Finite Group Databasebeta

← #17243189

Subgroups — #17243189

Order 4352.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537077C211yesmaximal, characteristic, complemented
2#14537070C211yesmaximal, characteristic, complemented
3#14536619C211yesmaximal, characteristic, complemented
4#14536167C211yesmaximal, characteristic, complemented
5#14536118C211yesmaximal, characteristic, complemented
6#14535845C211yesmaximal, characteristic, complemented
7#14535785C211yesmaximal, characteristic, complemented
8#14535705C211yesmaximal, characteristic, complemented
9#14535598C211yesmaximal, characteristic, complemented
10#14535554C211yesmaximal, characteristic, complemented
11#14535526C211yesmaximal, characteristic, complemented
12#14535452C211yesmaximal, characteristic, complemented
13#14535398C211yesmaximal, characteristic, complemented
14#14535388C211yesmaximal, characteristic, complemented
15#14535267C211yesmaximal, characteristic, complemented
16#14535195C211yesmaximal, characteristic, complemented
17#14535033C211yesmaximal, characteristic, complemented
18#14534588C211yesmaximal, characteristic, complemented
19#14534558C211yesmaximal, characteristic, complemented
20#14533967C211yesmaximal, characteristic, complemented
21#14533793C211yesmaximal, characteristic, complemented
22#14533036C211yesmaximal, characteristic, complemented
23#14533023C211yesmaximal, characteristic, complemented
24#14532914C211yesmaximal, characteristic, complemented
25#14532913C211yesmaximal, characteristic, complemented
26#14532434C211yesmaximal, characteristic, complemented
27#14532135C211yesmaximal, characteristic
28#14531513C211yesmaximal, characteristic, complemented
29#14531416C211yesmaximal, characteristic, complemented
30D17×#386C211yesmaximal, characteristic, complemented
31C17×#2751C211yesmaximal, characteristic, complemented
32C22×D4×D17C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34C2×#10587584C2211yescharacteristic, complemented
35C2×#10587565C2211yescharacteristic, complemented
36C2×#10587633C2211yescharacteristic, complemented
37C2×#10587561C2211yescharacteristic
38C2×#10587561C2211yescharacteristic, complemented
39C2×#10587622C2211yescharacteristic
40C2×#10587572C2211yescharacteristic, complemented
41C2×#10587615C2211yescharacteristic, complemented
42C2×#10587583C2211yescharacteristic
43C2×#10587582C2211yescharacteristic
44C2×#10587582C2211yescharacteristic, complemented
45C2×#10587564C2211yescharacteristic, complemented
46C2×#10587632C2211yescharacteristic
47C2×#10587570C2211yescharacteristic
48C2×#10587570C2211yescharacteristic
49C2×#10587568C2211yescharacteristic
50C2×#10587568C2211yescharacteristic
51C2×#10587579C2211yescharacteristic
52C2×C22⋊C4×D17C2211yescharacteristic
53C2×C22⋊C4×D17C2211yescharacteristic
54C2×C22⋊C4×D17C2211yescharacteristic
55#11762746C2211yescharacteristic, complemented
56#11762745C2211yescharacteristic, complemented
57#11762744C2211yescharacteristic, complemented
58#11762743C2211yescharacteristic, complemented
59#11762740C2211yescharacteristic, complemented
60#11762738C2211yescharacteristic, complemented
61#11762738C2211yescharacteristic, complemented
62#11762738C2211yescharacteristic, complemented
63#11762738C2211yescharacteristic, complemented
64#11762738C2211yescharacteristic, complemented
65#11762738C2211yescharacteristic, complemented
66#11762737C2211yescharacteristic, complemented
67#11762737C2211yescharacteristic, complemented
68#11762737C2211yescharacteristic, complemented
69#11762736C2211yescharacteristic, complemented
70#11762733C2211yescharacteristic, complemented
71#11762733C2211yescharacteristic, complemented
72#11762732C2211yescharacteristic, complemented
73#11762732C2211yescharacteristic, complemented
74#11762732C2211yescharacteristic, complemented
75#11762731C2211yescharacteristic, complemented
76#11762730C2211yescharacteristic, complemented
77#11762729C2211yescharacteristic, complemented
78#11762728C2211yescharacteristic, complemented
79#11762727C2211yescharacteristic, complemented
80#11762727C2211yescharacteristic, complemented
81#11762726C2211yescharacteristic
82#11762726C2211yescharacteristic, complemented
83#11762726C2211yescharacteristic, complemented
84#11762725C2211yescharacteristic
85#11762725C2211yescharacteristic
86#11762725C2211yescharacteristic
87#11762725C2211yescharacteristic
88#11762725C2211yescharacteristic, complemented
89#11762725C2211yescharacteristic, complemented
90#11762724C2211yescharacteristic, complemented
91#11762724C2211yescharacteristic, complemented
92#11762722C2211yescharacteristic, complemented
93#11762721C2211yescharacteristic, complemented
94#11762720C2211yescharacteristic, complemented
95#11762719C2211yescharacteristic
96#11762717C2211yescharacteristic
97#11762713C2211yescharacteristic, complemented
98#11762713C2211yescharacteristic, complemented
99#11762713C2211yescharacteristic, complemented
100#11762710C2211yescharacteristic
101#11762709C2211yescharacteristic
102#11762709C2211yescharacteristic
103#11762709C2211yescharacteristic, complemented
104#11762709C2211yescharacteristic, complemented
105#11762707C2211yescharacteristic, complemented
106#11762707C2211yescharacteristic, complemented
107#11762706C2211yescharacteristic, complemented
108#11762705C2211yescharacteristic, complemented
109#11762703C2211yescharacteristic, complemented
110#11762701C2211yescharacteristic, complemented
111#11762700C2211yescharacteristic, complemented
112#11762700C2211yescharacteristic, complemented
113#11762698C2211yescharacteristic, complemented
114#11762698C2211yescharacteristic, complemented
115#11762698C2211yescharacteristic, complemented
116#11762698C2211yescharacteristic, complemented
117#11762697C2211yescharacteristic, complemented
118#11762697C2211yescharacteristic, complemented
119#11762696C2211yescharacteristic, complemented
120#11762696C2211yescharacteristic, complemented
121#11762695C2211yescharacteristic, complemented
122#11762695C2211yescharacteristic, complemented
123#11762694C2211yescharacteristic, complemented
124#11762692C2211yescharacteristic, complemented
125#11762689C2211yescharacteristic
126#11762688C2211yescharacteristic
127#11762687C2211yescharacteristic
128#11762687C2211yescharacteristic
129#11762687C2211yescharacteristic
130#11762687C2211yescharacteristic
131#11762687C2211yescharacteristic
132#11762687C2211yescharacteristic
133#11762687C2211yescharacteristic, complemented
134#11762687C2211yescharacteristic, complemented
135#11762686C2211yescharacteristic
136#11762685C2211yescharacteristic
137#11762685C2211yescharacteristic
138#11762683C2211yescharacteristic
139#11762683C2211yescharacteristic
140#11762683C2211yescharacteristic
141#11762683C2211yescharacteristic
142#11762683C2211yescharacteristic, complemented
143#11762683C2211yescharacteristic, complemented
144#11762683C2211yescharacteristic, complemented
145#11762683C2211yescharacteristic, complemented
146#11762683C2211yescharacteristic, complemented
147#11762682C2211yescharacteristic, complemented
148#11762680C2211yescharacteristic
149#11762680C2211yescharacteristic
150#11762680C2211yescharacteristic, complemented
151#11762676C2211yescharacteristic, complemented
152#11762673C2211yescharacteristic, complemented
153#11762671C2211yescharacteristic, complemented
154#11762670C2211yescharacteristic, complemented
155#11762668C2211yescharacteristic
156#11762668C2211yescharacteristic
157#11762668C2211yescharacteristic
158#11762668C2211yescharacteristic, complemented
159#11762667C2211yescharacteristic, complemented
160#11762666C2211yescharacteristic, complemented
161#11762664C2211yescharacteristic
162#11762664C2211yescharacteristic
163#11762664C2211yescharacteristic
164#11762664C2211yescharacteristic
165#11762664C2211yescharacteristic
166#11762664C2211yescharacteristic
167C4×#63227C2211yescharacteristic
168C4×#63227C2211yescharacteristic
169#11762656C2211yescharacteristic
170#95×D17C2211yescharacteristic
171#95×D17C2211yescharacteristic
172C17×#400C2211yescharacteristic, complemented
173C17×#397C2211yescharacteristic, complemented
174C17×#397C2211yescharacteristic, complemented
175C17×#394C2211yescharacteristic
176C17×#393C2211yescharacteristic, complemented
177C17×#393C2211yescharacteristic, complemented
178C17×#391C2211yescharacteristic, complemented
179C17×#390C2211yescharacteristic
180C17×#388C2211yescharacteristic, complemented
181C17×#388C2211yescharacteristic, complemented
182C17×#387C2211yescharacteristic, complemented
183C17×#387C2211yescharacteristic, complemented
184C17×#386C2211yescharacteristic
185C17×#385C2211yescharacteristic, complemented
186C17×#381C2211yescharacteristic, complemented
187C24×D17C2311yescharacteristic
188C24×D17C2311yescharacteristic
189C22×Q8×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C22×C22⋊D17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C23×Dic17C2311yescharacteristic
197C2×D4×D17—24no—
198C2×D4×D17—42no—
199C2×D4×D17—42no—
200C22×D68C2311yescharacteristic
201C22×D68C2311yescharacteristic
202C22×D68C2311yescharacteristic
203C22×D68C2311yescharacteristic
204C22×C4×D17—42no—
205C22×C4×D17—42no—
206C22×C4×D17—42no—
207C22×C4×D17C2311yescharacteristic
208C22×C4×D17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×Dic34C2311yescharacteristic
216C22×Dic34C2311yescharacteristic
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C42×C17C2311yescharacteristic
234C2×C42×C17C2311yescharacteristic
235C2×C22⋊Dic17C2311yescharacteristic
236C2×C22⋊Dic17C2311yescharacteristic
237C2×C22⋊Dic17C2311yescharacteristic
238C2×C22⋊Dic17C2311yescharacteristic
239C2×C22⋊Dic17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244#10587633—42no—
245#10587632—42no—
246#10587622—42no—
247#10587615—42no—
248C2×#63227C2311yescharacteristic
249C2×#63227C2311yescharacteristic
250C2×#63227C2311yescharacteristic
251C2×#63227C2311yescharacteristic
252C2×#63227C2311yescharacteristic
253C2×#63227C2311yescharacteristic
254C2×#63227C2311yescharacteristic
255C2×#63227C2311yescharacteristic
256C2×#63227C2311yescharacteristic
257C2×#63227C2311yescharacteristic
258C2×#63227C2311yescharacteristic
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
261C2×#63227C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×C4⋊Dic17C2311yescharacteristic
285C2×C4⋊Dic17C2311yescharacteristic
286C2×C4⋊Dic17C2311yescharacteristic
287C2×C4⋊Dic17C2311yescharacteristic
288C2×C4⋊Dic17C2311yescharacteristic
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312#10587584—42no—
313#10587583—24no—
314#10587582—42no—
315#10587582—42no—
316#10587579—24no—
317#10587572—42no—
318#10587570—42no—
319#10587570—42no—
320#10587568—42no—
321#10587568—42no—
322C22⋊C4×D17—42no—
323C22⋊C4×D17—42no—
324C22⋊C4×D17—42no—
325#10587565—42no—
326#10587564—42no—
327#10587561—42no—
328#10587561—42no—
329C17×#95C2311yescharacteristic
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369C24×C17C2411yescharacteristic
370C24×C17C2411yescharacteristic
371C23×D17—22no—
372C23×D17—22no—
373C23×D17—22no—
374C23×D17—22no—
375C23×D17—22no—
376C23×D17—22no—
377C23×D17—22no—
378C23×D17—22no—
379C23×D17—41no—
380C23×D17—41no—
381C23×D17—41no—
382C23×D17—41no—
383C23×D17—41no—
384C23×D17—41no—
385C23×D17C2411yescharacteristic
386C23×D17C2411yescharacteristic
387C23×D17C2411yescharacteristic
388C23×D17C2411yescharacteristic
389C2×Q8×C17—41no—
390C2×Q8×C17—41no—
391C2×Q8×C17—41no—
392C2×D4×C17—22no—
393C2×D4×C17—22no—
394C2×D4×C17—41no—
395C22×C4×C17—22no—
396C22×C4×C17—41no—
397C22×C4×C17—41no—
398C22×C4×C17C2411yescharacteristic
399C22×C4×C17C2411yescharacteristic
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C2×C22⋊D17—22no—
412C2×C22⋊D17—22no—
413C2×C22⋊D17—22no—
414C2×C22⋊D17—22no—
415C2×C22⋊D17—22no—
416C2×C22⋊D17—41no—
417C2×C22⋊D17—41no—
418C2×C22⋊D17—41no—
419C2×C22⋊D17—41no—
420C2×C22⋊D17—41no—
421C2×C22⋊D17—41no—
422C2×C22⋊D17—41no—
423C22×Dic17—22no—
424C22×Dic17—22no—
425C22×Dic17—41no—
426C22×Dic17C2411yescharacteristic
427C22×Dic17C2411yescharacteristic
428C22×Dic17C2411yescharacteristic
429C22×Dic17C2411yescharacteristic
430C22×Dic17C2411yescharacteristic
431C22×Dic17C2411yescharacteristic
432C22×Dic17C2411yescharacteristic
433C22×Dic17C2411yescharacteristic
434C22×Dic17C2411yescharacteristic
435C22×Dic17C2411yescharacteristic
436C22×Dic17C2411yescharacteristic
437C22×Dic17C2411yescharacteristic
438D4×D17—416no—
439C2×D68—22no—
440C2×D68—22no—
441C2×D68—22no—
442C2×D68—22no—
443C2×D68—22no—
444C2×D68—22no—
445C2×D68—41no—
446C2×D68—41no—
447C2×D68—41no—
448C2×D68—41no—
449C2×D68—41no—
450C2×D68—41no—
451C2×C4×D17—22no—
452C2×C4×D17—22no—
453C2×C4×D17—22no—
454C2×C4×D17—22no—
455C2×C4×D17—22no—
456C2×C4×D17—22no—
457C2×C4×D17—22no—
458C2×C4×D17—41no—
459C2×C4×D17—41no—
460C2×C4×D17—41no—
461C2×C4×D17—41no—
462C2×C4×D17—41no—
463C2×C4×D17—41no—
464C2×C4×D17—41no—
465C2×C4×D17—41no—
466C2×C4×D17—41no—
467C2×C4×D17—41no—
468C2×C4×D17—416no—
469C2×C4×D17—41no—
470C2×C4×D17—41no—
471C2×C4×D17—41no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17—41no—
475C2×C4×D17#4114yes—
476C2×Dic34—22no—
477C2×Dic34—22no—
478C2×Dic34—41no—
479C2×Dic34—41no—
480C2×Dic34—41no—
481C2×Dic34—41no—
482C4⋊C4×C17—22no—
483C4⋊C4×C17—22no—
484C4⋊C4×C17—41no—
485C4⋊C4×C17—41no—
486C4⋊C4×C17—41no—
487C22⋊C4×C17—22no—
488C22⋊C4×C17—41no—
489C22⋊C4×C17—41no—
490C22⋊C4×C17—41no—
491C22⋊C4×C17—41no—
492C22⋊C4×C17—41no—
493C22⋊C4×C17—41no—
494C22⋊C4×C17—41no—
495C22⋊C4×C17—41no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C42×C17—41no—
499C42×C17—41no—
500C22⋊Dic17—22no—
501C22⋊Dic17—22no—
502C22⋊Dic17—22no—
503C22⋊Dic17—41no—
504C22⋊Dic17—41no—
505C22⋊Dic17—41no—
506C22⋊Dic17—41no—
507C22⋊Dic17—41no—
508C22⋊Dic17—41no—
509#63227—22no—
510#63227—22no—
511#63227—22no—
512#63227—22no—
513#63227—22no—
514#63227—22no—
515#63227—22no—
516#63227—22no—
517#63227—22no—
518#63227—22no—
519#63227—22no—
520#63227—22no—
521#63227—22no—
522#63227—22no—
523#63227—22no—
524#63227—41no—
525#63227—41no—
526#63227—41no—
527#63227—41no—
528#63227—41no—
529#63227—41no—
530#63227—41no—
531#63227—41no—
532#63227—41no—
533#63227—41no—
534#63227—41no—
535#63227—41no—
536#63227—41no—
537#63227—41no—
538#63227—41no—
539#63227—41no—
540#63227—41no—
541#63227—41no—
542#63227—41no—
543#63227—41no—
544#63227—41no—
545C4⋊Dic17—22no—
546C4⋊Dic17—22no—
547C4⋊Dic17—22no—
548C4⋊Dic17—41no—
549C4⋊Dic17—41no—
550C4⋊Dic17—41no—
551C4⋊Dic17—41no—
552#63225—22no—
553#63225—41no—
554#63225—41no—
555#63225—41no—
556#63225—41no—
557#63225—41no—
558#63225—41no—
559#63225—41no—
560#63225—41no—
561#63225—41no—
562#63225—41no—
563#63225—41no—
564#63225—41no—
565#63225—41no—
566#63225—41no—
567#63225—41no—
568C4×Dic17—22no—
569C4×Dic17—41no—
570C4×Dic17—41no—
571C4×Dic17—41no—
572C4×Dic17—41no—
573#36793—171nomaximal, Sylow
574C23×C17—21no—
575C23×C17—21no—
576C23×C17—21no—
577C23×C17—21no—
578C23×C17—21no—
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17H(5,𝔽2)12yes—
588C23×C17C2511yescharacteristic
589C22×D17—21no—
590C22×D17—21no—
591C22×D17—21no—
592C22×D17—21no—
593C22×D17—28no—
594C22×D17—21no—
595C22×D17—21no—
596C22×D17—21no—
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—21no—
600C22×D17—21no—
601C22×D17—21no—
602C22×D17—21no—
603C22×D17—21no—
604C22×D17—21no—
605C22×D17—21no—
606C22×D17—21no—
607C22×D17—21no—
608C22×D17—21no—
609C22×D17—21no—
610C22×D17—21no—
611C22×D17—21no—
612C22×D17—21no—
613C22×D17—21no—
614C22×D17—44no—
615C22×D17—44no—
616C22×D17—44no—
617C22×D17—44no—
618C22×D17—44no—
619C22×D17—44no—
620C22×D17—44no—
621C22×D17—44no—
622C22×D17—44no—
623C22×D17—82no—
624C22×D17—82no—
625C22×D17—82no—
626C22×D17—82no—
627C22×D17C2×#4112yes—
628C22×D17H(5,𝔽2)12yes—
629C22×D17H(5,𝔽2)12yes—
630C22×D172−1+412yes—
631Q8×C17—82no—
632D4×C17—44no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—44no—
672C2×C4×C17C2×#4112yes—
673C22⋊D17—44no—
674C22⋊D17—44no—
675C22⋊D17—82no—
676C22⋊D17—82no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—44no—
712C2×Dic17C2×#4112yes—
713C2×Dic17H(5,𝔽2)12yes—
714D68—44no—
715D68—44no—
716D68—82no—
717D68—82no—
718C4×D17—44no—
719C4×D17—44no—
720C4×D17—44no—
721C4×D17—44no—
722C4×D17—44no—
723C4×D17—82no—
724C4×D17—82no—
725C4×D17—82no—
726Dic34—82no—
727Dic34—82no—
728#2849—171no—
729#2848—171no—
730#2796—171no—
731#2761—171no—
732#2757—171no—
733#2751D1711yescharacteristic, complemented
734#2737—171no—
735#2730—171no—
736#2723—171no—
737#2715—171no—
738#2712—171no—
739#2710—171no—
740#2705—171no—
741#2701—171no—
742#2700—171no—
743#2691—171no—
744#2686—171no—
745#2672—171no—
746#2626—171no—
747#2622—171no—
748#2564—171no—
749#2549—171no—
750#2480—171no—
751#2480—171no—
752#2472—171no—
753#2472—171no—
754#2435—171no—
755#2408—171no—
756#2329—171no—
757#2318—171no—
758C2×#386—171no—
759C22×C17—22no—
760C22×C17—22no—
761C22×C17—22no—
762C22×C17—41no—
763C22×C17—41no—
764C22×C17—41no—
765C22×C17—41no—
766C22×C17—41no—
767C22×C17—41no—
768C22×C17—41no—
769C22×C17—41no—
770C22×C17—41no—
771C22×C17—41no—
772C22×C17—41no—
773C22×C17C22×#4111yescharacteristic
774C22×C17C2×H(5,𝔽2)11yescharacteristic
775C22×C17C2×H(5,𝔽2)11yescharacteristic
776C22×C17C2×H(5,𝔽2)11yescharacteristic
777C22×C17C2×H(5,𝔽2)11yescharacteristic
778C22×C17C2×2−1+411yescharacteristic
779C22×C17#58511yescharacteristic
780C2×D17—22no—
781C2×D17—22no—
782C2×D17—22no—
783C2×D17—22no—
784C2×D17—22no—
785C2×D17—22no—
786C2×D17—22no—
787C2×D17—22no—
788C2×D17—22no—
789C2×D17—416no—
790C2×D17—41no—
791C2×D17—41no—
792C2×D17—41no—
793C2×D17—41no—
794C2×D17—41no—
795C2×D17—41no—
796C2×D17—41no—
797C2×D17—41no—
798C2×D17—41no—
799C2×D17—41no—
800C2×D17—41no—
801C2×D17—41no—
802C2×D17—41no—
803C2×D17—41no—
804C2×D17—41no—
805C2×D17—41no—
806C2×D17—41no—
807C2×D17—41no—
808C2×D17—88no—
809C2×D17#54214yes—
810C4×C17—22no—
811C4×C17—41no—
812C4×C17—41no—
813C4×C17—41no—
814C4×C17—41no—
815C4×C17—41no—
816C4×C17—41no—
817C4×C17—41no—
818C4×C17—41no—
819C4×C17—41no—
820C4×C17—41no—
821C4×C17—41no—
822C4×C17—41no—
823Dic17—22no—
824Dic17—22no—
825Dic17—41no—
826Dic17—41no—
827Dic17—41no—
828Dic17—41no—
829Dic17—41no—
830Dic17—41no—
831Dic17—41no—
832Dic17—41no—
833Dic17—41no—
834Dic17—41no—
835C23×D4—171no—
836C24×C4—171no—
837C2×#126—171no—
838C2×#126—171no—
839C2×#124—171no—
840C2×#124—171no—
841C2×#124—171no—
842C2×#124—171no—
843C2×#123—171no—
844C2×#123—171no—
845C2×C22⋊Q8—171no—
846C2×C22⋊Q8—171no—
847C2×C22⋊Q8—171no—
848C2×C22⋊Q8—171no—
849C2×C22⋊Q8—171no—
850C2×#121—171no—
851C2×#121—171no—
852C2×#120—171no—
853C2×#120—171no—
854C2×C4×D4—171no—
855C22×C22⋊C4—171no—
856C22×C22⋊C4—171no—
857C22×C22⋊C4—171no—
858#400C2×D1711yescharacteristic, complemented
859#399—171no—
860#399—171no—
861#399—171no—
862#398—171no—
863#398—171no—
864#397—171no—
865#397—171no—
866#397—171no—
867#397—171no—
868#397—171no—
869#397—171no—
870#397—171no—
871#397—171no—
872#397—171no—
873#397—171no—
874#397C2×D1711yescharacteristic, complemented
875#397C2×D1711yescharacteristic, complemented
876#396—171no—
877#396—171no—
878#396—171no—
879#396—171no—
880#396—171no—
881#396—171no—
882#395—171no—
883#395—171no—
884#395—171no—
885#394—171no—
886#394—171no—
887#394—171no—
888#394—171no—
889#394—171no—
890#394—171no—
891#394—171no—
892#394—171no—
893#394—171no—
894#394—171no—
895#394—171no—
896#394—171no—
897#394—171no—
898#394C2×D1711yescharacteristic
899#393—171no—
900#393—171no—
901#393—171no—
902#393C2×D1711yescharacteristic, complemented
903#393C2×D1711yescharacteristic, complemented
904#392—171no—
905#392—171no—
906#391—171no—
907#391—171no—
908#391—171no—
909#391C2×D1711yescharacteristic, complemented
910#390—171no—
911#390—171no—
912#390—171no—
913#390—171no—
914#390—171no—
915#390C2×D1711yescharacteristic
916#389—171no—
917#389—171no—
918#389—171no—
919#389—171no—
920#388—171no—
921#388—171no—
922#388—171no—
923#388—171no—
924#388—171no—
925#388—171no—
926#388—171no—
927#388—171no—
928#388—171no—
929#388—171no—
930#388C2×D1711yescharacteristic, complemented
931#388C2×D1711yescharacteristic, complemented
932#387—171no—
933#387—171no—
934#387—171no—
935#387—171no—
936#387—171no—
937#387—171no—
938#387C2×D1711yescharacteristic, complemented
939#387C2×D1711yescharacteristic, complemented
940#386—171no—
941#386—171no—
942#386—171no—
943#386—171no—
944#386—171no—
945#386—171no—
946#386—171no—
947#386—171no—
948#386—171no—
949#386—171no—
950#386—171no—
951#386—171no—
952#386—171no—
953#386C2×D1711yescharacteristic
954#385—171no—
955#385—171no—
956#385—171no—
957#385—171no—
958#385—171no—
959#385—171no—
960#385—171no—
961#385—171no—
962#385—171no—
963#385—171no—
964#385—171no—
965#385—171no—
966#385—171no—
967#385C2×D1711yescharacteristic, complemented
968#383—171no—
969#382—171no—
970#381—171no—
971#381—171no—
972#381C2×D1711yescharacteristic, complemented
973#380—171no—
974#380—171no—
975#380—171no—
976#380—171no—
977#380—171no—
978#380—171no—
979#379—171no—
980#379—171no—
981#379—171no—
982#379—171no—
983#379—171no—
984#379—171no—
985C4×C22⋊C4—171no—
986C4×C22⋊C4—171no—
987C4×C22⋊C4—171no—
988C2×#95—171no—
989C2×#95—171no—
990C2×C17—42no—
991C2×C17—81no—
992C2×C17C2×#54211yescharacteristic
993C2×C17#349011yescharacteristic
994C2×C17#350611yescharacteristic
995C2×C17#353211yescharacteristic
996C2×C17#353411yescharacteristic
997C2×C17#353511yescharacteristic
998C2×C17#353611yescharacteristic
999D17—24no—
1000D17—42no—
1001D17—81no—
1002D17—81no—
1003C25—171no—
1004C25—171no—
1005C22×Q8—171no—
1006C22×Q8—171no—
1007C22×Q8C22×D1711yescharacteristic
1008C22×D4—171no—
1009C22×D4—171no—
1010C22×D4—171no—
1011C22×D4—171no—
1012C22×D4—171no—
1013C22×D4—171no—
1014C22×D4—171no—
1015C22×D4—171no—
1016C22×D4—344no—
1017C22×D4—682no—
1018C22×D4—682no—
1019C22×D4C22×D1711yescharacteristic
1020C23×C4—171no—
1021C23×C4—171no—
1022C23×C4—171no—
1023C23×C4—171no—
1024C23×C4—171no—
1025C23×C4—171no—
1026C23×C4—171no—
1027C23×C4—171no—
1028C23×C4—171no—
1029C23×C4—682no—
1030C23×C4—682no—
1031C23×C4—682no—
1032C23×C4C22×D1711yescharacteristic
1033#126—682no—
1034#126—682no—
1035#124—682no—
1036#124—682no—
1037#124—682no—
1038#124—682no—
1039#123—682no—
1040#123—682no—
1041C22⋊Q8—344no—
1042C22⋊Q8—682no—
1043C22⋊Q8—682no—
1044C22⋊Q8—682no—
1045C22⋊Q8—682no—
1046#121—682no—
1047#121—682no—
1048#120—682no—
1049#120—682no—
1050C4×D4—344no—
1051C2×C4⋊C4—171no—
1052C2×C4⋊C4—171no—
1053C2×C4⋊C4—171no—
1054C2×C4⋊C4—171no—
1055C2×C4⋊C4—171no—
1056C2×C4⋊C4—171no—
1057C2×C4⋊C4—171no—
1058C2×C4⋊C4—171no—
1059C2×C4⋊C4—171no—
1060C2×C4⋊C4—171no—
1061C2×C4⋊C4—171no—
1062C2×C4⋊C4—171no—
1063C2×C4⋊C4—171no—
1064C2×C4⋊C4—171no—
1065C2×C4⋊C4—171no—
1066C2×C4⋊C4—171no—
1067C2×C4⋊C4—171no—
1068C2×C4⋊C4—171no—
1069C2×C4⋊C4—171no—
1070C2×C4⋊C4—171no—
1071C2×C4⋊C4—171no—
1072C2×C4⋊C4—171no—
1073C2×C4⋊C4—171no—
1074C2×C4⋊C4C22×D1711yescharacteristic
1075C2×C4⋊C4C22×D1711yescharacteristic
1076C2×C4⋊C4C22×D1711yescharacteristic
1077C2×C4⋊C4C22×D1711yescharacteristic
1078C2×C4⋊C4C22×D1711yescharacteristic
1079C2×C22⋊C4—171no—
1080C2×C22⋊C4—171no—
1081C2×C22⋊C4—171no—
1082C2×C22⋊C4—171no—
1083C2×C22⋊C4—171no—
1084C2×C22⋊C4—171no—
1085C2×C22⋊C4—171no—
1086C2×C22⋊C4—171no—
1087C2×C22⋊C4—171no—
1088C2×C22⋊C4—171no—
1089C2×C22⋊C4—171no—
1090C2×C22⋊C4—171no—
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—171no—
1118C2×C22⋊C4—171no—
1119C2×C22⋊C4—171no—
1120C2×C22⋊C4—171no—
1121C2×C22⋊C4—171no—
1122C2×C22⋊C4—171no—
1123C2×C22⋊C4—171no—
1124C2×C22⋊C4—682no—
1125C2×C22⋊C4—682no—
1126C2×C22⋊C4—682no—
1127C2×C22⋊C4C22×D1711yescharacteristic
1128C2×C22⋊C4C22×D1711yescharacteristic
1129C2×C22⋊C4C22×D1711yescharacteristic
1130C2×C22⋊C4C22×D1711yescharacteristic
1131C2×C22⋊C4C22×D1711yescharacteristic
1132C2×C22⋊C4C22×D1711yescharacteristic
1133C2×C22⋊C4C22×D1711yescharacteristic
1134C2×C22⋊C4C22×D1711yescharacteristic
1135C2×C22⋊C4C22×D1711yescharacteristic
1136C2×C22⋊C4C22×D1711yescharacteristic
1137C2×C22⋊C4C22×D1711yescharacteristic
1138C2×C42—171no—
1139C2×C42—171no—
1140C2×C42—171no—
1141C2×C42—171no—
1142C2×C42—171no—
1143C2×C42C22×D1711yescharacteristic
1144C2×C42C22×D1711yescharacteristic
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154#95—171no—
1155#95—171no—
1156#95—171no—
1157#95—171no—
1158#95—171no—
1159#95—171no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95C22×D1711yescharacteristic
1172#95C22×D1711yescharacteristic
1173#95C22×D1711yescharacteristic
1174#95C22×D1711yescharacteristic
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178#95C22×D1711yescharacteristic
1179#95C22×D1711yescharacteristic
1180#95C22×D1711yescharacteristic
1181#95C22×D1711yescharacteristic
1182#95C22×D1711yescharacteristic
1183#95C22×D1711yescharacteristic
1184#95C22×D1711yescharacteristic
1185C17#3679311yescharacteristic, complemented, Sylow
1186C24—171no—
1187C24—171no—
1188C24—171no—
1189C24—171no—
1190C24—342no—
1191C24—342no—
1192C24—342no—
1193C24—342no—
1194C24—342no—
1195C24—342no—
1196C24—342no—
1197C24—342no—
1198C24—681no—
1199C24—681no—
1200C24—681no—
1201C24—681no—
1202C24—681no—
1203C24—681no—
1204C24C23×D1711yescharacteristic
1205C24C23×D1711yescharacteristic
1206C2×Q8—41no—
1207C2×Q8—41no—
1208C2×Q8—41no—
1209C2×Q8—342no—
1210C2×Q8—342no—
1211C2×Q8—681no—
1212C2×Q8—681no—
1213C2×Q8—681no—
1214C2×Q8—681no—
1215C2×D4—22no—
1216C2×D4—22no—
1217C2×D4—41no—
1218C2×D4—342no—
1219C2×D4—342no—
1220C2×D4—342no—
1221C2×D4—342no—
1222C2×D4—342no—
1223C2×D4—342no—
1224C2×D4—342no—
1225C2×D4—342no—
1226C2×D4—342no—
1227C2×D4—342no—
1228C2×D4—342no—
1229C2×D4—681no—
1230C2×D4—681no—
1231C2×D4—681no—
1232C2×D4—681no—
1233C2×D4—681no—
1234C2×D4—681no—
1235C2×D4—681no—
1236C2×D4—681no—
1237C2×D4—681no—
1238C2×D4—681no—
1239C2×D4—681no—
1240C2×D4—681no—
1241C2×D4—681no—
1242C2×D4—6816no—
1243C22×C4—22no—
1244C22×C4—41no—
1245C22×C4—41no—
1246C22×C4—171no—
1247C22×C4—171no—
1248C22×C4—174no—
1249C22×C4—171no—
1250C22×C4—171no—
1251C22×C4—171no—
1252C22×C4—171no—
1253C22×C4—171no—
1254C22×C4—171no—
1255C22×C4—171no—
1256C22×C4—171no—
1257C22×C4—171no—
1258C22×C4—171no—
1259C22×C4—342no—
1260C22×C4—342no—
1261C22×C4—342no—
1262C22×C4—342no—
1263C22×C4—342no—
1264C22×C4—342no—
1265C22×C4—342no—
1266C22×C4—342no—
1267C22×C4—342no—
1268C22×C4—681no—
1269C22×C4—681no—
1270C22×C4—681no—
1271C22×C4—681no—
1272C22×C4—681no—
1273C22×C4—681no—
1274C22×C4—681no—
1275C22×C4—681no—
1276C22×C4—681no—
1277C22×C4—681no—
1278C22×C4—681no—
1279C22×C4—681no—
1280C22×C4—681no—
1281C22×C4—681no—
1282C22×C4—681no—
1283C22×C4—681no—
1284C22×C4—6816no—
1285C22×C4—681no—
1286C22×C4C23×D1711yescharacteristic
1287C22×C4C23×D1711yescharacteristic
1288C22×C4C23×D1711yescharacteristic
1289C22×C4C23×D1711yescharacteristic
1290C22×C4C23×D1711yescharacteristic
1291C22×C4C23×D1711yescharacteristic
1292C22×C4C23×D1711yescharacteristic
1293C22×C4C23×D1711yescharacteristic
1294C22×C4C23×D1711yescharacteristic
1295C22×C4C23×D1711yescharacteristic
1296C22×C4C23×D1711yescharacteristic
1297C22×C4C23×D1711yescharacteristic
1298C22×C4C23×D1711yescharacteristic
1299C4⋊C4—22no—
1300C4⋊C4—22no—
1301C4⋊C4—41no—
1302C4⋊C4—41no—
1303C4⋊C4—41no—
1304C4⋊C4—342no—
1305C4⋊C4—342no—
1306C4⋊C4—342no—
1307C4⋊C4—342no—
1308C4⋊C4—681no—
1309C4⋊C4—681no—
1310C4⋊C4—681no—
1311C4⋊C4—681no—
1312C4⋊C4—681no—
1313C4⋊C4—681no—
1314C4⋊C4—681no—
1315C4⋊C4—681no—
1316C4⋊C4—681no—
1317C4⋊C4—681no—
1318C4⋊C4—681no—
1319C4⋊C4—681no—
1320C4⋊C4—681no—
1321C4⋊C4—681no—
1322C4⋊C4—681no—
1323C4⋊C4—681no—
1324C4⋊C4—681no—
1325C4⋊C4—681no—
1326C4⋊C4—681no—
1327C22⋊C4—22no—
1328C22⋊C4—41no—
1329C22⋊C4—41no—
1330C22⋊C4—41no—
1331C22⋊C4—41no—
1332C22⋊C4—41no—
1333C22⋊C4—41no—
1334C22⋊C4—41no—
1335C22⋊C4—41no—
1336C22⋊C4—41no—
1337C22⋊C4—41no—
1338C22⋊C4—342no—
1339C22⋊C4—342no—
1340C22⋊C4—342no—
1341C22⋊C4—342no—
1342C22⋊C4—342no—
1343C22⋊C4—342no—
1344C22⋊C4—342no—
1345C22⋊C4—342no—
1346C22⋊C4—342no—
1347C22⋊C4—342no—
1348C22⋊C4—342no—
1349C22⋊C4—342no—
1350C22⋊C4—342no—
1351C22⋊C4—342no—
1352C22⋊C4—342no—
1353C22⋊C4—342no—
1354C22⋊C4—342no—
1355C22⋊C4—342no—
1356C22⋊C4—681no—
1357C22⋊C4—681no—
1358C22⋊C4—681no—
1359C22⋊C4—681no—
1360C22⋊C4—681no—
1361C22⋊C4—681no—
1362C22⋊C4—681no—
1363C22⋊C4—681no—
1364C22⋊C4—681no—
1365C22⋊C4—681no—
1366C22⋊C4—681no—
1367C22⋊C4—681no—
1368C22⋊C4—681no—
1369C22⋊C4—681no—
1370C22⋊C4—681no—
1371C22⋊C4—681no—
1372C22⋊C4—681no—
1373C22⋊C4—681no—
1374C22⋊C4—681no—
1375C22⋊C4—681no—
1376C22⋊C4—681no—
1377C22⋊C4—681no—
1378C22⋊C4—681no—
1379C22⋊C4—681no—
1380C22⋊C4—681no—
1381C22⋊C4—681no—
1382C22⋊C4—681no—
1383C42—41no—
1384C42—41no—
1385C42—342no—
1386C42—681no—
1387C42—681no—
1388C42—681no—
1389C42—681no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—172no—
1404C23—172no—
1405C23—172no—
1406C23—172no—
1407C23—348no—
1408C23—341no—
1409C23—341no—
1410C23—341no—
1411C23—341no—
1412C23—341no—
1413C23—341no—
1414C23—341no—
1415C23—341no—
1416C23—341no—
1417C23—341no—
1418C23—341no—
1419C23—341no—
1420C23—341no—
1421C23—341no—
1422C23—341no—
1423C23—341no—
1424C23—341no—
1425C23—341no—
1426C23—341no—
1427C23—341no—
1428C23—341no—
1429C23—341no—
1430C23—341no—
1431C23—341no—
1432C23—684no—
1433C23—684no—
1434C23—684no—
1435C23—684no—
1436C23—684no—
1437C23—684no—
1438C23—684no—
1439C23—684no—
1440C23—684no—
1441C23—1362no—
1442C23—1362no—
1443C23—1362no—
1444C23—1362no—
1445C23#1058769612yes—
1446C23C24×D1711yescharacteristic
1447Q8—82no—
1448Q8—1362no—
1449Q8—1362no—
1450D4—44no—
1451D4—684no—
1452D4—684no—
1453D4—684no—
1454D4—684no—
1455D4—1362no—
1456D4—1362no—
1457D4—1362no—
1458D4—1362no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—44no—
1498C2×C4—172no—
1499C2×C4—172no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—341no—
1511C2×C4—341no—
1512C2×C4—341no—
1513C2×C4—341no—
1514C2×C4—341no—
1515C2×C4—341no—
1516C2×C4—341no—
1517C2×C4—341no—
1518C2×C4—341no—
1519C2×C4—341no—
1520C2×C4—341no—
1521C2×C4—341no—
1522C2×C4—341no—
1523C2×C4—341no—
1524C2×C4—341no—
1525C2×C4—341no—
1526C2×C4—341no—
1527C2×C4—341no—
1528C2×C4—341no—
1529C2×C4—341no—
1530C2×C4—341no—
1531C2×C4—341no—
1532C2×C4—341no—
1533C2×C4—341no—
1534C2×C4—684no—
1535C2×C4—684no—
1536C2×C4—684no—
1537C2×C4—684no—
1538C2×C4—684no—
1539C2×C4—684no—
1540C2×C4—1362no—
1541C2×C4—1362no—
1542C2×C4—1362no—
1543C2×C4#41×D1712yes—
1544C22—22no—
1545C22—22no—
1546C22—22no—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—174no—
1559C22—342no—
1560C22—342no—
1561C22—342no—
1562C22—342no—
1563C22—342no—
1564C22—342no—
1565C22—342no—
1566C22—342no—
1567C22—342no—
1568C22—6816no—
1569C22—681no—
1570C22—681no—
1571C22—681no—
1572C22—681no—
1573C22—681no—
1574C22—681no—
1575C22—681no—
1576C22—681no—
1577C22—681no—
1578C22—681no—
1579C22—681no—
1580C22—681no—
1581C22—681no—
1582C22—681no—
1583C22—681no—
1584C22—681no—
1585C22—681no—
1586C22—681no—
1587C22—1368no—
1588C22C2×#41×D1711yescharacteristic
1589C22H(5,𝔽2)×D1711yescharacteristic
1590C22H(5,𝔽2)×D1711yescharacteristic
1591C22H(5,𝔽2)×D1711yescharacteristic
1592C22C2×#1058769611yescharacteristic
1593C222−1+4×D1711yescharacteristic
1594C22#1176364511yescharacteristic
1595C4—22no—
1596C4—41no—
1597C4—41no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—41no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—41no—
1608C4—342no—
1609C4—342no—
1610C4—681no—
1611C4—681no—
1612C4—681no—
1613C4—681no—
1614C4—681no—
1615C4—681no—
1616C4—681no—
1617C4—681no—
1618C4—681no—
1619C4—681no—
1620C2—42no—
1621C2—81no—
1622C2—344no—
1623C2—682no—
1624C2—1361no—
1625C2—1361no—
1626C2D17×#54211yescharacteristic
1627C2#1454246811yescharacteristic
1628C2#1454263211yescharacteristic
1629C2#1454293511yescharacteristic
1630C2#1454297311yescharacteristic
1631C2#1454299611yescharacteristic
1632C2#1454300311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2751C2
prime radical#14532135C2
hypercenter#2751D17
hypocenterC17#36793
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2751

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14537077C2semidirect
2. #14537070C2semidirect
3. #14536619C2semidirect
4. #14536167C2semidirect
5. #14536118C2semidirect
6. #14535845C2semidirect
7. #14535785C2semidirect
8. #14535705C2semidirect
9. #14535598C2semidirect
10. #14535554C2semidirect
11. #14535526C2semidirect
12. #14535452C2semidirect
13. #14535398C2semidirect
14. #14535388C2semidirect
15. #14535267C2semidirect
16. #14535195C2semidirect
17. #14535033C2semidirect
18. #14534588C2semidirect
19. #14534558C2semidirect
20. #14533967C2semidirect
21. #14533793C2semidirect
22. #14533036C2semidirect
23. #14533023C2semidirect
24. #14532914C2semidirect
25. #14532913C2semidirect
26. #14532434C2semidirect
28. #14531513C2semidirect
29. #14531416C2semidirect
30. D17×#386C2semidirect
31. C17×#2751C2semidirect
34. C2×#10587584C22semidirect
35. C2×#10587565C22semidirect
36. C2×#10587633C22semidirect
38. C2×#10587561C22semidirect
40. C2×#10587572C22semidirect
41. C2×#10587615C22semidirect
44. C2×#10587582C22semidirect
45. C2×#10587564C22semidirect
55. #11762746C22semidirect
56. #11762745C22semidirect
57. #11762744C22semidirect
58. #11762743C22semidirect
59. #11762740C22semidirect
60. #11762738C22semidirect
61. #11762738C22semidirect
62. #11762738C22semidirect
63. #11762738C22semidirect
64. #11762738C22semidirect
65. #11762738C22semidirect
66. #11762737C22semidirect
67. #11762737C22semidirect
68. #11762737C22semidirect
69. #11762736C22semidirect
70. #11762733C22semidirect
71. #11762733C22semidirect
72. #11762732C22semidirect
73. #11762732C22semidirect
74. #11762732C22semidirect
75. #11762731C22semidirect
76. #11762730C22semidirect
77. #11762729C22semidirect
78. #11762728C22semidirect
79. #11762727C22semidirect
80. #11762727C22semidirect
82. #11762726C22semidirect
83. #11762726C22semidirect
88. #11762725C22semidirect
89. #11762725C22semidirect
90. #11762724C22semidirect
91. #11762724C22semidirect
92. #11762722C22semidirect
93. #11762721C22semidirect
94. #11762720C22semidirect
97. #11762713C22semidirect
98. #11762713C22semidirect
99. #11762713C22semidirect
103. #11762709C22semidirect
104. #11762709C22semidirect
105. #11762707C22semidirect
106. #11762707C22semidirect
107. #11762706C22semidirect
108. #11762705C22semidirect
109. #11762703C22semidirect
110. #11762701C22semidirect
111. #11762700C22semidirect
112. #11762700C22semidirect
113. #11762698C22semidirect
114. #11762698C22semidirect
115. #11762698C22semidirect
116. #11762698C22semidirect
117. #11762697C22semidirect
118. #11762697C22semidirect
119. #11762696C22semidirect
120. #11762696C22semidirect
121. #11762695C22semidirect
122. #11762695C22semidirect
123. #11762694C22semidirect
124. #11762692C22semidirect
133. #11762687C22semidirect
134. #11762687C22semidirect
142. #11762683C22semidirect
143. #11762683C22semidirect
144. #11762683C22semidirect
145. #11762683C22semidirect
146. #11762683C22semidirect
147. #11762682C22semidirect
150. #11762680C22semidirect
151. #11762676C22semidirect
152. #11762673C22semidirect
153. #11762671C22semidirect
154. #11762670C22semidirect
158. #11762668C22semidirect
159. #11762667C22semidirect
160. #11762666C22semidirect
172. C17×#400C22semidirect
173. C17×#397C22semidirect
174. C17×#397C22semidirect
176. C17×#393C22semidirect
177. C17×#393C22semidirect
178. C17×#391C22semidirect
180. C17×#388C22semidirect
181. C17×#388C22semidirect
182. C17×#387C22semidirect
183. C17×#387C22semidirect
185. C17×#385C22semidirect
186. C17×#381C22semidirect
733. #2751D17semidirect
858. #400C2×D17semidirect
874. #397C2×D17semidirect
875. #397C2×D17semidirect
902. #393C2×D17semidirect
903. #393C2×D17semidirect
909. #391C2×D17semidirect
930. #388C2×D17semidirect
931. #388C2×D17semidirect
938. #387C2×D17semidirect
939. #387C2×D17semidirect
967. #385C2×D17semidirect
972. #381C2×D17semidirect
1185. C17#36793semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145370772
#145370702
#145366192
#145361672
#145361182
#145358452
#145357852
#145357052
#145355982
#145355542
#145355262
#145354522
#145353982
#145353882
#145352672
#145351952
#145350332
#145345882
#145345582
#145339672
#145337932
#145330362
#145330232
#145329142
#145329132
#145324342
#145321352
#145315132
#145314162
D17×#3862
C17×#27512
#3679317