Finite Group Databasebeta

← #17242741

Subgroups — #17242741

Order 4352.

1994 conjugacy classes of subgroups.

The subgroup lattice has 1600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537102C211yesmaximal, characteristic, complemented
2#14537082C211yesmaximal, characteristic, complemented
3#14536454C211yesmaximal, characteristic, complemented
4#14536444C211yesmaximal, characteristic, complemented
5#14536398C211yesmaximal, characteristic, complemented
6#14536215C211yesmaximal, characteristic, complemented
7#14536205C211yesmaximal, characteristic, complemented
8#14536171C211yesmaximal, characteristic, complemented
9#14536103C211yesmaximal, characteristic, complemented
10#14536003C211yesmaximal, characteristic, complemented
11#14535906C211yesmaximal, characteristic, complemented
12#14535826C211yesmaximal, characteristic, complemented
13#14535820C211yesmaximal, characteristic, complemented
14#14535780C211yesmaximal, characteristic, complemented
15#14535414C211yesmaximal, characteristic, complemented
16#14535174C211yesmaximal, characteristic, complemented
17#14535161C211yesmaximal, characteristic, complemented
18#14534571C211yesmaximal, characteristic, complemented
19#14534531C211yesmaximal, characteristic, complemented
20#14533345C211yesmaximal, characteristic, complemented
21#14533105C211yesmaximal, characteristic, complemented
22#14532533C211yesmaximal, characteristic, complemented
23#14532451C211yesmaximal, characteristic, complemented
24#14532332C211yesmaximal, characteristic, complemented
25#14532175C211yesmaximal, characteristic, complemented
26#14532161C211yesmaximal, characteristic
27#14532113C211yesmaximal, characteristic, complemented
28#14531440C211yesmaximal, characteristic, complemented
29#14531361C211yesmaximal, characteristic, complemented
30D17×#388C211yesmaximal, characteristic, complemented
31C17×#2743C211yesmaximal, characteristic, complemented
32C23×D68C2211yescharacteristic
33C2×#10587584C2211yescharacteristic, complemented
34C2×#10587571C2211yescharacteristic, complemented
35C2×#10587580C2211yescharacteristic
36C2×#10587580C2211yescharacteristic
37C2×#10587569C2211yescharacteristic, complemented
38C2×#10587582C2211yescharacteristic, complemented
39C2×#10587582C2211yescharacteristic, complemented
40C2×#10587570C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587623C2211yescharacteristic
43C2×#10587623C2211yescharacteristic
44C2×C4×C22⋊D17C2211yescharacteristic, complemented
45C2×C4⋊C4×D17C2211yescharacteristic, complemented
46C2×C22⋊C4×D17C2211yescharacteristic
47C2×C22⋊C4×D17C2211yescharacteristic
48C2×C22⋊C4×D17C2211yescharacteristic
49C2×C22⋊C4×D17C2211yescharacteristic
50C2×C42×D17C2211yescharacteristic, complemented
51C17⋊#401C2211yescharacteristic, complemented
52#11762750C2211yescharacteristic, complemented
53#11762750C2211yescharacteristic, complemented
54#11762748C2211yescharacteristic, complemented
55#11762746C2211yescharacteristic, complemented
56#11762744C2211yescharacteristic, complemented
57#11762743C2211yescharacteristic, complemented
58#11762743C2211yescharacteristic, complemented
59#11762743C2211yescharacteristic, complemented
60#11762742C2211yescharacteristic, complemented
61#11762740C2211yescharacteristic, complemented
62#11762738C2211yescharacteristic, complemented
63#11762738C2211yescharacteristic, complemented
64#11762738C2211yescharacteristic, complemented
65#11762738C2211yescharacteristic, complemented
66#11762738C2211yescharacteristic, complemented
67#11762737C2211yescharacteristic
68#11762737C2211yescharacteristic, complemented
69#11762737C2211yescharacteristic, complemented
70#11762736C2211yescharacteristic, complemented
71#11762734C2211yescharacteristic
72#11762732C2211yescharacteristic
73#11762732C2211yescharacteristic
74#11762732C2211yescharacteristic, complemented
75#11762731C2211yescharacteristic, complemented
76#11762731C2211yescharacteristic, complemented
77#11762731C2211yescharacteristic, complemented
78#11762727C2211yescharacteristic
79#11762727C2211yescharacteristic
80#11762727C2211yescharacteristic
81#11762727C2211yescharacteristic
82#11762726C2211yescharacteristic
83#11762726C2211yescharacteristic
84#11762725C2211yescharacteristic, complemented
85#11762725C2211yescharacteristic, complemented
86#11762724C2211yescharacteristic, complemented
87#11762724C2211yescharacteristic, complemented
88#11762723C2211yescharacteristic
89#11762722C2211yescharacteristic, complemented
90#11762721C2211yescharacteristic
91#11762718C2211yescharacteristic
92#11762718C2211yescharacteristic
93#11762714C2211yescharacteristic, complemented
94#11762713C2211yescharacteristic, complemented
95#11762712C2211yescharacteristic
96#11762709C2211yescharacteristic, complemented
97#11762709C2211yescharacteristic, complemented
98#11762706C2211yescharacteristic, complemented
99#11762703C2211yescharacteristic
100#11762703C2211yescharacteristic, complemented
101#11762702C2211yescharacteristic
102#11762701C2211yescharacteristic, complemented
103#11762701C2211yescharacteristic, complemented
104#11762700C2211yescharacteristic, complemented
105#11762700C2211yescharacteristic, complemented
106#11762700C2211yescharacteristic, complemented
107#11762699C2211yescharacteristic, complemented
108#11762699C2211yescharacteristic, complemented
109#11762699C2211yescharacteristic, complemented
110#11762699C2211yescharacteristic, complemented
111#11762699C2211yescharacteristic, complemented
112#11762699C2211yescharacteristic, complemented
113#11762698C2211yescharacteristic, complemented
114#11762698C2211yescharacteristic, complemented
115#11762698C2211yescharacteristic, complemented
116#11762698C2211yescharacteristic, complemented
117#11762698C2211yescharacteristic, complemented
118#11762698C2211yescharacteristic, complemented
119#11762697C2211yescharacteristic
120#11762697C2211yescharacteristic
121#11762697C2211yescharacteristic
122#11762696C2211yescharacteristic, complemented
123#11762694C2211yescharacteristic, complemented
124#11762692C2211yescharacteristic, complemented
125#11762691C2211yescharacteristic, complemented
126#11762688C2211yescharacteristic, complemented
127#11762688C2211yescharacteristic, complemented
128#11762688C2211yescharacteristic, complemented
129#11762687C2211yescharacteristic
130#11762687C2211yescharacteristic
131#11762687C2211yescharacteristic
132#11762687C2211yescharacteristic
133#11762687C2211yescharacteristic
134#11762687C2211yescharacteristic
135#11762687C2211yescharacteristic
136#11762687C2211yescharacteristic
137#11762687C2211yescharacteristic
138#11762687C2211yescharacteristic
139#11762687C2211yescharacteristic
140#11762687C2211yescharacteristic
141#11762685C2211yescharacteristic, complemented
142#11762685C2211yescharacteristic, complemented
143#11762685C2211yescharacteristic, complemented
144#11762685C2211yescharacteristic, complemented
145#11762683C2211yescharacteristic, complemented
146#11762683C2211yescharacteristic, complemented
147#11762683C2211yescharacteristic, complemented
148#11762682C2211yescharacteristic
149#11762682C2211yescharacteristic
150#11762680C2211yescharacteristic, complemented
151#11762680C2211yescharacteristic, complemented
152#11762680C2211yescharacteristic, complemented
153#11762676C2211yescharacteristic, complemented
154#11762676C2211yescharacteristic, complemented
155#11762673C2211yescharacteristic, complemented
156#11762673C2211yescharacteristic, complemented
157#11762672C2211yescharacteristic
158#11762671C2211yescharacteristic, complemented
159#11762668C2211yescharacteristic, complemented
160#11762666C2211yescharacteristic, complemented
161#11762666C2211yescharacteristic, complemented
162#11762666C2211yescharacteristic, complemented
163#11762664C2211yescharacteristic
164#11762664C2211yescharacteristic
165#11762664C2211yescharacteristic
166#11762664C2211yescharacteristic
167#11762664C2211yescharacteristic
168#11762664C2211yescharacteristic
169#11762656C2211yescharacteristic, complemented
170#95×D17C2211yescharacteristic, complemented
171#95×D17C2211yescharacteristic, complemented
172C17×#400C2211yescharacteristic, complemented
173C17×#400C2211yescharacteristic, complemented
174C17×#400C2211yescharacteristic, complemented
175C17×#399C2211yescharacteristic
176C17×#396C2211yescharacteristic, complemented
177C17×#394C2211yescharacteristic
178C17×#388C2211yescharacteristic
179C17×#388C2211yescharacteristic, complemented
180C17×#387C2211yescharacteristic, complemented
181C17×#386C2211yescharacteristic
182C17×#386C2211yescharacteristic
183C17×#385C2211yescharacteristic
184C17×#381C2211yescharacteristic
185C17×#381C2211yescharacteristic, complemented
186C17×#380C2211yescharacteristic, complemented
187C24×D17C2311yescharacteristic
188C24×D17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C22×C22⋊D17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×D68—24no—
197C22×D68—42no—
198C22×D68—42no—
199C22×D68C2311yescharacteristic
200C22×D68C2311yescharacteristic
201C22×D68C2311yescharacteristic
202C22×D68C2311yescharacteristic
203C22×C4×D17C2311yescharacteristic
204C22×C4×D17C2311yescharacteristic
205C22×C4×D17C2311yescharacteristic
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2311yescharacteristic
208C22×C4×D17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×Dic34C2311yescharacteristic
212C2×C4⋊C4×C17C2311yescharacteristic
213C2×C4⋊C4×C17C2311yescharacteristic
214C2×C4⋊C4×C17C2311yescharacteristic
215C2×C4⋊C4×C17C2311yescharacteristic
216C2×C4⋊C4×C17C2311yescharacteristic
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C22⋊C4×C17C2311yescharacteristic
220C2×C22⋊C4×C17C2311yescharacteristic
221C2×C22⋊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×C42×C17C2311yescharacteristic
230C2×C22⋊Dic17C2311yescharacteristic
231C2×C22⋊Dic17C2311yescharacteristic
232C2×C22⋊Dic17C2311yescharacteristic
233C2×C22⋊Dic17C2311yescharacteristic
234C2×C22⋊Dic17C2311yescharacteristic
235C2×C22⋊Dic17C2311yescharacteristic
236C2×C22⋊Dic17C2311yescharacteristic
237C2×C22⋊Dic17C2311yescharacteristic
238C2×C22⋊Dic17C2311yescharacteristic
239C2×C22⋊Dic17C2311yescharacteristic
240#10587623—24no—
241#10587623—42no—
242C4×C22⋊D17—42no—
243C2×#63227C2311yescharacteristic
244C2×#63227C2311yescharacteristic
245C2×#63227C2311yescharacteristic
246C2×#63227C2311yescharacteristic
247C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
280C2×C4⋊Dic17C2311yescharacteristic
281C2×C4⋊Dic17C2311yescharacteristic
282C2×C4⋊Dic17C2311yescharacteristic
283C2×C4⋊Dic17C2311yescharacteristic
284C2×#63225C2311yescharacteristic
285C2×#63225C2311yescharacteristic
286C2×#63225C2311yescharacteristic
287C2×#63225C2311yescharacteristic
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×C4×Dic17C2311yescharacteristic
299C2×C4×Dic17C2311yescharacteristic
300C2×C4×Dic17C2311yescharacteristic
301C2×C4×Dic17C2311yescharacteristic
302C2×C4×Dic17C2311yescharacteristic
303C2×C4×Dic17C2311yescharacteristic
304#10587584—42no—
305#10587582—42no—
306#10587582—42no—
307#10587580—42no—
308#10587580—42no—
309C4⋊C4×D17—42no—
310#10587571—42no—
311#10587570—42no—
312#10587570—42no—
313#10587569—42no—
314C22⋊C4×D17—24no—
315C22⋊C4×D17—42no—
316C22⋊C4×D17—42no—
317C22⋊C4×D17—42no—
318C42×D17—42no—
319C17×#95C2311yescharacteristic
320C17×#95C2311yescharacteristic
321C17×#95C2311yescharacteristic
322C17×#95C2311yescharacteristic
323C17×#95C2311yescharacteristic
324C17×#95C2311yescharacteristic
325C17×#95C2311yescharacteristic
326C17×#95C2311yescharacteristic
327C17×#95C2311yescharacteristic
328C17×#95C2311yescharacteristic
329C17×#95C2311yescharacteristic
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333#10587502C2311yescharacteristic
334#10587502C2311yescharacteristic
335#10587502C2311yescharacteristic
336#10587502C2311yescharacteristic
337#10587502C2311yescharacteristic
338#10587502C2311yescharacteristic
339#10587502C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
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
363C24×C17C2411yescharacteristic
364C24×C17C2411yescharacteristic
365C23×D17—22no—
366C23×D17—22no—
367C23×D17—22no—
368C23×D17—41no—
369C23×D17—41no—
370C23×D17—41no—
371C23×D17—41no—
372C23×D17—41no—
373C23×D17—41no—
374C23×D17—41no—
375C23×D17—41no—
376C23×D17—41no—
377C23×D17—41no—
378C23×D17#4114yes—
379C23×D17C2411yescharacteristic
380C23×D17C2411yescharacteristic
381C23×D17C2411yescharacteristic
382C23×D17C2411yescharacteristic
383C2×D4×C17—22no—
384C2×D4×C17—41no—
385C2×D4×C17—41no—
386C22×C4×C17—22no—
387C22×C4×C17—41no—
388C22×C4×C17—41no—
389C22×C4×C17—41no—
390C22×C4×C17—41no—
391C22×C4×C17—41no—
392C22×C4×C17C2411yescharacteristic
393C22×C4×C17C2411yescharacteristic
394C22×C4×C17C2411yescharacteristic
395C22×C4×C17C2411yescharacteristic
396C22×C4×C17C2411yescharacteristic
397C22×C4×C17C2411yescharacteristic
398C22×C4×C17C2411yescharacteristic
399C22×C4×C17C2411yescharacteristic
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C2×C22⋊D17—22no—
406C2×C22⋊D17—22no—
407C2×C22⋊D17—22no—
408C2×C22⋊D17—22no—
409C2×C22⋊D17—22no—
410C2×C22⋊D17—41no—
411C2×C22⋊D17—41no—
412C2×C22⋊D17—41no—
413C2×C22⋊D17—41no—
414C2×C22⋊D17—41no—
415C2×C22⋊D17—41no—
416C2×C22⋊D17—41no—
417C22×Dic17C2411yescharacteristic
418C22×Dic17C2411yescharacteristic
419C22×Dic17C2411yescharacteristic
420C22×Dic17C2411yescharacteristic
421C22×Dic17C2411yescharacteristic
422C22×Dic17C2411yescharacteristic
423C22×Dic17C2411yescharacteristic
424C22×Dic17C2411yescharacteristic
425C22×Dic17C2411yescharacteristic
426C22×Dic17C2411yescharacteristic
427C22×Dic17C2411yescharacteristic
428C22×Dic17C2411yescharacteristic
429C2×D68—22no—
430C2×D68—22no—
431C2×D68—22no—
432C2×D68—22no—
433C2×D68—22no—
434C2×D68—22no—
435C2×D68—22no—
436C2×D68—22no—
437C2×D68—41no—
438C2×D68—41no—
439C2×D68—41no—
440C2×D68—41no—
441C2×D68—416no—
442C2×C4×D17—22no—
443C2×C4×D17—22no—
444C2×C4×D17—22no—
445C2×C4×D17—22no—
446C2×C4×D17—22no—
447C2×C4×D17—22no—
448C2×C4×D17—22no—
449C2×C4×D17—22no—
450C2×C4×D17—22no—
451C2×C4×D17—41no—
452C2×C4×D17—41no—
453C2×C4×D17—41no—
454C2×C4×D17—41no—
455C2×C4×D17—41no—
456C2×C4×D17—41no—
457C2×C4×D17—41no—
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×Dic34—22no—
467C2×Dic34—41no—
468C2×Dic34—41no—
469C4⋊C4×C17—41no—
470C4⋊C4×C17—41no—
471C4⋊C4×C17—41no—
472C4⋊C4×C17—41no—
473C4⋊C4×C17—41no—
474C4⋊C4×C17—41no—
475C4⋊C4×C17—41no—
476C22⋊C4×C17—22no—
477C22⋊C4×C17—41no—
478C22⋊C4×C17—41no—
479C22⋊C4×C17—41no—
480C22⋊C4×C17—41no—
481C22⋊C4×C17—41no—
482C22⋊C4×C17—41no—
483C22⋊C4×C17—41no—
484C22⋊C4×C17—41no—
485C22⋊C4×C17—41no—
486C42×C17—41no—
487C22⋊Dic17—22no—
488C22⋊Dic17—22no—
489C22⋊Dic17—22no—
490C22⋊Dic17—41no—
491C22⋊Dic17—41no—
492C22⋊Dic17—41no—
493C22⋊Dic17—41no—
494C22⋊Dic17—41no—
495C22⋊Dic17—41no—
496C22⋊Dic17—41no—
497#63227—22no—
498#63227—22no—
499#63227—22no—
500#63227—22no—
501#63227—22no—
502#63227—22no—
503#63227—22no—
504#63227—22no—
505#63227—22no—
506#63227—22no—
507#63227—41no—
508#63227—41no—
509#63227—41no—
510#63227—41no—
511#63227—41no—
512#63227—41no—
513#63227—41no—
514#63227—41no—
515#63227—41no—
516#63227—41no—
517#63227—41no—
518#63227—41no—
519#63227—41no—
520#63227—41no—
521#63227—41no—
522#63227—41no—
523#63227—41no—
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—
533C4⋊Dic17—41no—
534C4⋊Dic17—41no—
535C4⋊Dic17—41no—
536C4⋊Dic17—41no—
537C4⋊Dic17—41no—
538#63225—22no—
539#63225—41no—
540#63225—41no—
541#63225—41no—
542#63225—41no—
543#63225—41no—
544#63225—41no—
545#63225—41no—
546#63225—41no—
547#63225—41no—
548#63225—41no—
549#63225—41no—
550#63225—41no—
551#63225—41no—
552C4×Dic17—22no—
553C4×Dic17—22no—
554C4×Dic17—41no—
555C4×Dic17—41no—
556C4×Dic17—41no—
557C4×Dic17—41no—
558#36779—171nomaximal, Sylow
559C23×C17—21no—
560C23×C17—21no—
561C23×C17—21no—
562C23×C17—21no—
563C23×C17—21no—
564C23×C17—21no—
565C23×C17—21no—
566C23×C17—21no—
567C23×C17—21no—
568C23×C17—21no—
569C23×C17—21no—
570C23×C17—21no—
571C23×C17—21no—
572C23×C17C2×#4112yes—
573C23×C17C2511yescharacteristic
574C22×D17—21no—
575C22×D17—21no—
576C22×D17—21no—
577C22×D17—21no—
578C22×D17—21no—
579C22×D17—21no—
580C22×D17—21no—
581C22×D17—21no—
582C22×D17—21no—
583C22×D17—21no—
584C22×D17—28no—
585C22×D17—21no—
586C22×D17—21no—
587C22×D17—21no—
588C22×D17—21no—
589C22×D17—21no—
590C22×D17—21no—
591C22×D17—21no—
592C22×D17—21no—
593C22×D17—21no—
594C22×D17—21no—
595C22×D17—21no—
596C22×D17—21no—
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—44no—
600C22×D17—44no—
601C22×D17—44no—
602C22×D17—82no—
603C22×D17—82no—
604C22×D17—82no—
605C22×D17—82no—
606C22×D17—82no—
607C22×D17—82no—
608C22×D17—82no—
609C22×D17—82no—
610C22×D17—82no—
611C22×D17—82no—
612C22×D17C2×#4112yes—
613C22×D17C2×#4112yes—
614C22×D17H(5,𝔽2)12yes—
615C22×D17H(5,𝔽2)12yes—
616D4×C17—82no—
617C2×C4×C17—21no—
618C2×C4×C17—21no—
619C2×C4×C17—21no—
620C2×C4×C17—21no—
621C2×C4×C17—21no—
622C2×C4×C17—21no—
623C2×C4×C17—21no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
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—44no—
657C2×C4×C17—82no—
658C22⋊D17—44no—
659C22⋊D17—82no—
660C22⋊D17—82no—
661C22⋊D17—82no—
662C2×Dic17—21no—
663C2×Dic17—21no—
664C2×Dic17—21no—
665C2×Dic17—21no—
666C2×Dic17—21no—
667C2×Dic17—21no—
668C2×Dic17—21no—
669C2×Dic17—21no—
670C2×Dic17—21no—
671C2×Dic17—21no—
672C2×Dic17—21no—
673C2×Dic17—21no—
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
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×Dic17H(5,𝔽2)12yes—
698D68—44no—
699D68—44no—
700D68—44no—
701D68—44no—
702C4×D17—44no—
703C4×D17—44no—
704C4×D17—44no—
705C4×D17—44no—
706C4×D17—82no—
707C4×D17—82no—
708C4×D17—82no—
709C4×D17—82no—
710Dic34—82no—
711#2852—171no—
712#2850—171no—
713#2781—171no—
714#2781—171no—
715#2778—171no—
716#2765—171no—
717#2764—171no—
718#2761—171no—
719#2756—171no—
720#2749—171no—
721#2743D1711yescharacteristic, complemented
722#2741—171no—
723#2735—171no—
724#2735—171no—
725#2730—171no—
726#2702—171no—
727#2685—171no—
728#2684—171no—
729#2623—171no—
730#2618—171no—
731#2510—171no—
732#2488—171no—
733#2444—171no—
734#2437—171no—
735#2425—171no—
736#2412—171no—
737#2410—171no—
738#2405—171no—
739#2321—171no—
740#2308—171no—
741C2×#388—171no—
742C22×C17—22no—
743C22×C17—22no—
744C22×C17—22no—
745C22×C17—41no—
746C22×C17—41no—
747C22×C17—41no—
748C22×C17—41no—
749C22×C17—41no—
750C22×C17—41no—
751C22×C17—41no—
752C22×C17—41no—
753C22×C17—41no—
754C22×C17—41no—
755C22×C17—41no—
756C22×C17C22×#4111yescharacteristic
757C22×C17C2×H(5,𝔽2)11yescharacteristic
758C22×C17C2×H(5,𝔽2)11yescharacteristic
759C22×C17C2×H(5,𝔽2)11yescharacteristic
760C22×C17#58511yescharacteristic
761C22×C17#58511yescharacteristic
762C22×C17#58511yescharacteristic
763C2×D17—22no—
764C2×D17—22no—
765C2×D17—22no—
766C2×D17—22no—
767C2×D17—22no—
768C2×D17—22no—
769C2×D17—22no—
770C2×D17—22no—
771C2×D17—22no—
772C2×D17—41no—
773C2×D17—41no—
774C2×D17—41no—
775C2×D17—41no—
776C2×D17—41no—
777C2×D17—41no—
778C2×D17—41no—
779C2×D17—41no—
780C2×D17—41no—
781C2×D17—41no—
782C2×D17—41no—
783C2×D17—41no—
784C2×D17—41no—
785C2×D17—41no—
786C2×D17—41no—
787C2×D17—41no—
788C2×D17—41no—
789C2×D17—41no—
790C2×D17—88no—
791C2×D17—88no—
792C2×D17#53814yes—
793C4×C17—41no—
794C4×C17—41no—
795C4×C17—41no—
796C4×C17—41no—
797C4×C17—41no—
798C4×C17—41no—
799C4×C17—41no—
800C4×C17—41no—
801C4×C17—41no—
802C4×C17—41no—
803C4×C17—41no—
804C4×C17—41no—
805C4×C17—41no—
806Dic17—22no—
807Dic17—41no—
808Dic17—41no—
809Dic17—41no—
810Dic17—41no—
811Dic17—41no—
812Dic17—41no—
813Dic17—41no—
814Dic17—41no—
815Dic17—41no—
816Dic17—41no—
817Dic17—41no—
818C23×D4—171no—
819C2×#126—171no—
820C2×#124—171no—
821C2×#123—171no—
822C2×#123—171no—
823C2×#123—171no—
824C2×C22⋊Q8—171no—
825C2×C22⋊Q8—171no—
826C2×#121—171no—
827C2×#121—171no—
828C2×#120—171no—
829C2×#120—171no—
830C2×C4×D4—171no—
831C22×C4⋊C4—171no—
832C22×C22⋊C4—171no—
833C22×C22⋊C4—171no—
834C22×C22⋊C4—171no—
835C22×C22⋊C4—171no—
836C22×C42—171no—
837#401—171no—
838#400—171no—
839#400—171no—
840#400—171no—
841#400C2×D1711yescharacteristic, complemented
842#400C2×D1711yescharacteristic, complemented
843#400C2×D1711yescharacteristic, complemented
844#399—171no—
845#399—171no—
846#399C2×D1711yescharacteristic
847#398—171no—
848#398—171no—
849#398—171no—
850#398—171no—
851#398—171no—
852#397—171no—
853#397—171no—
854#397—171no—
855#397—171no—
856#397—171no—
857#397—171no—
858#397—171no—
859#397—171no—
860#397—171no—
861#397—171no—
862#396—171no—
863#396—171no—
864#396—171no—
865#396—171no—
866#396—171no—
867#396—171no—
868#396C2×D1711yescharacteristic, complemented
869#394—171no—
870#394—171no—
871#394—171no—
872#394—171no—
873#394—171no—
874#394—171no—
875#394—171no—
876#394—171no—
877#394—171no—
878#394—171no—
879#394—171no—
880#394C2×D1711yescharacteristic
881#393—171no—
882#393—171no—
883#392—171no—
884#392—171no—
885#391—171no—
886#391—171no—
887#390—171no—
888#390—171no—
889#390—171no—
890#389—171no—
891#388—171no—
892#388—171no—
893#388—171no—
894#388—171no—
895#388—171no—
896#388—171no—
897#388—171no—
898#388—171no—
899#388—171no—
900#388—171no—
901#388—171no—
902#388—171no—
903#388—171no—
904#388—171no—
905#388—171no—
906#388—171no—
907#388—171no—
908#388—171no—
909#388—171no—
910#388—171no—
911#388—171no—
912#388—171no—
913#388—171no—
914#388C2×D1711yescharacteristic
915#388C2×D1711yescharacteristic, complemented
916#387—171no—
917#387—171no—
918#387—171no—
919#387—171no—
920#387C2×D1711yescharacteristic, complemented
921#386—171no—
922#386—171no—
923#386—171no—
924#386—171no—
925#386—171no—
926#386—171no—
927#386—171no—
928#386—171no—
929#386—171no—
930#386—171no—
931#386—171no—
932#386—171no—
933#386—171no—
934#386—171no—
935#386—171no—
936#386—171no—
937#386—171no—
938#386—171no—
939#386—171no—
940#386C2×D1711yescharacteristic
941#386C2×D1711yescharacteristic
942#385—171no—
943#385—171no—
944#385—171no—
945#385—171no—
946#385—171no—
947#385—171no—
948#385—171no—
949#385—171no—
950#385C2×D1711yescharacteristic
951#383—171no—
952#383—171no—
953#382—171no—
954#382—171no—
955#381—171no—
956#381—171no—
957#381C2×D1711yescharacteristic
958#381C2×D1711yescharacteristic, complemented
959#380—171no—
960#380—171no—
961#380—171no—
962#380—171no—
963#380C2×D1711yescharacteristic, complemented
964#379—171no—
965#379—171no—
966#379—171no—
967#379—171no—
968#379—171no—
969#379—171no—
970C4×C22⋊C4—171no—
971C2×#95—171no—
972C2×#95—171no—
973C2×C17—42no—
974C2×C17—81no—
975C2×C17C2×#53811yescharacteristic
976C2×C17#349111yescharacteristic
977C2×C17#350511yescharacteristic
978C2×C17#353411yescharacteristic
979C2×C17#354211yescharacteristic
980C2×C17#354511yescharacteristic
981C2×C17#356011yescharacteristic
982D17—24no—
983D17—42no—
984D17—81no—
985D17—81no—
986C25—171no—
987C25—171no—
988C22×Q8—171no—
989C22×D4—171no—
990C22×D4—171no—
991C22×D4—171no—
992C22×D4—171no—
993C22×D4—171no—
994C22×D4—171no—
995C22×D4—171no—
996C22×D4—171no—
997C22×D4—344no—
998C22×D4—682no—
999C22×D4—682no—
1000C22×D4C22×D1711yescharacteristic
1001C23×C4—171no—
1002C23×C4—171no—
1003C23×C4—171no—
1004C23×C4—171no—
1005C23×C4—171no—
1006C23×C4—171no—
1007C23×C4—171no—
1008C23×C4—171no—
1009C23×C4C22×D1711yescharacteristic
1010C23×C4C22×D1711yescharacteristic
1011#126—682no—
1012#124—682no—
1013#123—682no—
1014#123—682no—
1015#123—682no—
1016C22⋊Q8—682no—
1017C22⋊Q8—682no—
1018#121—682no—
1019#121—682no—
1020#120—344no—
1021#120—682no—
1022C4×D4—682no—
1023C2×C4⋊C4—171no—
1024C2×C4⋊C4—171no—
1025C2×C4⋊C4—171no—
1026C2×C4⋊C4—171no—
1027C2×C4⋊C4—171no—
1028C2×C4⋊C4—171no—
1029C2×C4⋊C4—171no—
1030C2×C4⋊C4—171no—
1031C2×C4⋊C4—171no—
1032C2×C4⋊C4—171no—
1033C2×C4⋊C4—171no—
1034C2×C4⋊C4—171no—
1035C2×C4⋊C4—171no—
1036C2×C4⋊C4—171no—
1037C2×C4⋊C4—171no—
1038C2×C4⋊C4—171no—
1039C2×C4⋊C4—171no—
1040C2×C4⋊C4—171no—
1041C2×C4⋊C4—171no—
1042C2×C4⋊C4—682no—
1043C2×C4⋊C4C22×D1711yescharacteristic
1044C2×C4⋊C4C22×D1711yescharacteristic
1045C2×C4⋊C4C22×D1711yescharacteristic
1046C2×C4⋊C4C22×D1711yescharacteristic
1047C2×C4⋊C4C22×D1711yescharacteristic
1048C2×C4⋊C4C22×D1711yescharacteristic
1049C2×C4⋊C4C22×D1711yescharacteristic
1050C2×C22⋊C4—171no—
1051C2×C22⋊C4—171no—
1052C2×C22⋊C4—171no—
1053C2×C22⋊C4—171no—
1054C2×C22⋊C4—171no—
1055C2×C22⋊C4—171no—
1056C2×C22⋊C4—171no—
1057C2×C22⋊C4—171no—
1058C2×C22⋊C4—171no—
1059C2×C22⋊C4—171no—
1060C2×C22⋊C4—171no—
1061C2×C22⋊C4—171no—
1062C2×C22⋊C4—171no—
1063C2×C22⋊C4—171no—
1064C2×C22⋊C4—171no—
1065C2×C22⋊C4—171no—
1066C2×C22⋊C4—171no—
1067C2×C22⋊C4—171no—
1068C2×C22⋊C4—171no—
1069C2×C22⋊C4—171no—
1070C2×C22⋊C4—171no—
1071C2×C22⋊C4—171no—
1072C2×C22⋊C4—171no—
1073C2×C22⋊C4—171no—
1074C2×C22⋊C4—171no—
1075C2×C22⋊C4—171no—
1076C2×C22⋊C4—171no—
1077C2×C22⋊C4—171no—
1078C2×C22⋊C4—171no—
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—344no—
1097C2×C22⋊C4—682no—
1098C2×C22⋊C4—682no—
1099C2×C22⋊C4—682no—
1100C2×C22⋊C4C22×D1711yescharacteristic
1101C2×C22⋊C4C22×D1711yescharacteristic
1102C2×C22⋊C4C22×D1711yescharacteristic
1103C2×C22⋊C4C22×D1711yescharacteristic
1104C2×C22⋊C4C22×D1711yescharacteristic
1105C2×C22⋊C4C22×D1711yescharacteristic
1106C2×C22⋊C4C22×D1711yescharacteristic
1107C2×C22⋊C4C22×D1711yescharacteristic
1108C2×C22⋊C4C22×D1711yescharacteristic
1109C2×C22⋊C4C22×D1711yescharacteristic
1110C2×C42—171no—
1111C2×C42—171no—
1112C2×C42—171no—
1113C2×C42—171no—
1114C2×C42—171no—
1115C2×C42—171no—
1116C2×C42—682no—
1117C2×C42C22×D1711yescharacteristic
1118#95—171no—
1119#95—171no—
1120#95—171no—
1121#95—171no—
1122#95—171no—
1123#95—171no—
1124#95—171no—
1125#95—171no—
1126#95—171no—
1127#95—171no—
1128#95—171no—
1129#95—171no—
1130#95—171no—
1131#95—171no—
1132#95—171no—
1133#95—171no—
1134#95—171no—
1135#95—171no—
1136#95—171no—
1137#95—171no—
1138#95—171no—
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95C22×D1711yescharacteristic
1149#95C22×D1711yescharacteristic
1150#95C22×D1711yescharacteristic
1151#95C22×D1711yescharacteristic
1152#95C22×D1711yescharacteristic
1153#95C22×D1711yescharacteristic
1154#95C22×D1711yescharacteristic
1155#95C22×D1711yescharacteristic
1156#95C22×D1711yescharacteristic
1157#95C22×D1711yescharacteristic
1158#95C22×D1711yescharacteristic
1159#95C22×D1711yescharacteristic
1160#95C22×D1711yescharacteristic
1161#95C22×D1711yescharacteristic
1162C17#3677911yescharacteristic, complemented, Sylow
1163C24—171no—
1164C24—171no—
1165C24—174no—
1166C24—171no—
1167C24—171no—
1168C24—342no—
1169C24—342no—
1170C24—342no—
1171C24—681no—
1172C24—681no—
1173C24—681no—
1174C24—681no—
1175C24—681no—
1176C24—681no—
1177C24—681no—
1178C24—681no—
1179C24—681no—
1180C24—681no—
1181C24C23×D1711yescharacteristic
1182C24C23×D1711yescharacteristic
1183C2×Q8—342no—
1184C2×Q8—681no—
1185C2×Q8—681no—
1186C2×D4—22no—
1187C2×D4—41no—
1188C2×D4—41no—
1189C2×D4—342no—
1190C2×D4—342no—
1191C2×D4—342no—
1192C2×D4—342no—
1193C2×D4—342no—
1194C2×D4—342no—
1195C2×D4—342no—
1196C2×D4—342no—
1197C2×D4—342no—
1198C2×D4—342no—
1199C2×D4—342no—
1200C2×D4—342no—
1201C2×D4—342no—
1202C2×D4—681no—
1203C2×D4—681no—
1204C2×D4—681no—
1205C2×D4—681no—
1206C2×D4—6816no—
1207C2×D4—681no—
1208C2×D4—681no—
1209C2×D4—681no—
1210C2×D4—681no—
1211C2×D4—681no—
1212C2×D4—681no—
1213C2×D4—681no—
1214C22×C4—22no—
1215C22×C4—41no—
1216C22×C4—41no—
1217C22×C4—41no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—171no—
1221C22×C4—171no—
1222C22×C4—171no—
1223C22×C4—171no—
1224C22×C4—171no—
1225C22×C4—171no—
1226C22×C4—171no—
1227C22×C4—171no—
1228C22×C4—171no—
1229C22×C4—171no—
1230C22×C4—171no—
1231C22×C4—171no—
1232C22×C4—342no—
1233C22×C4—342no—
1234C22×C4—342no—
1235C22×C4—342no—
1236C22×C4—342no—
1237C22×C4—342no—
1238C22×C4—342no—
1239C22×C4—342no—
1240C22×C4—342no—
1241C22×C4—681no—
1242C22×C4—681no—
1243C22×C4—681no—
1244C22×C4—681no—
1245C22×C4—681no—
1246C22×C4—681no—
1247C22×C4—681no—
1248C22×C4—681no—
1249C22×C4—681no—
1250C22×C4—681no—
1251C22×C4—681no—
1252C22×C4—681no—
1253C22×C4—681no—
1254C22×C4—681no—
1255C22×C4—681no—
1256C22×C4C23×D1711yescharacteristic
1257C22×C4C23×D1711yescharacteristic
1258C22×C4C23×D1711yescharacteristic
1259C22×C4C23×D1711yescharacteristic
1260C22×C4C23×D1711yescharacteristic
1261C22×C4C23×D1711yescharacteristic
1262C22×C4C23×D1711yescharacteristic
1263C22×C4C23×D1711yescharacteristic
1264C22×C4C23×D1711yescharacteristic
1265C22×C4C23×D1711yescharacteristic
1266C22×C4C23×D1711yescharacteristic
1267C22×C4C23×D1711yescharacteristic
1268C22×C4C23×D1711yescharacteristic
1269C4⋊C4—41no—
1270C4⋊C4—41no—
1271C4⋊C4—41no—
1272C4⋊C4—41no—
1273C4⋊C4—41no—
1274C4⋊C4—41no—
1275C4⋊C4—41no—
1276C4⋊C4—342no—
1277C4⋊C4—681no—
1278C4⋊C4—681no—
1279C4⋊C4—681no—
1280C4⋊C4—681no—
1281C4⋊C4—681no—
1282C4⋊C4—681no—
1283C4⋊C4—681no—
1284C4⋊C4—681no—
1285C4⋊C4—681no—
1286C4⋊C4—681no—
1287C4⋊C4—681no—
1288C4⋊C4—681no—
1289C4⋊C4—681no—
1290C4⋊C4—681no—
1291C4⋊C4—681no—
1292C4⋊C4—681no—
1293C4⋊C4—681no—
1294C4⋊C4—681no—
1295C22⋊C4—22no—
1296C22⋊C4—41no—
1297C22⋊C4—41no—
1298C22⋊C4—41no—
1299C22⋊C4—41no—
1300C22⋊C4—41no—
1301C22⋊C4—41no—
1302C22⋊C4—41no—
1303C22⋊C4—41no—
1304C22⋊C4—41no—
1305C22⋊C4—342no—
1306C22⋊C4—342no—
1307C22⋊C4—342no—
1308C22⋊C4—342no—
1309C22⋊C4—342no—
1310C22⋊C4—342no—
1311C22⋊C4—342no—
1312C22⋊C4—342no—
1313C22⋊C4—342no—
1314C22⋊C4—342no—
1315C22⋊C4—342no—
1316C22⋊C4—342no—
1317C22⋊C4—342no—
1318C22⋊C4—681no—
1319C22⋊C4—681no—
1320C22⋊C4—681no—
1321C22⋊C4—681no—
1322C22⋊C4—681no—
1323C22⋊C4—681no—
1324C22⋊C4—681no—
1325C22⋊C4—681no—
1326C22⋊C4—681no—
1327C22⋊C4—681no—
1328C22⋊C4—681no—
1329C22⋊C4—681no—
1330C22⋊C4—681no—
1331C22⋊C4—681no—
1332C22⋊C4—681no—
1333C22⋊C4—681no—
1334C22⋊C4—681no—
1335C22⋊C4—681no—
1336C22⋊C4—681no—
1337C22⋊C4—681no—
1338C22⋊C4—681no—
1339C22⋊C4—681no—
1340C22⋊C4—681no—
1341C22⋊C4—681no—
1342C22⋊C4—681no—
1343C22⋊C4—681no—
1344C22⋊C4—681no—
1345C22⋊C4—681no—
1346C22⋊C4—681no—
1347C22⋊C4—681no—
1348C22⋊C4—681no—
1349C22⋊C4—681no—
1350C22⋊C4—681no—
1351C42—41no—
1352C42—342no—
1353C42—342no—
1354C42—681no—
1355C42—681no—
1356C42—681no—
1357C42—681no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—21no—
1370C23—21no—
1371C23—172no—
1372C23—172no—
1373C23—172no—
1374C23—172no—
1375C23—348no—
1376C23—341no—
1377C23—341no—
1378C23—341no—
1379C23—341no—
1380C23—341no—
1381C23—341no—
1382C23—341no—
1383C23—341no—
1384C23—341no—
1385C23—341no—
1386C23—341no—
1387C23—341no—
1388C23—341no—
1389C23—341no—
1390C23—341no—
1391C23—341no—
1392C23—341no—
1393C23—341no—
1394C23—341no—
1395C23—341no—
1396C23—341no—
1397C23—341no—
1398C23—341no—
1399C23—341no—
1400C23—684no—
1401C23—684no—
1402C23—684no—
1403C23—1362no—
1404C23—1362no—
1405C23—1362no—
1406C23—1362no—
1407C23—1362no—
1408C23—1362no—
1409C23—1362no—
1410C23—1362no—
1411C23—1362no—
1412C23—1362no—
1413C23#41×D1712yes—
1414C23C24×D1711yescharacteristic
1415Q8—1362no—
1416D4—82no—
1417D4—684no—
1418D4—684no—
1419D4—684no—
1420D4—684no—
1421D4—684no—
1422D4—1362no—
1423D4—1362no—
1424D4—1362no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—44no—
1465C2×C4—82no—
1466C2×C4—172no—
1467C2×C4—341no—
1468C2×C4—341no—
1469C2×C4—341no—
1470C2×C4—341no—
1471C2×C4—341no—
1472C2×C4—341no—
1473C2×C4—341no—
1474C2×C4—341no—
1475C2×C4—341no—
1476C2×C4—341no—
1477C2×C4—341no—
1478C2×C4—341no—
1479C2×C4—341no—
1480C2×C4—341no—
1481C2×C4—341no—
1482C2×C4—341no—
1483C2×C4—341no—
1484C2×C4—341no—
1485C2×C4—341no—
1486C2×C4—341no—
1487C2×C4—341no—
1488C2×C4—341no—
1489C2×C4—341no—
1490C2×C4—341no—
1491C2×C4—341no—
1492C2×C4—341no—
1493C2×C4—341no—
1494C2×C4—341no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—684no—
1503C2×C4—684no—
1504C2×C4—684no—
1505C2×C4—684no—
1506C2×C4—1362no—
1507C2×C4—1362no—
1508C2×C4—1362no—
1509C2×C4—1362no—
1510C22—22no—
1511C22—22no—
1512C22—22no—
1513C22—41no—
1514C22—41no—
1515C22—41no—
1516C22—41no—
1517C22—41no—
1518C22—41no—
1519C22—41no—
1520C22—41no—
1521C22—41no—
1522C22—41no—
1523C22—41no—
1524C22—174no—
1525C22—342no—
1526C22—342no—
1527C22—342no—
1528C22—342no—
1529C22—342no—
1530C22—342no—
1531C22—342no—
1532C22—342no—
1533C22—342no—
1534C22—681no—
1535C22—681no—
1536C22—681no—
1537C22—681no—
1538C22—681no—
1539C22—681no—
1540C22—681no—
1541C22—681no—
1542C22—681no—
1543C22—681no—
1544C22—681no—
1545C22—681no—
1546C22—681no—
1547C22—681no—
1548C22—681no—
1549C22—681no—
1550C22—681no—
1551C22—681no—
1552C22—1368no—
1553C22—1368no—
1554C22C2×#41×D1711yescharacteristic
1555C22H(5,𝔽2)×D1711yescharacteristic
1556C22H(5,𝔽2)×D1711yescharacteristic
1557C22H(5,𝔽2)×D1711yescharacteristic
1558C22#1176364511yescharacteristic
1559C22#1176364511yescharacteristic
1560C22#1176364611yescharacteristic
1561C4—41no—
1562C4—41no—
1563C4—41no—
1564C4—41no—
1565C4—41no—
1566C4—41no—
1567C4—41no—
1568C4—41no—
1569C4—41no—
1570C4—41no—
1571C4—41no—
1572C4—41no—
1573C4—41no—
1574C4—342no—
1575C4—681no—
1576C4—681no—
1577C4—681no—
1578C4—681no—
1579C4—681no—
1580C4—681no—
1581C4—681no—
1582C4—681no—
1583C4—681no—
1584C4—681no—
1585C4—681no—
1586C2—42no—
1587C2—81no—
1588C2—344no—
1589C2—682no—
1590C2—1361no—
1591C2—1361no—
1592C2D17×#53811yescharacteristic
1593C2#1454247911yescharacteristic
1594C2#1454261511yescharacteristic
1595C2#1454296711yescharacteristic
1596C2#1454309711yescharacteristic
1597C2#1454313711yescharacteristic
1598C2#1454333711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2743C2
prime radical#14532161C2
hypercenter#2743D17
hypocenterC17#36779
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2743

Complements

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

NH ≅ G/Ntype
1. #14537102C2semidirect
2. #14537082C2semidirect
3. #14536454C2semidirect
4. #14536444C2semidirect
5. #14536398C2semidirect
6. #14536215C2semidirect
7. #14536205C2semidirect
8. #14536171C2semidirect
9. #14536103C2semidirect
10. #14536003C2semidirect
11. #14535906C2semidirect
12. #14535826C2semidirect
13. #14535820C2semidirect
14. #14535780C2semidirect
15. #14535414C2semidirect
16. #14535174C2semidirect
17. #14535161C2semidirect
18. #14534571C2semidirect
19. #14534531C2semidirect
20. #14533345C2semidirect
21. #14533105C2semidirect
22. #14532533C2semidirect
23. #14532451C2semidirect
24. #14532332C2semidirect
25. #14532175C2semidirect
27. #14532113C2semidirect
28. #14531440C2semidirect
29. #14531361C2semidirect
30. D17×#388C2semidirect
31. C17×#2743C2semidirect
33. C2×#10587584C22semidirect
34. C2×#10587571C22semidirect
37. C2×#10587569C22semidirect
38. C2×#10587582C22semidirect
39. C2×#10587582C22semidirect
44. C2×C4×C22⋊D17C22semidirect
45. C2×C4⋊C4×D17C22semidirect
50. C2×C42×D17C22semidirect
51. C17⋊#401C22semidirect
52. #11762750C22semidirect
53. #11762750C22semidirect
54. #11762748C22semidirect
55. #11762746C22semidirect
56. #11762744C22semidirect
57. #11762743C22semidirect
58. #11762743C22semidirect
59. #11762743C22semidirect
60. #11762742C22semidirect
61. #11762740C22semidirect
62. #11762738C22semidirect
63. #11762738C22semidirect
64. #11762738C22semidirect
65. #11762738C22semidirect
66. #11762738C22semidirect
68. #11762737C22semidirect
69. #11762737C22semidirect
70. #11762736C22semidirect
74. #11762732C22semidirect
75. #11762731C22semidirect
76. #11762731C22semidirect
77. #11762731C22semidirect
84. #11762725C22semidirect
85. #11762725C22semidirect
86. #11762724C22semidirect
87. #11762724C22semidirect
89. #11762722C22semidirect
93. #11762714C22semidirect
94. #11762713C22semidirect
96. #11762709C22semidirect
97. #11762709C22semidirect
98. #11762706C22semidirect
100. #11762703C22semidirect
102. #11762701C22semidirect
103. #11762701C22semidirect
104. #11762700C22semidirect
105. #11762700C22semidirect
106. #11762700C22semidirect
107. #11762699C22semidirect
108. #11762699C22semidirect
109. #11762699C22semidirect
110. #11762699C22semidirect
111. #11762699C22semidirect
112. #11762699C22semidirect
113. #11762698C22semidirect
114. #11762698C22semidirect
115. #11762698C22semidirect
116. #11762698C22semidirect
117. #11762698C22semidirect
118. #11762698C22semidirect
122. #11762696C22semidirect
123. #11762694C22semidirect
124. #11762692C22semidirect
125. #11762691C22semidirect
126. #11762688C22semidirect
127. #11762688C22semidirect
128. #11762688C22semidirect
141. #11762685C22semidirect
142. #11762685C22semidirect
143. #11762685C22semidirect
144. #11762685C22semidirect
145. #11762683C22semidirect
146. #11762683C22semidirect
147. #11762683C22semidirect
150. #11762680C22semidirect
151. #11762680C22semidirect
152. #11762680C22semidirect
153. #11762676C22semidirect
154. #11762676C22semidirect
155. #11762673C22semidirect
156. #11762673C22semidirect
158. #11762671C22semidirect
159. #11762668C22semidirect
160. #11762666C22semidirect
161. #11762666C22semidirect
162. #11762666C22semidirect
169. #11762656C22semidirect
170. #95×D17C22semidirect
171. #95×D17C22semidirect
172. C17×#400C22semidirect
173. C17×#400C22semidirect
174. C17×#400C22semidirect
176. C17×#396C22semidirect
179. C17×#388C22semidirect
180. C17×#387C22semidirect
185. C17×#381C22semidirect
186. C17×#380C22semidirect
721. #2743D17semidirect
841. #400C2×D17semidirect
842. #400C2×D17semidirect
843. #400C2×D17semidirect
868. #396C2×D17semidirect
915. #388C2×D17semidirect
920. #387C2×D17semidirect
958. #381C2×D17semidirect
963. #380C2×D17semidirect
1162. C17#36779semidirect

Maximal subgroups

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

subgroupindex
#145371022
#145370822
#145364542
#145364442
#145363982
#145362152
#145362052
#145361712
#145361032
#145360032
#145359062
#145358262
#145358202
#145357802
#145354142
#145351742
#145351612
#145345712
#145345312
#145333452
#145331052
#145325332
#145324512
#145323322
#145321752
#145321612
#145321132
#145314402
#145313612
D17×#3882
C17×#27432
#3677917