Finite Group Databasebeta

← #17241183

Subgroups — #17241183

Order 4352.

2440 conjugacy classes of subgroups.

The subgroup lattice has 1676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763318C211yesmaximal, characteristic, complemented
2#14537073C211yesmaximal, characteristic, complemented
3#14537068C211yesmaximal, characteristic, complemented
4#14535328C211yesmaximal, characteristic, complemented
5#14535313C211yesmaximal, characteristic, complemented
6#14535274C211yesmaximal, characteristic, complemented
7#14535259C211yesmaximal, characteristic, complemented
8#14535229C211yesmaximal, characteristic, complemented
9#14535184C211yesmaximal, characteristic, complemented
10#14535169C211yesmaximal, characteristic, complemented
11#14535160C211yesmaximal, characteristic, complemented
12#14535094C211yesmaximal, characteristic, complemented
13#14535080C211yesmaximal, characteristic, complemented
14#14535060C211yesmaximal, characteristic, complemented
15#14535059C211yesmaximal, characteristic, complemented
16#14535030C211yesmaximal, characteristic, complemented
17#14535014C211yesmaximal, characteristic, complemented
18#14535005C211yesmaximal, characteristic, complemented
19#14534987C211yesmaximal, characteristic, complemented
20#14534702C211yesmaximal, characteristic, complemented
21#14534623C211yesmaximal, characteristic, complemented
22#14534456C211yesmaximal, characteristic, complemented
23#14534398C211yesmaximal, characteristic, complemented
24#14534355C211yesmaximal, characteristic, complemented
25#14534350C211yesmaximal, characteristic, complemented
26#14534142C211yesmaximal, characteristic, complemented
27#14533966C211yesmaximal, characteristic, complemented
28#14532413C211yesmaximal, characteristic, complemented
29#14532396C211yesmaximal, characteristic, complemented
30#14531417C211yesmaximal, characteristic, complemented
31C2×C17×#542C211yesmaximal, characteristic, complemented
32C22×#63252C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34C2×#10587630C2211yescharacteristic, complemented
35C2×#10587633C2211yescharacteristic
36#11763318—28no—
37C2×#10587580C2211yescharacteristic
38C2×#10587569C2211yescharacteristic
39C2×#10587621C2211yescharacteristic
40C2×#10587582C2211yescharacteristic
41C2×#10587564C2211yescharacteristic
42C2×#10587632C2211yescharacteristic
43C2×#10587632C2211yescharacteristic
44C2×#10587570C2211yescharacteristic
45C2×#10587625C2211yescharacteristic
46C2×#10587625C2211yescharacteristic
47C2×#10587625C2211yescharacteristic, complemented
48C2×#10587568C2211yescharacteristic
49C2×#10587623C2211yescharacteristic
50C2×#10587623C2211yescharacteristic
51C2×C4×D68C2211yescharacteristic
52C2×C4×C22⋊D17C2211yescharacteristic
53C2×C4×C22⋊D17C2211yescharacteristic
54C2×#10587558C2211yescharacteristic
55#11762748C2211yescharacteristic, complemented
56#11762747C2211yescharacteristic, complemented
57#11762745C2211yescharacteristic, complemented
58#11762744C2211yescharacteristic
59#11762744C2211yescharacteristic
60#11762744C2211yescharacteristic, complemented
61#11762742C2211yescharacteristic, complemented
62#11762742C2211yescharacteristic, complemented
63#11762740C2211yescharacteristic, complemented
64#11762740C2211yescharacteristic, complemented
65#11762737C2211yescharacteristic
66#11762737C2211yescharacteristic
67#11762737C2211yescharacteristic
68#11762737C2211yescharacteristic, complemented
69#11762735C2211yescharacteristic
70#11762735C2211yescharacteristic, complemented
71#11762732C2211yescharacteristic, complemented
72#11762732C2211yescharacteristic, complemented
73#11762731C2211yescharacteristic
74#11762731C2211yescharacteristic, complemented
75#11762729C2211yescharacteristic, complemented
76#11762728C2211yescharacteristic, complemented
77#11762728C2211yescharacteristic, complemented
78#11762728C2211yescharacteristic, complemented
79#11762726C2211yescharacteristic
80#11762726C2211yescharacteristic
81#11762725C2211yescharacteristic
82#11762725C2211yescharacteristic, complemented
83#11762724C2211yescharacteristic
84#11762724C2211yescharacteristic
85#11762724C2211yescharacteristic
86#11762724C2211yescharacteristic
87#11762724C2211yescharacteristic
88#11762724C2211yescharacteristic
89#11762724C2211yescharacteristic, complemented
90#11762724C2211yescharacteristic, complemented
91#11762723C2211yescharacteristic
92#11762723C2211yescharacteristic, complemented
93#11762721C2211yescharacteristic, complemented
94#11762720C2211yescharacteristic
95#11762720C2211yescharacteristic
96#11762720C2211yescharacteristic
97#11762720C2211yescharacteristic, complemented
98#11762720C2211yescharacteristic, complemented
99#11762718C2211yescharacteristic
100#11762718C2211yescharacteristic
101#11762717C2211yescharacteristic
102#11762717C2211yescharacteristic
103#11762714C2211yescharacteristic, complemented
104#11762711C2211yescharacteristic
105#11762711C2211yescharacteristic
106#11762710C2211yescharacteristic
107#11762709C2211yescharacteristic
108#11762707C2211yescharacteristic, complemented
109#11762707C2211yescharacteristic, complemented
110#11762704C2211yescharacteristic, complemented
111#11762703C2211yescharacteristic, complemented
112#11762702C2211yescharacteristic
113#11762702C2211yescharacteristic
114#11762700C2211yescharacteristic
115#11762700C2211yescharacteristic
116#11762700C2211yescharacteristic
117#11762700C2211yescharacteristic
118#11762700C2211yescharacteristic, complemented
119#11762699C2211yescharacteristic
120#11762697C2211yescharacteristic, complemented
121#11762695C2211yescharacteristic, complemented
122#11762695C2211yescharacteristic, complemented
123#11762693C2211yescharacteristic, complemented
124#11762693C2211yescharacteristic, complemented
125#11762693C2211yescharacteristic, complemented
126#11762690C2211yescharacteristic, complemented
127#11762690C2211yescharacteristic, complemented
128#11762690C2211yescharacteristic, complemented
129#11762689C2211yescharacteristic
130#11762689C2211yescharacteristic
131#11762688C2211yescharacteristic
132#11762688C2211yescharacteristic
133#11762688C2211yescharacteristic, complemented
134#11762686C2211yescharacteristic
135#11762686C2211yescharacteristic
136#11762686C2211yescharacteristic
137#11762686C2211yescharacteristic, complemented
138#11762685C2211yescharacteristic
139#11762685C2211yescharacteristic
140#11762685C2211yescharacteristic
141#11762685C2211yescharacteristic
142#11762685C2211yescharacteristic, complemented
143#11762684C2211yescharacteristic, complemented
144#11762684C2211yescharacteristic, complemented
145#11762682C2211yescharacteristic, complemented
146#11762681C2211yescharacteristic
147#11762681C2211yescharacteristic
148#11762680C2211yescharacteristic
149#11762680C2211yescharacteristic
150#11762680C2211yescharacteristic
151#11762680C2211yescharacteristic
152#11762680C2211yescharacteristic
153#11762680C2211yescharacteristic
154#11762680C2211yescharacteristic
155#11762680C2211yescharacteristic
156#11762680C2211yescharacteristic, complemented
157#11762680C2211yescharacteristic, complemented
158#11762680C2211yescharacteristic, complemented
159#11762677C2211yescharacteristic, complemented
160#11762675C2211yescharacteristic, complemented
161#11762672C2211yescharacteristic
162#11762670C2211yescharacteristic
163#11762669C2211yescharacteristic
164#11762667C2211yescharacteristic, complemented
165#11762667C2211yescharacteristic, complemented
166#11762666C2211yescharacteristic
167#11762666C2211yescharacteristic
168#11762664C2211yescharacteristic
169#11762664C2211yescharacteristic
170#11762664C2211yescharacteristic
171C4×C22⋊Dic17C2211yescharacteristic, complemented
172C2×#10587502C2211yescharacteristic, complemented
173C17×#542—28no—
174C2×C17×C4⋊Q8C2211yescharacteristic, complemented
175C2×C17×#126C2211yescharacteristic
176C2×C17×#126C2211yescharacteristic, complemented
177C2×C17×#124C2211yescharacteristic
178C2×C17×#124C2211yescharacteristic
179C2×C17×#124C2211yescharacteristic, complemented
180C2×C17×#123C2211yescharacteristic
181C2×C17×#123C2211yescharacteristic, complemented
182C2×C17×C22⋊Q8C2211yescharacteristic
183C2×C17×C22⋊Q8C2211yescharacteristic, complemented
184C2×C17×C22⋊Q8C2211yescharacteristic, complemented
185C2×C17×#121C2211yescharacteristic
186C2×C4×Q8×C17C2211yescharacteristic, complemented
187C2×C4×D4×C17C2211yescharacteristic
188C2×C17×#117C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C22×Q8×C17C2311yescharacteristic
191C22×Q8×C17C2311yescharacteristic
192C22×Q8×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C23×C4×C17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C2×#63252—24no—
210C2×#63252—42no—
211C2×#63252—42no—
212C22×D68C2311yescharacteristic
213C22×D68C2311yescharacteristic
214C22×C4×D17—24no—
215C22×C4×D17—42no—
216C22×C4×D17—42no—
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×Dic34C2311yescharacteristic
223C17×C4⋊Q8—24no—
224C17×#126—24no—
225C17×#126—24no—
226C17×#124—24no—
227C17×#124—24no—
228C17×#124—24no—
229C17×#123—24no—
230C17×#123—24no—
231C17×C22⋊Q8—24no—
232C17×C22⋊Q8—24no—
233C17×C22⋊Q8—24no—
234C17×#121—24no—
235C4×Q8×C17—24no—
236C4×D4×C17D418yescomplemented
237C17×#117—24no—
238C2×C4⋊C4×C17C2311yescharacteristic
239C2×C4⋊C4×C17C2311yescharacteristic
240C2×C4⋊C4×C17C2311yescharacteristic
241C2×C4⋊C4×C17C2311yescharacteristic
242C2×C4⋊C4×C17C2311yescharacteristic
243C2×C4⋊C4×C17C2311yescharacteristic
244C2×C4⋊C4×C17C2311yescharacteristic
245C2×C4⋊C4×C17C2311yescharacteristic
246C2×C4⋊C4×C17C2311yescharacteristic
247C2×C4⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C22⋊C4×C17C2311yescharacteristic
250C2×C22⋊C4×C17C2311yescharacteristic
251C2×C22⋊C4×C17C2311yescharacteristic
252C2×C22⋊C4×C17C2311yescharacteristic
253C2×C22⋊C4×C17C2311yescharacteristic
254C2×C22⋊C4×C17C2311yescharacteristic
255C2×C22⋊C4×C17C2311yescharacteristic
256C2×C22⋊C4×C17C2311yescharacteristic
257C2×C22⋊C4×C17C2311yescharacteristic
258C2×C22⋊C4×C17C2311yescharacteristic
259C2×C22⋊C4×C17C2311yescharacteristic
260C2×C42×C17C2311yescharacteristic
261C2×C42×C17C2311yescharacteristic
262C2×C42×C17C2311yescharacteristic
263C2×C42×C17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266C2×C22⋊Dic17C2311yescharacteristic
267C2×C22⋊Dic17C2311yescharacteristic
268C2×C22⋊Dic17C2311yescharacteristic
269C2×C22⋊Dic17C2311yescharacteristic
270C2×C22⋊Dic17C2311yescharacteristic
271C2×C22⋊Dic17C2311yescharacteristic
272C2×C22⋊Dic17C2311yescharacteristic
273C2×C22⋊Dic17C2311yescharacteristic
274C2×C22⋊Dic17C2311yescharacteristic
275C2×C22⋊Dic17C2311yescharacteristic
276C2×C22⋊Dic17C2311yescharacteristic
277#10587633—42no—
278#10587632—42no—
279#10587632—42no—
280#10587630—42no—
281#10587625—24no—
282#10587625—42no—
283#10587625—42no—
284#10587623—24no—
285#10587623—42no—
286#10587621—42no—
287C4×C22⋊D17—24no—
288C4×C22⋊D17—24no—
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295C2×#63227C2311yescharacteristic
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299C2×#63227C2311yescharacteristic
300C2×#63227C2311yescharacteristic
301C2×#63227C2311yescharacteristic
302C2×#63227C2311yescharacteristic
303C2×#63227C2311yescharacteristic
304C2×#63227C2311yescharacteristic
305C2×#63227C2311yescharacteristic
306C2×#63227C2311yescharacteristic
307C2×#63227C2311yescharacteristic
308C2×#63227C2311yescharacteristic
309C2×#63227C2311yescharacteristic
310C2×#63227C2311yescharacteristic
311C2×#63227C2311yescharacteristic
312C2×#63227C2311yescharacteristic
313C2×#63227C2311yescharacteristic
314C2×#63227C2311yescharacteristic
315C2×#63227C2311yescharacteristic
316C2×C4⋊Dic17C2311yescharacteristic
317C2×C4⋊Dic17C2311yescharacteristic
318C2×C4⋊Dic17C2311yescharacteristic
319C2×C4⋊Dic17C2311yescharacteristic
320C2×C4⋊Dic17C2311yescharacteristic
321C2×#63225C2311yescharacteristic
322C2×#63225C2311yescharacteristic
323C2×#63225C2311yescharacteristic
324C2×#63225C2311yescharacteristic
325C2×#63225C2311yescharacteristic
326C2×#63225C2311yescharacteristic
327C2×#63225C2311yescharacteristic
328C2×#63225C2311yescharacteristic
329C2×#63225C2311yescharacteristic
330C2×#63225C2311yescharacteristic
331C2×#63225C2311yescharacteristic
332C2×#63225C2311yescharacteristic
333C2×#63225C2311yescharacteristic
334C2×#63225C2311yescharacteristic
335C2×#63225C2311yescharacteristic
336C2×#63225C2311yescharacteristic
337C2×#63225C2311yescharacteristic
338C2×C4×Dic17C2311yescharacteristic
339C2×C4×Dic17C2311yescharacteristic
340C2×C4×Dic17C2311yescharacteristic
341#10587582—24no—
342#10587580—24no—
343#10587570—24no—
344#10587569—24no—
345#10587568—24no—
346#10587564—24no—
347C4×D68—24no—
348#10587558—24no—
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
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382#10587502C2311yescharacteristic
383#10587502C2311yescharacteristic
384#10587502C2311yescharacteristic
385C24×C17C2411yescharacteristic
386C24×C17C2411yescharacteristic
387C24×C17C2411yescharacteristic
388C23×D17—22no—
389C23×D17—22no—
390C23×D17—22no—
391C23×D17—41no—
392C23×D17—41no—
393C23×D17—41no—
394C23×D17—41no—
395C23×D17C2411yescharacteristic
396C23×D17C2411yescharacteristic
397C23×D17C2411yescharacteristic
398C2×Q8×C17—22no—
399C2×Q8×C17—22no—
400C2×Q8×C17—22no—
401C2×Q8×C17—41no—
402C2×Q8×C17—41no—
403C2×Q8×C17—41no—
404C2×Q8×C17—41no—
405C2×Q8×C17—41no—
406C2×Q8×C17—41no—
407C2×D4×C17—22no—
408C2×D4×C17—22no—
409C2×D4×C17—41no—
410C2×D4×C17—41no—
411C2×D4×C17—41no—
412C2×D4×C17—41no—
413C2×D4×C17—41no—
414C2×D4×C17—41no—
415C2×D4×C17C2×D414yes—
416C22×C4×C17—22no—
417C22×C4×C17—41no—
418C22×C4×C17—41no—
419C22×C4×C17—41no—
420C22×C4×C17—41no—
421C22×C4×C17—41no—
422C22×C4×C17—41no—
423C22×C4×C17C2×D414yes—
424C22×C4×C17C2×D414yes—
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C22×C4×C17C2411yescharacteristic
433C22×C4×C17C2411yescharacteristic
434C22×C4×C17C2411yescharacteristic
435C22×C4×C17C2411yescharacteristic
436C22×C4×C17C2411yescharacteristic
437C2×C22⋊D17—22no—
438C2×C22⋊D17—22no—
439C2×C22⋊D17—22no—
440C2×C22⋊D17—22no—
441C2×C22⋊D17—22no—
442C2×C22⋊D17—22no—
443C2×C22⋊D17—22no—
444C2×C22⋊D17—22no—
445C2×C22⋊D17—22no—
446C2×C22⋊D17—41no—
447C2×C22⋊D17—41no—
448C2×C22⋊D17—41no—
449C2×C22⋊D17—41no—
450C2×C22⋊D17—41no—
451C2×C22⋊D17—41no—
452C2×C22⋊D17—41no—
453C2×C22⋊D17—41no—
454C2×C22⋊D17—41no—
455C2×C22⋊D17—41no—
456C2×C22⋊D17—41no—
457C2×C22⋊D17—41no—
458C22×Dic17—22no—
459C22×Dic17—22no—
460C22×Dic17—41no—
461C22×Dic17—41no—
462C22×Dic17—41no—
463C22×Dic17—41no—
464C22×Dic17—41no—
465C22×Dic17—41no—
466C22×Dic17—41no—
467C22×Dic17C2411yescharacteristic
468C22×Dic17C2411yescharacteristic
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471C22×Dic17C2411yescharacteristic
472C22×Dic17C2411yescharacteristic
473C22×Dic17C2411yescharacteristic
474C22×Dic17C2411yescharacteristic
475C22×Dic17C2411yescharacteristic
476C22×Dic17C2411yescharacteristic
477C22×Dic17C2411yescharacteristic
478C22×Dic17C2411yescharacteristic
479C22×Dic17C2411yescharacteristic
480#63252—416no—
481C2×D68—22no—
482C2×D68—22no—
483C2×D68—22no—
484C2×D68—22no—
485C2×D68—41no—
486C2×D68—41no—
487C2×C4×D17—22no—
488C2×C4×D17—22no—
489C2×C4×D17—22no—
490C2×C4×D17—22no—
491C2×C4×D17—22no—
492C2×C4×D17—22no—
493C2×C4×D17—22no—
494C2×C4×D17—22no—
495C2×C4×D17—22no—
496C2×C4×D17—416no—
497C2×C4×D17—41no—
498C2×C4×D17—41no—
499C2×C4×D17—41no—
500C2×C4×D17—41no—
501C2×C4×D17—41no—
502C2×C4×D17—41no—
503C2×Dic34—22no—
504C2×Dic34—22no—
505C2×Dic34—41no—
506C4⋊C4×C17—22no—
507C4⋊C4×C17—22no—
508C4⋊C4×C17—22no—
509C4⋊C4×C17—22no—
510C4⋊C4×C17—22no—
511C4⋊C4×C17—22no—
512C4⋊C4×C17—22no—
513C4⋊C4×C17—22no—
514C4⋊C4×C17—22no—
515C4⋊C4×C17C2×D414yes—
516C22⋊C4×C17—22no—
517C22⋊C4×C17—22no—
518C22⋊C4×C17—22no—
519C22⋊C4×C17—22no—
520C22⋊C4×C17—22no—
521C22⋊C4×C17—22no—
522C22⋊C4×C17—22no—
523C22⋊C4×C17—22no—
524C22⋊C4×C17—22no—
525C22⋊C4×C17—22no—
526C22⋊C4×C17C2×D414yes—
527C22⋊C4×C17C2×D414yes—
528C42×C17—22no—
529C42×C17—22no—
530C42×C17—22no—
531C42×C17C2×D414yes—
532C22⋊Dic17—22no—
533C22⋊Dic17—22no—
534C22⋊Dic17—22no—
535C22⋊Dic17—41no—
536C22⋊Dic17—41no—
537C22⋊Dic17—41no—
538C22⋊Dic17—41no—
539C22⋊Dic17—41no—
540C22⋊Dic17—41no—
541C22⋊Dic17—41no—
542C22⋊Dic17—41no—
543C22⋊Dic17—41no—
544C22⋊Dic17—41no—
545#63227—22no—
546#63227—22no—
547#63227—22no—
548#63227—22no—
549#63227—22no—
550#63227—22no—
551#63227—22no—
552#63227—22no—
553#63227—22no—
554#63227—22no—
555#63227—41no—
556#63227—41no—
557#63227—41no—
558#63227—41no—
559#63227—41no—
560#63227—41no—
561#63227—41no—
562#63227—41no—
563#63227—41no—
564#63227—41no—
565#63227—41no—
566#63227—41no—
567#63227—41no—
568#63227—41no—
569#63227—41no—
570#63227—41no—
571#63227—41no—
572C4⋊Dic17—22no—
573C4⋊Dic17—41no—
574C4⋊Dic17—41no—
575C4⋊Dic17—41no—
576C4⋊Dic17—41no—
577#63225—22no—
578#63225—22no—
579#63225—22no—
580#63225—22no—
581#63225—22no—
582#63225—22no—
583#63225—22no—
584#63225—41no—
585#63225—41no—
586#63225—41no—
587#63225—41no—
588#63225—41no—
589#63225—41no—
590#63225—41no—
591#63225—41no—
592#63225—41no—
593#63225—41no—
594C4×Dic17—22no—
595C4×Dic17—41no—
596C4×Dic17—41no—
597#36712—171nomaximal, Sylow
598C23×C17—21no—
599C23×C17—21no—
600C23×C17—21no—
601C23×C17—21no—
602C23×C17—21no—
603C23×C17—21no—
604C23×C17—21no—
605C23×C17—21no—
606C23×C17—21no—
607C23×C17—21no—
608C23×C17—21no—
609C23×C17—21no—
610C23×C17—21no—
611C23×C17—21no—
612C23×C17—21no—
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17C22×D412yes—
618C23×C17C22×D412yes—
619C23×C17C2511yescharacteristic
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—21no—
624C22×D17—21no—
625C22×D17—21no—
626C22×D17—21no—
627C22×D17—21no—
628C22×D17—21no—
629C22×D17—21no—
630C22×D17—21no—
631C22×D17—21no—
632C22×D17—21no—
633C22×D17—21no—
634C22×D17—21no—
635C22×D17—21no—
636C22×D17—21no—
637C22×D17—21no—
638C22×D17—21no—
639C22×D17—44no—
640C22×D17—44no—
641C22×D17—44no—
642C22×D17—44no—
643C22×D17—44no—
644C22×D17—44no—
645C22×D17—44no—
646C22×D17H(5,𝔽2)12yes—
647C22×D172−1+412yes—
648Q8×C17—44no—
649Q8×C17—82no—
650Q8×C17—82no—
651D4×C17—44no—
652D4×C17—82no—
653D4×C17—82no—
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—21no—
672C2×C4×C17—21no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—21no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—21no—
685C2×C4×C17—44no—
686C2×C4×C17—44no—
687C2×C4×C17—44no—
688C2×C4×C17C22×D412yes—
689C2×C4×C17C22×D412yes—
690C2×C4×C17C22×D412yes—
691C2×C4×C17C22×D412yes—
692C2×C4×C17C22×D412yes—
693C22⋊D17—44no—
694C22⋊D17—44no—
695C22⋊D17—44no—
696C22⋊D17—44no—
697C22⋊D17—82no—
698C22⋊D17—82no—
699C22⋊D17—82no—
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—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—21no—
723C2×Dic17—21no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—21no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—21no—
734C2×Dic17—21no—
735C2×Dic17—21no—
736C2×Dic17—21no—
737C2×Dic17—21no—
738C2×Dic17—44no—
739C2×Dic17—82no—
740C2×Dic17—82no—
741C2×Dic17H(5,𝔽2)12yes—
742D68—44no—
743D68—44no—
744C4×D17—28no—
745C4×D17—44no—
746C4×D17—44no—
747C4×D17—44no—
748C4×D17—44no—
749Dic34—44no—
750C2×#542D1711yescharacteristic, complemented
751C2×#525—171no—
752#2849—171no—
753#2848—171no—
754#2696—171no—
755#2695—171no—
756#2692—171no—
757#2691—171no—
758#2689—171no—
759#2686—171no—
760#2685—171no—
761#2684—171no—
762#2677—171no—
763#2676—171no—
764#2674—171no—
765#2674—171no—
766#2672—171no—
767#2671—171no—
768#2670—171no—
769#2668—171no—
770#2638—171no—
771#2630—171no—
772#2609—171no—
773#2602—171no—
774#2599—171no—
775#2598—171no—
776#2580—171no—
777#2564—171no—
778#2432—171no—
779#2430—171no—
780#2318—171no—
781C22×C17—22no—
782C22×C17—22no—
783C22×C17—22no—
784C22×C17—22no—
785C22×C17—22no—
786C22×C17—22no—
787C22×C17—41no—
788C22×C17—41no—
789C22×C17—41no—
790C22×C17—41no—
791C22×C17—41no—
792C22×C17—41no—
793C22×C17—41no—
794C22×C17—41no—
795C22×C17—41no—
796C22×C17—41no—
797C22×C17—41no—
798C22×C17—41no—
799C22×C17—41no—
800C22×C17—41no—
801C22×C17—41no—
802C22×C17C23×D411yescharacteristic
803C22×C17C2×H(5,𝔽2)11yescharacteristic
804C22×C17C2×H(5,𝔽2)11yescharacteristic
805C22×C17C2×2−1+411yescharacteristic
806C22×C17#58511yescharacteristic
807C22×C17#58511yescharacteristic
808C22×C17#58511yescharacteristic
809C2×D17—22no—
810C2×D17—22no—
811C2×D17—22no—
812C2×D17—22no—
813C2×D17—22no—
814C2×D17—22no—
815C2×D17—416no—
816C2×D17—41no—
817C2×D17—41no—
818C2×D17—41no—
819C2×D17—41no—
820C2×D17—41no—
821C2×D17—41no—
822C2×D17—41no—
823C2×D17—41no—
824C2×D17—41no—
825C2×D17—41no—
826C2×D17—41no—
827C2×D17—41no—
828C2×D17—41no—
829C2×D17—41no—
830C2×D17—41no—
831C4×C17—22no—
832C4×C17—22no—
833C4×C17—22no—
834C4×C17—22no—
835C4×C17—22no—
836C4×C17—41no—
837C4×C17—41no—
838C4×C17—41no—
839C4×C17—41no—
840C4×C17—41no—
841C4×C17—41no—
842C4×C17—41no—
843Dic17—22no—
844Dic17—41no—
845Dic17—41no—
846Dic17—41no—
847Dic17—41no—
848Dic17—41no—
849Dic17—41no—
850Dic17—41no—
851Dic17—41no—
852Dic17—41no—
853Dic17—41no—
854Dic17—41no—
855Dic17—41no—
856C22×#41—171no—
857C24×C4—171no—
858#542—28no—
859C2×C4⋊Q8—171no—
860C2×C4⋊Q8C2×D1711yescharacteristic, complemented
861C2×#126C2×D1711yescharacteristic
862C2×#126C2×D1711yescharacteristic, complemented
863C2×#124—171no—
864C2×#124C2×D1711yescharacteristic
865C2×#124C2×D1711yescharacteristic
866C2×#124C2×D1711yescharacteristic, complemented
867#525—348no—
868C2×#123—171no—
869C2×#123—171no—
870C2×#123—171no—
871C2×#123C2×D1711yescharacteristic
872C2×#123C2×D1711yescharacteristic, complemented
873C2×C22⋊Q8—171no—
874C2×C22⋊Q8—171no—
875C2×C22⋊Q8—171no—
876C2×C22⋊Q8—171no—
877C2×C22⋊Q8C2×D1711yescharacteristic
878C2×C22⋊Q8C2×D1711yescharacteristic, complemented
879C2×C22⋊Q8C2×D1711yescharacteristic, complemented
880C2×#121—171no—
881C2×#121—171no—
882C2×#121—171no—
883C2×#121—171no—
884C2×#121C2×D1711yescharacteristic
885C2×#120—171no—
886C2×#120—171no—
887C2×#120—171no—
888C2×C4×Q8C2×D1711yescharacteristic, complemented
889C2×C4×D4—171no—
890C2×C4×D4—171no—
891C2×C4×D4—171no—
892C2×C4×D4C2×D1711yescharacteristic
893C2×#117—171no—
894C2×#117C2×D1711yescharacteristic, complemented
895#400—171no—
896#400—171no—
897#399—171no—
898#399—171no—
899#399—171no—
900#399—171no—
901#398—171no—
902#398—171no—
903#398—171no—
904#398—171no—
905#397—171no—
906#397—171no—
907#397—171no—
908#397—171no—
909#397—171no—
910#397—171no—
911#396—171no—
912#396—171no—
913#396—171no—
914#396—171no—
915#395—171no—
916#395—171no—
917#395—171no—
918#395—171no—
919#394—171no—
920#394—171no—
921#394—171no—
922#394—171no—
923#394—171no—
924#394—171no—
925#394—171no—
926#394—171no—
927#394—171no—
928#394—171no—
929#394—171no—
930#394—171no—
931#394—171no—
932#394—171no—
933#393—171no—
934#393—171no—
935#393—171no—
936#393—171no—
937#393—171no—
938#393—171no—
939#392—171no—
940#392—171no—
941#392—171no—
942#392—171no—
943#391—171no—
944#390—171no—
945#390—171no—
946#390—171no—
947#390—171no—
948#389—171no—
949#389—171no—
950#389—171no—
951#388—171no—
952#388—171no—
953#388—171no—
954#388—171no—
955#388—171no—
956#388—171no—
957#388—171no—
958#388—171no—
959#388—171no—
960#388—171no—
961#387—171no—
962#387—171no—
963#387—171no—
964#387—171no—
965#387—171no—
966#387—171no—
967#387—171no—
968#387—171no—
969#386—171no—
970#386—171no—
971#386—171no—
972#386—171no—
973#386—171no—
974#386—171no—
975#386—171no—
976#386—171no—
977#386—171no—
978#386—171no—
979#386—171no—
980#386—171no—
981#386—171no—
982#386—171no—
983#385—171no—
984#385—171no—
985#385—171no—
986#385—171no—
987#385—171no—
988#385—171no—
989#385—171no—
990#385—171no—
991#385—171no—
992#385—171no—
993#385—171no—
994#385—171no—
995#385—171no—
996#385—171no—
997#385—171no—
998#385—171no—
999#383—171no—
1000#382—171no—
1001#381—171no—
1002#381—171no—
1003#380—171no—
1004#380—171no—
1005#380—171no—
1006#380—171no—
1007#380—171no—
1008#379—171no—
1009#379—171no—
1010#379—171no—
1011C4×C22⋊C4—171no—
1012C2×#95—171no—
1013C2×C17—42no—
1014C2×C17—42no—
1015C2×C17—81no—
1016C2×C17#344911yescharacteristic
1017C2×C17#348411yescharacteristic
1018C2×C17#348911yescharacteristic
1019C2×C17#353311yescharacteristic
1020C2×C17#353511yescharacteristic
1021C2×C17#354011yescharacteristic
1022C2×C17#354111yescharacteristic
1023D17—42no—
1024D17—42no—
1025D17—81no—
1026C25—171no—
1027C2×#41—344no—
1028C2×#41—682no—
1029C2×#41—682no—
1030C22×Q8—171no—
1031C22×Q8C22×D1711yescharacteristic
1032C22×Q8C22×D1711yescharacteristic
1033C22×Q8C22×D1711yescharacteristic
1034C22×D4—171no—
1035C22×D4—171no—
1036C22×D4—171no—
1037C22×D4—171no—
1038C22×D4—171no—
1039C22×D4—171no—
1040C22×D4—171no—
1041C22×D4—171no—
1042C22×D4—171no—
1043C22×D4C22×D1711yescharacteristic
1044C22×D4C22×D1711yescharacteristic
1045C22×D4C22×D1711yescharacteristic
1046C23×C4—171no—
1047C23×C4—171no—
1048C23×C4—171no—
1049C23×C4—171no—
1050C23×C4—171no—
1051C23×C4—171no—
1052C23×C4—171no—
1053C23×C4—171no—
1054C23×C4—344no—
1055C23×C4—682no—
1056C23×C4—682no—
1057C23×C4C22×D1711yescharacteristic
1058C23×C4C22×D1711yescharacteristic
1059C23×C4C22×D1711yescharacteristic
1060C4⋊Q8—24no—
1061C4⋊Q8—682no—
1062#126—24no—
1063#126—24no—
1064#124—24no—
1065#124—24no—
1066#124—24no—
1067#124—682no—
1068#123—24no—
1069#123—24no—
1070#123—344no—
1071#123—344no—
1072#123—682no—
1073C22⋊Q8—24no—
1074C22⋊Q8—24no—
1075C22⋊Q8—24no—
1076C22⋊Q8—344no—
1077C22⋊Q8—344no—
1078C22⋊Q8—682no—
1079C22⋊Q8—682no—
1080#121—24no—
1081#121—344no—
1082#121—344no—
1083#121—682no—
1084#121—682no—
1085#120—344no—
1086#120—344no—
1087#120—682no—
1088C4×Q8—24no—
1089C4×D4—344no—
1090C4×D4—344no—
1091C4×D4—344no—
1092C4×D4C22⋊D1718yescomplemented
1093#117—24no—
1094#117—344no—
1095C2×C4⋊C4—171no—
1096C2×C4⋊C4—171no—
1097C2×C4⋊C4—171no—
1098C2×C4⋊C4—171no—
1099C2×C4⋊C4—171no—
1100C2×C4⋊C4—171no—
1101C2×C4⋊C4—171no—
1102C2×C4⋊C4—171no—
1103C2×C4⋊C4—171no—
1104C2×C4⋊C4—171no—
1105C2×C4⋊C4—171no—
1106C2×C4⋊C4—171no—
1107C2×C4⋊C4—171no—
1108C2×C4⋊C4—171no—
1109C2×C4⋊C4—171no—
1110C2×C4⋊C4—171no—
1111C2×C4⋊C4—171no—
1112C2×C4⋊C4—171no—
1113C2×C4⋊C4—171no—
1114C2×C4⋊C4—171no—
1115C2×C4⋊C4—171no—
1116C2×C4⋊C4—171no—
1117C2×C4⋊C4C22×D1711yescharacteristic
1118C2×C4⋊C4C22×D1711yescharacteristic
1119C2×C4⋊C4C22×D1711yescharacteristic
1120C2×C4⋊C4C22×D1711yescharacteristic
1121C2×C4⋊C4C22×D1711yescharacteristic
1122C2×C4⋊C4C22×D1711yescharacteristic
1123C2×C4⋊C4C22×D1711yescharacteristic
1124C2×C4⋊C4C22×D1711yescharacteristic
1125C2×C4⋊C4C22×D1711yescharacteristic
1126C2×C4⋊C4C22×D1711yescharacteristic
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—171no—
1134C2×C22⋊C4—171no—
1135C2×C22⋊C4—171no—
1136C2×C22⋊C4—171no—
1137C2×C22⋊C4—171no—
1138C2×C22⋊C4—171no—
1139C2×C22⋊C4—171no—
1140C2×C22⋊C4—171no—
1141C2×C22⋊C4—171no—
1142C2×C22⋊C4—171no—
1143C2×C22⋊C4—171no—
1144C2×C22⋊C4—171no—
1145C2×C22⋊C4—171no—
1146C2×C22⋊C4—171no—
1147C2×C22⋊C4—171no—
1148C2×C22⋊C4—171no—
1149C2×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
1153C2×C22⋊C4—171no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—171no—
1156C2×C22⋊C4—171no—
1157C2×C22⋊C4—171no—
1158C2×C22⋊C4—171no—
1159C2×C22⋊C4—171no—
1160C2×C22⋊C4—171no—
1161C2×C22⋊C4—171no—
1162C2×C22⋊C4—171no—
1163C2×C22⋊C4—171no—
1164C2×C22⋊C4—171no—
1165C2×C22⋊C4—171no—
1166C2×C22⋊C4—171no—
1167C2×C22⋊C4C22×D1711yescharacteristic
1168C2×C22⋊C4C22×D1711yescharacteristic
1169C2×C22⋊C4C22×D1711yescharacteristic
1170C2×C22⋊C4C22×D1711yescharacteristic
1171C2×C22⋊C4C22×D1711yescharacteristic
1172C2×C22⋊C4C22×D1711yescharacteristic
1173C2×C22⋊C4C22×D1711yescharacteristic
1174C2×C22⋊C4C22×D1711yescharacteristic
1175C2×C22⋊C4C22×D1711yescharacteristic
1176C2×C22⋊C4C22×D1711yescharacteristic
1177C2×C22⋊C4C22×D1711yescharacteristic
1178C2×C22⋊C4C22×D1711yescharacteristic
1179C2×C42—171no—
1180C2×C42—171no—
1181C2×C42—171no—
1182C2×C42C22×D1711yescharacteristic
1183C2×C42C22×D1711yescharacteristic
1184C2×C42C22×D1711yescharacteristic
1185C2×C42C22×D1711yescharacteristic
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196#95—171no—
1197#95—171no—
1198#95—171no—
1199#95—171no—
1200#95—171no—
1201#95—171no—
1202#95—171no—
1203#95—171no—
1204#95—171no—
1205#95—171no—
1206#95—171no—
1207#95—171no—
1208#95—171no—
1209#95—171no—
1210#95—171no—
1211#95—171no—
1212#95—171no—
1213#95—171no—
1214#95—171no—
1215#95—171no—
1216#95—171no—
1217#95—171no—
1218#95—171no—
1219#95—171no—
1220#95—171no—
1221#95—171no—
1222C17#3671211yescharacteristic, complemented, Sylow
1223C24—171no—
1224C24—171no—
1225C24—171no—
1226C24—342no—
1227C24—342no—
1228C24—342no—
1229C24—681no—
1230C24—681no—
1231C24—681no—
1232C24—681no—
1233C24C23×D1711yescharacteristic
1234C24C23×D1711yescharacteristic
1235C24C23×D1711yescharacteristic
1236#41—6816no—
1237C2×Q8—22no—
1238C2×Q8—22no—
1239C2×Q8—22no—
1240C2×Q8—41no—
1241C2×Q8—41no—
1242C2×Q8—41no—
1243C2×Q8—41no—
1244C2×Q8—41no—
1245C2×Q8—41no—
1246C2×Q8—342no—
1247C2×Q8—342no—
1248C2×Q8—681no—
1249C2×D4—22no—
1250C2×D4—22no—
1251C2×D4—41no—
1252C2×D4—41no—
1253C2×D4—41no—
1254C2×D4—41no—
1255C2×D4—41no—
1256C2×D4—41no—
1257C2×D4—342no—
1258C2×D4—342no—
1259C2×D4—342no—
1260C2×D4—342no—
1261C2×D4—342no—
1262C2×D4—342no—
1263C2×D4—342no—
1264C2×D4—342no—
1265C2×D4—342no—
1266C2×D4—342no—
1267C2×D4—342no—
1268C2×D4—342no—
1269C2×D4—342no—
1270C2×D4—681no—
1271C2×D4—681no—
1272C2×D4—681no—
1273C2×D4—681no—
1274C2×D4—681no—
1275C2×D4—681no—
1276C2×D4—681no—
1277C2×D4—681no—
1278C2×D4—681no—
1279C2×D4—681no—
1280C2×D4—681no—
1281C2×D4—681no—
1282C2×D4—681no—
1283C2×D4—681no—
1284C2×D4C2×C22⋊D1714yes—
1285C22×C4—22no—
1286C22×C4—41no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—41no—
1292C22×C4—171no—
1293C22×C4—171no—
1294C22×C4—171no—
1295C22×C4—171no—
1296C22×C4—171no—
1297C22×C4—171no—
1298C22×C4—171no—
1299C22×C4—171no—
1300C22×C4—171no—
1301C22×C4—171no—
1302C22×C4—171no—
1303C22×C4—171no—
1304C22×C4—171no—
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—681no—
1317C22×C4—681no—
1318C22×C4—681no—
1319C22×C4—681no—
1320C22×C4—681no—
1321C22×C4—681no—
1322C22×C4—6816no—
1323C22×C4—681no—
1324C22×C4—681no—
1325C22×C4—681no—
1326C22×C4—681no—
1327C22×C4—681no—
1328C22×C4—681no—
1329C22×C4—681no—
1330C22×C4C2×C22⋊D1714yes—
1331C22×C4C2×C22⋊D1714yes—
1332C22×C4C23×D1711yescharacteristic
1333C22×C4C23×D1711yescharacteristic
1334C22×C4C23×D1711yescharacteristic
1335C22×C4C23×D1711yescharacteristic
1336C22×C4C23×D1711yescharacteristic
1337C22×C4C23×D1711yescharacteristic
1338C22×C4C23×D1711yescharacteristic
1339C22×C4C23×D1711yescharacteristic
1340C22×C4C23×D1711yescharacteristic
1341C22×C4C23×D1711yescharacteristic
1342C22×C4C23×D1711yescharacteristic
1343C22×C4C23×D1711yescharacteristic
1344C4⋊C4—22no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—22no—
1350C4⋊C4—22no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—342no—
1354C4⋊C4—342no—
1355C4⋊C4—342no—
1356C4⋊C4—342no—
1357C4⋊C4—342no—
1358C4⋊C4—342no—
1359C4⋊C4—342no—
1360C4⋊C4—342no—
1361C4⋊C4—681no—
1362C4⋊C4—681no—
1363C4⋊C4—681no—
1364C4⋊C4—681no—
1365C4⋊C4—681no—
1366C4⋊C4—681no—
1367C4⋊C4—681no—
1368C4⋊C4—681no—
1369C4⋊C4—681no—
1370C4⋊C4—681no—
1371C4⋊C4—681no—
1372C4⋊C4—681no—
1373C4⋊C4—681no—
1374C4⋊C4—681no—
1375C4⋊C4C2×C22⋊D1714yes—
1376C22⋊C4—22no—
1377C22⋊C4—22no—
1378C22⋊C4—22no—
1379C22⋊C4—22no—
1380C22⋊C4—22no—
1381C22⋊C4—22no—
1382C22⋊C4—22no—
1383C22⋊C4—22no—
1384C22⋊C4—22no—
1385C22⋊C4—22no—
1386C22⋊C4—342no—
1387C22⋊C4—342no—
1388C22⋊C4—342no—
1389C22⋊C4—342no—
1390C22⋊C4—342no—
1391C22⋊C4—342no—
1392C22⋊C4—342no—
1393C22⋊C4—342no—
1394C22⋊C4—342no—
1395C22⋊C4—342no—
1396C22⋊C4—342no—
1397C22⋊C4—342no—
1398C22⋊C4—342no—
1399C22⋊C4—681no—
1400C22⋊C4—681no—
1401C22⋊C4—681no—
1402C22⋊C4—681no—
1403C22⋊C4—681no—
1404C22⋊C4—681no—
1405C22⋊C4—681no—
1406C22⋊C4—681no—
1407C22⋊C4—681no—
1408C22⋊C4—681no—
1409C22⋊C4—681no—
1410C22⋊C4—681no—
1411C22⋊C4—681no—
1412C22⋊C4—681no—
1413C22⋊C4—681no—
1414C22⋊C4—681no—
1415C22⋊C4—681no—
1416C22⋊C4—681no—
1417C22⋊C4—681no—
1418C22⋊C4—681no—
1419C22⋊C4—681no—
1420C22⋊C4—681no—
1421C22⋊C4—681no—
1422C22⋊C4—681no—
1423C22⋊C4—681no—
1424C22⋊C4—681no—
1425C22⋊C4—681no—
1426C22⋊C4C2×C22⋊D1714yes—
1427C22⋊C4C2×C22⋊D1714yes—
1428C42—22no—
1429C42—22no—
1430C42—22no—
1431C42—342no—
1432C42—681no—
1433C42—681no—
1434C42C2×C22⋊D1714yes—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—21no—
1453C23—21no—
1454C23—172no—
1455C23—172no—
1456C23—341no—
1457C23—341no—
1458C23—341no—
1459C23—341no—
1460C23—341no—
1461C23—341no—
1462C23—341no—
1463C23—341no—
1464C23—341no—
1465C23—341no—
1466C23—341no—
1467C23—341no—
1468C23—341no—
1469C23—341no—
1470C23—341no—
1471C23—341no—
1472C23—341no—
1473C23—341no—
1474C23—341no—
1475C23—684no—
1476C23—684no—
1477C23—684no—
1478C23—684no—
1479C23—684no—
1480C23—684no—
1481C23—684no—
1482C23C22×C22⋊D1712yes—
1483C23C22×C22⋊D1712yes—
1484C23C24×D1711yescharacteristic
1485Q8—44no—
1486Q8—82no—
1487Q8—82no—
1488Q8—684no—
1489D4—44no—
1490D4—82no—
1491D4—82no—
1492D4—684no—
1493D4—684no—
1494D4—684no—
1495D4—684no—
1496D4—684no—
1497D4—684no—
1498D4—1362no—
1499D4—1362no—
1500D4—1362no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—44no—
1533C2×C4—44no—
1534C2×C4—44no—
1535C2×C4—172no—
1536C2×C4—348no—
1537C2×C4—341no—
1538C2×C4—341no—
1539C2×C4—341no—
1540C2×C4—341no—
1541C2×C4—341no—
1542C2×C4—341no—
1543C2×C4—341no—
1544C2×C4—341no—
1545C2×C4—341no—
1546C2×C4—341no—
1547C2×C4—341no—
1548C2×C4—341no—
1549C2×C4—341no—
1550C2×C4—341no—
1551C2×C4—341no—
1552C2×C4—341no—
1553C2×C4—341no—
1554C2×C4—341no—
1555C2×C4—341no—
1556C2×C4—341no—
1557C2×C4—341no—
1558C2×C4—341no—
1559C2×C4—341no—
1560C2×C4—341no—
1561C2×C4—341no—
1562C2×C4—341no—
1563C2×C4—341no—
1564C2×C4—341no—
1565C2×C4—341no—
1566C2×C4—341no—
1567C2×C4—341no—
1568C2×C4—341no—
1569C2×C4—341no—
1570C2×C4—341no—
1571C2×C4—341no—
1572C2×C4—341no—
1573C2×C4—341no—
1574C2×C4—341no—
1575C2×C4—684no—
1576C2×C4—684no—
1577C2×C4—684no—
1578C2×C4—684no—
1579C2×C4—684no—
1580C2×C4—1362no—
1581C2×C4—1362no—
1582C2×C4C22×C22⋊D1712yes—
1583C2×C4C22×C22⋊D1712yes—
1584C2×C4C22×C22⋊D1712yes—
1585C2×C4C22×C22⋊D1712yes—
1586C2×C4C22×C22⋊D1712yes—
1587C22—22no—
1588C22—22no—
1589C22—22no—
1590C22—22no—
1591C22—22no—
1592C22—22no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—342no—
1609C22—342no—
1610C22—342no—
1611C22—342no—
1612C22—342no—
1613C22—342no—
1614C22—6816no—
1615C22—681no—
1616C22—681no—
1617C22—681no—
1618C22—681no—
1619C22—681no—
1620C22—681no—
1621C22—681no—
1622C22—681no—
1623C22—681no—
1624C22—681no—
1625C22—681no—
1626C22—681no—
1627C22—681no—
1628C22—681no—
1629C22—681no—
1630C22C23×C22⋊D1711yescharacteristic
1631C22H(5,𝔽2)×D1711yescharacteristic
1632C22H(5,𝔽2)×D1711yescharacteristic
1633C222−1+4×D1711yescharacteristic
1634C22#1176364511yescharacteristic
1635C22#1176364511yescharacteristic
1636C22#1176364611yescharacteristic
1637C4—22no—
1638C4—22no—
1639C4—22no—
1640C4—22no—
1641C4—22no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—41no—
1648C4—41no—
1649C4—342no—
1650C4—681no—
1651C4—681no—
1652C4—681no—
1653C4—681no—
1654C4—681no—
1655C4—681no—
1656C4—681no—
1657C4—681no—
1658C4—681no—
1659C4—681no—
1660C4—681no—
1661C4—681no—
1662C2—42no—
1663C2—42no—
1664C2—81no—
1665C2—682no—
1666C2—682no—
1667C2—1361no—
1668C2#1454211311yescharacteristic
1669C2#1454241511yescharacteristic
1670C2#1454245711yescharacteristic
1671C2#1454294711yescharacteristic
1672C2#1454298611yescharacteristic
1673C2#1454304911yescharacteristic
1674C2#1454306811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC2×C17×#542C2
hypercenterC2×#542D17
hypocenterC17#36712
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#11763318C2semidirect
2. #14537073C2semidirect
3. #14537068C2semidirect
4. #14535328C2semidirect
5. #14535313C2semidirect
6. #14535274C2semidirect
7. #14535259C2semidirect
8. #14535229C2semidirect
9. #14535184C2semidirect
10. #14535169C2semidirect
11. #14535160C2semidirect
12. #14535094C2semidirect
13. #14535080C2semidirect
14. #14535060C2semidirect
15. #14535059C2semidirect
16. #14535030C2semidirect
17. #14535014C2semidirect
18. #14535005C2semidirect
19. #14534987C2semidirect
20. #14534702C2semidirect
21. #14534623C2semidirect
22. #14534456C2semidirect
23. #14534398C2semidirect
24. #14534355C2semidirect
25. #14534350C2semidirect
26. #14534142C2semidirect
27. #14533966C2semidirect
28. #14532413C2semidirect
29. #14532396C2semidirect
30. #14531417C2semidirect
31. C2×C17×#542C2semidirect
34. C2×#10587630C22semidirect
47. C2×#10587625C22semidirect
55. #11762748C22semidirect
56. #11762747C22semidirect
57. #11762745C22semidirect
60. #11762744C22semidirect
61. #11762742C22semidirect
62. #11762742C22semidirect
63. #11762740C22semidirect
64. #11762740C22semidirect
68. #11762737C22semidirect
70. #11762735C22semidirect
71. #11762732C22semidirect
72. #11762732C22semidirect
74. #11762731C22semidirect
75. #11762729C22semidirect
76. #11762728C22semidirect
77. #11762728C22semidirect
78. #11762728C22semidirect
82. #11762725C22semidirect
89. #11762724C22semidirect
90. #11762724C22semidirect
92. #11762723C22semidirect
93. #11762721C22semidirect
97. #11762720C22semidirect
98. #11762720C22semidirect
103. #11762714C22semidirect
108. #11762707C22semidirect
109. #11762707C22semidirect
110. #11762704C22semidirect
111. #11762703C22semidirect
118. #11762700C22semidirect
120. #11762697C22semidirect
121. #11762695C22semidirect
122. #11762695C22semidirect
123. #11762693C22semidirect
124. #11762693C22semidirect
125. #11762693C22semidirect
126. #11762690C22semidirect
127. #11762690C22semidirect
128. #11762690C22semidirect
133. #11762688C22semidirect
137. #11762686C22semidirect
142. #11762685C22semidirect
143. #11762684C22semidirect
144. #11762684C22semidirect
145. #11762682C22semidirect
156. #11762680C22semidirect
157. #11762680C22semidirect
158. #11762680C22semidirect
159. #11762677C22semidirect
160. #11762675C22semidirect
164. #11762667C22semidirect
165. #11762667C22semidirect
171. C4×C22⋊Dic17C22semidirect
172. C2×#10587502C22semidirect
174. C2×C17×C4⋊Q8C22semidirect
176. C2×C17×#126C22semidirect
179. C2×C17×#124C22semidirect
181. C2×C17×#123C22semidirect
183. C2×C17×C22⋊Q8C22semidirect
184. C2×C17×C22⋊Q8C22semidirect
186. C2×C4×Q8×C17C22semidirect
188. C2×C17×#117C22semidirect
236. C4×D4×C17D4semidirect
750. C2×#542D17semidirect
860. C2×C4⋊Q8C2×D17semidirect
862. C2×#126C2×D17semidirect
866. C2×#124C2×D17semidirect
872. C2×#123C2×D17semidirect
878. C2×C22⋊Q8C2×D17semidirect
879. C2×C22⋊Q8C2×D17semidirect
888. C2×C4×Q8C2×D17semidirect
894. C2×#117C2×D17semidirect
1092. C4×D4C22⋊D17semidirect
1222. C17#36712semidirect

Maximal subgroups

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

subgroupindex
C2×#117633182
#145370732
#145370682
#145353282
#145353132
#145352742
#145352592
#145352292
#145351842
#145351692
#145351602
#145350942
#145350802
#145350602
#145350592
#145350302
#145350142
#145350052
#145349872
#145347022
#145346232
#145344562
#145343982
#145343552
#145343502
#145341422
#145339662
#145324132
#145323962
#145314172
C2×C17×#5422
#3671217