Finite Group Databasebeta

← #31965230

Subgroups — #31965230

Order 18176.

1074 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22597369C211yesmaximal, characteristic, complemented
2#22591250C211yesmaximal, characteristic, complemented
3#22586912C211yesmaximal, characteristic, complemented
4#22586908C211yesmaximal, characteristic, complemented
5#22586883C212yesmaximal, complemented
6#22586878C212yesmaximal, complemented
7#22586865C212yesmaximal, complemented
8#22586844C212yesmaximal, complemented
9C2×#17985736C211yesmaximal, characteristic, complemented
10C2×#17985733C211yesmaximal, characteristic, complemented
11C71×#3505C211yesmaximal, characteristic
12C2×D4×Dic71—21no—
13#17986071—22no—
14#17986071—22no—
15#17986056C2212yescomplemented
16#17985963C2212yescomplemented
17C2×C22⋊(C71⋊C8)C2211yescharacteristic
18C2×C22⋊(C71⋊C8)C2211yescharacteristic
19#17985898—21no—
20#17985874—21no—
21#17985874—21no—
22#17985865C2211yescharacteristic, complemented
23#17985859C2211yescharacteristic
24#17985859C2211yescharacteristic, complemented
25C4×C4⋊Dic71C2211yescharacteristic, complemented
26C2×C71⋊#95C2211yescharacteristic
27C2×C71⋊#95C2211yescharacteristic, complemented
28#17985736C2212yescomplemented
29#17985736C2212yescomplemented
30#17985736C2212yescomplemented
31#17985736C2212yescomplemented
32#17985733C2212yes—
33#17985733C2212yes—
34#17985733C2212yes—
35#17985733C2212yes—
36#553×C71—22no—
37#553×C71C412yescomplemented
38#552×C71C412yescomplemented
39#551×C71—22no—
40#548×C71C412yescomplemented
41#546×C71C412yescomplemented
42#539×C71—21no—
43#538×C71—21no—
44#534×C71—21no—
45#529×C71C2212yes—
46#525×C71C2212yes—
47C2×C22⋊Q8×C71C2211yescharacteristic
48C2×#121×C71C2211yescharacteristic
49#518×C71—21no—
50C2×C4×D4×C71C2211yescharacteristic
51C23×Dic71—21no—
52C23×Dic71—21no—
53C2×#11765849—22no—
54C22×C71⋊C8—21no—
55C22×C71⋊C8—21no—
56D4×Dic71—44no—
57C2×C4⋊Dic71—21no—
58C2×C4⋊Dic71—21no—
59C2×C4⋊Dic71—21no—
60C2×C4⋊Dic71—21no—
61C2×C22⋊Dic71—21no—
62C2×C22⋊Dic71—21no—
63C2×C4×Dic71—21no—
64C4⋊(C71⋊C8)—22no—
65C22⋊(C71⋊C8)—21no—
66C22⋊(C71⋊C8)—21no—
67C22⋊(C71⋊C8)—22no—
68C22⋊(C71⋊C8)C2312yes—
69C22⋊(C71⋊C8)C2312yes—
70#14556039—22no—
71C71⋊#95—21no—
72C71⋊#95—21no—
73C71⋊#95—21no—
74C71⋊#95C2311yescharacteristic
75C71⋊#95C2311yescharacteristic
76C71⋊#95C2311yescharacteristic
77C71⋊#95C2311yescharacteristic
78C2×#41×C71C2×C412yescomplemented
79C22×Q8×C71C2×C411yescharacteristic, complemented
80C22×D4×C71—21no—
81C22×D4×C71C2×C411yescharacteristic, complemented
82C22×D4×C71D411yescharacteristic
83C23×C4×C71C2311yescharacteristic
84C23×C4×C71C2311yescharacteristic
85#126×C71—22no—
86#126×C71—22no—
87#126×C71—22no—
88#125×C71—22no—
89#125×C71C2×C412yescomplemented
90#124×C71—22no—
91#124×C71C2×C412yescomplemented
92#123×C71—22no—
93#123×C71—22no—
94#123×C71—22no—
95#123×C71—22no—
96#123×C71—22no—
97C22⋊Q8×C71—21no—
98C22⋊Q8×C71—21no—
99C22⋊Q8×C71—22no—
100C22⋊Q8×C71C2×C412yescomplemented
101C22⋊Q8×C71C2×C412yescomplemented
102C22⋊Q8×C71C2312yes—
103#121×C71—22no—
104#121×C71—22no—
105#121×C71—21no—
106#121×C71—21no—
107#121×C71—22no—
108#121×C71C2×C412yescomplemented
109#121×C71C2×C412yescomplemented
110#121×C71C2312yes—
111#120×C71—22no—
112#120×C71—22no—
113C4×Q8×C71C2×C412yescomplemented
114C4×D4×C71—22no—
115C4×D4×C71—22no—
116C4×D4×C71—22no—
117C4×D4×C71—22no—
118C4×D4×C71—22no—
119C4×D4×C71C2×C412yes—
120C4×D4×C71C2×C412yes—
121C4×D4×C71C2×C412yescomplemented
122C4×D4×C71D412yes—
123C4×D4×C71D412yes—
124#117×C71—22no—
125#117×C71—22no—
126#117×C71C2×C412yescomplemented
127C2×C4⋊C4×C71—21no—
128C2×C4⋊C4×C71C2×C411yescharacteristic, complemented
129C2×C4⋊C4×C71C2×C411yescharacteristic, complemented
130C2×C4⋊C4×C71D411yescharacteristic
131C2×C22⋊C4×C71—21no—
132C2×C22⋊C4×C71—21no—
133C2×C22⋊C4×C71—22no—
134C2×C22⋊C4×C71D411yescharacteristic
135C2×C22⋊C4×C71D411yescharacteristic
136C2×C42×C71C2311yescharacteristic
137C22×Dic71—21no—
138C22×Dic71—21no—
139C22×Dic71—21no—
140C22×Dic71—21no—
141C22×Dic71—42no—
142C22×Dic71—42no—
143C22×Dic71—42no—
144C22×Dic71—42no—
145C22×Dic71—81no—
146C22×Dic71—81no—
147#11765849—82no—
148C2×C71⋊C8—22no—
149C2×C71⋊C8—22no—
150C2×C71⋊C8—81no—
151C2×C71⋊C8—81no—
152C4⋊Dic71—42no—
153C4⋊Dic71—42no—
154C4⋊Dic71—81no—
155C4⋊Dic71—81no—
156C22⋊Dic71—42no—
157C22⋊Dic71—42no—
158C4×Dic71—42no—
159C24×C71—21no—
160C24×C71C2×D411yescharacteristic
161C24×C71C2×D411yescharacteristic
162#41×C71—82no—
163C2×Q8×C71—21no—
164C2×Q8×C71—81no—
165C2×Q8×C71C22×C412yes—
166C2×D4×C71—22no—
167C2×D4×C71—22no—
168C2×D4×C71—22no—
169C2×D4×C71—22no—
170C2×D4×C71—22no—
171C2×D4×C71—22no—
172C2×D4×C71—21no—
173C2×D4×C71—42no—
174C2×D4×C71—42no—
175C2×D4×C71—81no—
176C2×D4×C71C22⋊C412yes—
177C2×D4×C71C22⋊C412yes—
178C2×D4×C71C22×C412yes—
179C22×C4×C71—21no—
180C22×C4×C71—21no—
181C22×C4×C71—21no—
182C22×C4×C71—22no—
183C22×C4×C71—22no—
184C22×C4×C71—81no—
185C22×C4×C71—81no—
186C22×C4×C71C22×C411yescharacteristic
187C22×C4×C71C22×C411yescharacteristic
188C22×C4×C71C22×C412yes—
189C22×C4×C71C2×D411yescharacteristic
190C22×C4×C71C2×D411yescharacteristic
191C22×C4×C71C2×D411yescharacteristic
192C22×C4×C71C2×D411yescharacteristic
193C22×C4×C71C2×D411yescharacteristic
194C22×C4×C71C2×D411yescharacteristic
195C22×C4×C71C2×D412yes—
196C22×C4×C71C2411yescharacteristic
197C4⋊C4×C71—22no—
198C4⋊C4×C71—21no—
199C4⋊C4×C71—21no—
200C4⋊C4×C71—22no—
201C4⋊C4×C71—22no—
202C4⋊C4×C71—22no—
203C4⋊C4×C71—22no—
204C4⋊C4×C71—22no—
205C4⋊C4×C71C22⋊C412yes—
206C4⋊C4×C71C22⋊C412yes—
207C4⋊C4×C71C22×C412yes—
208C4⋊C4×C71C22×C412yes—
209C22⋊C4×C71—22no—
210C22⋊C4×C71—22no—
211C22⋊C4×C71—22no—
212C22⋊C4×C71—22no—
213C22⋊C4×C71—22no—
214C22⋊C4×C71—22no—
215C22⋊C4×C71—22no—
216C22⋊C4×C71—22no—
217C22⋊C4×C71—22no—
218C22⋊C4×C71—22no—
219C22⋊C4×C71C22⋊C412yes—
220C22⋊C4×C71C22⋊C412yes—
221C22⋊C4×C71C22⋊C412yes—
222C22⋊C4×C71C22⋊C412yes—
223C42×C71—22no—
224C42×C71—22no—
225C42×C71C22×C412yes—
226C42×C71C2×D412yes—
227C23×C71—21no—
228C23×C71—21no—
229C23×C71—22no—
230C23×C71—41no—
231C23×C71—41no—
232C23×C71—41no—
233C23×C71—41no—
234C23×C71—42no—
235C23×C71—81no—
236C23×C71—81no—
237C23×C71C2×C22⋊C412yes—
238C23×C71C2×C22⋊C411yescharacteristic
239C23×C71C2×C22⋊C411yescharacteristic
240C23×C71AGL(1,ℤ/8)12yes—
241C23×C71#13712yes—
242C23×C71C22×D411yescharacteristic
243Q8×C71—42no—
244Q8×C71—81no—
245D4×C71—24no—
246D4×C71—24no—
247D4×C71—42no—
248D4×C71—42no—
249D4×C71—42no—
250D4×C71—44no—
251D4×C71—81no—
252D4×C71—82no—
253D4×C71—82no—
254C2×C4×C71—21no—
255C2×C4×C71—21no—
256C2×C4×C71—22no—
257C2×C4×C71—22no—
258C2×C4×C71—22no—
259C2×C4×C71—41no—
260C2×C4×C71—41no—
261C2×C4×C71—41no—
262C2×C4×C71—42no—
263C2×C4×C71—41no—
264C2×C4×C71—41no—
265C2×C4×C71—41no—
266C2×C4×C71—41no—
267C2×C4×C71—42no—
268C2×C4×C71—41no—
269C2×C4×C71—42no—
270C2×C4×C71—82no—
271C2×C4×C71—82no—
272C2×C4×C71—81no—
273C2×C4×C71—81no—
274C2×C4×C71C2×C22⋊C412yes—
275C2×C4×C71C2×C22⋊C412yes—
276C2×C4×C71C2×C22⋊C412yes—
277C2×C4×C71C2×C22⋊C411yescharacteristic
278C2×C4×C71C2×C22⋊C411yescharacteristic
279C2×C4×C71C23×C411yescharacteristic
280C2×C4×C71C22×D411yescharacteristic
281C2×Dic71—22no—
282C2×Dic71—41no—
283C2×Dic71—41no—
284C2×Dic71—41no—
285C2×Dic71—41no—
286C2×Dic71—41no—
287C2×Dic71—41no—
288C2×Dic71—41no—
289C2×Dic71—41no—
290C2×Dic71—41no—
291C2×Dic71—41no—
292C2×Dic71—41no—
293C2×Dic71—84no—
294C2×Dic71—84no—
295C71⋊C8—42no—
296C71⋊C8—42no—
297C22×C71—21no—
298C22×C71—21no—
299C22×C71—21no—
300C22×C71—21no—
301C22×C71—21no—
302C22×C71—21no—
303C22×C71—22no—
304C22×C71—22no—
305C22×C71—22no—
306C22×C71—42no—
307C22×C71—42no—
308C22×C71—42no—
309C22×C71—42no—
310C22×C71—42no—
311C22×C71—42no—
312C22×C71—42no—
313C22×C71—162no—
314C22×C71#41712yes—
315C22×C71#41712yes—
316C22×C71C22×C22⋊C411yescharacteristic
317C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C71C2×#13711yescharacteristic
319C4×C71—21no—
320C4×C71—21no—
321C4×C71—22no—
322C4×C71—21no—
323C4×C71—21no—
324C4×C71—22no—
325C4×C71—22no—
326C4×C71—42no—
327C4×C71—42no—
328C4×C71—42no—
329Dic71—42no—
330Dic71—81no—
331Dic71—81no—
332Dic71—81no—
333#17622—711nomaximal, Sylow
334C2×C71—21no—
335C2×C71—21no—
336C2×C71—22no—
337C2×C71—22no—
338C2×C71—42no—
339C2×C71—82no—
340C2×C71#288311yescharacteristic
341C2×C71C2×#41711yescharacteristic
342C2×C71#290111yescharacteristic
343#3505D7111yescharacteristic
344#2973—711no—
345#2349—711no—
346#1520—711no—
347#1519—711no—
348#1513—712no—
349#1512—712no—
350#1509—712no—
351#1504—712no—
352C2×#328—711no—
353C2×#327—711no—
354C71#1762211yescharacteristic, complemented, Sylow
355#553—22no—
356#553Dic7112yescomplemented
357#552Dic7112yescomplemented
358#551—22no—
359#548Dic7112yescomplemented
360#546Dic7112yescomplemented
361#539—21no—
362#538—21no—
363#534—21no—
364#529C2×D7112yes—
365#525C2×D7112yes—
366C2×C22⋊Q8C2×D7111yescharacteristic
367C2×#121C2×D7111yescharacteristic
368#518—21no—
369C2×C4×D4—1421no—
370C2×C4×D4C2×D7111yescharacteristic
371#435—1422no—
372#435—1422no—
373#432—712no—
374#407—712no—
375C2×C22⋊C8—711no—
376C2×C22⋊C8—711no—
377#389—1421no—
378#385—1421no—
379#385—1421no—
380#382—711no—
381#380—711no—
382#380—711no—
383C4×C4⋊C4—711no—
384C2×#95—711no—
385C2×#95—711no—
386#328—712no—
387#328—712no—
388#328—712no—
389#328—712no—
390#327—712no—
391#327—712no—
392#327—712no—
393#327—712no—
394C2×#41C2×Dic7112yescomplemented
395C22×Q8C2×Dic7111yescharacteristic, complemented
396C22×D4—21no—
397C22×D4C2×Dic7111yescharacteristic, complemented
398C22×D4C22⋊D7111yescharacteristic
399C23×C4—1421no—
400C23×C4—1421no—
401C23×C4C22×D7111yescharacteristic
402C23×C4C22×D7111yescharacteristic
403C2×M16—1422no—
404C22×C8—1421no—
405C22×C8—1421no—
406#126—22no—
407#126—22no—
408#126—22no—
409#125—22no—
410#125C2×Dic7112yescomplemented
411#124—22no—
412#124C2×Dic7112yescomplemented
413#123—22no—
414#123—22no—
415#123—22no—
416#123—22no—
417#123—22no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—22no—
421C22⋊Q8C2×Dic7112yescomplemented
422C22⋊Q8C2×Dic7112yescomplemented
423C22⋊Q8C22×D7112yes—
424#121—22no—
425#121—22no—
426#121—21no—
427#121—21no—
428#121—22no—
429#121C2×Dic7112yescomplemented
430#121C2×Dic7112yescomplemented
431#121C22×D7112yes—
432#120—22no—
433#120—22no—
434C4×Q8C2×Dic7112yescomplemented
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—2844no—
441C4×D4C2×Dic7112yes—
442C4×D4C2×Dic7112yes—
443C4×D4C2×Dic7112yescomplemented
444C4×D4C22⋊D7112yes—
445C4×D4C22⋊D7112yes—
446#117—22no—
447#117—22no—
448#117C2×Dic7112yescomplemented
449C2×C4⋊C4—21no—
450C2×C4⋊C4—1421no—
451C2×C4⋊C4—1421no—
452C2×C4⋊C4—1421no—
453C2×C4⋊C4—1421no—
454C2×C4⋊C4C2×Dic7111yescharacteristic, complemented
455C2×C4⋊C4C2×Dic7111yescharacteristic, complemented
456C2×C4⋊C4C22⋊D7111yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—1421no—
461C2×C22⋊C4—1421no—
462C2×C22⋊C4C22⋊D7111yescharacteristic
463C2×C22⋊C4C22⋊D7111yescharacteristic
464C2×C42—1421no—
465C2×C42C22×D7111yescharacteristic
466C4⋊C8—1422no—
467C22⋊C8—712no—
468C22⋊C8—712no—
469C22⋊C8—1421no—
470C22⋊C8—1421no—
471C22⋊C8—1422no—
472#97—1422no—
473#95—711no—
474#95—711no—
475#95—711no—
476#95—711no—
477#95—1421no—
478#95—1421no—
479#95—1421no—
480C24—21no—
481C24C2×C22⋊D7111yescharacteristic
482C24C2×C22⋊D7111yescharacteristic
483#41—82no—
484C2×Q8—21no—
485C2×Q8—81no—
486C2×Q8C22×Dic7112yes—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—81no—
497C2×D4C22⋊Dic7112yes—
498C2×D4C22⋊Dic7112yes—
499C2×D4C22×Dic7112yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—2842no—
508C22×C4—2842no—
509C22×C4—2842no—
510C22×C4—2842no—
511C22×C4—5681no—
512C22×C4—5681no—
513C22×C4—1421no—
514C22×C4—1421no—
515C22×C4—1421no—
516C22×C4—1421no—
517C22×C4C22×Dic7111yescharacteristic
518C22×C4C22×Dic7111yescharacteristic
519C22×C4C22×Dic7112yes—
520C22×C4C2×C22⋊D7111yescharacteristic
521C22×C4C2×C22⋊D7111yescharacteristic
522C22×C4C2×C22⋊D7111yescharacteristic
523C22×C4C2×C22⋊D7112yes—
524C22×C4C2×C22⋊D7111yescharacteristic
525C22×C4C2×C22⋊D7111yescharacteristic
526C22×C4C2×C22⋊D7111yescharacteristic
527C22×C4C23×D7111yescharacteristic
528M16—5682no—
529C2×C8—5681no—
530C2×C8—5681no—
531C2×C8—1422no—
532C2×C8—1422no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—2842no—
542C4⋊C4—2842no—
543C4⋊C4—5681no—
544C4⋊C4—5681no—
545C4⋊C4C22⋊Dic7112yes—
546C4⋊C4C22⋊Dic7112yes—
547C4⋊C4C22×Dic7112yes—
548C4⋊C4C22×Dic7112yes—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—2842no—
560C22⋊C4—2842no—
561C22⋊C4C22⋊Dic7112yes—
562C22⋊C4C22⋊Dic7112yes—
563C22⋊C4C22⋊Dic7112yes—
564C22⋊C4C22⋊Dic7112yes—
565C42—22no—
566C42—22no—
567C42—2842no—
568C42C22×Dic7112yes—
569C42C2×C22⋊D7112yes—
570C23—21no—
571C23—21no—
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—42no—
578C23—81no—
579C23—81no—
580C23C2×C22⋊Dic7112yes—
581C23C2×C22⋊Dic7111yescharacteristic
582C23C2×C22⋊Dic7111yescharacteristic
583C23#1455615312yes—
584C23#1455615812yes—
585C23C22×C22⋊D7111yescharacteristic
586Q8—42no—
587Q8—81no—
588D4—24no—
589D4—24no—
590D4—42no—
591D4—44no—
592D4—42no—
593D4—42no—
594D4—81no—
595D4—82no—
596D4—82no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—82no—
614C2×C4—82no—
615C2×C4—81no—
616C2×C4—81no—
617C2×C4—2841no—
618C2×C4—2841no—
619C2×C4—2841no—
620C2×C4—2841no—
621C2×C4—2841no—
622C2×C4—2841no—
623C2×C4—2841no—
624C2×C4—2841no—
625C2×C4—2841no—
626C2×C4—2841no—
627C2×C4—2841no—
628C2×C4—5684no—
629C2×C4—5684no—
630C2×C4—1422no—
631C2×C4C2×C22⋊Dic7112yes—
632C2×C4C2×C22⋊Dic7112yes—
633C2×C4C2×C22⋊Dic7112yes—
634C2×C4C2×C22⋊Dic7111yescharacteristic
635C2×C4C2×C22⋊Dic7111yescharacteristic
636C2×C4C23×Dic7111yescharacteristic
637C2×C4C22×C22⋊D7111yescharacteristic
638C8—2842no—
639C8—2842no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—162no—
657C22#1798600012yes—
658C22#1798600012yes—
659C22C22×C22⋊Dic7111yescharacteristic
660C22C2×#1455615311yescharacteristic
661C22C2×#1455615811yescharacteristic
662C4—22no—
663C4—21no—
664C4—21no—
665C4—22no—
666C4—21no—
667C4—21no—
668C4—22no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—2842no—
673C4—5681no—
674C4—5681no—
675C4—5681no—
676C2—21no—
677C2—21no—
678C2—22no—
679C2—22no—
680C2—42no—
681C2—82no—
682C2#2259680111yescharacteristic
683C2C2×#1798600011yescharacteristic
684C2#2259688711yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
Fitting, prime radicalC71×#3505C2
socleC22×C71C22×C22⋊C4
cosocleC22×C4×C71C24
hypercenter#3505D71
hypocenterC71#17622
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. #22597369C2semidirect
2. #22591250C2semidirect
3. #22586912C2semidirect
4. #22586908C2semidirect
5. #22586883C2semidirect
6. #22586878C2semidirect
7. #22586865C2semidirect
8. #22586844C2semidirect
9. C2×#17985736C2semidirect
10. C2×#17985733C2semidirect
15. #17986056C22semidirect
16. #17985963C22semidirect
22. #17985865C22semidirect
24. #17985859C22semidirect
25. C4×C4⋊Dic71C22semidirect
27. C2×C71⋊#95C22semidirect
28. #17985736C22semidirect
29. #17985736C22semidirect
30. #17985736C22semidirect
31. #17985736C22semidirect
37. #553×C71C4semidirect
38. #552×C71C4semidirect
40. #548×C71C4semidirect
41. #546×C71C4semidirect
78. C2×#41×C71C2×C4semidirect
79. C22×Q8×C71C2×C4semidirect
81. C22×D4×C71C2×C4semidirect
89. #125×C71C2×C4semidirect
91. #124×C71C2×C4semidirect
100. C22⋊Q8×C71C2×C4semidirect
101. C22⋊Q8×C71C2×C4semidirect
108. #121×C71C2×C4semidirect
109. #121×C71C2×C4semidirect
113. C4×Q8×C71C2×C4semidirect
121. C4×D4×C71C2×C4semidirect
126. #117×C71C2×C4semidirect
128. C2×C4⋊C4×C71C2×C4semidirect
129. C2×C4⋊C4×C71C2×C4semidirect
354. C71#17622semidirect
356. #553Dic71semidirect
357. #552Dic71semidirect
359. #548Dic71semidirect
360. #546Dic71semidirect
394. C2×#41C2×Dic71semidirect
395. C22×Q8C2×Dic71semidirect
397. C22×D4C2×Dic71semidirect
410. #125C2×Dic71semidirect
412. #124C2×Dic71semidirect
421. C22⋊Q8C2×Dic71semidirect
422. C22⋊Q8C2×Dic71semidirect
429. #121C2×Dic71semidirect
430. #121C2×Dic71semidirect
434. C4×Q8C2×Dic71semidirect
443. C4×D4C2×Dic71semidirect
448. #117C2×Dic71semidirect
454. C2×C4⋊C4C2×Dic71semidirect
455. C2×C4⋊C4C2×Dic71semidirect

Maximal subgroups

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

subgroupindex
#225973692
#225912502
#225869122
#225869082
#225868832
#225868782
#225868652
#225868442
C2×#179857362
C2×#179857332
C71×#35052
#1762271