Finite Group Databasebeta

← #31995263

Subgroups — #31995263

Order 18176.

1738 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986471C211yesmaximal, characteristic
2C2×#17986002C211yesmaximal, characteristic
3C2×#102×D71C211yesmaximal, characteristic
4C2×#17985956C211yesmaximal, characteristic, complemented
5#22590694C211yesmaximal, characteristic, complemented
6#22588167C211yesmaximal, characteristic, complemented
7#22588166C211yesmaximal, characteristic, complemented
8#22588164C211yesmaximal, characteristic, complemented
9C4×#14556048C211yesmaximal, characteristic, complemented
10#102×Dic71C211yesmaximal, characteristic, complemented
11C4×#14556049C211yesmaximal, characteristic, complemented
12#22588154C211yesmaximal, characteristic, complemented
13#22588058C211yesmaximal, characteristic, complemented
14#22588055C211yesmaximal, characteristic, complemented
15C71×#1762C211yesmaximal, characteristic, complemented
16C22×D4×D71C2211yescharacteristic
17C22×#11765848C2211yescharacteristic
18C22×C8×D71C2211yescharacteristic
19#17986471—24no—
20#17986471C418yescomplemented
21C2×C4×D284C2211yescharacteristic
22C2×D4×Dic71C2211yescharacteristic
23C2×#14556090C2211yescharacteristic
24C2×C4×C22⋊D71—21no—
25C2×(C22⋊D71)⋊C4—21no—
26C2×#14556086C2211yescharacteristic
27C2×#14556086C2211yescharacteristic
28C2×#14556085C2211yescharacteristic
29C2×C4⋊C4×D71C2211yescharacteristic
30C22×(C2×D71)⋊C4—21no—
31C2×C22⋊C4×D71—21no—
32#17986002C418yescomplemented
33C2×#14556050C2211yescharacteristic
34C2×#14556050C2211yescharacteristic
35C2×#14556049C2211yescharacteristic
36C2×#14556049C2211yescharacteristic
37C2×#14556048C2211yescharacteristic
38C2×#14556048C2211yescharacteristic
39#102×D71C418yescomplemented
40#17985956—24no—
41C2×#14556038C2211yescharacteristic, complemented
42C2×C4×C71⋊C8C2211yescharacteristic, complemented
43C2×C8×Dic71C2211yescharacteristic, complemented
44C4⋊C4×Dic71C2211yescharacteristic, complemented
45C4⋊C4×Dic71C2211yescharacteristic, complemented
46C4×Dic71⋊C4—21no—
47C4×C4⋊Dic71C2211yescharacteristic, complemented
48#17985850—21no—
49C4×(C2×D71)⋊C4—21no—
50#17985846—21no—
51#17985762C2211yescharacteristic, complemented
52#17985762C2211yescharacteristic, complemented
53#17985761C2211yescharacteristic, complemented
54#17985761C2211yescharacteristic, complemented
55#17985761C2211yescharacteristic, complemented
56#17985761C2211yescharacteristic, complemented
57C2×C4×D4×C71C2211yescharacteristic
58C2×#102×C71C2211yescharacteristic
59C2×#102×C71C2211yescharacteristic
60C2×#97×C71C2211yescharacteristic, complemented
61C4×C4⋊C4×C71C2211yescharacteristic, complemented
62#340×C71C2211yescharacteristic, complemented
63#340×C71C2211yescharacteristic, complemented
64C24×D71—21no—
65C22×D284C2311yescharacteristic
66C22×C22⋊D71—21no—
67C2×D4×D71—22no—
68C2×D4×D71—22no—
69C2×D4×D71—22no—
70C2×D4×D71C2×C414yes—
71C2×D4×D71C2×C414yes—
72C2×D4×D71C2×C414yes—
73C23×Dic71—21no—
74C22×C4×D71—21no—
75C22×C4×D71—21no—
76C22×C4×D71—21no—
77C22×C4×D71C2311yescharacteristic
78C2×#11765848—22no—
79C2×#11765848—22no—
80C2×#11765848C2×C414yescomplemented
81C22×C71⋊C8C2311yescharacteristic
82C22×C71⋊C8C2311yescharacteristic
83C2×C8×D71—22no—
84C2×C8×D71—22no—
85C2×C8×D71C2×C414yescomplemented
86C4×D284—22no—
87C4×D284C2×C414yescomplemented
88D4×Dic71—22no—
89D4×Dic71C2×C414yescomplemented
90#14556090—22no—
91#14556090C2×C414yescomplemented
92C4×C22⋊D71—28no—
93(C22⋊D71)⋊C4—28no—
94#14556086—22no—
95#14556086—22no—
96#14556086C2×C414yes—
97#14556086C2×C414yescomplemented
98#14556085C2×C414yes—
99#14556085D414yes—
100C2×C4⋊Dic71C2311yescharacteristic
101C2×C4⋊Dic71C2311yescharacteristic
102C2×C4⋊Dic71C2311yescharacteristic
103C2×Dic71⋊C4—21no—
104C2×Dic71⋊C4D411yescharacteristic
105C2×Dic71⋊C4D411yescharacteristic
106C4⋊C4×D71—22no—
107C4⋊C4×D71C2×C414yescomplemented
108C2×C22⋊Dic71—21no—
109C2×(C2×D71)⋊C4—21no—
110C2×(C2×D71)⋊C4—21no—
111C2×(C2×D71)⋊C4—21no—
112C2×(C2×D71)⋊C4—28no—
113C2×(C2×D71)⋊C4—21no—
114C2×(C2×D71)⋊C4D411yescharacteristic
115C2×(C2×D71)⋊C4D411yescharacteristic
116C22⋊C4×D71—28no—
117C2×C4×Dic71—21no—
118C2×C4×Dic71—21no—
119C2×C4×Dic71—21no—
120C2×C4×Dic71—21no—
121C2×C4×Dic71—21no—
122C2×C4×Dic71C2311yescharacteristic
123#14556050C2×C414yescomplemented
124#14556050C2×C414yescomplemented
125#14556049C2×C414yescomplemented
126#14556049C2×C414yescomplemented
127#14556048C2×C414yescomplemented
128#14556048C2×C414yescomplemented
129#14556038—22no—
130C4×C71⋊C8—22no—
131C8×Dic71—22no—
132C71⋊#95—21no—
133C71⋊#95—21no—
134C71⋊#95—21no—
135C22×D4×C71C2311yescharacteristic
136C23×C4×C71—21no—
137C22×C8×C71C2311yescharacteristic
138C22×C8×C71C2311yescharacteristic
139C4×D4×C71—22no—
140C4×D4×C71C2×C414yescomplemented
141C2×C4⋊C4×C71C2311yescharacteristic
142C2×C4⋊C4×C71C2311yescharacteristic
143C2×C4⋊C4×C71C2311yescharacteristic
144C2×C22⋊C4×C71—21no—
145C2×C42×C71—21no—
146C2×C42×C71C2311yescharacteristic
147#102×C71C2×C414yescomplemented
148#102×C71C2×C414yescomplemented
149#97×C71—22no—
150#95×C71—21no—
151C23×D71—21no—
152C23×D71—24no—
153C23×D71—24no—
154C23×D71—24no—
155C23×D71—81no—
156C23×D71—81no—
157C23×D71—81no—
158C23×D71—81no—
159C23×D71C2×D411yescharacteristic
160C2×D284—21no—
161C2×D284—21no—
162C2×D284—21no—
163C2×D284C22×C412yes—
164C2×D284C22×C412yes—
165C2×D284C22×C412yes—
166C2×C22⋊D71—24no—
167C2×C22⋊D71—24no—
168C2×C22⋊D71—24no—
169D4×D71—28no—
170D4×D71—28no—
171D4×D71—28no—
172D4×D71C42116yescomplemented
173C22×Dic71—21no—
174C22×Dic71—21no—
175C22×Dic71—21no—
176C22×Dic71—24no—
177C22×Dic71—81no—
178C22×Dic71—81no—
179C22×Dic71C2×D411yescharacteristic
180C22×Dic71C2×D411yescharacteristic
181C22×Dic71C2×D411yescharacteristic
182C2×C4×D71—24no—
183C2×C4×D71—24no—
184C2×C4×D71—24no—
185C2×C4×D71—81no—
186C2×C4×D71—81no—
187C2×C4×D71—81no—
188C2×C4×D71—81no—
189C2×C4×D71—81no—
190C2×C4×D71—81no—
191C2×C4×D71C22×C412yes—
192C2×C4×D71C22×C412yes—
193C2×C4×D71C22×C412yes—
194C2×C4×D71C2×D412yes—
195C2×C4×D71#4112yes—
196C2×C4×D71#4112yes—
197#11765848—28no—
198C2×C71⋊C8—21no—
199C2×C71⋊C8—21no—
200C2×C71⋊C8—21no—
201C2×C71⋊C8—21no—
202C2×C71⋊C8C22×C412yes—
203C2×C71⋊C8C22×C412yes—
204C8×D71—28no—
205C4⋊Dic71—21no—
206C4⋊Dic71—21no—
207C4⋊Dic71—21no—
208C4⋊Dic71C22×C412yes—
209C4⋊Dic71C22×C412yes—
210C4⋊Dic71C22×C412yes—
211Dic71⋊C4—24no—
212Dic71⋊C4C22⋊C414yes—
213Dic71⋊C4C22⋊C414yes—
214C22⋊Dic71—24no—
215(C2×D71)⋊C4—24no—
216(C2×D71)⋊C4—24no—
217(C2×D71)⋊C4—24no—
218(C2×D71)⋊C4—24no—
219(C2×D71)⋊C4C22⋊C414yes—
220(C2×D71)⋊C4C22⋊C414yes—
221C4×Dic71—24no—
222C4×Dic71—24no—
223C4×Dic71—81no—
224C4×Dic71—81no—
225C4×Dic71—81no—
226C4×Dic71C22×C412yes—
227C4×Dic71C2×D412yes—
228C24×C71—21no—
229C2×D4×C71—21no—
230C2×D4×C71—21no—
231C2×D4×C71—21no—
232C2×D4×C71C22×C412yes—
233C2×D4×C71C22×C412yes—
234C2×D4×C71C22×C412yes—
235C22×C4×C71—21no—
236C22×C4×C71—21no—
237C22×C4×C71—21no—
238C22×C4×C71—24no—
239C22×C4×C71—81no—
240C22×C4×C71—81no—
241C22×C4×C71C2×D411yescharacteristic
242C22×C4×C71C2×D411yescharacteristic
243C22×C4×C71C2411yescharacteristic
244C2×C8×C71—21no—
245C2×C8×C71—21no—
246C2×C8×C71—21no—
247C2×C8×C71—21no—
248C2×C8×C71C22×C412yes—
249C2×C8×C71C22×C412yes—
250C4⋊C4×C71—21no—
251C4⋊C4×C71—21no—
252C4⋊C4×C71—21no—
253C4⋊C4×C71C22×C412yes—
254C4⋊C4×C71C22×C412yes—
255C4⋊C4×C71C22×C412yes—
256C22⋊C4×C71—24no—
257C42×C71—81no—
258C42×C71C22×C412yes—
259C42×C71C2×D412yes—
260C23×C71—22no—
261C23×C71—22no—
262C23×C71—22no—
263C23×C71—41no—
264C23×C71—41no—
265C23×C71—41no—
266C23×C71—41no—
267C23×C71C22×D411yescharacteristic
268C22×D71—21no—
269C22×D71—21no—
270C22×D71—21no—
271C22×D71—21no—
272C22×D71—22no—
273C22×D71—22no—
274C22×D71—22no—
275C22×D71—216no—
276C22×D71—41no—
277C22×D71—41no—
278C22×D71—41no—
279C22×D71—41no—
280C22×D71—84no—
281C22×D71—84no—
282C22×D71—84no—
283C22×D71—84no—
284C22×D71—84no—
285C22×D71—84no—
286C22×D71C2×C22⋊C412yes—
287C22×D71C4×D412yes—
288C22×D71C4×D412yes—
289D4×C71—22no—
290D4×C71—22no—
291D4×C71—22no—
292D4×C71C2×C4214yes—
293C2×C4×C71—21no—
294C2×C4×C71—21no—
295C2×C4×C71—21no—
296C2×C4×C71—21no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—41no—
301C2×C4×C71—41no—
302C2×C4×C71—41no—
303C2×C4×C71—41no—
304C2×C4×C71—41no—
305C2×C4×C71—41no—
306C2×C4×C71—84no—
307C2×C4×C71C2×C22⋊C412yes—
308C2×C4×C71C2×C22⋊C412yes—
309C2×C4×C71C23×C411yescharacteristic
310C2×C4×C71C23×C411yescharacteristic
311C2×C4×C71C23×C411yescharacteristic
312C2×C4×C71C22×D411yescharacteristic
313C2×C4×C71C2×#4111yescharacteristic
314C2×C4×C71C2×#4111yescharacteristic
315C22⋊D71—216no—
316C2×Dic71—21no—
317C2×Dic71—21no—
318C2×Dic71—21no—
319C2×Dic71—21no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—41no—
324C2×Dic71—41no—
325C2×Dic71—41no—
326C2×Dic71—41no—
327C2×Dic71—41no—
328C2×Dic71—41no—
329C2×Dic71—84no—
330C2×Dic71C2×C22⋊C412yes—
331C2×Dic71C2×C22⋊C412yes—
332C2×Dic71C2×C22⋊C412yes—
333C2×Dic71C4×D412yes—
334C2×Dic71C4×D412yes—
335D284—22no—
336D284—22no—
337D284—22no—
338D284C2×C4214yes—
339C4×D71—84no—
340C4×D71—84no—
341C4×D71—84no—
342C4×D71C2×C4214yes—
343C4×D71#11714yes—
344C4×D71C4×D414yes—
345C4×D71C4×D414yes—
346C8×C71—22no—
347C8×C71—22no—
348C71⋊C8—22no—
349C71⋊C8—22no—
350C22×C71—24no—
351C22×C71—42no—
352C22×C71—42no—
353C22×C71—42no—
354C22×C71—42no—
355C22×C71—42no—
356C22×C71—42no—
357C22×C71C22×C22⋊C411yescharacteristic
358C22×C71C2×C4×D411yescharacteristic
359C22×C71C2×C4×D411yescharacteristic
360C22×C71#57611yescharacteristic
361C22×C71#57611yescharacteristic
362C22×C71#57711yescharacteristic
363C22×C71#57711yescharacteristic
364C2×D71—22no—
365C2×D71—22no—
366C2×D71—22no—
367C2×D71—22no—
368C2×D71—22no—
369C2×D71—22no—
370C2×D71—24no—
371C2×D71—42no—
372C2×D71—42no—
373C2×D71—42no—
374C2×D71—42no—
375C2×D71—42no—
376C2×D71—42no—
377C2×D71—816no—
378C2×D71C4×C22⋊C414yes—
379C4×C71—22no—
380C4×C71—22no—
381C4×C71—42no—
382C4×C71—42no—
383C4×C71—42no—
384C4×C71C22×C4211yescharacteristic
385C4×C71C2×#11711yescharacteristic
386C4×C71C2×C4×D411yescharacteristic
387C4×C71C2×C4×D411yescharacteristic
388Dic71—22no—
389Dic71—22no—
390Dic71—42no—
391Dic71—42no—
392Dic71—42no—
393Dic71C4×C22⋊C414yes—
394#20416—711nomaximal, Sylow
395C2×C71—44no—
396C2×C71C2×C4×C22⋊C411yescharacteristic
397C2×C71#289711yescharacteristic
398C2×C71#289711yescharacteristic
399C2×C71#294611yescharacteristic
400C2×C71#294611yescharacteristic
401C2×C71#294811yescharacteristic
402C2×C71#294911yescharacteristic
403D71—24no—
404D71—44no—
405C2×#518—711no—
406C2×#418—711no—
407C22×#102—711no—
408C2×#405—711no—
409#2274—711no—
410#1762—711no—
411#1762—711no—
412#1762—711no—
413#1762D7111yescharacteristic, complemented
414C4×#102—711no—
415C4×#102—711no—
416C4×#102—711no—
417C4×#102—711no—
418#1736—711no—
419#1735—711no—
420C71#2041611yescharacteristic, complemented, Sylow
421C23×D4—711no—
422C22×M16—711no—
423C23×C8—711no—
424#518—718no—
425#518—1424no—
426C2×C4×D4—711no—
427C2×C4×D4—711no—
428C2×C4×D4—711no—
429C2×C4×D4—1421no—
430C2×C4×D4—1421no—
431C2×C4×D4C2×D7111yescharacteristic
432C2×#117—711no—
433C2×#117—711no—
434C2×#117—711no—
435C22×C4⋊C4—711no—
436C22×C22⋊C4—1421no—
437C22×C22⋊C4—1421no—
438#418—718no—
439C2×#102—711no—
440C2×#102—711no—
441C2×#102—711no—
442C2×#102—711no—
443C2×#102—711no—
444C2×#102—711no—
445C2×#102—718no—
446C2×#102C2×D7111yescharacteristic
447C2×#102C2×D7111yescharacteristic
448#405—1424no—
449C2×#97—711no—
450C2×#97C2×D7111yescharacteristic, complemented
451C2×C4×C8—711no—
452C2×C4×C8—711no—
453C4×C4⋊C4—711no—
454C4×C4⋊C4—711no—
455C4×C4⋊C4—711no—
456C4×C4⋊C4—1421no—
457C4×C4⋊C4—1421no—
458C4×C4⋊C4C2×D7111yescharacteristic, complemented
459C4×C22⋊C4—1421no—
460C4×C22⋊C4—1421no—
461#340—711no—
462#340—711no—
463#340—711no—
464#340—711no—
465#340—711no—
466#340—711no—
467#340C2×D7111yescharacteristic, complemented
468#340C2×D7111yescharacteristic, complemented
469C25—1421no—
470C22×D4—714no—
471C22×D4—714no—
472C22×D4—714no—
473C22×D4—711no—
474C22×D4—1422no—
475C22×D4—1422no—
476C22×D4—1422no—
477C22×D4—1421no—
478C22×D4C22×D7111yescharacteristic
479C23×C4—21no—
480C23×C4—711no—
481C23×C4—1421no—
482C23×C4—1421no—
483C23×C4—1421no—
484C23×C4—1421no—
485C2×M16—714no—
486C2×M16—1422no—
487C2×M16—1422no—
488C22×C8—711no—
489C22×C8—711no—
490C22×C8—714no—
491C22×C8—1422no—
492C22×C8—1422no—
493C22×C8C22×D7111yescharacteristic
494C22×C8C22×D7111yescharacteristic
495C4×D4—22no—
496C4×D4—714no—
497C4×D4—714no—
498C4×D4—714no—
499C4×D4—1422no—
500C4×D4—1422no—
501C4×D4—1428no—
502C4×D4—1428no—
503C4×D4—1422no—
504C4×D4C4×D7114yescomplemented
505#117—714no—
506#117—714no—
507#117—714no—
508#117—714no—
509#117—1422no—
510#117—1422no—
511C2×C4⋊C4—711no—
512C2×C4⋊C4—711no—
513C2×C4⋊C4—711no—
514C2×C4⋊C4—711no—
515C2×C4⋊C4—711no—
516C2×C4⋊C4—714no—
517C2×C4⋊C4—1422no—
518C2×C4⋊C4—1421no—
519C2×C4⋊C4C22×D7111yescharacteristic
520C2×C4⋊C4C22×D7111yescharacteristic
521C2×C4⋊C4C22×D7111yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—711no—
524C2×C22⋊C4—711no—
525C2×C22⋊C4—1428no—
526C2×C22⋊C4—1428no—
527C2×C22⋊C4—1421no—
528C2×C22⋊C4—1421no—
529C2×C22⋊C4—1421no—
530C2×C22⋊C4—1421no—
531C2×C22⋊C4—1421no—
532C2×C42—21no—
533C2×C42—711no—
534C2×C42—1421no—
535C2×C42—1421no—
536C2×C42—1421no—
537C2×C42—1421no—
538C2×C42—1421no—
539C2×C42C22×D7111yescharacteristic
540#102—714no—
541#102—714no—
542#102—714no—
543#102—714no—
544#102—714no—
545#102—714no—
546#102C4×D7114yescomplemented
547#102C4×D7114yescomplemented
548#97—22no—
549#97—1422no—
550C4×C8—1422no—
551C4×C8—1422no—
552#95—21no—
553#95—1421no—
554#95—1421no—
555#95—1421no—
556C24—21no—
557C24—5681no—
558C24—5681no—
559C24—5681no—
560C24—5681no—
561C24—711no—
562C24—1424no—
563C24—1424no—
564C24—1424no—
565C24—1421no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—7116no—
570C2×D4—712no—
571C2×D4—712no—
572C2×D4—712no—
573C2×D4—1428no—
574C2×D4—1428no—
575C2×D4—1428no—
576C2×D4—1424no—
577C2×D4—1424no—
578C2×D4—1424no—
579C2×D4—1421no—
580C2×D4—1421no—
581C2×D4—1421no—
582C2×D4C2×C4×D7112yes—
583C2×D4C2×C4×D7112yes—
584C2×D4C2×C4×D7112yes—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4—5681no—
592C22×C4—5681no—
593C22×C4—5681no—
594C22×C4—5681no—
595C22×C4—5681no—
596C22×C4—5681no—
597C22×C4—5681no—
598C22×C4—5681no—
599C22×C4—711no—
600C22×C4—712no—
601C22×C4—712no—
602C22×C4—712no—
603C22×C4—712no—
604C22×C4—712no—
605C22×C4—712no—
606C22×C4—711no—
607C22×C4—711no—
608C22×C4—1424no—
609C22×C4—1424no—
610C22×C4—1421no—
611C22×C4—1421no—
612C22×C4—1421no—
613C22×C4—1424no—
614C22×C4—1424no—
615C22×C4D4×D7111yescharacteristic
616C22×C4D4×D7111yescharacteristic
617C22×C4C23×D7111yescharacteristic
618M16—1428no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—712no—
624C2×C8—712no—
625C2×C8—1428no—
626C2×C8—1421no—
627C2×C8—1421no—
628C2×C8—1421no—
629C2×C8—1421no—
630C2×C8C2×C4×D7112yes—
631C2×C8C2×C4×D7112yes—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—714no—
636C4⋊C4—714no—
637C4⋊C4—712no—
638C4⋊C4—712no—
639C4⋊C4—712no—
640C4⋊C4—1424no—
641C4⋊C4—1421no—
642C4⋊C4—1421no—
643C4⋊C4—1421no—
644C4⋊C4C2×C4×D7112yes—
645C4⋊C4C2×C4×D7112yes—
646C4⋊C4C2×C4×D7112yes—
647C22⋊C4—24no—
648C22⋊C4—714no—
649C22⋊C4—714no—
650C22⋊C4—1424no—
651C22⋊C4—1424no—
652C22⋊C4—1424no—
653C22⋊C4—1424no—
654C22⋊C4—1424no—
655C42—81no—
656C42—5681no—
657C42—5681no—
658C42—5681no—
659C42—712no—
660C42—712no—
661C42—1424no—
662C42—1424no—
663C42C2×C4×D7112yes—
664C42D4×D7112yes—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—2841no—
673C23—2841no—
674C23—2841no—
675C23—2841no—
676C23—5684no—
677C23—5684no—
678C23—5684no—
679C23—5684no—
680C23—5684no—
681C23—5684no—
682C23—712no—
683C23—712no—
684C23—712no—
685C23—14216no—
686C23—1422no—
687C23—1422no—
688C23—1422no—
689C23—1421no—
690C23—1421no—
691C23—1421no—
692C23—1421no—
693C23C2×D4×D7111yescharacteristic
694D4—22no—
695D4—22no—
696D4—22no—
697D4—714no—
698D4—14216no—
699D4—1422no—
700D4—1422no—
701D4—1422no—
702D4C42×D7114yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4—2841no—
718C2×C4—2841no—
719C2×C4—2841no—
720C2×C4—2841no—
721C2×C4—2841no—
722C2×C4—2841no—
723C2×C4—5684no—
724C2×C4—5684no—
725C2×C4—5684no—
726C2×C4—5684no—
727C2×C4—712no—
728C2×C4—712no—
729C2×C4—712no—
730C2×C4—714no—
731C2×C4—714no—
732C2×C4—714no—
733C2×C4—714no—
734C2×C4—712no—
735C2×C4—712no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4—1422no—
739C2×C4—1421no—
740C2×C4—1421no—
741C2×C4—1421no—
742C2×C4—1421no—
743C2×C4C22⋊C4×D7112yes—
744C2×C4C22⋊C4×D7112yes—
745C2×C4C22×C4×D7111yescharacteristic
746C2×C4C22×C4×D7111yescharacteristic
747C2×C4C22×C4×D7111yescharacteristic
748C2×C4C2×D4×D7111yescharacteristic
749C2×C4#41×D7111yescharacteristic
750C2×C4#41×D7111yescharacteristic
751C8—22no—
752C8—22no—
753C8—1422no—
754C8—1422no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—2842no—
763C22—2842no—
764C22—2842no—
765C22—2842no—
766C22—2842no—
767C22—2842no—
768C22—56816no—
769C22—714no—
770C22—1424no—
771C22—1422no—
772C22—1422no—
773C22—1422no—
774C22—1422no—
775C22—1422no—
776C22—1422no—
777C22C2×C22⋊C4×D7111yescharacteristic
778C22C4×D4×D7111yescharacteristic
779C22C4×D4×D7111yescharacteristic
780C22#1798680311yescharacteristic
781C22#1798680311yescharacteristic
782C22#1798680811yescharacteristic
783C22#1798680911yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—2842no—
790C4—2842no—
791C4—2842no—
792C4—714no—
793C4—1422no—
794C4—1422no—
795C4C2×C42×D7111yescharacteristic
796C4#117×D7111yescharacteristic
797C4C4×D4×D7111yescharacteristic
798C4C4×D4×D7111yescharacteristic
799C2—44no—
800C2—2844no—
801C2—1424no—
802C2C4×C22⋊C4×D7111yescharacteristic
803C2#2259686411yescharacteristic
804C2#2259686511yescharacteristic
805C2#2259716911yescharacteristic
806C2#2259717111yescharacteristic
807C2#2259718911yescharacteristic
808C2#2259719611yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutatorC4×C71C22×C42
FrattiniC22×C4C23×D71
FittingC71×#1762C2
socleC23×C71C22×D4
prime radicalC22×D4×D71C22
cosocleC22×C4×C71C24
hypercenter#1762D71
hypocenterC71#20416
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
4. C2×#17985956C2semidirect
5. #22590694C2semidirect
6. #22588167C2semidirect
7. #22588166C2semidirect
8. #22588164C2semidirect
9. C4×#14556048C2semidirect
10. #102×Dic71C2semidirect
11. C4×#14556049C2semidirect
12. #22588154C2semidirect
13. #22588058C2semidirect
14. #22588055C2semidirect
15. C71×#1762C2semidirect
20. #17986471C4semidirect
32. #17986002C4semidirect
39. #102×D71C4semidirect
41. C2×#14556038C22semidirect
42. C2×C4×C71⋊C8C22semidirect
43. C2×C8×Dic71C22semidirect
44. C4⋊C4×Dic71C22semidirect
45. C4⋊C4×Dic71C22semidirect
47. C4×C4⋊Dic71C22semidirect
51. #17985762C22semidirect
52. #17985762C22semidirect
53. #17985761C22semidirect
54. #17985761C22semidirect
55. #17985761C22semidirect
56. #17985761C22semidirect
60. C2×#97×C71C22semidirect
61. C4×C4⋊C4×C71C22semidirect
62. #340×C71C22semidirect
63. #340×C71C22semidirect
80. C2×#11765848C2×C4semidirect
85. C2×C8×D71C2×C4semidirect
87. C4×D284C2×C4semidirect
89. D4×Dic71C2×C4semidirect
91. #14556090C2×C4semidirect
97. #14556086C2×C4semidirect
107. C4⋊C4×D71C2×C4semidirect
123. #14556050C2×C4semidirect
124. #14556050C2×C4semidirect
125. #14556049C2×C4semidirect
126. #14556049C2×C4semidirect
127. #14556048C2×C4semidirect
128. #14556048C2×C4semidirect
140. C4×D4×C71C2×C4semidirect
147. #102×C71C2×C4semidirect
148. #102×C71C2×C4semidirect
172. D4×D71C42semidirect
413. #1762D71semidirect
420. C71#20416semidirect
450. C2×#97C2×D71semidirect
458. C4×C4⋊C4C2×D71semidirect
467. #340C2×D71semidirect
468. #340C2×D71semidirect
504. C4×D4C4×D71semidirect
546. #102C4×D71semidirect
547. #102C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179864712
C2×#179860022
C2×#102×D712
C2×#179859562
#225906942
#225881672
#225881662
#225881642
C4×#145560482
#102×Dic712
C4×#145560492
#225881542
#225880582
#225880552
C71×#17622
#2041671