Finite Group Databasebeta

← #32007508

Subgroups — #32007508

Order 18176.

950 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22590721C211yesmaximal, characteristic
2#22588956C211yesmaximal, characteristic, complemented
3#22588955C211yesmaximal, characteristic, complemented
4#22588954C211yesmaximal, characteristic, complemented
5#22588951C211yesmaximal, characteristic, complemented
6#22588946C211yesmaximal, characteristic, complemented
7#22588945C211yesmaximal, characteristic, complemented
8#22588943C211yesmaximal, characteristic, complemented
9#22588323C211yesmaximal, characteristic, complemented
10#22588321C211yesmaximal, characteristic, complemented
11#22588249C211yesmaximal, characteristic
12#22588249C211yesmaximal, characteristic
13#22588107C211yesmaximal, characteristic, complemented
14#22588105C211yesmaximal, characteristic, complemented
15C71×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D71C2211yescharacteristic
17C2×#14556085C2211yescharacteristic
18C2×#14556085C2211yescharacteristic
19C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
20C2×Dic71⋊C8C2211yescharacteristic, complemented
21C2×Dic71⋊C8C2211yescharacteristic, complemented
22C2×C22⋊(C71⋊C8)C2211yescharacteristic
23C2×C22⋊(C71⋊C8)C2211yescharacteristic
24C2×(C2×D71)⋊C8C2211yescharacteristic
25C2×(C2×D71)⋊C8C2211yescharacteristic
26C2×(C2×D71)⋊C8C2211yescharacteristic
27C2×(C2×D71)⋊C8C2211yescharacteristic
28C2×(C2×D71)⋊C8C2211yescharacteristic
29C2×(C2×D71)⋊C8C2211yescharacteristic
30C2×(C2×D71)⋊C8C2211yescharacteristic
31C2×(C2×D71)⋊C8C2211yescharacteristic
32C2×#14556039C2211yescharacteristic, complemented
33C2×#14556038C2211yescharacteristic, complemented
34C2×C8×Dic71C2211yescharacteristic, complemented
35#17985861C411yescharacteristic
36#17985861C411yescharacteristic
37#17985858C411yescharacteristic
38#17985858C411yescharacteristic
39#17985857C411yescharacteristic
40#17985857C411yescharacteristic
41#17985854C411yescharacteristic
42#17985854C411yescharacteristic
43C4×(C2×D71)⋊C4C2211yescharacteristic
44C4×(C2×D71)⋊C4C2211yescharacteristic
45C4×C22⋊Dic71C2211yescharacteristic
46#17985754C2211yescharacteristic, complemented
47#17985754C2211yescharacteristic, complemented
48#17985753C2211yescharacteristic, complemented
49#17985753C2211yescharacteristic, complemented
50#17985753C2211yescharacteristic, complemented
51#17985753C2211yescharacteristic, complemented
52C2×C4⋊C8×C71C2211yescharacteristic, complemented
53C2×C22⋊C8×C71C2211yescharacteristic
54C2×C22⋊C8×C71C2211yescharacteristic
55C2×C4×C8×C71C2211yescharacteristic, complemented
56C4×C22⋊C4×C71C2211yescharacteristic
57#336×C71C2211yescharacteristic, complemented
58#336×C71C2211yescharacteristic, complemented
59C24×D71C2×C411yescharacteristic
60C23×Dic71C2×C411yescharacteristic
61C22×C4×D71—22no—
62C22×C4×D71—22no—
63C22×C4×D71—41no—
64C22×C4×D71—41no—
65C22×C4×D71—41no—
66C22×C4×D71—41no—
67C22×C4×D71C2×C411yescharacteristic
68C22×C4×D71C2×C411yescharacteristic
69C22×C4×D71C2311yescharacteristic
70C22×C4×D71C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C22×C71⋊C8C2311yescharacteristic
73C22×C71⋊C8C2311yescharacteristic
74C22×C71⋊C8C2311yescharacteristic
75#14556085—41no—
76#14556085—41no—
77#14556085—41no—
78#14556085—41no—
79C2×Dic71⋊C4C2×C411yescharacteristic
80C2×Dic71⋊C4C2×C411yescharacteristic
81C2×Dic71⋊C4C2×C411yescharacteristic
82C2×Dic71⋊C4C2×C411yescharacteristic
83C2×C22⋊Dic71C2×C411yescharacteristic
84C2×C22⋊Dic71C2×C411yescharacteristic
85C2×(C2×D71)⋊C4C2×C411yescharacteristic
86C2×(C2×D71)⋊C4C2×C411yescharacteristic
87C2×(C2×D71)⋊C4C2×C411yescharacteristic
88C2×(C2×D71)⋊C4C2×C411yescharacteristic
89C2×(C2×D71)⋊C4C2×C411yescharacteristic
90C2×(C2×D71)⋊C4C2×C411yescharacteristic
91C2×(C2×D71)⋊C4C2×C411yescharacteristic
92C2×(C2×D71)⋊C4C2×C411yescharacteristic
93C2×C4×Dic71C2311yescharacteristic
94C2×C4×Dic71C2311yescharacteristic
95C4⋊(C71⋊C8)—41no—
96Dic71⋊C8—41no—
97Dic71⋊C8—41no—
98C22⋊(C71⋊C8)—41no—
99C22⋊(C71⋊C8)—41no—
100(C2×D71)⋊C8—22no—
101(C2×D71)⋊C8—22no—
102(C2×D71)⋊C8—22no—
103(C2×D71)⋊C8—22no—
104(C2×D71)⋊C8—41no—
105(C2×D71)⋊C8—41no—
106(C2×D71)⋊C8—41no—
107(C2×D71)⋊C8—41no—
108#14556039—41no—
109#14556038—41no—
110C8×Dic71—41no—
111C71⋊#95C2×C411yescharacteristic
112C71⋊#95C2×C411yescharacteristic
113C71⋊#95C2×C411yescharacteristic
114C71⋊#95C2×C411yescharacteristic
115C71⋊#95C2×C411yescharacteristic
116C71⋊#95C2×C411yescharacteristic
117C23×C4×C71C2311yescharacteristic
118C22×C8×C71C2311yescharacteristic
119C22×C8×C71C2311yescharacteristic
120C22×C8×C71C2311yescharacteristic
121C22×C8×C71C2311yescharacteristic
122C2×C22⋊C4×C71C2×C411yescharacteristic
123C2×C22⋊C4×C71C2×C411yescharacteristic
124C2×C42×C71C2311yescharacteristic
125C2×C42×C71C2311yescharacteristic
126C4⋊C8×C71—41no—
127C22⋊C8×C71—41no—
128C22⋊C8×C71—41no—
129C4×C8×C71—41no—
130#95×C71C2×C411yescharacteristic
131#95×C71C2×C411yescharacteristic
132C23×D71—22no—
133C23×D71—22no—
134C23×D71—22no—
135C23×D71—41no—
136C23×D71—41no—
137C23×D71—41no—
138C23×D71—41no—
139C23×D71C22×C411yescharacteristic
140C23×D71C22×C411yescharacteristic
141C22×Dic71—22no—
142C22×Dic71—41no—
143C22×Dic71—41no—
144C22×Dic71C22×C411yescharacteristic
145C22×Dic71C22×C411yescharacteristic
146C22×Dic71C22×C411yescharacteristic
147C22×Dic71C22×C411yescharacteristic
148C22×Dic71C22×C411yescharacteristic
149C22×Dic71C22×C411yescharacteristic
150C2×C4×D71—21no—
151C2×C4×D71—21no—
152C2×C4×D71—21no—
153C2×C4×D71—21no—
154C2×C4×D71—22no—
155C2×C4×D71—21no—
156C2×C4×D71—21no—
157C2×C4×D71—21no—
158C2×C4×D71—21no—
159C2×C4×D71—21no—
160C2×C4×D71—21no—
161C2×C4×D71—22no—
162C2×C4×D71—44no—
163C2×C4×D71—44no—
164C2×C4×D71—44no—
165C2×C4×D71—44no—
166C2×C4×D71—41no—
167C2×C4×D71—41no—
168C2×C4×D71—41no—
169C2×C4×D71—41no—
170C2×C4×D71#4112yes—
171C2×C4×D71#4112yes—
172C2×C71⋊C8—21no—
173C2×C71⋊C8—21no—
174C2×C71⋊C8—21no—
175C2×C71⋊C8—21no—
176C2×C71⋊C8—21no—
177C2×C71⋊C8—21no—
178C2×C71⋊C8—21no—
179C2×C71⋊C8—21no—
180C2×C71⋊C8—21no—
181C2×C71⋊C8—21no—
182C2×C71⋊C8—21no—
183C2×C71⋊C8—21no—
184Dic71⋊C4—41no—
185Dic71⋊C4—41no—
186Dic71⋊C4—41no—
187Dic71⋊C4—41no—
188C22⋊Dic71—22no—
189C22⋊Dic71—41no—
190(C2×D71)⋊C4—22no—
191(C2×D71)⋊C4—22no—
192(C2×D71)⋊C4—41no—
193(C2×D71)⋊C4—41no—
194(C2×D71)⋊C4—41no—
195(C2×D71)⋊C4—41no—
196(C2×D71)⋊C4—41no—
197(C2×D71)⋊C4—41no—
198C4×Dic71—21no—
199C4×Dic71—21no—
200C4×Dic71—21no—
201C4×Dic71—21no—
202C24×C71C22×C411yescharacteristic
203C22×C4×C71—21no—
204C22×C4×C71—21no—
205C22×C4×C71—21no—
206C22×C4×C71—21no—
207C22×C4×C71—21no—
208C22×C4×C71—21no—
209C22×C4×C71C22×C411yescharacteristic
210C22×C4×C71C22×C411yescharacteristic
211C22×C4×C71C22×C411yescharacteristic
212C22×C4×C71C22×C411yescharacteristic
213C22×C4×C71C22×C411yescharacteristic
214C22×C4×C71C2411yescharacteristic
215C2×C8×C71—21no—
216C2×C8×C71—21no—
217C2×C8×C71—21no—
218C2×C8×C71—21no—
219C2×C8×C71—21no—
220C2×C8×C71—21no—
221C2×C8×C71—21no—
222C2×C8×C71—21no—
223C2×C8×C71—21no—
224C2×C8×C71—21no—
225C2×C8×C71—21no—
226C2×C8×C71—21no—
227C22⋊C4×C71—22no—
228C22⋊C4×C71—41no—
229C42×C71—21no—
230C42×C71—21no—
231C42×C71—21no—
232C42×C71—21no—
233C23×C71—21no—
234C23×C71—21no—
235C23×C71—21no—
236C23×C71—21no—
237C23×C71—21no—
238C23×C71—21no—
239C23×C71#13112yes—
240C23×C71C23×C411yescharacteristic
241C22×D71—21no—
242C22×D71—21no—
243C22×D71—21no—
244C22×D71—21no—
245C22×D71—21no—
246C22×D71—21no—
247C22×D71—21no—
248C22×D71—21no—
249C22×D71—21no—
250C22×D71—21no—
251C22×D71—21no—
252C22×D71—21no—
253C22×D71—44no—
254C22×D71—44no—
255C22×D71—44no—
256C22×D71—44no—
257C22×D71—44no—
258C22×D71—44no—
259C22×D71—44no—
260C22×D71#11712yes—
261C22×D71#13112yes—
262C2×C4×C71—21no—
263C2×C4×C71—21no—
264C2×C4×C71—21no—
265C2×C4×C71—21no—
266C2×C4×C71—21no—
267C2×C4×C71—21no—
268C2×C4×C71—21no—
269C2×C4×C71—21no—
270C2×C4×C71—21no—
271C2×C4×C71—21no—
272C2×C4×C71—21no—
273C2×C4×C71—21no—
274C2×C4×C71—21no—
275C2×C4×C71—21no—
276C2×C4×C71—21no—
277C2×C4×C71—41no—
278C2×C4×C71—41no—
279C2×C4×C71—41no—
280C2×C4×C71—41no—
281C2×C4×C71C2×#4111yescharacteristic
282C2×C4×C71C2×#4111yescharacteristic
283C2×C4×C71H(5,𝔽2)11yescharacteristic
284C2×C4×C71H(5,𝔽2)11yescharacteristic
285C2×C4×C71H(5,𝔽2)11yescharacteristic
286C2×C4×C71H(5,𝔽2)11yescharacteristic
287C2×Dic71—21no—
288C2×Dic71—21no—
289C2×Dic71—21no—
290C2×Dic71—21no—
291C2×Dic71—21no—
292C2×Dic71—21no—
293C2×Dic71—21no—
294C2×Dic71—21no—
295C2×Dic71—21no—
296C2×Dic71—21no—
297C2×Dic71—21no—
298C2×Dic71—21no—
299C2×Dic71—21no—
300C2×Dic71—21no—
301C2×Dic71—21no—
302C2×Dic71—21no—
303C2×Dic71—21no—
304C2×Dic71—44no—
305C2×Dic71#11712yes—
306C4×D71—22no—
307C4×D71—22no—
308C4×D71—22no—
309C4×D71—22no—
310C4×D71—44no—
311C4×D71—44no—
312C4×D71—41no—
313C4×D71—41no—
314C4×D71—41no—
315C4×D71—41no—
316C8×C71—41no—
317C8×C71—41no—
318C8×C71—41no—
319C8×C71—41no—
320C71⋊C8—41no—
321C71⋊C8—41no—
322C71⋊C8—41no—
323C71⋊C8—41no—
324C22×C71—22no—
325C22×C71—22no—
326C22×C71—22no—
327C22×C71—41no—
328C22×C71—41no—
329C22×C71—41no—
330C22×C71—41no—
331C22×C71C2×#11711yescharacteristic
332C22×C71#51811yescharacteristic
333C22×C71#51811yescharacteristic
334C22×C71C2×#13111yescharacteristic
335C22×C71C2×#13111yescharacteristic
336C22×C71#56811yescharacteristic
337C22×C71#56811yescharacteristic
338C2×D71—22no—
339C2×D71—22no—
340C2×D71—22no—
341C2×D71—22no—
342C2×D71—22no—
343C2×D71—22no—
344C2×D71—416no—
345C2×D71—41no—
346C2×D71—41no—
347C2×D71—41no—
348C2×D71—41no—
349C2×D71—41no—
350C2×D71—41no—
351C2×D71—41no—
352C2×D71—41no—
353C4×C71—41no—
354C4×C71—41no—
355C4×C71—41no—
356C4×C71—41no—
357C4×C71—41no—
358C4×C71#53811yescharacteristic
359C4×C71#53811yescharacteristic
360C4×C71#53811yescharacteristic
361C4×C71#53811yescharacteristic
362Dic71—22no—
363Dic71—41no—
364Dic71—41no—
365Dic71—41no—
366Dic71—41no—
367Dic71—41no—
368#21908—711nomaximal, Sylow
369C2×C71—42no—
370C2×C71#231211yescharacteristic
371C2×C71#292411yescharacteristic
372C2×C71#292411yescharacteristic
373C2×C71#297611yescharacteristic
374C2×C71#297611yescharacteristic
375C2×C71#297711yescharacteristic
376C2×C71#297811yescharacteristic
377D71—42no—
378D71—42no—
379#2280—711no—
380#1924—711no—
381#1924—711no—
382#1924—711no—
383#1924—711no—
384#1923—711no—
385#1923—711no—
386#1923—711no—
387#1923D7111yescharacteristic, complemented
388#1798—711no—
389#1798—711no—
390#1779—711no—
391#1779—711no—
392#1750—711no—
393#1750—711no—
394C71#2190811yescharacteristic, complemented, Sylow
395C24×C4—711no—
396C2×#117—711no—
397C2×#117—711no—
398C2×C4⋊C8—711no—
399C2×C4⋊C8—711no—
400C2×C4⋊C8—711no—
401C2×C4⋊C8C2×D7111yescharacteristic, complemented
402C2×C22⋊C8—711no—
403C2×C22⋊C8—711no—
404C2×C22⋊C8—711no—
405C2×C22⋊C8—711no—
406C2×C22⋊C8—711no—
407C2×C22⋊C8—711no—
408C2×C22⋊C8—711no—
409C2×C22⋊C8—711no—
410C2×C22⋊C8—711no—
411C2×C22⋊C8—711no—
412C2×C22⋊C8C2×D7111yescharacteristic
413C2×C22⋊C8C2×D7111yescharacteristic
414C2×#97—711no—
415C2×#97—711no—
416C2×C4×C8—711no—
417C2×C4×C8C2×D7111yescharacteristic, complemented
418#381—711no—
419#381—711no—
420#380—711no—
421#380—711no—
422#380—711no—
423#380—711no—
424#379—711no—
425#379—711no—
426C4×C22⋊C4—711no—
427C4×C22⋊C4—711no—
428C4×C22⋊C4—711no—
429C4×C22⋊C4C2×D7111yescharacteristic
430#336—711no—
431#336—711no—
432#336—711no—
433#336—711no—
434#336—711no—
435#336—711no—
436#336C2×D7111yescharacteristic, complemented
437#336C2×D7111yescharacteristic, complemented
438C25—711no—
439C23×C4—2841no—
440C23×C4—2841no—
441C23×C4—2841no—
442C23×C4—2841no—
443C23×C4—711no—
444C23×C4—711no—
445C23×C4—711no—
446C23×C4—711no—
447C23×C4—711no—
448C23×C4—1422no—
449C23×C4—1422no—
450C23×C4C22×D7111yescharacteristic
451C22×C8—711no—
452C22×C8—711no—
453C22×C8—711no—
454C22×C8—711no—
455C22×C8C22×D7111yescharacteristic
456C22×C8C22×D7111yescharacteristic
457C22×C8C22×D7111yescharacteristic
458C22×C8C22×D7111yescharacteristic
459#117—2841no—
460#117—2841no—
461#117—2841no—
462#117—2841no—
463C2×C4⋊C4—711no—
464C2×C4⋊C4—711no—
465C2×C4⋊C4—711no—
466C2×C4⋊C4—711no—
467C2×C22⋊C4—711no—
468C2×C22⋊C4—711no—
469C2×C22⋊C4—711no—
470C2×C22⋊C4—711no—
471C2×C22⋊C4—711no—
472C2×C22⋊C4—711no—
473C2×C22⋊C4—711no—
474C2×C22⋊C4—711no—
475C2×C22⋊C4—711no—
476C2×C22⋊C4—711no—
477C2×C22⋊C4C4×D7111yescharacteristic
478C2×C22⋊C4C4×D7111yescharacteristic
479C2×C42—711no—
480C2×C42—711no—
481C2×C42C22×D7111yescharacteristic
482C2×C42C22×D7111yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—2841no—
485C4⋊C8—2841no—
486C4⋊C8—2841no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489C22⋊C8—2841no—
490C22⋊C8—2841no—
491C22⋊C8—2841no—
492C22⋊C8—2841no—
493C22⋊C8—2841no—
494C22⋊C8—2841no—
495C22⋊C8—1422no—
496C22⋊C8—1422no—
497C22⋊C8—1422no—
498C22⋊C8—1422no—
499#97—2841no—
500#97—2841no—
501C4×C8—41no—
502C4×C8—2841no—
503#95—711no—
504#95—711no—
505#95—711no—
506#95—711no—
507#95—711no—
508#95—711no—
509#95C4×D7111yescharacteristic
510#95C4×D7111yescharacteristic
511C24—2841no—
512C24—2841no—
513C24—2841no—
514C24—2841no—
515C24—711no—
516C24—711no—
517C24—1422no—
518C24—1422no—
519C24—1422no—
520C24C2×C4×D7111yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—2841no—
528C22×C4—2841no—
529C22×C4—2841no—
530C22×C4—2841no—
531C22×C4—2844no—
532C22×C4—2844no—
533C22×C4—2844no—
534C22×C4—2844no—
535C22×C4—2841no—
536C22×C4—2841no—
537C22×C4—711no—
538C22×C4—712no—
539C22×C4—712no—
540C22×C4—711no—
541C22×C4—711no—
542C22×C4—711no—
543C22×C4—711no—
544C22×C4—711no—
545C22×C4—1422no—
546C22×C4—1422no—
547C22×C4—1422no—
548C22×C4—1421no—
549C22×C4—1421no—
550C22×C4—1421no—
551C22×C4—1421no—
552C22×C4—1421no—
553C22×C4—1421no—
554C22×C4—1421no—
555C22×C4—1421no—
556C22×C4—1421no—
557C22×C4—1421no—
558C22×C4C2×C4×D7111yescharacteristic
559C22×C4C2×C4×D7111yescharacteristic
560C22×C4C2×C4×D7111yescharacteristic
561C22×C4C2×C4×D7111yescharacteristic
562C22×C4C2×C4×D7111yescharacteristic
563C22×C4C23×D7111yescharacteristic
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—1421no—
577C2×C8—1421no—
578C2×C8—1421no—
579C2×C8—1421no—
580C2×C8—1421no—
581C2×C8—1421no—
582C2×C8—1421no—
583C2×C8—1421no—
584C2×C8—1421no—
585C2×C8—1421no—
586C2×C8—1421no—
587C2×C8—1421no—
588C4⋊C4—2841no—
589C4⋊C4—2841no—
590C4⋊C4—2841no—
591C4⋊C4—2841no—
592C22⋊C4—22no—
593C22⋊C4—41no—
594C22⋊C4—2841no—
595C22⋊C4—2841no—
596C22⋊C4—2841no—
597C22⋊C4—2841no—
598C22⋊C4—2841no—
599C22⋊C4—2841no—
600C22⋊C4—2841no—
601C22⋊C4—1422no—
602C22⋊C4—1422no—
603C22⋊C4—1422no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—1421no—
609C42—1421no—
610C42—1421no—
611C42—1421no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—2844no—
619C23—2844no—
620C23—2844no—
621C23—2844no—
622C23—2844no—
623C23—2844no—
624C23—2844no—
625C23—712no—
626C23—712no—
627C23—1421no—
628C23—1421no—
629C23—1421no—
630C23—1421no—
631C23—1421no—
632C23—1421no—
633C23—1421no—
634C23—1421no—
635C23—1421no—
636C23—1421no—
637C23—1421no—
638C23—1421no—
639C23#1455613412yes—
640C23C22×C4×D7111yescharacteristic
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—2844no—
661C2×C4—2844no—
662C2×C4—2844no—
663C2×C4—2841no—
664C2×C4—2841no—
665C2×C4—2841no—
666C2×C4—2841no—
667C2×C4—712no—
668C2×C4—1421no—
669C2×C4—1421no—
670C2×C4—1421no—
671C2×C4—1421no—
672C2×C4—1421no—
673C2×C4—1421no—
674C2×C4—1421no—
675C2×C4—1421no—
676C2×C4—1421no—
677C2×C4—1421no—
678C2×C4—1421no—
679C2×C4—1421no—
680C2×C4—1421no—
681C2×C4—1421no—
682C2×C4—1421no—
683C2×C4—1421no—
684C2×C4—1421no—
685C2×C4—1422no—
686C2×C4—1422no—
687C2×C4—1422no—
688C2×C4—1422no—
689C2×C4#41×D7111yescharacteristic
690C2×C4#41×D7111yescharacteristic
691C2×C4#1455617311yescharacteristic
692C2×C4#1455617311yescharacteristic
693C2×C4#1455617411yescharacteristic
694C2×C4#1455617411yescharacteristic
695C8—41no—
696C8—41no—
697C8—41no—
698C8—41no—
699C8—2841no—
700C8—2841no—
701C8—2841no—
702C8—2841no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—28416no—
711C22—2841no—
712C22—2841no—
713C22—2841no—
714C22—2841no—
715C22—2841no—
716C22—2841no—
717C22—2841no—
718C22—2841no—
719C22—1422no—
720C22—1422no—
721C22—1422no—
722C22—1422no—
723C22—1422no—
724C22—1422no—
725C22#117×D7111yescharacteristic
726C22#1798647111yescharacteristic
727C22#1798647111yescharacteristic
728C22#131×D7111yescharacteristic
729C22C2×#1455613411yescharacteristic
730C22#1798676411yescharacteristic
731C22#1798676511yescharacteristic
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—2841no—
738C4—2841no—
739C4—2841no—
740C4—2841no—
741C4—2841no—
742C4—1422no—
743C4#1798658111yescharacteristic
744C4#1798658311yescharacteristic
745C4#1798658511yescharacteristic
746C4#1798658811yescharacteristic
747C2—42no—
748C2—2842no—
749C2—2842no—
750C2#2259093411yescharacteristic
751C2#2259699311yescharacteristic
752C2#2259699611yescharacteristic
753C2#2259738211yescharacteristic
754C2#2259738711yescharacteristic
755C2#2259739311yescharacteristic
756C2#2259739711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#1923C2
prime radicalC24×D71C2×C4
cosocleC22×C4×C71C24
hypercenter#1923D71
hypocenterC71#21908
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #22588956C2semidirect
3. #22588955C2semidirect
4. #22588954C2semidirect
5. #22588951C2semidirect
6. #22588946C2semidirect
7. #22588945C2semidirect
8. #22588943C2semidirect
9. #22588323C2semidirect
10. #22588321C2semidirect
13. #22588107C2semidirect
14. #22588105C2semidirect
15. C71×#1923C2semidirect
19. C2×C4⋊(C71⋊C8)C22semidirect
20. C2×Dic71⋊C8C22semidirect
21. C2×Dic71⋊C8C22semidirect
32. C2×#14556039C22semidirect
33. C2×#14556038C22semidirect
34. C2×C8×Dic71C22semidirect
46. #17985754C22semidirect
47. #17985754C22semidirect
48. #17985753C22semidirect
49. #17985753C22semidirect
50. #17985753C22semidirect
51. #17985753C22semidirect
52. C2×C4⋊C8×C71C22semidirect
55. C2×C4×C8×C71C22semidirect
57. #336×C71C22semidirect
58. #336×C71C22semidirect
387. #1923D71semidirect
394. C71#21908semidirect
401. C2×C4⋊C8C2×D71semidirect
417. C2×C4×C8C2×D71semidirect
436. #336C2×D71semidirect
437. #336C2×D71semidirect

Maximal subgroups

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

subgroupindex
#225907212
#225889562
#225889552
#225889542
#225889512
#225889462
#225889452
#225889432
#225883232
#225883212
#225882492
#225881072
#225881052
C71×#19232
#2190871