Finite Group Databasebeta

← #32015541

Subgroups — #32015541

Order 18176.

964 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986072C211yesmaximal, characteristic
2C2×#17986069C211yesmaximal, characteristic
3C2×#17986024C211yesmaximal, characteristic, complemented
4C2×#17986024C211yesmaximal, characteristic, complemented
5#22590801C211yesmaximal, characteristic
6#22589064C211yesmaximal, characteristic, complemented
7#22588524C211yesmaximal, characteristic, complemented
8#22588521C211yesmaximal, characteristic, complemented
9#22588519C211yesmaximal, characteristic, complemented
10#22588516C211yesmaximal, characteristic, complemented
11#22588491C211yesmaximal, characteristic, complemented
12#22588323C211yesmaximal, characteristic, complemented
13#22588323C211yesmaximal, characteristic, complemented
14#22588194C211yesmaximal, characteristic, complemented
15C71×#1940C211yesmaximal, characteristic, complemented
16C22×#11765848C2211yescharacteristic
17C22×#11765848C2211yescharacteristic
18C22×C8×D71C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20C2×C4×D284C2211yescharacteristic
21C2×#14556085C2211yescharacteristic
22C2×#14556085C2211yescharacteristic
23#17986072—24no—
24#17986069—24no—
25#17986024—24no—
26#17986024—24no—
27C2×C4⋊(C71⋊C8)C2211yescharacteristic
28C2×C4⋊(C71⋊C8)C2211yescharacteristic
29C2×C4⋊(C71⋊C8)C2211yescharacteristic
30C2×Dic71⋊C8C2211yescharacteristic
31C2×Dic71⋊C8C2211yescharacteristic
32C2×Dic71⋊C8C2211yescharacteristic
33C2×Dic71⋊C8C2211yescharacteristic
34C2×Dic71⋊C8C2211yescharacteristic
35C2×Dic71⋊C8C2211yescharacteristic
36C2×(C2×D71)⋊C8C2211yescharacteristic
37C2×(C2×D71)⋊C8C2211yescharacteristic
38C2×(C2×D71)⋊C8C2211yescharacteristic
39C2×(C2×D71)⋊C8C2211yescharacteristic
40C2×#14556039C2211yescharacteristic
41#17985900C411yescharacteristic
42#17985900C411yescharacteristic
43#17985895C411yescharacteristic
44#17985895C411yescharacteristic
45#17985888C411yescharacteristic
46#17985888C411yescharacteristic
47#17985888C411yescharacteristic
48#17985888C411yescharacteristic
49C4×(C2×D71)⋊C4C2211yescharacteristic
50C4×(C2×D71)⋊C4C2211yescharacteristic
51C42×Dic71C2211yescharacteristic
52#17985754C2211yescharacteristic
53#17985754C2211yescharacteristic
54#17985753C2211yescharacteristic
55#17985753C2211yescharacteristic
56C2×C4⋊C8×C71C2211yescharacteristic
57C2×C4⋊C8×C71C2211yescharacteristic
58C2×C4⋊C8×C71C2211yescharacteristic
59C2×#97×C71C2211yescharacteristic
60C4×C4⋊C4×C71C2211yescharacteristic
61#336×C71C2211yescharacteristic
62#336×C71C2211yescharacteristic
63C22×D284C2×C411yescharacteristic
64C22×C4×D71C2311yescharacteristic
65C22×C4×D71C2311yescharacteristic
66C2×#11765848—22no—
67C2×#11765848—22no—
68C2×#11765848—22no—
69C2×#11765848—22no—
70C2×#11765848—41no—
71C2×#11765848—41no—
72C22×C71⋊C8C2311yescharacteristic
73C22×C71⋊C8C2311yescharacteristic
74C22×C71⋊C8C2311yescharacteristic
75C22×C71⋊C8C2311yescharacteristic
76C2×C8×D71—22no—
77C2×C8×D71—22no—
78C2×C8×D71—22no—
79C2×C8×D71—22no—
80C2×C8×D71—41no—
81C2×C8×D71—41no—
82C4×D284D414yes—
83C4×D284Q814yes—
84#14556085—22no—
85#14556085—22no—
86#14556085—22no—
87#14556085—22no—
88C2×C4⋊Dic71C2×C411yescharacteristic
89C2×Dic71⋊C4C2×C411yescharacteristic
90C2×Dic71⋊C4C2×C411yescharacteristic
91C2×Dic71⋊C4C2×C411yescharacteristic
92C2×Dic71⋊C4C2×C411yescharacteristic
93C2×(C2×D71)⋊C4C2×C411yescharacteristic
94C2×(C2×D71)⋊C4C2×C411yescharacteristic
95C2×(C2×D71)⋊C4C2×C411yescharacteristic
96C2×(C2×D71)⋊C4C2×C411yescharacteristic
97C2×(C2×D71)⋊C4C2×C411yescharacteristic
98C2×(C2×D71)⋊C4C2×C411yescharacteristic
99C2×(C2×D71)⋊C4C2×C411yescharacteristic
100C2×(C2×D71)⋊C4C2×C411yescharacteristic
101C2×(C2×D71)⋊C4C2×C411yescharacteristic
102C2×(C2×D71)⋊C4C2×C411yescharacteristic
103C2×C4×Dic71C2×C411yescharacteristic
104C2×C4×Dic71C2×C411yescharacteristic
105C2×C4×Dic71C2×C411yescharacteristic
106C2×C4×Dic71C2×C411yescharacteristic
107C2×C4×Dic71C2311yescharacteristic
108C2×C4×Dic71C2311yescharacteristic
109C4⋊(C71⋊C8)—22no—
110C4⋊(C71⋊C8)—22no—
111C4⋊(C71⋊C8)—22no—
112Dic71⋊C8—22no—
113Dic71⋊C8—22no—
114Dic71⋊C8—22no—
115Dic71⋊C8—41no—
116Dic71⋊C8—41no—
117Dic71⋊C8D414yescomplemented
118(C2×D71)⋊C8—22no—
119(C2×D71)⋊C8—22no—
120(C2×D71)⋊C8—22no—
121(C2×D71)⋊C8—22no—
122#14556039—22no—
123C71⋊#95C2×C411yescharacteristic
124C71⋊#95C2×C411yescharacteristic
125C71⋊#95C2×C411yescharacteristic
126C71⋊#95C2×C411yescharacteristic
127C22×C8×C71C2311yescharacteristic
128C22×C8×C71C2311yescharacteristic
129C22×C8×C71C2311yescharacteristic
130C22×C8×C71C2311yescharacteristic
131C2×C4⋊C4×C71C2×C411yescharacteristic
132C2×C4⋊C4×C71C2×C411yescharacteristic
133C2×C42×C71C2311yescharacteristic
134C2×C42×C71C2311yescharacteristic
135C2×C42×C71C2311yescharacteristic
136C4⋊C8×C71—22no—
137C4⋊C8×C71—22no—
138C4⋊C8×C71—22no—
139#97×C71—22no—
140#95×C71C2×C411yescharacteristic
141#95×C71C2×C411yescharacteristic
142C23×D71C22×C411yescharacteristic
143C23×D71C22×C411yescharacteristic
144C2×D284—41no—
145C2×D284—41no—
146C2×D284C4⋊C414yes—
147C22×Dic71C22×C411yescharacteristic
148C22×Dic71C22×C411yescharacteristic
149C22×Dic71C22×C411yescharacteristic
150C22×Dic71C22×C411yescharacteristic
151C22×Dic71C22×C411yescharacteristic
152C22×Dic71C22×C411yescharacteristic
153C2×C4×D71—21no—
154C2×C4×D71—21no—
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×D71C2×D412yes—
162C2×C4×D71C2×D412yes—
163C2×C4×D71C2×Q812yes—
164C2×C4×D71C2×Q812yes—
165#11765848—44no—
166#11765848—44no—
167C2×C71⋊C8—21no—
168C2×C71⋊C8—21no—
169C2×C71⋊C8—21no—
170C2×C71⋊C8—21no—
171C2×C71⋊C8—21no—
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⋊C8C2×D412yes—
179C8×D71—44no—
180C8×D71—44no—
181C4⋊Dic71C4⋊C414yes—
182Dic71⋊C4—22no—
183Dic71⋊C4—22no—
184Dic71⋊C4—22no—
185Dic71⋊C4—22no—
186(C2×D71)⋊C4—22no—
187(C2×D71)⋊C4—22no—
188(C2×D71)⋊C4—22no—
189(C2×D71)⋊C4—22no—
190(C2×D71)⋊C4—22no—
191(C2×D71)⋊C4—22no—
192(C2×D71)⋊C4—41no—
193(C2×D71)⋊C4—41no—
194(C2×D71)⋊C4C4⋊C414yes—
195(C2×D71)⋊C4C4⋊C414yes—
196C4×Dic71—21no—
197C4×Dic71—21no—
198C4×Dic71—22no—
199C4×Dic71—41no—
200C4×Dic71—41no—
201C4×Dic71—41no—
202C4×Dic71C2×D412yes—
203C4×Dic71#4112yes—
204C22×C4×C71C22×C411yescharacteristic
205C22×C4×C71C22×C411yescharacteristic
206C22×C4×C71C22×C411yescharacteristic
207C22×C4×C71C22×C411yescharacteristic
208C22×C4×C71C22×C411yescharacteristic
209C22×C4×C71C22×C411yescharacteristic
210C22×C4×C71C2411yescharacteristic
211C2×C8×C71—21no—
212C2×C8×C71—21no—
213C2×C8×C71—21no—
214C2×C8×C71—21no—
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×C71C2×D412yes—
223C4⋊C4×C71—41no—
224C4⋊C4×C71—41no—
225C42×C71—21no—
226C42×C71—21no—
227C42×C71—21no—
228C42×C71—21no—
229C42×C71C2×D412yes—
230C42×C71C2×Q812yes—
231C23×C71C23×C411yescharacteristic
232C22×D71—21no—
233C22×D71—21no—
234C22×D71—21no—
235C22×D71—21no—
236C22×D71—21no—
237C22×D71—21no—
238C22×D71—21no—
239C22×D71—21no—
240C22×D71—21no—
241C22×D71—21no—
242C22×D71—21no—
243C22×D71—21no—
244C22×D71C2×C4⋊C412yes—
245C22×D71C2×C4⋊C412yes—
246C2×C4×C71—21no—
247C2×C4×C71—21no—
248C2×C4×C71—21no—
249C2×C4×C71—21no—
250C2×C4×C71—21no—
251C2×C4×C71—21no—
252C2×C4×C71—21no—
253C2×C4×C71—21no—
254C2×C4×C71—21no—
255C2×C4×C71—21no—
256C2×C4×C71—21no—
257C2×C4×C71—21no—
258C2×C4×C71—21no—
259C2×C4×C71—21no—
260C2×C4×C71—21no—
261C2×C4×C71—21no—
262C2×C4×C71C2×C4⋊C412yes—
263C2×C4×C71C2×C4⋊C412yes—
264C2×C4×C71C22×D411yescharacteristic
265C2×C4×C71C22×D411yescharacteristic
266C2×C4×C71C22×Q811yescharacteristic
267C2×C4×C71C2×#4111yescharacteristic
268C2×C4×C71H(5,𝔽2)11yescharacteristic
269C2×C4×C712−1+411yescharacteristic
270C2×Dic71—21no—
271C2×Dic71—21no—
272C2×Dic71—21no—
273C2×Dic71—21no—
274C2×Dic71—21no—
275C2×Dic71—21no—
276C2×Dic71—21no—
277C2×Dic71—21no—
278C2×Dic71—21no—
279C2×Dic71—21no—
280C2×Dic71—21no—
281C2×Dic71—21no—
282C2×Dic71—21no—
283C2×Dic71C2×C4⋊C412yes—
284C2×Dic71C2×C4⋊C412yes—
285C2×Dic71C4×D412yes—
286C2×Dic71C4×D412yes—
287C2×Dic71#13112yes—
288D284—44no—
289C4×D71—22no—
290C4×D71—22no—
291C4×D71—22no—
292C4×D71—22no—
293C4×D71—22no—
294C4×D71—22no—
295C4×D71—22no—
296C4×D71—22no—
297C8×C71—22no—
298C8×C71—41no—
299C8×C71—41no—
300C8×C71—41no—
301C71⋊C8—22no—
302C71⋊C8—41no—
303C71⋊C8—41no—
304C71⋊C8—41no—
305C22×C71C22×C4⋊C411yescharacteristic
306C22×C71C2×C4×D411yescharacteristic
307C22×C71#52011yescharacteristic
308C22×C71C2×#13111yescharacteristic
309C22×C71#56811yescharacteristic
310C22×C71#56811yescharacteristic
311C22×C71#56811yescharacteristic
312C2×D71—22no—
313C2×D71—22no—
314C2×D71—22no—
315C2×D71—22no—
316C2×D71—22no—
317C2×D71—22no—
318C2×D71—41no—
319C2×D71—41no—
320C2×D71—41no—
321C2×D71—41no—
322C2×D71—41no—
323C2×D71—41no—
324C2×D71—41no—
325C2×D71—41no—
326C4×C71—22no—
327C4×C71—22no—
328C4×C71—41no—
329C4×C71—41no—
330C4×C71—41no—
331C4×C71—41no—
332C4×C71D4211yescharacteristic
333C4×C71#54711yescharacteristic
334C4×C71D4×Q811yescharacteristic
335C4×C71#55411yescharacteristic
336Dic71—22no—
337Dic71—22no—
338Dic71—22no—
339Dic71—22no—
340Dic71—22no—
341Dic71—41no—
342#22652—711nomaximal, Sylow
343C2×C71D4×C4⋊C411yescharacteristic
344C2×C71#290511yescharacteristic
345C2×C71#290611yescharacteristic
346C2×C71#293211yescharacteristic
347C2×C71#293511yescharacteristic
348C2×C71#299211yescharacteristic
349C2×C71#299511yescharacteristic
350D71—42no—
351D71—42no—
352C2×#435—711no—
353C2×#435—711no—
354C2×#424—711no—
355C2×#424—711no—
356#2293—711no—
357#1940—711no—
358#1940D7111yescharacteristic, complemented
359#1851—711no—
360#1851—711no—
361#1850—711no—
362#1850—711no—
363#1842—711no—
364#1798—711no—
365#1798—711no—
366#1767—711no—
367C71#2265211yescharacteristic, complemented, Sylow
368C22×M16—711no—
369C22×M16—711no—
370C23×C8—711no—
371C23×C8—711no—
372C2×C4×D4—711no—
373C2×#117—711no—
374C2×#117—711no—
375#435—1424no—
376#435—1424no—
377#424—1424no—
378#424—1424no—
379C2×C4⋊C8—711no—
380C2×C4⋊C8—711no—
381C2×C4⋊C8—711no—
382C2×C4⋊C8—711no—
383C2×C4⋊C8—711no—
384C2×C4⋊C8—711no—
385C2×C4⋊C8—711no—
386C2×C4⋊C8—711no—
387C2×C4⋊C8—711no—
388C2×C4⋊C8C2×D7111yescharacteristic
389C2×C4⋊C8C2×D7111yescharacteristic
390C2×C4⋊C8C2×D7111yescharacteristic
391C2×C22⋊C8—711no—
392C2×C22⋊C8—711no—
393C2×C22⋊C8—711no—
394C2×C22⋊C8—711no—
395C2×#97—711no—
396C2×#97C2×D7111yescharacteristic
397#390—711no—
398#390—711no—
399#389—711no—
400#389—711no—
401#388—711no—
402#388—711no—
403#388—711no—
404#388—711no—
405C4×C4⋊C4C2×D7111yescharacteristic
406C4×C22⋊C4—711no—
407C4×C22⋊C4—711no—
408C43—711no—
409#336—711no—
410#336—711no—
411#336—711no—
412#336—711no—
413#336C2×D7111yescharacteristic
414#336C2×D7111yescharacteristic
415C22×D4—711no—
416C23×C4—711no—
417C23×C4—711no—
418C2×M16—2841no—
419C2×M16—2841no—
420C2×M16—1422no—
421C2×M16—1422no—
422C2×M16—1422no—
423C2×M16—1422no—
424C22×C8—2841no—
425C22×C8—2841no—
426C22×C8—711no—
427C22×C8—711no—
428C22×C8—711no—
429C22×C8—711no—
430C22×C8—1422no—
431C22×C8—1422no—
432C22×C8—1422no—
433C22×C8—1422no—
434C22×C8C22×D7111yescharacteristic
435C22×C8C22×D7111yescharacteristic
436C22×C8C22×D7111yescharacteristic
437C22×C8C22×D7111yescharacteristic
438C4×D4—714no—
439C4×D4—714no—
440#117—1422no—
441#117—1422no—
442#117—1422no—
443#117—1422no—
444C2×C4⋊C4—711no—
445C2×C4⋊C4—711no—
446C2×C4⋊C4—711no—
447C2×C4⋊C4—711no—
448C2×C4⋊C4—711no—
449C2×C4⋊C4C4×D7111yescharacteristic
450C2×C4⋊C4C4×D7111yescharacteristic
451C2×C22⋊C4—711no—
452C2×C22⋊C4—711no—
453C2×C22⋊C4—711no—
454C2×C22⋊C4—711no—
455C2×C22⋊C4—711no—
456C2×C22⋊C4—711no—
457C2×C22⋊C4—711no—
458C2×C22⋊C4—711no—
459C2×C22⋊C4—711no—
460C2×C22⋊C4—711no—
461C2×C42—711no—
462C2×C42—711no—
463C2×C42—711no—
464C2×C42—711no—
465C2×C42—711no—
466C2×C42—711no—
467C2×C42C22×D7111yescharacteristic
468C2×C42C22×D7111yescharacteristic
469C2×C42C22×D7111yescharacteristic
470C4⋊C8—22no—
471C4⋊C8—22no—
472C4⋊C8—22no—
473C4⋊C8—2841no—
474C4⋊C8—2841no—
475C4⋊C8—714no—
476C4⋊C8—1422no—
477C4⋊C8—1422no—
478C4⋊C8—1422no—
479C4⋊C8—1422no—
480C4⋊C8—1422no—
481C4⋊C8—1422no—
482C22⋊C8—1422no—
483C22⋊C8—1422no—
484C22⋊C8—1422no—
485C22⋊C8—1422no—
486#97—22no—
487#97—1422no—
488#95—711no—
489#95—711no—
490#95—711no—
491#95—711no—
492#95C4×D7111yescharacteristic
493#95C4×D7111yescharacteristic
494C24—711no—
495C24—711no—
496C2×D4—2841no—
497C2×D4—2841no—
498C2×D4—714no—
499C22×C4—711no—
500C22×C4—711no—
501C22×C4—711no—
502C22×C4—711no—
503C22×C4—711no—
504C22×C4—712no—
505C22×C4—712no—
506C22×C4—712no—
507C22×C4—712no—
508C22×C4—711no—
509C22×C4—1421no—
510C22×C4—1421no—
511C22×C4—1421no—
512C22×C4—1421no—
513C22×C4—1421no—
514C22×C4—1421no—
515C22×C4—1421no—
516C22×C4—1421no—
517C22×C4C2×C4×D7111yescharacteristic
518C22×C4C2×C4×D7111yescharacteristic
519C22×C4C2×C4×D7111yescharacteristic
520C22×C4C2×C4×D7111yescharacteristic
521C22×C4C2×C4×D7111yescharacteristic
522C22×C4C2×C4×D7111yescharacteristic
523C22×C4C23×D7111yescharacteristic
524M16—2844no—
525M16—2844no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—2844no—
538C2×C8—2844no—
539C2×C8—712no—
540C2×C8—1421no—
541C2×C8—1421no—
542C2×C8—1421no—
543C2×C8—1421no—
544C2×C8—1421no—
545C2×C8—1421no—
546C2×C8—1421no—
547C2×C8—1421no—
548C2×C8—1421no—
549C2×C8—1421no—
550C2×C8—1421no—
551C2×C8D4×D7112yes—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—714no—
555C4⋊C4—1422no—
556C4⋊C4—1422no—
557C4⋊C4—1422no—
558C4⋊C4—1422no—
559C22⋊C4—2841no—
560C22⋊C4—2841no—
561C22⋊C4—714no—
562C22⋊C4—714no—
563C22⋊C4—1422no—
564C22⋊C4—1422no—
565C22⋊C4—1422no—
566C22⋊C4—1422no—
567C22⋊C4—1422no—
568C22⋊C4—1422no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—2841no—
574C42—2841no—
575C42—2841no—
576C42—712no—
577C42—712no—
578C42—1422no—
579C42—1421no—
580C42—1421no—
581C42D4×D7112yes—
582C42Q8×D7112yes—
583C23—712no—
584C23—712no—
585C23—1421no—
586C23—1421no—
587C23—1421no—
588C23—1421no—
589C23—1421no—
590C23—1421no—
591C23—1421no—
592C23—1421no—
593C23—1421no—
594C23—1421no—
595C23—1421no—
596C23—1421no—
597C23C22×C4×D7111yescharacteristic
598D4—2844no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—712no—
616C2×C4—712no—
617C2×C4—712no—
618C2×C4—712no—
619C2×C4—712no—
620C2×C4—1421no—
621C2×C4—1421no—
622C2×C4—1421no—
623C2×C4—1421no—
624C2×C4—1421no—
625C2×C4—1421no—
626C2×C4—1421no—
627C2×C4—1421no—
628C2×C4—1421no—
629C2×C4—1421no—
630C2×C4—1421no—
631C2×C4—1421no—
632C2×C4—1421no—
633C2×C4—1422no—
634C2×C4—1422no—
635C2×C4—1422no—
636C2×C4—1422no—
637C2×C4—1422no—
638C2×C4—1422no—
639C2×C4—1422no—
640C2×C4—1422no—
641C2×C4C4⋊C4×D7112yes—
642C2×C4C4⋊C4×D7112yes—
643C2×C4C2×D4×D7111yescharacteristic
644C2×C4C2×D4×D7111yescharacteristic
645C2×C4C2×Q8×D7111yescharacteristic
646C2×C4#41×D7111yescharacteristic
647C2×C4#1455617411yescharacteristic
648C2×C4#1455617611yescharacteristic
649C8—22no—
650C8—41no—
651C8—41no—
652C8—41no—
653C8—2841no—
654C8—2841no—
655C8—2841no—
656C8—1422no—
657C22—2841no—
658C22—2841no—
659C22—2841no—
660C22—2841no—
661C22—2841no—
662C22—2841no—
663C22—2841no—
664C22—2841no—
665C22—1422no—
666C22—1422no—
667C22—1422no—
668C22—1422no—
669C22—1422no—
670C22—1422no—
671C22C2×C4⋊C4×D7111yescharacteristic
672C22C4×D4×D7111yescharacteristic
673C22#1798648111yescharacteristic
674C22#131×D7111yescharacteristic
675C22#1798676411yescharacteristic
676C22#1798676511yescharacteristic
677C22#1798676511yescharacteristic
678C4—22no—
679C4—22no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—2841no—
685C4—1422no—
686C4—1422no—
687C4—1422no—
688C4—1422no—
689C4—1422no—
690C4#1798663311yescharacteristic
691C4#1798665111yescharacteristic
692C4#1798666411yescharacteristic
693C4#1798670511yescharacteristic
694C2—2842no—
695C2—2842no—
696C2#2259124111yescharacteristic
697C2#2259690211yescharacteristic
698C2#2259690711yescharacteristic
699C2#2259705411yescharacteristic
700C2#2259708111yescharacteristic
701C2#2259747811yescharacteristic
702C2#2259750911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#1940C2
prime radicalC22×D284C2×C4
cosocleC22×C4×C71C24
hypercenter#1940D71
hypocenterC71#22652
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
3. C2×#17986024C2semidirect
4. C2×#17986024C2semidirect
6. #22589064C2semidirect
7. #22588524C2semidirect
8. #22588521C2semidirect
9. #22588519C2semidirect
10. #22588516C2semidirect
11. #22588491C2semidirect
12. #22588323C2semidirect
13. #22588323C2semidirect
14. #22588194C2semidirect
15. C71×#1940C2semidirect
117. Dic71⋊C8D4semidirect
358. #1940D71semidirect
367. C71#22652semidirect

Maximal subgroups

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

subgroupindex
C2×#179860722
C2×#179860692
C2×#179860242
#225908012
#225890642
#225885242
#225885212
#225885192
#225885162
#225884912
#225883232
#225881942
C71×#19402
#2265271