Finite Group Databasebeta

← #32015547

Subgroups — #32015547

Order 18176.

1126 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D71)⋊C8C211yesmaximal, characteristic
2C22×#14556059C211yesmaximal, characteristic, complemented
3C2×#106×D71C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D71C211yesmaximal, characteristic
5#22591236C211yesmaximal, characteristic
6#22589102C211yesmaximal, characteristic, complemented
7#22589100C211yesmaximal, characteristic, complemented
8#22588535C211yesmaximal, characteristic, complemented
9#22588534C211yesmaximal, characteristic, complemented
10#22588531C211yesmaximal, characteristic, complemented
11#22588495C211yesmaximal, characteristic, complemented
12#22588364C211yesmaximal, characteristic, complemented
13#22588363C211yesmaximal, characteristic, complemented
14#22588228C211yesmaximal, characteristic, complemented
15C71×#1853C211yesmaximal, characteristic, complemented
16C23×C71⋊C8C2211yescharacteristic
17C22×C8×D71C2211yescharacteristic
18C2×C4×C22⋊D71—21no—
19C2×C4×C22⋊D71C2211yescharacteristic
20C2×(C22⋊D71)⋊C4—21no—
21C22×C4⋊Dic71C2211yescharacteristic
22C2×C4⋊C4×D71C2211yescharacteristic
23C2×C4⋊C4×D71C2211yescharacteristic
24(C22⋊D71)⋊C8C418yescomplemented
25C2×#14556060C2211yescharacteristic
26C2×#14556060C2211yescharacteristic
27C2×#14556059—24no—
28C2×#14556059C2211yescharacteristic
29C2×#14556059C2211yescharacteristic
30C2×#14556059C2211yescharacteristic
31C2×#14556059C2211yescharacteristic
32C2×#14556059C2211yescharacteristic
33C2×#14556059C2211yescharacteristic
34#106×D71—24no—
35C2×Dic71⋊C8C2211yescharacteristic
36C2×(C2×D71)⋊C8C2211yescharacteristic
37C2×C8×Dic71C2211yescharacteristic
38#17985896—21no—
39#17985894—21no—
40#17985873—21no—
41#17985872—21no—
42#17985871—21no—
43#17985870—21no—
44#17985868C2211yescharacteristic
45#17985868C2211yescharacteristic
46#17985859C2211yescharacteristic
47#17985856C2211yescharacteristic
48#17985856C2211yescharacteristic
49C4⋊C4×Dic71C2211yescharacteristic
50C4⋊C4×Dic71C2211yescharacteristic
51#17985762C2211yescharacteristic
52#17985762C2211yescharacteristic
53#17985761C2211yescharacteristic
54#17985761C2211yescharacteristic
55C22×C4⋊C4×C71C2211yescharacteristic
56C2×#106×C71C2211yescharacteristic
57C2×#106×C71C2211yescharacteristic
58C2×C22⋊C8×C71C2211yescharacteristic
59#380×C71C2211yescharacteristic
60#340×C71C2211yescharacteristic
61#340×C71C2211yescharacteristic
62C22×C22⋊D71D411yescharacteristic
63C23×Dic71—21no—
64C22×C4×D71—21no—
65C22×C4×D71—21no—
66C22×C4×D71C2311yescharacteristic
67C22×C71⋊C8—22no—
68C22×C71⋊C8—22no—
69C22×C71⋊C8C2×C414yescomplemented
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C2×C8×D71—22no—
73C2×C8×D71—22no—
74C2×C8×D71C2×C414yescomplemented
75C4×C22⋊D71—44no—
76C4×C22⋊D71C2×C414yes—
77C4×C22⋊D71Q814yes—
78(C22⋊D71)⋊C4—44no—
79C2×C4⋊Dic71—22no—
80C2×C4⋊Dic71—21no—
81C2×C4⋊Dic71—41no—
82C2×C4⋊Dic71C2311yescharacteristic
83C2×C4⋊Dic71C2311yescharacteristic
84C2×C4⋊Dic71C2311yescharacteristic
85C2×C4⋊Dic71C2311yescharacteristic
86C2×Dic71⋊C4—21no—
87C2×Dic71⋊C4—21no—
88C2×Dic71⋊C4—21no—
89C2×Dic71⋊C4—21no—
90C2×Dic71⋊C4—21no—
91C2×Dic71⋊C4—21no—
92C2×Dic71⋊C4D411yescharacteristic
93C4⋊C4×D71—22no—
94C4⋊C4×D71—22no—
95C4⋊C4×D71—41no—
96C4⋊C4×D71—41no—
97C2×C22⋊Dic71—21no—
98C2×C22⋊Dic71D411yescharacteristic
99C2×(C2×D71)⋊C4—21no—
100C2×(C2×D71)⋊C4—21no—
101C2×(C2×D71)⋊C4D411yescharacteristic
102C2×C4×Dic71—21no—
103C2×C4×Dic71—21no—
104C2×C4×Dic71C2311yescharacteristic
105#14556060—22no—
106#14556060—41no—
107#14556059—22no—
108#14556059—22no—
109#14556059—22no—
110#14556059—22no—
111#14556059—22no—
112#14556059D414yescomplemented
113Dic71⋊C8C2×C414yescomplemented
114(C2×D71)⋊C8C2×C414yescomplemented
115C8×Dic71C2×C414yescomplemented
116C71⋊#95—21no—
117C71⋊#95—21no—
118C71⋊#95—21no—
119C71⋊#95—21no—
120C71⋊#95—21no—
121C23×C4×C71—21no—
122C23×C4×C71C2311yescharacteristic
123C22×C8×C71C2311yescharacteristic
124C22×C8×C71C2311yescharacteristic
125C2×C4⋊C4×C71—22no—
126C2×C4⋊C4×C71—21no—
127C2×C4⋊C4×C71—41no—
128C2×C4⋊C4×C71C2311yescharacteristic
129C2×C4⋊C4×C71C2311yescharacteristic
130C2×C4⋊C4×C71C2311yescharacteristic
131C2×C4⋊C4×C71C2311yescharacteristic
132C2×C22⋊C4×C71—21no—
133#106×C71—22no—
134#106×C71—41no—
135C22⋊C8×C71C2×C414yescomplemented
136#95×C71—21no—
137C23×D71C2×D411yescharacteristic
138C2×C22⋊D71C4⋊C414yes—
139C2×C22⋊D71SD1614yes—
140C2×C22⋊D71SD1614yes—
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—21no—
145C22×Dic71—42no—
146C22×Dic71—42no—
147C22×Dic71—81no—
148C22×Dic71C2×D411yescharacteristic
149C22×Dic71C2×D411yescharacteristic
150C22×Dic71C2×D411yescharacteristic
151C2×C4×D71—21no—
152C2×C4×D71—21no—
153C2×C4×D71—21no—
154C2×C4×D71—21no—
155C2×C4×D71—42no—
156C2×C4×D71—42no—
157C2×C4×D71—42no—
158C2×C4×D71—42no—
159C2×C4×D71—81no—
160C2×C4×D71—81no—
161C2×C4×D71C22×C412yes—
162C2×C4×D71C2×Q812yes—
163C2×C71⋊C8—21no—
164C2×C71⋊C8—21no—
165C2×C71⋊C8—28no—
166C2×C71⋊C8C22×C412yes—
167C2×C71⋊C8C22×C412yes—
168C2×C71⋊C8C2×D412yes—
169C2×C71⋊C8#4112yes—
170C8×D71—28no—
171C4⋊Dic71—21no—
172C4⋊Dic71—21no—
173C4⋊Dic71—21no—
174C4⋊Dic71—21no—
175C4⋊Dic71—21no—
176C4⋊Dic71—21no—
177C4⋊Dic71—21no—
178C4⋊Dic71—42no—
179C4⋊Dic71C2×D412yes—
180Dic71⋊C4—42no—
181Dic71⋊C4—42no—
182Dic71⋊C4—42no—
183Dic71⋊C4—42no—
184Dic71⋊C4—81no—
185Dic71⋊C4—81no—
186Dic71⋊C4C4⋊C414yes—
187C22⋊Dic71—42no—
188C22⋊Dic71C4⋊C414yes—
189(C2×D71)⋊C4—42no—
190(C2×D71)⋊C4—42no—
191(C2×D71)⋊C4C4⋊C414yes—
192C4×Dic71—42no—
193C4×Dic71—42no—
194C4×Dic71C22×C412yes—
195C4×Dic71C2×Q812yes—
196C24×C71C2×D411yescharacteristic
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—21no—
201C22×C4×C71—21no—
202C22×C4×C71—21no—
203C22×C4×C71—21no—
204C22×C4×C71—21no—
205C22×C4×C71—42no—
206C22×C4×C71—42no—
207C22×C4×C71—81no—
208C22×C4×C71C22×C412yes—
209C22×C4×C71C2×D411yescharacteristic
210C22×C4×C71C2×Q812yes—
211C22×C4×C71C2411yescharacteristic
212C2×C8×C71—21no—
213C2×C8×C71—21no—
214C2×C8×C71—21no—
215C2×C8×C71—21no—
216C2×C8×C71C22×C412yes—
217C2×C8×C71C22×C412yes—
218C4⋊C4×C71—21no—
219C4⋊C4×C71—21no—
220C4⋊C4×C71—21no—
221C4⋊C4×C71—21no—
222C4⋊C4×C71—21no—
223C4⋊C4×C71—21no—
224C4⋊C4×C71—21no—
225C4⋊C4×C71—42no—
226C4⋊C4×C71C2×D412yes—
227C22⋊C4×C71—42no—
228C23×C71—21no—
229C23×C71—21no—
230C23×C71—21no—
231C23×C71—21no—
232C23×C71C2×C4⋊C412yes—
233C23×C71C2×SD1612yes—
234C23×C71C2×SD1612yes—
235C23×C71C22×D411yescharacteristic
236C22×D71—21no—
237C22×D71—21no—
238C22×D71—21no—
239C22×D71—21no—
240C22×D71C2×C4⋊C412yes—
241C22×D71C2×SD1612yes—
242C22×D71C2×SD1612yes—
243C2×C4×C71—21no—
244C2×C4×C71—21no—
245C2×C4×C71—22no—
246C2×C4×C71—22no—
247C2×C4×C71—22no—
248C2×C4×C71—22no—
249C2×C4×C71—22no—
250C2×C4×C71—41no—
251C2×C4×C71—41no—
252C2×C4×C71—41no—
253C2×C4×C71—41no—
254C2×C4×C71—41no—
255C2×C4×C71—41no—
256C2×C4×C71—41no—
257C2×C4×C71—41no—
258C2×C4×C71—41no—
259C2×C4×C71—41no—
260C2×C4×C71—41no—
261C2×C4×C71—84no—
262C2×C4×C71C2×C4⋊C412yes—
263C2×C4×C71C23×C411yescharacteristic
264C2×C4×C71C22×D411yescharacteristic
265C2×C4×C71C22×Q811yescharacteristic
266C2×C4×C71C2×#4111yescharacteristic
267C2×C4×C71H(5,𝔽2)11yescharacteristic
268C2×C4×C712−1+411yescharacteristic
269C22⋊D71#106116yescomplemented
270C2×Dic71—21no—
271C2×Dic71—21no—
272C2×Dic71—21no—
273C2×Dic71—21no—
274C2×Dic71—22no—
275C2×Dic71—41no—
276C2×Dic71—41no—
277C2×Dic71—41no—
278C2×Dic71—41no—
279C2×Dic71—41no—
280C2×Dic71—41no—
281C2×Dic71—41no—
282C2×Dic71—41no—
283C2×Dic71—41no—
284C2×Dic71—41no—
285C2×Dic71—41no—
286C2×Dic71—84no—
287C2×Dic71C2×C4⋊C412yes—
288C2×Dic71C2×C4⋊C412yes—
289C2×Dic71C2×C4⋊C412yes—
290C2×Dic71C2×SD1612yes—
291C2×Dic71C2×SD1612yes—
292C4×D71—22no—
293C4×D71—22no—
294C4×D71—22no—
295C4×D71—22no—
296C4×D71—84no—
297C4×D71—84no—
298C8×C71—22no—
299C8×C71—22no—
300C71⋊C8—22no—
301C71⋊C8C4×D414yescomplemented
302C22×C71—22no—
303C22×C71—22no—
304C22×C71—22no—
305C22×C71—22no—
306C22×C71—22no—
307C22×C71—22no—
308C22×C71C2×#10614yescomplemented
309C22×C71C22×C4⋊C411yescharacteristic
310C22×C71D4211yescharacteristic
311C22×C71#54711yescharacteristic
312C22×C71C22×SD1611yescharacteristic
313C22×C71C22×SD1611yescharacteristic
314C22×C71#57711yescharacteristic
315C22×C71#57711yescharacteristic
316C2×D71—22no—
317C2×D71—22no—
318C2×D71—22no—
319C2×D71—22no—
320C2×D71—22no—
321C2×D71—22no—
322C2×D71C2×#10614yescomplemented
323C4×C71—22no—
324C4×C71—42no—
325C4×C71—81no—
326C4×C71—81no—
327C4×C71—81no—
328C4×C71C2×C4×D411yescharacteristic
329C4×C71#52011yescharacteristic
330C4×C71D4×Q811yescharacteristic
331C4×C71#55411yescharacteristic
332Dic71—22no—
333Dic71—22no—
334Dic71—42no—
335Dic71—81no—
336Dic71—81no—
337Dic71—81no—
338Dic71C2×#10614yescomplemented
339D4×#106—711nomaximal, Sylow
340C2×C71—24no—
341C2×C71D4×C4⋊C411yescharacteristic
342C2×C71C22×#10611yescharacteristic
343C2×C71#291211yescharacteristic
344C2×C71D4×SD1611yescharacteristic
345C2×C71D4×SD1611yescharacteristic
346C2×C71#333511yescharacteristic
347C2×C71#333511yescharacteristic
348D71—24no—
349C2×C8×D4—711no—
350C22×#106—711no—
351C22×#106—711no—
352D4×C4⋊C4—711no—
353D4×C4⋊C4—711no—
354#1948—711no—
355#1948—711no—
356#1853—711no—
357#1853—711no—
358#1853—711no—
359#1853D7111yescharacteristic, complemented
360#1844—711no—
361#1807—711no—
362#1807—711no—
363C4×#106—711no—
364C71D4×#10611yescharacteristic, complemented, Sylow
365C23×C8—711no—
366C23×C8—711no—
367C2×C4×D4—711no—
368C2×C4×D4—1421no—
369C2×C4×D4—1421no—
370C22×C4⋊C4—711no—
371C22×C4⋊C4—711no—
372C22×C4⋊C4—711no—
373C22×C4⋊C4C2×D7111yescharacteristic
374C8×D4—718no—
375C2×#106—711no—
376C2×#106—711no—
377C2×#106—711no—
378C2×#106—711no—
379C2×#106—711no—
380C2×#106—711no—
381C2×#106—711no—
382C2×#106—711no—
383C2×#106—1424no—
384C2×#106—1424no—
385C2×#106C2×D7111yescharacteristic
386C2×#106C2×D7111yescharacteristic
387C2×C4⋊C8—711no—
388C2×C22⋊C8—711no—
389C2×C22⋊C8C2×D7111yescharacteristic
390C2×C4×C8—711no—
391#389—1421no—
392#389—1421no—
393#385—1421no—
394#385—1421no—
395#385—1421no—
396#385—1421no—
397#384—711no—
398#384—711no—
399#380—711no—
400#380—711no—
401#380—711no—
402#380C2×D7111yescharacteristic
403C4×C4⋊C4—711no—
404C4×C4⋊C4—711no—
405#340—711no—
406#340—711no—
407#340—711no—
408#340—711no—
409#340C2×D7111yescharacteristic
410#340C2×D7111yescharacteristic
411C22×D4—711no—
412C23×C4—21no—
413C23×C4—711no—
414C23×C4—1421no—
415C23×C4—1421no—
416C23×C4—1421no—
417C23×C4C22×D7111yescharacteristic
418C22×C8—711no—
419C22×C8—714no—
420C22×C8—711no—
421C22×C8—714no—
422C22×C8—1422no—
423C22×C8—1422no—
424C22×C8—1422no—
425C22×C8—1422no—
426C22×C8C22×D7111yescharacteristic
427C22×C8C22×D7111yescharacteristic
428C4×D4—2844no—
429C4×D4—2844no—
430C4×D4—714no—
431C4×D4—714no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4—2841no—
436C2×C4⋊C4—2841no—
437C2×C4⋊C4—2841no—
438C2×C4⋊C4—711no—
439C2×C4⋊C4—711no—
440C2×C4⋊C4—711no—
441C2×C4⋊C4—711no—
442C2×C4⋊C4—711no—
443C2×C4⋊C4—1422no—
444C2×C4⋊C4—1421no—
445C2×C4⋊C4—1421no—
446C2×C4⋊C4—1421no—
447C2×C4⋊C4—1421no—
448C2×C4⋊C4—1421no—
449C2×C4⋊C4—1422no—
450C2×C4⋊C4—1422no—
451C2×C4⋊C4—1421no—
452C2×C4⋊C4—1421no—
453C2×C4⋊C4C22×D7111yescharacteristic
454C2×C4⋊C4C22×D7111yescharacteristic
455C2×C4⋊C4C22×D7111yescharacteristic
456C2×C4⋊C4C22×D7111yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—711no—
459C2×C22⋊C4—711no—
460C2×C22⋊C4—1421no—
461C2×C22⋊C4—1421no—
462C2×C22⋊C4—1421no—
463C2×C42—711no—
464C2×C42—1421no—
465C2×C42—1421no—
466#106—22no—
467#106—41no—
468#106—2841no—
469#106—714no—
470#106—1422no—
471#106—1422no—
472#106—1422no—
473#106—1422no—
474#106—1422no—
475#106—1422no—
476C4⋊C8—714no—
477C22⋊C8—714no—
478C22⋊C8C4×D7114yescomplemented
479C4×C8—714no—
480#95—21no—
481#95—1421no—
482#95—1421no—
483#95—1421no—
484#95—1421no—
485#95—1421no—
486C24—711no—
487C24D4×D7111yescharacteristic
488C2×D4—714no—
489C2×D4—714no—
490C2×D4—714no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—81no—
502C22×C4—2842no—
503C22×C4—2842no—
504C22×C4—2842no—
505C22×C4—2842no—
506C22×C4—2842no—
507C22×C4—2842no—
508C22×C4—5681no—
509C22×C4—5681no—
510C22×C4—5681no—
511C22×C4—711no—
512C22×C4—711no—
513C22×C4—711no—
514C22×C4—712no—
515C22×C4—712no—
516C22×C4—1421no—
517C22×C4—1421no—
518C22×C4—1421no—
519C22×C4—1421no—
520C22×C4—1421no—
521C22×C4—1421no—
522C22×C4—1421no—
523C22×C4—1421no—
524C22×C4C2×C4×D7112yes—
525C22×C4D4×D7111yescharacteristic
526C22×C4Q8×D7112yes—
527C22×C4C23×D7111yescharacteristic
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—712no—
533C2×C8—712no—
534C2×C8—712no—
535C2×C8—712no—
536C2×C8—1428no—
537C2×C8—1428no—
538C2×C8—1421no—
539C2×C8—1421no—
540C2×C8C2×C4×D7112yes—
541C2×C8C2×C4×D7112yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—2842no—
551C4⋊C4—2842no—
552C4⋊C4—2842no—
553C4⋊C4—2842no—
554C4⋊C4—2842no—
555C4⋊C4—5681no—
556C4⋊C4—5681no—
557C4⋊C4—714no—
558C4⋊C4—712no—
559C4⋊C4—1421no—
560C4⋊C4—1421no—
561C4⋊C4—1421no—
562C4⋊C4—1421no—
563C4⋊C4—1421no—
564C4⋊C4—1421no—
565C4⋊C4—1421no—
566C4⋊C4D4×D7112yes—
567C22⋊C4—42no—
568C22⋊C4—2842no—
569C22⋊C4—2842no—
570C22⋊C4—2842no—
571C22⋊C4—714no—
572C22⋊C4—714no—
573C42—2842no—
574C42—2842no—
575C42—712no—
576C42—712no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—712no—
582C23—712no—
583C23—712no—
584C23—1421no—
585C23—1421no—
586C23—1421no—
587C23—1421no—
588C23C4⋊C4×D7112yes—
589C23SD16×D7112yes—
590C23SD16×D7112yes—
591C23C2×D4×D7111yescharacteristic
592D4—7116no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—84no—
612C2×C4—2841no—
613C2×C4—2841no—
614C2×C4—2841no—
615C2×C4—2841no—
616C2×C4—2841no—
617C2×C4—2841no—
618C2×C4—2841no—
619C2×C4—2841no—
620C2×C4—2841no—
621C2×C4—2841no—
622C2×C4—2841no—
623C2×C4—5684no—
624C2×C4—5684no—
625C2×C4—5684no—
626C2×C4—712no—
627C2×C4—712no—
628C2×C4—712no—
629C2×C4—712no—
630C2×C4—712no—
631C2×C4—1422no—
632C2×C4—1421no—
633C2×C4—1421no—
634C2×C4—1421no—
635C2×C4—1421no—
636C2×C4—1422no—
637C2×C4—1422no—
638C2×C4—1422no—
639C2×C4—1422no—
640C2×C4C4⋊C4×D7112yes—
641C2×C4C22×C4×D7111yescharacteristic
642C2×C4C2×D4×D7111yescharacteristic
643C2×C4C2×Q8×D7111yescharacteristic
644C2×C4#41×D7111yescharacteristic
645C2×C4#1455617311yescharacteristic
646C2×C4#1455617511yescharacteristic
647C8—22no—
648C8—22no—
649C8—714no—
650C8—1422no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—714no—
658C22—1422no—
659C22—1422no—
660C22—1422no—
661C22—1422no—
662C22—1422no—
663C22—1422no—
664C22#106×D7114yescomplemented
665C22C2×C4⋊C4×D7111yescharacteristic
666C22#1798663111yescharacteristic
667C22#1798664711yescharacteristic
668C22C2×SD16×D7111yescharacteristic
669C22C2×SD16×D7111yescharacteristic
670C22#1798680811yescharacteristic
671C22#1798680911yescharacteristic
672C4—22no—
673C4—42no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4—2842no—
678C4—5681no—
679C4—5681no—
680C4—5681no—
681C4—714no—
682C4—1422no—
683C4—1422no—
684C4C4×D4×D7111yescharacteristic
685C4#1798647811yescharacteristic
686C4#1798666211yescharacteristic
687C4#1798670311yescharacteristic
688C2—24no—
689C2—1424no—
690C2#2259123811yescharacteristic
691C2C2×#106×D7111yescharacteristic
692C2#2259693411yescharacteristic
693C2#2260002911yescharacteristic
694C2#2260003411yescharacteristic
695C2#2260069011yescharacteristic
696C2#2260069511yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#1853C2
socleC23×C71C22×D4
prime radicalC22×C22⋊D71D4
cosocleC22×C4×C71C24
hypercenter#1853D71
hypocenterC71D4×#106
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
2. C22×#14556059C2semidirect
3. C2×#106×D71C2semidirect
6. #22589102C2semidirect
7. #22589100C2semidirect
8. #22588535C2semidirect
9. #22588534C2semidirect
10. #22588531C2semidirect
11. #22588495C2semidirect
12. #22588364C2semidirect
13. #22588363C2semidirect
14. #22588228C2semidirect
15. C71×#1853C2semidirect
24. (C22⋊D71)⋊C8C4semidirect
69. C22×C71⋊C8C2×C4semidirect
74. C2×C8×D71C2×C4semidirect
112. #14556059D4semidirect
113. Dic71⋊C8C2×C4semidirect
114. (C2×D71)⋊C8C2×C4semidirect
115. C8×Dic71C2×C4semidirect
135. C22⋊C8×C71C2×C4semidirect
269. C22⋊D71#106semidirect
301. C71⋊C8C4×D4semidirect
308. C22×C71C2×#106semidirect
322. C2×D71C2×#106semidirect
338. Dic71C2×#106semidirect
359. #1853D71semidirect
364. C71D4×#106semidirect
478. C22⋊C8C4×D71semidirect
664. C22#106×D71semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D71)⋊C82
C22×#145560592
C2×#106×D712
C4⋊C4×C22⋊D712
#225912362
#225891022
#225891002
#225885352
#225885342
#225885312
#225884952
#225883642
#225883632
#225882282
C71×#18532
D4×#10671