Finite Group Databasebeta

← #31964808

Subgroups — #31964808

Order 18176.

1470 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986510C211yesmaximal, characteristic
2C22×C22⋊(C71⋊C8)C211yesmaximal, characteristic, complemented
3#22586911C212yesmaximal, complemented
4#22586907C212yesmaximal, complemented
5#22586894C214yesmaximal, complemented
6#22586829C214yesmaximal, complemented
7C71×#2280C211yesmaximal, characteristic, complemented
8C22×#11765865C411yescharacteristic, complemented
9C23×C71⋊C8—21no—
10#17986510—21no—
11#17986510—21no—
12#17986510—21no—
13#17986510—21no—
14#17986510C412yescomplemented
15#17986510C412yescomplemented
16#17986510C2212yes—
17#17986510C2212yes—
18C2×#14556111—21no—
19C2×#14556107C411yescharacteristic, complemented
20C2×#14556107C2211yescharacteristic
21C2×#14556102C411yescharacteristic, complemented
22C2×#14556102C2211yescharacteristic
23C2×#14556097—21no—
24C2×C4×C22⋊D71—21no—
25C2×C4×C22⋊D71—21no—
26C2×#14556087C411yescharacteristic, complemented
27C2×C22⋊(C71⋊C8)—21no—
28C2×C22⋊(C71⋊C8)—21no—
29C2×C22⋊(C71⋊C8)—21no—
30C2×C22⋊(C71⋊C8)C2212yes—
31C2×C22⋊(C71⋊C8)C2212yescomplemented
32C2×C22⋊(C71⋊C8)C2212yescomplemented
33#17985735C2218yescomplemented
34#17985732C2218yescomplemented
35C24×C4×C71C2211yescharacteristic
36C2×#117×C71—21no—
37#381×C71C2212yescomplemented
38#380×C71—21no—
39#380×C71C2212yes—
40#379×C71—21no—
41C4×C22⋊C4×C71—21no—
42C4×C22⋊C4×C71C2212yescomplemented
43C2×#11765865—21no—
44C2×#11765865—21no—
45C2×#11765865—44no—
46C2×#11765865C2×C412yes—
47C2×#11765865C2×C412yes—
48C22×Dic142C2×C411yescharacteristic
49C22×D284C2×C411yescharacteristic
50C22×C22⋊D71—21no—
51C22×C22⋊D71—21no—
52C22×C22⋊D71—21no—
53C22×C4×D71—21no—
54C22×C71⋊C8—22no—
55C22×C71⋊C8—22no—
56C22×C71⋊C8—22no—
57C22×C71⋊C8—44no—
58#14556111—22no—
59#14556111—22no—
60#14556111—22no—
61#14556111—22no—
62#14556107—21no—
63#14556107—21no—
64#14556107—21no—
65#14556107—21no—
66#14556107C2×C412yes—
67#14556107C2×C412yes—
68#14556107C2×C412yes—
69#14556107C2312yes—
70#14556102—21no—
71#14556102—21no—
72#14556102—21no—
73#14556102—21no—
74#14556102C2×C412yes—
75#14556102C2×C412yes—
76#14556102C2×C412yes—
77#14556102C2312yes—
78#14556097—22no—
79#14556097—22no—
80#14556097—22no—
81#14556097—22no—
82C4×C22⋊D71—22no—
83C4×C22⋊D71—22no—
84C4×C22⋊D71—22no—
85C4×C22⋊D71—22no—
86C4×C22⋊D71—22no—
87C4×C22⋊D71—22no—
88C4×C22⋊D71—22no—
89C4×C22⋊D71—22no—
90#14556087—21no—
91#14556087—21no—
92#14556087C2×C412yes—
93#14556087C2×C412yes—
94C2×C4⋊Dic71C2×C411yescharacteristic
95C2×C4⋊Dic71C2×C411yescharacteristic
96C2×Dic71⋊C4—21no—
97C2×Dic71⋊C4—21no—
98C2×C22⋊Dic71—21no—
99C2×C22⋊Dic71—21no—
100C2×C22⋊Dic71—21no—
101C2×(C2×D71)⋊C4—21no—
102C2×(C2×D71)⋊C4—21no—
103C2×C4×Dic71—21no—
104C22⋊(C71⋊C8)—22no—
105C22⋊(C71⋊C8)—22no—
106C22⋊(C71⋊C8)—22no—
107C22⋊(C71⋊C8)C2314yes—
108C25×C71D411yescharacteristic
109C23×C4×C71—44no—
110C23×C4×C71C2×C411yescharacteristic
111C23×C4×C71C2×C411yescharacteristic
112C23×C4×C71C2×C411yescharacteristic
113C23×C4×C71C2×C411yescharacteristic
114C23×C4×C71D411yescharacteristic
115C23×C4×C71D411yescharacteristic
116C23×C4×C71D411yescharacteristic
117C23×C4×C71D411yescharacteristic
118C23×C4×C71D411yescharacteristic
119C23×C4×C71D411yescharacteristic
120C23×C4×C71D411yescharacteristic
121C23×C4×C71C2311yescharacteristic
122C23×C4×C71C2311yescharacteristic
123C23×C4×C71C2311yescharacteristic
124#117×C71—44no—
125C2×C4⋊C4×C71—22no—
126C2×C22⋊C4×C71—22no—
127C2×C22⋊C4×C71—22no—
128C2×C22⋊C4×C71—22no—
129C2×C42×C71—22no—
130#95×C71—22no—
131#95×C71C2314yes—
132C23×D71—21no—
133#11765865—44no—
134#11765865—44no—
135#11765865—44no—
136#11765865—44no—
137C2×Dic142—21no—
138C2×Dic142—42no—
139C2×Dic142C22×C412yes—
140C2×D284—21no—
141C2×D284—42no—
142C2×D284C22×C412yes—
143C2×C22⋊D71—22no—
144C2×C22⋊D71—22no—
145C2×C22⋊D71—22no—
146C2×C22⋊D71—22no—
147C2×C22⋊D71—22no—
148C2×C22⋊D71—22no—
149C2×C22⋊D71—44no—
150C2×C22⋊D71—44no—
151C2×C22⋊D71—44no—
152C22×Dic71—21no—
153C22×Dic71—21no—
154C22×Dic71—21no—
155C2×C4×D71—22no—
156C2×C4×D71—22no—
157C2×C4×D71—44no—
158C2×C71⋊C8—24no—
159C2×C71⋊C8—44no—
160C2×C71⋊C8—44no—
161C2×C71⋊C8—44no—
162C4⋊Dic71—21no—
163C4⋊Dic71—21no—
164C4⋊Dic71C22×C412yes—
165C4⋊Dic71C22×C412yes—
166Dic71⋊C4—22no—
167Dic71⋊C4—22no—
168Dic71⋊C4—22no—
169Dic71⋊C4—22no—
170C22⋊Dic71—22no—
171C22⋊Dic71—22no—
172C22⋊Dic71—22no—
173C22⋊Dic71—22no—
174C22⋊Dic71—22no—
175C22⋊Dic71—22no—
176(C2×D71)⋊C4—22no—
177(C2×D71)⋊C4—22no—
178(C2×D71)⋊C4—22no—
179(C2×D71)⋊C4—22no—
180C4×Dic71—22no—
181C4×Dic71—22no—
182C24×C71—24no—
183C24×C71—42no—
184C24×C71—42no—
185C24×C71C22⋊C411yescharacteristic
186C24×C71C22⋊C411yescharacteristic
187C24×C71C22⋊C411yescharacteristic
188C24×C71C22⋊C411yescharacteristic
189C24×C71C2×D411yescharacteristic
190C24×C71C2×D411yescharacteristic
191C24×C71C2×D411yescharacteristic
192C22×C4×C71—24no—
193C22×C4×C71—24no—
194C22×C4×C71—24no—
195C22×C4×C71—24no—
196C22×C4×C71—42no—
197C22×C4×C71—42no—
198C22×C4×C71—42no—
199C22×C4×C71—42no—
200C22×C4×C71—42no—
201C22×C4×C71—42no—
202C22×C4×C71—42no—
203C22×C4×C71—42no—
204C22×C4×C71—42no—
205C22×C4×C71—42no—
206C22×C4×C71—42no—
207C22×C4×C71C22⋊C411yescharacteristic
208C22×C4×C71C22⋊C411yescharacteristic
209C22×C4×C71C22⋊C411yescharacteristic
210C22×C4×C71C22⋊C411yescharacteristic
211C22×C4×C71C22⋊C411yescharacteristic
212C22×C4×C71C22⋊C411yescharacteristic
213C22×C4×C71C22⋊C411yescharacteristic
214C22×C4×C71C22⋊C411yescharacteristic
215C22×C4×C71C22⋊C411yescharacteristic
216C22×C4×C71C22⋊C411yescharacteristic
217C22×C4×C71C22⋊C411yescharacteristic
218C22×C4×C71C22⋊C411yescharacteristic
219C22×C4×C71C22×C411yescharacteristic
220C22×C4×C71C22×C411yescharacteristic
221C22×C4×C71C22×C411yescharacteristic
222C22×C4×C71C22×C411yescharacteristic
223C22×C4×C71C22×C411yescharacteristic
224C22×C4×C71C22×C411yescharacteristic
225C22×C4×C71C2×D411yescharacteristic
226C22×C4×C71C2×D411yescharacteristic
227C22×C4×C71C2×D411yescharacteristic
228C22×C4×C71C2×D411yescharacteristic
229C22×C4×C71C2×D411yescharacteristic
230C22×C4×C71C2×D411yescharacteristic
231C22×C4×C71C2×D411yescharacteristic
232C22×C4×C71C2×D411yescharacteristic
233C22×C4×C71C2×D411yescharacteristic
234C22×C4×C71C2411yescharacteristic
235C4⋊C4×C71—44no—
236C22⋊C4×C71—44no—
237C22⋊C4×C71—44no—
238C22⋊C4×C71—44no—
239C42×C71—44no—
240C23×C71—22no—
241C23×C71—22no—
242C23×C71—22no—
243C23×C71—22no—
244C23×C71—22no—
245C23×C71—22no—
246C23×C71—22no—
247C23×C71—22no—
248C23×C71—22no—
249C23×C71—22no—
250C23×C71—22no—
251C23×C71—22no—
252C23×C71—41no—
253C23×C71—41no—
254C23×C71—41no—
255C23×C71—41no—
256C23×C71—41no—
257C23×C71—41no—
258C23×C71—41no—
259C23×C71—41no—
260C23×C71—416no—
261C23×C71C2×C22⋊C411yescharacteristic
262C23×C71C2×C22⋊C411yescharacteristic
263C23×C71C2×C22⋊C411yescharacteristic
264C23×C71C2×C22⋊C411yescharacteristic
265C23×C71C2×C22⋊C411yescharacteristic
266C23×C71C2×C22⋊C411yescharacteristic
267C23×C71#13514yes—
268C23×C71C22×D411yescharacteristic
269C22×D71—22no—
270C22×D71—42no—
271C22×D71—42no—
272C22×D71—42no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—41no—
289C2×C4×C71—41no—
290C2×C4×C71—41no—
291C2×C4×C71—41no—
292C2×C4×C71—41no—
293C2×C4×C71—41no—
294C2×C4×C71—41no—
295C2×C4×C71—41no—
296C2×C4×C71—41no—
297C2×C4×C71—41no—
298C2×C4×C71—41no—
299C2×C4×C71—41no—
300C2×C4×C71—44no—
301C2×C4×C71—44no—
302C2×C4×C71—44no—
303C2×C4×C71#9914yes—
304C2×C4×C71C2×C22⋊C411yescharacteristic
305C2×C4×C71C2×C22⋊C411yescharacteristic
306C2×C4×C71C2×C22⋊C411yescharacteristic
307C2×C4×C71C2×C22⋊C411yescharacteristic
308C2×C4×C71C2×C22⋊C411yescharacteristic
309C2×C4×C71C2×C22⋊C411yescharacteristic
310C2×C4×C71C23×C411yescharacteristic
311C2×C4×C71C22×D411yescharacteristic
312C22⋊D71—44no—
313C22⋊D71—44no—
314C22⋊D71—44no—
315C22⋊D71—44no—
316C22⋊D71—44no—
317C22⋊D71—44no—
318C2×Dic71—22no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—42no—
322C2×Dic71—42no—
323C2×Dic71—42no—
324D284—42no—
325D284—42no—
326C4×D71—44no—
327C4×D71—44no—
328Dic142—42no—
329Dic142—42no—
330C71⋊C8—44no—
331C22×C71—28no—
332C22×C71—21no—
333C22×C71—21no—
334C22×C71—21no—
335C22×C71—21no—
336C22×C71—21no—
337C22×C71—21no—
338C22×C71—21no—
339C22×C71—21no—
340C22×C71—21no—
341C22×C71—21no—
342C22×C71—21no—
343C22×C71—21no—
344C22×C71—21no—
345C22×C71—21no—
346C22×C71—21no—
347C22×C71—21no—
348C22×C71—44no—
349C22×C71—44no—
350C22×C71—44no—
351C22×C71—44no—
352C22×C71—44no—
353C22×C71—44no—
354C22×C71C2×#9912yes—
355C22×C71#41612yes—
356C22×C71#41612yes—
357C22×C71#42112yes—
358C22×C71C22×C22⋊C411yescharacteristic
359C22×C71C2×#13512yes—
360C2×D71—42no—
361C2×D71—42no—
362C2×D71—42no—
363C2×D71—84no—
364C4×C71—21no—
365C4×C71—21no—
366C4×C71—21no—
367C4×C71—21no—
368C4×C71—21no—
369C4×C71—21no—
370C4×C71—84no—
371C4×C71C2×#9912yes—
372C4×C71C2×#9912yes—
373Dic71—42no—
374Dic71—42no—
375Dic71—42no—
376#17572—711nomaximal, Sylow
377C2×C71—22no—
378C2×C71—22no—
379C2×C71—22no—
380C2×C71—22no—
381C2×C71—22no—
382C2×C71—41no—
383C2×C71—41no—
384C2×C71C22×#9911yescharacteristic
385C2×C71C2×#41611yescharacteristic
386C2×C71C2×#42111yescharacteristic
387D71—82no—
388C2×#525—711no—
389C22×C22⋊C8—711no—
390#2280D7111yescharacteristic, complemented
391#1520—712no—
392#1519—712no—
393#1516—714no—
394#1501—714no—
395C71#1757211yescharacteristic, complemented, Sylow
396C22×#41—711no—
397C24×C4C2×D7111yescharacteristic
398C23×C8—1421no—
399#525—712no—
400#525—712no—
401#525—712no—
402#525—712no—
403#525—1421no—
404#525—1421no—
405#525—1421no—
406#525—1421no—
407C2×#123—1421no—
408C2×C22⋊Q8—711no—
409C2×C22⋊Q8—711no—
410C2×#121—711no—
411C2×#121—711no—
412C2×#120—1421no—
413C2×C4×D4—1421no—
414C2×C4×D4—1421no—
415C2×#117—21no—
416C2×#117—711no—
417C2×C22⋊C8—712no—
418C2×C22⋊C8—712no—
419C2×C22⋊C8—712no—
420C2×C22⋊C8—1421no—
421C2×C22⋊C8—1421no—
422C2×C22⋊C8—1421no—
423#381C2×D7112yescomplemented
424#380—21no—
425#380C2×D7112yes—
426#379—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4C2×D7112yescomplemented
429#328—718no—
430#327—718no—
431C25C22⋊D7111yescharacteristic
432C2×#41—2844no—
433C2×#41—712no—
434C2×#41—712no—
435C2×#41—1421no—
436C2×#41—1421no—
437C22×Q8—711no—
438C22×D4—711no—
439C22×D4—1421no—
440C22×D4—1421no—
441C22×D4—1421no—
442C23×C4—44no—
443C23×C4—1421no—
444C23×C4C4×D7111yescharacteristic
445C23×C4C4×D7111yescharacteristic
446C23×C4C4×D7111yescharacteristic
447C23×C4C4×D7111yescharacteristic
448C23×C4D28411yescharacteristic
449C23×C4D28411yescharacteristic
450C23×C4D28411yescharacteristic
451C23×C4D28411yescharacteristic
452C23×C4C22⋊D7111yescharacteristic
453C23×C4C22⋊D7111yescharacteristic
454C23×C4C22⋊D7111yescharacteristic
455C23×C4C22×D7111yescharacteristic
456C23×C4C22×D7111yescharacteristic
457C23×C4C22×D7111yescharacteristic
458C22×C8—2844no—
459C22×C8—1422no—
460C22×C8—1422no—
461C22×C8—1422no—
462#123—1422no—
463#123—1422no—
464#123—1422no—
465#123—1422no—
466C22⋊Q8—712no—
467C22⋊Q8—712no—
468C22⋊Q8—712no—
469C22⋊Q8—712no—
470C22⋊Q8—1421no—
471C22⋊Q8—1421no—
472C22⋊Q8—1421no—
473C22⋊Q8—1421no—
474#121—712no—
475#121—712no—
476#121—712no—
477#121—712no—
478#121—1421no—
479#121—1421no—
480#121—1421no—
481#121—1421no—
482#120—1422no—
483#120—1422no—
484#120—1422no—
485#120—1422no—
486C4×D4—1422no—
487C4×D4—1422no—
488C4×D4—1422no—
489C4×D4—1422no—
490C4×D4—1422no—
491C4×D4—1422no—
492C4×D4—1422no—
493C4×D4—1422no—
494#117—44no—
495#117—712no—
496#117—712no—
497#117—1421no—
498#117—1421no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—711no—
501C2×C4⋊C4—711no—
502C2×C4⋊C4—1421no—
503C2×C4⋊C4—1421no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—1421no—
508C2×C22⋊C4—1421no—
509C2×C22⋊C4—1421no—
510C2×C22⋊C4—1421no—
511C2×C22⋊C4—1421no—
512C2×C42—22no—
513C2×C42—1421no—
514C22⋊C8—714no—
515C22⋊C8—1422no—
516C22⋊C8—1422no—
517C22⋊C8—1422no—
518#95—22no—
519#95C22×D7114yes—
520C24—24no—
521C24—42no—
522C24—42no—
523C24—1421no—
524C24(C2×D71)⋊C411yescharacteristic
525C24(C2×D71)⋊C411yescharacteristic
526C24(C2×D71)⋊C411yescharacteristic
527C24(C2×D71)⋊C411yescharacteristic
528C24C2×C22⋊D7111yescharacteristic
529C24C2×C22⋊D7111yescharacteristic
530C24C2×C22⋊D7111yescharacteristic
531#41—2844no—
532#41—2844no—
533#41—2844no—
534#41—2844no—
535C2×Q8—2842no—
536C2×Q8—712no—
537C2×Q8—1421no—
538C2×D4—2842no—
539C2×D4—2844no—
540C2×D4—2844no—
541C2×D4—2844no—
542C2×D4—712no—
543C2×D4—1422no—
544C2×D4—1422no—
545C2×D4—1422no—
546C2×D4—1422no—
547C2×D4—1422no—
548C2×D4—1422no—
549C2×D4—1421no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—2844no—
566C22×C4—1421no—
567C22×C4—1421no—
568C22×C4—1421no—
569C22×C4—1422no—
570C22×C4—1422no—
571C22×C4(C2×D71)⋊C411yescharacteristic
572C22×C4(C2×D71)⋊C411yescharacteristic
573C22×C4(C2×D71)⋊C411yescharacteristic
574C22×C4(C2×D71)⋊C411yescharacteristic
575C22×C4(C2×D71)⋊C411yescharacteristic
576C22×C4(C2×D71)⋊C411yescharacteristic
577C22×C4(C2×D71)⋊C411yescharacteristic
578C22×C4(C2×D71)⋊C411yescharacteristic
579C22×C4(C2×D71)⋊C411yescharacteristic
580C22×C4(C2×D71)⋊C411yescharacteristic
581C22×C4(C2×D71)⋊C411yescharacteristic
582C22×C4(C2×D71)⋊C411yescharacteristic
583C22×C4C2×C4×D7111yescharacteristic
584C22×C4C2×C4×D7111yescharacteristic
585C22×C4C2×C4×D7111yescharacteristic
586C22×C4C2×C4×D7111yescharacteristic
587C22×C4C2×C4×D7111yescharacteristic
588C22×C4C2×C4×D7111yescharacteristic
589C22×C4C2×C22⋊D7111yescharacteristic
590C22×C4C2×C22⋊D7111yescharacteristic
591C22×C4C2×C22⋊D7111yescharacteristic
592C22×C4C2×D28411yescharacteristic
593C22×C4C2×D28411yescharacteristic
594C22×C4C2×D28411yescharacteristic
595C22×C4C2×D28411yescharacteristic
596C22×C4C2×D28411yescharacteristic
597C22×C4C2×D28411yescharacteristic
598C22×C4C23×D7111yescharacteristic
599C2×C8—2844no—
600C2×C8—2844no—
601C2×C8—2844no—
602C2×C8—1424no—
603C4⋊C4—44no—
604C4⋊C4—712no—
605C4⋊C4—712no—
606C4⋊C4—1422no—
607C4⋊C4—1422no—
608C4⋊C4—1422no—
609C4⋊C4—1422no—
610C4⋊C4—1421no—
611C4⋊C4—1421no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—1422no—
616C22⋊C4—1422no—
617C22⋊C4—1422no—
618C22⋊C4—1422no—
619C22⋊C4—1422no—
620C22⋊C4—1422no—
621C22⋊C4—1422no—
622C22⋊C4—1422no—
623C22⋊C4—1422no—
624C22⋊C4—1422no—
625C42—44no—
626C42—1422no—
627C42—1422no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—416no—
649C23—2842no—
650C23—2842no—
651C23—2842no—
652C23—1422no—
653C23C2×(C2×D71)⋊C411yescharacteristic
654C23C2×(C2×D71)⋊C411yescharacteristic
655C23C2×(C2×D71)⋊C411yescharacteristic
656C23C2×(C2×D71)⋊C411yescharacteristic
657C23C2×(C2×D71)⋊C411yescharacteristic
658C23C2×(C2×D71)⋊C411yescharacteristic
659C23#1455614814yes—
660C23C22×C22⋊D7111yescharacteristic
661Q8—2842no—
662Q8—2842no—
663D4—2842no—
664D4—2844no—
665D4—2844no—
666D4—2844no—
667D4—2844no—
668D4—2844no—
669D4—2844no—
670D4—2842no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—2844no—
702C2×C4—2842no—
703C2×C4—2842no—
704C2×C4—2842no—
705C2×C4—2844no—
706C2×C4—1422no—
707C2×C4—1422no—
708C2×C4—1422no—
709C2×C4#1455604214yes—
710C2×C4C2×(C2×D71)⋊C411yescharacteristic
711C2×C4C2×(C2×D71)⋊C411yescharacteristic
712C2×C4C2×(C2×D71)⋊C411yescharacteristic
713C2×C4C2×(C2×D71)⋊C411yescharacteristic
714C2×C4C2×(C2×D71)⋊C411yescharacteristic
715C2×C4C2×(C2×D71)⋊C411yescharacteristic
716C2×C4C22×C4×D7111yescharacteristic
717C2×C4C22×D28411yescharacteristic
718C8—2844no—
719C22—28no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—2842no—
743C22—2842no—
744C22—2842no—
745C22—5684no—
746C22C2×#1455604212yes—
747C22#1798599312yes—
748C22#1798599312yes—
749C22#1798601712yes—
750C22C22×(C2×D71)⋊C411yescharacteristic
751C22C2×#1455614812yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—84no—
759C4—2842no—
760C4—2842no—
761C4—2842no—
762C4C2×#1455604212yes—
763C4C2×#1455604212yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—5682no—
772C2C22×#1455604211yescharacteristic
773C2C2×#1798599311yescharacteristic
774C2C2×#1798601711yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D71)⋊C4
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#2280C2
socleC22×C71C22×C22⋊C4
prime radicalC2×#17986510C2
cosocleC22×C4×C71C24
hypercenter#2280D71
hypocenterC71#17572
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊(C71⋊C8)C2semidirect
3. #22586911C2semidirect
4. #22586907C2semidirect
5. #22586894C2semidirect
6. #22586829C2semidirect
7. C71×#2280C2semidirect
8. C22×#11765865C4semidirect
14. #17986510C4semidirect
15. #17986510C4semidirect
19. C2×#14556107C4semidirect
21. C2×#14556102C4semidirect
26. C2×#14556087C4semidirect
31. C2×C22⋊(C71⋊C8)C22semidirect
32. C2×C22⋊(C71⋊C8)C22semidirect
33. #17985735C22semidirect
34. #17985732C22semidirect
37. #381×C71C22semidirect
42. C4×C22⋊C4×C71C22semidirect
390. #2280D71semidirect
395. C71#17572semidirect
423. #381C2×D71semidirect
428. C4×C22⋊C4C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179865102
C22×C22⋊(C71⋊C8)2
#225869112
#225869072
#225868942
#225868292
C71×#22802
#1757271