Finite Group Databasebeta

← #31964943

Subgroups — #31964943

Order 18176.

1510 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986510C211yesmaximal, characteristic
2C2×#17985859C211yesmaximal, characteristic, complemented
3#22586913C212yesmaximal, complemented
4#22586909C212yesmaximal, complemented
5#22586884C214yesmaximal, complemented
6#22586845C214yesmaximal, complemented
7C2×#407×C71C211yesmaximal, characteristic, complemented
8C22×#11765865C411yescharacteristic, complemented
9#17986510—21no—
10#17986510—21no—
11#17986510—21no—
12#17986510—21no—
13#17986510C412yescomplemented
14#17986510C412yescomplemented
15#17986510C2212yes—
16#17986510C2212yes—
17C2×#14556111—21no—
18C2×#14556107C411yescharacteristic, complemented
19C2×#14556107C2211yescharacteristic
20C2×#14556102C411yescharacteristic, complemented
21C2×#14556102C2211yescharacteristic
22C2×#14556097—21no—
23C2×C4×C22⋊D71—21no—
24C2×C4×C22⋊D71—21no—
25C2×#14556087C411yescharacteristic, complemented
26C22×C4⋊Dic71—21no—
27C22×C22⋊Dic71—21no—
28#17985859—21no—
29#17985859—21no—
30#17985859C2212yes—
31#17985859C2212yescomplemented
32C2×C71⋊#95C2212yescomplemented
33#17985737C2218yescomplemented
34#17985734C2218yescomplemented
35C24×C4×C71C2211yescharacteristic
36C22×M16×C71—21no—
37#407×C71—21no—
38#407×C71—21no—
39#407×C71C2212yescomplemented
40#407×C71C2212yescomplemented
41C2×C22⋊C8×C71—21no—
42C2×C22⋊C8×C71C2212yes—
43C2×#11765865—21no—
44C2×#11765865—21no—
45C2×#11765865—44no—
46C2×#11765865C2×C412yes—
47C2×#11765865C2×C412yescomplemented
48C22×Dic142C2×C411yescharacteristic, complemented
49C22×D284C2×C411yescharacteristic, complemented
50C22×C22⋊D71—21no—
51C22×C22⋊D71—21no—
52C22×C22⋊D71—21no—
53C23×Dic71—22no—
54C22×C4×D71—21no—
55#14556111—22no—
56#14556111—22no—
57#14556111—22no—
58#14556111—22no—
59#14556107—21no—
60#14556107—21no—
61#14556107—21no—
62#14556107—21no—
63#14556107C2×C412yes—
64#14556107C2×C412yescomplemented
65#14556107C2×C412yescomplemented
66#14556107C2312yes—
67#14556102—21no—
68#14556102—21no—
69#14556102—21no—
70#14556102—21no—
71#14556102C2×C412yes—
72#14556102C2×C412yescomplemented
73#14556102C2×C412yescomplemented
74#14556102C2312yes—
75#14556097—22no—
76#14556097—22no—
77#14556097—22no—
78#14556097—22no—
79C4×C22⋊D71—22no—
80C4×C22⋊D71—22no—
81C4×C22⋊D71—22no—
82C4×C22⋊D71—22no—
83C4×C22⋊D71—22no—
84C4×C22⋊D71—22no—
85C4×C22⋊D71—22no—
86C4×C22⋊D71—22no—
87#14556087—21no—
88#14556087—21no—
89#14556087C2×C412yes—
90#14556087C2×C412yescomplemented
91C2×C4⋊Dic71—22no—
92C2×C4⋊Dic71—22no—
93C2×C4⋊Dic71—44no—
94C2×C4⋊Dic71C2×C411yescharacteristic, complemented
95C2×C4⋊Dic71C2×C411yescharacteristic, complemented
96C2×Dic71⋊C4—21no—
97C2×Dic71⋊C4—21no—
98C2×C22⋊Dic71—21no—
99C2×C22⋊Dic71—21no—
100C2×C22⋊Dic71—21no—
101C2×C22⋊Dic71—22no—
102C2×C22⋊Dic71—22no—
103C2×C22⋊Dic71—44no—
104C2×(C2×D71)⋊C4—21no—
105C2×(C2×D71)⋊C4—21no—
106C2×C4×Dic71—21no—
107C71⋊#95—22no—
108C71⋊#95C2314yes—
109C25×C71D411yescharacteristic
110C23×C4×C71—44no—
111C23×C4×C71C2×C411yescharacteristic
112C23×C4×C71C2×C411yescharacteristic
113C23×C4×C71C2×C411yescharacteristic
114C23×C4×C71C2×C411yescharacteristic
115C23×C4×C71D411yescharacteristic
116C23×C4×C71D411yescharacteristic
117C23×C4×C71D411yescharacteristic
118C23×C4×C71D411yescharacteristic
119C23×C4×C71D411yescharacteristic
120C23×C4×C71D411yescharacteristic
121C23×C4×C71D411yescharacteristic
122C23×C4×C71C2311yescharacteristic
123C23×C4×C71C2311yescharacteristic
124C23×C4×C71C2311yescharacteristic
125C2×M16×C71—22no—
126C2×M16×C71—22no—
127C2×M16×C71—44no—
128C22×C8×C71—22no—
129C22⋊C8×C71—22no—
130C22⋊C8×C71—22no—
131C22⋊C8×C71—22no—
132C22⋊C8×C71C2314yes—
133C23×D71—21no—
134#11765865—44no—
135#11765865—44no—
136#11765865—44no—
137#11765865—44no—
138C2×Dic142—21no—
139C2×Dic142—42no—
140C2×Dic142C22×C412yes—
141C2×D284—21no—
142C2×D284—42no—
143C2×D284C22×C412yes—
144C2×C22⋊D71—22no—
145C2×C22⋊D71—22no—
146C2×C22⋊D71—22no—
147C2×C22⋊D71—22no—
148C2×C22⋊D71—22no—
149C2×C22⋊D71—22no—
150C2×C22⋊D71—44no—
151C2×C22⋊D71—44no—
152C2×C22⋊D71—42no—
153C2×C22⋊D71—42no—
154C22×Dic71—21no—
155C22×Dic71—21no—
156C22×Dic71—21no—
157C22×Dic71—24no—
158C22×Dic71—44no—
159C22×Dic71—44no—
160C22×Dic71—44no—
161C2×C4×D71—22no—
162C2×C4×D71—22no—
163C2×C4×D71—44no—
164C4⋊Dic71—21no—
165C4⋊Dic71—21no—
166C4⋊Dic71—44no—
167C4⋊Dic71—44no—
168C4⋊Dic71C22×C412yes—
169C4⋊Dic71C22×C412yes—
170Dic71⋊C4—22no—
171Dic71⋊C4—22no—
172Dic71⋊C4—22no—
173Dic71⋊C4—22no—
174C22⋊Dic71—22no—
175C22⋊Dic71—22no—
176C22⋊Dic71—22no—
177C22⋊Dic71—22no—
178C22⋊Dic71—22no—
179C22⋊Dic71—22no—
180C22⋊Dic71—44no—
181C22⋊Dic71—44no—
182(C2×D71)⋊C4—22no—
183(C2×D71)⋊C4—22no—
184(C2×D71)⋊C4—22no—
185(C2×D71)⋊C4—22no—
186C4×Dic71—22no—
187C4×Dic71—22no—
188C24×C71—22no—
189C24×C71—22no—
190C24×C71—42no—
191C24×C71—42no—
192C24×C71C22⋊C411yescharacteristic
193C24×C71C22⋊C411yescharacteristic
194C24×C71C22⋊C411yescharacteristic
195C24×C71C22⋊C411yescharacteristic
196C24×C71C2×D411yescharacteristic
197C24×C71C2×D411yescharacteristic
198C24×C71C2×D411yescharacteristic
199C22×C4×C71—24no—
200C22×C4×C71—24no—
201C22×C4×C71—24no—
202C22×C4×C71—42no—
203C22×C4×C71—42no—
204C22×C4×C71—42no—
205C22×C4×C71—42no—
206C22×C4×C71—42no—
207C22×C4×C71—42no—
208C22×C4×C71—42no—
209C22×C4×C71—42no—
210C22×C4×C71—42no—
211C22×C4×C71—42no—
212C22×C4×C71—42no—
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×C71C22×C411yescharacteristic
226C22×C4×C71C22×C411yescharacteristic
227C22×C4×C71C22×C411yescharacteristic
228C22×C4×C71C22×C411yescharacteristic
229C22×C4×C71C22×C411yescharacteristic
230C22×C4×C71C22×C411yescharacteristic
231C22×C4×C71C2×D411yescharacteristic
232C22×C4×C71C2×D411yescharacteristic
233C22×C4×C71C2×D411yescharacteristic
234C22×C4×C71C2×D411yescharacteristic
235C22×C4×C71C2×D411yescharacteristic
236C22×C4×C71C2×D411yescharacteristic
237C22×C4×C71C2×D411yescharacteristic
238C22×C4×C71C2×D411yescharacteristic
239C22×C4×C71C2×D411yescharacteristic
240C22×C4×C71C2411yescharacteristic
241M16×C71—44no—
242M16×C71—44no—
243C2×C8×C71—24no—
244C2×C8×C71—44no—
245C23×C71—21no—
246C23×C71—21no—
247C23×C71—22no—
248C23×C71—22no—
249C23×C71—21no—
250C23×C71—21no—
251C23×C71—22no—
252C23×C71—22no—
253C23×C71—22no—
254C23×C71—22no—
255C23×C71—22no—
256C23×C71—22no—
257C23×C71—22no—
258C23×C71—22no—
259C23×C71—41no—
260C23×C71—41no—
261C23×C71—41no—
262C23×C71—41no—
263C23×C71—41no—
264C23×C71—41no—
265C23×C71—41no—
266C23×C71—41no—
267C23×C71—48no—
268C23×C71—48no—
269C23×C71C2×C22⋊C411yescharacteristic
270C23×C71C2×C22⋊C411yescharacteristic
271C23×C71C2×C22⋊C411yescharacteristic
272C23×C71C2×C22⋊C411yescharacteristic
273C23×C71C2×C22⋊C411yescharacteristic
274C23×C71C2×C22⋊C411yescharacteristic
275C23×C71AGL(1,ℤ/8)12yes—
276C23×C71#13712yes—
277C23×C71C22×D411yescharacteristic
278C22×D71—22no—
279C22×D71—42no—
280C22×D71—42no—
281C22×D71—42no—
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—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—41no—
298C2×C4×C71—41no—
299C2×C4×C71—41no—
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—41no—
307C2×C4×C71—41no—
308C2×C4×C71—41no—
309C2×C4×C71#9914yes—
310C2×C4×C71C2×C22⋊C411yescharacteristic
311C2×C4×C71C2×C22⋊C411yescharacteristic
312C2×C4×C71C2×C22⋊C411yescharacteristic
313C2×C4×C71C2×C22⋊C411yescharacteristic
314C2×C4×C71C2×C22⋊C411yescharacteristic
315C2×C4×C71C2×C22⋊C411yescharacteristic
316C2×C4×C71C23×C411yescharacteristic
317C2×C4×C71C22×D411yescharacteristic
318C22⋊D71—44no—
319C22⋊D71—44no—
320C22⋊D71—42no—
321C22⋊D71—42no—
322C22⋊D71—44no—
323C22⋊D71—44no—
324C22⋊D71—44no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—22no—
328C2×Dic71—42no—
329C2×Dic71—42no—
330C2×Dic71—42no—
331C2×Dic71—44no—
332C2×Dic71—44no—
333C2×Dic71—44no—
334C2×Dic71—88no—
335D284—42no—
336D284—42no—
337C4×D71—44no—
338C4×D71—44no—
339Dic142—42no—
340Dic142—42no—
341C8×C71—44no—
342C22×C71—24no—
343C22×C71—24no—
344C22×C71—21no—
345C22×C71—21no—
346C22×C71—21no—
347C22×C71—21no—
348C22×C71—21no—
349C22×C71—21no—
350C22×C71—21no—
351C22×C71—21no—
352C22×C71—21no—
353C22×C71—21no—
354C22×C71—21no—
355C22×C71—21no—
356C22×C71—21no—
357C22×C71—21no—
358C22×C71—21no—
359C22×C71—21no—
360C22×C71—42no—
361C22×C71—42no—
362C22×C71—44no—
363C22×C71—44no—
364C22×C71—44no—
365C22×C71—44no—
366C22×C71—42no—
367C22×C71—42no—
368C22×C71C2×#9912yes—
369C22×C71#41712yes—
370C22×C71#41712yes—
371C22×C71#42112yes—
372C22×C71C22×C22⋊C411yescharacteristic
373C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C71C2×#13711yescharacteristic
375C2×D71—42no—
376C2×D71—42no—
377C2×D71—42no—
378C2×D71—84no—
379C4×C71—21no—
380C4×C71—21no—
381C4×C71—21no—
382C4×C71—21no—
383C4×C71—21no—
384C4×C71—21no—
385C4×C71C2×#9912yes—
386C4×C71C2×#9912yes—
387Dic71—42no—
388Dic71—42no—
389Dic71—42no—
390Dic71—84no—
391#17592—711nomaximal, Sylow
392C2×C71—21no—
393C2×C71—22no—
394C2×C71—21no—
395C2×C71—22no—
396C2×C71—22no—
397C2×C71—22no—
398C2×C71—41no—
399C2×C71—41no—
400C2×C71C22×#9911yescharacteristic
401C2×C71C2×#41711yescharacteristic
402C2×C71C2×#42111yescharacteristic
403D71—82no—
404C2×#525—711no—
405C2×#407D7111yescharacteristic, complemented
406C2×#380—711no—
407#1520—712no—
408#1519—712no—
409#1513—714no—
410#1504—714no—
411C71#1759211yescharacteristic, complemented, Sylow
412C22×#41—711no—
413C24×C4C2×D7111yescharacteristic
414C22×M16—21no—
415#525—712no—
416#525—712no—
417#525—712no—
418#525—712no—
419#525—1421no—
420#525—1421no—
421#525—1421no—
422#525—1421no—
423C2×#123—1421no—
424C2×C22⋊Q8—711no—
425C2×C22⋊Q8—711no—
426C2×#121—711no—
427C2×#121—711no—
428C2×#120—1421no—
429C2×C4×D4—1421no—
430C2×C4×D4—1421no—
431C2×#117—711no—
432C22×C4⋊C4—1421no—
433C22×C22⋊C4—1421no—
434#407—21no—
435#407—21no—
436#407C2×D7112yescomplemented
437#407C2×D7112yescomplemented
438C2×C22⋊C8—21no—
439C2×C22⋊C8C2×D7112yes—
440#380—712no—
441#380—712no—
442#380—1421no—
443#380—1421no—
444C2×#95—712no—
445#328—718no—
446#327—718no—
447C25D28411yescharacteristic
448C2×#41—2844no—
449C2×#41—712no—
450C2×#41—712no—
451C2×#41—1421no—
452C2×#41—1421no—
453C22×Q8—711no—
454C22×D4—711no—
455C22×D4—1421no—
456C22×D4—1421no—
457C22×D4—1421no—
458C23×C4—44no—
459C23×C4—1422no—
460C23×C4—1421no—
461C23×C4C4×D7111yescharacteristic
462C23×C4C4×D7111yescharacteristic
463C23×C4C4×D7111yescharacteristic
464C23×C4C4×D7111yescharacteristic
465C23×C4D28411yescharacteristic
466C23×C4D28411yescharacteristic
467C23×C4D28411yescharacteristic
468C23×C4C22⋊D7111yescharacteristic
469C23×C4C22⋊D7111yescharacteristic
470C23×C4C22⋊D7111yescharacteristic
471C23×C4C22⋊D7111yescharacteristic
472C23×C4C22×D7111yescharacteristic
473C23×C4C22×D7111yescharacteristic
474C23×C4C22×D7111yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—44no—
478C22×C8—22no—
479#123—1422no—
480#123—1422no—
481#123—1422no—
482#123—1422no—
483C22⋊Q8—712no—
484C22⋊Q8—712no—
485C22⋊Q8—712no—
486C22⋊Q8—712no—
487C22⋊Q8—1421no—
488C22⋊Q8—1421no—
489C22⋊Q8—1421no—
490C22⋊Q8—1421no—
491#121—712no—
492#121—712no—
493#121—712no—
494#121—712no—
495#121—1421no—
496#121—1421no—
497#121—1421no—
498#121—1421no—
499#120—1422no—
500#120—1422no—
501#120—1422no—
502#120—1422no—
503C4×D4—1422no—
504C4×D4—1422no—
505C4×D4—1422no—
506C4×D4—1422no—
507C4×D4—1422no—
508C4×D4—1422no—
509C4×D4—1422no—
510C4×D4—1422no—
511#117—712no—
512#117—712no—
513#117—1421no—
514#117—1421no—
515C2×C4⋊C4—2844no—
516C2×C4⋊C4—711no—
517C2×C4⋊C4—711no—
518C2×C4⋊C4—1422no—
519C2×C4⋊C4—1422no—
520C2×C4⋊C4—1421no—
521C2×C4⋊C4—1421no—
522C2×C22⋊C4—2844no—
523C2×C22⋊C4—1422no—
524C2×C22⋊C4—1422no—
525C2×C22⋊C4—1421no—
526C2×C22⋊C4—1421no—
527C2×C22⋊C4—1421no—
528C2×C22⋊C4—1421no—
529C2×C22⋊C4—1421no—
530C2×C42—1421no—
531C22⋊C8—22no—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8C22×D7114yes—
535#95—714no—
536#95—1422no—
537C24—22no—
538C24—22no—
539C24—42no—
540C24—42no—
541C24—1421no—
542C24(C2×D71)⋊C411yescharacteristic
543C24(C2×D71)⋊C411yescharacteristic
544C24(C2×D71)⋊C411yescharacteristic
545C24(C2×D71)⋊C411yescharacteristic
546C24C2×D28411yescharacteristic
547C24C2×D28411yescharacteristic
548C24C2×D28411yescharacteristic
549#41—2844no—
550#41—2844no—
551#41—2844no—
552#41—2844no—
553C2×Q8—2842no—
554C2×Q8—712no—
555C2×Q8—1421no—
556C2×D4—2842no—
557C2×D4—2844no—
558C2×D4—2844no—
559C2×D4—2842no—
560C2×D4—2842no—
561C2×D4—712no—
562C2×D4—1422no—
563C2×D4—1422no—
564C2×D4—1422no—
565C2×D4—1422no—
566C2×D4—1422no—
567C2×D4—1422no—
568C2×D4—1421no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—2844no—
584C22×C4—2844no—
585C22×C4—2844no—
586C22×C4—2844no—
587C22×C4—1424no—
588C22×C4—1421no—
589C22×C4—1421no—
590C22×C4—1421no—
591C22×C4—1422no—
592C22×C4—1422no—
593C22×C4(C2×D71)⋊C411yescharacteristic
594C22×C4(C2×D71)⋊C411yescharacteristic
595C22×C4(C2×D71)⋊C411yescharacteristic
596C22×C4(C2×D71)⋊C411yescharacteristic
597C22×C4(C2×D71)⋊C411yescharacteristic
598C22×C4(C2×D71)⋊C411yescharacteristic
599C22×C4(C2×D71)⋊C411yescharacteristic
600C22×C4(C2×D71)⋊C411yescharacteristic
601C22×C4(C2×D71)⋊C411yescharacteristic
602C22×C4(C2×D71)⋊C411yescharacteristic
603C22×C4(C2×D71)⋊C411yescharacteristic
604C22×C4(C2×D71)⋊C411yescharacteristic
605C22×C4C2×C4×D7111yescharacteristic
606C22×C4C2×C4×D7111yescharacteristic
607C22×C4C2×C4×D7111yescharacteristic
608C22×C4C2×C4×D7111yescharacteristic
609C22×C4C2×C4×D7111yescharacteristic
610C22×C4C2×C4×D7111yescharacteristic
611C22×C4C2×C22⋊D7111yescharacteristic
612C22×C4C2×C22⋊D7111yescharacteristic
613C22×C4C2×C22⋊D7111yescharacteristic
614C22×C4C2×C22⋊D7111yescharacteristic
615C22×C4C2×C22⋊D7111yescharacteristic
616C22×C4C2×C22⋊D7111yescharacteristic
617C22×C4C2×D28411yescharacteristic
618C22×C4C2×D28411yescharacteristic
619C22×C4C2×D28411yescharacteristic
620C22×C4C23×D7111yescharacteristic
621M16—44no—
622M16—44no—
623C2×C8—24no—
624C2×C8—44no—
625C4⋊C4—2844no—
626C4⋊C4—2844no—
627C4⋊C4—712no—
628C4⋊C4—712no—
629C4⋊C4—1422no—
630C4⋊C4—1422no—
631C4⋊C4—1422no—
632C4⋊C4—1422no—
633C4⋊C4—1421no—
634C4⋊C4—1421no—
635C22⋊C4—2844no—
636C22⋊C4—2844no—
637C22⋊C4—1422no—
638C22⋊C4—1422no—
639C22⋊C4—1422no—
640C22⋊C4—1422no—
641C22⋊C4—1422no—
642C22⋊C4—1422no—
643C22⋊C4—1422no—
644C22⋊C4—1422no—
645C22⋊C4—1422no—
646C22⋊C4—1422no—
647C42—1422no—
648C42—1422no—
649C23—22no—
650C23—22no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—48no—
672C23—48no—
673C23—2842no—
674C23—2842no—
675C23—2842no—
676C23—1422no—
677C23C2×(C2×D71)⋊C411yescharacteristic
678C23C2×(C2×D71)⋊C411yescharacteristic
679C23C2×(C2×D71)⋊C411yescharacteristic
680C23C2×(C2×D71)⋊C411yescharacteristic
681C23C2×(C2×D71)⋊C411yescharacteristic
682C23C2×(C2×D71)⋊C411yescharacteristic
683C23#1455615612yes—
684C23#1455616112yes—
685C23C22×D28411yescharacteristic
686Q8—2842no—
687Q8—2842no—
688D4—2842no—
689D4—2844no—
690D4—2844no—
691D4—2844no—
692D4—2844no—
693D4—2844no—
694D4—2842no—
695D4—2842no—
696D4—2842no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—2844no—
725C2×C4—2842no—
726C2×C4—2842no—
727C2×C4—2842no—
728C2×C4—2844no—
729C2×C4—2844no—
730C2×C4—2844no—
731C2×C4—2844no—
732C2×C4—5688no—
733C2×C4—1422no—
734C2×C4—1422no—
735C2×C4—1422no—
736C2×C4#1455604214yes—
737C2×C4C2×(C2×D71)⋊C411yescharacteristic
738C2×C4C2×(C2×D71)⋊C411yescharacteristic
739C2×C4C2×(C2×D71)⋊C411yescharacteristic
740C2×C4C2×(C2×D71)⋊C411yescharacteristic
741C2×C4C2×(C2×D71)⋊C411yescharacteristic
742C2×C4C2×(C2×D71)⋊C411yescharacteristic
743C2×C4C22×C4×D7111yescharacteristic
744C2×C4C22×C22⋊D7111yescharacteristic
745C8—44no—
746C22—24no—
747C22—24no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—42no—
771C22—42no—
772C22—2842no—
773C22—2842no—
774C22—2842no—
775C22—5684no—
776C22C2×#1455604212yes—
777C22#1798600112yes—
778C22#1798600112yes—
779C22#1798601512yes—
780C22C22×(C2×D71)⋊C411yescharacteristic
781C22C2×#1455615611yescharacteristic
782C22C2×#1455616111yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—2842no—
790C4—2842no—
791C4—2842no—
792C4—5684no—
793C4C2×#1455604212yes—
794C4C2×#1455604212yes—
795C2—21no—
796C2—22no—
797C2—22no—
798C2—21no—
799C2—22no—
800C2—22no—
801C2—41no—
802C2—41no—
803C2—5682no—
804C2C22×#1455604211yescharacteristic
805C2C2×#1798600111yescharacteristic
806C2C2×#1798601511yescharacteristic
subgroupG/H
centerC22C22×(C2×D71)⋊C4
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC2×#407×C71C2
socleC22×C71C22×C22⋊C4
prime radicalC2×#17986510C2
cosocleC22×C4×C71C24
hypercenterC2×#407D71
hypocenterC71#17592
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#17985859C2semidirect
3. #22586913C2semidirect
4. #22586909C2semidirect
5. #22586884C2semidirect
6. #22586845C2semidirect
7. C2×#407×C71C2semidirect
8. C22×#11765865C4semidirect
13. #17986510C4semidirect
14. #17986510C4semidirect
18. C2×#14556107C4semidirect
20. C2×#14556102C4semidirect
25. C2×#14556087C4semidirect
31. #17985859C22semidirect
32. C2×C71⋊#95C22semidirect
33. #17985737C22semidirect
34. #17985734C22semidirect
39. #407×C71C22semidirect
40. #407×C71C22semidirect
47. C2×#11765865C2×C4semidirect
48. C22×Dic142C2×C4semidirect
49. C22×D284C2×C4semidirect
64. #14556107C2×C4semidirect
65. #14556107C2×C4semidirect
72. #14556102C2×C4semidirect
73. #14556102C2×C4semidirect
90. #14556087C2×C4semidirect
94. C2×C4⋊Dic71C2×C4semidirect
95. C2×C4⋊Dic71C2×C4semidirect
405. C2×#407D71semidirect
411. C71#17592semidirect
436. #407C2×D71semidirect
437. #407C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179865102
C2×#179858592
#225869132
#225869092
#225868842
#225868452
C2×#407×C712
#1759271