Finite Group Databasebeta

← #31964617

Subgroups — #31964617

Order 18176.

1574 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986510C211yesmaximal, characteristic
2C2×C4×C22⋊Dic71C211yesmaximal, characteristic, complemented
3#22586861C212yesmaximal, complemented
4#22586857C212yesmaximal, complemented
5#22586845C214yesmaximal, complemented
6#22586832C214yesmaximal, 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×C22⋊Dic71—21no—
27C22×C4×Dic71—21no—
28C4×C22⋊Dic71—21no—
29C4×C22⋊Dic71—21no—
30C4×C22⋊Dic71C2212yes—
31C4×C22⋊Dic71C2212yescomplemented
32C2×C71⋊#95C2212yescomplemented
33#17985737C2218yescomplemented
34#17985734C2218yescomplemented
35C24×C4×C71C2211yescharacteristic
36C22×M16×C71—21no—
37#407×C71—21no—
38#407×C71—21no—
39#407×C71C2212yes—
40#407×C71C2212yescomplemented
41C2×C22⋊C8×C71—21no—
42C2×C22⋊C8×C71C2212yescomplemented
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⋊Dic71C2×C411yescharacteristic, complemented
92C2×C4⋊Dic71C2×C411yescharacteristic, complemented
93C2×Dic71⋊C4—21no—
94C2×Dic71⋊C4—21no—
95C2×C22⋊Dic71—28no—
96C2×C22⋊Dic71—21no—
97C2×C22⋊Dic71—21no—
98C2×C22⋊Dic71—22no—
99C2×C22⋊Dic71—22no—
100C2×C22⋊Dic71—21no—
101C2×(C2×D71)⋊C4—21no—
102C2×(C2×D71)⋊C4—21no—
103C2×C4×Dic71—21no—
104C2×C4×Dic71—22no—
105C2×C4×Dic71—22no—
106C2×C4×Dic71—44no—
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—44no—
153C22×Dic71—28no—
154C22×Dic71—21no—
155C22×Dic71—21no—
156C22×Dic71—21no—
157C22×Dic71—24no—
158C22×Dic71—44no—
159C22×Dic71—44no—
160C2×C4×D71—22no—
161C2×C4×D71—22no—
162C2×C4×D71—44no—
163C4⋊Dic71—21no—
164C4⋊Dic71—21no—
165C4⋊Dic71C22×C412yes—
166C4⋊Dic71C22×C412yes—
167Dic71⋊C4—22no—
168Dic71⋊C4—22no—
169Dic71⋊C4—22no—
170Dic71⋊C4—22no—
171C22⋊Dic71—28no—
172C22⋊Dic71—28no—
173C22⋊Dic71—22no—
174C22⋊Dic71—22no—
175C22⋊Dic71—22no—
176C22⋊Dic71—22no—
177C22⋊Dic71—22no—
178C22⋊Dic71—22no—
179(C2×D71)⋊C4—22no—
180(C2×D71)⋊C4—22no—
181(C2×D71)⋊C4—22no—
182(C2×D71)⋊C4—22no—
183C4×Dic71—22no—
184C4×Dic71—22no—
185C4×Dic71—44no—
186C4×Dic71—44no—
187C24×C71—24no—
188C24×C71—42no—
189C24×C71—42no—
190C24×C71C22⋊C411yescharacteristic
191C24×C71C22⋊C411yescharacteristic
192C24×C71C22⋊C411yescharacteristic
193C24×C71C22⋊C411yescharacteristic
194C24×C71C2×D411yescharacteristic
195C24×C71C2×D411yescharacteristic
196C24×C71C2×D411yescharacteristic
197C22×C4×C71—24no—
198C22×C4×C71—24no—
199C22×C4×C71—24no—
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×C71—42no—
208C22×C4×C71—42no—
209C22×C4×C71—42no—
210C22×C4×C71—42no—
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×C71C22×C411yescharacteristic
226C22×C4×C71C22×C411yescharacteristic
227C22×C4×C71C22×C411yescharacteristic
228C22×C4×C71C22×C411yescharacteristic
229C22×C4×C71C2×D411yescharacteristic
230C22×C4×C71C2×D411yescharacteristic
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×C71C2411yescharacteristic
239M16×C71—44no—
240M16×C71—44no—
241C2×C8×C71—24no—
242C2×C8×C71—44no—
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—22no—
253C23×C71—22no—
254C23×C71—22no—
255C23×C71—41no—
256C23×C71—41no—
257C23×C71—41no—
258C23×C71—41no—
259C23×C71—41no—
260C23×C71—41no—
261C23×C71—41no—
262C23×C71—41no—
263C23×C71—416no—
264C23×C71#10414yes—
265C23×C71C2×C22⋊C411yescharacteristic
266C23×C71C2×C22⋊C411yescharacteristic
267C23×C71C2×C22⋊C411yescharacteristic
268C23×C71C2×C22⋊C411yescharacteristic
269C23×C71C2×C22⋊C411yescharacteristic
270C23×C71C2×C22⋊C411yescharacteristic
271C23×C71C22×D411yescharacteristic
272C22×D71—22no—
273C22×D71—42no—
274C22×D71—42no—
275C22×D71—42no—
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—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
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—41no—
301C2×C4×C71—41no—
302C2×C4×C71—41no—
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—28no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—44no—
323C2×Dic71—42no—
324C2×Dic71—416no—
325C2×Dic71—42no—
326C2×Dic71—44no—
327C2×Dic71—42no—
328D284—42no—
329D284—42no—
330C4×D71—44no—
331C4×D71—44no—
332Dic142—42no—
333Dic142—42no—
334C8×C71—44no—
335C22×C71—28no—
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—21no—
349C22×C71—21no—
350C22×C71—21no—
351C22×C71—21no—
352C22×C71—44no—
353C22×C71—44no—
354C22×C71—44no—
355C22×C71—44no—
356C22×C71—44no—
357C22×C71—44no—
358C22×C71C2×#9912yes—
359C22×C71C2×#10412yes—
360C22×C71C2×#10412yes—
361C22×C71C2×#10412yes—
362C22×C71C22×C22⋊C411yescharacteristic
363C22×C71#57512yes—
364C2×D71—42no—
365C2×D71—42no—
366C2×D71—42no—
367C2×D71—84no—
368C4×C71—21no—
369C4×C71—21no—
370C4×C71—21no—
371C4×C71—21no—
372C4×C71—21no—
373C4×C71—21no—
374C4×C71C2×#9912yes—
375C4×C71C2×#9912yes—
376Dic71—48no—
377Dic71—42no—
378Dic71—42no—
379Dic71—42no—
380#17542—711nomaximal, Sylow
381C2×C71—22no—
382C2×C71—22no—
383C2×C71—22no—
384C2×C71—22no—
385C2×C71—22no—
386C2×C71—41no—
387C2×C71—41no—
388C2×C71C22×#9911yescharacteristic
389C2×C71#289611yescharacteristic
390C2×C71C22×#10411yescharacteristic
391D71—82no—
392C2×#525—711no—
393C2×#407D7111yescharacteristic, complemented
394C2×C4×C22⋊C4—711no—
395#1508—712no—
396#1507—712no—
397#1504—714no—
398#1501—714no—
399C71#1754211yescharacteristic, complemented, Sylow
400C22×#41—711no—
401C24×C4C2×D7111yescharacteristic
402C22×M16—21no—
403#525—712no—
404#525—712no—
405#525—712no—
406#525—712no—
407#525—1421no—
408#525—1421no—
409#525—1421no—
410#525—1421no—
411C2×#123—1421no—
412C2×C22⋊Q8—711no—
413C2×C22⋊Q8—711no—
414C2×#121—711no—
415C2×#121—711no—
416C2×#120—1421no—
417C2×C4×D4—1421no—
418C2×C4×D4—1421no—
419C2×#117—711no—
420C22×C22⋊C4—1421no—
421C22×C42—1421no—
422#407—21no—
423#407—21no—
424#407C2×D7112yes—
425#407C2×D7112yescomplemented
426C2×C22⋊C8—21no—
427C2×C22⋊C8C2×D7112yescomplemented
428C4×C22⋊C4—712no—
429C4×C22⋊C4—712no—
430C4×C22⋊C4—1421no—
431C4×C22⋊C4—1421no—
432C2×#95—712no—
433#328—718no—
434#327—718no—
435C25D28411yescharacteristic
436C2×#41—2844no—
437C2×#41—712no—
438C2×#41—712no—
439C2×#41—1421no—
440C2×#41—1421no—
441C22×Q8—711no—
442C22×D4—711no—
443C22×D4—1421no—
444C22×D4—1421no—
445C22×D4—1421no—
446C23×C4—44no—
447C23×C4—1422no—
448C23×C4—1421no—
449C23×C4C4×D7111yescharacteristic
450C23×C4C4×D7111yescharacteristic
451C23×C4C4×D7111yescharacteristic
452C23×C4C4×D7111yescharacteristic
453C23×C4D28411yescharacteristic
454C23×C4D28411yescharacteristic
455C23×C4D28411yescharacteristic
456C23×C4C22⋊D7111yescharacteristic
457C23×C4C22⋊D7111yescharacteristic
458C23×C4C22⋊D7111yescharacteristic
459C23×C4C22⋊D7111yescharacteristic
460C23×C4C22×D7111yescharacteristic
461C23×C4C22×D7111yescharacteristic
462C23×C4C22×D7111yescharacteristic
463C2×M16—22no—
464C2×M16—22no—
465C2×M16—44no—
466C22×C8—22no—
467#123—1422no—
468#123—1422no—
469#123—1422no—
470#123—1422no—
471C22⋊Q8—712no—
472C22⋊Q8—712no—
473C22⋊Q8—712no—
474C22⋊Q8—712no—
475C22⋊Q8—1421no—
476C22⋊Q8—1421no—
477C22⋊Q8—1421no—
478C22⋊Q8—1421no—
479#121—712no—
480#121—712no—
481#121—712no—
482#121—712no—
483#121—1421no—
484#121—1421no—
485#121—1421no—
486#121—1421no—
487#120—1422no—
488#120—1422no—
489#120—1422no—
490#120—1422no—
491C4×D4—1422no—
492C4×D4—1422no—
493C4×D4—1422no—
494C4×D4—1422no—
495C4×D4—1422no—
496C4×D4—1422no—
497C4×D4—1422no—
498C4×D4—1422no—
499#117—712no—
500#117—712no—
501#117—1421no—
502#117—1421no—
503C2×C4⋊C4—711no—
504C2×C4⋊C4—711no—
505C2×C4⋊C4—1421no—
506C2×C4⋊C4—1421no—
507C2×C22⋊C4—1428no—
508C2×C22⋊C4—1421no—
509C2×C22⋊C4—1421no—
510C2×C22⋊C4—1422no—
511C2×C22⋊C4—1422no—
512C2×C22⋊C4—1421no—
513C2×C22⋊C4—1421no—
514C2×C22⋊C4—1421no—
515C2×C42—2844no—
516C2×C42—1422no—
517C2×C42—1422no—
518C2×C42—1421no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8—22no—
522C22⋊C8C22×D7114yes—
523#95—714no—
524#95—1422no—
525C24—24no—
526C24—42no—
527C24—42no—
528C24—1421no—
529C24(C2×D71)⋊C411yescharacteristic
530C24(C2×D71)⋊C411yescharacteristic
531C24(C2×D71)⋊C411yescharacteristic
532C24(C2×D71)⋊C411yescharacteristic
533C24C2×D28411yescharacteristic
534C24C2×D28411yescharacteristic
535C24C2×D28411yescharacteristic
536#41—2844no—
537#41—2844no—
538#41—2844no—
539#41—2844no—
540C2×Q8—2842no—
541C2×Q8—712no—
542C2×Q8—1421no—
543C2×D4—2842no—
544C2×D4—2844no—
545C2×D4—2844no—
546C2×D4—2844no—
547C2×D4—712no—
548C2×D4—1422no—
549C2×D4—1422no—
550C2×D4—1422no—
551C2×D4—1422no—
552C2×D4—1422no—
553C2×D4—1422no—
554C2×D4—1421no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—2844no—
570C22×C4—2844no—
571C22×C4—2844no—
572C22×C4—1428no—
573C22×C4—1424no—
574C22×C4—1421no—
575C22×C4—1421no—
576C22×C4—1421no—
577C22×C4—1422no—
578C22×C4—1422no—
579C22×C4(C2×D71)⋊C411yescharacteristic
580C22×C4(C2×D71)⋊C411yescharacteristic
581C22×C4(C2×D71)⋊C411yescharacteristic
582C22×C4(C2×D71)⋊C411yescharacteristic
583C22×C4(C2×D71)⋊C411yescharacteristic
584C22×C4(C2×D71)⋊C411yescharacteristic
585C22×C4(C2×D71)⋊C411yescharacteristic
586C22×C4(C2×D71)⋊C411yescharacteristic
587C22×C4(C2×D71)⋊C411yescharacteristic
588C22×C4(C2×D71)⋊C411yescharacteristic
589C22×C4(C2×D71)⋊C411yescharacteristic
590C22×C4(C2×D71)⋊C411yescharacteristic
591C22×C4C2×C4×D7111yescharacteristic
592C22×C4C2×C4×D7111yescharacteristic
593C22×C4C2×C4×D7111yescharacteristic
594C22×C4C2×C4×D7111yescharacteristic
595C22×C4C2×C4×D7111yescharacteristic
596C22×C4C2×C4×D7111yescharacteristic
597C22×C4C2×C22⋊D7111yescharacteristic
598C22×C4C2×C22⋊D7111yescharacteristic
599C22×C4C2×C22⋊D7111yescharacteristic
600C22×C4C2×C22⋊D7111yescharacteristic
601C22×C4C2×C22⋊D7111yescharacteristic
602C22×C4C2×C22⋊D7111yescharacteristic
603C22×C4C2×D28411yescharacteristic
604C22×C4C2×D28411yescharacteristic
605C22×C4C2×D28411yescharacteristic
606C22×C4C23×D7111yescharacteristic
607M16—44no—
608M16—44no—
609C2×C8—24no—
610C2×C8—44no—
611C4⋊C4—712no—
612C4⋊C4—712no—
613C4⋊C4—1422no—
614C4⋊C4—1422no—
615C4⋊C4—1422no—
616C4⋊C4—1422no—
617C4⋊C4—1421no—
618C4⋊C4—1421no—
619C22⋊C4—1428no—
620C22⋊C4—1428no—
621C22⋊C4—1422no—
622C22⋊C4—1422no—
623C22⋊C4—1422no—
624C22⋊C4—1422no—
625C22⋊C4—1422no—
626C22⋊C4—1422no—
627C22⋊C4—1422no—
628C22⋊C4—1422no—
629C22⋊C4—1422no—
630C22⋊C4—1422no—
631C42—2844no—
632C42—2844no—
633C42—1422no—
634C42—1422no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—416no—
656C23—2842no—
657C23—2842no—
658C23—2842no—
659C23—1422no—
660C23#1455605414yes—
661C23C2×(C2×D71)⋊C411yescharacteristic
662C23C2×(C2×D71)⋊C411yescharacteristic
663C23C2×(C2×D71)⋊C411yescharacteristic
664C23C2×(C2×D71)⋊C411yescharacteristic
665C23C2×(C2×D71)⋊C411yescharacteristic
666C23C2×(C2×D71)⋊C411yescharacteristic
667C23C22×D28411yescharacteristic
668Q8—2842no—
669Q8—2842no—
670D4—2842no—
671D4—2844no—
672D4—2844no—
673D4—2844no—
674D4—2844no—
675D4—2844no—
676D4—2844no—
677D4—2842no—
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—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—2844no—
706C2×C4—2844no—
707C2×C4—2842no—
708C2×C4—28416no—
709C2×C4—2842no—
710C2×C4—2842no—
711C2×C4—2844no—
712C2×C4—2844no—
713C2×C4—1428no—
714C2×C4—1422no—
715C2×C4—1422no—
716C2×C4—1422no—
717C2×C4#1455604214yes—
718C2×C4C2×(C2×D71)⋊C411yescharacteristic
719C2×C4C2×(C2×D71)⋊C411yescharacteristic
720C2×C4C2×(C2×D71)⋊C411yescharacteristic
721C2×C4C2×(C2×D71)⋊C411yescharacteristic
722C2×C4C2×(C2×D71)⋊C411yescharacteristic
723C2×C4C2×(C2×D71)⋊C411yescharacteristic
724C2×C4C22×C4×D7111yescharacteristic
725C2×C4C22×C22⋊D7111yescharacteristic
726C8—44no—
727C22—28no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—2842no—
751C22—2842no—
752C22—2842no—
753C22—5684no—
754C22C2×#1455604212yes—
755C22C2×#1455605412yes—
756C22C2×#1455605412yes—
757C22C2×#1455605412yes—
758C22C22×(C2×D71)⋊C411yescharacteristic
759C22#1798679912yes—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—2848no—
767C4—2842no—
768C4—2842no—
769C4—2842no—
770C4C2×#1455604212yes—
771C4C2×#1455604212yes—
772C2—22no—
773C2—22no—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—41no—
778C2—41no—
779C2—5682no—
780C2C22×#1455604211yescharacteristic
781C2#2259686011yescharacteristic
782C2C22×#1455605411yescharacteristic
subgroupG/H
centerC2×C4C2×(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#17542
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊Dic71C2semidirect
3. #22586861C2semidirect
4. #22586857C2semidirect
5. #22586845C2semidirect
6. #22586832C2semidirect
7. C2×#407×C71C2semidirect
8. C22×#11765865C4semidirect
13. #17986510C4semidirect
14. #17986510C4semidirect
18. C2×#14556107C4semidirect
20. C2×#14556102C4semidirect
25. C2×#14556087C4semidirect
31. C4×C22⋊Dic71C22semidirect
32. C2×C71⋊#95C22semidirect
33. #17985737C22semidirect
34. #17985734C22semidirect
40. #407×C71C22semidirect
42. C2×C22⋊C8×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
91. C2×C4⋊Dic71C2×C4semidirect
92. C2×C4⋊Dic71C2×C4semidirect
393. C2×#407D71semidirect
399. C71#17542semidirect
425. #407C2×D71semidirect
427. C2×C22⋊C8C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179865102
C2×C4×C22⋊Dic712
#225868612
#225868572
#225868452
#225868322
C2×#407×C712
#1754271