Finite Group Databasebeta

← #31918945

Subgroups — #31918945

Order 18176.

2882 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D71C211yesmaximal, characteristic
2C2×#17985878C212yesmaximal
3C2×C4×C22⋊Dic71C212yesmaximal, complemented
4C2×#17985846C211yesmaximal, characteristic, complemented
5#22586576C212yesmaximal, complemented
6#22586571C212yesmaximal, complemented
7#22586566C211yesmaximal, characteristic, complemented
8#22586563C211yesmaximal, characteristic, complemented
9(C2×D71)⋊#95C211yesmaximal, characteristic, complemented
10#95×Dic71C211yesmaximal, characteristic, complemented
11C22×#95×C71C211yesmaximal, characteristic, complemented
12C23×C22⋊D71C2211yescharacteristic
13C23×C4×D71C2211yescharacteristic
14C2×C4×C22⋊D71—28no—
15C2×C4×C22⋊D71C418yescomplemented
16C22×Dic71⋊C4C2211yescharacteristic
17C22×C22⋊Dic71C2212yes—
18C22×C22⋊Dic71C2211yescharacteristic
19C22×(C2×D71)⋊C4C2211yescharacteristic
20C22×(C2×D71)⋊C4C2212yes—
21C22×(C2×D71)⋊C4C2212yes—
22C22×C4×Dic71C2212yes—
23C22×C4×Dic71C2212yes—
24C22×C4×Dic71C2211yescharacteristic
25#17985878C4116yescomplemented
26C4×C22⋊Dic71—28no—
27#17985846—24no—
28C2×C71⋊#95C2211yescharacteristic
29C2×C71⋊#95C2212yes—
30C2×C71⋊#95C2211yescharacteristic
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2212yes—
35C24×C4×C71C2211yescharacteristic
36C24×C4×C71C2212yes—
37C2×#95×C71—24no—
38C2×#95×C71C2211yescharacteristic
39C2×#95×C71C2212yes—
40C2×#95×C71C2211yescharacteristic
41C24×D71C2311yescharacteristic
42C22×C22⋊D71—24no—
43C22×C22⋊D71—22no—
44C22×C22⋊D71—22no—
45C22×C22⋊D71C2×C418yes—
46C22×C22⋊D71C2×C414yes—
47C23×Dic71C2312yes—
48C23×Dic71C2312yes—
49C23×Dic71C2311yescharacteristic
50C23×Dic71C2311yescharacteristic
51C23×Dic71C2311yescharacteristic
52C22×C4×D71—24no—
53C22×C4×D71—22no—
54C22×C4×D71—22no—
55C22×C4×D71—42no—
56C22×C4×D71C2×C414yescomplemented
57C4×C22⋊D71—232no—
58C2×Dic71⋊C4—24no—
59C2×Dic71⋊C4C2×C414yescomplemented
60C2×C22⋊Dic71—24no—
61C2×C22⋊Dic71—24no—
62C2×C22⋊Dic71C2×C414yes—
63C2×C22⋊Dic71C2×C418yescomplemented
64C2×C22⋊Dic71D418yes—
65C2×(C2×D71)⋊C4—24no—
66C2×(C2×D71)⋊C4—24no—
67C2×(C2×D71)⋊C4—24no—
68C2×(C2×D71)⋊C4—42no—
69C2×(C2×D71)⋊C4—42no—
70C2×(C2×D71)⋊C4C2×C418yescomplemented
71C2×(C2×D71)⋊C4C2×C414yescomplemented
72C2×(C2×D71)⋊C4C2×C418yescomplemented
73C2×C4×Dic71—24no—
74C2×C4×Dic71—24no—
75C2×C4×Dic71—24no—
76C2×C4×Dic71—24no—
77C2×C4×Dic71—24no—
78C2×C4×Dic71—42no—
79C2×C4×Dic71—42no—
80C2×C4×Dic71C2×C414yescomplemented
81C71⋊#95—24no—
82C71⋊#95—24no—
83C71⋊#95—22no—
84C71⋊#95—22no—
85C71⋊#95—42no—
86C71⋊#95C2×C418yescomplemented
87C71⋊#95C2×C418yescomplemented
88C25×C71C2311yescharacteristic
89C23×C4×C71—24no—
90C23×C4×C71—24no—
91C23×C4×C71—24no—
92C23×C4×C71—22no—
93C23×C4×C71—24no—
94C23×C4×C71—22no—
95C23×C4×C71—24no—
96C23×C4×C71—42no—
97C23×C4×C71—42no—
98C23×C4×C71—42no—
99C23×C4×C71C2×C414yes—
100C23×C4×C71C2×C418yescomplemented
101C23×C4×C71C2312yes—
102C23×C4×C71C2311yescharacteristic
103C23×C4×C71C2311yescharacteristic
104C23×C4×C71C2312yes—
105#95×C71—22no—
106#95×C71—24no—
107#95×C71D414yescomplemented
108C23×D71—22no—
109C23×D71—21no—
110C23×D71—21no—
111C23×D71—21no—
112C23×D71—21no—
113C23×D71—22no—
114C23×D71—22no—
115C23×D71—21no—
116C23×D71—21no—
117C23×D71C22×C412yes—
118C23×D71C22×C414yes—
119C2×C22⋊D71—28no—
120C2×C22⋊D71—28no—
121C2×C22⋊D71—216no—
122C2×C22⋊D71—216no—
123C2×C22⋊D71C42116yescomplemented
124C22×Dic71—21no—
125C22×Dic71—22no—
126C22×Dic71—21no—
127C22×Dic71—21no—
128C22×Dic71—21no—
129C22×Dic71—22no—
130C22×Dic71—22no—
131C22×Dic71—21no—
132C22×Dic71—21no—
133C22×Dic71—22no—
134C22×Dic71—22no—
135C22×Dic71—22no—
136C22×Dic71—22no—
137C22×Dic71—22no—
138C22×Dic71—22no—
139C22×Dic71—22no—
140C22×Dic71—22no—
141C22×Dic71—22no—
142C22×Dic71—22no—
143C22×Dic71—22no—
144C22×Dic71—22no—
145C22×Dic71C22×C414yes—
146C22×Dic71C22×C414yes—
147C22×Dic71C22×C414yes—
148C22×Dic71C22×C412yes—
149C22×Dic71C22×C412yes—
150C22×Dic71C22×C412yes—
151C22×Dic71C2×D414yes—
152C22×Dic71C2×D414yes—
153C2×C4×D71—28no—
154C2×C4×D71—28no—
155C2×C4×D71—44no—
156C2×C4×D71—48no—
157C2×C4×D71—48no—
158Dic71⋊C4—28no—
159C22⋊Dic71—216no—
160C22⋊Dic71C22⋊C4116yescomplemented
161(C2×D71)⋊C4—216no—
162(C2×D71)⋊C4—28no—
163(C2×D71)⋊C4—48no—
164C4×Dic71—28no—
165C4×Dic71—48no—
166C4×Dic71—48no—
167C24×C71—21no—
168C24×C71—21no—
169C24×C71—22no—
170C24×C71—22no—
171C24×C71—21no—
172C24×C71—21no—
173C24×C71C22×C412yes—
174C24×C71C22×C414yes—
175C24×C71C2×D414yes—
176C24×C71#4112yes—
177C24×C71#4112yes—
178C24×C71C2411yescharacteristic
179C22×C4×C71—22no—
180C22×C4×C71—22no—
181C22×C4×C71—22no—
182C22×C4×C71—22no—
183C22×C4×C71—22no—
184C22×C4×C71—22no—
185C22×C4×C71—28no—
186C22×C4×C71—216no—
187C22×C4×C71—21no—
188C22×C4×C71—22no—
189C22×C4×C71—22no—
190C22×C4×C71—22no—
191C22×C4×C71—22no—
192C22×C4×C71—21no—
193C22×C4×C71—22no—
194C22×C4×C71—22no—
195C22×C4×C71—22no—
196C22×C4×C71—22no—
197C22×C4×C71—28no—
198C22×C4×C71—216no—
199C22×C4×C71—44no—
200C22×C4×C71—48no—
201C22×C4×C71—48no—
202C22×C4×C71—48no—
203C22×C4×C71—48no—
204C22×C4×C71—48no—
205C22×C4×C71—48no—
206C22×C4×C71—48no—
207C22×C4×C71C22×C412yes—
208C22×C4×C71C22×C414yes—
209C22×C4×C71C22×C412yes—
210C22×C4×C71C22×C414yes—
211C22×C4×C71C2×D412yes—
212C22×C4×C71C2×D414yes—
213C22×C4×C71#4112yes—
214C22×C4×C71#4114yes—
215C23×C71—22no—
216C23×C71—24no—
217C23×C71—22no—
218C23×C71—24no—
219C23×C71—22no—
220C23×C71—24no—
221C23×C71—22no—
222C23×C71—24no—
223C23×C71—24no—
224C23×C71—22no—
225C23×C71—24no—
226C23×C71—24no—
227C23×C71—24no—
228C23×C71—22no—
229C23×C71—24no—
230C23×C71—22no—
231C23×C71—22no—
232C23×C71—24no—
233C23×C71C2×C4214yes—
234C23×C71C2×C22⋊C414yes—
235C23×C71#11714yes—
236C23×C71C4×D418yes—
237C23×C71C4×D418yes—
238C23×C71C23×C411yescharacteristic
239C23×C71C23×C412yes—
240C23×C71C22×D412yes—
241C23×C71C22×D411yescharacteristic
242C23×C71C2×#4111yescharacteristic
243C23×C71C2×#4111yescharacteristic
244C23×C71C2×#4112yes—
245C23×C71C2×#4111yescharacteristic
246C23×C71H(5,𝔽2)12yes—
247C23×C71H(5,𝔽2)11yescharacteristic
248C23×C712−1+411yescharacteristic
249C22×D71—22no—
250C22×D71—22no—
251C22×D71—24no—
252C22×D71—22no—
253C22×D71—24no—
254C22×D71—24no—
255C22×D71—22no—
256C22×D71—24no—
257C22×D71—24no—
258C22×D71—22no—
259C22×D71—22no—
260C22×D71—24no—
261C22×D71—42no—
262C22×D71—42no—
263C22×D71—42no—
264C22×D71—41no—
265C22×D71—42no—
266C22×D71—41no—
267C22×D71—42no—
268C22×D71—41no—
269C22×D71—41no—
270C22×D71—42no—
271C22×D71C2×C4214yes—
272C2×C4×C71—22no—
273C2×C4×C71—24no—
274C2×C4×C71—24no—
275C2×C4×C71—22no—
276C2×C4×C71—24no—
277C2×C4×C71—24no—
278C2×C4×C71—24no—
279C2×C4×C71—24no—
280C2×C4×C71—24no—
281C2×C4×C71—24no—
282C2×C4×C71—22no—
283C2×C4×C71—24no—
284C2×C4×C71—22no—
285C2×C4×C71—24no—
286C2×C4×C71—22no—
287C2×C4×C71—24no—
288C2×C4×C71—416no—
289C2×C4×C71—432no—
290C2×C4×C71—42no—
291C2×C4×C71—42no—
292C2×C4×C71—42no—
293C2×C4×C71—42no—
294C2×C4×C71—42no—
295C2×C4×C71—42no—
296C2×C4×C71C4×D414yes—
297C2×C4×C71C4×D418yescomplemented
298C22⋊D71—232no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—24no—
303C2×Dic71—24no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—24no—
308C2×Dic71—24no—
309C2×Dic71—24no—
310C2×Dic71—24no—
311C2×Dic71—24no—
312C2×Dic71—24no—
313C2×Dic71—24no—
314C2×Dic71—24no—
315C2×Dic71—24no—
316C2×Dic71—24no—
317C2×Dic71—42no—
318C2×Dic71—42no—
319C2×Dic71—42no—
320C2×Dic71—42no—
321C2×Dic71—42no—
322C2×Dic71—42no—
323C2×Dic71—42no—
324C2×Dic71—42no—
325C2×Dic71C2×C4214yes—
326C2×Dic71C2×C22⋊C414yes—
327C2×Dic71C2×C22⋊C414yes—
328C4×D71—416no—
329C22×C71—24no—
330C22×C71—24no—
331C22×C71—24no—
332C22×C71—24no—
333C22×C71—28no—
334C22×C71—28no—
335C22×C71—28no—
336C22×C71—28no—
337C22×C71—24no—
338C22×C71—24no—
339C22×C71C4×C22⋊C418yescomplemented
340C22×C71C22×C4211yescharacteristic
341C22×C71C22×C22⋊C411yescharacteristic
342C22×C71C2×#11711yescharacteristic
343C22×C71C2×C4×D412yes—
344C22×C71C2×C4×D411yescharacteristic
345C22×C71C2×C4×D412yes—
346C22×C71C2×C4×D412yes—
347C22×C71C4×#4111yescharacteristic
348C22×C71C4×#4112yes—
349C22×C71#51811yescharacteristic
350C22×C71#51812yes—
351C22×C71#52011yescharacteristic
352C22×C71#52012yes—
353C22×C71D4212yes—
354C22×C71#54612yes—
355C22×C71#54612yes—
356C22×C71#54611yescharacteristic
357C22×C71#54712yes—
358C22×C71#54811yescharacteristic
359C22×C71#55112yes—
360C22×C71#55211yescharacteristic
361C22×C71#55311yescharacteristic
362C22×C71#55312yes—
363C2×D71—24no—
364C2×D71—24no—
365C2×D71—24no—
366C2×D71—42no—
367C2×D71—42no—
368C2×D71—42no—
369C2×D71—42no—
370C2×D71—44no—
371C2×D71—44no—
372C2×D71—44no—
373C2×D71—44no—
374C4×C71—24no—
375C4×C71—28no—
376C4×C71—42no—
377C4×C71—44no—
378Dic71—24no—
379Dic71—24no—
380Dic71—24no—
381Dic71—44no—
382Dic71—44no—
383#13813—711nomaximal, Sylow
384C2×C71—28no—
385C2×C71C2×C4×C22⋊C411yescharacteristic
386C2×C71C42×D411yescharacteristic
387C2×C71#227511yescharacteristic
388C2×C71D4×C22⋊C411yescharacteristic
389C2×C71#233911yescharacteristic
390C2×C71#235211yescharacteristic
391C2×C71#235311yescharacteristic
392C2×C71#235812yes—
393C2×C71#235912yes—
394C2×C71#236112yes—
395C2×C71#236412yes—
396D71—44no—
397C22×C4×D4—711no—
398C2×#386—712no—
399C2×C4×C22⋊C4—711no—
400C2×C4×C22⋊C4—712no—
401C22×#95D7111yescharacteristic, complemented
402#1437—712no—
403#1436—712no—
404#1434—711no—
405C22⋊#95—711no—
406C22⋊#95—711no—
407C4×#95—711no—
408C71#1381311yescharacteristic, complemented, Sylow
409C23×D4—711no—
410C24×C4—711no—
411C24×C4C2×D7111yescharacteristic
412C24×C4C2×D7112yes—
413C2×C4×D4—718no—
414C2×C4×D4—1428no—
415C22×C4⋊C4—711no—
416C22×C22⋊C4—712no—
417C22×C22⋊C4—711no—
418C22×C22⋊C4—712no—
419C22×C22⋊C4—711no—
420C22×C22⋊C4—712no—
421C22×C42—712no—
422C22×C42—712no—
423C22×C42—711no—
424#386—7116no—
425C4×C22⋊C4—1428no—
426C4×C22⋊C4—1424no—
427C2×#95—24no—
428C2×#95—712no—
429C2×#95—712no—
430C2×#95—712no—
431C2×#95—711no—
432C2×#95—711no—
433C2×#95—712no—
434C2×#95—712no—
435C2×#95C2×D7111yescharacteristic
436C2×#95C2×D7112yes—
437C2×#95C2×D7111yescharacteristic
438C25—711no—
439C25C22×D7111yescharacteristic
440C22×D4—714no—
441C22×D4—718no—
442C22×D4—1424no—
443C22×D4—1422no—
444C22×D4—1422no—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—22no—
449C23×C4—24no—
450C23×C4—22no—
451C23×C4—24no—
452C23×C4—42no—
453C23×C4—42no—
454C23×C4—42no—
455C23×C4—2842no—
456C23×C4—714no—
457C23×C4—711no—
458C23×C4—711no—
459C23×C4—711no—
460C23×C4—712no—
461C23×C4—712no—
462C23×C4—1424no—
463C23×C4—1422no—
464C23×C4—1422no—
465C23×C4C4×D7114yes—
466C23×C4C4×D7118yescomplemented
467C23×C4C22×D7111yescharacteristic
468C23×C4C22×D7112yes—
469C23×C4C22×D7112yes—
470C23×C4C22×D7111yescharacteristic
471C4×D4—14232no—
472C2×C4⋊C4—714no—
473C2×C4⋊C4—1424no—
474C2×C22⋊C4—2842no—
475C2×C22⋊C4—2842no—
476C2×C22⋊C4—718no—
477C2×C22⋊C4—714no—
478C2×C22⋊C4—718no—
479C2×C22⋊C4—718no—
480C2×C22⋊C4—714no—
481C2×C22⋊C4—718no—
482C2×C22⋊C4—1424no—
483C2×C22⋊C4—1424no—
484C2×C22⋊C4—1424no—
485C2×C22⋊C4—1424no—
486C2×C22⋊C4—1424no—
487C2×C42—2842no—
488C2×C42—2842no—
489C2×C42—714no—
490C2×C42—1424no—
491C2×C42—1424no—
492C2×C42—1424no—
493C2×C42—1424no—
494C2×C42—1424no—
495#95—22no—
496#95—24no—
497#95—2842no—
498#95—718no—
499#95—718no—
500#95—1424no—
501#95—1424no—
502#95—1422no—
503#95—1422no—
504#95C22⋊D7114yescomplemented
505C24—21no—
506C24—21no—
507C24—22no—
508C24—22no—
509C24—21no—
510C24—21no—
511C24—714no—
512C24—712no—
513C24—1422no—
514C24—1421no—
515C24—1421no—
516C24—1422no—
517C24—1421no—
518C24—1421no—
519C24—1421no—
520C24—1422no—
521C24—1421no—
522C24C2×C4×D7112yes—
523C24C2×C4×D7114yes—
524C24D4×D7114yes—
525C24#1176586412yes—
526C24#1176586612yes—
527C24C23×D7111yescharacteristic
528C2×D4—7116no—
529C2×D4—1428no—
530C2×D4—1428no—
531C2×D4—14216no—
532C2×D4—14216no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—216no—
551C22×C4—28no—
552C22×C4—216no—
553C22×C4—44no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—2848no—
562C22×C4—2848no—
563C22×C4—2844no—
564C22×C4—714no—
565C22×C4—712no—
566C22×C4—712no—
567C22×C4—712no—
568C22×C4—714no—
569C22×C4—714no—
570C22×C4—714no—
571C22×C4—714no—
572C22×C4—1428no—
573C22×C4—1422no—
574C22×C4—1422no—
575C22×C4—1422no—
576C22×C4—1422no—
577C22×C4—1422no—
578C22×C4—1422no—
579C22×C4—1422no—
580C22×C4—1422no—
581C22×C4—1422no—
582C22×C4—1422no—
583C22×C4—1422no—
584C22×C4—1422no—
585C22×C4—1428no—
586C22×C4—1422no—
587C22×C4—1421no—
588C22×C4—1421no—
589C22×C4—1422no—
590C22×C4—1421no—
591C22×C4—1421no—
592C22×C4—1421no—
593C22×C4—1422no—
594C22×C4—1421no—
595C22×C4C2×C4×D7114yes—
596C22×C4C2×C4×D7112yes—
597C22×C4C2×C4×D7112yes—
598C22×C4C2×C4×D7114yes—
599C22×C4C2×C22⋊D7112yes—
600C22×C4C2×C22⋊D7114yes—
601C22×C4#1176586512yes—
602C22×C4#1176586514yes—
603C4⋊C4—1428no—
604C22⋊C4—2848no—
605C22⋊C4—7116no—
606C22⋊C4—1428no—
607C22⋊C4—14216no—
608C22⋊C4—14216no—
609C42—2848no—
610C42—2848no—
611C42—1428no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—22no—
616C23—24no—
617C23—22no—
618C23—24no—
619C23—22no—
620C23—22no—
621C23—24no—
622C23—22no—
623C23—24no—
624C23—22no—
625C23—24no—
626C23—22no—
627C23—24no—
628C23—22no—
629C23—24no—
630C23—2842no—
631C23—2842no—
632C23—2842no—
633C23—2841no—
634C23—2842no—
635C23—2841no—
636C23—2842no—
637C23—2841no—
638C23—2841no—
639C23—2842no—
640C23—714no—
641C23—1422no—
642C23—1422no—
643C23—1424no—
644C23—1424no—
645C23—1422no—
646C23—1424no—
647C23—1422no—
648C23—1424no—
649C23—1424no—
650C23—1422no—
651C23—1422no—
652C23—1424no—
653C23C42×D7114yes—
654C23C22⋊C4×D7114yes—
655C23#1455608614yes—
656C23(C22⋊D71)⋊C418yes—
657C23#1455609018yes—
658C23C22×C4×D7111yescharacteristic
659C23C22×C4×D7112yes—
660C23C2×D4×D7112yes—
661C23C22×C22⋊D7111yescharacteristic
662C23C2×#1176586411yescharacteristic
663C23C2×#1176586511yescharacteristic
664C23C2×#1176586512yes—
665C23C2×#1176586611yescharacteristic
666C23#1455617312yes—
667C23#1455617311yescharacteristic
668C23#1455617611yescharacteristic
669D4—14232no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—432no—
687C2×C4—416no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—28416no—
695C2×C4—2842no—
696C2×C4—2842no—
697C2×C4—2842no—
698C2×C4—2842no—
699C2×C4—2842no—
700C2×C4—2842no—
701C2×C4—2842no—
702C2×C4—2842no—
703C2×C4—714no—
704C2×C4—714no—
705C2×C4—714no—
706C2×C4—1424no—
707C2×C4—1424no—
708C2×C4—1424no—
709C2×C4—1424no—
710C2×C4—1424no—
711C2×C4—1424no—
712C2×C4—1424no—
713C2×C4—1424no—
714C2×C4—1424no—
715C2×C4—1424no—
716C2×C4—1422no—
717C2×C4—1422no—
718C2×C4—1424no—
719C2×C4—1422no—
720C2×C4—1424no—
721C2×C4—1422no—
722C2×C4—1422no—
723C2×C4—1422no—
724C2×C4C4×C22⋊D7114yes—
725C2×C4C4×C22⋊D7118yescomplemented
726C22—24no—
727C22—24no—
728C22—28no—
729C22—28no—
730C22—28no—
731C22—28no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—2842no—
737C22—2842no—
738C22—2844no—
739C22—2844no—
740C22—2844no—
741C22—2844no—
742C22—2842no—
743C22—2842no—
744C22—1424no—
745C22—1424no—
746C22—1424no—
747C22#1798584618yescomplemented
748C22C2×C42×D7111yescharacteristic
749C22C2×C22⋊C4×D7111yescharacteristic
750C22C2×#1455608611yescharacteristic
751C22C2×(C22⋊D71)⋊C412yes—
752C22C2×C4×C22⋊D7111yescharacteristic
753C22C2×C4×C22⋊D7112yes—
754C22C2×#1455609012yes—
755C22C4×#1176586511yescharacteristic
756C22C4×#1176586512yes—
757C22#1798647211yescharacteristic
758C22#1798647212yes—
759C22#1798648011yescharacteristic
760C22#1798648012yes—
761C22D4×C22⋊D7112yes—
762C22#1798663912yes—
763C22#1798663912yes—
764C22#1798664311yescharacteristic
765C22#1798665012yes—
766C22#1798666011yescharacteristic
767C22#1798667512yes—
768C22#1798668411yescharacteristic
769C22#1798669711yescharacteristic
770C22#1798669712yes—
771C4—28no—
772C4—24no—
773C4—44no—
774C4—42no—
775C4—2844no—
776C4—2844no—
777C4—1424no—
778C4—1424no—
779C4—1424no—
780C2—28no—
781C2—2844no—
782C2C2×#1798584611yescharacteristic
783C2C42×C22⋊D7111yescharacteristic
784C2#2259069811yescharacteristic
785C2C22⋊C4×C22⋊D7111yescharacteristic
786C2#2259116711yescharacteristic
787C2#2259126511yescharacteristic
788C2#2259127611yescharacteristic
789C2#2259131912yes—
790C2#2259132812yes—
791C2#2259135612yes—
792C2#2259138712yes—
subgroupG/H
center, FrattiniC24C23×D71
commutatorC22×C71C22×C42
FittingC22×#95×C71C2
socle, cosocleC24×C71C24
prime radicalC23×C22⋊D71C22
hypercenterC22×#95D71
hypocenterC71#13813
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊Dic71C2semidirect
4. C2×#17985846C2semidirect
5. #22586576C2semidirect
6. #22586571C2semidirect
7. #22586566C2semidirect
8. #22586563C2semidirect
9. (C2×D71)⋊#95C2semidirect
10. #95×Dic71C2semidirect
11. C22×#95×C71C2semidirect
15. C2×C4×C22⋊D71C4semidirect
25. #17985878C4semidirect
56. C22×C4×D71C2×C4semidirect
59. C2×Dic71⋊C4C2×C4semidirect
63. C2×C22⋊Dic71C2×C4semidirect
70. C2×(C2×D71)⋊C4C2×C4semidirect
71. C2×(C2×D71)⋊C4C2×C4semidirect
72. C2×(C2×D71)⋊C4C2×C4semidirect
80. C2×C4×Dic71C2×C4semidirect
86. C71⋊#95C2×C4semidirect
87. C71⋊#95C2×C4semidirect
100. C23×C4×C71C2×C4semidirect
107. #95×C71D4semidirect
123. C2×C22⋊D71C42semidirect
160. C22⋊Dic71C22⋊C4semidirect
297. C2×C4×C71C4×D4semidirect
339. C22×C71C4×C22⋊C4semidirect
401. C22×#95D71semidirect
408. C71#13813semidirect
466. C23×C4C4×D71semidirect
504. #95C22⋊D71semidirect
725. C2×C4C4×C22⋊D71semidirect
747. C22#17985846semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D712
C2×#179858782
C2×C4×C22⋊Dic712
C2×#179858462
#225865762
#225865712
#225865662
#225865632
(C2×D71)⋊#952
#95×Dic712
C22×#95×C712
#1381371