Finite Group Databasebeta

← #31918864

Subgroups — #31918864

Order 18176.

2574 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic71⋊C4C211yesmaximal, characteristic
2C2×#17985857C211yesmaximal, characteristic
3C2×#17985850C212yesmaximal, complemented
4C2×C22⋊C4×Dic71C211yesmaximal, characteristic
5C2×C22⋊C4×Dic71C211yesmaximal, characteristic
6C2×C4×C22⋊Dic71C211yesmaximal, characteristic
7#22586575C212yesmaximal, complemented
8#22586571C212yesmaximal, complemented
9Dic71⋊#95C212yesmaximal, complemented
10#22586562C211yesmaximal, characteristic
11C71×C22⋊#95C211yesmaximal, characteristic
12C24×Dic71C2211yescharacteristic
13C24×Dic71C2211yescharacteristic
14C22×Dic71⋊C4—28no—
15C22×Dic71⋊C4C418yescomplemented
16C22×Dic71⋊C4C2211yescharacteristic
17C22×Dic71⋊C4C2211yescharacteristic
18C22×Dic71⋊C4C2211yescharacteristic
19C22×Dic71⋊C4C2212yes—
20C22×Dic71⋊C4C2211yescharacteristic
21C22×C22⋊Dic71C2211yescharacteristic
22C22×C22⋊Dic71C2211yescharacteristic
23C22×C4×Dic71C2212yes—
24C22×C4×Dic71C2212yes—
25C22×C4×Dic71C2212yes—
26#17985857C418yescomplemented
27#17985850—28no—
28C22⋊C4×Dic71—24no—
29C22⋊C4×Dic71C418yescomplemented
30C4×C22⋊Dic71—24no—
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2212yes—
35C2×C71⋊#95C2212yes—
36C2×C71⋊#95C2212yes—
37C24×C4×C71C2211yescharacteristic
38C22×C22⋊C4×C71C2211yescharacteristic
39C22×C22⋊C4×C71C2211yescharacteristic
40C2×#95×C71C2212yes—
41C2×#95×C71C2212yes—
42C23×Dic71—24no—
43C23×Dic71—24no—
44C23×Dic71—24no—
45C23×Dic71—22no—
46C23×Dic71—22no—
47C23×Dic71—42no—
48C23×Dic71C2×C414yes—
49C23×Dic71C2×C414yes—
50C23×Dic71C2×C414yes—
51C23×Dic71C2×C414yes—
52C23×Dic71C2311yescharacteristic
53C23×Dic71C2312yes—
54C23×Dic71C2311yescharacteristic
55C23×Dic71C2311yescharacteristic
56C23×Dic71C2312yes—
57C23×Dic71C2311yescharacteristic
58C2×Dic71⋊C4—24no—
59C2×Dic71⋊C4—24no—
60C2×Dic71⋊C4—24no—
61C2×Dic71⋊C4—24no—
62C2×Dic71⋊C4—232no—
63C2×Dic71⋊C4—24no—
64C2×Dic71⋊C4C2×C414yes—
65C2×Dic71⋊C4C2×C414yes—
66C2×Dic71⋊C4C2×C414yes—
67C2×Dic71⋊C4C2×C414yes—
68C2×Dic71⋊C4C2×C418yescomplemented
69C2×Dic71⋊C4D418yes—
70C2×C22⋊Dic71—22no—
71C2×C22⋊Dic71—22no—
72C2×C22⋊Dic71C2×C414yes—
73C2×C22⋊Dic71C2×C414yes—
74C2×C22⋊Dic71D414yes—
75C2×C22⋊Dic71Q814yes—
76C2×C4×Dic71—24no—
77C2×C4×Dic71—24no—
78C2×C4×Dic71—24no—
79C2×C4×Dic71—24no—
80C2×C4×Dic71—24no—
81C2×C4×Dic71—24no—
82C2×C4×Dic71—42no—
83C2×C4×Dic71—42no—
84C2×C4×Dic71C2×C418yescomplemented
85C71⋊#95—24no—
86C71⋊#95—24no—
87C71⋊#95—24no—
88C71⋊#95—42no—
89C71⋊#95C2×C418yescomplemented
90C71⋊#95C2×C418yescomplemented
91C25×C71C2311yescharacteristic
92C23×C4×C71—22no—
93C23×C4×C71—22no—
94C23×C4×C71—24no—
95C23×C4×C71—42no—
96C23×C4×C71C2×C414yes—
97C23×C4×C71C2312yes—
98C23×C4×C71C2312yes—
99C23×C4×C71C2311yescharacteristic
100C23×C4×C71C2311yescharacteristic
101C2×C22⋊C4×C71—22no—
102C2×C22⋊C4×C71—22no—
103C2×C22⋊C4×C71—22no—
104C2×C22⋊C4×C71—22no—
105C2×C22⋊C4×C71C2×C414yes—
106C2×C22⋊C4×C71C2×C414yes—
107#95×C71—24no—
108#95×C71—42no—
109C22×Dic71—21no—
110C22×Dic71—22no—
111C22×Dic71—22no—
112C22×Dic71—22no—
113C22×Dic71—21no—
114C22×Dic71—22no—
115C22×Dic71—22no—
116C22×Dic71—22no—
117C22×Dic71—22no—
118C22×Dic71—28no—
119C22×Dic71—28no—
120C22×Dic71—216no—
121C22×Dic71—216no—
122C22×Dic71—28no—
123C22×Dic71—21no—
124C22×Dic71—22no—
125C22×Dic71—22no—
126C22×Dic71—22no—
127C22×Dic71—21no—
128C22×Dic71—22no—
129C22×Dic71—22no—
130C22×Dic71—22no—
131C22×Dic71—22no—
132C22×Dic71—22no—
133C22×Dic71—28no—
134C22×Dic71—44no—
135C22×Dic71—48no—
136C22×Dic71—48no—
137C22×Dic71C42116yescomplemented
138C22×Dic71C22×C412yes—
139C22×Dic71C22×C414yes—
140C22×Dic71C22×C412yes—
141C22×Dic71C22×C412yes—
142C22×Dic71C22×C412yes—
143C22×Dic71C22×C412yes—
144C22×Dic71C22×C414yes—
145C22×Dic71C22×C412yes—
146C22×Dic71C22×C412yes—
147C22×Dic71C22×C412yes—
148C22×Dic71C2×D414yes—
149C22×Dic71C2×D414yes—
150C22×Dic71C2×D414yes—
151C22×Dic71C2×Q814yes—
152C22×Dic71#4114yes—
153Dic71⋊C4—28no—
154Dic71⋊C4—28no—
155Dic71⋊C4—28no—
156Dic71⋊C4—216no—
157Dic71⋊C4C22⋊C4116yescomplemented
158C22⋊Dic71—28no—
159C22⋊Dic71C4⋊C4116yescomplemented
160C4×Dic71—216no—
161C4×Dic71—48no—
162C4×Dic71—48no—
163C24×C71—22no—
164C24×C71—22no—
165C24×C71—22no—
166C24×C71—22no—
167C24×C71C22×C412yes—
168C24×C71C22×C412yes—
169C24×C71C22×C412yes—
170C24×C71C2×D412yes—
171C24×C71C2×Q812yes—
172C24×C71#4112yes—
173C24×C71#4112yes—
174C24×C71C2411yescharacteristic
175C22×C4×C71—21no—
176C22×C4×C71—21no—
177C22×C4×C71—22no—
178C22×C4×C71—28no—
179C22×C4×C71—22no—
180C22×C4×C71—22no—
181C22×C4×C71—22no—
182C22×C4×C71—21no—
183C22×C4×C71—22no—
184C22×C4×C71—22no—
185C22×C4×C71—22no—
186C22×C4×C71—22no—
187C22×C4×C71—21no—
188C22×C4×C71—22no—
189C22×C4×C71—22no—
190C22×C4×C71—22no—
191C22×C4×C71—22no—
192C22×C4×C71—22no—
193C22×C4×C71—22no—
194C22×C4×C71—22no—
195C22×C4×C71—28no—
196C22×C4×C71—44no—
197C22×C4×C71—48no—
198C22×C4×C71—48no—
199C22×C4×C71C22×C414yes—
200C22×C4×C71C22×C414yes—
201C22×C4×C71C22×C412yes—
202C22×C4×C71C22×C412yes—
203C22×C4×C71C2×D414yes—
204C22⋊C4×C71—28no—
205C22⋊C4×C71—28no—
206C23×C71—22no—
207C23×C71—22no—
208C23×C71—24no—
209C23×C71—24no—
210C23×C71—22no—
211C23×C71—22no—
212C23×C71—24no—
213C23×C71—24no—
214C23×C71—24no—
215C23×C71—24no—
216C23×C71—24no—
217C23×C71—24no—
218C23×C71—24no—
219C23×C71—24no—
220C23×C71—24no—
221C23×C71—24no—
222C23×C71C2×C4214yes—
223C23×C71C2×C4⋊C414yes—
224C23×C71#11714yes—
225C23×C71C4×D414yes—
226C23×C71C4×D414yes—
227C23×C71C4×Q814yes—
228C23×C71C4×Q814yes—
229C23×C71C23×C411yescharacteristic
230C23×C71C23×C411yescharacteristic
231C23×C71C23×C411yescharacteristic
232C23×C71C22×D412yes—
233C23×C71C22×D411yescharacteristic
234C23×C71C22×Q811yescharacteristic
235C23×C71C2×#4112yes—
236C23×C71C2×#4111yescharacteristic
237C23×C71C2×#4111yescharacteristic
238C23×C71H(5,𝔽2)12yes—
239C23×C712−1+412yes—
240C2×C4×C71—22no—
241C2×C4×C71—22no—
242C2×C4×C71—24no—
243C2×C4×C71—24no—
244C2×C4×C71—22no—
245C2×C4×C71—24no—
246C2×C4×C71—24no—
247C2×C4×C71—22no—
248C2×C4×C71—24no—
249C2×C4×C71—24no—
250C2×C4×C71—22no—
251C2×C4×C71—24no—
252C2×C4×C71—24no—
253C2×C4×C71—416no—
254C2×C4×C71—42no—
255C2×C4×C71—42no—
256C2×C4×C71—42no—
257C2×C4×C71—42no—
258C2×C4×C71—42no—
259C2×C4×C71—42no—
260C2×C4×C71—42no—
261C2×C4×C71—42no—
262C2×C4×C71—42no—
263C2×C4×C71—42no—
264C2×C4×C71C2×C22⋊C414yes—
265C2×Dic71—22no—
266C2×Dic71—22no—
267C2×Dic71—24no—
268C2×Dic71—24no—
269C2×Dic71—24no—
270C2×Dic71—22no—
271C2×Dic71—22no—
272C2×Dic71—24no—
273C2×Dic71—24no—
274C2×Dic71—24no—
275C2×Dic71—24no—
276C2×Dic71—24no—
277C2×Dic71—24no—
278C2×Dic71—24no—
279C2×Dic71—232no—
280C2×Dic71—22no—
281C2×Dic71—24no—
282C2×Dic71—24no—
283C2×Dic71—22no—
284C2×Dic71—22no—
285C2×Dic71—24no—
286C2×Dic71—416no—
287C2×Dic71—42no—
288C2×Dic71—42no—
289C2×Dic71—42no—
290C2×Dic71—42no—
291C2×Dic71—42no—
292C2×Dic71—42no—
293C2×Dic71C2×C4214yes—
294C2×Dic71C2×C4214yes—
295C2×Dic71C2×C22⋊C414yes—
296C2×Dic71C2×C22⋊C414yes—
297C2×Dic71C2×C4⋊C418yescomplemented
298C2×Dic71#11714yes—
299C2×Dic71C4×D418yes—
300C2×Dic71C4×D418yes—
301C22×C71—24no—
302C22×C71—24no—
303C22×C71—24no—
304C22×C71—24no—
305C22×C71—28no—
306C22×C71—28no—
307C22×C71—28no—
308C22×C71—28no—
309C22×C71—24no—
310C22×C71—24no—
311C22×C71C4×C4⋊C418yescomplemented
312C22×C71C22×C4211yescharacteristic
313C22×C71C22×C22⋊C411yescharacteristic
314C22×C71C22×C4⋊C411yescharacteristic
315C22×C71C2×#11711yescharacteristic
316C22×C71C2×#11711yescharacteristic
317C22×C71C2×C4×D412yes—
318C22×C71C2×C4×D412yes—
319C22×C71C2×C4×D411yescharacteristic
320C22×C71C2×C4×D411yescharacteristic
321C22×C71C2×C4×Q811yescharacteristic
322C22×C71C2×C4×Q811yescharacteristic
323C22×C71#51811yescharacteristic
324C22×C71#51911yescharacteristic
325C22×C71#52012yes—
326C22×C71#52012yes—
327C22×C71D4212yes—
328C22×C71#54612yes—
329C22×C71#54712yes—
330C22×C71#54812yes—
331C22×C71D4×Q812yes—
332C22×C71#55212yes—
333C22×C71#55312yes—
334C22×C71#55412yes—
335C4×C71—24no—
336C4×C71—42no—
337C4×C71—44no—
338C4×C71—44no—
339Dic71—24no—
340Dic71—28no—
341Dic71—24no—
342Dic71—42no—
343Dic71—44no—
344Dic71C4×C22⋊C418yescomplemented
345C22⋊C4×C4⋊C4—711nomaximal, Sylow
346C2×C71—28no—
347C2×C71C2×C4×C22⋊C411yescharacteristic
348C2×C71C2×C4×C4⋊C411yescharacteristic
349C2×C71#227411yescharacteristic
350C2×C71D4×C22⋊C411yescharacteristic
351C2×C71Q8×C22⋊C411yescharacteristic
352C2×C71#234411yescharacteristic
353C2×C71#234511yescharacteristic
354C2×C71D4×C4⋊C412yes—
355C2×C71#235212yes—
356C2×C71#236012yes—
357C2×C71#236112yes—
358C23×C4⋊C4—711no—
359C2×#380—711no—
360C2×C4×C4⋊C4—712no—
361C2×C4×C22⋊C4—711no—
362C2×C4×C22⋊C4—711no—
363C2×C4×C22⋊C4—711no—
364#1436—712no—
365#1436—712no—
366C4⋊#95—712no—
367C22⋊#95—711no—
368C22⋊#95D7111yescharacteristic
369C71C22⋊C4×C4⋊C411yescharacteristic, complemented, Sylow
370C24×C4—711no—
371C24×C4—711no—
372C24×C4C2×D7111yescharacteristic
373C22×C4⋊C4—711no—
374C22×C4⋊C4—718no—
375C22×C4⋊C4—711no—
376C22×C4⋊C4—711no—
377C22×C4⋊C4—711no—
378C22×C4⋊C4—712no—
379C22×C4⋊C4—1428no—
380C22×C22⋊C4—711no—
381C22×C22⋊C4—711no—
382C22×C22⋊C4C2×D7111yescharacteristic
383C22×C22⋊C4C2×D7111yescharacteristic
384C22×C42—712no—
385C22×C42—712no—
386C22×C42—712no—
387#380—718no—
388C4×C4⋊C4—1428no—
389C4×C22⋊C4—718no—
390C4×C22⋊C4—1424no—
391C4×C22⋊C4—1424no—
392C2×#95—712no—
393C2×#95—712no—
394C2×#95—712no—
395C2×#95—712no—
396C2×#95—712no—
397C2×#95—712no—
398C2×#95C2×D7112yes—
399C2×#95C2×D7112yes—
400C25C22×D7111yescharacteristic
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—24no—
404C23×C4—42no—
405C23×C4—2842no—
406C23×C4—714no—
407C23×C4—711no—
408C23×C4—714no—
409C23×C4—714no—
410C23×C4—714no—
411C23×C4—712no—
412C23×C4—711no—
413C23×C4—711no—
414C23×C4—712no—
415C23×C4—711no—
416C23×C4—1424no—
417C23×C4—1422no—
418C23×C4—1422no—
419C23×C4—1424no—
420C23×C4—1424no—
421C23×C4C4×D7114yes—
422C23×C4C22×D7112yes—
423C23×C4C22×D7112yes—
424C23×C4C22×D7111yescharacteristic
425C23×C4C22×D7111yescharacteristic
426C2×C4⋊C4—714no—
427C2×C4⋊C4—718no—
428C2×C4⋊C4—714no—
429C2×C4⋊C4—714no—
430C2×C4⋊C4—714no—
431C2×C4⋊C4—718no—
432C2×C4⋊C4—14232no—
433C2×C4⋊C4—1424no—
434C2×C4⋊C4—1424no—
435C2×C4⋊C4—1424no—
436C2×C4⋊C4—1424no—
437C2×C4⋊C4—1424no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—714no—
443C2×C22⋊C4—714no—
444C2×C22⋊C4—714no—
445C2×C22⋊C4—714no—
446C2×C22⋊C4—1422no—
447C2×C22⋊C4—1422no—
448C2×C22⋊C4C4×D7114yes—
449C2×C22⋊C4C4×D7114yes—
450C2×C42—2842no—
451C2×C42—2842no—
452C2×C42—718no—
453C2×C42—1424no—
454C2×C42—1424no—
455C2×C42—1424no—
456C2×C42—1424no—
457C2×C42—1424no—
458C2×C42—1424no—
459#95—24no—
460#95—42no—
461#95—2842no—
462#95—718no—
463#95—718no—
464#95—1424no—
465#95—1424no—
466#95—1424no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24C2×C4×D7112yes—
472C24C2×C4×D7112yes—
473C24C2×C4×D7112yes—
474C24D4×D7112yes—
475C24Q8×D7112yes—
476C24#1176586412yes—
477C24#1176586412yes—
478C24C23×D7111yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—44no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—2848no—
504C22×C4—2848no—
505C22×C4—2844no—
506C22×C4—712no—
507C22×C4—712no—
508C22×C4—712no—
509C22×C4—714no—
510C22×C4—714no—
511C22×C4—712no—
512C22×C4—712no—
513C22×C4—714no—
514C22×C4—712no—
515C22×C4—712no—
516C22×C4—714no—
517C22×C4—714no—
518C22×C4—714no—
519C22×C4—7116no—
520C22×C4—714no—
521C22×C4—712no—
522C22×C4—1428no—
523C22×C4—1421no—
524C22×C4—1422no—
525C22×C4—1422no—
526C22×C4—1422no—
527C22×C4—1422no—
528C22×C4—1422no—
529C22×C4—1421no—
530C22×C4—1422no—
531C22×C4—1422no—
532C22×C4—1422no—
533C22×C4—1428no—
534C22×C4—1428no—
535C22×C4—1428no—
536C22×C4—14216no—
537C22×C4—14216no—
538C22×C4—1422no—
539C22×C4—1421no—
540C22×C4—1422no—
541C22×C4—1422no—
542C22×C4—1422no—
543C22×C4—1421no—
544C22×C4—1422no—
545C22×C4—1422no—
546C22×C4—1422no—
547C22×C4C2×C4×D7114yes—
548C22×C4C2×C4×D7114yes—
549C22×C4C2×C4×D7112yes—
550C22×C4C2×C4×D7112yes—
551C22×C4D4×D7114yes—
552C4⋊C4—7116no—
553C4⋊C4—14216no—
554C4⋊C4—1428no—
555C4⋊C4—1428no—
556C4⋊C4—1428no—
557C22⋊C4—28no—
558C22⋊C4—28no—
559C22⋊C4—7116no—
560C22⋊C4—1428no—
561C42—2848no—
562C42—2848no—
563C42—14216no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—22no—
572C23—24no—
573C23—22no—
574C23—24no—
575C23—24no—
576C23—22no—
577C23—22no—
578C23—24no—
579C23—24no—
580C23C42×D7114yes—
581C23C4⋊C4×D7114yes—
582C23#1455608414yes—
583C23(C22⋊D71)⋊C414yes—
584C23(C22⋊D71)⋊C414yes—
585C23#1455609314yes—
586C23#1455609314yes—
587C23C22×C4×D7111yescharacteristic
588C23C22×C4×D7111yescharacteristic
589C23C22×C4×D7111yescharacteristic
590C23C2×D4×D7111yescharacteristic
591C23C2×D4×D7112yes—
592C23C2×Q8×D7111yescharacteristic
593C23#41×D7112yes—
594C23C2×#1176586411yescharacteristic
595C23C2×#1176586411yescharacteristic
596C23#1455617312yes—
597C23#1455617512yes—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—416no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—2842no—
623C2×C4—2842no—
624C2×C4—2842no—
625C2×C4—2842no—
626C2×C4—2842no—
627C2×C4—2842no—
628C2×C4—28416no—
629C2×C4—714no—
630C2×C4—714no—
631C2×C4—714no—
632C2×C4—718no—
633C2×C4—718no—
634C2×C4—714no—
635C2×C4—714no—
636C2×C4—718no—
637C2×C4—1422no—
638C2×C4—1424no—
639C2×C4—1424no—
640C2×C4—1422no—
641C2×C4—1422no—
642C2×C4—1424no—
643C2×C4—14232no—
644C2×C4—1424no—
645C2×C4—1424no—
646C2×C4—1424no—
647C2×C4—1424no—
648C2×C4—1424no—
649C2×C4—1422no—
650C2×C4—1424no—
651C2×C4—1422no—
652C2×C4—1424no—
653C2×C4—1424no—
654C2×C4—1424no—
655C2×C4—1422no—
656C2×C4—1422no—
657C2×C4—1424no—
658C2×C4C22⋊C4×D7114yes—
659C22—28no—
660C22—28no—
661C22—28no—
662C22—28no—
663C22—24no—
664C22—24no—
665C22—24no—
666C22—24no—
667C22—24no—
668C22—24no—
669C22#1798585018yescomplemented
670C22C2×C42×D7111yescharacteristic
671C22C2×C22⋊C4×D7111yescharacteristic
672C22C2×C4⋊C4×D7111yescharacteristic
673C22#117×D7111yescharacteristic
674C22C2×#1455608411yescharacteristic
675C22C4×D4×D7112yes—
676C22C4×D4×D7112yes—
677C22C2×(C22⋊D71)⋊C411yescharacteristic
678C22C2×(C22⋊D71)⋊C411yescharacteristic
679C22C2×#1455609311yescharacteristic
680C22C2×#1455609311yescharacteristic
681C22#1798647211yescharacteristic
682C22#1798647611yescharacteristic
683C22#1798647812yes—
684C22#1798647812yes—
685C22#1798663112yes—
686C22#1798663612yes—
687C22#1798664712yes—
688C22#1798665512yes—
689C22#1798666212yes—
690C22#1798668612yes—
691C22#1798669212yes—
692C22#1798670312yes—
693C4—24no—
694C4—44no—
695C4—44no—
696C4—42no—
697C4—2844no—
698C4—2842no—
699C4—718no—
700C4—1428no—
701C4—1424no—
702C4—1424no—
703C2—28no—
704C2C4×C22⋊C4×D7111yescharacteristic
705C2C2×#1798585011yescharacteristic
706C2#2259069511yescharacteristic
707C2#2259115611yescharacteristic
708C2#2259117211yescharacteristic
709C2#2259120411yescharacteristic
710C2#2259121211yescharacteristic
711C2#2259123812yes—
712C2#2259126712yes—
713C2#2259134012yes—
714C2#2259135112yes—
subgroupG/H
center, FrattiniC24C23×D71
commutatorC22×C71C22×C42
FittingC71×C22⋊#95C2
socle, cosocleC24×C71C24
prime radicalC25×C71C23
hypercenterC22⋊#95D71
hypocenterC71C22⋊C4×C4⋊C4
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#17985850C2semidirect
7. #22586575C2semidirect
8. #22586571C2semidirect
9. Dic71⋊#95C2semidirect
15. C22×Dic71⋊C4C4semidirect
26. #17985857C4semidirect
29. C22⋊C4×Dic71C4semidirect
68. C2×Dic71⋊C4C2×C4semidirect
84. C2×C4×Dic71C2×C4semidirect
89. C71⋊#95C2×C4semidirect
90. C71⋊#95C2×C4semidirect
137. C22×Dic71C42semidirect
157. Dic71⋊C4C22⋊C4semidirect
159. C22⋊Dic71C4⋊C4semidirect
297. C2×Dic71C2×C4⋊C4semidirect
311. C22×C71C4×C4⋊C4semidirect
344. Dic71C4×C22⋊C4semidirect
369. C71C22⋊C4×C4⋊C4semidirect
669. C22#17985850semidirect

Maximal subgroups

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

subgroupindex
C23×Dic71⋊C42
C2×#179858572
C2×#179858502
C2×C22⋊C4×Dic712
C2×C4×C22⋊Dic712
#225865752
#225865712
Dic71⋊#952
#225865622
C71×C22⋊#952
C22⋊C4×C4⋊C471