Finite Group Databasebeta

← #31919435

Subgroups — #31919435

Order 18176.

2510 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic71⋊C4C211yesmaximal, characteristic
2C2×#17985874C211yesmaximal, characteristic
3C2×#17985872C211yesmaximal, characteristic
4C2×#17985871C211yesmaximal, characteristic
5C2×#17985868C212yesmaximal, complemented
6C2×#17985857C211yesmaximal, characteristic
7C2×C22⋊C4×Dic71C211yesmaximal, characteristic
8#22586604C212yesmaximal, complemented
9#22586603C212yesmaximal, complemented
10Dic71⋊#95C212yesmaximal, complemented
11C2×#385×C71C211yesmaximal, characteristic
12C24×Dic71C2211yescharacteristic
13C24×Dic71C2211yescharacteristic
14C22×C4⋊Dic71C2212yes—
15C22×Dic71⋊C4—28no—
16C22×Dic71⋊C4—24no—
17C22×Dic71⋊C4C2211yescharacteristic
18C22×Dic71⋊C4C2212yes—
19C22×Dic71⋊C4C2211yescharacteristic
20C22×Dic71⋊C4C2212yes—
21C22×Dic71⋊C4C2212yes—
22C22×Dic71⋊C4C2212yes—
23C22×C22⋊Dic71C2211yescharacteristic
24C22×C22⋊Dic71C2211yescharacteristic
25C22×C4×Dic71C2212yes—
26#17985874—24no—
27#17985872—24no—
28#17985871—24no—
29#17985868—28no—
30#17985857—24no—
31C22⋊C4×Dic71C418yescomplemented
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2212yes—
35C2×C71⋊#95C2211yescharacteristic
36C2×C71⋊#95C2211yescharacteristic
37C2×C71⋊#95C2212yes—
38C24×C4×C71C2211yescharacteristic
39C22×C4⋊C4×C71C2212yes—
40C22×C22⋊C4×C71C2211yescharacteristic
41C22×C22⋊C4×C71C2211yescharacteristic
42#385×C71—24no—
43C2×#95×C71C2212yes—
44C23×Dic71—24no—
45C23×Dic71—24no—
46C23×Dic71—24no—
47C23×Dic71—22no—
48C23×Dic71—22no—
49C23×Dic71—22no—
50C23×Dic71—42no—
51C23×Dic71C2×C414yes—
52C23×Dic71D414yes—
53C23×Dic71Q814yes—
54C23×Dic71C2311yescharacteristic
55C23×Dic71C2311yescharacteristic
56C23×Dic71C2312yes—
57C23×Dic71C2311yescharacteristic
58C23×Dic71C2312yes—
59C23×Dic71C2311yescharacteristic
60C2×C4⋊Dic71—24no—
61C2×C4⋊Dic71—24no—
62C2×C4⋊Dic71—42no—
63C2×Dic71⋊C4—232no—
64C2×Dic71⋊C4—24no—
65C2×Dic71⋊C4—24no—
66C2×Dic71⋊C4—24no—
67C2×Dic71⋊C4—24no—
68C2×Dic71⋊C4—22no—
69C2×Dic71⋊C4—22no—
70C2×Dic71⋊C4—24no—
71C2×Dic71⋊C4—24no—
72C2×Dic71⋊C4—24no—
73C2×Dic71⋊C4—24no—
74C2×Dic71⋊C4—24no—
75C2×Dic71⋊C4—24no—
76C2×Dic71⋊C4—24no—
77C2×Dic71⋊C4—42no—
78C2×Dic71⋊C4—42no—
79C2×Dic71⋊C4D418yes—
80C2×C22⋊Dic71—22no—
81C2×C22⋊Dic71—22no—
82C2×C22⋊Dic71—22no—
83C2×C22⋊Dic71C2×C414yes—
84C2×C22⋊Dic71D414yes—
85C2×C22⋊Dic71Q814yes—
86C2×C4×Dic71—24no—
87C2×C4×Dic71—24no—
88C2×C4×Dic71C2×C418yescomplemented
89C71⋊#95—22no—
90C71⋊#95—22no—
91C71⋊#95—24no—
92C71⋊#95—24no—
93C71⋊#95—24no—
94C71⋊#95C2×C418yescomplemented
95C25×C71C2311yescharacteristic
96C23×C4×C71—22no—
97C23×C4×C71—24no—
98C23×C4×C71—22no—
99C23×C4×C71—22no—
100C23×C4×C71—42no—
101C23×C4×C71C2311yescharacteristic
102C23×C4×C71C2311yescharacteristic
103C23×C4×C71C2312yes—
104C23×C4×C71C2312yes—
105C2×C4⋊C4×C71—24no—
106C2×C4⋊C4×C71—24no—
107C2×C4⋊C4×C71—42no—
108C2×C22⋊C4×C71—22no—
109C2×C22⋊C4×C71—22no—
110C2×C22⋊C4×C71—22no—
111C2×C22⋊C4×C71C2×C414yes—
112C2×C22⋊C4×C71D414yes—
113C2×C22⋊C4×C71Q814yes—
114#95×C71—24no—
115C22×Dic71—22no—
116C22×Dic71—22no—
117C22×Dic71—22no—
118C22×Dic71—22no—
119C22×Dic71—22no—
120C22×Dic71—22no—
121C22×Dic71—216no—
122C22×Dic71—28no—
123C22×Dic71—216no—
124C22×Dic71—28no—
125C22×Dic71—28no—
126C22×Dic71—22no—
127C22×Dic71—22no—
128C22×Dic71—22no—
129C22×Dic71—22no—
130C22×Dic71—22no—
131C22×Dic71—22no—
132C22×Dic71—21no—
133C22×Dic71—21no—
134C22×Dic71—21no—
135C22×Dic71—21no—
136C22×Dic71—21no—
137C22×Dic71—21no—
138C22×Dic71—22no—
139C22×Dic71—22no—
140C22×Dic71—22no—
141C22×Dic71—22no—
142C22×Dic71—48no—
143C22×Dic71—48no—
144C22×Dic71—44no—
145C22×Dic71—44no—
146C22×Dic71C4⋊C4116yescomplemented
147C22×Dic71C22×C412yes—
148C22×Dic71C22×C414yes—
149C22×Dic71C22×C412yes—
150C22×Dic71C2×D414yes—
151C22×Dic71C2×D412yes—
152C22×Dic71C2×D414yes—
153C22×Dic71C2×D412yes—
154C22×Dic71C2×D414yes—
155C22×Dic71C2×Q812yes—
156C22×Dic71C2×Q814yes—
157C22×Dic71C2×Q812yes—
158C22×Dic71#4114yes—
159C4⋊Dic71—48no—
160Dic71⋊C4—216no—
161Dic71⋊C4—216no—
162Dic71⋊C4—48no—
163Dic71⋊C4—48no—
164Dic71⋊C4—44no—
165Dic71⋊C4—44no—
166C22⋊Dic71—44no—
167C22⋊Dic71C4⋊C4116yescomplemented
168C4×Dic71—216no—
169C24×C71—22no—
170C24×C71—22no—
171C24×C71—22no—
172C24×C71—22no—
173C24×C71C22×C412yes—
174C24×C71C2×D412yes—
175C24×C71C2×D412yes—
176C24×C71C2×D412yes—
177C24×C71C2×Q812yes—
178C24×C71C2×Q812yes—
179C24×C71C2×Q812yes—
180C24×C71C2411yescharacteristic
181C22×C4×C71—22no—
182C22×C4×C71—22no—
183C22×C4×C71—22no—
184C22×C4×C71—22no—
185C22×C4×C71—28no—
186C22×C4×C71—22no—
187C22×C4×C71—22no—
188C22×C4×C71—22no—
189C22×C4×C71—22no—
190C22×C4×C71—22no—
191C22×C4×C71—22no—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—22no—
199C22×C4×C71—22no—
200C22×C4×C71—22no—
201C22×C4×C71—22no—
202C22×C4×C71—48no—
203C22×C4×C71—48no—
204C22×C4×C71—44no—
205C22×C4×C71—44no—
206C22×C4×C71C22×C414yes—
207C22×C4×C71C2×D414yes—
208C22×C4×C71C2×D414yes—
209C22×C4×C71C2×Q814yes—
210C4⋊C4×C71—48no—
211C22⋊C4×C71—44no—
212C22⋊C4×C71C4⋊C4116yescomplemented
213C23×C71—24no—
214C23×C71—24no—
215C23×C71—22no—
216C23×C71—24no—
217C23×C71—22no—
218C23×C71—22no—
219C23×C71—22no—
220C23×C71—24no—
221C23×C71—24no—
222C23×C71—24no—
223C23×C71—24no—
224C23×C71—24no—
225C23×C71—24no—
226C23×C71—24no—
227C23×C71—24no—
228C23×C71—24no—
229C23×C71C2×C4⋊C414yes—
230C23×C71C2×C4⋊C414yes—
231C23×C71C2×C4⋊C414yes—
232C23×C71#12714yes—
233C23×C71C4⋊Q814yes—
234C23×C71C4⋊Q814yes—
235C23×C71C4⋊Q814yes—
236C23×C71C23×C411yescharacteristic
237C23×C71C22×D411yescharacteristic
238C23×C71C22×D411yescharacteristic
239C23×C71C22×D412yes—
240C23×C71C22×D411yescharacteristic
241C23×C71C22×Q811yescharacteristic
242C23×C71C22×Q811yescharacteristic
243C23×C71C22×Q811yescharacteristic
244C23×C71C2×#4112yes—
245C23×C71H(5,𝔽2)12yes—
246C23×C712−1+412yes—
247C2×C4×C71—24no—
248C2×C4×C71—24no—
249C2×C4×C71—24no—
250C2×C4×C71—24no—
251C2×C4×C71—24no—
252C2×C4×C71—24no—
253C2×C4×C71—24no—
254C2×C4×C71—24no—
255C2×C4×C71—24no—
256C2×C4×C71—416no—
257C2×C4×C71—42no—
258C2×C4×C71—42no—
259C2×C4×C71—42no—
260C2×C4×C71—42no—
261C2×C4×C71—41no—
262C2×C4×C71—41no—
263C2×C4×C71—41no—
264C2×C4×C71—41no—
265C2×C4×C71—41no—
266C2×C4×C71—41no—
267C2×C4×C71—42no—
268C2×C4×C71—42no—
269C2×C4×C71—42no—
270C2×C4×C71—42no—
271C2×C4×C71C2×C4⋊C418yescomplemented
272C2×Dic71—24no—
273C2×Dic71—24no—
274C2×Dic71—24no—
275C2×Dic71—22no—
276C2×Dic71—24no—
277C2×Dic71—22no—
278C2×Dic71—24no—
279C2×Dic71—24no—
280C2×Dic71—24no—
281C2×Dic71—24no—
282C2×Dic71—232no—
283C2×Dic71—24no—
284C2×Dic71—24no—
285C2×Dic71—24no—
286C2×Dic71—416no—
287C2×Dic71—42no—
288C2×Dic71—42no—
289C2×Dic71—42no—
290C2×Dic71—42no—
291C2×Dic71—41no—
292C2×Dic71—41no—
293C2×Dic71—41no—
294C2×Dic71—41no—
295C2×Dic71—41no—
296C2×Dic71—41no—
297C2×Dic71—42no—
298C2×Dic71—42no—
299C2×Dic71—42no—
300C2×Dic71—42no—
301C2×Dic71C2×C4⋊C414yes—
302C2×Dic71C2×C4⋊C414yes—
303C2×Dic71C2×C4⋊C418yescomplemented
304C2×Dic71C4×D418yes—
305C2×Dic71#12014yes—
306C2×Dic71C22⋊Q818yes—
307C2×Dic71#12314yes—
308C22×C71—24no—
309C22×C71—28no—
310C22×C71—28no—
311C22×C71—24no—
312C22×C71—24no—
313C22×C71—28no—
314C22×C71—28no—
315C22×C71—24no—
316C22×C71—24no—
317C22×C71—24no—
318C22×C71#38418yescomplemented
319C22×C71C22×C4⋊C411yescharacteristic
320C22×C71C22×C4⋊C411yescharacteristic
321C22×C71C22×C4⋊C411yescharacteristic
322C22×C71C2×C4×D412yes—
323C22×C71#52012yes—
324C22×C71C2×#12011yescharacteristic
325C22×C71C2×C22⋊Q812yes—
326C22×C71C2×#12311yescharacteristic
327C22×C71C2×#12711yescharacteristic
328C22×C71C2×C4⋊Q811yescharacteristic
329C22×C71C2×C4⋊Q811yescharacteristic
330C22×C71C2×C4⋊Q811yescharacteristic
331C22×C71#53511yescharacteristic
332C22×C71#53611yescharacteristic
333C22×C71#54412yes—
334C22×C71D4212yes—
335C22×C71D4212yes—
336C22×C71#54712yes—
337C22×C71#54712yes—
338C22×C71D4×Q812yes—
339C22×C71D4×Q812yes—
340C22×C71#55412yes—
341C22×C71#55412yes—
342C4×C71—28no—
343C4×C71—44no—
344C4×C71—81no—
345C4×C71—81no—
346Dic71—28no—
347Dic71—24no—
348Dic71—44no—
349Dic71—81no—
350Dic71—81no—
351Dic71#38518yescomplemented
352#13880—711nomaximal, Sylow
353C2×C71—28no—
354C2×C71C2×#38411yescharacteristic
355C2×C71C2×#38511yescharacteristic
356C2×C71#231711yescharacteristic
357C2×C71D4×C4⋊C412yes—
358C2×C71D4×C4⋊C412yes—
359C2×C71#243311yescharacteristic
360C2×C71#243411yescharacteristic
361C2×C71#244012yes—
362C2×C71#244012yes—
363C2×C71#250111yescharacteristic
364C2×C71#250211yescharacteristic
365C23×C4⋊C4—711no—
366C2×#385—711no—
367C2×#385—711no—
368C2×#385—711no—
369C2×#385D7111yescharacteristic
370C2×#384—712no—
371C2×#380—711no—
372C2×C4×C22⋊C4—711no—
373#1444—712no—
374#1444—712no—
375C4⋊#95—712no—
376C71#1388011yescharacteristic, complemented, Sylow
377C24×C4—711no—
378C24×C4—711no—
379C24×C4C2×D7111yescharacteristic
380C22×C4⋊C4—712no—
381C22×C4⋊C4—712no—
382C22×C4⋊C4—712no—
383C22×C4⋊C4—712no—
384C22×C4⋊C4—712no—
385C22×C4⋊C4—711no—
386C22×C4⋊C4—711no—
387C22×C4⋊C4—1428no—
388C22×C4⋊C4—1424no—
389C22×C4⋊C4C2×D7112yes—
390C22×C22⋊C4—711no—
391C22×C22⋊C4—711no—
392C22×C22⋊C4C2×D7111yescharacteristic
393C22×C22⋊C4C2×D7111yescharacteristic
394C22×C42—712no—
395#385—24no—
396#385—1424no—
397#385—1424no—
398#385—1424no—
399#384—1428no—
400#380—1424no—
401C4×C22⋊C4—718no—
402C2×#95—712no—
403C2×#95—712no—
404C2×#95—712no—
405C2×#95—712no—
406C2×#95—711no—
407C2×#95—711no—
408C2×#95C2×D7112yes—
409C25C22×D7111yescharacteristic
410C23×C4—22no—
411C23×C4—24no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—42no—
415C23×C4—2842no—
416C23×C4—711no—
417C23×C4—714no—
418C23×C4—714no—
419C23×C4—714no—
420C23×C4—712no—
421C23×C4—711no—
422C23×C4—712no—
423C23×C4—711no—
424C23×C4—711no—
425C23×C4—1422no—
426C23×C4—1422no—
427C23×C4—1424no—
428C23×C4—1422no—
429C23×C4—1424no—
430C23×C4—1424no—
431C23×C4C22×D7111yescharacteristic
432C23×C4C22×D7111yescharacteristic
433C23×C4C22×D7112yes—
434C23×C4C22×D7112yes—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—2842no—
439C2×C4⋊C4—2842no—
440C2×C4⋊C4—2842no—
441C2×C4⋊C4—718no—
442C2×C4⋊C4—1422no—
443C2×C4⋊C4—1422no—
444C2×C4⋊C4—1424no—
445C2×C4⋊C4—1424no—
446C2×C4⋊C4—1424no—
447C2×C4⋊C4—1424no—
448C2×C4⋊C4—1424no—
449C2×C4⋊C4—1424no—
450C2×C4⋊C4—1424no—
451C2×C4⋊C4—1424no—
452C2×C4⋊C4—1424no—
453C2×C4⋊C4—1424no—
454C2×C4⋊C4—1424no—
455C2×C4⋊C4—1424no—
456C2×C4⋊C4—14232no—
457C2×C4⋊C4—1424no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—714no—
462C2×C22⋊C4—714no—
463C2×C22⋊C4—714no—
464C2×C22⋊C4—1422no—
465C2×C22⋊C4—1422no—
466C2×C22⋊C4—1422no—
467C2×C22⋊C4Dic14214yes—
468C2×C22⋊C4C4×D7114yes—
469C2×C22⋊C4C22⋊D7114yes—
470C2×C42—718no—
471C2×C42—1424no—
472C2×C42—1424no—
473#95—24no—
474#95—718no—
475#95—1422no—
476#95—1422no—
477#95—1424no—
478#95—1424no—
479#95—1424no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24C2×C4×D7112yes—
485C24D4×D7112yes—
486C24D4×D7112yes—
487C24C2×C22⋊D7112yes—
488C24Q8×D7112yes—
489C24Q8×D7112yes—
490C24C2×Dic14212yes—
491C24C23×D7111yescharacteristic
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—2844no—
518C22×C4—2844no—
519C22×C4—2848no—
520C22×C4—2848no—
521C22×C4—712no—
522C22×C4—714no—
523C22×C4—712no—
524C22×C4—712no—
525C22×C4—714no—
526C22×C4—712no—
527C22×C4—714no—
528C22×C4—714no—
529C22×C4—712no—
530C22×C4—714no—
531C22×C4—712no—
532C22×C4—7116no—
533C22×C4—714no—
534C22×C4—1421no—
535C22×C4—1421no—
536C22×C4—1421no—
537C22×C4—1421no—
538C22×C4—1422no—
539C22×C4—1421no—
540C22×C4—1421no—
541C22×C4—1422no—
542C22×C4—1422no—
543C22×C4—1422no—
544C22×C4—1428no—
545C22×C4—1422no—
546C22×C4—1422no—
547C22×C4—1422no—
548C22×C4—1422no—
549C22×C4—1422no—
550C22×C4—1422no—
551C22×C4—1428no—
552C22×C4—14216no—
553C22×C4—14216no—
554C22×C4—1428no—
555C22×C4—1422no—
556C22×C4—1422no—
557C22×C4—1422no—
558C22×C4—1422no—
559C22×C4—1422no—
560C22×C4—1422no—
561C22×C4C2×C4×D7114yes—
562C22×C4D4×D7114yes—
563C22×C4C2×C22⋊D7114yes—
564C22×C4C2×Dic14214yes—
565C4⋊C4—48no—
566C4⋊C4—2848no—
567C4⋊C4—2848no—
568C4⋊C4—2844no—
569C4⋊C4—2844no—
570C4⋊C4—2848no—
571C4⋊C4—14216no—
572C4⋊C4—14216no—
573C22⋊C4—44no—
574C22⋊C4—2844no—
575C22⋊C4—7116no—
576C22⋊C4Dic71⋊C4116yescomplemented
577C42—14216no—
578C23—22no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—22no—
592C23—24no—
593C23—22no—
594C23C4⋊C4×D7114yes—
595C23C4⋊C4×D7114yes—
596C23C2×Dic71⋊C414yes—
597C23#1455612414yes—
598C23#1455612614yes—
599C23#1455612714yes—
600C23#1455612714yes—
601C23C22×C4×D7111yescharacteristic
602C23C2×D4×D7111yescharacteristic
603C23C2×D4×D7111yescharacteristic
604C23C2×D4×D7112yes—
605C23C22×C22⋊D7111yescharacteristic
606C23C2×Q8×D7111yescharacteristic
607C23C2×Q8×D7111yescharacteristic
608C23C22×Dic14211yescharacteristic
609C23#41×D7112yes—
610C23#1455617312yes—
611C23#1455617512yes—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—416no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—28416no—
637C2×C4—2842no—
638C2×C4—2842no—
639C2×C4—2842no—
640C2×C4—2842no—
641C2×C4—2841no—
642C2×C4—2841no—
643C2×C4—2842no—
644C2×C4—2842no—
645C2×C4—2842no—
646C2×C4—2842no—
647C2×C4—2841no—
648C2×C4—2841no—
649C2×C4—2841no—
650C2×C4—2841no—
651C2×C4—714no—
652C2×C4—718no—
653C2×C4—714no—
654C2×C4—718no—
655C2×C4—714no—
656C2×C4—718no—
657C2×C4—714no—
658C2×C4—1424no—
659C2×C4—1424no—
660C2×C4—1424no—
661C2×C4—14232no—
662C2×C4—1424no—
663C2×C4—1424no—
664C2×C4—1424no—
665C2×C4—1424no—
666C2×C4—1424no—
667C2×C4—1424no—
668C2×C4—1424no—
669C2×C4—1422no—
670C2×C4—1424no—
671C2×C4—1422no—
672C2×C4C2×Dic71⋊C418yescomplemented
673C22—28no—
674C22—28no—
675C22—24no—
676C22—28no—
677C22—28no—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—24no—
682C22—24no—
683C22#1798586818yescomplemented
684C22C2×C4⋊C4×D7111yescharacteristic
685C22C2×C4⋊C4×D7111yescharacteristic
686C22C22×Dic71⋊C411yescharacteristic
687C22C4×D4×D7112yes—
688C22#1798647812yes—
689C22#120×D7111yescharacteristic
690C22C22⋊Q8×D7112yes—
691C22#123×D7111yescharacteristic
692C22C2×#1455612411yescharacteristic
693C22C2×#1455612611yescharacteristic
694C22C2×#1455612711yescharacteristic
695C22C2×#1455612711yescharacteristic
696C22#1798656411yescharacteristic
697C22#1798657111yescharacteristic
698C22#1798662812yes—
699C22#1798663112yes—
700C22D4×C22⋊D7112yes—
701C22#1798664712yes—
702C22#1798664812yes—
703C22#1798666212yes—
704C22D4×Dic14212yes—
705C22#1798670312yes—
706C22#1798670812yes—
707C4—28no—
708C4—44no—
709C4—81no—
710C4—81no—
711C4—2844no—
712C4—5681no—
713C4—5681no—
714C4—718no—
715C4—1428no—
716C4—1424no—
717C2—28no—
718C2C2×#1798586811yescharacteristic
719C2#385×D7111yescharacteristic
720C2#2259095911yescharacteristic
721C2D4×Dic71⋊C412yes—
722C2#2259123812yes—
723C2#2259197511yescharacteristic
724C2#2259198211yescharacteristic
725C2#2259203912yes—
726C2#2259204112yes—
727C2#2259280911yescharacteristic
728C2#2259281611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC2×#385×C71C2
socle, cosocleC24×C71C24
prime radicalC25×C71C23
hypercenterC2×#385D71
hypocenterC71#13880
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
5. C2×#17985868C2semidirect
8. #22586604C2semidirect
9. #22586603C2semidirect
10. Dic71⋊#95C2semidirect
31. C22⋊C4×Dic71C4semidirect
88. C2×C4×Dic71C2×C4semidirect
94. C71⋊#95C2×C4semidirect
146. C22×Dic71C4⋊C4semidirect
167. C22⋊Dic71C4⋊C4semidirect
212. C22⋊C4×C71C4⋊C4semidirect
271. C2×C4×C71C2×C4⋊C4semidirect
303. C2×Dic71C2×C4⋊C4semidirect
318. C22×C71#384semidirect
351. Dic71#385semidirect
376. C71#13880semidirect
576. C22⋊C4Dic71⋊C4semidirect
672. C2×C4C2×Dic71⋊C4semidirect
683. C22#17985868semidirect

Maximal subgroups

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

subgroupindex
C23×Dic71⋊C42
C2×#179858742
C2×#179858722
C2×#179858712
C2×#179858682
C2×#179858572
C2×C22⋊C4×Dic712
#225866042
#225866032
Dic71⋊#952
C2×#385×C712
#1388071