Finite Group Databasebeta

← C2×#23777283 #35196708

Subgroups — C2×#23777283 #35196708

Order 20224.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777283C2132yesmaximal, direct product factor
2C2×#19099291C211yesmaximal, characteristic, complemented
3C2×#19099288C212yesmaximal, complemented
4C2×#19099287C211yesmaximal, characteristic, complemented
5C2×#19099286C211yesmaximal, characteristic, complemented
6C2×#19099285C212yesmaximal, complemented
7C2×#19099254C212yesmaximal, complemented
8C2×#19099251C212yesmaximal, complemented
9C2×#19099245C214yesmaximal, complemented
10C2×#19099172C214yesmaximal, complemented
11C2×#19099138C212yesmaximal
12C2×#19099119C212yesmaximal, complemented
13C2×#19099117C212yesmaximal, complemented
14C2×#19099117C211yesmaximal, characteristic, complemented
15C2×C4⋊Q8×D79C211yesmaximal, characteristic, complemented
16C2×#19099039C212yesmaximal, complemented
17C2×C4×#11929625C211yesmaximal, characteristic
18C2×#557×C79C211yesmaximal, characteristic, complemented
19C22×#11929625C2211yescharacteristic
20C22×Q8×D79C2212yes—
21#19099291C22116yescomplemented
22#19099288C22132yescomplemented
23#19099287C22116yescomplemented
24#19099286C22116yescomplemented
25#19099285C22132yescomplemented
26#19099254C22132yescomplemented
27#19099251C22132yescomplemented
28#19099245C22164yescomplemented
29#19099172C22164yescomplemented
30#19099138C22132yes—
31#19099119C22132yescomplemented
32#19099117C22132yescomplemented
33#19099117C22116yescomplemented
34C2×#14579161C2211yescharacteristic
35C2×#14579160C2212yes—
36C2×#14579160C2212yes—
37C2×#14579160C2211yescharacteristic
38C2×#14579159C2212yes—
39C2×#14579159C2211yescharacteristic
40C2×#14579159C2212yes—
41C4⋊Q8×D79C22116yescomplemented
42C2×#14579156C2214yes—
43C2×#14579156C2214yes—
44C2×#14579156C2214yes—
45C2×#14579155C2214yes—
46C2×#14579153C2212yes—
47C2×#14579152C2214yes—
48C2×#14579151C2214yes—
49C2×#14579151C2214yes—
50C2×#14579151C2214yes—
51C2×#14579151C2212yes—
52C2×#14579150C2212yes—
53C2×#14579149C2212yes—
54C2×#14579146C2214yes—
55C2×#14579146C2214yes—
56C2×#14579141C2211yescharacteristic
57C2×#14579141C2212yes—
58C2×#14579139C2212yes—
59C2×#14579139C2214yes—
60C2×#14579139C2214yes—
61C2×#14579139C2214yes—
62C2×#14579137C2211yescharacteristic
63C2×#14579137C2212yes—
64#19099039C22132yescomplemented
65C4×#11929625C22116yes—
66C2×Q8×Dic79C2211yescharacteristic
67C2×Q8×Dic79C2212yes—
68C2×C4×Dic158C2214yes—
69C2×C4×Dic158C2212yes—
70C2×C4×Dic158C2212yes—
71C2×C4×Dic158C2212yes—
72C2×C4×Dic158C2211yescharacteristic
73C2×#14579126C2214yes—
74C2×#14579126C2212yes—
75C2×#14579126C2214yes—
76C2×C4×D316C2212yes—
77C2×C4×D316C2211yescharacteristic
78C2×#14579123C2212yes—
79C2×#14579123C2211yescharacteristic
80C2×#14579119C2211yescharacteristic
81C2×#14579119C2212yes—
82C2×#14579119C2214yes—
83C2×#14579119C2212yes—
84C2×#14579119C2212yes—
85C2×#14579118C2214yes—
86C2×#14579118C2212yes—
87C2×#14579118C2214yes—
88C2×C4⋊C4×D79C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C2×C42×D79C2211yescharacteristic
91C2×C42×D79C2212yes—
92#557×C79C22116yescomplemented
93C2×C4⋊Q8×C79C2211yescharacteristic
94C2×C4⋊Q8×C79C2212yes—
95C2×#125×C79C2214yes—
96C2×#125×C79C2212yes—
97C2×C4×Q8×C79C2211yescharacteristic
98C2×C4×Q8×C79C2212yes—
99C2×C4×Q8×C79C2212yes—
100C2×C4×Q8×C79C2211yescharacteristic
101C2×#11929625—28no—
102C2×#11929625C2318yes—
103C22×Dic158C2312yes—
104C22×Dic158C2314yes—
105C22×Dic158C2312yes—
106C22×Dic158C2311yescharacteristic
107C2×Q8×D79—216no—
108C2×Q8×D79C23116yes—
109C22×D316C2312yes—
110C22×D316C2311yescharacteristic
111C22×C4×D79C2311yescharacteristic
112C22×C4×D79C2311yescharacteristic
113C22×C4×D79C2312yes—
114C22×C4×D79C2312yes—
115C22×C4×D79C2312yes—
116C22×C4×D79C2314yes—
117C22×C4×D79C2311yescharacteristic
118#14579161C2318yes—
119#14579160C23116yes—
120#14579160C23116yes—
121#14579160C2318yes—
122#14579159C23116yes—
123#14579159C23116yes—
124#14579159C2318yes—
125#14579156C23132yes—
126#14579156C23132yes—
127#14579156C23132yes—
128#14579155C23132yes—
129#14579153C23116yes—
130#14579152C23132yes—
131#14579151C23116yes—
132#14579151C23132yes—
133#14579151C23132yes—
134#14579151C23132yes—
135#14579150C23116yes—
136#14579149C23116yes—
137#14579146C23132yes—
138#14579146C23132yes—
139#14579141C2318yes—
140#14579141C23116yes—
141#14579139C23132yes—
142#14579139C23132yes—
143#14579139C23116yes—
144#14579139C23132yes—
145#14579137C2318yes—
146#14579137C23116yes—
147Q8×Dic79C23116yes—
148Q8×Dic79C2318yes—
149C4×Dic158C23132yes—
150C4×Dic158C23116yes—
151C4×Dic158C23116yes—
152C4×Dic158C23116yes—
153C4×Dic158C2318yes—
154#14579126C23132yes—
155#14579126C23132yes—
156#14579126C23116yes—
157C4×D316C23116yes—
158C4×D316C2318yes—
159#14579123C23116yes—
160#14579123C2318yes—
161#14579119C23116yes—
162#14579119C23132yes—
163#14579119C23116yes—
164#14579119C23116yes—
165#14579119C2318yes—
166#14579118C23116yes—
167#14579118C23132yes—
168#14579118C23132yes—
169C2×C4⋊Dic79C2312yes—
170C2×C4⋊Dic79C2312yes—
171C2×C4⋊Dic79C2311yescharacteristic
172C2×C4⋊Dic79C2311yescharacteristic
173C2×C4⋊Dic79C2312yes—
174C2×C4⋊Dic79C2314yes—
175C2×C4⋊Dic79C2312yes—
176C2×Dic79⋊C4C2314yes—
177C2×Dic79⋊C4C2314yes—
178C2×Dic79⋊C4C2312yes—
179C2×Dic79⋊C4C2312yes—
180C2×Dic79⋊C4C2314yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2312yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2314yes—
186C2×Dic79⋊C4C2312yes—
187C4⋊C4×D79C23116yes—
188C4⋊C4×D79C23116yes—
189C2×(C2×D79)⋊C4C2312yes—
190C2×(C2×D79)⋊C4C2312yes—
191C2×(C2×D79)⋊C4C2312yes—
192C2×(C2×D79)⋊C4C2314yes—
193C2×(C2×D79)⋊C4C2314yes—
194C2×(C2×D79)⋊C4C2312yes—
195C2×(C2×D79)⋊C4C2312yes—
196C2×(C2×D79)⋊C4C2314yes—
197C2×(C2×D79)⋊C4C2314yes—
198C2×C4×Dic79C2311yescharacteristic
199C2×C4×Dic79C2312yes—
200C2×C4×Dic79C2311yescharacteristic
201C2×C4×Dic79C2312yes—
202C2×C4×Dic79C2311yescharacteristic
203C2×C4×Dic79C2314yes—
204C2×C4×Dic79C2314yes—
205C2×C4×Dic79C2312yes—
206C2×C4×Dic79C2314yes—
207C42×D79C2318yes—
208C42×D79C23116yes—
209C22×Q8×C79C2311yescharacteristic
210C22×Q8×C79C2312yes—
211C22×Q8×C79C2311yescharacteristic
212C4⋊Q8×C79C23116yes—
213C4⋊Q8×C79C2318yes—
214#125×C79C23132yes—
215#125×C79C23116yes—
216C4×Q8×C79C23116yes—
217C4×Q8×C79C23116yes—
218C4×Q8×C79C2318yes—
219C4×Q8×C79C2318yes—
220C2×C4⋊C4×C79C2311yescharacteristic
221C2×C4⋊C4×C79C2311yescharacteristic
222C2×C4⋊C4×C79C2312yes—
223C2×C4⋊C4×C79C2314yes—
224C2×C4⋊C4×C79C2312yes—
225C2×C4⋊C4×C79C2312yes—
226C2×C4⋊C4×C79C2314yes—
227C2×C4⋊C4×C79C2312yes—
228C2×C4⋊C4×C79C2314yes—
229C2×C42×C79C2312yes—
230C2×C42×C79C2314yes—
231C2×C42×C79C2311yescharacteristic
232C2×C42×C79C2312yes—
233C23×D79C2412yes—
234C23×D79C2411yescharacteristic
235#11929625—232no—
236C2×Dic158—216no—
237C2×Dic158—28no—
238C2×Dic158—28no—
239C2×Dic158—24no—
240C2×Dic158C24116yes—
241C2×Dic158C2418yes—
242C2×Dic158C2418yes—
243C2×Dic158C2414yes—
244Q8×D79—264no—
245C2×D316—28no—
246C2×D316—24no—
247C2×D316C2418yes—
248C2×D316C2414yes—
249C22×Dic79C2414yes—
250C22×Dic79C2412yes—
251C22×Dic79C2412yes—
252C22×Dic79C2412yes—
253C22×Dic79C2411yescharacteristic
254C22×Dic79C2411yescharacteristic
255C22×Dic79C2411yescharacteristic
256C2×C4×D79—28no—
257C2×C4×D79—24no—
258C2×C4×D79—28no—
259C2×C4×D79—216no—
260C2×C4×D79—24no—
261C2×C4×D79—28no—
262C2×C4×D79#4118yes—
263C2×C4×D79C24116yes—
264C2×C4×D79C2418yes—
265C2×C4×D79C2414yes—
266C2×C4×D79C2414yes—
267C2×C4×D79C2418yes—
268C2×C4×D79C2418yes—
269C2×C4×D79C2414yes—
270C4⋊Dic79C2418yes—
271C4⋊Dic79C2418yes—
272C4⋊Dic79C2414yes—
273C4⋊Dic79C2414yes—
274C4⋊Dic79C2418yes—
275C4⋊Dic79C24116yes—
276C4⋊Dic79C2418yes—
277Dic79⋊C4C24116yes—
278Dic79⋊C4C24116yes—
279Dic79⋊C4C2418yes—
280Dic79⋊C4C2418yes—
281Dic79⋊C4C24116yes—
282Dic79⋊C4C24116yes—
283Dic79⋊C4C2418yes—
284Dic79⋊C4C24116yes—
285Dic79⋊C4C2418yes—
286Dic79⋊C4C24116yes—
287Dic79⋊C4C2418yes—
288(C2×D79)⋊C4C2418yes—
289(C2×D79)⋊C4C2418yes—
290(C2×D79)⋊C4C2418yes—
291(C2×D79)⋊C4C24116yes—
292(C2×D79)⋊C4C24116yes—
293(C2×D79)⋊C4C2418yes—
294(C2×D79)⋊C4C2418yes—
295(C2×D79)⋊C4C24116yes—
296(C2×D79)⋊C4C24116yes—
297C4×Dic79C2414yes—
298C4×Dic79C2418yes—
299C4×Dic79C2414yes—
300C4×Dic79C2418yes—
301C4×Dic79C2414yes—
302C4×Dic79C24116yes—
303C4×Dic79C24116yes—
304C4×Dic79C2418yes—
305C4×Dic79C24116yes—
306C2×Q8×C79—28no—
307C2×Q8×C79—24no—
308C2×Q8×C79—24no—
309C2×Q8×C79C2418yes—
310C2×Q8×C79C2414yes—
311C2×Q8×C79C2414yes—
312C22×C4×C79C2412yes—
313C22×C4×C79C2414yes—
314C22×C4×C79C2412yes—
315C22×C4×C79C2412yes—
316C22×C4×C79C2411yescharacteristic
317C22×C4×C79C2412yes—
318C22×C4×C79C2411yescharacteristic
319C22×C4×C79C2411yescharacteristic
320C4⋊C4×C79C2414yes—
321C4⋊C4×C79C2414yes—
322C4⋊C4×C79C2418yes—
323C4⋊C4×C79C24116yes—
324C4⋊C4×C79C2418yes—
325C4⋊C4×C79C2418yes—
326C4⋊C4×C79C24116yes—
327C4⋊C4×C79C2418yes—
328C4⋊C4×C79C24116yes—
329C42×C79C2418yes—
330C42×C79C24116yes—
331C42×C79C2414yes—
332C42×C79C2418yes—
333C23×C79C2511yescharacteristic
334C22×D79—22no—
335C22×D79—22no—
336C22×D79—24no—
337C22×D79—24no—
338C22×D79—24no—
339C22×D79C2×#4114yes—
340C22×D79C2514yes—
341C22×D79C2512yes—
342Q8×C79—216no—
343Q8×C79—28no—
344Q8×C79—28no—
345C2×C4×C79—24no—
346C2×C4×C79—28no—
347C2×C4×C79—24no—
348C2×C4×C79—22no—
349C2×C4×C79—24no—
350C2×C4×C79—24no—
351C2×C4×C79C2×#4114yes—
352C2×C4×C792−1+414yes—
353C2×C4×C79C2514yes—
354C2×C4×C79C2514yes—
355C2×C4×C79C2512yes—
356C2×C4×C79C2518yes—
357C2×C4×C79C2514yes—
358C2×C4×C79C2514yes—
359C2×C4×C79C2512yes—
360C2×C4×C79C2512yes—
361C2×Dic79—28no—
362C2×Dic79—24no—
363C2×Dic79—22no—
364C2×Dic79—24no—
365C2×Dic79—24no—
366C2×Dic79C2×#4114yes—
367C2×Dic792−1+414yes—
368C2×Dic79C2514yes—
369C2×Dic79C2514yes—
370C2×Dic79C2514yes—
371C2×Dic79C2512yes—
372C2×Dic79C2518yes—
373C2×Dic79C2512yes—
374C2×Dic79C2512yes—
375D316—216no—
376D316—28no—
377C4×D79—232no—
378C4×D79—28no—
379C4×D79—216no—
380C4×D79—216no—
381C4×D79—28no—
382C4×D79—216no—
383C4×D79C2×#41116yes—
384Dic158—216no—
385Dic158—28no—
386Dic158—232no—
387Dic158—216no—
388C22×C79C22×#4112yes—
389C22×C79C2×2−1+412yes—
390C22×C79C2×2−1+412yes—
391C22×C79C2611yescharacteristic
392C2×D79—22no—
393C2×D79—22no—
394C2×D79—28no—
395C2×D79—24no—
396C2×D79—24no—
397C2×D79—24no—
398C2×D79—48no—
399C2×D79C22×#4114yes—
400C4×C79—28no—
401C4×C79—24no—
402C4×C79—24no—
403C4×C79—24no—
404C4×C79—24no—
405C4×C79—22no—
406C4×C79C22×#4114yes—
407C4×C79C2×2−1+414yes—
408Dic79—28no—
409Dic79—24no—
410Dic79—24no—
411Dic79—24no—
412Dic79—22no—
413Dic79C22×#4114yes—
414Dic79C2×2−1+414yes—
415C2×#3509—791nomaximal, Sylow
416C2×C79#350914yescomplemented
417C2×C79C23×#4111yescharacteristic
418C2×C79C22×2−1+411yescharacteristic
419C2×C79C22×2−1+411yescharacteristic
420D79—24no—
421D79—44no—
422#3509—7932no—
423C2×#557—792no—
424C2×#557—791no—
425C2×#557D7911yescharacteristic, complemented
426C2×#556—791no—
427C2×#556—792no—
428C2×#556—791no—
429C2×#552—794no—
430C2×#552—792no—
431C2×#552—792no—
432C2×#541—794no—
433C2×#536—792no—
434C2×#533—792no—
435C2×#533—791no—
436C2×#533—792no—
437C22×C4⋊Q8—791no—
438C2×#519—792no—
439C2×C4×#41—791no—
440C79C2×#350911yescharacteristic, complemented, Sylow
441C22×#41—791no—
442C23×Q8—792no—
443#557—7932no—
444#557—7916no—
445#557C2×D79116yescomplemented
446#556—7916no—
447#556—7932no—
448#556—7916no—
449#552—7964no—
450#552—7932no—
451#552—7932no—
452#541—7964no—
453#536—7932no—
454#533—7932no—
455#533—7916no—
456#533—7932no—
457C2×C4⋊Q8—792no—
458C2×C4⋊Q8—791no—
459C2×C4⋊Q8—792no—
460C2×C4⋊Q8—7916no—
461C2×C4⋊Q8—792no—
462C2×C4⋊Q8—792no—
463C2×C4⋊Q8—791no—
464C2×C4⋊Q8—791no—
465C2×C4⋊Q8C2×D7911yescharacteristic
466C2×C4⋊Q8C2×D7912yes—
467C2×#126—794no—
468C2×#126—794no—
469C2×#126—794no—
470C2×#126—794no—
471C2×#125—792no—
472C2×#125—794no—
473C2×#125—794no—
474C2×#125—794no—
475C2×#125—794no—
476C2×#125—792no—
477C2×#125C2×D7912yes—
478C2×#125C2×D7914yes—
479C2×#124—792no—
480C2×#124—792no—
481C2×#123—794no—
482C2×#123—794no—
483C2×C22⋊Q8—791no—
484C2×C22⋊Q8—792no—
485C2×C22⋊Q8—794no—
486C2×C22⋊Q8—794no—
487C2×C22⋊Q8—792no—
488C2×C22⋊Q8—791no—
489C2×C22⋊Q8—794no—
490C2×C22⋊Q8—792no—
491#519—7932no—
492C4×#41—7916no—
493C2×C4×Q8—791no—
494C2×C4×Q8—792no—
495C2×C4×Q8—794no—
496C2×C4×Q8—792no—
497C2×C4×Q8—794no—
498C2×C4×Q8—794no—
499C2×C4×Q8—792no—
500C2×C4×Q8—792no—
501C2×C4×Q8—791no—
502C2×C4×Q8—792no—
503C2×C4×Q8C2×D7911yescharacteristic
504C2×C4×Q8C2×D7912yes—
505C2×C4×Q8C2×D7912yes—
506C2×C4×Q8C2×D7911yescharacteristic
507C2×C4×D4—792no—
508C2×C4×D4—791no—
509C2×C4×D4—792no—
510C2×C4×D4—791no—
511C2×#117—791no—
512C2×#117—792no—
513C2×#117—794no—
514C2×#117—792no—
515C2×#117—792no—
516C2×#117—792no—
517C2×#117—794no—
518C2×#117—794no—
519C22×C4⋊C4—792no—
520C22×C4⋊C4—792no—
521C22×C42—791no—
522C22×C42—792no—
523C2×#41—798no—
524C2×#41—1588no—
525C22×Q8—7916no—
526C22×Q8—792no—
527C22×Q8—791no—
528C22×Q8—794no—
529C22×Q8—792no—
530C22×Q8—15816no—
531C22×Q8C22×D7912yes—
532C22×Q8C22×D7911yescharacteristic
533C22×Q8C22×D7911yescharacteristic
534C22×D4—792no—
535C22×D4—791no—
536C23×C4—791no—
537C23×C4—794no—
538C23×C4—791no—
539C23×C4—791no—
540C23×C4—792no—
541C23×C4—792no—
542C23×C4—792no—
543C4⋊Q8—7916no—
544C4⋊Q8—798no—
545C4⋊Q8—7916no—
546C4⋊Q8—7916no—
547C4⋊Q8—7916no—
548C4⋊Q8—798no—
549C4⋊Q8—798no—
550C4⋊Q8C22×D7918yes—
551C4⋊Q8C22×D79116yes—
552#126—7932no—
553#126—7932no—
554#126—7932no—
555#126—7932no—
556#125—7916no—
557#125—7932no—
558#125—7932no—
559#125—7932no—
560#125—7932no—
561#125—7916no—
562#125C22×D79116yes—
563#125C22×D79132yes—
564#124—7916no—
565#124—7916no—
566#123—7932no—
567#123—7932no—
568C22⋊Q8—798no—
569C22⋊Q8—7916no—
570C22⋊Q8—7932no—
571C22⋊Q8—7932no—
572C22⋊Q8—7916no—
573C22⋊Q8—798no—
574C22⋊Q8—7932no—
575C22⋊Q8—7916no—
576C4×Q8—798no—
577C4×Q8—7916no—
578C4×Q8—7932no—
579C4×Q8—7916no—
580C4×Q8—7932no—
581C4×Q8—7932no—
582C4×Q8—7916no—
583C4×Q8—7916no—
584C4×Q8—7916no—
585C4×Q8—798no—
586C4×Q8C22×D7918yes—
587C4×Q8C22×D79116yes—
588C4×Q8C22×D79116yes—
589C4×Q8C22×D7918yes—
590C4×D4—7916no—
591C4×D4—798no—
592C4×D4—7916no—
593C4×D4—798no—
594#117—798no—
595#117—7916no—
596#117—7932no—
597#117—7916no—
598#117—7916no—
599#117—7916no—
600#117—7932no—
601#117—7932no—
602C2×C4⋊C4—794no—
603C2×C4⋊C4—792no—
604C2×C4⋊C4—794no—
605C2×C4⋊C4—792no—
606C2×C4⋊C4—792no—
607C2×C4⋊C4—791no—
608C2×C4⋊C4—791no—
609C2×C4⋊C4—792no—
610C2×C4⋊C4—792no—
611C2×C4⋊C4—792no—
612C2×C4⋊C4—794no—
613C2×C4⋊C4—794no—
614C2×C4⋊C4—794no—
615C2×C4⋊C4—794no—
616C2×C4⋊C4—794no—
617C2×C4⋊C4—792no—
618C2×C4⋊C4—792no—
619C2×C4⋊C4—792no—
620C2×C4⋊C4—7916no—
621C2×C4⋊C4—7916no—
622C2×C4⋊C4C22×D7912yes—
623C2×C4⋊C4C22×D7912yes—
624C2×C4⋊C4C22×D7911yescharacteristic
625C2×C4⋊C4C22×D7911yescharacteristic
626C2×C4⋊C4C22×D7912yes—
627C2×C4⋊C4C22×D7914yes—
628C2×C4⋊C4C22×D7914yes—
629C2×C4⋊C4C22×D7914yes—
630C2×C4⋊C4C22×D7912yes—
631C2×C22⋊C4—792no—
632C2×C22⋊C4—792no—
633C2×C22⋊C4—792no—
634C2×C22⋊C4—792no—
635C2×C22⋊C4—792no—
636C2×C22⋊C4—794no—
637C2×C22⋊C4—794no—
638C2×C22⋊C4—794no—
639C2×C22⋊C4—794no—
640C2×C42—792no—
641C2×C42—794no—
642C2×C42—794no—
643C2×C42—794no—
644C2×C42—791no—
645C2×C42—792no—
646C2×C42—792no—
647C2×C42—791no—
648C2×C42—791no—
649C2×C42—798no—
650C2×C42—7916no—
651C2×C42C22×D7914yes—
652C2×C42C22×D7912yes—
653C2×C42C22×D7912yes—
654C2×C42C22×D7911yescharacteristic
655C24—791no—
656C24—792no—
657#41—15832no—
658C2×Q8—28no—
659C2×Q8—24no—
660C2×Q8—24no—
661C2×Q8—798no—
662C2×Q8—794no—
663C2×Q8—7916no—
664C2×Q8—798no—
665C2×Q8—1588no—
666C2×Q8—15816no—
667C2×Q8—15864no—
668C2×Q8—1588no—
669C2×Q8—1584no—
670C2×Q8C23×D7918yes—
671C2×Q8C23×D7914yes—
672C2×Q8C23×D7914yes—
673C2×D4—798no—
674C2×D4—794no—
675C2×D4—1588no—
676C2×D4—1584no—
677C22×C4—791no—
678C22×C4—791no—
679C22×C4—798no—
680C22×C4—794no—
681C22×C4—792no—
682C22×C4—792no—
683C22×C4—792no—
684C22×C4—791no—
685C22×C4—794no—
686C22×C4—794no—
687C22×C4—794no—
688C22×C4—798no—
689C22×C4—798no—
690C22×C4—798no—
691C22×C4—7916no—
692C22×C4—1588no—
693C22×C4—1584no—
694C22×C4—1588no—
695C22×C4—15816no—
696C22×C4—1588no—
697C22×C4—1584no—
698C22×C4C23×D7912yes—
699C22×C4C23×D7912yes—
700C22×C4C23×D7911yescharacteristic
701C22×C4C23×D7914yes—
702C22×C4C23×D7912yes—
703C22×C4C23×D7912yes—
704C22×C4C23×D7911yescharacteristic
705C22×C4C23×D7911yescharacteristic
706C4⋊C4—7916no—
707C4⋊C4—7916no—
708C4⋊C4—798no—
709C4⋊C4—798no—
710C4⋊C4—798no—
711C4⋊C4—7916no—
712C4⋊C4—7916no—
713C4⋊C4—7916no—
714C4⋊C4—7916no—
715C4⋊C4—798no—
716C4⋊C4—798no—
717C4⋊C4—798no—
718C4⋊C4—798no—
719C4⋊C4—794no—
720C4⋊C4—794no—
721C4⋊C4—798no—
722C4⋊C4—7916no—
723C4⋊C4—798no—
724C4⋊C4C23×D7918yes—
725C4⋊C4C23×D7918yes—
726C4⋊C4C23×D7914yes—
727C4⋊C4C23×D7914yes—
728C4⋊C4C23×D7918yes—
729C4⋊C4C23×D79116yes—
730C4⋊C4C23×D79116yes—
731C4⋊C4C23×D79116yes—
732C4⋊C4C23×D7918yes—
733C22⋊C4—798no—
734C22⋊C4—798no—
735C22⋊C4—798no—
736C22⋊C4—798no—
737C22⋊C4—798no—
738C22⋊C4—7916no—
739C22⋊C4—7916no—
740C22⋊C4—7916no—
741C22⋊C4—7916no—
742C42—794no—
743C42—798no—
744C42—794no—
745C42—798no—
746C42—794no—
747C42—7916no—
748C42—7916no—
749C42—7916no—
750C42—798no—
751C42C23×D7918yes—
752C42C23×D7914yes—
753C42C23×D79116yes—
754C42C23×D7918yes—
755C23—792no—
756C23—794no—
757C23—794no—
758C23—1584no—
759C23—1584no—
760C23—1584no—
761C23—1582no—
762C23—1582no—
763C23C24×D7911yescharacteristic
764Q8—28no—
765Q8—216no—
766Q8—28no—
767Q8—15832no—
768Q8—15816no—
769Q8—1588no—
770Q8—15816no—
771D4—15816no—
772D4—1588no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—28no—
779C2×C4—794no—
780C2×C4—792no—
781C2×C4—792no—
782C2×C4—794no—
783C2×C4—7916no—
784C2×C4—794no—
785C2×C4—794no—
786C2×C4—794no—
787C2×C4—792no—
788C2×C4—798no—
789C2×C4—15816no—
790C2×C4—15816no—
791C2×C4—1588no—
792C2×C4—15832no—
793C2×C4—1584no—
794C2×C4—1584no—
795C2×C4—1582no—
796C2×C4—1584no—
797C2×C4—1588no—
798C2×C4—15816no—
799C2×C4—1588no—
800C2×C4#41×D7914yes—
801C2×C4#1457920914yes—
802C2×C4C24×D7914yes—
803C2×C4C24×D7914yes—
804C2×C4C24×D7912yes—
805C2×C4C24×D7918yes—
806C2×C4C24×D7914yes—
807C2×C4C24×D7914yes—
808C2×C4C24×D7912yes—
809C2×C4C24×D7912yes—
810C22—3168no—
811C22—794no—
812C22—1584no—
813C22—1584no—
814C22—1584no—
815C22—1588no—
816C22—1582no—
817C22—1582no—
818C22C2×#41×D7912yes—
819C222−1+4×D7912yes—
820C22C2×#1457920912yes—
821C22C25×D7911yescharacteristic
822C4—24no—
823C4—28no—
824C4—24no—
825C4—22no—
826C4—24no—
827C4—24no—
828C4—794no—
829C4—794no—
830C4—1588no—
831C4—1584no—
832C4—1584no—
833C4—1582no—
834C4—1584no—
835C4C2×#41×D7914yes—
836C4C2×#1457920914yes—
837C2—3164no—
838C2—1584no—
839C2#2377728314yesdirect product factor
840C2C22×#41×D7911yescharacteristic
841C2C2×2−1+4×D7911yescharacteristic
842C2C22×#1457920911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#557×C79C2
socleC23×C79C25
prime radicalC22×#11929625C22
hypercenterC2×#557D79
hypocenterC79C2×#3509
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #23777283C2direct (N × H)
2. C2×#19099291C2semidirect
3. C2×#19099288C2semidirect
4. C2×#19099287C2semidirect
5. C2×#19099286C2semidirect
6. C2×#19099285C2semidirect
7. C2×#19099254C2semidirect
8. C2×#19099251C2semidirect
9. C2×#19099245C2semidirect
10. C2×#19099172C2semidirect
12. C2×#19099119C2semidirect
13. C2×#19099117C2semidirect
14. C2×#19099117C2semidirect
15. C2×C4⋊Q8×D79C2semidirect
16. C2×#19099039C2semidirect
18. C2×#557×C79C2semidirect
21. #19099291C22semidirect
22. #19099288C22semidirect
23. #19099287C22semidirect
24. #19099286C22semidirect
25. #19099285C22semidirect
26. #19099254C22semidirect
27. #19099251C22semidirect
28. #19099245C22semidirect
29. #19099172C22semidirect
31. #19099119C22semidirect
32. #19099117C22semidirect
33. #19099117C22semidirect
41. C4⋊Q8×D79C22semidirect
64. #19099039C22semidirect
92. #557×C79C22semidirect
416. C2×C79#3509semidirect
425. C2×#557D79semidirect
440. C79C2×#3509semidirect
445. #557C2×D79semidirect
839. C2#23777283direct (N × H)

Maximal subgroups

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

subgroupindex
#237772832
C2×#190992912
C2×#190992882
C2×#190992872
C2×#190992862
C2×#190992852
C2×#190992542
C2×#190992512
C2×#190992452
C2×#190991722
C2×#190991382
C2×#190991192
C2×#190991172
C2×C4⋊Q8×D792
C2×#190990392
C2×C4×#119296252
C2×#557×C792
C2×#350979