Finite Group Databasebeta

← C2×#23777409 #35196531

Subgroups — C2×#23777409 #35196531

Order 20224.

7118 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777409C2132yesmaximal, direct product factor
2C2×#19099293C211yesmaximal, characteristic, complemented
3C2×#19099287C211yesmaximal, characteristic, complemented
4C2×#19099285C214yesmaximal, complemented
5C2×#19099284C212yesmaximal, complemented
6C2×#19099281C212yesmaximal, complemented
7C2×#19099279C211yesmaximal, characteristic, complemented
8C2×#19099276C212yesmaximal, complemented
9C2×#19099228C211yesmaximal, characteristic, complemented
10C2×#19099223C212yesmaximal, complemented
11C2×#19099185C212yesmaximal, complemented
12C2×#19099183C214yesmaximal, complemented
13C2×#19099119C212yesmaximal, complemented
14C2×#19099098C212yesmaximal, complemented
15C2×#19099097C211yesmaximal, characteristic, complemented
16C2×#19099039C212yesmaximal, complemented
17C2×C4×#11929624C211yesmaximal, characteristic, complemented
18C2×#533×C79C211yesmaximal, characteristic, complemented
19C22×#11929624C2211yescharacteristic
20C22×Q8×D79C2212yes—
21#19099293C22116yescomplemented
22#19099287C22116yescomplemented
23#19099285C22164yescomplemented
24#19099284C22132yescomplemented
25#19099281C22132yescomplemented
26#19099279C22116yescomplemented
27#19099276C22132yescomplemented
28#19099228C22116yescomplemented
29#19099223C22132yescomplemented
30#19099185C22132yescomplemented
31#19099183C22164yescomplemented
32#19099119C22132yescomplemented
33C2×#14579160C2212yes—
34C2×#14579160C2212yes—
35C2×#14579160C2212yes—
36C2×#14579159C2214yes—
37#19099098C22132yescomplemented
38#19099097C22116yescomplemented
39C2×#14579156C2214yes—
40C2×#14579156C2214yes—
41C2×#14579155C2214yes—
42C2×#14579155C2212yes—
43C2×#14579154C2214yes—
44C2×#14579153C2211yescharacteristic
45C2×#14579150C2214yes—
46C2×#14579150C2212yes—
47C2×#14579149C2214yes—
48C2×#14579149C2211yescharacteristic
49C2×#14579147C2214yes—
50C2×#14579147C2214yes—
51C2×#14579146C2214yes—
52C2×#14579144C2212yes—
53C2×#14579141C2212yes—
54C2×#14579140C2211yescharacteristic
55C2×#14579139C2214yes—
56C2×#14579139C2214yes—
57C2×#14579139C2214yes—
58C2×#14579137C2212yes—
59C2×#14579136C2212yes—
60C2×#14579136C2212yes—
61C2×#14579135C2211yescharacteristic
62C2×#14579134C2214yes—
63#19099039C22132yescomplemented
64C4×#11929624C22116yescomplemented
65C2×Q8×Dic79C2212yes—
66C2×C4×Dic158C2211yescharacteristic
67C2×C4×Dic158C2211yescharacteristic
68C2×C4×Dic158C2214yes—
69C2×C4×Dic158C2211yescharacteristic
70C2×#14579126C2214yes—
71C2×#14579126C2212yes—
72C2×#14579126C2212yes—
73C2×#14579126C2214yes—
74C2×C4×D316C2211yescharacteristic
75C2×C4×D316C2211yescharacteristic
76C2×C4×D316C2211yescharacteristic
77C2×#14579123C2214yes—
78C2×#14579123C2212yes—
79C2×C4×C22⋊D79C2212yes—
80C2×C4×C22⋊D79C2212yes—
81C2×C4×C22⋊D79C2212yes—
82C2×#14579120C2211yescharacteristic
83C2×#14579119C2214yes—
84C2×#14579119C2212yes—
85C2×#14579119C2212yes—
86C2×#14579119C2212yes—
87C2×#14579118C2212yes—
88C2×#14579118C2212yes—
89C2×#14579118C2214yes—
90C2×C42×D79C2212yes—
91#533×C79C22116yescomplemented
92C2×C4⋊Q8×C79C2211yescharacteristic
93C2×C4⋊Q8×C79C2211yescharacteristic
94C2×#125×C79C2212yes—
95C2×C22⋊Q8×C79C2212yes—
96C2×C22⋊Q8×C79C2212yes—
97C2×C4×Q8×C79C2212yes—
98C2×C4×Q8×C79C2212yes—
99C2×#117×C79C2212yes—
100C22×C42×C79C2211yescharacteristic
101C2×#11929624—28no—
102C2×#11929624C2318yes—
103C22×Dic158C2311yescharacteristic
104C22×Dic158C2314yes—
105C22×Dic158C2314yes—
106C22×Dic158C2311yescharacteristic
107C2×Q8×D79—216no—
108C2×Q8×D79C23116yes—
109C22×D316C2311yescharacteristic
110C22×D316C2311yescharacteristic
111C22×D316C2314yes—
112C22×C22⋊D79C2312yes—
113C22×C22⋊D79C2312yes—
114C22×C4×D79C2312yes—
115C22×C4×D79C2312yes—
116C22×C4×D79C2312yes—
117C22×C4×D79C2314yes—
118C22×C4×D79C2312yes—
119#14579160C23116yes—
120#14579160C23116yes—
121#14579160C23116yes—
122#14579159C23132yes—
123#14579156C23132yes—
124#14579156C23132yes—
125#14579155C23132yes—
126#14579155C23116yes—
127#14579154C23132yes—
128#14579153C2318yes—
129#14579150C23132yes—
130#14579150C23116yes—
131#14579149C23132yes—
132#14579149C2318yes—
133#14579147C23132yes—
134#14579147C23132yes—
135#14579146C23132yes—
136#14579144C23116yes—
137#14579141C23116yes—
138#14579140C2318yes—
139#14579139C23132yes—
140#14579139C23132yes—
141#14579139C23132yes—
142#14579137C23116yes—
143#14579136C23116yes—
144#14579136C23116yes—
145#14579135C2318yes—
146#14579134C23132yes—
147Q8×Dic79C23116yes—
148C4×Dic158C2318yes—
149C4×Dic158C23132yes—
150C4×Dic158C2318yes—
151C4×Dic158C2318yes—
152#14579126C23132yes—
153#14579126C23116yes—
154#14579126C23116yes—
155#14579126C23132yes—
156C4×D316C2318yes—
157C4×D316C2318yes—
158C4×D316C2318yes—
159#14579123C23132yes—
160#14579123C23116yes—
161C4×C22⋊D79C23116yes—
162C4×C22⋊D79C23116yes—
163C4×C22⋊D79C23116yes—
164#14579120C2318yes—
165#14579119C23132yes—
166#14579119C23116yes—
167#14579119C23116yes—
168#14579119C23116yes—
169#14579118C23116yes—
170#14579118C23132yes—
171#14579118C23116yes—
172C2×C4⋊Dic79C2311yescharacteristic
173C2×C4⋊Dic79C2311yescharacteristic
174C2×C4⋊Dic79C2311yescharacteristic
175C2×C4⋊Dic79C2314yes—
176C2×C4⋊Dic79C2311yescharacteristic
177C2×Dic79⋊C4C2312yes—
178C2×Dic79⋊C4C2312yes—
179C2×Dic79⋊C4C2314yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2312yes—
182C2×Dic79⋊C4C2312yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2314yes—
185C2×Dic79⋊C4C2312yes—
186C2×C22⋊Dic79C2312yes—
187C2×C22⋊Dic79C2312yes—
188C2×(C2×D79)⋊C4C2312yes—
189C2×(C2×D79)⋊C4C2314yes—
190C2×(C2×D79)⋊C4C2312yes—
191C2×(C2×D79)⋊C4C2312yes—
192C2×(C2×D79)⋊C4C2312yes—
193C2×(C2×D79)⋊C4C2314yes—
194C2×(C2×D79)⋊C4C2314yes—
195C2×(C2×D79)⋊C4C2312yes—
196C2×(C2×D79)⋊C4C2314yes—
197C2×(C2×D79)⋊C4C2314yes—
198C2×(C2×D79)⋊C4C2312yes—
199C2×C4×Dic79C2312yes—
200C2×C4×Dic79C2312yes—
201C2×C4×Dic79C2312yes—
202C2×C4×Dic79C2314yes—
203C2×C4×Dic79C2312yes—
204C2×C4×Dic79C2314yes—
205C2×C4×Dic79C2314yes—
206C42×D79C23116yes—
207C22×Q8×C79C2312yes—
208C22×Q8×C79C2312yes—
209C23×C4×C79C2311yescharacteristic
210C23×C4×C79C2311yescharacteristic
211C23×C4×C79C2311yescharacteristic
212C4⋊Q8×C79C2318yes—
213C4⋊Q8×C79C2318yes—
214#125×C79C23116yes—
215C22⋊Q8×C79C23116yes—
216C22⋊Q8×C79C23116yes—
217C4×Q8×C79C23116yes—
218C4×Q8×C79C23116yes—
219#117×C79C23116yes—
220C2×C4⋊C4×C79C2312yes—
221C2×C4⋊C4×C79C2312yes—
222C2×C4⋊C4×C79C2314yes—
223C2×C4⋊C4×C79C2314yes—
224C2×C4⋊C4×C79C2312yes—
225C2×C4⋊C4×C79C2312yes—
226C2×C22⋊C4×C79C2314yes—
227C2×C42×C79C2311yescharacteristic
228C2×C42×C79C2311yescharacteristic
229C2×C42×C79C2311yescharacteristic
230C2×C42×C79C2311yescharacteristic
231C2×C42×C79C2318yes—
232C2×C42×C79C2314yes—
233C23×D79C2412yes—
234C23×D79C2412yes—
235#11929624—232no—
236C2×Dic158—216no—
237C2×Dic158—24no—
238C2×Dic158—48no—
239C2×Dic158#4118yes—
240C2×Dic158C24116yes—
241C2×Dic158C2414yes—
242C2×Dic158C24116yes—
243C2×Dic158C2414yes—
244Q8×D79—264no—
245C2×D316—24no—
246C2×D316—24no—
247C2×D316—48no—
248C2×D316C2414yes—
249C2×D316C2414yes—
250C2×D316C24116yes—
251C2×C22⋊D79—28no—
252C2×C22⋊D79—44no—
253C2×C22⋊D79C2418yes—
254C2×C22⋊D79C2418yes—
255C22×Dic79C2412yes—
256C22×Dic79C2412yes—
257C22×Dic79C2412yes—
258C22×Dic79C2412yes—
259C22×Dic79C2412yes—
260C22×Dic79C2412yes—
261C2×C4×D79—216no—
262C2×C4×D79—28no—
263C2×C4×D79—28no—
264C2×C4×D79—28no—
265C2×C4×D79—44no—
266C2×C4×D79C2418yes—
267C2×C4×D79C24116yes—
268C2×C4×D79C2418yes—
269C2×C4×D79C2418yes—
270C2×C4×D79C2418yes—
271C4⋊Dic79C2414yes—
272C4⋊Dic79C2414yes—
273C4⋊Dic79C2414yes—
274C4⋊Dic79C24116yes—
275C4⋊Dic79C2414yes—
276Dic79⋊C4C2418yes—
277Dic79⋊C4C2418yes—
278Dic79⋊C4C24116yes—
279Dic79⋊C4C2418yes—
280Dic79⋊C4C2418yes—
281Dic79⋊C4C2418yes—
282Dic79⋊C4C24116yes—
283Dic79⋊C4C24116yes—
284Dic79⋊C4C2418yes—
285C22⋊Dic79C2418yes—
286C22⋊Dic79C2418yes—
287(C2×D79)⋊C4C2418yes—
288(C2×D79)⋊C4C24116yes—
289(C2×D79)⋊C4C2418yes—
290(C2×D79)⋊C4C2418yes—
291(C2×D79)⋊C4C2418yes—
292(C2×D79)⋊C4C24116yes—
293(C2×D79)⋊C4C24116yes—
294(C2×D79)⋊C4C2418yes—
295(C2×D79)⋊C4C24116yes—
296(C2×D79)⋊C4C24116yes—
297(C2×D79)⋊C4C2418yes—
298C4×Dic79C2418yes—
299C4×Dic79C2418yes—
300C4×Dic79C2418yes—
301C4×Dic79C24116yes—
302C4×Dic79C2418yes—
303C4×Dic79C24116yes—
304C4×Dic79C24116yes—
305C24×C79C2411yescharacteristic
306C2×Q8×C79—28no—
307C2×Q8×C79—44no—
308C2×Q8×C79C2418yes—
309C2×Q8×C79C2418yes—
310C22×C4×C79—24no—
311C22×C4×C79—24no—
312C22×C4×C79—42no—
313C22×C4×C79C2414yes—
314C22×C4×C79C2414yes—
315C22×C4×C79C2414yes—
316C22×C4×C79C2411yescharacteristic
317C22×C4×C79C2411yescharacteristic
318C22×C4×C79C2411yescharacteristic
319C22×C4×C79C2411yescharacteristic
320C22×C4×C79C2414yes—
321C22×C4×C79C2414yes—
322C22×C4×C79C2411yescharacteristic
323C22×C4×C79C2411yescharacteristic
324C4⋊C4×C79C2418yes—
325C4⋊C4×C79C2418yes—
326C4⋊C4×C79C24116yes—
327C4⋊C4×C79C24116yes—
328C4⋊C4×C79C2418yes—
329C4⋊C4×C79C2418yes—
330C22⋊C4×C79C24116yes—
331C42×C79C2414yes—
332C42×C79C2414yes—
333C42×C79C2414yes—
334C42×C79C2414yes—
335C42×C79C24116yes—
336C23×C79—22no—
337C23×C79—22no—
338C23×C79—22no—
339C23×C79C2512yes—
340C23×C79C2511yescharacteristic
341C22×D79—24no—
342C22×D79—24no—
343C22×D79—24no—
344C22×D79—24no—
345C22×D79—24no—
346C22×D79—24no—
347C22×D79C2514yes—
348C22×D79C2514yes—
349Q8×C79—216no—
350Q8×C79—48no—
351C2×C4×C79—22no—
352C2×C4×C79—28no—
353C2×C4×C79—22no—
354C2×C4×C79—22no—
355C2×C4×C79—28no—
356C2×C4×C79—22no—
357C2×C4×C79—28no—
358C2×C4×C79—28no—
359C2×C4×C79—44no—
360C2×C4×C79C2×#4114yes—
361C2×C4×C792−1+414yes—
362C2×C4×C79C2512yes—
363C2×C4×C79C2512yes—
364C2×C4×C79C2518yes—
365C2×C4×C79C2518yes—
366C2×C4×C79C2512yes—
367C2×C4×C79C2512yes—
368C2×C4×C79C2512yes—
369C2×C4×C79C2512yes—
370C22⋊D79—216no—
371C22⋊D79—48no—
372C2×Dic79—24no—
373C2×Dic79—24no—
374C2×Dic79—24no—
375C2×Dic79—24no—
376C2×Dic79—24no—
377C2×Dic79C2×#4118yes—
378C2×Dic79C2514yes—
379C2×Dic79C2514yes—
380C2×Dic79C2514yes—
381C2×Dic79C2514yes—
382C2×Dic79C2514yes—
383C2×Dic79C2514yes—
384D316—28no—
385D316—28no—
386D316—416no—
387C4×D79—216no—
388C4×D79—216no—
389C4×D79—232no—
390C4×D79—216no—
391C4×D79—48no—
392Dic158—28no—
393Dic158—232no—
394Dic158—416no—
395Dic158C2×#41116yes—
396C22×C79—22no—
397C22×C79—22no—
398C22×C79—22no—
399C22×C79—44no—
400C22×C79C22×#4112yes—
401C22×C79C2×2−1+412yes—
402C22×C79#58512yes—
403C22×C79C2611yescharacteristic
404C2×D79—24no—
405C2×D79—24no—
406C2×D79—24no—
407C2×D79—24no—
408C2×D79—24no—
409C2×D79—24no—
410C2×D79—48no—
411C2×D79—48no—
412C4×C79—22no—
413C4×C79—28no—
414C4×C79—22no—
415C4×C79—22no—
416C4×C79—22no—
417C4×C79—28no—
418C4×C79C22×#4114yes—
419C4×C79C2×2−1+414yes—
420Dic79—24no—
421Dic79—24no—
422Dic79—24no—
423Dic79—24no—
424Dic79—24no—
425Dic79C22×#4118yes—
426C2×#3518—791nomaximal, Sylow
427C2×C79—42no—
428C2×C79#351814yescomplemented
429C2×C79C23×#4111yescharacteristic
430C2×C79C22×2−1+411yescharacteristic
431C2×C79C2×#58511yescharacteristic
432D79—44no—
433D79—44no—
434#3518—7932no—
435C2×Q82—791no—
436C2×#556—791no—
437C2×#556—792no—
438C2×#556—794no—
439C2×#556—792no—
440C2×#555—791no—
441C2×#555—792no—
442C2×D4×Q8—791no—
443C2×#548—792no—
444C2×#542—794no—
445C2×#542—792no—
446C2×#533—792no—
447C2×#533D7911yescharacteristic, complemented
448C2×#529—791no—
449C2×#529—792no—
450C2×#519—792no—
451C2×C4×#41—791no—
452C79C2×#351811yescharacteristic, complemented, Sylow
453C22×#41—791no—
454C23×Q8—792no—
455Q82—7916no—
456#556—7916no—
457#556—7932no—
458#556—7964no—
459#556—7932no—
460#555—7916no—
461#555—7932no—
462D4×Q8—7916no—
463#548—7932no—
464#542—7964no—
465#542—7932no—
466#533—7932no—
467#533C2×D79116yescomplemented
468C2×C4⋊Q8—794no—
469C2×C4⋊Q8—792no—
470C2×C4⋊Q8—792no—
471C2×C4⋊Q8—792no—
472C2×C4⋊Q8C2×D7911yescharacteristic
473C2×C4⋊Q8C2×D7911yescharacteristic
474#529—7932no—
475#529—7916no—
476C2×#126—794no—
477C2×#126—794no—
478C2×#126—794no—
479C2×#126—792no—
480C2×#126—794no—
481C2×#125—791no—
482C2×#125C2×D7912yes—
483C2×#124—792no—
484C2×#124—794no—
485C2×#124—794no—
486C2×#124—794no—
487C2×#124—791no—
488C2×#124—794no—
489C2×#123—792no—
490C2×#123—794no—
491C2×C22⋊Q8—792no—
492C2×C22⋊Q8—791no—
493C2×C22⋊Q8—792no—
494C2×C22⋊Q8—794no—
495C2×C22⋊Q8—794no—
496C2×C22⋊Q8—794no—
497C2×C22⋊Q8C2×D7912yes—
498C2×C22⋊Q8C2×D7912yes—
499C2×#121—791no—
500C2×#121—792no—
501C2×#121—792no—
502C2×#121—794no—
503#519—7932no—
504C4×#41—7916no—
505C2×C4×Q8—792no—
506C2×C4×Q8—794no—
507C2×C4×Q8—792no—
508C2×C4×Q8—792no—
509C2×C4×Q8—794no—
510C2×C4×Q8—791no—
511C2×C4×Q8—791no—
512C2×C4×Q8—794no—
513C2×C4×Q8—791no—
514C2×C4×Q8C2×D7912yes—
515C2×C4×Q8C2×D7912yes—
516C2×C4×D4—792no—
517C2×C4×D4—792no—
518C2×C4×D4—792no—
519C2×C4×D4—794no—
520C2×C4×D4—792no—
521C2×C4×D4—791no—
522C2×C4×D4—791no—
523C2×C4×D4—791no—
524C2×#117—791no—
525C2×#117—794no—
526C2×#117—792no—
527C2×#117—792no—
528C2×#117—792no—
529C2×#117—792no—
530C2×#117—792no—
531C2×#117—794no—
532C2×#117C2×D7912yes—
533C22×C42—792no—
534C22×C42C2×D7911yescharacteristic
535C2×#41—798no—
536C2×#41—1588no—
537C22×Q8—7916no—
538C22×Q8—794no—
539C22×Q8—791no—
540C22×Q8—791no—
541C22×Q8—794no—
542C22×Q8—15816no—
543C22×Q8C22×D7912yes—
544C22×Q8C22×D7912yes—
545C22×D4—792no—
546C22×D4—792no—
547C22×D4—794no—
548C22×D4—791no—
549C22×D4—791no—
550C23×C4—792no—
551C23×C4—794no—
552C23×C4—792no—
553C23×C4—792no—
554C23×C4—792no—
555C23×C4C22×D7911yescharacteristic
556C23×C4C22×D7911yescharacteristic
557C23×C4C22×D7911yescharacteristic
558C4⋊Q8—7932no—
559C4⋊Q8—7916no—
560C4⋊Q8—7916no—
561C4⋊Q8—7916no—
562C4⋊Q8C22×D7918yes—
563C4⋊Q8C22×D7918yes—
564#126—7932no—
565#126—7932no—
566#126—7932no—
567#126—7916no—
568#126—7932no—
569#125—798no—
570#125C22×D79116yes—
571#124—7916no—
572#124—7932no—
573#124—7932no—
574#124—7932no—
575#124—798no—
576#124—7932no—
577#123—7916no—
578#123—7932no—
579C22⋊Q8—7916no—
580C22⋊Q8—798no—
581C22⋊Q8—7916no—
582C22⋊Q8—7932no—
583C22⋊Q8—7932no—
584C22⋊Q8—7932no—
585C22⋊Q8C22×D79116yes—
586C22⋊Q8C22×D79116yes—
587#121—798no—
588#121—7916no—
589#121—7916no—
590#121—7932no—
591C4×Q8—7916no—
592C4×Q8—7932no—
593C4×Q8—7916no—
594C4×Q8—7916no—
595C4×Q8—7932no—
596C4×Q8—798no—
597C4×Q8—798no—
598C4×Q8—7932no—
599C4×Q8—798no—
600C4×Q8C22×D79116yes—
601C4×Q8C22×D79116yes—
602C4×D4—7916no—
603C4×D4—7916no—
604C4×D4—7916no—
605C4×D4—7932no—
606C4×D4—7916no—
607C4×D4—798no—
608C4×D4—798no—
609C4×D4—798no—
610#117—798no—
611#117—7932no—
612#117—7916no—
613#117—7916no—
614#117—7916no—
615#117—7916no—
616#117—7916no—
617#117—7932no—
618#117C22×D79116yes—
619C2×C4⋊C4—792no—
620C2×C4⋊C4—791no—
621C2×C4⋊C4—791no—
622C2×C4⋊C4—791no—
623C2×C4⋊C4—792no—
624C2×C4⋊C4—791no—
625C2×C4⋊C4—794no—
626C2×C4⋊C4—792no—
627C2×C4⋊C4—792no—
628C2×C4⋊C4—794no—
629C2×C4⋊C4—792no—
630C2×C4⋊C4—794no—
631C2×C4⋊C4—792no—
632C2×C4⋊C4—794no—
633C2×C4⋊C4C22×D7912yes—
634C2×C4⋊C4C22×D7912yes—
635C2×C4⋊C4C22×D7912yes—
636C2×C4⋊C4C22×D7914yes—
637C2×C4⋊C4C22×D7914yes—
638C2×C4⋊C4C22×D7912yes—
639C2×C22⋊C4—792no—
640C2×C22⋊C4—792no—
641C2×C22⋊C4—794no—
642C2×C22⋊C4—792no—
643C2×C22⋊C4—792no—
644C2×C22⋊C4—792no—
645C2×C22⋊C4—792no—
646C2×C22⋊C4—794no—
647C2×C22⋊C4—794no—
648C2×C22⋊C4—792no—
649C2×C22⋊C4—794no—
650C2×C22⋊C4—792no—
651C2×C22⋊C4—794no—
652C2×C22⋊C4C22×D7914yes—
653C2×C42—792no—
654C2×C42—794no—
655C2×C42—794no—
656C2×C42—792no—
657C2×C42—794no—
658C2×C42—792no—
659C2×C42—792no—
660C2×C42—7916no—
661C2×C42C22×D7911yescharacteristic
662C2×C42C22×D7911yescharacteristic
663C2×C42C22×D7914yes—
664C2×C42C22×D7911yescharacteristic
665C2×C42C22×D7918yes—
666C2×C42C22×D7911yescharacteristic
667C24—792no—
668C24—792no—
669C24C23×D7911yescharacteristic
670#41—15832no—
671C2×Q8—28no—
672C2×Q8—44no—
673C2×Q8—3168no—
674C2×Q8—798no—
675C2×Q8—7916no—
676C2×Q8—794no—
677C2×Q8—794no—
678C2×Q8—7916no—
679C2×Q8—15816no—
680C2×Q8—15864no—
681C2×Q8—1584no—
682C2×Q8C23×D7918yes—
683C2×Q8C23×D7918yes—
684C2×D4—3168no—
685C2×D4—3164no—
686C2×D4—798no—
687C2×D4—798no—
688C2×D4—7916no—
689C2×D4—794no—
690C2×D4—794no—
691C2×D4—1588no—
692C2×D4—1584no—
693C2×D4—1584no—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—42no—
697C22×C4—3164no—
698C22×C4—798no—
699C22×C4—792no—
700C22×C4—792no—
701C22×C4—792no—
702C22×C4—792no—
703C22×C4—792no—
704C22×C4—792no—
705C22×C4—798no—
706C22×C4—798no—
707C22×C4—7916no—
708C22×C4—798no—
709C22×C4—15816no—
710C22×C4—1588no—
711C22×C4—1588no—
712C22×C4—1588no—
713C22×C4C23×D7914yes—
714C22×C4C23×D7914yes—
715C22×C4C23×D7911yescharacteristic
716C22×C4C23×D7911yescharacteristic
717C22×C4C23×D7914yes—
718C22×C4C23×D7914yes—
719C22×C4C23×D7911yescharacteristic
720C22×C4C23×D7911yescharacteristic
721C22×C4C23×D7914yes—
722C22×C4C23×D7911yescharacteristic
723C22×C4C23×D7911yescharacteristic
724C4⋊C4—798no—
725C4⋊C4—798no—
726C4⋊C4—7916no—
727C4⋊C4—798no—
728C4⋊C4—798no—
729C4⋊C4—798no—
730C4⋊C4—7916no—
731C4⋊C4—798no—
732C4⋊C4—7916no—
733C4⋊C4—794no—
734C4⋊C4—794no—
735C4⋊C4—794no—
736C4⋊C4—794no—
737C4⋊C4—7916no—
738C4⋊C4C23×D7918yes—
739C4⋊C4C23×D7918yes—
740C4⋊C4C23×D7918yes—
741C4⋊C4C23×D79116yes—
742C4⋊C4C23×D79116yes—
743C4⋊C4C23×D7918yes—
744C22⋊C4—798no—
745C22⋊C4—798no—
746C22⋊C4—7916no—
747C22⋊C4—798no—
748C22⋊C4—798no—
749C22⋊C4—798no—
750C22⋊C4—798no—
751C22⋊C4—7916no—
752C22⋊C4—7916no—
753C22⋊C4—798no—
754C22⋊C4—7916no—
755C22⋊C4—798no—
756C22⋊C4—7916no—
757C22⋊C4C23×D79116yes—
758C42—798no—
759C42—798no—
760C42—798no—
761C42—7916no—
762C42—7916no—
763C42—7916no—
764C42—798no—
765C42C23×D7914yes—
766C42C23×D7914yes—
767C42C23×D7914yes—
768C42C23×D7914yes—
769C42C23×D79116yes—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—794no—
774C23—794no—
775C23—1584no—
776C23—1584no—
777C23—1584no—
778C23—1584no—
779C23—1584no—
780C23—1584no—
781C23C24×D7912yes—
782C23C24×D7911yescharacteristic
783Q8—216no—
784Q8—48no—
785Q8—31616no—
786Q8—7916no—
787Q8—15832no—
788Q8—1588no—
789D4—31616no—
790D4—3168no—
791D4—15816no—
792D4—1588no—
793D4—1588no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—28no—
798C2×C4—22no—
799C2×C4—28no—
800C2×C4—28no—
801C2×C4—28no—
802C2×C4—44no—
803C2×C4—3168no—
804C2×C4—794no—
805C2×C4—798no—
806C2×C4—794no—
807C2×C4—794no—
808C2×C4—794no—
809C2×C4—794no—
810C2×C4—794no—
811C2×C4—15832no—
812C2×C4—15816no—
813C2×C4—1584no—
814C2×C4—1584no—
815C2×C4—1584no—
816C2×C4—1584no—
817C2×C4—1584no—
818C2×C4—15816no—
819C2×C4—15816no—
820C2×C4#41×D7914yes—
821C2×C4#1457920914yes—
822C2×C4C24×D7912yes—
823C2×C4C24×D7912yes—
824C2×C4C24×D7918yes—
825C2×C4C24×D7918yes—
826C2×C4C24×D7912yes—
827C2×C4C24×D7912yes—
828C2×C4C24×D7912yes—
829C2×C4C24×D7912yes—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—44no—
834C22—3168no—
835C22—3168no—
836C22—1584no—
837C22—1584no—
838C22—1584no—
839C22—1584no—
840C22—1584no—
841C22—1584no—
842C22C2×#41×D7912yes—
843C22C2×#1457920912yes—
844C22#1909939912yes—
845C22C25×D7911yescharacteristic
846C4—22no—
847C4—28no—
848C4—22no—
849C4—22no—
850C4—22no—
851C4—28no—
852C4—798no—
853C4—1584no—
854C4—1584no—
855C4—1584no—
856C4—1584no—
857C4—1584no—
858C4C2×#41×D7914yes—
859C4C2×#1457920914yes—
860C2—42no—
861C2—3164no—
862C2—3164no—
863C2#2377740914yesdirect product factor
864C2C22×#41×D7911yescharacteristic
865C2C22×#1457920911yescharacteristic
866C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#533×C79C2
socleC23×C79C25
hypercenterC2×#533D79
hypocenterC79C2×#3518
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #23777409C2direct (N × H)
2. C2×#19099293C2semidirect
3. C2×#19099287C2semidirect
4. C2×#19099285C2semidirect
5. C2×#19099284C2semidirect
6. C2×#19099281C2semidirect
7. C2×#19099279C2semidirect
8. C2×#19099276C2semidirect
9. C2×#19099228C2semidirect
10. C2×#19099223C2semidirect
11. C2×#19099185C2semidirect
12. C2×#19099183C2semidirect
13. C2×#19099119C2semidirect
14. C2×#19099098C2semidirect
15. C2×#19099097C2semidirect
16. C2×#19099039C2semidirect
17. C2×C4×#11929624C2semidirect
18. C2×#533×C79C2semidirect
21. #19099293C22semidirect
22. #19099287C22semidirect
23. #19099285C22semidirect
24. #19099284C22semidirect
25. #19099281C22semidirect
26. #19099279C22semidirect
27. #19099276C22semidirect
28. #19099228C22semidirect
29. #19099223C22semidirect
30. #19099185C22semidirect
31. #19099183C22semidirect
32. #19099119C22semidirect
37. #19099098C22semidirect
38. #19099097C22semidirect
63. #19099039C22semidirect
64. C4×#11929624C22semidirect
91. #533×C79C22semidirect
428. C2×C79#3518semidirect
447. C2×#533D79semidirect
452. C79C2×#3518semidirect
467. #533C2×D79semidirect
863. C2#23777409direct (N × H)

Maximal subgroups

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

subgroupindex
#237774092
C2×#190992932
C2×#190992872
C2×#190992852
C2×#190992842
C2×#190992812
C2×#190992792
C2×#190992762
C2×#190992282
C2×#190992232
C2×#190991852
C2×#190991832
C2×#190991192
C2×#190990982
C2×#190990972
C2×#190990392
C2×C4×#119296242
C2×#533×C792
C2×#351879