Finite Group Databasebeta

← C2×#23777015 #35195365

Subgroups — C2×#23777015 #35195365

Order 20224.

7706 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777015C2132yesmaximal, direct product factor
2C2×#19099291C211yesmaximal, characteristic, complemented
3C2×#19099286C211yesmaximal, characteristic, complemented
4C2×#19099281C212yesmaximal, complemented
5C2×#19099253C212yesmaximal, complemented
6C2×#19099246C214yesmaximal, complemented
7C2×D4×Dic158C211yesmaximal, characteristic, complemented
8C2×#19099222C212yesmaximal, complemented
9C2×#19099217C211yesmaximal, characteristic, complemented
10C2×#19099212C212yesmaximal, complemented
11C2×#19099120C211yesmaximal, characteristic, complemented
12C2×#19099117C212yesmaximal, complemented
13C2×#19099097C212yesmaximal, complemented
14C2×#19099093C214yesmaximal, complemented
15C2×C4×#11929624C211yesmaximal, characteristic, complemented
16C2×C4×#11929623C212yesmaximal, complemented
17C22×C4×Dic158C212yesmaximal, complemented
18C2×C4×#41×C79C211yesmaximal, characteristic, complemented
19C22×#11929624C2211yescharacteristic
20C22×#11929623C2212yes—
21C23×Dic158C2212yes—
22#19099291C22116yescomplemented
23#19099286C22116yescomplemented
24#19099281C22132yescomplemented
25#19099253C22132yescomplemented
26#19099246C22164yescomplemented
27D4×Dic158C22116yescomplemented
28#19099222C22132yescomplemented
29#19099217C22116yescomplemented
30#19099212C22132yescomplemented
31#19099120C22116yescomplemented
32#19099117C22132yescomplemented
33C2×#14579161C2211yescharacteristic
34C2×#14579161C2211yescharacteristic
35C2×#14579160C2212yes—
36C2×#14579159C2212yes—
37#19099097C22132yescomplemented
38#19099093C22164yescomplemented
39C2×#14579156C2214yes—
40C2×#14579155C2214yes—
41C2×#14579154C2214yes—
42C2×#14579153C2212yes—
43C2×#14579153C2212yes—
44C2×#14579151C2214yes—
45C2×#14579151C2214yes—
46C2×#14579149C2212yes—
47C2×#14579147C2214yes—
48C2×#14579145C2214yes—
49C2×#14579144C2214yes—
50C2×#14579142C2214yes—
51C2×#14579141C2212yes—
52C2×#14579140C2212yes—
53C2×#14579140C2212yes—
54C2×#14579140C2212yes—
55C2×#14579139C2214yes—
56C2×#14579138C2214yes—
57C2×#14579137C2212yes—
58C2×#14579135C2212yes—
59C2×#14579133C2214yes—
60C4×#11929624C22116yescomplemented
61C4×#11929623C22132yescomplemented
62C2×C4×Dic158C2211yescharacteristic
63C2×C4×Dic158C2212yes—
64C2×C4×Dic158C2214yes—
65C2×C4×Dic158C2212yes—
66C2×C4×Dic158C2214yes—
67C2×C4×Dic158C2212yes—
68C2×C4×Dic158C2212yes—
69C2×C4×Dic158C2211yescharacteristic
70C2×C4×Dic158C22132yescomplemented
71C2×#14579126C2212yes—
72C2×C4×D316C2211yescharacteristic
73C2×C4×D316C2211yescharacteristic
74C2×D4×Dic79C2212yes—
75C2×C4×C22⋊D79C2214yes—
76C2×C4×C22⋊D79C2212yes—
77C2×C4×C22⋊D79C2212yes—
78C2×(C22⋊D79)⋊C4C2214yes—
79C2×#14579120C2211yescharacteristic
80C2×#14579120C2212yes—
81C2×#14579119C2212yes—
82C2×#14579118C2212yes—
83C2×#14579118C2214yes—
84C2×#14579117C2214yes—
85C22×C4⋊Dic79C2212yes—
86C22×Dic79⋊C4C2214yes—
87C22×C4×Dic79C2214yes—
88C2×C42×D79C2212yes—
89C22×#41×C79C2211yescharacteristic
90C4×#41×C79C22116yescomplemented
91C2×C4×Q8×C79C2211yescharacteristic
92C2×C4×Q8×C79C2211yescharacteristic
93C2×C4×D4×C79C2211yescharacteristic
94C2×C4×D4×C79C2211yescharacteristic
95C2×C4×D4×C79C2212yes—
96C2×C4×D4×C79C2212yes—
97C2×#117×C79C2212yes—
98C2×#117×C79C2211yescharacteristic
99C22×C42×C79C2212yes—
100C22×C42×C79C2211yescharacteristic
101C2×#11929624—28no—
102C2×#11929624C2318yes—
103C2×#11929623—216no—
104C2×#11929623C23116yes—
105C22×Dic158—216no—
106C22×Dic158C23116yes—
107C22×Dic158C2312yes—
108C22×Dic158C2314yes—
109C22×Dic158C2312yes—
110C22×Dic158C2311yescharacteristic
111C22×D316C2311yescharacteristic
112C22×C22⋊D79C2314yes—
113C22×C22⋊D79C2312yes—
114C23×Dic79C2314yes—
115C23×Dic79C2314yes—
116C22×C4×D79C2312yes—
117C22×C4×D79C2312yes—
118C22×C4×D79C2312yes—
119#14579161C2318yes—
120#14579161C2318yes—
121#14579160C23116yes—
122#14579159C23116yes—
123#14579156C23132yes—
124#14579155C23132yes—
125#14579154C23132yes—
126#14579153C23116yes—
127#14579153C23116yes—
128#14579151C23132yes—
129#14579151C23132yes—
130#14579149C23116yes—
131#14579147C23132yes—
132#14579145C23132yes—
133#14579144C23132yes—
134#14579142C23132yes—
135#14579141C23116yes—
136#14579140C23116yes—
137#14579140C23116yes—
138#14579140C23116yes—
139#14579139C23132yes—
140#14579138C23132yes—
141#14579137C23116yes—
142#14579135C23116yes—
143#14579133C23132yes—
144C4×Dic158C23116yes—
145C4×Dic158C2318yes—
146C4×Dic158C23132yes—
147C4×Dic158C23116yes—
148C4×Dic158C2318yes—
149C4×Dic158C23132yes—
150C4×Dic158C23116yes—
151C4×Dic158C23116yes—
152#14579126C23116yes—
153C4×D316C2318yes—
154C4×D316C2318yes—
155D4×Dic79C23116yes—
156C4×C22⋊D79C23116yes—
157C4×C22⋊D79C23132yes—
158C4×C22⋊D79C23116yes—
159(C22⋊D79)⋊C4C23132yes—
160#14579120C2318yes—
161#14579120C23116yes—
162#14579119C23116yes—
163#14579118C23116yes—
164#14579118C23132yes—
165#14579117C23132yes—
166C2×C4⋊Dic79C23116yes—
167C2×C4⋊Dic79C2311yescharacteristic
168C2×C4⋊Dic79C2312yes—
169C2×C4⋊Dic79C2314yes—
170C2×C4⋊Dic79C2312yes—
171C2×C4⋊Dic79C2311yescharacteristic
172C2×C4⋊Dic79C2312yes—
173C2×C4⋊Dic79C2312yes—
174C2×Dic79⋊C4C23132yes—
175C2×Dic79⋊C4C2312yes—
176C2×Dic79⋊C4C2314yes—
177C2×Dic79⋊C4C2314yes—
178C2×Dic79⋊C4C2314yes—
179C2×Dic79⋊C4C2314yes—
180C2×Dic79⋊C4C2314yes—
181C2×Dic79⋊C4C2312yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2314yes—
184C2×C22⋊Dic79C2314yes—
185C2×C22⋊Dic79C2312yes—
186C2×C22⋊Dic79C2314yes—
187C2×(C2×D79)⋊C4C2312yes—
188C2×(C2×D79)⋊C4C2312yes—
189C2×(C2×D79)⋊C4C2314yes—
190C2×(C2×D79)⋊C4C2314yes—
191C2×(C2×D79)⋊C4C2314yes—
192C2×C4×Dic79C2312yes—
193C2×C4×Dic79C2312yes—
194C2×C4×Dic79C2312yes—
195C2×C4×Dic79C2314yes—
196C2×C4×Dic79C2314yes—
197C2×C4×Dic79C2314yes—
198C2×C4×Dic79C23132yes—
199C42×D79C23116yes—
200C2×#41×C79—28no—
201C2×#41×C79C2318yes—
202C22×Q8×C79C2311yescharacteristic
203C22×D4×C79C2312yes—
204C22×D4×C79C2311yescharacteristic
205C23×C4×C79C2312yes—
206C23×C4×C79C2311yescharacteristic
207C23×C4×C79C2312yes—
208C23×C4×C79C2312yes—
209C23×C4×C79C2311yescharacteristic
210C23×C4×C79C2311yescharacteristic
211C4×Q8×C79C2318yes—
212C4×Q8×C79C2318yes—
213C4×D4×C79C2318yes—
214C4×D4×C79C23116yes—
215C4×D4×C79C2318yes—
216C4×D4×C79C23116yes—
217#117×C79C23116yes—
218#117×C79C2318yes—
219C2×C4⋊C4×C79C2311yescharacteristic
220C2×C4⋊C4×C79C2312yes—
221C2×C4⋊C4×C79C2311yescharacteristic
222C2×C4⋊C4×C79C2312yes—
223C2×C22⋊C4×C79C2312yes—
224C2×C22⋊C4×C79C2312yes—
225C2×C22⋊C4×C79C2312yes—
226C2×C42×C79C2311yescharacteristic
227C2×C42×C79C2311yescharacteristic
228C2×C42×C79C2312yes—
229C2×C42×C79C2311yescharacteristic
230C2×C42×C79C2312yes—
231C2×C42×C79C2311yescharacteristic
232C2×C42×C79C2312yes—
233C2×C42×C79C23116yes—
234C2×C42×C79C2318yes—
235C23×D79C2412yes—
236#11929624—232no—
237#11929623—264no—
238C2×Dic158—216no—
239C2×Dic158—264no—
240C2×Dic158—28no—
241C2×Dic158—28no—
242C2×Dic158#4118yescomplemented
243C2×Dic158C24116yes—
244C2×Dic158C2418yes—
245C2×Dic158C2418yes—
246C2×Dic158C2414yes—
247C2×D316—24no—
248C2×D316C2414yes—
249C2×C22⋊D79—28no—
250C2×C22⋊D79—216no—
251C2×C22⋊D79C24116yes—
252C2×C22⋊D79C2418yes—
253C22×Dic79—216no—
254C22×Dic79—216no—
255C22×Dic79C2414yes—
256C22×Dic79C24116yes—
257C22×Dic79C2414yes—
258C22×Dic79C24116yes—
259C22×Dic79C2412yes—
260C22×Dic79C2412yes—
261C22×Dic79C2412yes—
262C2×C4×D79—28no—
263C2×C4×D79—28no—
264C2×C4×D79—28no—
265C2×C4×D79C2418yes—
266C2×C4×D79C2418yes—
267C2×C4×D79C2418yes—
268C4⋊Dic79C2414yes—
269C4⋊Dic79C2418yes—
270C4⋊Dic79C24116yes—
271C4⋊Dic79C2418yes—
272C4⋊Dic79C2414yes—
273C4⋊Dic79C2418yes—
274C4⋊Dic79C2418yes—
275Dic79⋊C4C2418yes—
276Dic79⋊C4C24116yes—
277Dic79⋊C4C24116yes—
278Dic79⋊C4C24116yes—
279Dic79⋊C4C24116yes—
280Dic79⋊C4C24116yes—
281Dic79⋊C4C2418yes—
282Dic79⋊C4C24116yes—
283Dic79⋊C4C24116yes—
284C22⋊Dic79C24116yes—
285C22⋊Dic79C2418yes—
286C22⋊Dic79C24116yes—
287(C2×D79)⋊C4C2418yes—
288(C2×D79)⋊C4C2418yes—
289(C2×D79)⋊C4C24116yes—
290(C2×D79)⋊C4C24116yes—
291(C2×D79)⋊C4C24116yes—
292C4×Dic79C2418yes—
293C4×Dic79C2418yes—
294C4×Dic79C2418yes—
295C4×Dic79C24116yes—
296C4×Dic79C24116yes—
297C4×Dic79C24116yes—
298C24×C79C2411yescharacteristic
299C24×C79C2412yes—
300#41×C79—232no—
301C2×Q8×C79—24no—
302C2×Q8×C79C2414yes—
303C2×D4×C79—28no—
304C2×D4×C79#4118yescomplemented
305C2×D4×C79C2418yes—
306C2×D4×C79C2414yes—
307C22×C4×C79—28no—
308C22×C4×C79—28no—
309C22×C4×C79—24no—
310C22×C4×C79—24no—
311C22×C4×C79—28no—
312C22×C4×C79—24no—
313C22×C4×C79C2412yes—
314C22×C4×C79C2418yes—
315C22×C4×C79C2414yes—
316C22×C4×C79C2411yescharacteristic
317C22×C4×C79C2412yes—
318C22×C4×C79C2411yescharacteristic
319C22×C4×C79C2411yescharacteristic
320C22×C4×C79C2412yes—
321C22×C4×C79C2418yes—
322C22×C4×C79C2414yes—
323C22×C4×C79C2418yes—
324C22×C4×C79C2414yes—
325C22×C4×C79C2411yescharacteristic
326C22×C4×C79C2411yescharacteristic
327C22×C4×C79C2411yescharacteristic
328C4⋊C4×C79C2414yes—
329C4⋊C4×C79C2418yes—
330C4⋊C4×C79C2414yes—
331C4⋊C4×C79C2418yes—
332C22⋊C4×C79C2418yes—
333C22⋊C4×C79C2418yes—
334C22⋊C4×C79C2418yes—
335C42×C79C2414yes—
336C42×C79C2414yes—
337C42×C79C2418yes—
338C42×C79C2414yes—
339C42×C79C2418yes—
340C42×C79C2414yes—
341C42×C79C2418yes—
342C23×C79—24no—
343C23×C79—24no—
344C23×C79—22no—
345C23×C79—22no—
346C23×C79—22no—
347C23×C79C2×#4118yes—
348C23×C79C2512yes—
349C23×C79C2514yes—
350C23×C79C2511yescharacteristic
351C22×D79—24no—
352C22×D79—24no—
353C22×D79—24no—
354C22×D79C2514yes—
355Q8×C79—28no—
356D4×C79—216no—
357D4×C79C2×#41116yescomplemented
358C2×C4×C79—22no—
359C2×C4×C79—24no—
360C2×C4×C79—22no—
361C2×C4×C79—24no—
362C2×C4×C79—216no—
363C2×C4×C79—24no—
364C2×C4×C79—22no—
365C2×C4×C79—216no—
366C2×C4×C79—28no—
367C2×C4×C79—28no—
368C2×C4×C79—216no—
369C2×C4×C79—28no—
370C2×C4×C79C2×#4114yes—
371C2×C4×C79C2×#4114yes—
372C2×C4×C792−1+414yes—
373C2×C4×C79C2514yes—
374C2×C4×C79C2512yes—
375C2×C4×C79C2512yes—
376C2×C4×C79C2514yes—
377C2×C4×C79C2512yes—
378C2×C4×C79C2514yes—
379C2×C4×C79C2512yes—
380C2×C4×C79C2512yes—
381C2×C4×C79C2512yes—
382C22⋊D79—232no—
383C22⋊D79—216no—
384C2×Dic79—24no—
385C2×Dic79—28no—
386C2×Dic79—28no—
387C2×Dic79—232no—
388C2×Dic79—24no—
389C2×Dic79—232no—
390C2×Dic79C2×#4118yes—
391C2×Dic79C2514yes—
392C2×Dic79C2518yes—
393C2×Dic79C2514yes—
394C2×Dic79C2518yes—
395C2×Dic79C2514yes—
396D316—28no—
397C4×D79—216no—
398C4×D79—216no—
399C4×D79—216no—
400Dic158—216no—
401Dic158—216no—
402Dic158—232no—
403Dic158C2×#41116yescomplemented
404C22×C79—24no—
405C22×C79—24no—
406C22×C79—216no—
407C22×C79—22no—
408C22×C79—22no—
409C22×C79—22no—
410C22×C79—44no—
411C22×C79C22×#4112yes—
412C22×C79C22×#4118yes—
413C22×C79C22×#4112yes—
414C22×C79C2×2−1+412yes—
415C22×C79C2611yescharacteristic
416C2×D79—24no—
417C2×D79—24no—
418C2×D79—24no—
419C2×D79—48no—
420C4×C79—22no—
421C4×C79—24no—
422C4×C79—24no—
423C4×C79—22no—
424C4×C79—24no—
425C4×C79—22no—
426C4×C79C22×#4114yes—
427C4×C79C22×#4114yes—
428C4×C79C2×2−1+414yes—
429Dic79—28no—
430Dic79—28no—
431Dic79—24no—
432Dic79—24no—
433Dic79C22×#4118yes—
434C2×#3482—791nomaximal, Sylow
435C2×C79—28no—
436C2×C79—42no—
437C2×C79#348214yescomplemented
438C2×C79C23×#4111yescharacteristic
439C2×C79C23×#4111yescharacteristic
440C2×C79C22×2−1+411yescharacteristic
441D79—44no—
442#3482—7932no—
443C2×#557—791no—
444C2×#556—791no—
445C2×#556—792no—
446C2×#552—792no—
447C2×#552—794no—
448C2×D4×Q8—791no—
449C2×#548—792no—
450C2×#547—792no—
451C2×#547—791no—
452C2×#533—791no—
453C2×#533—792no—
454C2×#529—792no—
455C2×#529—794no—
456C2×C4×#41—791no—
457C2×C4×#41—792no—
458C2×C4×#41D7911yescharacteristic, complemented
459C22×C4×Q8—792no—
460C79C2×#348211yescharacteristic, complemented, Sylow
461C22×#41—792no—
462C22×#41—791no—
463C22×#41C2×D7911yescharacteristic
464C23×Q8—792no—
465#557—7916no—
466#556—7916no—
467#556—7932no—
468#552—7932no—
469#552—7964no—
470D4×Q8—7916no—
471#548—7932no—
472#547—7932no—
473#547—7916no—
474#533—7932no—
475#533—7916no—
476C2×C4⋊Q8—792no—
477C2×C4⋊Q8—792no—
478C2×C4⋊Q8—791no—
479C2×C4⋊Q8—791no—
480#529—7964no—
481#529—7932no—
482C2×#126—794no—
483C2×#126—794no—
484C2×#126—794no—
485C2×#125—794no—
486C2×#125—794no—
487C2×#125—792no—
488C2×#125—792no—
489C2×#124—794no—
490C2×#124—792no—
491C2×#123—794no—
492C2×#123—794no—
493C2×#123—794no—
494C2×C22⋊Q8—792no—
495C2×C22⋊Q8—792no—
496C2×C22⋊Q8—792no—
497C2×C22⋊Q8—792no—
498C2×C22⋊Q8—792no—
499C2×C22⋊Q8—794no—
500C2×C22⋊Q8—794no—
501C2×#121—794no—
502C2×#121—792no—
503C4×#41—7932no—
504C4×#41—7916no—
505C4×#41C2×D79116yescomplemented
506C2×C4×Q8—792no—
507C2×C4×Q8—791no—
508C2×C4×Q8—792no—
509C2×C4×Q8—794no—
510C2×C4×Q8—792no—
511C2×C4×Q8—792no—
512C2×C4×Q8—794no—
513C2×C4×Q8—7932no—
514C2×C4×Q8—792no—
515C2×C4×Q8—791no—
516C2×C4×Q8C2×D7911yescharacteristic
517C2×C4×Q8C2×D7911yescharacteristic
518C2×C4×D4—792no—
519C2×C4×D4—794no—
520C2×C4×D4—792no—
521C2×C4×D4—792no—
522C2×C4×D4—794no—
523C2×C4×D4—791no—
524C2×C4×D4—791no—
525C2×C4×D4C2×D7911yescharacteristic
526C2×C4×D4C2×D7912yes—
527C2×C4×D4C2×D7911yescharacteristic
528C2×C4×D4C2×D7912yes—
529C2×#117—791no—
530C2×#117—792no—
531C2×#117—792no—
532C2×#117—794no—
533C2×#117—792no—
534C2×#117—794no—
535C2×#117C2×D7912yes—
536C2×#117C2×D7911yescharacteristic
537C22×C4⋊C4—794no—
538C22×C4⋊C4—792no—
539C22×C42—794no—
540C22×C42—792no—
541C22×C42C2×D7912yes—
542C22×C42C2×D7911yescharacteristic
543C2×#41—28no—
544C2×#41—7916no—
545C2×#41—798no—
546C2×#41—1588no—
547C2×#41—15816no—
548C2×#41C22×D7918yes—
549C22×Q8—791no—
550C22×Q8—794no—
551C22×Q8—792no—
552C22×Q8—792no—
553C22×Q8—7916no—
554C22×Q8—15816no—
555C22×Q8C22×D7911yescharacteristic
556C22×D4—794no—
557C22×D4—792no—
558C22×D4—791no—
559C22×D4C22×D7912yes—
560C22×D4C22×D7911yescharacteristic
561C23×C4—794no—
562C23×C4—794no—
563C23×C4—792no—
564C23×C4—792no—
565C23×C4—792no—
566C23×C4C22×D7912yes—
567C23×C4C22×D7912yes—
568C23×C4C22×D7911yescharacteristic
569C23×C4C22×D7911yescharacteristic
570C23×C4C22×D7911yescharacteristic
571C23×C4C22×D7912yes—
572C4⋊Q8—7916no—
573C4⋊Q8—7916no—
574C4⋊Q8—798no—
575C4⋊Q8—798no—
576#126—7932no—
577#126—7932no—
578#126—7932no—
579#125—7932no—
580#125—7932no—
581#125—7916no—
582#125—7916no—
583#124—7932no—
584#124—7916no—
585#123—7932no—
586#123—7932no—
587#123—7932no—
588C22⋊Q8—7916no—
589C22⋊Q8—7916no—
590C22⋊Q8—7916no—
591C22⋊Q8—7916no—
592C22⋊Q8—7916no—
593C22⋊Q8—7932no—
594C22⋊Q8—7932no—
595#121—7932no—
596#121—7916no—
597C4×Q8—7916no—
598C4×Q8—798no—
599C4×Q8—7932no—
600C4×Q8—7916no—
601C4×Q8—7916no—
602C4×Q8—7916no—
603C4×Q8—7932no—
604C4×Q8—7916no—
605C4×Q8—798no—
606C4×Q8C22×D7918yes—
607C4×Q8C22×D7918yes—
608C4×D4—7916no—
609C4×D4—7916no—
610C4×D4—7932no—
611C4×D4—7916no—
612C4×D4—7932no—
613C4×D4—798no—
614C4×D4—798no—
615C4×D4C22×D7918yes—
616C4×D4C22×D79116yes—
617C4×D4C22×D7918yes—
618C4×D4C22×D79116yes—
619#117—798no—
620#117—7916no—
621#117—7916no—
622#117—7932no—
623#117—7916no—
624#117—7932no—
625#117C22×D79116yes—
626#117C22×D7918yes—
627C2×C4⋊C4—792no—
628C2×C4⋊C4—791no—
629C2×C4⋊C4—794no—
630C2×C4⋊C4—792no—
631C2×C4⋊C4—794no—
632C2×C4⋊C4—794no—
633C2×C4⋊C4—794no—
634C2×C4⋊C4—7932no—
635C2×C4⋊C4—7916no—
636C2×C4⋊C4—792no—
637C2×C4⋊C4—794no—
638C2×C4⋊C4—791no—
639C2×C4⋊C4—792no—
640C2×C4⋊C4—794no—
641C2×C4⋊C4—794no—
642C2×C4⋊C4—792no—
643C2×C4⋊C4—794no—
644C2×C4⋊C4—792no—
645C2×C4⋊C4C22×D7911yescharacteristic
646C2×C4⋊C4C22×D7912yes—
647C2×C4⋊C4C22×D7911yescharacteristic
648C2×C4⋊C4C22×D7912yes—
649C2×C22⋊C4—794no—
650C2×C22⋊C4—792no—
651C2×C22⋊C4—794no—
652C2×C22⋊C4—792no—
653C2×C22⋊C4—792no—
654C2×C22⋊C4—794no—
655C2×C22⋊C4—794no—
656C2×C22⋊C4—794no—
657C2×C22⋊C4C22×D7912yes—
658C2×C22⋊C4C22×D7912yes—
659C2×C22⋊C4C22×D7912yes—
660C2×C42—792no—
661C2×C42—794no—
662C2×C42—792no—
663C2×C42—794no—
664C2×C42—7932no—
665C2×C42—794no—
666C2×C42—792no—
667C2×C42—7916no—
668C2×C42C22×D7911yescharacteristic
669C2×C42C22×D7912yes—
670C2×C42C22×D7911yescharacteristic
671C2×C42C22×D7912yes—
672C2×C42C22×D79116yes—
673C2×C42C22×D7918yes—
674C2×C42C22×D7912yes—
675C2×C42C22×D7911yescharacteristic
676C2×C42C22×D7911yescharacteristic
677C24—792no—
678C24C23×D7911yescharacteristic
679C24C23×D7912yes—
680#41—232no—
681#41—15832no—
682#41—15864no—
683C2×Q8—24no—
684C2×Q8—798no—
685C2×Q8—794no—
686C2×Q8—7916no—
687C2×Q8—798no—
688C2×Q8—798no—
689C2×Q8—15816no—
690C2×Q8—15864no—
691C2×Q8—1588no—
692C2×Q8—1588no—
693C2×Q8C23×D7914yes—
694C2×D4—28no—
695C2×D4—7916no—
696C2×D4—798no—
697C2×D4—794no—
698C2×D4—1588no—
699C2×D4—15816no—
700C2×D4—1584no—
701C2×D4#1192962418yescomplemented
702C2×D4C23×D7918yes—
703C2×D4C23×D7914yes—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—28no—
709C22×C4—24no—
710C22×C4—792no—
711C22×C4—792no—
712C22×C4—792no—
713C22×C4—794no—
714C22×C4—794no—
715C22×C4—7916no—
716C22×C4—7916no—
717C22×C4—798no—
718C22×C4—798no—
719C22×C4—798no—
720C22×C4—1588no—
721C22×C4—15816no—
722C22×C4—15816no—
723C22×C4—1588no—
724C22×C4—1588no—
725C22×C4C23×D7912yes—
726C22×C4C23×D7918yes—
727C22×C4C23×D7911yescharacteristic
728C22×C4C23×D7911yescharacteristic
729C22×C4C23×D7911yescharacteristic
730C22×C4C23×D7912yes—
731C22×C4C23×D7912yes—
732C22×C4C23×D7918yes—
733C22×C4C23×D7918yes—
734C22×C4C23×D7914yes—
735C22×C4C23×D7914yes—
736C22×C4C23×D7914yes—
737C22×C4C23×D7911yescharacteristic
738C22×C4C23×D7911yescharacteristic
739C22×C4C23×D7911yescharacteristic
740C4⋊C4—798no—
741C4⋊C4—7916no—
742C4⋊C4—7916no—
743C4⋊C4—7916no—
744C4⋊C4—798no—
745C4⋊C4—7916no—
746C4⋊C4—7916no—
747C4⋊C4—7916no—
748C4⋊C4—7916no—
749C4⋊C4—794no—
750C4⋊C4—798no—
751C4⋊C4—7916no—
752C4⋊C4—794no—
753C4⋊C4—798no—
754C4⋊C4—798no—
755C4⋊C4—798no—
756C4⋊C4C23×D7914yes—
757C4⋊C4C23×D7918yes—
758C4⋊C4C23×D7914yes—
759C4⋊C4C23×D7918yes—
760C22⋊C4—7916no—
761C22⋊C4—798no—
762C22⋊C4—7916no—
763C22⋊C4—798no—
764C22⋊C4—798no—
765C22⋊C4—7916no—
766C22⋊C4—7916no—
767C22⋊C4—7916no—
768C22⋊C4C23×D7918yes—
769C22⋊C4C23×D7918yes—
770C22⋊C4C23×D7918yes—
771C42—798no—
772C42—798no—
773C42—7916no—
774C42—7916no—
775C42—798no—
776C42—7916no—
777C42C23×D7914yes—
778C42C23×D7914yes—
779C42C23×D7914yes—
780C42C23×D7918yes—
781C42C23×D7918yes—
782C42C23×D7914yes—
783C42C23×D7918yes—
784C23—24no—
785C23—24no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—794no—
790C23—1584no—
791C23—1584no—
792C23—1584no—
793C23C2×#1192962418yes—
794C23C24×D7912yes—
795C23C24×D7914yes—
796C23C24×D7911yescharacteristic
797Q8—28no—
798Q8—7916no—
799Q8—15832no—
800Q8—15816no—
801Q8—15816no—
802D4—216no—
803D4—15816no—
804D4—15832no—
805D4—1588no—
806D4C2×#11929624116yescomplemented
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—216no—
814C2×C4—216no—
815C2×C4—28no—
816C2×C4—216no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—794no—
820C2×C4—798no—
821C2×C4—794no—
822C2×C4—794no—
823C2×C4—798no—
824C2×C4—798no—
825C2×C4—15816no—
826C2×C4—15832no—
827C2×C4—1584no—
828C2×C4—1588no—
829C2×C4—1584no—
830C2×C4—1588no—
831C2×C4—15832no—
832C2×C4—15816no—
833C2×C4—15816no—
834C2×C4#41×D7914yes—
835C2×C4C2×#1192962414yes—
836C2×C4#1457920814yes—
837C2×C4C24×D7914yes—
838C2×C4C24×D7912yes—
839C2×C4C24×D7912yes—
840C2×C4C24×D7912yes—
841C2×C4C24×D7914yes—
842C2×C4C24×D7914yes—
843C2×C4C24×D7912yes—
844C2×C4C24×D7912yes—
845C2×C4C24×D7912yes—
846C22—24no—
847C22—24no—
848C22—216no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—3168no—
854C22—1584no—
855C22—1584no—
856C22—1584no—
857C22C2×#41×D7912yes—
858C22C22×#1192962418yes—
859C22C22×#1192962412yes—
860C22C2×#1457920812yes—
861C22C25×D7911yescharacteristic
862C4—22no—
863C4—24no—
864C4—22no—
865C4—24no—
866C4—24no—
867C4—22no—
868C4—798no—
869C4—1588no—
870C4—1584no—
871C4—1588no—
872C4—1584no—
873C4C2×#41×D7914yes—
874C4C22×#1192962414yes—
875C4C2×#1457920814yes—
876C2—28no—
877C2—42no—
878C2—3164no—
879C2#2377701514yesdirect product factor
880C2C22×#41×D7911yescharacteristic
881C2C23×#1192962411yescharacteristic
882C2C22×#1457920811yescharacteristic
subgroupG/H
centerC22×C4C23×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×C4×#41×C79C2
socleC23×C79C25
hypercenterC2×C4×#41D79
hypocenterC79C2×#3482
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #23777015C2direct (N × H)
2. C2×#19099291C2semidirect
3. C2×#19099286C2semidirect
4. C2×#19099281C2semidirect
5. C2×#19099253C2semidirect
6. C2×#19099246C2semidirect
7. C2×D4×Dic158C2semidirect
8. C2×#19099222C2semidirect
9. C2×#19099217C2semidirect
10. C2×#19099212C2semidirect
11. C2×#19099120C2semidirect
12. C2×#19099117C2semidirect
13. C2×#19099097C2semidirect
14. C2×#19099093C2semidirect
15. C2×C4×#11929624C2semidirect
16. C2×C4×#11929623C2semidirect
17. C22×C4×Dic158C2semidirect
18. C2×C4×#41×C79C2semidirect
22. #19099291C22semidirect
23. #19099286C22semidirect
24. #19099281C22semidirect
25. #19099253C22semidirect
26. #19099246C22semidirect
27. D4×Dic158C22semidirect
28. #19099222C22semidirect
29. #19099217C22semidirect
30. #19099212C22semidirect
31. #19099120C22semidirect
32. #19099117C22semidirect
37. #19099097C22semidirect
38. #19099093C22semidirect
60. C4×#11929624C22semidirect
61. C4×#11929623C22semidirect
70. C2×C4×Dic158C22semidirect
90. C4×#41×C79C22semidirect
242. C2×Dic158#41semidirect
304. C2×D4×C79#41semidirect
357. D4×C79C2×#41semidirect
403. Dic158C2×#41semidirect
437. C2×C79#3482semidirect
458. C2×C4×#41D79semidirect
460. C79C2×#3482semidirect
505. C4×#41C2×D79semidirect
701. C2×D4#11929624semidirect
806. D4C2×#11929624semidirect
879. C2#23777015direct (N × H)

Maximal subgroups

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

subgroupindex
#237770152
C2×#190992912
C2×#190992862
C2×#190992812
C2×#190992532
C2×#190992462
C2×D4×Dic1582
C2×#190992222
C2×#190992172
C2×#190992122
C2×#190991202
C2×#190991172
C2×#190990972
C2×#190990932
C2×C4×#119296242
C2×C4×#119296232
C22×C4×Dic1582
C2×C4×#41×C792
C2×#348279