Finite Group Databasebeta

← C2×#23777308 #35196641

Subgroups — C2×#23777308 #35196641

Order 20224.

7758 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777308C2132yesmaximal, direct product factor
2C2×#19099284C212yesmaximal, complemented
3C2×#19099279C211yesmaximal, characteristic, complemented
4C2×#19099278C211yesmaximal, characteristic, complemented
5C2×#19099273C211yesmaximal, characteristic, complemented
6C2×#19099266C212yesmaximal, complemented
7C2×#19099263C212yesmaximal, complemented
8C2×#19099223C214yesmaximal, complemented
9C2×#19099214C212yesmaximal, complemented
10C2×#19099183C214yesmaximal, complemented
11C2×#19099143C212yesmaximal, complemented
12C2×#19099119C212yesmaximal, complemented
13C2×#19099110C212yesmaximal, complemented
14C2×#19099110C211yesmaximal, characteristic, complemented
15C2×C4⋊Q8×D79C211yesmaximal, characteristic, complemented
16C2×#19099044C212yesmaximal, complemented
17C2×C4×#11929625C211yesmaximal, characteristic, complemented
18C2×#554×C79C211yesmaximal, characteristic, complemented
19C22×#11929625C2211yescharacteristic
20C22×#11929624C2212yes—
21C22×#11929624C2214yes—
22C22×Q8×D79C2212yes—
23#19099284C22132yescomplemented
24#19099279C22116yescomplemented
25#19099278C22116yescomplemented
26#19099273C22116yescomplemented
27#19099266C22132yescomplemented
28#19099263C22132yescomplemented
29#19099223C22164yescomplemented
30#19099214C22132yescomplemented
31#19099183C22164yescomplemented
32#19099143C22132yescomplemented
33#19099119C22132yescomplemented
34#19099110C22116yescomplemented
35#19099110C22132yescomplemented
36C2×#14579161C2211yescharacteristic
37C2×#14579160C2212yes—
38C2×#14579160C2212yes—
39C2×#14579160C2211yescharacteristic
40C2×#14579159C2212yes—
41C4⋊Q8×D79C22116yescomplemented
42C2×#14579157C2211yescharacteristic
43C2×#14579156C2214yes—
44C2×#14579154C2214yes—
45C2×#14579153C2212yes—
46C2×#14579150C2214yes—
47C2×#14579147C2212yes—
48C2×#14579147C2214yes—
49C2×#14579147C2214yes—
50C2×#14579146C2214yes—
51C2×#14579144C2214yes—
52C2×#14579139C2214yes—
53C2×#14579139C2214yes—
54C2×#14579139C2214yes—
55C2×#14579137C2212yes—
56C2×#14579136C2212yes—
57C2×#14579136C2214yes—
58C2×#14579136C2211yescharacteristic
59C2×#14579136C2212yes—
60C2×#14579135C2212yes—
61C2×#14579134C2214yes—
62C2×#14579134C2212yes—
63C2×#14579134C2214yes—
64C2×#14579132C2211yescharacteristic
65C2×#14579132C2212yes—
66#19099044C22132yescomplemented
67C4×#11929625C22116yescomplemented
68C2×Q8×Dic79C2211yescharacteristic
69C2×#14579126C2214yes—
70C2×#14579126C2214yes—
71C2×C4×D316C2212yes—
72C2×C4×D316C2211yescharacteristic
73C2×C4×D316C2212yes—
74C2×C4×D316C2211yescharacteristic
75C2×#14579123C2211yescharacteristic
76C2×#14579123C2212yes—
77C2×#14579123C2214yes—
78C2×C4×C22⋊D79C2214yes—
79C2×C4×C22⋊D79C2214yes—
80C2×C4×C22⋊D79C2212yes—
81C2×#14579120C2212yes—
82C2×#14579119C2212yes—
83C2×#14579119C2211yescharacteristic
84C2×#14579119C2212yes—
85C2×#14579119C2212yes—
86C2×#14579119C2212yes—
87C2×C4⋊C4×D79C2212yes—
88C2×C4⋊C4×D79C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C2×C42×D79C2211yescharacteristic
91C2×C42×D79C2212yes—
92#554×C79C22116yescomplemented
93C2×C4⋊Q8×C79C2211yescharacteristic
94C2×#125×C79C2212yes—
95C2×C22⋊Q8×C79C2214yes—
96C2×C22⋊Q8×C79C2212yes—
97C2×C4×Q8×C79C2211yescharacteristic
98C2×C4×D4×C79C2212yes—
99C2×C4×D4×C79C2211yescharacteristic
100C22×C4⋊C4×C79C2212yes—
101C2×#11929625—28no—
102C2×#11929625C2318yes—
103C2×#11929624—216no—
104C2×#11929624—416no—
105C2×#11929624C23116yes—
106C2×#11929624C23132yes—
107C22×Dic158C2312yes—
108C22×Dic158C2314yes—
109C22×Dic158C2312yes—
110C2×Q8×D79—48no—
111C2×Q8×D79C23116yes—
112C22×D316C2312yes—
113C22×D316C2312yes—
114C22×D316C2311yescharacteristic
115C22×D316C2311yescharacteristic
116C22×D316C2314yes—
117C22×C22⋊D79C2312yes—
118C22×C22⋊D79C2312yes—
119C22×C22⋊D79C2312yes—
120C22×C22⋊D79C2314yes—
121C22×C4×D79C2311yescharacteristic
122C22×C4×D79C2312yes—
123C22×C4×D79C2312yes—
124C22×C4×D79C2311yescharacteristic
125C22×C4×D79C2312yes—
126C22×C4×D79C2312yes—
127C22×C4×D79C2314yes—
128C22×C4×D79C2314yes—
129C22×C4×D79C2311yescharacteristic
130#14579161C2318yes—
131#14579160C23116yes—
132#14579160C23116yes—
133#14579160C2318yes—
134#14579159C23116yes—
135#14579157C2318yes—
136#14579156C23132yes—
137#14579154C23132yes—
138#14579153C23116yes—
139#14579150C23132yes—
140#14579147C23116yes—
141#14579147C23132yes—
142#14579147C23132yes—
143#14579146C23132yes—
144#14579144C23132yes—
145#14579139C23132yes—
146#14579139C23132yes—
147#14579139C23132yes—
148#14579137C23116yes—
149#14579136C23116yes—
150#14579136C23132yes—
151#14579136C2318yes—
152#14579136C23116yes—
153#14579135C23116yes—
154#14579134C23132yes—
155#14579134C23132yes—
156#14579134C23116yes—
157#14579132C2318yes—
158#14579132C23116yes—
159Q8×Dic79C2318yes—
160#14579126C23132yes—
161#14579126C23132yes—
162C4×D316C23116yes—
163C4×D316C23116yes—
164C4×D316C2318yes—
165C4×D316C2318yes—
166#14579123C2318yes—
167#14579123C23116yes—
168#14579123C23132yes—
169C4×C22⋊D79C23132yes—
170C4×C22⋊D79C23116yes—
171C4×C22⋊D79C23132yes—
172#14579120C23116yes—
173#14579119C23116yes—
174#14579119C23116yes—
175#14579119C23116yes—
176#14579119C23116yes—
177#14579119C2318yes—
178C2×C4⋊Dic79C2312yes—
179C2×C4⋊Dic79C2312yes—
180C2×C4⋊Dic79C2311yescharacteristic
181C2×C4⋊Dic79C2311yescharacteristic
182C2×C4⋊Dic79C2312yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2314yes—
185C2×Dic79⋊C4C2314yes—
186C2×Dic79⋊C4C2312yes—
187C2×Dic79⋊C4C2314yes—
188C4⋊C4×D79C23116yes—
189C4⋊C4×D79C23116yes—
190C4⋊C4×D79C23116yes—
191C2×C22⋊Dic79C2314yes—
192C2×C22⋊Dic79C2312yes—
193C2×(C2×D79)⋊C4C2312yes—
194C2×(C2×D79)⋊C4C2314yes—
195C2×(C2×D79)⋊C4C2312yes—
196C2×(C2×D79)⋊C4C2312yes—
197C2×(C2×D79)⋊C4C2314yes—
198C2×(C2×D79)⋊C4C2314yes—
199C2×(C2×D79)⋊C4C2312yes—
200C2×(C2×D79)⋊C4C2314yes—
201C2×(C2×D79)⋊C4C2312yes—
202C2×C4×Dic79C2311yescharacteristic
203C2×C4×Dic79C2312yes—
204C2×C4×Dic79C2311yescharacteristic
205C2×C4×Dic79C2311yescharacteristic
206C2×C4×Dic79C2312yes—
207C2×C4×Dic79C2314yes—
208C2×C4×Dic79C2314yes—
209C42×D79C2318yes—
210C42×D79C23116yes—
211C22×Q8×C79C2311yescharacteristic
212C22×Q8×C79C2312yes—
213C22×D4×C79C2311yescharacteristic
214C23×C4×C79C2312yes—
215C23×C4×C79C2314yes—
216C4⋊Q8×C79C2318yes—
217#125×C79C23116yes—
218C22⋊Q8×C79C23116yes—
219C22⋊Q8×C79C23132yes—
220C4×Q8×C79C2318yes—
221C4×D4×C79C23116yes—
222C4×D4×C79C2318yes—
223C2×C4⋊C4×C79C23116yes—
224C2×C4⋊C4×C79C2311yescharacteristic
225C2×C4⋊C4×C79C2314yes—
226C2×C4⋊C4×C79C2312yes—
227C2×C4⋊C4×C79C2311yescharacteristic
228C2×C4⋊C4×C79C2312yes—
229C2×C4⋊C4×C79C2312yes—
230C2×C4⋊C4×C79C2314yes—
231C2×C22⋊C4×C79C2314yes—
232C2×C22⋊C4×C79C2312yes—
233C2×C42×C79C2312yes—
234C2×C42×C79C2311yescharacteristic
235C23×D79C2412yes—
236C23×D79C2412yes—
237C23×D79C2411yescharacteristic
238#11929625—232no—
239#11929624—264no—
240#11929624—464no—
241C2×Dic158—28no—
242C2×Dic158—216no—
243C2×Dic158—44no—
244C2×Dic158C24116yes—
245C2×Dic158C2418yes—
246C2×Dic158C2418yes—
247Q8×D79—432no—
248C2×D316—28no—
249C2×D316—28no—
250C2×D316—24no—
251C2×D316—24no—
252C2×D316—48no—
253C2×D316C2418yes—
254C2×D316C2418yes—
255C2×D316C2414yes—
256C2×D316C2414yes—
257C2×D316C24116yes—
258C2×C22⋊D79—28no—
259C2×C22⋊D79—28no—
260C2×C22⋊D79—28no—
261C2×C22⋊D79—48no—
262C2×C22⋊D79C2418yes—
263C2×C22⋊D79C2418yes—
264C2×C22⋊D79C2418yes—
265C2×C22⋊D79C24116yes—
266C22×Dic79C2414yes—
267C22×Dic79C2412yes—
268C22×Dic79C2412yes—
269C22×Dic79C2411yescharacteristic
270C22×Dic79C2411yescharacteristic
271C22×Dic79C2411yescharacteristic
272C2×C4×D79—28no—
273C2×C4×D79—24no—
274C2×C4×D79—28no—
275C2×C4×D79—28no—
276C2×C4×D79—24no—
277C2×C4×D79—28no—
278C2×C4×D79—48no—
279C2×C4×D79—48no—
280C2×C4×D79#4118yescomplemented
281C2×C4×D79C2414yes—
282C2×C4×D79C2418yes—
283C2×C4×D79C2418yes—
284C2×C4×D79C2418yes—
285C2×C4×D79C2414yes—
286C2×C4×D79C2418yes—
287C2×C4×D79C24116yes—
288C2×C4×D79C24116yes—
289C2×C4×D79C2414yes—
290C4⋊Dic79C2418yes—
291C4⋊Dic79C2418yes—
292C4⋊Dic79C2414yes—
293C4⋊Dic79C2414yes—
294C4⋊Dic79C2418yes—
295Dic79⋊C4C24116yes—
296Dic79⋊C4C24116yes—
297Dic79⋊C4C24116yes—
298Dic79⋊C4C2418yes—
299Dic79⋊C4C24116yes—
300C22⋊Dic79C24116yes—
301C22⋊Dic79C2418yes—
302(C2×D79)⋊C4C2418yes—
303(C2×D79)⋊C4C24116yes—
304(C2×D79)⋊C4C2418yes—
305(C2×D79)⋊C4C2418yes—
306(C2×D79)⋊C4C24116yes—
307(C2×D79)⋊C4C24116yes—
308(C2×D79)⋊C4C2418yes—
309(C2×D79)⋊C4C24116yes—
310(C2×D79)⋊C4C2418yes—
311C4×Dic79C2414yes—
312C4×Dic79C2418yes—
313C4×Dic79C2414yes—
314C4×Dic79C2414yes—
315C4×Dic79C2418yes—
316C4×Dic79C24116yes—
317C4×Dic79C24116yes—
318C24×C79C2412yes—
319C2×Q8×C79—24no—
320C2×Q8×C79—44no—
321C2×Q8×C79C2414yes—
322C2×Q8×C79C2418yes—
323C2×D4×C79—24no—
324C2×D4×C79C2414yes—
325C22×C4×C79—28no—
326C22×C4×C79—48no—
327C22×C4×C79C2411yescharacteristic
328C22×C4×C79C2412yes—
329C22×C4×C79C2414yes—
330C22×C4×C79C2418yes—
331C22×C4×C79C2412yes—
332C22×C4×C79C2412yes—
333C22×C4×C79C24116yes—
334C22×C4×C79C2411yescharacteristic
335C22×C4×C79C2411yescharacteristic
336C4⋊C4×C79C2414yes—
337C4⋊C4×C79C24116yes—
338C4⋊C4×C79C2418yes—
339C4⋊C4×C79C2414yes—
340C4⋊C4×C79C2418yes—
341C4⋊C4×C79C2418yes—
342C4⋊C4×C79C24116yes—
343C22⋊C4×C79C24116yes—
344C22⋊C4×C79C2418yes—
345C42×C79C2418yes—
346C42×C79C2414yes—
347C23×C79—24no—
348C23×C79—24no—
349C23×C79—24no—
350C23×C79C2514yes—
351C23×C79C2511yescharacteristic
352C22×D79—22no—
353C22×D79—22no—
354C22×D79—24no—
355C22×D79—24no—
356C22×D79—24no—
357C22×D79—24no—
358C22×D79—24no—
359C22×D79—24no—
360C22×D79C2×#4114yes—
361C22×D79C2514yes—
362C22×D79C2514yes—
363C22×D79C2512yes—
364Q8×C79—28no—
365Q8×C79—48no—
366D4×C79—28no—
367C2×C4×C79—24no—
368C2×C4×C79—24no—
369C2×C4×C79—24no—
370C2×C4×C79—22no—
371C2×C4×C79—28no—
372C2×C4×C79—216no—
373C2×C4×C79—416no—
374C2×C4×C79C2×#4114yes—
375C2×C4×C792−1+414yes—
376C2×C4×C79C2514yes—
377C2×C4×C79C2512yes—
378C2×C4×C79C2514yes—
379C2×C4×C79C2514yes—
380C2×C4×C79C2518yes—
381C2×C4×C79C2512yes—
382C2×C4×C79C2512yes—
383C22⋊D79—216no—
384C22⋊D79—216no—
385C22⋊D79—216no—
386C22⋊D79—416no—
387C2×Dic79—24no—
388C2×Dic79—28no—
389C2×Dic79—24no—
390C2×Dic79—22no—
391C2×Dic79C2×#4114yes—
392C2×Dic79H(5,𝔽2)14yes—
393C2×Dic79C2514yes—
394C2×Dic79C2512yes—
395C2×Dic79C2514yes—
396C2×Dic79C2518yes—
397C2×Dic79C2512yes—
398C2×Dic79C2512yes—
399D316—216no—
400D316—216no—
401D316—28no—
402D316—28no—
403D316—416no—
404C4×D79—216no—
405C4×D79—28no—
406C4×D79—216no—
407C4×D79—216no—
408C4×D79—28no—
409C4×D79—216no—
410C4×D79—416no—
411C4×D79—416no—
412C4×D79C2×#41116yescomplemented
413Dic158—216no—
414Dic158—232no—
415Dic158—48no—
416C22×C79—24no—
417C22×C79—24no—
418C22×C79—24no—
419C22×C79—48no—
420C22×C79C22×#4112yes—
421C22×C79C2×H(5,𝔽2)12yes—
422C22×C79C2×2−1+412yes—
423C22×C79C2611yescharacteristic
424C2×D79—22no—
425C2×D79—22no—
426C2×D79—28no—
427C2×D79—24no—
428C2×D79—24no—
429C2×D79—24no—
430C2×D79—24no—
431C2×D79—24no—
432C2×D79—24no—
433C2×D79—48no—
434C2×D79—48no—
435C2×D79C22×#4114yes—
436C4×C79—24no—
437C4×C79—24no—
438C4×C79—24no—
439C4×C79—28no—
440C4×C79—22no—
441C4×C79C22×#4114yes—
442C4×C79C2×2−1+414yes—
443Dic79—24no—
444Dic79—28no—
445Dic79—24no—
446Dic79—22no—
447Dic79C22×#4114yes—
448Dic79C2×H(5,𝔽2)14yes—
449C2×#3511—791nomaximal, Sylow
450C2×C79—44no—
451C2×C79#351114yescomplemented
452C2×C79C23×#4111yescharacteristic
453C2×C79C22×H(5,𝔽2)11yescharacteristic
454C2×C79C22×2−1+411yescharacteristic
455D79—24no—
456D79—44no—
457D79—44no—
458#3511—7932no—
459C2×#556—792no—
460C2×#555—791no—
461C2×#555—791no—
462C2×#554—791no—
463C2×#554D7911yescharacteristic, complemented
464C2×#553—792no—
465C2×#553—792no—
466C2×#548—794no—
467C2×#547—792no—
468C2×#542—794no—
469C2×#537—792no—
470C2×#533—792no—
471C2×#532—792no—
472C2×#532—791no—
473C22×C4⋊Q8—791no—
474C2×#520—792no—
475C2×C4×#41—791no—
476C79C2×#351111yescharacteristic, complemented, Sylow
477C22×#41—791no—
478C22×#41—794no—
479C22×#41—792no—
480C23×Q8—792no—
481#556—7932no—
482#555—7916no—
483#555—7916no—
484#554—7916no—
485#554C2×D79116yescomplemented
486#553—7932no—
487#553—7932no—
488#548—7964no—
489#547—7932no—
490#542—7964no—
491#537—7932no—
492#533—7932no—
493#532—7916no—
494#532—7932no—
495C2×C4⋊Q8—792no—
496C2×C4⋊Q8—7916no—
497C2×C4⋊Q8—792no—
498C2×C4⋊Q8—792no—
499C2×C4⋊Q8—791no—
500C2×C4⋊Q8—791no—
501C2×C4⋊Q8C2×D7911yescharacteristic
502C2×#127—791no—
503C2×#126—794no—
504C2×#126—794no—
505C2×#125—792no—
506C2×#125C2×D7912yes—
507C2×#124—794no—
508C2×#124—792no—
509C2×#124—794no—
510C2×#124—794no—
511C2×#123—794no—
512C2×#123—794no—
513C2×C22⋊Q8—792no—
514C2×C22⋊Q8—794no—
515C2×C22⋊Q8—794no—
516C2×C22⋊Q8—794no—
517C2×C22⋊Q8C2×D7912yes—
518C2×C22⋊Q8C2×D7914yes—
519C2×#121—791no—
520C2×#121—792no—
521C2×#121—792no—
522C2×#121—791no—
523C2×#121—792no—
524C2×#121—792no—
525C2×#121—794no—
526C2×#121—794no—
527C2×#121—792no—
528C2×#121—794no—
529#520—7932no—
530C4×#41—7916no—
531C2×C4×Q8—791no—
532C2×C4×Q8—794no—
533C2×C4×Q8—794no—
534C2×C4×Q8C2×D7911yescharacteristic
535C2×C4×D4—794no—
536C2×C4×D4—794no—
537C2×C4×D4—792no—
538C2×C4×D4—791no—
539C2×C4×D4—792no—
540C2×C4×D4—794no—
541C2×C4×D4—792no—
542C2×C4×D4—791no—
543C2×C4×D4—792no—
544C2×C4×D4—791no—
545C2×C4×D4C2×D7912yes—
546C2×C4×D4C2×D7911yescharacteristic
547C2×#117—792no—
548C2×#117—791no—
549C2×#117—792no—
550C2×#117—792no—
551C2×#117—792no—
552C2×#117—792no—
553C22×C4⋊C4—792no—
554C22×C4⋊C4—792no—
555C22×C4⋊C4—792no—
556C22×C4⋊C4C2×D7912yes—
557C22×C42—791no—
558C22×C42—792no—
559C2×#41—31616no—
560C2×#41—798no—
561C2×#41—7932no—
562C2×#41—7916no—
563C2×#41—15816no—
564C2×#41—1588no—
565C22×Q8—3168no—
566C22×Q8—7916no—
567C22×Q8—792no—
568C22×Q8—792no—
569C22×Q8—794no—
570C22×Q8C22×D7911yescharacteristic
571C22×Q8C22×D7912yes—
572C22×D4—794no—
573C22×D4—792no—
574C22×D4—792no—
575C22×D4—792no—
576C22×D4—794no—
577C22×D4—791no—
578C22×D4—792no—
579C22×D4—792no—
580C22×D4—791no—
581C22×D4C22×D7911yescharacteristic
582C23×C4—794no—
583C23×C4—794no—
584C23×C4—791no—
585C23×C4—791no—
586C23×C4—792no—
587C23×C4—792no—
588C23×C4—792no—
589C23×C4—791no—
590C23×C4—792no—
591C23×C4C22×D7912yes—
592C23×C4C22×D7914yes—
593C4⋊Q8—7916no—
594C4⋊Q8—7916no—
595C4⋊Q8—7916no—
596C4⋊Q8—798no—
597C4⋊Q8—798no—
598C4⋊Q8C22×D7918yes—
599#127—798no—
600#126—7932no—
601#126—7932no—
602#125—7916no—
603#125C22×D79116yes—
604#124—7932no—
605#124—7916no—
606#124—7932no—
607#124—7932no—
608#123—7932no—
609#123—7932no—
610C22⋊Q8—7916no—
611C22⋊Q8—7932no—
612C22⋊Q8—7932no—
613C22⋊Q8—7932no—
614C22⋊Q8C22×D79116yes—
615C22⋊Q8C22×D79132yes—
616#121—798no—
617#121—7916no—
618#121—7916no—
619#121—798no—
620#121—7916no—
621#121—7916no—
622#121—7932no—
623#121—7932no—
624#121—7916no—
625#121—7932no—
626C4×Q8—798no—
627C4×Q8—7932no—
628C4×Q8—7932no—
629C4×Q8C22×D7918yes—
630C4×D4—7932no—
631C4×D4—7932no—
632C4×D4—7916no—
633C4×D4—798no—
634C4×D4—7916no—
635C4×D4—7932no—
636C4×D4—7916no—
637C4×D4—798no—
638C4×D4—7916no—
639C4×D4—798no—
640C4×D4C22×D79116yes—
641C4×D4C22×D7918yes—
642#117—7916no—
643#117—798no—
644#117—7916no—
645#117—7916no—
646#117—7916no—
647#117—7916no—
648C2×C4⋊C4—792no—
649C2×C4⋊C4—792no—
650C2×C4⋊C4—794no—
651C2×C4⋊C4—794no—
652C2×C4⋊C4—794no—
653C2×C4⋊C4—791no—
654C2×C4⋊C4—791no—
655C2×C4⋊C4—792no—
656C2×C4⋊C4—792no—
657C2×C4⋊C4—794no—
658C2×C4⋊C4—7916no—
659C2×C4⋊C4—7916no—
660C2×C4⋊C4—7916no—
661C2×C4⋊C4C22×D7911yescharacteristic
662C2×C4⋊C4C22×D7912yes—
663C2×C4⋊C4C22×D7912yes—
664C2×C4⋊C4C22×D7914yes—
665C2×C4⋊C4C22×D79116yes—
666C2×C4⋊C4C22×D7911yescharacteristic
667C2×C4⋊C4C22×D7912yes—
668C2×C4⋊C4C22×D7914yes—
669C2×C22⋊C4—794no—
670C2×C22⋊C4—792no—
671C2×C22⋊C4—792no—
672C2×C22⋊C4—794no—
673C2×C22⋊C4—792no—
674C2×C22⋊C4—792no—
675C2×C22⋊C4—794no—
676C2×C22⋊C4—794no—
677C2×C22⋊C4—794no—
678C2×C22⋊C4—792no—
679C2×C22⋊C4—792no—
680C2×C22⋊C4C22×D7914yes—
681C2×C22⋊C4C22×D7912yes—
682C2×C42—792no—
683C2×C42—794no—
684C2×C42—794no—
685C2×C42—791no—
686C2×C42—791no—
687C2×C42—792no—
688C2×C42—791no—
689C2×C42—798no—
690C2×C42—7916no—
691C2×C42C22×D7912yes—
692C2×C42C22×D7911yescharacteristic
693C24—791no—
694C24—792no—
695C24—792no—
696C24C23×D7912yes—
697#41—31664no—
698#41—15864no—
699#41—15832no—
700C2×Q8—24no—
701C2×Q8—44no—
702C2×Q8—3164no—
703C2×Q8—31632no—
704C2×Q8—798no—
705C2×Q8—798no—
706C2×Q8—7916no—
707C2×Q8—15816no—
708C2×Q8—1588no—
709C2×Q8C23×D7914yes—
710C2×Q8C23×D7918yes—
711C2×D4—24no—
712C2×D4—3168no—
713C2×D4—3168no—
714C2×D4—7916no—
715C2×D4—798no—
716C2×D4—798no—
717C2×D4—798no—
718C2×D4—7916no—
719C2×D4—794no—
720C2×D4—798no—
721C2×D4—798no—
722C2×D4—794no—
723C2×D4—1588no—
724C2×D4—1588no—
725C2×D4—1588no—
726C2×D4—1588no—
727C2×D4—1588no—
728C2×D4—1584no—
729C2×D4—1584no—
730C2×D4C23×D7914yes—
731C22×C4—28no—
732C22×C4—48no—
733C22×C4—3168no—
734C22×C4—3168no—
735C22×C4—7916no—
736C22×C4—7916no—
737C22×C4—791no—
738C22×C4—791no—
739C22×C4—798no—
740C22×C4—794no—
741C22×C4—792no—
742C22×C4—791no—
743C22×C4—792no—
744C22×C4—794no—
745C22×C4—794no—
746C22×C4—798no—
747C22×C4—798no—
748C22×C4—794no—
749C22×C4—798no—
750C22×C4—798no—
751C22×C4—1584no—
752C22×C4—1588no—
753C22×C4—1588no—
754C22×C4—1588no—
755C22×C4—1588no—
756C22×C4—1584no—
757C22×C4C23×D7918yes—
758C22×C4C23×D7912yes—
759C22×C4C23×D7911yescharacteristic
760C22×C4C23×D7912yes—
761C22×C4C23×D7912yes—
762C22×C4C23×D7914yes—
763C22×C4C23×D79116yes—
764C22×C4C23×D7911yescharacteristic
765C22×C4C23×D7911yescharacteristic
766C4⋊C4—7916no—
767C4⋊C4—7916no—
768C4⋊C4—7916no—
769C4⋊C4—798no—
770C4⋊C4—7916no—
771C4⋊C4—798no—
772C4⋊C4—798no—
773C4⋊C4—794no—
774C4⋊C4—794no—
775C4⋊C4—798no—
776C4⋊C4C23×D7914yes—
777C4⋊C4C23×D7918yes—
778C4⋊C4C23×D7918yes—
779C4⋊C4C23×D79116yes—
780C4⋊C4C23×D7914yes—
781C4⋊C4C23×D7918yes—
782C4⋊C4C23×D79116yes—
783C22⋊C4—7916no—
784C22⋊C4—798no—
785C22⋊C4—798no—
786C22⋊C4—7916no—
787C22⋊C4—798no—
788C22⋊C4—798no—
789C22⋊C4—7916no—
790C22⋊C4—7916no—
791C22⋊C4—7916no—
792C22⋊C4—798no—
793C22⋊C4—798no—
794C22⋊C4C23×D79116yes—
795C22⋊C4C23×D7918yes—
796C42—794no—
797C42—798no—
798C42—794no—
799C42—794no—
800C42—798no—
801C42—7916no—
802C42—7916no—
803C42C23×D7918yes—
804C42C23×D7914yes—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—792no—
809C23—794no—
810C23—794no—
811C23—794no—
812C23—1584no—
813C23—1584no—
814C23—1584no—
815C23—1584no—
816C23—1584no—
817C23—1584no—
818C23—1582no—
819C23—1582no—
820C23C24×D7914yes—
821C23C24×D7911yescharacteristic
822Q8—28no—
823Q8—48no—
824Q8—3168no—
825Q8—15832no—
826Q8—15816no—
827D4—28no—
828D4—31616no—
829D4—31616no—
830D4—15816no—
831D4—15816no—
832D4—15816no—
833D4—15816no—
834D4—15816no—
835D4—1588no—
836D4—1588no—
837C2×C4—24no—
838C2×C4—28no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—216no—
843C2×C4—416no—
844C2×C4—31616no—
845C2×C4—31616no—
846C2×C4—794no—
847C2×C4—792no—
848C2×C4—792no—
849C2×C4—794no—
850C2×C4—7916no—
851C2×C4—794no—
852C2×C4—792no—
853C2×C4—794no—
854C2×C4—798no—
855C2×C4—1588no—
856C2×C4—15816no—
857C2×C4—15816no—
858C2×C4—1588no—
859C2×C4—1584no—
860C2×C4—1582no—
861C2×C4—1584no—
862C2×C4—15816no—
863C2×C4—1588no—
864C2×C4—15816no—
865C2×C4#41×D7914yes—
866C2×C4#1457920914yes—
867C2×C4C24×D7914yes—
868C2×C4C24×D7912yes—
869C2×C4C24×D7914yes—
870C2×C4C24×D7914yes—
871C2×C4C24×D7918yes—
872C2×C4C24×D7912yes—
873C2×C4C24×D7912yes—
874C22—24no—
875C22—24no—
876C22—24no—
877C22—48no—
878C22—3168no—
879C22—3168no—
880C22—794no—
881C22—1584no—
882C22—1584no—
883C22—1584no—
884C22—1584no—
885C22—1584no—
886C22—1584no—
887C22—1588no—
888C22—1582no—
889C22—1582no—
890C22C2×#41×D7912yes—
891C22H(5,𝔽2)×D7912yes—
892C22C2×#1457920912yes—
893C22C25×D7911yescharacteristic
894C4—24no—
895C4—24no—
896C4—24no—
897C4—28no—
898C4—22no—
899C4—794no—
900C4—794no—
901C4—1584no—
902C4—1588no—
903C4—1584no—
904C4—1582no—
905C4C2×#41×D7914yes—
906C4C2×#1457920914yes—
907C2—44no—
908C2—3164no—
909C2—3164no—
910C2—1584no—
911C2#2377730814yesdirect product factor
912C2C22×#41×D7911yescharacteristic
913C2C2×H(5,𝔽2)×D7911yescharacteristic
914C2C22×#1457920911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#554×C79C2
socleC23×C79C25
hypercenterC2×#554D79
hypocenterC79C2×#3511
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #23777308C2direct (N × H)
2. C2×#19099284C2semidirect
3. C2×#19099279C2semidirect
4. C2×#19099278C2semidirect
5. C2×#19099273C2semidirect
6. C2×#19099266C2semidirect
7. C2×#19099263C2semidirect
8. C2×#19099223C2semidirect
9. C2×#19099214C2semidirect
10. C2×#19099183C2semidirect
11. C2×#19099143C2semidirect
12. C2×#19099119C2semidirect
13. C2×#19099110C2semidirect
14. C2×#19099110C2semidirect
15. C2×C4⋊Q8×D79C2semidirect
16. C2×#19099044C2semidirect
17. C2×C4×#11929625C2semidirect
18. C2×#554×C79C2semidirect
23. #19099284C22semidirect
24. #19099279C22semidirect
25. #19099278C22semidirect
26. #19099273C22semidirect
27. #19099266C22semidirect
28. #19099263C22semidirect
29. #19099223C22semidirect
30. #19099214C22semidirect
31. #19099183C22semidirect
32. #19099143C22semidirect
33. #19099119C22semidirect
34. #19099110C22semidirect
35. #19099110C22semidirect
41. C4⋊Q8×D79C22semidirect
66. #19099044C22semidirect
67. C4×#11929625C22semidirect
92. #554×C79C22semidirect
280. C2×C4×D79#41semidirect
412. C4×D79C2×#41semidirect
451. C2×C79#3511semidirect
463. C2×#554D79semidirect
476. C79C2×#3511semidirect
485. #554C2×D79semidirect
911. C2#23777308direct (N × H)

Maximal subgroups

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

subgroupindex
#237773082
C2×#190992842
C2×#190992792
C2×#190992782
C2×#190992732
C2×#190992662
C2×#190992632
C2×#190992232
C2×#190992142
C2×#190991832
C2×#190991432
C2×#190991192
C2×#190991102
C2×C4⋊Q8×D792
C2×#190990442
C2×C4×#119296252
C2×#554×C792
C2×#351179