Finite Group Databasebeta

← C2×#23777797 #35196060

Subgroups — C2×#23777797 #35196060

Order 20224.

7810 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777797C2132yesmaximal, direct product factor
2C2×#19099310C214yesmaximal, complemented
3C2×#19099271C212yesmaximal, complemented
4C2×#19099268C212yesmaximal, complemented
5C2×#19099232C212yesmaximal, complemented
6C2×#19099231C212yesmaximal, complemented
7C2×#19099218C211yesmaximal, characteristic, complemented
8C2×#19099217C211yesmaximal, characteristic, complemented
9C2×#19099216C211yesmaximal, characteristic, complemented
10C2×#19099165C214yesmaximal, complemented
11C2×#19099144C212yesmaximal, complemented
12C2×#19099143C212yesmaximal, complemented
13C2×#19099142C212yesmaximal, complemented
14C2×#19099141C212yesmaximal, complemented
15C2×#19099118C211yesmaximal, characteristic, complemented
16C2×#19099110C211yesmaximal, characteristic, complemented
17C2×#19099110C211yesmaximal, characteristic, complemented
18C2×#547×C79C211yesmaximal, characteristic, complemented
19C22×#11929625C2212yes—
20C22×#11929624C2212yes—
21C22×#11929624C2212yes—
22C22×#11929624C2212yes—
23C22×#11929623C2212yes—
24#19099310C22164yescomplemented
25#19099271C22132yescomplemented
26#19099268C22132yescomplemented
27#19099232C22132yescomplemented
28#19099231C22132yescomplemented
29#19099218C22116yescomplemented
30#19099217C22116yescomplemented
31#19099216C22116yescomplemented
32#19099165C22164yescomplemented
33#19099144C22132yescomplemented
34#19099143C22132yescomplemented
35#19099142C22132yescomplemented
36#19099141C22132yescomplemented
37#19099118C22116yescomplemented
38#19099110C22116yescomplemented
39#19099110C22116yescomplemented
40C2×#14579161C2211yescharacteristic
41C2×#14579160C2211yescharacteristic
42C2×#14579160C2211yescharacteristic
43C2×#14579157C2211yescharacteristic
44C2×#14579157C2214yes—
45C2×#14579157C2211yescharacteristic
46C2×#14579152C2212yes—
47C2×#14579151C2214yes—
48C2×#14579147C2212yes—
49C2×#14579147C2212yes—
50C2×#14579146C2214yes—
51C2×#14579145C2214yes—
52C2×#14579143C2214yes—
53C2×#14579141C2212yes—
54C2×#14579141C2214yes—
55C2×#14579141C2212yes—
56C2×#14579140C2212yes—
57C2×#14579140C2214yes—
58C2×#14579139C2214yes—
59C2×#14579138C2214yes—
60C2×#14579137C2212yes—
61C2×#14579137C2212yes—
62C2×#14579136C2212yes—
63C2×#14579136C2211yescharacteristic
64C2×#14579136C2211yescharacteristic
65C2×#14579136C2214yes—
66C2×#14579135C2212yes—
67C2×#14579135C2214yes—
68C2×#14579135C2214yes—
69C2×#14579134C2214yes—
70C2×#14579134C2212yes—
71C2×#14579134C2212yes—
72C2×#14579134C2214yes—
73C2×#14579133C2214yes—
74C2×#14579133C2214yes—
75C2×#14579132C2212yes—
76C2×#14579132C2214yes—
77C2×#14579132C2211yescharacteristic
78C2×#14579132C2211yescharacteristic
79C2×Q8×Dic79C2212yes—
80C2×#14579126C2212yes—
81C2×C4×D316C2211yescharacteristic
82C2×C4×D316C2211yescharacteristic
83C2×C4×C22⋊D79C2212yes—
84C2×C4×C22⋊D79C2214yes—
85C2×C4×C22⋊D79C2212yes—
86C2×(C22⋊D79)⋊C4C2214yes—
87C2×#14579119C2212yes—
88C22×C4⋊Dic79C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C2×C4⋊C4×D79C2212yes—
91C2×C42×D79C2211yescharacteristic
92C22×#41×C79C2212yes—
93#547×C79C22116yescomplemented
94C2×C4⋊Q8×C79C2211yescharacteristic
95C2×#123×C79C2214yes—
96C2×C22⋊Q8×C79C2212yes—
97C2×#121×C79C2212yes—
98C2×C4×D4×C79C2211yescharacteristic
99C2×C4×D4×C79C2211yescharacteristic
100C22×C4⋊C4×C79C2212yes—
101C2×#11929625—48no—
102C2×#11929625C23116yes—
103C2×#11929624—48no—
104C2×#11929624—48no—
105C2×#11929624—48no—
106C2×#11929624C23116yes—
107C2×#11929624C23116yes—
108C2×#11929624C23116yes—
109C2×#11929623—48no—
110C2×#11929623C23116yes—
111C22×Dic158C2312yes—
112C22×Dic158C2312yes—
113C22×Dic158C2312yes—
114C22×D316C2311yescharacteristic
115C22×D316C2311yescharacteristic
116C22×D316C2312yes—
117C22×D316C2312yes—
118C22×D316C2314yes—
119C22×C22⋊D79C2312yes—
120C22×C22⋊D79C2312yes—
121C22×C22⋊D79C2312yes—
122C22×C22⋊D79C2312yes—
123C22×C22⋊D79C2312yes—
124C22×C22⋊D79C2314yes—
125C22×C22⋊D79C2314yes—
126C22×C22⋊D79C2312yes—
127C23×Dic79C2314yes—
128C22×C4×D79C2311yescharacteristic
129C22×C4×D79C2311yescharacteristic
130C22×C4×D79C2311yescharacteristic
131C22×C4×D79C2312yes—
132C22×C4×D79C2312yes—
133C22×C4×D79C2314yes—
134C22×C4×D79C2314yes—
135#14579161C2318yes—
136#14579160C2318yes—
137#14579160C2318yes—
138#14579157C23132yes—
139#14579157C2318yes—
140#14579157C2318yes—
141#14579152C23116yes—
142#14579151C23132yes—
143#14579147C23116yes—
144#14579147C23116yes—
145#14579146C23132yes—
146#14579145C23132yes—
147#14579143C23132yes—
148#14579141C23116yes—
149#14579141C23116yes—
150#14579141C23132yes—
151#14579140C23132yes—
152#14579140C23116yes—
153#14579139C23132yes—
154#14579138C23132yes—
155#14579137C23116yes—
156#14579137C23116yes—
157#14579136C2318yes—
158#14579136C23132yes—
159#14579136C2318yes—
160#14579136C23116yes—
161#14579135C23132yes—
162#14579135C23116yes—
163#14579135C23132yes—
164#14579134C23132yes—
165#14579134C23132yes—
166#14579134C23116yes—
167#14579134C23116yes—
168#14579133C23132yes—
169#14579133C23132yes—
170#14579132C2318yes—
171#14579132C23116yes—
172#14579132C2318yes—
173#14579132C23132yes—
174Q8×Dic79C23116yes—
175#14579126C23116yes—
176C4×D316C2318yes—
177C4×D316C2318yes—
178C4×C22⋊D79C23132yes—
179C4×C22⋊D79C23116yes—
180C4×C22⋊D79C23116yes—
181(C22⋊D79)⋊C4C23132yes—
182#14579119C23116yes—
183C2×C4⋊Dic79C23116yes—
184C2×C4⋊Dic79C2311yescharacteristic
185C2×C4⋊Dic79C2312yes—
186C2×C4⋊Dic79C2311yescharacteristic
187C2×C4⋊Dic79C2314yes—
188C2×C4⋊Dic79C2312yes—
189C2×C4⋊Dic79C2314yes—
190C2×Dic79⋊C4C2314yes—
191C2×Dic79⋊C4C2314yes—
192C2×Dic79⋊C4C2312yes—
193C2×Dic79⋊C4C2312yes—
194C2×Dic79⋊C4C2314yes—
195C4⋊C4×D79C23116yes—
196C4⋊C4×D79C23116yes—
197C2×C22⋊Dic79C2312yes—
198C2×C22⋊Dic79C2314yes—
199C2×C22⋊Dic79C2312yes—
200C2×(C2×D79)⋊C4C2314yes—
201C2×(C2×D79)⋊C4C2314yes—
202C2×(C2×D79)⋊C4C2312yes—
203C2×(C2×D79)⋊C4C2314yes—
204C2×(C2×D79)⋊C4C2312yes—
205C2×(C2×D79)⋊C4C2312yes—
206C2×(C2×D79)⋊C4C2312yes—
207C2×C4×Dic79C2311yescharacteristic
208C2×C4×Dic79C2311yescharacteristic
209C2×C4×Dic79C2311yescharacteristic
210C2×C4×Dic79C2314yes—
211C42×D79C2318yes—
212C2×#41×C79—48no—
213C2×#41×C79C23116yes—
214C22×Q8×C79C2312yes—
215C22×D4×C79C2311yescharacteristic
216C22×D4×C79C2311yescharacteristic
217C22×D4×C79C2314yes—
218C23×C4×C79C2312yes—
219C23×C4×C79C2312yes—
220C23×C4×C79C2314yes—
221C4⋊Q8×C79C2318yes—
222#123×C79C23132yes—
223C22⋊Q8×C79C23116yes—
224#121×C79C23116yes—
225C4×D4×C79C2318yes—
226C4×D4×C79C2318yes—
227C2×C4⋊C4×C79C23116yes—
228C2×C4⋊C4×C79C2311yescharacteristic
229C2×C4⋊C4×C79C2312yes—
230C2×C4⋊C4×C79C2314yes—
231C2×C4⋊C4×C79C2311yescharacteristic
232C2×C4⋊C4×C79C2312yes—
233C2×C22⋊C4×C79C2312yes—
234C2×C22⋊C4×C79C2312yes—
235C2×C22⋊C4×C79C2314yes—
236C2×C42×C79C2311yescharacteristic
237C23×D79C2412yes—
238C23×D79C2411yescharacteristic
239C23×D79C2412yes—
240#11929625—432no—
241#11929624—432no—
242#11929624—432no—
243#11929624—432no—
244#11929623—432no—
245C2×Dic158—28no—
246C2×Dic158—44no—
247C2×Dic158—44no—
248C2×Dic158C2418yes—
249C2×Dic158C2418yes—
250C2×Dic158C2418yes—
251C2×D316—24no—
252C2×D316—24no—
253C2×D316—44no—
254C2×D316—44no—
255C2×D316—48no—
256C2×D316C2414yes—
257C2×D316C2414yes—
258C2×D316C2418yes—
259C2×D316C2418yes—
260C2×D316C24116yes—
261C2×C22⋊D79—28no—
262C2×C22⋊D79—28no—
263C2×C22⋊D79—48no—
264C2×C22⋊D79—44no—
265C2×C22⋊D79—44no—
266C2×C22⋊D79—44no—
267C2×C22⋊D79—44no—
268C2×C22⋊D79—48no—
269C2×C22⋊D79C2418yes—
270C2×C22⋊D79C2418yes—
271C2×C22⋊D79C24116yes—
272C2×C22⋊D79C2418yes—
273C2×C22⋊D79C2418yes—
274C2×C22⋊D79C2418yes—
275C2×C22⋊D79C24116yes—
276C2×C22⋊D79C2418yes—
277C22×Dic79—48no—
278C22×Dic79C2411yescharacteristic
279C22×Dic79C2411yescharacteristic
280C22×Dic79C2414yes—
281C22×Dic79C2412yes—
282C22×Dic79C2412yes—
283C22×Dic79C24116yes—
284C22×Dic79C2411yescharacteristic
285C2×C4×D79—24no—
286C2×C4×D79—28no—
287C2×C4×D79—24no—
288C2×C4×D79—24no—
289C2×C4×D79—28no—
290C2×C4×D79—48no—
291C2×C4×D79—48no—
292C2×C4×D79C2418yes—
293C2×C4×D79C2414yes—
294C2×C4×D79C2414yes—
295C2×C4×D79C2418yes—
296C2×C4×D79C2414yes—
297C2×C4×D79C24116yes—
298C2×C4×D79C24116yes—
299C4⋊Dic79C2414yes—
300C4⋊Dic79C2418yes—
301C4⋊Dic79C2414yes—
302C4⋊Dic79C24116yes—
303C4⋊Dic79C2418yes—
304C4⋊Dic79C24116yes—
305Dic79⋊C4C24116yes—
306Dic79⋊C4C24116yes—
307Dic79⋊C4C2418yes—
308Dic79⋊C4C2418yes—
309Dic79⋊C4C24116yes—
310C22⋊Dic79C2418yes—
311C22⋊Dic79C24116yes—
312C22⋊Dic79C2418yes—
313(C2×D79)⋊C4C24116yes—
314(C2×D79)⋊C4C24116yes—
315(C2×D79)⋊C4C2418yes—
316(C2×D79)⋊C4C24116yes—
317(C2×D79)⋊C4C2418yes—
318(C2×D79)⋊C4C2418yes—
319(C2×D79)⋊C4C2418yes—
320C4×Dic79C2414yes—
321C4×Dic79C2414yes—
322C4×Dic79C2414yes—
323C4×Dic79C24116yes—
324C24×C79C2412yes—
325C24×C79C2412yes—
326#41×C79—432no—
327C2×Q8×C79—28no—
328C2×Q8×C79C2418yes—
329C2×D4×C79—24no—
330C2×D4×C79—24no—
331C2×D4×C79—48no—
332C2×D4×C79C2414yes—
333C2×D4×C79C2414yes—
334C2×D4×C79C24116yes—
335C22×C4×C79—28no—
336C22×C4×C79—28no—
337C22×C4×C79—48no—
338C22×C4×C79C2412yes—
339C22×C4×C79C2412yes—
340C22×C4×C79C2418yes—
341C22×C4×C79C2418yes—
342C22×C4×C79C2411yescharacteristic
343C22×C4×C79C2414yes—
344C22×C4×C79C24116yes—
345C22×C4×C79C2411yescharacteristic
346C22×C4×C79C2411yescharacteristic
347C4⋊C4×C79C2414yes—
348C4⋊C4×C79C2418yes—
349C4⋊C4×C79C24116yes—
350C4⋊C4×C79C2414yes—
351C4⋊C4×C79C2418yes—
352C22⋊C4×C79C2418yes—
353C22⋊C4×C79C2418yes—
354C22⋊C4×C79C24116yes—
355C42×C79C2414yes—
356C23×C79—24no—
357C23×C79—24no—
358C23×C79—24no—
359C23×C79—24no—
360C23×C79—24no—
361C23×C79—24no—
362C23×C79C2514yes—
363C23×C79C2514yes—
364C23×C79C2511yescharacteristic
365C22×D79—24no—
366C22×D79—22no—
367C22×D79—22no—
368C22×D79—24no—
369C22×D79—24no—
370C22×D79—24no—
371C22×D79—22no—
372C22×D79—24no—
373C22×D79—24no—
374C22×D79C2514yes—
375C22×D79C2512yes—
376C22×D79C2514yes—
377Q8×C79—216no—
378D4×C79—28no—
379D4×C79—28no—
380D4×C79—416no—
381C2×C4×C79—24no—
382C2×C4×C79—28no—
383C2×C4×C79—24no—
384C2×C4×C79—22no—
385C2×C4×C79—216no—
386C2×C4×C79—216no—
387C2×C4×C79—416no—
388C2×C4×C79H(5,𝔽2)14yes—
389C2×C4×C79H(5,𝔽2)14yes—
390C2×C4×C79C2512yes—
391C2×C4×C79C2518yes—
392C2×C4×C79C2514yes—
393C2×C4×C79C2514yes—
394C2×C4×C79C2512yes—
395C2×C4×C79C2512yes—
396C22⋊D79—216no—
397C22⋊D79—216no—
398C22⋊D79—416no—
399C22⋊D79—416no—
400C22⋊D79—48no—
401C22⋊D79—48no—
402C22⋊D79—48no—
403C22⋊D79—48no—
404C2×Dic79—24no—
405C2×Dic79—24no—
406C2×Dic79—22no—
407C2×Dic79—22no—
408C2×Dic79—28no—
409C2×Dic79—416no—
410C2×Dic792−1+414yes—
411C2×Dic79C2512yes—
412C2×Dic79C2512yes—
413C2×Dic79C2518yes—
414C2×Dic79C2514yes—
415C2×Dic79C2514yes—
416C2×Dic79C2512yes—
417D316—28no—
418D316—28no—
419D316—48no—
420D316—48no—
421D316—416no—
422C4×D79—216no—
423C4×D79—28no—
424C4×D79—28no—
425C4×D79—216no—
426C4×D79—28no—
427C4×D79—416no—
428C4×D79—416no—
429Dic158—216no—
430Dic158—48no—
431Dic158—48no—
432C22×C79—24no—
433C22×C79—24no—
434C22×C79—24no—
435C22×C79—24no—
436C22×C79—24no—
437C22×C79—24no—
438C22×C79—48no—
439C22×C79—48no—
440C22×C79C2×H(5,𝔽2)12yes—
441C22×C79C2×H(5,𝔽2)12yes—
442C22×C79C2×2−1+412yes—
443C22×C79C2611yescharacteristic
444C2×D79—24no—
445C2×D79—22no—
446C2×D79—22no—
447C2×D79—24no—
448C2×D79—24no—
449C2×D79—24no—
450C2×D79—24no—
451C2×D79—24no—
452C2×D79—22no—
453C2×D79—48no—
454C2×D79—44no—
455C2×D79—48no—
456C4×C79—24no—
457C4×C79—24no—
458C4×C79—28no—
459C4×C79—22no—
460C4×C79C2×H(5,𝔽2)14yes—
461C4×C79C2×H(5,𝔽2)14yes—
462Dic79—28no—
463Dic79—22no—
464Dic79—22no—
465Dic79—24no—
466Dic79—24no—
467Dic79C2×2−1+414yes—
468C2×#3548—791nomaximal, Sylow
469C2×C79—44no—
470C2×C79—44no—
471C2×C79#354814yescomplemented
472C2×C79C22×H(5,𝔽2)11yescharacteristic
473C2×C79C22×H(5,𝔽2)11yescharacteristic
474C2×C79C22×2−1+411yescharacteristic
475D79—44no—
476D79—42no—
477D79—44no—
478#3548—7932no—
479C2×#562—794no—
480C2×#554—792no—
481C2×#554—792no—
482C2×#550—792no—
483C2×#550—792no—
484C2×#547—791no—
485C2×#547—791no—
486C2×#547—791no—
487C2×#547D7911yescharacteristic, complemented
488C2×#540—794no—
489C2×#537—792no—
490C2×#537—792no—
491C2×#537—792no—
492C2×#537—792no—
493C2×#533—791no—
494C2×#532—791no—
495C2×#532—791no—
496C79C2×#354811yescharacteristic, complemented, Sylow
497C22×#41—792no—
498C22×#41—792no—
499C22×#41—792no—
500C22×#41—792no—
501C22×#41—792no—
502C22×#41C2×D7912yes—
503#562—7964no—
504#554—7932no—
505#554—7932no—
506#550—7932no—
507#550—7932no—
508#547—7916no—
509#547—7916no—
510#547—7916no—
511#547C2×D79116yescomplemented
512#540—7964no—
513#537—7932no—
514#537—7932no—
515#537—7932no—
516#537—7932no—
517#533—7916no—
518#532—7916no—
519#532—7916no—
520C2×C4⋊Q8—791no—
521C2×C4⋊Q8—791no—
522C2×C4⋊Q8—791no—
523C2×C4⋊Q8C2×D7911yescharacteristic
524C2×#127—791no—
525C2×#127—791no—
526C2×#127—794no—
527C2×#125—792no—
528C2×#125—794no—
529C2×#124—792no—
530C2×#124—792no—
531C2×#123—794no—
532C2×#123—794no—
533C2×#123—794no—
534C2×#123C2×D7914yes—
535C2×C22⋊Q8—792no—
536C2×C22⋊Q8—792no—
537C2×C22⋊Q8—792no—
538C2×C22⋊Q8—794no—
539C2×C22⋊Q8—792no—
540C2×C22⋊Q8—792no—
541C2×C22⋊Q8—794no—
542C2×C22⋊Q8—794no—
543C2×C22⋊Q8—794no—
544C2×C22⋊Q8C2×D7912yes—
545C2×#121—791no—
546C2×#121—791no—
547C2×#121—794no—
548C2×#121—792no—
549C2×#121—794no—
550C2×#121—794no—
551C2×#121—794no—
552C2×#121—792no—
553C2×#121—794no—
554C2×#121—791no—
555C2×#121—791no—
556C2×#121—794no—
557C2×#121—792no—
558C2×#121—792no—
559C2×#121—792no—
560C2×#121—794no—
561C2×#121—794no—
562C2×#121C2×D7912yes—
563C2×C4×Q8—792no—
564C2×C4×Q8—792no—
565C2×C4×D4—792no—
566C2×C4×D4—792no—
567C2×C4×D4—794no—
568C2×C4×D4—794no—
569C2×C4×D4—791no—
570C2×C4×D4—791no—
571C2×C4×D4C2×D7911yescharacteristic
572C2×C4×D4C2×D7911yescharacteristic
573C2×#117—792no—
574C22×C4⋊C4—792no—
575C22×C4⋊C4—792no—
576C22×C4⋊C4—792no—
577C22×C4⋊C4C2×D7912yes—
578C22×C42—791no—
579C2×#41—48no—
580C2×#41—3168no—
581C2×#41—3168no—
582C2×#41—3168no—
583C2×#41—3168no—
584C2×#41—3168no—
585C2×#41—7916no—
586C2×#41—7916no—
587C2×#41—7916no—
588C2×#41—7916no—
589C2×#41—7916no—
590C2×#41C22×D79116yes—
591C22×Q8—792no—
592C22×Q8—792no—
593C22×Q8—792no—
594C22×Q8C22×D7912yes—
595C22×D4—792no—
596C22×D4—792no—
597C22×D4—794no—
598C22×D4—794no—
599C22×D4—792no—
600C22×D4—792no—
601C22×D4—792no—
602C22×D4—792no—
603C22×D4—792no—
604C22×D4—792no—
605C22×D4—794no—
606C22×D4—791no—
607C22×D4—791no—
608C22×D4C22×D7911yescharacteristic
609C22×D4C22×D7911yescharacteristic
610C22×D4C22×D7914yes—
611C23×C4—794no—
612C23×C4—794no—
613C23×C4—794no—
614C23×C4—792no—
615C23×C4—792no—
616C23×C4—791no—
617C23×C4—791no—
618C23×C4—791no—
619C23×C4C22×D7912yes—
620C23×C4C22×D7912yes—
621C23×C4C22×D7914yes—
622C4⋊Q8—798no—
623C4⋊Q8—798no—
624C4⋊Q8—798no—
625C4⋊Q8C22×D7918yes—
626#127—798no—
627#127—798no—
628#127—7932no—
629#125—7916no—
630#125—7932no—
631#124—7916no—
632#124—7916no—
633#123—7932no—
634#123—7932no—
635#123—7932no—
636#123C22×D79132yes—
637C22⋊Q8—7916no—
638C22⋊Q8—7916no—
639C22⋊Q8—7916no—
640C22⋊Q8—7932no—
641C22⋊Q8—7916no—
642C22⋊Q8—7916no—
643C22⋊Q8—7932no—
644C22⋊Q8—7932no—
645C22⋊Q8—7932no—
646C22⋊Q8C22×D79116yes—
647#121—798no—
648#121—798no—
649#121—7932no—
650#121—7916no—
651#121—7932no—
652#121—7932no—
653#121—7932no—
654#121—7916no—
655#121—7932no—
656#121—798no—
657#121—798no—
658#121—7932no—
659#121—7916no—
660#121—7916no—
661#121—7916no—
662#121—7932no—
663#121—7932no—
664#121C22×D79116yes—
665C4×Q8—7916no—
666C4×Q8—7916no—
667C4×D4—7916no—
668C4×D4—7916no—
669C4×D4—7932no—
670C4×D4—7932no—
671C4×D4—798no—
672C4×D4—798no—
673C4×D4C22×D7918yes—
674C4×D4C22×D7918yes—
675#117—7916no—
676C2×C4⋊C4—791no—
677C2×C4⋊C4—791no—
678C2×C4⋊C4—792no—
679C2×C4⋊C4—794no—
680C2×C4⋊C4—794no—
681C2×C4⋊C4—794no—
682C2×C4⋊C4—7916no—
683C2×C4⋊C4—792no—
684C2×C4⋊C4—792no—
685C2×C4⋊C4—792no—
686C2×C4⋊C4—794no—
687C2×C4⋊C4—794no—
688C2×C4⋊C4—7916no—
689C2×C4⋊C4—7916no—
690C2×C4⋊C4C22×D7911yescharacteristic
691C2×C4⋊C4C22×D7912yes—
692C2×C4⋊C4C22×D7911yescharacteristic
693C2×C4⋊C4C22×D7914yes—
694C2×C4⋊C4C22×D79116yes—
695C2×C4⋊C4C22×D7912yes—
696C2×C22⋊C4—794no—
697C2×C22⋊C4—792no—
698C2×C22⋊C4—792no—
699C2×C22⋊C4—794no—
700C2×C22⋊C4—794no—
701C2×C22⋊C4—794no—
702C2×C22⋊C4—792no—
703C2×C22⋊C4—792no—
704C2×C22⋊C4—792no—
705C2×C22⋊C4—792no—
706C2×C22⋊C4C22×D7914yes—
707C2×C22⋊C4C22×D7912yes—
708C2×C22⋊C4C22×D7912yes—
709C2×C42—794no—
710C2×C42—791no—
711C2×C42—791no—
712C2×C42—791no—
713C2×C42—798no—
714C2×C42C22×D7911yescharacteristic
715C24—792no—
716C24—792no—
717C24—791no—
718C24C23×D7912yes—
719C24C23×D7912yes—
720#41—432no—
721#41—31632no—
722#41—31632no—
723#41—31632no—
724#41—31632no—
725#41—31632no—
726C2×Q8—28no—
727C2×Q8—3164no—
728C2×Q8—3164no—
729C2×Q8—798no—
730C2×Q8—798no—
731C2×Q8—798no—
732C2×Q8—1588no—
733C2×Q8C23×D7918yes—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—48no—
737C2×D4—3164no—
738C2×D4—3168no—
739C2×D4—3164no—
740C2×D4—3164no—
741C2×D4—3164no—
742C2×D4—3164no—
743C2×D4—3168no—
744C2×D4—3168no—
745C2×D4—3164no—
746C2×D4—798no—
747C2×D4—798no—
748C2×D4—7916no—
749C2×D4—7916no—
750C2×D4—798no—
751C2×D4—798no—
752C2×D4—798no—
753C2×D4—798no—
754C2×D4—798no—
755C2×D4—798no—
756C2×D4—7916no—
757C2×D4—794no—
758C2×D4—794no—
759C2×D4—1588no—
760C2×D4—1588no—
761C2×D4—1584no—
762C2×D4—1584no—
763C2×D4C23×D7914yes—
764C2×D4C23×D7914yes—
765C2×D4C23×D79116yes—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—48no—
769C22×C4—3168no—
770C22×C4—3168no—
771C22×C4—3168no—
772C22×C4—7916no—
773C22×C4—7916no—
774C22×C4—7916no—
775C22×C4—791no—
776C22×C4—791no—
777C22×C4—791no—
778C22×C4—794no—
779C22×C4—792no—
780C22×C4—792no—
781C22×C4—794no—
782C22×C4—794no—
783C22×C4—794no—
784C22×C4—798no—
785C22×C4—798no—
786C22×C4—1584no—
787C22×C4—1588no—
788C22×C4—1584no—
789C22×C4—1588no—
790C22×C4—1584no—
791C22×C4C23×D7918yes—
792C22×C4C23×D7918yes—
793C22×C4C23×D7911yescharacteristic
794C22×C4C23×D7914yes—
795C22×C4C23×D7912yes—
796C22×C4C23×D7912yes—
797C22×C4C23×D79116yes—
798C22×C4C23×D7911yescharacteristic
799C22×C4C23×D7911yescharacteristic
800C4⋊C4—7916no—
801C4⋊C4—7916no—
802C4⋊C4—798no—
803C4⋊C4—798no—
804C4⋊C4—7916no—
805C4⋊C4—794no—
806C4⋊C4—794no—
807C4⋊C4—798no—
808C4⋊C4—7916no—
809C4⋊C4—798no—
810C4⋊C4—7916no—
811C4⋊C4C23×D7914yes—
812C4⋊C4C23×D7918yes—
813C4⋊C4C23×D7914yes—
814C4⋊C4C23×D79116yes—
815C4⋊C4C23×D7918yes—
816C22⋊C4—7916no—
817C22⋊C4—798no—
818C22⋊C4—798no—
819C22⋊C4—7916no—
820C22⋊C4—7916no—
821C22⋊C4—7916no—
822C22⋊C4—798no—
823C22⋊C4—798no—
824C22⋊C4—798no—
825C22⋊C4—798no—
826C22⋊C4C23×D79116yes—
827C22⋊C4C23×D7918yes—
828C22⋊C4C23×D7918yes—
829C42—794no—
830C42—794no—
831C42—794no—
832C42—7916no—
833C42C23×D7914yes—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—24no—
840C23—794no—
841C23—794no—
842C23—792no—
843C23—1584no—
844C23—1582no—
845C23—1584no—
846C23—1584no—
847C23—1584no—
848C23—1582no—
849C23—1582no—
850C23—1584no—
851C23—1584no—
852C23C24×D7914yes—
853C23C24×D7914yes—
854C23C24×D7911yescharacteristic
855Q8—216no—
856Q8—3168no—
857Q8—3168no—
858Q8—15816no—
859D4—28no—
860D4—28no—
861D4—416no—
862D4—3168no—
863D4—31616no—
864D4—3168no—
865D4—3168no—
866D4—3168no—
867D4—3168no—
868D4—31616no—
869D4—31616no—
870D4—3168no—
871D4—15816no—
872D4—15816no—
873D4—1588no—
874D4—1588no—
875C2×C4—24no—
876C2×C4—28no—
877C2×C4—24no—
878C2×C4—22no—
879C2×C4—216no—
880C2×C4—216no—
881C2×C4—416no—
882C2×C4—31616no—
883C2×C4—31616no—
884C2×C4—31616no—
885C2×C4—794no—
886C2×C4—792no—
887C2×C4—792no—
888C2×C4—792no—
889C2×C4—798no—
890C2×C4—794no—
891C2×C4—794no—
892C2×C4—1588no—
893C2×C4—1584no—
894C2×C4—1582no—
895C2×C4—1584no—
896C2×C4—1588no—
897C2×C4—1582no—
898C2×C4—15816no—
899C2×C4—1588no—
900C2×C4—15816no—
901C2×C4—1588no—
902C2×C4#1457920614yes—
903C2×C4#1457920714yes—
904C2×C4C24×D7912yes—
905C2×C4C24×D7918yes—
906C2×C4C24×D7914yes—
907C2×C4C24×D7914yes—
908C2×C4C24×D7912yes—
909C2×C4C24×D7912yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—48no—
917C22—48no—
918C22—3168no—
919C22—3168no—
920C22—3164no—
921C22—1584no—
922C22—1584no—
923C22—1582no—
924C22—1584no—
925C22—1582no—
926C22—1584no—
927C22—1582no—
928C22—1584no—
929C22—1584no—
930C22C2×#1457920612yes—
931C22C2×#1457920712yes—
932C222−1+4×D7912yes—
933C22C25×D7911yescharacteristic
934C4—24no—
935C4—28no—
936C4—24no—
937C4—22no—
938C4—794no—
939C4—1584no—
940C4—1582no—
941C4—1584no—
942C4—1588no—
943C4—1582no—
944C4C2×#1457920614yes—
945C4C2×#1457920714yes—
946C2—44no—
947C2—44no—
948C2—3164no—
949C2—3164no—
950C2—3162no—
951C2#2377779714yesdirect product factor
952C2C22×#1457920611yescharacteristic
953C2C22×#1457920711yescharacteristic
954C2C2×2−1+4×D7911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#547×C79C2
socleC23×C79C25
hypercenterC2×#547D79
hypocenterC79C2×#3548
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #23777797C2direct (N × H)
2. C2×#19099310C2semidirect
3. C2×#19099271C2semidirect
4. C2×#19099268C2semidirect
5. C2×#19099232C2semidirect
6. C2×#19099231C2semidirect
7. C2×#19099218C2semidirect
8. C2×#19099217C2semidirect
9. C2×#19099216C2semidirect
10. C2×#19099165C2semidirect
11. C2×#19099144C2semidirect
12. C2×#19099143C2semidirect
13. C2×#19099142C2semidirect
14. C2×#19099141C2semidirect
15. C2×#19099118C2semidirect
16. C2×#19099110C2semidirect
17. C2×#19099110C2semidirect
18. C2×#547×C79C2semidirect
24. #19099310C22semidirect
25. #19099271C22semidirect
26. #19099268C22semidirect
27. #19099232C22semidirect
28. #19099231C22semidirect
29. #19099218C22semidirect
30. #19099217C22semidirect
31. #19099216C22semidirect
32. #19099165C22semidirect
33. #19099144C22semidirect
34. #19099143C22semidirect
35. #19099142C22semidirect
36. #19099141C22semidirect
37. #19099118C22semidirect
38. #19099110C22semidirect
39. #19099110C22semidirect
93. #547×C79C22semidirect
471. C2×C79#3548semidirect
487. C2×#547D79semidirect
496. C79C2×#3548semidirect
511. #547C2×D79semidirect
951. C2#23777797direct (N × H)

Maximal subgroups

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

subgroupindex
#237777972
C2×#190993102
C2×#190992712
C2×#190992682
C2×#190992322
C2×#190992312
C2×#190992182
C2×#190992172
C2×#190992162
C2×#190991652
C2×#190991442
C2×#190991432
C2×#190991422
C2×#190991412
C2×#190991182
C2×#190991102
C2×#547×C792
C2×#354879