Finite Group Databasebeta

← C2×#23777799 #35196065

Subgroups — C2×#23777799 #35196065

Order 20224.

7810 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777799C2132yesmaximal, direct product factor
2C2×#19099309C214yesmaximal, complemented
3C2×#19099274C211yesmaximal, characteristic, complemented
4C2×#19099269C212yesmaximal, complemented
5C2×#19099235C211yesmaximal, characteristic, complemented
6C2×#19099234C211yesmaximal, characteristic, complemented
7C2×#19099234C212yesmaximal, complemented
8C2×#19099215C212yesmaximal, complemented
9C2×#19099214C212yesmaximal, complemented
10C2×#19099169C212yesmaximal, complemented
11C2×#19099164C212yesmaximal, complemented
12C2×#19099144C212yesmaximal, complemented
13C2×#19099143C212yesmaximal, complemented
14C2×#19099143C214yesmaximal, complemented
15C2×#19099117C211yesmaximal, characteristic, complemented
16C2×#19099114C211yesmaximal, characteristic, complemented
17C2×#19099110C211yesmaximal, characteristic, complemented
18C2×#554×C79C211yesmaximal, characteristic, complemented
19C22×#11929625C2212yes—
20C22×#11929625C2212yes—
21C22×#11929624C2214yes—
22C22×#11929624C2212yes—
23C22×#11929624C2212yes—
24#19099309C22164yescomplemented
25#19099274C22116yescomplemented
26#19099269C22132yescomplemented
27#19099235C22116yescomplemented
28#19099234C22132yescomplemented
29#19099234C22116yescomplemented
30#19099215C22132yescomplemented
31#19099214C22132yescomplemented
32#19099169C22132yescomplemented
33#19099164C22132yescomplemented
34#19099144C22132yescomplemented
35#19099143C22132yescomplemented
36#19099143C22164yescomplemented
37#19099117C22116yescomplemented
38#19099114C22116yescomplemented
39#19099110C22116yescomplemented
40C2×#14579160C2211yescharacteristic
41C2×#14579160C2211yescharacteristic
42C2×#14579159C2211yescharacteristic
43C2×#14579158C2211yescharacteristic
44C2×#14579158C2212yes—
45C2×#14579157C2211yescharacteristic
46C2×#14579157C2212yes—
47C2×#14579152C2212yes—
48C2×#14579151C2212yes—
49C2×#14579150C2212yes—
50C2×#14579147C2212yes—
51C2×#14579146C2214yes—
52C2×#14579146C2214yes—
53C2×#14579144C2214yes—
54C2×#14579143C2214yes—
55C2×#14579141C2212yes—
56C2×#14579141C2214yes—
57C2×#14579141C2211yescharacteristic
58C2×#14579139C2214yes—
59C2×#14579139C2214yes—
60C2×#14579139C2212yes—
61C2×#14579137C2214yes—
62C2×#14579137C2211yescharacteristic
63C2×#14579136C2212yes—
64C2×#14579136C2214yes—
65C2×#14579136C2211yescharacteristic
66C2×#14579136C2212yes—
67C2×#14579136C2212yes—
68C2×#14579136C2214yes—
69C2×#14579136C2214yes—
70C2×#14579135C2212yes—
71C2×#14579135C2214yes—
72C2×#14579135C2214yes—
73C2×#14579134C2214yes—
74C2×#14579134C2214yes—
75C2×#14579134C2214yes—
76C2×#14579134C2212yes—
77C2×#14579134C2214yes—
78C2×#14579132C2211yescharacteristic
79C2×C4×Dic158C2212yes—
80C2×C4×Dic158C2211yescharacteristic
81C2×C4×D316C2212yes—
82C2×C4×D316C2211yescharacteristic
83C2×#14579123C2212yes—
84C2×#14579123C2212yes—
85C2×#14579123C2212yes—
86C2×#14579123C2212yes—
87C2×C4×C22⋊D79C2212yes—
88C2×#14579118C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C2×C4⋊C4×D79C2214yes—
91C2×C42×D79C2211yescharacteristic
92#554×C79C22116yescomplemented
93C2×C4⋊Q8×C79C2211yescharacteristic
94C2×#125×C79C2212yes—
95C2×C22⋊Q8×C79C2212yes—
96C2×C22⋊Q8×C79C2214yes—
97C2×C4×Q8×C79C2211yescharacteristic
98C2×C4×D4×C79C2211yescharacteristic
99C2×C4×D4×C79C2212yes—
100C22×C4⋊C4×C79C2212yes—
101C2×#11929625—48no—
102C2×#11929625—48no—
103C2×#11929625C23116yes—
104C2×#11929625C23116yes—
105C2×#11929624—48no—
106C2×#11929624—416no—
107C2×#11929624—48no—
108C2×#11929624C23116yes—
109C2×#11929624C23132yes—
110C2×#11929624C23116yes—
111C22×Dic158C2312yes—
112C22×Dic158C2311yescharacteristic
113C22×Dic158C2312yes—
114C22×D316C2312yes—
115C22×D316C2311yescharacteristic
116C22×D316C2312yes—
117C22×D316C2314yes—
118C22×D316C2312yes—
119C22×D316C2314yes—
120C22×D316C2312yes—
121C22×D316C2314yes—
122C22×C22⋊D79C2312yes—
123C22×C22⋊D79C2312yes—
124C22×C22⋊D79C2314yes—
125C22×C22⋊D79C2314yes—
126C22×C22⋊D79C2312yes—
127C22×C4×D79C2311yescharacteristic
128C22×C4×D79C2311yescharacteristic
129C22×C4×D79C2311yescharacteristic
130C22×C4×D79C2312yes—
131C22×C4×D79C2314yes—
132C22×C4×D79C2314yes—
133C22×C4×D79C2314yes—
134C22×C4×D79C2314yes—
135#14579160C2318yes—
136#14579160C2318yes—
137#14579159C2318yes—
138#14579158C23116yes—
139#14579158C2318yes—
140#14579157C23116yes—
141#14579157C2318yes—
142#14579152C23116yes—
143#14579151C23116yes—
144#14579150C23116yes—
145#14579147C23116yes—
146#14579146C23132yes—
147#14579146C23132yes—
148#14579144C23132yes—
149#14579143C23132yes—
150#14579141C2318yes—
151#14579141C23116yes—
152#14579141C23132yes—
153#14579139C23116yes—
154#14579139C23132yes—
155#14579139C23132yes—
156#14579137C2318yes—
157#14579137C23132yes—
158#14579136C23132yes—
159#14579136C23132yes—
160#14579136C23116yes—
161#14579136C23132yes—
162#14579136C23116yes—
163#14579136C23116yes—
164#14579136C2318yes—
165#14579135C23132yes—
166#14579135C23116yes—
167#14579135C23132yes—
168#14579134C23132yes—
169#14579134C23116yes—
170#14579134C23132yes—
171#14579134C23132yes—
172#14579134C23132yes—
173#14579132C2318yes—
174C4×Dic158C23116yes—
175C4×Dic158C2318yes—
176C4×D316C23116yes—
177C4×D316C2318yes—
178#14579123C23116yes—
179#14579123C23116yes—
180#14579123C23116yes—
181#14579123C23116yes—
182C4×C22⋊D79C23116yes—
183#14579118C23116yes—
184C2×C4⋊Dic79C2311yescharacteristic
185C2×C4⋊Dic79C2314yes—
186C2×C4⋊Dic79C2311yescharacteristic
187C2×C4⋊Dic79C2312yes—
188C2×Dic79⋊C4C2312yes—
189C2×Dic79⋊C4C2312yes—
190C2×Dic79⋊C4C2314yes—
191C2×Dic79⋊C4C2312yes—
192C2×Dic79⋊C4C2312yes—
193C2×Dic79⋊C4C2312yes—
194C2×Dic79⋊C4C2312yes—
195C4⋊C4×D79C23116yes—
196C4⋊C4×D79C23132yes—
197C2×C22⋊Dic79C2312yes—
198C2×(C2×D79)⋊C4C2312yes—
199C2×(C2×D79)⋊C4C2312yes—
200C2×(C2×D79)⋊C4C2312yes—
201C2×(C2×D79)⋊C4C2314yes—
202C2×(C2×D79)⋊C4C2314yes—
203C2×(C2×D79)⋊C4C2314yes—
204C2×(C2×D79)⋊C4C2314yes—
205C2×(C2×D79)⋊C4C2312yes—
206C2×(C2×D79)⋊C4C2314yes—
207C2×C4×Dic79C2311yescharacteristic
208C2×C4×Dic79C2311yescharacteristic
209C2×C4×Dic79C2311yescharacteristic
210C2×C4×Dic79C2312yes—
211C42×D79C2318yes—
212C22×Q8×C79C2311yescharacteristic
213C22×Q8×C79C2312yes—
214C22×D4×C79C2311yescharacteristic
215C23×C4×C79C2312yes—
216C23×C4×C79C2314yes—
217C4⋊Q8×C79C2318yes—
218#125×C79C23116yes—
219C22⋊Q8×C79C23116yes—
220C22⋊Q8×C79C23132yes—
221C4×Q8×C79C2318yes—
222C4×D4×C79C23116yes—
223C4×D4×C79C2318yes—
224C2×C4⋊C4×C79C23116yes—
225C2×C4⋊C4×C79C2311yescharacteristic
226C2×C4⋊C4×C79C2314yes—
227C2×C4⋊C4×C79C2312yes—
228C2×C4⋊C4×C79C2311yescharacteristic
229C2×C4⋊C4×C79C2312yes—
230C2×C4⋊C4×C79C2312yes—
231C2×C4⋊C4×C79C2314yes—
232C2×C22⋊C4×C79C2314yes—
233C2×C22⋊C4×C79C2312yes—
234C2×C42×C79C2312yes—
235C2×C42×C79C2311yescharacteristic
236C23×D79C2411yescharacteristic
237C23×D79C2412yes—
238C23×D79C2414yes—
239#11929625—432no—
240#11929625—432no—
241#11929624—464no—
242#11929624—432no—
243#11929624—432no—
244C2×Dic158—28no—
245C2×Dic158—24no—
246C2×Dic158—44no—
247C2×Dic158C2418yes—
248C2×Dic158C2414yes—
249C2×Dic158C2418yes—
250C2×D316—28no—
251C2×D316—28no—
252C2×D316—24no—
253C2×D316—44no—
254C2×D316—48no—
255C2×D316—48no—
256C2×D316—44no—
257C2×D316—48no—
258C2×D316C2418yes—
259C2×D316C2418yes—
260C2×D316C2414yes—
261C2×D316C2418yes—
262C2×D316C24116yes—
263C2×D316C24116yes—
264C2×D316C2418yes—
265C2×D316C24116yes—
266C2×C22⋊D79—28no—
267C2×C22⋊D79—44no—
268C2×C22⋊D79—48no—
269C2×C22⋊D79—44no—
270C2×C22⋊D79—48no—
271C2×C22⋊D79C2418yes—
272C2×C22⋊D79C2418yes—
273C2×C22⋊D79C24116yes—
274C2×C22⋊D79C24116yes—
275C2×C22⋊D79C2418yes—
276C22×Dic79C2411yescharacteristic
277C22×Dic79C2412yes—
278C22×Dic79C2412yes—
279C22×Dic79C2412yes—
280C22×Dic79C2411yescharacteristic
281C22×Dic79C2411yescharacteristic
282C2×C4×D79—216no—
283C2×C4×D79—24no—
284C2×C4×D79—24no—
285C2×C4×D79—28no—
286C2×C4×D79—24no—
287C2×C4×D79—48no—
288C2×C4×D79—48no—
289C2×C4×D79—48no—
290C2×C4×D79C2414yes—
291C2×C4×D79C2418yes—
292C2×C4×D79C24116yes—
293C2×C4×D79C2414yes—
294C2×C4×D79C2414yes—
295C2×C4×D79C24116yes—
296C2×C4×D79C24116yes—
297C2×C4×D79C24116yes—
298C4⋊Dic79C2414yes—
299C4⋊Dic79C24116yes—
300C4⋊Dic79C2414yes—
301C4⋊Dic79C2418yes—
302Dic79⋊C4C2418yes—
303Dic79⋊C4C2418yes—
304Dic79⋊C4C24116yes—
305Dic79⋊C4C2418yes—
306Dic79⋊C4C2418yes—
307Dic79⋊C4C2418yes—
308Dic79⋊C4C2418yes—
309C22⋊Dic79C2418yes—
310(C2×D79)⋊C4C2418yes—
311(C2×D79)⋊C4C2418yes—
312(C2×D79)⋊C4C2418yes—
313(C2×D79)⋊C4C24116yes—
314(C2×D79)⋊C4C24116yes—
315(C2×D79)⋊C4C24116yes—
316(C2×D79)⋊C4C24116yes—
317(C2×D79)⋊C4C2418yes—
318(C2×D79)⋊C4C24116yes—
319C4×Dic79C2414yes—
320C4×Dic79C2414yes—
321C4×Dic79C2414yes—
322C4×Dic79C2418yes—
323C24×C79C2412yes—
324C2×Q8×C79—24no—
325C2×Q8×C79—44no—
326C2×Q8×C79C2414yes—
327C2×Q8×C79C2418yes—
328C2×D4×C79—24no—
329C2×D4×C79C2414yes—
330C22×C4×C79—28no—
331C22×C4×C79—48no—
332C22×C4×C79C2412yes—
333C22×C4×C79C2412yes—
334C22×C4×C79C2418yes—
335C22×C4×C79C2412yes—
336C22×C4×C79C2411yescharacteristic
337C22×C4×C79C2414yes—
338C22×C4×C79C24116yes—
339C22×C4×C79C2411yescharacteristic
340C22×C4×C79C2411yescharacteristic
341C4⋊C4×C79C2414yes—
342C4⋊C4×C79C24116yes—
343C4⋊C4×C79C2418yes—
344C4⋊C4×C79C2414yes—
345C4⋊C4×C79C2418yes—
346C4⋊C4×C79C2418yes—
347C4⋊C4×C79C24116yes—
348C22⋊C4×C79C24116yes—
349C22⋊C4×C79C2418yes—
350C42×C79C2418yes—
351C42×C79C2414yes—
352C23×C79—24no—
353C23×C79—24no—
354C23×C79—24no—
355C23×C79C2514yes—
356C23×C79C2511yescharacteristic
357C22×D79—22no—
358C22×D79—28no—
359C22×D79—24no—
360C22×D79—22no—
361C22×D79—24no—
362C22×D79—28no—
363C22×D79—22no—
364C22×D79—24no—
365C22×D79—28no—
366C22×D79C2514yes—
367C22×D79C2512yes—
368C22×D79C2518yes—
369Q8×C79—28no—
370Q8×C79—48no—
371D4×C79—28no—
372C2×C4×C79—28no—
373C2×C4×C79—22no—
374C2×C4×C79—24no—
375C2×C4×C79—24no—
376C2×C4×C79—24no—
377C2×C4×C79—216no—
378C2×C4×C79—416no—
379C2×C4×C79H(5,𝔽2)14yes—
380C2×C4×C792−1+414yes—
381C2×C4×C79C2512yes—
382C2×C4×C79C2518yes—
383C2×C4×C79C2514yes—
384C2×C4×C79C2514yes—
385C2×C4×C79C2514yes—
386C2×C4×C79C2512yes—
387C2×C4×C79C2512yes—
388C22⋊D79—216no—
389C22⋊D79—416no—
390C22⋊D79—416no—
391C22⋊D79—48no—
392C22⋊D79—48no—
393C2×Dic79—24no—
394C2×Dic79—22no—
395C2×Dic79—24no—
396C2×Dic79—24no—
397C2×Dic79—22no—
398C2×Dic79H(5,𝔽2)14yes—
399C2×Dic79C2512yes—
400C2×Dic79C2512yes—
401C2×Dic79C2514yes—
402C2×Dic79C2514yes—
403C2×Dic79C2514yes—
404C2×Dic79C2512yes—
405D316—216no—
406D316—216no—
407D316—28no—
408D316—48no—
409D316—416no—
410D316—416no—
411D316—416no—
412D316—48no—
413C4×D79—28no—
414C4×D79—216no—
415C4×D79—28no—
416C4×D79—232no—
417C4×D79—28no—
418C4×D79—416no—
419C4×D79—416no—
420C4×D79—416no—
421Dic158—28no—
422Dic158—216no—
423Dic158—48no—
424C22×C79—24no—
425C22×C79—24no—
426C22×C79—24no—
427C22×C79—48no—
428C22×C79C2×H(5,𝔽2)12yes—
429C22×C79C2×H(5,𝔽2)12yes—
430C22×C79C2×2−1+412yes—
431C22×C79C2611yescharacteristic
432C2×D79—24no—
433C2×D79—22no—
434C2×D79—28no—
435C2×D79—24no—
436C2×D79—28no—
437C2×D79—22no—
438C2×D79—22no—
439C2×D79—24no—
440C2×D79—28no—
441C2×D79—44no—
442C2×D79—48no—
443C2×D79—416no—
444C4×C79—24no—
445C4×C79—24no—
446C4×C79—28no—
447C4×C79—24no—
448C4×C79—22no—
449C4×C79C2×H(5,𝔽2)14yes—
450C4×C79C2×2−1+414yes—
451Dic79—24no—
452Dic79—24no—
453Dic79—22no—
454Dic79—24no—
455Dic79—22no—
456Dic79C2×H(5,𝔽2)14yes—
457C2×#3548—791nomaximal, Sylow
458C2×C79—44no—
459C2×C79#354814yescomplemented
460C2×C79C22×H(5,𝔽2)11yescharacteristic
461C2×C79C22×H(5,𝔽2)11yescharacteristic
462C2×C79C22×2−1+411yescharacteristic
463D79—44no—
464D79—42no—
465D79—48no—
466#3548—7932no—
467C2×#562—794no—
468C2×#554—791no—
469C2×#554—792no—
470C2×#554D7911yescharacteristic, complemented
471C2×#550—791no—
472C2×#550—792no—
473C2×#550—791no—
474C2×#547—792no—
475C2×#547—792no—
476C2×#540—792no—
477C2×#540—792no—
478C2×#537—794no—
479C2×#537—792no—
480C2×#537—792no—
481C2×#533—791no—
482C2×#532—791no—
483C2×#532—791no—
484C79C2×#354811yescharacteristic, complemented, Sylow
485C22×#41—792no—
486C22×#41—792no—
487C22×#41—792no—
488C22×#41—792no—
489C22×#41—794no—
490#562—7964no—
491#554—7916no—
492#554—7932no—
493#554C2×D79116yescomplemented
494#550—7916no—
495#550—7932no—
496#550—7916no—
497#547—7932no—
498#547—7932no—
499#540—7932no—
500#540—7932no—
501#537—7964no—
502#537—7932no—
503#537—7932no—
504#533—7916no—
505#532—7916no—
506#532—7916no—
507C2×C4⋊Q8—791no—
508C2×C4⋊Q8—791no—
509C2×C4⋊Q8—791no—
510C2×C4⋊Q8C2×D7911yescharacteristic
511C2×#127—791no—
512C2×#127—792no—
513C2×#127—791no—
514C2×#127—792no—
515C2×#125—792no—
516C2×#125—792no—
517C2×#125C2×D7912yes—
518C2×#124—792no—
519C2×#124—792no—
520C2×#123—794no—
521C2×#123—794no—
522C2×#123—794no—
523C2×#123—794no—
524C2×C22⋊Q8—791no—
525C2×C22⋊Q8—794no—
526C2×C22⋊Q8—792no—
527C2×C22⋊Q8—791no—
528C2×C22⋊Q8—794no—
529C2×C22⋊Q8—792no—
530C2×C22⋊Q8—794no—
531C2×C22⋊Q8—794no—
532C2×C22⋊Q8C2×D7912yes—
533C2×C22⋊Q8C2×D7914yes—
534C2×#121—791no—
535C2×#121—794no—
536C2×#121—792no—
537C2×#121—794no—
538C2×#121—792no—
539C2×#121—792no—
540C2×#121—791no—
541C2×#121—794no—
542C2×#121—794no—
543C2×#121—792no—
544C2×#121—794no—
545C2×#121—792no—
546C2×#121—794no—
547C2×#121—794no—
548C2×#121—794no—
549C2×#121—794no—
550C2×C4×Q8—791no—
551C2×C4×Q8—792no—
552C2×C4×Q8C2×D7911yescharacteristic
553C2×C4×D4—792no—
554C2×C4×D4—792no—
555C2×C4×D4—792no—
556C2×C4×D4—792no—
557C2×C4×D4—792no—
558C2×C4×D4—791no—
559C2×C4×D4—792no—
560C2×C4×D4C2×D7911yescharacteristic
561C2×C4×D4C2×D7912yes—
562C2×#117—792no—
563C22×C4⋊C4—794no—
564C22×C4⋊C4—792no—
565C22×C4⋊C4C2×D7912yes—
566C22×C42—791no—
567C2×#41—3168no—
568C2×#41—3168no—
569C2×#41—31616no—
570C2×#41—3168no—
571C2×#41—3168no—
572C2×#41—7916no—
573C2×#41—7916no—
574C2×#41—7916no—
575C2×#41—7916no—
576C2×#41—7932no—
577C22×Q8—792no—
578C22×Q8—792no—
579C22×Q8—791no—
580C22×Q8C22×D7911yescharacteristic
581C22×Q8C22×D7912yes—
582C22×D4—792no—
583C22×D4—794no—
584C22×D4—794no—
585C22×D4—792no—
586C22×D4—792no—
587C22×D4—794no—
588C22×D4—792no—
589C22×D4—794no—
590C22×D4—794no—
591C22×D4—792no—
592C22×D4—792no—
593C22×D4—791no—
594C22×D4—792no—
595C22×D4C22×D7911yescharacteristic
596C23×C4—794no—
597C23×C4—794no—
598C23×C4—794no—
599C23×C4—794no—
600C23×C4—792no—
601C23×C4—791no—
602C23×C4—791no—
603C23×C4—791no—
604C23×C4C22×D7912yes—
605C23×C4C22×D7914yes—
606C4⋊Q8—798no—
607C4⋊Q8—798no—
608C4⋊Q8—798no—
609C4⋊Q8C22×D7918yes—
610#127—798no—
611#127—7916no—
612#127—798no—
613#127—7916no—
614#125—7916no—
615#125—7916no—
616#125C22×D79116yes—
617#124—7916no—
618#124—7916no—
619#123—7932no—
620#123—7932no—
621#123—7932no—
622#123—7932no—
623C22⋊Q8—798no—
624C22⋊Q8—7932no—
625C22⋊Q8—7916no—
626C22⋊Q8—798no—
627C22⋊Q8—7932no—
628C22⋊Q8—7916no—
629C22⋊Q8—7932no—
630C22⋊Q8—7932no—
631C22⋊Q8C22×D79116yes—
632C22⋊Q8C22×D79132yes—
633#121—798no—
634#121—7932no—
635#121—7916no—
636#121—7932no—
637#121—7916no—
638#121—7916no—
639#121—798no—
640#121—7932no—
641#121—7932no—
642#121—7916no—
643#121—7932no—
644#121—7916no—
645#121—7932no—
646#121—7932no—
647#121—7932no—
648#121—7932no—
649C4×Q8—7916no—
650C4×Q8—798no—
651C4×Q8C22×D7918yes—
652C4×D4—7916no—
653C4×D4—7916no—
654C4×D4—7916no—
655C4×D4—7916no—
656C4×D4—7916no—
657C4×D4—798no—
658C4×D4—7916no—
659C4×D4C22×D7918yes—
660C4×D4C22×D79116yes—
661#117—7916no—
662C2×C4⋊C4—792no—
663C2×C4⋊C4—792no—
664C2×C4⋊C4—791no—
665C2×C4⋊C4—794no—
666C2×C4⋊C4—794no—
667C2×C4⋊C4—792no—
668C2×C4⋊C4—792no—
669C2×C4⋊C4—791no—
670C2×C4⋊C4—792no—
671C2×C4⋊C4—792no—
672C2×C4⋊C4—792no—
673C2×C4⋊C4—7932no—
674C2×C4⋊C4—7916no—
675C2×C4⋊C4C22×D7912yes—
676C2×C4⋊C4C22×D7914yes—
677C2×C4⋊C4C22×D7911yescharacteristic
678C2×C4⋊C4C22×D7914yes—
679C2×C4⋊C4C22×D79116yes—
680C2×C4⋊C4C22×D7912yes—
681C2×C4⋊C4C22×D7911yescharacteristic
682C2×C4⋊C4C22×D7912yes—
683C2×C22⋊C4—792no—
684C2×C22⋊C4—792no—
685C2×C22⋊C4—792no—
686C2×C22⋊C4—794no—
687C2×C22⋊C4—794no—
688C2×C22⋊C4—794no—
689C2×C22⋊C4—794no—
690C2×C22⋊C4—792no—
691C2×C22⋊C4—794no—
692C2×C22⋊C4—792no—
693C2×C22⋊C4C22×D7914yes—
694C2×C22⋊C4C22×D7912yes—
695C2×C42—792no—
696C2×C42—791no—
697C2×C42—791no—
698C2×C42—791no—
699C2×C42—798no—
700C2×C42C22×D7912yes—
701C2×C42C22×D7911yescharacteristic
702C24—792no—
703C24—794no—
704C24—791no—
705C24C23×D7912yes—
706#41—31632no—
707#41—31632no—
708#41—31664no—
709#41—31632no—
710#41—31632no—
711C2×Q8—24no—
712C2×Q8—44no—
713C2×Q8—3164no—
714C2×Q8—798no—
715C2×Q8—798no—
716C2×Q8—794no—
717C2×Q8—1588no—
718C2×Q8—1584no—
719C2×Q8C23×D7914yes—
720C2×Q8C23×D7918yes—
721C2×D4—24no—
722C2×D4—3168no—
723C2×D4—3168no—
724C2×D4—3164no—
725C2×D4—3164no—
726C2×D4—3168no—
727C2×D4—3168no—
728C2×D4—3164no—
729C2×D4—3168no—
730C2×D4—3164no—
731C2×D4—798no—
732C2×D4—7916no—
733C2×D4—7916no—
734C2×D4—798no—
735C2×D4—798no—
736C2×D4—7916no—
737C2×D4—798no—
738C2×D4—7916no—
739C2×D4—7916no—
740C2×D4—798no—
741C2×D4—798no—
742C2×D4—794no—
743C2×D4—798no—
744C2×D4—1588no—
745C2×D4—1588no—
746C2×D4—1588no—
747C2×D4—1584no—
748C2×D4C23×D7914yes—
749C22×C4—28no—
750C22×C4—48no—
751C22×C4—3168no—
752C22×C4—3168no—
753C22×C4—3168no—
754C22×C4—7916no—
755C22×C4—7916no—
756C22×C4—7916no—
757C22×C4—791no—
758C22×C4—791no—
759C22×C4—791no—
760C22×C4—792no—
761C22×C4—792no—
762C22×C4—792no—
763C22×C4—794no—
764C22×C4—794no—
765C22×C4—794no—
766C22×C4—7916no—
767C22×C4—798no—
768C22×C4—15816no—
769C22×C4—1584no—
770C22×C4—1588no—
771C22×C4—1584no—
772C22×C4—1584no—
773C22×C4C23×D7918yes—
774C22×C4C23×D7911yescharacteristic
775C22×C4C23×D7912yes—
776C22×C4C23×D7912yes—
777C22×C4C23×D7914yes—
778C22×C4C23×D7912yes—
779C22×C4C23×D79116yes—
780C22×C4C23×D7911yescharacteristic
781C22×C4C23×D7911yescharacteristic
782C4⋊C4—798no—
783C4⋊C4—798no—
784C4⋊C4—7916no—
785C4⋊C4—798no—
786C4⋊C4—798no—
787C4⋊C4—798no—
788C4⋊C4—798no—
789C4⋊C4—794no—
790C4⋊C4—7916no—
791C4⋊C4—794no—
792C4⋊C4—798no—
793C4⋊C4C23×D7918yes—
794C4⋊C4C23×D79116yes—
795C4⋊C4C23×D7914yes—
796C4⋊C4C23×D79116yes—
797C4⋊C4C23×D7918yes—
798C4⋊C4C23×D7914yes—
799C4⋊C4C23×D7918yes—
800C22⋊C4—798no—
801C22⋊C4—798no—
802C22⋊C4—798no—
803C22⋊C4—7916no—
804C22⋊C4—7916no—
805C22⋊C4—7916no—
806C22⋊C4—7916no—
807C22⋊C4—798no—
808C22⋊C4—7916no—
809C22⋊C4—798no—
810C22⋊C4C23×D79116yes—
811C22⋊C4C23×D7918yes—
812C42—794no—
813C42—794no—
814C42—794no—
815C42—798no—
816C42C23×D7914yes—
817C42C23×D7918yes—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—794no—
822C23—798no—
823C23—792no—
824C23—1584no—
825C23—1588no—
826C23—1582no—
827C23—1588no—
828C23—1582no—
829C23—1584no—
830C23—1582no—
831C23—1584no—
832C23—1588no—
833C23C24×D7914yes—
834C23C24×D7911yescharacteristic
835Q8—28no—
836Q8—48no—
837Q8—3168no—
838Q8—15816no—
839Q8—1588no—
840D4—28no—
841D4—31616no—
842D4—31616no—
843D4—3168no—
844D4—3168no—
845D4—31616no—
846D4—31616no—
847D4—3168no—
848D4—31616no—
849D4—3168no—
850D4—15816no—
851D4—15816no—
852D4—15816no—
853D4—1588no—
854C2×C4—24no—
855C2×C4—28no—
856C2×C4—22no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—216no—
860C2×C4—416no—
861C2×C4—31616no—
862C2×C4—31616no—
863C2×C4—31616no—
864C2×C4—794no—
865C2×C4—792no—
866C2×C4—792no—
867C2×C4—792no—
868C2×C4—794no—
869C2×C4—794no—
870C2×C4—794no—
871C2×C4—15832no—
872C2×C4—1588no—
873C2×C4—1584no—
874C2×C4—1584no—
875C2×C4—1584no—
876C2×C4—1582no—
877C2×C4—1582no—
878C2×C4—15816no—
879C2×C4—1588no—
880C2×C4—1588no—
881C2×C4#1457920714yes—
882C2×C4#1457920914yes—
883C2×C4C24×D7912yes—
884C2×C4C24×D7914yes—
885C2×C4C24×D7914yes—
886C2×C4C24×D7918yes—
887C2×C4C24×D7914yes—
888C2×C4C24×D7912yes—
889C2×C4C24×D7912yes—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—48no—
894C22—3168no—
895C22—31616no—
896C22—3164no—
897C22—1584no—
898C22—1582no—
899C22—1588no—
900C22—1588no—
901C22—1584no—
902C22—1582no—
903C22—1582no—
904C22—1584no—
905C22—1588no—
906C22H(5,𝔽2)×D7912yes—
907C22C2×#1457920712yes—
908C22C2×#1457920912yes—
909C22C25×D7911yescharacteristic
910C4—24no—
911C4—28no—
912C4—22no—
913C4—24no—
914C4—24no—
915C4—794no—
916C4—1584no—
917C4—1584no—
918C4—1584no—
919C4—1582no—
920C4—1582no—
921C4C2×#1457920714yes—
922C4C2×#1457920914yes—
923C2—44no—
924C2—3164no—
925C2—3168no—
926C2—3162no—
927C2#2377779914yesdirect product factor
928C2C2×H(5,𝔽2)×D7911yescharacteristic
929C2C22×#1457920711yescharacteristic
930C2C22×#1457920911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#554×C79C2
socleC23×C79C25
hypercenterC2×#554D79
hypocenterC79C2×#3548
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #23777799C2direct (N × H)
2. C2×#19099309C2semidirect
3. C2×#19099274C2semidirect
4. C2×#19099269C2semidirect
5. C2×#19099235C2semidirect
6. C2×#19099234C2semidirect
7. C2×#19099234C2semidirect
8. C2×#19099215C2semidirect
9. C2×#19099214C2semidirect
10. C2×#19099169C2semidirect
11. C2×#19099164C2semidirect
12. C2×#19099144C2semidirect
13. C2×#19099143C2semidirect
14. C2×#19099143C2semidirect
15. C2×#19099117C2semidirect
16. C2×#19099114C2semidirect
17. C2×#19099110C2semidirect
18. C2×#554×C79C2semidirect
24. #19099309C22semidirect
25. #19099274C22semidirect
26. #19099269C22semidirect
27. #19099235C22semidirect
28. #19099234C22semidirect
29. #19099234C22semidirect
30. #19099215C22semidirect
31. #19099214C22semidirect
32. #19099169C22semidirect
33. #19099164C22semidirect
34. #19099144C22semidirect
35. #19099143C22semidirect
36. #19099143C22semidirect
37. #19099117C22semidirect
38. #19099114C22semidirect
39. #19099110C22semidirect
92. #554×C79C22semidirect
459. C2×C79#3548semidirect
470. C2×#554D79semidirect
484. C79C2×#3548semidirect
493. #554C2×D79semidirect
927. C2#23777799direct (N × H)

Maximal subgroups

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

subgroupindex
#237777992
C2×#190993092
C2×#190992742
C2×#190992692
C2×#190992352
C2×#190992342
C2×#190992152
C2×#190992142
C2×#190991692
C2×#190991642
C2×#190991442
C2×#190991432
C2×#190991172
C2×#190991142
C2×#190991102
C2×#554×C792
C2×#354879