Finite Group Databasebeta

← C2×#23777934 #35195636

Subgroups — C2×#23777934 #35195636

Order 20224.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777934C2132yesmaximal, direct product factor
2C2×#19099317C212yesmaximal, complemented
3C2×#19099311C212yesmaximal, complemented
4C2×#19099269C212yesmaximal, complemented
5C2×#19099266C212yesmaximal, complemented
6C2×#19099261C212yesmaximal, complemented
7C2×#19099214C212yesmaximal, complemented
8C2×#19099214C214yesmaximal, complemented
9C2×#19099193C212yesmaximal, complemented
10C2×#19099169C212yesmaximal, complemented
11C2×#19099161C214yesmaximal, complemented
12C2×#19099160C212yesmaximal, complemented
13C2×#19099144C212yesmaximal, complemented
14C2×#19099113C211yesmaximal, characteristic, complemented
15C2×#19099097C211yesmaximal, characteristic, complemented
16C22×#125×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2212yes—
18C22×#11929624C2214yes—
19#19099317C22132yescomplemented
20#19099311C22132yescomplemented
21#19099269C22132yescomplemented
22#19099266C22132yescomplemented
23#19099261C22132yescomplemented
24#19099214C22132yescomplemented
25#19099214C22164yescomplemented
26#19099193C22132yescomplemented
27#19099169C22132yescomplemented
28#19099161C22164yescomplemented
29#19099160C22132yescomplemented
30#19099144C22132yescomplemented
31#19099113C22116yescomplemented
32C2×#14579161C2211yescharacteristic
33C2×#14579160C2212yes—
34C2×#14579160C2214yes—
35C2×#14579158C2211yescharacteristic
36#19099097C22116yescomplemented
37C2×#14579156C2214yes—
38C2×#14579156C2214yes—
39C2×#14579155C2212yes—
40C2×#14579153C2211yescharacteristic
41C2×#14579152C2212yes—
42C2×#14579151C2214yes—
43C2×#14579149C2211yescharacteristic
44C2×#14579149C2212yes—
45C2×#14579146C2214yes—
46C2×#14579146C2214yes—
47C2×#14579146C2214yes—
48C2×#14579146C2214yes—
49C2×#14579146C2214yes—
50C2×#14579144C2212yes—
51C2×#14579144C2214yes—
52C2×#14579141C2214yes—
53C2×#14579141C2214yes—
54C2×#14579140C2211yescharacteristic
55C2×#14579139C2214yes—
56C2×#14579139C2214yes—
57C2×#14579139C2214yes—
58C2×#14579139C2214yes—
59C2×#14579136C2212yes—
60C2×#14579136C2214yes—
61C2×#14579136C2212yes—
62C2×#14579136C2214yes—
63C2×#14579136C2214yes—
64C2×#14579135C2212yes—
65C2×#14579135C2214yes—
66C2×#14579135C2211yescharacteristic
67C2×#14579135C2212yes—
68C2×C4×Dic158C2211yescharacteristic
69C2×C4×D316C2211yescharacteristic
70C2×C4×D316C2212yes—
71C2×C4×D316C2212yes—
72C2×#14579123C2214yes—
73C2×#14579123C2212yes—
74C2×#14579123C2212yes—
75C2×C4×C22⋊D79C2212yes—
76C2×C4×C22⋊D79C2214yes—
77C2×#14579119C2212yes—
78C2×#14579118C2212yes—
79C2×C4⋊C4×D79C2212yes—
80C2×C4⋊C4×D79C2214yes—
81C2×#125×C79C2212yes—
82C2×#125×C79C2212yes—
83C2×#125×C79C2212yes—
84C2×#125×C79C2212yes—
85C2×#125×C79C22116yescomplemented
86C22×C4⋊C4×C79C2211yescharacteristic
87C22×C4⋊C4×C79C2212yes—
88C22×C4⋊C4×C79C2211yescharacteristic
89C22×C4⋊C4×C79C2212yes—
90C22×C42×C79C2211yescharacteristic
91C2×#11929624—48no—
92C2×#11929624—416no—
93C2×#11929624C23132yes—
94C2×#11929624C23116yes—
95C22×Dic158C2311yescharacteristic
96C22×Dic158C2314yes—
97C22×Dic158C2312yes—
98C22×D316C2312yes—
99C22×D316C2314yes—
100C22×D316C2311yescharacteristic
101C22×D316C2312yes—
102C22×D316C2314yes—
103C22×D316C2312yes—
104C22×C22⋊D79C2312yes—
105C22×C22⋊D79C2314yes—
106C22×C4×D79C2312yes—
107C22×C4×D79C2314yes—
108C22×C4×D79C2314yes—
109C22×C4×D79C2314yes—
110C22×C4×D79C2314yes—
111#14579161C2318yes—
112#14579160C23116yes—
113#14579160C23132yes—
114#14579158C2318yes—
115#14579156C23132yes—
116#14579156C23132yes—
117#14579155C23116yes—
118#14579153C2318yes—
119#14579152C23116yes—
120#14579151C23132yes—
121#14579149C2318yes—
122#14579149C23116yes—
123#14579146C23132yes—
124#14579146C23132yes—
125#14579146C23132yes—
126#14579146C23132yes—
127#14579146C23132yes—
128#14579144C23132yes—
129#14579144C23116yes—
130#14579141C23132yes—
131#14579141C23132yes—
132#14579140C2318yes—
133#14579139C23132yes—
134#14579139C23132yes—
135#14579139C23132yes—
136#14579139C23132yes—
137#14579136C23132yes—
138#14579136C23132yes—
139#14579136C23116yes—
140#14579136C23132yes—
141#14579136C23116yes—
142#14579135C2318yes—
143#14579135C23116yes—
144#14579135C23132yes—
145#14579135C23116yes—
146C4×Dic158C2318yes—
147C4×D316C23116yes—
148C4×D316C2318yes—
149C4×D316C23116yes—
150#14579123C23132yes—
151#14579123C23116yes—
152#14579123C23116yes—
153C4×C22⋊D79C23132yes—
154C4×C22⋊D79C23116yes—
155#14579119C23116yes—
156#14579118C23116yes—
157C2×C4⋊Dic79C2312yes—
158C2×C4⋊Dic79C2314yes—
159C2×C4⋊Dic79C2312yes—
160C2×C4⋊Dic79C2311yescharacteristic
161C2×C4⋊Dic79C2311yescharacteristic
162C2×Dic79⋊C4C2312yes—
163C2×Dic79⋊C4C2314yes—
164C2×Dic79⋊C4C2314yes—
165C2×Dic79⋊C4C2312yes—
166C2×Dic79⋊C4C2312yes—
167C2×Dic79⋊C4C2314yes—
168C2×Dic79⋊C4C2312yes—
169C4⋊C4×D79C23132yes—
170C4⋊C4×D79C23116yes—
171C2×C22⋊Dic79C2312yes—
172C2×(C2×D79)⋊C4C2312yes—
173C2×(C2×D79)⋊C4C2312yes—
174C2×(C2×D79)⋊C4C2314yes—
175C2×(C2×D79)⋊C4C2314yes—
176C2×(C2×D79)⋊C4C2312yes—
177C2×(C2×D79)⋊C4C2312yes—
178C2×(C2×D79)⋊C4C2314yes—
179C2×(C2×D79)⋊C4C2314yes—
180C2×(C2×D79)⋊C4C2314yes—
181C2×(C2×D79)⋊C4C2314yes—
182C2×(C2×D79)⋊C4C2314yes—
183C2×C4×Dic79C2312yes—
184C2×C4×Dic79C2314yes—
185C23×C4×C79C2311yescharacteristic
186C23×C4×C79C2311yescharacteristic
187C23×C4×C79C2312yes—
188C23×C4×C79C2311yescharacteristic
189C23×C4×C79C2312yes—
190#125×C79C23116yes—
191#125×C79C23116yes—
192#125×C79C23116yes—
193#125×C79C23116yes—
194C2×C4⋊C4×C79C23116yes—
195C2×C4⋊C4×C79C2318yes—
196C2×C4⋊C4×C79C23116yes—
197C2×C4⋊C4×C79C2312yes—
198C2×C4⋊C4×C79C2314yes—
199C2×C4⋊C4×C79C2312yes—
200C2×C4⋊C4×C79C2314yes—
201C2×C4⋊C4×C79C2314yes—
202C2×C4⋊C4×C79C2314yes—
203C2×C4⋊C4×C79C2312yes—
204C2×C4⋊C4×C79C2312yes—
205C2×C4⋊C4×C79C2318yes—
206C2×C42×C79C2311yescharacteristic
207C2×C42×C79C2311yescharacteristic
208C2×C42×C79C2311yescharacteristic
209C2×C42×C79C2311yescharacteristic
210C2×C42×C79C2318yes—
211C23×D79C2412yes—
212C23×D79C2414yes—
213#11929624—464no—
214#11929624—432no—
215C2×Dic158—42no—
216C2×Dic158—48no—
217C2×Dic158—44no—
218C2×Dic158C24116yes—
219C2×Dic158C2418yes—
220C2×Dic158C2414yes—
221C2×D316—28no—
222C2×D316—48no—
223C2×D316—44no—
224C2×D316—48no—
225C2×D316—44no—
226C2×D316—42no—
227C2×D316C2418yes—
228C2×D316C24116yes—
229C2×D316C2418yes—
230C2×D316C24116yes—
231C2×D316C2414yes—
232C2×D316C2418yes—
233C2×C22⋊D79—216no—
234C2×C22⋊D79—28no—
235C2×C22⋊D79C2418yes—
236C2×C22⋊D79C24116yes—
237C22×Dic79C2412yes—
238C22×Dic79C2414yes—
239C22×Dic79C2412yes—
240C22×Dic79C2412yes—
241C2×C4×D79—28no—
242C2×C4×D79—48no—
243C2×C4×D79—48no—
244C2×C4×D79—48no—
245C2×C4×D79—48no—
246C2×C4×D79C2418yes—
247C2×C4×D79C24116yes—
248C2×C4×D79C24116yes—
249C2×C4×D79C24116yes—
250C2×C4×D79C24116yes—
251C4⋊Dic79C2418yes—
252C4⋊Dic79C24116yes—
253C4⋊Dic79C2418yes—
254C4⋊Dic79C2414yes—
255C4⋊Dic79C2414yes—
256Dic79⋊C4C2418yes—
257Dic79⋊C4C24116yes—
258Dic79⋊C4C24116yes—
259Dic79⋊C4C2418yes—
260Dic79⋊C4C2418yes—
261Dic79⋊C4C24116yes—
262Dic79⋊C4C2418yes—
263C22⋊Dic79C2418yes—
264(C2×D79)⋊C4C2418yes—
265(C2×D79)⋊C4C2418yes—
266(C2×D79)⋊C4C24116yes—
267(C2×D79)⋊C4C24116yes—
268(C2×D79)⋊C4C2418yes—
269(C2×D79)⋊C4C2418yes—
270(C2×D79)⋊C4C24116yes—
271(C2×D79)⋊C4C24116yes—
272(C2×D79)⋊C4C24116yes—
273(C2×D79)⋊C4C24116yes—
274(C2×D79)⋊C4C24116yes—
275C4×Dic79C2418yes—
276C4×Dic79C24116yes—
277C24×C79C2411yescharacteristic
278C22×C4×C79—24no—
279C22×C4×C79—28no—
280C22×C4×C79—24no—
281C22×C4×C79—44no—
282C22×C4×C79—42no—
283C22×C4×C79C2411yescharacteristic
284C22×C4×C79C2411yescharacteristic
285C22×C4×C79C2414yes—
286C22×C4×C79C2414yes—
287C22×C4×C79C2418yes—
288C22×C4×C79C2411yescharacteristic
289C22×C4×C79C2411yescharacteristic
290C22×C4×C79C2411yescharacteristic
291C22×C4×C79C2414yes—
292C22×C4×C79C2414yes—
293C22×C4×C79C2414yes—
294C22×C4×C79C2418yes—
295C22×C4×C79C2411yescharacteristic
296C4⋊C4×C79C2418yes—
297C4⋊C4×C79C24116yes—
298C4⋊C4×C79C2418yes—
299C4⋊C4×C79C24116yes—
300C4⋊C4×C79C24116yes—
301C4⋊C4×C79C24116yes—
302C4⋊C4×C79C2418yes—
303C4⋊C4×C79C2418yes—
304C42×C79C2414yes—
305C42×C79C2414yes—
306C42×C79C2414yes—
307C42×C79C2414yes—
308C23×C79—22no—
309C23×C79—22no—
310C23×C79H(5,𝔽2)14yes—
311C23×C79C2512yes—
312C23×C79C2511yescharacteristic
313C22×D79—24no—
314C22×D79—28no—
315C22×D79—24no—
316C22×D79—28no—
317C22×D79—28no—
318C22×D79—24no—
319C22×D79C2514yes—
320C22×D79C2518yes—
321C2×C4×C79—22no—
322C2×C4×C79—28no—
323C2×C4×C79—22no—
324C2×C4×C79—28no—
325C2×C4×C79—216no—
326C2×C4×C79—22no—
327C2×C4×C79—28no—
328C2×C4×C79—22no—
329C2×C4×C79—22no—
330C2×C4×C79—28no—
331C2×C4×C79—44no—
332C2×C4×C79—48no—
333C2×C4×C792−1+414yes—
334C2×C4×C79C2518yes—
335C2×C4×C79C2512yes—
336C2×C4×C79C2512yes—
337C2×C4×C79C2512yes—
338C2×C4×C79C2512yes—
339C2×C4×C79C2518yes—
340C2×C4×C79C2512yes—
341C2×C4×C79C2512yes—
342C22⋊D79—216no—
343C22⋊D79—232no—
344C2×Dic79—28no—
345C2×Dic79—24no—
346C2×Dic79—24no—
347C2×Dic79—24no—
348C2×Dic79C2514yes—
349C2×Dic79C2514yes—
350C2×Dic79C2514yes—
351C2×Dic79C2518yes—
352D316—216no—
353D316—44no—
354D316—416no—
355D316—48no—
356D316—48no—
357D316—416no—
358C4×D79—216no—
359C4×D79—416no—
360C4×D79—416no—
361C4×D79—416no—
362C4×D79—416no—
363Dic158—44no—
364Dic158—48no—
365Dic158—416no—
366C22×C79—22no—
367C22×C79—22no—
368C22×C79—28no—
369C22×C79C2×H(5,𝔽2)14yes—
370C22×C79C2×H(5,𝔽2)12yes—
371C22×C79C2×2−1+412yes—
372C22×C79#58512yes—
373C22×C79C2611yescharacteristic
374C2×D79—24no—
375C2×D79—28no—
376C2×D79—24no—
377C2×D79—28no—
378C2×D79—28no—
379C2×D79—24no—
380C2×D79—48no—
381C2×D79—416no—
382C4×C79—22no—
383C4×C79—28no—
384C4×C79—22no—
385C4×C79—22no—
386C4×C79—22no—
387C4×C79—28no—
388C4×C79—22no—
389C4×C79C2×2−1+414yes—
390Dic79—28no—
391Dic79—24no—
392Dic79—24no—
393Dic79—24no—
394C2×#3559—791nomaximal, Sylow
395C2×C79—24no—
396C2×C79#355914yescomplemented
397C2×C79C22×H(5,𝔽2)11yescharacteristic
398C2×C79C22×2−1+411yescharacteristic
399C2×C79C2×#58511yescharacteristic
400D79—44no—
401D79—48no—
402#3559—7932no—
403C2×#563—792no—
404C2×#562—792no—
405C2×#554—792no—
406C2×#553—792no—
407C2×#553—792no—
408C2×#547—794no—
409C2×#547—792no—
410C2×#544—792no—
411C2×#540—792no—
412C2×#539—794no—
413C2×#539—792no—
414C2×#537—792no—
415C2×#532—791no—
416C2×#529—791no—
417C22×#125D7911yescharacteristic, complemented
418C79C2×#355911yescharacteristic, complemented, Sylow
419C22×#41—792no—
420C22×#41—794no—
421#563—7932no—
422#562—7932no—
423#554—7932no—
424#553—7932no—
425#553—7932no—
426#547—7964no—
427#547—7932no—
428#544—7932no—
429#540—7932no—
430#539—7964no—
431#539—7932no—
432#537—7932no—
433#532—7916no—
434C2×C4⋊Q8—792no—
435C2×C4⋊Q8—794no—
436C2×C4⋊Q8—791no—
437C2×#127—791no—
438#529—7916no—
439C2×#126—794no—
440C2×#126—794no—
441C2×#126—792no—
442C2×#125—794no—
443C2×#125—792no—
444C2×#125—791no—
445C2×#125C2×D7912yes—
446C2×#125C2×D7912yes—
447C2×#125C2×D7912yes—
448C2×#125C2×D7912yes—
449C2×#125C2×D79116yescomplemented
450C2×#124—791no—
451C2×#124—792no—
452C2×#123—792no—
453C2×#123—794no—
454C2×#123—794no—
455C2×#123—794no—
456C2×#123—794no—
457C2×#123—794no—
458C2×#123—794no—
459C2×C22⋊Q8—791no—
460C2×C22⋊Q8—794no—
461C2×C22⋊Q8—794no—
462C2×C22⋊Q8—794no—
463C2×C22⋊Q8—794no—
464C2×C22⋊Q8—794no—
465C2×C22⋊Q8—794no—
466C2×#121—791no—
467C2×#121—792no—
468C2×#121—792no—
469C2×#121—794no—
470C2×#121—794no—
471C2×#121—794no—
472C2×#121—792no—
473C2×#121—794no—
474C2×#121—792no—
475C2×C4×Q8—791no—
476C2×C4×D4—792no—
477C2×C4×D4—794no—
478C2×C4×D4—794no—
479C2×C4×D4—792no—
480C2×C4×D4—792no—
481C2×C4×D4—791no—
482C2×C4×D4—792no—
483C2×C4×D4—792no—
484C2×#117—792no—
485C2×#117—792no—
486C22×C4⋊C4—794no—
487C22×C4⋊C4—792no—
488C22×C4⋊C4C2×D7912yes—
489C22×C4⋊C4C2×D7911yescharacteristic
490C22×C4⋊C4C2×D7912yes—
491C22×C4⋊C4C2×D7911yescharacteristic
492C22×C42C2×D7911yescharacteristic
493C2×#41—3168no—
494C2×#41—31616no—
495C2×#41—7916no—
496C2×#41—7932no—
497C22×Q8—791no—
498C22×Q8—794no—
499C22×Q8—792no—
500C22×D4—792no—
501C22×D4—794no—
502C22×D4—794no—
503C22×D4—791no—
504C22×D4—792no—
505C22×D4—794no—
506C22×D4—792no—
507C22×D4—792no—
508C23×C4—794no—
509C23×C4—794no—
510C23×C4—794no—
511C23×C4—794no—
512C23×C4—792no—
513C23×C4C22×D7912yes—
514C23×C4C22×D7911yescharacteristic
515C23×C4C22×D7911yescharacteristic
516C23×C4C22×D7912yes—
517C23×C4C22×D7911yescharacteristic
518C4⋊Q8—7916no—
519C4⋊Q8—7932no—
520C4⋊Q8—798no—
521#127—798no—
522#126—7932no—
523#126—7932no—
524#126—7916no—
525#125—7932no—
526#125—7916no—
527#125—798no—
528#125C22×D79116yes—
529#125C22×D79116yes—
530#125C22×D79116yes—
531#125C22×D79116yes—
532#124—798no—
533#124—7916no—
534#123—7916no—
535#123—7932no—
536#123—7932no—
537#123—7932no—
538#123—7932no—
539#123—7932no—
540#123—7932no—
541C22⋊Q8—798no—
542C22⋊Q8—7932no—
543C22⋊Q8—7932no—
544C22⋊Q8—7932no—
545C22⋊Q8—7932no—
546C22⋊Q8—7932no—
547C22⋊Q8—7932no—
548#121—798no—
549#121—7916no—
550#121—7916no—
551#121—7932no—
552#121—7932no—
553#121—7932no—
554#121—7916no—
555#121—7932no—
556#121—7916no—
557C4×Q8—798no—
558C4×D4—7916no—
559C4×D4—7932no—
560C4×D4—7932no—
561C4×D4—7916no—
562C4×D4—7916no—
563C4×D4—798no—
564C4×D4—7916no—
565C4×D4—7916no—
566#117—7916no—
567#117—7916no—
568C2×C4⋊C4—792no—
569C2×C4⋊C4—792no—
570C2×C4⋊C4—794no—
571C2×C4⋊C4—794no—
572C2×C4⋊C4—794no—
573C2×C4⋊C4—792no—
574C2×C4⋊C4—792no—
575C2×C4⋊C4—792no—
576C2×C4⋊C4—794no—
577C2×C4⋊C4—792no—
578C2×C4⋊C4—791no—
579C2×C4⋊C4—791no—
580C2×C4⋊C4—7932no—
581C2×C4⋊C4—7916no—
582C2×C4⋊C4C22×D7912yes—
583C2×C4⋊C4C22×D7914yes—
584C2×C4⋊C4C22×D7912yes—
585C2×C4⋊C4C22×D7914yes—
586C2×C4⋊C4C22×D7914yes—
587C2×C4⋊C4C22×D7914yes—
588C2×C4⋊C4C22×D7912yes—
589C2×C4⋊C4C22×D7912yes—
590C2×C4⋊C4C22×D79116yes—
591C2×C4⋊C4C22×D7918yes—
592C2×C4⋊C4C22×D79116yes—
593C2×C4⋊C4C22×D7918yes—
594C2×C22⋊C4—792no—
595C2×C22⋊C4—792no—
596C2×C22⋊C4—794no—
597C2×C22⋊C4—792no—
598C2×C22⋊C4—792no—
599C2×C22⋊C4—794no—
600C2×C22⋊C4—794no—
601C2×C22⋊C4—794no—
602C2×C22⋊C4—794no—
603C2×C22⋊C4—794no—
604C2×C22⋊C4—794no—
605C2×C22⋊C4—792no—
606C2×C42—792no—
607C2×C42—794no—
608C2×C42C22×D7911yescharacteristic
609C2×C42C22×D7911yescharacteristic
610C2×C42C22×D7911yescharacteristic
611C2×C42C22×D7911yescharacteristic
612C2×C42C22×D7918yes—
613C24—792no—
614C24—794no—
615C24C23×D7911yescharacteristic
616#41—31632no—
617#41—31664no—
618C2×Q8—3162no—
619C2×Q8—3168no—
620C2×Q8—3164no—
621C2×Q8—794no—
622C2×Q8—7916no—
623C2×Q8—798no—
624C2×D4—3168no—
625C2×D4—3164no—
626C2×D4—3162no—
627C2×D4—3168no—
628C2×D4—3164no—
629C2×D4—798no—
630C2×D4—7916no—
631C2×D4—7916no—
632C2×D4—794no—
633C2×D4—798no—
634C2×D4—7916no—
635C2×D4—798no—
636C2×D4—798no—
637C2×D4—1588no—
638C2×D4—15816no—
639C2×D4—1588no—
640C22×C4—24no—
641C22×C4—28no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—42no—
645C22×C4—3168no—
646C22×C4—3168no—
647C22×C4—3168no—
648C22×C4—3168no—
649C22×C4—7916no—
650C22×C4—7916no—
651C22×C4—7916no—
652C22×C4—7916no—
653C22×C4—792no—
654C22×C4—792no—
655C22×C4—792no—
656C22×C4—794no—
657C22×C4—798no—
658C22×C4—1588no—
659C22×C4C23×D7914yes—
660C22×C4C23×D7914yes—
661C22×C4C23×D7918yes—
662C22×C4C23×D7914yes—
663C22×C4C23×D7911yescharacteristic
664C22×C4C23×D7911yescharacteristic
665C22×C4C23×D7911yescharacteristic
666C22×C4C23×D7911yescharacteristic
667C22×C4C23×D7911yescharacteristic
668C22×C4C23×D7914yes—
669C22×C4C23×D7914yes—
670C22×C4C23×D7918yes—
671C22×C4C23×D7911yescharacteristic
672C4⋊C4—798no—
673C4⋊C4—7916no—
674C4⋊C4—7916no—
675C4⋊C4—798no—
676C4⋊C4—798no—
677C4⋊C4—7916no—
678C4⋊C4—798no—
679C4⋊C4—798no—
680C4⋊C4—7916no—
681C4⋊C4—798no—
682C4⋊C4—794no—
683C4⋊C4—794no—
684C4⋊C4C23×D7918yes—
685C4⋊C4C23×D79116yes—
686C4⋊C4C23×D7918yes—
687C4⋊C4C23×D79116yes—
688C4⋊C4C23×D79116yes—
689C4⋊C4C23×D79116yes—
690C4⋊C4C23×D7918yes—
691C4⋊C4C23×D7918yes—
692C22⋊C4—798no—
693C22⋊C4—798no—
694C22⋊C4—7916no—
695C22⋊C4—798no—
696C22⋊C4—798no—
697C22⋊C4—7916no—
698C22⋊C4—7916no—
699C22⋊C4—7916no—
700C22⋊C4—7916no—
701C22⋊C4—7916no—
702C22⋊C4—7916no—
703C22⋊C4—798no—
704C42—798no—
705C42—7916no—
706C42C23×D7914yes—
707C42C23×D7914yes—
708C42C23×D7914yes—
709C42C23×D7914yes—
710C23—22no—
711C23—22no—
712C23—794no—
713C23—798no—
714C23—1584no—
715C23—1588no—
716C23—1584no—
717C23—1588no—
718C23—1588no—
719C23—1584no—
720C23#1457920714yes—
721C23C24×D7912yes—
722C23C24×D7911yescharacteristic
723Q8—31616no—
724Q8—3168no—
725Q8—3164no—
726D4—31616no—
727D4—3168no—
728D4—31616no—
729D4—3168no—
730D4—3164no—
731D4—15816no—
732D4—15832no—
733D4—15816no—
734C2×C4—22no—
735C2×C4—28no—
736C2×C4—22no—
737C2×C4—28no—
738C2×C4—216no—
739C2×C4—22no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—28no—
744C2×C4—48no—
745C2×C4—44no—
746C2×C4—31616no—
747C2×C4—31616no—
748C2×C4—31616no—
749C2×C4—31616no—
750C2×C4—794no—
751C2×C4—794no—
752C2×C4—794no—
753C2×C4—798no—
754C2×C4—1588no—
755C2×C4—1584no—
756C2×C4—1584no—
757C2×C4—1584no—
758C2×C4—15816no—
759C2×C4#1457920914yes—
760C2×C4C24×D7918yes—
761C2×C4C24×D7912yes—
762C2×C4C24×D7912yes—
763C2×C4C24×D7912yes—
764C2×C4C24×D7912yes—
765C2×C4C24×D7912yes—
766C2×C4C24×D7918yes—
767C2×C4C24×D7912yes—
768C22—28no—
769C22—22no—
770C22—22no—
771C22—3168no—
772C22—31616no—
773C22—1584no—
774C22—1588no—
775C22—1584no—
776C22—1588no—
777C22—1588no—
778C22—1584no—
779C22C2×#1457920714yes—
780C22C2×#1457920712yes—
781C22C2×#1457920912yes—
782C22#1909939912yes—
783C22C25×D7911yescharacteristic
784C4—22no—
785C4—28no—
786C4—22no—
787C4—22no—
788C4—28no—
789C4—22no—
790C4—22no—
791C4—1588no—
792C4—1584no—
793C4—1584no—
794C4—1584no—
795C4C2×#1457920914yes—
796C2—24no—
797C2—3164no—
798C2—3168no—
799C2#2377793414yesdirect product factor
800C2C22×#1457920711yescharacteristic
801C2C22×#1457920911yescharacteristic
802C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC22×#125×C79C2
socleC23×C79C25
hypercenterC22×#125D79
hypocenterC79C2×#3559
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. #23777934C2direct (N × H)
2. C2×#19099317C2semidirect
3. C2×#19099311C2semidirect
4. C2×#19099269C2semidirect
5. C2×#19099266C2semidirect
6. C2×#19099261C2semidirect
7. C2×#19099214C2semidirect
8. C2×#19099214C2semidirect
9. C2×#19099193C2semidirect
10. C2×#19099169C2semidirect
11. C2×#19099161C2semidirect
12. C2×#19099160C2semidirect
13. C2×#19099144C2semidirect
14. C2×#19099113C2semidirect
15. C2×#19099097C2semidirect
16. C22×#125×C79C2semidirect
19. #19099317C22semidirect
20. #19099311C22semidirect
21. #19099269C22semidirect
22. #19099266C22semidirect
23. #19099261C22semidirect
24. #19099214C22semidirect
25. #19099214C22semidirect
26. #19099193C22semidirect
27. #19099169C22semidirect
28. #19099161C22semidirect
29. #19099160C22semidirect
30. #19099144C22semidirect
31. #19099113C22semidirect
36. #19099097C22semidirect
85. C2×#125×C79C22semidirect
396. C2×C79#3559semidirect
417. C22×#125D79semidirect
418. C79C2×#3559semidirect
449. C2×#125C2×D79semidirect
799. C2#23777934direct (N × H)

Maximal subgroups

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

subgroupindex
#237779342
C2×#190993172
C2×#190993112
C2×#190992692
C2×#190992662
C2×#190992612
C2×#190992142
C2×#190991932
C2×#190991692
C2×#190991612
C2×#190991602
C2×#190991442
C2×#190991132
C2×#190990972
C22×#125×C792
C2×#355979