Finite Group Databasebeta

← C2×#23775785 #35166722

Subgroups — C2×#23775785 #35166722

Order 20224.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099265C211yesmaximal, characteristic
2C2×#19099255C211yesmaximal, characteristic, complemented
3#23775785C2116yesmaximal, direct product factor
4C2×#19098963C211yesmaximal, characteristic, complemented
5C2×#19098896C211yesmaximal, characteristic, complemented
6C2×#19098902C211yesmaximal, characteristic, complemented
7C2×#19098886C211yesmaximal, characteristic, complemented
8C2×#19098874C211yesmaximal, characteristic, complemented
9C2×#19098868C211yesmaximal, characteristic, complemented
10C2×#19098865C211yesmaximal, characteristic, complemented
11C2×#19098789C211yesmaximal, characteristic, complemented
12C2×SD16×Dic79C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D79C211yesmaximal, characteristic, complemented
14C2×#19098598C211yesmaximal, characteristic, complemented
15C22×#14579093C211yesmaximal, characteristic, complemented
16C2×#465×C79C211yesmaximal, characteristic, complemented
17C22×C8×D79C2211yescharacteristic
18#19099265—24no—
19#19099265C2218yes—
20#19099255—24no—
21#19099255C2218yescomplemented
22C2×#14579156—21no—
23C2×#14579154—21no—
24C2×#14579152—21no—
25C2×#14579152C2211yescharacteristic
26C2×#14579152C2211yescharacteristic
27C2×#14579145—21no—
28C2×#14579145—21no—
29C2×#14579137C2211yescharacteristic
30C2×#14579133—21no—
31C2×#14579132C2211yescharacteristic
32C2×Q8×Dic79C2211yescharacteristic
33C2×D4×Dic79—21no—
34C2×D4×Dic79C2211yescharacteristic
35C2×C4×C22⋊D79C2211yescharacteristic
36C2×#14579119C2211yescharacteristic
37C2×#14579119C2211yescharacteristic
38C2×#14579117—21no—
39C22×C4⋊Dic79C2211yescharacteristic
40C22×C4⋊Dic79C2211yescharacteristic
41#19098963C2218yescomplemented
42#19098902C2218yescomplemented
43#19098896C2218yescomplemented
44#19098886C2218yescomplemented
45#19098874C2218yescomplemented
46#19098868C2218yescomplemented
47#19098865C2218yescomplemented
48#19098789C2218yescomplemented
49SD16×Dic79C2218yescomplemented
50C8×C22⋊D79C2218yescomplemented
51#19098598C2218yescomplemented
52C2×#14579094C2211yescharacteristic
53C2×#14579094C2211yescharacteristic
54C2×#14579094C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579093C2211yescharacteristic
58C2×#14579093C2211yescharacteristic
59C2×#14579093C2211yescharacteristic
60C2×#14579093C2218yescomplemented
61C2×Dic79⋊C8C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C23×C8×C79C2211yescharacteristic
71C2×C22⋊Q8×C79C2211yescharacteristic
72C2×#121×C79C2211yescharacteristic
73#465×C79C2218yescomplemented
74C2×#106×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C22×C22⋊D79—21no—
78C22×C22⋊D79D411yescharacteristic
79C23×Dic79—21no—
80C23×Dic79—21no—
81C23×Dic79—21no—
82C22×C4×D79C2311yescharacteristic
83C22×C79⋊C8C2311yescharacteristic
84C22×C79⋊C8C2311yescharacteristic
85C2×C8×D79—24no—
86C2×C8×D79C2314yes—
87#14579156—28no—
88#14579154—28no—
89#14579152—28no—
90#14579152—22no—
91#14579152—22no—
92#14579152C2314yes—
93#14579152C2314yes—
94#14579145—28no—
95#14579145—28no—
96#14579137—22no—
97#14579137C2314yes—
98#14579133—28no—
99#14579132—22no—
100#14579132C2314yes—
101Q8×Dic79—22no—
102Q8×Dic79C2314yes—
103D4×Dic79—28no—
104D4×Dic79—22no—
105D4×Dic79C2314yes—
106C4×C22⋊D79D414yes—
107C4×C22⋊D79C2314yes—
108#14579119—22no—
109#14579119—22no—
110#14579119C2314yes—
111#14579119C2314yes—
112#14579117—28no—
113C2×C4⋊Dic79—22no—
114C2×C4⋊Dic79—22no—
115C2×C4⋊Dic79—21no—
116C2×C4⋊Dic79—21no—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79C2314yes—
121C2×C4⋊Dic79C2314yes—
122C2×C4⋊Dic79C2311yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
125C2×C4⋊Dic79C2311yescharacteristic
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4D411yescharacteristic
130C2×C22⋊Dic79—21no—
131C2×C22⋊Dic79—21no—
132C2×C22⋊Dic79D411yescharacteristic
133C2×(C2×D79)⋊C4—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4D411yescharacteristic
137C2×C4×Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79C2311yescharacteristic
141#14579094C2314yes—
142#14579094C2314yes—
143#14579094C2314yes—
144#14579094C2314yes—
145#14579093C2314yes—
146#14579093C2314yes—
147#14579093C2314yes—
148#14579093C2314yes—
149Dic79⋊C8C2314yes—
150#14579085C2314yes—
151#14579085C2314yes—
152#14579082C2314yes—
153#14579082C2314yes—
154C22⋊(C79⋊C8)C2314yes—
155(C2×D79)⋊C8C2314yes—
156C8×Dic79C2314yes—
157C22×Q8×C79C2311yescharacteristic
158C22×D4×C79—21no—
159C22×D4×C79C2311yescharacteristic
160C23×C4×C79C2311yescharacteristic
161C2×SD16×C79—24no—
162C2×SD16×C79C2314yes—
163C22×C8×C79—24no—
164C22×C8×C79C2314yes—
165C22×C8×C79C2311yescharacteristic
166C22×C8×C79C2311yescharacteristic
167C22⋊Q8×C79—22no—
168C22⋊Q8×C79C2314yes—
169#121×C79—22no—
170#121×C79C2314yes—
171C2×C4⋊C4×C79—21no—
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176#106×C79C2314yes—
177#103×C79C2314yes—
178#102×C79C2314yes—
179C23×D79C2×D411yescharacteristic
180C2×C22⋊D79—24no—
181C2×C22⋊D79—24no—
182C2×C22⋊D79—82no—
183C2×C22⋊D79C2×D414yes—
184C22×Dic79—24no—
185C22×Dic79—21no—
186C22×Dic79—21no—
187C22×Dic79—21no—
188C22×Dic79—21no—
189C22×Dic79—24no—
190C22×Dic79—24no—
191C22×Dic79—44no—
192C22×Dic79—82no—
193C22×Dic79—82no—
194C22×Dic79C2×D411yescharacteristic
195C22×Dic79C2×D411yescharacteristic
196C22×Dic79C2×D411yescharacteristic
197C2×C4×D79—22no—
198C2×C4×D79—22no—
199C2×C4×D79C2×D412yes—
200C2×C4×D79C2412yes—
201C2×C79⋊C8—22no—
202C2×C79⋊C8—22no—
203C2×C79⋊C8C2412yes—
204C2×C79⋊C8C2412yes—
205C8×D79—28no—
206C4⋊Dic79—24no—
207C4⋊Dic79—24no—
208C4⋊Dic79—24no—
209C4⋊Dic79—21no—
210C4⋊Dic79—21no—
211C4⋊Dic79—21no—
212C4⋊Dic79—21no—
213C4⋊Dic79—24no—
214C4⋊Dic79—24no—
215C4⋊Dic79C2412yes—
216C4⋊Dic79C2412yes—
217C4⋊Dic79C2412yes—
218C4⋊Dic79C2412yes—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4C2×D414yes—
223C22⋊Dic79—24no—
224C22⋊Dic79—24no—
225C22⋊Dic79C2×D414yes—
226(C2×D79)⋊C4—24no—
227(C2×D79)⋊C4—24no—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4C2×D414yes—
230C4×Dic79—24no—
231C4×Dic79—24no—
232C4×Dic79—24no—
233C4×Dic79C2×D412yes—
234C4×Dic79C2412yes—
235C24×C79—21no—
236C24×C79C2×D411yescharacteristic
237C2×Q8×C79—21no—
238C2×Q8×C79—22no—
239C2×Q8×C79—22no—
240C2×Q8×C79C2412yes—
241C2×D4×C79—24no—
242C2×D4×C79—21no—
243C2×D4×C79—22no—
244C2×D4×C79—22no—
245C2×D4×C79—44no—
246C2×D4×C79C2412yes—
247C22×C4×C79—22no—
248C22×C4×C79—22no—
249C22×C4×C79—21no—
250C22×C4×C79—21no—
251C22×C4×C79—21no—
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D412yes—
254C22×C4×C79C2412yes—
255C22×C4×C79C2411yescharacteristic
256SD16×C79—28no—
257C2×C8×C79—28no—
258C2×C8×C79—22no—
259C2×C8×C79#4114yes—
260C2×C8×C79C2412yes—
261C2×C8×C79C2412yes—
262C4⋊C4×C79—24no—
263C4⋊C4×C79—21no—
264C4⋊C4×C79—21no—
265C4⋊C4×C79C2412yes—
266C4⋊C4×C79C2412yes—
267C22⋊C4×C79—24no—
268C22⋊C4×C79—24no—
269C23×C79—22no—
270C23×C79—22no—
271C23×C79—22no—
272C23×C79—42no—
273C23×C79—42no—
274C23×C79—42no—
275C23×C79#13514yes—
276C23×C79C22×D412yes—
277C23×C79C22×D411yescharacteristic
278C22×D79—22no—
279C22×D79—22no—
280C22×D79—22no—
281C22×D79C22×D412yes—
282Q8×C79—22no—
283Q8×C79—22no—
284Q8×C79—42no—
285D4×C79—22no—
286D4×C79—22no—
287D4×C79—48no—
288D4×C79—42no—
289C2×C4×C79—22no—
290C2×C4×C79—24no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—42no—
297C2×C4×C79—42no—
298C2×C4×C79—42no—
299C2×C4×C79C22×D412yes—
300C2×C4×C79C22×D411yescharacteristic
301C2×C4×C79C2×#4112yes—
302C2×C4×C792−1+412yes—
303C2×C4×C79C2511yescharacteristic
304C22⋊D79—28no—
305C22⋊D79—84no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—48no—
314C2×Dic79—42no—
315C2×Dic79—42no—
316C2×Dic79—42no—
317C2×Dic79—42no—
318C2×Dic79—84no—
319C2×Dic79—84no—
320C2×Dic79C22×D412yes—
321C2×Dic79C22×D412yes—
322C2×Dic79C22×D412yes—
323C4×D79—24no—
324C4×D79—22no—
325C4×D79—22no—
326C8×C79—22no—
327C8×C79C2×#4114yes—
328C79⋊C8—22no—
329C79⋊C8—22no—
330C22×C79—28no—
331C22×C79—22no—
332C22×C79—22no—
333C22×C79—42no—
334C22×C79—42no—
335C22×C79—42no—
336C22×C79—84no—
337C22×C79#54712yes—
338C22×C79C2×#13514yes—
339C22×C79C2×#13512yes—
340C22×C79#57712yes—
341C22×C79C23×D411yescharacteristic
342C2×D79—22no—
343C2×D79—22no—
344C2×D79—22no—
345C2×D79—44no—
346C4×C79—22no—
347C4×C79—42no—
348C4×C79—42no—
349C4×C79—42no—
350C4×C79#54712yes—
351C4×C79C22×#4111yescharacteristic
352C4×C79C2×2−1+411yescharacteristic
353Dic79—22no—
354Dic79—22no—
355Dic79—22no—
356Dic79—42no—
357Dic79—42no—
358Dic79—42no—
359Dic79—42no—
360C2×#3337—791nomaximal, Sylow
361C2×C79—24no—
362C2×C79—82no—
363C2×C79#333714yescomplemented
364C2×C79C2×#54711yescharacteristic
365C2×C79C22×#13511yescharacteristic
366C2×C79C2×#57711yescharacteristic
367D79—42no—
368C2×#553—791no—
369C2×#552—791no—
370#3337—7916no—
371C2×#499—791no—
372C2×#484—791no—
373C2×#485—791no—
374C2×#482—791no—
375C2×#480—791no—
376C2×#479—791no—
377C2×#478—791no—
378C2×#465—791no—
379C2×#465D7911yescharacteristic, complemented
380C2×C4×SD16—791no—
381C2×C8×D4—791no—
382C2×#427—791no—
383C22×#106—791no—
384C79C2×#333711yescharacteristic, complemented, Sylow
385C22×SD16C2×D7911yescharacteristic
386C23×C8—791no—
387C23×C8C2×D7911yescharacteristic
388#553—798no—
389#553—1584no—
390#552—798no—
391#552—1584no—
392C2×#126—1581no—
393C2×#126—1581no—
394C2×#125—791no—
395C2×#125—791no—
396C2×#125—1581no—
397C2×#123—1581no—
398C2×#123—1581no—
399C2×C22⋊Q8—791no—
400C2×C22⋊Q8C2×D7911yescharacteristic
401C2×#121—791no—
402C2×#121—1581no—
403C2×#121C2×D7911yescharacteristic
404C2×C4×Q8—791no—
405C2×C4×D4—791no—
406C2×C4×D4—791no—
407C2×C4×D4—1581no—
408C2×#117—791no—
409C2×#117—791no—
410C2×#117—1581no—
411C22×C4⋊C4—791no—
412C22×C4⋊C4—791no—
413#499—798no—
414#485—798no—
415#484—798no—
416#482—798no—
417#480—798no—
418#479—798no—
419#478—798no—
420#465—798no—
421#465C2×D7918yescomplemented
422C4×SD16—798no—
423C8×D4—798no—
424#427—798no—
425C2×#107—791no—
426C2×#107—791no—
427C2×#107—791no—
428C2×#107—791no—
429C2×#106—791no—
430C2×#106—791no—
431C2×#106—798no—
432C2×#106—791no—
433C2×#106—791no—
434C2×#106C2×D7911yescharacteristic
435C2×C4⋊C8—791no—
436C2×#103—791no—
437C2×#103—791no—
438C2×#103C2×D7911yescharacteristic
439C2×#102—791no—
440C2×#102—791no—
441C2×#102C2×D7911yescharacteristic
442C2×C22⋊C8—791no—
443C2×C22⋊C8—791no—
444C2×C4×C8—791no—
445C22×Q8C22×D7911yescharacteristic
446C22×D4—21no—
447C22×D4—791no—
448C22×D4—1581no—
449C22×D4C22×D7911yescharacteristic
450C23×C4—791no—
451C23×C4—1581no—
452C23×C4—1581no—
453C23×C4—1581no—
454C23×C4C22×D7911yescharacteristic
455C2×SD16—24no—
456C2×SD16C22×D7914yes—
457C22×C8—24no—
458C22×C8—791no—
459C22×C8—791no—
460C22×C8—794no—
461C22×C8—1584no—
462C22×C8C22×D7911yescharacteristic
463C22×C8C22×D7914yes—
464C22×C8C22×D7911yescharacteristic
465#126—1588no—
466#126—1588no—
467#125—794no—
468#125—794no—
469#125—1582no—
470#125—1582no—
471#125—1588no—
472#123—1588no—
473#123—1588no—
474C22⋊Q8—22no—
475C22⋊Q8—794no—
476C22⋊Q8—1582no—
477C22⋊Q8C22×D7914yes—
478#121—22no—
479#121—794no—
480#121—1582no—
481#121—1588no—
482#121C22×D7914yes—
483C4×Q8—794no—
484C4×Q8—1582no—
485C4×D4—794no—
486C4×D4—794no—
487C4×D4—794no—
488C4×D4—1582no—
489C4×D4—1588no—
490#117—794no—
491#117—794no—
492#117—1588no—
493#117—1582no—
494#117—1582no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—791no—
497C2×C4⋊C4—791no—
498C2×C4⋊C4—791no—
499C2×C4⋊C4—791no—
500C2×C4⋊C4—791no—
501C2×C4⋊C4—794no—
502C2×C4⋊C4—794no—
503C2×C4⋊C4—1581no—
504C2×C4⋊C4—1581no—
505C2×C4⋊C4—1581no—
506C2×C4⋊C4—1581no—
507C2×C4⋊C4—1581no—
508C2×C4⋊C4—1581no—
509C2×C4⋊C4—1581no—
510C2×C4⋊C4—1581no—
511C2×C4⋊C4—1582no—
512C2×C4⋊C4—1582no—
513C2×C4⋊C4C22×D7911yescharacteristic
514C2×C4⋊C4C22×D7911yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—791no—
518C2×C22⋊C4—791no—
519C2×C22⋊C4—1581no—
520C2×C22⋊C4—1581no—
521C2×C22⋊C4—1581no—
522C2×C22⋊C4—1581no—
523C2×C22⋊C4—1581no—
524C2×C42—791no—
525C2×C42—1581no—
526C2×C42—1581no—
527C2×C42—1581no—
528#107—794no—
529#107—794no—
530#107—794no—
531#107—794no—
532#106—794no—
533#106—794no—
534#106—794no—
535#106—794no—
536#106C22×D7914yes—
537C4⋊C8—794no—
538#103—794no—
539#103—794no—
540#103C22×D7914yes—
541#102—794no—
542#102—794no—
543#102C22×D7914yes—
544C22⋊C8—794no—
545C22⋊C8—794no—
546C4×C8—794no—
547C24—21no—
548C24—791no—
549C24D4×D7911yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8C23×D7912yes—
554C2×D4—24no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—44no—
559C2×D4—794no—
560C2×D4—6322no—
561C2×D4—1584no—
562C2×D4—1584no—
563C2×D4C23×D7912yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—3164no—
570C22×C4—791no—
571C22×C4—791no—
572C22×C4—791no—
573C22×C4—792no—
574C22×C4—792no—
575C22×C4—6322no—
576C22×C4—6322no—
577C22×C4—1584no—
578C22×C4—1581no—
579C22×C4—1581no—
580C22×C4—1581no—
581C22×C4—1581no—
582C22×C4—1584no—
583C22×C4—1584no—
584C22×C4—1582no—
585C22×C4—1582no—
586C22×C4D4×D7912yes—
587C22×C4D4×D7911yescharacteristic
588C22×C4C23×D7912yes—
589C22×C4C23×D7911yescharacteristic
590SD16—28no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—792no—
594C2×C8—792no—
595C2×C8—1582no—
596C2×C8—1582no—
597C2×C8—1588no—
598C2×C8#1192962314yes—
599C2×C8C23×D7912yes—
600C2×C8C23×D7912yes—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—794no—
605C4⋊C4—792no—
606C4⋊C4—792no—
607C4⋊C4—792no—
608C4⋊C4—792no—
609C4⋊C4—1584no—
610C4⋊C4—1584no—
611C4⋊C4—1584no—
612C4⋊C4—1584no—
613C4⋊C4—1584no—
614C4⋊C4—1584no—
615C4⋊C4—1581no—
616C4⋊C4—1581no—
617C4⋊C4—1581no—
618C4⋊C4—1581no—
619C4⋊C4—1584no—
620C4⋊C4—1584no—
621C4⋊C4C23×D7912yes—
622C4⋊C4C23×D7912yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—794no—
626C22⋊C4—794no—
627C22⋊C4—1584no—
628C22⋊C4—1584no—
629C22⋊C4—1584no—
630C22⋊C4—1584no—
631C22⋊C4—1584no—
632C42—792no—
633C42—792no—
634C42—1584no—
635C42—1584no—
636C42—1584no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—792no—
644C23—1582no—
645C23—1582no—
646C23—1582no—
647C23#1457918214yes—
648C23C2×D4×D7912yes—
649C23C2×D4×D7911yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—42no—
657D4—6324no—
658D4—1588no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—3168no—
670C2×C4—3162no—
671C2×C4—3162no—
672C2×C4—3162no—
673C2×C4—3162no—
674C2×C4—792no—
675C2×C4—792no—
676C2×C4—792no—
677C2×C4—6324no—
678C2×C4—6324no—
679C2×C4—1582no—
680C2×C4—1582no—
681C2×C4—1582no—
682C2×C4—1582no—
683C2×C4—1582no—
684C2×C4—1582no—
685C2×C4—1582no—
686C2×C4—1582no—
687C2×C4—1584no—
688C2×C4—1582no—
689C2×C4C2×D4×D7912yes—
690C2×C4C2×D4×D7911yescharacteristic
691C2×C4C2×#1192962312yes—
692C2×C4#1457920812yes—
693C2×C4C24×D7911yescharacteristic
694C8—22no—
695C8—1582no—
696C8—1582no—
697C8C2×#1192962314yes—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—84no—
705C22—3164no—
706C22—1582no—
707C22—1582no—
708C22—1582no—
709C22#1909921312yes—
710C22C2×#1457918214yes—
711C22C2×#1457918212yes—
712C22#1909937012yes—
713C22C22×D4×D7911yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—3162no—
719C4—3162no—
720C4—3162no—
721C4—3162no—
722C4—1582no—
723C4—1582no—
724C4—1582no—
725C4#1909921312yes—
726C4C22×#1192962311yescharacteristic
727C4C2×#1457920811yescharacteristic
728C2—24no—
729C2—82no—
730C2—3162no—
731C2#2377578514yesdirect product factor
732C2C2×#1909921311yescharacteristic
733C2C22×#1457918211yescharacteristic
734C2C2×#1909937011yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#465×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099265C2
hypercenterC2×#465D79
hypocenterC79C2×#3337
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
2. C2×#19099255C2semidirect
3. #23775785C2direct (N × H)
4. C2×#19098963C2semidirect
5. C2×#19098896C2semidirect
6. C2×#19098902C2semidirect
7. C2×#19098886C2semidirect
8. C2×#19098874C2semidirect
9. C2×#19098868C2semidirect
10. C2×#19098865C2semidirect
11. C2×#19098789C2semidirect
12. C2×SD16×Dic79C2semidirect
13. C2×C8×C22⋊D79C2semidirect
14. C2×#19098598C2semidirect
15. C22×#14579093C2semidirect
16. C2×#465×C79C2semidirect
21. #19099255C22semidirect
41. #19098963C22semidirect
42. #19098902C22semidirect
43. #19098896C22semidirect
44. #19098886C22semidirect
45. #19098874C22semidirect
46. #19098868C22semidirect
47. #19098865C22semidirect
48. #19098789C22semidirect
49. SD16×Dic79C22semidirect
50. C8×C22⋊D79C22semidirect
51. #19098598C22semidirect
60. C2×#14579093C22semidirect
73. #465×C79C22semidirect
363. C2×C79#3337semidirect
379. C2×#465D79semidirect
384. C79C2×#3337semidirect
421. #465C2×D79semidirect
731. C2#23775785direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992652
C2×#190992552
#237757852
C2×#190989632
C2×#190988962
C2×#190989022
C2×#190988862
C2×#190988742
C2×#190988682
C2×#190988652
C2×#190987892
C2×SD16×Dic792
C2×C8×C22⋊D792
C2×#190985982
C22×#145790932
C2×#465×C792
C2×#333779