Finite Group Databasebeta

← #34294078

Subgroups — #34294078

Order 20224.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098708C211yesmaximal, characteristic
2C2×#19098673C211yesmaximal, characteristic, complemented
3C2×C4×#11929611C211yesmaximal, characteristic, complemented
4#23766093C211yesmaximal, characteristic, complemented
5#23763755C211yesmaximal, characteristic, complemented
6#23763748C211yesmaximal, characteristic, complemented
7#23763717C211yesmaximal, characteristic, complemented
8#23763668C211yesmaximal, characteristic, complemented
9#23763661C211yesmaximal, characteristic, complemented
10#23763593C211yesmaximal, characteristic, complemented
11#23763340C211yesmaximal, characteristic, complemented
12#23763230C211yesmaximal, characteristic, complemented
13C4×#14579082C211yesmaximal, characteristic, complemented
14#23763166C211yesmaximal, characteristic, complemented
15C2×#520×C79C211yesmaximal, characteristic, complemented
16C22×#11929611C2211yescharacteristic
17C22×#11929609C2211yescharacteristic
18C2×#14579135C2211yescharacteristic
19C2×C4×D316C2211yescharacteristic
20#19098708C418yescomplemented
21#19098673—24no—
22C4×#11929611—24no—
23C2×#14579092C2211yescharacteristic
24C2×#14579092C2211yescharacteristic
25C2×#14579085C2211yescharacteristic
26C2×#14579085C2211yescharacteristic
27C2×#14579085C2211yescharacteristic
28C2×#14579082C2211yescharacteristic
29C2×#14579082C2211yescharacteristic
30C2×#14579082C2211yescharacteristic
31C2×#14579081C2211yescharacteristic
32C2×#14579081C2211yescharacteristic
33C2×C22⋊(C79⋊C8)C2211yescharacteristic
34C2×C22⋊(C79⋊C8)C2211yescharacteristic
35C2×#14579072C2211yescharacteristic
36C2×C4×C79⋊C8C2211yescharacteristic
37#19098465C2211yescharacteristic
38#19098463—21no—
39#19098461C2211yescharacteristic
40#19098453—21no—
41#19098439—21no—
42#19098434—21no—
43#19098423C2211yescharacteristic
44C4×C4⋊Dic79C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098318C2211yescharacteristic
50#19098318C2211yescharacteristic
51C22×#41×C79C2211yescharacteristic
52#520×C79—24no—
53#520×C79—24no—
54C2×C4×Q8×C79C2211yescharacteristic
55C2×C4×Q8×C79C2211yescharacteristic
56C2×C4×D4×C79—21no—
57C2×C4×D4×C79—21no—
58C2×C4×D4×C79C2211yescharacteristic
59C2×C4×D4×C79C2211yescharacteristic
60C2×#117×C79—21no—
61C2×#117×C79C2211yescharacteristic
62C22×C4⋊C4×C79—21no—
63C22×C4⋊C4×C79C2211yescharacteristic
64C22×D316C2311yescharacteristic
65C22×C22⋊D79—21no—
66C22×C4×D79—21no—
67C2×#11929611—22no—
68C2×#11929611—22no—
69C2×#11929611C2×C414yescomplemented
70C2×#11929609—22no—
71C2×#11929609—22no—
72C2×#11929609C2×C414yescomplemented
73C22×C79⋊C8C2311yescharacteristic
74C22×C79⋊C8C2311yescharacteristic
75C22×C79⋊C8C2311yescharacteristic
76C22×C79⋊C8C2311yescharacteristic
77#14579135—22no—
78#14579135C2×C414yescomplemented
79C4×D316—22no—
80C4×D316—22no—
81C2×C4⋊Dic79C2311yescharacteristic
82C2×C4⋊Dic79C2311yescharacteristic
83C2×C4⋊Dic79C2311yescharacteristic
84C2×Dic79⋊C4—21no—
85C2×C22⋊Dic79—21no—
86C2×(C2×D79)⋊C4—21no—
87C2×(C2×D79)⋊C4—21no—
88C2×(C2×D79)⋊C4—21no—
89C2×(C2×D79)⋊C4—21no—
90C2×C4×Dic79—21no—
91#14579092—22no—
92#14579092—22no—
93#14579085—22no—
94#14579085—22no—
95#14579085C2×C414yescomplemented
96#14579082—22no—
97#14579082—22no—
98#14579082C2×C414yescomplemented
99#14579081—22no—
100#14579081—22no—
101C22⋊(C79⋊C8)—22no—
102C22⋊(C79⋊C8)C2×C414yescomplemented
103#14579072—22no—
104C4×C79⋊C8—22no—
105C79⋊#95—21no—
106C79⋊#95—21no—
107C79⋊#95—21no—
108C2×#41×C79—22no—
109C2×#41×C79—22no—
110C2×#41×C79—22no—
111C2×#41×C79—22no—
112C2×#41×C79—22no—
113C2×#41×C79C2×C414yescomplemented
114C22×Q8×C79C2311yescharacteristic
115C22×D4×C79—21no—
116C22×D4×C79C2311yescharacteristic
117C23×C4×C79—21no—
118C23×C4×C79—21no—
119C23×C4×C79—21no—
120C23×C4×C79—21no—
121C23×C4×C79C2311yescharacteristic
122C4×Q8×C79—22no—
123C4×Q8×C79—22no—
124C4×Q8×C79—22no—
125C4×Q8×C79D414yescomplemented
126C4×D4×C79—28no—
127C4×D4×C79—28no—
128C4×D4×C79—22no—
129C4×D4×C79—22no—
130C4×D4×C79—22no—
131C4×D4×C79D414yescomplemented
132#117×C79—28no—
133#117×C79—22no—
134#117×C79—22no—
135C2×C4⋊C4×C79—28no—
136C2×C4⋊C4×C79—21no—
137C2×C4⋊C4×C79—21no—
138C2×C4⋊C4×C79—21no—
139C2×C4⋊C4×C79—22no—
140C2×C4⋊C4×C79—22no—
141C2×C4⋊C4×C79D411yescharacteristic
142C2×C4⋊C4×C79D411yescharacteristic
143C2×C4⋊C4×C79C2311yescharacteristic
144C2×C4⋊C4×C79C2311yescharacteristic
145C2×C22⋊C4×C79—21no—
146C2×C22⋊C4×C79—21no—
147C2×C22⋊C4×C79D411yescharacteristic
148C2×C22⋊C4×C79D411yescharacteristic
149C2×C42×C79—21no—
150C2×C42×C79—21no—
151C2×C42×C79C2311yescharacteristic
152C2×C42×C79C2311yescharacteristic
153C23×D79—21no—
154C2×D316—21no—
155C2×D316—21no—
156C2×D316—21no—
157C2×D316—21no—
158C2×D316—21no—
159C2×D316C22×C412yes—
160C2×C22⋊D79—24no—
161C2×C22⋊D79—81no—
162C2×C22⋊D79—81no—
163C22×Dic79—21no—
164C22×Dic79—21no—
165C22×Dic79—21no—
166C2×C4×D79—42no—
167C2×C4×D79—81no—
168C2×C4×D79—81no—
169#11929611—28no—
170#11929609—28no—
171C2×C79⋊C8—21no—
172C2×C79⋊C8—21no—
173C2×C79⋊C8—21no—
174C2×C79⋊C8—21no—
175C2×C79⋊C8—21no—
176C2×C79⋊C8—21no—
177C2×C79⋊C8—21no—
178C2×C79⋊C8—21no—
179C2×C79⋊C8—21no—
180C2×C79⋊C8—21no—
181C2×C79⋊C8C22×C412yes—
182C2×C79⋊C8C22×C412yes—
183C4⋊Dic79—21no—
184C4⋊Dic79—21no—
185C4⋊Dic79—21no—
186C4⋊Dic79—21no—
187C4⋊Dic79—21no—
188C4⋊Dic79C22×C412yes—
189Dic79⋊C4—81no—
190C22⋊Dic79—81no—
191(C2×D79)⋊C4—24no—
192(C2×D79)⋊C4—42no—
193(C2×D79)⋊C4—81no—
194(C2×D79)⋊C4—81no—
195C4×Dic79—81no—
196C24×C79—21no—
197C24×C79C2×D411yescharacteristic
198#41×C79—28no—
199#41×C79—28no—
200#41×C79—28no—
201#41×C79—28no—
202C2×Q8×C79—21no—
203C2×Q8×C79—21no—
204C2×Q8×C79—21no—
205C2×Q8×C79C22×C412yes—
206C2×Q8×C79C2×D412yes—
207C2×Q8×C79#4112yes—
208C2×D4×C79—24no—
209C2×D4×C79—24no—
210C2×D4×C79—24no—
211C2×D4×C79—21no—
212C2×D4×C79—21no—
213C2×D4×C79—21no—
214C2×D4×C79C22×C412yes—
215C2×D4×C79C2×D412yes—
216C2×D4×C79#4112yes—
217C22×C4×C79—24no—
218C22×C4×C79—24no—
219C22×C4×C79—21no—
220C22×C4×C79—24no—
221C22×C4×C79—21no—
222C22×C4×C79—21no—
223C22×C4×C79—21no—
224C22×C4×C79—21no—
225C22×C4×C79—21no—
226C22×C4×C79—21no—
227C22×C4×C79—24no—
228C22×C4×C79—24no—
229C22×C4×C79—24no—
230C22×C4×C79—81no—
231C22×C4×C79—81no—
232C22×C4×C79—81no—
233C22×C4×C79—81no—
234C22×C4×C79—81no—
235C22×C4×C79—81no—
236C22×C4×C79C22×C412yes—
237C22×C4×C79C2×D411yescharacteristic
238C22×C4×C79C2×D411yescharacteristic
239C22×C4×C79C2×D411yescharacteristic
240C22×C4×C79C2×D411yescharacteristic
241C22×C4×C79C2×D411yescharacteristic
242C22×C4×C79#4112yes—
243C22×C4×C79C2411yescharacteristic
244C4⋊C4×C79—24no—
245C4⋊C4×C79—24no—
246C4⋊C4×C79—22no—
247C4⋊C4×C79—24no—
248C4⋊C4×C79—22no—
249C4⋊C4×C79—21no—
250C4⋊C4×C79—21no—
251C4⋊C4×C79C2×D412yes—
252C4⋊C4×C79C2×D412yes—
253C22⋊C4×C79—24no—
254C22⋊C4×C79—24no—
255C22⋊C4×C79—22no—
256C22⋊C4×C79—22no—
257C42×C79—24no—
258C42×C79—24no—
259C42×C79—21no—
260C42×C79—21no—
261C42×C79C2×D412yes—
262C42×C79C2×D412yes—
263C23×C79—22no—
264C23×C79—21no—
265C23×C79—22no—
266C23×C79—21no—
267C23×C79—22no—
268C23×C79—21no—
269C23×C79—21no—
270C23×C79—21no—
271C23×C79—21no—
272C23×C79—41no—
273C23×C79—41no—
274C23×C79—41no—
275C23×C79—41no—
276C23×C79C4×D412yes—
277C23×C79C22×D411yescharacteristic
278C22×D79—22no—
279C22×D79—41no—
280C22×D79—41no—
281C22×D79—41no—
282C22×D79—41no—
283C22×D79—41no—
284C22×D79—41no—
285Q8×C79—22no—
286Q8×C79—22no—
287Q8×C79—22no—
288Q8×C79C4×D414yes—
289D4×C79—216no—
290D4×C79—22no—
291D4×C79—22no—
292D4×C79—22no—
293D4×C79C4×D414yes—
294C2×C4×C79—216no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—21no—
298C2×C4×C79—21no—
299C2×C4×C79—22no—
300C2×C4×C79—21no—
301C2×C4×C79—21no—
302C2×C4×C79—21no—
303C2×C4×C79—21no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—21no—
309C2×C4×C79—21no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—21no—
313C2×C4×C79—21no—
314C2×C4×C79—21no—
315C2×C4×C79—21no—
316C2×C4×C79—41no—
317C2×C4×C79—41no—
318C2×C4×C79—41no—
319C2×C4×C79—41no—
320C2×C4×C79—84no—
321C2×C4×C79—84no—
322C2×C4×C79—84no—
323C2×C4×C79C4×D412yes—
324C2×C4×C79#12012yes—
325C2×C4×C79#12012yes—
326C2×C4×C79C23×C411yescharacteristic
327C2×C4×C79C22×D411yescharacteristic
328C2×C4×C79C22×D411yescharacteristic
329C2×C4×C79C2×#4111yescharacteristic
330C2×C4×C79C2×#4111yescharacteristic
331C2×C4×C79C2×#4111yescharacteristic
332C22⋊D79—84no—
333C2×Dic79—22no—
334C2×Dic79—41no—
335C2×Dic79—41no—
336C2×Dic79—41no—
337C2×Dic79—41no—
338C2×Dic79—41no—
339C2×Dic79—41no—
340C2×Dic79—41no—
341C2×Dic79—41no—
342D316—22no—
343D316—22no—
344D316—41no—
345D316—41no—
346C4×D79—84no—
347C79⋊C8—22no—
348C79⋊C8—22no—
349C79⋊C8—41no—
350C79⋊C8—41no—
351C22×C79—22no—
352C22×C79—22no—
353C22×C79—22no—
354C22×C79—24no—
355C22×C79—41no—
356C22×C79—42no—
357C22×C79—41no—
358C22×C79—42no—
359C22×C79—42no—
360C22×C79—42no—
361C22×C79—41no—
362C22×C79—42no—
363C22×C79—41no—
364C22×C79—42no—
365C22×C79C2×C4×D411yescharacteristic
366C22×C79C2×#12011yescharacteristic
367C22×C79#52511yescharacteristic
368C22×C79#57611yescharacteristic
369C22×C79#57711yescharacteristic
370C22×C79#57711yescharacteristic
371C22×C79#57711yescharacteristic
372C2×D79—42no—
373C2×D79—42no—
374C2×D79—42no—
375C2×D79—81no—
376C2×D79—81no—
377C2×D79—81no—
378C2×D79—81no—
379C4×C79—22no—
380C4×C79—22no—
381C4×C79—22no—
382C4×C79—24no—
383C4×C79—41no—
384C4×C79—41no—
385C4×C79—42no—
386C4×C79—42no—
387C4×C79C2×C4×D411yescharacteristic
388C4×C79C2×C4×D411yescharacteristic
389C4×C79#52511yescharacteristic
390C4×C79#52511yescharacteristic
391Dic79—42no—
392Dic79—81no—
393Dic79—81no—
394#21464—791nomaximal, Sylow
395C2×C79—42no—
396C2×C79—44no—
397C2×C79C4×#12011yescharacteristic
398C2×C79#294611yescharacteristic
399C2×C79#295211yescharacteristic
400C2×C79#301011yescharacteristic
401C2×C79#301211yescharacteristic
402C2×C79#311911yescharacteristic
403C2×C79#312511yescharacteristic
404D79—82no—
405C2×#520D7911yescharacteristic, complemented
406C2×#449—791no—
407C2×#442—791no—
408C2×C4×SD16—791no—
409#2324—791no—
410#1880—791no—
411#1879—791no—
412#1874—791no—
413#1865—791no—
414#1864—791no—
415#1853—791no—
416#1788—791no—
417#1763—791no—
418C4×#102—791no—
419#1750—791no—
420C79#2146411yescharacteristic, complemented, Sylow
421C22×#41C2×D7911yescharacteristic
422C22×SD16—791no—
423C22×D8—791no—
424C2×#121—791no—
425#520—24no—
426#520—24no—
427C2×C4×Q8C2×D7911yescharacteristic
428C2×C4×Q8C2×D7911yescharacteristic
429C2×C4×D4—21no—
430C2×C4×D4—21no—
431C2×C4×D4—791no—
432C2×C4×D4C2×D7911yescharacteristic
433C2×C4×D4C2×D7911yescharacteristic
434C2×#117—21no—
435C2×#117C2×D7911yescharacteristic
436C22×C4⋊C4—21no—
437C22×C4⋊C4C2×D7911yescharacteristic
438#449—798no—
439#442—1584no—
440C4×SD16—1584no—
441C2×#106—791no—
442C2×#106—791no—
443C2×#103—791no—
444C2×#103—791no—
445C2×#103—791no—
446C2×#102—791no—
447C2×#102—791no—
448C2×#102—791no—
449C2×#102—791no—
450C2×#102—791no—
451C2×C22⋊C8—791no—
452C2×C22⋊C8—791no—
453C2×#97—791no—
454C2×C4×C8—791no—
455#390—791no—
456#390—1581no—
457#389—791no—
458#388—1581no—
459#386—1581no—
460#385—1581no—
461#380—791no—
462C4×C4⋊C4—791no—
463#340—791no—
464#340—791no—
465#340—791no—
466#340—791no—
467#336—791no—
468#336—791no—
469C2×#41—22no—
470C2×#41—22no—
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—22no—
474C2×#41C4×D7914yescomplemented
475C22×Q8C22×D7911yescharacteristic
476C22×D4—21no—
477C22×D4—791no—
478C22×D4—1581no—
479C22×D4C22×D7911yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—1581no—
485C23×C4C22×D7911yescharacteristic
486C2×SD16—794no—
487C2×SD16—1582no—
488C2×SD16—1582no—
489C2×D8—794no—
490C2×D8—1582no—
491C2×D8—1582no—
492C22×C8—791no—
493C22×C8—791no—
494C22×C8—791no—
495C22×C8—791no—
496#121—794no—
497#121—1582no—
498C4×Q8—22no—
499C4×Q8—22no—
500C4×Q8—22no—
501C4×Q8C22⋊D7914yescomplemented
502C4×D4—28no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—1582no—
508C4×D4—1582no—
509C4×D4C22⋊D7914yescomplemented
510#117—28no—
511#117—22no—
512#117—22no—
513C2×C4⋊C4—28no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—791no—
520C2×C4⋊C4—791no—
521C2×C4⋊C4—791no—
522C2×C4⋊C4—1581no—
523C2×C4⋊C4C22⋊D7911yescharacteristic
524C2×C4⋊C4C22⋊D7911yescharacteristic
525C2×C4⋊C4C22×D7911yescharacteristic
526C2×C4⋊C4C22×D7911yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—1581no—
530C2×C22⋊C4—1581no—
531C2×C22⋊C4—1581no—
532C2×C22⋊C4—1581no—
533C2×C22⋊C4—1581no—
534C2×C22⋊C4C22⋊D7911yescharacteristic
535C2×C22⋊C4C22⋊D7911yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—1581no—
539C2×C42C22×D7911yescharacteristic
540C2×C42C22×D7911yescharacteristic
541#106—1582no—
542#106—1582no—
543#103—794no—
544#103—1582no—
545#103—1582no—
546#102—794no—
547#102—1582no—
548#102—1582no—
549#102—1582no—
550#102—1582no—
551C22⋊C8—794no—
552C22⋊C8—1582no—
553#97—1582no—
554C4×C8—1582no—
555#95—1581no—
556#95—1581no—
557#95—1581no—
558C24—21no—
559C24—1581no—
560C24C2×C22⋊D7911yescharacteristic
561#41—28no—
562#41—28no—
563#41—28no—
564#41—28no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8C2×C4×D7912yes—
569C2×Q8C2×C22⋊D7912yes—
570C2×Q8#1192962412yes—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—792no—
578C2×D4—6321no—
579C2×D4—6321no—
580C2×D4—1584no—
581C2×D4—1581no—
582C2×D4—1581no—
583C2×D4—1581no—
584C2×D4—1581no—
585C2×D4—1581no—
586C2×D4C2×C4×D7912yes—
587C2×D4C2×C22⋊D7912yes—
588C2×D4#1192962412yes—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—3162no—
609C22×C4—6321no—
610C22×C4—6321no—
611C22×C4—1581no—
612C22×C4—1581no—
613C22×C4—1581no—
614C22×C4C2×C4×D7912yes—
615C22×C4C2×C22⋊D7911yescharacteristic
616C22×C4C2×C22⋊D7911yescharacteristic
617C22×C4C2×C22⋊D7911yescharacteristic
618C22×C4C2×C22⋊D7911yescharacteristic
619C22×C4C2×C22⋊D7911yescharacteristic
620C22×C4#1192962412yes—
621C22×C4C23×D7911yescharacteristic
622SD16—1588no—
623D8—1588no—
624C2×C8—792no—
625C2×C8—792no—
626C2×C8—1581no—
627C2×C8—1581no—
628C2×C8—1581no—
629C2×C8—1581no—
630C2×C8—1581no—
631C2×C8—1581no—
632C2×C8—1581no—
633C2×C8—1581no—
634C2×C8—1581no—
635C2×C8—1581no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—24no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—792no—
644C4⋊C4—6321no—
645C4⋊C4—1581no—
646C4⋊C4—1581no—
647C4⋊C4—1581no—
648C4⋊C4—1581no—
649C4⋊C4—1581no—
650C4⋊C4C2×C22⋊D7912yes—
651C4⋊C4C2×C22⋊D7912yes—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—3162no—
657C22⋊C4—6321no—
658C22⋊C4—6321no—
659C22⋊C4—6321no—
660C22⋊C4—1584no—
661C42—24no—
662C42—24no—
663C42—21no—
664C42—21no—
665C42—6321no—
666C42C2×C22⋊D7912yes—
667C42C2×C22⋊D7912yes—
668C23—22no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—3161no—
682C23—3161no—
683C23—3161no—
684C23—3161no—
685C23—3161no—
686C23—3161no—
687C23—1582no—
688C23C4×C22⋊D7912yes—
689C23C22×C22⋊D7911yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8C4×C22⋊D7914yes—
694D4—216no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—3161no—
699D4—3161no—
700D4—6324no—
701D4—1582no—
702D4—1582no—
703D4C4×C22⋊D7914yes—
704C2×C4—216no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—3161no—
734C2×C4—3161no—
735C2×C4—3161no—
736C2×C4—3161no—
737C2×C4—3161no—
738C2×C4—3161no—
739C2×C4—3161no—
740C2×C4—3161no—
741C2×C4—6324no—
742C2×C4—1582no—
743C2×C4C4×C22⋊D7912yes—
744C2×C4#1457913012yes—
745C2×C4#1457913012yes—
746C2×C4C22×C4×D7911yescharacteristic
747C2×C4C22×C22⋊D7911yescharacteristic
748C2×C4C22×C22⋊D7911yescharacteristic
749C2×C4C2×#1192962411yescharacteristic
750C2×C4C2×#1192962411yescharacteristic
751C2×C4C2×#1192962411yescharacteristic
752C8—3161no—
753C8—3161no—
754C8—1582no—
755C8—1582no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—3162no—
771C22—3162no—
772C22—3162no—
773C22—6321no—
774C22—6321no—
775C22—6321no—
776C22—6321no—
777C22C2×C4×C22⋊D7911yescharacteristic
778C22C2×#1457913011yescharacteristic
779C22#1909907411yescharacteristic
780C22#1909936611yescharacteristic
781C22#1909937111yescharacteristic
782C22#1909937111yescharacteristic
783C22#1909937411yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—24no—
788C4—41no—
789C4—41no—
790C4—42no—
791C4—42no—
792C4—3162no—
793C4—6321no—
794C4—6321no—
795C4C2×C4×C22⋊D7911yescharacteristic
796C4C2×C4×C22⋊D7911yescharacteristic
797C4#1909907411yescharacteristic
798C4#1909907411yescharacteristic
799C2—42no—
800C2—44no—
801C2—6322no—
802C2C4×#1457913011yescharacteristic
803C2#2377222811yescharacteristic
804C2#2377228111yescharacteristic
805C2#2377268611yescharacteristic
806C2#2377270411yescharacteristic
807C2#2377359911yescharacteristic
808C2#2377367711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC2×#520×C79C2
socleC23×C79C22×D4
prime radicalC2×#19098708C2
cosocleC22×C4×C79C24
hypercenterC2×#520D79
hypocenterC79#21464
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#19098673C2semidirect
3. C2×C4×#11929611C2semidirect
4. #23766093C2semidirect
5. #23763755C2semidirect
6. #23763748C2semidirect
7. #23763717C2semidirect
8. #23763668C2semidirect
9. #23763661C2semidirect
10. #23763593C2semidirect
11. #23763340C2semidirect
12. #23763230C2semidirect
13. C4×#14579082C2semidirect
14. #23763166C2semidirect
15. C2×#520×C79C2semidirect
20. #19098708C4semidirect
69. C2×#11929611C2×C4semidirect
72. C2×#11929609C2×C4semidirect
78. #14579135C2×C4semidirect
95. #14579085C2×C4semidirect
98. #14579082C2×C4semidirect
102. C22⋊(C79⋊C8)C2×C4semidirect
113. C2×#41×C79C2×C4semidirect
125. C4×Q8×C79D4semidirect
131. C4×D4×C79D4semidirect
405. C2×#520D79semidirect
420. C79#21464semidirect
474. C2×#41C4×D79semidirect
501. C4×Q8C22⋊D79semidirect
509. C4×D4C22⋊D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190987082
C2×#190986732
C2×C4×#119296112
#237660932
#237637552
#237637482
#237637172
#237636682
#237636612
#237635932
#237633402
#237632302
C4×#145790822
#237631662
C2×#520×C792
#2146479