Finite Group Databasebeta

← #34310863

Subgroups — #34310863

Order 20224.

1066 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098794C211yesmaximal, characteristic
2C2×C4×#11929611C211yesmaximal, characteristic, complemented
3C22×#14579092C211yesmaximal, characteristic, complemented
4#23766414C211yesmaximal, characteristic
5#23764257C211yesmaximal, characteristic, complemented
6#23764125C211yesmaximal, characteristic, complemented
7#23764031C211yesmaximal, characteristic, complemented
8#23764027C211yesmaximal, characteristic, complemented
9#23763717C211yesmaximal, characteristic
10#23763708C211yesmaximal, characteristic, complemented
11#23763668C211yesmaximal, characteristic, complemented
12#23763660C211yesmaximal, characteristic, complemented
13C4×#14579092C211yesmaximal, characteristic, complemented
14C22⋊C4×C79⋊C8C211yesmaximal, characteristic, complemented
15C79×#2360C211yesmaximal, characteristic, complemented
16C22×#11929611C2211yescharacteristic
17C23×C79⋊C8C2211yescharacteristic
18C2×#14579135C2211yescharacteristic
19C2×C4×D316C2211yescharacteristic
20C2×(C22⋊D79)⋊C4—21no—
21C22×C4⋊Dic79C2211yescharacteristic
22#19098794C418yescomplemented
23C4×#11929611—24no—
24C2×#14579092—24no—
25C2×#14579092C2211yescharacteristic
26C2×#14579092C2211yescharacteristic
27C2×#14579092C2211yescharacteristic
28C2×#14579092C2211yescharacteristic
29C2×#14579092C2211yescharacteristic
30C2×#14579085C2211yescharacteristic
31C2×#14579085C2211yescharacteristic
32C2×#14579085C2211yescharacteristic
33C2×#14579081C2211yescharacteristic
34C2×#14579081C2211yescharacteristic
35C2×#14579081C2211yescharacteristic
36C2×C22⋊(C79⋊C8)C2211yescharacteristic
37C2×C4×C79⋊C8C2211yescharacteristic
38C2×C4×C79⋊C8C2211yescharacteristic
39#19098465C2211yescharacteristic
40#19098461C2211yescharacteristic
41#19098455—21no—
42#19098440—21no—
43#19098437—21no—
44C4×C4⋊Dic79C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098318C2211yescharacteristic
50#19098318C2211yescharacteristic
51C2×C22⋊Q8×C79C2211yescharacteristic
52C2×C4×Q8×C79C2211yescharacteristic
53C22×C4⋊C4×C79C2211yescharacteristic
54#391×C79C2211yescharacteristic
55#389×C79—21no—
56#389×C79C2211yescharacteristic
57#387×C79—21no—
58#385×C79—21no—
59C4×C4⋊C4×C79C2211yescharacteristic
60C4×C22⋊C4×C79—21no—
61C4×C22⋊C4×C79C2211yescharacteristic
62C22×D316C2311yescharacteristic
63C22×C22⋊D79—21no—
64C23×Dic79—21no—
65C22×C4×D79—21no—
66C2×#11929611—22no—
67C2×#11929611—22no—
68C2×#11929611C2×C414yescomplemented
69C22×C79⋊C8—22no—
70C22×C79⋊C8—22no—
71C22×C79⋊C8C2×C414yescomplemented
72C22×C79⋊C8C2311yescharacteristic
73C22×C79⋊C8C2311yescharacteristic
74C22×C79⋊C8C2311yescharacteristic
75C22×C79⋊C8C2311yescharacteristic
76#14579135—22no—
77#14579135C2×C414yes—
78C4×D316—22no—
79C4×D316—41no—
80(C22⋊D79)⋊C4—44no—
81C2×C4⋊Dic79—22no—
82C2×C4⋊Dic79—21no—
83C2×C4⋊Dic79—41no—
84C2×C4⋊Dic79C2311yescharacteristic
85C2×C4⋊Dic79C2311yescharacteristic
86C2×C4⋊Dic79C2311yescharacteristic
87C2×Dic79⋊C4—21no—
88C2×(C2×D79)⋊C4—21no—
89C2×(C2×D79)⋊C4—21no—
90C2×(C2×D79)⋊C4—21no—
91C2×(C2×D79)⋊C4—21no—
92C2×C4×Dic79—21no—
93#14579092—22no—
94#14579092—22no—
95#14579092—22no—
96#14579092C2×C414yescomplemented
97#14579092D414yescomplemented
98#14579085—22no—
99#14579085—41no—
100#14579085C2×C414yescomplemented
101#14579081—22no—
102#14579081—41no—
103#14579081C2×C414yescomplemented
104C22⋊(C79⋊C8)—22no—
105C4×C79⋊C8—22no—
106C4×C79⋊C8—22no—
107C79⋊#95—21no—
108C79⋊#95—21no—
109C22×Q8×C79C2311yescharacteristic
110C23×C4×C79—21no—
111C23×C4×C79C2311yescharacteristic
112C22⋊Q8×C79—22no—
113C22⋊Q8×C79C2×C414yescomplemented
114C4×Q8×C79—22no—
115C4×Q8×C79—41no—
116C2×C4⋊C4×C79—21no—
117C2×C4⋊C4×C79—22no—
118C2×C4⋊C4×C79—21no—
119C2×C4⋊C4×C79—21no—
120C2×C4⋊C4×C79—21no—
121C2×C4⋊C4×C79—41no—
122C2×C4⋊C4×C79C2311yescharacteristic
123C2×C4⋊C4×C79C2311yescharacteristic
124C2×C4⋊C4×C79C2311yescharacteristic
125C2×C22⋊C4×C79—21no—
126C2×C22⋊C4×C79D411yescharacteristic
127C2×C22⋊C4×C79D411yescharacteristic
128C2×C42×C79—21no—
129C2×C42×C79—21no—
130C2×C42×C79C2311yescharacteristic
131C2×C42×C79C2311yescharacteristic
132#95×C79—21no—
133#95×C79—21no—
134#95×C79—21no—
135#95×C79—21no—
136#95×C79D411yescharacteristic
137#95×C79D411yescharacteristic
138C23×D79—21no—
139C2×D316—21no—
140C2×D316—21no—
141C2×D316—21no—
142C2×D316—21no—
143C2×D316—21no—
144C2×D316C22×C412yes—
145C2×C22⋊D79—24no—
146C2×C22⋊D79—42no—
147C2×C22⋊D79—42no—
148C22×Dic79—21no—
149C22×Dic79—21no—
150C22×Dic79—21no—
151C22×Dic79—42no—
152C22×Dic79—42no—
153C22×Dic79—81no—
154C2×C4×D79—42no—
155C2×C4×D79—42no—
156C2×C4×D79—81no—
157#11929611—28no—
158C2×C79⋊C8—28no—
159C2×C79⋊C8—21no—
160C2×C79⋊C8—21no—
161C2×C79⋊C8—21no—
162C2×C79⋊C8—21no—
163C2×C79⋊C8—21no—
164C2×C79⋊C8—21no—
165C2×C79⋊C8—21no—
166C2×C79⋊C8—21no—
167C2×C79⋊C8C22×C412yes—
168C2×C79⋊C8C22×C412yes—
169C2×C79⋊C8C2×D412yes—
170C2×C79⋊C8#4112yes—
171C4⋊Dic79—21no—
172C4⋊Dic79—21no—
173C4⋊Dic79—21no—
174C4⋊Dic79—21no—
175C4⋊Dic79—42no—
176C4⋊Dic79C22×C412yes—
177C4⋊Dic79C2×D412yes—
178Dic79⋊C4—42no—
179(C2×D79)⋊C4—24no—
180(C2×D79)⋊C4—42no—
181(C2×D79)⋊C4—42no—
182(C2×D79)⋊C4—81no—
183C4×Dic79—42no—
184C24×C79C2×D411yescharacteristic
185C2×Q8×C79—21no—
186C2×Q8×C79—21no—
187C2×Q8×C79—21no—
188C2×Q8×C79—21no—
189C2×Q8×C79—21no—
190C2×Q8×C79C22×C412yes—
191C22×C4×C79—21no—
192C22×C4×C79—21no—
193C22×C4×C79—21no—
194C22×C4×C79—21no—
195C22×C4×C79—21no—
196C22×C4×C79—21no—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—42no—
200C22×C4×C79—42no—
201C22×C4×C79—81no—
202C22×C4×C79C22×C412yes—
203C22×C4×C79C2×D411yescharacteristic
204C22×C4×C79C2×D411yescharacteristic
205C22×C4×C79C2×D411yescharacteristic
206C22×C4×C79C2×D411yescharacteristic
207C22×C4×C79C2×D411yescharacteristic
208C22×C4×C79#4112yes—
209C22×C4×C79C2411yescharacteristic
210C4⋊C4×C79—24no—
211C4⋊C4×C79—21no—
212C4⋊C4×C79—21no—
213C4⋊C4×C79—21no—
214C4⋊C4×C79—21no—
215C4⋊C4×C79—42no—
216C4⋊C4×C79—42no—
217C4⋊C4×C79—81no—
218C4⋊C4×C79C22×C412yes—
219C4⋊C4×C79C2×D412yes—
220C22⋊C4×C79—24no—
221C22⋊C4×C79—22no—
222C22⋊C4×C79SD1614yescomplemented
223C42×C79—21no—
224C42×C79—21no—
225C42×C79—21no—
226C42×C79—21no—
227C42×C79—42no—
228C42×C79—81no—
229C23×C79—21no—
230C23×C79—21no—
231C23×C79—21no—
232C23×C79—21no—
233C23×C79C4×D412yes—
234C23×C79C2×SD1612yes—
235C23×C79#13512yes—
236C23×C79C22×D411yescharacteristic
237C22×D79—22no—
238C22×D79—41no—
239C22×D79—41no—
240C22×D79—41no—
241C22×D79—41no—
242C22×D79—41no—
243C22×D79—41no—
244Q8×C79—22no—
245Q8×C79—22no—
246Q8×C79—41no—
247Q8×C79—41no—
248C2×C4×C79—21no—
249C2×C4×C79—21no—
250C2×C4×C79—21no—
251C2×C4×C79—21no—
252C2×C4×C79—21no—
253C2×C4×C79—21no—
254C2×C4×C79—22no—
255C2×C4×C79—22no—
256C2×C4×C79—22no—
257C2×C4×C79—22no—
258C2×C4×C79—22no—
259C2×C4×C79—22no—
260C2×C4×C79—21no—
261C2×C4×C79—22no—
262C2×C4×C79—21no—
263C2×C4×C79—21no—
264C2×C4×C79—21no—
265C2×C4×C79—21no—
266C2×C4×C79—21no—
267C2×C4×C79—41no—
268C2×C4×C79—41no—
269C2×C4×C79—41no—
270C2×C4×C79—41no—
271C2×C4×C79—41no—
272C2×C4×C79—41no—
273C2×C4×C79—41no—
274C2×C4×C79—41no—
275C2×C4×C79—41no—
276C2×C4×C79—84no—
277C2×C4×C79C4×D412yes—
278C2×C4×C79C2×SD1612yes—
279C2×C4×C79C2×SD1612yes—
280C2×C4×C79C23×C411yescharacteristic
281C2×C4×C79C22×D411yescharacteristic
282C2×C4×C79C2×#4111yescharacteristic
283C2×C4×C79C2×#4111yescharacteristic
284C2×C4×C79H(5,𝔽2)11yescharacteristic
285C2×C4×C792−1+411yescharacteristic
286C22⋊D79—48no—
287C2×Dic79—22no—
288C2×Dic79—22no—
289C2×Dic79—41no—
290C2×Dic79—41no—
291C2×Dic79—41no—
292C2×Dic79—41no—
293C2×Dic79—41no—
294C2×Dic79—41no—
295C2×Dic79—41no—
296C2×Dic79—84no—
297D316—22no—
298D316—22no—
299D316—41no—
300D316—41no—
301C4×D79—84no—
302C79⋊C8—22no—
303C79⋊C8—41no—
304C79⋊C8—41no—
305C79⋊C8C4×D414yescomplemented
306C22×C79—22no—
307C22×C79—22no—
308C22×C79—22no—
309C22×C79—22no—
310C22×C79—22no—
311C22×C79—22no—
312C22×C79C4×SD1614yescomplemented
313C22×C79C2×C4×D411yescharacteristic
314C22×C79D4211yescharacteristic
315C22×C79#54711yescharacteristic
316C22×C79C22×SD1611yescharacteristic
317C22×C79C2×#13511yescharacteristic
318C22×C79#57711yescharacteristic
319C22×C79#57711yescharacteristic
320C2×D79—42no—
321C2×D79—42no—
322C2×D79—42no—
323C2×D79—81no—
324C2×D79—81no—
325C2×D79—81no—
326C2×D79—81no—
327C4×C79—22no—
328C4×C79—22no—
329C4×C79—22no—
330C4×C79—41no—
331C4×C79—42no—
332C4×C79—42no—
333C4×C79—41no—
334C4×C79—42no—
335C4×C79—81no—
336C4×C79C2×C4×D411yescharacteristic
337C4×C79#52011yescharacteristic
338C4×C79#54811yescharacteristic
339C4×C79#55311yescharacteristic
340Dic79—42no—
341Dic79—42no—
342Dic79—81no—
343#23022—791nomaximal, Sylow
344C2×C79—24no—
345C2×C79#236111yescharacteristic
346C2×C79C2×C4×SD1611yescharacteristic
347C2×C79#295211yescharacteristic
348C2×C79D4×SD1611yescharacteristic
349C2×C79#328211yescharacteristic
350C2×C79#333511yescharacteristic
351C2×C79#333711yescharacteristic
352D79—82no—
353C2×#465—791no—
354C2×C4×SD16—791no—
355C22×#106—791no—
356#2361—791no—
357#2360D7911yescharacteristic, complemented
358#1968—791no—
359#1941—791no—
360#1927—791no—
361#1926—791no—
362#1874—791no—
363#1872—791no—
364#1865—791no—
365#1864—791no—
366C4×#106—791no—
367C8×C22⋊C4—791no—
368C79#2302211yescharacteristic, complemented, Sylow
369C22×SD16—791no—
370C23×C8—791no—
371C2×C22⋊Q8C2×D7911yescharacteristic
372C2×#121—791no—
373C2×C4×Q8C2×D7911yescharacteristic
374C2×C4×D4—791no—
375C2×C4×D4—1581no—
376C22×C4⋊C4—791no—
377C22×C4⋊C4C2×D7911yescharacteristic
378#465—798no—
379C4×SD16—1584no—
380C2×#106—791no—
381C2×#106—791no—
382C2×#106—791no—
383C2×#106—791no—
384C2×#106—791no—
385C2×#106—1584no—
386C2×#103—791no—
387C2×#103—791no—
388C2×#103—791no—
389C2×#102—791no—
390C2×#102—791no—
391C2×#102—791no—
392C2×C22⋊C8—791no—
393C2×C4×C8—791no—
394C2×C4×C8—791no—
395#391C2×D7911yescharacteristic
396#390—791no—
397#389—21no—
398#389—791no—
399#389C2×D7911yescharacteristic
400#388—1581no—
401#387—21no—
402#386—1581no—
403#385—21no—
404#385—1581no—
405C4×C4⋊C4—791no—
406C4×C4⋊C4C2×D7911yescharacteristic
407C4×C22⋊C4—21no—
408C4×C22⋊C4C2×D7911yescharacteristic
409#340—791no—
410#340—791no—
411#340—791no—
412#340—791no—
413#336—791no—
414#336—791no—
415C22×Q8C22×D7911yescharacteristic
416C22×D4—791no—
417C22×D4—1581no—
418C23×C4—21no—
419C23×C4—1581no—
420C23×C4—1581no—
421C23×C4C22×D7911yescharacteristic
422C2×SD16—794no—
423C2×SD16—1582no—
424C2×SD16—1582no—
425C22×C8—791no—
426C22×C8—794no—
427C22×C8—791no—
428C22×C8—791no—
429C22×C8—791no—
430C22×C8—1582no—
431C22×C8—1582no—
432C22⋊Q8—22no—
433C22⋊Q8C4×D7914yescomplemented
434#121—794no—
435#121—1582no—
436C4×Q8—22no—
437C4×Q8—41no—
438C4×D4—3161no—
439C4×D4—3164no—
440C4×D4—1582no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4—3161no—
448C2×C4⋊C4—791no—
449C2×C4⋊C4—791no—
450C2×C4⋊C4—791no—
451C2×C4⋊C4—1581no—
452C2×C4⋊C4—1581no—
453C2×C4⋊C4—1582no—
454C2×C4⋊C4C22×D7911yescharacteristic
455C2×C4⋊C4C22×D7911yescharacteristic
456C2×C4⋊C4C22×D7911yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—1581no—
459C2×C22⋊C4—1581no—
460C2×C22⋊C4—1581no—
461C2×C22⋊C4—1581no—
462C2×C22⋊C4C22⋊D7911yescharacteristic
463C2×C22⋊C4C22⋊D7911yescharacteristic
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—1581no—
467C2×C42C22×D7911yescharacteristic
468C2×C42C22×D7911yescharacteristic
469#106—794no—
470#106—794no—
471#106—1582no—
472#106—1582no—
473#106—1582no—
474#103—3161no—
475#103—794no—
476#103—1582no—
477#102—3161no—
478#102—794no—
479#102—1582no—
480C22⋊C8—1582no—
481C4×C8—1582no—
482C4×C8—1582no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—1581no—
488#95—1581no—
489#95C22⋊D7911yescharacteristic
490#95C22⋊D7911yescharacteristic
491C24—1581no—
492C24C2×C22⋊D7911yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8C2×C4×D7912yes—
499C2×D4—3162no—
500C2×D4—3162no—
501C2×D4—792no—
502C2×D4—1584no—
503C2×D4—1581no—
504C2×D4—1581no—
505C2×D4—1581no—
506C2×D4—1581no—
507C2×D4—1581no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—81no—
519C22×C4—3162no—
520C22×C4—3162no—
521C22×C4—3162no—
522C22×C4—3162no—
523C22×C4—6321no—
524C22×C4—6321no—
525C22×C4—1581no—
526C22×C4—1581no—
527C22×C4—1581no—
528C22×C4C2×C4×D7912yes—
529C22×C4C2×C22⋊D7911yescharacteristic
530C22×C4C2×C22⋊D7911yescharacteristic
531C22×C4C2×C22⋊D7911yescharacteristic
532C22×C4C2×C22⋊D7911yescharacteristic
533C22×C4C2×C22⋊D7911yescharacteristic
534C22×C4#1192962412yes—
535C22×C4C23×D7911yescharacteristic
536SD16—1588no—
537C2×C8—792no—
538C2×C8—792no—
539C2×C8—792no—
540C2×C8—792no—
541C2×C8—1581no—
542C2×C8—1581no—
543C2×C8—1581no—
544C2×C8—1581no—
545C2×C8—1581no—
546C2×C8—1581no—
547C2×C8—1588no—
548C2×C8—1581no—
549C2×C8—1581no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—24no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—81no—
558C4⋊C4—3162no—
559C4⋊C4—3162no—
560C4⋊C4—792no—
561C4⋊C4—792no—
562C4⋊C4—1581no—
563C4⋊C4—1581no—
564C4⋊C4—1581no—
565C4⋊C4—1581no—
566C4⋊C4C2×C4×D7912yes—
567C4⋊C4D4×D7912yes—
568C22⋊C4—24no—
569C22⋊C4—22no—
570C22⋊C4—3162no—
571C22⋊C4—3162no—
572C22⋊C4—6321no—
573C22⋊C4—1584no—
574C22⋊C4#1192961114yescomplemented
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—81no—
581C42—3162no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—3161no—
587C23—3161no—
588C23—3161no—
589C23—3161no—
590C23—3161no—
591C23—3161no—
592C23—1582no—
593C23C4×C22⋊D7912yes—
594C23C2×#1192961112yes—
595C23#1457918112yes—
596C23C22×C22⋊D7911yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—41no—
600Q8—41no—
601D4—3168no—
602D4—3161no—
603D4—3161no—
604D4—1582no—
605D4—1582no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—84no—
635C2×C4—3161no—
636C2×C4—3161no—
637C2×C4—3161no—
638C2×C4—3161no—
639C2×C4—3161no—
640C2×C4—3161no—
641C2×C4—3161no—
642C2×C4—6324no—
643C2×C4—6324no—
644C2×C4—1582no—
645C2×C4—1582no—
646C2×C4C4×C22⋊D7912yes—
647C2×C4C2×#1192961112yes—
648C2×C4C2×#1192961112yes—
649C2×C4C22×C4×D7911yescharacteristic
650C2×C4C2×D4×D7911yescharacteristic
651C2×C4#41×D7911yescharacteristic
652C2×C4C2×#1192962411yescharacteristic
653C2×C4#1457920611yescharacteristic
654C2×C4#1457920811yescharacteristic
655C8—3161no—
656C8—3161no—
657C8—794no—
658C8—1582no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—3162no—
666C22—3162no—
667C22—3162no—
668C22—6321no—
669C22—6321no—
670C22—6321no—
671C22—6321no—
672C22C4×#1192961114yescomplemented
673C22C2×C4×C22⋊D7911yescharacteristic
674C22D4×C22⋊D7911yescharacteristic
675C22#1909921211yescharacteristic
676C22C22×#1192961111yescharacteristic
677C22C2×#1457918111yescharacteristic
678C22#1909937111yescharacteristic
679C22#1909937411yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—41no—
684C4—42no—
685C4—41no—
686C4—42no—
687C4—42no—
688C4—81no—
689C4—3162no—
690C4—3162no—
691C4—6321no—
692C4C4×D4×D7911yescharacteristic
693C4#1909904211yescharacteristic
694C4#1909922211yescharacteristic
695C4#1909926211yescharacteristic
696C2—24no—
697C2—6322no—
698C2#2376641711yescharacteristic
699C2C2×C4×#1192961111yescharacteristic
700C2#2377228111yescharacteristic
701C2D4×#1192961111yescharacteristic
702C2#2377510311yescharacteristic
703C2#2377575111yescharacteristic
704C2#2377577911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2360C2
socleC23×C79C22×D4
prime radicalC2×#14579135C22
cosocleC22×C4×C79C24
hypercenter#2360D79
hypocenterC79#23022
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11929611C2semidirect
3. C22×#14579092C2semidirect
5. #23764257C2semidirect
6. #23764125C2semidirect
7. #23764031C2semidirect
8. #23764027C2semidirect
10. #23763708C2semidirect
11. #23763668C2semidirect
12. #23763660C2semidirect
13. C4×#14579092C2semidirect
14. C22⋊C4×C79⋊C8C2semidirect
15. C79×#2360C2semidirect
22. #19098794C4semidirect
68. C2×#11929611C2×C4semidirect
71. C22×C79⋊C8C2×C4semidirect
96. #14579092C2×C4semidirect
97. #14579092D4semidirect
100. #14579085C2×C4semidirect
103. #14579081C2×C4semidirect
113. C22⋊Q8×C79C2×C4semidirect
222. C22⋊C4×C79SD16semidirect
305. C79⋊C8C4×D4semidirect
312. C22×C79C4×SD16semidirect
357. #2360D79semidirect
368. C79#23022semidirect
433. C22⋊Q8C4×D79semidirect
574. C22⋊C4#11929611semidirect
672. C22C4×#11929611semidirect

Maximal subgroups

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

subgroupindex
C2×#190987942
C2×C4×#119296112
C22×#145790922
#237664142
#237642572
#237641252
#237640312
#237640272
#237637172
#237637082
#237636682
#237636602
C4×#145790922
C22⋊C4×C79⋊C82
C79×#23602
#2302279