Finite Group Databasebeta

← #34304611

Subgroups — #34304611

Order 20224.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099217C211yesmaximal, characteristic
2C2×#19098635C211yesmaximal, characteristic, complemented
3#23764372C211yesmaximal, characteristic, complemented
4#23764348C211yesmaximal, characteristic, complemented
5#23763836C211yesmaximal, characteristic, complemented
6#23763826C211yesmaximal, characteristic, complemented
7#23763722C211yesmaximal, characteristic, complemented
8#23763717C211yesmaximal, characteristic, complemented
9#23763488C211yesmaximal, characteristic, complemented
10#23763484C211yesmaximal, characteristic, complemented
11#23763407C211yesmaximal, characteristic, complemented
12#23763228C211yesmaximal, characteristic, complemented
13#23763121C211yesmaximal, characteristic, complemented
14C2×#19098325C211yesmaximal, characteristic, complemented
15C79×#2352C211yesmaximal, characteristic, complemented
16C22×#11929623—21no—
17C22×#11929608C2211yescharacteristic
18C23×C79⋊C8C2211yescharacteristic
19#19099217—24no—
20#19099217C418yescomplemented
21C2×#14579161C2211yescharacteristic
22C2×#14579145—21no—
23C2×#14579145—21no—
24C2×#14579141—21no—
25C2×#14579135C2211yescharacteristic
26C2×#14579135C2211yescharacteristic
27C2×C4×D316C2211yescharacteristic
28C22×C4⋊Dic79C2211yescharacteristic
29C22×C4⋊Dic79C2211yescharacteristic
30#19098635—24no—
31C2×C4⋊(C79⋊C8)C2211yescharacteristic
32C2×#14579081C2211yescharacteristic
33C2×#14579081C2211yescharacteristic
34C2×#14579081C2211yescharacteristic
35C2×#14579081C2211yescharacteristic
36C2×C22⋊(C79⋊C8)C2211yescharacteristic
37C2×C22⋊(C79⋊C8)C2211yescharacteristic
38C2×#14579072C2211yescharacteristic
39#19098325C2211yescharacteristic
40#19098325C2211yescharacteristic
41#19098325C2211yescharacteristic
42#19098325C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51C2×C4×D4×C79C2211yescharacteristic
52C2×#117×C79C2211yescharacteristic
53C22×C4⋊C4×C79C2211yescharacteristic
54#388×C79—21no—
55#387×C79—21no—
56#386×C79—21no—
57#382×C79C2211yescharacteristic
58#380×C79C2211yescharacteristic
59#380×C79C2211yescharacteristic
60C4×C4⋊C4×C79C2211yescharacteristic
61C4×C22⋊C4×C79—21no—
62C2×#11929623—28no—
63C2×#11929623—44no—
64C2×#11929623—44no—
65C22×Dic158—21no—
66C22×D316C2311yescharacteristic
67C22×C22⋊D79—21no—
68C22×C22⋊D79—21no—
69C23×Dic79—21no—
70C23×Dic79—21no—
71C22×C4×D79—21no—
72C2×#11929608—22no—
73C2×#11929608—22no—
74C2×#11929608—41no—
75C22×C79⋊C8—22no—
76C22×C79⋊C8—22no—
77C22×C79⋊C8—41no—
78C22×C79⋊C8C2311yescharacteristic
79C22×C79⋊C8C2311yescharacteristic
80C22×C79⋊C8C2311yescharacteristic
81C22×C79⋊C8C2311yescharacteristic
82#14579161—22no—
83#14579161C2×C414yescomplemented
84#14579145—28no—
85#14579145—28no—
86#14579141—28no—
87#14579135—22no—
88#14579135—22no—
89#14579135C2×C414yes—
90#14579135C2×C414yescomplemented
91C4×D316—22no—
92C4×D316C2×C414yescomplemented
93C2×C4⋊Dic79—22no—
94C2×C4⋊Dic79—22no—
95C2×C4⋊Dic79—21no—
96C2×C4⋊Dic79—21no—
97C2×C4⋊Dic79—21no—
98C2×C4⋊Dic79C2×C414yes—
99C2×C4⋊Dic79C2×C414yescomplemented
100C2×C4⋊Dic79C2311yescharacteristic
101C2×C4⋊Dic79C2311yescharacteristic
102C2×C4⋊Dic79C2311yescharacteristic
103C2×(C2×D79)⋊C4—21no—
104C2×(C2×D79)⋊C4—21no—
105C2×(C2×D79)⋊C4—21no—
106C4⋊(C79⋊C8)—22no—
107#14579081—22no—
108#14579081—22no—
109#14579081—41no—
110#14579081—41no—
111C22⋊(C79⋊C8)—22no—
112C22⋊(C79⋊C8)—22no—
113#14579072—22no—
114C22×D4×C79D411yescharacteristic
115C23×C4×C79—21no—
116C23×C4×C79C2311yescharacteristic
117C23×C4×C79C2311yescharacteristic
118C4×D4×C79C2×C414yes—
119C4×D4×C79D414yes—
120#117×C79—22no—
121#117×C79—41no—
122C2×C4⋊C4×C79—22no—
123C2×C4⋊C4×C79—21no—
124C2×C4⋊C4×C79—41no—
125C2×C4⋊C4×C79D411yescharacteristic
126C2×C4⋊C4×C79C2311yescharacteristic
127C2×C4⋊C4×C79C2311yescharacteristic
128C2×C4⋊C4×C79C2311yescharacteristic
129C2×C4⋊C4×C79C2311yescharacteristic
130C2×C22⋊C4×C79—21no—
131C2×C22⋊C4×C79—21no—
132C2×C22⋊C4×C79—21no—
133C2×C22⋊C4×C79D411yescharacteristic
134C2×C22⋊C4×C79D411yescharacteristic
135C2×C42×C79—21no—
136C2×C42×C79—21no—
137C2×C42×C79C2311yescharacteristic
138#95×C79—21no—
139#95×C79—21no—
140#95×C79—21no—
141#95×C79—21no—
142#95×C79—21no—
143C23×D79—21no—
144#11929623—432no—
145C2×Dic158—24no—
146C2×Dic158—42no—
147C2×Dic158—42no—
148C2×D316—21no—
149C2×D316—21no—
150C2×D316—21no—
151C2×D316—21no—
152C2×D316—21no—
153C2×D316C22×C412yes—
154C2×C22⋊D79—24no—
155C2×C22⋊D79—24no—
156C2×C22⋊D79—42no—
157C2×C22⋊D79—42no—
158C2×C22⋊D79—42no—
159C2×C22⋊D79—42no—
160C22×Dic79—24no—
161C22×Dic79—24no—
162C22×Dic79—21no—
163C22×Dic79—21no—
164C22×Dic79—21no—
165C22×Dic79—42no—
166C22×Dic79—42no—
167C22×Dic79—42no—
168C22×Dic79—42no—
169C2×C4×D79—24no—
170C2×C4×D79—42no—
171C2×C4×D79—42no—
172#11929608—44no—
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⋊C8—21no—
182C2×C79⋊C8—21no—
183C2×C79⋊C8—21no—
184C2×C79⋊C8—44no—
185C2×C79⋊C8#4112yescomplemented
186C4⋊Dic79—24no—
187C4⋊Dic79—24no—
188C4⋊Dic79—24no—
189C4⋊Dic79—21no—
190C4⋊Dic79—21no—
191C4⋊Dic79—21no—
192C4⋊Dic79C22×C412yes—
193C4⋊Dic79C22×C412yes—
194C4⋊Dic79C22×C412yes—
195(C2×D79)⋊C4—24no—
196(C2×D79)⋊C4—24no—
197(C2×D79)⋊C4—24no—
198C24×C79C2×D411yescharacteristic
199C24×C79C2×D411yescharacteristic
200C2×D4×C79—22no—
201C2×D4×C79—22no—
202C2×D4×C79C22⋊C414yes—
203C22×C4×C79—21no—
204C22×C4×C79—21no—
205C22×C4×C79—21no—
206C22×C4×C79—21no—
207C22×C4×C79—21no—
208C22×C4×C79—21no—
209C22×C4×C79—21no—
210C22×C4×C79—21no—
211C22×C4×C79—21no—
212C22×C4×C79—21no—
213C22×C4×C79—21no—
214C22×C4×C79—21no—
215C22×C4×C79—42no—
216C22×C4×C79—42no—
217C22×C4×C79—81no—
218C22×C4×C79C22×C412yes—
219C22×C4×C79C22×C412yes—
220C22×C4×C79C2×D411yescharacteristic
221C22×C4×C79C2×D411yescharacteristic
222C22×C4×C79C2×D411yescharacteristic
223C22×C4×C79C2×D411yescharacteristic
224C22×C4×C79C2×D412yes—
225C22×C4×C79C2×D412yes—
226C22×C4×C79C2411yescharacteristic
227C4⋊C4×C79—21no—
228C4⋊C4×C79—21no—
229C4⋊C4×C79—21no—
230C4⋊C4×C79—21no—
231C4⋊C4×C79—21no—
232C4⋊C4×C79—21no—
233C4⋊C4×C79—21no—
234C4⋊C4×C79—42no—
235C4⋊C4×C79C22⋊C414yes—
236C4⋊C4×C79#4112yescomplemented
237C22⋊C4×C79—42no—
238C22⋊C4×C79—42no—
239C22⋊C4×C79—81no—
240C22⋊C4×C79C22⋊C414yes—
241C22⋊C4×C79C22⋊C414yes—
242C42×C79—42no—
243C42×C79—81no—
244C42×C79C22×C412yes—
245C42×C79C2×D412yes—
246C23×C79—21no—
247C23×C79—21no—
248C23×C79—21no—
249C23×C79—21no—
250C23×C79—21no—
251C23×C79—21no—
252C23×C79—21no—
253C23×C79—21no—
254C23×C79—21no—
255C23×C79—21no—
256C23×C79C2×C22⋊C412yes—
257C23×C79C2×C22⋊C412yes—
258C23×C79AGL(1,ℤ/8)12yes—
259C23×C79AGL(1,ℤ/8)12yes—
260C23×C79C22×D411yescharacteristic
261C22×D79—22no—
262C22×D79—41no—
263C22×D79—41no—
264C22×D79—41no—
265C22×D79—41no—
266C22×D79—41no—
267C22×D79—41no—
268D4×C79—28no—
269C2×C4×C79—21no—
270C2×C4×C79—21no—
271C2×C4×C79—21no—
272C2×C4×C79—21no—
273C2×C4×C79—21no—
274C2×C4×C79—21no—
275C2×C4×C79—21no—
276C2×C4×C79—21no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—41no—
287C2×C4×C79—41no—
288C2×C4×C79—41no—
289C2×C4×C79—41no—
290C2×C4×C79—41no—
291C2×C4×C79—41no—
292C2×C4×C79—41no—
293C2×C4×C79—41no—
294C2×C4×C79—41no—
295C2×C4×C79—41no—
296C2×C4×C79—41no—
297C2×C4×C79—84no—
298C2×C4×C79C2×C22⋊C412yes—
299C2×C4×C79C2×C22⋊C412yes—
300C2×C4×C79C2×C22⋊C412yes—
301C2×C4×C79C2×C22⋊C412yes—
302C2×C4×C79C23×C411yescharacteristic
303C2×C4×C79C22×D411yescharacteristic
304C2×C4×C79C2×#4111yescharacteristic
305C2×C4×C79C2×#4111yescharacteristic
306C2×C4×C79H(5,𝔽2)11yescharacteristic
307C2×C4×C792−1+411yescharacteristic
308C22⋊D79—48no—
309C22⋊D79—48no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—48no—
314C2×Dic79—41no—
315C2×Dic79—41no—
316C2×Dic79—41no—
317C2×Dic79—41no—
318C2×Dic79—41no—
319C2×Dic79—41no—
320C2×Dic79—48no—
321D316—22no—
322D316—22no—
323D316—41no—
324D316—41no—
325C4×D79—48no—
326Dic158—48no—
327C79⋊C8—22no—
328C79⋊C8—41no—
329C79⋊C8—41no—
330C79⋊C8—41no—
331C22×C79—22no—
332C22×C79—22no—
333C22×C79—22no—
334C22×C79—22no—
335C22×C79—22no—
336C22×C79—22no—
337C22×C79—22no—
338C22×C79—22no—
339C22×C79—22no—
340C22×C79—41no—
341C22×C79—41no—
342C22×C79—41no—
343C22×C79—41no—
344C22×C79#41814yes—
345C22×C79C22×C22⋊C411yescharacteristic
346C22×C79#54611yescharacteristic
347C22×C79#54711yescharacteristic
348C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C79#57711yescharacteristic
351C22×C79#57811yescharacteristic
352C2×D79—42no—
353C2×D79—42no—
354C2×D79—42no—
355C2×D79—81no—
356C2×D79—81no—
357C2×D79—81no—
358C2×D79—81no—
359C4×C79—22no—
360C4×C79—22no—
361C4×C79—22no—
362C4×C79—22no—
363C4×C79—42no—
364C4×C79—81no—
365C4×C79—81no—
366C4×C79—81no—
367C4×C79C4×#4111yescharacteristic
368C4×C79#52011yescharacteristic
369C4×C79#54611yescharacteristic
370C4×C79#54711yescharacteristic
371Dic79—42no—
372Dic79—42no—
373Dic79—42no—
374#22495—791nomaximal, Sylow
375C2×C79—24no—
376C2×C79—42no—
377C2×C79#233911yescharacteristic
378C2×C79C2×#41811yescharacteristic
379C2×C79#289811yescharacteristic
380C2×C79#330611yescharacteristic
381C2×C79#330811yescharacteristic
382C2×C79#334311yescharacteristic
383C2×C79#334511yescharacteristic
384D79—82no—
385C2×#547—791no—
386C2×#435—791no—
387#2352D7911yescharacteristic, complemented
388#1993—791no—
389#1987—791no—
390#1895—791no—
391#1893—791no—
392#1875—791no—
393#1874—791no—
394#1824—791no—
395#1823—791no—
396#1804—791no—
397#1762—791no—
398#1736—791no—
399C2×#340—791no—
400C79#2249511yescharacteristic, complemented, Sylow
401C22×#41—1581no—
402C22×M16—791no—
403C23×C8—791no—
404#547—798no—
405#547—1584no—
406C2×C4⋊Q8—791no—
407C2×#123—1581no—
408C2×#123—1581no—
409C2×C22⋊Q8—1581no—
410C2×#121—791no—
411C2×#121—791no—
412C2×C4×D4—791no—
413C2×C4×D4C2×D7911yescharacteristic
414C2×#117C2×D7911yescharacteristic
415C22×C4⋊C4—791no—
416C22×C4⋊C4—791no—
417C22×C4⋊C4C2×D7911yescharacteristic
418#435—1584no—
419C2×C4⋊C8—791no—
420C2×#102—791no—
421C2×#102—791no—
422C2×#102—791no—
423C2×#102—791no—
424C2×C22⋊C8—791no—
425C2×C22⋊C8—791no—
426C2×#97—791no—
427#388—21no—
428#387—21no—
429#386—21no—
430#382C2×D7911yescharacteristic
431#380C2×D7911yescharacteristic
432#380C2×D7911yescharacteristic
433C4×C4⋊C4C2×D7911yescharacteristic
434C4×C22⋊C4—21no—
435#340—791no—
436#340—791no—
437#340—791no—
438#340—791no—
439#340—791no—
440#340—791no—
441#340—791no—
442#340—791no—
443#340—791no—
444#340—791no—
445#340—791no—
446#340—791no—
447C2×#41—3164no—
448C2×#41—3164no—
449C2×#41—1588no—
450C22×Q8—1581no—
451C22×D4—791no—
452C22×D4—1581no—
453C22×D4—1581no—
454C22×D4C22⋊D7911yescharacteristic
455C23×C4—21no—
456C23×C4—1581no—
457C23×C4—1581no—
458C23×C4—1581no—
459C23×C4C22×D7911yescharacteristic
460C23×C4C22×D7911yescharacteristic
461C2×M16—3161no—
462C2×M16—1582no—
463C2×M16—1582no—
464C22×C8—3161no—
465C22×C8—791no—
466C22×C8—791no—
467C22×C8—791no—
468C22×C8—791no—
469C22×C8—1582no—
470C22×C8—1582no—
471C4⋊Q8—794no—
472C4⋊Q8—1582no—
473#123—1588no—
474#123—1588no—
475C22⋊Q8—1588no—
476#121—794no—
477#121—794no—
478#121—1582no—
479#121—1582no—
480C4×D4—794no—
481C4×D4—1582no—
482C4×D4C4×D7914yes—
483C4×D4D31614yes—
484#117—22no—
485#117—41no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—41no—
489C2×C4⋊C4—794no—
490C2×C4⋊C4—794no—
491C2×C4⋊C4—791no—
492C2×C4⋊C4—791no—
493C2×C4⋊C4—791no—
494C2×C4⋊C4—1581no—
495C2×C4⋊C4—1581no—
496C2×C4⋊C4—1581no—
497C2×C4⋊C4—1582no—
498C2×C4⋊C4—1582no—
499C2×C4⋊C4C22⋊D7911yescharacteristic
500C2×C4⋊C4C22×D7911yescharacteristic
501C2×C4⋊C4C22×D7911yescharacteristic
502C2×C4⋊C4C22×D7911yescharacteristic
503C2×C4⋊C4C22×D7911yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—1581no—
508C2×C22⋊C4—1581no—
509C2×C22⋊C4—1581no—
510C2×C22⋊C4C22⋊D7911yescharacteristic
511C2×C22⋊C4C22⋊D7911yescharacteristic
512C2×C42—21no—
513C2×C42—21no—
514C2×C42C22×D7911yescharacteristic
515C4⋊C8—1582no—
516#102—3161no—
517#102—3161no—
518#102—1582no—
519#102—1582no—
520C22⋊C8—1582no—
521C22⋊C8—1582no—
522#97—1582no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528C24—1581no—
529C24C2×C22⋊D7911yescharacteristic
530C24C2×C22⋊D7911yescharacteristic
531#41—31632no—
532C2×Q8—3162no—
533C2×Q8—3162no—
534C2×Q8—1584no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—3162no—
538C2×D4—3162no—
539C2×D4—3162no—
540C2×D4—3162no—
541C2×D4—792no—
542C2×D4—1584no—
543C2×D4—1584no—
544C2×D4—1581no—
545C2×D4—1581no—
546C2×D4—1581no—
547C2×D4—1581no—
548C2×D4—1581no—
549C2×D4(C2×D79)⋊C414yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4—3162no—
566C22×C4—3162no—
567C22×C4—3162no—
568C22×C4—3162no—
569C22×C4—3162no—
570C22×C4—3162no—
571C22×C4—1584no—
572C22×C4—1584no—
573C22×C4—1581no—
574C22×C4—1581no—
575C22×C4—1581no—
576C22×C4—1584no—
577C22×C4C2×C4×D7912yes—
578C22×C4C2×C4×D7912yes—
579C22×C4C2×C22⋊D7911yescharacteristic
580C22×C4C2×C22⋊D7911yescharacteristic
581C22×C4C2×C22⋊D7911yescharacteristic
582C22×C4C2×C22⋊D7911yescharacteristic
583C22×C4C2×D31612yes—
584C22×C4C2×D31612yes—
585C22×C4C23×D7911yescharacteristic
586M16—3164no—
587C2×C8—3164no—
588C2×C8—792no—
589C2×C8—1581no—
590C2×C8—1581no—
591C2×C8—1581no—
592C2×C8—1581no—
593C2×C8—1581no—
594C2×C8—1581no—
595C2×C8—1581no—
596C2×C8—1581no—
597C2×C8—1581no—
598C2×C8—1581no—
599C2×C8—1581no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—792no—
609C4⋊C4—792no—
610C4⋊C4—792no—
611C4⋊C4—1584no—
612C4⋊C4—1584no—
613C4⋊C4—1584no—
614C4⋊C4—1581no—
615C4⋊C4—1581no—
616C4⋊C4—1581no—
617C4⋊C4(C2×D79)⋊C414yes—
618C4⋊C4#1192962312yescomplemented
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C22⋊C4—1584no—
623C22⋊C4—1584no—
624C22⋊C4—1584no—
625C22⋊C4(C2×D79)⋊C414yes—
626C22⋊C4(C2×D79)⋊C414yes—
627C42—42no—
628C42—81no—
629C42C2×C4×D7912yes—
630C42C2×D31612yes—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—3161no—
642C23—3161no—
643C23—3161no—
644C23—3161no—
645C23—3161no—
646C23—3161no—
647C23—1582no—
648C23C2×(C2×D79)⋊C412yes—
649C23C2×(C2×D79)⋊C412yes—
650C23#1457918612yes—
651C23#1457918612yes—
652C23C22×C22⋊D7911yescharacteristic
653Q8—3168no—
654D4—28no—
655D4—3168no—
656D4—3168no—
657D4—3161no—
658D4—3161no—
659D4—1582no—
660D4—1582no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4—3168no—
691C2×C4—3168no—
692C2×C4—3168no—
693C2×C4—3161no—
694C2×C4—3161no—
695C2×C4—3161no—
696C2×C4—3161no—
697C2×C4—3161no—
698C2×C4—3161no—
699C2×C4—1582no—
700C2×C4—1582no—
701C2×C4—1582no—
702C2×C4C2×(C2×D79)⋊C412yes—
703C2×C4C2×(C2×D79)⋊C412yes—
704C2×C4C2×(C2×D79)⋊C412yes—
705C2×C4C2×(C2×D79)⋊C412yes—
706C2×C4C22×C4×D7911yescharacteristic
707C2×C4C22×D31611yescharacteristic
708C2×C4#41×D7911yescharacteristic
709C2×C4C2×#1192962311yescharacteristic
710C2×C4#1457920611yescharacteristic
711C2×C4#1457920811yescharacteristic
712C8—3161no—
713C8—3161no—
714C8—3161no—
715C8—1582no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—3162no—
730C22—3162no—
731C22—3162no—
732C22—6321no—
733C22—6321no—
734C22—6321no—
735C22—6321no—
736C22#1909856714yes—
737C22C22×(C2×D79)⋊C411yescharacteristic
738C22#1909920711yescharacteristic
739C22#1909921211yescharacteristic
740C22C2×#1457918611yescharacteristic
741C22C2×#1457918611yescharacteristic
742C22#1909937411yescharacteristic
743C22#1909937811yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—3162no—
753C4—3162no—
754C4—3162no—
755C4C4×#1192962311yescharacteristic
756C4#1909904211yescharacteristic
757C4#1909920811yescharacteristic
758C4#1909921711yescharacteristic
759C2—24no—
760C2—42no—
761C2—6322no—
762C2#2376622511yescharacteristic
763C2C2×#1909856711yescharacteristic
764C2#2377193011yescharacteristic
765C2#2377536111yescharacteristic
766C2#2377539111yescharacteristic
767C2#2377584011yescharacteristic
768C2#2377586411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2352C2
socleC23×C79C22×D4
prime radicalC2×#19099217C2
cosocleC22×C4×C79C24
hypercenter#2352D79
hypocenterC79#22495
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#19098635C2semidirect
3. #23764372C2semidirect
4. #23764348C2semidirect
5. #23763836C2semidirect
6. #23763826C2semidirect
7. #23763722C2semidirect
8. #23763717C2semidirect
9. #23763488C2semidirect
10. #23763484C2semidirect
11. #23763407C2semidirect
12. #23763228C2semidirect
13. #23763121C2semidirect
14. C2×#19098325C2semidirect
15. C79×#2352C2semidirect
20. #19099217C4semidirect
83. #14579161C2×C4semidirect
90. #14579135C2×C4semidirect
92. C4×D316C2×C4semidirect
99. C2×C4⋊Dic79C2×C4semidirect
185. C2×C79⋊C8#41semidirect
236. C4⋊C4×C79#41semidirect
387. #2352D79semidirect
400. C79#22495semidirect
618. C4⋊C4#11929623semidirect

Maximal subgroups

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

subgroupindex
C2×#190992172
C2×#190986352
#237643722
#237643482
#237638362
#237638262
#237637222
#237637172
#237634882
#237634842
#237634072
#237632282
#237631212
C2×#190983252
C79×#23522
#2249579