Finite Group Databasebeta

← #34304559

Subgroups — #34304559

Order 20224.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099253C211yesmaximal, characteristic
2D4×C4⋊Dic79C211yesmaximal, characteristic
3#23764369C211yesmaximal, characteristic, complemented
4#23764355C211yesmaximal, characteristic, complemented
5#23763833C211yesmaximal, characteristic, complemented
6#23763823C211yesmaximal, characteristic, complemented
7#23763705C211yesmaximal, characteristic, complemented
8#23763705C211yesmaximal, characteristic, complemented
9#23763496C211yesmaximal, characteristic, complemented
10#23763487C211yesmaximal, characteristic, complemented
11#23763406C211yesmaximal, characteristic, complemented
12#23763231C211yesmaximal, characteristic, complemented
13#23763120C211yesmaximal, characteristic, complemented
14C2×#19098326C211yesmaximal, characteristic, complemented
15C2×#435×C79C211yesmaximal, characteristic
16#19099253—24no—
17#19099253C418yescomplemented
18C2×#14579154—21no—
19C2×#14579153C2211yescharacteristic
20C2×#14579151—21no—
21C2×#14579142—21no—
22C2×#14579140C2211yescharacteristic
23C2×#14579140C2211yescharacteristic
24C2×C4×Dic158C2211yescharacteristic
25C2×D4×Dic79—21no—
26C2×#14579120C2211yescharacteristic
27C2×#14579117—21no—
28C22×C4⋊Dic79C2211yescharacteristic
29C22×C4⋊Dic79C2211yescharacteristic
30C22×C4⋊Dic79C2211yescharacteristic
31C2×#14579086C2211yescharacteristic
32C2×#14579086C2211yescharacteristic
33C2×#14579086C2211yescharacteristic
34C2×#14579086C2211yescharacteristic
35#19098462—21no—
36#19098438—21no—
37#19098438—21no—
38#19098433C2211yescharacteristic
39#19098423C2211yescharacteristic
40#19098423C2211yescharacteristic
41C4×C4⋊Dic79C2211yescharacteristic
42#19098326C2211yescharacteristic
43#19098326C2211yescharacteristic
44#19098326C2211yescharacteristic
45#19098326C2211yescharacteristic
46#19098326C2211yescharacteristic
47#19098326C2211yescharacteristic
48#19098326C2211yescharacteristic
49#19098326C2211yescharacteristic
50#19098326C2211yescharacteristic
51#19098326C2211yescharacteristic
52#19098326C2211yescharacteristic
53#19098326C2211yescharacteristic
54C22×M16×C79C2211yescharacteristic
55C23×C8×C79C2211yescharacteristic
56C2×C4×D4×C79C2211yescharacteristic
57#435×C79—24no—
58C2×C4⋊C8×C79C2211yescharacteristic
59C2×C22⋊C8×C79C2211yescharacteristic
60C2×C22⋊C8×C79C2211yescharacteristic
61C2×#97×C79C2211yescharacteristic
62C22×Dic158C2311yescharacteristic
63C23×Dic79—21no—
64C23×Dic79—21no—
65C23×Dic79—21no—
66#14579154—28no—
67#14579153—22no—
68#14579153C2×C414yescomplemented
69#14579151—28no—
70#14579142—28no—
71#14579140—22no—
72#14579140—22no—
73#14579140C2×C414yescomplemented
74#14579140C2×C414yescomplemented
75C4×Dic158—22no—
76C4×Dic158C2×C414yescomplemented
77D4×Dic79—44no—
78#14579120—22no—
79#14579120C2×C414yescomplemented
80#14579117—28no—
81C2×C4⋊Dic79—22no—
82C2×C4⋊Dic79—21no—
83C2×C4⋊Dic79—22no—
84C2×C4⋊Dic79—22no—
85C2×C4⋊Dic79—21no—
86C2×C4⋊Dic79—21no—
87C2×C4⋊Dic79—21no—
88C2×C4⋊Dic79—21no—
89C2×C4⋊Dic79—41no—
90C2×C4⋊Dic79—41no—
91C2×C4⋊Dic79C2×C414yescomplemented
92C2×C4⋊Dic79C2311yescharacteristic
93C2×C4⋊Dic79C2311yescharacteristic
94C2×C4⋊Dic79C2311yescharacteristic
95C2×C4⋊Dic79C2311yescharacteristic
96C2×C4⋊Dic79C2311yescharacteristic
97C2×C4⋊Dic79C2311yescharacteristic
98C2×C4⋊Dic79C2311yescharacteristic
99C2×Dic79⋊C4—21no—
100C2×Dic79⋊C4—21no—
101C2×Dic79⋊C4—21no—
102C2×Dic79⋊C4—21no—
103C2×Dic79⋊C4—21no—
104C2×C22⋊Dic79—21no—
105C2×C22⋊Dic79—21no—
106C2×C22⋊Dic79—21no—
107C2×C22⋊Dic79—21no—
108C2×C22⋊Dic79—21no—
109C2×C4×Dic79—21no—
110C2×C4×Dic79—21no—
111C2×C4×Dic79—21no—
112#14579086—22no—
113#14579086—22no—
114#14579086—41no—
115#14579086—41no—
116C79⋊#95—21no—
117C79⋊#95—21no—
118C79⋊#95—21no—
119C22×D4×C79D411yescharacteristic
120C23×C4×C79C2311yescharacteristic
121C23×C4×C79C2311yescharacteristic
122C2×M16×C79—22no—
123C2×M16×C79—22no—
124C2×M16×C79—41no—
125C22×C8×C79—22no—
126C22×C8×C79—22no—
127C22×C8×C79—41no—
128C22×C8×C79C2311yescharacteristic
129C22×C8×C79C2311yescharacteristic
130C22×C8×C79C2311yescharacteristic
131C22×C8×C79C2311yescharacteristic
132C4×D4×C79C2×C414yes—
133C4×D4×C79D414yes—
134C2×C4⋊C4×C79D411yescharacteristic
135C2×C22⋊C4×C79D411yescharacteristic
136C2×C22⋊C4×C79D411yescharacteristic
137C2×C42×C79C2311yescharacteristic
138C4⋊C8×C79—22no—
139C22⋊C8×C79—22no—
140C22⋊C8×C79—22no—
141#97×C79—22no—
142C2×Dic158—21no—
143C2×Dic158—21no—
144C2×Dic158—21no—
145C2×Dic158—21no—
146C2×Dic158—21no—
147C2×Dic158C22×C412yes—
148C22×Dic79—24no—
149C22×Dic79—21no—
150C22×Dic79—21no—
151C22×Dic79—21no—
152C22×Dic79—21no—
153C22×Dic79—21no—
154C22×Dic79—21no—
155C22×Dic79—21no—
156C22×Dic79—21no—
157C22×Dic79—42no—
158C22×Dic79—42no—
159C22×Dic79—42no—
160C22×Dic79—42no—
161C22×Dic79—42no—
162C22×Dic79—42no—
163C22×Dic79—81no—
164C22×Dic79—81no—
165C4⋊Dic79—24no—
166C4⋊Dic79—21no—
167C4⋊Dic79—21no—
168C4⋊Dic79—21no—
169C4⋊Dic79—21no—
170C4⋊Dic79—21no—
171C4⋊Dic79—21no—
172C4⋊Dic79—21no—
173C4⋊Dic79—21no—
174C4⋊Dic79—21no—
175C4⋊Dic79—21no—
176C4⋊Dic79—42no—
177C4⋊Dic79—42no—
178C4⋊Dic79—42no—
179C4⋊Dic79—81no—
180C4⋊Dic79C22×C412yes—
181C4⋊Dic79C22×C412yes—
182C4⋊Dic79C22×C412yes—
183C4⋊Dic79#4112yes—
184Dic79⋊C4—24no—
185Dic79⋊C4—24no—
186Dic79⋊C4—24no—
187Dic79⋊C4—24no—
188Dic79⋊C4—24no—
189C22⋊Dic79—24no—
190C22⋊Dic79—24no—
191C22⋊Dic79—24no—
192C22⋊Dic79—42no—
193C22⋊Dic79—42no—
194C4×Dic79—24no—
195C4×Dic79—24no—
196C4×Dic79—42no—
197C24×C79C2×D411yescharacteristic
198C24×C79C2×D411yescharacteristic
199C2×D4×C79—22no—
200C2×D4×C79—22no—
201C2×D4×C79C22⋊C414yes—
202C22×C4×C79—21no—
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×C79C22×C412yes—
211C22×C4×C79C22×C412yes—
212C22×C4×C79C2×D411yescharacteristic
213C22×C4×C79C2×D411yescharacteristic
214C22×C4×C79C2×D411yescharacteristic
215C22×C4×C79C2×D411yescharacteristic
216C22×C4×C79C2×D412yes—
217C22×C4×C79C2×D412yes—
218C22×C4×C79C2411yescharacteristic
219M16×C79—44no—
220C2×C8×C79—21no—
221C2×C8×C79—21no—
222C2×C8×C79—21no—
223C2×C8×C79—21no—
224C2×C8×C79—21no—
225C2×C8×C79—21no—
226C2×C8×C79—21no—
227C2×C8×C79—21no—
228C2×C8×C79—21no—
229C2×C8×C79—21no—
230C2×C8×C79—21no—
231C2×C8×C79—44no—
232C2×C8×C79#4112yes—
233C4⋊C4×C79C22⋊C414yes—
234C22⋊C4×C79C22⋊C414yes—
235C22⋊C4×C79C22⋊C414yes—
236C42×C79C22×C412yes—
237C42×C79C2×D412yes—
238C23×C79—21no—
239C23×C79—21no—
240C23×C79—21no—
241C23×C79—21no—
242C23×C79—21no—
243C23×C79—21no—
244C23×C79—21no—
245C23×C79—21no—
246C23×C79—21no—
247C23×C79—21no—
248C23×C79C2×C22⋊C412yes—
249C23×C79C2×C22⋊C412yes—
250C23×C79AGL(1,ℤ/8)12yes—
251C23×C79#13712yes—
252C23×C79C22×D411yescharacteristic
253D4×C79—28no—
254C2×C4×C79—21no—
255C2×C4×C79—21no—
256C2×C4×C79—21no—
257C2×C4×C79—21no—
258C2×C4×C79—21no—
259C2×C4×C79—21no—
260C2×C4×C79—21no—
261C2×C4×C79—21no—
262C2×C4×C79—22no—
263C2×C4×C79—22no—
264C2×C4×C79—22no—
265C2×C4×C79—22no—
266C2×C4×C79—22no—
267C2×C4×C79—22no—
268C2×C4×C79—22no—
269C2×C4×C79—22no—
270C2×C4×C79C2×C22⋊C412yes—
271C2×C4×C79C2×C22⋊C412yes—
272C2×C4×C79C2×C22⋊C412yes—
273C2×C4×C79C2×C22⋊C412yes—
274C2×C4×C79C23×C411yescharacteristic
275C2×C4×C79C22×D411yescharacteristic
276C2×C4×C79C2×#4111yescharacteristic
277C2×C4×C79C2×#4111yescharacteristic
278C2×C4×C79H(5,𝔽2)11yescharacteristic
279C2×C4×C792−1+411yescharacteristic
280C2×Dic79—22no—
281C2×Dic79—22no—
282C2×Dic79—22no—
283C2×Dic79—22no—
284C2×Dic79—22no—
285C2×Dic79—41no—
286C2×Dic79—41no—
287C2×Dic79—41no—
288C2×Dic79—41no—
289C2×Dic79—41no—
290C2×Dic79—41no—
291C2×Dic79—41no—
292C2×Dic79—41no—
293C2×Dic79—41no—
294C2×Dic79—41no—
295C2×Dic79—48no—
296C2×Dic79—41no—
297C2×Dic79—41no—
298C2×Dic79—41no—
299C2×Dic79—41no—
300C2×Dic79—41no—
301C2×Dic79—41no—
302C2×Dic79—41no—
303C2×Dic79—41no—
304C2×Dic79—41no—
305C2×Dic79—84no—
306C2×Dic79—84no—
307Dic158—22no—
308Dic158—22no—
309Dic158—41no—
310Dic158—41no—
311C8×C79—22no—
312C8×C79—41no—
313C8×C79—41no—
314C8×C79—41no—
315C22×C79—22no—
316C22×C79—22no—
317C22×C79—22no—
318C22×C79—22no—
319C22×C79—22no—
320C22×C79—22no—
321C22×C79—22no—
322C22×C79—22no—
323C22×C79—22no—
324C22×C79—41no—
325C22×C79—41no—
326C22×C79—41no—
327C22×C79—41no—
328C22×C79#41714yes—
329C22×C79C22×C22⋊C411yescharacteristic
330C22×C79#54611yescharacteristic
331C22×C79#54711yescharacteristic
332C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C79C2×#13711yescharacteristic
334C22×C79#57711yescharacteristic
335C22×C79#57811yescharacteristic
336C4×C79—22no—
337C4×C79—22no—
338C4×C79—22no—
339C4×C79—22no—
340C4×C79C4×#4111yescharacteristic
341C4×C79#52011yescharacteristic
342C4×C79#54611yescharacteristic
343C4×C79#54711yescharacteristic
344Dic79—42no—
345Dic79—42no—
346Dic79—42no—
347Dic79—42no—
348Dic79—42no—
349Dic79—81no—
350Dic79—81no—
351Dic79—81no—
352#22491—791nomaximal, Sylow
353C2×C79—24no—
354C2×C79—42no—
355C2×C79#233911yescharacteristic
356C2×C79C2×#41711yescharacteristic
357C2×C79#289811yescharacteristic
358C2×C79#331011yescharacteristic
359C2×C79#331211yescharacteristic
360C2×C79#334311yescharacteristic
361C2×C79#334411yescharacteristic
362C2×#552—791no—
363C2×#435D7911yescharacteristic
364D4×C4⋊C4—791no—
365#1992—791no—
366#1989—791no—
367#1894—791no—
368#1892—791no—
369#1872—791no—
370#1872—791no—
371#1825—791no—
372#1823—791no—
373#1803—791no—
374#1763—791no—
375#1736—791no—
376C2×#340—791no—
377C79#2249111yescharacteristic, complemented, Sylow
378C22×M16C2×D7911yescharacteristic
379C23×C8C2×D7911yescharacteristic
380#552—798no—
381#552—1584no—
382C2×#126—1581no—
383C2×#125—791no—
384C2×#125—1581no—
385C2×#123—1581no—
386C2×C22⋊Q8—791no—
387C2×C22⋊Q8—791no—
388C2×C4×Q8—791no—
389C2×C4×D4—1581no—
390C2×C4×D4C2×D7911yescharacteristic
391C2×#117—791no—
392C2×#117—1581no—
393C22×C4⋊C4—791no—
394C22×C4⋊C4—791no—
395C22×C4⋊C4—791no—
396#435—24no—
397C2×C4⋊C8C2×D7911yescharacteristic
398C2×#103—791no—
399C2×#103—791no—
400C2×#103—791no—
401C2×#103—791no—
402C2×C22⋊C8C2×D7911yescharacteristic
403C2×C22⋊C8C2×D7911yescharacteristic
404C2×#97C2×D7911yescharacteristic
405#389—1581no—
406#385—1581no—
407#385—1581no—
408#384—791no—
409#380—791no—
410#380—791no—
411C4×C4⋊C4—791no—
412#340—791no—
413#340—791no—
414#340—791no—
415#340—791no—
416#340—791no—
417#340—791no—
418#340—791no—
419#340—791no—
420#340—791no—
421#340—791no—
422#340—791no—
423#340—791no—
424C22×Q8—791no—
425C22×D4D31611yescharacteristic
426C23×C4—1581no—
427C23×C4—1581no—
428C23×C4—1581no—
429C23×C4C22×D7911yescharacteristic
430C23×C4C22×D7911yescharacteristic
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—41no—
434C22×C8—22no—
435C22×C8—22no—
436C22×C8—41no—
437C22×C8C22×D7911yescharacteristic
438C22×C8C22×D7911yescharacteristic
439C22×C8C22×D7911yescharacteristic
440C22×C8C22×D7911yescharacteristic
441#126—1588no—
442#125—794no—
443#125—1588no—
444#125—1582no—
445#123—1588no—
446C22⋊Q8—794no—
447C22⋊Q8—794no—
448C22⋊Q8—1582no—
449C22⋊Q8—1582no—
450C4×Q8—794no—
451C4×Q8—1582no—
452C4×D4—3164no—
453C4×D4C4×D7914yes—
454C4×D4C22⋊D7914yes—
455#117—794no—
456#117—1582no—
457#117—1588no—
458C2×C4⋊C4—3161no—
459C2×C4⋊C4—3161no—
460C2×C4⋊C4—794no—
461C2×C4⋊C4—791no—
462C2×C4⋊C4—791no—
463C2×C4⋊C4—791no—
464C2×C4⋊C4—791no—
465C2×C4⋊C4—791no—
466C2×C4⋊C4—791no—
467C2×C4⋊C4—791no—
468C2×C4⋊C4—1581no—
469C2×C4⋊C4—1581no—
470C2×C4⋊C4—1581no—
471C2×C4⋊C4—1582no—
472C2×C4⋊C4—1582no—
473C2×C4⋊C4—1581no—
474C2×C4⋊C4—1582no—
475C2×C4⋊C4—1581no—
476C2×C4⋊C4—1581no—
477C2×C4⋊C4—1581no—
478C2×C4⋊C4—1581no—
479C2×C4⋊C4—1581no—
480C2×C4⋊C4—1581no—
481C2×C4⋊C4D31611yescharacteristic
482C2×C22⋊C4—1581no—
483C2×C22⋊C4—1581no—
484C2×C22⋊C4—1581no—
485C2×C22⋊C4—1581no—
486C2×C22⋊C4—1581no—
487C2×C22⋊C4D31611yescharacteristic
488C2×C22⋊C4D31611yescharacteristic
489C2×C42—1581no—
490C2×C42—1581no—
491C2×C42—1581no—
492C2×C42C22×D7911yescharacteristic
493C4⋊C8—22no—
494#103—3161no—
495#103—3161no—
496#103—1582no—
497#103—1582no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500#97—22no—
501#95—1581no—
502#95—1581no—
503#95—1581no—
504C24C2×D31611yescharacteristic
505C24C2×D31611yescharacteristic
506C2×Q8—792no—
507C2×Q8—1581no—
508C2×Q8—1581no—
509C2×Q8—1581no—
510C2×Q8—1581no—
511C2×Q8—1581no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4(C2×D79)⋊C414yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—3162no—
524C22×C4—3162no—
525C22×C4—3162no—
526C22×C4—3162no—
527C22×C4—3162no—
528C22×C4—3162no—
529C22×C4—6321no—
530C22×C4—6321no—
531C22×C4—1581no—
532C22×C4—1581no—
533C22×C4—1581no—
534C22×C4—1584no—
535C22×C4—1581no—
536C22×C4—1581no—
537C22×C4—1581no—
538C22×C4—1581no—
539C22×C4—1581no—
540C22×C4C2×C4×D7912yes—
541C22×C4C2×C4×D7912yes—
542C22×C4C2×C22⋊D7912yes—
543C22×C4C2×C22⋊D7912yes—
544C22×C4C2×D31611yescharacteristic
545C22×C4C2×D31611yescharacteristic
546C22×C4C2×D31611yescharacteristic
547C22×C4C2×D31611yescharacteristic
548C22×C4C23×D7911yescharacteristic
549M16—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—44no—
562C2×C8#1192962312yes—
563C4⋊C4—3162no—
564C4⋊C4—3162no—
565C4⋊C4—3162no—
566C4⋊C4—792no—
567C4⋊C4—792no—
568C4⋊C4—792no—
569C4⋊C4—792no—
570C4⋊C4—6321no—
571C4⋊C4—1581no—
572C4⋊C4—1581no—
573C4⋊C4—1581no—
574C4⋊C4—1581no—
575C4⋊C4—1581no—
576C4⋊C4—1581no—
577C4⋊C4—1581no—
578C4⋊C4—1584no—
579C4⋊C4—1584no—
580C4⋊C4—1584no—
581C4⋊C4—1584no—
582C4⋊C4—1584no—
583C4⋊C4—1584no—
584C4⋊C4—1581no—
585C4⋊C4—1581no—
586C4⋊C4—1581no—
587C4⋊C4(C2×D79)⋊C414yes—
588C22⋊C4—3162no—
589C22⋊C4—3162no—
590C22⋊C4—1584no—
591C22⋊C4—1584no—
592C22⋊C4—1584no—
593C22⋊C4(C2×D79)⋊C414yes—
594C22⋊C4(C2×D79)⋊C414yes—
595C42—3162no—
596C42—1584no—
597C42—1584no—
598C42C2×C4×D7912yes—
599C42C2×C22⋊D7912yes—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23C2×(C2×D79)⋊C412yes—
611C23C2×(C2×D79)⋊C412yes—
612C23#1457918912yes—
613C23#1457919412yes—
614C23C22×D31611yescharacteristic
615Q8—3161no—
616Q8—3161no—
617Q8—1582no—
618Q8—1582no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—3161no—
637C2×C4—3161no—
638C2×C4—3168no—
639C2×C4—3161no—
640C2×C4—3161no—
641C2×C4—3161no—
642C2×C4—3161no—
643C2×C4—3161no—
644C2×C4—3161no—
645C2×C4—3161no—
646C2×C4—3161no—
647C2×C4—3161no—
648C2×C4—3161no—
649C2×C4—3161no—
650C2×C4—3161no—
651C2×C4—3161no—
652C2×C4—3161no—
653C2×C4—3161no—
654C2×C4—3161no—
655C2×C4—3161no—
656C2×C4—6324no—
657C2×C4—6324no—
658C2×C4—1582no—
659C2×C4—1582no—
660C2×C4—1582no—
661C2×C4—1582no—
662C2×C4—1582no—
663C2×C4C2×(C2×D79)⋊C412yes—
664C2×C4C2×(C2×D79)⋊C412yes—
665C2×C4C2×(C2×D79)⋊C412yes—
666C2×C4C2×(C2×D79)⋊C412yes—
667C2×C4C22×C4×D7911yescharacteristic
668C2×C4C22×C22⋊D7911yescharacteristic
669C2×C4#41×D7911yescharacteristic
670C2×C4C2×#1192962311yescharacteristic
671C2×C4#1457920611yescharacteristic
672C2×C4#1457920811yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1909856514yes—
691C22C22×(C2×D79)⋊C411yescharacteristic
692C22#1909920811yescharacteristic
693C22#1909921711yescharacteristic
694C22C2×#1457918911yescharacteristic
695C22C2×#1457919411yescharacteristic
696C22#1909937511yescharacteristic
697C22#1909938011yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—3162no—
703C4—3162no—
704C4—3162no—
705C4—3162no—
706C4—3162no—
707C4—6321no—
708C4—6321no—
709C4—6321no—
710C4C4×#1192962311yescharacteristic
711C4#1909904211yescharacteristic
712C4#1909920711yescharacteristic
713C4#1909921211yescharacteristic
714C2—24no—
715C2—42no—
716C2#2376622511yescharacteristic
717C2C2×#1909856511yescharacteristic
718C2#2377193411yescharacteristic
719C2#2377542311yescharacteristic
720C2#2377545311yescharacteristic
721C2#2377584211yescharacteristic
722C2#2377585711yescharacteristic
subgroupG/H
centerC23C22×D316
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC2×#435×C79C2
socleC23×C79C22×D4
prime radicalC22×D4×C79D4
cosocleC22×C4×C79C24
hypercenterC2×#435D79
hypocenterC79#22491
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #23764369C2semidirect
4. #23764355C2semidirect
5. #23763833C2semidirect
6. #23763823C2semidirect
7. #23763705C2semidirect
8. #23763705C2semidirect
9. #23763496C2semidirect
10. #23763487C2semidirect
11. #23763406C2semidirect
12. #23763231C2semidirect
13. #23763120C2semidirect
14. C2×#19098326C2semidirect
17. #19099253C4semidirect
68. #14579153C2×C4semidirect
73. #14579140C2×C4semidirect
74. #14579140C2×C4semidirect
76. C4×Dic158C2×C4semidirect
79. #14579120C2×C4semidirect
91. C2×C4⋊Dic79C2×C4semidirect
377. C79#22491semidirect

Maximal subgroups

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

subgroupindex
C2×#190992532
D4×C4⋊Dic792
#237643692
#237643552
#237638332
#237638232
#237637052
#237634962
#237634872
#237634062
#237632312
#237631202
C2×#190983262
C2×#435×C792
#2249179