Finite Group Databasebeta

← #34308717

Subgroups — #34308717

Order 20224.

1106 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098725C211yesmaximal, characteristic
2C2×#19098668C211yesmaximal, characteristic, complemented
3C2×#19098564C211yesmaximal, characteristic
4#23766403C211yesmaximal, characteristic, complemented
5#23764253C211yesmaximal, characteristic, complemented
6#23764100C211yesmaximal, characteristic, complemented
7#23764024C211yesmaximal, characteristic, complemented
8#23763831C211yesmaximal, characteristic, complemented
9#23763758C211yesmaximal, characteristic, complemented
10#23763741C211yesmaximal, characteristic, complemented
11#23763668C211yesmaximal, characteristic, complemented
12#23763592C211yesmaximal, characteristic, complemented
13C4×#14579085C211yesmaximal, characteristic, complemented
14#23763184C211yesmaximal, characteristic, complemented
15C79×#2341C211yesmaximal, characteristic
16C22×#11929614C2211yescharacteristic
17C22×#11929612C2211yescharacteristic
18C22×#11929608C2211yescharacteristic
19C2×#14579140C2211yescharacteristic
20C2×C4×Dic158C2211yescharacteristic
21C22×C4⋊Dic79C2211yescharacteristic
22#19098725C418yescomplemented
23#19098668—24no—
24C2×#14579092C2211yescharacteristic
25C2×#14579092C2211yescharacteristic
26#19098564—24no—
27C2×#14579085C2211yescharacteristic
28C2×#14579085C2211yescharacteristic
29C2×#14579085C2211yescharacteristic
30C2×#14579084C2211yescharacteristic
31C2×#14579084C2211yescharacteristic
32C2×#14579082C2211yescharacteristic
33C2×#14579082C2211yescharacteristic
34C2×#14579082C2211yescharacteristic
35C2×C22⋊(C79⋊C8)C2211yescharacteristic
36C2×#14579072C2211yescharacteristic
37C2×C4×C79⋊C8C2211yescharacteristic
38#19098469C2211yescharacteristic
39#19098461C2211yescharacteristic
40#19098460—21no—
41#19098450—21no—
42#19098435—21no—
43C4×C4⋊Dic79C2211yescharacteristic
44C22⋊C4×Dic79—21no—
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098318C2211yescharacteristic
50#19098318C2211yescharacteristic
51C22×#41×C79C2211yescharacteristic
52C2×C4×Q8×C79C2211yescharacteristic
53C2×C4×Q8×C79C2211yescharacteristic
54#390×C79—21no—
55#390×C79—21no—
56#390×C79C2211yescharacteristic
57#390×C79C2211yescharacteristic
58#380×C79—21no—
59#380×C79C2211yescharacteristic
60C4×C22⋊C4×C79—21no—
61C4×C22⋊C4×C79C2211yescharacteristic
62C22×Dic158C2311yescharacteristic
63C23×Dic79—21no—
64C2×#11929614—22no—
65C2×#11929614—22no—
66C2×#11929614C2×C414yescomplemented
67C2×#11929612—41no—
68C2×#11929612—41no—
69C2×#11929612C2×C414yescomplemented
70C2×#11929608—22no—
71C2×#11929608—22no—
72C2×#11929608—41no—
73C22×C79⋊C8C2311yescharacteristic
74C22×C79⋊C8C2311yescharacteristic
75C22×C79⋊C8C2311yescharacteristic
76C22×C79⋊C8C2311yescharacteristic
77#14579140—22no—
78#14579140C2×C414yes—
79C4×Dic158—22no—
80C4×Dic158—41no—
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×Dic79⋊C4—21no—
89C2×Dic79⋊C4—21no—
90C2×C22⋊Dic79—21no—
91C2×C4×Dic79—21no—
92C2×C4×Dic79—21no—
93#14579092—22no—
94#14579092—41no—
95#14579085—22no—
96#14579085C2×C414yescomplemented
97#14579085D414yes—
98#14579084—22no—
99#14579084—41no—
100#14579082—22no—
101#14579082—22no—
102#14579082C2×C414yescomplemented
103C22⋊(C79⋊C8)C2×C414yes—
104#14579072—22no—
105C4×C79⋊C8—41no—
106C79⋊#95—21no—
107C79⋊#95—21no—
108C79⋊#95—21no—
109C79⋊#95—21no—
110C2×#41×C79—22no—
111C2×#41×C79—22no—
112C2×#41×C79—22no—
113C2×#41×C79—41no—
114C2×#41×C79—41no—
115C2×#41×C79C2×C414yes—
116C22×Q8×C79C2311yescharacteristic
117C22×D4×C79—21no—
118C22×D4×C79C2311yescharacteristic
119C23×C4×C79—21no—
120C23×C4×C79C2311yescharacteristic
121C4×Q8×C79—22no—
122C4×Q8×C79—22no—
123C4×Q8×C79—41no—
124C4×Q8×C79—41no—
125C2×C4⋊C4×C79—21no—
126C2×C4⋊C4×C79—21no—
127C2×C4⋊C4×C79C2311yescharacteristic
128C2×C4⋊C4×C79C2311yescharacteristic
129C2×C22⋊C4×C79—21no—
130C2×C22⋊C4×C79—21no—
131C2×C22⋊C4×C79—21no—
132C2×C22⋊C4×C79—21no—
133C2×C22⋊C4×C79—21no—
134C2×C22⋊C4×C79D411yescharacteristic
135C2×C22⋊C4×C79D411yescharacteristic
136C2×C42×C79—21no—
137C2×C42×C79—21no—
138C2×C42×C79C2311yescharacteristic
139C2×C42×C79C2311yescharacteristic
140#95×C79—21no—
141#95×C79D411yescharacteristic
142#95×C79D411yescharacteristic
143C2×Dic158—21no—
144C2×Dic158—21no—
145C2×Dic158—21no—
146C2×Dic158—21no—
147C2×Dic158—21no—
148C2×Dic158C22×C412yes—
149C22×Dic79—21no—
150C22×Dic79—21no—
151C22×Dic79—21no—
152C22×Dic79—21no—
153C22×Dic79—42no—
154C22×Dic79—42no—
155C22×Dic79—81no—
156#11929614—28no—
157#11929612—44no—
158#11929608—44no—
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⋊C8—21no—
168C2×C79⋊C8C22×C412yes—
169C2×C79⋊C8C22×C412yes—
170C2×C79⋊C8C2×D412yes—
171C4⋊Dic79—21no—
172C4⋊Dic79—21no—
173C4⋊Dic79—21no—
174C4⋊Dic79—21no—
175C4⋊Dic79—42no—
176C4⋊Dic79C22×C412yes—
177C4⋊Dic79C2×D412yes—
178Dic79⋊C4—24no—
179Dic79⋊C4—42no—
180Dic79⋊C4—81no—
181C22⋊Dic79—24no—
182C4×Dic79—42no—
183C4×Dic79—81no—
184C24×C79—21no—
185C24×C79C2×D411yescharacteristic
186#41×C79—28no—
187#41×C79—44no—
188#41×C79—44no—
189#41×C79—44no—
190C2×Q8×C79—21no—
191C2×Q8×C79—21no—
192C2×Q8×C79—21no—
193C2×Q8×C79C22×C412yes—
194C2×Q8×C79C2×D412yes—
195C2×Q8×C79#4112yes—
196C2×D4×C79—24no—
197C2×D4×C79—21no—
198C2×D4×C79—21no—
199C2×D4×C79—21no—
200C2×D4×C79—21no—
201C2×D4×C79—21no—
202C2×D4×C79—42no—
203C2×D4×C79—42no—
204C2×D4×C79C22×C412yes—
205C22×C4×C79—21no—
206C22×C4×C79—21no—
207C22×C4×C79—21no—
208C22×C4×C79—21no—
209C22×C4×C79—21no—
210C22×C4×C79—24no—
211C22×C4×C79—21no—
212C22×C4×C79—21no—
213C22×C4×C79—42no—
214C22×C4×C79—42no—
215C22×C4×C79C22×C412yes—
216C22×C4×C79C2×D411yescharacteristic
217C22×C4×C79C2×D411yescharacteristic
218C22×C4×C79C2×D411yescharacteristic
219C22×C4×C79C2×D411yescharacteristic
220C22×C4×C79C2×D411yescharacteristic
221C22×C4×C79#4112yes—
222C22×C4×C79C2411yescharacteristic
223C4⋊C4×C79—21no—
224C4⋊C4×C79—21no—
225C4⋊C4×C79—21no—
226C4⋊C4×C79—21no—
227C4⋊C4×C79—42no—
228C4⋊C4×C79—42no—
229C22⋊C4×C79—22no—
230C22⋊C4×C79—41no—
231C22⋊C4×C79—42no—
232C22⋊C4×C79—42no—
233C22⋊C4×C79—81no—
234C22⋊C4×C79—81no—
235C22⋊C4×C79—81no—
236C42×C79—21no—
237C42×C79—21no—
238C42×C79—21no—
239C42×C79—21no—
240C42×C79—42no—
241C42×C79—42no—
242C23×C79—21no—
243C23×C79—21no—
244C23×C79—21no—
245C23×C79—21no—
246C23×C79—21no—
247C23×C79—21no—
248C23×C79—22no—
249C23×C79—41no—
250C23×C79—41no—
251C23×C79—41no—
252C23×C79—41no—
253C23×C79—41no—
254C23×C79—41no—
255C23×C79C4×D412yes—
256C23×C79C22×D411yescharacteristic
257Q8×C79—22no—
258Q8×C79—22no—
259Q8×C79—22no—
260Q8×C79C4×D414yes—
261D4×C79—22no—
262D4×C79—22no—
263D4×C79—48no—
264D4×C79—41no—
265D4×C79—41no—
266C2×C4×C79—22no—
267C2×C4×C79—21no—
268C2×C4×C79—22no—
269C2×C4×C79—21no—
270C2×C4×C79—22no—
271C2×C4×C79—21no—
272C2×C4×C79—21no—
273C2×C4×C79—22no—
274C2×C4×C79—22no—
275C2×C4×C79—22no—
276C2×C4×C79—22no—
277C2×C4×C79—21no—
278C2×C4×C79—21no—
279C2×C4×C79—21no—
280C2×C4×C79—21no—
281C2×C4×C79—21no—
282C2×C4×C79—21no—
283C2×C4×C79—21no—
284C2×C4×C79—21no—
285C2×C4×C79—21no—
286C2×C4×C79—48no—
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×C79C4×D412yes—
294C2×C4×C79#13712yes—
295C2×C4×C79C23×C411yescharacteristic
296C2×C4×C79C22×D411yescharacteristic
297C2×C4×C79C2×#4111yescharacteristic
298C2×C4×C79C2×#4111yescharacteristic
299C2×C4×C79H(5,𝔽2)11yescharacteristic
300C2×C4×C79H(5,𝔽2)11yescharacteristic
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—41no—
305C2×Dic79—41no—
306C2×Dic79—41no—
307C2×Dic79—41no—
308C2×Dic79—41no—
309C2×Dic79—41no—
310C2×Dic79—41no—
311C2×Dic79—41no—
312C2×Dic79—41no—
313C2×Dic79—84no—
314Dic158—22no—
315Dic158—22no—
316Dic158—41no—
317Dic158—41no—
318C79⋊C8—22no—
319C79⋊C8—22no—
320C79⋊C8—22no—
321C79⋊C8—41no—
322C22×C79—22no—
323C22×C79—22no—
324C22×C79—22no—
325C22×C79—41no—
326C22×C79—41no—
327C22×C79—41no—
328C22×C79—41no—
329C22×C79—42no—
330C22×C79—42no—
331C22×C79—42no—
332C22×C79—81no—
333C22×C79—81no—
334C22×C79—81no—
335C22×C79—81no—
336C22×C79C2×C4×D411yescharacteristic
337C22×C79D4211yescharacteristic
338C22×C79#54611yescharacteristic
339C22×C79C2×#13711yescharacteristic
340C22×C79#57511yescharacteristic
341C22×C79#57711yescharacteristic
342C22×C79#57711yescharacteristic
343C4×C79—22no—
344C4×C79—24no—
345C4×C79—22no—
346C4×C79—41no—
347C4×C79—41no—
348C4×C79—41no—
349C4×C79—81no—
350C4×C79—81no—
351C4×C79C2×C4×D411yescharacteristic
352C4×C79#51811yescharacteristic
353C4×C79#54611yescharacteristic
354C4×C79#55111yescharacteristic
355Dic79—42no—
356Dic79—42no—
357Dic79—42no—
358Dic79—81no—
359#22867—791nomaximal, Sylow
360C2×C79—42no—
361C2×C79—82no—
362C2×C79#235811yescharacteristic
363C2×C79C4×#13711yescharacteristic
364C2×C79#295211yescharacteristic
365C2×C79#327511yescharacteristic
366C2×C79#327811yescharacteristic
367C2×C79#331611yescharacteristic
368C2×C79#331711yescharacteristic
369C2×#452—791no—
370C2×#441—791no—
371C2×#417—791no—
372#2360—791no—
373#2341D7911yescharacteristic
374#1968—791no—
375#1936—791no—
376#1926—791no—
377#1894—791no—
378#1880—791no—
379#1878—791no—
380#1865—791no—
381#1853—791no—
382C4×#103—791no—
383#1753—791no—
384C79#2286711yescharacteristic, complemented, Sylow
385C22×#41C2×D7911yescharacteristic
386C22×Q16—791no—
387C22×SD16—791no—
388C22×M16—791no—
389C2×C22⋊Q8—791no—
390C2×C4×Q8—791no—
391C2×C4×Q8C2×D7911yescharacteristic
392C2×C4×Q8C2×D7911yescharacteristic
393C22×C4⋊C4—791no—
394#452—798no—
395#441—1584no—
396C2×#106—791no—
397C2×#106—791no—
398#417—1584no—
399C2×#103—791no—
400C2×#103—791no—
401C2×#103—791no—
402C2×#103—791no—
403C2×#103—791no—
404C2×#102—791no—
405C2×#102—791no—
406C2×#102—791no—
407C2×C22⋊C8—791no—
408C2×#97—791no—
409C2×C4×C8—791no—
410#391—791no—
411#390—21no—
412#390—21no—
413#390C2×D7911yescharacteristic
414#390C2×D7911yescharacteristic
415#389—791no—
416#389—1581no—
417#387—1581no—
418#385—1581no—
419#380—21no—
420#380C2×D7911yescharacteristic
421C4×C4⋊C4—791no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—1581no—
424C4×C22⋊C4C2×D7911yescharacteristic
425#340—791no—
426#340—791no—
427#340—791no—
428#340—791no—
429#336—791no—
430#336—791no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—41no—
435C2×#41—41no—
436C2×#41C4×D7914yes—
437C22×Q8—791no—
438C22×Q8C22×D7911yescharacteristic
439C22×D4—21no—
440C22×D4C22×D7911yescharacteristic
441C23×C4—21no—
442C23×C4—1581no—
443C23×C4C22×D7911yescharacteristic
444C2×Q16—794no—
445C2×Q16—1582no—
446C2×Q16—1582no—
447C2×SD16—3161no—
448C2×SD16—3161no—
449C2×SD16—794no—
450C2×M16—3161no—
451C2×M16—1582no—
452C2×M16—1582no—
453C22×C8—791no—
454C22×C8—791no—
455C22×C8—791no—
456C22×C8—791no—
457C22⋊Q8—794no—
458C22⋊Q8—1582no—
459C4×Q8—22no—
460C4×Q8—22no—
461C4×Q8—41no—
462C4×Q8—41no—
463C4×Q8—3161no—
464C4×Q8—1582no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—3161no—
468C2×C4⋊C4—791no—
469C2×C4⋊C4—791no—
470C2×C4⋊C4—791no—
471C2×C4⋊C4—1581no—
472C2×C4⋊C4—1581no—
473C2×C4⋊C4—1582no—
474C2×C4⋊C4—1581no—
475C2×C4⋊C4—1581no—
476C2×C4⋊C4C22×D7911yescharacteristic
477C2×C4⋊C4C22×D7911yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—1581no—
484C2×C22⋊C4C22⋊D7911yescharacteristic
485C2×C22⋊C4C22⋊D7911yescharacteristic
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—1581no—
489C2×C42—1581no—
490C2×C42C22×D7911yescharacteristic
491C2×C42C22×D7911yescharacteristic
492#106—3161no—
493#106—1582no—
494#103—3161no—
495#103—794no—
496#103—794no—
497#103—1582no—
498#103—1582no—
499#102—794no—
500#102—1582no—
501#102—1582no—
502C22⋊C8—794no—
503#97—1582no—
504C4×C8—3161no—
505#95—21no—
506#95—1581no—
507#95—1581no—
508#95—1581no—
509#95—1581no—
510#95C22⋊D7911yescharacteristic
511#95C22⋊D7911yescharacteristic
512C24—21no—
513C24C2×C22⋊D7911yescharacteristic
514#41—28no—
515#41—44no—
516#41—44no—
517#41—44no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—792no—
522C2×Q8—1581no—
523C2×Q8—1581no—
524C2×Q8—1581no—
525C2×Q8—1581no—
526C2×Q8—1581no—
527C2×Q8C2×C4×D7912yes—
528C2×Q8D4×D7912yes—
529C2×Q8#1192962312yes—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4C2×C4×D7912yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—24no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—3162no—
550C22×C4—3162no—
551C22×C4—6321no—
552C22×C4—1581no—
553C22×C4—1581no—
554C22×C4—1581no—
555C22×C4—1581no—
556C22×C4C2×C4×D7912yes—
557C22×C4C2×C22⋊D7911yescharacteristic
558C22×C4C2×C22⋊D7911yescharacteristic
559C22×C4C2×C22⋊D7911yescharacteristic
560C22×C4C2×C22⋊D7911yescharacteristic
561C22×C4C2×C22⋊D7911yescharacteristic
562C22×C4#1192962412yes—
563C22×C4C23×D7911yescharacteristic
564Q16—1588no—
565SD16—3164no—
566M16—3164no—
567C2×C8—792no—
568C2×C8—792no—
569C2×C8—792no—
570C2×C8—1581no—
571C2×C8—1581no—
572C2×C8—1581no—
573C2×C8—1581no—
574C2×C8—1581no—
575C2×C8—1581no—
576C2×C8—1581no—
577C2×C8—1581no—
578C2×C8—1581no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—3162no—
586C4⋊C4—3162no—
587C4⋊C4—792no—
588C4⋊C4—792no—
589C4⋊C4—6321no—
590C4⋊C4—1581no—
591C4⋊C4—1581no—
592C4⋊C4—1581no—
593C4⋊C4—1581no—
594C4⋊C4—1584no—
595C22⋊C4—22no—
596C22⋊C4—41no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—81no—
600C22⋊C4—81no—
601C22⋊C4—81no—
602C22⋊C4—1584no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—42no—
608C42—42no—
609C42—3162no—
610C42—6321no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23C4×C22⋊D7912yes—
625C23C22×C22⋊D7911yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—3161no—
630Q8—3161no—
631Q8—1582no—
632Q8—1582no—
633Q8(C22⋊D79)⋊C414yes—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—48no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—3161no—
667C2×C4—3161no—
668C2×C4—3161no—
669C2×C4—3161no—
670C2×C4—3161no—
671C2×C4—3161no—
672C2×C4—3161no—
673C2×C4—3161no—
674C2×C4—3161no—
675C2×C4—6324no—
676C2×C4—1582no—
677C2×C4—1582no—
678C2×C4—1582no—
679C2×C4C4×C22⋊D7912yes—
680C2×C4#1457919112yes—
681C2×C4C22×C4×D7911yescharacteristic
682C2×C4C2×D4×D7911yescharacteristic
683C2×C4C2×#1192962311yescharacteristic
684C2×C4C2×#1192962411yescharacteristic
685C2×C4#1457920611yescharacteristic
686C2×C4#1457920611yescharacteristic
687C8—3161no—
688C8—1582no—
689C8—1582no—
690C8—1582no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22C2×C4×C22⋊D7911yescharacteristic
706C22D4×C22⋊D7911yescharacteristic
707C22#1909920711yescharacteristic
708C22C2×#1457919111yescharacteristic
709C22#1909936111yescharacteristic
710C22#1909937111yescharacteristic
711C22#1909937411yescharacteristic
712C4—22no—
713C4—22no—
714C4—24no—
715C4—41no—
716C4—41no—
717C4—41no—
718C4—81no—
719C4—81no—
720C4—3162no—
721C4—3162no—
722C4—3162no—
723C4—6321no—
724C4C2×(C22⋊D79)⋊C411yescharacteristic
725C4#1909903611yescharacteristic
726C4#1909920311yescharacteristic
727C4#1909923911yescharacteristic
728C2—42no—
729C2—82no—
730C2#2376637911yescharacteristic
731C2C4×#1457919111yescharacteristic
732C2#2377228111yescharacteristic
733C2#2377503211yescharacteristic
734C2#2377506611yescharacteristic
735C2#2377551111yescharacteristic
736C2#2377552611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2341C2
socleC23×C79C22×D4
prime radicalC22×#41×C79C22
cosocleC22×C4×C79C24
hypercenter#2341D79
hypocenterC79#22867
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#19098668C2semidirect
4. #23766403C2semidirect
5. #23764253C2semidirect
6. #23764100C2semidirect
7. #23764024C2semidirect
8. #23763831C2semidirect
9. #23763758C2semidirect
10. #23763741C2semidirect
11. #23763668C2semidirect
12. #23763592C2semidirect
13. C4×#14579085C2semidirect
14. #23763184C2semidirect
22. #19098725C4semidirect
66. C2×#11929614C2×C4semidirect
69. C2×#11929612C2×C4semidirect
96. #14579085C2×C4semidirect
102. #14579082C2×C4semidirect
384. C79#22867semidirect

Maximal subgroups

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

subgroupindex
C2×#190987252
C2×#190986682
C2×#190985642
#237664032
#237642532
#237641002
#237640242
#237638312
#237637582
#237637412
#237636682
#237635922
C4×#145790852
#237631842
C79×#23412
#2286779