Finite Group Databasebeta

← #34257063

Subgroups — #34257063

Order 20224.

982 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777276C211yesmaximal, characteristic
2#23772517C211yesmaximal, characteristic, complemented
3#23762133C211yesmaximal, characteristic, complemented
4#23762131C211yesmaximal, characteristic, complemented
5#23762120C211yesmaximal, characteristic, complemented
6#23762113C211yesmaximal, characteristic, complemented
7#23762108C211yesmaximal, characteristic, complemented
8#23762106C211yesmaximal, characteristic, complemented
9#23762096C211yesmaximal, characteristic, complemented
10#23762093C211yesmaximal, characteristic, complemented
11#23762075C211yesmaximal, characteristic, complemented
12#23762067C211yesmaximal, characteristic, complemented
13#23762060C211yesmaximal, characteristic, complemented
14#23762047C211yesmaximal, characteristic, complemented
15C79×#2925C211yesmaximal, characteristic, complemented
16#19099298—21no—
17#19099298C412yes—
18#19099234—21no—
19#19099234C412yes—
20#19099209—21no—
21#19099209—21no—
22#19099209C412yes—
23#19099209C412yes—
24#19099168—21no—
25#19099168—21no—
26#19099127—21no—
27#19099120C2211yescharacteristic
28#19099113C2211yescharacteristic
29#19099113C2211yescharacteristic
30#19099113C2211yescharacteristic
31#19099113C2211yescharacteristic
32C2×#14579158C2211yescharacteristic
33#19099037—21no—
34#19098694—21no—
35#19098641—21no—
36#19098635—21no—
37#19098635—21no—
38#19098620C2211yescharacteristic
39#19098620C2211yescharacteristic, complemented
40#19098616C2211yescharacteristic, complemented
41#19098587C2211yescharacteristic
42#19098587C2211yescharacteristic, complemented
43C2×C4⋊(C79⋊C8)C2211yescharacteristic, complemented
44#19098311C2211yescharacteristic, complemented
45#19098311C2211yescharacteristic, complemented
46#19098311C2211yescharacteristic, complemented
47#19098311C2211yescharacteristic, complemented
48#19098308C2211yescharacteristic, complemented
49#19098308C2211yescharacteristic, complemented
50#19098308C2211yescharacteristic, complemented
51#19098308C2211yescharacteristic, complemented
52#19098306C2211yescharacteristic
53#19098306C2211yescharacteristic
54#19098306C2211yescharacteristic
55#19098306C2211yescharacteristic
56#19098306C2211yescharacteristic
57#19098306C2211yescharacteristic
58#19098306C2211yescharacteristic
59#19098306C2211yescharacteristic
60C4×#41×C79C2211yescharacteristic
61#433×C79—21no—
62#433×C79—21no—
63#432×C79C2211yescharacteristic
64#432×C79C2211yescharacteristic, complemented
65#431×C79C2211yescharacteristic
66#431×C79C2211yescharacteristic, complemented
67#423×C79C2211yescharacteristic, complemented
68C2×C4⋊C8×C79C2211yescharacteristic, complemented
69#408×C79—21no—
70#405×C79—21no—
71C2×#11929624—21no—
72C2×#11929624—21no—
73C2×#11929624C2×C412yes—
74C2×#11929624C2×C412yes—
75C22×D316—21no—
76C22×D316—21no—
77C22×D316C2×C412yes—
78C2×#11929608—21no—
79C2×#11929608—21no—
80C22×C79⋊C8—21no—
81#14579161C2311yescharacteristic
82#14579161C2311yescharacteristic
83#14579158—21no—
84#14579158—21no—
85#14579158C2×C412yes—
86#14579158C2311yescharacteristic
87#14579158C2311yescharacteristic
88#14579157—22no—
89#14579153—21no—
90#14579150—22no—
91#14579149—21no—
92#14579149—21no—
93#14579149C2×C412yes—
94#14579149C2×C412yes—
95#14579146—22no—
96#14579146—22no—
97#14579146—22no—
98#14579146—22no—
99#14579140—21no—
100#14579140C2×C412yes—
101#14579135—21no—
102#14579135—21no—
103#14579135—21no—
104#14579135—21no—
105#14579135—21no—
106#14579135—21no—
107#14579135C2×C412yes—
108#14579135C2×C412yes—
109#14579134—22no—
110#14579134—22no—
111#14579134—22no—
112#14579134—22no—
113#14579129—22no—
114#14579129—22no—
115C4×Dic158—21no—
116C4×Dic158C2×C412yes—
117C4×D316—21no—
118C4×D316—21no—
119C4×D316—21no—
120C4×D316—21no—
121C4×D316—21no—
122C4×D316—21no—
123C4×D316C2×C412yes—
124C4×D316C2×C412yes—
125#14579123—22no—
126#14579123—22no—
127#14579120—21no—
128C22⋊C4×D79—22no—
129C22⋊C4×D79—22no—
130C4⋊(C79⋊C8)—21no—
131C4⋊(C79⋊C8)—21no—
132C4⋊(C79⋊C8)—21no—
133C4⋊(C79⋊C8)C2311yescharacteristic
134C4⋊(C79⋊C8)C2311yescharacteristic
135C4⋊(C79⋊C8)C2311yescharacteristic
136C4⋊(C79⋊C8)C2311yescharacteristic
137C22⋊(C79⋊C8)—21no—
138C22⋊(C79⋊C8)—21no—
139C22⋊(C79⋊C8)—21no—
140#14579072—21no—
141#14579072—21no—
142C4×C79⋊C8—21no—
143C2×#41×C79D411yescharacteristic
144C2×M16×C79—21no—
145C22×C8×C79—21no—
146C4×Q8×C79C2×C411yescharacteristic
147C4×Q8×C79D411yescharacteristic
148C4×D4×C79C2×C411yescharacteristic
149C4×D4×C79C2×C411yescharacteristic
150C4×D4×C79C2×C411yescharacteristic
151C4×D4×C79D411yescharacteristic
152C4×D4×C79D411yescharacteristic
153C4×D4×C79D411yescharacteristic
154#117×C79D411yescharacteristic
155#117×C79D411yescharacteristic
156#117×C79D411yescharacteristic
157C2×C42×C79C2311yescharacteristic
158C2×C42×C79C2311yescharacteristic
159C2×C42×C79C2311yescharacteristic
160C4⋊C8×C79—21no—
161C4⋊C8×C79—21no—
162C4⋊C8×C79C2311yescharacteristic
163C4⋊C8×C79C2311yescharacteristic
164C4⋊C8×C79C2311yescharacteristic
165C4⋊C8×C79C2311yescharacteristic
166C22⋊C8×C79—21no—
167C22⋊C8×C79—21no—
168C22⋊C8×C79—21no—
169C22⋊C8×C79—21no—
170#97×C79—21no—
171#97×C79—21no—
172C4×C8×C79—21no—
173C4×C8×C79—21no—
174C23×D79—22no—
175#11929624—81no—
176#11929624—81no—
177#11929624—81no—
178#11929624—81no—
179#11929624—82no—
180#11929624—82no—
181C2×Dic158—21no—
182C2×Dic158C22×C412yes—
183C2×D316—22no—
184C2×D316—22no—
185C2×D316—22no—
186C2×D316—21no—
187C2×D316—21no—
188C2×D316—21no—
189C2×D316—21no—
190C2×D316—42no—
191C2×D316—42no—
192C2×D316—81no—
193C2×D316—81no—
194C2×D316—82no—
195C2×D316C22×C412yes—
196C2×D316C22×C412yes—
197C2×C22⋊D79—22no—
198C2×C22⋊D79—22no—
199C2×C22⋊D79—22no—
200C2×C22⋊D79—22no—
201C2×C4×D79—22no—
202C2×C4×D79—22no—
203C2×C4×D79—22no—
204C2×C4×D79—22no—
205#11929608—81no—
206#11929608—81no—
207C2×C79⋊C8—21no—
208C2×C79⋊C8—21no—
209C2×C79⋊C8—21no—
210C2×C79⋊C8—21no—
211C2×C79⋊C8—81no—
212C4⋊Dic79—21no—
213C4⋊Dic79—21no—
214C4⋊Dic79—21no—
215C4⋊Dic79C22×C412yes—
216Dic79⋊C4—22no—
217Dic79⋊C4—22no—
218C22⋊Dic79—22no—
219(C2×D79)⋊C4—22no—
220(C2×D79)⋊C4—22no—
221(C2×D79)⋊C4—22no—
222(C2×D79)⋊C4—22no—
223(C2×D79)⋊C4—22no—
224(C2×D79)⋊C4—22no—
225(C2×D79)⋊C4—22no—
226(C2×D79)⋊C4—22no—
227C4×Dic79—22no—
228#41×C79—41no—
229#41×C79—41no—
230C2×Q8×C79C22⋊C411yescharacteristic
231C2×D4×C79C22⋊C411yescharacteristic
232C2×D4×C79C22⋊C411yescharacteristic
233C2×D4×C79C22⋊C411yescharacteristic
234C22×C4×C79C22×C411yescharacteristic
235C22×C4×C79C22×C411yescharacteristic
236C22×C4×C79C22×C411yescharacteristic
237C22×C4×C79C2×D411yescharacteristic
238C22×C4×C79C2×D411yescharacteristic
239C22×C4×C79C2×D411yescharacteristic
240C22×C4×C79C2×D411yescharacteristic
241C22×C4×C79C2×D411yescharacteristic
242C22×C4×C79C2×D411yescharacteristic
243M16×C79—42no—
244C2×C8×C79—21no—
245C2×C8×C79—21no—
246C2×C8×C79—21no—
247C2×C8×C79—21no—
248C2×C8×C79—42no—
249C4⋊C4×C79C22⋊C411yescharacteristic
250C4⋊C4×C79C22⋊C411yescharacteristic
251C4⋊C4×C79C22⋊C411yescharacteristic
252C4⋊C4×C79C22⋊C411yescharacteristic
253C4⋊C4×C79C22⋊C411yescharacteristic
254C4⋊C4×C79C22⋊C411yescharacteristic
255C22⋊C4×C79C22⋊C411yescharacteristic
256C22⋊C4×C79C22⋊C411yescharacteristic
257C22⋊C4×C79C22⋊C411yescharacteristic
258C22⋊C4×C79C22⋊C411yescharacteristic
259C22⋊C4×C79C22⋊C411yescharacteristic
260C22⋊C4×C79C22⋊C411yescharacteristic
261C42×C79C22×C411yescharacteristic
262C42×C79C22×C411yescharacteristic
263C42×C79C22×C411yescharacteristic
264C42×C79C2×D411yescharacteristic
265C42×C79C2×D411yescharacteristic
266C42×C79C2×D411yescharacteristic
267C42×C79C2×D411yescharacteristic
268C42×C79C2×D411yescharacteristic
269C42×C79C2×D411yescharacteristic
270C42×C79C2411yescharacteristic
271C23×C79C2×C22⋊C411yescharacteristic
272C23×C79C2×C22⋊C411yescharacteristic
273C23×C79C2×C22⋊C411yescharacteristic
274C22×D79—22no—
275C22×D79—22no—
276C22×D79—44no—
277C22×D79—82no—
278C22×D79—82no—
279Q8×C79—41no—
280D4×C79—41no—
281D4×C79—41no—
282D4×C79—41no—
283C2×C4×C79—21no—
284C2×C4×C79—21no—
285C2×C4×C79—21no—
286C2×C4×C79—21no—
287C2×C4×C79—21no—
288C2×C4×C79—21no—
289C2×C4×C79—21no—
290C2×C4×C79—21no—
291C2×C4×C79—21no—
292C2×C4×C79—21no—
293C2×C4×C79—21no—
294C2×C4×C79—21no—
295C2×C4×C79—41no—
296C2×C4×C79—41no—
297C2×C4×C79—41no—
298C2×C4×C79C2×C22⋊C411yescharacteristic
299C2×C4×C79C2×C22⋊C411yescharacteristic
300C2×C4×C79C2×C22⋊C411yescharacteristic
301C2×C4×C79C2×C22⋊C411yescharacteristic
302C2×C4×C79C2×C22⋊C411yescharacteristic
303C2×C4×C79C2×C22⋊C411yescharacteristic
304C2×C4×C79C2×C22⋊C411yescharacteristic
305C2×C4×C79C2×C22⋊C411yescharacteristic
306C2×C4×C79C2×C22⋊C411yescharacteristic
307C2×C4×C79C23×C411yescharacteristic
308C2×C4×C79C22×D411yescharacteristic
309C2×C4×C79C22×D411yescharacteristic
310C22⋊D79—82no—
311C22⋊D79—82no—
312C22⋊D79—82no—
313C22⋊D79—82no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316D316—42no—
317D316—42no—
318D316—44no—
319D316—41no—
320D316—41no—
321D316—41no—
322D316—41no—
323D316—41no—
324D316—41no—
325D316—41no—
326D316—41no—
327D316—82no—
328D316—82no—
329C4×D79—82no—
330C4×D79—82no—
331C4×D79—82no—
332C4×D79—82no—
333Dic158—41no—
334Dic158—41no—
335Dic158—42no—
336C8×C79—41no—
337C8×C79—41no—
338C8×C79—41no—
339C8×C79—41no—
340C79⋊C8—41no—
341C79⋊C8—41no—
342C79⋊C8—41no—
343C79⋊C8—41no—
344C22×C79—21no—
345C22×C79—21no—
346C22×C79—21no—
347C22×C79—21no—
348C22×C79—21no—
349C22×C79—21no—
350C22×C79—21no—
351C22×C79—21no—
352C22×C79—21no—
353C22×C79C22×C22⋊C411yescharacteristic
354C2×D79—42no—
355C2×D79—42no—
356C2×D79—42no—
357C2×D79—42no—
358C2×D79—42no—
359C2×D79—42no—
360C2×D79—164no—
361C4×C79—21no—
362C4×C79—21no—
363C4×C79—21no—
364C4×C79—21no—
365C4×C79—21no—
366C4×C79—21no—
367C4×C79—21no—
368C4×C79—21no—
369C4×C79—21no—
370C4×C79—21no—
371C4×C79#57511yescharacteristic
372C4×C79#57511yescharacteristic
373C4×C79#57611yescharacteristic
374C4×C79#57711yescharacteristic
375Dic79—42no—
376Dic79—42no—
377#17766—791nomaximal, Sylow
378C2×C79—41no—
379C2×C79—41no—
380C2×C79—41no—
381C2×C79#288811yescharacteristic
382C2×C79#289611yescharacteristic
383C2×C79#289711yescharacteristic
384D79—82no—
385D79—82no—
386#3508—791no—
387#2989—791no—
388#2925D7911yescharacteristic, complemented
389#1560—791no—
390#1559—791no—
391#1557—791no—
392#1555—791no—
393#1554—791no—
394#1553—791no—
395#1551—791no—
396#1551—791no—
397#1547—791no—
398#1545—791no—
399#1543—791no—
400#1540—791no—
401C79#1776611yescharacteristic, complemented, Sylow
402#559—792no—
403#559—1581no—
404#550—792no—
405#550—1581no—
406#546—792no—
407#546—792no—
408#546—1581no—
409#546—1581no—
410#540—1581no—
411#540—1581no—
412#535—1581no—
413#533—791no—
414#532—791no—
415#532—791no—
416#532—791no—
417#532—791no—
418C2×#127—791no—
419#518—1581no—
420C4×#41C2×D7911yescharacteristic
421#446—1581no—
422#436—1581no—
423#435—1581no—
424#435—1581no—
425#433—21no—
426#433—21no—
427#432—791no—
428#432—791no—
429#432C2×D7911yescharacteristic
430#432C2×D7911yescharacteristic, complemented
431#431—791no—
432#431C2×D7911yescharacteristic
433#431C2×D7911yescharacteristic, complemented
434#423—791no—
435#423—791no—
436#423C2×D7911yescharacteristic, complemented
437C2×C4⋊C8—791no—
438C2×C4⋊C8C2×D7911yescharacteristic, complemented
439#408—21no—
440#405—21no—
441#333—791no—
442#333—791no—
443#333—791no—
444#333—791no—
445#332—791no—
446#332—791no—
447#332—791no—
448#332—791no—
449#331—791no—
450#331—791no—
451#331—791no—
452#331—791no—
453#331—791no—
454#331—791no—
455#331—791no—
456#331—791no—
457C2×#41—792no—
458C2×#41—792no—
459C2×#41—1581no—
460C2×#41—1581no—
461C2×#41C22⋊D7911yescharacteristic
462C22×D4—792no—
463C22×D4—1581no—
464C22×D4—1581no—
465C2×M16—21no—
466C2×M16—1581no—
467C2×M16—1581no—
468C22×C8—21no—
469C22×C8—1581no—
470C4⋊Q8—791no—
471C4⋊Q8—791no—
472#127—792no—
473#127—791no—
474#127—791no—
475#127—1582no—
476#127—1581no—
477#127—1581no—
478#125—1581no—
479#124—792no—
480#124—792no—
481#124—1582no—
482#124—1581no—
483#124—1581no—
484#123—1582no—
485#123—1582no—
486#123—1582no—
487#123—1582no—
488C22⋊Q8—792no—
489C22⋊Q8—1581no—
490#121—792no—
491#121—792no—
492#121—1581no—
493#121—1581no—
494#121—1581no—
495#121—1581no—
496#121—1581no—
497#121—1581no—
498#121—1582no—
499#121—1582no—
500#121—1582no—
501#121—1582no—
502#120—1582no—
503#120—1582no—
504C4×Q8—792no—
505C4×Q8—1581no—
506C4×Q8C4×D7911yescharacteristic
507C4×Q8D31611yescharacteristic
508C4×D4—792no—
509C4×D4—792no—
510C4×D4—1582no—
511C4×D4—1582no—
512C4×D4—1581no—
513C4×D4—1581no—
514C4×D4—1581no—
515C4×D4—1581no—
516C4×D4—1581no—
517C4×D4—1581no—
518C4×D4C4×D7911yescharacteristic
519C4×D4C4×D7911yescharacteristic
520C4×D4C4×D7911yescharacteristic
521C4×D4D31611yescharacteristic
522C4×D4D31611yescharacteristic
523C4×D4D31611yescharacteristic
524#117—1581no—
525#117C22⋊D7911yescharacteristic
526#117C22⋊D7911yescharacteristic
527#117C22⋊D7911yescharacteristic
528C2×C22⋊C4—1582no—
529C2×C22⋊C4—1582no—
530C2×C42C22×D7911yescharacteristic
531C2×C42C22×D7911yescharacteristic
532C2×C42C22×D7911yescharacteristic
533C4⋊C8—21no—
534C4⋊C8—21no—
535C4⋊C8—791no—
536C4⋊C8—791no—
537C4⋊C8—791no—
538C4⋊C8—791no—
539C4⋊C8—1581no—
540C4⋊C8—1581no—
541C4⋊C8—1581no—
542C4⋊C8C22×D7911yescharacteristic
543C4⋊C8C22×D7911yescharacteristic
544C4⋊C8C22×D7911yescharacteristic
545C4⋊C8C22×D7911yescharacteristic
546C22⋊C8—21no—
547C22⋊C8—21no—
548C22⋊C8—21no—
549C22⋊C8—21no—
550C22⋊C8—1581no—
551C22⋊C8—1581no—
552C22⋊C8—1581no—
553#97—21no—
554#97—21no—
555#97—1581no—
556#97—1581no—
557C4×C8—21no—
558C4×C8—21no—
559C4×C8—1581no—
560C24—1582no—
561#41—41no—
562#41—41no—
563#41—6321no—
564#41—6321no—
565#41—6321no—
566#41—6321no—
567#41—6322no—
568#41—6322no—
569C2×Q8—792no—
570C2×Q8—1581no—
571C2×Q8(C2×D79)⋊C411yescharacteristic
572C2×D4—3162no—
573C2×D4—3162no—
574C2×D4—792no—
575C2×D4—792no—
576C2×D4—6321no—
577C2×D4—6321no—
578C2×D4—6322no—
579C2×D4—1582no—
580C2×D4—1582no—
581C2×D4—1582no—
582C2×D4—1582no—
583C2×D4—1582no—
584C2×D4—1582no—
585C2×D4—1582no—
586C2×D4—1581no—
587C2×D4—1581no—
588C2×D4—1581no—
589C2×D4—1581no—
590C2×D4(C2×D79)⋊C411yescharacteristic
591C2×D4(C2×D79)⋊C411yescharacteristic
592C2×D4(C2×D79)⋊C411yescharacteristic
593C22×C4—1582no—
594C22×C4—1582no—
595C22×C4—1582no—
596C22×C4—1582no—
597C22×C4C2×C4×D7911yescharacteristic
598C22×C4C2×C4×D7911yescharacteristic
599C22×C4C2×C4×D7911yescharacteristic
600C22×C4C2×C22⋊D7911yescharacteristic
601C22×C4C2×C22⋊D7911yescharacteristic
602C22×C4C2×C22⋊D7911yescharacteristic
603C22×C4C2×D31611yescharacteristic
604C22×C4C2×D31611yescharacteristic
605C22×C4C2×D31611yescharacteristic
606M16—42no—
607M16—6321no—
608M16—6321no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—42no—
614C2×C8—6321no—
615C2×C8—1581no—
616C2×C8—1581no—
617C2×C8—1581no—
618C2×C8—1581no—
619C4⋊C4—792no—
620C4⋊C4—1582no—
621C4⋊C4—1582no—
622C4⋊C4—1581no—
623C4⋊C4—1581no—
624C4⋊C4—1581no—
625C4⋊C4(C2×D79)⋊C411yescharacteristic
626C4⋊C4(C2×D79)⋊C411yescharacteristic
627C4⋊C4(C2×D79)⋊C411yescharacteristic
628C4⋊C4(C2×D79)⋊C411yescharacteristic
629C4⋊C4(C2×D79)⋊C411yescharacteristic
630C4⋊C4(C2×D79)⋊C411yescharacteristic
631C22⋊C4—1582no—
632C22⋊C4—1582no—
633C22⋊C4—1582no—
634C22⋊C4—1582no—
635C22⋊C4—1582no—
636C22⋊C4—1582no—
637C22⋊C4—1582no—
638C22⋊C4—1582no—
639C22⋊C4—1582no—
640C22⋊C4(C2×D79)⋊C411yescharacteristic
641C22⋊C4(C2×D79)⋊C411yescharacteristic
642C22⋊C4(C2×D79)⋊C411yescharacteristic
643C22⋊C4(C2×D79)⋊C411yescharacteristic
644C22⋊C4(C2×D79)⋊C411yescharacteristic
645C22⋊C4(C2×D79)⋊C411yescharacteristic
646C42—1582no—
647C42C2×C4×D7911yescharacteristic
648C42C2×C4×D7911yescharacteristic
649C42C2×C4×D7911yescharacteristic
650C42C2×C22⋊D7911yescharacteristic
651C42C2×C22⋊D7911yescharacteristic
652C42C2×C22⋊D7911yescharacteristic
653C42C2×D31611yescharacteristic
654C42C2×D31611yescharacteristic
655C42C2×D31611yescharacteristic
656C42C23×D7911yescharacteristic
657C23—3164no—
658C23—6322no—
659C23—6322no—
660C23—1582no—
661C23—1582no—
662C23C2×(C2×D79)⋊C411yescharacteristic
663C23C2×(C2×D79)⋊C411yescharacteristic
664C23C2×(C2×D79)⋊C411yescharacteristic
665Q8—41no—
666Q8—3162no—
667Q8—3161no—
668Q8—3161no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—3162no—
673D4—3162no—
674D4—3164no—
675D4—3161no—
676D4—3161no—
677D4—3161no—
678D4—3161no—
679D4—3161no—
680D4—3161no—
681D4—3161no—
682D4—3161no—
683D4—6322no—
684D4—6322no—
685D4—6322no—
686D4—6322no—
687D4—6322no—
688D4—6322no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—6322no—
705C2×C4—6322no—
706C2×C4—6322no—
707C2×C4—6322no—
708C2×C4—1582no—
709C2×C4—1582no—
710C2×C4C2×(C2×D79)⋊C411yescharacteristic
711C2×C4C2×(C2×D79)⋊C411yescharacteristic
712C2×C4C2×(C2×D79)⋊C411yescharacteristic
713C2×C4C2×(C2×D79)⋊C411yescharacteristic
714C2×C4C2×(C2×D79)⋊C411yescharacteristic
715C2×C4C2×(C2×D79)⋊C411yescharacteristic
716C2×C4C2×(C2×D79)⋊C411yescharacteristic
717C2×C4C2×(C2×D79)⋊C411yescharacteristic
718C2×C4C2×(C2×D79)⋊C411yescharacteristic
719C2×C4C22×C4×D7911yescharacteristic
720C2×C4C22×C22⋊D7911yescharacteristic
721C2×C4C22×D31611yescharacteristic
722C8—41no—
723C8—41no—
724C8—41no—
725C8—41no—
726C8—3161no—
727C8—3161no—
728C8—3161no—
729C8—3161no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—3162no—
740C22—3162no—
741C22—3162no—
742C22—3162no—
743C22—3162no—
744C22—3162no—
745C22—12644no—
746C22C22×(C2×D79)⋊C411yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—3162no—
758C4—3162no—
759C4#1909936111yescharacteristic
760C4#1909936111yescharacteristic
761C4#1909936811yescharacteristic
762C4#1909937511yescharacteristic
763C2—41no—
764C2—41no—
765C2—41no—
766C2—6322no—
767C2—6322no—
768C2#2377187811yescharacteristic
769C2#2377191711yescharacteristic
770C2#2377192711yescharacteristic
subgroupG/H
centerC22C22×(C2×D79)⋊C4
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#2925C2
socleC22×C79C22×C22⋊C4
prime radical#23777276C2
cosocleC42×C79C24
hypercenter#2925D79
hypocenterC79#17766
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #23772517C2semidirect
3. #23762133C2semidirect
4. #23762131C2semidirect
5. #23762120C2semidirect
6. #23762113C2semidirect
7. #23762108C2semidirect
8. #23762106C2semidirect
9. #23762096C2semidirect
10. #23762093C2semidirect
11. #23762075C2semidirect
12. #23762067C2semidirect
13. #23762060C2semidirect
14. #23762047C2semidirect
15. C79×#2925C2semidirect
39. #19098620C22semidirect
40. #19098616C22semidirect
42. #19098587C22semidirect
43. C2×C4⋊(C79⋊C8)C22semidirect
44. #19098311C22semidirect
45. #19098311C22semidirect
46. #19098311C22semidirect
47. #19098311C22semidirect
48. #19098308C22semidirect
49. #19098308C22semidirect
50. #19098308C22semidirect
51. #19098308C22semidirect
64. #432×C79C22semidirect
66. #431×C79C22semidirect
67. #423×C79C22semidirect
68. C2×C4⋊C8×C79C22semidirect
388. #2925D79semidirect
401. C79#17766semidirect
430. #432C2×D79semidirect
433. #431C2×D79semidirect
436. #423C2×D79semidirect
438. C2×C4⋊C8C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237772762
#237725172
#237621332
#237621312
#237621202
#237621132
#237621082
#237621062
#237620962
#237620932
#237620752
#237620672
#237620602
#237620472
C79×#29252
#1776679