Finite Group Databasebeta

← #34299565

Subgroups — #34299565

Order 20224.

1024 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098708C211yesmaximal, characteristic
2#23766093C211yesmaximal, characteristic, complemented
3#23764275C211yesmaximal, characteristic, complemented
4#23764257C211yesmaximal, characteristic, complemented
5#23764093C211yesmaximal, characteristic, complemented
6#23764086C211yesmaximal, characteristic, complemented
7#23764031C211yesmaximal, characteristic, complemented
8#23764024C211yesmaximal, characteristic, complemented
9#23763751C211yesmaximal, characteristic, complemented
10#23763737C211yesmaximal, characteristic, complemented
11#23763717C211yesmaximal, characteristic, complemented
12#23763593C211yesmaximal, characteristic, complemented
13#23763340C211yesmaximal, characteristic, complemented
14#23763166C211yesmaximal, characteristic, complemented
15C79×#2311C211yesmaximal, characteristic, complemented
16C22×#11929611C2211yescharacteristic
17C22×#11929609C2211yescharacteristic
18C2×#14579135C2211yescharacteristic
19C2×C4×D316C2211yescharacteristic
20#19098708C418yescomplemented
21C2×#14579092C2211yescharacteristic
22C2×#14579092C2211yescharacteristic
23C2×#14579085C2211yescharacteristic
24C2×#14579085C2211yescharacteristic
25C2×#14579085C2211yescharacteristic
26C2×#14579082C2211yescharacteristic
27C2×#14579082C2211yescharacteristic
28C2×#14579082C2211yescharacteristic
29C2×#14579081C2211yescharacteristic
30C2×#14579081C2211yescharacteristic
31C2×C22⋊(C79⋊C8)C2211yescharacteristic
32C2×C22⋊(C79⋊C8)C2211yescharacteristic
33C2×#14579072C2211yescharacteristic
34C2×C4×C79⋊C8C2211yescharacteristic
35#19098465C2211yescharacteristic
36#19098463—21no—
37#19098461C2211yescharacteristic
38#19098453—21no—
39#19098439—21no—
40#19098434—21no—
41#19098423C2211yescharacteristic
42C4×C4⋊Dic79C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098318C2211yescharacteristic
48#19098318C2211yescharacteristic
49C22×#41×C79C2211yescharacteristic
50C2×#117×C79C2211yescharacteristic
51C22×C4⋊C4×C79C2211yescharacteristic
52#391×C79C2211yescharacteristic
53#391×C79C2211yescharacteristic
54#390×C79C2211yescharacteristic
55#390×C79C2211yescharacteristic
56#386×C79—21no—
57#386×C79—21no—
58#380×C79—21no—
59#380×C79—21no—
60C22×D316C2311yescharacteristic
61C22×C22⋊D79—21no—
62C22×C4×D79—21no—
63C2×#11929611—41no—
64C2×#11929611—41no—
65C2×#11929611C2×C414yescomplemented
66C2×#11929609—41no—
67C2×#11929609—41no—
68C2×#11929609C2×C414yescomplemented
69C22×C79⋊C8C2311yescharacteristic
70C22×C79⋊C8C2311yescharacteristic
71C22×C79⋊C8C2311yescharacteristic
72C22×C79⋊C8C2311yescharacteristic
73#14579135—22no—
74#14579135C2×C414yes—
75C4×D316—41no—
76C4×D316—41no—
77C2×C4⋊Dic79C2311yescharacteristic
78C2×C4⋊Dic79C2311yescharacteristic
79C2×C4⋊Dic79C2311yescharacteristic
80C2×Dic79⋊C4—21no—
81C2×C22⋊Dic79—21no—
82C2×(C2×D79)⋊C4—21no—
83C2×(C2×D79)⋊C4—21no—
84C2×(C2×D79)⋊C4—21no—
85C2×(C2×D79)⋊C4—21no—
86C2×C4×Dic79—21no—
87#14579092—41no—
88#14579092—41no—
89#14579085—41no—
90#14579085—41no—
91#14579085C2×C414yescomplemented
92#14579082—41no—
93#14579082—41no—
94#14579082C2×C414yescomplemented
95#14579081—41no—
96#14579081—41no—
97C22⋊(C79⋊C8)—22no—
98C22⋊(C79⋊C8)C2×C414yescomplemented
99#14579072—41no—
100C4×C79⋊C8—41no—
101C79⋊#95—21no—
102C79⋊#95—21no—
103C79⋊#95—21no—
104C2×#41×C79—22no—
105C2×#41×C79—41no—
106C2×#41×C79—41no—
107C2×#41×C79—41no—
108C2×#41×C79—41no—
109C2×#41×C79C2×C414yescomplemented
110C22×Q8×C79C2311yescharacteristic
111C22×D4×C79—21no—
112C22×D4×C79C2311yescharacteristic
113C23×C4×C79—21no—
114C23×C4×C79—21no—
115C23×C4×C79C2311yescharacteristic
116#117×C79—41no—
117#117×C79—41no—
118C2×C4⋊C4×C79—21no—
119C2×C4⋊C4×C79—41no—
120C2×C4⋊C4×C79—41no—
121C2×C4⋊C4×C79D411yescharacteristic
122C2×C4⋊C4×C79D411yescharacteristic
123C2×C4⋊C4×C79C2311yescharacteristic
124C2×C4⋊C4×C79C2311yescharacteristic
125C2×C22⋊C4×C79—21no—
126C2×C22⋊C4×C79—21no—
127C2×C22⋊C4×C79—21no—
128C2×C22⋊C4×C79—21no—
129C2×C22⋊C4×C79D411yescharacteristic
130C2×C22⋊C4×C79D411yescharacteristic
131C2×C42×C79C2311yescharacteristic
132C2×C42×C79C2311yescharacteristic
133#95×C79—21no—
134#95×C79—21no—
135#95×C79—21no—
136#95×C79—21no—
137C23×D79—21no—
138C2×D316—21no—
139C2×D316—21no—
140C2×D316—21no—
141C2×D316—21no—
142C2×D316—21no—
143C2×D316C22×C412yes—
144C2×C22⋊D79—24no—
145C2×C22⋊D79—81no—
146C2×C22⋊D79—81no—
147C22×Dic79—21no—
148C22×Dic79—21no—
149C22×Dic79—21no—
150C2×C4×D79—42no—
151C2×C4×D79—81no—
152C2×C4×D79—81no—
153#11929611—44no—
154#11929609—44no—
155C2×C79⋊C8—21no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8—21no—
158C2×C79⋊C8—21no—
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⋊C8C22×C412yes—
166C2×C79⋊C8C22×C412yes—
167C4⋊Dic79—21no—
168C4⋊Dic79—21no—
169C4⋊Dic79—21no—
170C4⋊Dic79—21no—
171C4⋊Dic79—21no—
172C4⋊Dic79C22×C412yes—
173Dic79⋊C4—81no—
174C22⋊Dic79—81no—
175(C2×D79)⋊C4—24no—
176(C2×D79)⋊C4—42no—
177(C2×D79)⋊C4—81no—
178(C2×D79)⋊C4—81no—
179C4×Dic79—81no—
180C24×C79—21no—
181C24×C79C2×D411yescharacteristic
182#41×C79—44no—
183#41×C79—44no—
184#41×C79—44no—
185#41×C79—44no—
186C2×Q8×C79—21no—
187C2×Q8×C79—21no—
188C2×Q8×C79—21no—
189C2×Q8×C79—21no—
190C2×Q8×C79—21no—
191C2×Q8×C79C22×C412yes—
192C2×D4×C79—24no—
193C2×D4×C79—21no—
194C2×D4×C79—21no—
195C2×D4×C79—21no—
196C2×D4×C79—21no—
197C2×D4×C79—21no—
198C2×D4×C79—42no—
199C2×D4×C79—42no—
200C2×D4×C79C22×C412yes—
201C22×C4×C79—21no—
202C22×C4×C79—21no—
203C22×C4×C79—21no—
204C22×C4×C79—21no—
205C22×C4×C79—21no—
206C22×C4×C79—24no—
207C22×C4×C79—21no—
208C22×C4×C79—21no—
209C22×C4×C79—42no—
210C22×C4×C79—42no—
211C22×C4×C79—42no—
212C22×C4×C79—81no—
213C22×C4×C79—81no—
214C22×C4×C79C22×C412yes—
215C22×C4×C79C2×D411yescharacteristic
216C22×C4×C79C2×D411yescharacteristic
217C22×C4×C79C2×D411yescharacteristic
218C22×C4×C79C2×D411yescharacteristic
219C22×C4×C79C2×D411yescharacteristic
220C22×C4×C79#4112yes—
221C22×C4×C79C2411yescharacteristic
222C4⋊C4×C79—21no—
223C4⋊C4×C79—21no—
224C4⋊C4×C79—21no—
225C4⋊C4×C79—21no—
226C4⋊C4×C79—41no—
227C4⋊C4×C79—41no—
228C4⋊C4×C79—42no—
229C22⋊C4×C79—41no—
230C22⋊C4×C79—41no—
231C22⋊C4×C79—81no—
232C22⋊C4×C79—81no—
233C22⋊C4×C79—81no—
234C22⋊C4×C79—81no—
235C42×C79—21no—
236C42×C79—21no—
237C42×C79—21no—
238C42×C79—21no—
239C23×C79—21no—
240C23×C79—21no—
241C23×C79—21no—
242C23×C79—21no—
243C23×C79—21no—
244C23×C79—21no—
245C23×C79—22no—
246C23×C79—41no—
247C23×C79—41no—
248C23×C79—41no—
249C23×C79—41no—
250C23×C79—41no—
251C23×C79—41no—
252C23×C79C4×D412yes—
253C23×C79C22×D411yescharacteristic
254C22×D79—22no—
255C22×D79—41no—
256C22×D79—41no—
257C22×D79—41no—
258C22×D79—41no—
259C22×D79—41no—
260C22×D79—41no—
261Q8×C79—22no—
262Q8×C79—22no—
263Q8×C79—41no—
264Q8×C79—41no—
265D4×C79—22no—
266D4×C79—22no—
267D4×C79—48no—
268D4×C79—41no—
269D4×C79—41no—
270C2×C4×C79—21no—
271C2×C4×C79—21no—
272C2×C4×C79—22no—
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—21no—
287C2×C4×C79—21no—
288C2×C4×C79—21no—
289C2×C4×C79—48no—
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—41no—
298C2×C4×C79—84no—
299C2×C4×C79C4×D412yes—
300C2×C4×C79C23×C411yescharacteristic
301C2×C4×C79C2×#4111yescharacteristic
302C2×C4×C79H(5,𝔽2)11yescharacteristic
303C2×C4×C79H(5,𝔽2)11yescharacteristic
304C2×C4×C79H(5,𝔽2)11yescharacteristic
305C2×C4×C79H(5,𝔽2)11yescharacteristic
306C22⋊D79—84no—
307C2×Dic79—22no—
308C2×Dic79—41no—
309C2×Dic79—41no—
310C2×Dic79—41no—
311C2×Dic79—41no—
312C2×Dic79—41no—
313C2×Dic79—41no—
314C2×Dic79—41no—
315C2×Dic79—41no—
316D316—22no—
317D316—22no—
318D316—41no—
319D316—41no—
320C4×D79—84no—
321C79⋊C8—22no—
322C79⋊C8—22no—
323C79⋊C8—41no—
324C79⋊C8—41no—
325C22×C79—22no—
326C22×C79—22no—
327C22×C79—22no—
328C22×C79—41no—
329C22×C79—41no—
330C22×C79—41no—
331C22×C79—41no—
332C22×C79—42no—
333C22×C79—42no—
334C22×C79—42no—
335C22×C79—81no—
336C22×C79—81no—
337C22×C79—81no—
338C22×C79—81no—
339C22×C79C2×C4×D411yescharacteristic
340C22×C79#53411yescharacteristic
341C22×C79#53511yescharacteristic
342C22×C79#57611yescharacteristic
343C22×C79#57711yescharacteristic
344C22×C79#57711yescharacteristic
345C22×C79#57711yescharacteristic
346C2×D79—42no—
347C2×D79—42no—
348C2×D79—42no—
349C2×D79—81no—
350C2×D79—81no—
351C2×D79—81no—
352C2×D79—81no—
353C4×C79—22no—
354C4×C79—42no—
355C4×C79—41no—
356C4×C79—41no—
357C4×C79—41no—
358C4×C79—41no—
359C4×C79—81no—
360C4×C79—81no—
361C4×C79#51811yescharacteristic
362C4×C79#51811yescharacteristic
363C4×C79#53811yescharacteristic
364C4×C79#53811yescharacteristic
365Dic79—42no—
366Dic79—81no—
367Dic79—81no—
368#22053—791nomaximal, Sylow
369C2×C79—42no—
370C2×C79—82no—
371C2×C79#232111yescharacteristic
372C2×C79#294611yescharacteristic
373C2×C79#295211yescharacteristic
374C2×C79#319811yescharacteristic
375C2×C79#320411yescharacteristic
376C2×C79#322111yescharacteristic
377C2×C79#322411yescharacteristic
378D79—82no—
379C2×#449—791no—
380#2324—791no—
381#2311D7911yescharacteristic, complemented
382#1972—791no—
383#1968—791no—
384#1935—791no—
385#1934—791no—
386#1927—791no—
387#1926—791no—
388#1879—791no—
389#1877—791no—
390#1874—791no—
391#1853—791no—
392#1788—791no—
393#1750—791no—
394C79#2205311yescharacteristic, complemented, Sylow
395C22×#41C2×D7911yescharacteristic
396C22×SD16—791no—
397C22×D8—791no—
398C2×#121—791no—
399C2×C4×D4—791no—
400C2×#117C2×D7911yescharacteristic
401C22×C4⋊C4C2×D7911yescharacteristic
402#449—798no—
403C2×#106—791no—
404C2×#106—791no—
405C2×#103—791no—
406C2×#103—791no—
407C2×#103—791no—
408C2×#102—791no—
409C2×#102—791no—
410C2×#102—791no—
411C2×#102—791no—
412C2×#102—791no—
413C2×C22⋊C8—791no—
414C2×C22⋊C8—791no—
415C2×#97—791no—
416C2×C4×C8—791no—
417#391C2×D7911yescharacteristic
418#391C2×D7911yescharacteristic
419#390—791no—
420#390—1581no—
421#390C2×D7911yescharacteristic
422#390C2×D7911yescharacteristic
423#389—791no—
424#388—1581no—
425#386—21no—
426#386—21no—
427#386—1581no—
428#385—1581no—
429#380—21no—
430#380—21no—
431#380—791no—
432C4×C4⋊C4—791no—
433#340—791no—
434#340—791no—
435#340—791no—
436#340—791no—
437#336—791no—
438#336—791no—
439C2×#41—22no—
440C2×#41—41no—
441C2×#41—41no—
442C2×#41—41no—
443C2×#41—41no—
444C2×#41C4×D7914yescomplemented
445C22×Q8C22×D7911yescharacteristic
446C22×D4—21no—
447C22×D4—791no—
448C22×D4—1581no—
449C22×D4C22×D7911yescharacteristic
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—1581no—
453C23×C4C22×D7911yescharacteristic
454C2×SD16—3161no—
455C2×SD16—3161no—
456C2×SD16—794no—
457C2×D8—3161no—
458C2×D8—3161no—
459C2×D8—794no—
460C22×C8—791no—
461C22×C8—791no—
462C22×C8—791no—
463C22×C8—791no—
464#121—794no—
465#121—1582no—
466C4×D4—3161no—
467C4×D4—3161no—
468#117—41no—
469#117—41no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—41no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4—791no—
474C2×C4⋊C4—791no—
475C2×C4⋊C4—791no—
476C2×C4⋊C4—1581no—
477C2×C4⋊C4C22⋊D7911yescharacteristic
478C2×C4⋊C4C22⋊D7911yescharacteristic
479C2×C4⋊C4C22×D7911yescharacteristic
480C2×C4⋊C4C22×D7911yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1581no—
486C2×C22⋊C4—1581no—
487C2×C22⋊C4—1581no—
488C2×C22⋊C4—1581no—
489C2×C22⋊C4—1581no—
490C2×C22⋊C4C22⋊D7911yescharacteristic
491C2×C22⋊C4C22⋊D7911yescharacteristic
492C2×C42—1581no—
493C2×C42C22×D7911yescharacteristic
494C2×C42C22×D7911yescharacteristic
495#106—3161no—
496#106—3161no—
497#103—3161no—
498#103—3161no—
499#103—794no—
500#102—3161no—
501#102—3161no—
502#102—3161no—
503#102—3161no—
504#102—794no—
505C22⋊C8—794no—
506C22⋊C8—1582no—
507#97—3161no—
508C4×C8—3161no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—1581no—
514#95—1581no—
515#95—1581no—
516C24—21no—
517C24—1581no—
518C24C2×C22⋊D7911yescharacteristic
519#41—44no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C2×C4×D7912yes—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—792no—
538C2×D4—6321no—
539C2×D4—6321no—
540C2×D4—1584no—
541C2×D4—1581no—
542C2×D4—1581no—
543C2×D4—1581no—
544C2×D4—1581no—
545C2×D4—1581no—
546C2×D4C2×C4×D7912yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4—3162no—
561C22×C4—6321no—
562C22×C4—6321no—
563C22×C4—1581no—
564C22×C4—1581no—
565C22×C4—1581no—
566C22×C4C2×C4×D7912yes—
567C22×C4C2×C22⋊D7911yescharacteristic
568C22×C4C2×C22⋊D7911yescharacteristic
569C22×C4C2×C22⋊D7911yescharacteristic
570C22×C4C2×C22⋊D7911yescharacteristic
571C22×C4C2×C22⋊D7911yescharacteristic
572C22×C4#1192962412yes—
573C22×C4C23×D7911yescharacteristic
574SD16—3164no—
575D8—3164no—
576C2×C8—792no—
577C2×C8—792no—
578C2×C8—1581no—
579C2×C8—1581no—
580C2×C8—1581no—
581C2×C8—1581no—
582C2×C8—1581no—
583C2×C8—1581no—
584C2×C8—1581no—
585C2×C8—1581no—
586C2×C8—1581no—
587C2×C8—1581no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—42no—
595C4⋊C4—792no—
596C4⋊C4—6321no—
597C4⋊C4—1581no—
598C4⋊C4—1581no—
599C4⋊C4—1581no—
600C4⋊C4—1581no—
601C4⋊C4—1581no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—3162no—
609C22⋊C4—6321no—
610C22⋊C4—6321no—
611C22⋊C4—6321no—
612C22⋊C4—1584no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—6321no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—3161no—
632C23—3161no—
633C23—3161no—
634C23—3161no—
635C23—3161no—
636C23—3161no—
637C23—1582no—
638C23C4×C22⋊D7912yes—
639C23C22×C22⋊D7911yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644D4—22no—
645D4—22no—
646D4—48no—
647D4—41no—
648D4—41no—
649D4—3161no—
650D4—3161no—
651D4—6324no—
652D4—1582no—
653D4—1582no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
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—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—48no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—84no—
683C2×C4—3161no—
684C2×C4—3161no—
685C2×C4—3161no—
686C2×C4—3161no—
687C2×C4—3161no—
688C2×C4—3161no—
689C2×C4—3161no—
690C2×C4—3161no—
691C2×C4—6324no—
692C2×C4—1582no—
693C2×C4C4×C22⋊D7912yes—
694C2×C4C22×C4×D7911yescharacteristic
695C2×C4C2×#1192962411yescharacteristic
696C2×C4#1457920611yescharacteristic
697C2×C4#1457920611yescharacteristic
698C2×C4#1457920611yescharacteristic
699C2×C4#1457920611yescharacteristic
700C8—3161no—
701C8—3161no—
702C8—1582no—
703C8—1582no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—3162no—
719C22—3162no—
720C22—3162no—
721C22—6321no—
722C22—6321no—
723C22—6321no—
724C22—6321no—
725C22C2×C4×C22⋊D7911yescharacteristic
726C22#1909912211yescharacteristic
727C22#1909913011yescharacteristic
728C22#1909936611yescharacteristic
729C22#1909937111yescharacteristic
730C22#1909937111yescharacteristic
731C22#1909937411yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—41no—
738C4—81no—
739C4—81no—
740C4—3162no—
741C4—6321no—
742C4—6321no—
743C4#1909903611yescharacteristic
744C4#1909903611yescharacteristic
745C4#1909915111yescharacteristic
746C4#1909915111yescharacteristic
747C2—42no—
748C2—82no—
749C2—6322no—
750C2#2376605811yescharacteristic
751C2#2377222811yescharacteristic
752C2#2377228111yescharacteristic
753C2#2377424611yescharacteristic
754C2#2377430611yescharacteristic
755C2#2377446111yescharacteristic
756C2#2377449411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2311C2
socleC23×C79C22×D4
prime radicalC2×#19098708C2
cosocleC22×C4×C79C24
hypercenter#2311D79
hypocenterC79#22053
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #23766093C2semidirect
3. #23764275C2semidirect
4. #23764257C2semidirect
5. #23764093C2semidirect
6. #23764086C2semidirect
7. #23764031C2semidirect
8. #23764024C2semidirect
9. #23763751C2semidirect
10. #23763737C2semidirect
11. #23763717C2semidirect
12. #23763593C2semidirect
13. #23763340C2semidirect
14. #23763166C2semidirect
15. C79×#2311C2semidirect
20. #19098708C4semidirect
65. C2×#11929611C2×C4semidirect
68. C2×#11929609C2×C4semidirect
91. #14579085C2×C4semidirect
94. #14579082C2×C4semidirect
98. C22⋊(C79⋊C8)C2×C4semidirect
109. C2×#41×C79C2×C4semidirect
381. #2311D79semidirect
394. C79#22053semidirect
444. C2×#41C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190987082
#237660932
#237642752
#237642572
#237640932
#237640862
#237640312
#237640242
#237637512
#237637372
#237637172
#237635932
#237633402
#237631662
C79×#23112
#2205379