Finite Group Databasebeta

← #34308567

Subgroups — #34308567

Order 20224.

1146 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×#19098708C211yesmaximal, characteristic
2C2×#19098661C211yesmaximal, characteristic, complemented
3C2×#19098559C211yesmaximal, characteristic, complemented
4#23766436C211yesmaximal, characteristic, complemented
5#23764275C211yesmaximal, characteristic, complemented
6#23764100C211yesmaximal, characteristic, complemented
7#23764017C211yesmaximal, characteristic, complemented
8#23763826C211yesmaximal, characteristic, complemented
9#23763755C211yesmaximal, characteristic, complemented
10#23763751C211yesmaximal, characteristic, complemented
11#23763668C211yesmaximal, characteristic, complemented
12#23763597C211yesmaximal, characteristic, complemented
13#23763230C211yesmaximal, characteristic, complemented
14#23763178C211yesmaximal, characteristic, complemented
15C79×#2341C211yesmaximal, characteristic, complemented
16C22×#11929611C2211yescharacteristic
17C22×#11929609C2211yescharacteristic
18C23×C79⋊C8C2211yescharacteristic
19C2×#14579135C2211yescharacteristic
20C2×C4×D316C2211yescharacteristic
21C2×#14579120C2211yescharacteristic
22#19098708C418yescomplemented
23#19098661—24no—
24C2×#14579094C2211yescharacteristic
25C2×#14579092C2211yescharacteristic
26#19098559—24no—
27C2×#14579085C2211yescharacteristic
28C2×#14579085C2211yescharacteristic
29C2×#14579085C2211yescharacteristic
30C2×#14579082C2211yescharacteristic
31C2×#14579082C2211yescharacteristic
32C2×#14579082C2211yescharacteristic
33C2×#14579081C2211yescharacteristic
34C2×#14579081C2211yescharacteristic
35C2×C22⋊(C79⋊C8)C2211yescharacteristic
36C2×#14579072C2211yescharacteristic
37C2×#14579072C2211yescharacteristic
38#19098465C2211yescharacteristic
39#19098463—21no—
40#19098461C2211yescharacteristic
41#19098452—21no—
42#19098439—21no—
43C4×C4⋊Dic79C2211yescharacteristic
44#19098410—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×D316C2311yescharacteristic
63C22×C22⋊D79—21no—
64C22×C4×D79—21no—
65C2×#11929611—22no—
66C2×#11929611—22no—
67C2×#11929611C2×C414yes—
68C2×#11929609—41no—
69C2×#11929609—41no—
70C2×#11929609C2×C414yes—
71C22×C79⋊C8—22no—
72C22×C79⋊C8—22no—
73C22×C79⋊C8—41no—
74C22×C79⋊C8C2311yescharacteristic
75C22×C79⋊C8C2311yescharacteristic
76C22×C79⋊C8C2311yescharacteristic
77C22×C79⋊C8C2311yescharacteristic
78#14579135—22no—
79#14579135C2×C414yes—
80C4×D316—22no—
81C4×D316—41no—
82#14579120—22no—
83#14579120—41no—
84C2×C4⋊Dic79C2311yescharacteristic
85C2×C4⋊Dic79C2311yescharacteristic
86C2×C4⋊Dic79C2311yescharacteristic
87C2×Dic79⋊C4—21no—
88C2×C22⋊Dic79—21no—
89C2×(C2×D79)⋊C4—21no—
90C2×(C2×D79)⋊C4—21no—
91C2×(C2×D79)⋊C4—21no—
92C2×(C2×D79)⋊C4—21no—
93C2×C4×Dic79—21no—
94C2×C4×Dic79—21no—
95#14579094—22no—
96#14579092—41no—
97#14579085—22no—
98#14579085C2×C414yescomplemented
99#14579085D414yescomplemented
100#14579082—22no—
101#14579082—22no—
102#14579082C2×C414yescomplemented
103#14579081—22no—
104#14579081—41no—
105C22⋊(C79⋊C8)C2×C414yescomplemented
106#14579072—22no—
107#14579072—41no—
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×C414yescomplemented
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
143C23×D79—21no—
144C2×D316—21no—
145C2×D316—21no—
146C2×D316—21no—
147C2×D316—21no—
148C2×D316—21no—
149C2×D316C22×C412yes—
150C2×C22⋊D79—24no—
151C2×C22⋊D79—81no—
152C2×C22⋊D79—81no—
153C22×Dic79—21no—
154C22×Dic79—21no—
155C22×Dic79—21no—
156C2×C4×D79—42no—
157C2×C4×D79—42no—
158C2×C4×D79—81no—
159#11929611—28no—
160#11929609—44no—
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⋊C8—21no—
169C2×C79⋊C8—21no—
170C2×C79⋊C8—44no—
171C2×C79⋊C8C22×C412yes—
172C2×C79⋊C8C22×C412yes—
173C2×C79⋊C8C2×D412yes—
174C4⋊Dic79—21no—
175C4⋊Dic79—21no—
176C4⋊Dic79—21no—
177C4⋊Dic79—21no—
178C4⋊Dic79C22×C412yes—
179C4⋊Dic79C2×D412yes—
180Dic79⋊C4—81no—
181C22⋊Dic79—42no—
182(C2×D79)⋊C4—24no—
183(C2×D79)⋊C4—42no—
184(C2×D79)⋊C4—42no—
185(C2×D79)⋊C4—81no—
186C4×Dic79—42no—
187C4×Dic79—81no—
188C24×C79—21no—
189C24×C79C2×D411yescharacteristic
190#41×C79—28no—
191#41×C79—44no—
192#41×C79—44no—
193#41×C79—44no—
194C2×Q8×C79—21no—
195C2×Q8×C79—21no—
196C2×Q8×C79—21no—
197C2×Q8×C79C22×C412yes—
198C2×Q8×C79C2×D412yes—
199C2×Q8×C79#4112yes—
200C2×D4×C79—24no—
201C2×D4×C79—21no—
202C2×D4×C79—21no—
203C2×D4×C79—21no—
204C2×D4×C79—21no—
205C2×D4×C79—21no—
206C2×D4×C79—42no—
207C2×D4×C79—42no—
208C2×D4×C79C22×C412yes—
209C22×C4×C79—21no—
210C22×C4×C79—21no—
211C22×C4×C79—21no—
212C22×C4×C79—21no—
213C22×C4×C79—21no—
214C22×C4×C79—24no—
215C22×C4×C79—21no—
216C22×C4×C79—21no—
217C22×C4×C79—42no—
218C22×C4×C79—42no—
219C22×C4×C79C22×C412yes—
220C22×C4×C79C2×D411yescharacteristic
221C22×C4×C79C2×D411yescharacteristic
222C22×C4×C79C2×D411yescharacteristic
223C22×C4×C79C2×D411yescharacteristic
224C22×C4×C79C2×D411yescharacteristic
225C22×C4×C79#4112yes—
226C22×C4×C79C2411yescharacteristic
227C4⋊C4×C79—21no—
228C4⋊C4×C79—21no—
229C4⋊C4×C79—21no—
230C4⋊C4×C79—21no—
231C4⋊C4×C79—42no—
232C4⋊C4×C79—42no—
233C22⋊C4×C79—41no—
234C22⋊C4×C79—41no—
235C22⋊C4×C79—42no—
236C22⋊C4×C79—42no—
237C22⋊C4×C79—81no—
238C22⋊C4×C79—81no—
239C22⋊C4×C79—81no—
240C42×C79—21no—
241C42×C79—21no—
242C42×C79—21no—
243C42×C79—21no—
244C42×C79—42no—
245C42×C79—42no—
246C23×C79—21no—
247C23×C79—21no—
248C23×C79—21no—
249C23×C79—21no—
250C23×C79—21no—
251C23×C79—21no—
252C23×C79—22no—
253C23×C79—41no—
254C23×C79—41no—
255C23×C79—41no—
256C23×C79—41no—
257C23×C79—41no—
258C23×C79—41no—
259C23×C79C4×D412yes—
260C23×C79C22×D411yescharacteristic
261C22×D79—22no—
262C22×D79—41no—
263C22×D79—41no—
264C22×D79—41no—
265C22×D79—41no—
266C22×D79—41no—
267C22×D79—41no—
268Q8×C79—22no—
269Q8×C79—22no—
270Q8×C79—22no—
271Q8×C79C4×D414yes—
272D4×C79—22no—
273D4×C79—22no—
274D4×C79—48no—
275D4×C79—41no—
276D4×C79—41no—
277C2×C4×C79—22no—
278C2×C4×C79—21no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—21no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
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—21no—
296C2×C4×C79—21no—
297C2×C4×C79—21no—
298C2×C4×C79—48no—
299C2×C4×C79—41no—
300C2×C4×C79—41no—
301C2×C4×C79—41no—
302C2×C4×C79—41no—
303C2×C4×C79—41no—
304C2×C4×C79—41no—
305C2×C4×C79C4×D412yes—
306C2×C4×C79C23×C411yescharacteristic
307C2×C4×C79C22×D411yescharacteristic
308C2×C4×C79C2×#4111yescharacteristic
309C2×C4×C79C2×#4111yescharacteristic
310C2×C4×C79H(5,𝔽2)11yescharacteristic
311C2×C4×C79H(5,𝔽2)11yescharacteristic
312C22⋊D79—84no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—41no—
316C2×Dic79—41no—
317C2×Dic79—41no—
318C2×Dic79—41no—
319C2×Dic79—41no—
320C2×Dic79—41no—
321C2×Dic79—41no—
322D316—22no—
323D316—22no—
324D316—41no—
325D316—41no—
326C4×D79—84no—
327C79⋊C8—22no—
328C79⋊C8—22no—
329C79⋊C8—22no—
330C79⋊C8—41no—
331C22×C79—22no—
332C22×C79—22no—
333C22×C79—22no—
334C22×C79—41no—
335C22×C79—41no—
336C22×C79—41no—
337C22×C79—41no—
338C22×C79—42no—
339C22×C79—42no—
340C22×C79—42no—
341C22×C79—81no—
342C22×C79—81no—
343C22×C79—81no—
344C22×C79—81no—
345C22×C79C2×C4×D411yescharacteristic
346C22×C79D4211yescharacteristic
347C22×C79#54611yescharacteristic
348C22×C79#57511yescharacteristic
349C22×C79#57511yescharacteristic
350C22×C79#57611yescharacteristic
351C22×C79#57711yescharacteristic
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—24no—
361C4×C79—41no—
362C4×C79—41no—
363C4×C79—41no—
364C4×C79—41no—
365C4×C79—81no—
366C4×C79—81no—
367C4×C79C2×C4×D411yescharacteristic
368C4×C79#51811yescharacteristic
369C4×C79#54611yescharacteristic
370C4×C79#55111yescharacteristic
371Dic79—42no—
372Dic79—42no—
373Dic79—81no—
374#22857—791nomaximal, Sylow
375C2×C79—42no—
376C2×C79—82no—
377C2×C79#235811yescharacteristic
378C2×C79#294311yescharacteristic
379C2×C79#294611yescharacteristic
380C2×C79#326811yescharacteristic
381C2×C79#327111yescharacteristic
382C2×C79#330911yescharacteristic
383C2×C79#332111yescharacteristic
384D79—82no—
385C2×#449—791no—
386C2×#440—791no—
387C2×#416—791no—
388#2363—791no—
389#2341D7911yescharacteristic, complemented
390#1972—791no—
391#1936—791no—
392#1925—791no—
393#1893—791no—
394#1880—791no—
395#1879—791no—
396#1865—791no—
397#1854—791no—
398#1763—791no—
399#1752—791no—
400C79#2285711yescharacteristic, complemented, Sylow
401C22×#41C2×D7911yescharacteristic
402C22×SD16—791no—
403C22×D8—791no—
404C23×C8—791no—
405C2×#121—791no—
406C2×C4×Q8C2×D7911yescharacteristic
407C2×C4×Q8C2×D7911yescharacteristic
408C2×C4×D4—791no—
409C2×#117—791no—
410#449—798no—
411#440—1584no—
412C2×#107—791no—
413C2×#106—791no—
414#416—1584no—
415C2×#103—791no—
416C2×#103—791no—
417C2×#103—791no—
418C2×#102—791no—
419C2×#102—791no—
420C2×#102—791no—
421C2×#102—791no—
422C2×#102—791no—
423C2×C22⋊C8—791no—
424C2×#97—791no—
425C2×#97—791no—
426#390—21no—
427#390—21no—
428#390—791no—
429#390—1581no—
430#390C2×D7911yescharacteristic
431#390C2×D7911yescharacteristic
432#389—791no—
433#388—1581no—
434#386—1581no—
435#380—21no—
436#380C2×D7911yescharacteristic
437C4×C4⋊C4—791no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—1581no—
440C4×C22⋊C4C2×D7911yescharacteristic
441#340—791no—
442#340—791no—
443#340—791no—
444#340—791no—
445#336—791no—
446#336—791no—
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—22no—
450C2×#41—41no—
451C2×#41—41no—
452C2×#41C4×D7914yescomplemented
453C22×Q8C22×D7911yescharacteristic
454C22×D4—21no—
455C22×D4—791no—
456C22×D4—1581no—
457C22×D4C22×D7911yescharacteristic
458C23×C4—21no—
459C23×C4—1581no—
460C23×C4C22×D7911yescharacteristic
461C2×SD16—794no—
462C2×SD16—1582no—
463C2×SD16—1582no—
464C2×D8—3161no—
465C2×D8—3161no—
466C2×D8—794no—
467C22×C8—3161no—
468C22×C8—791no—
469C22×C8—791no—
470C22×C8—791no—
471C22×C8—791no—
472C22×C8—1582no—
473C22×C8—1582no—
474#121—794no—
475#121—1582no—
476C4×Q8—22no—
477C4×Q8—22no—
478C4×Q8—41no—
479C4×Q8—41no—
480C4×D4—3161no—
481C4×D4—1582no—
482#117—3161no—
483#117—1582no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—791no—
487C2×C4⋊C4—791no—
488C2×C4⋊C4—791no—
489C2×C4⋊C4—1581no—
490C2×C4⋊C4C22×D7911yescharacteristic
491C2×C4⋊C4C22×D7911yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1581no—
498C2×C22⋊C4—1581no—
499C2×C22⋊C4—1581no—
500C2×C22⋊C4—1581no—
501C2×C22⋊C4—1581no—
502C2×C22⋊C4C22⋊D7911yescharacteristic
503C2×C22⋊C4C22⋊D7911yescharacteristic
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—1581no—
507C2×C42—1581no—
508C2×C42C22×D7911yescharacteristic
509C2×C42C22×D7911yescharacteristic
510#107—1582no—
511#106—3161no—
512#103—794no—
513#103—794no—
514#103—1582no—
515#102—3161no—
516#102—794no—
517#102—1582no—
518#102—1582no—
519#102—1582no—
520C22⋊C8—794no—
521#97—3161no—
522#97—1582no—
523#95—21no—
524#95—1581no—
525#95—1581no—
526#95C22⋊D7911yescharacteristic
527#95C22⋊D7911yescharacteristic
528C24—21no—
529C24—1581no—
530C24C2×C22⋊D7911yescharacteristic
531#41—28no—
532#41—44no—
533#41—44no—
534#41—44no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8C2×C4×D7912yes—
539C2×Q8D4×D7912yes—
540C2×Q8#1192962312yes—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—792no—
550C2×D4—6321no—
551C2×D4—6321no—
552C2×D4—1584no—
553C2×D4—1581no—
554C2×D4—1581no—
555C2×D4—1581no—
556C2×D4—1581no—
557C2×D4—1581no—
558C2×D4C2×C4×D7912yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—3162no—
570C22×C4—3162no—
571C22×C4—6321no—
572C22×C4—1581no—
573C22×C4—1581no—
574C22×C4—1581no—
575C22×C4C2×C4×D7912yes—
576C22×C4C2×C22⋊D7911yescharacteristic
577C22×C4C2×C22⋊D7911yescharacteristic
578C22×C4C2×C22⋊D7911yescharacteristic
579C22×C4C2×C22⋊D7911yescharacteristic
580C22×C4C2×C22⋊D7911yescharacteristic
581C22×C4#1192962412yes—
582C22×C4C23×D7911yescharacteristic
583SD16—1588no—
584D8—3164no—
585C2×C8—3164no—
586C2×C8—792no—
587C2×C8—792no—
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—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—792no—
605C4⋊C4—792no—
606C4⋊C4—6321no—
607C4⋊C4—1581no—
608C4⋊C4—1581no—
609C4⋊C4—1581no—
610C4⋊C4—1581no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C22⋊C4—81no—
618C22⋊C4—3162no—
619C22⋊C4—3162no—
620C22⋊C4—3162no—
621C22⋊C4—6321no—
622C22⋊C4—1584no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—42no—
628C42—42no—
629C42—3162no—
630C42—6321no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—3161no—
645C23—3161no—
646C23—3161no—
647C23—3161no—
648C23—3161no—
649C23—3161no—
650C23—1582no—
651C23C4×C22⋊D7912yes—
652C23C22×C22⋊D7911yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8(C22⋊D79)⋊C414yes—
657D4—22no—
658D4—22no—
659D4—48no—
660D4—41no—
661D4—41no—
662D4—3161no—
663D4—3161no—
664D4—6324no—
665D4—1582no—
666D4—1582no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—48no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—3161no—
696C2×C4—3161no—
697C2×C4—3161no—
698C2×C4—3161no—
699C2×C4—3161no—
700C2×C4—3161no—
701C2×C4—3161no—
702C2×C4—6324no—
703C2×C4—1582no—
704C2×C4—1582no—
705C2×C4C4×C22⋊D7912yes—
706C2×C4C22×C4×D7911yescharacteristic
707C2×C4C2×D4×D7911yescharacteristic
708C2×C4C2×#1192962311yescharacteristic
709C2×C4C2×#1192962411yescharacteristic
710C2×C4#1457920611yescharacteristic
711C2×C4#1457920611yescharacteristic
712C8—3161no—
713C8—1582no—
714C8—1582no—
715C8—1582no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—3162no—
731C22—3162no—
732C22—3162no—
733C22—6321no—
734C22—6321no—
735C22—6321no—
736C22—6321no—
737C22C2×C4×C22⋊D7911yescharacteristic
738C22D4×C22⋊D7911yescharacteristic
739C22#1909920711yescharacteristic
740C22#1909936111yescharacteristic
741C22#1909936111yescharacteristic
742C22#1909936611yescharacteristic
743C22#1909937111yescharacteristic
744C4—22no—
745C4—24no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—81no—
751C4—81no—
752C4—3162no—
753C4—3162no—
754C4—6321no—
755C4C2×(C22⋊D79)⋊C411yescharacteristic
756C4#1909903611yescharacteristic
757C4#1909920311yescharacteristic
758C4#1909923911yescharacteristic
759C2—42no—
760C2—82no—
761C2—6322no—
762C2#2376637911yescharacteristic
763C2#2377219811yescharacteristic
764C2#2377222811yescharacteristic
765C2#2377494111yescharacteristic
766C2#2377498611yescharacteristic
767C2#2377540611yescharacteristic
768C2#2377558611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2341C2
socleC23×C79C22×D4
prime radicalC2×#19098708C2
cosocleC22×C4×C79C24
hypercenter#2341D79
hypocenterC79#22857
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×#19098661C2semidirect
3. C2×#19098559C2semidirect
4. #23766436C2semidirect
5. #23764275C2semidirect
6. #23764100C2semidirect
7. #23764017C2semidirect
8. #23763826C2semidirect
9. #23763755C2semidirect
10. #23763751C2semidirect
11. #23763668C2semidirect
12. #23763597C2semidirect
13. #23763230C2semidirect
14. #23763178C2semidirect
15. C79×#2341C2semidirect
22. #19098708C4semidirect
98. #14579085C2×C4semidirect
99. #14579085D4semidirect
102. #14579082C2×C4semidirect
105. C22⋊(C79⋊C8)C2×C4semidirect
115. C2×#41×C79C2×C4semidirect
389. #2341D79semidirect
400. C79#22857semidirect
452. 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
C2×#190986612
C2×#190985592
#237664362
#237642752
#237641002
#237640172
#237638262
#237637552
#237637512
#237636682
#237635972
#237632302
#237631782
C79×#23412
#2285779