Finite Group Databasebeta

← #34299529

Subgroups — #34299529

Order 20224.

1084 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098706C211yesmaximal, characteristic
2#23765890C211yesmaximal, characteristic, complemented
3#23764280C211yesmaximal, characteristic, complemented
4#23764275C211yesmaximal, characteristic, complemented
5#23764096C211yesmaximal, characteristic, complemented
6#23764089C211yesmaximal, characteristic, complemented
7#23764034C211yesmaximal, characteristic, complemented
8#23764020C211yesmaximal, characteristic, complemented
9#23763748C211yesmaximal, characteristic, complemented
10#23763734C211yesmaximal, characteristic, complemented
11#23763723C211yesmaximal, characteristic, complemented
12#23763597C211yesmaximal, characteristic, complemented
13#23763338C211yesmaximal, characteristic, complemented
14#23763162C211yesmaximal, characteristic, complemented
15C4×#121×C79C211yesmaximal, characteristic, complemented
16C22×#11929624C2211yescharacteristic
17C22×#11929612C2211yescharacteristic
18C22×#11929609C2211yescharacteristic
19C2×#14579120C2211yescharacteristic
20#19098706C418yescomplemented
21C2×#14579094C2211yescharacteristic
22C2×#14579092C2211yescharacteristic
23C2×#14579084C2211yescharacteristic
24C2×#14579084C2211yescharacteristic
25C2×#14579084C2211yescharacteristic
26C2×#14579082C2211yescharacteristic
27C2×#14579082C2211yescharacteristic
28C2×#14579081C2211yescharacteristic
29C2×#14579081C2211yescharacteristic
30C2×#14579081C2211yescharacteristic
31C2×C22⋊(C79⋊C8)C2211yescharacteristic
32C2×C22⋊(C79⋊C8)C2211yescharacteristic
33C2×#14579072C2211yescharacteristic
34C2×#14579072C2211yescharacteristic
35#19098469C2211yescharacteristic
36#19098469C2211yescharacteristic
37#19098465C2211yescharacteristic
38#19098465C2211yescharacteristic
39#19098442—21no—
40#19098442—21no—
41C4×(C2×D79)⋊C4—21no—
42C4×(C2×D79)⋊C4—21no—
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098318C2211yescharacteristic
48#19098318C2211yescharacteristic
49C2×#121×C79C2211yescharacteristic
50C2×C4×D4×C79—21no—
51C2×C4×D4×C79C2211yescharacteristic
52C22×C42×C79C2211yescharacteristic
53#390×C79C2211yescharacteristic
54#389×C79C2211yescharacteristic
55#388×C79—21no—
56#386×C79—21no—
57#380×C79C2211yescharacteristic
58C4×C4⋊C4×C79C2211yescharacteristic
59C4×C22⋊C4×C79—21no—
60C2×#11929624—22no—
61C2×#11929624—41no—
62C2×#11929624—41no—
63C2×#11929624—41no—
64C2×#11929624—41no—
65C2×#11929624C2×C414yescomplemented
66C22×Dic158C2311yescharacteristic
67C22×D316C2311yescharacteristic
68C22×C22⋊D79—21no—
69C22×C4×D79—21no—
70C2×#11929612—41no—
71C2×#11929612—41no—
72C2×#11929612C2×C414yescomplemented
73C2×#11929609—41no—
74C2×#11929609—41no—
75C2×#11929609C2×C414yescomplemented
76C22×C79⋊C8C2311yescharacteristic
77C22×C79⋊C8C2311yescharacteristic
78C22×C79⋊C8C2311yescharacteristic
79C22×C79⋊C8C2311yescharacteristic
80#14579120—41no—
81#14579120—41no—
82C2×C4⋊Dic79C2311yescharacteristic
83C2×C4⋊Dic79C2311yescharacteristic
84C2×C22⋊Dic79—21no—
85C2×(C2×D79)⋊C4—21no—
86C2×(C2×D79)⋊C4—21no—
87C2×(C2×D79)⋊C4—21no—
88C2×(C2×D79)⋊C4—21no—
89C2×C4×Dic79—21no—
90#14579094—41no—
91#14579092—41no—
92#14579084—41no—
93#14579084—41no—
94#14579084C2×C414yescomplemented
95#14579082—41no—
96#14579082—41no—
97#14579081—41no—
98#14579081—41no—
99#14579081C2×C414yescomplemented
100C22⋊(C79⋊C8)—22no—
101C22⋊(C79⋊C8)C2×C414yescomplemented
102#14579072—41no—
103#14579072—41no—
104C79⋊#95—21no—
105C79⋊#95—21no—
106C79⋊#95—21no—
107C79⋊#95—21no—
108C22×D4×C79—21no—
109C22×D4×C79C2311yescharacteristic
110C23×C4×C79—21no—
111C23×C4×C79D411yescharacteristic
112C23×C4×C79D411yescharacteristic
113C23×C4×C79C2311yescharacteristic
114#121×C79—22no—
115#121×C79C2×C414yes—
116C4×D4×C79—41no—
117C4×D4×C79—41no—
118C4×D4×C79—44no—
119C2×C4⋊C4×C79—21no—
120C2×C4⋊C4×C79C2311yescharacteristic
121C2×C4⋊C4×C79C2311yescharacteristic
122C2×C4⋊C4×C79C2311yescharacteristic
123C2×C22⋊C4×C79—21no—
124C2×C22⋊C4×C79—21no—
125C2×C22⋊C4×C79—21no—
126C2×C22⋊C4×C79—21no—
127C2×C22⋊C4×C79—21no—
128C2×C42×C79—21no—
129C2×C42×C79—41no—
130C2×C42×C79—41no—
131C2×C42×C79D411yescharacteristic
132C2×C42×C79D411yescharacteristic
133C2×C42×C79C2311yescharacteristic
134C2×C42×C79C2311yescharacteristic
135#95×C79—21no—
136#95×C79—21no—
137#95×C79—21no—
138C23×D79—21no—
139#11929624—44no—
140#11929624—44no—
141#11929624—44no—
142#11929624—44no—
143C2×Dic158—21no—
144C2×Dic158—21no—
145C2×Dic158—21no—
146C2×Dic158—21no—
147C2×Dic158—21no—
148C2×Dic158C22×C412yes—
149C2×D316—21no—
150C2×D316—21no—
151C2×D316—21no—
152C2×D316—21no—
153C2×D316—21no—
154C2×D316C22×C412yes—
155C2×C22⋊D79—24no—
156C2×C22⋊D79—42no—
157C2×C22⋊D79—42no—
158C22×Dic79—21no—
159C22×Dic79—21no—
160C22×Dic79—21no—
161C2×C4×D79—24no—
162C2×C4×D79—42no—
163C2×C4×D79—42no—
164#11929612—44no—
165#11929609—44no—
166C2×C79⋊C8—21no—
167C2×C79⋊C8—21no—
168C2×C79⋊C8—21no—
169C2×C79⋊C8—21no—
170C2×C79⋊C8—21no—
171C2×C79⋊C8—21no—
172C2×C79⋊C8—21no—
173C2×C79⋊C8—21no—
174C2×C79⋊C8—21no—
175C2×C79⋊C8—21no—
176C2×C79⋊C8C22×C412yes—
177C2×C79⋊C8C22×C412yes—
178C4⋊Dic79—21no—
179C4⋊Dic79—21no—
180C4⋊Dic79—21no—
181C4⋊Dic79—21no—
182C22⋊Dic79—42no—
183(C2×D79)⋊C4—42no—
184(C2×D79)⋊C4—42no—
185(C2×D79)⋊C4—42no—
186(C2×D79)⋊C4—42no—
187C4×Dic79—42no—
188C24×C79—21no—
189C24×C79C2×D411yescharacteristic
190C2×D4×C79—24no—
191C2×D4×C79—21no—
192C2×D4×C79—21no—
193C2×D4×C79—21no—
194C2×D4×C79—21no—
195C2×D4×C79—21no—
196C2×D4×C79—42no—
197C2×D4×C79—42no—
198C2×D4×C79C22×C412yes—
199C22×C4×C79—21no—
200C22×C4×C79—21no—
201C22×C4×C79—21no—
202C22×C4×C79—21no—
203C22×C4×C79—21no—
204C22×C4×C79—22no—
205C22×C4×C79—21no—
206C22×C4×C79—21no—
207C22×C4×C79—41no—
208C22×C4×C79—41no—
209C22×C4×C79—41no—
210C22×C4×C79—41no—
211C22×C4×C79—41no—
212C22×C4×C79—42no—
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—21no—
228C4⋊C4×C79—42no—
229C4⋊C4×C79C22×C412yes—
230C22⋊C4×C79—24no—
231C22⋊C4×C79—42no—
232C22⋊C4×C79—42no—
233C22⋊C4×C79—42no—
234C22⋊C4×C79—42no—
235C42×C79—21no—
236C42×C79—21no—
237C42×C79—21no—
238C42×C79—21no—
239C42×C79—41no—
240C42×C79—41no—
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
257C22×D79—22no—
258C22×D79—41no—
259C22×D79—41no—
260C22×D79—41no—
261C22×D79—41no—
262C22×D79—41no—
263C22×D79—41no—
264D4×C79—22no—
265D4×C79—22no—
266D4×C79—48no—
267D4×C79—41no—
268D4×C79—41no—
269C2×C4×C79—21no—
270C2×C4×C79—21no—
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—22no—
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—44no—
288C2×C4×C79—44no—
289C2×C4×C79—41no—
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—84no—
298C2×C4×C79C4×D412yes—
299C2×C4×C79AGL(1,ℤ/8)12yes—
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—48no—
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—48no—
321Dic158—22no—
322Dic158—22no—
323Dic158—41no—
324Dic158—41no—
325C79⋊C8—22no—
326C79⋊C8—22no—
327C79⋊C8—41no—
328C79⋊C8—41no—
329C22×C79—22no—
330C22×C79—22no—
331C22×C79—22no—
332C22×C79—41no—
333C22×C79—41no—
334C22×C79—41no—
335C22×C79—41no—
336C22×C79—42no—
337C22×C79—42no—
338C22×C79—42no—
339C22×C79—81no—
340C22×C79—81no—
341C22×C79—81no—
342C22×C79—81no—
343C22×C79C2×C4×D411yescharacteristic
344C22×C79#53411yescharacteristic
345C22×C79#53511yescharacteristic
346C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C79#57511yescharacteristic
348C22×C79#57511yescharacteristic
349C22×C79#57511yescharacteristic
350C2×D79—42no—
351C2×D79—42no—
352C2×D79—42no—
353C2×D79—81no—
354C2×D79—81no—
355C2×D79—81no—
356C2×D79—81no—
357C4×C79—22no—
358C4×C79—22no—
359C4×C79—41no—
360C4×C79—41no—
361C4×C79—41no—
362C4×C79—42no—
363C4×C79—81no—
364C4×C79—81no—
365C4×C79#51811yescharacteristic
366C4×C79#51811yescharacteristic
367C4×C79#53811yescharacteristic
368C4×C79#53811yescharacteristic
369Dic79—42no—
370Dic79—81no—
371Dic79—81no—
372#22051—791nomaximal, Sylow
373C2×C79—42no—
374C2×C79—82no—
375C2×C79#232111yescharacteristic
376C2×C79#294311yescharacteristic
377C2×C79C4×AGL(1,ℤ/8)11yescharacteristic
378C2×C79#319411yescharacteristic
379C2×C79#319711yescharacteristic
380C2×C79#321411yescharacteristic
381C2×C79#321911yescharacteristic
382D79—82no—
383C2×#449—791no—
384C4×#121D7911yescharacteristic, complemented
385#2297—791no—
386#1973—791no—
387#1972—791no—
388#1936—791no—
389#1935—791no—
390#1927—791no—
391#1925—791no—
392#1879—791no—
393#1877—791no—
394#1875—791no—
395#1854—791no—
396#1788—791no—
397#1749—791no—
398C79#2205111yescharacteristic, complemented, Sylow
399C22×#41—791no—
400C22×SD16—791no—
401C22×D8—791no—
402C2×#121C2×D7911yescharacteristic
403C2×C4×D4—21no—
404C2×C4×D4C2×D7911yescharacteristic
405C2×#117—791no—
406C22×C42C2×D7911yescharacteristic
407#449—798no—
408C2×#107—791no—
409C2×#106—791no—
410C2×#103—791no—
411C2×#103—791no—
412C2×#103—791no—
413C2×#102—791no—
414C2×#102—791no—
415C2×#102—791no—
416C2×#102—791no—
417C2×#102—791no—
418C2×C22⋊C8—791no—
419C2×C22⋊C8—791no—
420C2×#97—791no—
421C2×#97—791no—
422#391—791no—
423#391—791no—
424#390—791no—
425#390—791no—
426#390C2×D7911yescharacteristic
427#389C2×D7911yescharacteristic
428#388—21no—
429#386—21no—
430#386—1581no—
431#386—1581no—
432#380C2×D7911yescharacteristic
433C4×C4⋊C4C2×D7911yescharacteristic
434C4×C22⋊C4—21no—
435C4×C22⋊C4—1581no—
436C4×C22⋊C4—1581no—
437#340—791no—
438#340—791no—
439#340—791no—
440#340—791no—
441#336—791no—
442#336—791no—
443C2×#41—3161no—
444C2×#41—3161no—
445C2×#41—3161no—
446C2×#41—3161no—
447C2×#41—794no—
448C2×#41—1582no—
449C22×Q8—791no—
450C22×D4—21no—
451C22×D4—791no—
452C22×D4—1581no—
453C22×D4C22×D7911yescharacteristic
454C23×C4—21no—
455C23×C4—1581no—
456C23×C4C22⋊D7911yescharacteristic
457C23×C4C22⋊D7911yescharacteristic
458C23×C4C22×D7911yescharacteristic
459C2×SD16—3161no—
460C2×SD16—3161no—
461C2×SD16—794no—
462C2×D8—3161no—
463C2×D8—3161no—
464C2×D8—794no—
465C22×C8—791no—
466C22×C8—791no—
467C22×C8—791no—
468C22×C8—791no—
469#121—22no—
470#121C4×D7914yes—
471C4×D4—41no—
472C4×D4—41no—
473C4×D4—44no—
474#117—3161no—
475#117—3161no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—791no—
478C2×C4⋊C4—791no—
479C2×C4⋊C4C22×D7911yescharacteristic
480C2×C4⋊C4C22×D7911yescharacteristic
481C2×C4⋊C4C22×D7911yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—1581no—
488C2×C22⋊C4—1581no—
489C2×C22⋊C4—1581no—
490C2×C22⋊C4—1581no—
491C2×C22⋊C4—1581no—
492C2×C42—21no—
493C2×C42—41no—
494C2×C42—41no—
495C2×C42—1581no—
496C2×C42C22⋊D7911yescharacteristic
497C2×C42C22⋊D7911yescharacteristic
498C2×C42C22×D7911yescharacteristic
499C2×C42C22×D7911yescharacteristic
500#107—3161no—
501#106—3161no—
502#103—3161no—
503#103—3161no—
504#103—794no—
505#102—3161no—
506#102—3161no—
507#102—3161no—
508#102—3161no—
509#102—794no—
510C22⋊C8—794no—
511C22⋊C8—1582no—
512#97—3161no—
513#97—3161no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—1581no—
518#95—1581no—
519#95—1581no—
520#95—1581no—
521C24—21no—
522C24—1581no—
523C24C2×C22⋊D7911yescharacteristic
524#41—3164no—
525#41—3164no—
526#41—3164no—
527#41—3164no—
528C2×Q8—792no—
529C2×Q8—1581no—
530C2×Q8—1581no—
531C2×Q8—1581no—
532C2×Q8—1581no—
533C2×Q8—1581no—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—3162no—
543C2×D4—3162no—
544C2×D4—792no—
545C2×D4—1584no—
546C2×D4—1581no—
547C2×D4—1581no—
548C2×D4—1581no—
549C2×D4—1581no—
550C2×D4—1581no—
551C2×D4C2×C4×D7912yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—3162no—
569C22×C4—3162no—
570C22×C4—1581no—
571C22×C4—1581no—
572C22×C4—1581no—
573C22×C4—1584no—
574C22×C4C2×C4×D7912yes—
575C22×C4C2×C22⋊D7911yescharacteristic
576C22×C4C2×C22⋊D7911yescharacteristic
577C22×C4C2×C22⋊D7911yescharacteristic
578C22×C4C2×C22⋊D7911yescharacteristic
579C22×C4C2×C22⋊D7911yescharacteristic
580C22×C4#1192962412yes—
581C22×C4C23×D7911yescharacteristic
582SD16—3164no—
583D8—3164no—
584C2×C8—792no—
585C2×C8—792no—
586C2×C8—1581no—
587C2×C8—1581no—
588C2×C8—1581no—
589C2×C8—1581no—
590C2×C8—1581no—
591C2×C8—1581no—
592C2×C8—1581no—
593C2×C8—1581no—
594C2×C8—1581no—
595C2×C8—1581no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
602C4⋊C4—1581no—
603C4⋊C4—1581no—
604C4⋊C4—1581no—
605C4⋊C4—1581no—
606C4⋊C4C2×C4×D7912yes—
607C22⋊C4—24no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—3162no—
613C22⋊C4—3162no—
614C22⋊C4—3162no—
615C22⋊C4—3162no—
616C22⋊C4—3162no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—41no—
622C42—41no—
623C42—42no—
624C42—3162no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—3161no—
639C23—3161no—
640C23—3161no—
641C23—3161no—
642C23—3161no—
643C23—3161no—
644C23—1582no—
645C23C4×C22⋊D7912yes—
646C23C22×C22⋊D7911yescharacteristic
647Q8—3161no—
648Q8—3161no—
649Q8—1582no—
650Q8—1582no—
651D4—22no—
652D4—22no—
653D4—48no—
654D4—41no—
655D4—41no—
656D4—3168no—
657D4—3161no—
658D4—3161no—
659D4—1582no—
660D4—1582no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4—3168no—
691C2×C4—3161no—
692C2×C4—3161no—
693C2×C4—3161no—
694C2×C4—3161no—
695C2×C4—3161no—
696C2×C4—3161no—
697C2×C4—3161no—
698C2×C4—3161no—
699C2×C4—1582no—
700C2×C4C4×C22⋊D7912yes—
701C2×C4#1457918712yes—
702C2×C4C22×C4×D7911yescharacteristic
703C2×C4C2×#1192962411yescharacteristic
704C2×C4#1457920611yescharacteristic
705C2×C4#1457920611yescharacteristic
706C2×C4#1457920711yescharacteristic
707C2×C4#1457920711yescharacteristic
708C8—3161no—
709C8—3161no—
710C8—1582no—
711C8—1582no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—3162no—
727C22—3162no—
728C22—3162no—
729C22—6321no—
730C22—6321no—
731C22—6321no—
732C22—6321no—
733C22C2×C4×C22⋊D7911yescharacteristic
734C22#1909912211yescharacteristic
735C22#1909912711yescharacteristic
736C22C2×#1457918711yescharacteristic
737C22#1909936111yescharacteristic
738C22#1909936111yescharacteristic
739C22#1909936111yescharacteristic
740C4—22no—
741C4—22no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—42no—
746C4—81no—
747C4—81no—
748C4—3162no—
749C4—6321no—
750C4—6321no—
751C4#1909903511yescharacteristic
752C4#1909903511yescharacteristic
753C4#1909914611yescharacteristic
754C4#1909914611yescharacteristic
755C2—42no—
756C2—82no—
757C2—6322no—
758C2#2376605411yescharacteristic
759C2#2377219811yescharacteristic
760C2C4×#1457918711yescharacteristic
761C2#2377421411yescharacteristic
762C2#2377423711yescharacteristic
763C2#2377439111yescharacteristic
764C2#2377443311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC4×#121×C79C2
socleC23×C79C22×D4
prime radicalC2×#19098706C2
cosocleC22×C4×C79C24
hypercenterC4×#121D79
hypocenterC79#22051
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. #23765890C2semidirect
3. #23764280C2semidirect
4. #23764275C2semidirect
5. #23764096C2semidirect
6. #23764089C2semidirect
7. #23764034C2semidirect
8. #23764020C2semidirect
9. #23763748C2semidirect
10. #23763734C2semidirect
11. #23763723C2semidirect
12. #23763597C2semidirect
13. #23763338C2semidirect
14. #23763162C2semidirect
15. C4×#121×C79C2semidirect
20. #19098706C4semidirect
65. C2×#11929624C2×C4semidirect
72. C2×#11929612C2×C4semidirect
75. C2×#11929609C2×C4semidirect
94. #14579084C2×C4semidirect
99. #14579081C2×C4semidirect
101. C22⋊(C79⋊C8)C2×C4semidirect
384. C4×#121D79semidirect
398. C79#22051semidirect

Maximal subgroups

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

subgroupindex
C2×#190987062
#237658902
#237642802
#237642752
#237640962
#237640892
#237640342
#237640202
#237637482
#237637342
#237637232
#237635972
#237633382
#237631622
C4×#121×C792
#2205179