Finite Group Databasebeta

← #34299550

Subgroups — #34299550

Order 20224.

1080 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×#19098714C211yesmaximal, characteristic
2#23766082C211yesmaximal, characteristic, complemented
3#23764280C211yesmaximal, characteristic, complemented
4#23764253C211yesmaximal, characteristic, complemented
5#23764100C211yesmaximal, characteristic, complemented
6#23764086C211yesmaximal, characteristic, complemented
7#23764024C211yesmaximal, characteristic, complemented
8#23764017C211yesmaximal, characteristic, complemented
9#23763758C211yesmaximal, characteristic, complemented
10#23763758C211yesmaximal, characteristic, complemented
11#23763712C211yesmaximal, characteristic, complemented
12#23763599C211yesmaximal, characteristic, complemented
13#23763331C211yesmaximal, characteristic
14#23763166C211yesmaximal, characteristic, complemented
15C79×#2309C211yesmaximal, characteristic
16C22×#11929612C2211yescharacteristic
17C22×#11929612C2211yescharacteristic
18C2×#14579140C2211yescharacteristic
19C2×C4×Dic158C2211yescharacteristic, complemented
20#19098714C418yescomplemented
21C2×#14579094C2211yescharacteristic, complemented
22C2×#14579092C2211yescharacteristic, complemented
23C2×#14579084C2211yescharacteristic, complemented
24C2×#14579084C2211yescharacteristic, complemented
25C2×#14579082C2211yescharacteristic
26C2×#14579082C2211yescharacteristic
27C2×#14579082C2211yescharacteristic
28C2×#14579082C2211yescharacteristic
29C2×#14579082C2211yescharacteristic
30C2×#14579082C2211yescharacteristic
31C2×C22⋊(C79⋊C8)C2211yescharacteristic
32C2×C22⋊(C79⋊C8)C2211yescharacteristic
33C2×#14579072C2211yescharacteristic, complemented
34C2×C4×C79⋊C8C2211yescharacteristic, complemented
35#19098469C2211yescharacteristic, complemented
36#19098461C2211yescharacteristic, complemented
37#19098458—21no—
38#19098457—21no—
39#19098451—21no—
40#19098444—21no—
41#19098423C2211yescharacteristic
42C4×C4⋊Dic79C2211yescharacteristic, complemented
43#19098325C2211yescharacteristic, complemented
44#19098325C2211yescharacteristic, complemented
45#19098325C2211yescharacteristic, complemented
46#19098325C2211yescharacteristic, complemented
47#19098318C2211yescharacteristic, complemented
48#19098318C2211yescharacteristic, complemented
49C23×D4×C79C2211yescharacteristic
50C2×#117×C79C2211yescharacteristic
51C2×#117×C79C2211yescharacteristic
52#390×C79—21no—
53#390×C79—21no—
54#390×C79C2211yescharacteristic
55#390×C79C2211yescharacteristic
56#390×C79C2211yescharacteristic
57#390×C79C2211yescharacteristic
58#379×C79—21no—
59#379×C79—21no—
60C22×Dic158C2311yescharacteristic
61C2×#11929612—41no—
62C2×#11929612—41no—
63C2×#11929612—41no—
64C2×#11929612—41no—
65C2×#11929612C2×C414yes—
66C2×#11929612C2×C414yes—
67C22×C79⋊C8C2311yescharacteristic
68C22×C79⋊C8C2311yescharacteristic
69C22×C79⋊C8C2311yescharacteristic
70C22×C79⋊C8C2311yescharacteristic
71#14579140—22no—
72#14579140C2×C414yes—
73C4×Dic158—41no—
74C4×Dic158—41no—
75C2×C4⋊Dic79C2311yescharacteristic
76C2×C4⋊Dic79C2311yescharacteristic
77C2×C4⋊Dic79C2311yescharacteristic
78C2×Dic79⋊C4—21no—
79C2×Dic79⋊C4—21no—
80C2×Dic79⋊C4—21no—
81C2×C22⋊Dic79—21no—
82C2×C22⋊Dic79—21no—
83C2×C4×Dic79—21no—
84C2×C4×Dic79—21no—
85#14579094—41no—
86#14579092—41no—
87#14579084—41no—
88#14579084—41no—
89#14579082—41no—
90#14579082—41no—
91#14579082—41no—
92#14579082—41no—
93#14579082C2×C414yes—
94#14579082C2×C414yes—
95C22⋊(C79⋊C8)—22no—
96C22⋊(C79⋊C8)C2×C414yes—
97#14579072—41no—
98C4×C79⋊C8—41no—
99C79⋊#95—21no—
100C79⋊#95—21no—
101C79⋊#95—21no—
102C79⋊#95—21no—
103C79⋊#95—21no—
104C25×C79—21no—
105C22×D4×C79—21no—
106C22×D4×C79—22no—
107C22×D4×C79—41no—
108C22×D4×C79—41no—
109C22×D4×C79—41no—
110C22×D4×C79—41no—
111C22×D4×C79C2×C414yes—
112C22×D4×C79C2311yescharacteristic
113C22×D4×C79C2311yescharacteristic
114C23×C4×C79C2311yescharacteristic
115#117×C79—41no—
116#117×C79—41no—
117#117×C79—41no—
118#117×C79—41no—
119C2×C4⋊C4×C79D411yescharacteristic
120C2×C4⋊C4×C79D411yescharacteristic
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×C22⋊C4×C79—21no—
129C2×C22⋊C4×C79—21no—
130C2×C22⋊C4×C79—21no—
131C2×C22⋊C4×C79—21no—
132C2×C22⋊C4×C79D411yescharacteristic
133C2×C22⋊C4×C79D411yescharacteristic
134C2×C42×C79—21no—
135C2×C42×C79C2311yescharacteristic
136C2×C42×C79C2311yescharacteristic
137C2×Dic158—21no—
138C2×Dic158—21no—
139C2×Dic158—21no—
140C2×Dic158—21no—
141C2×Dic158—21no—
142C2×Dic158C22×C412yes—
143C22×Dic79—21no—
144C22×Dic79—21no—
145C22×Dic79—21no—
146C22×Dic79—21no—
147#11929612—44no—
148#11929612—44no—
149C2×C79⋊C8—21no—
150C2×C79⋊C8—21no—
151C2×C79⋊C8—21no—
152C2×C79⋊C8—21no—
153C2×C79⋊C8—21no—
154C2×C79⋊C8—21no—
155C2×C79⋊C8—21no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8—21no—
158C2×C79⋊C8—21no—
159C2×C79⋊C8C22×C412yes—
160C2×C79⋊C8C22×C412yes—
161C4⋊Dic79—21no—
162C4⋊Dic79—21no—
163C4⋊Dic79—21no—
164C4⋊Dic79—21no—
165C4⋊Dic79—21no—
166C4⋊Dic79C22×C412yes—
167Dic79⋊C4—24no—
168Dic79⋊C4—42no—
169Dic79⋊C4—81no—
170C22⋊Dic79—24no—
171C22⋊Dic79—81no—
172C4×Dic79—42no—
173C4×Dic79—81no—
174C24×C79—21no—
175C24×C79—21no—
176C24×C79—24no—
177C24×C79—42no—
178C24×C79—42no—
179C24×C79—81no—
180C24×C79—81no—
181C24×C79—81no—
182C24×C79—81no—
183C24×C79C2×D411yescharacteristic
184C2×D4×C79—24no—
185C2×D4×C79—21no—
186C2×D4×C79—21no—
187C2×D4×C79—21no—
188C2×D4×C79—21no—
189C2×D4×C79—21no—
190C2×D4×C79—21no—
191C2×D4×C79—21no—
192C2×D4×C79—21no—
193C2×D4×C79—21no—
194C2×D4×C79—21no—
195C2×D4×C79—44no—
196C2×D4×C79—44no—
197C2×D4×C79—42no—
198C2×D4×C79—42no—
199C2×D4×C79—44no—
200C2×D4×C79—44no—
201C2×D4×C79C22×C412yes—
202C2×D4×C79C22×C412yes—
203C22×C4×C79—21no—
204C22×C4×C79—21no—
205C22×C4×C79—21no—
206C22×C4×C79—21no—
207C22×C4×C79—21no—
208C22×C4×C79—21no—
209C22×C4×C79C22×C412yes—
210C22×C4×C79C2×D411yescharacteristic
211C22×C4×C79C2×D411yescharacteristic
212C22×C4×C79C2×D411yescharacteristic
213C22×C4×C79C2×D411yescharacteristic
214C22×C4×C79C2×D411yescharacteristic
215C22×C4×C79#4112yes—
216C22×C4×C79C2411yescharacteristic
217C4⋊C4×C79—21no—
218C4⋊C4×C79—21no—
219C4⋊C4×C79—21no—
220C4⋊C4×C79—21no—
221C4⋊C4×C79—41no—
222C4⋊C4×C79—41no—
223C22⋊C4×C79—41no—
224C22⋊C4×C79—41no—
225C22⋊C4×C79—42no—
226C22⋊C4×C79—81no—
227C22⋊C4×C79—81no—
228C22⋊C4×C79—81no—
229C22⋊C4×C79—81no—
230C22⋊C4×C79—81no—
231C22⋊C4×C79—81no—
232C22⋊C4×C79—81no—
233C22⋊C4×C79—81no—
234C42×C79—21no—
235C42×C79—21no—
236C42×C79—21no—
237C42×C79—21no—
238C42×C79—42no—
239C23×C79—21no—
240C23×C79—21no—
241C23×C79—21no—
242C23×C79—21no—
243C23×C79—21no—
244C23×C79—21no—
245C23×C79—22no—
246C23×C79—22no—
247C23×C79—48no—
248C23×C79—41no—
249C23×C79—41no—
250C23×C79—41no—
251C23×C79—41no—
252C23×C79—41no—
253C23×C79—41no—
254C23×C79—41no—
255C23×C79—41no—
256C23×C79—41no—
257C23×C79—41no—
258C23×C79—41no—
259C23×C79—41no—
260C23×C79—84no—
261C23×C79—84no—
262C23×C79—84no—
263C23×C79—84no—
264C23×C79—84no—
265C23×C79—84no—
266C23×C79C4×D412yes—
267C23×C79C22×D411yescharacteristic
268D4×C79—22no—
269D4×C79—22no—
270D4×C79—22no—
271D4×C79—22no—
272D4×C79—48no—
273D4×C79—41no—
274D4×C79—41no—
275D4×C79—41no—
276D4×C79—41no—
277C2×C4×C79—21no—
278C2×C4×C79—21no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
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×C79—41no—
299C2×C4×C79—41no—
300C2×C4×C79—41no—
301C2×C4×C79C4×D412yes—
302C2×C4×C79C23×C411yescharacteristic
303C2×C4×C79C2×#4111yescharacteristic
304C2×C4×C79H(5,𝔽2)11yescharacteristic
305C2×C4×C79H(5,𝔽2)11yescharacteristic
306C2×C4×C79H(5,𝔽2)11yescharacteristic
307C2×C4×C79H(5,𝔽2)11yescharacteristic
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—41no—
311C2×Dic79—41no—
312C2×Dic79—41no—
313C2×Dic79—41no—
314C2×Dic79—41no—
315C2×Dic79—41no—
316C2×Dic79—41no—
317C2×Dic79—41no—
318C2×Dic79—41no—
319C2×Dic79—41no—
320Dic158—22no—
321Dic158—22no—
322Dic158—41no—
323Dic158—41no—
324C79⋊C8—22no—
325C79⋊C8—22no—
326C79⋊C8—41no—
327C79⋊C8—41no—
328C22×C79—22no—
329C22×C79—22no—
330C22×C79—22no—
331C22×C79—41no—
332C22×C79—41no—
333C22×C79—41no—
334C22×C79—41no—
335C22×C79—42no—
336C22×C79—42no—
337C22×C79—42no—
338C22×C79—42no—
339C22×C79—42no—
340C22×C79—42no—
341C22×C79—816no—
342C22×C79—81no—
343C22×C79—81no—
344C22×C79—81no—
345C22×C79—81no—
346C22×C79—81no—
347C22×C79—81no—
348C22×C79—81no—
349C22×C79—81no—
350C22×C79C2×C4×D411yescharacteristic
351C22×C79#53411yescharacteristic
352C22×C79#53511yescharacteristic
353C22×C79#57611yescharacteristic
354C22×C79#57711yescharacteristic
355C22×C79#57711yescharacteristic
356C22×C79#57711yescharacteristic
357C4×C79—22no—
358C4×C79—41no—
359C4×C79—41no—
360C4×C79—41no—
361C4×C79—41no—
362C4×C79—81no—
363C4×C79—81no—
364C4×C79#51811yescharacteristic
365C4×C79#51811yescharacteristic
366C4×C79#53811yescharacteristic
367C4×C79#53811yescharacteristic
368Dic79—42no—
369Dic79—42no—
370Dic79—81no—
371Dic79—81no—
372#22052—791nomaximal, Sylow
373C2×C79—42no—
374C2×C79—82no—
375C2×C79—82no—
376C2×C79#232111yescharacteristic
377C2×C79#294611yescharacteristic
378C2×C79#294911yescharacteristic
379C2×C79#319811yescharacteristic
380C2×C79#320011yescharacteristic
381C2×C79#322211yescharacteristic
382C2×C79#322411yescharacteristic
383C2×#450—791no—
384#2323—791no—
385#2309D7911yescharacteristic
386#1973—791no—
387#1968—791no—
388#1936—791no—
389#1934—791no—
390#1926—791no—
391#1925—791no—
392#1880—791no—
393#1880—791no—
394#1873—791no—
395#1854—791no—
396#1786—791no—
397#1750—791no—
398C79#2205211yescharacteristic, complemented, Sylow
399C23×D4C2×D7911yescharacteristic
400C22×SD16—791no—
401C22×SD16—791no—
402C2×C22⋊Q8—791no—
403C2×C4×Q8—791no—
404C2×#117C2×D7911yescharacteristic
405C2×#117C2×D7911yescharacteristic
406#450—798no—
407C2×#107—791no—
408C2×#106—791no—
409C2×#103—791no—
410C2×#103—791no—
411C2×#102—791no—
412C2×#102—791no—
413C2×#102—791no—
414C2×#102—791no—
415C2×#102—791no—
416C2×#102—791no—
417C2×C22⋊C8—791no—
418C2×C22⋊C8—791no—
419C2×#97—791no—
420C2×C4×C8—791no—
421#391—791no—
422#390—21no—
423#390—21no—
424#390C2×D7911yescharacteristic
425#390C2×D7911yescharacteristic
426#390C2×D7911yescharacteristic
427#390C2×D7911yescharacteristic
428#389—791no—
429#389—1581no—
430#388—1581no—
431#388—1581no—
432#387—1581no—
433#380—791no—
434#379—21no—
435#379—21no—
436C4×C4⋊C4—791no—
437#340—791no—
438#340—791no—
439#340—791no—
440#340—791no—
441#336—791no—
442#336—791no—
443C25—21no—
444C22×Q8—791no—
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—41no—
448C22×D4—41no—
449C22×D4—41no—
450C22×D4—41no—
451C22×D4C4×D7914yes—
452C22×D4C22×D7911yescharacteristic
453C22×D4C22×D7911yescharacteristic
454C23×C4C22×D7911yescharacteristic
455C2×SD16—3161no—
456C2×SD16—3161no—
457C2×SD16—3161no—
458C2×SD16—3161no—
459C2×SD16—794no—
460C2×SD16—794no—
461C22×C8—791no—
462C22×C8—791no—
463C22×C8—791no—
464C22×C8—791no—
465C22⋊Q8—794no—
466C22⋊Q8—1582no—
467C4×Q8—3161no—
468C4×Q8—3161no—
469#117—41no—
470#117—41no—
471#117—41no—
472#117—41no—
473C2×C4⋊C4—791no—
474C2×C4⋊C4—791no—
475C2×C4⋊C4—791no—
476C2×C4⋊C4—1581no—
477C2×C4⋊C4—1581no—
478C2×C4⋊C4—1581no—
479C2×C4⋊C4C22⋊D7911yescharacteristic
480C2×C4⋊C4C22⋊D7911yescharacteristic
481C2×C4⋊C4C22×D7911yescharacteristic
482C2×C4⋊C4C22×D7911yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—1581no—
493C2×C22⋊C4—1581no—
494C2×C22⋊C4C22⋊D7911yescharacteristic
495C2×C22⋊C4C22⋊D7911yescharacteristic
496C2×C42—21no—
497C2×C42—1581no—
498C2×C42—1581no—
499C2×C42C22×D7911yescharacteristic
500C2×C42C22×D7911yescharacteristic
501#107—3161no—
502#106—3161no—
503#103—3161no—
504#103—3161no—
505#102—3161no—
506#102—3161no—
507#102—3161no—
508#102—3161no—
509#102—794no—
510#102—794no—
511C22⋊C8—794no—
512C22⋊C8—1582no—
513#97—3161no—
514C4×C8—3161no—
515#95—1581no—
516#95—1581no—
517#95—1581no—
518#95—1581no—
519#95—1581no—
520C24—21no—
521C24—21no—
522C24—24no—
523C24—42no—
524C24—42no—
525C24—81no—
526C24—81no—
527C24—81no—
528C24—81no—
529C24C2×C22⋊D7911yescharacteristic
530C2×Q8—792no—
531C2×Q8—1581no—
532C2×Q8—1581no—
533C2×Q8—1581no—
534C2×Q8—1581no—
535C2×Q8—1581no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—24no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4C2×C4×D7912yes—
554C2×D4C2×C4×D7912yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—1581no—
562C22×C4—1581no—
563C22×C4—1581no—
564C22×C4—1581no—
565C22×C4C2×C4×D7912yes—
566C22×C4C2×C22⋊D7911yescharacteristic
567C22×C4C2×C22⋊D7911yescharacteristic
568C22×C4C2×C22⋊D7911yescharacteristic
569C22×C4C2×C22⋊D7911yescharacteristic
570C22×C4C2×C22⋊D7911yescharacteristic
571C22×C4#1192962412yes—
572C22×C4C23×D7911yescharacteristic
573SD16—3164no—
574SD16—3164no—
575C2×C8—792no—
576C2×C8—792no—
577C2×C8—1581no—
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—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—3162no—
594C4⋊C4—792no—
595C4⋊C4—6321no—
596C4⋊C4—1581no—
597C4⋊C4—1581no—
598C4⋊C4—1581no—
599C4⋊C4—1581no—
600C4⋊C4—1581no—
601C4⋊C4—1584no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—6321no—
614C22⋊C4—1584no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—42no—
620C42—3162no—
621C42—6321no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—22no—
630C23—48no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23C4×C22⋊D7912yes—
650C23C22×C22⋊D7911yescharacteristic
651Q8—3161no—
652Q8—3161no—
653Q8—1582no—
654Q8—1582no—
655D4—22no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—48no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664C2×C4—21no—
665C2×C4—21no—
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—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—3161no—
689C2×C4—3161no—
690C2×C4—3161no—
691C2×C4—3161no—
692C2×C4—3161no—
693C2×C4—3161no—
694C2×C4—3161no—
695C2×C4—3161no—
696C2×C4—3161no—
697C2×C4—3161no—
698C2×C4—1582no—
699C2×C4—1582no—
700C2×C4C4×C22⋊D7912yes—
701C2×C4C22×C4×D7911yescharacteristic
702C2×C4C2×#1192962411yescharacteristic
703C2×C4#1457920611yescharacteristic
704C2×C4#1457920611yescharacteristic
705C2×C4#1457920611yescharacteristic
706C2×C4#1457920611yescharacteristic
707C8—3161no—
708C8—3161no—
709C8—1582no—
710C8—1582no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—816no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C2×C4×C22⋊D7911yescharacteristic
734C22#1909912211yescharacteristic
735C22#1909913011yescharacteristic
736C22#1909936611yescharacteristic
737C22#1909937411yescharacteristic
738C22#1909937411yescharacteristic
739C22#1909937411yescharacteristic
740C4—22no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—81no—
746C4—81no—
747C4—3162no—
748C4—3162no—
749C4—6321no—
750C4—6321no—
751C4#1909903611yescharacteristic
752C4#1909903611yescharacteristic
753C4#1909915111yescharacteristic
754C4#1909915111yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2#2376605811yescharacteristic
759C2#2377223211yescharacteristic
760C2#2377225711yescharacteristic
761C2#2377425211yescharacteristic
762C2#2377427211yescharacteristic
763C2#2377447211yescharacteristic
764C2#2377449411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2309C2
socleC23×C79C22×D4
prime radicalC23×D4×C79C22
cosocleC22×C4×C79C24
hypercenter#2309D79
hypocenterC79#22052
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. #23766082C2semidirect
3. #23764280C2semidirect
4. #23764253C2semidirect
5. #23764100C2semidirect
6. #23764086C2semidirect
7. #23764024C2semidirect
8. #23764017C2semidirect
9. #23763758C2semidirect
10. #23763758C2semidirect
11. #23763712C2semidirect
12. #23763599C2semidirect
14. #23763166C2semidirect
19. C2×C4×Dic158C22semidirect
20. #19098714C4semidirect
21. C2×#14579094C22semidirect
22. C2×#14579092C22semidirect
23. C2×#14579084C22semidirect
24. C2×#14579084C22semidirect
33. C2×#14579072C22semidirect
34. C2×C4×C79⋊C8C22semidirect
35. #19098469C22semidirect
36. #19098461C22semidirect
42. C4×C4⋊Dic79C22semidirect
43. #19098325C22semidirect
44. #19098325C22semidirect
45. #19098325C22semidirect
46. #19098325C22semidirect
47. #19098318C22semidirect
48. #19098318C22semidirect
398. C79#22052semidirect

Maximal subgroups

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

subgroupindex
C2×#190987142
#237660822
#237642802
#237642532
#237641002
#237640862
#237640242
#237640172
#237637582
#237637122
#237635992
#237633312
#237631662
C79×#23092
#2205279