Finite Group Databasebeta

← #34310813

Subgroups — #34310813

Order 20224.

892 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772978C211yesmaximal, characteristic
2C2×#19098678C211yesmaximal, characteristic, complemented
3#23772121C211yesmaximal, characteristic, complemented
4C22×#14579096C211yesmaximal, characteristic, complemented
5#23764287C211yesmaximal, characteristic, complemented
6#23764145C211yesmaximal, characteristic, complemented
7#23764048C211yesmaximal, characteristic, complemented
8#23764045C211yesmaximal, characteristic, complemented
9#23763703C211yesmaximal, characteristic, complemented
10#23763702C211yesmaximal, characteristic, complemented
11#23763675C211yesmaximal, characteristic, complemented
12#23763674C211yesmaximal, characteristic, complemented
13#23763280C211yesmaximal, characteristic, complemented
14#23763174C211yesmaximal, characteristic, complemented
15C79×#2933C211yesmaximal, characteristic, complemented
16C2×#14579181C2211yescharacteristic
17C2×#14579167C2211yescharacteristic
18C22×#11929608C2211yescharacteristic
19C23×C79⋊C8C2211yescharacteristic
20#19099074C2211yescharacteristic
21#19098802C411yescharacteristic, complemented
22#19098802C411yescharacteristic, complemented
23#19098797C411yescharacteristic, complemented
24#19098797C411yescharacteristic, complemented
25#19098794C411yescharacteristic, complemented
26#19098794C411yescharacteristic, complemented
27#19098790C411yescharacteristic, complemented
28#19098790C411yescharacteristic, complemented
29#19098678—24no—
30#19098638—21no—
31#19098637—21no—
32#19098631—21no—
33(C22⋊D79)⋊C8—21no—
34C2×#14579096—24no—
35C2×#14579096C2211yescharacteristic
36C2×#14579096C2211yescharacteristic
37C2×#14579096C2211yescharacteristic
38C2×#14579096C2211yescharacteristic
39#19098599C2211yescharacteristic
40#19098589C2211yescharacteristic
41C2×#14579088C2211yescharacteristic
42C2×#14579088C2211yescharacteristic
43C2×#14579087C2211yescharacteristic
44C2×#14579087C2211yescharacteristic
45#19098559C2211yescharacteristic
46#19098557C2211yescharacteristic
47#19098529C2211yescharacteristic
48#19098518C2211yescharacteristic
49C2×C8×Dic79C2211yescharacteristic
50C2×C8×Dic79C2211yescharacteristic
51C4×C22⋊Dic79C2211yescharacteristic
52#19098324C2211yescharacteristic
53#19098324C2211yescharacteristic
54#19098322C2211yescharacteristic
55#19098322C2211yescharacteristic
56#19098317C2211yescharacteristic
57#19098317C2211yescharacteristic
58C2×#131×C79C2211yescharacteristic
59C22×M16×C79C2211yescharacteristic
60#525×C79C2211yescharacteristic
61#436×C79—21no—
62#435×C79—21no—
63#435×C79—21no—
64C8×D4×C79—21no—
65#424×C79C2211yescharacteristic
66#408×C79C2211yescharacteristic
67C2×C22⋊C8×C79C2211yescharacteristic
68#405×C79C2211yescharacteristic
69C2×#11929624C2311yescharacteristic
70#14579181—22no—
71#14579181—22no—
72C2×#11929614C2×C411yescharacteristic
73C2×#11929612C2×C411yescharacteristic
74C2×#11929611C2×C411yescharacteristic
75C2×#11929609C2×C411yescharacteristic
76#14579167—22no—
77#14579167—41no—
78C2×#11929608—21no—
79C2×#11929608—22no—
80C2×#11929608—41no—
81C2×#11929608C2311yescharacteristic
82C2×#11929608C2311yescharacteristic
83C2×#11929607—21no—
84C22×C79⋊C8—22no—
85C22×C79⋊C8—22no—
86C22×C79⋊C8—21no—
87C22×C79⋊C8C2×C411yescharacteristic
88C22×C79⋊C8C2×C411yescharacteristic
89C22×C79⋊C8C2×C411yescharacteristic
90C22×C79⋊C8C2×C411yescharacteristic
91C22×C79⋊C8C2311yescharacteristic
92C22×C79⋊C8C2311yescharacteristic
93C2×C8×D79—21no—
94#14579144—21no—
95#14579140C2×C411yescharacteristic
96#14579140C2×C411yescharacteristic
97#14579135C2×C411yescharacteristic
98#14579135C2×C411yescharacteristic
99#14579130—21no—
100C4×C22⋊D79—21no—
101C4×C22⋊D79—21no—
102#14579120C2311yescharacteristic
103C2×C22⋊Dic79—21no—
104C2×C4×Dic79C2311yescharacteristic
105C2×C4×Dic79C2311yescharacteristic
106#14579096—22no—
107#14579096—22no—
108#14579096—22no—
109#14579096D414yescomplemented
110#14579094C2×C411yescharacteristic
111#14579094C2×C411yescharacteristic
112#14579092C2×C411yescharacteristic
113#14579092C2×C411yescharacteristic
114Dic79⋊C8—21no—
115Dic79⋊C8—21no—
116#14579088—22no—
117#14579088—41no—
118#14579087—22no—
119#14579087—41no—
120#14579085C2×C411yescharacteristic
121#14579085C2×C411yescharacteristic
122#14579084C2×C411yescharacteristic
123#14579084C2×C411yescharacteristic
124#14579082C2×C411yescharacteristic
125#14579082C2×C411yescharacteristic
126#14579081C2×C411yescharacteristic
127#14579081C2×C411yescharacteristic
128(C2×D79)⋊C8—21no—
129(C2×D79)⋊C8—21no—
130#14579071—21no—
131C8×Dic79—21no—
132C8×Dic79—22no—
133C8×Dic79—22no—
134C79⋊#95—21no—
135C2×#41×C79C2311yescharacteristic
136C23×C4×C79C2311yescharacteristic
137#131×C79—22no—
138#131×C79—41no—
139C2×M16×C79—21no—
140C2×M16×C79—21no—
141C2×M16×C79—22no—
142C2×M16×C79—41no—
143C2×M16×C79C2311yescharacteristic
144C2×M16×C79C2311yescharacteristic
145C22×C8×C79—21no—
146C22×C8×C79—21no—
147C22×C8×C79C2311yescharacteristic
148C22×C8×C79C2311yescharacteristic
149#123×C79—21no—
150C22⋊Q8×C79C2×C411yescharacteristic
151C22⋊Q8×C79C2×C411yescharacteristic
152#121×C79C2×C411yescharacteristic
153#121×C79C2×C411yescharacteristic
154#120×C79—21no—
155C4×D4×C79—21no—
156C4×D4×C79—21no—
157#117×C79C2311yescharacteristic
158C4⋊C8×C79—21no—
159C4⋊C8×C79—21no—
160C22⋊C8×C79—21no—
161C22⋊C8×C79—21no—
162C22⋊C8×C79D411yescharacteristic
163C22⋊C8×C79D411yescharacteristic
164C22⋊C8×C79D411yescharacteristic
165C22⋊C8×C79D411yescharacteristic
166#97×C79—21no—
167C4×C8×C79—21no—
168#11929624—21no—
169#11929624—21no—
170#11929624—21no—
171#11929624—21no—
172C2×Dic158C22×C411yescharacteristic
173C2×D316C22×C411yescharacteristic
174C2×C22⋊D79—21no—
175C2×C22⋊D79—21no—
176C2×C22⋊D79—21no—
177C22×Dic79—21no—
178C22×Dic79—21no—
179C2×C4×D79—21no—
180#11929614—22no—
181#11929612—22no—
182#11929611—22no—
183#11929609—22no—
184#11929608—21no—
185#11929608—21no—
186#11929608—21no—
187#11929608—42no—
188#11929608C2×D412yes—
189#11929607—42no—
190C2×C79⋊C8—22no—
191C2×C79⋊C8—22no—
192C2×C79⋊C8—22no—
193C2×C79⋊C8—22no—
194C2×C79⋊C8—21no—
195C2×C79⋊C8—21no—
196C2×C79⋊C8—21no—
197C2×C79⋊C8—21no—
198C2×C79⋊C8—42no—
199C2×C79⋊C8C22×C411yescharacteristic
200C2×C79⋊C8C22×C411yescharacteristic
201C2×C79⋊C8C22×C411yescharacteristic
202C2×C79⋊C8C22×C411yescharacteristic
203C2×C79⋊C8C2×D412yes—
204C2×C79⋊C8#4112yes—
205C8×D79—42no—
206C4⋊Dic79C22×C411yescharacteristic
207C4⋊Dic79C22×C411yescharacteristic
208Dic79⋊C4—21no—
209Dic79⋊C4—21no—
210C22⋊Dic79—24no—
211C22⋊Dic79—21no—
212C22⋊Dic79—21no—
213C22⋊Dic79—21no—
214(C2×D79)⋊C4—21no—
215(C2×D79)⋊C4—21no—
216C4×Dic79—21no—
217C4×Dic79—21no—
218C4×Dic79—21no—
219C4×Dic79—21no—
220C4×Dic79—21no—
221C24×C79#4111yescharacteristic
222#41×C79—21no—
223#41×C79—21no—
224#41×C79—21no—
225#41×C79—21no—
226C2×Q8×C79C22×C411yescharacteristic
227C2×D4×C79—21no—
228C2×D4×C79—21no—
229C2×D4×C79—21no—
230C2×D4×C79C22×C411yescharacteristic
231C22×C4×C79—21no—
232C22×C4×C79—21no—
233C22×C4×C79—21no—
234C22×C4×C79—21no—
235C22×C4×C79—21no—
236C22×C4×C79C22×C411yescharacteristic
237C22×C4×C79C22×C411yescharacteristic
238C22×C4×C79C2×D411yescharacteristic
239C22×C4×C79C2×D411yescharacteristic
240C22×C4×C79#4111yescharacteristic
241C22×C4×C79C2411yescharacteristic
242M16×C79—21no—
243M16×C79—21no—
244M16×C79—21no—
245M16×C79—42no—
246M16×C79—42no—
247M16×C79C2×D412yes—
248C2×C8×C79—21no—
249C2×C8×C79—21no—
250C2×C8×C79—21no—
251C2×C8×C79—21no—
252C2×C8×C79—21no—
253C2×C8×C79—21no—
254C2×C8×C79—42no—
255C2×C8×C79—42no—
256C2×C8×C79C2×D411yescharacteristic
257C2×C8×C79C2×D411yescharacteristic
258C2×C8×C79C2×D411yescharacteristic
259C2×C8×C79C2×D411yescharacteristic
260C4⋊C4×C79—21no—
261C4⋊C4×C79—21no—
262C4⋊C4×C79C22×C411yescharacteristic
263C4⋊C4×C79C22×C411yescharacteristic
264C22⋊C4×C79—21no—
265C22⋊C4×C79—21no—
266C22⋊C4×C79—21no—
267C22⋊C4×C79—21no—
268C22⋊C4×C79—21no—
269C42×C79—21no—
270C23×C79—21no—
271C23×C79—21no—
272C23×C79—22no—
273C23×C79—21no—
274C23×C79—41no—
275C23×C79C4×D411yescharacteristic
276C23×C79C4×D411yescharacteristic
277C23×C79C2×#4111yescharacteristic
278C22×D79—21no—
279Q8×C79—21no—
280Q8×C79—21no—
281D4×C79—21no—
282D4×C79—21no—
283D4×C79—41no—
284D4×C79—41no—
285D4×C79—42no—
286D4×C79—81no—
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—21no—
299C2×C4×C79—21no—
300C2×C4×C79—41no—
301C2×C4×C79—41no—
302C2×C4×C79C4×D411yescharacteristic
303C2×C4×C79C4×D411yescharacteristic
304C2×C4×C79C23×C411yescharacteristic
305C2×C4×C79C22×D411yescharacteristic
306C2×C4×C79C22×D411yescharacteristic
307C2×C4×C79C2×#4111yescharacteristic
308C2×C4×C79H(5,𝔽2)11yescharacteristic
309C2×C4×C792−1+411yescharacteristic
310C22⋊D79—41no—
311C22⋊D79—41no—
312C22⋊D79—42no—
313C22⋊D79—81no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—21no—
317C2×Dic79—21no—
318C2×Dic79—21no—
319C2×Dic79—41no—
320C2×Dic79—41no—
321C2×Dic79—41no—
322C2×Dic79—41no—
323D316—21no—
324D316—21no—
325C4×D79—41no—
326C4×D79—41no—
327Dic158—21no—
328Dic158—21no—
329C8×C79—21no—
330C8×C79—21no—
331C8×C79—22no—
332C8×C79—21no—
333C8×C79—21no—
334C8×C79—41no—
335C79⋊C8—21no—
336C79⋊C8—21no—
337C79⋊C8—22no—
338C79⋊C8—41no—
339C79⋊C8C4×D412yes—
340C79⋊C8C4×D412yes—
341C22×C79—21no—
342C22×C79—21no—
343C22×C79—21no—
344C22×C79—21no—
345C22×C79—21no—
346C22×C79—21no—
347C22×C79—21no—
348C22×C79—42no—
349C22×C79—42no—
350C22×C79—41no—
351C22×C79—41no—
352C22×C79—41no—
353C22×C79#44312yescomplemented
354C22×C79C2×C4×D411yescharacteristic
355C22×C79#54811yescharacteristic
356C22×C79#55311yescharacteristic
357C2×D79—41no—
358C2×D79—41no—
359C2×D79—41no—
360C4×C79—21no—
361C4×C79—21no—
362C4×C79—41no—
363C4×C79—41no—
364C4×C79—41no—
365C4×C79C2×C4×D411yescharacteristic
366C4×C79#52011yescharacteristic
367C4×C79D4211yescharacteristic
368C4×C79#54711yescharacteristic
369Dic79—42no—
370Dic79—42no—
371Dic79—41no—
372Dic79—41no—
373Dic79—41no—
374#23018—791nomaximal, Sylow
375C2×C79—21no—
376C2×C79—21no—
377C2×C79—22no—
378C2×C79—41no—
379C2×C79—81no—
380C2×C79#236111yescharacteristic
381C2×C79C2×#44311yescharacteristic
382C2×C79#295711yescharacteristic
383D79—81no—
384#3050—791no—
385C2×#443—791no—
386#2933—791no—
387#2933D7911yescharacteristic, complemented
388C22×#108—791no—
389#1974—791no—
390#1945—791no—
391#1929—791no—
392#1929—791no—
393#1871—791no—
394#1871—791no—
395#1866—791no—
396#1866—791no—
397#1772—791no—
398C8×C22⋊C4—791no—
399C79#2301811yescharacteristic, complemented, Sylow
400C2×#135—791no—
401C2×#131—791no—
402C2×#131C2×D7911yescharacteristic
403C22×M16—791no—
404C22×M16C2×D7911yescharacteristic
405C23×C8—791no—
406#525—791no—
407#525C2×D7911yescharacteristic
408#467—791no—
409#467—791no—
410#466—791no—
411#466—791no—
412#465—791no—
413#465—791no—
414#465—791no—
415#465—791no—
416#443—1584no—
417#436—21no—
418#436—1581no—
419#435—21no—
420#435—21no—
421#435—1581no—
422#435—1581no—
423C8×D4—21no—
424C8×D4—1581no—
425C2×#108—791no—
426C2×#108—791no—
427C2×#108—791no—
428C2×#108—791no—
429C2×#108—1584no—
430#427—791no—
431#424—791no—
432#424C2×D7911yescharacteristic
433C2×#104—791no—
434C2×#104—791no—
435C2×#104—791no—
436C2×#104—791no—
437#416—791no—
438#416—791no—
439#408—791no—
440#408C2×D7911yescharacteristic
441C2×C22⋊C8C2×D7911yescharacteristic
442#405—791no—
443#405C2×D7911yescharacteristic
444C2×C4×C8—791no—
445C2×C4×C8—791no—
446C4×C22⋊C4—791no—
447#339—791no—
448#339—791no—
449#339—791no—
450#339—791no—
451#336—791no—
452#336—791no—
453C2×#41—791no—
454C2×#41C22×D7911yescharacteristic
455C23×C4C22×D7911yescharacteristic
456#135—1582no—
457#135—1582no—
458C2×Q16—791no—
459C2×SD16—791no—
460C2×SD16—791no—
461C2×D8—791no—
462#131—22no—
463#131—41no—
464#131—3161no—
465#131—1582no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—22no—
469C2×M16—41no—
470C2×M16—3161no—
471C2×M16—791no—
472C2×M16—791no—
473C2×M16—1582no—
474C2×M16—1581no—
475C2×M16—1581no—
476C2×M16C22×D7911yescharacteristic
477C2×M16C22×D7911yescharacteristic
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—791no—
481C22×C8—791no—
482C22×C8—791no—
483C22×C8—791no—
484C22×C8—791no—
485C22×C8—791no—
486C22×C8—1581no—
487C22×C8—1581no—
488C22×C8—1582no—
489C22×C8—1582no—
490C22×C8C22×D7911yescharacteristic
491C22×C8C22×D7911yescharacteristic
492#123—21no—
493#123—1581no—
494C22⋊Q8—791no—
495C22⋊Q8—791no—
496C22⋊Q8C4×D7911yescharacteristic
497C22⋊Q8C4×D7911yescharacteristic
498#121—791no—
499#121—791no—
500#121C4×D7911yescharacteristic
501#121C4×D7911yescharacteristic
502#120—21no—
503#120—1581no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—1581no—
507C4×D4—1581no—
508#117—791no—
509#117C22×D7911yescharacteristic
510C2×C22⋊C4—1581no—
511C2×C42—791no—
512C2×C42—791no—
513#108—794no—
514#108—1582no—
515#108—1582no—
516#108—1582no—
517#107—791no—
518#107—791no—
519#106—791no—
520#106—791no—
521C4⋊C8—21no—
522C4⋊C8—21no—
523C4⋊C8—1581no—
524C4⋊C8—1581no—
525#104—3161no—
526#104—3161no—
527#104—1582no—
528#104—1582no—
529#103—791no—
530#103—791no—
531#103—791no—
532#103—791no—
533#102—791no—
534#102—791no—
535#102—791no—
536#102—791no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8—1581no—
540C22⋊C8—1581no—
541C22⋊C8C22⋊D7911yescharacteristic
542C22⋊C8C22⋊D7911yescharacteristic
543C22⋊C8C22⋊D7911yescharacteristic
544C22⋊C8C22⋊D7911yescharacteristic
545#97—21no—
546#97—1581no—
547C4×C8—21no—
548C4×C8—1582no—
549C4×C8—1582no—
550C4×C8—1581no—
551#95—1581no—
552C24#1192962411yescharacteristic
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557#41—1581no—
558#41—1581no—
559#41—1581no—
560#41—1581no—
561C2×Q8—791no—
562C2×Q8C2×C4×D7911yescharacteristic
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—791no—
567C2×D4—1581no—
568C2×D4—1581no—
569C2×D4—1581no—
570C2×D4C2×C4×D7911yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—1581no—
577C22×C4—1581no—
578C22×C4—1581no—
579C22×C4C2×C4×D7911yescharacteristic
580C22×C4C2×C4×D7911yescharacteristic
581C22×C4C2×C22⋊D7911yescharacteristic
582C22×C4C2×C22⋊D7911yescharacteristic
583C22×C4#1192962411yescharacteristic
584C22×C4C23×D7911yescharacteristic
585Q16—1582no—
586SD16—1582no—
587SD16—1582no—
588D8—1582no—
589M16—21no—
590M16—21no—
591M16—21no—
592M16—42no—
593M16—42no—
594M16—3162no—
595M16—3162no—
596M16—792no—
597M16—1581no—
598M16—1581no—
599M16—1581no—
600M16D4×D7912yes—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—42no—
608C2×C8—42no—
609C2×C8—3162no—
610C2×C8—3162no—
611C2×C8—792no—
612C2×C8—791no—
613C2×C8—791no—
614C2×C8—792no—
615C2×C8—791no—
616C2×C8—791no—
617C2×C8—1581no—
618C2×C8—1582no—
619C2×C8—1582no—
620C2×C8—1582no—
621C2×C8—1582no—
622C2×C8—1581no—
623C2×C8—1581no—
624C2×C8—1581no—
625C2×C8C2×C22⋊D7911yescharacteristic
626C2×C8C2×C22⋊D7911yescharacteristic
627C2×C8C2×C22⋊D7911yescharacteristic
628C2×C8C2×C22⋊D7911yescharacteristic
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—791no—
632C4⋊C4—791no—
633C4⋊C4—1581no—
634C4⋊C4—1581no—
635C4⋊C4C2×C4×D7911yescharacteristic
636C4⋊C4C2×C4×D7911yescharacteristic
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—1584no—
643C22⋊C4—1581no—
644C22⋊C4—1581no—
645C22⋊C4—1581no—
646C22⋊C4—1581no—
647C22⋊C4—1581no—
648C42—21no—
649C42—1581no—
650C42—1581no—
651C42—1581no—
652C42—1581no—
653C42—1581no—
654C23—22no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—41no—
659C23—1581no—
660C23C4×C22⋊D7911yescharacteristic
661C23C4×C22⋊D7911yescharacteristic
662C23C2×#1192962411yescharacteristic
663Q8—21no—
664Q8—21no—
665Q8—1581no—
666Q8—1581no—
667D4—21no—
668D4—21no—
669D4—42no—
670D4—41no—
671D4—41no—
672D4—81no—
673D4—3162no—
674D4—3161no—
675D4—3161no—
676D4—6321no—
677D4—1581no—
678D4—1581no—
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—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—3161no—
695C2×C4—3161no—
696C2×C4—3161no—
697C2×C4—3161no—
698C2×C4—3161no—
699C2×C4—3161no—
700C2×C4—1582no—
701C2×C4—1582no—
702C2×C4—1581no—
703C2×C4—1581no—
704C2×C4—1581no—
705C2×C4C4×C22⋊D7911yescharacteristic
706C2×C4C4×C22⋊D7911yescharacteristic
707C2×C4C22×C4×D7911yescharacteristic
708C2×C4C2×D4×D7911yescharacteristic
709C2×C4C22×C22⋊D7911yescharacteristic
710C2×C4#41×D7911yescharacteristic
711C2×C4#1457920611yescharacteristic
712C2×C4#1457920811yescharacteristic
713C8—21no—
714C8—21no—
715C8—22no—
716C8—21no—
717C8—21no—
718C8—41no—
719C8—3161no—
720C8—792no—
721C8—792no—
722C8—1582no—
723C8—1581no—
724C8—1581no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—3161no—
738C22—3161no—
739C22—3161no—
740C22#1909867812yescomplemented
741C22C2×C4×C22⋊D7911yescharacteristic
742C22#1909922211yescharacteristic
743C22#1909926211yescharacteristic
744C4—21no—
745C4—21no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—3162no—
750C4—3162no—
751C4—3161no—
752C4—3161no—
753C4—3161no—
754C4C4×D4×D7911yescharacteristic
755C4#1909904211yescharacteristic
756C4D4×C22⋊D7911yescharacteristic
757C4#1909921211yescharacteristic
758C2—21no—
759C2—21no—
760C2—22no—
761C2—41no—
762C2—81no—
763C2—6321no—
764C2#2376641711yescharacteristic
765C2C2×#1909867811yescharacteristic
766C2#2377231511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2933C2
socleC22×C79C2×C4×D4
prime radical#23772978C2
cosocleC22×C4×C79C24
hypercenter#2933D79
hypocenterC79#23018
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2933

Complements

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

NH ≅ G/Ntype
2. C2×#19098678C2semidirect
3. #23772121C2semidirect
4. C22×#14579096C2semidirect
5. #23764287C2semidirect
6. #23764145C2semidirect
7. #23764048C2semidirect
8. #23764045C2semidirect
9. #23763703C2semidirect
10. #23763702C2semidirect
11. #23763675C2semidirect
12. #23763674C2semidirect
13. #23763280C2semidirect
14. #23763174C2semidirect
15. C79×#2933C2semidirect
21. #19098802C4semidirect
22. #19098802C4semidirect
23. #19098797C4semidirect
24. #19098797C4semidirect
25. #19098794C4semidirect
26. #19098794C4semidirect
27. #19098790C4semidirect
28. #19098790C4semidirect
109. #14579096D4semidirect
353. C22×C79#443semidirect
387. #2933D79semidirect
399. C79#23018semidirect
740. C22#19098678semidirect

Maximal subgroups

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

subgroupindex
#237729782
C2×#190986782
#237721212
C22×#145790962
#237642872
#237641452
#237640482
#237640452
#237637032
#237637022
#237636752
#237636742
#237632802
#237631742
C79×#29332
#2301879