Finite Group Databasebeta

← #34310799

Subgroups — #34310799

Order 20224.

864 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772855C211yesmaximal, characteristic
2C2×#19098683C211yesmaximal, characteristic, complemented
3C2×#19098678C211yesmaximal, characteristic, complemented
4#23772143C211yesmaximal, characteristic, complemented
5#23764231C211yesmaximal, characteristic, complemented
6#23764173C211yesmaximal, characteristic, complemented
7#23764110C211yesmaximal, characteristic, complemented
8#23764103C211yesmaximal, characteristic, complemented
9#23763727C211yesmaximal, characteristic, complemented
10#23763727C211yesmaximal, characteristic, complemented
11#23763674C211yesmaximal, characteristic, complemented
12#23763674C211yesmaximal, characteristic, complemented
13#23763259C211yesmaximal, characteristic, complemented
14#23763210C211yesmaximal, characteristic, complemented
15C79×#2906C211yesmaximal, characteristic, complemented
16C2×#14579181C2211yescharacteristic
17C2×#14579181C2211yescharacteristic
18C2×#14579167C2211yescharacteristic
19C2×#14579167C2211yescharacteristic
20#19099113C2211yescharacteristic
21#19098785C411yescharacteristic, complemented
22#19098785C411yescharacteristic, complemented
23#19098778C411yescharacteristic, complemented
24#19098778C411yescharacteristic, complemented
25#19098773C411yescharacteristic, complemented
26#19098768C411yescharacteristic, complemented
27#19098763C411yescharacteristic, complemented
28#19098758C411yescharacteristic, complemented
29#19098683—24no—
30#19098678—24no—
31#19098640—21no—
32#19098633—21no—
33#19098633—21no—
34#19098628—21no—
35C2×#14579096C2211yescharacteristic
36C2×#14579096C2211yescharacteristic
37C2×C4⋊(C79⋊C8)C2211yescharacteristic
38C2×#14579088C2211yescharacteristic
39C2×#14579088C2211yescharacteristic
40C2×#14579087C2211yescharacteristic
41C2×#14579087C2211yescharacteristic
42C2×#14579087C2211yescharacteristic
43C2×#14579087C2211yescharacteristic
44#19098557C2211yescharacteristic
45#19098557C2211yescharacteristic
46#19098529C2211yescharacteristic
47#19098529C2211yescharacteristic
48C4×#11929608C2211yescharacteristic
49C2×#14579071C2211yescharacteristic
50C2×C8×Dic79C2211yescharacteristic
51#19098409C2211yescharacteristic
52#19098327C2211yescharacteristic
53#19098327C2211yescharacteristic
54#19098322C2211yescharacteristic
55#19098322C2211yescharacteristic
56#19098317C2211yescharacteristic
57#19098317C2211yescharacteristic
58C2×#131×C79C2211yescharacteristic
59C2×#131×C79C2211yescharacteristic
60C4×#41×C79C2211yescharacteristic
61#424×C79—21no—
62#424×C79—21no—
63#424×C79C2211yescharacteristic
64#424×C79C2211yescharacteristic
65#423×C79—21no—
66#423×C79C2211yescharacteristic
67C2×C4⋊C8×C79—21no—
68C2×C4⋊C8×C79C2211yescharacteristic
69C2×#11929624C2311yescharacteristic
70C2×#11929624C2311yescharacteristic
71#14579181—22no—
72#14579181—22no—
73#14579181—22no—
74#14579181—22no—
75C2×#11929614C2×C411yescharacteristic
76C2×#11929614C2×C411yescharacteristic
77C2×#11929612C2×C411yescharacteristic
78C2×#11929612C2×C411yescharacteristic
79C2×#11929611C2×C411yescharacteristic
80C2×#11929611C2×C411yescharacteristic
81C2×#11929609C2×C411yescharacteristic
82C2×#11929609C2×C411yescharacteristic
83#14579167—22no—
84#14579167—22no—
85#14579167—41no—
86#14579167—41no—
87C2×#11929608C2311yescharacteristic
88C2×#11929608C2311yescharacteristic
89C2×#11929607—21no—
90C2×#11929607—21no—
91C22×C79⋊C8C2311yescharacteristic
92C22×C79⋊C8C2311yescharacteristic
93C2×C8×D79—21no—
94C2×C8×D79—21no—
95#14579161C2×C411yescharacteristic
96#14579158C2×C411yescharacteristic
97#14579149C2×C411yescharacteristic
98#14579149C2×C411yescharacteristic
99#14579135—21no—
100#14579135—21no—
101C4×D316—21no—
102C4×D316—21no—
103C2×C4×Dic79C2311yescharacteristic
104C2×C4×Dic79C2311yescharacteristic
105#14579096—22no—
106#14579096—22no—
107C4⋊(C79⋊C8)C2×C411yescharacteristic
108C4⋊(C79⋊C8)C2×C411yescharacteristic
109C4⋊(C79⋊C8)C2×C411yescharacteristic
110C4⋊(C79⋊C8)C2×C411yescharacteristic
111#14579088—22no—
112#14579088D414yescomplemented
113#14579087—22no—
114#14579087—22no—
115#14579087—41no—
116#14579087—41no—
117#14579084C2×C411yescharacteristic
118#14579084C2×C411yescharacteristic
119#14579084C2×C411yescharacteristic
120#14579084C2×C411yescharacteristic
121#14579081C2×C411yescharacteristic
122#14579081C2×C411yescharacteristic
123#14579081C2×C411yescharacteristic
124#14579081C2×C411yescharacteristic
125(C2×D79)⋊C8—21no—
126(C2×D79)⋊C8—21no—
127(C2×D79)⋊C8—21no—
128(C2×D79)⋊C8—21no—
129#14579072—21no—
130#14579071—22no—
131C4×C79⋊C8—21no—
132C8×Dic79—22no—
133C79⋊#95—21no—
134C79⋊#95—21no—
135C2×#41×C79C2311yescharacteristic
136#131×C79—22no—
137#131×C79—22no—
138#131×C79—41no—
139#131×C79—41no—
140C2×M16×C79—21no—
141C2×M16×C79—21no—
142C2×M16×C79C2311yescharacteristic
143C2×M16×C79C2311yescharacteristic
144C22×C8×C79—21no—
145C22×C8×C79—21no—
146C22×C8×C79C2311yescharacteristic
147C22×C8×C79C2311yescharacteristic
148C4×Q8×C79C2×C411yescharacteristic
149C4×Q8×C79C2×C411yescharacteristic
150C4×D4×C79—21no—
151C4×D4×C79—21no—
152C4×D4×C79C2×C411yescharacteristic
153C4×D4×C79C2×C411yescharacteristic
154#117×C79—21no—
155#117×C79C2311yescharacteristic
156C2×C42×C79—21no—
157C2×C42×C79C2311yescharacteristic
158C4⋊C8×C79—21no—
159C4⋊C8×C79—21no—
160C4⋊C8×C79—21no—
161C4⋊C8×C79—21no—
162C4⋊C8×C79—21no—
163C4⋊C8×C79—21no—
164C4⋊C8×C79D411yescharacteristic
165C4⋊C8×C79D411yescharacteristic
166C4⋊C8×C79D411yescharacteristic
167C4⋊C8×C79D411yescharacteristic
168#11929624—21no—
169#11929624—21no—
170#11929624—21no—
171#11929624—21no—
172#11929624—21no—
173#11929624—21no—
174#11929624—21no—
175#11929624—21no—
176C2×Dic158C22×C411yescharacteristic
177C2×Dic158C22×C411yescharacteristic
178C2×D316—21no—
179C2×D316—21no—
180C2×D316C22×C411yescharacteristic
181C2×D316C22×C411yescharacteristic
182C2×C22⋊D79—21no—
183C2×C22⋊D79—21no—
184C22×Dic79—21no—
185C22×Dic79—21no—
186C2×C4×D79—21no—
187C2×C4×D79—21no—
188#11929614—22no—
189#11929614—22no—
190#11929612—22no—
191#11929612—22no—
192#11929611—22no—
193#11929611—22no—
194#11929609—22no—
195#11929609—22no—
196#11929608—21no—
197#11929608—21no—
198#11929608—21no—
199#11929608C2×D412yes—
200#11929607—42no—
201#11929607—42no—
202C2×C79⋊C8—21no—
203C2×C79⋊C8—21no—
204C2×C79⋊C8—21no—
205C2×C79⋊C8—21no—
206C2×C79⋊C8—21no—
207C2×C79⋊C8—21no—
208C2×C79⋊C8C22×C411yescharacteristic
209C2×C79⋊C8C22×C411yescharacteristic
210C2×C79⋊C8C22×C411yescharacteristic
211C2×C79⋊C8C22×C411yescharacteristic
212C8×D79—42no—
213C8×D79—42no—
214C4⋊Dic79—21no—
215C4⋊Dic79—21no—
216(C2×D79)⋊C4—21no—
217(C2×D79)⋊C4—21no—
218(C2×D79)⋊C4—21no—
219(C2×D79)⋊C4—21no—
220C4×Dic79—21no—
221C4×Dic79—21no—
222C4×Dic79—21no—
223C4×Dic79C2×D412yes—
224#41×C79—21no—
225#41×C79—21no—
226#41×C79C2×D412yes—
227#41×C79#4112yes—
228C2×Q8×C79C22×C411yescharacteristic
229C2×D4×C79—21no—
230C2×D4×C79C22×C411yescharacteristic
231C22×C4×C79—21no—
232C22×C4×C79—21no—
233C22×C4×C79—21no—
234C22×C4×C79#4111yescharacteristic
235C22×C4×C79#4111yescharacteristic
236C22×C4×C79C2411yescharacteristic
237M16×C79—21no—
238M16×C79—21no—
239M16×C79—21no—
240M16×C79—21no—
241M16×C79—42no—
242M16×C79—42no—
243C2×C8×C79—21no—
244C2×C8×C79—21no—
245C2×C8×C79—21no—
246C2×C8×C79—21no—
247C2×C8×C79—21no—
248C2×C8×C79—21no—
249C2×C8×C79—42no—
250C2×C8×C79—42no—
251C2×C8×C79C2×D411yescharacteristic
252C2×C8×C79C2×D411yescharacteristic
253C2×C8×C79C2×D411yescharacteristic
254C2×C8×C79C2×D411yescharacteristic
255C4⋊C4×C79—21no—
256C4⋊C4×C79—21no—
257C4⋊C4×C79C22×C411yescharacteristic
258C4⋊C4×C79C22×C411yescharacteristic
259C22⋊C4×C79—21no—
260C22⋊C4×C79—21no—
261C22⋊C4×C79—21no—
262C42×C79—21no—
263C42×C79—21no—
264C42×C79—21no—
265C42×C79C22×C411yescharacteristic
266C42×C79C22×C411yescharacteristic
267C42×C79C2×D411yescharacteristic
268C42×C79C2×D411yescharacteristic
269C23×C79—21no—
270C23×C79C2×#4111yescharacteristic
271C22×D79—21no—
272C22×D79—21no—
273Q8×C79—21no—
274Q8×C79C4×D412yes—
275D4×C79—22no—
276D4×C79—22no—
277D4×C79—21no—
278D4×C79C4×D412yes—
279C2×C4×C79—21no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—21no—
283C2×C4×C79—21no—
284C2×C4×C79—41no—
285C2×C4×C79—41no—
286C2×C4×C79—42no—
287C2×C4×C79—81no—
288C2×C4×C79C4×D411yescharacteristic
289C2×C4×C79C4×D411yescharacteristic
290C2×C4×C79C4×D411yescharacteristic
291C2×C4×C79C4×D411yescharacteristic
292C2×C4×C79C23×C411yescharacteristic
293C2×C4×C79C22×D411yescharacteristic
294C2×C4×C79C22×D411yescharacteristic
295C2×C4×C79C2×#4111yescharacteristic
296C2×C4×C79H(5,𝔽2)11yescharacteristic
297C2×C4×C792−1+411yescharacteristic
298C22⋊D79—41no—
299C22⋊D79—41no—
300C22⋊D79—41no—
301C22⋊D79—41no—
302C2×Dic79—21no—
303C2×Dic79—21no—
304C2×Dic79—22no—
305C2×Dic79—41no—
306C2×Dic79—41no—
307C2×Dic79—41no—
308C2×Dic79—41no—
309C2×Dic79—41no—
310D316—21no—
311D316—21no—
312D316—21no—
313D316—21no—
314D316—42no—
315D316—81no—
316C4×D79—41no—
317C4×D79—41no—
318C4×D79—41no—
319C4×D79—41no—
320Dic158—21no—
321Dic158—21no—
322Dic158—21no—
323Dic158—21no—
324C8×C79—21no—
325C8×C79—21no—
326C8×C79—21no—
327C8×C79—21no—
328C8×C79—41no—
329C8×C79—41no—
330C79⋊C8—21no—
331C79⋊C8—21no—
332C79⋊C8—21no—
333C79⋊C8—21no—
334C79⋊C8—22no—
335C79⋊C8—41no—
336C22×C79—21no—
337C22×C79—21no—
338C22×C79—22no—
339C22×C79—41no—
340C22×C79—41no—
341C22×C79C2×C4×D411yescharacteristic
342C22×C79#54711yescharacteristic
343C22×C79#55311yescharacteristic
344C2×D79—41no—
345C2×D79—41no—
346C2×D79—41no—
347C2×D79—41no—
348C2×D79—41no—
349C2×D79—41no—
350C4×C79—22no—
351C4×C79—21no—
352C4×C79—21no—
353C4×C79—21no—
354C4×C79—21no—
355C4×C79—41no—
356C4×C79—41no—
357C4×C79C2×C4×D411yescharacteristic
358C4×C79#52011yescharacteristic
359C4×C79D4211yescharacteristic
360C4×C79#54811yescharacteristic
361Dic79—42no—
362Dic79—41no—
363Dic79—41no—
364Dic79—81no—
365#23017—791nomaximal, Sylow
366C2×C79—21no—
367C2×C79—21no—
368C2×C79—42no—
369C2×C79#236111yescharacteristic
370C2×C79#295511yescharacteristic
371C2×C79#295711yescharacteristic
372D79—81no—
373D79—81no—
374#3035—791no—
375C2×#444—791no—
376C2×#443—791no—
377#2935—791no—
378#2906D7911yescharacteristic, complemented
379#1963—791no—
380#1950—791no—
381#1938—791no—
382#1937—791no—
383#1876—791no—
384#1876—791no—
385#1866—791no—
386#1866—791no—
387#1768—791no—
388#1759—791no—
389C79#2301711yescharacteristic, complemented, Sylow
390C2×#135—791no—
391C2×#135—791no—
392C2×#131—791no—
393C2×#131—791no—
394C2×#131C2×D7911yescharacteristic
395C2×#131C2×D7911yescharacteristic
396#532—791no—
397C4×#41C2×D7911yescharacteristic
398#464—791no—
399#464—791no—
400#463—791no—
401#463—791no—
402#462—791no—
403#461—791no—
404#460—791no—
405#459—791no—
406#444—1584no—
407#443—1584no—
408#436—1581no—
409#435—1581no—
410#435—1581no—
411C8×D4—1581no—
412C2×#108—791no—
413C2×#108—791no—
414#424—21no—
415#424—21no—
416#424C2×D7911yescharacteristic
417#424C2×D7911yescharacteristic
418#423—21no—
419#423C2×D7911yescharacteristic
420C2×C4⋊C8—21no—
421C2×C4⋊C8—791no—
422C2×C4⋊C8C2×D7911yescharacteristic
423C2×#104—791no—
424C2×#104—791no—
425C2×#104—791no—
426C2×#104—791no—
427C2×#104—791no—
428C2×#104—791no—
429#416—791no—
430#416—791no—
431#408—791no—
432#408—791no—
433C4×M16—791no—
434C2×#97—791no—
435C2×C4×C8—791no—
436#376—791no—
437#341—791no—
438#341—791no—
439#339—791no—
440#339—791no—
441#336—791no—
442#336—791no—
443C2×#41—791no—
444C2×#41—791no—
445C2×#41C22×D7911yescharacteristic
446#135—1582no—
447#135—1582no—
448#135—1582no—
449#135—1582no—
450C2×Q16—791no—
451C2×Q16—791no—
452C2×SD16—791no—
453C2×SD16—791no—
454C2×SD16—791no—
455C2×SD16—791no—
456C2×D8—791no—
457C2×D8—791no—
458#131—22no—
459#131—22no—
460#131—41no—
461#131—41no—
462#131—3161no—
463#131—3161no—
464#131—1582no—
465#131—1582no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—791no—
469C2×M16—791no—
470C2×M16—1581no—
471C2×M16—1581no—
472C2×M16C22×D7911yescharacteristic
473C2×M16C22×D7911yescharacteristic
474C22×C8—21no—
475C22×C8—21no—
476C22×C8—791no—
477C22×C8—791no—
478C22×C8—1581no—
479C22×C8—1581no—
480C22×C8C22×D7911yescharacteristic
481C22×C8C22×D7911yescharacteristic
482C4⋊Q8—791no—
483#127—791no—
484#124—791no—
485#124—791no—
486#121—1581no—
487#121—1581no—
488C4×Q8C4×D7911yescharacteristic
489C4×Q8C4×D7911yescharacteristic
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—1581no—
493C4×D4—1581no—
494C4×D4C4×D7911yescharacteristic
495C4×D4C4×D7911yescharacteristic
496#117—21no—
497#117C22×D7911yescharacteristic
498C2×C42—21no—
499C2×C42—791no—
500C2×C42—791no—
501C2×C42C22×D7911yescharacteristic
502#108—1582no—
503#108—1582no—
504C4⋊C8—21no—
505C4⋊C8—21no—
506C4⋊C8—21no—
507C4⋊C8—21no—
508C4⋊C8—21no—
509C4⋊C8—21no—
510C4⋊C8—791no—
511C4⋊C8—791no—
512C4⋊C8—791no—
513C4⋊C8—791no—
514C4⋊C8C22⋊D7911yescharacteristic
515C4⋊C8C22⋊D7911yescharacteristic
516C4⋊C8C22⋊D7911yescharacteristic
517C4⋊C8C22⋊D7911yescharacteristic
518#104—3161no—
519#104—3161no—
520#104—794no—
521#104—1582no—
522#104—1582no—
523#104—1582no—
524#103—791no—
525#103—791no—
526#103—791no—
527#103—791no—
528#102—791no—
529#102—791no—
530#102—791no—
531#102—791no—
532C22⋊C8—1581no—
533C22⋊C8—1581no—
534C22⋊C8—1581no—
535C22⋊C8—1581no—
536#97—1582no—
537#97—1581no—
538C4×C8—1582no—
539C4×C8—1581no—
540#95—1581no—
541#95—1581no—
542#41—21no—
543#41—21no—
544#41—1581no—
545#41—1581no—
546#41—1581no—
547#41—1581no—
548#41—1581no—
549#41—1581no—
550#41—1581no—
551#41—1581no—
552#41D4×D7912yes—
553#41#1192962512yes—
554C2×Q8—791no—
555C2×Q8—791no—
556C2×Q8C2×C4×D7911yescharacteristic
557C2×D4—21no—
558C2×D4—791no—
559C2×D4—791no—
560C2×D4—1581no—
561C2×D4—1581no—
562C2×D4—1581no—
563C2×D4—1581no—
564C2×D4C2×C4×D7911yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—1581no—
569C22×C4—1581no—
570C22×C4—1581no—
571C22×C4—1581no—
572C22×C4#1192962411yescharacteristic
573C22×C4#1192962411yescharacteristic
574C22×C4C23×D7911yescharacteristic
575Q16—1582no—
576Q16—1582no—
577SD16—1582no—
578SD16—1582no—
579SD16—1582no—
580SD16—1582no—
581D8—1582no—
582D8—1582no—
583M16—21no—
584M16—21no—
585M16—21no—
586M16—21no—
587M16—42no—
588M16—42no—
589M16—3162no—
590M16—3162no—
591M16—792no—
592M16—1581no—
593M16—1581no—
594M16—1581no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—42no—
602C2×C8—42no—
603C2×C8—3162no—
604C2×C8—3162no—
605C2×C8—791no—
606C2×C8—791no—
607C2×C8—791no—
608C2×C8—791no—
609C2×C8—1581no—
610C2×C8—1581no—
611C2×C8—1581no—
612C2×C8—1581no—
613C2×C8—1581no—
614C2×C8—1581no—
615C2×C8C2×C22⋊D7911yescharacteristic
616C2×C8C2×C22⋊D7911yescharacteristic
617C2×C8C2×C22⋊D7911yescharacteristic
618C2×C8C2×C22⋊D7911yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—1581no—
622C4⋊C4—1581no—
623C4⋊C4C2×C4×D7911yescharacteristic
624C4⋊C4C2×C4×D7911yescharacteristic
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—1581no—
629C22⋊C4—1581no—
630C22⋊C4—1581no—
631C22⋊C4—1581no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—792no—
636C42—1581no—
637C42—1581no—
638C42—1581no—
639C42C2×C4×D7911yescharacteristic
640C42C2×C4×D7911yescharacteristic
641C42C2×C22⋊D7911yescharacteristic
642C42C2×C22⋊D7911yescharacteristic
643C23—21no—
644C23—1581no—
645C23—1581no—
646C23C2×#1192962411yescharacteristic
647Q8—21no—
648Q8—1581no—
649Q8—1581no—
650Q8—1581no—
651Q8—1581no—
652Q8#1457912312yes—
653D4—22no—
654D4—22no—
655D4—21no—
656D4—3162no—
657D4—3161no—
658D4—3161no—
659D4—3161no—
660D4—3161no—
661D4—6321no—
662D4—1581no—
663D4—1581no—
664D4—1581no—
665D4—1581no—
666D4#1457912312yes—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—81no—
676C2×C4—3161no—
677C2×C4—3161no—
678C2×C4—3161no—
679C2×C4—3161no—
680C2×C4—3161no—
681C2×C4—3161no—
682C2×C4—3161no—
683C2×C4—3161no—
684C2×C4—3161no—
685C2×C4—1582no—
686C2×C4—1581no—
687C2×C4—1581no—
688C2×C4C4×C22⋊D7911yescharacteristic
689C2×C4C4×C22⋊D7911yescharacteristic
690C2×C4C4×C22⋊D7911yescharacteristic
691C2×C4C4×C22⋊D7911yescharacteristic
692C2×C4C22×C4×D7911yescharacteristic
693C2×C4C2×D4×D7911yescharacteristic
694C2×C4C22×C22⋊D7911yescharacteristic
695C2×C4C2×#1192962511yescharacteristic
696C2×C4#1457920611yescharacteristic
697C2×C4#1457920911yescharacteristic
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—41no—
703C8—41no—
704C8—3161no—
705C8—1582no—
706C8—1581no—
707C8—1581no—
708C8—1581no—
709C8—1581no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—3161no—
716C22—3161no—
717C22—3161no—
718C22—3161no—
719C22—3161no—
720C22—3161no—
721C22C2×C4×C22⋊D7911yescharacteristic
722C22#1909921411yescharacteristic
723C22#1909926111yescharacteristic
724C4—21no—
725C4—21no—
726C4—22no—
727C4—21no—
728C4—21no—
729C4—41no—
730C4—41no—
731C4—3162no—
732C4—3161no—
733C4—3161no—
734C4—6321no—
735C4C2×#1457912311yescharacteristic
736C4#1909904411yescharacteristic
737C4D4×C22⋊D7911yescharacteristic
738C4#1909922411yescharacteristic
739C2—21no—
740C2—21no—
741C2—42no—
742C2—6321no—
743C2—6321no—
744C2#2376641611yescharacteristic
745C2#2377230111yescharacteristic
746C2#2377231511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2906C2
socleC22×C79C2×C4×D4
prime radical#23772855C2
cosocleC22×C4×C79C24
hypercenter#2906D79
hypocenterC79#23017
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. C2×#19098683C2semidirect
3. C2×#19098678C2semidirect
4. #23772143C2semidirect
5. #23764231C2semidirect
6. #23764173C2semidirect
7. #23764110C2semidirect
8. #23764103C2semidirect
9. #23763727C2semidirect
10. #23763727C2semidirect
11. #23763674C2semidirect
12. #23763674C2semidirect
13. #23763259C2semidirect
14. #23763210C2semidirect
15. C79×#2906C2semidirect
21. #19098785C4semidirect
22. #19098785C4semidirect
23. #19098778C4semidirect
24. #19098778C4semidirect
25. #19098773C4semidirect
26. #19098768C4semidirect
27. #19098763C4semidirect
28. #19098758C4semidirect
112. #14579088D4semidirect
378. #2906D79semidirect
389. C79#23017semidirect

Maximal subgroups

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

subgroupindex
#237728552
C2×#190986832
C2×#190986782
#237721432
#237642312
#237641732
#237641102
#237641032
#237637272
#237636742
#237632592
#237632102
C79×#29062
#2301779