Finite Group Databasebeta

← #34294735

Subgroups — #34294735

Order 20224.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 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#23772119C211yesmaximal, characteristic, complemented
5#23764319C211yesmaximal, characteristic, complemented
6#23764175C211yesmaximal, characteristic, complemented
7#23764048C211yesmaximal, characteristic, complemented
8#23764048C211yesmaximal, characteristic, complemented
9#23763727C211yesmaximal, characteristic, complemented
10#23763727C211yesmaximal, characteristic, complemented
11#23763420C211yesmaximal, characteristic, complemented
12#23763272C211yesmaximal, characteristic, complemented
13#23763246C211yesmaximal, characteristic, complemented
14#23763239C211yesmaximal, characteristic, complemented
15C79×#2875C211yesmaximal, 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#19098636—21no—
32#19098636—21no—
33#19098636—21no—
34#19098636—21no—
35C2×#14579096C2211yescharacteristic
36C2×#14579096C2211yescharacteristic
37#19098587C2211yescharacteristic
38C2×C4⋊(C79⋊C8)C2211yescharacteristic
39C2×#14579088C2211yescharacteristic
40C2×#14579088C2211yescharacteristic
41C2×#14579087C2211yescharacteristic
42C2×#14579087C2211yescharacteristic
43C2×#14579087C2211yescharacteristic
44C2×#14579087C2211yescharacteristic
45#19098557C2211yescharacteristic
46#19098557C2211yescharacteristic
47#19098529C2211yescharacteristic
48#19098529C2211yescharacteristic
49C2×#14579071C2211yescharacteristic
50C2×C8×Dic79C2211yescharacteristic
51C4×C4⋊Dic79C2211yescharacteristic
52#19098327C2211yescharacteristic
53#19098327C2211yescharacteristic
54#19098322C2211yescharacteristic
55#19098322C2211yescharacteristic
56#19098317C2211yescharacteristic
57#19098317C2211yescharacteristic
58C2×#131×C79C2211yescharacteristic
59C2×#131×C79C2211yescharacteristic
60C4×#41×C79C2211yescharacteristic
61#405×C79—21no—
62#405×C79—21no—
63#405×C79C2211yescharacteristic
64#405×C79C2211yescharacteristic
65C4×M16×C79—21no—
66C4×M16×C79C2211yescharacteristic
67C2×#97×C79—21no—
68C2×#97×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—22no—
86#14579167—22no—
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⋊Dic79—21no—
104C2×C4×Dic79C2311yescharacteristic
105C2×C4×Dic79C2311yescharacteristic
106#14579096—22no—
107#14579096—22no—
108C4⋊(C79⋊C8)—21no—
109C4⋊(C79⋊C8)—21no—
110C4⋊(C79⋊C8)C2×C411yescharacteristic
111C4⋊(C79⋊C8)C2×C411yescharacteristic
112C4⋊(C79⋊C8)C2×C411yescharacteristic
113C4⋊(C79⋊C8)C2×C411yescharacteristic
114#14579088—22no—
115#14579088—22no—
116#14579087—22no—
117#14579087—22no—
118#14579087—22no—
119#14579087—22no—
120#14579084C2×C411yescharacteristic
121#14579084C2×C411yescharacteristic
122#14579084C2×C411yescharacteristic
123#14579084C2×C411yescharacteristic
124#14579081C2×C411yescharacteristic
125#14579081C2×C411yescharacteristic
126#14579081C2×C411yescharacteristic
127#14579081C2×C411yescharacteristic
128(C2×D79)⋊C8—21no—
129(C2×D79)⋊C8—21no—
130(C2×D79)⋊C8—21no—
131(C2×D79)⋊C8—21no—
132#14579071—22no—
133C8×Dic79—22no—
134C79⋊#95—21no—
135C2×#41×C79C2311yescharacteristic
136#131×C79—22no—
137#131×C79—22no—
138#131×C79—22no—
139#131×C79D414yescomplemented
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
158#97×C79—21no—
159#97×C79—21no—
160#97×C79—21no—
161#97×C79D411yescharacteristic
162#97×C79D411yescharacteristic
163#97×C79D411yescharacteristic
164#97×C79D411yescharacteristic
165C4×C8×C79—21no—
166C4×C8×C79—21no—
167C4×C8×C79—21no—
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#11929608—21no—
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—
216C4⋊Dic79—42no—
217(C2×D79)⋊C4—21no—
218(C2×D79)⋊C4—21no—
219(C2×D79)⋊C4—21no—
220(C2×D79)⋊C4—21no—
221C4×Dic79—21no—
222C4×Dic79—21no—
223C4×Dic79—21no—
224C4×Dic79—21no—
225#41×C79—21no—
226#41×C79—21no—
227#41×C79C2×D412yes—
228#41×C79#4112yes—
229C2×Q8×C79C22×C411yescharacteristic
230C2×D4×C79—21no—
231C2×D4×C79C22×C411yescharacteristic
232C22×C4×C79—21no—
233C22×C4×C79—21no—
234C22×C4×C79—21no—
235C22×C4×C79#4111yescharacteristic
236C22×C4×C79#4111yescharacteristic
237C22×C4×C79C2411yescharacteristic
238M16×C79—24no—
239M16×C79—24no—
240M16×C79—21no—
241M16×C79—21no—
242M16×C79C2×D412yes—
243M16×C79#4112yes—
244C2×C8×C79—24no—
245C2×C8×C79—24no—
246C2×C8×C79—21no—
247C2×C8×C79—21no—
248C2×C8×C79—21no—
249C2×C8×C79—21no—
250C2×C8×C79C2×D411yescharacteristic
251C2×C8×C79C2×D411yescharacteristic
252C2×C8×C79C2×D411yescharacteristic
253C2×C8×C79C2×D411yescharacteristic
254C2×C8×C79C2×D412yes—
255C2×C8×C79#4112yes—
256C4⋊C4×C79—21no—
257C4⋊C4×C79—21no—
258C4⋊C4×C79C22×C411yescharacteristic
259C4⋊C4×C79C22×C411yescharacteristic
260C22⋊C4×C79—21no—
261C22⋊C4×C79—21no—
262C22⋊C4×C79—21no—
263C42×C79—21no—
264C42×C79—21no—
265C42×C79—21no—
266C42×C79C22×C411yescharacteristic
267C42×C79C22×C411yescharacteristic
268C42×C79C2×D411yescharacteristic
269C42×C79C2×D411yescharacteristic
270C23×C79—21no—
271C23×C79C2×#4111yescharacteristic
272C22×D79—21no—
273C22×D79—21no—
274Q8×C79—21no—
275Q8×C79C4×D412yes—
276D4×C79—22no—
277D4×C79—22no—
278D4×C79—21no—
279D4×C79C4×D412yes—
280C2×C4×C79—21no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—21no—
284C2×C4×C79—21no—
285C2×C4×C79—41no—
286C2×C4×C79—41no—
287C2×C4×C79—81no—
288C2×C4×C79—81no—
289C2×C4×C79C4×D411yescharacteristic
290C2×C4×C79C4×D411yescharacteristic
291C2×C4×C79C4×D411yescharacteristic
292C2×C4×C79C4×D411yescharacteristic
293C2×C4×C79C23×C411yescharacteristic
294C2×C4×C79C22×D411yescharacteristic
295C2×C4×C79C22×D411yescharacteristic
296C2×C4×C79C2×#4111yescharacteristic
297C2×C4×C79C2×#4111yescharacteristic
298C2×C4×C79C2×#4111yescharacteristic
299C22⋊D79—41no—
300C22⋊D79—41no—
301C22⋊D79—41no—
302C22⋊D79—41no—
303C2×Dic79—22no—
304C2×Dic79—21no—
305C2×Dic79—21no—
306C2×Dic79—41no—
307C2×Dic79—41no—
308C2×Dic79—41no—
309C2×Dic79—41no—
310C2×Dic79—41no—
311D316—21no—
312D316—21no—
313D316—21no—
314D316—21no—
315D316—81no—
316D316—81no—
317C4×D79—41no—
318C4×D79—41no—
319C4×D79—41no—
320C4×D79—41no—
321Dic158—21no—
322Dic158—21no—
323Dic158—21no—
324Dic158—21no—
325C8×C79—22no—
326C8×C79—21no—
327C8×C79—22no—
328C8×C79—21no—
329C8×C79#12112yes—
330C8×C79#12112yes—
331C79⋊C8—21no—
332C79⋊C8—21no—
333C79⋊C8—21no—
334C79⋊C8—21no—
335C79⋊C8—41no—
336C79⋊C8—41no—
337C22×C79—21no—
338C22×C79—21no—
339C22×C79—22no—
340C22×C79—41no—
341C22×C79—41no—
342C22×C79C2×C4×D411yescharacteristic
343C22×C79#52911yescharacteristic
344C22×C79#53211yescharacteristic
345C2×D79—41no—
346C2×D79—41no—
347C2×D79—41no—
348C2×D79—41no—
349C2×D79—41no—
350C2×D79—41no—
351C4×C79—21no—
352C4×C79—21no—
353C4×C79—21no—
354C4×C79—21no—
355C4×C79—22no—
356C4×C79—41no—
357C4×C79—41no—
358C4×C79C2×C4×D411yescharacteristic
359C4×C79C4×#4111yescharacteristic
360C4×C79C2×#12111yescharacteristic
361C4×C79#52511yescharacteristic
362Dic79—42no—
363Dic79—41no—
364Dic79—41no—
365Dic79—81no—
366#21519—791nomaximal, Sylow
367C2×C79—21no—
368C2×C79—21no—
369C2×C79—42no—
370C2×C79C4×#12111yescharacteristic
371C2×C79#295611yescharacteristic
372C2×C79#295711yescharacteristic
373D79—81no—
374D79—81no—
375#3035—791no—
376C2×#444—791no—
377C2×#443—791no—
378#2932—791no—
379#2875D7911yescharacteristic, complemented
380#1980—791no—
381#1950—791no—
382#1929—791no—
383#1929—791no—
384#1876—791no—
385#1876—791no—
386#1806—791no—
387#1771—791no—
388#1765—791no—
389#1764—791no—
390C79#2151911yescharacteristic, complemented, Sylow
391C2×#135—791no—
392C2×#135—791no—
393C2×#131—791no—
394C2×#131—791no—
395C2×#131C2×D7911yescharacteristic
396C2×#131C2×D7911yescharacteristic
397#532—791no—
398C4×#41C2×D7911yescharacteristic
399#464—791no—
400#464—791no—
401#463—791no—
402#463—791no—
403#462—791no—
404#461—791no—
405#460—791no—
406#459—791no—
407#444—1584no—
408#443—1584no—
409#435—1581no—
410#435—1581no—
411#435—1581no—
412#435—1581no—
413C2×#108—791no—
414C2×#108—791no—
415#423—791no—
416C2×C4⋊C8—791no—
417C2×#104—791no—
418C2×#104—791no—
419C2×#104—791no—
420C2×#104—791no—
421C2×#104—791no—
422C2×#104—791no—
423#416—791no—
424#416—791no—
425#408—791no—
426#408—791no—
427#405—21no—
428#405—21no—
429#405C2×D7911yescharacteristic
430#405C2×D7911yescharacteristic
431C4×M16—21no—
432C4×M16C2×D7911yescharacteristic
433C2×#97—21no—
434C2×#97—791no—
435C2×#97C2×D7911yescharacteristic
436C2×C4×C8—791no—
437C4×C4⋊C4—791no—
438#341—791no—
439#341—791no—
440#339—791no—
441#339—791no—
442#336—791no—
443#336—791no—
444C2×#41—791no—
445C2×#41—791no—
446C2×#41C22×D7911yescharacteristic
447#135—1582no—
448#135—1582no—
449#135—1582no—
450#135—1582no—
451C2×Q16—791no—
452C2×Q16—791no—
453C2×SD16—791no—
454C2×SD16—791no—
455C2×SD16—791no—
456C2×SD16—791no—
457C2×D8—791no—
458C2×D8—791no—
459#131—22no—
460#131—22no—
461#131—22no—
462#131—1582no—
463#131—1582no—
464#131—1582no—
465#131—1582no—
466#131D31614yescomplemented
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—791no—
470C2×M16—791no—
471C2×M16—1581no—
472C2×M16—1581no—
473C2×M16C22×D7911yescharacteristic
474C2×M16C22×D7911yescharacteristic
475C22×C8—21no—
476C22×C8—21no—
477C22×C8—791no—
478C22×C8—791no—
479C22×C8—1581no—
480C22×C8—1581no—
481C22×C8C22×D7911yescharacteristic
482C22×C8C22×D7911yescharacteristic
483C4⋊Q8—791no—
484#127—791no—
485#124—791no—
486#124—791no—
487#121—1581no—
488#121—1581no—
489C4×Q8C4×D7911yescharacteristic
490C4×Q8C4×D7911yescharacteristic
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—1581no—
494C4×D4—1581no—
495C4×D4C4×D7911yescharacteristic
496C4×D4C4×D7911yescharacteristic
497#117—21no—
498#117C22×D7911yescharacteristic
499C2×C4⋊C4—1581no—
500C2×C42—21no—
501C2×C42—791no—
502C2×C42—791no—
503C2×C42C22×D7911yescharacteristic
504#108—1582no—
505#108—1582no—
506C4⋊C8—791no—
507C4⋊C8—791no—
508C4⋊C8—791no—
509C4⋊C8—791no—
510C4⋊C8—1581no—
511C4⋊C8—1581no—
512#104—1582no—
513#104—1582no—
514#104—1582no—
515#104—1582no—
516#104—1582no—
517#104—1582no—
518#103—791no—
519#103—791no—
520#103—791no—
521#103—791no—
522#102—791no—
523#102—791no—
524#102—791no—
525#102—791no—
526C22⋊C8—1581no—
527C22⋊C8—1581no—
528C22⋊C8—1581no—
529C22⋊C8—1581no—
530#97—21no—
531#97—21no—
532#97—21no—
533#97—1582no—
534#97C22⋊D7911yescharacteristic
535#97C22⋊D7911yescharacteristic
536#97C22⋊D7911yescharacteristic
537#97C22⋊D7911yescharacteristic
538C4×C8—21no—
539C4×C8—21no—
540C4×C8—21no—
541C4×C8—1582no—
542#95—1581no—
543#41—21no—
544#41—21no—
545#41—1581no—
546#41—1581no—
547#41—1581no—
548#41—1581no—
549#41—1581no—
550#41—1581no—
551#41—1581no—
552#41—1581no—
553#41C2×D31612yes—
554#41#1192962412yes—
555C2×Q8—791no—
556C2×Q8—791no—
557C2×Q8C2×C4×D7911yescharacteristic
558C2×D4—21no—
559C2×D4—791no—
560C2×D4—791no—
561C2×D4—1581no—
562C2×D4—1581no—
563C2×D4—1581no—
564C2×D4—1581no—
565C2×D4C2×C4×D7911yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—1581no—
570C22×C4—1581no—
571C22×C4—1581no—
572C22×C4—1581no—
573C22×C4#1192962411yescharacteristic
574C22×C4#1192962411yescharacteristic
575C22×C4C23×D7911yescharacteristic
576Q16—1582no—
577Q16—1582no—
578SD16—1582no—
579SD16—1582no—
580SD16—1582no—
581SD16—1582no—
582D8—1582no—
583D8—1582no—
584M16—24no—
585M16—21no—
586M16—21no—
587M16—24no—
588M16—3162no—
589M16—3162no—
590M16—1581no—
591M16—1581no—
592M16—1581no—
593M16—1581no—
594M16C2×D31612yes—
595M16#1192962412yes—
596C2×C8—24no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—24no—
602C2×C8—3162no—
603C2×C8—3162no—
604C2×C8—791no—
605C2×C8—791no—
606C2×C8—791no—
607C2×C8—791no—
608C2×C8—1581no—
609C2×C8—1581no—
610C2×C8—1581no—
611C2×C8—1581no—
612C2×C8—1581no—
613C2×C8—1581no—
614C2×C8C2×C22⋊D7911yescharacteristic
615C2×C8C2×C22⋊D7911yescharacteristic
616C2×C8C2×C22⋊D7911yescharacteristic
617C2×C8C2×C22⋊D7911yescharacteristic
618C2×C8C2×D31612yes—
619C2×C8#1192962412yes—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—3162no—
623C4⋊C4—1581no—
624C4⋊C4—1581no—
625C4⋊C4C2×C4×D7911yescharacteristic
626C4⋊C4C2×C4×D7911yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—1581no—
631C22⋊C4—1581no—
632C22⋊C4—1581no—
633C22⋊C4—1581no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—1581no—
638C42—1581no—
639C42—1581no—
640C42—1581no—
641C42C2×C4×D7911yescharacteristic
642C42C2×C4×D7911yescharacteristic
643C42C2×C22⋊D7911yescharacteristic
644C42C2×C22⋊D7911yescharacteristic
645C23—21no—
646C23—1581no—
647C23—1581no—
648C23C2×#1192962411yescharacteristic
649Q8—21no—
650Q8—1581no—
651Q8—1581no—
652Q8—1581no—
653Q8—1581no—
654Q8C4×D31612yes—
655D4—22no—
656D4—22no—
657D4—21no—
658D4—3161no—
659D4—3161no—
660D4—3161no—
661D4—3161no—
662D4—6321no—
663D4—6321no—
664D4—1581no—
665D4—1581no—
666D4—1581no—
667D4—1581no—
668D4C4×D31612yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—3161no—
679C2×C4—3161no—
680C2×C4—3161no—
681C2×C4—3161no—
682C2×C4—3161no—
683C2×C4—3161no—
684C2×C4—3161no—
685C2×C4—3161no—
686C2×C4—3161no—
687C2×C4—1582no—
688C2×C4—1581no—
689C2×C4—1581no—
690C2×C4C4×C22⋊D7911yescharacteristic
691C2×C4C4×C22⋊D7911yescharacteristic
692C2×C4C4×C22⋊D7911yescharacteristic
693C2×C4C4×C22⋊D7911yescharacteristic
694C2×C4C22×C4×D7911yescharacteristic
695C2×C4C22×C22⋊D7911yescharacteristic
696C2×C4C22×D31611yescharacteristic
697C2×C4C2×#1192962411yescharacteristic
698C2×C4C2×#1192962411yescharacteristic
699C2×C4C2×#1192962411yescharacteristic
700C8—22no—
701C8—21no—
702C8—22no—
703C8—21no—
704C8—3161no—
705C8—3161no—
706C8—1581no—
707C8—1581no—
708C8—1581no—
709C8—1581no—
710C8#1457913512yes—
711C8#1457913512yes—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—3161no—
718C22—3161no—
719C22—3161no—
720C22—3161no—
721C22—3161no—
722C22—3161no—
723C22C2×C4×C22⋊D7911yescharacteristic
724C22#1909909711yescharacteristic
725C22#1909911311yescharacteristic
726C4—21no—
727C4—21no—
728C4—22no—
729C4—21no—
730C4—21no—
731C4—41no—
732C4—41no—
733C4—3162no—
734C4—3161no—
735C4—3161no—
736C4—6321no—
737C4C2×C4×D31611yescharacteristic
738C4C4×#1192962411yescharacteristic
739C4C2×#1457913511yescharacteristic
740C4#1909907411yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—6321no—
745C2—6321no—
746C2C4×#1457913511yescharacteristic
747C2#2377230711yescharacteristic
748C2#2377231511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2875C2
socleC22×C79C2×C4×D4
prime radical#23772855C2
cosocleC22×C4×C79C24
hypercenter#2875D79
hypocenterC79#21519
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2875

Complements

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

NH ≅ G/Ntype
2. C2×#19098683C2semidirect
3. C2×#19098678C2semidirect
4. #23772119C2semidirect
5. #23764319C2semidirect
6. #23764175C2semidirect
7. #23764048C2semidirect
8. #23764048C2semidirect
9. #23763727C2semidirect
10. #23763727C2semidirect
11. #23763420C2semidirect
12. #23763272C2semidirect
13. #23763246C2semidirect
14. #23763239C2semidirect
15. C79×#2875C2semidirect
21. #19098785C4semidirect
22. #19098785C4semidirect
23. #19098778C4semidirect
24. #19098778C4semidirect
25. #19098773C4semidirect
26. #19098768C4semidirect
27. #19098763C4semidirect
28. #19098758C4semidirect
139. #131×C79D4semidirect
379. #2875D79semidirect
390. C79#21519semidirect
466. #131D316semidirect

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
#237721192
#237643192
#237641752
#237640482
#237637272
#237634202
#237632722
#237632462
#237632392
C79×#28752
#2151979