Finite Group Databasebeta

← #34309017

Subgroups — #34309017

Order 20224.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772618C211yesmaximal, characteristic
2C2×#19098683C211yesmaximal, characteristic, complemented
3#23772121C211yesmaximal, characteristic, complemented
4C2×#19098580C211yesmaximal, characteristic, complemented
5#23764287C211yesmaximal, characteristic, complemented
6#23764114C211yesmaximal, characteristic, complemented
7#23764045C211yesmaximal, characteristic, complemented
8#23763846C211yesmaximal, characteristic, complemented
9#23763730C211yesmaximal, characteristic, complemented
10#23763727C211yesmaximal, characteristic, complemented
11#23763675C211yesmaximal, characteristic, complemented
12#23763604C211yesmaximal, characteristic, complemented
13#23763235C211yesmaximal, characteristic, complemented
14#23763168C211yesmaximal, characteristic, complemented
15C79×#2880C211yesmaximal, characteristic, complemented
16C2×#14579181C2211yescharacteristic
17C2×#14579181C2211yescharacteristic
18C2×#14579167C2211yescharacteristic, complemented
19C22×#11929608C2211yescharacteristic
20#19099074C2211yescharacteristic
21C2×#14579120C2211yescharacteristic
22#19098725C411yescharacteristic, complemented
23#19098725C411yescharacteristic, complemented
24#19098719C411yescharacteristic, complemented
25#19098714C411yescharacteristic, complemented
26#19098708C411yescharacteristic, complemented
27#19098708C411yescharacteristic, complemented
28#19098702C411yescharacteristic, complemented
29#19098697C411yescharacteristic, complemented
30#19098683—24no—
31#19098638—21no—
32#19098637—21no—
33#19098631—21no—
34(C22⋊D79)⋊C8—21no—
35C2×#14579096C2211yescharacteristic, complemented
36C2×#14579096C2211yescharacteristic, complemented
37#19098589C2211yescharacteristic, complemented
38#19098580—24no—
39C2×#14579088C2211yescharacteristic
40C2×#14579088C2211yescharacteristic
41C2×#14579088C2211yescharacteristic
42C2×#14579088C2211yescharacteristic
43C2×#14579087C2211yescharacteristic, complemented
44C2×#14579087C2211yescharacteristic, complemented
45#19098559C2211yescharacteristic
46#19098559C2211yescharacteristic
47#19098529C2211yescharacteristic, complemented
48C2×C22⋊(C79⋊C8)C2211yescharacteristic
49#19098518C2211yescharacteristic, complemented
50C2×#14579071C2211yescharacteristic, complemented
51C2×C8×Dic79C2211yescharacteristic, complemented
52#19098327C2211yescharacteristic, complemented
53#19098327C2211yescharacteristic, complemented
54#19098324C2211yescharacteristic, complemented
55#19098324C2211yescharacteristic, complemented
56#19098317C2211yescharacteristic, complemented
57#19098317C2211yescharacteristic, complemented
58C22×#41×C79C2211yescharacteristic
59C2×#131×C79C2211yescharacteristic
60C2×#131×C79C2211yescharacteristic
61#408×C79—21no—
62#408×C79—21no—
63#408×C79C2211yescharacteristic
64#408×C79C2211yescharacteristic
65#407×C79—21no—
66#407×C79C2211yescharacteristic
67C2×C22⋊C8×C79—21no—
68C2×C22⋊C8×C79C2211yescharacteristic
69C2×#11929624C2311yescharacteristic
70#14579181—22no—
71#14579181—22no—
72#14579181—41no—
73#14579181—41no—
74C2×#11929614C2×C411yescharacteristic
75C2×#11929614C2×C411yescharacteristic
76C2×#11929612C2×C411yescharacteristic
77C2×#11929612C2×C411yescharacteristic
78C2×#11929611C2×C411yescharacteristic
79C2×#11929611C2×C411yescharacteristic
80C2×#11929609C2×C411yescharacteristic
81C2×#11929609C2×C411yescharacteristic
82#14579167—22no—
83#14579167—41no—
84C2×#11929608—21no—
85C2×#11929608—22no—
86C2×#11929608—41no—
87C2×#11929608C2311yescharacteristic
88C2×#11929608C2311yescharacteristic
89C2×#11929607—21no—
90C22×C79⋊C8—21no—
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#14579120—22no—
103#14579120—41no—
104#14579120C2311yescharacteristic
105C2×C4⋊Dic79—21no—
106C2×C22⋊Dic79—21no—
107C2×C4×Dic79C2311yescharacteristic
108C2×C4×Dic79C2311yescharacteristic
109#14579096—22no—
110#14579096—41no—
111Dic79⋊C8—21no—
112Dic79⋊C8—21no—
113#14579088—22no—
114#14579088—22no—
115#14579088—22no—
116#14579088D414yescomplemented
117#14579087—22no—
118#14579087—41no—
119#14579085C2×C411yescharacteristic
120#14579085C2×C411yescharacteristic
121#14579085C2×C411yescharacteristic
122#14579085C2×C411yescharacteristic
123#14579082C2×C411yescharacteristic
124#14579082C2×C411yescharacteristic
125#14579082C2×C411yescharacteristic
126#14579082C2×C411yescharacteristic
127C22⋊(C79⋊C8)C2×C411yescharacteristic
128C22⋊(C79⋊C8)C2×C411yescharacteristic
129C22⋊(C79⋊C8)C2×C411yescharacteristic
130C22⋊(C79⋊C8)C2×C411yescharacteristic
131(C2×D79)⋊C8—21no—
132(C2×D79)⋊C8—21no—
133#14579071—21no—
134#14579071—22no—
135C8×Dic79—21no—
136C8×Dic79—41no—
137C2×#41×C79—21no—
138C2×#41×C79—21no—
139C2×#41×C79—22no—
140C2×#41×C79—22no—
141C2×#41×C79—41no—
142C2×#41×C79—41no—
143C2×#41×C79C2×C411yescharacteristic
144C2×#41×C79C2×C411yescharacteristic
145C2×#41×C79C2311yescharacteristic
146C2×#41×C79C2311yescharacteristic
147C22×Q8×C79C2×C411yescharacteristic
148C22×D4×C79—21no—
149C22×D4×C79C2×C411yescharacteristic
150C23×C4×C79—21no—
151C23×C4×C79C2311yescharacteristic
152#131×C79—22no—
153#131×C79—22no—
154#131×C79—41no—
155#131×C79—41no—
156C2×M16×C79—21no—
157C2×M16×C79—21no—
158C2×M16×C79C2311yescharacteristic
159C2×M16×C79C2311yescharacteristic
160C22×C8×C79—21no—
161C22×C8×C79—21no—
162C22×C8×C79C2311yescharacteristic
163C22×C8×C79C2311yescharacteristic
164C22⋊C8×C79—21no—
165C22⋊C8×C79—21no—
166C22⋊C8×C79—21no—
167C22⋊C8×C79—21no—
168C22⋊C8×C79—21no—
169C22⋊C8×C79—21no—
170C22⋊C8×C79D411yescharacteristic
171C22⋊C8×C79D411yescharacteristic
172C22⋊C8×C79D411yescharacteristic
173C22⋊C8×C79D411yescharacteristic
174#11929624—21no—
175#11929624—21no—
176#11929624—21no—
177#11929624—21no—
178C2×Dic158C22×C411yescharacteristic
179C2×D316C22×C411yescharacteristic
180C2×C22⋊D79—21no—
181C2×C22⋊D79—21no—
182C2×C22⋊D79—21no—
183C22×Dic79—21no—
184C22×Dic79—21no—
185C2×C4×D79—21no—
186#11929614—22no—
187#11929614—41no—
188#11929612—22no—
189#11929612—41no—
190#11929611—22no—
191#11929611—41no—
192#11929609—22no—
193#11929609—41no—
194#11929608—21no—
195#11929608—21no—
196#11929608—21no—
197#11929608—42no—
198#11929608C2×D412yes—
199#11929607—42no—
200C2×C79⋊C8—21no—
201C2×C79⋊C8—21no—
202C2×C79⋊C8—21no—
203C2×C79⋊C8—21no—
204C2×C79⋊C8—21no—
205C2×C79⋊C8—21no—
206C2×C79⋊C8—42no—
207C2×C79⋊C8C22×C411yescharacteristic
208C2×C79⋊C8C22×C411yescharacteristic
209C2×C79⋊C8C22×C411yescharacteristic
210C2×C79⋊C8C22×C411yescharacteristic
211C8×D79—42no—
212C4⋊Dic79—42no—
213C4⋊Dic79C22×C411yescharacteristic
214C4⋊Dic79C22×C411yescharacteristic
215Dic79⋊C4—21no—
216Dic79⋊C4—21no—
217C22⋊Dic79—21no—
218C22⋊Dic79—21no—
219C22⋊Dic79—21no—
220C22⋊Dic79—42no—
221(C2×D79)⋊C4—21no—
222(C2×D79)⋊C4—21no—
223C4×Dic79—21no—
224C4×Dic79—21no—
225C4×Dic79—21no—
226C4×Dic79—21no—
227C4×Dic79C2×D412yes—
228C24×C79—21no—
229C24×C79#4111yescharacteristic
230#41×C79—21no—
231#41×C79—21no—
232#41×C79—22no—
233#41×C79—22no—
234#41×C79—21no—
235#41×C79—21no—
236#41×C79—21no—
237#41×C79—21no—
238#41×C79—42no—
239#41×C79—42no—
240#41×C79—41no—
241#41×C79—41no—
242#41×C79—42no—
243#41×C79—42no—
244#41×C79C2×D412yes—
245#41×C79#4112yes—
246C2×Q8×C79—21no—
247C2×Q8×C79—22no—
248C2×Q8×C79—41no—
249C2×Q8×C79C22×C411yescharacteristic
250C2×Q8×C79C22×C411yescharacteristic
251C2×D4×C79—21no—
252C2×D4×C79—22no—
253C2×D4×C79—21no—
254C2×D4×C79—21no—
255C2×D4×C79—21no—
256C2×D4×C79—21no—
257C2×D4×C79—41no—
258C2×D4×C79—42no—
259C2×D4×C79—42no—
260C2×D4×C79C22×C411yescharacteristic
261C2×D4×C79C22×C411yescharacteristic
262C22×C4×C79—21no—
263C22×C4×C79—21no—
264C22×C4×C79—21no—
265C22×C4×C79—21no—
266C22×C4×C79—21no—
267C22×C4×C79—21no—
268C22×C4×C79—21no—
269C22×C4×C79—21no—
270C22×C4×C79—21no—
271C22×C4×C79—42no—
272C22×C4×C79—42no—
273C22×C4×C79C22×C411yescharacteristic
274C22×C4×C79C22×C411yescharacteristic
275C22×C4×C79C2×D411yescharacteristic
276C22×C4×C79C2×D411yescharacteristic
277C22×C4×C79#4111yescharacteristic
278C22×C4×C79C2411yescharacteristic
279M16×C79—21no—
280M16×C79—21no—
281M16×C79—21no—
282M16×C79—21no—
283M16×C79—42no—
284M16×C79—42no—
285C2×C8×C79—21no—
286C2×C8×C79—21no—
287C2×C8×C79—21no—
288C2×C8×C79—21no—
289C2×C8×C79—21no—
290C2×C8×C79—21no—
291C2×C8×C79—42no—
292C2×C8×C79—42no—
293C2×C8×C79C2×D411yescharacteristic
294C2×C8×C79C2×D411yescharacteristic
295C2×C8×C79C2×D411yescharacteristic
296C2×C8×C79C2×D411yescharacteristic
297C23×C79—21no—
298C23×C79—21no—
299C23×C79—21no—
300C23×C79—21no—
301C23×C79—41no—
302C23×C79—41no—
303C23×C79—42no—
304C23×C79—42no—
305C23×C79—81no—
306C23×C79C4×D411yescharacteristic
307C23×C79C4×D411yescharacteristic
308C23×C79C2×#4111yescharacteristic
309C22×D79—21no—
310Q8×C79—21no—
311Q8×C79—21no—
312Q8×C79—21no—
313Q8×C79—42no—
314Q8×C79C4×D412yes—
315D4×C79—22no—
316D4×C79—22no—
317D4×C79—21no—
318D4×C79—21no—
319D4×C79—21no—
320D4×C79—42no—
321D4×C79—42no—
322D4×C79—42no—
323D4×C79—41no—
324D4×C79—41no—
325D4×C79C4×D412yes—
326C2×C4×C79—21no—
327C2×C4×C79—21no—
328C2×C4×C79—21no—
329C2×C4×C79—21no—
330C2×C4×C79—21no—
331C2×C4×C79—21no—
332C2×C4×C79—21no—
333C2×C4×C79—21no—
334C2×C4×C79—21no—
335C2×C4×C79—22no—
336C2×C4×C79—22no—
337C2×C4×C79—21no—
338C2×C4×C79—21no—
339C2×C4×C79—21no—
340C2×C4×C79—42no—
341C2×C4×C79—42no—
342C2×C4×C79—42no—
343C2×C4×C79—41no—
344C2×C4×C79—41no—
345C2×C4×C79C4×D411yescharacteristic
346C2×C4×C79C4×D411yescharacteristic
347C2×C4×C79C23×C411yescharacteristic
348C2×C4×C79C22×D411yescharacteristic
349C2×C4×C79C22×D411yescharacteristic
350C2×C4×C79C2×#4111yescharacteristic
351C2×C4×C79H(5,𝔽2)11yescharacteristic
352C2×C4×C79H(5,𝔽2)11yescharacteristic
353C22⋊D79—42no—
354C22⋊D79—41no—
355C22⋊D79—41no—
356C22⋊D79—81no—
357C2×Dic79—21no—
358C2×Dic79—21no—
359C2×Dic79—21no—
360C2×Dic79—22no—
361C2×Dic79—41no—
362C2×Dic79—41no—
363C2×Dic79—41no—
364C2×Dic79—41no—
365C2×Dic79—41no—
366D316—21no—
367D316—21no—
368C4×D79—41no—
369C4×D79—41no—
370Dic158—21no—
371Dic158—21no—
372C8×C79—21no—
373C8×C79—21no—
374C8×C79—21no—
375C8×C79—21no—
376C8×C79—41no—
377C8×C79—41no—
378C79⋊C8—21no—
379C79⋊C8—21no—
380C79⋊C8—21no—
381C79⋊C8—21no—
382C79⋊C8—22no—
383C79⋊C8—41no—
384C22×C79—21no—
385C22×C79—21no—
386C22×C79—21no—
387C22×C79—21no—
388C22×C79—22no—
389C22×C79—21no—
390C22×C79—21no—
391C22×C79—21no—
392C22×C79—21no—
393C22×C79—41no—
394C22×C79—41no—
395C22×C79—41no—
396C22×C79—41no—
397C22×C79—41no—
398C22×C79—81no—
399C22×C79—81no—
400C22×C79—84no—
401C22×C79C2×C4×D411yescharacteristic
402C22×C79#54611yescharacteristic
403C22×C79#55111yescharacteristic
404C2×D79—41no—
405C2×D79—41no—
406C2×D79—41no—
407C4×C79—21no—
408C4×C79—21no—
409C4×C79—22no—
410C4×C79—41no—
411C4×C79C2×C4×D411yescharacteristic
412C4×C79#51811yescharacteristic
413C4×C79D4211yescharacteristic
414C4×C79#54611yescharacteristic
415Dic79—42no—
416Dic79—41no—
417Dic79—41no—
418Dic79—41no—
419Dic79—81no—
420#22887—791nomaximal, Sylow
421C2×C79—21no—
422C2×C79—21no—
423C2×C79—41no—
424C2×C79—41no—
425C2×C79—42no—
426C2×C79—81no—
427C2×C79#235811yescharacteristic
428C2×C79#295511yescharacteristic
429C2×C79#295711yescharacteristic
430D79—81no—
431#3002—791no—
432C2×#444—791no—
433#2933—791no—
434C2×#421—791no—
435#2880D7911yescharacteristic, complemented
436#1974—791no—
437#1938—791no—
438#1929—791no—
439#1897—791no—
440#1876—791no—
441#1876—791no—
442#1866—791no—
443#1855—791no—
444#1764—791no—
445#1750—791no—
446C79#2288711yescharacteristic, complemented, Sylow
447C22×#41C2×D7911yescharacteristic
448C2×#135—791no—
449C2×#135—791no—
450C2×#131—791no—
451C2×#131C2×D7911yescharacteristic
452C2×#131C2×D7911yescharacteristic
453C22×M16—791no—
454#525—791no—
455C2×#117—791no—
456#452—791no—
457#452—791no—
458#451—791no—
459#450—791no—
460#449—791no—
461#449—791no—
462#448—791no—
463#447—791no—
464#444—1584no—
465#436—1581no—
466#435—1581no—
467#435—1581no—
468C8×D4—1581no—
469C2×#108—791no—
470C2×#108—791no—
471#424—791no—
472#421—1584no—
473C2×#104—791no—
474C2×#104—791no—
475C2×#104—791no—
476C2×#104—791no—
477C2×#104—791no—
478C2×#104—791no—
479#416—791no—
480#416—791no—
481#408—21no—
482#408—21no—
483#408—791no—
484#408C2×D7911yescharacteristic
485#408C2×D7911yescharacteristic
486#407—21no—
487#407C2×D7911yescharacteristic
488C2×C22⋊C8—21no—
489C2×C22⋊C8—791no—
490C2×C22⋊C8C2×D7911yescharacteristic
491#405—791no—
492C2×#97—791no—
493C2×C4×C8—791no—
494#341—791no—
495#341—791no—
496#339—791no—
497#339—791no—
498#336—791no—
499#336—791no—
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—791no—
507C2×#41C4×D7911yescharacteristic
508C2×#41C4×D7911yescharacteristic
509C2×#41C22×D7911yescharacteristic
510C2×#41C22×D7911yescharacteristic
511C22×Q8C4×D7911yescharacteristic
512C22×D4—21no—
513C22×D4C4×D7911yescharacteristic
514C23×C4—21no—
515C23×C4C22×D7911yescharacteristic
516#135—3161no—
517#135—3161no—
518#135—1582no—
519#135—1582no—
520C2×Q16—791no—
521C2×Q16—791no—
522C2×SD16—791no—
523C2×SD16—791no—
524C2×SD16—791no—
525C2×SD16—791no—
526C2×D8—791no—
527C2×D8—791no—
528#131—22no—
529#131—22no—
530#131—41no—
531#131—41no—
532#131—3161no—
533#131—1582no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—3161no—
537C2×M16—791no—
538C2×M16—791no—
539C2×M16—1582no—
540C2×M16—1581no—
541C2×M16—1581no—
542C2×M16C22×D7911yescharacteristic
543C2×M16C22×D7911yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—791no—
547C22×C8—791no—
548C22×C8—1581no—
549C22×C8—1581no—
550C22×C8C22×D7911yescharacteristic
551C22×C8C22×D7911yescharacteristic
552#123—1581no—
553C22⋊Q8—791no—
554C22⋊Q8—791no—
555#121—791no—
556#121—791no—
557#120—1581no—
558C4×D4—1581no—
559C4×D4—1581no—
560#117—3161no—
561#117—791no—
562#117—1582no—
563C2×C4⋊C4—1581no—
564C2×C22⋊C4—1581no—
565C2×C42—791no—
566C2×C42—791no—
567#108—3161no—
568#108—1582no—
569C4⋊C8—1581no—
570C4⋊C8—1581no—
571#104—3161no—
572#104—794no—
573#104—1582no—
574#104—1582no—
575#104—1582no—
576#104—1582no—
577#103—791no—
578#103—791no—
579#103—791no—
580#103—791no—
581#102—791no—
582#102—791no—
583#102—791no—
584#102—791no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—791no—
592C22⋊C8—791no—
593C22⋊C8—791no—
594C22⋊C8—791no—
595C22⋊C8—1581no—
596C22⋊C8—1581no—
597C22⋊C8C22⋊D7911yescharacteristic
598C22⋊C8C22⋊D7911yescharacteristic
599C22⋊C8C22⋊D7911yescharacteristic
600C22⋊C8C22⋊D7911yescharacteristic
601#97—1582no—
602#97—1581no—
603C4×C8—3161no—
604C4×C8—1581no—
605C24—21no—
606C24#1192962411yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—42no—
616#41—42no—
617#41—41no—
618#41—41no—
619#41—42no—
620#41—42no—
621#41—1581no—
622#41—1581no—
623#41—1581no—
624#41—1581no—
625#41D4×D7912yes—
626#41#1192962312yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8—791no—
631C2×Q8C2×C4×D7911yescharacteristic
632C2×Q8C2×C4×D7911yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—41no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—791no—
643C2×D4—1581no—
644C2×D4—1581no—
645C2×D4—1581no—
646C2×D4C2×C4×D7911yescharacteristic
647C2×D4C2×C4×D7911yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—1581no—
660C22×C4—1581no—
661C22×C4—1581no—
662C22×C4C2×C4×D7911yescharacteristic
663C22×C4C2×C4×D7911yescharacteristic
664C22×C4C2×C22⋊D7911yescharacteristic
665C22×C4C2×C22⋊D7911yescharacteristic
666C22×C4#1192962411yescharacteristic
667C22×C4C23×D7911yescharacteristic
668Q16—3161no—
669Q16—1582no—
670SD16—3161no—
671SD16—3161no—
672SD16—1582no—
673SD16—1582no—
674D8—3161no—
675D8—1582no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—42no—
681M16—42no—
682M16—3162no—
683M16—3162no—
684M16—792no—
685M16—1581no—
686M16—1581no—
687M16—1581no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8—3162no—
697C2×C8—3162no—
698C2×C8—791no—
699C2×C8—791no—
700C2×C8—791no—
701C2×C8—791no—
702C2×C8—1581no—
703C2×C8—1581no—
704C2×C8—1581no—
705C2×C8—1581no—
706C2×C8—1581no—
707C2×C8—1581no—
708C2×C8C2×C22⋊D7911yescharacteristic
709C2×C8C2×C22⋊D7911yescharacteristic
710C2×C8C2×C22⋊D7911yescharacteristic
711C2×C8C2×C22⋊D7911yescharacteristic
712C4⋊C4—3162no—
713C4⋊C4—791no—
714C4⋊C4—791no—
715C4⋊C4—1581no—
716C4⋊C4—1581no—
717C22⋊C4—3162no—
718C22⋊C4—1581no—
719C22⋊C4—1581no—
720C22⋊C4—1581no—
721C22⋊C4—1581no—
722C22⋊C4—1581no—
723C42—792no—
724C42—1581no—
725C42—1581no—
726C42—1581no—
727C42—1581no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—81no—
737C23—1581no—
738C23C4×C22⋊D7911yescharacteristic
739C23C4×C22⋊D7911yescharacteristic
740C23C2×#1192962411yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—42no—
745Q8—1581no—
746Q8—1581no—
747Q8(C22⋊D79)⋊C412yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—3162no—
759D4—3161no—
760D4—3161no—
761D4—6321no—
762D4—1581no—
763D4—1581no—
764D4(C22⋊D79)⋊C412yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—3161no—
785C2×C4—3161no—
786C2×C4—3161no—
787C2×C4—3161no—
788C2×C4—3161no—
789C2×C4—3161no—
790C2×C4—3161no—
791C2×C4—1582no—
792C2×C4—1581no—
793C2×C4—1581no—
794C2×C4—1581no—
795C2×C4C4×C22⋊D7911yescharacteristic
796C2×C4C4×C22⋊D7911yescharacteristic
797C2×C4C22×C4×D7911yescharacteristic
798C2×C4C2×D4×D7911yescharacteristic
799C2×C4C22×C22⋊D7911yescharacteristic
800C2×C4C2×#1192962311yescharacteristic
801C2×C4#1457920611yescharacteristic
802C2×C4#1457920611yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—41no—
808C8—41no—
809C8—3161no—
810C8—1582no—
811C8—1581no—
812C8—1581no—
813C8—1581no—
814C8—1581no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—81no—
830C22—81no—
831C22—84no—
832C22—3161no—
833C22—3161no—
834C22—3161no—
835C22C2×C4×C22⋊D7911yescharacteristic
836C22#1909920311yescharacteristic
837C22#1909923911yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—3162no—
843C4—3161no—
844C4—3161no—
845C4—3161no—
846C4—6321no—
847C4C2×(C22⋊D79)⋊C411yescharacteristic
848C4#1909903611yescharacteristic
849C4D4×C22⋊D7911yescharacteristic
850C4#1909920711yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—6321no—
858C2#2376637911yescharacteristic
859C2#2377230111yescharacteristic
860C2#2377231511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2880C2
socleC22×C79C2×C4×D4
prime radical#23772618C2
cosocleC22×C4×C79C24
hypercenter#2880D79
hypocenterC79#22887
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#19098683C2semidirect
3. #23772121C2semidirect
4. C2×#19098580C2semidirect
5. #23764287C2semidirect
6. #23764114C2semidirect
7. #23764045C2semidirect
8. #23763846C2semidirect
9. #23763730C2semidirect
10. #23763727C2semidirect
11. #23763675C2semidirect
12. #23763604C2semidirect
13. #23763235C2semidirect
14. #23763168C2semidirect
15. C79×#2880C2semidirect
18. C2×#14579167C22semidirect
22. #19098725C4semidirect
23. #19098725C4semidirect
24. #19098719C4semidirect
25. #19098714C4semidirect
26. #19098708C4semidirect
27. #19098708C4semidirect
28. #19098702C4semidirect
29. #19098697C4semidirect
35. C2×#14579096C22semidirect
36. C2×#14579096C22semidirect
37. #19098589C22semidirect
43. C2×#14579087C22semidirect
44. C2×#14579087C22semidirect
47. #19098529C22semidirect
49. #19098518C22semidirect
50. C2×#14579071C22semidirect
51. C2×C8×Dic79C22semidirect
52. #19098327C22semidirect
53. #19098327C22semidirect
54. #19098324C22semidirect
55. #19098324C22semidirect
56. #19098317C22semidirect
57. #19098317C22semidirect
116. #14579088D4semidirect
435. #2880D79semidirect
446. C79#22887semidirect

Maximal subgroups

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

subgroupindex
#237726182
C2×#190986832
#237721212
C2×#190985802
#237642872
#237641142
#237640452
#237638462
#237637302
#237637272
#237636752
#237636042
#237632352
#237631682
C79×#28802
#2288779