Finite Group Databasebeta

← #34288844

Subgroups — #34288844

Order 20224.

810 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098519C211yesmaximal, characteristic
2#23766009C211yesmaximal, characteristic
3#23763569C211yesmaximal, characteristic, complemented
4#23763566C211yesmaximal, characteristic, complemented
5#23763530C211yesmaximal, characteristic, complemented
6#23763527C211yesmaximal, characteristic, complemented
7#23763431C211yesmaximal, characteristic
8#23763431C211yesmaximal, characteristic
9#23763427C211yesmaximal, characteristic
10#23763423C211yesmaximal, characteristic
11#23763298C211yesmaximal, characteristic, complemented
12#23763298C211yesmaximal, characteristic, complemented
13C4×#14579094C211yesmaximal, characteristic, complemented
14C4×#14579092C211yesmaximal, characteristic, complemented
15C79×#2314C211yesmaximal, characteristic
16C22×#11929608C2211yescharacteristic
17C23×C79⋊C8C2211yescharacteristic
18C2×#14579094C2211yescharacteristic
19C2×#14579094C2211yescharacteristic
20C2×#14579094C2211yescharacteristic
21C2×#14579094C2211yescharacteristic
22C2×#14579092C2211yescharacteristic
23C2×#14579092C2211yescharacteristic
24C2×#14579092C2211yescharacteristic
25C2×#14579092C2211yescharacteristic
26#19098519C418yescomplemented
27C2×#14579072C2211yescharacteristic
28C2×#14579072C2211yescharacteristic
29C2×C4×C79⋊C8C2211yescharacteristic
30C2×C4×C79⋊C8C2211yescharacteristic
31#19098456—21no—
32#19098456—21no—
33#19098449—21no—
34#19098449—21no—
35#19098433C2211yescharacteristic
36#19098429C2211yescharacteristic
37#19098423C2211yescharacteristic
38#19098423C2211yescharacteristic
39C4×C4⋊Dic79C2211yescharacteristic
40C4×C4⋊Dic79C2211yescharacteristic
41#19098325C2211yescharacteristic
42#19098325C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49C2×#117×C79C2211yescharacteristic
50#388×C79—21no—
51#388×C79—21no—
52#387×C79—21no—
53#387×C79—21no—
54#384×C79C2211yescharacteristic
55#382×C79C2211yescharacteristic
56#380×C79C2211yescharacteristic
57#380×C79C2211yescharacteristic
58C4×C4⋊C4×C79C2211yescharacteristic
59C4×C4⋊C4×C79C2211yescharacteristic
60C2×#11929608—22no—
61C2×#11929608—22no—
62C2×#11929608C2×C414yes—
63C22×C79⋊C8—22no—
64C22×C79⋊C8—22no—
65C22×C79⋊C8C2×C414yes—
66C22×C79⋊C8C2311yescharacteristic
67C22×C79⋊C8C2311yescharacteristic
68C22×C79⋊C8C2311yescharacteristic
69C22×C79⋊C8C2311yescharacteristic
70C2×C4⋊Dic79—21no—
71C2×C4⋊Dic79—21no—
72C2×C4⋊Dic79C2311yescharacteristic
73C2×C4⋊Dic79C2311yescharacteristic
74C2×C4⋊Dic79C2311yescharacteristic
75C2×C4⋊Dic79C2311yescharacteristic
76C2×C22⋊Dic79—21no—
77C2×C22⋊Dic79—21no—
78C2×C4×Dic79—21no—
79C2×C4×Dic79—21no—
80#14579094—22no—
81#14579094—22no—
82#14579094—22no—
83#14579094—22no—
84#14579092—22no—
85#14579092—22no—
86#14579092—22no—
87#14579092—22no—
88#14579072C2×C414yes—
89#14579072C2×C414yes—
90C4×C79⋊C8C2×C414yes—
91C4×C79⋊C8C2×C414yes—
92C79⋊#95—21no—
93C79⋊#95—21no—
94C79⋊#95—21no—
95C79⋊#95—21no—
96C79⋊#95—21no—
97C79⋊#95—21no—
98C23×C4×C79C2311yescharacteristic
99#117×C79C2×C414yes—
100#117×C79Q814yes—
101C2×C4⋊C4×C79—21no—
102C2×C4⋊C4×C79—21no—
103C2×C4⋊C4×C79D411yescharacteristic
104C2×C4⋊C4×C79D411yescharacteristic
105C2×C4⋊C4×C79C2311yescharacteristic
106C2×C4⋊C4×C79C2311yescharacteristic
107C2×C4⋊C4×C79C2311yescharacteristic
108C2×C4⋊C4×C79C2311yescharacteristic
109C2×C22⋊C4×C79—21no—
110C2×C22⋊C4×C79—21no—
111C2×C22⋊C4×C79D411yescharacteristic
112C2×C22⋊C4×C79D411yescharacteristic
113C2×C42×C79—21no—
114C2×C42×C79—21no—
115C2×C42×C79C2311yescharacteristic
116C2×C42×C79C2311yescharacteristic
117#95×C79—21no—
118#95×C79—21no—
119#95×C79—21no—
120#95×C79—21no—
121#95×C79—21no—
122#95×C79—21no—
123C22×Dic79—21no—
124C22×Dic79—21no—
125C22×Dic79—21no—
126C22×Dic79—21no—
127#11929608—28no—
128C2×C79⋊C8—28no—
129C2×C79⋊C8—21no—
130C2×C79⋊C8—21no—
131C2×C79⋊C8—21no—
132C2×C79⋊C8—21no—
133C2×C79⋊C8C22×C412yes—
134C2×C79⋊C8C22×C412yes—
135C2×C79⋊C8C22×C412yes—
136C2×C79⋊C8C22×C412yes—
137C2×C79⋊C8#4112yes—
138C2×C79⋊C8#4112yes—
139C2×C79⋊C8#4112yes—
140C2×C79⋊C8#4112yes—
141C4⋊Dic79—21no—
142C4⋊Dic79—21no—
143C4⋊Dic79—21no—
144C4⋊Dic79—21no—
145C4⋊Dic79—21no—
146C4⋊Dic79—21no—
147C4⋊Dic79—21no—
148C4⋊Dic79—21no—
149C4⋊Dic79—81no—
150C4⋊Dic79—81no—
151C22⋊Dic79—81no—
152C22⋊Dic79—81no—
153C4×Dic79—81no—
154C4×Dic79—81no—
155C24×C79C2×D411yescharacteristic
156C22×C4×C79—21no—
157C22×C4×C79—21no—
158C22×C4×C79—21no—
159C22×C4×C79—21no—
160C22×C4×C79—21no—
161C22×C4×C79—21no—
162C22×C4×C79—21no—
163C22×C4×C79—21no—
164C22×C4×C79C22×C412yes—
165C22×C4×C79C2×D411yescharacteristic
166C22×C4×C79C2×D411yescharacteristic
167C22×C4×C79C2×D411yescharacteristic
168C22×C4×C79C2×D411yescharacteristic
169C22×C4×C79C2×D411yescharacteristic
170C22×C4×C79C2×Q812yes—
171C22×C4×C79C2411yescharacteristic
172C4⋊C4×C79—21no—
173C4⋊C4×C79—21no—
174C4⋊C4×C79—21no—
175C4⋊C4×C79—21no—
176C4⋊C4×C79—21no—
177C4⋊C4×C79—21no—
178C4⋊C4×C79—21no—
179C4⋊C4×C79—21no—
180C4⋊C4×C79—81no—
181C4⋊C4×C79—81no—
182C4⋊C4×C79C4⋊C414yes—
183C4⋊C4×C79C4⋊C414yes—
184C22⋊C4×C79—81no—
185C22⋊C4×C79—81no—
186C22⋊C4×C79C4⋊C414yes—
187C22⋊C4×C79C4⋊C414yes—
188C42×C79—81no—
189C42×C79—81no—
190C42×C79C22×C412yes—
191C42×C79C22×C412yes—
192C42×C79C2×Q812yes—
193C42×C79C2×Q812yes—
194C23×C79—21no—
195C23×C79—21no—
196C23×C79—21no—
197C23×C79—21no—
198C23×C79—21no—
199C23×C79—21no—
200C23×C79C2×C4⋊C412yes—
201C23×C79C22×D411yescharacteristic
202C2×C4×C79—21no—
203C2×C4×C79—21no—
204C2×C4×C79—21no—
205C2×C4×C79—21no—
206C2×C4×C79—21no—
207C2×C4×C79—21no—
208C2×C4×C79—21no—
209C2×C4×C79—21no—
210C2×C4×C79—21no—
211C2×C4×C79—21no—
212C2×C4×C79—22no—
213C2×C4×C79—22no—
214C2×C4×C79—22no—
215C2×C4×C79—22no—
216C2×C4×C79—41no—
217C2×C4×C79—41no—
218C2×C4×C79—41no—
219C2×C4×C79—41no—
220C2×C4×C79—41no—
221C2×C4×C79—41no—
222C2×C4×C79—41no—
223C2×C4×C79—41no—
224C2×C4×C79—41no—
225C2×C4×C79—41no—
226C2×C4×C79—41no—
227C2×C4×C79—41no—
228C2×C4×C79C2×C4⋊C412yes—
229C2×C4×C79C2×C4⋊C412yes—
230C2×C4×C79C2×C4⋊C412yes—
231C2×C4×C79C2×C4⋊C412yes—
232C2×C4×C79C2×C4⋊C412yes—
233C2×C4×C79C23×C411yescharacteristic
234C2×C4×C79C22×Q811yescharacteristic
235C2×C4×C79C2×#4111yescharacteristic
236C2×C4×C79C2×#4111yescharacteristic
237C2×C4×C79C2×#4111yescharacteristic
238C2×C4×C79C2×#4111yescharacteristic
239C2×Dic79—41no—
240C2×Dic79—41no—
241C2×Dic79—41no—
242C2×Dic79—41no—
243C2×Dic79—41no—
244C2×Dic79—41no—
245C2×Dic79—41no—
246C2×Dic79—41no—
247C2×Dic79—41no—
248C2×Dic79—41no—
249C2×Dic79—41no—
250C2×Dic79—41no—
251C79⋊C8—22no—
252C79⋊C8—22no—
253C79⋊C8#11714yes—
254C79⋊C8#11714yes—
255C22×C79—22no—
256C22×C79—22no—
257C22×C79—22no—
258C22×C79—41no—
259C22×C79—41no—
260C22×C79—41no—
261C22×C79—41no—
262C22×C79C22×C4⋊C411yescharacteristic
263C22×C79#53211yescharacteristic
264C22×C79#53211yescharacteristic
265C22×C79#57611yescharacteristic
266C22×C79#57711yescharacteristic
267C22×C79#57711yescharacteristic
268C22×C79#57811yescharacteristic
269C4×C79—22no—
270C4×C79—22no—
271C4×C79—22no—
272C4×C79—22no—
273C4×C79—22no—
274C4×C79—81no—
275C4×C79—81no—
276C4×C79—81no—
277C4×C79—81no—
278C4×C79C2×#11711yescharacteristic
279C4×C79C2×#11711yescharacteristic
280C4×C79#53311yescharacteristic
281C4×C79#53311yescharacteristic
282Dic79—81no—
283Dic79—81no—
284Dic79—81no—
285Dic79—81no—
286#20822—791nomaximal, Sylow
287C2×C79—42no—
288C2×C79#228511yescharacteristic
289C2×C79#291211yescharacteristic
290C2×C79#291311yescharacteristic
291C2×C79#317811yescharacteristic
292C2×C79#317811yescharacteristic
293C2×C79#317911yescharacteristic
294C2×C79#317911yescharacteristic
295C2×#405—791no—
296#2314—791no—
297#2314D7911yescharacteristic
298#1847—791no—
299#1847—791no—
300#1835—791no—
301#1834—791no—
302#1809—791no—
303#1809—791no—
304#1808—791no—
305#1807—791no—
306#1776—791no—
307#1776—791no—
308C4×#107—791no—
309C4×#106—791no—
310C79#2082211yescharacteristic, complemented, Sylow
311C22×M16—791no—
312C23×C8—791no—
313C2×#117C2×D7911yescharacteristic
314C2×#107—791no—
315C2×#107—791no—
316C2×#107—791no—
317C2×#107—791no—
318C2×#106—791no—
319C2×#106—791no—
320C2×#106—791no—
321C2×#106—791no—
322#405—798no—
323C2×#97—791no—
324C2×#97—791no—
325C2×C4×C8—791no—
326C2×C4×C8—791no—
327#388—21no—
328#388—21no—
329#388—1581no—
330#388—1581no—
331#387—21no—
332#387—21no—
333#387—1581no—
334#387—1581no—
335#384—791no—
336#384C2×D7911yescharacteristic
337#382—791no—
338#382C2×D7911yescharacteristic
339#380—791no—
340#380—791no—
341#380C2×D7911yescharacteristic
342#380C2×D7911yescharacteristic
343C4×C4⋊C4—791no—
344C4×C4⋊C4—791no—
345C4×C4⋊C4C2×D7911yescharacteristic
346C4×C4⋊C4C2×D7911yescharacteristic
347#340—791no—
348#340—791no—
349#340—791no—
350#340—791no—
351#340—791no—
352#340—791no—
353#340—791no—
354#340—791no—
355C23×C4C22×D7911yescharacteristic
356C2×M16—794no—
357C2×M16—1582no—
358C2×M16—1582no—
359C22×C8—791no—
360C22×C8—791no—
361C22×C8—794no—
362C22×C8—791no—
363C22×C8—791no—
364C22×C8—1582no—
365C22×C8—1582no—
366#117Dic15814yes—
367#117C4×D7914yes—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—791no—
371C2×C4⋊C4—791no—
372C2×C4⋊C4—791no—
373C2×C4⋊C4—791no—
374C2×C4⋊C4—1581no—
375C2×C4⋊C4—1581no—
376C2×C4⋊C4C22⋊D7911yescharacteristic
377C2×C4⋊C4C22⋊D7911yescharacteristic
378C2×C4⋊C4C22×D7911yescharacteristic
379C2×C4⋊C4C22×D7911yescharacteristic
380C2×C4⋊C4C22×D7911yescharacteristic
381C2×C4⋊C4C22×D7911yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—1581no—
385C2×C22⋊C4—1581no—
386C2×C22⋊C4C22⋊D7911yescharacteristic
387C2×C22⋊C4C22⋊D7911yescharacteristic
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—1581no—
391C2×C42—1581no—
392C2×C42C22×D7911yescharacteristic
393C2×C42C22×D7911yescharacteristic
394#107—1582no—
395#107—1582no—
396#107—1582no—
397#107—1582no—
398#106—1582no—
399#106—1582no—
400#106—1582no—
401#106—1582no—
402#97—794no—
403#97—794no—
404C4×C8—794no—
405C4×C8—794no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—1581no—
413#95—1581no—
414#95—1581no—
415#95—1581no—
416#95—1581no—
417#95—1581no—
418C24C2×C22⋊D7911yescharacteristic
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—1581no—
428C22×C4—1581no—
429C22×C4—1581no—
430C22×C4—1581no—
431C22×C4C2×C4×D7912yes—
432C22×C4C2×C22⋊D7911yescharacteristic
433C22×C4C2×C22⋊D7911yescharacteristic
434C22×C4C2×C22⋊D7911yescharacteristic
435C22×C4C2×C22⋊D7911yescharacteristic
436C22×C4C2×C22⋊D7911yescharacteristic
437C22×C4C2×Dic15812yes—
438C22×C4C23×D7911yescharacteristic
439M16—1588no—
440C2×C8—792no—
441C2×C8—792no—
442C2×C8—792no—
443C2×C8—792no—
444C2×C8—792no—
445C2×C8—792no—
446C2×C8—792no—
447C2×C8—792no—
448C2×C8—1588no—
449C2×C8—1581no—
450C2×C8—1581no—
451C2×C8—1581no—
452C2×C8—1581no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—6321no—
464C4⋊C4—6321no—
465C4⋊C4—1581no—
466C4⋊C4—1581no—
467C4⋊C4—1581no—
468C4⋊C4—1581no—
469C4⋊C4—1581no—
470C4⋊C4—1581no—
471C4⋊C4—1581no—
472C4⋊C4—1581no—
473C4⋊C4Dic79⋊C414yes—
474C4⋊C4Dic79⋊C414yes—
475C22⋊C4—81no—
476C22⋊C4—81no—
477C22⋊C4—6321no—
478C22⋊C4—6321no—
479C22⋊C4Dic79⋊C414yes—
480C22⋊C4Dic79⋊C414yes—
481C42—81no—
482C42—81no—
483C42—6321no—
484C42—6321no—
485C42C2×C4×D7912yes—
486C42C2×C4×D7912yes—
487C42C2×Dic15812yes—
488C42C2×Dic15812yes—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23C2×Dic79⋊C412yes—
496C23C22×C22⋊D7911yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—3161no—
524C2×C4—3161no—
525C2×C4—3161no—
526C2×C4—3161no—
527C2×C4—3161no—
528C2×C4—3161no—
529C2×C4—3161no—
530C2×C4—3161no—
531C2×C4—3161no—
532C2×C4—3161no—
533C2×C4—3161no—
534C2×C4—3161no—
535C2×C4C2×Dic79⋊C412yes—
536C2×C4C2×Dic79⋊C412yes—
537C2×C4C2×Dic79⋊C412yes—
538C2×C4C2×Dic79⋊C412yes—
539C2×C4C2×Dic79⋊C412yes—
540C2×C4C22×C4×D7911yescharacteristic
541C2×C4C22×Dic15811yescharacteristic
542C2×C4#41×D7911yescharacteristic
543C2×C4#41×D7911yescharacteristic
544C2×C4#41×D7911yescharacteristic
545C2×C4#41×D7911yescharacteristic
546C8—794no—
547C8—794no—
548C8—1582no—
549C8—1582no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C22×Dic79⋊C411yescharacteristic
558C22#1909910911yescharacteristic
559C22#1909910911yescharacteristic
560C22#1909936611yescharacteristic
561C22#1909937111yescharacteristic
562C22#1909937411yescharacteristic
563C22#1909937811yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—22no—
568C4—22no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—6321no—
574C4—6321no—
575C4—6321no—
576C4—6321no—
577C4#117×D7911yescharacteristic
578C4#117×D7911yescharacteristic
579C4#1909911611yescharacteristic
580C4#1909911611yescharacteristic
581C2—42no—
582C2#2376580311yescharacteristic
583C2#2377199311yescharacteristic
584C2#2377199811yescharacteristic
585C2#2377406211yescharacteristic
586C2#2377407011yescharacteristic
587C2#2377407711yescharacteristic
588C2#2377408511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2314C2
socleC23×C79C22×D4
prime radicalC24×C79C2×D4
cosocleC22×C4×C79C24
hypercenter#2314D79
hypocenterC79#20822
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
3. #23763569C2semidirect
4. #23763566C2semidirect
5. #23763530C2semidirect
6. #23763527C2semidirect
11. #23763298C2semidirect
12. #23763298C2semidirect
13. C4×#14579094C2semidirect
14. C4×#14579092C2semidirect
26. #19098519C4semidirect
310. C79#20822semidirect

Maximal subgroups

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

subgroupindex
C2×#190985192
#237660092
#237635692
#237635662
#237635302
#237635272
#237634312
#237634272
#237634232
#237632982
C4×#145790942
C4×#145790922
C79×#23142
#2082279