Finite Group Databasebeta

← #34298847

Subgroups — #34298847

Order 20224.

786 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098619C211yesmaximal, characteristic
2#23765806C211yesmaximal, characteristic
3#23765796C211yesmaximal, characteristic
4#23764170C211yesmaximal, characteristic, complemented
5#23764168C211yesmaximal, characteristic, complemented
6#23764166C211yesmaximal, characteristic, complemented
7#23763602C211yesmaximal, characteristic
8#23763600C211yesmaximal, characteristic
9#23763598C211yesmaximal, characteristic
10#23763596C211yesmaximal, characteristic
11#23763567C211yesmaximal, characteristic, complemented
12#23763565C211yesmaximal, characteristic, complemented
13#23763532C211yesmaximal, characteristic, complemented
14#23763532C211yesmaximal, characteristic, complemented
15C79×#1949C211yesmaximal, characteristic, complemented
16C2×#14579119C2211yescharacteristic
17C2×#14579119C2211yescharacteristic
18C2×C42×D79C2211yescharacteristic
19#19098619C418yescomplemented
20C2×#14579095C2211yescharacteristic
21C2×#14579094C2211yescharacteristic
22C2×#14579094C2211yescharacteristic
23C2×#14579093C2211yescharacteristic
24C2×#14579092C2211yescharacteristic
25C2×#14579092C2211yescharacteristic
26C2×C4⋊(C79⋊C8)C2211yescharacteristic
27C2×(C2×D79)⋊C8C2211yescharacteristic
28C2×(C2×D79)⋊C8C2211yescharacteristic
29C2×#14579071C2211yescharacteristic
30C2×#14579071C2211yescharacteristic
31#19098432C2211yescharacteristic
32#19098432C2211yescharacteristic
33#19098430—21no—
34#19098429C2211yescharacteristic
35#19098428C2211yescharacteristic
36#19098428C2211yescharacteristic
37#19098425—21no—
38#19098422—21no—
39#19098422—21no—
40#19098420C2211yescharacteristic
41#19098420C2211yescharacteristic
42C4×C4⋊Dic79C2211yescharacteristic
43#19098414—21no—
44#19098414—21no—
45C4×(C2×D79)⋊C4—21no—
46#19098409—21no—
47#19098326C2211yescharacteristic
48#19098326C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51#19098325C2211yescharacteristic
52#19098325C2211yescharacteristic
53C2×#107×C79C2211yescharacteristic
54C2×#106×C79C2211yescharacteristic
55C2×C4⋊C8×C79C2211yescharacteristic
56#382×C79C2211yescharacteristic
57C4×C4⋊C4×C79C2211yescharacteristic
58#340×C79C2211yescharacteristic
59#340×C79C2211yescharacteristic
60C22×C4×D79D411yescharacteristic
61C22×C4×D79D411yescharacteristic
62C22×C4×D79C2311yescharacteristic
63C22×C79⋊C8C2311yescharacteristic
64C22×C79⋊C8C2311yescharacteristic
65#14579119—41no—
66#14579119—41no—
67#14579119—41no—
68#14579119—41no—
69C2×C4⋊Dic79C2311yescharacteristic
70C2×C4⋊Dic79C2311yescharacteristic
71C2×C4⋊Dic79C2311yescharacteristic
72C2×C4⋊Dic79C2311yescharacteristic
73C2×Dic79⋊C4—21no—
74C2×Dic79⋊C4—21no—
75C2×Dic79⋊C4—21no—
76C2×Dic79⋊C4—21no—
77C2×(C2×D79)⋊C4—21no—
78C2×(C2×D79)⋊C4—21no—
79C2×(C2×D79)⋊C4—21no—
80C2×(C2×D79)⋊C4—21no—
81C2×C4×Dic79—21no—
82C2×C4×Dic79—21no—
83C2×C4×Dic79—21no—
84C2×C4×Dic79D411yescharacteristic
85C2×C4×Dic79D411yescharacteristic
86C2×C4×Dic79C2311yescharacteristic
87C42×D79C2×C414yes—
88C42×D79Q814yes—
89#14579095—41no—
90#14579094—41no—
91#14579094—41no—
92#14579093—41no—
93#14579092—41no—
94#14579092—41no—
95C4⋊(C79⋊C8)C2×C414yes—
96(C2×D79)⋊C8C2×C414yes—
97(C2×D79)⋊C8C2×C414yes—
98#14579071C2×C414yes—
99#14579071C2×C414yes—
100C79⋊#95—21no—
101C79⋊#95—21no—
102C79⋊#95—21no—
103C79⋊#95—21no—
104C79⋊#95—21no—
105C79⋊#95—21no—
106C79⋊#95—21no—
107C79⋊#95—21no—
108C79⋊#95—21no—
109C22×C8×C79C2311yescharacteristic
110C22×C8×C79C2311yescharacteristic
111C2×C4⋊C4×C79C2311yescharacteristic
112C2×C4⋊C4×C79C2311yescharacteristic
113C2×C4⋊C4×C79C2311yescharacteristic
114C2×C4⋊C4×C79C2311yescharacteristic
115C2×C42×C79—21no—
116C2×C42×C79C2311yescharacteristic
117#107×C79—41no—
118#106×C79—41no—
119C4⋊C8×C79C2×C414yes—
120#95×C79—21no—
121#95×C79—21no—
122#95×C79—21no—
123C23×D79C2×D411yescharacteristic
124C22×Dic79—21no—
125C22×Dic79—21no—
126C22×Dic79—21no—
127C22×Dic79—21no—
128C22×Dic79C2×D411yescharacteristic
129C22×Dic79C2×D411yescharacteristic
130C22×Dic79C2×D411yescharacteristic
131C2×C4×D79—21no—
132C2×C4×D79—21no—
133C2×C4×D79—21no—
134C2×C4×D79—21no—
135C2×C4×D79—41no—
136C2×C4×D79—41no—
137C2×C4×D79—41no—
138C2×C4×D79—41no—
139C2×C4×D79C4⋊C414yes—
140C2×C4×D79C4⋊C414yes—
141C2×C4×D79C22×C412yes—
142C2×C4×D79C2×Q812yes—
143C2×C79⋊C8—21no—
144C2×C79⋊C8—21no—
145C2×C79⋊C8—21no—
146C2×C79⋊C8—21no—
147C2×C79⋊C8C22×C412yes—
148C2×C79⋊C8C22×C412yes—
149C4⋊Dic79—21no—
150C4⋊Dic79—21no—
151C4⋊Dic79—21no—
152C4⋊Dic79—21no—
153C4⋊Dic79—21no—
154C4⋊Dic79—21no—
155C4⋊Dic79—21no—
156C4⋊Dic79—21no—
157Dic79⋊C4—42no—
158Dic79⋊C4—42no—
159Dic79⋊C4—42no—
160Dic79⋊C4—42no—
161(C2×D79)⋊C4—42no—
162(C2×D79)⋊C4—42no—
163(C2×D79)⋊C4—42no—
164(C2×D79)⋊C4—42no—
165C4×Dic79—42no—
166C4×Dic79—42no—
167C4×Dic79—42no—
168C4×Dic79C4⋊C414yes—
169C4×Dic79C4⋊C414yes—
170C4×Dic79C22×C412yes—
171C4×Dic79C2×Q812yes—
172C22×C4×C79—21no—
173C22×C4×C79—21no—
174C22×C4×C79—21no—
175C22×C4×C79—21no—
176C22×C4×C79C2×D411yescharacteristic
177C22×C4×C79C2×D411yescharacteristic
178C22×C4×C79C2411yescharacteristic
179C2×C8×C79—21no—
180C2×C8×C79—21no—
181C2×C8×C79—21no—
182C2×C8×C79—21no—
183C2×C8×C79C22×C412yes—
184C2×C8×C79C22×C412yes—
185C4⋊C4×C79—21no—
186C4⋊C4×C79—21no—
187C4⋊C4×C79—21no—
188C4⋊C4×C79—21no—
189C4⋊C4×C79—21no—
190C4⋊C4×C79—21no—
191C4⋊C4×C79—21no—
192C4⋊C4×C79—21no—
193C42×C79—42no—
194C42×C79C22×C412yes—
195C42×C79C2×Q812yes—
196C23×C79C22×D411yescharacteristic
197C22×D79—21no—
198C22×D79—21no—
199C22×D79—21no—
200C22×D79—21no—
201C22×D79—21no—
202C22×D79—21no—
203C22×D79C2×C4⋊C412yes—
204C2×C4×C79—21no—
205C2×C4×C79—21no—
206C2×C4×C79—21no—
207C2×C4×C79—21no—
208C2×C4×C79—41no—
209C2×C4×C79—41no—
210C2×C4×C79—41no—
211C2×C4×C79—41no—
212C2×C4×C79—41no—
213C2×C4×C79—41no—
214C2×C4×C79—41no—
215C2×C4×C79—41no—
216C2×C4×C79—41no—
217C2×C4×C79—41no—
218C2×C4×C79—41no—
219C2×C4×C79—41no—
220C2×C4×C79C2×C4⋊C412yes—
221C2×C4×C79C2×C4⋊C412yes—
222C2×C4×C79C23×C411yescharacteristic
223C2×C4×C79C22×Q811yescharacteristic
224C2×C4×C79H(5,𝔽2)11yescharacteristic
225C2×C4×C79H(5,𝔽2)11yescharacteristic
226C2×C4×C792−1+411yescharacteristic
227C2×C4×C792−1+411yescharacteristic
228C2×Dic79—21no—
229C2×Dic79—21no—
230C2×Dic79—21no—
231C2×Dic79—21no—
232C2×Dic79—21no—
233C2×Dic79—21no—
234C2×Dic79—41no—
235C2×Dic79—41no—
236C2×Dic79—41no—
237C2×Dic79—41no—
238C2×Dic79—41no—
239C2×Dic79—41no—
240C2×Dic79—41no—
241C2×Dic79—41no—
242C2×Dic79—41no—
243C2×Dic79—41no—
244C2×Dic79—41no—
245C2×Dic79—41no—
246C2×Dic79C2×C4⋊C412yes—
247C2×Dic79C2×C4⋊C412yes—
248C2×Dic79C2×C4⋊C412yes—
249C4×D79—22no—
250C4×D79—22no—
251C4×D79—22no—
252C4×D79—22no—
253C4×D79—44no—
254C4×D79—44no—
255C8×C79—22no—
256C8×C79—22no—
257C79⋊C8—22no—
258C79⋊C8—22no—
259C22×C79C22×C4⋊C411yescharacteristic
260C22×C79#53511yescharacteristic
261C22×C79#53611yescharacteristic
262C22×C79#57511yescharacteristic
263C22×C79#57511yescharacteristic
264C22×C79#57511yescharacteristic
265C22×C79#57511yescharacteristic
266C2×D79—22no—
267C2×D79—22no—
268C2×D79—22no—
269C2×D79—41no—
270C2×D79—41no—
271C2×D79—41no—
272C2×D79—41no—
273C4×C79—22no—
274C4×C79—22no—
275C4×C79—81no—
276C4×C79—81no—
277C4×C79—81no—
278C4×C79—81no—
279C4×C79#52011yescharacteristic
280C4×C79#52011yescharacteristic
281C4×C79#54411yescharacteristic
282C4×C79#54411yescharacteristic
283Dic79—22no—
284Dic79—22no—
285Dic79—22no—
286Dic79—81no—
287Dic79—81no—
288Dic79—81no—
289Dic79—81no—
290#21989—791nomaximal, Sylow
291C2×C79#231711yescharacteristic
292C2×C79#291111yescharacteristic
293C2×C79#291111yescharacteristic
294C2×C79#321911yescharacteristic
295C2×C79#321911yescharacteristic
296C2×C79#324011yescharacteristic
297C2×C79#324011yescharacteristic
298D79—42no—
299C2×#432—791no—
300#2285—791no—
301#2283—791no—
302#1949—791no—
303#1949—791no—
304#1949—791no—
305#1949D7911yescharacteristic, complemented
306#1854—791no—
307#1854—791no—
308#1854—791no—
309#1854—791no—
310#1847—791no—
311#1847—791no—
312#1836—791no—
313#1836—791no—
314C79#2198911yescharacteristic, complemented, Sylow
315C2×#117—791no—
316C2×#117—791no—
317C22×C42—791no—
318#432—798no—
319C2×#107—791no—
320C2×#107—791no—
321C2×#107—791no—
322C2×#107C2×D7911yescharacteristic
323C2×#106—791no—
324C2×#106—791no—
325C2×#106—791no—
326C2×#106C2×D7911yescharacteristic
327C2×C4⋊C8—791no—
328C2×C4⋊C8C2×D7911yescharacteristic
329C2×C22⋊C8—791no—
330C2×C22⋊C8—791no—
331C2×#97—791no—
332C2×#97—791no—
333#384—791no—
334#384—791no—
335#383—1581no—
336#382—791no—
337#382—791no—
338#382—791no—
339#382C2×D7911yescharacteristic
340#381—1581no—
341#380—791no—
342#380—791no—
343#380—1581no—
344#380—1581no—
345C4×C4⋊C4—791no—
346C4×C4⋊C4—1581no—
347C4×C4⋊C4—1581no—
348C4×C4⋊C4C2×D7911yescharacteristic
349C4×C22⋊C4—1581no—
350#376—1581no—
351#340—791no—
352#340—791no—
353#340—791no—
354#340—791no—
355#340—791no—
356#340—791no—
357#340C2×D7911yescharacteristic
358#340C2×D7911yescharacteristic
359C23×C4—791no—
360C23×C4—791no—
361C23×C4—791no—
362C22×C8—791no—
363C22×C8—791no—
364C22×C8C22×D7911yescharacteristic
365C22×C8C22×D7911yescharacteristic
366#117—3161no—
367#117—3161no—
368#117—3161no—
369#117—3161no—
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⋊C4—1581no—
377C2×C4⋊C4—1581no—
378C2×C4⋊C4C22×D7911yescharacteristic
379C2×C4⋊C4C22×D7911yescharacteristic
380C2×C4⋊C4C22×D7911yescharacteristic
381C2×C4⋊C4C22×D7911yescharacteristic
382C2×C22⋊C4—1581no—
383C2×C22⋊C4—1581no—
384C2×C22⋊C4—1581no—
385C2×C22⋊C4—1581no—
386C2×C42—21no—
387C2×C42—791no—
388C2×C42—791no—
389C2×C42—791no—
390C2×C42—794no—
391C2×C42—794no—
392C2×C42—1581no—
393C2×C42—1581no—
394C2×C42—1581no—
395C2×C42C22×D7911yescharacteristic
396#107—41no—
397#107—3161no—
398#107—3161no—
399#107—3161no—
400#106—41no—
401#106—3161no—
402#106—3161no—
403#106—3161no—
404C4⋊C8—794no—
405C4⋊C8C4×D7914yes—
406C22⋊C8—794no—
407C22⋊C8—794no—
408#97—794no—
409#97—794no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—1581no—
414#95—1581no—
415#95—1581no—
416#95—1581no—
417#95—1581no—
418#95—1581no—
419#95—1581no—
420#95—1581no—
421#95—1581no—
422C24—791no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—3161no—
428C22×C4—3161no—
429C22×C4—3161no—
430C22×C4—3161no—
431C22×C4—794no—
432C22×C4—794no—
433C22×C4—791no—
434C22×C4—791no—
435C22×C4—791no—
436C22×C4—792no—
437C22×C4—792no—
438C22×C4—1581no—
439C22×C4—1581no—
440C22×C4—1581no—
441C22×C4—1581no—
442C22×C4—1581no—
443C22×C4—1581no—
444C22×C4—1581no—
445C22×C4—1581no—
446C22×C4D4×D7911yescharacteristic
447C22×C4D4×D7911yescharacteristic
448C22×C4C23×D7911yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—792no—
454C2×C8—792no—
455C2×C8—1581no—
456C2×C8—1581no—
457C2×C8—1581no—
458C2×C8—1581no—
459C2×C8C2×C4×D7912yes—
460C2×C8C2×C4×D7912yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—3162no—
470C4⋊C4—3162no—
471C4⋊C4—3162no—
472C4⋊C4—3162no—
473C4⋊C4—1581no—
474C4⋊C4—1581no—
475C4⋊C4—1581no—
476C4⋊C4—1581no—
477C4⋊C4—1581no—
478C4⋊C4—1581no—
479C4⋊C4—1581no—
480C4⋊C4—1581no—
481C22⋊C4—3162no—
482C22⋊C4—3162no—
483C22⋊C4—3162no—
484C22⋊C4—3162no—
485C42—42no—
486C42—3162no—
487C42—3162no—
488C42—3162no—
489C42—792no—
490C42—794no—
491C42—794no—
492C42—792no—
493C42C2×C4×D7912yes—
494C42Q8×D7912yes—
495C23—792no—
496C23—1581no—
497C23—1581no—
498C23—1581no—
499C23—1581no—
500C23—1581no—
501C23—1581no—
502C23C2×D4×D7911yescharacteristic
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
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—3164no—
520C2×C4—3164no—
521C2×C4—3161no—
522C2×C4—3161no—
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—792no—
534C2×C4—792no—
535C2×C4—792no—
536C2×C4—1581no—
537C2×C4—1581no—
538C2×C4—1581no—
539C2×C4—1581no—
540C2×C4—1581no—
541C2×C4—1581no—
542C2×C4—1582no—
543C2×C4—1582no—
544C2×C4—1582no—
545C2×C4—1582no—
546C2×C4C4⋊C4×D7912yes—
547C2×C4C4⋊C4×D7912yes—
548C2×C4C22×C4×D7911yescharacteristic
549C2×C4C2×Q8×D7911yescharacteristic
550C2×C4#1457920611yescharacteristic
551C2×C4#1457920711yescharacteristic
552C2×C4#1457920811yescharacteristic
553C2×C4#1457920911yescharacteristic
554C8—22no—
555C8—22no—
556C8—1582no—
557C8—1582no—
558C22—3161no—
559C22—3161no—
560C22—3161no—
561C22—3161no—
562C22—1582no—
563C22—1582no—
564C22—1582no—
565C22C2×C4⋊C4×D7911yescharacteristic
566C22#1909912911yescharacteristic
567C22#1909913611yescharacteristic
568C22#1909935911yescharacteristic
569C22#1909936011yescharacteristic
570C22#1909936011yescharacteristic
571C22#1909936211yescharacteristic
572C4—22no—
573C4—22no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—6321no—
579C4—6321no—
580C4—6321no—
581C4—6321no—
582C4—1582no—
583C4—1582no—
584C4—1582no—
585C4#1909904211yescharacteristic
586C4#1909904511yescharacteristic
587C4#1909919011yescharacteristic
588C4#1909919311yescharacteristic
589C2—3162no—
590C2#2376602211yescharacteristic
591C2#2377198711yescharacteristic
592C2#2377198811yescharacteristic
593C2#2377443611yescharacteristic
594C2#2377444211yescharacteristic
595C2#2377463911yescharacteristic
596C2#2377464511yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#1949C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
cosocleC22×C4×C79C24
hypercenter#1949D79
hypocenterC79#21989
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #23764170C2semidirect
5. #23764168C2semidirect
6. #23764166C2semidirect
11. #23763567C2semidirect
12. #23763565C2semidirect
13. #23763532C2semidirect
14. #23763532C2semidirect
15. C79×#1949C2semidirect
19. #19098619C4semidirect
305. #1949D79semidirect
314. C79#21989semidirect

Maximal subgroups

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

subgroupindex
C2×#190986192
#237658062
#237657962
#237641702
#237641682
#237641662
#237636022
#237636002
#237635982
#237635962
#237635672
#237635652
#237635322
C79×#19492
#2198979