Finite Group Databasebeta

← #34298876

Subgroups — #34298876

Order 20224.

762 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098622C211yesmaximal, characteristic
2#23766025C211yesmaximal, characteristic
3#23766010C211yesmaximal, characteristic
4#23764169C211yesmaximal, characteristic, complemented
5#23764165C211yesmaximal, characteristic, complemented
6#23764160C211yesmaximal, characteristic, complemented
7#23764155C211yesmaximal, characteristic, complemented
8#23763598C211yesmaximal, characteristic
9#23763596C211yesmaximal, characteristic
10#23763591C211yesmaximal, characteristic
11#23763586C211yesmaximal, characteristic
12#23763569C211yesmaximal, characteristic, complemented
13#23763533C211yesmaximal, characteristic, complemented
14#23763528C211yesmaximal, characteristic, complemented
15C79×#1846C211yesmaximal, characteristic, complemented
16C2×#14579119C2211yescharacteristic
17C2×#14579118C2211yescharacteristic
18C2×C4⋊C4×D79C2211yescharacteristic
19#19098622C418yescomplemented
20C2×#14579094C2211yescharacteristic
21C2×#14579094C2211yescharacteristic
22C2×#14579092C2211yescharacteristic
23C2×#14579092C2211yescharacteristic
24C2×Dic79⋊C8C2211yescharacteristic
25C2×Dic79⋊C8C2211yescharacteristic
26C2×(C2×D79)⋊C8C2211yescharacteristic
27C2×(C2×D79)⋊C8C2211yescharacteristic
28C2×#14579072C2211yescharacteristic
29#19098460—21no—
30#19098460—21no—
31#19098455—21no—
32#19098455—21no—
33#19098450—21no—
34#19098450—21no—
35#19098437—21no—
36#19098437—21no—
37#19098433C2211yescharacteristic
38#19098433C2211yescharacteristic
39#19098432C2211yescharacteristic
40#19098428C2211yescharacteristic
41#19098420C2211yescharacteristic
42#19098420C2211yescharacteristic
43C4⋊C4×Dic79C2211yescharacteristic
44C4⋊C4×Dic79C2211yescharacteristic
45#19098326C2211yescharacteristic
46#19098326C2211yescharacteristic
47#19098326C2211yescharacteristic
48#19098326C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51#19098325C2211yescharacteristic
52#19098325C2211yescharacteristic
53C2×#107×C79C2211yescharacteristic
54C2×#107×C79C2211yescharacteristic
55C2×#106×C79C2211yescharacteristic
56C2×#106×C79C2211yescharacteristic
57C2×C4×C8×C79C2211yescharacteristic
58#382×C79C2211yescharacteristic
59#382×C79C2211yescharacteristic
60C22×C4×D79—21no—
61C22×C4×D79C2311yescharacteristic
62C22×C79⋊C8C2311yescharacteristic
63C22×C79⋊C8C2311yescharacteristic
64#14579119—41no—
65#14579119—41no—
66#14579118C2×C414yes—
67#14579118Q814yes—
68C2×C4⋊Dic79—21no—
69C2×C4⋊Dic79—21no—
70C2×C4⋊Dic79—21no—
71C2×C4⋊Dic79—21no—
72C2×C4⋊Dic79C2311yescharacteristic
73C2×C4⋊Dic79C2311yescharacteristic
74C2×C4⋊Dic79C2311yescharacteristic
75C2×C4⋊Dic79C2311yescharacteristic
76C2×Dic79⋊C4—21no—
77C2×Dic79⋊C4—21no—
78C2×Dic79⋊C4—21no—
79C2×Dic79⋊C4D411yescharacteristic
80C2×Dic79⋊C4D411yescharacteristic
81C4⋊C4×D79—41no—
82C4⋊C4×D79—41no—
83C2×(C2×D79)⋊C4—21no—
84C2×(C2×D79)⋊C4—21no—
85C2×(C2×D79)⋊C4—21no—
86C2×(C2×D79)⋊C4D411yescharacteristic
87C2×(C2×D79)⋊C4D411yescharacteristic
88C2×C4×Dic79—21no—
89C2×C4×Dic79—21no—
90C2×C4×Dic79—21no—
91C2×C4×Dic79C2311yescharacteristic
92#14579094—41no—
93#14579094—41no—
94#14579092—41no—
95#14579092—41no—
96Dic79⋊C8C2×C414yescomplemented
97Dic79⋊C8C2×C414yescomplemented
98(C2×D79)⋊C8C2×C414yes—
99(C2×D79)⋊C8C2×C414yes—
100#14579072C2×C414yescomplemented
101C79⋊#95—21no—
102C79⋊#95—21no—
103C79⋊#95—21no—
104C79⋊#95—21no—
105C79⋊#95—21no—
106C79⋊#95—21no—
107C22×C8×C79C2311yescharacteristic
108C22×C8×C79C2311yescharacteristic
109C2×C4⋊C4×C79C2311yescharacteristic
110C2×C4⋊C4×C79C2311yescharacteristic
111C2×C4⋊C4×C79C2311yescharacteristic
112C2×C4⋊C4×C79C2311yescharacteristic
113C2×C42×C79C2311yescharacteristic
114#107×C79—41no—
115#107×C79—41no—
116#106×C79—41no—
117#106×C79—41no—
118C4×C8×C79C2×C414yescomplemented
119#95×C79—21no—
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—42no—
136C2×C4×D79—81no—
137C2×C4×D79—81no—
138C2×C4×D79C22×C412yes—
139C2×C4×D79C2×Q812yes—
140C2×C79⋊C8—21no—
141C2×C79⋊C8—21no—
142C2×C79⋊C8—21no—
143C2×C79⋊C8—21no—
144C2×C79⋊C8C22×C412yes—
145C2×C79⋊C8C22×C412yes—
146C4⋊Dic79—21no—
147C4⋊Dic79—21no—
148C4⋊Dic79—21no—
149C4⋊Dic79—21no—
150C4⋊Dic79—21no—
151C4⋊Dic79—21no—
152C4⋊Dic79—21no—
153C4⋊Dic79—21no—
154C4⋊Dic79—81no—
155C4⋊Dic79—81no—
156C4⋊Dic79—81no—
157C4⋊Dic79—81no—
158Dic79⋊C4—42no—
159Dic79⋊C4—81no—
160Dic79⋊C4—81no—
161Dic79⋊C4C4⋊C414yes—
162Dic79⋊C4C4⋊C414yes—
163(C2×D79)⋊C4—42no—
164(C2×D79)⋊C4—81no—
165(C2×D79)⋊C4—81no—
166(C2×D79)⋊C4C4⋊C414yes—
167(C2×D79)⋊C4C4⋊C414yes—
168C4×Dic79—42no—
169C4×Dic79—81no—
170C4×Dic79—81no—
171C4×Dic79C22×C412yes—
172C4×Dic79C2×Q812yes—
173C22×C4×C79—21no—
174C22×C4×C79—21no—
175C22×C4×C79—21no—
176C22×C4×C79—21no—
177C22×C4×C79C2×D411yescharacteristic
178C22×C4×C79C2×D411yescharacteristic
179C22×C4×C79C2411yescharacteristic
180C2×C8×C79—21no—
181C2×C8×C79—21no—
182C2×C8×C79—21no—
183C2×C8×C79—21no—
184C2×C8×C79C22×C412yes—
185C2×C8×C79C22×C412yes—
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—
193C4⋊C4×C79—21no—
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—84no—
254C8×C79—22no—
255C8×C79—22no—
256C79⋊C8—22no—
257C79⋊C8—22no—
258C22×C79C22×C4⋊C411yescharacteristic
259C22×C79#53511yescharacteristic
260C22×C79#53611yescharacteristic
261C22×C79#57611yescharacteristic
262C22×C79#57711yescharacteristic
263C22×C79#57711yescharacteristic
264C22×C79#57811yescharacteristic
265C2×D79—22no—
266C2×D79—22no—
267C2×D79—22no—
268C2×D79—41no—
269C2×D79—41no—
270C2×D79—41no—
271C2×D79—41no—
272C4×C79—22no—
273C4×C79—22no—
274C4×C79—81no—
275C4×C79—81no—
276C4×C79—81no—
277C4×C79—81no—
278C4×C79#52011yescharacteristic
279C4×C79#52011yescharacteristic
280C4×C79#54411yescharacteristic
281C4×C79#54411yescharacteristic
282Dic79—22no—
283Dic79—22no—
284Dic79—22no—
285Dic79—81no—
286Dic79—81no—
287Dic79—81no—
288Dic79—81no—
289#21992—791nomaximal, Sylow
290C2×C79#231711yescharacteristic
291C2×C79#291211yescharacteristic
292C2×C79#291311yescharacteristic
293C2×C79#322411yescharacteristic
294C2×C79#322511yescharacteristic
295C2×C79#324111yescharacteristic
296C2×C79#324211yescharacteristic
297D79—42no—
298C2×#433—791no—
299#2317—791no—
300#2314—791no—
301#1949—791no—
302#1949—791no—
303#1948—791no—
304#1947—791no—
305#1854—791no—
306#1854—791no—
307#1853—791no—
308#1852—791no—
309#1847—791no—
310#1846D7911yescharacteristic, complemented
311#1836—791no—
312#1834—791no—
313C79#2199211yescharacteristic, complemented, Sylow
314C2×#117—791no—
315C2×#117—791no—
316C22×C4⋊C4—791no—
317#433—798no—
318C2×#107—791no—
319C2×#107—791no—
320C2×#107C2×D7911yescharacteristic
321C2×#107C2×D7911yescharacteristic
322C2×#106—791no—
323C2×#106—791no—
324C2×#106C2×D7911yescharacteristic
325C2×#106C2×D7911yescharacteristic
326C2×C4⋊C8—791no—
327C2×C4⋊C8—791no—
328C2×C22⋊C8—791no—
329C2×C22⋊C8—791no—
330C2×#97—791no—
331C2×C4×C8C2×D7911yescharacteristic
332#389—1581no—
333#389—1581no—
334#388—1581no—
335#388—1581no—
336#387—1581no—
337#387—1581no—
338#385—1581no—
339#385—1581no—
340#384—791no—
341#384—791no—
342#384—791no—
343#382—791no—
344#382C2×D7911yescharacteristic
345#382C2×D7911yescharacteristic
346#380—791no—
347#380—791no—
348C4×C4⋊C4—791no—
349C4×C4⋊C4—791no—
350#340—791no—
351#340—791no—
352#340—791no—
353#340—791no—
354#340—791no—
355#340—791no—
356#340—791no—
357#340—791no—
358C23×C4—791no—
359C23×C4—1581no—
360C22×C8—791no—
361C22×C8—791no—
362C22×C8C22×D7911yescharacteristic
363C22×C8C22×D7911yescharacteristic
364#117—3161no—
365#117—3161no—
366#117—794no—
367#117—794no—
368C2×C4⋊C4—3161no—
369C2×C4⋊C4—3161no—
370C2×C4⋊C4—791no—
371C2×C4⋊C4—791no—
372C2×C4⋊C4—791no—
373C2×C4⋊C4—791no—
374C2×C4⋊C4—791no—
375C2×C4⋊C4—791no—
376C2×C4⋊C4—1581no—
377C2×C4⋊C4—1581no—
378C2×C4⋊C4—1581no—
379C2×C4⋊C4—1581no—
380C2×C4⋊C4—1581no—
381C2×C4⋊C4—1581no—
382C2×C4⋊C4—1581no—
383C2×C4⋊C4C22×D7911yescharacteristic
384C2×C4⋊C4C22×D7911yescharacteristic
385C2×C4⋊C4C22×D7911yescharacteristic
386C2×C4⋊C4C22×D7911yescharacteristic
387C2×C22⋊C4—791no—
388C2×C22⋊C4—791no—
389C2×C22⋊C4—1581no—
390C2×C22⋊C4—1581no—
391C2×C22⋊C4—1581no—
392C2×C42—791no—
393C2×C42—1581no—
394C2×C42—1581no—
395C2×C42—1581no—
396C2×C42C22×D7911yescharacteristic
397#107—41no—
398#107—41no—
399#107—3161no—
400#107—3161no—
401#106—41no—
402#106—41no—
403#106—3161no—
404#106—3161no—
405C4⋊C8—794no—
406C4⋊C8—794no—
407C22⋊C8—794no—
408C22⋊C8—794no—
409#97—794no—
410C4×C8C4×D7914yescomplemented
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—1581no—
416#95—1581no—
417#95—1581no—
418#95—1581no—
419#95—1581no—
420#95—1581no—
421C24—791no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—3162no—
427C22×C4—791no—
428C22×C4—791no—
429C22×C4—791no—
430C22×C4—792no—
431C22×C4—792no—
432C22×C4—6321no—
433C22×C4—6321no—
434C22×C4—1581no—
435C22×C4—1581no—
436C22×C4—1581no—
437C22×C4—1581no—
438C22×C4—1581no—
439C22×C4—1581no—
440C22×C4—1581no—
441C22×C4—1581no—
442C22×C4D4×D7911yescharacteristic
443C22×C4D4×D7911yescharacteristic
444C22×C4C23×D7911yescharacteristic
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—792no—
450C2×C8—792no—
451C2×C8—1581no—
452C2×C8—1581no—
453C2×C8—1581no—
454C2×C8—1581no—
455C2×C8C2×C4×D7912yes—
456C2×C8C2×C4×D7912yes—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—3162no—
466C4⋊C4—794no—
467C4⋊C4—794no—
468C4⋊C4—6321no—
469C4⋊C4—6321no—
470C4⋊C4—6321no—
471C4⋊C4—6321no—
472C4⋊C4—6321no—
473C4⋊C4—6321no—
474C4⋊C4—1581no—
475C4⋊C4—1581no—
476C4⋊C4—1581no—
477C4⋊C4—1581no—
478C4⋊C4—1581no—
479C4⋊C4—1581no—
480C4⋊C4—1581no—
481C4⋊C4—1581no—
482C22⋊C4—3162no—
483C22⋊C4—794no—
484C22⋊C4—794no—
485C22⋊C4—6321no—
486C22⋊C4—6321no—
487C42—3162no—
488C42—792no—
489C42—792no—
490C42—6321no—
491C42—6321no—
492C42C2×C4×D7912yes—
493C42Q8×D7912yes—
494C23—792no—
495C23—1581no—
496C23—1581no—
497C23—1581no—
498C23—1581no—
499C23—1581no—
500C23—1581no—
501C23C2×D4×D7911yescharacteristic
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
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—3161no—
519C2×C4—3161no—
520C2×C4—3161no—
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—792no—
531C2×C4—792no—
532C2×C4—792no—
533C2×C4—6324no—
534C2×C4—1581no—
535C2×C4—1581no—
536C2×C4—1581no—
537C2×C4—1581no—
538C2×C4—1581no—
539C2×C4—1581no—
540C2×C4—1582no—
541C2×C4—1582no—
542C2×C4—1582no—
543C2×C4—1582no—
544C2×C4C4⋊C4×D7912yes—
545C2×C4C4⋊C4×D7912yes—
546C2×C4C22×C4×D7911yescharacteristic
547C2×C4C2×Q8×D7911yescharacteristic
548C2×C4#1457920611yescharacteristic
549C2×C4#1457920611yescharacteristic
550C2×C4#1457920911yescharacteristic
551C2×C4#1457920911yescharacteristic
552C8—22no—
553C8—22no—
554C8—1582no—
555C8—1582no—
556C22—3161no—
557C22—3161no—
558C22—3161no—
559C22—3161no—
560C22—1582no—
561C22—1582no—
562C22—1582no—
563C22C2×C4⋊C4×D7911yescharacteristic
564C22#1909912611yescharacteristic
565C22#1909913811yescharacteristic
566C22#1909936511yescharacteristic
567C22#1909937011yescharacteristic
568C22#1909937011yescharacteristic
569C22#1909937711yescharacteristic
570C4—22no—
571C4—22no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—6321no—
577C4—6321no—
578C4—6321no—
579C4—6321no—
580C4—1582no—
581C4—1582no—
582C4—1582no—
583C4#1909904411yescharacteristic
584C4#1909904411yescharacteristic
585C4#1909919011yescharacteristic
586C4#1909919011yescharacteristic
587C2—3162no—
588C2#2376602111yescharacteristic
589C2#2377199211yescharacteristic
590C2#2377199711yescharacteristic
591C2#2377448711yescharacteristic
592C2#2377450211yescharacteristic
593C2#2377465611yescharacteristic
594C2#2377467111yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#1846C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
cosocleC22×C4×C79C24
hypercenter#1846D79
hypocenterC79#21992
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1846

Complements

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

NH ≅ G/Ntype
4. #23764169C2semidirect
5. #23764165C2semidirect
6. #23764160C2semidirect
7. #23764155C2semidirect
12. #23763569C2semidirect
13. #23763533C2semidirect
14. #23763528C2semidirect
15. C79×#1846C2semidirect
19. #19098622C4semidirect
96. Dic79⋊C8C2×C4semidirect
97. Dic79⋊C8C2×C4semidirect
100. #14579072C2×C4semidirect
118. C4×C8×C79C2×C4semidirect
310. #1846D79semidirect
313. C79#21992semidirect
410. C4×C8C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190986222
#237660252
#237660102
#237641692
#237641652
#237641602
#237641552
#237635982
#237635962
#237635912
#237635862
#237635692
#237635332
#237635282
C79×#18462
#2199279