Finite Group Databasebeta

← #29699719

Subgroups — #29699719

Order 15616.

710 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519797C211yesmaximal, characteristic
2#21454484C211yesmaximal, characteristic, complemented
3#21446711C212yesmaximal
4#21446467C212yesmaximal, complemented
5#21446464C212yesmaximal, complemented
6#21445990C211yesmaximal, characteristic, complemented
7#21445839C211yesmaximal, characteristic, complemented
8#21445836C211yesmaximal, characteristic, complemented
9#21445704C212yesmaximal, complemented
10#21445689C211yesmaximal, characteristic, complemented
11C61×#2925C211yesmaximal, characteristic, complemented
12C2×#14519797C2211yescharacteristic
13C4×#11758222C2211yescharacteristic
14C4×#11758202C411yescharacteristic, complemented
15C4×#11758202C411yescharacteristic, complemented
16C4×#11758201C411yescharacteristic, complemented
17C4×#11758201C411yescharacteristic, complemented
18C4×#11758200C411yescharacteristic, complemented
19C4×#11758200C411yescharacteristic, complemented
20C4×#11758199C411yescharacteristic, complemented
21C4×#11758199C411yescharacteristic, complemented
22#16839822—22no—
23#16839818—21no—
24#16839814—21no—
25C2×#14519712C2212yes—
26C2×#14519712C2212yes—
27#16839798C2211yescharacteristic
28#16839786C2211yescharacteristic
29C2×#14519704C2212yes—
30C2×#14519703C2212yes—
31#16839758C2211yescharacteristic
32#16839756C2211yescharacteristic
33#16839728C2212yes—
34#16839717C2212yes—
35C2×#14519687C2212yes—
36C2×C4×#92418C2211yescharacteristic
37C4×C4⋊Dic61C2211yescharacteristic
38#16839523C2212yes—
39#16839521C2212yes—
40#16839516C2212yes—
41C4×#41×C61C2211yescharacteristic
42C61×#433—22no—
43C61×#432—21no—
44C61×#431—21no—
45C61×#423C2211yescharacteristic
46C2×C4⋊C8×C61C2211yescharacteristic
47C61×#408C2212yes—
48C61×#405C2212yes—
49C2×#11758222C2311yescharacteristic
50#14519797—22no—
51#14519797—22no—
52C2×#11758202C2×C411yescharacteristic
53C2×#11758200C2×C411yescharacteristic
54C2×#11758201C2×C411yescharacteristic
55C2×#11758199C2×C411yescharacteristic
56C2×#11758194C2312yes—
57C22×#92418C2311yescharacteristic
58C22×#92418C2311yescharacteristic
59C4×Dic122C2×C411yescharacteristic
60C4×Dic122C2×C411yescharacteristic
61C4×D244C2×C411yescharacteristic
62C4×D244C2×C411yescharacteristic
63C4×C22⋊D61—21no—
64C4×C22⋊D61—21no—
65#14519736C2311yescharacteristic
66#14519734—21no—
67C2×C4⋊Dic61—21no—
68C2×C4×Dic61C2312yes—
69C42×D61—21no—
70#14519712—24no—
71#14519712—42no—
72#14519710C2×C411yescharacteristic
73#14519710C2×C411yescharacteristic
74#14519708C2×C411yescharacteristic
75#14519708C2×C411yescharacteristic
76C4⋊#92418—21no—
77C4⋊#92418—21no—
78#14519704—42no—
79#14519703—42no—
80#14519701C2×C411yescharacteristic
81#14519701C2×C411yescharacteristic
82#14519700C2×C411yescharacteristic
83#14519700C2×C411yescharacteristic
84#14519698C2×C411yescharacteristic
85#14519698C2×C411yescharacteristic
86#14519697C2×C411yescharacteristic
87#14519697C2×C411yescharacteristic
88#14519689—22no—
89#14519689—22no—
90#14519687—22no—
91#14519687—24no—
92C4×#92418C2×C411yescharacteristic
93C4×#92418C2×C411yescharacteristic
94C4×#92418C2×C411yescharacteristic
95C4×#92418C2×C411yescharacteristic
96C8×Dic61—22no—
97#14519684—21no—
98C2×#41×C61C2311yescharacteristic
99C2×M16×C61C2312yes—
100C22×C8×C61C2312yes—
101C4×Q8×C61C2×C411yescharacteristic
102C4×Q8×C61C2×C411yescharacteristic
103C4×D4×C61—21no—
104C4×D4×C61—21no—
105C4×D4×C61C2×C411yescharacteristic
106C4×D4×C61C2×C411yescharacteristic
107#117×C61—21no—
108#117×C61C2311yescharacteristic
109C2×C42×C61—21no—
110C2×C42×C61C2311yescharacteristic
111C4⋊C8×C61—21no—
112C4⋊C8×C61—21no—
113C4⋊C8×C61D411yescharacteristic
114C4⋊C8×C61D411yescharacteristic
115C4⋊C8×C61D412yes—
116C22⋊C8×C61—22no—
117C22⋊C8×C61—22no—
118#97×C61—22no—
119C4×C8×C61—22no—
120#41×C61—21no—
121#41×C61—21no—
122#41×C61—21no—
123#41×C61—21no—
124C2×Q8×C61C22×C411yescharacteristic
125C2×D4×C61—21no—
126C2×D4×C61C22×C411yescharacteristic
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61#4111yescharacteristic
131C22×C4×C61#4111yescharacteristic
132C22×C4×C61C2411yescharacteristic
133C2×C22⋊D61—21no—
134C22×Dic61—22no—
135#11758222—21no—
136#11758222—21no—
137#11758222—21no—
138#11758222—21no—
139C2×D244C22×C411yescharacteristic
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×Dic122C22×C411yescharacteristic
144M16×C61—22no—
145M16×C61—22no—
146C2×C8×C61—22no—
147C2×C8×C61—22no—
148C2×C8×C61—22no—
149C2×C8×C61C2×D412yes—
150C2×C8×C61C2×D412yes—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61C22×C411yescharacteristic
154C4⋊C4×C61C22×C411yescharacteristic
155C22⋊C4×C61—21no—
156C22⋊C4×C61—21no—
157C22⋊C4×C61—21no—
158C42×C61—21no—
159C42×C61—21no—
160C42×C61—21no—
161C42×C61C22×C411yescharacteristic
162C42×C61C22×C411yescharacteristic
163C42×C61C2×D411yescharacteristic
164C42×C61C2×D411yescharacteristic
165C22⋊Dic61—21no—
166#11758202—22no—
167#11758201—22no—
168#11758200—22no—
169#11758199—22no—
170#11758198—21no—
171#11758198—21no—
172C4⋊Dic61—42no—
173C4⋊Dic61C22×C411yescharacteristic
174C4⋊Dic61C22×C411yescharacteristic
175#11758196—21no—
176#11758196—21no—
177C4×Dic61—21no—
178C4×Dic61—21no—
179C4×Dic61—21no—
180C4×Dic61—22no—
181C4×Dic61—22no—
182#11758194—22no—
183#11758194—22no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—22no—
187C2×#92418C22×C411yescharacteristic
188C2×#92418C22×C411yescharacteristic
189C2×#92418C22×C411yescharacteristic
190C2×#92418C22×C411yescharacteristic
191C2×#92418#4112yes—
192C2×#92418#4112yes—
193C23×C61—21no—
194C23×C61C2×#4111yescharacteristic
195C22×D61—21no—
196Q8×C61—21no—
197Q8×C61—21no—
198D4×C61—21no—
199D4×C61—21no—
200D4×C61—41no—
201D4×C61—41no—
202C2×C4×C61—22no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—41no—
207C2×C4×C61—41no—
208C2×C4×C61—41no—
209C2×C4×C61—42no—
210C2×C4×C61—81no—
211C2×C4×C61C4×D411yescharacteristic
212C2×C4×C61C4×D411yescharacteristic
213C2×C4×C61C4×D411yescharacteristic
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61C23×C411yescharacteristic
216C2×C4×C61C22×D411yescharacteristic
217C2×C4×C61C2×#4111yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×C4×C61H(5,𝔽2)11yescharacteristic
220C2×C4×C612−1+411yescharacteristic
221C22⋊D61—41no—
222C22⋊D61—41no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—42no—
227C2×Dic61—42no—
228C2×Dic61—42no—
229D244—21no—
230D244—21no—
231C4×D61—41no—
232C4×D61—41no—
233C4×D61—42no—
234C4×D61—81no—
235Dic122—21no—
236Dic122—21no—
237C8×C61—22no—
238C8×C61—22no—
239C8×C61—42no—
240#92418—21no—
241#92418—21no—
242#92418—42no—
243#92418#11712yes—
244#92418#11712yes—
245#22803—611nomaximal, Sylow
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—41no—
249C22×C61—41no—
250C22×C61—41no—
251C22×C61C2×C4×D411yescharacteristic
252C22×C61#55511yescharacteristic
253C22×C61#55611yescharacteristic
254C2×D61—41no—
255C2×D61—41no—
256C2×D61—41no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—41no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61#44412yes—
264C4×C61C2×#11711yescharacteristic
265C4×C61#52011yescharacteristic
266C4×C61#54711yescharacteristic
267C4×C61#55011yescharacteristic
268Dic61—41no—
269Dic61—41no—
270Dic61—41no—
271Dic61—82no—
272C4×#135—611no—
273#2925—611no—
274#2925D6111yescharacteristic, complemented
275#1975—612no—
276#1929—612no—
277#1929—612no—
278#1848—611no—
279#1806—611no—
280#1806—611no—
281#1773—612no—
282#1770—611no—
283C2×C61—21no—
284C2×C61—21no—
285C2×C61—81no—
286C2×C61#235411yescharacteristic
287C2×C61C2×#44411yescharacteristic
288C2×C61#295711yescharacteristic
289D61—81no—
290C2×#135—611no—
291C4×#41—611no—
292C4×#41C2×D6111yescharacteristic
293C4×Q16—611no—
294C4×Q16—611no—
295C4×SD16—611no—
296C4×SD16—611no—
297C4×SD16—611no—
298C4×SD16—611no—
299C4×D8—611no—
300C4×D8—611no—
301#433—22no—
302#433—1222no—
303#432—21no—
304#432—1221no—
305#431—21no—
306#431—1221no—
307C2×#108—612no—
308C2×#108—612no—
309#427—611no—
310#423—611no—
311#423C2×D6111yescharacteristic
312C2×C4⋊C8C2×D6111yescharacteristic
313C2×#104—612no—
314C2×#104—612no—
315#416—611no—
316#416—611no—
317#408—612no—
318#408C2×D6112yes—
319#405—612no—
320#405C2×D6112yes—
321C2×#97—612no—
322C2×C4×C8—611no—
323C4×C4⋊C4—611no—
324#339—612no—
325#339—612no—
326#336—612no—
327C61#2280311yescharacteristic, complemented, Sylow
328C2×#41—611no—
329C2×#41C22×D6111yescharacteristic
330#135—1222no—
331#135—1222no—
332C2×Q16—611no—
333C2×SD16—611no—
334C2×SD16—611no—
335C2×D8—611no—
336C2×M16—612no—
337C2×M16C22×D6112yes—
338C22×C8—611no—
339C22×C8—611no—
340C22×C8C22×D6112yes—
341C4×Q8—611no—
342C4×Q8—611no—
343C4×Q8C4×D6111yescharacteristic
344C4×Q8C4×D6111yescharacteristic
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—611no—
348C4×D4—611no—
349C4×D4—1221no—
350C4×D4—1221no—
351C4×D4C4×D6111yescharacteristic
352C4×D4C4×D6111yescharacteristic
353#117—21no—
354#117—611no—
355#117—1221no—
356#117C22×D6111yescharacteristic
357C2×C4⋊C4—1221no—
358C2×C42—21no—
359C2×C42—612no—
360C2×C42—1221no—
361C2×C42C22×D6111yescharacteristic
362#108—1224no—
363#108—2442no—
364#107—611no—
365#107—611no—
366#106—611no—
367#106—611no—
368C4⋊C8—21no—
369C4⋊C8—21no—
370C4⋊C8—1221no—
371C4⋊C8—1221no—
372C4⋊C8C22⋊D6111yescharacteristic
373C4⋊C8C22⋊D6111yescharacteristic
374C4⋊C8C22⋊D6112yes—
375#104—2442no—
376#104—2442no—
377#103—611no—
378#103—611no—
379#103—611no—
380#103—611no—
381#102—611no—
382#102—611no—
383#102—611no—
384#102—611no—
385C22⋊C8—22no—
386C22⋊C8—22no—
387C22⋊C8—1222no—
388C22⋊C8—1222no—
389#97—22no—
390#97—1224no—
391#97—1222no—
392C4×C8—22no—
393C4×C8—611no—
394C4×C8—611no—
395C4×C8—611no—
396C4×C8—611no—
397C4×C8—1222no—
398#95—1221no—
399#41—21no—
400#41—21no—
401#41—21no—
402#41—21no—
403#41—1221no—
404#41—1221no—
405#41—1221no—
406#41—1221no—
407C2×Q8—611no—
408C2×Q8C2×C4×D6111yescharacteristic
409C2×D4—21no—
410C2×D4—611no—
411C2×D4—1221no—
412C2×D4C2×C4×D6111yescharacteristic
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—1221no—
417C22×C4—1221no—
418C22×C4—1221no—
419C22×C4—1222no—
420C22×C4#1175822211yescharacteristic
421C22×C4#1175822211yescharacteristic
422C22×C4C23×D6111yescharacteristic
423Q16—1222no—
424SD16—1222no—
425SD16—1222no—
426D8—1222no—
427M16—22no—
428M16—22no—
429M16—1222no—
430M16—1222no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—611no—
435C2×C8—611no—
436C2×C8—612no—
437C2×C8—612no—
438C2×C8—611no—
439C2×C8—611no—
440C2×C8—1221no—
441C2×C8—1221no—
442C2×C8—1222no—
443C2×C8C2×C22⋊D6112yes—
444C2×C8C2×C22⋊D6112yes—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—611no—
448C4⋊C4—611no—
449C4⋊C4—1221no—
450C4⋊C4—1221no—
451C4⋊C4—2442no—
452C4⋊C4C2×C4×D6111yescharacteristic
453C4⋊C4C2×C4×D6111yescharacteristic
454C22⋊C4—21no—
455C22⋊C4—21no—
456C22⋊C4—21no—
457C22⋊C4—1221no—
458C22⋊C4—1221no—
459C22⋊C4—1221no—
460C42—21no—
461C42—21no—
462C42—21no—
463C42—1221no—
464C42—1221no—
465C42—1221no—
466C42—1222no—
467C42—1222no—
468C42C2×C4×D6111yescharacteristic
469C42C2×C4×D6111yescharacteristic
470C42C2×C22⋊D6111yescharacteristic
471C42C2×C22⋊D6111yescharacteristic
472C23—21no—
473C23—1221no—
474C23C2×#1175822211yescharacteristic
475Q8—21no—
476Q8—21no—
477Q8—1221no—
478Q8—1221no—
479D4—21no—
480D4—21no—
481D4—41no—
482D4—41no—
483D4—1221no—
484D4—1221no—
485D4—2441no—
486D4—2441no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—81no—
496C2×C4—1221no—
497C2×C4—1221no—
498C2×C4—1221no—
499C2×C4—4881no—
500C2×C4—2442no—
501C2×C4—2442no—
502C2×C4—2442no—
503C2×C4—2442no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4C4×C22⋊D6111yescharacteristic
507C2×C4C4×C22⋊D6111yescharacteristic
508C2×C4C4×C22⋊D6111yescharacteristic
509C2×C4C4×C22⋊D6111yescharacteristic
510C2×C4C22×C4×D6111yescharacteristic
511C2×C4C22×C22⋊D6111yescharacteristic
512C2×C4#41×D6111yescharacteristic
513C2×C4#41×D6111yescharacteristic
514C2×C4#1451982311yescharacteristic
515C2×C4#1451982411yescharacteristic
516C8—22no—
517C8—22no—
518C8—42no—
519C8—612no—
520C8—612no—
521C8—1221no—
522C8—1221no—
523C8—2442no—
524C22—21no—
525C22—21no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—2441no—
530C22—2441no—
531C22—2441no—
532C22C2×C4×C22⋊D6111yescharacteristic
533C22#1684047511yescharacteristic
534C22#1684048011yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—4882no—
542C4—2441no—
543C4—2441no—
544C4—2441no—
545C4#1683988212yes—
546C4#117×D6111yescharacteristic
547C4#1684024211yescharacteristic
548C4#1684041111yescharacteristic
549C4#1684043111yescharacteristic
550C2—21no—
551C2—21no—
552C2—81no—
553C2—4881no—
554C2#2144876911yescharacteristic
555C2C2×#1683988211yescharacteristic
556C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2925C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C22
cosocleC22×C4×C61C24
hypercenter#2925D61
hypocenterC61#22803
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #21454484C2semidirect
4. #21446467C2semidirect
5. #21446464C2semidirect
6. #21445990C2semidirect
7. #21445839C2semidirect
8. #21445836C2semidirect
9. #21445704C2semidirect
10. #21445689C2semidirect
11. C61×#2925C2semidirect
14. C4×#11758202C4semidirect
15. C4×#11758202C4semidirect
16. C4×#11758201C4semidirect
17. C4×#11758201C4semidirect
18. C4×#11758200C4semidirect
19. C4×#11758200C4semidirect
20. C4×#11758199C4semidirect
21. C4×#11758199C4semidirect
274. #2925D61semidirect
327. C61#22803semidirect

Maximal subgroups

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

subgroupindex
C4×#145197972
#214544842
#214467112
#214464672
#214464642
#214459902
#214458392
#214458362
#214457042
#214456892
C61×#29252
#2280361