Finite Group Databasebeta

← #29699713

Subgroups — #29699713

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#21454487C211yesmaximal, characteristic, complemented
3#21454485C211yesmaximal, characteristic, complemented
4#21446709C212yesmaximal
5#21446470C212yesmaximal, complemented
6#21446465C212yesmaximal, complemented
7#21445990C211yesmaximal, characteristic, complemented
8#21445840C211yesmaximal, characteristic, complemented
9#21445702C212yesmaximal, complemented
10#21445688C211yesmaximal, characteristic, complemented
11C61×#1806C211yesmaximal, 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#16839823—22no—
23#16839822—22no—
24#16839819—21no—
25#16839818—21no—
26#16839815—21no—
27#16839814—21no—
28C2×#14519712C2212yes—
29C2×#14519712C2212yes—
30#16839798C2211yescharacteristic
31#16839786C2211yescharacteristic
32C2×C4⋊#92418C2211yescharacteristic
33C2×#14519705C2212yes—
34#16839758C2211yescharacteristic
35#16839756C2211yescharacteristic
36#16839730C2212yes—
37#16839729C2212yes—
38#16839720C2212yes—
39#16839718C2212yes—
40C2×#14519688C2212yes—
41C2×C4×#92418C2211yescharacteristic
42#16839522C2212yes—
43#16839517C2212yes—
44C4×#41×C61C2211yescharacteristic
45C61×#423C2211yescharacteristic
46C2×#104×C61C2212yes—
47C4×C4⋊C4×C61C2211yescharacteristic
48C61×#339C2212yes—
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×#92418C2312yes—
59C22×#92418C2311yescharacteristic
60C4×Dic122C2×C411yescharacteristic
61C4×Dic122C2×C411yescharacteristic
62C4×D244C2×C411yescharacteristic
63C4×D244C2×C411yescharacteristic
64C4×C22⋊D61—21no—
65C4×C22⋊D61—21no—
66#14519736C2311yescharacteristic
67#14519734—21no—
68C42×D61—21no—
69#14519712—24no—
70#14519712—42no—
71#14519710C2×C411yescharacteristic
72#14519710C2×C411yescharacteristic
73#14519708C2×C411yescharacteristic
74#14519708C2×C411yescharacteristic
75C4⋊#92418—21no—
76C4⋊#92418—21no—
77C4⋊#92418D411yescharacteristic
78C4⋊#92418D411yescharacteristic
79C4⋊#92418D412yes—
80#14519705—42no—
81#14519701C2×C411yescharacteristic
82#14519701C2×C411yescharacteristic
83#14519700C2×C411yescharacteristic
84#14519700C2×C411yescharacteristic
85#14519698C2×C411yescharacteristic
86#14519698C2×C411yescharacteristic
87#14519697C2×C411yescharacteristic
88#14519697C2×C411yescharacteristic
89C22⋊#92418—22no—
90C22⋊#92418—22no—
91#14519689—22no—
92#14519689—22no—
93#14519688—22no—
94#14519688—24no—
95#14519687—22no—
96C4×#92418—22no—
97C4×#92418C2×C411yescharacteristic
98C4×#92418C2×C411yescharacteristic
99C4×#92418C2×C411yescharacteristic
100C4×#92418C2×C411yescharacteristic
101C8×Dic61—22no—
102C2×#41×C61C2311yescharacteristic
103C2×M16×C61C2312yes—
104C4×Q8×C61C2×C411yescharacteristic
105C4×Q8×C61C2×C411yescharacteristic
106C4×D4×C61—21no—
107C4×D4×C61—21no—
108C4×D4×C61C2×C411yescharacteristic
109C4×D4×C61C2×C411yescharacteristic
110#117×C61—21no—
111#117×C61C2311yescharacteristic
112C2×C4⋊C4×C61—21no—
113C2×C42×C61—21no—
114C2×C42×C61C2312yes—
115C2×C42×C61C2311yescharacteristic
116C4⋊C8×C61—21no—
117C4⋊C8×C61—21no—
118#104×C61—42no—
119#95×C61—21no—
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—22no—
131C22×C4×C61#4111yescharacteristic
132C22×C4×C61#4111yescharacteristic
133C22×C4×C61C2411yescharacteristic
134C2×C22⋊D61—21no—
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—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—42no—
150C4⋊C4×C61C22×C411yescharacteristic
151C4⋊C4×C61C22×C411yescharacteristic
152C22⋊C4×C61—21no—
153C22⋊C4×C61—21no—
154C22⋊C4×C61—21no—
155C42×C61—21no—
156C42×C61—21no—
157C42×C61—21no—
158C42×C61—22no—
159C42×C61—22no—
160C42×C61C22×C411yescharacteristic
161C42×C61C22×C411yescharacteristic
162C42×C61C2×D411yescharacteristic
163C42×C61C2×D411yescharacteristic
164C22⋊Dic61—21no—
165#11758202—22no—
166#11758201—22no—
167#11758200—22no—
168#11758199—22no—
169#11758198—21no—
170#11758198—21no—
171C4⋊Dic61C22×C411yescharacteristic
172C4⋊Dic61C22×C411yescharacteristic
173#11758196—21no—
174#11758196—21no—
175C4×Dic61—21no—
176C4×Dic61—21no—
177C4×Dic61—21no—
178#11758194—22no—
179#11758194—22no—
180C2×#92418—22no—
181C2×#92418—21no—
182C2×#92418—21no—
183C2×#92418—22no—
184C2×#92418—22no—
185C2×#92418C22×C411yescharacteristic
186C2×#92418C22×C411yescharacteristic
187C2×#92418C22×C411yescharacteristic
188C2×#92418C22×C411yescharacteristic
189C2×#92418C2×D412yes—
190C2×#92418C2×D412yes—
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—42no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61—81no—
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61C4×D411yescharacteristic
216C2×C4×C61C4×D411yescharacteristic
217C2×C4×C61C4×D411yescharacteristic
218C2×C4×C61C23×C411yescharacteristic
219C2×C4×C61C22×D411yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C61C2×#4111yescharacteristic
222C2×C4×C61H(5,𝔽2)11yescharacteristic
223C2×C4×C612−1+411yescharacteristic
224C22⋊D61—41no—
225C22⋊D61—41no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229D244—21no—
230D244—21no—
231C4×D61—41no—
232C4×D61—41no—
233C4×D61—42no—
234C4×D61—81no—
235Dic122—21no—
236Dic122—21no—
237C8×C61—42no—
238#92418—21no—
239#92418—21no—
240#92418—22no—
241#92418—22no—
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—82no—
264C4×C61#44412yes—
265C4×C61C2×#11711yescharacteristic
266C4×C61#52011yescharacteristic
267C4×C61#54711yescharacteristic
268C4×C61#55011yescharacteristic
269Dic61—41no—
270Dic61—41no—
271Dic61—41no—
272C4×#135—611no—
273#2925—611no—
274#2925—611no—
275#1975—612no—
276#1929—612no—
277#1929—612no—
278#1848—611no—
279#1806—611no—
280#1806D6111yescharacteristic, complemented
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—1222no—
302#433—1222no—
303#432—1221no—
304#432—1221no—
305#431—1221no—
306#431—1221no—
307C2×#108—612no—
308C2×#108—612no—
309#427—611no—
310#423—611no—
311#423C2×D6111yescharacteristic
312C2×C4⋊C8—611no—
313C2×#104—612no—
314C2×#104C2×D6112yes—
315#416—611no—
316#416—611no—
317#408—612no—
318#408—612no—
319#405—612no—
320#405—612no—
321C2×#97—612no—
322C2×C4×C8—611no—
323C4×C4⋊C4C2×D6111yescharacteristic
324#339—612no—
325#339C2×D6112yes—
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×C8—612no—
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—21no—
358C2×C42—21no—
359C2×C42—1221no—
360C2×C42C22×D6112yes—
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—611no—
371C4⋊C8—611no—
372C4⋊C8—612no—
373C4⋊C8—1221no—
374C4⋊C8—1221no—
375#104—42no—
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—1222no—
386C22⋊C8—1222no—
387C22⋊C8—1222no—
388C22⋊C8—1222no—
389#97—1224no—
390#97—1222no—
391#97—1222no—
392C4×C8—611no—
393C4×C8—611no—
394C4×C8—611no—
395C4×C8—611no—
396C4×C8—1222no—
397C4×C8—1222no—
398#95—21no—
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—22no—
417C22×C4—1221no—
418C22×C4—1221no—
419C22×C4—1221no—
420C22×C4#1175822411yescharacteristic
421C22×C4#1175822411yescharacteristic
422C22×C4C23×D6111yescharacteristic
423Q16—1222no—
424SD16—1222no—
425SD16—1222no—
426D8—1222no—
427M16—22no—
428M16—22no—
429M16—1222no—
430M16—1222no—
431C2×C8—22no—
432C2×C8—611no—
433C2×C8—611no—
434C2×C8—612no—
435C2×C8—612no—
436C2×C8—611no—
437C2×C8—611no—
438C2×C8—612no—
439C2×C8—612no—
440C2×C8—1222no—
441C2×C8—1221no—
442C2×C8—1221no—
443C2×C8—1222no—
444C2×C8—1222no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—42no—
448C4⋊C4—611no—
449C4⋊C4—611no—
450C4⋊C4—1221no—
451C4⋊C4—1221no—
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—22no—
464C42—22no—
465C42—1221no—
466C42—1221no—
467C42—1221no—
468C42C2×C4×D6111yescharacteristic
469C42C2×C4×D6111yescharacteristic
470C42D4×D6111yescharacteristic
471C42D4×D6111yescharacteristic
472C23—21no—
473C23—1221no—
474C23C2×#1175822411yescharacteristic
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—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—81no—
499C2×C4—1221no—
500C2×C4—1221no—
501C2×C4—1221no—
502C2×C4—4881no—
503C2×C4—2442no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4#1451973711yescharacteristic
507C2×C4#1451973711yescharacteristic
508C2×C4#1451973711yescharacteristic
509C2×C4#1451973711yescharacteristic
510C2×C4C22×C4×D6111yescharacteristic
511C2×C4C2×D4×D6111yescharacteristic
512C2×C4#41×D6111yescharacteristic
513C2×C4#41×D6111yescharacteristic
514C2×C4#1451982211yescharacteristic
515C2×C4#1451982511yescharacteristic
516C8—42no—
517C8—612no—
518C8—612no—
519C8—1221no—
520C8—1221no—
521C8—1222no—
522C8—1222no—
523C8—2442no—
524C22—21no—
525C22—21no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—2441no—
530C22—2441no—
531C22—2441no—
532C22C2×#1451973711yescharacteristic
533C22#1684047611yescharacteristic
534C22#1684048311yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—82no—
542C4—2441no—
543C4—2441no—
544C4—2441no—
545C4#1683988112yes—
546C4#117×D6111yescharacteristic
547C4#1684024311yescharacteristic
548C4#1684041411yescharacteristic
549C4#1684043011yescharacteristic
550C2—21no—
551C2—21no—
552C2—81no—
553C2—4881no—
554C2#2144876311yescharacteristic
555C2C2×#1683988111yescharacteristic
556C2#2145473211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1806C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C22
cosocleC22×C4×C61C24
hypercenter#1806D61
hypocenterC61#22803
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #21454487C2semidirect
3. #21454485C2semidirect
5. #21446470C2semidirect
6. #21446465C2semidirect
7. #21445990C2semidirect
8. #21445840C2semidirect
9. #21445702C2semidirect
10. #21445688C2semidirect
11. C61×#1806C2semidirect
14. C4×#11758202C4semidirect
15. C4×#11758202C4semidirect
16. C4×#11758201C4semidirect
17. C4×#11758201C4semidirect
18. C4×#11758200C4semidirect
19. C4×#11758200C4semidirect
20. C4×#11758199C4semidirect
21. C4×#11758199C4semidirect
280. #1806D61semidirect
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
#214544872
#214544852
#214467092
#214464702
#214464652
#214459902
#214458402
#214457022
#214456882
C61×#18062
#2280361