Subgroups — #27136183

Order 12352.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20259969	C₂	1	1	yes	maximal, characteristic
2	#20259967	C₂	1	1	yes	maximal, characteristic
3	#20259838	C₂	1	1	yes	maximal, characteristic
4	#15690565	—	2	1	no	—
5	C₄⋊#11715871	—	2	1	no	—
6	C₈×D₁₉₃	C₂²	1	1	yes	characteristic
7	#15690530	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₁₉₃	C₄	1	1	yes	characteristic, complemented
9	C₂×#11715871	—	4	1	no	—
10	#13095400	—	4	1	no	—
11	C₄×D₁₉₃	D₄	1	1	yes	characteristic
12	#13095393	Q₈	1	1	yes	characteristic
13	C₈×C₁₉₃	C₂×C₄	1	1	yes	characteristic
14	C₂×D₁₉₃	SD₁₆	1	1	yes	characteristic
15	#11715871	—	8	1	no	—
16	C₄×C₁₉₃	C₄⋊C₄	1	1	yes	characteristic
17	Dic₁₉₃	SD₁₆	1	1	yes	characteristic
18	C₂×C₁₉₃	#106	1	1	yes	characteristic
19	D₁₉₃	—	2	1	no	—
20	C₁₉₃	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	193	1	no	maximal, Sylow
22	M₃₂	—	193	1	no	—
23	#108	—	193	1	no	—
24	#106	—	193	1	no	—
25	M₁₆	—	386	1	no	—
26	C₂×C₈	—	193	1	no	—
27	C₄⋊C₄	—	386	1	no	—
28	C₁₆	—	193	1	no	—
29	C₁₆	#11715871	1	1	yes	characteristic, complemented
30	C₂×C₄	—	772	1	no	—
31	C₂×C₄	—	193	1	no	—
32	C₈	—	772	1	no	—
33	C₈	—	193	1	no	—
34	C₈	C₂×#11715871	1	1	yes	characteristic
35	C₂²	—	193	1	no	—
36	C₄	—	1544	1	no	—
37	C₄	—	193	1	no	—
38	C₄	C₄⋊#11715871	1	1	yes	characteristic
39	C₂	—	386	1	no	—
40	C₂	#20259967	1	1	yes	characteristic

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

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