Subgroups — #27136348

Order 12352.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#13095402	C₂	1	2	yes	maximal
2	C₈×#11715871	C₂	1	1	yes	maximal, characteristic
3	C₂×#13095402	—	2	2	no	—
4	#15690563	C₄	1	1	yes	characteristic
5	C₄×#11715871	C₂²	1	1	yes	characteristic
6	C₈×D₁₉₃	C₄	1	1	yes	characteristic
7	#13095402	—	4	2	no	—
8	C₂×#11715871	D₄	1	1	yes	characteristic
9	C₂×#11715871	Q₈	1	1	yes	characteristic
10	#13095400	—	2	1	no	—
11	C₄×D₁₉₃	C₂×C₄	1	1	yes	characteristic
12	#13095393	C₈	1	1	yes	characteristic, complemented
13	C₈×C₁₉₃	C₈	1	1	yes	characteristic, complemented
14	C₂×D₁₉₃	C₄⋊C₄	1	1	yes	characteristic
15	#11715871	—	2	1	no	—
16	#11715871	SD₁₆	1	2	yes	—
17	C₄×C₁₉₃	C₂×C₈	1	1	yes	characteristic
18	Dic₁₉₃	M₁₆	1	1	yes	characteristic
19	C₂×C₁₉₃	C₄⋊C₈	1	1	yes	characteristic
20	D₁₉₃	#106	1	1	yes	characteristic
21	D₁₉₃	#108	1	1	yes	characteristic
22	C₁₉₃	#334	1	1	yes	characteristic, complemented, Sylow
23	#334	—	193	1	no	maximal, Sylow
24	C₄⋊C₈	—	193	2	no	—
25	C₄×C₈	—	193	1	no	—
26	C₂×C₈	—	386	2	no	—
27	C₂×C₈	—	193	1	no	—
28	C₂×C₈	—	193	1	no	—
29	C₄²	—	193	1	no	—
30	C₂×C₄	—	193	1	no	—
31	C₂×C₄	—	193	1	no	—
32	C₂×C₄	—	193	1	no	—
33	C₈	—	772	2	no	—
34	C₈	—	386	1	no	—
35	C₈	—	193	1	no	—
36	C₈	#13095402	1	1	yes	characteristic, complemented
37	C₂²	—	193	1	no	—
38	C₄	—	386	1	no	—
39	C₄	—	193	2	no	—
40	C₄	—	193	1	no	—
41	C₄	C₂×#13095402	1	1	yes	characteristic
42	C₂	—	193	1	no	—
43	C₂	—	193	1	no	—
44	C₂	C₄⋊#13095402	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.