Subgroups — #27136100

Order 12352.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13095400	C₂	1	2	yes	maximal
2	C₈×Dic₁₉₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#13095400	C₄	1	4	yes	—
4	C₂×#13095393	C₄	1	1	yes	characteristic
5	C₄×Dic₁₉₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₉₃	C₄	1	1	yes	characteristic
7	#13095400	—	2	4	no	—
8	C₂×Dic₁₉₃	C₂×C₄	1	2	yes	—
9	#13095393	C₈	1	2	yes	complemented
10	C₂×C₄×C₁₉₃	C₂×C₄	1	1	yes	characteristic
11	C₈×C₁₉₃	C₈	1	2	yes	complemented
12	C₂²×C₁₉₃	C₄²	1	1	yes	characteristic
13	C₄×C₁₉₃	C₂×C₈	1	1	yes	characteristic
14	C₄×C₁₉₃	C₂×C₈	1	1	yes	characteristic
15	Dic₁₉₃	M₁₆	1	4	yes	—
16	C₂×C₁₉₃	C₄×C₈	1	1	yes	characteristic
17	C₂×C₁₉₃	#97	1	2	yes	—
18	C₁₉₃	#322	1	1	yes	characteristic, complemented, Sylow
19	#322	—	193	1	no	maximal, Sylow
20	C₄×C₈	—	193	2	no	—
21	C₄×C₈	—	193	1	no	—
22	C₂×C₈	—	193	4	no	—
23	C₂×C₈	—	193	1	no	—
24	C₂×C₈	#11715871	1	1	yes	characteristic
25	C₄²	—	193	1	no	—
26	C₂×C₄	—	193	2	no	—
27	C₂×C₄	C₂×#11715871	1	1	yes	characteristic
28	C₈	—	386	4	no	—
29	C₈	—	193	2	no	—
30	C₈	#13095400	1	2	yes	complemented
31	C₂²	C₄×#11715871	1	1	yes	characteristic
32	C₄	—	193	4	no	—
33	C₄	C₂×#13095400	1	1	yes	characteristic
34	C₄	#15690563	1	1	yes	characteristic
35	C₂	C₄×#13095400	1	1	yes	characteristic
36	C₂	#20259953	1	2	yes	—

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.