Subgroups — #38762390

Order 25408.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27163003	C₂	1	6	yes	maximal
2	C₂×C₄²×C₃₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₃₉₇	C₂²	1	4	yes	—
4	C₂²×C₄×C₃₉₇	C₂²	1	3	yes	—
5	C₄²×C₃₉₇	C₄	1	4	yes	complemented
6	C₂×Dic₃₉₇	—	2	12	no	—
7	C₂³×C₃₉₇	C₂³	1	1	yes	characteristic
8	C₂×C₄×C₃₉₇	—	2	6	no	—
9	C₂×C₄×C₃₉₇	C₂×C₄	1	6	yes	—
10	C₂²×C₃₉₇	C₂²×C₄	1	1	yes	characteristic
11	C₂²×C₃₉₇	#41	1	6	yes	—
12	C₄×C₃₉₇	—	2	6	no	—
13	Dic₃₉₇	—	4	4	no	—
14	C₂×C₃₉₇	#117	1	3	yes	—
15	C₂×C₃₉₇	#126	1	4	yes	—
16	C₃₉₇	#383	1	1	yes	characteristic, complemented, Sylow
17	#383	—	397	1	no	maximal, Sylow
18	C₂×C₄²	D₃₉₇	1	1	yes	characteristic
19	#95	—	397	6	no	—
20	C₂²×C₄	—	397	4	no	—
21	C₂²×C₄	C₂×D₃₉₇	1	3	yes	—
22	C₄²	Dic₃₉₇	1	4	yes	complemented
23	C₂³	C₂²×D₃₉₇	1	1	yes	characteristic
24	C₂×C₄	—	2	6	no	—
25	C₂×C₄	—	794	12	no	—
26	C₂×C₄	C₂×Dic₃₉₇	1	6	yes	—
27	C₂²	C₂²×Dic₃₉₇	1	1	yes	characteristic
28	C₂²	#20263731	1	6	yes	—
29	C₄	—	2	6	no	—
30	C₄	—	1588	4	no	—
31	C₂	#27163055	1	3	yes	—
32	C₂	#27163090	1	4	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.