Subgroups — #27164398

Order 12736.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₇₉₆	C₂	1	4	yes	maximal
2	#20263955	C₂	1	2	yes	maximal
3	C₄×C₈×C₁₉₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₉₈	C₂²	1	4	yes	—
5	Dic₇₉₆	—	2	8	no	—
6	C₄⋊Dic₁₉₉	—	2	4	no	—
7	C₂×C₈×C₁₉₉	C₂²	1	2	yes	—
8	C₄²×C₁₉₉	C₂²	1	1	yes	characteristic
9	Dic₃₉₈	—	2	8	no	—
10	C₂×Dic₁₉₉	—	2	4	no	—
11	C₂×C₄×C₁₉₉	D₄	1	2	yes	—
12	C₂×C₄×C₁₉₉	C₂³	1	1	yes	characteristic
13	C₈×C₁₉₉	D₄	1	4	yes	—
14	C₂²×C₁₉₉	C₂×D₄	1	1	yes	characteristic
15	C₄×C₁₉₉	Q₁₆	1	4	yes	complemented
16	C₄×C₁₉₉	C₂×D₄	1	2	yes	—
17	Dic₁₉₉	—	4	4	no	—
18	C₂×C₁₉₉	#127	1	1	yes	characteristic
19	C₂×C₁₉₉	C₂×Q₁₆	1	2	yes	—
20	C₁₉₉	#494	1	1	yes	characteristic, complemented, Sylow
21	#494	—	199	1	no	maximal, Sylow
22	C₂×Q₁₆	—	199	4	no	—
23	C₄⋊Q₈	—	199	2	no	—
24	C₄×C₈	D₁₉₉	1	1	yes	characteristic
25	C₂×Q₈	—	199	4	no	—
26	Q₁₆	—	398	8	no	—
27	C₂×C₈	C₂×D₁₉₉	1	2	yes	—
28	C₄⋊C₄	—	398	4	no	—
29	C₄²	C₂×D₁₉₉	1	1	yes	characteristic
30	Q₈	—	398	8	no	—
31	C₂×C₄	—	398	4	no	—
32	C₂×C₄	D₇₉₆	1	2	yes	—
33	C₂×C₄	C₂²×D₁₉₉	1	1	yes	characteristic
34	C₈	D₇₉₆	1	4	yes	—
35	C₂²	C₂×D₇₉₆	1	1	yes	characteristic
36	C₄	—	796	4	no	—
37	C₄	Dic₇₉₆	1	4	yes	complemented
38	C₄	C₂×D₇₉₆	1	2	yes	—
39	C₂	#20263952	1	1	yes	characteristic
40	C₂	C₂×Dic₇₉₆	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.