Subgroups — C₂²⋊#11764047 #17984144

Order 4384.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11764047	C₂	1	2	yes	maximal, complemented
2	C₂²×Dic₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#11764047	—	2	2	no	—
4	C₂×Dic₁₃₇	—	2	2	no	—
5	C₂×Dic₁₃₇	C₄	1	1	yes	characteristic
6	C₂×Dic₁₃₇	C₂²	1	1	yes	characteristic
7	C₂³×C₁₃₇	C₄	1	1	yes	characteristic
8	C₂²×C₁₃₇	—	2	1	no	—
9	C₂²×C₁₃₇	—	2	1	no	—
10	C₂²×C₁₃₇	C₈	1	2	yes	complemented
11	C₂²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
12	Dic₁₃₇	—	2	1	no	—
13	Dic₁₃₇	D₄	1	2	yes	—
14	C₂×C₁₃₇	—	2	2	no	—
15	C₂×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×C₁₃₇	C₂×C₈	1	1	yes	characteristic
17	C₂×C₁₃₇	M₁₆	1	1	yes	characteristic
18	C₁₃₇	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂²⋊C₈	—	137	1	no	maximal, Sylow
20	C₂²×C₄	—	137	1	no	—
21	C₂×C₈	—	137	2	no	—
22	C₂³	#10587739	1	1	yes	characteristic
23	C₂×C₄	—	274	2	no	—
24	C₂×C₄	—	137	1	no	—
25	C₂×C₄	—	137	1	no	—
26	C₈	—	274	2	no	—
27	C₂²	—	2	1	no	—
28	C₂²	—	2	1	no	—
29	C₂²	#11764047	1	2	yes	complemented
30	C₂²	C₂×#10587739	1	1	yes	characteristic
31	C₄	—	274	1	no	—
32	C₄	—	137	2	no	—
33	C₂	—	2	2	no	—
34	C₂	C₂²⋊#10587739	1	1	yes	characteristic
35	C₂	C₂×#11764047	1	1	yes	characteristic
36	C₂	#14555519	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.