Subgroups — C₇²×#108 #13096169

Order 1568.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₇²×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₇²	C₂²	1	1	yes	characteristic
4	C₇²×C₈	—	2	2	no	—
5	C₇²×C₈	C₄	1	2	yes	—
6	C₇×#108	C₇	1	8	yes	maximal, direct product factor
7	C₂²×C₇²	Q₈	1	1	yes	characteristic
8	C₄×C₇²	C₂×C₄	1	1	yes	characteristic
9	C₄×C₇²	D₄	1	1	yes	characteristic
10	C₇×M₁₆	C₂×C₇	1	16	yes	—
11	C₂×C₇×C₈	C₂×C₇	1	8	yes	—
12	C₂×C₇²	—	2	1	no	—
13	C₂×C₇²	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₄×C₇	C₂²×C₇	1	8	yes	—
15	C₇×C₈	—	2	16	no	—
16	C₇×C₈	C₄×C₇	1	16	yes	—
17	C₇²	#108	1	1	yes	characteristic, direct product factor, Sylow
18	#108	C₇²	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²×C₇	C₇×Q₈	1	8	yes	—
20	C₄×C₇	C₂×C₄×C₇	1	8	yes	—
21	C₄×C₇	C₇×D₄	1	8	yes	—
22	M₁₆	C₂×C₇²	1	2	yes	—
23	C₂×C₈	C₂×C₇²	1	1	yes	characteristic
24	C₂×C₇	—	2	8	no	—
25	C₂×C₇	C₇×C₄⋊C₄	1	8	yes	—
26	C₂×C₄	C₂²×C₇²	1	1	yes	characteristic
27	C₈	—	2	2	no	—
28	C₈	C₄×C₇²	1	2	yes	—
29	C₇	C₇×#108	1	8	yes	direct product factor
30	C₂²	C₇²×Q₈	1	1	yes	characteristic
31	C₄	C₂×C₄×C₇²	1	1	yes	characteristic
32	C₄	C₇²×D₄	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₇²×C₄⋊C₄	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.