Subgroups — D₉₇⋊#108 #20261748

Order 6208.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₇⋊M₁₆	C₂	1	2	yes	maximal
2	#15690881	C₂	1	2	yes	maximal, complemented
3	#15690880	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₉₇	C₂	1	1	yes	maximal, characteristic
5	#13095521	C₂²	1	4	yes	—
6	#13095520	—	2	2	no	—
7	#13095519	—	2	2	no	—
8	C₂×C₄×D₉₇	C₂²	1	1	yes	characteristic
9	C₂×#11715895	C₄	1	1	yes	characteristic
10	C₈×D₉₇	C₄	1	1	yes	characteristic
11	C₈×D₉₇	C₄	1	1	yes	characteristic
12	C₈×D₉₇	C₂²	1	1	yes	characteristic
13	C₈×D₉₇	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₉₇	C₄	1	1	yes	characteristic
15	C₂²×D₉₇	Q₈	1	1	yes	characteristic
16	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₉₇	D₄	1	1	yes	characteristic
18	C₄×D₉₇	C₂×C₄	1	1	yes	characteristic
19	C₄×D₉₇	D₄	1	1	yes	characteristic
20	C₄×D₉₇	Q₈	1	1	yes	characteristic
21	C₄×D₉₇	C₂³	1	1	yes	characteristic
22	#11715897	—	2	4	no	—
23	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
24	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
25	#11715895	C₂×C₄	1	1	yes	characteristic
26	#11715895	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₉₇	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₉₇	—	2	2	no	—
29	C₂×D₉₇	C₄⋊C₄	1	1	yes	characteristic
30	C₂×D₉₇	C₂×Q₈	1	1	yes	characteristic
31	C₄×C₉₇	C₄⋊C₄	1	1	yes	characteristic
32	C₄×C₉₇	C₂²×C₄	1	1	yes	characteristic
33	Dic₉₇	C₄⋊C₄	1	1	yes	characteristic
34	Dic₉₇	C₂×D₄	1	1	yes	characteristic
35	C₂×C₉₇	—	2	1	no	—
36	C₂×C₉₇	C₂×C₄⋊C₄	1	1	yes	characteristic
37	D₉₇	—	2	1	no	—
38	D₉₇	#108	1	2	yes	complemented
39	C₉₇	C₂×#108	1	1	yes	characteristic, complemented, Sylow
40	C₂×#108	—	97	1	no	maximal, Sylow
41	C₂×M₁₆	—	97	2	no	—
42	C₂²×C₈	—	97	1	no	—
43	#108	—	97	2	no	—
44	#108	—	97	2	no	—
45	C₂²×C₄	—	97	1	no	—
46	M₁₆	—	97	4	no	—
47	M₁₆	—	194	2	no	—
48	C₂×C₈	—	97	1	no	—
49	C₂×C₈	—	97	1	no	—
50	C₂×C₈	—	97	1	no	—
51	C₂×C₈	—	97	1	no	—
52	C₂×C₈	—	97	1	no	—
53	C₂×C₈	—	194	2	no	—
54	C₂×C₈	#87604	1	1	yes	characteristic
55	C₂³	—	97	1	no	—
56	C₂×C₄	—	97	1	no	—
57	C₂×C₄	—	97	1	no	—
58	C₂×C₄	—	97	1	no	—
59	C₂×C₄	—	97	1	no	—
60	C₂×C₄	—	97	1	no	—
61	C₂×C₄	C₂×#87604	1	1	yes	characteristic
62	C₈	—	97	1	no	—
63	C₈	—	97	1	no	—
64	C₈	—	194	4	no	—
65	C₈	C₂×#87604	1	1	yes	characteristic
66	C₈	C₂×#87604	1	1	yes	characteristic
67	C₂²	—	97	1	no	—
68	C₂²	—	97	1	no	—
69	C₂²	—	194	2	no	—
70	C₂²	C₄⋊#87604	1	1	yes	characteristic
71	C₄	—	97	1	no	—
72	C₄	—	97	1	no	—
73	C₄	C₄⋊#87604	1	1	yes	characteristic
74	C₄	C₂²×#87604	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	97	2	no	—
77	C₂	—	194	1	no	—
78	C₂	C₂×C₄⋊#87604	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#87604
commutator	C₄×C₉₇	C₂²×C₄
Frattini	C₄	C₂²×#87604
Fitting	C₂×C₈×C₉₇	C₄
socle	C₂×C₉₇	C₂×C₄⋊C₄
hypercenter	C₂×C₈	#87604
hypocenter	C₉₇	C₂×#108
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #15690881	C₂	semidirect
3. #15690880	C₂	semidirect
38. D₉₇	#108	semidirect
39. C₉₇	C₂×#108	semidirect

Subgroups — D97⋊#108 #20261748

Conjugacy classes of subgroups

Complements

Subgroups — D₉₇⋊#108 #20261748