Subgroups — C₂×C₄×#13095523 #27158888

Order 12416.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13095523	C₂	1	2	yes	maximal
2	C₄×#13095523	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×#11715897	C₂	1	1	yes	maximal, characteristic
4	C₂×#13095523	C₄	1	8	yes	direct product factor
5	C₂×#13095523	C₂²	1	4	yes	—
6	C₂²×#11715897	C₄	1	1	yes	characteristic
7	C₂²×#11715897	C₂²	1	1	yes	characteristic
8	C₄×#11715897	C₄	1	2	yes	—
9	C₄×#11715897	C₂²	1	2	yes	—
10	C₂×C₄×Dic₉₇	C₄	1	1	yes	characteristic
11	#13095523	C₂×C₄	1	8	yes	direct product factor
12	C₂×#11715897	C₈	1	4	yes	—
13	C₂×#11715897	C₂×C₄	1	1	yes	characteristic
14	C₂×#11715897	C₂×C₄	1	4	yes	—
15	C₂×#11715897	C₂×C₄	1	2	yes	—
16	C₂×#11715897	C₂³	1	1	yes	characteristic
17	C₂²×Dic₉₇	C₈	1	1	yes	characteristic
18	C₂²×Dic₉₇	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₉₇	C₈	1	2	yes	—
20	C₄×Dic₉₇	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₉₇	C₈	1	1	yes	characteristic
22	C₂³×C₉₇	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₉₇	C₁₆	1	4	yes	complemented
24	C₂×C₄×C₉₇	C₂×C₈	1	2	yes	—
25	C₂×Dic₉₇	C₁₆	1	4	yes	complemented
26	C₂×Dic₉₇	C₄²	1	2	yes	—
27	C₂×Dic₉₇	C₂×C₈	1	1	yes	characteristic
28	C₂×Dic₉₇	C₂×C₈	1	2	yes	—
29	C₂×Dic₉₇	C₂×C₈	1	2	yes	—
30	C₂×Dic₉₇	C₂²×C₄	1	1	yes	characteristic
31	#11715897	C₄²	1	2	yes	—
32	#11715897	C₂×C₈	1	4	yes	—
33	#11715897	C₂²×C₄	1	2	yes	—
34	C₂²×C₉₇	C₄×C₈	1	2	yes	—
35	C₂²×C₉₇	C₂×C₁₆	1	2	yes	—
36	C₂²×C₉₇	C₂×C₁₆	1	2	yes	—
37	C₂²×C₉₇	C₂²×C₈	1	1	yes	characteristic
38	C₄×C₉₇	C₂×C₁₆	1	4	yes	complemented
39	Dic₉₇	C₄×C₈	1	2	yes	—
40	Dic₉₇	C₂×C₁₆	1	4	yes	complemented
41	Dic₉₇	C₂×C₄²	1	1	yes	characteristic
42	Dic₉₇	C₂²×C₈	1	1	yes	characteristic
43	C₂×C₉₇	C₄×C₁₆	1	4	yes	complemented
44	C₂×C₉₇	C₂×C₄×C₈	1	1	yes	characteristic
45	C₂×C₉₇	C₂²×C₁₆	1	1	yes	characteristic
46	C₂×C₉₇	C₂²×C₁₆	1	1	yes	characteristic
47	C₂×C₄×C₁₆	—	97	1	no	maximal, Sylow
48	C₉₇	C₂×C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₁₆	—	97	2	no	—
50	C₂×C₄×C₈	—	97	1	no	—
51	C₄×C₁₆	—	97	4	no	—
52	C₂²×C₈	—	97	1	no	—
53	C₂²×C₈	—	97	1	no	—
54	C₂×C₄²	—	97	1	no	—
55	C₂×C₁₆	—	97	4	no	—
56	C₂×C₁₆	—	97	8	no	—
57	C₄×C₈	—	97	2	no	—
58	C₄×C₈	—	97	2	no	—
59	C₂²×C₄	—	97	1	no	—
60	C₂²×C₄	—	97	1	no	—
61	C₂²×C₄	#11715906	1	1	yes	characteristic
62	C₂×C₈	—	97	4	no	—
63	C₂×C₈	—	97	1	no	—
64	C₂×C₈	—	97	2	no	—
65	C₂×C₈	—	97	4	no	—
66	C₂×C₈	—	97	1	no	—
67	C₄²	—	97	2	no	—
68	C₄²	—	97	2	no	—
69	C₁₆	—	97	8	no	—
70	C₂³	C₂×#11715906	1	1	yes	characteristic
71	C₂×C₄	—	97	2	no	—
72	C₂×C₄	—	97	2	no	—
73	C₂×C₄	—	97	4	no	—
74	C₂×C₄	—	97	1	no	—
75	C₂×C₄	—	97	1	no	—
76	C₂×C₄	—	97	2	no	—
77	C₂×C₄	#13095523	1	4	yes	direct product factor
78	C₂×C₄	C₂×#11715906	1	2	yes	—
79	C₈	—	97	2	no	—
80	C₈	—	97	2	no	—
81	C₈	—	97	4	no	—
82	C₂²	C₄×#11715906	1	2	yes	—
83	C₂²	C₂×#13095523	1	2	yes	—
84	C₂²	#15690905	1	2	yes	—
85	C₂²	C₂²×#11715906	1	1	yes	characteristic
86	C₄	—	97	1	no	—
87	C₄	—	97	1	no	—
88	C₄	—	97	2	no	—
89	C₄	—	97	4	no	—
90	C₄	C₂×#13095523	1	4	yes	direct product factor
91	C₂	C₄×#13095523	1	4	yes	direct product factor
92	C₂	C₂×C₄×#11715906	1	1	yes	characteristic
93	C₂	C₂²×#13095523	1	1	yes	characteristic
94	C₂	C₂×#15690905	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	#11715906
commutator, hypocenter	C₉₇	C₂×C₄×C₁₆
Frattini	C₂²	C₂²×#11715906
Fitting	C₂²×C₄×C₉₇	C₈
socle, prime radical	C₂³×C₉₇	C₂×C₈
cosocle	C₂×#11715897	C₂³
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₄×#13095523	C₂	direct (N × H)
4. C₂×#13095523	C₄	direct (N × H)
11. #13095523	C₂×C₄	direct (N × H)
23. C₂×C₄×C₉₇	C₁₆	semidirect
25. C₂×Dic₉₇	C₁₆	semidirect
38. C₄×C₉₇	C₂×C₁₆	semidirect
40. Dic₉₇	C₂×C₁₆	semidirect
43. C₂×C₉₇	C₄×C₁₆	semidirect
48. C₉₇	C₂×C₄×C₁₆	semidirect
77. C₂×C₄	#13095523	direct (N × H)
90. C₄	C₂×#13095523	direct (N × H)
91. C₂	C₄×#13095523	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#13095523	2
C₄×#13095523	2
C₂×C₄×#11715897	2
C₂×C₄×C₁₆	97

Subgroups — C2×C4×#13095523 #27158888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#13095523 #27158888