Subgroups — C₁₇×C₄⋊#95 #14524441

Order 2176.

656 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₄×C₁₇	C₂	1	2	yes	maximal
2	C₂²×C₄²×C₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₇×#95	C₂	1	4	yes	maximal
4	C₂³×C₄×C₁₇	C₂²	1	4	yes	—
5	C₂³×C₄×C₁₇	C₂²	1	2	yes	—
6	C₂³×C₄×C₁₇	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₇	—	2	4	no	—
8	C₂×C₄⋊C₄×C₁₇	—	2	4	no	—
9	C₂×C₄⋊C₄×C₁₇	C₄	1	8	yes	complemented
10	C₂×C₄²×C₁₇	—	2	4	no	—
11	C₂×C₄²×C₁₇	C₄	1	4	yes	complemented
12	C₁₇×#95	—	2	8	no	—
13	C₂⁴×C₁₇	C₂³	1	1	yes	characteristic
14	C₂²×C₄×C₁₇	—	2	4	no	—
15	C₂²×C₄×C₁₇	—	2	4	no	—
16	C₂²×C₄×C₁₇	—	2	8	no	—
17	C₂²×C₄×C₁₇	—	2	4	no	—
18	C₂²×C₄×C₁₇	—	2	4	no	—
19	C₂²×C₄×C₁₇	—	2	8	no	—
20	C₂²×C₄×C₁₇	C₂×C₄	1	8	yes	—
21	C₂²×C₄×C₁₇	C₂×C₄	1	4	yes	—
22	C₂²×C₄×C₁₇	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₁₇	C₂×C₄	1	4	yes	—
24	C₂²×C₄×C₁₇	D₄	1	4	yes	—
25	C₂²×C₄×C₁₇	D₄	1	4	yes	—
26	C₂²×C₄×C₁₇	D₄	1	2	yes	—
27	C₂²×C₄×C₁₇	Q₈	1	4	yes	—
28	C₂²×C₄×C₁₇	Q₈	1	2	yes	—
29	C₄⋊C₄×C₁₇	—	2	16	no	—
30	C₄²×C₁₇	—	2	8	no	—
31	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
32	C₂³×C₁₇	C₂²×C₄	1	2	yes	—
33	C₂³×C₁₇	C₂×D₄	1	2	yes	—
34	C₂³×C₁₇	C₂×D₄	1	1	yes	characteristic
35	C₂³×C₁₇	C₂×D₄	1	2	yes	—
36	C₂³×C₁₇	C₂×Q₈	1	1	yes	characteristic
37	C₂³×C₁₇	C₂×Q₈	1	2	yes	—
38	C₂³×C₁₇	#41	1	4	yes	—
39	C₂×C₄×C₁₇	—	2	4	no	—
40	C₂×C₄×C₁₇	—	2	4	no	—
41	C₂×C₄×C₁₇	—	2	8	no	—
42	C₂×C₄×C₁₇	—	2	8	no	—
43	C₂×C₄×C₁₇	—	2	8	no	—
44	C₂×C₄×C₁₇	—	2	16	no	—
45	C₂×C₄×C₁₇	—	4	8	no	—
46	C₂×C₄×C₁₇	—	4	4	no	—
47	C₂×C₄×C₁₇	—	4	4	no	—
48	C₂×C₄×C₁₇	C₄²	1	4	yes	—
49	C₂×C₄×C₁₇	C₂²⋊C₄	1	4	yes	—
50	C₂×C₄×C₁₇	C₂²⋊C₄	1	8	yes	—
51	C₂×C₄×C₁₇	C₄⋊C₄	1	4	yes	—
52	C₂×C₄×C₁₇	C₄⋊C₄	1	8	yes	—
53	C₂×C₄×C₁₇	C₄⋊C₄	1	8	yes	complemented
54	C₄⋊#95	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
56	C₂²×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₁₇	C₂×C₂²⋊C₄	1	2	yes	—
58	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂²×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
60	C₂²×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
61	C₂²×C₁₇	#117	1	2	yes	—
62	C₂²×C₁₇	C₄×D₄	1	4	yes	—
63	C₂²×C₁₇	C₄×Q₈	1	4	yes	—
64	C₂²×C₁₇	#121	1	4	yes	—
65	C₂²×C₁₇	C₂²⋊Q₈	1	4	yes	—
66	C₂²×C₁₇	#124	1	2	yes	—
67	C₂²×C₁₇	#125	1	2	yes	—
68	C₂²×C₁₇	#127	1	1	yes	characteristic
69	C₂²×C₁₇	C₄⋊Q₈	1	2	yes	—
70	C₂²×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
71	C₄×C₁₇	—	2	8	no	—
72	C₄×C₁₇	—	4	8	no	—
73	C₄×C₁₇	#95	1	8	yes	complemented
74	C₂²×C₄⋊C₄	C₂×C₁₇	1	2	yes	—
75	C₂²×C₄²	C₂×C₁₇	1	1	yes	characteristic
76	C₂×#95	C₂×C₁₇	1	4	yes	—
77	C₂×C₁₇	C₂×#95	1	1	yes	characteristic
78	C₂×C₁₇	C₄×C₄⋊C₄	1	2	yes	—
79	C₂×C₁₇	#380	1	2	yes	—
80	C₂×C₁₇	#382	1	1	yes	characteristic
81	C₂×C₁₇	#384	1	1	yes	characteristic
82	C₂×C₁₇	#389	1	4	yes	—
83	C₂×C₁₇	#390	1	2	yes	—
84	C₂×C₁₇	#391	1	2	yes	—
85	C₂³×C₄	C₂²×C₁₇	1	4	yes	—
86	C₂³×C₄	C₂²×C₁₇	1	2	yes	—
87	C₂³×C₄	C₂²×C₁₇	1	1	yes	characteristic
88	C₂×C₄⋊C₄	—	2	4	no	—
89	C₂×C₄⋊C₄	—	2	4	no	—
90	C₂×C₄⋊C₄	C₄×C₁₇	1	8	yes	complemented
91	C₂×C₄²	—	2	4	no	—
92	C₂×C₄²	C₄×C₁₇	1	4	yes	complemented
93	#95	—	2	8	no	—
94	C₁₇	C₄⋊#95	1	1	yes	characteristic, direct product factor, Sylow
95	C₂⁴	C₂³×C₁₇	1	1	yes	characteristic
96	C₂²×C₄	—	2	4	no	—
97	C₂²×C₄	—	2	4	no	—
98	C₂²×C₄	—	2	8	no	—
99	C₂²×C₄	—	2	4	no	—
100	C₂²×C₄	—	2	4	no	—
101	C₂²×C₄	—	2	8	no	—
102	C₂²×C₄	C₂×C₄×C₁₇	1	8	yes	—
103	C₂²×C₄	C₂×C₄×C₁₇	1	4	yes	—
104	C₂²×C₄	C₂×C₄×C₁₇	1	2	yes	—
105	C₂²×C₄	C₂×C₄×C₁₇	1	4	yes	—
106	C₂²×C₄	D₄×C₁₇	1	4	yes	—
107	C₂²×C₄	D₄×C₁₇	1	4	yes	—
108	C₂²×C₄	D₄×C₁₇	1	2	yes	—
109	C₂²×C₄	Q₈×C₁₇	1	4	yes	—
110	C₂²×C₄	Q₈×C₁₇	1	2	yes	—
111	C₄⋊C₄	—	2	16	no	—
112	C₄²	—	2	8	no	—
113	C₂³	C₂²×C₄×C₁₇	1	1	yes	characteristic
114	C₂³	C₂²×C₄×C₁₇	1	2	yes	—
115	C₂³	C₂×D₄×C₁₇	1	2	yes	—
116	C₂³	C₂×D₄×C₁₇	1	1	yes	characteristic
117	C₂³	C₂×D₄×C₁₇	1	2	yes	—
118	C₂³	C₂×Q₈×C₁₇	1	2	yes	—
119	C₂³	C₂×Q₈×C₁₇	1	1	yes	characteristic
120	C₂³	#41×C₁₇	1	4	yes	—
121	C₂×C₄	—	2	8	no	—
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	—	2	4	no	—
124	C₂×C₄	—	2	8	no	—
125	C₂×C₄	—	2	8	no	—
126	C₂×C₄	—	2	16	no	—
127	C₂×C₄	—	4	4	no	—
128	C₂×C₄	—	4	4	no	—
129	C₂×C₄	—	4	8	no	—
130	C₂×C₄	C₄²×C₁₇	1	4	yes	—
131	C₂×C₄	C₂²⋊C₄×C₁₇	1	4	yes	—
132	C₂×C₄	C₂²⋊C₄×C₁₇	1	8	yes	—
133	C₂×C₄	C₄⋊C₄×C₁₇	1	4	yes	—
134	C₂×C₄	C₄⋊C₄×C₁₇	1	8	yes	—
135	C₂×C₄	C₄⋊C₄×C₁₇	1	8	yes	complemented
136	C₂²	C₂×C₄²×C₁₇	1	1	yes	characteristic
137	C₂²	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
138	C₂²	C₂×C₂²⋊C₄×C₁₇	1	2	yes	—
139	C₂²	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
140	C₂²	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
141	C₂²	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
142	C₂²	C₁₇×#117	1	2	yes	—
143	C₂²	C₄×D₄×C₁₇	1	4	yes	—
144	C₂²	C₄×Q₈×C₁₇	1	4	yes	—
145	C₂²	C₁₇×#121	1	4	yes	—
146	C₂²	C₁₇×C₂²⋊Q₈	1	4	yes	—
147	C₂²	C₁₇×#124	1	2	yes	—
148	C₂²	C₁₇×#125	1	2	yes	—
149	C₂²	C₁₇×#127	1	1	yes	characteristic
150	C₂²	C₁₇×C₄⋊Q₈	1	2	yes	—
151	C₂²	C₁₇×C₄⋊Q₈	1	1	yes	characteristic
152	C₄	—	2	8	no	—
153	C₄	—	4	8	no	—
154	C₄	C₁₇×#95	1	8	yes	complemented
155	C₂	C₂×C₁₇×#95	1	1	yes	characteristic
156	C₂	C₄×C₄⋊C₄×C₁₇	1	2	yes	—
157	C₂	C₁₇×#380	1	2	yes	—
158	C₂	C₁₇×#382	1	1	yes	characteristic
159	C₂	C₁₇×#384	1	1	yes	characteristic
160	C₂	C₁₇×#389	1	4	yes	—
161	C₂	C₁₇×#390	1	2	yes	—
162	C₂	C₁₇×#391	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₇	C₂³
commutator	C₂²	C₂×C₄²×C₁₇
Frattini, cosocle	C₂⁴	C₂³×C₁₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₂×C₄⋊C₄×C₁₇	C₄	semidirect
11. C₂×C₄²×C₁₇	C₄	semidirect
53. C₂×C₄×C₁₇	C₄⋊C₄	semidirect
54. C₄⋊#95	C₁₇	direct (N × H)
73. C₄×C₁₇	#95	semidirect
90. C₂×C₄⋊C₄	C₄×C₁₇	semidirect
92. C₂×C₄²	C₄×C₁₇	semidirect
94. C₁₇	C₄⋊#95	direct (N × H)
135. C₂×C₄	C₄⋊C₄×C₁₇	semidirect
154. C₄	C₁₇×#95	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊C₄×C₁₇	2
C₂²×C₄²×C₁₇	2
C₂×C₁₇×#95	2
C₄⋊#95	17

Subgroups — C17×C4⋊#95 #14524441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₄⋊#95 #14524441