Group #35324593 — subgroups

Subgroups — C₂²⋊C₃₂×D₈₃ #35324593

Order 21248.

342 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×D₈₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₂×D₈₃	C₂	1	2	yes	maximal, complemented
3	C₂²⋊(C₈₃⋊C₃₂)	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₈₃)⋊C₃₂	C₂	1	2	yes	maximal, complemented
5	C₈₃×C₂²⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₈₃	C₄	1	1	yes	characteristic
7	C₂²×C₈₃⋊C₁₆	C₄	1	1	yes	characteristic
8	C₂×C₁₆×D₈₃	—	2	4	no	—
9	C₂×C₁₆×D₈₃	C₄	1	1	yes	characteristic
10	C₂×C₁₆×D₈₃	C₄	1	1	yes	characteristic
11	C₂×C₁₆×D₈₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×D₈₃	C₂²	1	1	yes	characteristic
13	C₂×C₈₃⋊C₃₂	C₂²	1	2	yes	complemented
14	C₃₂×D₈₃	—	2	4	no	—
15	C₂²×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
16	C₂×C₃₂×C₈₃	C₂²	1	2	yes	complemented
17	C₂²×C₄×D₈₃	C₈	1	1	yes	characteristic
18	C₂²×C₈₃⋊C₈	C₈	1	1	yes	characteristic
19	C₂×C₈×D₈₃	—	2	2	no	—
20	C₂×C₈×D₈₃	—	2	2	no	—
21	C₂×C₈×D₈₃	C₈	1	1	yes	characteristic
22	C₂×C₈×D₈₃	C₈	1	1	yes	characteristic
23	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈₃⋊C₁₆	—	2	2	no	—
26	C₂×C₈₃⋊C₁₆	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈₃⋊C₁₆	C₂×C₄	1	1	yes	characteristic
28	C₁₆×D₈₃	—	2	2	no	—
29	C₁₆×D₈₃	—	2	2	no	—
30	C₁₆×D₈₃	—	2	2	no	—
31	C₁₆×D₈₃	D₄	1	4	yes	—
32	C₈₃⋊C₃₂	—	2	2	no	—
33	C₂²×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₁₆×C₈₃	—	2	2	no	—
35	C₂×C₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₁₆×C₈₃	C₂³	1	1	yes	characteristic
37	C₃₂×C₈₃	—	2	2	no	—
38	C₂³×D₈₃	C₁₆	1	1	yes	characteristic
39	C₂²×Dic₈₃	C₁₆	1	1	yes	characteristic
40	C₂×C₄×D₈₃	—	2	2	no	—
41	C₂×C₄×D₈₃	—	2	2	no	—
42	C₂×C₄×D₈₃	C₁₆	1	1	yes	characteristic
43	C₂×C₄×D₈₃	C₁₆	1	1	yes	characteristic
44	C₂×C₄×D₈₃	C₂×C₈	1	1	yes	characteristic
45	C₂×C₄×D₈₃	C₂×C₈	1	1	yes	characteristic
46	C₂×C₈₃⋊C₈	—	2	2	no	—
47	C₂×C₈₃⋊C₈	C₂×C₈	1	1	yes	characteristic
48	C₂×C₈₃⋊C₈	C₂×C₈	1	1	yes	characteristic
49	C₈×D₈₃	—	2	2	no	—
50	C₈×D₈₃	—	2	1	no	—
51	C₈×D₈₃	—	2	1	no	—
52	C₈×D₈₃	—	2	2	no	—
53	C₈×D₈₃	C₂²⋊C₄	1	2	yes	—
54	C₈×D₈₃	M₁₆	1	2	yes	—
55	C₈₃⋊C₁₆	—	2	1	no	—
56	C₈₃⋊C₁₆	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₈₃	C₂×C₈	1	1	yes	characteristic
58	C₂×C₈×C₈₃	—	2	1	no	—
59	C₂×C₈×C₈₃	—	2	1	no	—
60	C₂×C₈×C₈₃	C₂×C₈	1	1	yes	characteristic
61	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
62	C₁₆×C₈₃	—	2	1	no	—
63	C₁₆×C₈₃	C₂×D₄	1	2	yes	—
64	C₂³×C₈₃	C₂×C₁₆	1	1	yes	characteristic
65	C₂²×D₈₃	—	2	2	no	—
66	C₂²×D₈₃	—	2	2	no	—
67	C₂²×D₈₃	C₃₂	1	4	yes	complemented
68	C₂²×D₈₃	C₂×C₁₆	1	1	yes	characteristic
69	C₂²×D₈₃	C₂×C₁₆	1	1	yes	characteristic
70	C₂×C₄×C₈₃	—	2	1	no	—
71	C₂×C₄×C₈₃	—	2	1	no	—
72	C₂×C₄×C₈₃	C₂×C₁₆	1	1	yes	characteristic
73	C₂×C₄×C₈₃	C₂²×C₈	1	1	yes	characteristic
74	C₂×Dic₈₃	—	2	2	no	—
75	C₂×Dic₈₃	C₂×C₁₆	1	1	yes	characteristic
76	C₂×Dic₈₃	C₂×C₁₆	1	1	yes	characteristic
77	C₄×D₈₃	—	2	2	no	—
78	C₄×D₈₃	—	2	1	no	—
79	C₄×D₈₃	—	2	1	no	—
80	C₄×D₈₃	—	2	2	no	—
81	C₄×D₈₃	C₂²⋊C₈	1	2	yes	—
82	C₄×D₈₃	M₃₂	1	2	yes	—
83	C₈×C₈₃	—	2	1	no	—
84	C₈×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₈×C₈₃	C₂×M₁₆	1	1	yes	characteristic
86	C₈₃⋊C₈	—	2	1	no	—
87	C₈₃⋊C₈	C₂²⋊C₈	1	2	yes	—
88	C₂²×C₈₃	—	2	1	no	—
89	C₂²×C₈₃	—	2	1	no	—
90	C₂²×C₈₃	C₂×C₃₂	1	2	yes	complemented
91	C₂²×C₈₃	C₂²×C₁₆	1	1	yes	characteristic
92	C₂×D₈₃	—	2	1	no	—
93	C₂×D₈₃	—	2	1	no	—
94	C₂×D₈₃	—	2	8	no	—
95	C₂×D₈₃	C₂²⋊C₁₆	1	2	yes	—
96	C₂×D₈₃	C₂×C₃₂	1	2	yes	—
97	C₂×D₈₃	C₂×C₃₂	1	2	yes	complemented
98	C₂×D₈₃	M₆₄	1	2	yes	—
99	C₄×C₈₃	—	2	1	no	—
100	C₄×C₈₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
101	C₄×C₈₃	C₂×M₃₂	1	1	yes	characteristic
102	Dic₈₃	—	2	1	no	—
103	Dic₈₃	C₂²⋊C₁₆	1	2	yes	—
104	C₂×C₂²⋊C₃₂	—	83	1	no	maximal, Sylow
105	C₂×C₈₃	—	2	2	no	—
106	C₂×C₈₃	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
107	C₂×C₈₃	C₂²×C₃₂	1	1	yes	characteristic
108	C₂×C₈₃	C₂×M₆₄	1	1	yes	characteristic
109	D₈₃	—	2	2	no	—
110	D₈₃	C₂²⋊C₃₂	1	4	yes	direct product factor
111	C₂³×C₁₆	—	83	1	no	—
112	C₂²×C₃₂	—	83	2	no	—
113	C₂²⋊C₃₂	—	83	1	no	—
114	C₂²⋊C₃₂	—	83	2	no	—
115	C₂²⋊C₃₂	D₈₃	1	1	yes	characteristic, direct product factor
116	C₈₃	C₂×C₂²⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
117	C₂³×C₈	—	83	1	no	—
118	C₂²×C₁₆	—	83	1	no	—
119	C₂²×C₁₆	—	83	1	no	—
120	C₂²×C₁₆	—	83	1	no	—
121	C₂²×C₁₆	—	83	1	no	—
122	C₂²×C₁₆	—	83	1	no	—
123	C₂²×C₁₆	—	166	4	no	—
124	C₂²×C₁₆	C₂×D₈₃	1	1	yes	characteristic
125	C₂×C₃₂	—	83	2	no	—
126	C₂×C₃₂	—	166	4	no	—
127	C₂×C₃₂	C₂×D₈₃	1	2	yes	complemented
128	C₂³×C₄	—	83	1	no	—
129	C₂²×C₈	—	83	1	no	—
130	C₂²×C₈	—	83	1	no	—
131	C₂²×C₈	—	83	1	no	—
132	C₂²×C₈	—	83	1	no	—
133	C₂²×C₈	—	83	1	no	—
134	C₂²×C₈	—	166	2	no	—
135	C₂²×C₈	—	166	2	no	—
136	C₂²×C₈	C₄×D₈₃	1	1	yes	characteristic
137	C₂×C₁₆	—	2	2	no	—
138	C₂×C₁₆	—	83	1	no	—
139	C₂×C₁₆	—	83	4	no	—
140	C₂×C₁₆	—	83	1	no	—
141	C₂×C₁₆	—	166	2	no	—
142	C₂×C₁₆	—	166	2	no	—
143	C₂×C₁₆	—	166	2	no	—
144	C₂×C₁₆	—	166	2	no	—
145	C₂×C₁₆	C₄×D₈₃	1	1	yes	characteristic
146	C₂×C₁₆	C₂²×D₈₃	1	1	yes	characteristic
147	C₃₂	—	2	2	no	—
148	C₃₂	—	166	2	no	—
149	C₂⁴	—	83	1	no	—
150	C₂²×C₄	—	83	1	no	—
151	C₂²×C₄	—	83	1	no	—
152	C₂²×C₄	—	83	1	no	—
153	C₂²×C₄	—	83	1	no	—
154	C₂²×C₄	—	83	1	no	—
155	C₂²×C₄	—	166	2	no	—
156	C₂²×C₄	—	166	2	no	—
157	C₂²×C₄	C₈×D₈₃	1	1	yes	characteristic
158	C₂×C₈	—	2	1	no	—
159	C₂×C₈	—	2	1	no	—
160	C₂×C₈	—	83	1	no	—
161	C₂×C₈	—	83	2	no	—
162	C₂×C₈	—	83	2	no	—
163	C₂×C₈	—	83	1	no	—
164	C₂×C₈	—	166	2	no	—
165	C₂×C₈	—	166	2	no	—
166	C₂×C₈	—	166	2	no	—
167	C₂×C₈	—	166	1	no	—
168	C₂×C₈	—	166	1	no	—
169	C₂×C₈	C₈×D₈₃	1	1	yes	characteristic
170	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
171	C₁₆	—	2	1	no	—
172	C₁₆	—	83	2	no	—
173	C₁₆	—	166	1	no	—
174	C₁₆	D₄×D₈₃	1	2	yes	—
175	C₂³	—	83	1	no	—
176	C₂³	—	83	1	no	—
177	C₂³	—	83	4	no	—
178	C₂³	—	166	2	no	—
179	C₂³	—	166	2	no	—
180	C₂³	C₁₆×D₈₃	1	1	yes	characteristic
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	83	1	no	—
184	C₂×C₄	—	83	2	no	—
185	C₂×C₄	—	83	2	no	—
186	C₂×C₄	—	83	1	no	—
187	C₂×C₄	—	166	2	no	—
188	C₂×C₄	—	166	2	no	—
189	C₂×C₄	—	166	2	no	—
190	C₂×C₄	—	166	1	no	—
191	C₂×C₄	—	166	1	no	—
192	C₂×C₄	C₁₆×D₈₃	1	1	yes	characteristic
193	C₂×C₄	C₂×C₈×D₈₃	1	1	yes	characteristic
194	C₈	—	2	1	no	—
195	C₈	—	83	2	no	—
196	C₈	—	166	1	no	—
197	C₈	C₂²⋊C₄×D₈₃	1	1	yes	characteristic
198	C₈	M₁₆×D₈₃	1	1	yes	characteristic
199	C₂²	—	2	1	no	—
200	C₂²	—	2	1	no	—
201	C₂²	—	83	2	no	—
202	C₂²	—	83	2	no	—
203	C₂²	—	83	2	no	—
204	C₂²	—	83	2	no	—
205	C₂²	—	166	8	no	—
206	C₂²	—	166	1	no	—
207	C₂²	—	166	1	no	—
208	C₂²	C₃₂×D₈₃	1	2	yes	complemented
209	C₂²	C₂×C₁₆×D₈₃	1	1	yes	characteristic
210	C₄	—	2	1	no	—
211	C₄	—	83	2	no	—
212	C₄	—	166	1	no	—
213	C₄	C₂²⋊C₈×D₈₃	1	1	yes	characteristic
214	C₄	M₃₂×D₈₃	1	1	yes	characteristic
215	C₂	—	2	2	no	—
216	C₂	—	83	4	no	—
217	C₂	—	166	2	no	—
218	C₂	C₂²⋊C₁₆×D₈₃	1	1	yes	characteristic
219	C₂	C₂×C₃₂×D₈₃	1	1	yes	characteristic
220	C₂	M₆₄×D₈₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₆×D₈₃

C₂

yes

maximal, characteristic

C₂×C₃₂×D₈₃

C₂

yes

maximal, complemented

C₂²⋊(C₈₃⋊C₃₂)

C₂

yes

maximal, characteristic, complemented

(C₂×D₈₃)⋊C₃₂

C₂

yes

maximal, complemented

C₈₃×C₂²⋊C₃₂

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₈₃

C₄

yes

characteristic

C₂²×C₈₃⋊C₁₆

C₄

yes

characteristic

C₂×C₁₆×D₈₃

—

C₂×C₁₆×D₈₃

C₄

yes

characteristic

C₂×C₁₆×D₈₃

C₄

yes

characteristic

C₂×C₁₆×D₈₃

C₂²

yes

characteristic

C₂×C₁₆×D₈₃

C₂²

yes

characteristic

C₂×C₈₃⋊C₃₂

C₂²

yes

complemented

C₃₂×D₈₃

—

C₂²×C₁₆×C₈₃

C₂²

yes

characteristic

C₂×C₃₂×C₈₃

C₂²

yes

complemented

C₂²×C₄×D₈₃

C₈

yes

characteristic

C₂²×C₈₃⋊C₈

C₈

yes

characteristic

C₂×C₈×D₈₃

—

C₂×C₈×D₈₃

—

C₂×C₈×D₈₃

C₈

yes

characteristic

C₂×C₈×D₈₃

C₈

yes

characteristic

C₂×C₈×D₈₃

C₂×C₄

yes

characteristic

C₂×C₈×D₈₃

C₂×C₄

yes

characteristic

C₂×C₈₃⋊C₁₆

—

C₂×C₈₃⋊C₁₆

C₂×C₄

yes

characteristic

C₂×C₈₃⋊C₁₆

C₂×C₄

yes

characteristic

C₁₆×D₈₃

—

C₁₆×D₈₃

—

C₁₆×D₈₃

—

C₁₆×D₈₃

D₄

yes

—

C₈₃⋊C₃₂

—

C₂²×C₈×C₈₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₃

—

C₂×C₁₆×C₈₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₃

C₂³

yes

characteristic

C₃₂×C₈₃

—

C₂³×D₈₃

C₁₆

yes

characteristic

C₂²×Dic₈₃

C₁₆

yes

characteristic

C₂×C₄×D₈₃

—

C₂×C₄×D₈₃

—

C₂×C₄×D₈₃

C₁₆

yes

characteristic

C₂×C₄×D₈₃

C₁₆

yes

characteristic

C₂×C₄×D₈₃

C₂×C₈

yes

characteristic

C₂×C₄×D₈₃

C₂×C₈

yes

characteristic

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

C₂×C₈

yes

characteristic

C₂×C₈₃⋊C₈

C₂×C₈

yes

characteristic

C₈×D₈₃

—

C₈×D₈₃

—

C₈×D₈₃

—

C₈×D₈₃

—

C₈×D₈₃

C₂²⋊C₄

yes

—

C₈×D₈₃

M₁₆

yes

—

C₈₃⋊C₁₆

—

C₈₃⋊C₁₆

C₂²⋊C₄

yes

—

C₂²×C₄×C₈₃

C₂×C₈

yes

characteristic

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂×C₈

yes

characteristic

C₂×C₈×C₈₃

C₂²×C₄

yes

characteristic

C₁₆×C₈₃

—

C₁₆×C₈₃

C₂×D₄

yes

—

C₂³×C₈₃

C₂×C₁₆

yes

characteristic

C₂²×D₈₃

—

C₂²×D₈₃

—

C₂²×D₈₃

C₃₂

yes

complemented

C₂²×D₈₃

C₂×C₁₆

yes

characteristic

C₂²×D₈₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₈₃

C₂²×C₈

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

C₂×C₁₆

yes

characteristic

C₂×Dic₈₃

C₂×C₁₆

yes

characteristic

C₄×D₈₃

—

C₄×D₈₃

—

C₄×D₈₃

—

C₄×D₈₃

—

C₄×D₈₃

C₂²⋊C₈

yes

—

C₄×D₈₃

M₃₂

yes

—

C₈×C₈₃

—

C₈×C₈₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₈₃

C₂×M₁₆

yes

characteristic

C₈₃⋊C₈

—

C₈₃⋊C₈

C₂²⋊C₈

yes

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

C₂×C₃₂

yes

complemented

C₂²×C₈₃

C₂²×C₁₆

yes

characteristic

C₂×D₈₃

—

C₂×D₈₃

—

C₂×D₈₃

—

C₂×D₈₃

C₂²⋊C₁₆

yes

—

C₂×D₈₃

C₂×C₃₂

yes

—

C₂×D₈₃

C₂×C₃₂

yes

complemented

C₂×D₈₃

M₆₄

yes

—

C₄×C₈₃

—

100

C₄×C₈₃

C₂×C₂²⋊C₈

yes

characteristic

101

C₄×C₈₃

C₂×M₃₂

yes

characteristic

102

Dic₈₃

—

103

Dic₈₃

C₂²⋊C₁₆

yes

—

104

C₂×C₂²⋊C₃₂

—

maximal, Sylow

105

C₂×C₈₃

—

106

C₂×C₈₃

C₂×C₂²⋊C₁₆

yes

characteristic

107

C₂×C₈₃

C₂²×C₃₂

yes

characteristic

108

C₂×C₈₃

C₂×M₆₄

yes

characteristic

109

D₈₃

—

110

D₈₃

C₂²⋊C₃₂

yes

direct product factor

111

C₂³×C₁₆

—

112

C₂²×C₃₂

—

113

C₂²⋊C₃₂

—

114

C₂²⋊C₃₂

—

115

C₂²⋊C₃₂

D₈₃

yes

characteristic, direct product factor

116

C₈₃

C₂×C₂²⋊C₃₂

yes

characteristic, complemented, Sylow

117

C₂³×C₈

—

118

C₂²×C₁₆

—

119

C₂²×C₁₆

—

120

C₂²×C₁₆

—

121

C₂²×C₁₆

—

122

C₂²×C₁₆

—

123

C₂²×C₁₆

—

166

—

124

C₂²×C₁₆

C₂×D₈₃

yes

characteristic

125

C₂×C₃₂

—

126

C₂×C₃₂

—

166

—

127

C₂×C₃₂

C₂×D₈₃

yes

complemented

128

C₂³×C₄

—

129

C₂²×C₈

—

130

C₂²×C₈

—

131

C₂²×C₈

—

132

C₂²×C₈

—

133

C₂²×C₈

—

134

C₂²×C₈

—

166

—

135

C₂²×C₈

—

166

—

136

C₂²×C₈

C₄×D₈₃

yes

characteristic

137

C₂×C₁₆

—

138

C₂×C₁₆

—

139

C₂×C₁₆

—

140

C₂×C₁₆

—

141

C₂×C₁₆

—

166

—

142

C₂×C₁₆

—

166

—

143

C₂×C₁₆

—

166

—

144

C₂×C₁₆

—

166

—

145

C₂×C₁₆

C₄×D₈₃

yes

characteristic

146

C₂×C₁₆

C₂²×D₈₃

yes

characteristic

147

C₃₂

—

148

C₃₂

—

166

—

149

C₂⁴

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

—

166

—

156

C₂²×C₄

—

166

—

157

C₂²×C₄

C₈×D₈₃

yes

characteristic

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

166

—

165

C₂×C₈

—

166

—

166

C₂×C₈

—

166

—

167

C₂×C₈

—

166

—

168

C₂×C₈

—

166

—

169

C₂×C₈

C₈×D₈₃

yes

characteristic

170

C₂×C₈

C₂×C₄×D₈₃

yes

characteristic

171

C₁₆

—

172

C₁₆

—

173

C₁₆

—

166

—

174

C₁₆

D₄×D₈₃

yes

—

175

C₂³

—

176

C₂³

—

177

C₂³

—

178

C₂³

—

166

—

179

C₂³

—

166

—

180

C₂³

C₁₆×D₈₃

yes

characteristic

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

166

—

188

C₂×C₄

—

166

—

189

C₂×C₄

—

166

—

190

C₂×C₄

—

166

—

191

C₂×C₄

—

166

—

192

C₂×C₄

C₁₆×D₈₃

yes

characteristic

193

C₂×C₄

C₂×C₈×D₈₃

yes

characteristic

194

C₈

—

195

C₈

—

196

C₈

—

166

—

197

C₈

C₂²⋊C₄×D₈₃

yes

characteristic

198

C₈

M₁₆×D₈₃

yes

characteristic

199

C₂²

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

166

—

206

C₂²

—

166

—

207

C₂²

—

166

—

208

C₂²

C₃₂×D₈₃

yes

complemented

209

C₂²

C₂×C₁₆×D₈₃

yes

characteristic

210

C₄

—

211

C₄

—

212

C₄

—

166

—

213

C₄

C₂²⋊C₈×D₈₃

yes

characteristic

214

C₄

M₃₂×D₈₃

yes

characteristic

215

C₂

—

216

C₂

—

217

C₂

—

166

—

218

C₂

C₂²⋊C₁₆×D₈₃

yes

characteristic

219

C₂

C₂×C₃₂×D₈₃

yes

characteristic

220

C₂

M₆₄×D₈₃

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂²×D₈₃
commutator	C₂×C₈₃	C₂²×C₃₂
Fitting	C₈₃×C₂²⋊C₃₂	C₂
socle	C₂²×C₈₃	C₂²×C₁₆
prime radical	C₂³×D₈₃	C₁₆
cosocle	C₂×C₁₆×C₈₃	C₂³
hypercenter	C₂²⋊C₃₂	D₈₃
hypocenter	C₈₃	C₂×C₂²⋊C₃₂
LCS	G ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂²⋊C₃₂

subgroup

G/H

center, Frattini

C₂×C₁₆

C₂²×D₈₃

commutator

C₂×C₈₃

C₂²×C₃₂

Fitting

C₈₃×C₂²⋊C₃₂

C₂

socle

C₂²×C₈₃

C₂²×C₁₆

prime radical

C₂³×D₈₃

C₁₆

cosocle

C₂×C₁₆×C₈₃

C₂³

hypercenter

C₂²⋊C₃₂

D₈₃

hypocenter

C₈₃

C₂×C₂²⋊C₃₂

LCS

G ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₁₆ ◁ C₂²⋊C₃₂

N	H ≅ G/N	type
2. C₂×C₃₂×D₈₃	C₂	semidirect
3. C₂²⋊(C₈₃⋊C₃₂)	C₂	semidirect
4. (C₂×D₈₃)⋊C₃₂	C₂	semidirect
5. C₈₃×C₂²⋊C₃₂	C₂	semidirect
13. C₂×C₈₃⋊C₃₂	C₂²	semidirect
16. C₂×C₃₂×C₈₃	C₂²	semidirect
67. C₂²×D₈₃	C₃₂	semidirect
90. C₂²×C₈₃	C₂×C₃₂	semidirect
97. C₂×D₈₃	C₂×C₃₂	semidirect
110. D₈₃	C₂²⋊C₃₂	direct (N × H)
115. C₂²⋊C₃₂	D₈₃	direct (N × H)
116. C₈₃	C₂×C₂²⋊C₃₂	semidirect
127. C₂×C₃₂	C₂×D₈₃	semidirect
208. C₂²	C₃₂×D₈₃	semidirect

H ≅ G/N

type

2. C₂×C₃₂×D₈₃

C₂

semidirect

3. C₂²⋊(C₈₃⋊C₃₂)

C₂

semidirect

4. (C₂×D₈₃)⋊C₃₂

C₂

semidirect

5. C₈₃×C₂²⋊C₃₂

C₂

semidirect

13. C₂×C₈₃⋊C₃₂

C₂²

semidirect

16. C₂×C₃₂×C₈₃

C₂²

semidirect

67. C₂²×D₈₃

C₃₂

semidirect

90. C₂²×C₈₃

C₂×C₃₂

semidirect

97. C₂×D₈₃

C₂×C₃₂

semidirect

110. D₈₃

C₂²⋊C₃₂

direct (N × H)

115. C₂²⋊C₃₂

D₈₃

direct (N × H)

116. C₈₃

C₂×C₂²⋊C₃₂

semidirect

127. C₂×C₃₂

C₂×D₈₃

semidirect

208. C₂²

C₃₂×D₈₃

semidirect

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

subgroup	index
C₂²×C₁₆×D₈₃	2
C₂×C₃₂×D₈₃	2
C₂²⋊(C₈₃⋊C₃₂)	2
(C₂×D₈₃)⋊C₃₂	2
C₈₃×C₂²⋊C₃₂	2
C₂×C₂²⋊C₃₂	83

subgroup

index

C₂²×C₁₆×D₈₃

C₂×C₃₂×D₈₃

C₂²⋊(C₈₃⋊C₃₂)

(C₂×D₈₃)⋊C₃₂

C₈₃×C₂²⋊C₃₂

C₂×C₂²⋊C₃₂

Subgroups — C₂²⋊C₃₂×D₈₃ #35324593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C22⋊C32×D83 #35324593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊C₃₂×D₈₃ #35324593