Group #35323761 — subgroups

Subgroups — #35323761

Order 21248.

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

normal subgroups only

This group has 462 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	C₂×#19128081	C₂	1	1	yes	maximal, characteristic
2	C₂×#19127506	C₂	1	2	yes	maximal
3	C₂×#19127506	C₂	1	2	yes	maximal
4	#24908196	C₂	1	1	yes	maximal, characteristic
5	C₈₃×#1374	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₃₂	—	2	1	no	—
7	C₂²×Dic₃₃₂	C₂²	1	2	yes	—
8	C₂×#14581792	—	2	1	no	—
9	#19128081	—	2	4	no	—
10	C₂×#14581726	C₂²	1	1	yes	characteristic
11	C₂×#14581726	C₂²	1	1	yes	characteristic
12	#19127599	—	2	1	no	—
13	#19127506	—	2	4	no	—
14	#19127506	—	2	4	no	—
15	#19127464	—	2	1	no	—
16	C₂²×C₁₆×C₈₃	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
18	C₂²×Dic₁₆₆	—	2	2	no	—
19	C₂×Dic₃₃₂	—	2	4	no	—
20	C₂×Dic₃₃₂	—	2	2	no	—
21	C₂×Dic₃₃₂	—	2	2	no	—
22	C₂×Dic₃₃₂	—	2	2	no	—
23	C₂×Dic₃₃₂	—	2	2	no	—
24	C₂×Dic₃₃₂	—	2	2	no	—
25	C₂×Dic₃₃₂	—	4	2	no	—
26	C₂×Dic₃₃₂	—	4	2	no	—
27	C₂×Dic₃₃₂	D₄	1	4	yes	—
28	#14581792	—	2	4	no	—
29	#14581792	—	4	2	no	—
30	C₂×C₄⋊Dic₈₃	—	2	1	no	—
31	C₂×C₄⋊Dic₈₃	—	2	1	no	—
32	C₂×C₄⋊Dic₈₃	—	4	1	no	—
33	C₂×C₄⋊Dic₈₃	—	4	1	no	—
34	C₂×Dic₈₃⋊C₄	—	4	1	no	—
35	#14581726	—	2	2	no	—
36	#14581726	—	2	1	no	—
37	#14581726	D₄	1	2	yes	—
38	C₈₃⋊#95	—	4	1	no	—
39	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
41	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
42	C₂×C₁₆×C₈₃	—	2	2	no	—
43	C₂×C₁₆×C₈₃	—	2	2	no	—
44	C₂×C₁₆×C₈₃	—	2	2	no	—
45	C₄×C₈×C₈₃	—	2	2	no	—
46	C₂×Dic₁₆₆	—	2	4	no	—
47	C₂×Dic₁₆₆	—	4	2	no	—
48	C₂×Dic₁₆₆	—	4	2	no	—
49	C₂×Dic₁₆₆	—	4	2	no	—
50	C₂×Dic₁₆₆	—	4	2	no	—
51	C₂×Dic₁₆₆	—	4	2	no	—
52	C₂²×Dic₈₃	—	4	2	no	—
53	C₂²×Dic₈₃	—	4	1	no	—
54	C₂²×Dic₈₃	—	4	1	no	—
55	Dic₃₃₂	—	2	4	no	—
56	Dic₃₃₂	—	2	4	no	—
57	Dic₃₃₂	—	4	8	no	—
58	Dic₃₃₂	—	4	2	no	—
59	Dic₃₃₂	—	4	2	no	—
60	C₄⋊Dic₈₃	—	2	2	no	—
61	C₄⋊Dic₈₃	—	4	4	no	—
62	C₄⋊Dic₈₃	—	4	4	no	—
63	C₄⋊Dic₈₃	—	4	1	no	—
64	C₄⋊Dic₈₃	—	4	1	no	—
65	C₄⋊Dic₈₃	—	4	1	no	—
66	Dic₈₃⋊C₄	—	8	2	no	—
67	C₂²×C₄×C₈₃	D₈	1	1	yes	characteristic
68	C₂²×C₄×C₈₃	D₈	1	1	yes	characteristic
69	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₈₃	—	2	1	no	—
71	C₂×C₈×C₈₃	—	2	1	no	—
72	C₂×C₈×C₈₃	SD₁₆	1	2	yes	—
73	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
74	C₂×C₈×C₈₃	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₈₃	#41	1	2	yes	—
76	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
77	C₄²×C₈₃	—	2	1	no	—
78	C₄²×C₈₃	—	2	1	no	—
79	C₁₆×C₈₃	—	4	2	no	—
80	C₂³×C₈₃	C₂×D₈	1	1	yes	characteristic
81	C₂×C₄×C₈₃	—	2	1	no	—
82	C₂×C₄×C₈₃	—	2	1	no	—
83	C₂×C₄×C₈₃	—	2	1	no	—
84	C₂×C₄×C₈₃	—	2	1	no	—
85	C₂×C₄×C₈₃	SD₃₂	1	2	yes	—
86	C₂×C₄×C₈₃	Q₃₂	1	2	yes	—
87	C₂×C₄×C₈₃	#120	1	1	yes	characteristic
88	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
89	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
90	C₂×C₄×C₈₃	C₂×SD₁₆	1	1	yes	characteristic
91	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
92	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
93	C₂×Dic₈₃	—	4	4	no	—
94	C₂×Dic₈₃	—	4	2	no	—
95	C₂×Dic₈₃	—	8	2	no	—
96	C₂×Dic₈₃	—	8	2	no	—
97	C₂×Dic₈₃	—	8	1	no	—
98	C₂×Dic₈₃	—	8	1	no	—
99	C₂×Dic₈₃	—	8	1	no	—
100	C₂×Dic₈₃	—	8	1	no	—
101	C₂×Dic₈₃	—	8	1	no	—
102	Dic₁₆₆	—	4	4	no	—
103	Dic₁₆₆	—	4	4	no	—
104	Dic₁₆₆	—	8	2	no	—
105	Dic₁₆₆	—	8	2	no	—
106	C₈×C₈₃	—	2	2	no	—
107	C₈×C₈₃	#121	1	2	yes	—
108	C₈×C₈₃	#123	1	2	yes	—
109	C₂²×C₈₃	#447	1	1	yes	characteristic
110	C₂²×C₈₃	#459	1	1	yes	characteristic
111	C₂²×C₈₃	#486	1	1	yes	characteristic
112	C₂²×C₈₃	C₂×SD₃₂	1	1	yes	characteristic
113	C₂²×C₈₃	C₂×Q₃₂	1	1	yes	characteristic
114	C₂²×C₈₃	#510	1	1	yes	characteristic
115	C₂²×C₈₃	#510	1	1	yes	characteristic
116	C₄×C₈₃	—	2	2	no	—
117	C₄×C₈₃	—	2	2	no	—
118	C₄×C₈₃	#394	1	1	yes	characteristic
119	C₄×C₈₃	#450	1	1	yes	characteristic
120	C₄×C₈₃	#460	1	1	yes	characteristic
121	C₄×C₈₃	#490	1	1	yes	characteristic
122	Dic₈₃	—	8	2	no	—
123	Dic₈₃	—	8	4	no	—
124	Dic₈₃	—	16	1	no	—
125	#13409	—	83	1	no	maximal, Sylow
126	C₂×C₈₃	#2041	1	1	yes	characteristic
127	C₂×C₈₃	#2185	1	1	yes	characteristic
128	C₂×C₈₃	#2188	1	1	yes	characteristic
129	C₂×C₈₃	#2208	1	1	yes	characteristic
130	C₂×C₈₃	#2209	1	1	yes	characteristic
131	C₂×C₈₃	#2241	1	1	yes	characteristic
132	C₂×C₈₃	#2245	1	1	yes	characteristic
133	C₂×#494	—	83	1	no	—
134	C₂×#358	—	83	2	no	—
135	C₂×#358	—	83	2	no	—
136	#1942	—	83	1	no	—
137	#1374	D₈₃	1	1	yes	characteristic
138	C₈₃	#13409	1	1	yes	characteristic, complemented, Sylow
139	C₂²×Q₁₆	—	83	2	no	—
140	C₂²×Q₁₆	—	166	1	no	—
141	C₂×C₄⋊Q₈	—	166	1	no	—
142	C₂²×C₁₆	C₂×D₈₃	1	2	yes	—
143	#494	—	166	4	no	—
144	C₂×#107	—	83	1	no	—
145	C₂×#107	—	83	1	no	—
146	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
147	#389	—	166	1	no	—
148	#358	—	166	4	no	—
149	#358	—	166	4	no	—
150	#340	—	166	1	no	—
151	C₂²×Q₈	—	166	2	no	—
152	C₂×Q₁₆	—	332	2	no	—
153	C₂×Q₁₆	—	332	2	no	—
154	C₂×Q₁₆	—	83	4	no	—
155	C₂×Q₁₆	—	166	4	no	—
156	C₂×Q₁₆	—	166	2	no	—
157	C₂×Q₁₆	—	166	2	no	—
158	C₂×Q₁₆	—	166	2	no	—
159	C₂×Q₁₆	—	166	2	no	—
160	C₂×Q₁₆	—	166	2	no	—
161	C₂²×C₈	D₃₃₂	1	1	yes	characteristic
162	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
163	C₄⋊Q₈	—	332	2	no	—
164	C₄⋊Q₈	—	166	4	no	—
165	C₂×C₄⋊C₄	—	332	1	no	—
166	C₂×C₄⋊C₄	—	332	1	no	—
167	C₂×C₄⋊C₄	—	332	1	no	—
168	C₂×C₄⋊C₄	—	166	1	no	—
169	C₂×C₄⋊C₄	—	166	1	no	—
170	C₂×C₄²	D₃₃₂	1	1	yes	characteristic
171	C₂×C₁₆	—	2	2	no	—
172	C₂×C₁₆	—	2	2	no	—
173	C₂×C₁₆	—	2	2	no	—
174	#107	—	83	2	no	—
175	#107	—	166	2	no	—
176	#107	—	166	1	no	—
177	C₄×C₈	—	2	2	no	—
178	#95	—	332	1	no	—
179	C₂×Q₈	—	332	2	no	—
180	C₂×Q₈	—	332	2	no	—
181	C₂×Q₈	—	332	2	no	—
182	C₂×Q₈	—	332	2	no	—
183	C₂×Q₈	—	332	2	no	—
184	C₂×Q₈	—	166	4	no	—
185	C₂²×C₄	—	332	1	no	—
186	C₂²×C₄	—	332	2	no	—
187	C₂²×C₄	—	332	1	no	—
188	C₂²×C₄	D₆₆₄	1	1	yes	characteristic
189	C₂²×C₄	D₆₆₄	1	1	yes	characteristic
190	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
191	Q₁₆	—	332	8	no	—
192	Q₁₆	—	332	2	no	—
193	Q₁₆	—	332	2	no	—
194	Q₁₆	—	166	4	no	—
195	Q₁₆	—	166	4	no	—
196	C₂×C₈	—	2	1	no	—
197	C₂×C₈	—	2	1	no	—
198	C₂×C₈	#13050579	1	2	yes	—
199	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
200	C₂×C₈	D₄×D₈₃	1	2	yes	—
201	C₂×C₈	#13050590	1	2	yes	—
202	C₂×C₈	#13050591	1	1	yes	characteristic
203	C₄⋊C₄	—	332	4	no	—
204	C₄⋊C₄	—	332	4	no	—
205	C₄⋊C₄	—	332	1	no	—
206	C₄⋊C₄	—	332	1	no	—
207	C₄⋊C₄	—	332	1	no	—
208	C₄⋊C₄	—	664	2	no	—
209	C₄⋊C₄	—	166	2	no	—
210	C₄²	—	2	1	no	—
211	C₄²	—	2	1	no	—
212	C₁₆	—	4	2	no	—
213	C₂³	C₂×D₆₆₄	1	1	yes	characteristic
214	Q₈	—	332	4	no	—
215	Q₈	—	332	4	no	—
216	Q₈	—	664	2	no	—
217	Q₈	—	664	2	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	332	4	no	—
223	C₂×C₄	—	332	2	no	—
224	C₂×C₄	—	664	1	no	—
225	C₂×C₄	—	664	1	no	—
226	C₂×C₄	—	664	1	no	—
227	C₂×C₄	—	664	1	no	—
228	C₂×C₄	—	664	1	no	—
229	C₂×C₄	—	664	2	no	—
230	C₂×C₄	—	664	2	no	—
231	C₂×C₄	#14581737	1	2	yes	—
232	C₂×C₄	Dic₆₆₄	1	2	yes	—
233	C₂×C₄	#14581762	1	1	yes	characteristic
234	C₂×C₄	#14581767	1	1	yes	characteristic
235	C₂×C₄	#14581780	1	1	yes	characteristic
236	C₂×C₄	C₂×#13050579	1	1	yes	characteristic
237	C₂×C₄	#14581820	1	1	yes	characteristic
238	C₂×C₄	#14581820	1	1	yes	characteristic
239	C₈	—	2	2	no	—
240	C₈	#14581765	1	2	yes	—
241	C₈	#14581777	1	2	yes	—
242	C₂²	#19127837	1	1	yes	characteristic
243	C₂²	#19127897	1	1	yes	characteristic
244	C₂²	#19128048	1	1	yes	characteristic
245	C₂²	C₂×#14581737	1	1	yes	characteristic
246	C₂²	C₂×Dic₆₆₄	1	1	yes	characteristic
247	C₂²	#19128144	1	1	yes	characteristic
248	C₂²	#19128144	1	1	yes	characteristic
249	C₄	—	2	2	no	—
250	C₄	—	2	2	no	—
251	C₄	—	1328	1	no	—
252	C₄	—	664	4	no	—
253	C₄	—	664	2	no	—
254	C₄	#19127619	1	1	yes	characteristic
255	C₄	#19127854	1	1	yes	characteristic
256	C₄	#19127902	1	1	yes	characteristic
257	C₄	#19128066	1	1	yes	characteristic
258	C₂	#24908698	1	1	yes	characteristic
259	C₂	#24909382	1	1	yes	characteristic
260	C₂	#24909399	1	1	yes	characteristic
261	C₂	#24909509	1	1	yes	characteristic
262	C₂	#24909514	1	1	yes	characteristic
263	C₂	#24909691	1	1	yes	characteristic
264	C₂	#24909709	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19128081

C₂

yes

maximal, characteristic

C₂×#19127506

C₂

yes

maximal

C₂×#19127506

C₂

yes

maximal

#24908196

C₂

yes

maximal, characteristic

C₈₃×#1374

C₂

yes

maximal, characteristic

C₂²×Dic₃₃₂

—

C₂²×Dic₃₃₂

C₂²

yes

—

C₂×#14581792

—

#19128081

—

C₂×#14581726

C₂²

yes

characteristic

C₂×#14581726

C₂²

yes

—

—

—

—

C₂²×C₁₆×C₈₃

C₂²

yes

—

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

C₂²×Dic₁₆₆

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

D₄

yes

—

#14581792

—

#14581792

—

C₂×C₄⋊Dic₈₃

—

C₂×C₄⋊Dic₈₃

—

C₂×C₄⋊Dic₈₃

—

C₂×C₄⋊Dic₈₃

—

C₂×Dic₈₃⋊C₄

—

#14581726

—

#14581726

—

#14581726

D₄

yes

—

C₈₃⋊#95

—

C₂²×C₈×C₈₃

D₄

yes

characteristic

C₂²×C₈×C₈₃

C₂³

yes

characteristic

C₂×C₄²×C₈₃

D₄

yes

characteristic

C₂×C₁₆×C₈₃

—

C₂×C₁₆×C₈₃

—

C₂×C₁₆×C₈₃

—

C₄×C₈×C₈₃

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂²×Dic₈₃

—

C₂²×Dic₈₃

—

C₂²×Dic₈₃

—

Dic₃₃₂

—

Dic₃₃₂

—

Dic₃₃₂

—

Dic₃₃₂

—

Dic₃₃₂

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

Dic₈₃⋊C₄

—

C₂²×C₄×C₈₃

D₈

yes

characteristic

C₂²×C₄×C₈₃

D₈

yes

characteristic

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

SD₁₆

yes

—

C₂×C₈×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

—

C₂×C₈×C₈₃

#41

yes

—

C₂×C₈×C₈₃

#41

yes

characteristic

C₄²×C₈₃

—

C₄²×C₈₃

—

C₁₆×C₈₃

—

C₂³×C₈₃

C₂×D₈

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

SD₃₂

yes

—

C₂×C₄×C₈₃

Q₃₂

yes

—

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

C₂×SD₁₆

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

100

C₂×Dic₈₃

—

101

C₂×Dic₈₃

—

102

Dic₁₆₆

—

103

Dic₁₆₆

—

104

Dic₁₆₆

—

105

Dic₁₆₆

—

106

C₈×C₈₃

—

107

C₈×C₈₃

#121

yes

—

108

C₈×C₈₃

#123

yes

—

109

C₂²×C₈₃

#447

yes

characteristic

110

C₂²×C₈₃

#459

yes

characteristic

111

C₂²×C₈₃

#486

yes

characteristic

112

C₂²×C₈₃

C₂×SD₃₂

yes

characteristic

113

C₂²×C₈₃

C₂×Q₃₂

yes

characteristic

114

C₂²×C₈₃

#510

yes

characteristic

115

C₂²×C₈₃

#510

yes

characteristic

116

C₄×C₈₃

—

117

C₄×C₈₃

—

118

C₄×C₈₃

#394

yes

characteristic

119

C₄×C₈₃

#450

yes

characteristic

120

C₄×C₈₃

#460

yes

characteristic

121

C₄×C₈₃

#490

yes

characteristic

122

Dic₈₃

—

123

Dic₈₃

—

124

Dic₈₃

—

125

#13409

—

maximal, Sylow

126

C₂×C₈₃

#2041

yes

characteristic

127

C₂×C₈₃

#2185

yes

characteristic

128

C₂×C₈₃

#2188

yes

characteristic

129

C₂×C₈₃

#2208

yes

characteristic

130

C₂×C₈₃

#2209

yes

characteristic

131

C₂×C₈₃

#2241

yes

characteristic

132

C₂×C₈₃

#2245

yes

characteristic

133

C₂×#494

—

134

C₂×#358

—

135

C₂×#358

—

136

#1942

—

137

#1374

D₈₃

yes

characteristic

138

C₈₃

#13409

yes

characteristic, complemented, Sylow

139

C₂²×Q₁₆

—

140

C₂²×Q₁₆

—

166

—

141

C₂×C₄⋊Q₈

—

166

—

142

C₂²×C₁₆

C₂×D₈₃

yes

—

143

#494

—

166

—

144

C₂×#107

—

145

C₂×#107

—

146

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

147

#389

—

166

—

148

#358

—

166

—

149

#358

—

166

—

150

#340

—

166

—

151

C₂²×Q₈

—

166

—

152

C₂×Q₁₆

—

332

—

153

C₂×Q₁₆

—

332

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

166

—

156

C₂×Q₁₆

—

166

—

157

C₂×Q₁₆

—

166

—

158

C₂×Q₁₆

—

166

—

159

C₂×Q₁₆

—

166

—

160

C₂×Q₁₆

—

166

—

161

C₂²×C₈

D₃₃₂

yes

characteristic

162

C₂²×C₈

C₂²×D₈₃

yes

characteristic

163

C₄⋊Q₈

—

332

—

164

C₄⋊Q₈

—

166

—

165

C₂×C₄⋊C₄

—

332

—

166

C₂×C₄⋊C₄

—

332

—

167

C₂×C₄⋊C₄

—

332

—

168

C₂×C₄⋊C₄

—

166

—

169

C₂×C₄⋊C₄

—

166

—

170

C₂×C₄²

D₃₃₂

yes

characteristic

171

C₂×C₁₆

—

172

C₂×C₁₆

—

173

C₂×C₁₆

—

174

#107

—

175

#107

—

166

—

176

#107

—

166

—

177

C₄×C₈

—

178

#95

—

332

—

179

C₂×Q₈

—

332

—

180

C₂×Q₈

—

332

—

181

C₂×Q₈

—

332

—

182

C₂×Q₈

—

332

—

183

C₂×Q₈

—

332

—

184

C₂×Q₈

—

166

—

185

C₂²×C₄

—

332

—

186

C₂²×C₄

—

332

—

187

C₂²×C₄

—

332

—

188

C₂²×C₄

D₆₆₄

yes

characteristic

189

C₂²×C₄

D₆₆₄

yes

characteristic

190

C₂²×C₄

C₂×D₃₃₂

yes

characteristic

191

Q₁₆

—

332

—

192

Q₁₆

—

332

—

193

Q₁₆

—

332

—

194

Q₁₆

—

166

—

195

Q₁₆

—

166

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

#13050579

yes

—

199

C₂×C₈

D₄×D₈₃

yes

characteristic

200

C₂×C₈

D₄×D₈₃

yes

—

201

C₂×C₈

#13050590

yes

—

202

C₂×C₈

#13050591

yes

characteristic

203

C₄⋊C₄

—

332

—

204

C₄⋊C₄

—

332

—

205

C₄⋊C₄

—

332

—

206

C₄⋊C₄

—

332

—

207

C₄⋊C₄

—

332

—

208

C₄⋊C₄

—

664

—

209

C₄⋊C₄

—

166

—

210

C₄²

—

211

C₄²

—

212

C₁₆

—

213

C₂³

C₂×D₆₆₄

yes

characteristic

214

Q₈

—

332

—

215

Q₈

—

332

—

216

Q₈

—

664

—

217

Q₈

—

664

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

332

—

223

C₂×C₄

—

332

—

224

C₂×C₄

—

664

—

225

C₂×C₄

—

664

—

226

C₂×C₄

—

664

—

227

C₂×C₄

—

664

—

228

C₂×C₄

—

664

—

229

C₂×C₄

—

664

—

230

C₂×C₄

—

664

—

231

C₂×C₄

#14581737

yes

—

232

C₂×C₄

Dic₆₆₄

yes

—

233

C₂×C₄

#14581762

yes

characteristic

234

C₂×C₄

#14581767

yes

characteristic

235

C₂×C₄

#14581780

yes

characteristic

236

C₂×C₄

C₂×#13050579

yes

characteristic

237

C₂×C₄

#14581820

yes

characteristic

238

C₂×C₄

#14581820

yes

characteristic

239

C₈

—

240

C₈

#14581765

yes

—

241

C₈

#14581777

yes

—

242

C₂²

#19127837

yes

characteristic

243

C₂²

#19127897

yes

characteristic

244

C₂²

#19128048

yes

characteristic

245

C₂²

C₂×#14581737

yes

characteristic

246

C₂²

C₂×Dic₆₆₄

yes

characteristic

247

C₂²

#19128144

yes

characteristic

248

C₂²

#19128144

yes

characteristic

249

C₄

—

250

C₄

—

251

C₄

—

1328

—

252

C₄

—

664

—

253

C₄

—

664

—

254

C₄

#19127619

yes

characteristic

255

C₄

#19127854

yes

characteristic

256

C₄

#19127902

yes

characteristic

257

C₄

#19128066

yes

characteristic

258

C₂

#24908698

yes

characteristic

259

C₂

#24909382

yes

characteristic

260

C₂

#24909399

yes

characteristic

261

C₂

#24909509

yes

characteristic

262

C₂

#24909514

yes

characteristic

263

C₂

#24909691

yes

characteristic

264

C₂

#24909709

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₆₆₄
commutator, cosocle	C₂²×C₈×C₈₃	C₂³
Frattini	C₂²×C₈	C₂²×D₈₃
Fitting	C₈₃×#1374	C₂
socle, prime radical	C₂³×C₈₃	C₂×D₈
hypercenter	#1374	D₈₃
hypocenter	C₈₃	#13409
LCS	G ▷ C₂²×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

subgroup

G/H

center

C₂³

C₂×D₆₆₄

commutator, cosocle

C₂²×C₈×C₈₃

C₂³

Frattini

C₂²×C₈

C₂²×D₈₃

Fitting

C₈₃×#1374

C₂

socle, prime radical

C₂³×C₈₃

C₂×D₈

D₈₃

C₈₃

G ▷ C₂²×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

N	H ≅ G/N	type
138. C₈₃	#13409	semidirect

H ≅ G/N

type

138. C₈₃

#13409

semidirect

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

subgroup	index
C₂×#19128081	2
C₂×#19127506	2
#24908196	2
C₈₃×#1374	2
#13409	83

subgroup

index

C₈₃×#1374

Subgroups — #35323761

Conjugacy classes of subgroups

Complements

Maximal subgroups