Group #35307012 — subgroups

Subgroups — #35307012

Order 21248.

574 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 139 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×#19127986	C₂	1	2	yes	maximal
3	C₂×#19127448	C₂	1	2	yes	maximal
4	#24905298	C₂	1	1	yes	maximal, characteristic
5	C₈₃×#1984	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₃₂	—	2	2	no	—
7	C₂×#14581792	C₂²	1	2	yes	—
8	#19128081	—	2	4	no	—
9	#19127986	—	2	4	no	—
10	#19127986	—	2	4	no	—
11	C₂×#14581723	—	2	2	no	—
12	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
13	C₂×#14581716	—	2	2	no	—
14	#19127448	—	2	4	no	—
15	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
18	#336×C₈₃	—	2	2	no	—
19	C₂²×Dic₁₆₆	—	2	2	no	—
20	C₂×Dic₃₃₂	—	2	8	no	—
21	C₂×Dic₃₃₂	—	4	4	no	—
22	C₂×Dic₃₃₂	—	4	4	no	—
23	C₂²×C₈₃⋊C₈	—	2	2	no	—
24	#14581792	—	2	2	no	—
25	#14581792	—	2	2	no	—
26	#14581792	—	2	2	no	—
27	#14581792	D₄	1	4	yes	—
28	C₂×C₄⋊Dic₈₃	—	2	2	no	—
29	C₂×C₄⋊Dic₈₃	—	2	2	no	—
30	#14581723	—	2	8	no	—
31	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
32	C₄⋊(C₈₃⋊C₈)	D₄	1	4	yes	—
33	#14581716	—	2	8	no	—
34	C₂²×Q₈×C₈₃	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₈₃	—	2	1	no	—
36	C₂²×C₈×C₈₃	D₄	1	2	yes	—
37	C₄×Q₈×C₈₃	—	2	2	no	—
38	C₄×Q₈×C₈₃	—	2	2	no	—
39	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
40	C₂×C₄⋊C₄×C₈₃	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₈₃	—	2	1	no	—
42	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₈₃	—	2	2	no	—
44	C₄×C₈×C₈₃	—	2	2	no	—
45	C₂×Dic₁₆₆	—	2	4	no	—
46	C₂×Dic₁₆₆	—	4	4	no	—
47	C₂×Dic₁₆₆	—	4	4	no	—
48	C₂×Dic₁₆₆	—	4	2	no	—
49	C₂²×Dic₈₃	—	4	2	no	—
50	Dic₃₃₂	—	4	16	no	—
51	C₂×C₈₃⋊C₈	—	2	4	no	—
52	C₂×C₈₃⋊C₈	—	4	2	no	—
53	C₂×C₈₃⋊C₈	—	4	2	no	—
54	C₄⋊Dic₈₃	—	2	4	no	—
55	C₄⋊Dic₈₃	—	2	4	no	—
56	C₄⋊Dic₈₃	—	4	2	no	—
57	C₄⋊Dic₈₃	—	4	2	no	—
58	C₂×Q₈×C₈₃	—	2	1	no	—
59	C₂×Q₈×C₈₃	—	2	2	no	—
60	C₂×Q₈×C₈₃	—	2	2	no	—
61	C₂×Q₈×C₈₃	Q₁₆	1	2	yes	complemented
62	C₂²×C₄×C₈₃	—	2	1	no	—
63	C₂²×C₄×C₈₃	—	2	1	no	—
64	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
67	C₂×C₈×C₈₃	—	2	2	no	—
68	C₂×C₈×C₈₃	—	2	2	no	—
69	C₂×C₈×C₈₃	—	4	1	no	—
70	C₂×C₈×C₈₃	—	4	2	no	—
71	C₂×C₈×C₈₃	SD₁₆	1	4	yes	—
72	C₄⋊C₄×C₈₃	—	2	2	no	—
73	C₄⋊C₄×C₈₃	—	4	2	no	—
74	C₄²×C₈₃	—	4	1	no	—
75	C₄²×C₈₃	—	4	1	no	—
76	C₄²×C₈₃	C₂×D₄	1	2	yes	—
77	C₄²×C₈₃	C₂×D₄	1	2	yes	—
78	C₂³×C₈₃	#121	1	1	yes	characteristic
79	Q₈×C₈₃	—	2	4	no	—
80	Q₈×C₈₃	—	4	2	no	—
81	C₂×C₄×C₈₃	—	2	2	no	—
82	C₂×C₄×C₈₃	—	2	2	no	—
83	C₂×C₄×C₈₃	—	4	1	no	—
84	C₂×C₄×C₈₃	—	4	1	no	—
85	C₂×C₄×C₈₃	—	4	1	no	—
86	C₂×C₄×C₈₃	—	4	2	no	—
87	C₂×C₄×C₈₃	#120	1	1	yes	characteristic
88	C₂×C₄×C₈₃	#120	1	2	yes	—
89	C₂×C₄×C₈₃	#121	1	2	yes	—
90	C₂×C₄×C₈₃	#127	1	1	yes	characteristic
91	C₂×C₄×C₈₃	C₂×SD₁₆	1	2	yes	—
92	C₂×C₄×C₈₃	C₂×Q₁₆	1	1	yes	characteristic
93	C₂×C₄×C₈₃	#135	1	1	yes	characteristic
94	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	2	yes	—
95	C₂×C₄×C₈₃	#137	1	2	yes	—
96	C₂×Dic₈₃	—	4	4	no	—
97	C₂×Dic₈₃	—	8	4	no	—
98	Dic₁₆₆	—	4	8	no	—
99	Dic₁₆₆	—	8	2	no	—
100	Dic₁₆₆	—	8	2	no	—
101	C₈×C₈₃	—	2	4	no	—
102	C₈×C₈₃	—	8	1	no	—
103	C₈₃⋊C₈	—	4	4	no	—
104	C₂²×C₈₃	#392	1	1	yes	characteristic
105	C₂²×C₈₃	#460	1	2	yes	—
106	C₂²×C₈₃	#467	1	1	yes	characteristic
107	C₂²×C₈₃	#470	1	1	yes	characteristic
108	C₂²×C₈₃	#473	1	2	yes	—
109	C₄×C₈₃	—	2	2	no	—
110	C₄×C₈₃	—	4	2	no	—
111	C₄×C₈₃	—	8	1	no	—
112	C₄×C₈₃	#450	1	2	yes	—
113	C₄×C₈₃	#451	1	2	yes	—
114	C₄×C₈₃	#452	1	2	yes	—
115	C₄×C₈₃	#492	1	1	yes	characteristic
116	C₄×C₈₃	#496	1	1	yes	characteristic
117	Dic₈₃	—	8	4	no	—
118	#10276	—	83	1	no	maximal, Sylow
119	C₂×C₈₃	#1670	1	2	yes	—
120	C₂×C₈₃	#1690	1	2	yes	—
121	C₂×C₈₃	#2001	1	1	yes	characteristic
122	C₂×C₈₃	#2014	1	1	yes	characteristic
123	C₂×C₈₃	#2020	1	1	yes	characteristic
124	C₂×#494	—	83	1	no	—
125	C₂×#475	—	83	2	no	—
126	#1984	D₈₃	1	1	yes	characteristic
127	C₂×#332	—	83	2	no	—
128	#1277	—	83	1	no	—
129	C₈₃	#10276	1	1	yes	characteristic, complemented, Sylow
130	C₂²×Q₁₆	—	166	2	no	—
131	C₂×C₄⋊Q₈	—	83	2	no	—
132	C₂×C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic
133	#494	—	166	4	no	—
134	#475	—	166	4	no	—
135	#475	—	166	4	no	—
136	C₂×#106	—	166	2	no	—
137	C₂×C₄⋊C₈	—	83	2	no	—
138	C₂×C₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
139	C₂×#103	—	166	2	no	—
140	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
141	#336	—	2	2	no	—
142	#332	—	166	4	no	—
143	C₂²×Q₈	—	166	2	no	—
144	C₂²×Q₈	D₃₃₂	1	1	yes	characteristic
145	C₂×Q₁₆	—	332	4	no	—
146	C₂×Q₁₆	—	332	4	no	—
147	C₂×Q₁₆	—	166	8	no	—
148	C₂²×C₈	—	2	1	no	—
149	C₂²×C₈	—	166	2	no	—
150	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
151	C₄⋊Q₈	—	83	4	no	—
152	C₄⋊Q₈	—	166	2	no	—
153	C₄⋊Q₈	—	166	2	no	—
154	C₄⋊Q₈	—	166	2	no	—
155	C₄×Q₈	—	2	2	no	—
156	C₄×Q₈	—	2	2	no	—
157	C₂×C₄⋊C₄	—	2	1	no	—
158	C₂×C₄⋊C₄	—	166	2	no	—
159	C₂×C₄⋊C₄	—	166	2	no	—
160	C₂×C₄⋊C₄	D₃₃₂	1	1	yes	characteristic
161	C₂×C₄²	—	2	1	no	—
162	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
163	#106	—	166	8	no	—
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	83	4	no	—
166	C₄⋊C₈	—	166	2	no	—
167	#103	—	166	8	no	—
168	C₄×C₈	—	2	2	no	—
169	C₂×Q₈	—	2	1	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	—	2	2	no	—
172	C₂×Q₈	—	332	2	no	—
173	C₂×Q₈	—	332	4	no	—
174	C₂×Q₈	—	332	4	no	—
175	C₂×Q₈	—	166	4	no	—
176	C₂×Q₈	Dic₃₃₂	1	2	yes	complemented
177	C₂²×C₄	—	2	1	no	—
178	C₂²×C₄	—	2	1	no	—
179	C₂²×C₄	—	332	2	no	—
180	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
181	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
182	C₂²×C₄	#13050590	1	1	yes	characteristic
183	Q₁₆	—	332	16	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	2	no	—
186	C₂×C₈	—	4	1	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	332	2	no	—
189	C₂×C₈	—	332	2	no	—
190	C₂×C₈	—	166	4	no	—
191	C₂×C₈	#13050577	1	4	yes	—
192	C₄⋊C₄	—	2	2	no	—
193	C₄⋊C₄	—	4	2	no	—
194	C₄⋊C₄	—	332	2	no	—
195	C₄⋊C₄	—	332	2	no	—
196	C₄⋊C₄	—	166	4	no	—
197	C₄⋊C₄	—	166	4	no	—
198	C₄²	—	4	1	no	—
199	C₄²	—	4	1	no	—
200	C₄²	D₄×D₈₃	1	2	yes	—
201	C₄²	D₄×D₈₃	1	2	yes	—
202	C₂³	#14581766	1	1	yes	characteristic
203	Q₈	—	2	4	no	—
204	Q₈	—	4	2	no	—
205	Q₈	—	332	8	no	—
206	Q₈	—	664	2	no	—
207	Q₈	—	664	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	332	4	no	—
215	C₂×C₄	—	664	4	no	—
216	C₂×C₄	#14581760	1	1	yes	characteristic
217	C₂×C₄	#14581762	1	2	yes	—
218	C₂×C₄	#14581765	1	2	yes	—
219	C₂×C₄	#14581788	1	1	yes	characteristic
220	C₂×C₄	C₂×#13050577	1	2	yes	—
221	C₂×C₄	C₂×Dic₃₃₂	1	1	yes	characteristic
222	C₂×C₄	#14581814	1	1	yes	characteristic
223	C₂×C₄	#14581817	1	2	yes	—
224	C₂×C₄	#14581825	1	2	yes	—
225	C₈	—	2	4	no	—
226	C₈	—	8	1	no	—
227	C₈	—	332	4	no	—
228	C₂²	#19127610	1	1	yes	characteristic
229	C₂²	#19127901	1	2	yes	—
230	C₂²	#19127942	1	1	yes	characteristic
231	C₂²	#19127959	1	1	yes	characteristic
232	C₂²	#19127976	1	2	yes	—
233	C₄	—	2	2	no	—
234	C₄	—	4	2	no	—
235	C₄	—	8	1	no	—
236	C₄	—	664	4	no	—
237	C₄	#19127851	1	2	yes	—
238	C₄	#19127859	1	2	yes	—
239	C₄	#19127865	1	2	yes	—
240	C₄	#19128075	1	1	yes	characteristic
241	C₄	#19128091	1	1	yes	characteristic
242	C₂	#24906833	1	2	yes	—
243	C₂	#24906957	1	2	yes	—
244	C₂	#24908473	1	1	yes	characteristic
245	C₂	#24908550	1	1	yes	characteristic
246	C₂	#24908584	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19128081

C₂

yes

maximal, characteristic

C₂×#19127986

C₂

yes

maximal

C₂×#19127448

C₂

yes

maximal

#24905298

C₂

yes

maximal, characteristic

C₈₃×#1984

C₂

yes

maximal, characteristic

C₂²×Dic₃₃₂

—

C₂×#14581792

C₂²

yes

—

—

—

—

—

C₂×C₄⋊(C₈₃⋊C₈)

C₂²

yes

—

C₂×#14581716

—

#19127448

—

C₂×C₄×Q₈×C₈₃

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₈₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

#336×C₈₃

—

C₂²×Dic₁₆₆

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂²×C₈₃⋊C₈

—

—

—

—

D₄

yes

—

C₂×C₄⋊Dic₈₃

—

C₂×C₄⋊Dic₈₃

—

#14581723

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

D₄

yes

—

#14581716

—

C₂²×Q₈×C₈₃

D₄

yes

characteristic

C₂²×C₈×C₈₃

—

C₂²×C₈×C₈₃

D₄

yes

—

C₄×Q₈×C₈₃

—

C₄×Q₈×C₈₃

—

C₂×C₄⋊C₄×C₈₃

—

C₂×C₄⋊C₄×C₈₃

D₄

yes

characteristic

C₂×C₄²×C₈₃

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

C₄⋊C₈×C₈₃

—

C₄×C₈×C₈₃

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂²×Dic₈₃

—

Dic₃₃₂

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

Q₁₆

yes

complemented

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₃

#41

yes

characteristic

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

SD₁₆

yes

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄²×C₈₃

—

C₄²×C₈₃

—

C₄²×C₈₃

C₂×D₄

yes

—

C₄²×C₈₃

C₂×D₄

yes

—

C₂³×C₈₃

#121

yes

characteristic

Q₈×C₈₃

—

Q₈×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

#120

yes

characteristic

C₂×C₄×C₈₃

#120

yes

—

C₂×C₄×C₈₃

#121

yes

—

C₂×C₄×C₈₃

#127

yes

characteristic

C₂×C₄×C₈₃

C₂×SD₁₆

yes

—

C₂×C₄×C₈₃

C₂×Q₁₆

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

—

C₂×C₄×C₈₃

#137

yes

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

Dic₁₆₆

—

Dic₁₆₆

—

100

Dic₁₆₆

—

101

C₈×C₈₃

—

102

C₈×C₈₃

—

103

C₈₃⋊C₈

—

104

C₂²×C₈₃

#392

yes

characteristic

105

C₂²×C₈₃

#460

yes

—

106

C₂²×C₈₃

#467

yes

characteristic

107

C₂²×C₈₃

#470

yes

characteristic

108

C₂²×C₈₃

#473

yes

—

109

C₄×C₈₃

—

110

C₄×C₈₃

—

111

C₄×C₈₃

—

112

C₄×C₈₃

#450

yes

—

113

C₄×C₈₃

#451

yes

—

114

C₄×C₈₃

#452

yes

—

115

C₄×C₈₃

#492

yes

characteristic

116

C₄×C₈₃

#496

yes

characteristic

117

Dic₈₃

—

118

#10276

—

maximal, Sylow

119

C₂×C₈₃

#1670

yes

—

120

C₂×C₈₃

#1690

yes

—

121

C₂×C₈₃

#2001

yes

characteristic

122

C₂×C₈₃

#2014

yes

characteristic

123

C₂×C₈₃

#2020

yes

characteristic

124

C₂×#494

—

125

C₂×#475

—

126

#1984

D₈₃

yes

characteristic

127

C₂×#332

—

128

#1277

—

129

C₈₃

#10276

yes

characteristic, complemented, Sylow

130

C₂²×Q₁₆

—

166

—

131

C₂×C₄⋊Q₈

—

132

C₂×C₄×Q₈

C₂×D₈₃

yes

characteristic

133

#494

—

166

—

134

#475

—

166

—

135

#475

—

166

—

136

C₂×#106

—

166

—

137

C₂×C₄⋊C₈

—

138

C₂×C₄⋊C₈

C₂×D₈₃

yes

characteristic

139

C₂×#103

—

166

—

140

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

141

#336

—

142

#332

—

166

—

143

C₂²×Q₈

—

166

—

144

C₂²×Q₈

D₃₃₂

yes

characteristic

145

C₂×Q₁₆

—

332

—

146

C₂×Q₁₆

—

332

—

147

C₂×Q₁₆

—

166

—

148

C₂²×C₈

—

149

C₂²×C₈

—

166

—

150

C₂²×C₈

C₂²⋊D₈₃

yes

—

151

C₄⋊Q₈

—

152

C₄⋊Q₈

—

166

—

153

C₄⋊Q₈

—

166

—

154

C₄⋊Q₈

—

166

—

155

C₄×Q₈

—

156

C₄×Q₈

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

166

—

159

C₂×C₄⋊C₄

—

166

—

160

C₂×C₄⋊C₄

D₃₃₂

yes

characteristic

161

C₂×C₄²

—

162

C₂×C₄²

C₂²×D₈₃

yes

characteristic

163

#106

—

166

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

166

—

167

#103

—

166

—

168

C₄×C₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

332

—

173

C₂×Q₈

—

332

—

174

C₂×Q₈

—

332

—

175

C₂×Q₈

—

166

—

176

C₂×Q₈

Dic₃₃₂

yes

complemented

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

332

—

180

C₂²×C₄

C₂×C₂²⋊D₈₃

yes

characteristic

181

C₂²×C₄

C₂×D₃₃₂

yes

characteristic

182

C₂²×C₄

#13050590

yes

characteristic

183

Q₁₆

—

332

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

332

—

189

C₂×C₈

—

332

—

190

C₂×C₈

—

166

—

191

C₂×C₈

#13050577

yes

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

332

—

195

C₄⋊C₄

—

332

—

196

C₄⋊C₄

—

166

—

197

C₄⋊C₄

—

166

—

198

C₄²

—

199

C₄²

—

200

C₄²

D₄×D₈₃

yes

—

201

C₄²

D₄×D₈₃

yes

—

202

C₂³

#14581766

yes

characteristic

203

Q₈

—

204

Q₈

—

205

Q₈

—

332

—

206

Q₈

—

664

—

207

Q₈

—

664

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

332

—

215

C₂×C₄

—

664

—

216

C₂×C₄

#14581760

yes

characteristic

217

C₂×C₄

#14581762

yes

—

218

C₂×C₄

#14581765

yes

—

219

C₂×C₄

#14581788

yes

characteristic

220

C₂×C₄

C₂×#13050577

yes

—

221

C₂×C₄

C₂×Dic₃₃₂

yes

characteristic

222

C₂×C₄

#14581814

yes

characteristic

223

C₂×C₄

#14581817

yes

—

224

C₂×C₄

#14581825

yes

—

225

C₈

—

226

C₈

—

227

C₈

—

332

—

228

C₂²

#19127610

yes

characteristic

229

C₂²

#19127901

yes

—

230

C₂²

#19127942

yes

characteristic

231

C₂²

#19127959

yes

characteristic

232

C₂²

#19127976

yes

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

664

—

237

C₄

#19127851

yes

—

238

C₄

#19127859

yes

—

239

C₄

#19127865

yes

—

240

C₄

#19128075

yes

characteristic

241

C₄

#19128091

yes

characteristic

242

C₂

#24906833

yes

—

243

C₂

#24906957

yes

—

244

C₂

#24908473

yes

characteristic

245

C₂

#24908550

yes

characteristic

246

C₂

#24908584

yes

characteristic

	subgroup	G/H
center	C₂³	#14581766
commutator, cosocle	C₂×C₄²×C₈₃	C₂³
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₈₃×#1984	C₂
socle, prime radical	C₂³×C₈₃	#121
hypercenter	#1984	D₈₃
hypocenter	C₈₃	#10276
LCS	G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

subgroup

G/H

center

C₂³

#14581766

commutator, cosocle

C₂×C₄²×C₈₃

C₂³

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₈₃×#1984

C₂

C₂³×C₈₃

D₈₃

C₈₃

G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

N	H ≅ G/N	type
61. C₂×Q₈×C₈₃	Q₁₆	semidirect
129. C₈₃	#10276	semidirect
176. C₂×Q₈	Dic₃₃₂	semidirect

H ≅ G/N

type

61. C₂×Q₈×C₈₃

Q₁₆

semidirect

129. C₈₃

#10276

semidirect

176. C₂×Q₈

Dic₃₃₂

semidirect

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

subgroup	index
C₂×#19128081	2
C₂×#19127986	2
C₂×#19127448	2
#24905298	2
C₈₃×#1984	2
#10276	83

subgroup

index

C₈₃×#1984

Subgroups — #35307012

Conjugacy classes of subgroups

Complements

Maximal subgroups