Group #26031626 — subgroups

Subgroups — #26031626

Order 11392.

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

normal subgroups only

This group has 348 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	#19152155	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152132	C₂	1	1	yes	maximal, characteristic
3	#19151906	C₂	1	2	yes	maximal, complemented
4	#19151894	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151889	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151856	C₂	1	2	yes	maximal, complemented
7	#19151844	C₂	1	2	yes	maximal
8	#19151821	C₂	1	2	yes	maximal, complemented
9	#19151809	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151804	C₂	1	1	yes	maximal, characteristic, complemented
11	#423×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Dic₃₅₆	C₂²	1	2	yes	—
13	C₂×#13083563	C₂²	1	2	yes	—
14	#15668012	C₂²	1	1	yes	characteristic
15	#15668012	C₂²	1	1	yes	characteristic
16	#15668006	—	2	1	no	—
17	#15668004	—	2	1	no	—
18	#15668004	C₂²	1	1	yes	characteristic
19	#15668000	C₂²	1	1	yes	characteristic
20	#15667995	—	2	1	no	—
21	#15667991	—	2	1	no	—
22	#15667991	C₂²	1	1	yes	characteristic
23	#15667991	C₂²	1	2	yes	—
24	#15667986	C₂²	1	1	yes	characteristic
25	C₄×Dic₁₇₈	—	2	1	no	—
26	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
27	C₄×Dic₁₇₈	C₂²	1	2	yes	—
28	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊D₈₉	—	2	1	no	—
30	#15667971	—	2	1	no	—
31	#15667969	—	2	1	no	—
32	#15667946	C₂²	1	2	yes	—
33	#15667944	C₂²	1	2	yes	—
34	#15667937	C₂²	1	2	yes	—
35	#15667937	C₂²	1	2	yes	—
36	#15667937	C₂²	1	2	yes	—
37	#15667934	C₂²	1	2	yes	—
38	C₂×M₁₆×C₈₉	C₂²	1	2	yes	—
39	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
42	C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
43	C₂×Dic₁₇₈	—	2	1	no	—
44	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
45	C₂×Dic₁₇₈	C₂³	1	2	yes	—
46	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
47	C₂×C₂²⋊D₈₉	—	2	1	no	—
48	C₂×C₄×D₈₉	—	2	1	no	—
49	Dic₃₅₆	—	4	2	no	—
50	#13083563	—	4	2	no	—
51	C₄⋊Dic₈₉	—	2	1	no	—
52	C₄⋊Dic₈₉	—	2	1	no	—
53	C₄⋊Dic₈₉	—	2	1	no	—
54	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
55	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
56	C₄⋊Dic₈₉	C₂³	1	2	yes	—
57	#13083553	—	2	1	no	—
58	#13083553	—	2	1	no	—
59	#13083553	—	2	1	no	—
60	#13083553	—	2	2	no	—
61	#13083553	—	2	2	no	—
62	#13083553	—	2	1	no	—
63	C₂²⋊Dic₈₉	—	2	2	no	—
64	C₂²⋊Dic₈₉	—	2	1	no	—
65	#13083551	—	2	1	no	—
66	#13083551	—	2	1	no	—
67	#13083551	—	2	1	no	—
68	#13083551	—	2	1	no	—
69	C₄×Dic₈₉	—	2	1	no	—
70	C₄×Dic₈₉	—	2	2	no	—
71	C₂²×C₄×C₈₉	D₄	1	1	yes	characteristic
72	C₂²×C₄×C₈₉	D₄	1	1	yes	characteristic
73	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
74	M₁₆×C₈₉	—	4	2	no	—
75	C₂×C₈×C₈₉	C₂³	1	2	yes	—
76	C₂×C₈×C₈₉	C₂³	1	2	yes	—
77	C₄²×C₈₉	D₄	1	1	yes	characteristic
78	C₄²×C₈₉	D₄	1	1	yes	characteristic
79	C₄²×C₈₉	C₂³	1	1	yes	characteristic
80	C₄²×C₈₉	C₂³	1	1	yes	characteristic
81	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×D₈₉	—	2	1	no	—
83	C₂×C₄×C₈₉	—	2	2	no	—
84	C₂×C₄×C₈₉	—	2	1	no	—
85	C₂×C₄×C₈₉	—	2	1	no	—
86	C₂×C₄×C₈₉	—	4	1	no	—
87	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
92	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
93	C₂²⋊D₈₉	—	4	2	no	—
94	C₂×Dic₈₉	—	2	1	no	—
95	C₂×Dic₈₉	—	2	1	no	—
96	C₂×Dic₈₉	—	2	2	no	—
97	C₂×Dic₈₉	—	2	2	no	—
98	C₂×Dic₈₉	—	2	1	no	—
99	D₃₅₆	—	2	1	no	—
100	D₃₅₆	—	2	1	no	—
101	C₄×D₈₉	—	4	2	no	—
102	Dic₁₇₈	—	2	2	no	—
103	Dic₁₇₈	—	2	1	no	—
104	Dic₁₇₈	—	2	1	no	—
105	Dic₁₇₈	—	2	2	no	—
106	Dic₁₇₈	—	4	2	no	—
107	C₈×C₈₉	—	2	2	no	—
108	C₈×C₈₉	—	2	2	no	—
109	C₂²×C₈₉	—	2	1	no	—
110	C₂²×C₈₉	—	2	1	no	—
111	C₂²×C₈₉	—	2	1	no	—
112	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
113	C₂×D₈₉	—	4	1	no	—
114	C₂×D₈₉	—	4	1	no	—
115	C₂×D₈₉	—	4	1	no	—
116	C₄×C₈₉	—	2	1	no	—
117	C₄×C₈₉	—	2	1	no	—
118	C₄×C₈₉	—	2	1	no	—
119	C₄×C₈₉	—	2	1	no	—
120	C₄×C₈₉	#137	1	2	yes	—
121	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
122	C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
123	Dic₈₉	—	4	2	no	—
124	Dic₈₉	—	4	1	no	—
125	Dic₈₉	—	4	1	no	—
126	Dic₈₉	—	4	2	no	—
127	Dic₈₉	—	4	1	no	—
128	C₂×C₈₉	—	4	1	no	—
129	C₂×C₈₉	#537	1	1	yes	characteristic
130	C₂×C₈₉	C₂×#137	1	1	yes	characteristic
131	C₂×C₈₉	#575	1	1	yes	characteristic
132	D₈₉	—	8	1	no	—
133	#3252	—	89	1	no	maximal, Sylow
134	C₈₉	#3252	1	1	yes	characteristic, complemented, Sylow
135	#533	—	89	1	no	—
136	#529	—	89	1	no	—
137	#479	—	89	2	no	—
138	#477	—	89	1	no	—
139	#476	—	89	1	no	—
140	#470	—	89	2	no	—
141	#468	—	89	2	no	—
142	#464	—	89	2	no	—
143	#462	—	89	1	no	—
144	#461	—	89	1	no	—
145	#423	D₈₉	1	1	yes	characteristic, complemented
146	C₂×Q₁₆	—	89	2	no	—
147	C₂×SD₁₆	—	89	2	no	—
148	C₂×M₁₆	C₂×D₈₉	1	2	yes	—
149	C₄⋊Q₈	—	89	1	no	—
150	C₄⋊Q₈	—	89	1	no	—
151	#126	—	178	1	no	—
152	#125	—	89	1	no	—
153	#125	—	178	1	no	—
154	#124	—	89	1	no	—
155	#123	—	178	1	no	—
156	C₂²⋊Q₈	—	89	1	no	—
157	C₂²⋊Q₈	—	89	2	no	—
158	C₂²⋊Q₈	—	178	1	no	—
159	#121	—	89	1	no	—
160	C₄×Q₈	—	89	1	no	—
161	C₄×Q₈	—	89	2	no	—
162	C₄×Q₈	—	178	1	no	—
163	C₄×D₄	—	89	1	no	—
164	C₄×D₄	—	178	1	no	—
165	#117	—	178	1	no	—
166	#117	—	178	1	no	—
167	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic
168	#107	—	89	2	no	—
169	#106	—	89	2	no	—
170	C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
171	C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
172	C₄⋊C₈	C₂×D₈₉	1	2	yes	—
173	#103	—	89	2	no	—
174	#103	—	89	2	no	—
175	#103	—	89	2	no	—
176	#102	—	89	2	no	—
177	C₂×Q₈	—	89	1	no	—
178	C₂×Q₈	—	89	2	no	—
179	C₂×Q₈	—	178	1	no	—
180	C₂×D₄	—	89	1	no	—
181	C₂×D₄	—	178	1	no	—
182	C₂²×C₄	—	178	1	no	—
183	C₂²×C₄	D₃₅₆	1	1	yes	characteristic
184	C₂²×C₄	D₃₅₆	1	1	yes	characteristic
185	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
186	Q₁₆	—	356	2	no	—
187	SD₁₆	—	356	2	no	—
188	M₁₆	—	4	2	no	—
189	C₂×C₈	C₂²×D₈₉	1	2	yes	—
190	C₂×C₈	C₂²×D₈₉	1	2	yes	—
191	C₄⋊C₄	—	89	2	no	—
192	C₄⋊C₄	—	89	1	no	—
193	C₄⋊C₄	—	89	1	no	—
194	C₄⋊C₄	—	178	1	no	—
195	C₄⋊C₄	—	178	1	no	—
196	C₄⋊C₄	—	178	1	no	—
197	C₄⋊C₄	—	178	1	no	—
198	C₄⋊C₄	—	178	1	no	—
199	C₄⋊C₄	—	178	2	no	—
200	C₄⋊C₄	—	178	1	no	—
201	C₄⋊C₄	—	178	2	no	—
202	C₄⋊C₄	—	178	1	no	—
203	C₂²⋊C₄	—	178	2	no	—
204	C₂²⋊C₄	—	178	1	no	—
205	C₂²⋊C₄	—	178	1	no	—
206	C₂²⋊C₄	—	178	1	no	—
207	C₂²⋊C₄	—	178	1	no	—
208	C₂²⋊C₄	—	178	1	no	—
209	C₄²	—	178	1	no	—
210	C₄²	—	178	2	no	—
211	C₄²	D₃₅₆	1	1	yes	characteristic
212	C₄²	D₃₅₆	1	1	yes	characteristic
213	C₄²	C₂²×D₈₉	1	1	yes	characteristic
214	C₄²	C₂²×D₈₉	1	1	yes	characteristic
215	C₂³	—	178	1	no	—
216	C₂³	C₂×D₃₅₆	1	1	yes	characteristic
217	Q₈	—	356	2	no	—
218	Q₈	—	178	2	no	—
219	Q₈	—	178	1	no	—
220	Q₈	—	178	1	no	—
221	Q₈	—	178	2	no	—
222	D₄	—	356	2	no	—
223	D₄	—	178	1	no	—
224	D₄	—	178	1	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	356	2	no	—
230	C₂×C₄	—	178	1	no	—
231	C₂×C₄	—	178	1	no	—
232	C₂×C₄	—	178	2	no	—
233	C₂×C₄	—	178	2	no	—
234	C₂×C₄	—	178	1	no	—
235	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
236	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
237	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
238	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
239	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
240	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
241	C₈	—	2	2	no	—
242	C₈	—	2	2	no	—
243	C₂²	—	2	1	no	—
244	C₂²	—	2	1	no	—
245	C₂²	—	2	1	no	—
246	C₂²	—	356	1	no	—
247	C₂²	—	356	1	no	—
248	C₂²	—	356	1	no	—
249	C₂²	C₂²×D₃₅₆	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	1	no	—
253	C₄	—	2	1	no	—
254	C₄	—	356	1	no	—
255	C₄	—	356	1	no	—
256	C₄	—	356	2	no	—
257	C₄	—	356	1	no	—
258	C₄	—	356	2	no	—
259	C₄	#15668045	1	2	yes	—
260	C₄	#15668057	1	1	yes	characteristic
261	C₄	#15668060	1	1	yes	characteristic
262	C₂	—	4	1	no	—
263	C₂	—	712	1	no	—
264	C₂	#19152179	1	1	yes	characteristic
265	C₂	C₂×#15668045	1	1	yes	characteristic
266	C₂	#19152398	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19152155

C₂

yes

maximal, characteristic, complemented

#19152132

C₂

yes

maximal, characteristic

#19151906

C₂

yes

maximal, complemented

#19151894

C₂

yes

maximal, characteristic, complemented

#19151889

C₂

yes

maximal, characteristic, complemented

#19151856

C₂

yes

maximal, complemented

#19151844

C₂

yes

maximal

#19151821

C₂

yes

maximal, complemented

#19151809

C₂

yes

maximal, characteristic, complemented

#19151804

C₂

yes

maximal, characteristic, complemented

#423×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₃₅₆

C₂²

yes

—

C₂×#13083563

C₂²

yes

—

#15668012

C₂²

yes

characteristic

#15668012

C₂²

yes

—

—

C₂²

yes

characteristic

#15668000

C₂²

yes

—

—

C₂²

yes

characteristic

#15667991

C₂²

yes

—

#15667986

C₂²

yes

characteristic

C₄×Dic₁₇₈

—

C₄×Dic₁₇₈

C₂²

yes

characteristic

C₄×Dic₁₇₈

C₂²

yes

—

C₄×D₃₅₆

C₂²

yes

characteristic

C₄×C₂²⋊D₈₉

—

#15667971

—

#15667969

—

#15667946

C₂²

yes

—

#15667944

C₂²

yes

—

#15667937

C₂²

yes

—

#15667937

C₂²

yes

—

#15667937

C₂²

yes

—

#15667934

C₂²

yes

—

C₂×M₁₆×C₈₉

C₂²

yes

—

C₂×C₄²×C₈₉

C₂²

yes

characteristic

C₄⋊C₈×C₈₉

C₂²

yes

characteristic

C₄⋊C₈×C₈₉

C₂²

yes

characteristic

C₄⋊C₈×C₈₉

C₂²

yes

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

C₂³

yes

characteristic

C₂×Dic₁₇₈

C₂³

yes

—

C₂×D₃₅₆

C₂³

yes

characteristic

C₂×C₂²⋊D₈₉

—

C₂×C₄×D₈₉

—

Dic₃₅₆

—

#13083563

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

C₂³

yes

characteristic

C₄⋊Dic₈₉

C₂³

yes

characteristic

C₄⋊Dic₈₉

C₂³

yes

—

—

—

—

—

—

—

C₂²⋊Dic₈₉

—

C₂²⋊Dic₈₉

—

—

—

—

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

D₄

yes

characteristic

C₂²×C₄×C₈₉

D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂³

yes

characteristic

M₁₆×C₈₉

—

C₂×C₈×C₈₉

C₂³

yes

—

C₂×C₈×C₈₉

C₂³

yes

—

C₄²×C₈₉

D₄

yes

characteristic

C₄²×C₈₉

D₄

yes

characteristic

C₄²×C₈₉

C₂³

yes

characteristic

C₄²×C₈₉

C₂³

yes

characteristic

C₂³×C₈₉

C₂×D₄

yes

characteristic

C₂²×D₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂⁴

yes

characteristic

C₂²⋊D₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

D₃₅₆

—

100

D₃₅₆

—

101

C₄×D₈₉

—

102

Dic₁₇₈

—

103

Dic₁₇₈

—

104

Dic₁₇₈

—

105

Dic₁₇₈

—

106

Dic₁₇₈

—

107

C₈×C₈₉

—

108

C₈×C₈₉

—

109

C₂²×C₈₉

—

110

C₂²×C₈₉

—

111

C₂²×C₈₉

—

112

C₂²×C₈₉

C₂²×D₄

yes

characteristic

113

C₂×D₈₉

—

114

C₂×D₈₉

—

115

C₂×D₈₉

—

116

C₄×C₈₉

—

117

C₄×C₈₉

—

118

C₄×C₈₉

—

119

C₄×C₈₉

—

120

C₄×C₈₉

#137

yes

—

121

C₄×C₈₉

H(5,𝔽₂)

yes

characteristic

122

C₄×C₈₉

2₋¹⁺⁴

yes

characteristic

123

Dic₈₉

—

124

Dic₈₉

—

125

Dic₈₉

—

126

Dic₈₉

—

127

Dic₈₉

—

128

C₂×C₈₉

—

129

C₂×C₈₉

#537

yes

characteristic

130

C₂×C₈₉

C₂×#137

yes

characteristic

131

C₂×C₈₉

#575

yes

characteristic

132

D₈₉

—

133

#3252

—

maximal, Sylow

134

C₈₉

#3252

yes

characteristic, complemented, Sylow

135

#533

—

136

#529

—

137

#479

—

138

#477

—

139

#476

—

140

#470

—

141

#468

—

142

#464

—

143

#462

—

144

#461

—

145

#423

D₈₉

yes

characteristic, complemented

146

C₂×Q₁₆

—

147

C₂×SD₁₆

—

148

C₂×M₁₆

C₂×D₈₉

yes

—

149

C₄⋊Q₈

—

150

C₄⋊Q₈

—

151

#126

—

178

—

152

#125

—

153

#125

—

178

—

154

#124

—

155

#123

—

178

—

156

C₂²⋊Q₈

—

157

C₂²⋊Q₈

—

158

C₂²⋊Q₈

—

178

—

159

#121

—

160

C₄×Q₈

—

161

C₄×Q₈

—

162

C₄×Q₈

—

178

—

163

C₄×D₄

—

164

C₄×D₄

—

178

—

165

#117

—

178

—

166

#117

—

178

—

167

C₂×C₄²

C₂×D₈₉

yes

characteristic

168

#107

—

169

#106

—

170

C₄⋊C₈

C₂×D₈₉

yes

characteristic

171

C₄⋊C₈

C₂×D₈₉

yes

characteristic

172

C₄⋊C₈

C₂×D₈₉

yes

—

173

#103

—

174

#103

—

175

#103

—

176

#102

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

178

—

180

C₂×D₄

—

181

C₂×D₄

—

178

—

182

C₂²×C₄

—

178

—

183

C₂²×C₄

D₃₅₆

yes

characteristic

184

C₂²×C₄

D₃₅₆

yes

characteristic

185

C₂²×C₄

C₂²×D₈₉

yes

characteristic

186

Q₁₆

—

356

—

187

SD₁₆

—

356

—

188

M₁₆

—

189

C₂×C₈

C₂²×D₈₉

yes

—

190

C₂×C₈

C₂²×D₈₉

yes

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

178

—

195

C₄⋊C₄

—

178

—

196

C₄⋊C₄

—

178

—

197

C₄⋊C₄

—

178

—

198

C₄⋊C₄

—

178

—

199

C₄⋊C₄

—

178

—

200

C₄⋊C₄

—

178

—

201

C₄⋊C₄

—

178

—

202

C₄⋊C₄

—

178

—

203

C₂²⋊C₄

—

178

—

204

C₂²⋊C₄

—

178

—

205

C₂²⋊C₄

—

178

—

206

C₂²⋊C₄

—

178

—

207

C₂²⋊C₄

—

178

—

208

C₂²⋊C₄

—

178

—

209

C₄²

—

178

—

210

C₄²

—

178

—

211

C₄²

D₃₅₆

yes

characteristic

212

C₄²

D₃₅₆

yes

characteristic

213

C₄²

C₂²×D₈₉

yes

characteristic

214

C₄²

C₂²×D₈₉

yes

characteristic

215

C₂³

—

178

—

216

C₂³

C₂×D₃₅₆

yes

characteristic

217

Q₈

—

356

—

218

Q₈

—

178

—

219

Q₈

—

178

—

220

Q₈

—

178

—

221

Q₈

—

178

—

222

D₄

—

356

—

223

D₄

—

178

—

224

D₄

—

178

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

356

—

230

C₂×C₄

—

178

—

231

C₂×C₄

—

178

—

232

C₂×C₄

—

178

—

233

C₂×C₄

—

178

—

234

C₂×C₄

—

178

—

235

C₂×C₄

C₂×D₃₅₆

yes

characteristic

236

C₂×C₄

C₂×D₃₅₆

yes

characteristic

237

C₂×C₄

C₂×D₃₅₆

yes

characteristic

238

C₂×C₄

C₂×D₃₅₆

yes

characteristic

239

C₂×C₄

C₂×D₃₅₆

yes

characteristic

240

C₂×C₄

C₂³×D₈₉

yes

characteristic

241

C₈

—

242

C₈

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

356

—

247

C₂²

—

356

—

248

C₂²

—

356

—

249

C₂²

C₂²×D₃₅₆

yes

characteristic

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

356

—

255

C₄

—

356

—

256

C₄

—

356

—

257

C₄

—

356

—

258

C₄

—

356

—

259

C₄

#15668045

yes

—

260

C₄

#15668057

yes

characteristic

261

C₄

#15668060

yes

characteristic

262

C₂

—

263

C₂

—

712

—

264

C₂

#19152179

yes

characteristic

265

C₂

C₂×#15668045

yes

characteristic

266

C₂

#19152398

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×D₃₅₆
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#423×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	#15667986	C₂²
hypercenter	#423	D₈₉
hypocenter	C₈₉	#3252
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂²

C₂²×D₃₅₆

commutator, cosocle

C₂×C₄×C₈₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₈₉

Fitting

#423×C₈₉

C₂

socle

C₂²×C₈₉

C₂²×D₄

C₂²

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
1. #19152155	C₂	semidirect
3. #19151906	C₂	semidirect
4. #19151894	C₂	semidirect
5. #19151889	C₂	semidirect
6. #19151856	C₂	semidirect
8. #19151821	C₂	semidirect
9. #19151809	C₂	semidirect
10. #19151804	C₂	semidirect
11. #423×C₈₉	C₂	semidirect
134. C₈₉	#3252	semidirect
145. #423	D₈₉	semidirect

H ≅ G/N

type

1. #19152155

C₂

semidirect

3. #19151906

C₂

semidirect

4. #19151894

C₂

semidirect

5. #19151889

C₂

semidirect

6. #19151856

C₂

semidirect

8. #19151821

C₂

semidirect

9. #19151809

C₂

semidirect

10. #19151804

C₂

semidirect

11. #423×C₈₉

C₂

semidirect

134. C₈₉

#3252

semidirect

145. #423

D₈₉

semidirect

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

subgroup	index
#19152155	2
#19152132	2
#19151906	2
#19151894	2
#19151889	2
#19151856	2
#19151844	2
#19151821	2
#19151809	2
#19151804	2
#423×C₈₉	2
#3252	89

subgroup

index

#423×C₈₉

Subgroups — #26031626

Conjugacy classes of subgroups

Complements

Maximal subgroups