Group #36453536 — subgroups

Subgroups — #36453536

Order 22784.

486 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 155 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	#26028630	C₂	1	1	yes	maximal, characteristic
2	#26020404	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151345	C₂	1	2	yes	maximal
4	C₂×#19151343	C₂	1	2	yes	maximal
5	C₈₉×#1767	C₂	1	1	yes	maximal, characteristic
6	C₂×#15668012	C₂²	1	1	yes	characteristic
7	C₂×#15668012	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊#10623494	—	2	2	no	—
9	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
10	#19151504	—	2	2	no	—
11	#19151504	—	2	1	no	—
12	#19151504	—	2	1	no	—
13	#19151464	C₄	1	4	yes	—
14	#19151345	—	2	4	no	—
15	#19151343	—	2	4	no	—
16	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
17	C₂×#97×C₈₉	—	2	1	no	—
18	C₄³×C₈₉	C₂²	1	1	yes	characteristic
19	#336×C₈₉	—	2	1	no	—
20	C₂²×Dic₁₇₈	—	2	1	no	—
21	C₂²×Dic₁₇₈	—	2	1	no	—
22	C₂²×#10623494	—	2	2	no	—
23	#15668012	—	2	2	no	—
24	#15668012	—	2	2	no	—
25	#15668012	—	2	2	no	—
26	#15668012	—	2	2	no	—
27	C₂×C₄⋊Dic₈₉	—	2	1	no	—
28	C₂×C₄⋊Dic₈₉	—	2	1	no	—
29	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
30	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
31	C₄⋊#10623494	—	2	2	no	—
32	C₄⋊#10623494	—	2	2	no	—
33	C₄⋊#10623494	—	4	4	no	—
34	#15667919	—	2	4	no	—
35	#15667919	—	2	4	no	—
36	C₂²×C₈×C₈₉	—	2	2	no	—
37	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₈₉	D₄	1	2	yes	—
39	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₈₉	—	2	2	no	—
43	C₄⋊C₈×C₈₉	D₄	1	4	yes	—
44	#97×C₈₉	—	4	2	no	—
45	C₂×Dic₁₇₈	—	4	2	no	—
46	C₂×Dic₁₇₈	—	4	1	no	—
47	C₂×Dic₁₇₈	—	4	1	no	—
48	C₂×Dic₁₇₈	—	4	2	no	—
49	C₂×Dic₁₇₈	—	4	1	no	—
50	C₂×Dic₁₇₈	—	4	2	no	—
51	C₂×Dic₁₇₈	—	4	1	no	—
52	C₂×Dic₁₇₈	—	4	2	no	—
53	C₂²×Dic₈₉	—	2	2	no	—
54	C₂²×Dic₈₉	—	2	2	no	—
55	C₂×#10623494	—	4	2	no	—
56	C₂×#10623494	—	4	4	no	—
57	C₄⋊Dic₈₉	—	2	4	no	—
58	C₄⋊Dic₈₉	—	2	4	no	—
59	C₄⋊Dic₈₉	—	4	2	no	—
60	C₄⋊Dic₈₉	—	4	1	no	—
61	C₄⋊Dic₈₉	—	4	1	no	—
62	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₈₉	—	2	4	no	—
68	C₂×C₈×C₈₉	—	4	2	no	—
69	C₂×C₈×C₈₉	—	4	2	no	—
70	C₄²×C₈₉	—	2	4	no	—
71	C₄²×C₈₉	—	2	2	no	—
72	C₄²×C₈₉	—	2	1	no	—
73	C₄²×C₈₉	—	2	2	no	—
74	C₄²×C₈₉	—	2	2	no	—
75	C₄²×C₈₉	—	2	1	no	—
76	C₄²×C₈₉	C₂×D₄	1	2	yes	—
77	C₄²×C₈₉	#41	1	2	yes	—
78	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₈₉	—	2	2	no	—
80	C₂×C₄×C₈₉	—	2	2	no	—
81	C₂×C₄×C₈₉	—	2	2	no	—
82	C₂×C₄×C₈₉	—	2	2	no	—
83	C₂×C₄×C₈₉	—	2	2	no	—
84	C₂×C₄×C₈₉	—	2	2	no	—
85	C₂×C₄×C₈₉	#101	1	4	yes	—
86	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
87	C₂×C₄×C₈₉	#121	1	2	yes	—
88	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
89	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
90	C₂×C₄×C₈₉	#135	1	2	yes	—
91	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
92	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
93	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
94	C₂×C₄×C₈₉	#137	1	2	yes	—
95	C₂×Dic₈₉	—	4	2	no	—
96	C₂×Dic₈₉	—	4	2	no	—
97	C₂×Dic₈₉	—	4	2	no	—
98	C₂×Dic₈₉	—	4	2	no	—
99	C₂×Dic₈₉	—	4	4	no	—
100	Dic₁₇₈	—	8	2	no	—
101	Dic₁₇₈	—	8	2	no	—
102	Dic₁₇₈	—	8	2	no	—
103	Dic₁₇₈	—	8	1	no	—
104	Dic₁₇₈	—	8	1	no	—
105	C₈×C₈₉	—	4	4	no	—
106	#10623494	—	8	2	no	—
107	C₂²×C₈₉	#390	1	1	yes	characteristic
108	C₂²×C₈₉	C₂×#101	1	2	yes	—
109	C₂²×C₈₉	#416	1	1	yes	characteristic
110	C₂²×C₈₉	#417	1	2	yes	—
111	C₂²×C₈₉	#417	1	1	yes	characteristic
112	C₄×C₈₉	—	2	4	no	—
113	C₄×C₈₉	—	2	2	no	—
114	C₄×C₈₉	—	4	2	no	—
115	C₄×C₈₉	#463	1	2	yes	—
116	C₄×C₈₉	#464	1	2	yes	—
117	C₄×C₈₉	#489	1	2	yes	—
118	C₄×C₈₉	#496	1	1	yes	characteristic
119	C₄×C₈₉	#497	1	1	yes	characteristic
120	Dic₈₉	—	8	2	no	—
121	Dic₈₉	—	8	2	no	—
122	#9708	—	89	1	no	maximal, Sylow
123	C₂×C₈₉	#1552	1	2	yes	—
124	C₂×C₈₉	#1561	1	2	yes	—
125	C₂×C₈₉	#1959	1	1	yes	characteristic
126	C₂×C₈₉	#1966	1	1	yes	characteristic
127	C₂×C₈₉	#1983	1	1	yes	characteristic
128	#2862	—	89	1	no	—
129	#1842	—	89	1	no	—
130	#1767	D₈₉	1	1	yes	characteristic
131	C₂×#332	—	89	2	no	—
132	C₂×#332	—	89	2	no	—
133	C₈₉	#9708	1	1	yes	characteristic, complemented, Sylow
134	C₂×C₄⋊Q₈	—	89	1	no	—
135	C₂×C₄⋊Q₈	—	89	1	no	—
136	C₂×C₄⋊C₈	—	89	2	no	—
137	C₂×C₄⋊C₈	—	178	2	no	—
138	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
139	C₂×#97	—	2	1	no	—
140	#391	—	178	2	no	—
141	#391	—	178	1	no	—
142	#391	—	178	1	no	—
143	#382	—	89	4	no	—
144	C₄³	C₂×D₈₉	1	1	yes	characteristic
145	#336	—	2	1	no	—
146	#332	—	178	4	no	—
147	#332	—	178	4	no	—
148	C₂²×Q₈	—	178	1	no	—
149	C₂²×Q₈	—	178	1	no	—
150	C₂²×C₈	—	2	2	no	—
151	C₂²×C₈	—	178	2	no	—
152	C₄⋊Q₈	—	178	2	no	—
153	C₄⋊Q₈	—	178	2	no	—
154	C₄⋊Q₈	—	178	2	no	—
155	C₄⋊Q₈	—	178	2	no	—
156	C₂×C₄⋊C₄	—	89	2	no	—
157	C₂×C₄⋊C₄	—	89	2	no	—
158	C₂×C₄⋊C₄	—	178	1	no	—
159	C₂×C₄⋊C₄	—	178	1	no	—
160	C₂×C₄²	C₄×D₈₉	1	2	yes	—
161	C₂×C₄²	D₃₅₆	1	2	yes	—
162	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
163	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
164	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
165	C₄⋊C₈	—	2	2	no	—
166	C₄⋊C₈	—	356	4	no	—
167	C₄⋊C₈	—	178	2	no	—
168	C₄⋊C₈	—	178	2	no	—
169	C₄⋊C₈	D₃₅₆	1	4	yes	—
170	#97	—	4	2	no	—
171	#95	—	178	4	no	—
172	#95	—	178	4	no	—
173	C₂×Q₈	—	356	2	no	—
174	C₂×Q₈	—	356	1	no	—
175	C₂×Q₈	—	356	1	no	—
176	C₂×Q₈	—	356	2	no	—
177	C₂×Q₈	—	356	1	no	—
178	C₂×Q₈	—	356	2	no	—
179	C₂×Q₈	—	356	1	no	—
180	C₂×Q₈	—	356	2	no	—
181	C₂²×C₄	—	178	2	no	—
182	C₂²×C₄	—	178	2	no	—
183	C₂²×C₄	#13083551	1	2	yes	—
184	C₂²×C₄	#13083551	1	2	yes	—
185	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
187	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
188	C₂×C₈	—	2	4	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	356	2	no	—
192	C₂×C₈	—	356	4	no	—
193	C₄⋊C₄	—	356	2	no	—
194	C₄⋊C₄	—	356	1	no	—
195	C₄⋊C₄	—	356	1	no	—
196	C₄⋊C₄	—	178	4	no	—
197	C₄⋊C₄	—	178	4	no	—
198	C₄²	—	2	2	no	—
199	C₄²	—	2	1	no	—
200	C₄²	—	2	2	no	—
201	C₄²	—	2	1	no	—
202	C₄²	—	2	2	no	—
203	C₄²	—	2	4	no	—
204	C₄²	C₂×D₃₅₆	1	2	yes	—
205	C₄²	#13083574	1	2	yes	—
206	C₂³	C₂×#13083551	1	1	yes	characteristic
207	Q₈	—	712	2	no	—
208	Q₈	—	712	1	no	—
209	Q₈	—	712	1	no	—
210	Q₈	—	712	2	no	—
211	Q₈	—	712	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	356	2	no	—
219	C₂×C₄	—	356	2	no	—
220	C₂×C₄	—	356	2	no	—
221	C₂×C₄	—	356	2	no	—
222	C₂×C₄	—	356	4	no	—
223	C₂×C₄	#15667930	1	4	yes	—
224	C₂×C₄	C₄×D₃₅₆	1	2	yes	—
225	C₂×C₄	#15667986	1	2	yes	—
226	C₂×C₄	#15668000	1	1	yes	characteristic
227	C₂×C₄	#15668009	1	1	yes	characteristic
228	C₂×C₄	#15668032	1	2	yes	—
229	C₂×C₄	#15668038	1	1	yes	characteristic
230	C₂×C₄	#15668040	1	2	yes	—
231	C₂×C₄	#15668043	1	1	yes	characteristic
232	C₂×C₄	#15668045	1	2	yes	—
233	C₈	—	4	4	no	—
234	C₈	—	712	2	no	—
235	C₂²	#19151500	1	1	yes	characteristic
236	C₂²	C₂×#15667930	1	2	yes	—
237	C₂²	#19151592	1	1	yes	characteristic
238	C₂²	#19151597	1	1	yes	characteristic
239	C₂²	#19151600	1	2	yes	—
240	C₄	—	2	4	no	—
241	C₄	—	2	2	no	—
242	C₄	—	4	2	no	—
243	C₄	—	712	2	no	—
244	C₄	—	712	2	no	—
245	C₄	#19151813	1	2	yes	—
246	C₄	#19151820	1	2	yes	—
247	C₄	#19151958	1	2	yes	—
248	C₄	#19151987	1	1	yes	characteristic
249	C₄	#19151992	1	1	yes	characteristic
250	C₂	#26018953	1	2	yes	—
251	C₂	#26018989	1	2	yes	—
252	C₂	#26021068	1	1	yes	characteristic
253	C₂	#26021096	1	1	yes	characteristic
254	C₂	#26021184	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26028630

C₂

yes

maximal, characteristic

#26020404

C₂

yes

maximal, characteristic

C₂×#19151345

C₂

yes

maximal

C₂×#19151343

C₂

yes

maximal

C₈₉×#1767

C₂

yes

maximal, characteristic

C₂×#15668012

C₂²

yes

characteristic

C₂×#15668012

C₂²

yes

characteristic

C₂×C₄⋊#10623494

—

C₂×C₄⋊#10623494

C₂²

yes

—

—

—

—

C₄

yes

—

#19151345

—

#19151343

—

C₂×C₄⋊C₈×C₈₉

C₂²

yes

—

C₂×#97×C₈₉

—

C₄³×C₈₉

C₂²

yes

characteristic

#336×C₈₉

—

C₂²×Dic₁₇₈

—

C₂²×Dic₁₇₈

—

—

—

—

—

—

C₂×C₄⋊Dic₈₉

—

C₂×C₄⋊Dic₈₉

—

C₂×C₄⋊Dic₈₉

C₂×C₄

yes

—

C₂×C₄⋊Dic₈₉

C₂×C₄

yes

—

—

—

—

—

—

C₂²×C₈×C₈₉

—

C₂×C₄²×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

D₄

yes

characteristic

C₂×C₄²×C₈₉

D₄

yes

characteristic

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

C₄⋊C₈×C₈₉

D₄

yes

—

#97×C₈₉

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

C₂×#10623494

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#101

yes

—

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

#121

yes

—

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

—

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₈₉

#137

yes

characteristic

C₂×C₄×C₈₉

#137

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

100

Dic₁₇₈

—

101

Dic₁₇₈

—

102

Dic₁₇₈

—

103

Dic₁₇₈

—

104

Dic₁₇₈

—

105

C₈×C₈₉

—

106

#10623494

—

107

C₂²×C₈₉

#390

yes

characteristic

108

C₂²×C₈₉

C₂×#101

yes

—

109

C₂²×C₈₉

#416

yes

characteristic

110

C₂²×C₈₉

#417

yes

—

111

C₂²×C₈₉

#417

yes

characteristic

112

C₄×C₈₉

—

113

C₄×C₈₉

—

114

C₄×C₈₉

—

115

C₄×C₈₉

#463

yes

—

116

C₄×C₈₉

#464

yes

—

117

C₄×C₈₉

#489

yes

—

118

C₄×C₈₉

#496

yes

characteristic

119

C₄×C₈₉

#497

yes

characteristic

120

Dic₈₉

—

121

Dic₈₉

—

122

#9708

—

maximal, Sylow

123

C₂×C₈₉

#1552

yes

—

124

C₂×C₈₉

#1561

yes

—

125

C₂×C₈₉

#1959

yes

characteristic

126

C₂×C₈₉

#1966

yes

characteristic

127

C₂×C₈₉

#1983

yes

characteristic

128

#2862

—

129

#1842

—

130

#1767

D₈₉

yes

characteristic

131

C₂×#332

—

132

C₂×#332

—

133

C₈₉

#9708

yes

characteristic, complemented, Sylow

134

C₂×C₄⋊Q₈

—

135

C₂×C₄⋊Q₈

—

136

C₂×C₄⋊C₈

—

137

C₂×C₄⋊C₈

—

178

—

138

C₂×C₄⋊C₈

C₂×D₈₉

yes

—

139

C₂×#97

—

140

#391

—

178

—

141

#391

—

178

—

142

#391

—

178

—

143

#382

—

144

C₄³

C₂×D₈₉

yes

characteristic

145

#336

—

146

#332

—

178

—

147

#332

—

178

—

148

C₂²×Q₈

—

178

—

149

C₂²×Q₈

—

178

—

150

C₂²×C₈

—

151

C₂²×C₈

—

178

—

152

C₄⋊Q₈

—

178

—

153

C₄⋊Q₈

—

178

—

154

C₄⋊Q₈

—

178

—

155

C₄⋊Q₈

—

178

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

178

—

159

C₂×C₄⋊C₄

—

178

—

160

C₂×C₄²

C₄×D₈₉

yes

—

161

C₂×C₄²

D₃₅₆

yes

—

162

C₂×C₄²

C₂²⋊D₈₉

yes

characteristic

163

C₂×C₄²

C₂²⋊D₈₉

yes

characteristic

164

C₂×C₄²

C₂²×D₈₉

yes

characteristic

165

C₄⋊C₈

—

166

C₄⋊C₈

—

356

—

167

C₄⋊C₈

—

178

—

168

C₄⋊C₈

—

178

—

169

C₄⋊C₈

D₃₅₆

yes

—

170

#97

—

171

#95

—

178

—

172

#95

—

178

—

173

C₂×Q₈

—

356

—

174

C₂×Q₈

—

356

—

175

C₂×Q₈

—

356

—

176

C₂×Q₈

—

356

—

177

C₂×Q₈

—

356

—

178

C₂×Q₈

—

356

—

179

C₂×Q₈

—

356

—

180

C₂×Q₈

—

356

—

181

C₂²×C₄

—

178

—

182

C₂²×C₄

—

178

—

183

C₂²×C₄

#13083551

yes

—

184

C₂²×C₄

#13083551

yes

—

185

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

186

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

187

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

356

—

192

C₂×C₈

—

356

—

193

C₄⋊C₄

—

356

—

194

C₄⋊C₄

—

356

—

195

C₄⋊C₄

—

356

—

196

C₄⋊C₄

—

178

—

197

C₄⋊C₄

—

178

—

198

C₄²

—

199

C₄²

—

200

C₄²

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

C₂×D₃₅₆

yes

—

205

C₄²

#13083574

yes

—

206

C₂³

C₂×#13083551

yes

characteristic

207

Q₈

—

712

—

208

Q₈

—

712

—

209

Q₈

—

712

—

210

Q₈

—

712

—

211

Q₈

—

712

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

356

—

219

C₂×C₄

—

356

—

220

C₂×C₄

—

356

—

221

C₂×C₄

—

356

—

222

C₂×C₄

—

356

—

223

C₂×C₄

#15667930

yes

—

224

C₂×C₄

C₄×D₃₅₆

yes

—

225

C₂×C₄

#15667986

yes

—

226

C₂×C₄

#15668000

yes

characteristic

227

C₂×C₄

#15668009

yes

characteristic

228

C₂×C₄

#15668032

yes

—

229

C₂×C₄

#15668038

yes

characteristic

230

C₂×C₄

#15668040

yes

—

231

C₂×C₄

#15668043

yes

characteristic

232

C₂×C₄

#15668045

yes

—

233

C₈

—

234

C₈

—

712

—

235

C₂²

#19151500

yes

characteristic

236

C₂²

C₂×#15667930

yes

—

237

C₂²

#19151592

yes

characteristic

238

C₂²

#19151597

yes

characteristic

239

C₂²

#19151600

yes

—

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

712

—

244

C₄

—

712

—

245

C₄

#19151813

yes

—

246

C₄

#19151820

yes

—

247

C₄

#19151958

yes

—

248

C₄

#19151987

yes

characteristic

249

C₄

#19151992

yes

characteristic

250

C₂

#26018953

yes

—

251

C₂

#26018989

yes

—

252

C₂

#26021068

yes

characteristic

253

C₂

#26021096

yes

characteristic

254

C₂

#26021184

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×#13083551
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1767	C₂
socle, prime radical	C₂³×C₈₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1767	D₈₉
hypocenter	C₈₉	#9708
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

subgroup

G/H

center

C₂³

C₂×#13083551

commutator

C₂²×C₄×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1767

C₂

socle, prime radical

C₂³×C₈₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

N	H ≅ G/N	type
133. C₈₉	#9708	semidirect

H ≅ G/N

type

133. C₈₉

#9708

semidirect

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

subgroup	index
#26028630	2
#26020404	2
C₂×#19151345	2
C₂×#19151343	2
C₈₉×#1767	2
#9708	89

subgroup

index

C₈₉×#1767

Subgroups — #36453536

Conjugacy classes of subgroups

Complements

Maximal subgroups