Group #26031472 — subgroups

Subgroups — #26031472

Order 11392.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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	C₄⋊Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152130	C₂	1	1	yes	maximal, characteristic
3	#19152005	C₂	1	2	yes	maximal, complemented
4	#19151956	C₂	1	2	yes	maximal, complemented
5	#19151930	C₂	1	2	yes	maximal, complemented
6	#19151910	C₂	1	2	yes	maximal
7	#19151894	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151890	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151888	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151654	C₂	1	1	yes	maximal, characteristic, complemented
11	#476×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×D₈₉	—	2	1	no	—
13	#15668012	C₂²	1	1	yes	characteristic
14	#15668011	—	2	1	no	—
15	#15668011	C₂²	1	2	yes	—
16	#15668010	—	2	1	no	—
17	#15668005	—	2	1	no	—
18	#15668003	C₂²	1	1	yes	characteristic
19	#15667999	C₂²	1	1	yes	characteristic
20	#15667994	—	2	1	no	—
21	#15667992	C₂²	1	1	yes	characteristic
22	#15667983	C₂²	1	1	yes	characteristic
23	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊D₈₉	—	2	1	no	—
25	#15667971	—	2	1	no	—
26	C₄⋊C₄×D₈₉	—	2	1	no	—
27	C₄⋊C₄×D₈₉	C₂²	1	2	yes	—
28	C₄²×D₈₉	C₂²	1	1	yes	characteristic
29	#15667946	C₂²	1	2	yes	—
30	#15667945	C₂²	1	2	yes	—
31	#15667943	C₂²	1	2	yes	—
32	C₄⋊#10623494	C₂²	1	1	yes	characteristic
33	#15667937	C₂²	1	2	yes	—
34	#15667935	C₂²	1	2	yes	—
35	#15667933	C₂²	1	2	yes	—
36	#15667924	C₂²	1	2	yes	—
37	#15667922	C₂²	1	2	yes	—
38	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
40	#106×C₈₉	C₂²	1	2	yes	—
41	C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
42	#102×C₈₉	C₂²	1	2	yes	—
43	C₂×Dic₁₇₈	—	2	1	no	—
44	C₂×Dic₁₇₈	—	2	2	no	—
45	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
46	Q₈×D₈₉	—	4	4	no	—
47	C₂×C₂²⋊D₈₉	—	2	1	no	—
48	C₂×C₄×D₈₉	—	2	2	no	—
49	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
50	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
51	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
52	C₂×#10623494	C₂³	1	2	yes	—
53	C₄⋊Dic₈₉	—	2	1	no	—
54	C₄⋊Dic₈₉	—	2	1	no	—
55	C₄⋊Dic₈₉	—	2	1	no	—
56	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
57	C₄⋊Dic₈₉	C₂³	1	2	yes	—
58	#13083553	—	2	1	no	—
59	#13083553	—	2	1	no	—
60	#13083553	—	2	2	no	—
61	#13083553	—	2	2	no	—
62	C₂²⋊Dic₈₉	—	2	1	no	—
63	C₂²⋊Dic₈₉	—	2	1	no	—
64	C₂²⋊Dic₈₉	—	2	1	no	—
65	#13083551	—	2	1	no	—
66	C₄×Dic₈₉	—	2	1	no	—
67	C₄×Dic₈₉	D₄	1	1	yes	characteristic
68	C₄×Dic₈₉	D₄	1	1	yes	characteristic
69	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
70	C₂×Q₈×C₈₉	—	2	1	no	—
71	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₈₉	—	2	1	no	—
73	C₂×C₈×C₈₉	C₂³	1	2	yes	—
74	C₄⋊C₄×C₈₉	—	2	1	no	—
75	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
76	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
77	C₂²⋊C₄×C₈₉	—	2	1	no	—
78	C₄²×C₈₉	C₂³	1	1	yes	characteristic
79	C₂³×C₈₉	—	2	1	no	—
80	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
81	Q₈×C₈₉	—	4	2	no	—
82	D₄×C₈₉	—	2	1	no	—
83	D₄×C₈₉	—	2	1	no	—
84	C₂×C₄×C₈₉	—	2	1	no	—
85	C₂×C₄×C₈₉	—	2	2	no	—
86	C₂×C₄×C₈₉	—	4	2	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	C₂⁴	1	1	yes	characteristic
90	C₂²⋊D₈₉	—	4	2	no	—
91	C₂×Dic₈₉	—	2	1	no	—
92	C₂×Dic₈₉	—	2	1	no	—
93	C₂×Dic₈₉	—	2	2	no	—
94	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
95	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
96	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
97	C₄×D₈₉	—	2	2	no	—
98	C₄×D₈₉	—	2	2	no	—
99	C₄×D₈₉	—	2	1	no	—
100	C₄×D₈₉	—	2	1	no	—
101	C₄×D₈₉	—	4	4	no	—
102	Dic₁₇₈	—	2	1	no	—
103	Dic₁₇₈	—	2	1	no	—
104	Dic₁₇₈	—	4	4	no	—
105	Dic₁₇₈	—	4	2	no	—
106	C₈×C₈₉	—	2	2	no	—
107	#10623494	—	2	2	no	—
108	C₂²×C₈₉	—	4	1	no	—
109	C₂²×C₈₉	—	4	1	no	—
110	C₂²×C₈₉	—	4	1	no	—
111	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
112	C₂×D₈₉	—	2	1	no	—
113	C₂×D₈₉	—	2	1	no	—
114	C₂×D₈₉	AGL(1,ℤ/8)	1	2	yes	—
115	C₄×C₈₉	—	2	1	no	—
116	C₄×C₈₉	—	4	2	no	—
117	C₄×C₈₉	—	4	1	no	—
118	C₄×C₈₉	#137	1	2	yes	—
119	C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
120	C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
121	Dic₈₉	—	2	1	no	—
122	Dic₈₉	—	2	1	no	—
123	Dic₈₉	—	2	1	no	—
124	Dic₈₉	—	4	1	no	—
125	Dic₈₉	—	4	2	no	—
126	Dic₈₉	—	4	1	no	—
127	C₂×C₈₉	—	8	1	no	—
128	C₂×C₈₉	#536	1	1	yes	characteristic
129	C₂×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
130	C₂×C₈₉	C₂×#137	1	1	yes	characteristic
131	D₈₉	—	2	2	no	—
132	#3238	—	89	1	no	maximal, Sylow
133	C₈₉	#3238	1	1	yes	characteristic, complemented, Sylow
134	C₂×C₄⋊Q₈	—	89	1	no	—
135	#529	—	89	1	no	—
136	#501	—	89	2	no	—
137	#489	—	89	2	no	—
138	#483	—	89	2	no	—
139	#480	—	89	2	no	—
140	#477	—	89	1	no	—
141	#477	—	89	1	no	—
142	#476	—	89	1	no	—
143	#476	D₈₉	1	1	yes	characteristic, complemented
144	#432	—	89	1	no	—
145	C₂²×Q₈	—	178	1	no	—
146	C₄⋊Q₈	—	89	2	no	—
147	C₄⋊Q₈	—	89	1	no	—
148	C₄⋊Q₈	—	178	1	no	—
149	C₄⋊Q₈	—	178	1	no	—
150	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
151	#126	—	178	1	no	—
152	#125	—	89	1	no	—
153	#124	—	89	1	no	—
154	#123	—	178	1	no	—
155	C₂²⋊Q₈	—	89	1	no	—
156	#121	—	89	1	no	—
157	C₄×Q₈	—	89	1	no	—
158	C₄×D₄	—	178	1	no	—
159	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
160	#117	—	178	1	no	—
161	C₂×C₄⋊C₄	—	89	2	no	—
162	C₂×C₄⋊C₄	—	178	1	no	—
163	C₂×C₄²	—	89	1	no	—
164	#107	—	89	2	no	—
165	#107	—	89	2	no	—
166	#106	—	89	2	no	—
167	#106	C₂×D₈₉	1	2	yes	—
168	C₄⋊C₈	—	89	1	no	—
169	C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
170	#103	—	89	2	no	—
171	#103	—	89	2	no	—
172	#102	—	89	2	no	—
173	#102	C₂×D₈₉	1	2	yes	—
174	C₂²⋊C₈	—	89	2	no	—
175	#97	—	89	2	no	—
176	C₂×Q₈	—	2	1	no	—
177	C₂×Q₈	—	89	1	no	—
178	C₂×Q₈	—	356	4	no	—
179	C₂×Q₈	—	178	2	no	—
180	C₂×Q₈	—	178	1	no	—
181	C₂×D₄	—	178	1	no	—
182	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	89	1	no	—
185	C₂²×C₄	—	89	1	no	—
186	C₂²×C₄	—	89	1	no	—
187	C₂²×C₄	—	178	2	no	—
188	C₂×C₈	—	89	2	no	—
189	C₂×C₈	C₂²×D₈₉	1	2	yes	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	89	2	no	—
192	C₄⋊C₄	—	89	1	no	—
193	C₄⋊C₄	—	178	2	no	—
194	C₄⋊C₄	—	178	2	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	1	no	—
200	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
201	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
202	C₂²⋊C₄	—	2	1	no	—
203	C₂²⋊C₄	—	178	1	no	—
204	C₂²⋊C₄	—	178	1	no	—
205	C₂²⋊C₄	—	178	1	no	—
206	C₂²⋊C₄	—	178	1	no	—
207	C₄²	—	89	1	no	—
208	C₄²	—	89	1	no	—
209	C₄²	—	89	1	no	—
210	C₄²	—	178	1	no	—
211	C₄²	C₂²×D₈₉	1	1	yes	characteristic
212	C₂³	—	2	1	no	—
213	C₂³	—	89	1	no	—
214	Q₈	—	4	2	no	—
215	Q₈	—	356	2	no	—
216	Q₈	—	356	4	no	—
217	Q₈	—	178	1	no	—
218	Q₈	—	178	1	no	—
219	D₄	—	2	1	no	—
220	D₄	—	2	1	no	—
221	D₄	—	356	2	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	89	1	no	—
226	C₂×C₄	—	89	1	no	—
227	C₂×C₄	—	89	1	no	—
228	C₂×C₄	—	356	4	no	—
229	C₂×C₄	—	178	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	—	178	1	no	—
236	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
237	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
238	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
239	C₈	—	2	2	no	—
240	C₈	—	178	2	no	—
241	C₂²	—	4	1	no	—
242	C₂²	—	4	1	no	—
243	C₂²	—	4	1	no	—
244	C₂²	—	89	2	no	—
245	C₂²	—	178	1	no	—
246	C₂²	—	178	1	no	—
247	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
248	C₄	—	2	1	no	—
249	C₄	—	4	1	no	—
250	C₄	—	4	2	no	—
251	C₄	—	356	1	no	—
252	C₄	—	356	2	no	—
253	C₄	—	356	1	no	—
254	C₄	—	178	1	no	—
255	C₄	—	178	1	no	—
256	C₄	—	178	1	no	—
257	C₄	#15668041	1	2	yes	—
258	C₄	#15668059	1	1	yes	characteristic
259	C₄	#15668060	1	1	yes	characteristic
260	C₂	—	8	1	no	—
261	C₂	—	178	2	no	—
262	C₂	#19152171	1	1	yes	characteristic
263	C₂	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
264	C₂	C₂×#15668041	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊Q₈×D₈₉

C₂

yes

maximal, characteristic, complemented

#19152130

C₂

yes

maximal, characteristic

#19152005

C₂

yes

maximal, complemented

#19151956

C₂

yes

maximal, complemented

#19151930

C₂

yes

maximal, complemented

#19151910

C₂

yes

maximal

#19151894

C₂

yes

maximal, characteristic, complemented

#19151890

C₂

yes

maximal, characteristic, complemented

#19151888

C₂

yes

maximal, characteristic, complemented

#19151654

C₂

yes

maximal, characteristic, complemented

#476×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₈₉

—

#15668012

C₂²

yes

characteristic

#15668011

—

#15668011

C₂²

yes

—

#15668010

—

#15668005

—

#15668003

C₂²

yes

characteristic

#15667999

C₂²

yes

characteristic

#15667994

—

#15667992

C₂²

yes

characteristic

#15667983

C₂²

yes

characteristic

C₄×Dic₁₇₈

C₂²

yes

characteristic

C₄×C₂²⋊D₈₉

—

#15667971

—

C₄⋊C₄×D₈₉

—

C₄⋊C₄×D₈₉

C₂²

yes

—

C₄²×D₈₉

C₂²

yes

characteristic

#15667946

C₂²

yes

—

#15667945

C₂²

yes

—

#15667943

C₂²

yes

—

C₄⋊#10623494

C₂²

yes

characteristic

#15667937

C₂²

yes

—

#15667935

C₂²

yes

—

#15667933

C₂²

yes

—

#15667924

C₂²

yes

—

#15667922

C₂²

yes

—

C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

C₄×D₄×C₈₉

C₂²

yes

characteristic

#106×C₈₉

C₂²

yes

—

C₄⋊C₈×C₈₉

C₂²

yes

characteristic

#102×C₈₉

C₂²

yes

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

C₂³

yes

characteristic

Q₈×D₈₉

—

C₂×C₂²⋊D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

D₄

yes

characteristic

C₂×C₄×D₈₉

D₄

yes

characteristic

C₂×C₄×D₈₉

C₂³

yes

characteristic

C₂×#10623494

C₂³

yes

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

C₂³

yes

characteristic

C₄⋊Dic₈₉

C₂³

yes

—

—

—

—

—

C₂²⋊Dic₈₉

—

C₂²⋊Dic₈₉

—

C₂²⋊Dic₈₉

—

#13083551

—

C₄×Dic₈₉

—

C₄×Dic₈₉

D₄

yes

characteristic

C₄×Dic₈₉

D₄

yes

characteristic

C₄×Dic₈₉

C₂³

yes

characteristic

C₂×Q₈×C₈₉

—

C₂×D₄×C₈₉

C₂³

yes

characteristic

C₂²×C₄×C₈₉

—

C₂×C₈×C₈₉

C₂³

yes

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

C₂³

yes

characteristic

C₄⋊C₄×C₈₉

C₂³

yes

—

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

C₂³

yes

characteristic

C₂³×C₈₉

—

C₂²×D₈₉

C₂×D₄

yes

characteristic

Q₈×C₈₉

—

D₄×C₈₉

—

D₄×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

C₂⁴

yes

characteristic

C₂²⋊D₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

C₂×D₄

yes

characteristic

C₂×Dic₈₉

C₂×D₄

yes

characteristic

C₂×Dic₈₉

C₂×D₄

yes

characteristic

C₄×D₈₉

—

C₄×D₈₉

—

C₄×D₈₉

—

100

C₄×D₈₉

—

101

C₄×D₈₉

—

102

Dic₁₇₈

—

103

Dic₁₇₈

—

104

Dic₁₇₈

—

105

Dic₁₇₈

—

106

C₈×C₈₉

—

107

#10623494

—

108

C₂²×C₈₉

—

109

C₂²×C₈₉

—

110

C₂²×C₈₉

—

111

C₂²×C₈₉

C₂²×D₄

yes

characteristic

112

C₂×D₈₉

—

113

C₂×D₈₉

—

114

C₂×D₈₉

AGL(1,ℤ/8)

yes

—

115

C₄×C₈₉

—

116

C₄×C₈₉

—

117

C₄×C₈₉

—

118

C₄×C₈₉

#137

yes

—

119

C₄×C₈₉

2₋¹⁺⁴

yes

characteristic

120

C₄×C₈₉

2₋¹⁺⁴

yes

characteristic

121

Dic₈₉

—

122

Dic₈₉

—

123

Dic₈₉

—

124

Dic₈₉

—

125

Dic₈₉

—

126

Dic₈₉

—

127

C₂×C₈₉

—

128

C₂×C₈₉

#536

yes

characteristic

129

C₂×C₈₉

C₂×AGL(1,ℤ/8)

yes

characteristic

130

C₂×C₈₉

C₂×#137

yes

characteristic

131

D₈₉

—

132

#3238

—

maximal, Sylow

133

C₈₉

#3238

yes

characteristic, complemented, Sylow

134

C₂×C₄⋊Q₈

—

135

#529

—

136

#501

—

137

#489

—

138

#483

—

139

#480

—

140

#477

—

141

#477

—

142

#476

—

143

#476

D₈₉

yes

characteristic, complemented

144

#432

—

145

C₂²×Q₈

—

178

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

178

—

149

C₄⋊Q₈

—

178

—

150

C₄⋊Q₈

C₂×D₈₉

yes

characteristic

151

#126

—

178

—

152

#125

—

153

#124

—

154

#123

—

178

—

155

C₂²⋊Q₈

—

156

#121

—

157

C₄×Q₈

—

158

C₄×D₄

—

178

—

159

C₄×D₄

C₂×D₈₉

yes

characteristic

160

#117

—

178

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

178

—

163

C₂×C₄²

—

164

#107

—

165

#107

—

166

#106

—

167

#106

C₂×D₈₉

yes

—

168

C₄⋊C₈

—

169

C₄⋊C₈

C₂×D₈₉

yes

characteristic

170

#103

—

171

#103

—

172

#102

—

173

#102

C₂×D₈₉

yes

—

174

C₂²⋊C₈

—

175

#97

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

356

—

179

C₂×Q₈

—

178

—

180

C₂×Q₈

—

178

—

181

C₂×D₄

—

178

—

182

C₂×D₄

C₂²×D₈₉

yes

characteristic

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

178

—

188

C₂×C₈

—

189

C₂×C₈

C₂²×D₈₉

yes

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

178

—

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

C₂²×D₈₉

yes

—

201

C₄⋊C₄

C₂²×D₈₉

yes

characteristic

202

C₂²⋊C₄

—

203

C₂²⋊C₄

—

178

—

204

C₂²⋊C₄

—

178

—

205

C₂²⋊C₄

—

178

—

206

C₂²⋊C₄

—

178

—

207

C₄²

—

208

C₄²

—

209

C₄²

—

210

C₄²

—

178

—

211

C₄²

C₂²×D₈₉

yes

characteristic

212

C₂³

—

213

C₂³

—

214

Q₈

—

215

Q₈

—

356

—

216

Q₈

—

356

—

217

Q₈

—

178

—

218

Q₈

—

178

—

219

D₄

—

220

D₄

—

221

D₄

—

356

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

356

—

229

C₂×C₄

—

178

—

230

C₂×C₄

—

178

—

231

C₂×C₄

—

178

—

232

C₂×C₄

—

178

—

233

C₂×C₄

—

178

—

234

C₂×C₄

—

178

—

235

C₂×C₄

—

178

—

236

C₂×C₄

D₄×D₈₉

yes

characteristic

237

C₂×C₄

D₄×D₈₉

yes

characteristic

238

C₂×C₄

C₂³×D₈₉

yes

characteristic

239

C₈

—

240

C₈

—

178

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

178

—

246

C₂²

—

178

—

247

C₂²

C₂×D₄×D₈₉

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

356

—

252

C₄

—

356

—

253

C₄

—

356

—

254

C₄

—

178

—

255

C₄

—

178

—

256

C₄

—

178

—

257

C₄

#15668041

yes

—

258

C₄

#15668059

yes

characteristic

259

C₄

#15668060

yes

characteristic

260

C₂

—

261

C₂

—

178

—

262

C₂

#19152171

yes

characteristic

263

C₂

AGL(1,ℤ/8)×D₈₉

yes

characteristic

264

C₂

C₂×#15668041

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#476×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	#15667983	C₂²
hypercenter	#476	D₈₉
hypocenter	C₈₉	#3238
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #476

subgroup

G/H

center

C₂²

C₂×D₄×D₈₉

commutator, cosocle

C₂×C₄×C₈₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₈₉

Fitting

#476×C₈₉

C₂

socle

C₂²×C₈₉

C₂²×D₄

C₂²

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #476

N	H ≅ G/N	type
1. C₄⋊Q₈×D₈₉	C₂	semidirect
3. #19152005	C₂	semidirect
4. #19151956	C₂	semidirect
5. #19151930	C₂	semidirect
7. #19151894	C₂	semidirect
8. #19151890	C₂	semidirect
9. #19151888	C₂	semidirect
10. #19151654	C₂	semidirect
11. #476×C₈₉	C₂	semidirect
133. C₈₉	#3238	semidirect
143. #476	D₈₉	semidirect

H ≅ G/N

type

1. C₄⋊Q₈×D₈₉

C₂

semidirect

3. #19152005

C₂

semidirect

4. #19151956

C₂

semidirect

5. #19151930

C₂

semidirect

7. #19151894

C₂

semidirect

8. #19151890

C₂

semidirect

9. #19151888

C₂

semidirect

10. #19151654

C₂

semidirect

11. #476×C₈₉

C₂

semidirect

133. C₈₉

#3238

semidirect

143. #476

D₈₉

semidirect

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

subgroup	index
C₄⋊Q₈×D₈₉	2
#19152130	2
#19152005	2
#19151956	2
#19151930	2
#19151910	2
#19151894	2
#19151890	2
#19151888	2
#19151654	2
#476×C₈₉	2
#3238	89

subgroup

index

C₄⋊Q₈×D₈₉

#476×C₈₉

Subgroups — #26031472

Conjugacy classes of subgroups

Complements

Maximal subgroups