Group #36469493 — subgroups

Subgroups — #36469493

Order 22784.

494 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 143 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×C₄×#13083557	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151379	C₂	1	2	yes	maximal
3	C₂×#19151375	C₂	1	2	yes	maximal, complemented
4	#26018334	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13083557	C₄	1	1	yes	characteristic
7	C₂²×#13083557	C₂²	1	1	yes	characteristic
8	C₂×C₄²×D₈₉	C₄	1	1	yes	characteristic
9	C₂×#15667952	C₂²	1	2	yes	—
10	C₄×#13083557	—	2	4	no	—
11	C₂×#15667922	C₄	1	1	yes	characteristic
12	C₂×#15667922	C₂²	1	1	yes	characteristic
13	C₂×C₄×#10623494	C₄	1	1	yes	characteristic
14	#19151379	C₄	1	8	yes	complemented
15	#19151375	—	2	4	no	—
16	C₂×M₃₂×C₈₉	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₈₉	—	2	1	no	—
19	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
20	C₂×#13083557	—	2	2	no	—
21	C₂×#13083557	—	2	2	no	—
22	C₂×#13083557	—	2	2	no	—
23	C₂×#13083557	—	2	2	no	—
24	C₂×#13083557	—	2	1	no	—
25	C₂×#13083557	—	2	1	no	—
26	C₂×#13083557	C₂×C₄	1	4	yes	—
27	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
28	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×Dic₈₉	—	2	1	no	—
30	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
31	C₄²×D₈₉	—	2	2	no	—
32	C₄²×D₈₉	—	2	2	no	—
33	#15667952	—	2	2	no	—
34	#15667952	C₂×C₄	1	4	yes	complemented
35	C₂×#13083549	—	2	2	no	—
36	#15667922	—	2	2	no	—
37	#15667922	D₄	1	4	yes	—
38	C₄×#10623494	—	2	2	no	—
39	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
41	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
42	M₃₂×C₈₉	—	2	2	no	—
43	M₃₂×C₈₉	C₂×C₄	1	4	yes	complemented
44	C₂×C₁₆×C₈₉	—	2	2	no	—
45	C₄×C₈×C₈₉	—	2	2	no	—
46	C₂³×D₈₉	M₁₆	1	1	yes	characteristic
47	C₂²×Dic₈₉	—	2	1	no	—
48	C₂²×Dic₈₉	M₁₆	1	1	yes	characteristic
49	C₂×C₄×D₈₉	—	2	1	no	—
50	C₂×C₄×D₈₉	—	2	1	no	—
51	C₂×C₄×D₈₉	—	2	1	no	—
52	C₂×C₄×D₈₉	—	2	1	no	—
53	C₂×C₄×D₈₉	—	2	4	no	—
54	C₂×C₄×D₈₉	—	4	4	no	—
55	C₂×C₄×D₈₉	C₄²	1	2	yes	—
56	C₂×C₄×D₈₉	M₁₆	1	2	yes	—
57	#13083557	—	2	8	no	—
58	#13083557	—	2	4	no	—
59	#13083557	—	2	4	no	—
60	C₂×#10623494	—	2	1	no	—
61	C₂×#10623494	—	2	1	no	—
62	C₂×#10623494	—	2	1	no	—
63	C₂×#10623494	—	2	1	no	—
64	C₂×#10623494	C₄²	1	2	yes	—
65	C₂×#10623494	C₂²⋊C₄	1	2	yes	—
66	C₄×Dic₈₉	—	2	4	no	—
67	C₄×Dic₈₉	—	2	1	no	—
68	C₄×Dic₈₉	C₂²⋊C₄	1	2	yes	—
69	#13083549	—	2	4	no	—
70	C₂²×C₄×C₈₉	—	2	1	no	—
71	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₈×C₈₉	—	2	1	no	—
73	C₂×C₈×C₈₉	—	2	1	no	—
74	C₂×C₈×C₈₉	M₁₆	1	2	yes	—
75	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
76	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
77	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
78	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
79	C₄²×C₈₉	—	2	1	no	—
80	C₄²×C₈₉	M₁₆	1	2	yes	—
81	C₁₆×C₈₉	—	2	4	no	—
82	C₂³×C₈₉	C₂×M₁₆	1	1	yes	characteristic
83	C₂²×D₈₉	—	2	1	no	—
84	C₂²×D₈₉	—	2	1	no	—
85	C₂²×D₈₉	—	4	2	no	—
86	C₂²×D₈₉	#97	1	2	yes	—
87	C₂×C₄×C₈₉	—	2	4	no	—
88	C₂×C₄×C₈₉	—	2	2	no	—
89	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
90	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
92	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
93	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
94	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
95	C₂×Dic₈₉	—	2	1	no	—
96	C₂×Dic₈₉	—	2	1	no	—
97	C₂×Dic₈₉	—	2	2	no	—
98	C₂×Dic₈₉	—	4	2	no	—
99	C₂×Dic₈₉	#97	1	2	yes	—
100	C₄×D₈₉	—	2	2	no	—
101	C₄×D₈₉	—	2	2	no	—
102	C₄×D₈₉	—	2	2	no	—
103	C₄×D₈₉	—	2	2	no	—
104	C₄×D₈₉	—	4	8	no	—
105	C₈×C₈₉	—	2	2	no	—
106	C₈×C₈₉	C₄×D₄	1	2	yes	—
107	C₈×C₈₉	C₄×D₄	1	2	yes	—
108	#10623494	—	2	2	no	—
109	#10623494	—	2	2	no	—
110	C₂²×C₈₉	—	2	2	no	—
111	C₂²×C₈₉	C₂×#97	1	1	yes	characteristic
112	C₂²×C₈₉	#407	1	1	yes	characteristic
113	C₂²×C₈₉	#432	1	1	yes	characteristic
114	C₂×D₈₉	—	2	2	no	—
115	C₂×D₈₉	—	4	2	no	—
116	C₂×D₈₉	—	4	2	no	—
117	C₂×D₈₉	—	4	2	no	—
118	C₄×C₈₉	—	2	4	no	—
119	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
120	C₄×C₈₉	C₄×M₁₆	1	1	yes	characteristic
121	C₄×C₈₉	#407	1	1	yes	characteristic
122	C₄×C₈₉	#432	1	1	yes	characteristic
123	Dic₈₉	—	2	2	no	—
124	Dic₈₉	—	4	2	no	—
125	#12607	—	89	1	no	maximal, Sylow
126	C₂×C₈₉	—	2	1	no	—
127	C₂×C₈₉	—	2	1	no	—
128	C₂×C₈₉	#1749	1	1	yes	characteristic
129	C₂×C₈₉	#2165	1	2	yes	—
130	D₈₉	—	4	2	no	—
131	C₂×C₄×M₁₆	—	89	1	no	—
132	C₂×#349	—	89	2	no	—
133	C₂×#347	—	89	2	no	—
134	#1376	—	89	1	no	—
135	#1376	D₈₉	1	1	yes	characteristic, complemented
136	C₈₉	#12607	1	1	yes	characteristic, complemented, Sylow
137	C₂²×M₁₆	—	89	1	no	—
138	C₂²×M₁₆	—	89	1	no	—
139	C₂²×C₄²	—	89	1	no	—
140	C₂×M₃₂	—	89	2	no	—
141	C₂×M₃₂	C₂×D₈₉	1	2	yes	—
142	C₄×M₁₆	—	178	4	no	—
143	C₂×#97	—	89	1	no	—
144	C₂×#97	—	89	1	no	—
145	C₂×C₄×C₈	—	89	1	no	—
146	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
147	#349	—	89	8	no	—
148	#347	—	178	4	no	—
149	C₂³×C₄	—	89	1	no	—
150	C₂³×C₄	—	178	1	no	—
151	C₂×M₁₆	—	89	4	no	—
152	C₂×M₁₆	—	178	2	no	—
153	C₂×M₁₆	—	178	2	no	—
154	C₂×M₁₆	—	178	2	no	—
155	C₂×M₁₆	—	178	2	no	—
156	C₂×M₁₆	—	178	1	no	—
157	C₂×M₁₆	—	178	1	no	—
158	C₂²×C₈	—	89	1	no	—
159	C₂²×C₈	—	89	1	no	—
160	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
161	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
162	C₂×C₄²	—	89	1	no	—
163	C₂×C₄²	—	178	2	no	—
164	C₂×C₄²	—	178	1	no	—
165	C₂×C₄²	—	178	2	no	—
166	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
167	M₃₂	—	2	2	no	—
168	M₃₂	—	89	4	no	—
169	M₃₂	—	178	2	no	—
170	M₃₂	C₄×D₈₉	1	4	yes	complemented
171	C₂×C₁₆	—	2	2	no	—
172	C₂×C₁₆	—	178	2	no	—
173	#97	—	89	4	no	—
174	#97	—	178	2	no	—
175	C₄×C₈	—	2	2	no	—
176	C₄×C₈	—	178	2	no	—
177	C₂⁴	—	89	1	no	—
178	C₂²×C₄	—	2	1	no	—
179	C₂²×C₄	—	89	1	no	—
180	C₂²×C₄	—	89	2	no	—
181	C₂²×C₄	—	89	2	no	—
182	C₂²×C₄	—	356	4	no	—
183	C₂²×C₄	—	178	4	no	—
184	C₂²×C₄	—	178	1	no	—
185	C₂²×C₄	—	178	1	no	—
186	C₂²×C₄	—	178	1	no	—
187	C₂²×C₄	—	178	1	no	—
188	C₂²×C₄	—	178	1	no	—
189	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
190	M₁₆	—	178	8	no	—
191	M₁₆	—	178	4	no	—
192	M₁₆	—	178	4	no	—
193	C₂×C₈	—	2	1	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	89	2	no	—
196	C₂×C₈	—	89	2	no	—
197	C₂×C₈	—	178	1	no	—
198	C₂×C₈	—	178	1	no	—
199	C₂×C₈	—	178	1	no	—
200	C₂×C₈	—	178	1	no	—
201	C₂×C₈	#13083557	1	2	yes	—
202	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
203	C₂×C₈	D₄×D₈₉	1	2	yes	—
204	C₂×C₈	#13083573	1	1	yes	characteristic
205	C₂×C₈	#13083575	1	1	yes	characteristic
206	C₄²	—	2	1	no	—
207	C₄²	—	89	2	no	—
208	C₄²	—	178	4	no	—
209	C₄²	—	178	1	no	—
210	C₄²	#13083557	1	2	yes	—
211	C₁₆	—	2	4	no	—
212	C₁₆	—	178	4	no	—
213	C₂³	—	89	2	no	—
214	C₂³	—	356	2	no	—
215	C₂³	—	178	1	no	—
216	C₂³	—	178	1	no	—
217	C₂³	M₁₆×D₈₉	1	1	yes	characteristic
218	C₂×C₄	—	2	4	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	89	2	no	—
221	C₂×C₄	—	356	8	no	—
222	C₂×C₄	—	356	2	no	—
223	C₂×C₄	—	178	2	no	—
224	C₂×C₄	—	178	1	no	—
225	C₂×C₄	—	178	1	no	—
226	C₂×C₄	—	178	2	no	—
227	C₂×C₄	—	178	2	no	—
228	C₂×C₄	—	178	2	no	—
229	C₂×C₄	—	178	2	no	—
230	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
231	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
232	C₂×C₄	#15667970	1	1	yes	characteristic
233	C₂×C₄	M₁₆×D₈₉	1	1	yes	characteristic
234	C₂×C₄	C₂×#13083557	1	1	yes	characteristic
235	C₂×C₄	C₂×#13083557	1	1	yes	characteristic
236	C₈	—	2	2	no	—
237	C₈	—	178	2	no	—
238	C₈	—	178	2	no	—
239	C₈	#15667972	1	2	yes	—
240	C₈	#15667974	1	2	yes	—
241	C₂²	—	2	2	no	—
242	C₂²	—	356	2	no	—
243	C₂²	—	356	2	no	—
244	C₂²	—	356	2	no	—
245	C₂²	—	178	2	no	—
246	C₂²	#97×D₈₉	1	1	yes	characteristic
247	C₂²	#19151560	1	1	yes	characteristic
248	C₂²	#19151654	1	1	yes	characteristic
249	C₄	—	2	4	no	—
250	C₄	—	356	2	no	—
251	C₄	—	178	2	no	—
252	C₄	#19151445	1	1	yes	characteristic
253	C₄	C₄×#13083557	1	1	yes	characteristic
254	C₄	#19151560	1	1	yes	characteristic
255	C₄	#19151654	1	1	yes	characteristic
256	C₂	—	2	1	no	—
257	C₂	—	2	1	no	—
258	C₂	—	356	2	no	—
259	C₂	#26020013	1	1	yes	characteristic
260	C₂	#26022063	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×#13083557

C₂

yes

maximal, characteristic

C₂×#19151379

C₂

yes

maximal

C₂×#19151375

C₂

yes

maximal, complemented

#26018334

C₂

yes

maximal, characteristic, complemented

C₈₉×#1376

C₂

yes

maximal, characteristic, complemented

C₂²×#13083557

C₄

yes

characteristic

C₂²×#13083557

C₂²

yes

characteristic

C₂×C₄²×D₈₉

C₄

yes

characteristic

C₂×#15667952

C₂²

yes

—

C₄×#13083557

—

C₂×#15667922

C₄

yes

characteristic

C₂×#15667922

C₂²

yes

characteristic

C₂×C₄×#10623494

C₄

yes

characteristic

#19151379

C₄

yes

complemented

#19151375

—

C₂×M₃₂×C₈₉

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

C₂²×C₄×D₈₉

—

C₂²×C₄×D₈₉

C₂×C₄

yes

—

—

—

—

—

—

C₂×C₄

yes

—

C₂²×#10623494

C₂×C₄

yes

characteristic

C₂²×#10623494

C₂×C₄

yes

characteristic

C₂×C₄×Dic₈₉

—

C₂×C₄×Dic₈₉

C₂×C₄

yes

characteristic

C₄²×D₈₉

—

C₄²×D₈₉

—

#15667952

—

#15667952

C₂×C₄

yes

—

—

D₄

yes

—

C₄×#10623494

—

C₂²×C₈×C₈₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₈₉

C₂³

yes

characteristic

C₂×C₄²×C₈₉

C₂×C₄

yes

characteristic

M₃₂×C₈₉

—

M₃₂×C₈₉

C₂×C₄

yes

complemented

C₂×C₁₆×C₈₉

—

C₄×C₈×C₈₉

—

C₂³×D₈₉

M₁₆

yes

characteristic

C₂²×Dic₈₉

—

C₂²×Dic₈₉

M₁₆

yes

characteristic

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

C₄²

yes

—

C₂×C₄×D₈₉

M₁₆

yes

—

—

—

—

—

—

—

—

C₄²

yes

—

C₂×#10623494

C₂²⋊C₄

yes

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

C₂²⋊C₄

yes

—

#13083549

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

M₁₆

yes

—

C₂×C₈×C₈₉

C₂²×C₄

yes

—

C₂×C₈×C₈₉

C₂×D₄

yes

—

C₂×C₈×C₈₉

yes

C₂×C₈×C₈₉

yes

C₄²×C₈₉

—

C₄²×C₈₉

M₁₆

yes

—

C₁₆×C₈₉

—

C₂³×C₈₉

C₂×M₁₆

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

#97

yes

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

#117

yes

characteristic

C₂×C₄×C₈₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₈₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₈₉

C₂×M₁₆

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

#97

yes

—

100

C₄×D₈₉

—

101

C₄×D₈₉

—

102

C₄×D₈₉

—

103

C₄×D₈₉

—

104

C₄×D₈₉

—

105

C₈×C₈₉

—

106

C₈×C₈₉

C₄×D₄

yes

—

107

C₈×C₈₉

C₄×D₄

yes

—

108

#10623494

—

109

#10623494

—

110

C₂²×C₈₉

—

111

C₂²×C₈₉

C₂×#97

yes

characteristic

112

C₂²×C₈₉

#407

yes

characteristic

113

C₂²×C₈₉

#432

yes

characteristic

114

C₂×D₈₉

—

115

C₂×D₈₉

—

116

C₂×D₈₉

—

117

C₂×D₈₉

—

118

C₄×C₈₉

—

119

C₄×C₈₉

C₄×C₂²⋊C₄

yes

characteristic

120

C₄×C₈₉

C₄×M₁₆

yes

characteristic

121

C₄×C₈₉

#407

yes

characteristic

122

C₄×C₈₉

#432

yes

characteristic

123

Dic₈₉

—

124

Dic₈₉

—

125

#12607

—

maximal, Sylow

126

C₂×C₈₉

—

127

C₂×C₈₉

—

128

C₂×C₈₉

#1749

yes

characteristic

129

C₂×C₈₉

#2165

yes

—

130

D₈₉

—

131

C₂×C₄×M₁₆

—

132

C₂×#349

—

133

C₂×#347

—

134

#1376

—

135

#1376

D₈₉

yes

characteristic, complemented

136

C₈₉

#12607

yes

characteristic, complemented, Sylow

137

C₂²×M₁₆

—

138

C₂²×M₁₆

—

139

C₂²×C₄²

—

140

C₂×M₃₂

—

141

C₂×M₃₂

C₂×D₈₉

yes

—

142

C₄×M₁₆

—

178

—

143

C₂×#97

—

144

C₂×#97

—

145

C₂×C₄×C₈

—

146

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

147

#349

—

148

#347

—

178

—

149

C₂³×C₄

—

150

C₂³×C₄

—

178

—

151

C₂×M₁₆

—

152

C₂×M₁₆

—

178

—

153

C₂×M₁₆

—

178

—

154

C₂×M₁₆

—

178

—

155

C₂×M₁₆

—

178

—

156

C₂×M₁₆

—

178

—

157

C₂×M₁₆

—

178

—

158

C₂²×C₈

—

159

C₂²×C₈

—

160

C₂²×C₈

C₄×D₈₉

yes

characteristic

161

C₂²×C₈

C₂²×D₈₉

yes

characteristic

162

C₂×C₄²

—

163

C₂×C₄²

—

178

—

164

C₂×C₄²

—

178

—

165

C₂×C₄²

—

178

—

166

C₂×C₄²

C₄×D₈₉

yes

characteristic

167

M₃₂

—

168

M₃₂

—

169

M₃₂

—

178

—

170

M₃₂

C₄×D₈₉

yes

complemented

171

C₂×C₁₆

—

172

C₂×C₁₆

—

178

—

173

#97

—

174

#97

—

178

—

175

C₄×C₈

—

176

C₄×C₈

—

178

—

177

C₂⁴

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

356

—

183

C₂²×C₄

—

178

—

184

C₂²×C₄

—

178

—

185

C₂²×C₄

—

178

—

186

C₂²×C₄

—

178

—

187

C₂²×C₄

—

178

—

188

C₂²×C₄

—

178

—

189

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

190

M₁₆

—

178

—

191

M₁₆

—

178

—

192

M₁₆

—

178

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

178

—

198

C₂×C₈

—

178

—

199

C₂×C₈

—

178

—

200

C₂×C₈

—

178

—

201

C₂×C₈

#13083557

yes

—

202

C₂×C₈

C₂×C₄×D₈₉

yes

—

203

C₂×C₈

D₄×D₈₉

yes

—

204

C₂×C₈

#13083573

yes

characteristic

205

C₂×C₈

#13083575

yes

characteristic

206

C₄²

—

207

C₄²

—

208

C₄²

—

178

—

209

C₄²

—

178

—

210

C₄²

#13083557

yes

—

211

C₁₆

—

212

C₁₆

—

178

—

213

C₂³

—

214

C₂³

—

356

—

215

C₂³

—

178

—

216

C₂³

—

178

—

217

C₂³

M₁₆×D₈₉

yes

characteristic

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

356

—

222

C₂×C₄

—

356

—

223

C₂×C₄

—

178

—

224

C₂×C₄

—

178

—

225

C₂×C₄

—

178

—

226

C₂×C₄

—

178

—

227

C₂×C₄

—

178

—

228

C₂×C₄

—

178

—

229

C₂×C₄

—

178

—

230

C₂×C₄

C₄²×D₈₉

yes

characteristic

231

C₂×C₄

C₂²⋊C₄×D₈₉

yes

characteristic

232

C₂×C₄

#15667970

yes

characteristic

233

C₂×C₄

M₁₆×D₈₉

yes

characteristic

234

C₂×C₄

C₂×#13083557

yes

characteristic

235

C₂×C₄

C₂×#13083557

yes

characteristic

236

C₈

—

237

C₈

—

178

—

238

C₈

—

178

—

239

C₈

#15667972

yes

—

240

C₈

#15667974

yes

—

241

C₂²

—

242

C₂²

—

356

—

243

C₂²

—

356

—

244

C₂²

—

356

—

245

C₂²

—

178

—

246

C₂²

#97×D₈₉

yes

characteristic

247

C₂²

#19151560

yes

characteristic

248

C₂²

#19151654

yes

characteristic

249

C₄

—

250

C₄

—

356

—

251

C₄

—

178

—

252

C₄

#19151445

yes

characteristic

253

C₄

C₄×#13083557

yes

characteristic

254

C₄

#19151560

yes

characteristic

255

C₄

#19151654

yes

characteristic

256

C₂

—

257

C₂

—

258

C₂

—

356

—

259

C₂

#26020013

yes

characteristic

260

C₂

#26022063

yes

—

	subgroup	G/H
center	C₂×C₄	#15667970
commutator	C₂×C₄×C₈₉	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₈₉×#1376	C₂
socle	C₂²×C₈₉	#432
prime radical	C₂³×D₈₉	M₁₆
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	#1376	D₈₉
hypocenter	C₈₉	#12607
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1376

subgroup

G/H

center

C₂×C₄

#15667970

commutator

C₂×C₄×C₈₉

C₂×C₄²

Frattini

C₂²×C₈

C₂²×D₈₉

Fitting

C₈₉×#1376

C₂

socle

C₂²×C₈₉

#432

prime radical

C₂³×D₈₉

M₁₆

cosocle

C₂²×C₈×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1376

N	H ≅ G/N	type
3. C₂×#19151375	C₂	semidirect
4. #26018334	C₂	semidirect
5. C₈₉×#1376	C₂	semidirect
14. #19151379	C₄	semidirect
34. #15667952	C₂×C₄	semidirect
43. M₃₂×C₈₉	C₂×C₄	semidirect
135. #1376	D₈₉	semidirect
136. C₈₉	#12607	semidirect
170. M₃₂	C₄×D₈₉	semidirect

H ≅ G/N

type

3. C₂×#19151375

C₂

semidirect

4. #26018334

C₂

semidirect

5. C₈₉×#1376

C₂

semidirect

14. #19151379

C₄

semidirect

34. #15667952

C₂×C₄

semidirect

43. M₃₂×C₈₉

C₂×C₄

semidirect

135. #1376

D₈₉

semidirect

136. C₈₉

#12607

semidirect

170. M₃₂

C₄×D₈₉

semidirect

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

subgroup	index
C₂×C₄×#13083557	2
C₂×#19151379	2
C₂×#19151375	2
#26018334	2
C₈₉×#1376	2
#12607	89

subgroup

index

C₈₉×#1376

Subgroups — #36469493

Conjugacy classes of subgroups

Complements

Maximal subgroups