Group #36452273 — subgroups

Subgroups — #36452273

Order 22784.

474 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 135 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	#26029333	C₂	1	1	yes	maximal, characteristic
2	#26020248	C₂	1	1	yes	maximal, characteristic
3	#26018681	C₂	1	2	yes	maximal
4	#26018110	C₂	1	2	yes	maximal
5	C₈₉×#2581	C₂	1	1	yes	maximal, characteristic
6	Q₈×#10623494	—	2	4	no	—
7	#19151651	—	2	2	no	—
8	#19151651	C₂²	1	2	yes	—
9	#19151622	C₂²	1	2	yes	—
10	C₂×#15667931	—	2	1	no	—
11	#19151367	—	2	1	no	—
12	Q₈⋊#10623494	—	2	4	no	—
13	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
15	#400×C₈₉	C₄	1	2	yes	—
16	#395×C₈₉	C₄	1	2	yes	—
17	#391×C₈₉	—	2	1	no	—
18	#389×C₈₉	—	2	1	no	—
19	#387×C₈₉	—	2	2	no	—
20	#382×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#13083558	—	2	2	no	—
22	C₄⋊#10623494	—	2	4	no	—
23	C₄⋊#10623494	—	2	2	no	—
24	C₄⋊#10623494	—	2	2	no	—
25	C₄⋊#10623494	—	2	2	no	—
26	#15667931	—	4	2	no	—
27	C₂²⋊#10623494	—	2	2	no	—
28	C₄×#10623494	—	2	4	no	—
29	C₄×#10623494	D₄	1	4	yes	—
30	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
32	C₄×Q₈×C₈₉	—	2	2	no	—
33	C₄×Q₈×C₈₉	—	2	2	no	—
34	C₄×Q₈×C₈₉	—	2	2	no	—
35	C₄×Q₈×C₈₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
37	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
41	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₈₉	—	2	1	no	—
43	C₂×C₄²×C₈₉	D₄	1	2	yes	—
44	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
45	#95×C₈₉	—	2	2	no	—
46	#95×C₈₉	—	2	2	no	—
47	#95×C₈₉	—	2	2	no	—
48	#95×C₈₉	—	2	1	no	—
49	#95×C₈₉	C₂×C₄	1	2	yes	—
50	#13083558	—	4	2	no	—
51	#13083558	—	4	2	no	—
52	C₂×#10623494	—	2	4	no	—
53	C₂×#10623494	—	4	2	no	—
54	C₂×Q₈×C₈₉	—	2	2	no	—
55	C₂×Q₈×C₈₉	—	2	2	no	—
56	C₂×Q₈×C₈₉	—	2	2	no	—
57	C₂×Q₈×C₈₉	—	4	2	no	—
58	C₂×Q₈×C₈₉	SD₁₆	1	2	yes	—
59	C₂×Q₈×C₈₉	Q₁₆	1	2	yes	—
60	C₂²×C₄×C₈₉	—	2	1	no	—
61	C₂²×C₄×C₈₉	—	2	2	no	—
62	C₂²×C₄×C₈₉	—	2	1	no	—
63	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
68	C₄⋊C₄×C₈₉	—	2	4	no	—
69	C₄⋊C₄×C₈₉	—	2	2	no	—
70	C₄⋊C₄×C₈₉	—	2	2	no	—
71	C₄⋊C₄×C₈₉	—	4	4	no	—
72	C₄⋊C₄×C₈₉	—	4	1	no	—
73	C₄⋊C₄×C₈₉	—	4	1	no	—
74	C₄⋊C₄×C₈₉	—	4	2	no	—
75	C₄²×C₈₉	—	2	2	no	—
76	C₄²×C₈₉	—	2	2	no	—
77	C₄²×C₈₉	—	4	2	no	—
78	C₄²×C₈₉	C₂×D₄	1	2	yes	—
79	C₄²×C₈₉	#41	1	2	yes	—
80	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	Q₈×C₈₉	—	2	4	no	—
82	Q₈×C₈₉	—	2	4	no	—
83	Q₈×C₈₉	—	2	4	no	—
84	Q₈×C₈₉	—	4	2	no	—
85	C₂×C₄×C₈₉	—	2	2	no	—
86	C₂×C₄×C₈₉	—	2	2	no	—
87	C₂×C₄×C₈₉	—	2	2	no	—
88	C₂×C₄×C₈₉	—	2	2	no	—
89	C₂×C₄×C₈₉	—	4	1	no	—
90	C₂×C₄×C₈₉	—	4	1	no	—
91	C₂×C₄×C₈₉	—	4	1	no	—
92	C₂×C₄×C₈₉	—	4	1	no	—
93	C₂×C₄×C₈₉	—	4	2	no	—
94	C₂×C₄×C₈₉	—	4	2	no	—
95	C₂×C₄×C₈₉	—	4	2	no	—
96	C₂×C₄×C₈₉	—	4	2	no	—
97	C₂×C₄×C₈₉	—	4	1	no	—
98	C₂×C₄×C₈₉	—	4	2	no	—
99	C₂×C₄×C₈₉	#103	1	4	yes	—
100	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
101	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
102	C₂×C₄×C₈₉	#121	1	2	yes	—
103	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
104	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
105	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
106	C₂×C₄×C₈₉	#135	1	2	yes	—
107	#10623494	—	4	4	no	—
108	#10623494	—	8	2	no	—
109	C₂²×C₈₉	—	2	1	no	—
110	C₂²×C₈₉	—	2	1	no	—
111	C₂²×C₈₉	#386	1	1	yes	characteristic
112	C₂²×C₈₉	C₂×#103	1	1	yes	characteristic
113	C₂²×C₈₉	#416	1	1	yes	characteristic
114	C₄×C₈₉	—	2	2	no	—
115	C₄×C₈₉	—	2	4	no	—
116	C₄×C₈₉	—	2	1	no	—
117	C₄×C₈₉	—	2	1	no	—
118	C₄×C₈₉	—	4	2	no	—
119	C₄×C₈₉	—	4	2	no	—
120	C₄×C₈₉	—	8	2	no	—
121	C₄×C₈₉	—	8	1	no	—
122	C₄×C₈₉	#465	1	2	yes	—
123	C₄×C₈₉	#467	1	2	yes	—
124	#9484	—	89	1	no	maximal, Sylow
125	C₂×C₈₉	—	2	1	no	—
126	C₂×C₈₉	—	2	1	no	—
127	C₂×C₈₉	#1891	1	1	yes	characteristic
128	C₂×C₈₉	#1892	1	1	yes	characteristic
129	C₂×C₈₉	#1912	1	1	yes	characteristic
130	#2982	—	89	1	no	—
131	#2581	D₈₉	1	1	yes	characteristic
132	#1801	—	89	1	no	—
133	#1487	—	89	2	no	—
134	#1286	—	89	2	no	—
135	C₈₉	#9484	1	1	yes	characteristic, complemented, Sylow
136	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
137	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
138	C₈×Q₈	—	178	4	no	—
139	#431	—	89	2	no	—
140	#431	—	178	2	no	—
141	#423	—	89	2	no	—
142	C₂×#101	—	178	1	no	—
143	#400	Dic₈₉	1	2	yes	—
144	#395	Dic₈₉	1	2	yes	—
145	#391	—	2	1	no	—
146	#389	—	2	1	no	—
147	#387	—	2	2	no	—
148	#382	C₂×D₈₉	1	1	yes	characteristic
149	#343	—	178	1	no	—
150	Q₈⋊C₈	—	178	4	no	—
151	C₂²×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
152	C₂²×Q₈	C₂²⋊D₈₉	1	1	yes	characteristic
153	C₂×M₁₆	—	178	2	no	—
154	C₄×Q₈	—	2	2	no	—
155	C₄×Q₈	—	2	2	no	—
156	C₄×Q₈	—	2	2	no	—
157	C₄×Q₈	—	2	2	no	—
158	C₂×C₄⋊C₄	—	2	2	no	—
159	C₂×C₄⋊C₄	—	2	1	no	—
160	C₂×C₄⋊C₄	—	2	1	no	—
161	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
162	C₂×C₄⋊C₄	C₂×Dic₈₉	1	2	yes	—
163	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
164	C₂×C₄²	—	2	1	no	—
165	C₂×C₄²	C₂²⋊D₈₉	1	2	yes	—
166	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
167	C₄⋊C₈	—	178	4	no	—
168	C₄⋊C₈	—	178	2	no	—
169	C₄⋊C₈	—	178	2	no	—
170	C₄⋊C₈	—	178	2	no	—
171	#101	—	356	2	no	—
172	C₂²⋊C₈	—	178	2	no	—
173	C₄×C₈	—	89	4	no	—
174	C₄×C₈	—	178	4	no	—
175	#95	—	2	2	no	—
176	#95	—	2	2	no	—
177	#95	—	2	2	no	—
178	#95	—	2	1	no	—
179	#95	C₂×Dic₈₉	1	2	yes	—
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	2	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	#13083561	1	2	yes	—
185	C₂×Q₈	#13083564	1	2	yes	—
186	C₂²×C₄	—	2	1	no	—
187	C₂²×C₄	—	2	2	no	—
188	C₂²×C₄	—	2	1	no	—
189	C₂²×C₄	C₂²⋊Dic₈₉	1	2	yes	—
190	C₂²×C₄	C₂²⋊Dic₈₉	1	2	yes	—
191	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
192	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
193	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
194	M₁₆	—	356	2	no	—
195	M₁₆	—	356	2	no	—
196	C₂×C₈	—	356	2	no	—
197	C₂×C₈	—	178	4	no	—
198	C₄⋊C₄	—	2	4	no	—
199	C₄⋊C₄	—	2	2	no	—
200	C₄⋊C₄	—	2	2	no	—
201	C₄⋊C₄	—	4	4	no	—
202	C₄⋊C₄	—	4	1	no	—
203	C₄⋊C₄	—	4	1	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	2	2	no	—
207	C₄²	—	4	2	no	—
208	C₄²	D₄×D₈₉	1	2	yes	—
209	C₄²	#13083573	1	2	yes	—
210	C₂³	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
211	Q₈	—	2	4	no	—
212	Q₈	—	2	4	no	—
213	Q₈	—	2	4	no	—
214	Q₈	—	4	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	4	1	no	—
220	C₂×C₄	—	4	1	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	—	4	1	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	4	1	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	#15667936	1	4	yes	—
230	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
231	C₂×C₄	#15667980	1	1	yes	characteristic
232	C₂×C₄	#15667984	1	2	yes	—
233	C₂×C₄	#15667993	1	1	yes	characteristic
234	C₂×C₄	C₂×#13083561	1	1	yes	characteristic
235	C₂×C₄	C₂×#13083564	1	1	yes	characteristic
236	C₂×C₄	#15668032	1	2	yes	—
237	C₈	—	356	4	no	—
238	C₈	—	712	2	no	—
239	C₂²	—	2	1	no	—
240	C₂²	—	2	1	no	—
241	C₂²	#19151478	1	1	yes	characteristic
242	C₂²	C₂×#15667936	1	1	yes	characteristic
243	C₂²	#19151594	1	1	yes	characteristic
244	C₄	—	2	2	no	—
245	C₄	—	2	4	no	—
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	4	2	no	—
249	C₄	—	4	2	no	—
250	C₄	—	8	2	no	—
251	C₄	—	8	1	no	—
252	C₄	#19151829	1	2	yes	—
253	C₄	#19151837	1	2	yes	—
254	C₂	—	2	1	no	—
255	C₂	—	2	1	no	—
256	C₂	#26020671	1	1	yes	characteristic
257	C₂	#26020676	1	1	yes	characteristic
258	C₂	#26020790	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26029333

C₂

yes

maximal, characteristic

#26020248

C₂

yes

maximal, characteristic

#26018681

C₂

yes

maximal

#26018110

C₂

yes

maximal

C₈₉×#2581

C₂

yes

maximal, characteristic

Q₈×#10623494

—

#19151651

—

#19151651

C₂²

yes

—

#19151622

C₂²

yes

—

C₂×#15667931

—

#19151367

—

Q₈⋊#10623494

—

C₂×C₄×Q₈×C₈₉

C₂²

yes

characteristic

C₂×C₄×Q₈×C₈₉

C₂²

yes

characteristic

#400×C₈₉

C₄

yes

—

#395×C₈₉

C₄

yes

—

#391×C₈₉

—

#389×C₈₉

—

#387×C₈₉

—

#382×C₈₉

C₂²

yes

—

—

—

—

—

—

—

—

D₄

yes

—

C₂²×Q₈×C₈₉

C₂×C₄

yes

characteristic

C₂²×Q₈×C₈₉

D₄

yes

characteristic

C₄×Q₈×C₈₉

—

C₄×Q₈×C₈₉

—

C₄×Q₈×C₈₉

—

C₄×Q₈×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₈₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

characteristic

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

#95×C₈₉

—

#95×C₈₉

—

#95×C₈₉

—

#95×C₈₉

—

#95×C₈₉

C₂×C₄

yes

—

—

—

—

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

SD₁₆

yes

—

C₂×Q₈×C₈₉

Q₁₆

yes

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

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

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#103

yes

—

100

C₂×C₄×C₈₉

C₄×D₄

yes

—

101

C₂×C₄×C₈₉

#120

yes

characteristic

102

C₂×C₄×C₈₉

#121

yes

—

103

C₂×C₄×C₈₉

#123

yes

characteristic

104

C₂×C₄×C₈₉

C₂×SD₁₆

yes

characteristic

105

C₂×C₄×C₈₉

C₂×Q₁₆

yes

characteristic

106

C₂×C₄×C₈₉

#135

yes

—

107

#10623494

—

108

#10623494

—

109

C₂²×C₈₉

—

110

C₂²×C₈₉

—

111

C₂²×C₈₉

#386

yes

characteristic

112

C₂²×C₈₉

C₂×#103

yes

characteristic

113

C₂²×C₈₉

#416

yes

characteristic

114

C₄×C₈₉

—

115

C₄×C₈₉

—

116

C₄×C₈₉

—

117

C₄×C₈₉

—

118

C₄×C₈₉

—

119

C₄×C₈₉

—

120

C₄×C₈₉

—

121

C₄×C₈₉

—

122

C₄×C₈₉

#465

yes

—

123

C₄×C₈₉

#467

yes

—

124

#9484

—

maximal, Sylow

125

C₂×C₈₉

—

126

C₂×C₈₉

—

127

C₂×C₈₉

#1891

yes

characteristic

128

C₂×C₈₉

#1892

yes

characteristic

129

C₂×C₈₉

#1912

yes

characteristic

130

#2982

—

131

#2581

D₈₉

yes

characteristic

132

#1801

—

133

#1487

—

134

#1286

—

135

C₈₉

#9484

yes

characteristic, complemented, Sylow

136

C₂×C₄×Q₈

C₂×D₈₉

yes

characteristic

137

C₂×C₄×Q₈

C₂×D₈₉

yes

characteristic

138

C₈×Q₈

—

178

—

139

#431

—

140

#431

—

178

—

141

#423

—

142

C₂×#101

—

178

—

143

#400

Dic₈₉

yes

—

144

#395

Dic₈₉

yes

—

145

#391

—

146

#389

—

147

#387

—

148

#382

C₂×D₈₉

yes

characteristic

149

#343

—

178

—

150

Q₈⋊C₈

—

178

—

151

C₂²×Q₈

C₂×Dic₈₉

yes

characteristic

152

C₂²×Q₈

C₂²⋊D₈₉

yes

characteristic

153

C₂×M₁₆

—

178

—

154

C₄×Q₈

—

155

C₄×Q₈

—

156

C₄×Q₈

—

157

C₄×Q₈

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

C₂×Dic₈₉

yes

characteristic

162

C₂×C₄⋊C₄

C₂×Dic₈₉

yes

—

163

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

characteristic

164

C₂×C₄²

—

165

C₂×C₄²

C₂²⋊D₈₉

yes

—

166

C₂×C₄²

C₂²×D₈₉

yes

characteristic

167

C₄⋊C₈

—

178

—

168

C₄⋊C₈

—

178

—

169

C₄⋊C₈

—

178

—

170

C₄⋊C₈

—

178

—

171

#101

—

356

—

172

C₂²⋊C₈

—

178

—

173

C₄×C₈

—

174

C₄×C₈

—

178

—

175

#95

—

176

#95

—

177

#95

—

178

#95

—

179

#95

C₂×Dic₈₉

yes

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

#13083561

yes

—

185

C₂×Q₈

#13083564

yes

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

C₂²⋊Dic₈₉

yes

—

190

C₂²×C₄

C₂²⋊Dic₈₉

yes

—

191

C₂²×C₄

C₂²×Dic₈₉

yes

characteristic

192

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

193

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

194

M₁₆

—

356

—

195

M₁₆

—

356

—

196

C₂×C₈

—

356

—

197

C₂×C₈

—

178

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

D₄×D₈₉

yes

—

209

C₄²

#13083573

yes

—

210

C₂³

C₂×C₂²⋊Dic₈₉

yes

characteristic

211

Q₈

—

212

Q₈

—

213

Q₈

—

214

Q₈

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

#15667936

yes

—

230

C₂×C₄

D₄×Dic₈₉

yes

—

231

C₂×C₄

#15667980

yes

characteristic

232

C₂×C₄

#15667984

yes

—

233

C₂×C₄

#15667993

yes

characteristic

234

C₂×C₄

C₂×#13083561

yes

characteristic

235

C₂×C₄

C₂×#13083564

yes

characteristic

236

C₂×C₄

#15668032

yes

—

237

C₈

—

356

—

238

C₈

—

712

—

239

C₂²

—

240

C₂²

—

241

C₂²

#19151478

yes

characteristic

242

C₂²

C₂×#15667936

yes

characteristic

243

C₂²

#19151594

yes

characteristic

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

#19151829

yes

—

253

C₄

#19151837

yes

—

254

C₂

—

255

C₂

—

256

C₂

#26020671

yes

characteristic

257

C₂

#26020676

yes

characteristic

258

C₂

#26020790

yes

characteristic

	subgroup	G/H
center	C₂²	#19151478
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#2581	C₂
socle	C₂²×C₈₉	#386
prime radical	C₂³×C₈₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#2581	D₈₉
hypocenter	C₈₉	#9484
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2581

subgroup

G/H

center

C₂²

#19151478

commutator

C₂²×C₄×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#2581

C₂

socle

C₂²×C₈₉

#386

prime radical

C₂³×C₈₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2581

N	H ≅ G/N	type
135. C₈₉	#9484	semidirect

H ≅ G/N

type

135. C₈₉

#9484

semidirect

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

subgroup	index
#26029333	2
#26020248	2
#26018681	2
#26018110	2
C₈₉×#2581	2
#9484	89

subgroup

index

C₈₉×#2581

Subgroups — #36452273

Conjugacy classes of subgroups

Complements

Maximal subgroups