Group #36708853 — subgroups

Subgroups — C₂×#26022344 #36708853

Order 22784.

702 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 195 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	C₂²×Dic₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151840	C₂	1	2	yes	maximal
4	#26022344	C₂	1	8	yes	maximal, direct product factor
5	C₂×#19151401	C₂	1	2	yes	maximal, complemented
6	C₂×#366×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Dic₃₅₆	C₂²	1	2	yes	—
8	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
9	C₂×#15667992	—	2	2	no	—
10	C₂×Dic₇₁₂	—	2	4	no	—
11	C₂×Dic₇₁₂	C₂²	1	4	yes	complemented
12	C₂²×#13083549	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×D₈₉	—	2	4	no	—
14	C₂×C₁₆×D₈₉	C₂²	1	4	yes	—
15	#19151840	—	2	4	no	—
16	#19151840	C₂²	1	8	yes	—
17	C₂×#15667935	—	2	2	no	—
18	#19151401	C₂²	1	8	yes	complemented
19	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#107×C₈₉	C₂²	1	2	yes	—
21	#366×C₈₉	C₂²	1	4	yes	complemented
22	C₂²×Dic₁₇₈	—	2	2	no	—
23	C₂²×C₄×D₈₉	D₄	1	1	yes	characteristic
24	C₂×Dic₃₅₆	—	2	4	no	—
25	C₂×Dic₃₅₆	—	2	2	no	—
26	C₂×Dic₃₅₆	—	2	4	no	—
27	C₂×Dic₃₅₆	C₂³	1	4	yes	—
28	C₂²×#10623494	D₄	1	1	yes	characteristic
29	C₂×C₈×D₈₉	—	2	2	no	—
30	C₂×C₈×D₈₉	—	2	2	no	—
31	C₂×C₈×D₈₉	D₄	1	2	yes	—
32	C₂×C₈×D₈₉	C₂³	1	2	yes	—
33	#15667992	—	2	8	no	—
34	#15667992	—	4	4	no	—
35	C₂×C₄⋊Dic₈₉	—	4	2	no	—
36	C₂×#13083551	—	4	2	no	—
37	Dic₇₁₂	—	2	8	no	—
38	C₂×#13083549	—	2	2	no	—
39	C₂×#13083549	C₂³	1	2	yes	—
40	C₁₆×D₈₉	—	2	8	no	—
41	#15667935	—	2	8	no	—
42	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
44	C₂×C₁₆×C₈₉	D₄	1	4	yes	—
45	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
46	#107×C₈₉	—	2	2	no	—
47	#107×C₈₉	C₂³	1	4	yes	—
48	C₂³×D₈₉	D₈	1	1	yes	characteristic
49	C₂×Dic₁₇₈	—	2	4	no	—
50	C₂×Dic₁₇₈	—	4	4	no	—
51	C₂×Dic₁₇₈	—	4	4	no	—
52	C₂×Dic₁₇₈	—	4	2	no	—
53	C₂²×Dic₈₉	—	4	2	no	—
54	C₂²×Dic₈₉	D₈	1	1	yes	characteristic
55	C₂×C₄×D₈₉	—	2	2	no	—
56	C₂×C₄×D₈₉	—	2	2	no	—
57	C₂×C₄×D₈₉	D₈	1	2	yes	—
58	C₂×C₄×D₈₉	C₂×D₄	1	2	yes	—
59	Dic₃₅₆	—	2	4	no	—
60	Dic₃₅₆	—	2	4	no	—
61	Dic₃₅₆	—	4	4	no	—
62	C₂×#10623494	—	2	2	no	—
63	C₂×#10623494	C₂×D₄	1	2	yes	—
64	C₈×D₈₉	—	2	4	no	—
65	C₈×D₈₉	—	2	2	no	—
66	C₈×D₈₉	—	2	2	no	—
67	C₄⋊Dic₈₉	—	4	8	no	—
68	#13083551	—	4	8	no	—
69	#13083549	—	2	2	no	—
70	C₂²×C₄×C₈₉	—	4	2	no	—
71	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
74	C₂×C₈×C₈₉	#41	1	2	yes	—
75	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
76	C₄⋊C₄×C₈₉	—	2	4	no	—
77	C₄⋊C₄×C₈₉	—	4	2	no	—
78	C₁₆×C₈₉	C₂×D₄	1	4	yes	—
79	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
80	C₂²×D₈₉	—	2	2	no	—
81	C₂²×D₈₉	—	2	2	no	—
82	C₂²×D₈₉	Q₃₂	1	4	yes	complemented
83	C₂²×D₈₉	C₂×D₈	1	2	yes	—
84	C₂×C₄×C₈₉	—	4	4	no	—
85	C₂×C₄×C₈₉	—	8	4	no	—
86	C₂×C₄×C₈₉	#121	1	2	yes	—
87	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
88	C₂×C₄×C₈₉	#135	1	2	yes	—
89	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
90	C₂×Dic₈₉	—	2	2	no	—
91	C₂×Dic₈₉	—	4	4	no	—
92	C₂×Dic₈₉	—	8	4	no	—
93	C₂×Dic₈₉	C₂×D₈	1	2	yes	—
94	C₄×D₈₉	—	2	2	no	—
95	C₄×D₈₉	—	2	2	no	—
96	C₄×D₈₉	—	2	4	no	—
97	Dic₁₇₈	—	4	4	no	—
98	Dic₁₇₈	—	4	4	no	—
99	Dic₁₇₈	—	8	4	no	—
100	C₈×C₈₉	#121	1	2	yes	—
101	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
102	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
103	#10623494	—	2	2	no	—
104	C₂²×C₈₉	#466	1	2	yes	—
105	C₂²×C₈₉	C₂×Q₃₂	1	2	yes	—
106	C₂²×C₈₉	#508	1	2	yes	—
107	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
108	C₂×D₈₉	—	2	2	no	—
109	C₂×D₈₉	—	2	8	no	—
110	C₂×D₈₉	—	2	2	no	—
111	C₂×D₈₉	C₂×Q₃₂	1	4	yes	complemented
112	C₄×C₈₉	—	8	4	no	—
113	C₄×C₈₉	#466	1	2	yes	—
114	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
115	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
116	Dic₈₉	—	2	2	no	—
117	Dic₈₉	—	8	4	no	—
118	C₂×#2216	—	89	1	no	maximal, Sylow
119	C₂×C₈₉	#2216	1	4	yes	complemented
120	C₂×C₈₉	C₂×#466	1	1	yes	characteristic
121	C₂×C₈₉	C₂²×Q₃₂	1	1	yes	characteristic
122	C₂×C₈₉	C₂×#508	1	1	yes	characteristic
123	D₈₉	—	2	4	no	—
124	C₂²×Q₃₂	—	89	1	no	—
125	C₂³×C₁₆	—	89	1	no	—
126	C₂×#467	—	89	2	no	—
127	#2216	—	89	8	no	—
128	C₂×#366	D₈₉	1	1	yes	characteristic, complemented
129	C₂×#358	—	89	2	no	—
130	C₈₉	C₂×#2216	1	1	yes	characteristic, complemented, Sylow
131	C₂²×Q₁₆	—	89	2	no	—
132	C₂³×C₈	—	89	1	no	—
133	C₂×C₂²⋊Q₈	—	178	2	no	—
134	C₂×Q₃₂	—	89	4	no	—
135	C₂×Q₃₂	—	178	4	no	—
136	C₂²×C₁₆	—	89	1	no	—
137	C₂²×C₁₆	—	89	4	no	—
138	C₂²×C₁₆	—	178	4	no	—
139	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
140	#467	—	89	8	no	—
141	#467	—	178	4	no	—
142	C₂×#107	C₂×D₈₉	1	2	yes	—
143	C₂×#103	—	178	2	no	—
144	#366	C₂×D₈₉	1	4	yes	complemented
145	#358	—	89	8	no	—
146	C₂²×Q₈	—	178	2	no	—
147	C₂³×C₄	—	89	1	no	—
148	C₂×Q₁₆	—	89	4	no	—
149	C₂×Q₁₆	—	178	2	no	—
150	C₂×Q₁₆	—	178	4	no	—
151	C₂×Q₁₆	—	178	4	no	—
152	C₂²×C₈	—	89	1	no	—
153	C₂²×C₈	—	89	2	no	—
154	C₂²×C₈	—	89	2	no	—
155	C₂²×C₈	—	178	2	no	—
156	C₂²×C₈	—	178	2	no	—
157	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
158	C₂²⋊Q₈	—	356	4	no	—
159	C₂²⋊Q₈	—	178	8	no	—
160	C₂×C₄⋊C₄	—	2	2	no	—
161	C₂×C₄⋊C₄	—	356	2	no	—
162	C₂×C₂²⋊C₄	—	356	2	no	—
163	Q₃₂	—	178	8	no	—
164	C₂×C₁₆	—	89	2	no	—
165	C₂×C₁₆	—	178	2	no	—
166	C₂×C₁₆	—	178	8	no	—
167	C₂×C₁₆	D₃₅₆	1	4	yes	—
168	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
169	#107	—	2	2	no	—
170	#107	C₂²×D₈₉	1	4	yes	—
171	#103	—	178	8	no	—
172	C₂⁴	—	89	1	no	—
173	C₂×Q₈	—	356	2	no	—
174	C₂×Q₈	—	356	4	no	—
175	C₂×Q₈	—	356	4	no	—
176	C₂×Q₈	—	178	4	no	—
177	C₂²×C₄	—	4	2	no	—
178	C₂²×C₄	—	89	1	no	—
179	C₂²×C₄	—	89	2	no	—
180	C₂²×C₄	—	89	2	no	—
181	C₂²×C₄	—	356	2	no	—
182	C₂²×C₄	—	178	2	no	—
183	C₂²×C₄	—	178	2	no	—
184	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
185	Q₁₆	—	356	4	no	—
186	Q₁₆	—	178	4	no	—
187	Q₁₆	—	178	4	no	—
188	C₂×C₈	—	89	2	no	—
189	C₂×C₈	—	178	2	no	—
190	C₂×C₈	—	178	4	no	—
191	C₂×C₈	—	178	2	no	—
192	C₂×C₈	—	178	2	no	—
193	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
194	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
195	C₂×C₈	#13083575	1	2	yes	—
196	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
197	C₄⋊C₄	—	2	4	no	—
198	C₄⋊C₄	—	4	2	no	—
199	C₄⋊C₄	—	356	8	no	—
200	C₂²⋊C₄	—	356	8	no	—
201	C₁₆	—	178	2	no	—
202	C₁₆	C₂×D₃₅₆	1	4	yes	—
203	C₂³	—	89	4	no	—
204	C₂³	—	89	2	no	—
205	C₂³	—	178	2	no	—
206	C₂³	—	178	2	no	—
207	C₂³	D₈×D₈₉	1	1	yes	characteristic
208	Q₈	—	356	4	no	—
209	Q₈	—	356	4	no	—
210	Q₈	—	712	4	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	8	4	no	—
213	C₂×C₄	—	89	2	no	—
214	C₂×C₄	—	356	4	no	—
215	C₂×C₄	—	178	2	no	—
216	C₂×C₄	—	178	4	no	—
217	C₂×C₄	—	178	2	no	—
218	C₂×C₄	—	178	2	no	—
219	C₂×C₄	—	712	4	no	—
220	C₂×C₄	#15667987	1	2	yes	—
221	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
222	C₂×C₄	#15668035	1	2	yes	—
223	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
224	C₈	—	178	2	no	—
225	C₈	#15667987	1	2	yes	—
226	C₈	C₂²×D₃₅₆	1	1	yes	characteristic
227	C₈	C₂×#13083575	1	1	yes	characteristic
228	C₂²	—	89	4	no	—
229	C₂²	—	178	8	no	—
230	C₂²	—	178	2	no	—
231	C₂²	—	178	2	no	—
232	C₂²	#19151835	1	2	yes	—
233	C₂²	Q₃₂×D₈₉	1	2	yes	—
234	C₂²	#19152027	1	2	yes	—
235	C₂²	C₂×D₈×D₈₉	1	1	yes	characteristic
236	C₄	—	8	4	no	—
237	C₄	—	178	2	no	—
238	C₄	—	712	4	no	—
239	C₄	#19151835	1	2	yes	—
240	C₄	C₂×#15667987	1	1	yes	characteristic
241	C₄	C₂×#15668035	1	1	yes	characteristic
242	C₂	—	178	4	no	—
243	C₂	#26022344	1	4	yes	direct product factor
244	C₂	C₂×#19151835	1	1	yes	characteristic
245	C₂	C₂×Q₃₂×D₈₉	1	1	yes	characteristic
246	C₂	C₂×#19152027	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₇₁₂

C₂

yes

maximal, characteristic, complemented

C₂²×C₁₆×D₈₉

C₂

yes

maximal, characteristic

C₂×#19151840

C₂

yes

maximal

#26022344

C₂

yes

maximal, direct product factor

C₂×#19151401

C₂

yes

maximal, complemented

C₂×#366×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₃₅₆

C₂²

yes

—

C₂²×C₈×D₈₉

C₂²

yes

characteristic

C₂×#15667992

—

C₂×Dic₇₁₂

—

C₂×Dic₇₁₂

C₂²

yes

complemented

C₂²×#13083549

C₂²

yes

characteristic

C₂×C₁₆×D₈₉

—

C₂×C₁₆×D₈₉

C₂²

yes

—

#19151840

—

#19151840

C₂²

yes

—

C₂×#15667935

—

#19151401

C₂²

yes

complemented

C₂²×C₁₆×C₈₉

C₂²

yes

characteristic

C₂×#107×C₈₉

C₂²

yes

—

#366×C₈₉

C₂²

yes

complemented

C₂²×Dic₁₇₈

—

C₂²×C₄×D₈₉

D₄

yes

characteristic

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

C₂³

yes

—

C₂²×#10623494

D₄

yes

characteristic

C₂×C₈×D₈₉

—

C₂×C₈×D₈₉

—

C₂×C₈×D₈₉

D₄

yes

—

C₂×C₈×D₈₉

C₂³

yes

—

#15667992

—

#15667992

—

C₂×C₄⋊Dic₈₉

—

C₂×#13083551

—

Dic₇₁₂

—

C₂×#13083549

—

C₂×#13083549

C₂³

yes

—

C₁₆×D₈₉

—

#15667935

—

C₂²×C₈×C₈₉

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₈₉

—

C₂×C₁₆×C₈₉

D₄

yes

—

C₂×C₁₆×C₈₉

C₂³

yes

—

#107×C₈₉

—

#107×C₈₉

C₂³

yes

—

C₂³×D₈₉

D₈

yes

characteristic

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

D₈

yes

characteristic

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

D₈

yes

—

C₂×C₄×D₈₉

C₂×D₄

yes

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

C₂×#10623494

—

C₂×#10623494

C₂×D₄

yes

—

C₈×D₈₉

—

C₈×D₈₉

—

C₈×D₈₉

—

C₄⋊Dic₈₉

—

#13083551

—

#13083549

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

—

C₂×C₈×C₈₉

#41

yes

—

C₂×C₈×C₈₉

C₂⁴

yes

characteristic

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₁₆×C₈₉

C₂×D₄

yes

—

C₂³×C₈₉

C₂×D₈

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

Q₃₂

yes

complemented

C₂²×D₈₉

C₂×D₈

yes

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#121

yes

—

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×C₄×C₈₉

#135

yes

—

C₂×C₄×C₈₉

C₂²×D₄

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

C₂×D₈

yes

—

C₄×D₈₉

—

C₄×D₈₉

—

C₄×D₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

Dic₁₇₈

—

100

C₈×C₈₉

#121

yes

—

101

C₈×C₈₉

C₂²×D₄

yes

characteristic

102

C₈×C₈₉

C₂×#41

yes

characteristic

103

#10623494

—

104

C₂²×C₈₉

#466

yes

—

105

C₂²×C₈₉

C₂×Q₃₂

yes

—

106

C₂²×C₈₉

#508

yes

—

107

C₂²×C₈₉

C₂²×D₈

yes

characteristic

108

C₂×D₈₉

—

109

C₂×D₈₉

—

110

C₂×D₈₉

—

111

C₂×D₈₉

C₂×Q₃₂

yes

complemented

112

C₄×C₈₉

—

113

C₄×C₈₉

#466

yes

—

114

C₄×C₈₉

C₂×#121

yes

characteristic

115

C₄×C₈₉

C₂×#135

yes

characteristic

116

Dic₈₉

—

117

Dic₈₉

—

118

C₂×#2216

—

maximal, Sylow

119

C₂×C₈₉

#2216

yes

complemented

120

C₂×C₈₉

C₂×#466

yes

characteristic

121

C₂×C₈₉

C₂²×Q₃₂

yes

characteristic

122

C₂×C₈₉

C₂×#508

yes

characteristic

123

D₈₉

—

124

C₂²×Q₃₂

—

125

C₂³×C₁₆

—

126

C₂×#467

—

127

#2216

—

128

C₂×#366

D₈₉

yes

characteristic, complemented

129

C₂×#358

—

130

C₈₉

C₂×#2216

yes

characteristic, complemented, Sylow

131

C₂²×Q₁₆

—

132

C₂³×C₈

—

133

C₂×C₂²⋊Q₈

—

178

—

134

C₂×Q₃₂

—

135

C₂×Q₃₂

—

178

—

136

C₂²×C₁₆

—

137

C₂²×C₁₆

—

138

C₂²×C₁₆

—

178

—

139

C₂²×C₁₆

C₂×D₈₉

yes

characteristic

140

#467

—

141

#467

—

178

—

142

C₂×#107

C₂×D₈₉

yes

—

143

C₂×#103

—

178

—

144

#366

C₂×D₈₉

yes

complemented

145

#358

—

146

C₂²×Q₈

—

178

—

147

C₂³×C₄

—

148

C₂×Q₁₆

—

149

C₂×Q₁₆

—

178

—

150

C₂×Q₁₆

—

178

—

151

C₂×Q₁₆

—

178

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

—

178

—

156

C₂²×C₈

—

178

—

157

C₂²×C₈

C₂²×D₈₉

yes

characteristic

158

C₂²⋊Q₈

—

356

—

159

C₂²⋊Q₈

—

178

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

356

—

162

C₂×C₂²⋊C₄

—

356

—

163

Q₃₂

—

178

—

164

C₂×C₁₆

—

165

C₂×C₁₆

—

178

—

166

C₂×C₁₆

—

178

—

167

C₂×C₁₆

D₃₅₆

yes

—

168

C₂×C₁₆

C₂²×D₈₉

yes

—

169

#107

—

170

#107

C₂²×D₈₉

yes

—

171

#103

—

178

—

172

C₂⁴

—

173

C₂×Q₈

—

356

—

174

C₂×Q₈

—

356

—

175

C₂×Q₈

—

356

—

176

C₂×Q₈

—

178

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

356

—

182

C₂²×C₄

—

178

—

183

C₂²×C₄

—

178

—

184

C₂²×C₄

D₄×D₈₉

yes

characteristic

185

Q₁₆

—

356

—

186

Q₁₆

—

178

—

187

Q₁₆

—

178

—

188

C₂×C₈

—

189

C₂×C₈

—

178

—

190

C₂×C₈

—

178

—

191

C₂×C₈

—

178

—

192

C₂×C₈

—

178

—

193

C₂×C₈

D₄×D₈₉

yes

characteristic

194

C₂×C₈

C₂×D₃₅₆

yes

—

195

C₂×C₈

#13083575

yes

—

196

C₂×C₈

C₂³×D₈₉

yes

characteristic

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

356

—

200

C₂²⋊C₄

—

356

—

201

C₁₆

—

178

—

202

C₁₆

C₂×D₃₅₆

yes

—

203

C₂³

—

204

C₂³

—

205

C₂³

—

178

—

206

C₂³

—

178

—

207

C₂³

D₈×D₈₉

yes

characteristic

208

Q₈

—

356

—

209

Q₈

—

356

—

210

Q₈

—

712

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

356

—

215

C₂×C₄

—

178

—

216

C₂×C₄

—

178

—

217

C₂×C₄

—

178

—

218

C₂×C₄

—

178

—

219

C₂×C₄

—

712

—

220

C₂×C₄

#15667987

yes

—

221

C₂×C₄

D₈×D₈₉

yes

characteristic

222

C₂×C₄

#15668035

yes

—

223

C₂×C₄

C₂×D₄×D₈₉

yes

characteristic

224

C₈

—

178

—

225

C₈

#15667987

yes

—

226

C₈

C₂²×D₃₅₆

yes

characteristic

227

C₈

C₂×#13083575

yes

characteristic

228

C₂²

—

229

C₂²

—

178

—

230

C₂²

—

178

—

231

C₂²

—

178

—

232

C₂²

#19151835

yes

—

233

C₂²

Q₃₂×D₈₉

yes

—

234

C₂²

#19152027

yes

—

235

C₂²

C₂×D₈×D₈₉

yes

characteristic

236

C₄

—

237

C₄

—

178

—

238

C₄

—

712

—

239

C₄

#19151835

yes

—

240

C₄

C₂×#15667987

yes

characteristic

241

C₄

C₂×#15668035

yes

characteristic

242

C₂

—

178

—

243

C₂

#26022344

yes

direct product factor

244

C₂

C₂×#19151835

yes

characteristic

245

C₂

C₂×Q₃₂×D₈₉

yes

characteristic

246

C₂

C₂×#19152027

yes

characteristic

	subgroup	G/H
center	C₂³	D₈×D₈₉
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₂×#366×C₈₉	C₂
socle	C₂³×C₈₉	C₂×D₈
prime radical	C₂³×D₈₉	D₈
hypercenter	C₂×#366	D₈₉
hypocenter	C₈₉	C₂×#2216
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

subgroup

G/H

center

C₂³

D₈×D₈₉

commutator, cosocle

C₂×C₈×C₈₉

C₂⁴

Frattini

C₂×C₈

C₂³×D₈₉

Fitting

C₂×#366×C₈₉

C₂

socle

C₂³×C₈₉

C₂×D₈

prime radical

C₂³×D₈₉

D₈

D₈₉

C₈₉

G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

N	H ≅ G/N	type
1. C₂²×Dic₇₁₂	C₂	semidirect
4. #26022344	C₂	direct (N × H)
5. C₂×#19151401	C₂	semidirect
6. C₂×#366×C₈₉	C₂	semidirect
11. C₂×Dic₇₁₂	C₂²	semidirect
18. #19151401	C₂²	semidirect
21. #366×C₈₉	C₂²	semidirect
82. C₂²×D₈₉	Q₃₂	semidirect
111. C₂×D₈₉	C₂×Q₃₂	semidirect
119. C₂×C₈₉	#2216	semidirect
128. C₂×#366	D₈₉	semidirect
130. C₈₉	C₂×#2216	semidirect
144. #366	C₂×D₈₉	semidirect
243. C₂	#26022344	direct (N × H)

H ≅ G/N

type

1. C₂²×Dic₇₁₂

C₂

semidirect

4. #26022344

C₂

direct (N × H)

5. C₂×#19151401

C₂

semidirect

6. C₂×#366×C₈₉

C₂

semidirect

11. C₂×Dic₇₁₂

C₂²

semidirect

18. #19151401

C₂²

semidirect

21. #366×C₈₉

C₂²

semidirect

82. C₂²×D₈₉

Q₃₂

semidirect

111. C₂×D₈₉

C₂×Q₃₂

semidirect

119. C₂×C₈₉

#2216

semidirect

128. C₂×#366

D₈₉

semidirect

130. C₈₉

C₂×#2216

semidirect

144. #366

C₂×D₈₉

semidirect

243. C₂

#26022344

direct (N × H)

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

subgroup	index
C₂²×Dic₇₁₂	2
C₂²×C₁₆×D₈₉	2
C₂×#19151840	2
#26022344	2
C₂×#19151401	2
C₂×#366×C₈₉	2
C₂×#2216	89

subgroup

index

C₂²×Dic₇₁₂

C₂²×C₁₆×D₈₉

C₂×#366×C₈₉

Subgroups — C₂×#26022344 #36708853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#26022344 #36708853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26022344 #36708853