Group #36447568 — subgroups

Subgroups — #36447568

Order 22784.

378 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 123 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×C₈×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic
2	#26020390	C₂	1	1	yes	maximal, characteristic
3	#26018682	C₂	1	2	yes	maximal
4	#26018148	C₂	1	2	yes	maximal
5	C₈₉×#1564	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
7	C₈×Dic₁₇₈	—	2	1	no	—
8	C₈×Dic₁₇₈	—	2	1	no	—
9	C₈×Dic₁₇₈	C₄	1	2	yes	—
10	C₈×Dic₁₇₈	C₄	1	2	yes	—
11	#19151622	C₂²	1	2	yes	—
12	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
13	C₂×#15667941	—	2	1	no	—
14	C₂×C₈×Dic₈₉	—	2	1	no	—
15	#19151363	—	2	1	no	—
16	#19151363	—	2	1	no	—
17	#19151330	—	2	4	no	—
18	#431×C₈₉	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	#335×C₈₉	—	2	1	no	—
21	#334×C₈₉	—	2	1	no	—
22	C₂²×Dic₁₇₈	Q₈	1	1	yes	characteristic
23	C₂×#13083558	—	2	2	no	—
24	C₂²×#10623494	—	2	1	no	—
25	C₄×Dic₁₇₈	—	2	1	no	—
26	C₄×Dic₁₇₈	—	2	1	no	—
27	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
28	C₄×Dic₁₇₈	D₄	1	2	yes	—
29	C₂×C₄⋊Dic₈₉	Q₈	1	1	yes	characteristic
30	C₂×#13083553	—	2	1	no	—
31	C₂×C₄×Dic₈₉	—	2	1	no	—
32	C₄⋊#10623494	—	2	1	no	—
33	C₄⋊#10623494	—	2	2	no	—
34	C₄⋊#10623494	—	2	2	no	—
35	C₄⋊#10623494	C₂×C₄	1	2	yes	—
36	#15667941	—	2	2	no	—
37	#15667941	—	2	2	no	—
38	C₈×Dic₈₉	—	2	2	no	—
39	C₈×Dic₈₉	—	2	2	no	—
40	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₈₉	—	2	2	no	—
44	C₂²⋊C₈×C₈₉	—	2	2	no	—
45	C₄×C₈×C₈₉	—	2	2	no	—
46	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
50	C₂×Dic₁₇₈	—	2	1	no	—
51	C₂×Dic₁₇₈	—	2	4	no	—
52	C₂×Dic₁₇₈	C₄⋊C₄	1	2	yes	—
53	C₂²×Dic₈₉	—	2	1	no	—
54	C₂²×Dic₈₉	—	2	1	no	—
55	#13083558	—	4	2	no	—
56	#13083558	—	4	2	no	—
57	C₂×#10623494	—	2	2	no	—
58	C₂×#10623494	—	4	2	no	—
59	C₂×#10623494	—	4	2	no	—
60	C₄⋊Dic₈₉	—	2	1	no	—
61	C₄⋊Dic₈₉	C₄⋊C₄	1	2	yes	—
62	#13083553	—	2	2	no	—
63	#13083553	—	2	2	no	—
64	C₄×Dic₈₉	—	2	2	no	—
65	C₄×Dic₈₉	—	2	2	no	—
66	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
69	C₂×C₈×C₈₉	—	2	2	no	—
70	C₂×C₈×C₈₉	—	2	2	no	—
71	C₂×C₈×C₈₉	—	4	2	no	—
72	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₈₉	#41	1	1	yes	characteristic
80	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₈₉	—	2	2	no	—
82	C₂×C₄×C₈₉	—	4	1	no	—
83	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
86	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
88	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₈₉	#135	1	2	yes	—
90	C₂×C₄×C₈₉	#137	1	2	yes	—
91	C₂×Dic₈₉	—	2	4	no	—
92	C₂×Dic₈₉	—	2	2	no	—
93	C₂×Dic₈₉	—	2	2	no	—
94	C₂×Dic₈₉	—	4	2	no	—
95	Dic₁₇₈	—	2	4	no	—
96	Dic₁₇₈	—	2	2	no	—
97	Dic₁₇₈	#108	1	4	yes	—
98	C₈×C₈₉	—	2	1	no	—
99	C₈×C₈₉	—	2	1	no	—
100	C₈×C₈₉	—	2	1	no	—
101	C₈×C₈₉	—	2	1	no	—
102	C₈×C₈₉	—	8	2	no	—
103	#10623494	—	4	2	no	—
104	#10623494	—	8	2	no	—
105	C₂²×C₈₉	—	2	1	no	—
106	C₂²×C₈₉	—	2	1	no	—
107	C₂²×C₈₉	#380	1	1	yes	characteristic
108	C₂²×C₈₉	#479	1	2	yes	—
109	C₄×C₈₉	—	2	1	no	—
110	C₄×C₈₉	—	2	1	no	—
111	C₄×C₈₉	—	2	1	no	—
112	C₄×C₈₉	#416	1	1	yes	characteristic
113	C₄×C₈₉	#419	1	1	yes	characteristic
114	C₄×C₈₉	C₂×#108	1	2	yes	—
115	C₄×C₈₉	#464	1	2	yes	—
116	Dic₈₉	—	2	4	no	—
117	Dic₈₉	—	4	2	no	—
118	#8661	—	89	1	no	maximal, Sylow
119	C₂×C₈₉	—	2	2	no	—
120	C₂×C₈₉	#1805	1	1	yes	characteristic
121	C₂×C₈₉	#1810	1	1	yes	characteristic
122	C₂×C₈₉	#1814	1	1	yes	characteristic
123	C₂×C₈×Q₈	—	89	1	no	—
124	#1837	—	89	1	no	—
125	#1564	D₈₉	1	1	yes	characteristic
126	#1487	—	89	2	no	—
127	#1301	—	89	2	no	—
128	C₈₉	#8661	1	1	yes	characteristic, complemented, Sylow
129	C₂×C₄×Q₈	—	89	1	no	—
130	C₈×Q₈	—	89	2	no	—
131	C₈×Q₈	—	89	2	no	—
132	C₈×Q₈	—	178	1	no	—
133	C₈×Q₈	—	178	1	no	—
134	#431	C₂×D₈₉	1	2	yes	—
135	#423	—	89	2	no	—
136	C₂×C₄⋊C₈	—	89	1	no	—
137	C₂×C₄⋊C₈	—	178	1	no	—
138	C₂×C₄×C₈	—	178	1	no	—
139	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
140	#341	—	178	1	no	—
141	#341	—	178	1	no	—
142	#335	—	2	1	no	—
143	#334	—	2	1	no	—
144	Q₈⋊C₈	—	178	4	no	—
145	C₂²×Q₈	—	89	1	no	—
146	C₂×M₁₆	—	178	2	no	—
147	C₂²×C₈	—	178	1	no	—
148	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
149	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
150	C₄×Q₈	—	89	2	no	—
151	C₄×Q₈	—	89	2	no	—
152	C₄×Q₈	—	178	1	no	—
153	C₄×Q₈	—	178	1	no	—
154	C₂×C₄⋊C₄	—	89	1	no	—
155	C₂×C₄⋊C₄	—	178	1	no	—
156	C₂×C₄²	—	178	1	no	—
157	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	89	2	no	—
160	C₄⋊C₈	—	178	2	no	—
161	C₄⋊C₈	—	178	2	no	—
162	C₄⋊C₈	—	178	2	no	—
163	C₄⋊C₈	—	178	1	no	—
164	C₄⋊C₈	—	178	2	no	—
165	C₂²⋊C₈	—	2	2	no	—
166	C₄×C₈	—	2	2	no	—
167	C₄×C₈	—	178	2	no	—
168	C₄×C₈	—	178	2	no	—
169	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
170	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
171	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
172	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
173	C₂×Q₈	—	89	2	no	—
174	C₂×Q₈	—	178	4	no	—
175	C₂×Q₈	—	178	1	no	—
176	C₂²×C₄	—	178	1	no	—
177	C₂²×C₄	—	178	1	no	—
178	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
179	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
180	C₂²×C₄	#13083573	1	1	yes	characteristic
181	M₁₆	—	356	2	no	—
182	M₁₆	—	356	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	356	2	no	—
187	C₂×C₈	—	356	2	no	—
188	C₂×C₈	—	178	2	no	—
189	C₂×C₈	#13083551	1	1	yes	characteristic
190	C₂×C₈	#13083551	1	1	yes	characteristic
191	C₂×C₈	#13083551	1	1	yes	characteristic
192	C₂×C₈	#13083551	1	1	yes	characteristic
193	C₄⋊C₄	—	89	2	no	—
194	C₄⋊C₄	—	178	2	no	—
195	C₄⋊C₄	—	178	2	no	—
196	C₄⋊C₄	—	178	1	no	—
197	C₄²	—	178	2	no	—
198	C₄²	—	178	2	no	—
199	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
200	C₄²	D₄×D₈₉	1	1	yes	characteristic
201	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
202	C₄²	#13083575	1	1	yes	characteristic
203	C₂³	#15667992	1	1	yes	characteristic
204	Q₈	—	89	4	no	—
205	Q₈	—	178	4	no	—
206	Q₈	—	178	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	356	2	no	—
210	C₂×C₄	—	178	2	no	—
211	C₂×C₄	—	178	4	no	—
212	C₂×C₄	—	178	2	no	—
213	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
214	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
215	C₂×C₄	#15667970	1	1	yes	characteristic
216	C₂×C₄	#15667983	1	1	yes	characteristic
217	C₂×C₄	#15667987	1	1	yes	characteristic
218	C₂×C₄	#15667988	1	1	yes	characteristic
219	C₂×C₄	#15668034	1	2	yes	—
220	C₂×C₄	#15668045	1	2	yes	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	2	1	no	—
224	C₈	—	2	1	no	—
225	C₈	—	8	2	no	—
226	C₈	—	356	2	no	—
227	C₈	—	712	2	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	#19151455	1	1	yes	characteristic
231	C₂²	#19151906	1	2	yes	—
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	356	2	no	—
236	C₄	—	178	4	no	—
237	C₄	#19151595	1	1	yes	characteristic
238	C₄	#19151608	1	1	yes	characteristic
239	C₄	#108×D₈₉	1	2	yes	—
240	C₄	#19151821	1	2	yes	—
241	C₂	—	2	2	no	—
242	C₂	#26020268	1	1	yes	characteristic
243	C₂	#26020287	1	1	yes	characteristic
244	C₂	#26020303	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₁₇₈

C₂

yes

maximal, characteristic

#26020390

C₂

yes

maximal, characteristic

#26018682

C₂

yes

maximal

#26018148

C₂

yes

maximal

C₈₉×#1564

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₇₈

C₂²

yes

characteristic

C₈×Dic₁₇₈

—

C₈×Dic₁₇₈

—

C₈×Dic₁₇₈

C₄

yes

—

C₈×Dic₁₇₈

C₄

yes

—

#19151622

C₂²

yes

—

C₂×C₄⋊#10623494

C₂²

yes

characteristic

C₂×#15667941

—

C₂×C₈×Dic₈₉

—

#19151363

—

#19151363

—

#19151330

—

#431×C₈₉

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

#335×C₈₉

—

#334×C₈₉

—

C₂²×Dic₁₇₈

Q₈

yes

characteristic

C₂×#13083558

—

C₂²×#10623494

—

C₄×Dic₁₇₈

—

C₄×Dic₁₇₈

—

C₄×Dic₁₇₈

C₂×C₄

yes

—

C₄×Dic₁₇₈

D₄

yes

—

C₂×C₄⋊Dic₈₉

Q₈

yes

characteristic

C₂×#13083553

—

C₂×C₄×Dic₈₉

—

—

—

—

C₂×C₄

yes

—

#15667941

—

#15667941

—

C₈×Dic₈₉

—

C₈×Dic₈₉

—

C₂²×C₈×C₈₉

D₄

yes

characteristic

C₂²×C₈×C₈₉

D₄

yes

characteristic

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

C₂²⋊C₈×C₈₉

—

C₄×C₈×C₈₉

—

C₄×C₈×C₈₉

C₂×C₄

yes

characteristic

C₄×C₈×C₈₉

C₂×C₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

C₄⋊C₄

yes

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

—

—

—

—

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

C₄⋊C₄

yes

—

#13083553

—

#13083553

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₈₉

#41

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₄²×C₈₉

C₂²×C₄

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

#41

yes

characteristic

C₂³×C₈₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₉

#135

yes

—

C₂×C₄×C₈₉

#137

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

Dic₁₇₈

#108

yes

—

C₈×C₈₉

—

C₈×C₈₉

—

100

C₈×C₈₉

—

101

C₈×C₈₉

—

102

C₈×C₈₉

—

103

#10623494

—

104

#10623494

—

105

C₂²×C₈₉

—

106

C₂²×C₈₉

—

107

C₂²×C₈₉

#380

yes

characteristic

108

C₂²×C₈₉

#479

yes

—

109

C₄×C₈₉

—

110

C₄×C₈₉

—

111

C₄×C₈₉

—

112

C₄×C₈₉

#416

yes

characteristic

113

C₄×C₈₉

#419

yes

characteristic

114

C₄×C₈₉

C₂×#108

yes

—

115

C₄×C₈₉

#464

yes

—

116

Dic₈₉

—

117

Dic₈₉

—

118

#8661

—

maximal, Sylow

119

C₂×C₈₉

—

120

C₂×C₈₉

#1805

yes

characteristic

121

C₂×C₈₉

#1810

yes

characteristic

122

C₂×C₈₉

#1814

yes

characteristic

123

C₂×C₈×Q₈

—

124

#1837

—

125

#1564

D₈₉

yes

characteristic

126

#1487

—

127

#1301

—

128

C₈₉

#8661

yes

characteristic, complemented, Sylow

129

C₂×C₄×Q₈

—

130

C₈×Q₈

—

131

C₈×Q₈

—

132

C₈×Q₈

—

178

—

133

C₈×Q₈

—

178

—

134

#431

C₂×D₈₉

yes

—

135

#423

—

136

C₂×C₄⋊C₈

—

137

C₂×C₄⋊C₈

—

178

—

138

C₂×C₄×C₈

—

178

—

139

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

140

#341

—

178

—

141

#341

—

178

—

142

#335

—

143

#334

—

144

Q₈⋊C₈

—

178

—

145

C₂²×Q₈

—

146

C₂×M₁₆

—

178

—

147

C₂²×C₈

—

178

—

148

C₂²×C₈

D₃₅₆

yes

characteristic

149

C₂²×C₈

D₃₅₆

yes

characteristic

150

C₄×Q₈

—

151

C₄×Q₈

—

152

C₄×Q₈

—

178

—

153

C₄×Q₈

—

178

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

178

—

156

C₂×C₄²

—

178

—

157

C₂×C₄²

C₂²×D₈₉

yes

characteristic

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

178

—

161

C₄⋊C₈

—

178

—

162

C₄⋊C₈

—

178

—

163

C₄⋊C₈

—

178

—

164

C₄⋊C₈

—

178

—

165

C₂²⋊C₈

—

166

C₄×C₈

—

167

C₄×C₈

—

178

—

168

C₄×C₈

—

178

—

169

C₄×C₈

C₄×D₈₉

yes

characteristic

170

C₄×C₈

C₄×D₈₉

yes

characteristic

171

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

172

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

173

C₂×Q₈

—

174

C₂×Q₈

—

178

—

175

C₂×Q₈

—

178

—

176

C₂²×C₄

—

178

—

177

C₂²×C₄

—

178

—

178

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

179

C₂²×C₄

Q₈×D₈₉

yes

characteristic

180

C₂²×C₄

#13083573

yes

characteristic

181

M₁₆

—

356

—

182

M₁₆

—

356

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

356

—

187

C₂×C₈

—

356

—

188

C₂×C₈

—

178

—

189

C₂×C₈

#13083551

yes

characteristic

190

C₂×C₈

#13083551

yes

characteristic

191

C₂×C₈

#13083551

yes

characteristic

192

C₂×C₈

#13083551

yes

characteristic

193

C₄⋊C₄

—

194

C₄⋊C₄

—

178

—

195

C₄⋊C₄

—

178

—

196

C₄⋊C₄

—

178

—

197

C₄²

—

178

—

198

C₄²

—

178

—

199

C₄²

C₂×C₄×D₈₉

yes

characteristic

200

C₄²

D₄×D₈₉

yes

characteristic

201

C₄²

C₂×C₂²⋊D₈₉

yes

characteristic

202

C₄²

#13083575

yes

characteristic

203

C₂³

#15667992

yes

characteristic

204

Q₈

—

205

Q₈

—

178

—

206

Q₈

—

178

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

356

—

210

C₂×C₄

—

178

—

211

C₂×C₄

—

178

—

212

C₂×C₄

—

178

—

213

C₂×C₄

C₂×#13083551

yes

characteristic

214

C₂×C₄

C₄⋊C₄×D₈₉

yes

characteristic

215

C₂×C₄

#15667970

yes

characteristic

216

C₂×C₄

#15667983

yes

characteristic

217

C₂×C₄

#15667987

yes

characteristic

218

C₂×C₄

#15667988

yes

characteristic

219

C₂×C₄

#15668034

yes

—

220

C₂×C₄

#15668045

yes

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

225

C₈

—

226

C₈

—

356

—

227

C₈

—

712

—

228

C₂²

—

229

C₂²

—

230

C₂²

#19151455

yes

characteristic

231

C₂²

#19151906

yes

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

356

—

236

C₄

—

178

—

237

C₄

#19151595

yes

characteristic

238

C₄

#19151608

yes

characteristic

239

C₄

#108×D₈₉

yes

—

240

C₄

#19151821

yes

—

241

C₂

—

242

C₂

#26020268

yes

characteristic

243

C₂

#26020287

yes

characteristic

244

C₂

#26020303

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#15667987
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1564	C₂
socle	C₂²×C₈₉	#380
prime radical	C₂³×C₈₉	C₂²⋊Q₈
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1564	D₈₉
hypocenter	C₈₉	#8661
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

subgroup

G/H

center

C₂×C₄

#15667987

commutator

C₄²×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1564

C₂

socle

C₂²×C₈₉

#380

prime radical

C₂³×C₈₉

C₂²⋊Q₈

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

N	H ≅ G/N	type
128. C₈₉	#8661	semidirect

H ≅ G/N

type

128. C₈₉

#8661

semidirect

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

subgroup	index
C₂×C₈×Dic₁₇₈	2
#26020390	2
#26018682	2
#26018148	2
C₈₉×#1564	2
#8661	89

subgroup

index

C₂×C₈×Dic₁₇₈

C₈₉×#1564

Subgroups — #36447568

Conjugacy classes of subgroups

Complements

Maximal subgroups