Group #30755724 — subgroups

Subgroups — #30755724

Order 17152.

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

normal subgroups only

This group has 498 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	#22570788	C₂	1	1	yes	maximal, characteristic
2	#22561036	C₂	1	2	yes	maximal, complemented
3	#22559954	C₂	1	1	yes	maximal, characteristic, complemented
4	#22558659	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1567	C₂	1	1	yes	maximal, characteristic, complemented
6	#16863946	C₂²	1	2	yes	—
7	#16863801	C₄	1	1	yes	characteristic, complemented
8	#16863773	C₄	1	1	yes	characteristic, complemented
9	#16863743	C₄	1	2	yes	complemented
10	#16863632	—	2	2	no	—
11	C₄×D₅₃₆	—	2	2	no	—
12	C₂×#14523969	—	2	4	no	—
13	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic
15	#16863150	—	2	2	no	—
16	#16863123	—	2	4	no	—
17	#423×C₆₇	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
19	#335×C₆₇	—	2	2	no	—
20	C₂×#11761628	—	2	2	no	—
21	C₂×D₅₃₆	—	2	2	no	—
22	C₂²×C₆₇⋊C₈	—	2	1	no	—
23	#14524043	C₂×C₄	1	2	yes	—
24	#14524040	C₂×C₄	1	2	yes	—
25	#14524031	—	2	2	no	—
26	#14524017	—	2	2	no	—
27	#14524017	—	2	2	no	—
28	C₄×D₂₆₈	—	2	2	no	—
29	C₄×D₂₆₈	—	2	2	no	—
30	C₂×C₄×Dic₆₇	—	2	1	no	—
31	C₂×C₄×Dic₆₇	—	2	1	no	—
32	C₂×C₄×Dic₆₇	D₄	1	2	yes	—
33	#14523977	—	2	2	no	—
34	#14523969	—	4	8	no	—
35	#14523965	—	2	4	no	—
36	C₄×C₆₇⋊C₈	—	2	1	no	—
37	C₄×C₆₇⋊C₈	D₄	1	2	yes	—
38	C₂×M₁₆×C₆₇	—	2	2	no	—
39	C₂²×C₈×C₆₇	D₄	1	2	yes	—
40	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
41	C₄⋊C₈×C₆₇	—	2	2	no	—
42	C₄⋊C₈×C₆₇	—	2	2	no	—
43	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₆₇	D₄	1	2	yes	—
46	#11761628	—	4	4	no	—
47	#11761628	—	4	4	no	—
48	C₂×Dic₁₃₄	—	2	2	no	—
49	C₂×D₂₆₈	—	2	2	no	—
50	C₂×D₂₆₈	—	2	2	no	—
51	C₂×D₂₆₈	—	2	2	no	—
52	C₂×C₂²⋊D₆₇	—	4	2	no	—
53	C₂²×Dic₆₇	—	2	2	no	—
54	C₂×C₄×D₆₇	—	4	2	no	—
55	D₅₃₆	—	4	4	no	—
56	C₂×C₆₇⋊C₈	—	2	2	no	—
57	C₂×C₆₇⋊C₈	—	4	2	no	—
58	C₄⋊Dic₆₇	—	2	2	no	—
59	C₄⋊Dic₆₇	—	2	2	no	—
60	(C₂×D₆₇)⋊C₄	—	4	2	no	—
61	(C₂×D₆₇)⋊C₄	—	4	2	no	—
62	C₄×Dic₆₇	—	2	2	no	—
63	C₄×Dic₆₇	—	4	2	no	—
64	C₄×Dic₆₇	—	4	2	no	—
65	C₄×Dic₆₇	D₈	1	4	yes	complemented
66	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
69	M₁₆×C₆₇	—	4	4	no	—
70	C₂×C₈×C₆₇	—	4	2	no	—
71	C₂×C₈×C₆₇	—	4	2	no	—
72	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
74	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₆₇	#41	1	1	yes	characteristic
78	C₂³×C₆₇	#121	1	1	yes	characteristic
79	C₂²×D₆₇	—	4	2	no	—
80	C₂×C₄×C₆₇	—	2	2	no	—
81	C₂×C₄×C₆₇	—	2	2	no	—
82	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
86	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
87	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
88	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
89	C₂×C₄×C₆₇	#135	1	2	yes	—
90	C₂²⋊D₆₇	—	8	4	no	—
91	C₂×Dic₆₇	—	2	4	no	—
92	C₂×Dic₆₇	—	4	2	no	—
93	C₂×Dic₆₇	—	4	2	no	—
94	C₂×Dic₆₇	—	4	2	no	—
95	D₂₆₈	—	4	4	no	—
96	D₂₆₈	—	4	4	no	—
97	D₂₆₈	—	4	4	no	—
98	C₄×D₆₇	—	8	2	no	—
99	C₄×D₆₇	—	8	2	no	—
100	Dic₁₃₄	—	4	4	no	—
101	C₈×C₆₇	—	2	2	no	—
102	C₈×C₆₇	—	2	2	no	—
103	C₈×C₆₇	—	8	2	no	—
104	C₆₇⋊C₈	—	4	2	no	—
105	C₂²×C₆₇	—	2	1	no	—
106	C₂²×C₆₇	—	2	1	no	—
107	C₂²×C₆₇	#390	1	1	yes	characteristic
108	C₂²×C₆₇	#466	1	2	yes	—
109	C₂×D₆₇	—	8	2	no	—
110	C₂×D₆₇	—	8	2	no	—
111	C₂×D₆₇	—	8	2	no	—
112	C₄×C₆₇	—	2	1	no	—
113	C₄×C₆₇	—	2	1	no	—
114	C₄×C₆₇	#421	1	2	yes	—
115	C₄×C₆₇	C₄×D₈	1	2	yes	—
116	C₄×C₆₇	#444	1	2	yes	—
117	C₄×C₆₇	#493	1	1	yes	characteristic
118	C₄×C₆₇	#495	1	1	yes	characteristic
119	Dic₆₇	—	4	4	no	—
120	Dic₆₇	—	8	2	no	—
121	#9847	—	67	1	no	maximal, Sylow
122	C₂×C₆₇	—	2	2	no	—
123	C₂×C₆₇	#1963	1	1	yes	characteristic
124	C₂×C₆₇	#1970	1	1	yes	characteristic
125	C₂×C₆₇	#1975	1	1	yes	characteristic
126	D₆₇	—	16	2	no	—
127	#3169	—	67	1	no	—
128	#1962	—	67	2	no	—
129	#1744	—	67	1	no	—
130	#1567	D₆₇	1	1	yes	characteristic, complemented
131	#1492	—	67	2	no	—
132	C₆₇	#9847	1	1	yes	characteristic, complemented, Sylow
133	#532	—	67	2	no	—
134	#500	—	67	1	no	—
135	#493	—	67	1	no	—
136	#486	—	67	2	no	—
137	#466	—	134	2	no	—
138	C₄×D₈	—	134	2	no	—
139	#423	C₂×D₆₇	1	2	yes	—
140	C₂×#104	—	134	4	no	—
141	C₂×C₄×C₈	—	67	1	no	—
142	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
143	C₄³	—	67	1	no	—
144	#336	—	134	2	no	—
145	#335	—	2	2	no	—
146	D₄⋊C₈	—	134	4	no	—
147	C₂×#41	—	134	2	no	—
148	C₂×D₈	—	134	2	no	—
149	C₂×M₁₆	—	2	2	no	—
150	C₂²×C₈	—	134	1	no	—
151	C₂²×C₈	D₂₆₈	1	2	yes	—
152	C₄⋊Q₈	—	67	2	no	—
153	#127	—	67	2	no	—
154	#124	—	134	2	no	—
155	#121	—	134	2	no	—
156	#121	—	134	2	no	—
157	C₄×D₄	—	134	2	no	—
158	C₄×D₄	—	134	2	no	—
159	C₂×C₄²	—	67	2	no	—
160	C₂×C₄²	—	134	1	no	—
161	C₂×C₄²	—	134	1	no	—
162	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
163	#107	—	134	2	no	—
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	2	2	no	—
166	#104	—	268	8	no	—
167	#102	—	134	4	no	—
168	C₄×C₈	—	67	2	no	—
169	C₄×C₈	—	134	1	no	—
170	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
171	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
172	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
173	#41	—	268	4	no	—
174	#41	—	268	4	no	—
175	C₂×Q₈	—	134	2	no	—
176	C₂×D₄	—	268	2	no	—
177	C₂×D₄	—	134	2	no	—
178	C₂×D₄	—	134	2	no	—
179	C₂×D₄	—	134	2	no	—
180	C₂²×C₄	—	268	2	no	—
181	C₂²×C₄	—	134	2	no	—
182	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
183	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
184	C₂²×C₄	#11761629	1	1	yes	characteristic
185	D₈	—	268	4	no	—
186	M₁₆	—	4	4	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	4	2	no	—
189	C₂×C₈	—	268	2	no	—
190	C₂×C₈	—	134	2	no	—
191	C₂×C₈	(C₂×D₆₇)⋊C₄	1	2	yes	—
192	C₂×C₈	(C₂×D₆₇)⋊C₄	1	2	yes	—
193	C₄⋊C₄	—	134	2	no	—
194	C₄⋊C₄	—	134	2	no	—
195	C₂²⋊C₄	—	268	2	no	—
196	C₂²⋊C₄	—	268	2	no	—
197	C₄²	—	268	2	no	—
198	C₄²	—	268	2	no	—
199	C₄²	—	67	4	no	—
200	C₄²	—	134	2	no	—
201	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
202	C₄²	D₄×D₆₇	1	1	yes	characteristic
203	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
204	C₄²	#11761629	1	1	yes	characteristic
205	C₂³	—	268	2	no	—
206	C₂³	#14524018	1	1	yes	characteristic
207	Q₈	—	268	4	no	—
208	D₄	—	268	4	no	—
209	D₄	—	268	4	no	—
210	D₄	—	268	4	no	—
211	D₄	—	536	4	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	268	2	no	—
215	C₂×C₄	—	268	2	no	—
216	C₂×C₄	—	268	2	no	—
217	C₂×C₄	—	536	2	no	—
218	C₂×C₄	—	536	2	no	—
219	C₂×C₄	—	134	4	no	—
220	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
221	C₂×C₄	#14524005	1	1	yes	characteristic
222	C₂×C₄	#14524005	1	1	yes	characteristic
223	C₂×C₄	#14524018	1	1	yes	characteristic
224	C₂×C₄	#14524032	1	1	yes	characteristic
225	C₂×C₄	#14524039	1	1	yes	characteristic
226	C₂×C₄	D₈×D₆₇	1	2	yes	—
227	C₂×C₄	#14524066	1	2	yes	—
228	C₈	—	2	2	no	—
229	C₈	—	2	2	no	—
230	C₈	—	8	2	no	—
231	C₈	—	268	2	no	—
232	C₂²	—	2	1	no	—
233	C₂²	—	2	1	no	—
234	C₂²	—	536	2	no	—
235	C₂²	—	536	2	no	—
236	C₂²	—	536	2	no	—
237	C₂²	#16863297	1	1	yes	characteristic
238	C₂²	#16863633	1	2	yes	—
239	C₄	—	2	1	no	—
240	C₄	—	2	1	no	—
241	C₄	—	268	4	no	—
242	C₄	—	536	2	no	—
243	C₄	#16863412	1	2	yes	—
244	C₄	#16863478	1	2	yes	—
245	C₄	#16863517	1	2	yes	—
246	C₄	#16863771	1	1	yes	characteristic
247	C₄	#16863781	1	1	yes	characteristic
248	C₂	—	2	2	no	—
249	C₂	—	1072	2	no	—
250	C₂	#22561040	1	1	yes	characteristic
251	C₂	#22561073	1	1	yes	characteristic
252	C₂	#22561100	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22570788

C₂

yes

maximal, characteristic

#22561036

C₂

yes

maximal, complemented

#22559954

C₂

yes

maximal, characteristic, complemented

#22558659

C₂

yes

maximal, complemented

C₆₇×#1567

C₂

yes

maximal, characteristic, complemented

#16863946

C₂²

yes

—

#16863801

C₄

yes

characteristic, complemented

#16863773

C₄

yes

characteristic, complemented

#16863743

C₄

yes

complemented

#16863632

—

C₄×D₅₃₆

—

C₂×#14523969

—

C₂×C₄×C₆₇⋊C₈

C₂²

yes

characteristic

C₄²×Dic₆₇

C₂²

yes

characteristic

#16863150

—

#16863123

—

#423×C₆₇

C₂²

yes

—

C₂×C₄×C₈×C₆₇

C₂²

yes

characteristic

#335×C₆₇

—

C₂×#11761628

—

C₂×D₅₃₆

—

C₂²×C₆₇⋊C₈

—

#14524043

C₂×C₄

yes

—

#14524040

C₂×C₄

yes

—

#14524031

—

#14524017

—

#14524017

—

C₄×D₂₆₈

—

C₄×D₂₆₈

—

C₂×C₄×Dic₆₇

—

C₂×C₄×Dic₆₇

—

C₂×C₄×Dic₆₇

D₄

yes

—

#14523977

—

#14523969

—

#14523965

—

C₄×C₆₇⋊C₈

—

C₄×C₆₇⋊C₈

D₄

yes

—

C₂×M₁₆×C₆₇

—

C₂²×C₈×C₆₇

D₄

yes

—

C₂×C₄²×C₆₇

C₂³

yes

characteristic

C₄⋊C₈×C₆₇

—

C₄⋊C₈×C₆₇

—

C₄×C₈×C₆₇

C₂×C₄

yes

characteristic

C₄×C₈×C₆₇

C₂×C₄

yes

characteristic

C₄×C₈×C₆₇

D₄

yes

—

#11761628

—

#11761628

—

C₂×Dic₁₃₄

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×C₂²⋊D₆₇

—

C₂²×Dic₆₇

—

C₂×C₄×D₆₇

—

D₅₃₆

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

(C₂×D₆₇)⋊C₄

—

(C₂×D₆₇)⋊C₄

—

C₄×Dic₆₇

—

C₄×Dic₆₇

—

C₄×Dic₆₇

—

C₄×Dic₆₇

D₈

yes

complemented

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₇

#41

yes

characteristic

M₁₆×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

C₂²⋊C₄

yes

—

C₂×C₈×C₆₇

C₂²⋊C₄

yes

—

C₄²×C₆₇

C₂²×C₄

yes

characteristic

C₄²×C₆₇

C₂×D₄

yes

characteristic

C₄²×C₆₇

C₂×D₄

yes

C₄²×C₆₇

yes

C₂³×C₆₇

yes

C₂²×D₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₇

C₄×D₄

yes

characteristic

C₂×C₄×C₆₇

C₄×D₄

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

C₂×D₈

yes

—

C₂×C₄×C₆₇

#135

yes

—

C₂²⋊D₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

D₂₆₈

—

D₂₆₈

—

D₂₆₈

—

C₄×D₆₇

—

C₄×D₆₇

—

100

Dic₁₃₄

—

101

C₈×C₆₇

—

102

C₈×C₆₇

—

103

C₈×C₆₇

—

104

C₆₇⋊C₈

—

105

C₂²×C₆₇

—

106

C₂²×C₆₇

—

107

C₂²×C₆₇

#390

yes

characteristic

108

C₂²×C₆₇

#466

yes

—

109

C₂×D₆₇

—

110

C₂×D₆₇

—

111

C₂×D₆₇

—

112

C₄×C₆₇

—

113

C₄×C₆₇

—

114

C₄×C₆₇

#421

yes

—

115

C₄×C₆₇

C₄×D₈

yes

—

116

C₄×C₆₇

#444

yes

—

117

C₄×C₆₇

#493

yes

characteristic

118

C₄×C₆₇

#495

yes

characteristic

119

Dic₆₇

—

120

Dic₆₇

—

121

#9847

—

maximal, Sylow

122

C₂×C₆₇

—

123

C₂×C₆₇

#1963

yes

characteristic

124

C₂×C₆₇

#1970

yes

characteristic

125

C₂×C₆₇

#1975

yes

characteristic

126

D₆₇

—

127

#3169

—

128

#1962

—

129

#1744

—

130

#1567

D₆₇

yes

characteristic, complemented

131

#1492

—

132

C₆₇

#9847

yes

characteristic, complemented, Sylow

133

#532

—

134

#500

—

135

#493

—

136

#486

—

137

#466

—

134

—

138

C₄×D₈

—

134

—

139

#423

C₂×D₆₇

yes

—

140

C₂×#104

—

134

—

141

C₂×C₄×C₈

—

142

C₂×C₄×C₈

C₂×D₆₇

yes

characteristic

143

C₄³

—

144

#336

—

134

—

145

#335

—

146

D₄⋊C₈

—

134

—

147

C₂×#41

—

134

—

148

C₂×D₈

—

134

—

149

C₂×M₁₆

—

150

C₂²×C₈

—

134

—

151

C₂²×C₈

D₂₆₈

yes

—

152

C₄⋊Q₈

—

153

#127

—

154

#124

—

134

—

155

#121

—

134

—

156

#121

—

134

—

157

C₄×D₄

—

134

—

158

C₄×D₄

—

134

—

159

C₂×C₄²

—

160

C₂×C₄²

—

134

—

161

C₂×C₄²

—

134

—

162

C₂×C₄²

C₂²×D₆₇

yes

characteristic

163

#107

—

134

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

#104

—

268

—

167

#102

—

134

—

168

C₄×C₈

—

169

C₄×C₈

—

134

—

170

C₄×C₈

C₄×D₆₇

yes

characteristic

171

C₄×C₈

C₄×D₆₇

yes

characteristic

172

C₄×C₈

C₂²⋊D₆₇

yes

—

173

#41

—

268

—

174

#41

—

268

—

175

C₂×Q₈

—

134

—

176

C₂×D₄

—

268

—

177

C₂×D₄

—

134

—

178

C₂×D₄

—

134

—

179

C₂×D₄

—

134

—

180

C₂²×C₄

—

268

—

181

C₂²×C₄

—

134

—

182

C₂²×C₄

D₄×D₆₇

yes

characteristic

183

C₂²×C₄

C₂×D₂₆₈

yes

characteristic

184

C₂²×C₄

#11761629

yes

characteristic

185

D₈

—

268

—

186

M₁₆

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

268

—

190

C₂×C₈

—

134

—

191

C₂×C₈

(C₂×D₆₇)⋊C₄

yes

—

192

C₂×C₈

(C₂×D₆₇)⋊C₄

yes

—

193

C₄⋊C₄

—

134

—

194

C₄⋊C₄

—

134

—

195

C₂²⋊C₄

—

268

—

196

C₂²⋊C₄

—

268

—

197

C₄²

—

268

—

198

C₄²

—

268

—

199

C₄²

—

200

C₄²

—

134

—

201

C₄²

C₂×C₄×D₆₇

yes

characteristic

202

C₄²

D₄×D₆₇

yes

characteristic

203

C₄²

C₂×C₂²⋊D₆₇

yes

characteristic

204

C₄²

#11761629

yes

characteristic

205

C₂³

—

268

—

206

C₂³

#14524018

yes

characteristic

207

Q₈

—

268

—

208

D₄

—

268

—

209

D₄

—

268

—

210

D₄

—

268

—

211

D₄

—

536

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

268

—

215

C₂×C₄

—

268

—

216

C₂×C₄

—

268

—

217

C₂×C₄

—

536

—

218

C₂×C₄

—

536

—

219

C₂×C₄

—

134

—

220

C₂×C₄

C₂×(C₂×D₆₇)⋊C₄

yes

characteristic

221

C₂×C₄

#14524005

yes

characteristic

222

C₂×C₄

#14524005

yes

characteristic

223

C₂×C₄

#14524018

yes

characteristic

224

C₂×C₄

#14524032

yes

characteristic

225

C₂×C₄

#14524039

yes

characteristic

226

C₂×C₄

D₈×D₆₇

yes

—

227

C₂×C₄

#14524066

yes

—

228

C₈

—

229

C₈

—

230

C₈

—

231

C₈

—

268

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

536

—

235

C₂²

—

536

—

236

C₂²

—

536

—

237

C₂²

#16863297

yes

characteristic

238

C₂²

#16863633

yes

—

239

C₄

—

240

C₄

—

241

C₄

—

268

—

242

C₄

—

536

—

243

C₄

#16863412

yes

—

244

C₄

#16863478

yes

—

245

C₄

#16863517

yes

—

246

C₄

#16863771

yes

characteristic

247

C₄

#16863781

yes

characteristic

248

C₂

—

249

C₂

—

1072

—

250

C₂

#22561040

yes

characteristic

251

C₂

#22561073

yes

characteristic

252

C₂

#22561100

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14524039
commutator	C₄²×C₆₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₆₇×#1567	C₂
socle	C₂²×C₆₇	#390
prime radical	#22570788	C₂
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	#1567	D₆₇
hypocenter	C₆₇	#9847
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

subgroup

G/H

center

C₂×C₄

#14524039

commutator

C₄²×C₆₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₆₇

Fitting

C₆₇×#1567

C₂

C₂²×C₆₇

C₂

C₂×C₄²×C₆₇

C₂³

D₆₇

C₆₇

G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

N	H ≅ G/N	type
2. #22561036	C₂	semidirect
3. #22559954	C₂	semidirect
4. #22558659	C₂	semidirect
5. C₆₇×#1567	C₂	semidirect
7. #16863801	C₄	semidirect
8. #16863773	C₄	semidirect
9. #16863743	C₄	semidirect
65. C₄×Dic₆₇	D₈	semidirect
130. #1567	D₆₇	semidirect
132. C₆₇	#9847	semidirect

H ≅ G/N

type

2. #22561036

C₂

semidirect

3. #22559954

C₂

semidirect

4. #22558659

C₂

semidirect

5. C₆₇×#1567

C₂

semidirect

7. #16863801

C₄

semidirect

8. #16863773

C₄

semidirect

9. #16863743

C₄

semidirect

65. C₄×Dic₆₇

D₈

semidirect

130. #1567

D₆₇

semidirect

132. C₆₇

#9847

semidirect

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

subgroup	index
#22570788	2
#22561036	2
#22559954	2
#22558659	2
C₆₇×#1567	2
#9847	67

subgroup

index

C₆₇×#1567

Subgroups — #30755724

Conjugacy classes of subgroups

Complements

Maximal subgroups