Group #30750303 — subgroups

Subgroups — #30750303

Order 17152.

476 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 155 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	#22563299	C₂	1	1	yes	maximal, characteristic
2	#22561012	C₂	1	1	yes	maximal, characteristic
3	#22560968	C₂	1	2	yes	maximal
4	#22558048	C₂	1	2	yes	maximal
5	C₂×#333×C₆₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#14523977	—	2	2	no	—
7	C₂×#14523967	—	2	2	no	—
8	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
9	#16863303	—	2	2	no	—
10	#16863295	—	2	2	no	—
11	#16863266	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×Dic₆₇	—	2	2	no	—
13	C₄×C₄⋊Dic₆₇	C₂²	1	2	yes	—
14	#16863159	—	2	2	no	—
15	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
17	#333×C₆₇	C₄	1	4	yes	complemented
18	C₂²×C₆₇⋊C₈	—	2	1	no	—
19	C₂×C₄⋊Dic₆₇	—	2	2	no	—
20	C₂×C₄⋊Dic₆₇	—	2	1	no	—
21	C₂×C₄⋊Dic₆₇	—	2	2	no	—
22	C₂×C₄⋊Dic₆₇	D₄	1	2	yes	—
23	C₂×C₄⋊Dic₆₇	D₄	1	2	yes	—
24	C₂×C₄×Dic₆₇	—	2	2	no	—
25	C₂×C₄×Dic₆₇	—	2	2	no	—
26	#14523977	—	4	4	no	—
27	#14523967	—	4	4	no	—
28	C₄×C₆₇⋊C₈	—	2	2	no	—
29	C₆₇⋊#95	—	2	4	no	—
30	C₆₇⋊#95	—	2	2	no	—
31	C₂²×Q₈×C₆₇	D₄	1	2	yes	—
32	C₂²×C₈×C₆₇	—	2	2	no	—
33	C₄⋊Q₈×C₆₇	—	2	2	no	—
34	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
35	C₄⋊Q₈×C₆₇	Q₈	1	2	yes	—
36	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
37	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
38	C₄⋊C₈×C₆₇	—	2	2	no	—
39	C₄⋊C₈×C₆₇	C₂×C₄	1	4	yes	—
40	C₂²×Dic₆₇	—	2	2	no	—
41	C₂²×Dic₆₇	—	2	2	no	—
42	C₂²×Dic₆₇	—	4	1	no	—
43	C₂×C₆₇⋊C₈	—	2	2	no	—
44	C₂×C₆₇⋊C₈	—	4	1	no	—
45	C₂×C₆₇⋊C₈	—	4	1	no	—
46	C₄⋊Dic₆₇	—	2	2	no	—
47	C₄⋊Dic₆₇	—	2	2	no	—
48	C₄⋊Dic₆₇	—	2	2	no	—
49	C₄⋊Dic₆₇	—	4	2	no	—
50	C₄⋊Dic₆₇	—	4	2	no	—
51	C₄⋊Dic₆₇	—	4	2	no	—
52	C₄⋊Dic₆₇	—	8	2	no	—
53	C₄⋊Dic₆₇	Q₁₆	1	4	yes	—
54	C₄×Dic₆₇	—	4	2	no	—
55	C₄×Dic₆₇	—	4	2	no	—
56	C₄×Dic₆₇	—	8	2	no	—
57	C₂×Q₈×C₆₇	—	2	2	no	—
58	C₂×Q₈×C₆₇	—	4	2	no	—
59	C₂×Q₈×C₆₇	—	4	2	no	—
60	C₂×Q₈×C₆₇	C₄⋊C₄	1	4	yes	—
61	C₂²×C₄×C₆₇	—	2	2	no	—
62	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
63	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₆₇	—	2	4	no	—
65	C₂×C₈×C₆₇	—	4	2	no	—
66	C₂×C₈×C₆₇	—	4	2	no	—
67	C₄⋊C₄×C₆₇	—	2	4	no	—
68	C₄⋊C₄×C₆₇	—	2	4	no	—
69	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
70	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
71	C₄²×C₆₇	#41	1	2	yes	—
72	C₂³×C₆₇	#120	1	1	yes	characteristic
73	Q₈×C₆₇	—	4	4	no	—
74	Q₈×C₆₇	—	8	2	no	—
75	C₂×C₄×C₆₇	—	2	1	no	—
76	C₂×C₄×C₆₇	—	2	1	no	—
77	C₂×C₄×C₆₇	—	2	4	no	—
78	C₂×C₄×C₆₇	—	4	2	no	—
79	C₂×C₄×C₆₇	—	4	2	no	—
80	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
82	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
83	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
84	C₂×C₄×C₆₇	C₂×Q₁₆	1	2	yes	—
85	C₂×C₄×C₆₇	#135	1	2	yes	—
86	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
87	C₂×C₄×C₆₇	#137	1	2	yes	—
88	C₂×Dic₆₇	—	2	4	no	—
89	C₂×Dic₆₇	—	4	2	no	—
90	C₂×Dic₆₇	—	4	2	no	—
91	C₂×Dic₆₇	—	4	2	no	—
92	C₂×Dic₆₇	—	4	2	no	—
93	C₂×Dic₆₇	—	4	2	no	—
94	C₂×Dic₆₇	—	8	2	no	—
95	C₂×Dic₆₇	—	8	1	no	—
96	C₈×C₆₇	—	4	4	no	—
97	C₆₇⋊C₈	—	4	2	no	—
98	C₂²×C₆₇	#385	1	1	yes	characteristic
99	C₂²×C₆₇	#449	1	2	yes	—
100	C₂²×C₆₇	#451	1	2	yes	—
101	C₂²×C₆₇	#453	1	1	yes	characteristic
102	C₂²×C₆₇	#455	1	1	yes	characteristic
103	C₄×C₆₇	—	2	1	no	—
104	C₄×C₆₇	—	2	1	no	—
105	C₄×C₆₇	—	4	4	no	—
106	C₄×C₆₇	C₄×Q₁₆	1	2	yes	—
107	C₄×C₆₇	#440	1	2	yes	—
108	C₄×C₆₇	#477	1	2	yes	—
109	C₄×C₆₇	#479	1	2	yes	—
110	Dic₆₇	—	4	4	no	—
111	Dic₆₇	—	8	2	no	—
112	Dic₆₇	—	16	1	no	—
113	#8929	—	67	1	no	maximal, Sylow
114	C₂×C₆₇	#1624	1	1	yes	characteristic
115	C₂×C₆₇	#1633	1	1	yes	characteristic
116	C₂×C₆₇	#1644	1	2	yes	—
117	C₂×C₆₇	#1856	1	1	yes	characteristic
118	C₂×C₆₇	#1863	1	2	yes	—
119	#2369	—	67	1	no	—
120	#1956	—	67	1	no	—
121	#1947	—	67	2	no	—
122	C₂×#333	D₆₇	1	1	yes	characteristic
123	#1279	—	67	2	no	—
124	C₆₇	#8929	1	1	yes	characteristic, complemented, Sylow
125	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
126	C₂×#107	—	134	2	no	—
127	C₂×C₄⋊C₈	C₂×D₆₇	1	2	yes	—
128	C₂×#103	—	134	2	no	—
129	C₂×C₄×C₈	—	67	1	no	—
130	#391	—	134	2	no	—
131	#389	—	134	2	no	—
132	#384	—	67	1	no	—
133	C₄×C₄⋊C₄	—	67	2	no	—
134	C₄×C₄⋊C₄	—	134	2	no	—
135	#340	—	134	2	no	—
136	#333	Dic₆₇	1	4	yes	complemented
137	C₂²×Q₈	D₂₆₈	1	2	yes	—
138	C₂²×C₈	—	2	2	no	—
139	C₂²×C₈	—	134	1	no	—
140	C₄⋊Q₈	—	2	2	no	—
141	C₄⋊Q₈	Dic₁₃₄	1	2	yes	—
142	C₄⋊Q₈	C₂×Dic₆₇	1	2	yes	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	67	2	no	—
145	C₂×C₄⋊C₄	—	67	2	no	—
146	C₂×C₄⋊C₄	—	134	2	no	—
147	C₂×C₄⋊C₄	—	134	1	no	—
148	C₂×C₄⋊C₄	—	134	2	no	—
149	C₂×C₄²	—	134	2	no	—
150	C₂×C₄²	—	134	2	no	—
151	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
152	#107	—	268	4	no	—
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	C₂×Dic₆₇	1	4	yes	—
155	#103	—	268	4	no	—
156	C₄×C₈	—	134	2	no	—
157	#95	—	134	4	no	—
158	#95	—	134	2	no	—
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	4	2	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂×Q₈	C₄⋊Dic₆₇	1	4	yes	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	268	1	no	—
165	C₂²×C₄	—	134	2	no	—
166	C₂²×C₄	—	134	2	no	—
167	C₂²×C₄	D₄×D₆₇	1	2	yes	—
168	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
169	C₂×C₈	—	2	4	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	—	268	1	no	—
173	C₂×C₈	—	268	1	no	—
174	C₂×C₈	—	134	2	no	—
175	C₄⋊C₄	—	2	4	no	—
176	C₄⋊C₄	—	2	4	no	—
177	C₄⋊C₄	—	268	2	no	—
178	C₄⋊C₄	—	268	2	no	—
179	C₄⋊C₄	—	268	2	no	—
180	C₄⋊C₄	—	536	2	no	—
181	C₄⋊C₄	—	67	4	no	—
182	C₄⋊C₄	—	134	2	no	—
183	C₄⋊C₄	—	134	2	no	—
184	C₄⋊C₄	—	134	2	no	—
185	C₄²	—	268	2	no	—
186	C₄²	—	268	2	no	—
187	C₄²	—	536	2	no	—
188	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
189	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
190	C₄²	#11761627	1	2	yes	—
191	C₂³	#14524013	1	1	yes	characteristic
192	Q₈	—	4	4	no	—
193	Q₈	—	8	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	268	2	no	—
200	C₂×C₄	—	268	2	no	—
201	C₂×C₄	—	268	2	no	—
202	C₂×C₄	—	268	2	no	—
203	C₂×C₄	—	268	2	no	—
204	C₂×C₄	—	536	2	no	—
205	C₂×C₄	—	536	1	no	—
206	C₂×C₄	—	134	4	no	—
207	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
208	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
209	C₂×C₄	#14524020	1	2	yes	—
210	C₂×C₄	#14524027	1	1	yes	characteristic
211	C₂×C₄	Q₁₆×D₆₇	1	2	yes	—
212	C₂×C₄	#14524066	1	2	yes	—
213	C₂×C₄	#14524070	1	2	yes	—
214	C₂×C₄	#14524072	1	2	yes	—
215	C₈	—	4	4	no	—
216	C₈	—	268	2	no	—
217	C₂²	#16863271	1	1	yes	characteristic
218	C₂²	#16863544	1	2	yes	—
219	C₂²	#16863553	1	2	yes	—
220	C₂²	#16863566	1	1	yes	characteristic
221	C₂²	#16863576	1	1	yes	characteristic
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	4	4	no	—
225	C₄	—	268	4	no	—
226	C₄	—	536	2	no	—
227	C₄	—	1072	1	no	—
228	C₄	Q₁₆×Dic₆₇	1	2	yes	—
229	C₄	#16863497	1	2	yes	—
230	C₄	#16863689	1	2	yes	—
231	C₄	#16863705	1	2	yes	—
232	C₂	#22559293	1	1	yes	characteristic
233	C₂	#22559350	1	1	yes	characteristic
234	C₂	#22559424	1	2	yes	—
235	C₂	#22560421	1	1	yes	characteristic
236	C₂	#22560465	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22563299

C₂

yes

maximal, characteristic

#22561012

C₂

yes

maximal, characteristic

#22560968

C₂

yes

maximal

#22558048

C₂

yes

maximal

C₂×#333×C₆₇

C₂

yes

maximal, characteristic

C₂×#14523977

—

C₂×#14523967

—

C₂×C₄×C₆₇⋊C₈

C₂²

yes

—

—

C₂²

yes

characteristic

C₄⋊C₄×Dic₆₇

—

C₄×C₄⋊Dic₆₇

C₂²

yes

—

#16863159

—

C₂×C₄⋊Q₈×C₆₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₆₇

C₂²

yes

—

#333×C₆₇

C₄

yes

complemented

C₂²×C₆₇⋊C₈

—

C₂×C₄⋊Dic₆₇

—

C₂×C₄⋊Dic₆₇

—

C₂×C₄⋊Dic₆₇

—

C₂×C₄⋊Dic₆₇

D₄

yes

—

C₂×C₄⋊Dic₆₇

D₄

yes

—

C₂×C₄×Dic₆₇

—

C₂×C₄×Dic₆₇

—

#14523977

—

#14523967

—

C₄×C₆₇⋊C₈

—

C₆₇⋊#95

—

C₆₇⋊#95

—

C₂²×Q₈×C₆₇

D₄

yes

—

C₂²×C₈×C₆₇

—

C₄⋊Q₈×C₆₇

—

C₄⋊Q₈×C₆₇

C₂×C₄

yes

—

C₄⋊Q₈×C₆₇

Q₈

yes

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄²×C₆₇

C₂³

yes

characteristic

C₄⋊C₈×C₆₇

—

C₄⋊C₈×C₆₇

C₂×C₄

yes

—

C₂²×Dic₆₇

—

C₂²×Dic₆₇

—

C₂²×Dic₆₇

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

Q₁₆

yes

—

C₄×Dic₆₇

—

C₄×Dic₆₇

—

C₄×Dic₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

C₄⋊C₄

yes

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂×D₄

yes

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄²×C₆₇

C₂²×C₄

yes

characteristic

C₄²×C₆₇

C₂×Q₈

yes

characteristic

C₄²×C₆₇

#41

yes

—

C₂³×C₆₇

#120

yes

characteristic

Q₈×C₆₇

—

Q₈×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₇

C₄×D₄

yes

—

C₂×C₄×C₆₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₆₇

#123

yes

characteristic

C₂×C₄×C₆₇

C₂×Q₁₆

yes

—

C₂×C₄×C₆₇

#135

yes

—

C₂×C₄×C₆₇

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₆₇

#137

yes

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₈×C₆₇

—

C₆₇⋊C₈

—

C₂²×C₆₇

#385

yes

characteristic

C₂²×C₆₇

#449

yes

—

100

C₂²×C₆₇

#451

yes

—

101

C₂²×C₆₇

#453

yes

characteristic

102

C₂²×C₆₇

#455

yes

characteristic

103

C₄×C₆₇

—

104

C₄×C₆₇

—

105

C₄×C₆₇

—

106

C₄×C₆₇

C₄×Q₁₆

yes

—

107

C₄×C₆₇

#440

yes

—

108

C₄×C₆₇

#477

yes

—

109

C₄×C₆₇

#479

yes

—

110

Dic₆₇

—

111

Dic₆₇

—

112

Dic₆₇

—

113

#8929

—

maximal, Sylow

114

C₂×C₆₇

#1624

yes

characteristic

115

C₂×C₆₇

#1633

yes

characteristic

116

C₂×C₆₇

#1644

yes

—

117

C₂×C₆₇

#1856

yes

characteristic

118

C₂×C₆₇

#1863

yes

—

119

#2369

—

120

#1956

—

121

#1947

—

122

C₂×#333

D₆₇

yes

characteristic

123

#1279

—

124

C₆₇

#8929

yes

characteristic, complemented, Sylow

125

C₂×C₄⋊Q₈

C₂×D₆₇

yes

characteristic

126

C₂×#107

—

134

—

127

C₂×C₄⋊C₈

C₂×D₆₇

yes

—

128

C₂×#103

—

134

—

129

C₂×C₄×C₈

—

130

#391

—

134

—

131

#389

—

134

—

132

#384

—

133

C₄×C₄⋊C₄

—

134

C₄×C₄⋊C₄

—

134

—

135

#340

—

134

—

136

#333

Dic₆₇

yes

complemented

137

C₂²×Q₈

D₂₆₈

yes

—

138

C₂²×C₈

—

139

C₂²×C₈

—

134

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

Dic₁₃₄

yes

—

142

C₄⋊Q₈

C₂×Dic₆₇

yes

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

134

—

147

C₂×C₄⋊C₄

—

134

—

148

C₂×C₄⋊C₄

—

134

—

149

C₂×C₄²

—

134

—

150

C₂×C₄²

—

134

—

151

C₂×C₄²

C₂²×D₆₇

yes

characteristic

152

#107

—

268

—

153

C₄⋊C₈

—

154

C₄⋊C₈

C₂×Dic₆₇

yes

—

155

#103

—

268

—

156

C₄×C₈

—

134

—

157

#95

—

134

—

158

#95

—

134

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

C₄⋊Dic₆₇

yes

—

163

C₂²×C₄

—

164

C₂²×C₄

—

268

—

165

C₂²×C₄

—

134

—

166

C₂²×C₄

—

134

—

167

C₂²×C₄

D₄×D₆₇

yes

—

168

C₂²×C₄

C₂×D₂₆₈

yes

characteristic

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

268

—

173

C₂×C₈

—

268

—

174

C₂×C₈

—

134

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

268

—

178

C₄⋊C₄

—

268

—

179

C₄⋊C₄

—

268

—

180

C₄⋊C₄

—

536

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

134

—

183

C₄⋊C₄

—

134

—

184

C₄⋊C₄

—

134

—

185

C₄²

—

268

—

186

C₄²

—

268

—

187

C₄²

—

536

—

188

C₄²

C₂²×Dic₆₇

yes

characteristic

189

C₄²

C₂×Dic₁₃₄

yes

characteristic

190

C₄²

#11761627

yes

—

191

C₂³

#14524013

yes

characteristic

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

268

—

200

C₂×C₄

—

268

—

201

C₂×C₄

—

268

—

202

C₂×C₄

—

268

—

203

C₂×C₄

—

268

—

204

C₂×C₄

—

536

—

205

C₂×C₄

—

536

—

206

C₂×C₄

—

134

—

207

C₂×C₄

C₂×C₄⋊Dic₆₇

yes

characteristic

208

C₂×C₄

D₄×Dic₆₇

yes

—

209

C₂×C₄

#14524020

yes

—

210

C₂×C₄

#14524027

yes

characteristic

211

C₂×C₄

Q₁₆×D₆₇

yes

—

212

C₂×C₄

#14524066

yes

—

213

C₂×C₄

#14524070

yes

—

214

C₂×C₄

#14524072

yes

—

215

C₈

—

216

C₈

—

268

—

217

C₂²

#16863271

yes

characteristic

218

C₂²

#16863544

yes

—

219

C₂²

#16863553

yes

—

220

C₂²

#16863566

yes

characteristic

221

C₂²

#16863576

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

268

—

226

C₄

—

536

—

227

C₄

—

1072

—

228

C₄

Q₁₆×Dic₆₇

yes

—

229

C₄

#16863497

yes

—

230

C₄

#16863689

yes

—

231

C₄

#16863705

yes

—

232

C₂

#22559293

yes

characteristic

233

C₂

#22559350

yes

characteristic

234

C₂

#22559424

yes

—

235

C₂

#22560421

yes

characteristic

236

C₂

#22560465

yes

—

	subgroup	G/H
center	C₂³	#14524013
commutator	C₄²×C₆₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₂×#333×C₆₇	C₂
socle, prime radical	C₂³×C₆₇	#120
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	C₂×#333	D₆₇
hypocenter	C₆₇	#8929
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

subgroup

G/H

center

C₂³

#14524013

commutator

C₄²×C₆₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₆₇

Fitting

C₂×#333×C₆₇

C₂

socle, prime radical

C₂³×C₆₇

#120

cosocle

C₂×C₄²×C₆₇

C₂³

D₆₇

C₆₇

G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

N	H ≅ G/N	type
17. #333×C₆₇	C₄	semidirect
124. C₆₇	#8929	semidirect
136. #333	Dic₆₇	semidirect

H ≅ G/N

type

17. #333×C₆₇

C₄

semidirect

124. C₆₇

#8929

semidirect

136. #333

Dic₆₇

semidirect

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

subgroup	index
#22563299	2
#22561012	2
#22560968	2
#22558048	2
C₂×#333×C₆₇	2
#8929	67

subgroup

index

C₂×#333×C₆₇

Subgroups — #30750303

Conjugacy classes of subgroups

Complements

Maximal subgroups