Group #30774325 — subgroups

Subgroups — #30774325

Order 17152.

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

normal subgroups only

This group has 482 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	#22561965	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863212	C₂	1	2	yes	maximal, complemented
3	C₂×#16863209	C₂	1	2	yes	maximal
4	C₄×#14523979	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#495×C₆₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#14523983	C₂²	1	2	yes	—
7	C₂×#14523979	C₂²	1	2	yes	—
8	C₄×#11761612	—	2	1	no	—
9	C₄⋊(C₆₇⋊C₁₆)	—	2	2	no	—
10	#16863212	—	2	4	no	—
11	#16863209	—	2	4	no	—
12	#16863161	—	2	1	no	—
13	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₆₇	—	2	1	no	—
15	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×#124×C₆₇	—	2	1	no	—
17	#495×C₆₇	—	2	2	no	—
18	#495×C₆₇	C₄	1	4	yes	—
19	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×#11761612	—	2	2	no	—
21	#14523983	—	2	2	no	—
22	#14523983	—	2	2	no	—
23	C₂×C₆₇⋊C₁₆	—	2	2	no	—
24	#14523979	—	2	2	no	—
25	#14523979	D₄	1	4	yes	—
26	#14523954	—	4	1	no	—
27	C₄×C₆₇⋊C₈	—	4	1	no	—
28	C₂²×Q₈×C₆₇	—	2	1	no	—
29	C₂²×D₄×C₆₇	—	2	1	no	—
30	C₂×Q₁₆×C₆₇	—	2	2	no	—
31	C₂×Q₁₆×C₆₇	—	2	1	no	—
32	C₂×Q₁₆×C₆₇	—	2	2	no	—
33	C₂×Q₁₆×C₆₇	C₂×C₄	1	2	yes	—
34	C₂×SD₁₆×C₆₇	—	2	4	no	—
35	C₂×SD₁₆×C₆₇	—	4	4	no	—
36	C₂×D₈×C₆₇	—	2	2	no	—
37	C₂×D₈×C₆₇	—	2	1	no	—
38	C₂×D₈×C₆₇	—	2	2	no	—
39	C₂×D₈×C₆₇	C₂×C₄	1	2	yes	—
40	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
42	#124×C₆₇	—	2	4	no	—
43	#124×C₆₇	—	4	1	no	—
44	#124×C₆₇	—	4	1	no	—
45	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
46	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
47	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
48	C₄×C₈×C₆₇	D₄	1	2	yes	—
49	#11761612	—	2	4	no	—
50	#11761612	—	4	2	no	—
51	C₂×C₆₇⋊C₈	—	4	2	no	—
52	C₆₇⋊C₁₆	—	4	2	no	—
53	C₂⁴×C₆₇	—	4	1	no	—
54	C₂×Q₈×C₆₇	—	2	2	no	—
55	C₂×Q₈×C₆₇	—	4	1	no	—
56	C₂×Q₈×C₆₇	—	4	2	no	—
57	C₂×Q₈×C₆₇	—	4	2	no	—
58	C₂×D₄×C₆₇	—	2	2	no	—
59	C₂×D₄×C₆₇	—	4	2	no	—
60	C₂×D₄×C₆₇	—	4	1	no	—
61	C₂×D₄×C₆₇	—	4	2	no	—
62	C₂²×C₄×C₆₇	—	4	1	no	—
63	C₂²×C₄×C₆₇	SD₁₆	1	2	yes	—
64	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
65	Q₁₆×C₆₇	—	2	4	no	—
66	Q₁₆×C₆₇	—	4	1	no	—
67	Q₁₆×C₆₇	—	4	1	no	—
68	SD₁₆×C₆₇	—	4	8	no	—
69	D₈×C₆₇	—	2	4	no	—
70	D₈×C₆₇	—	4	1	no	—
71	D₈×C₆₇	—	4	1	no	—
72	C₂×C₈×C₆₇	—	2	2	no	—
73	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
74	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
76	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₆₇	#41	1	2	yes	—
78	C₂²⋊C₄×C₆₇	—	4	4	no	—
79	C₂²⋊C₄×C₆₇	—	4	4	no	—
80	C₄²×C₆₇	C₂²⋊C₄	1	2	yes	—
81	C₄²×C₆₇	D₈	1	1	yes	characteristic
82	C₄²×C₆₇	D₈	1	1	yes	characteristic
83	C₂³×C₆₇	—	4	2	no	—
84	C₂³×C₆₇	—	8	4	no	—
85	C₂³×C₆₇	—	8	2	no	—
86	C₂³×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
87	Q₈×C₆₇	—	4	2	no	—
88	Q₈×C₆₇	—	4	2	no	—
89	Q₈×C₆₇	—	8	2	no	—
90	D₄×C₆₇	—	4	2	no	—
91	D₄×C₆₇	—	4	2	no	—
92	D₄×C₆₇	—	8	2	no	—
93	C₂×C₄×C₆₇	—	4	2	no	—
94	C₂×C₄×C₆₇	—	4	2	no	—
95	C₂×C₄×C₆₇	—	8	2	no	—
96	C₂×C₄×C₆₇	#102	1	2	yes	—
97	C₂×C₄×C₆₇	#102	1	2	yes	—
98	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₆₇	#121	1	2	yes	—
100	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
101	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
102	C₈×C₆₇	—	2	2	no	—
103	C₈×C₆₇	C₄×D₄	1	2	yes	—
104	C₈×C₆₇	#124	1	1	yes	characteristic
105	C₈×C₆₇	#127	1	1	yes	characteristic
106	C₆₇⋊C₈	—	4	4	no	—
107	C₂²×C₆₇	—	2	2	no	—
108	C₂²×C₆₇	—	8	4	no	—
109	C₂²×C₆₇	—	8	2	no	—
110	C₂²×C₆₇	—	16	4	no	—
111	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
112	C₂²×C₆₇	#460	1	2	yes	—
113	C₄×C₆₇	—	2	2	no	—
114	C₄×C₆₇	—	2	2	no	—
115	C₄×C₆₇	—	8	2	no	—
116	C₄×C₆₇	#390	1	1	yes	characteristic
117	C₄×C₆₇	#418	1	1	yes	characteristic
118	C₄×C₆₇	#459	1	2	yes	—
119	#13258	—	67	1	no	maximal, Sylow
120	C₂×C₆₇	—	2	2	no	—
121	C₂×C₆₇	—	16	2	no	—
122	C₂×C₆₇	#1982	1	1	yes	characteristic
123	C₂×C₆₇	#2148	1	2	yes	—
124	C₂×#495	D₆₇	1	1	yes	characteristic
125	#2150	—	67	1	no	—
126	C₂×#362	—	67	2	no	—
127	C₂×#361	—	67	2	no	—
128	C₄×#108	—	67	1	no	—
129	C₆₇	#13258	1	1	yes	characteristic, complemented, Sylow
130	C₂²×Q₁₆	C₂×D₆₇	1	1	yes	characteristic
131	C₂²×SD₁₆	—	2	1	no	—
132	C₂²×D₈	C₂×D₆₇	1	1	yes	characteristic
133	C₂×#124	—	2	1	no	—
134	C₂×M₃₂	—	67	2	no	—
135	#495	—	2	2	no	—
136	#495	Dic₆₇	1	4	yes	—
137	C₂×#108	—	67	2	no	—
138	C₄×M₁₆	—	134	1	no	—
139	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
140	C₄⋊C₁₆	—	134	2	no	—
141	#362	—	134	4	no	—
142	#361	—	134	4	no	—
143	#341	—	134	1	no	—
144	C₂²×Q₈	—	2	1	no	—
145	C₂²×D₄	—	2	1	no	—
146	C₂×Q₁₆	—	2	2	no	—
147	C₂×Q₁₆	—	2	1	no	—
148	C₂×Q₁₆	—	2	2	no	—
149	C₂×Q₁₆	C₂×Dic₆₇	1	2	yes	—
150	C₂×SD₁₆	—	2	4	no	—
151	C₂×SD₁₆	—	4	4	no	—
152	C₂×D₈	—	2	2	no	—
153	C₂×D₈	—	2	1	no	—
154	C₂×D₈	—	2	2	no	—
155	C₂×D₈	C₂×Dic₆₇	1	2	yes	—
156	C₂×M₁₆	—	134	2	no	—
157	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
158	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
159	#124	—	2	4	no	—
160	#124	—	4	1	no	—
161	#124	—	4	1	no	—
162	C₂×C₂²⋊C₄	—	4	2	no	—
163	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
164	M₃₂	—	134	2	no	—
165	M₃₂	—	134	2	no	—
166	C₂×C₁₆	—	134	2	no	—
167	#108	—	67	4	no	—
168	#108	—	134	2	no	—
169	#97	—	268	1	no	—
170	C₄×C₈	—	268	1	no	—
171	C₄×C₈	C₂×Dic₆₇	1	2	yes	—
172	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
173	C₂⁴	—	4	1	no	—
174	C₂×Q₈	—	2	2	no	—
175	C₂×Q₈	—	4	1	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	—	4	2	no	—
178	C₂×D₄	—	2	2	no	—
179	C₂×D₄	—	4	2	no	—
180	C₂×D₄	—	4	1	no	—
181	C₂×D₄	—	4	2	no	—
182	C₂²×C₄	—	4	1	no	—
183	C₂²×C₄	#11761616	1	2	yes	—
184	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
185	Q₁₆	—	2	4	no	—
186	Q₁₆	—	4	1	no	—
187	Q₁₆	—	4	1	no	—
188	SD₁₆	—	4	8	no	—
189	D₈	—	2	4	no	—
190	D₈	—	4	1	no	—
191	D₈	—	4	1	no	—
192	M₁₆	—	268	2	no	—
193	M₁₆	—	134	4	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	268	2	no	—
196	C₂×C₈	C₂²⋊Dic₆₇	1	2	yes	—
197	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
198	C₂×C₈	D₄×D₆₇	1	2	yes	—
199	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
200	C₂×C₈	#11761627	1	2	yes	—
201	C₂²⋊C₄	—	4	4	no	—
202	C₂²⋊C₄	—	4	4	no	—
203	C₄²	C₂²⋊Dic₆₇	1	2	yes	—
204	C₄²	#11761613	1	1	yes	characteristic
205	C₄²	#11761613	1	1	yes	characteristic
206	C₁₆	—	268	2	no	—
207	C₂³	—	4	2	no	—
208	C₂³	—	8	4	no	—
209	C₂³	—	8	2	no	—
210	C₂³	C₂×#11761616	1	1	yes	characteristic
211	Q₈	—	4	2	no	—
212	Q₈	—	4	2	no	—
213	Q₈	—	8	2	no	—
214	D₄	—	4	2	no	—
215	D₄	—	4	2	no	—
216	D₄	—	8	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	8	2	no	—
220	C₂×C₄	#14523964	1	2	yes	—
221	C₂×C₄	#14523964	1	2	yes	—
222	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
223	C₂×C₄	#14524014	1	2	yes	—
224	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
225	C₂×C₄	#14524069	1	2	yes	—
226	C₈	—	2	2	no	—
227	C₈	—	268	4	no	—
228	C₈	D₄×Dic₆₇	1	2	yes	—
229	C₈	#14524030	1	1	yes	characteristic
230	C₈	#14524039	1	1	yes	characteristic
231	C₂²	—	2	2	no	—
232	C₂²	—	8	2	no	—
233	C₂²	—	8	4	no	—
234	C₂²	—	16	4	no	—
235	C₂²	C₂×#14523964	1	1	yes	characteristic
236	C₂²	#16863593	1	2	yes	—
237	C₄	—	2	2	no	—
238	C₄	—	2	2	no	—
239	C₄	—	8	2	no	—
240	C₄	#16863299	1	1	yes	characteristic
241	C₄	#16863401	1	1	yes	characteristic
242	C₄	#16863588	1	2	yes	—
243	C₂	—	2	2	no	—
244	C₂	—	16	2	no	—
245	C₂	#22561137	1	1	yes	characteristic
246	C₂	#22561958	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22561965

C₂

yes

maximal, characteristic, complemented

C₂×#16863212

C₂

yes

maximal, complemented

C₂×#16863209

C₂

yes

maximal

C₄×#14523979

C₂

yes

maximal, characteristic, complemented

C₂×#495×C₆₇

C₂

yes

maximal, characteristic

C₂×#14523983

C₂²

yes

—

C₂×#14523979

C₂²

yes

—

C₄×#11761612

—

C₄⋊(C₆₇⋊C₁₆)

—

#16863212

—

#16863209

—

#16863161

—

C₂²×Q₁₆×C₆₇

C₂²

yes

characteristic

C₂²×SD₁₆×C₆₇

—

C₂²×D₈×C₆₇

C₂²

yes

characteristic

C₂×#124×C₆₇

—

#495×C₆₇

—

#495×C₆₇

C₄

yes

—

C₂×C₄×C₈×C₆₇

C₂²

yes

—

—

—

C₂×C₆₇⋊C₁₆

—

#14523979

—

#14523979

D₄

yes

—

#14523954

—

C₄×C₆₇⋊C₈

—

C₂²×Q₈×C₆₇

—

C₂²×D₄×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

C₂×C₄

yes

—

C₂×SD₁₆×C₆₇

—

C₂×SD₁₆×C₆₇

—

C₂×D₈×C₆₇

—

C₂×D₈×C₆₇

—

C₂×D₈×C₆₇

—

C₂×D₈×C₆₇

C₂×C₄

yes

—

C₂²×C₈×C₆₇

D₄

yes

characteristic

C₂²×C₈×C₆₇

C₂³

yes

characteristic

#124×C₆₇

—

#124×C₆₇

—

#124×C₆₇

—

C₂×C₂²⋊C₄×C₆₇

—

C₂×C₄²×C₆₇

D₄

yes

characteristic

C₄×C₈×C₆₇

C₂×C₄

yes

—

C₄×C₈×C₆₇

D₄

yes

—

#11761612

—

#11761612

—

C₂×C₆₇⋊C₈

—

C₆₇⋊C₁₆

—

C₂⁴×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

SD₁₆

yes

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

Q₁₆×C₆₇

—

Q₁₆×C₆₇

—

Q₁₆×C₆₇

—

SD₁₆×C₆₇

—

D₈×C₆₇

—

D₈×C₆₇

—

D₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

C₂²⋊C₄

yes

—

C₂×C₈×C₆₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

—

C₂×C₈×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

#41

yes

—

C₂²⋊C₄×C₆₇

—

C₂²⋊C₄×C₆₇

—

C₄²×C₆₇

C₂²⋊C₄

yes

—

C₄²×C₆₇

D₈

yes

characteristic

C₄²×C₆₇

D₈

yes

characteristic

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

C₂×SD₁₆

yes

characteristic

Q₈×C₆₇

—

Q₈×C₆₇

—

Q₈×C₆₇

—

D₄×C₆₇

—

D₄×C₆₇

—

D₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

#102

yes

—

C₂×C₄×C₆₇

#102

yes

—

C₂×C₄×C₆₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₇

#121

yes

—

100

C₂×C₄×C₆₇

C₂×D₈

yes

characteristic

101

C₂×C₄×C₆₇

AGL(1,ℤ/8)

yes

—

102

C₈×C₆₇

—

103

C₈×C₆₇

C₄×D₄

yes

—

104

C₈×C₆₇

#124

yes

characteristic

105

C₈×C₆₇

#127

yes

characteristic

106

C₆₇⋊C₈

—

107

C₂²×C₆₇

—

108

C₂²×C₆₇

—

109

C₂²×C₆₇

—

110

C₂²×C₆₇

—

111

C₂²×C₆₇

C₂×#102

yes

characteristic

112

C₂²×C₆₇

#460

yes

—

113

C₄×C₆₇

—

114

C₄×C₆₇

—

115

C₄×C₆₇

—

116

C₄×C₆₇

#390

yes

characteristic

117

C₄×C₆₇

#418

yes

characteristic

118

C₄×C₆₇

#459

yes

—

119

#13258

—

maximal, Sylow

120

C₂×C₆₇

—

121

C₂×C₆₇

—

122

C₂×C₆₇

#1982

yes

characteristic

123

C₂×C₆₇

#2148

yes

—

124

C₂×#495

D₆₇

yes

characteristic

125

#2150

—

126

C₂×#362

—

127

C₂×#361

—

128

C₄×#108

—

129

C₆₇

#13258

yes

characteristic, complemented, Sylow

130

C₂²×Q₁₆

C₂×D₆₇

yes

characteristic

131

C₂²×SD₁₆

—

132

C₂²×D₈

C₂×D₆₇

yes

characteristic

133

C₂×#124

—

134

C₂×M₃₂

—

135

#495

—

136

#495

Dic₆₇

yes

—

137

C₂×#108

—

138

C₄×M₁₆

—

134

—

139

C₂×C₄×C₈

C₂×D₆₇

yes

characteristic

140

C₄⋊C₁₆

—

134

—

141

#362

—

134

—

142

#361

—

134

—

143

#341

—

134

—

144

C₂²×Q₈

—

145

C₂²×D₄

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

148

C₂×Q₁₆

—

149

C₂×Q₁₆

C₂×Dic₆₇

yes

—

150

C₂×SD₁₆

—

151

C₂×SD₁₆

—

152

C₂×D₈

—

153

C₂×D₈

—

154

C₂×D₈

—

155

C₂×D₈

C₂×Dic₆₇

yes

—

156

C₂×M₁₆

—

134

—

157

C₂²×C₈

C₂²⋊D₆₇

yes

characteristic

158

C₂²×C₈

C₂²×D₆₇

yes

characteristic

159

#124

—

160

#124

—

161

#124

—

162

C₂×C₂²⋊C₄

—

163

C₂×C₄²

C₂²⋊D₆₇

yes

characteristic

164

M₃₂

—

134

—

165

M₃₂

—

134

—

166

C₂×C₁₆

—

134

—

167

#108

—

168

#108

—

134

—

169

#97

—

268

—

170

C₄×C₈

—

268

—

171

C₄×C₈

C₂×Dic₆₇

yes

—

172

C₄×C₈

C₂²⋊D₆₇

yes

—

173

C₂⁴

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂²×C₄

—

183

C₂²×C₄

#11761616

yes

—

184

C₂²×C₄

C₂×C₂²⋊D₆₇

yes

characteristic

185

Q₁₆

—

186

Q₁₆

—

187

Q₁₆

—

188

SD₁₆

—

189

D₈

—

190

D₈

—

191

D₈

—

192

M₁₆

—

268

—

193

M₁₆

—

134

—

194

C₂×C₈

—

195

C₂×C₈

—

268

—

196

C₂×C₈

C₂²⋊Dic₆₇

yes

—

197

C₂×C₈

C₂²×Dic₆₇

yes

characteristic

198

C₂×C₈

D₄×D₆₇

yes

—

199

C₂×C₈

C₂×C₂²⋊D₆₇

yes

characteristic

200

C₂×C₈

#11761627

yes

—

201

C₂²⋊C₄

—

202

C₂²⋊C₄

—

203

C₄²

C₂²⋊Dic₆₇

yes

—

204

C₄²

#11761613

yes

characteristic

205

C₄²

#11761613

yes

characteristic

206

C₁₆

—

268

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

C₂×#11761616

yes

characteristic

211

Q₈

—

212

Q₈

—

213

Q₈

—

214

D₄

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

#14523964

yes

—

221

C₂×C₄

#14523964

yes

—

222

C₂×C₄

C₂×C₂²⋊Dic₆₇

yes

characteristic

223

C₂×C₄

#14524014

yes

—

224

C₂×C₄

C₂×#11761613

yes

characteristic

225

C₂×C₄

#14524069

yes

—

226

C₈

—

227

C₈

—

268

—

228

C₈

D₄×Dic₆₇

yes

—

229

C₈

#14524030

yes

characteristic

230

C₈

#14524039

yes

characteristic

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

C₂×#14523964

yes

characteristic

236

C₂²

#16863593

yes

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

#16863299

yes

characteristic

241

C₄

#16863401

yes

characteristic

242

C₄

#16863588

yes

—

243

C₂

—

244

C₂

—

245

C₂

#22561137

yes

characteristic

246

C₂

#22561958

yes

—

	subgroup	G/H
center	C₂²	C₂×#14523964
commutator	C₂×C₈×C₆₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₂×#495×C₆₇	C₂
socle	C₂²×C₆₇	C₂×#102
prime radical	C₂²×D₈×C₆₇	C₂²
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	C₂×#495	D₆₇
hypocenter	C₆₇	#13258
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#495

subgroup

G/H

center

C₂²

C₂×#14523964

commutator

C₂×C₈×C₆₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₆₇

Fitting

C₂×#495×C₆₇

C₂

socle

C₂²×C₆₇

C₂×#102

prime radical

C₂²×D₈×C₆₇

C₂²

cosocle

C₂²×C₈×C₆₇

C₂³

D₆₇

C₆₇

G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#495

N	H ≅ G/N	type
1. #22561965	C₂	semidirect
2. C₂×#16863212	C₂	semidirect
4. C₄×#14523979	C₂	semidirect
129. C₆₇	#13258	semidirect

H ≅ G/N

type

1. #22561965

C₂

semidirect

2. C₂×#16863212

C₂

semidirect

4. C₄×#14523979

C₂

semidirect

129. C₆₇

#13258

semidirect

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

subgroup	index
#22561965	2
C₂×#16863212	2
C₂×#16863209	2
C₄×#14523979	2
C₂×#495×C₆₇	2
#13258	67

subgroup

index

C₂×#495×C₆₇

Subgroups — #30774325

Conjugacy classes of subgroups

Complements

Maximal subgroups