Group #30759389 — subgroups

Subgroups — #30759389

Order 17152.

478 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 133 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	#22560368	C₂	1	1	yes	maximal, characteristic
2	#22560214	C₂	1	2	yes	maximal
3	C₂×Q₈⋊(C₆₇⋊C₈)	C₂	1	2	yes	maximal
4	#22558092	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#2582	C₂	1	1	yes	maximal, characteristic
6	C₂×#14523976	—	2	2	no	—
7	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
8	C₂×#14523967	—	2	2	no	—
9	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
10	#16863266	C₂²	1	1	yes	characteristic
11	#16863158	—	2	2	no	—
12	Q₈⋊(C₆₇⋊C₈)	—	2	4	no	—
13	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
14	#398×C₆₇	—	2	2	no	—
15	#391×C₆₇	—	2	2	no	—
16	#389×C₆₇	—	2	2	no	—
17	#384×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×C₆₇⋊C₈	—	2	1	no	—
19	C₂²×C₆₇⋊C₈	—	2	2	no	—
20	C₂×C₄⋊Dic₆₇	—	2	2	no	—
21	C₂×C₄⋊Dic₆₇	—	2	1	no	—
22	#14523976	—	4	4	no	—
23	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
24	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
25	#14523967	—	4	4	no	—
26	C₄×C₆₇⋊C₈	—	2	1	no	—
27	C₄×C₆₇⋊C₈	D₄	1	2	yes	—
28	C₂²×Q₈×C₆₇	D₄	1	2	yes	—
29	C₄×Q₈×C₆₇	—	2	2	no	—
30	C₄×Q₈×C₆₇	—	2	2	no	—
31	C₄×Q₈×C₆₇	—	2	2	no	—
32	C₄×Q₈×C₆₇	—	2	2	no	—
33	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
34	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
35	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
36	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
37	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
38	C₂×C₄²×C₆₇	—	2	2	no	—
39	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
40	#95×C₆₇	—	2	4	no	—
41	#95×C₆₇	—	2	2	no	—
42	C₂²×Dic₆₇	—	4	1	no	—
43	C₂×C₆₇⋊C₈	—	2	2	no	—
44	C₂×C₆₇⋊C₈	—	2	2	no	—
45	C₂×C₆₇⋊C₈	—	2	2	no	—
46	C₂×C₆₇⋊C₈	—	4	2	no	—
47	C₂×C₆₇⋊C₈	—	4	2	no	—
48	C₂×C₆₇⋊C₈	—	4	2	no	—
49	C₄⋊Dic₆₇	—	4	2	no	—
50	C₄⋊Dic₆₇	—	4	2	no	—
51	C₄⋊Dic₆₇	—	4	2	no	—
52	C₂×Q₈×C₆₇	—	2	2	no	—
53	C₂×Q₈×C₆₇	—	2	2	no	—
54	C₂×Q₈×C₆₇	—	2	2	no	—
55	C₂×Q₈×C₆₇	—	2	2	no	—
56	C₂×Q₈×C₆₇	—	2	2	no	—
57	C₂×Q₈×C₆₇	Q₁₆	1	4	yes	—
58	C₂²×C₄×C₆₇	—	2	2	no	—
59	C₂²×C₄×C₆₇	—	2	2	no	—
60	C₂²×C₄×C₆₇	—	2	2	no	—
61	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
63	C₄⋊C₄×C₆₇	—	2	2	no	—
64	C₄⋊C₄×C₆₇	—	2	2	no	—
65	C₄⋊C₄×C₆₇	—	4	2	no	—
66	C₄⋊C₄×C₆₇	—	4	2	no	—
67	C₄⋊C₄×C₆₇	—	4	2	no	—
68	C₄⋊C₄×C₆₇	—	4	2	no	—
69	C₄⋊C₄×C₆₇	—	4	2	no	—
70	C₄⋊C₄×C₆₇	—	8	2	no	—
71	C₄²×C₆₇	—	4	2	no	—
72	C₄²×C₆₇	—	4	2	no	—
73	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₆₇	#41	1	1	yes	characteristic
75	C₄²×C₆₇	#41	1	2	yes	—
76	C₂³×C₆₇	#120	1	1	yes	characteristic
77	Q₈×C₆₇	—	2	4	no	—
78	Q₈×C₆₇	—	2	4	no	—
79	Q₈×C₆₇	—	4	2	no	—
80	Q₈×C₆₇	—	4	2	no	—
81	C₂×C₄×C₆₇	—	2	1	no	—
82	C₂×C₄×C₆₇	—	2	1	no	—
83	C₂×C₄×C₆₇	—	2	4	no	—
84	C₂×C₄×C₆₇	—	4	2	no	—
85	C₂×C₄×C₆₇	—	4	2	no	—
86	C₂×C₄×C₆₇	—	4	2	no	—
87	C₂×C₄×C₆₇	—	4	4	no	—
88	C₂×C₄×C₆₇	—	4	2	no	—
89	C₂×C₄×C₆₇	—	4	2	no	—
90	C₂×C₄×C₆₇	—	4	2	no	—
91	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
92	C₂×C₄×C₆₇	#121	1	2	yes	—
93	C₂×C₄×C₆₇	#123	1	2	yes	—
94	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
95	C₂×C₄×C₆₇	C₂×Q₁₆	1	2	yes	—
96	C₂×C₄×C₆₇	#135	1	2	yes	—
97	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
98	C₂×C₄×C₆₇	#137	1	2	yes	—
99	C₂×Dic₆₇	—	8	2	no	—
100	C₂×Dic₆₇	—	8	1	no	—
101	C₆₇⋊C₈	—	2	4	no	—
102	C₆₇⋊C₈	—	8	2	no	—
103	C₂²×C₆₇	#394	1	1	yes	characteristic
104	C₂²×C₆₇	#449	1	2	yes	—
105	C₂²×C₆₇	#451	1	2	yes	—
106	C₂²×C₆₇	#453	1	1	yes	characteristic
107	C₂²×C₆₇	#456	1	1	yes	characteristic
108	C₄×C₆₇	—	2	1	no	—
109	C₄×C₆₇	—	2	1	no	—
110	C₄×C₆₇	—	4	4	no	—
111	C₄×C₆₇	—	8	2	no	—
112	C₄×C₆₇	—	8	2	no	—
113	C₄×C₆₇	#467	1	2	yes	—
114	C₄×C₆₇	#468	1	2	yes	—
115	C₄×C₆₇	#484	1	2	yes	—
116	C₄×C₆₇	#485	1	2	yes	—
117	Dic₆₇	—	16	1	no	—
118	#10439	—	67	1	no	maximal, Sylow
119	C₂×C₆₇	#1620	1	1	yes	characteristic
120	C₂×C₆₇	#1633	1	1	yes	characteristic
121	C₂×C₆₇	#1648	1	2	yes	—
122	C₂×C₆₇	#2036	1	2	yes	—
123	C₂×C₆₇	#2039	1	1	yes	characteristic
124	#2582	D₆₇	1	1	yes	characteristic
125	#1845	—	67	1	no	—
126	#1803	—	67	2	no	—
127	C₂×Q₈⋊C₈	—	67	2	no	—
128	#1296	—	67	1	no	—
129	C₆₇	#10439	1	1	yes	characteristic, complemented, Sylow
130	C₂×C₄×Q₈	C₂×D₆₇	1	2	yes	—
131	C₂×#107	—	134	2	no	—
132	C₂×C₄⋊C₈	—	67	2	no	—
133	C₂×#103	—	134	2	no	—
134	C₂×C₄×C₈	—	67	1	no	—
135	#398	—	2	2	no	—
136	#391	—	2	2	no	—
137	#389	—	2	2	no	—
138	#384	—	67	1	no	—
139	#384	C₂×D₆₇	1	1	yes	characteristic
140	#340	—	134	2	no	—
141	Q₈⋊C₈	—	134	4	no	—
142	C₂²×Q₈	C₂²⋊D₆₇	1	2	yes	—
143	C₂²×C₈	—	134	2	no	—
144	C₂²×C₈	—	134	1	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₄×Q₈	—	2	2	no	—
148	C₄×Q₈	—	2	2	no	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	2	2	no	—
152	C₂×C₄⋊C₄	—	134	2	no	—
153	C₂×C₄⋊C₄	—	134	1	no	—
154	C₂×C₄⋊C₄	C₂²⋊D₆₇	1	2	yes	—
155	C₂×C₄⋊C₄	C₂²⋊D₆₇	1	2	yes	—
156	C₂×C₄²	—	2	2	no	—
157	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
158	#107	—	268	4	no	—
159	C₄⋊C₈	—	134	2	no	—
160	C₄⋊C₈	—	134	2	no	—
161	#103	—	268	4	no	—
162	C₄×C₈	—	67	2	no	—
163	C₄×C₈	—	134	1	no	—
164	#95	—	2	4	no	—
165	#95	—	2	2	no	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	2	no	—
169	C₂×Q₈	—	2	2	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	#11761618	1	4	yes	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	—	268	1	no	—
176	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₂²⋊D₆₇	1	2	yes	—
178	C₂×C₈	—	268	2	no	—
179	C₂×C₈	—	268	2	no	—
180	C₂×C₈	—	268	2	no	—
181	C₂×C₈	—	134	2	no	—
182	C₂×C₈	—	134	2	no	—
183	C₂×C₈	—	134	2	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	4	2	no	—
190	C₄⋊C₄	—	4	2	no	—
191	C₄⋊C₄	—	8	2	no	—
192	C₄⋊C₄	—	268	2	no	—
193	C₄⋊C₄	—	268	2	no	—
194	C₄⋊C₄	—	268	2	no	—
195	C₄²	—	4	2	no	—
196	C₄²	—	4	2	no	—
197	C₄²	D₄×D₆₇	1	1	yes	characteristic
198	C₄²	#11761627	1	1	yes	characteristic
199	C₄²	#11761627	1	2	yes	—
200	C₂³	#14524012	1	1	yes	characteristic
201	Q₈	—	2	4	no	—
202	Q₈	—	2	4	no	—
203	Q₈	—	4	2	no	—
204	Q₈	—	4	2	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	4	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	4	no	—
211	C₂×C₄	—	4	2	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	536	2	no	—
216	C₂×C₄	—	536	1	no	—
217	C₂×C₄	#14524014	1	1	yes	characteristic
218	C₂×C₄	#14524015	1	2	yes	—
219	C₂×C₄	#14524024	1	2	yes	—
220	C₂×C₄	#14524030	1	1	yes	characteristic
221	C₂×C₄	C₂×#11761618	1	2	yes	—
222	C₂×C₄	#14524063	1	2	yes	—
223	C₂×C₄	#14524068	1	2	yes	—
224	C₂×C₄	#14524074	1	2	yes	—
225	C₈	—	536	2	no	—
226	C₈	—	134	4	no	—
227	C₂²	#16863310	1	1	yes	characteristic
228	C₂²	#16863541	1	2	yes	—
229	C₂²	#16863552	1	2	yes	—
230	C₂²	#16863564	1	1	yes	characteristic
231	C₂²	#16863579	1	1	yes	characteristic
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	4	4	no	—
235	C₄	—	8	2	no	—
236	C₄	—	8	2	no	—
237	C₄	—	1072	1	no	—
238	C₄	#16863635	1	2	yes	—
239	C₄	#16863644	1	2	yes	—
240	C₄	#16863729	1	2	yes	—
241	C₄	#16863734	1	2	yes	—
242	C₂	#22559268	1	1	yes	characteristic
243	C₂	#22559349	1	1	yes	characteristic
244	C₂	#22559451	1	2	yes	—
245	C₂	#22561409	1	2	yes	—
246	C₂	#22561430	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22560368

C₂

yes

maximal, characteristic

#22560214

C₂

yes

maximal

C₂×Q₈⋊(C₆₇⋊C₈)

C₂

yes

maximal

#22558092

C₂

yes

maximal, characteristic

C₆₇×#2582

C₂

yes

maximal, characteristic

C₂×#14523976

—

C₂×C₄⋊(C₆₇⋊C₈)

C₂²

yes

—

C₂×#14523967

—

C₂×C₄×C₆₇⋊C₈

C₂²

yes

characteristic

#16863266

C₂²

yes

characteristic

#16863158

—

Q₈⋊(C₆₇⋊C₈)

—

C₂×C₄×Q₈×C₆₇

C₂²

yes

—

#398×C₆₇

—

#391×C₆₇

—

#389×C₆₇

—

#384×C₆₇

C₂²

yes

characteristic

C₂²×C₆₇⋊C₈

—

C₂²×C₆₇⋊C₈

—

C₂×C₄⋊Dic₆₇

—

C₂×C₄⋊Dic₆₇

—

#14523976

—

C₄⋊(C₆₇⋊C₈)

—

C₄⋊(C₆₇⋊C₈)

—

#14523967

—

C₄×C₆₇⋊C₈

—

C₄×C₆₇⋊C₈

D₄

yes

—

C₂²×Q₈×C₆₇

D₄

yes

—

C₄×Q₈×C₆₇

—

C₄×Q₈×C₆₇

—

C₄×Q₈×C₆₇

—

C₄×Q₈×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

D₄

yes

—

C₂×C₄⋊C₄×C₆₇

D₄

yes

—

C₂×C₄²×C₆₇

—

C₂×C₄²×C₆₇

C₂³

yes

characteristic

#95×C₆₇

—

#95×C₆₇

—

C₂²×Dic₆₇

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

Q₁₆

yes

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×D₄

yes

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

C₂×D₄

yes

C₄²×C₆₇

yes

C₄²×C₆₇

yes

—

C₂³×C₆₇

#120

yes

characteristic

Q₈×C₆₇

—

Q₈×C₆₇

—

Q₈×C₆₇

—

Q₈×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

#121

yes

characteristic

C₂×C₄×C₆₇

#121

yes

—

C₂×C₄×C₆₇

#123

yes

—

C₂×C₄×C₆₇

#124

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

—

100

C₂×Dic₆₇

—

101

C₆₇⋊C₈

—

102

C₆₇⋊C₈

—

103

C₂²×C₆₇

#394

yes

characteristic

104

C₂²×C₆₇

#449

yes

—

105

C₂²×C₆₇

#451

yes

—

106

C₂²×C₆₇

#453

yes

characteristic

107

C₂²×C₆₇

#456

yes

characteristic

108

C₄×C₆₇

—

109

C₄×C₆₇

—

110

C₄×C₆₇

—

111

C₄×C₆₇

—

112

C₄×C₆₇

—

113

C₄×C₆₇

#467

yes

—

114

C₄×C₆₇

#468

yes

—

115

C₄×C₆₇

#484

yes

—

116

C₄×C₆₇

#485

yes

—

117

Dic₆₇

—

118

#10439

—

maximal, Sylow

119

C₂×C₆₇

#1620

yes

characteristic

120

C₂×C₆₇

#1633

yes

characteristic

121

C₂×C₆₇

#1648

yes

—

122

C₂×C₆₇

#2036

yes

—

123

C₂×C₆₇

#2039

yes

characteristic

124

#2582

D₆₇

yes

characteristic

125

#1845

—

126

#1803

—

127

C₂×Q₈⋊C₈

—

128

#1296

—

129

C₆₇

#10439

yes

characteristic, complemented, Sylow

130

C₂×C₄×Q₈

C₂×D₆₇

yes

—

131

C₂×#107

—

134

—

132

C₂×C₄⋊C₈

—

133

C₂×#103

—

134

—

134

C₂×C₄×C₈

—

135

#398

—

136

#391

—

137

#389

—

138

#384

—

139

#384

C₂×D₆₇

yes

characteristic

140

#340

—

134

—

141

Q₈⋊C₈

—

134

—

142

C₂²×Q₈

C₂²⋊D₆₇

yes

—

143

C₂²×C₈

—

134

—

144

C₂²×C₈

—

134

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

134

—

153

C₂×C₄⋊C₄

—

134

—

154

C₂×C₄⋊C₄

C₂²⋊D₆₇

yes

—

155

C₂×C₄⋊C₄

C₂²⋊D₆₇

yes

—

156

C₂×C₄²

—

157

C₂×C₄²

C₂²×D₆₇

yes

characteristic

158

#107

—

268

—

159

C₄⋊C₈

—

134

—

160

C₄⋊C₈

—

134

—

161

#103

—

268

—

162

C₄×C₈

—

163

C₄×C₈

—

134

—

164

#95

—

165

#95

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

#11761618

yes

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

268

—

176

C₂²×C₄

C₂×C₂²⋊D₆₇

yes

characteristic

177

C₂²×C₄

C₂×C₂²⋊D₆₇

yes

—

178

C₂×C₈

—

268

—

179

C₂×C₈

—

268

—

180

C₂×C₈

—

268

—

181

C₂×C₈

—

134

—

182

C₂×C₈

—

134

—

183

C₂×C₈

—

134

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

268

—

193

C₄⋊C₄

—

268

—

194

C₄⋊C₄

—

268

—

195

C₄²

—

196

C₄²

—

197

C₄²

D₄×D₆₇

yes

characteristic

198

C₄²

#11761627

yes

characteristic

199

C₄²

#11761627

yes

—

200

C₂³

#14524012

yes

characteristic

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

536

—

216

C₂×C₄

—

536

—

217

C₂×C₄

#14524014

yes

characteristic

218

C₂×C₄

#14524015

yes

—

219

C₂×C₄

#14524024

yes

—

220

C₂×C₄

#14524030

yes

characteristic

221

C₂×C₄

C₂×#11761618

yes

—

222

C₂×C₄

#14524063

yes

—

223

C₂×C₄

#14524068

yes

—

224

C₂×C₄

#14524074

yes

—

225

C₈

—

536

—

226

C₈

—

134

—

227

C₂²

#16863310

yes

characteristic

228

C₂²

#16863541

yes

—

229

C₂²

#16863552

yes

—

230

C₂²

#16863564

yes

characteristic

231

C₂²

#16863579

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

1072

—

238

C₄

#16863635

yes

—

239

C₄

#16863644

yes

—

240

C₄

#16863729

yes

—

241

C₄

#16863734

yes

—

242

C₂

#22559268

yes

characteristic

243

C₂

#22559349

yes

characteristic

244

C₂

#22559451

yes

—

245

C₂

#22561409

yes

—

246

C₂

#22561430

yes

characteristic

	subgroup	G/H
center	C₂³	#14524012
commutator, cosocle	C₂×C₄²×C₆₇	C₂³
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₆₇×#2582	C₂
socle, prime radical	C₂³×C₆₇	#120
hypercenter	#2582	D₆₇
hypocenter	C₆₇	#10439
LCS	G ▷ C₂×C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2582

subgroup

G/H

center

C₂³

#14524012

commutator, cosocle

C₂×C₄²×C₆₇

C₂³

Frattini

C₂×C₄²

C₂²×D₆₇

Fitting

C₆₇×#2582

C₂

C₂³×C₆₇

D₆₇

C₆₇

G ▷ C₂×C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2582

N	H ≅ G/N	type
129. C₆₇	#10439	semidirect

H ≅ G/N

type

129. C₆₇

#10439

semidirect

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

subgroup	index
#22560368	2
#22560214	2
C₂×Q₈⋊(C₆₇⋊C₈)	2
#22558092	2
C₆₇×#2582	2
#10439	67

subgroup

index

C₂×Q₈⋊(C₆₇⋊C₈)

C₆₇×#2582

Subgroups — #30759389

Conjugacy classes of subgroups

Complements

Maximal subgroups