Group #26109107 — subgroups

Subgroups — #26109107

Order 12032.

476 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 149 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	C₄⋊Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	#20243504	C₂	1	2	yes	maximal
3	C₂×#15688872	C₂	1	1	yes	maximal, characteristic
4	#20241272	C₂	1	2	yes	maximal
5	C₂×C₄₇×#333	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×Dic₄₇	C₄	1	2	yes	—
7	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
8	#15689030	C₄	1	2	yes	—
9	#15689022	—	2	2	no	—
10	#15688993	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×Dic₄₇	—	2	2	no	—
12	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
13	#15688877	—	2	2	no	—
14	#15688877	—	2	2	no	—
15	#15688872	—	2	2	no	—
16	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
18	C₄₇×#333	—	2	2	no	—
19	C₂²×C₄₇⋊C₈	—	2	2	no	—
20	Q₈×Dic₄₇	—	4	4	no	—
21	C₂×C₄⋊Dic₄₇	—	2	2	no	—
22	C₂×C₄⋊Dic₄₇	—	2	2	no	—
23	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
24	C₂×C₄×Dic₄₇	—	2	2	no	—
25	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
28	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
29	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
30	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
31	C₄₇⋊#95	—	2	4	no	—
32	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₄₇	—	2	2	no	—
34	C₄⋊Q₈×C₄₇	—	2	2	no	—
35	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
36	C₄⋊Q₈×C₄₇	Q₈	1	2	yes	—
37	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
38	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
39	C₄⋊C₈×C₄₇	—	2	2	no	—
40	C₄⋊C₈×C₄₇	—	2	2	no	—
41	C₂×Q₈×C₄₇	—	2	2	no	—
42	C₂×Q₈×C₄₇	—	4	2	no	—
43	C₂×Q₈×C₄₇	—	4	2	no	—
44	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	—
45	C₂²×C₄×C₄₇	—	2	2	no	—
46	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
48	C₂²×Dic₄₇	—	2	2	no	—
49	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
50	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×C₈×C₄₇	—	4	2	no	—
53	C₂×C₈×C₄₇	—	4	2	no	—
54	C₂×C₈×C₄₇	—	4	2	no	—
55	C₄⋊C₄×C₄₇	—	2	4	no	—
56	C₄⋊C₄×C₄₇	—	2	4	no	—
57	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
59	C₄²×C₄₇	#41	1	2	yes	—
60	C₄⋊Dic₄₇	—	4	4	no	—
61	C₄⋊Dic₄₇	—	4	2	no	—
62	C₄⋊Dic₄₇	—	4	2	no	—
63	C₄⋊Dic₄₇	—	4	2	no	—
64	C₄×Dic₄₇	—	2	2	no	—
65	C₄×Dic₄₇	—	2	2	no	—
66	C₄×Dic₄₇	—	2	2	no	—
67	C₄×Dic₄₇	—	2	2	no	—
68	C₄×Dic₄₇	—	2	2	no	—
69	C₄×Dic₄₇	—	4	1	no	—
70	C₄×Dic₄₇	—	4	4	no	—
71	C₂×C₄₇⋊C₈	—	4	2	no	—
72	C₂×C₄₇⋊C₈	—	4	2	no	—
73	C₂×C₄₇⋊C₈	—	4	2	no	—
74	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	Q₈×C₄₇	—	4	4	no	—
76	Q₈×C₄₇	—	4	4	no	—
77	C₂×C₄×C₄₇	—	2	1	no	—
78	C₂×C₄×C₄₇	—	2	1	no	—
79	C₂×C₄×C₄₇	—	2	4	no	—
80	C₂×C₄×C₄₇	—	4	2	no	—
81	C₂×C₄×C₄₇	—	4	2	no	—
82	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
84	C₂×C₄×C₄₇	#121	1	2	yes	—
85	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
86	C₂×C₄×C₄₇	#135	1	2	yes	—
87	C₂×C₄×C₄₇	#135	1	2	yes	—
88	C₂×C₄×C₄₇	#137	1	2	yes	—
89	C₂×C₄×C₄₇	#137	1	2	yes	—
90	C₂×Dic₄₇	—	2	2	no	—
91	C₂×Dic₄₇	—	2	1	no	—
92	C₂×Dic₄₇	—	2	2	no	—
93	C₂×Dic₄₇	—	2	2	no	—
94	C₂×Dic₄₇	—	2	2	no	—
95	C₂×Dic₄₇	—	2	2	no	—
96	C₂×Dic₄₇	—	4	2	no	—
97	C₂×Dic₄₇	—	4	4	no	—
98	C₂×Dic₄₇	#100	1	2	yes	—
99	C₈×C₄₇	—	8	2	no	—
100	C₄₇⋊C₈	—	8	2	no	—
101	#8594	—	47	1	no	maximal, Sylow
102	C₂²×C₄₇	#380	1	1	yes	characteristic
103	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
104	C₂²×C₄₇	#413	1	1	yes	characteristic
105	C₂²×C₄₇	#416	1	2	yes	—
106	C₂²×C₄₇	#419	1	2	yes	—
107	C₄×C₄₇	—	2	1	no	—
108	C₄×C₄₇	—	2	1	no	—
109	C₄×C₄₇	—	4	4	no	—
110	C₄×C₄₇	#464	1	2	yes	—
111	C₄×C₄₇	#464	1	2	yes	—
112	C₄×C₄₇	#479	1	2	yes	—
113	C₄×C₄₇	#479	1	2	yes	—
114	Dic₄₇	—	2	2	no	—
115	Dic₄₇	—	4	1	no	—
116	Dic₄₇	—	4	2	no	—
117	Dic₄₇	—	8	2	no	—
118	C₄×C₄⋊Q₈	—	47	1	no	—
119	#1831	—	47	2	no	—
120	C₂×#333	—	47	1	no	—
121	C₂×#333	D₄₇	1	1	yes	characteristic
122	#1296	—	47	2	no	—
123	C₂×C₄₇	#1543	1	1	yes	characteristic
124	C₂×C₄₇	#1554	1	2	yes	—
125	C₂×C₄₇	#1558	1	1	yes	characteristic
126	C₂×C₄₇	#1800	1	1	yes	characteristic
127	C₂×C₄₇	#1805	1	2	yes	—
128	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
129	C₂×C₄×Q₈	—	47	2	no	—
130	C₂×C₄⋊C₈	—	47	2	no	—
131	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
132	#391	—	47	2	no	—
133	#389	—	94	2	no	—
134	#384	—	47	1	no	—
135	C₄×C₄⋊C₄	—	94	2	no	—
136	C₄³	—	47	1	no	—
137	#336	—	94	2	no	—
138	#336	—	94	2	no	—
139	#333	—	2	2	no	—
140	#333	—	94	2	no	—
141	C₄₇	#8594	1	1	yes	characteristic, complemented, Sylow
142	C₂²×Q₈	C₄×D₄₇	1	2	yes	—
143	C₂²×C₈	—	2	2	no	—
144	C₂²×C₈	—	94	2	no	—
145	C₄⋊Q₈	—	2	2	no	—
146	C₄⋊Q₈	Dic₉₄	1	2	yes	—
147	C₄⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
148	C₄×Q₈	—	188	4	no	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	47	2	no	—
151	C₂×C₄⋊C₄	—	94	2	no	—
152	C₂×C₄⋊C₄	—	94	2	no	—
153	C₂×C₄²	—	47	1	no	—
154	C₂×C₄²	—	47	2	no	—
155	C₂×C₄²	—	47	2	no	—
156	C₂×C₄²	—	47	1	no	—
157	C₂×C₄²	—	94	2	no	—
158	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
159	C₄⋊C₈	—	2	2	no	—
160	C₄⋊C₈	—	2	2	no	—
161	C₄⋊C₈	—	94	2	no	—
162	C₄⋊C₈	—	94	2	no	—
163	#95	—	94	4	no	—
164	C₂×Q₈	—	2	2	no	—
165	C₂×Q₈	—	4	2	no	—
166	C₂×Q₈	—	4	2	no	—
167	C₂×Q₈	Dic₄₇⋊C₄	1	4	yes	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	47	1	no	—
170	C₂²×C₄	—	47	2	no	—
171	C₂²×C₄	—	47	1	no	—
172	C₂²×C₄	—	94	2	no	—
173	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
174	C₂²×C₄	D₄×D₄₇	1	2	yes	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	—	4	2	no	—
178	C₂×C₈	—	188	2	no	—
179	C₂×C₈	—	188	2	no	—
180	C₂×C₈	—	188	2	no	—
181	C₄⋊C₄	—	2	4	no	—
182	C₄⋊C₄	—	2	4	no	—
183	C₄⋊C₄	—	188	2	no	—
184	C₄⋊C₄	—	188	4	no	—
185	C₄⋊C₄	—	188	2	no	—
186	C₄⋊C₄	—	188	2	no	—
187	C₄²	—	94	2	no	—
188	C₄²	—	94	2	no	—
189	C₄²	—	94	2	no	—
190	C₄²	—	94	2	no	—
191	C₄²	—	94	2	no	—
192	C₄²	—	188	1	no	—
193	C₄²	—	188	4	no	—
194	C₄²	C₂×Dic₉₄	1	1	yes	characteristic
195	C₄²	#10625352	1	2	yes	—
196	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
197	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
198	Q₈	—	4	4	no	—
199	Q₈	—	4	4	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	47	2	no	—
206	C₂×C₄	—	94	2	no	—
207	C₂×C₄	—	94	1	no	—
208	C₂×C₄	—	94	2	no	—
209	C₂×C₄	—	94	2	no	—
210	C₂×C₄	—	94	2	no	—
211	C₂×C₄	—	94	2	no	—
212	C₂×C₄	—	188	2	no	—
213	C₂×C₄	—	188	4	no	—
214	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
215	C₂×C₄	#13093980	1	1	yes	characteristic
216	C₂×C₄	#13093996	1	2	yes	—
217	C₂×C₄	#13094001	1	2	yes	—
218	C₂×C₄	#13094045	1	2	yes	—
219	C₂×C₄	#13094047	1	2	yes	—
220	C₂×C₄	#13094053	1	2	yes	—
221	C₂×C₄	#13094056	1	2	yes	—
222	C₈	—	8	2	no	—
223	C₈	—	376	2	no	—
224	C₂²	#15688981	1	1	yes	characteristic
225	C₂²	#100×D₄₇	1	1	yes	characteristic
226	C₂²	#15689104	1	1	yes	characteristic
227	C₂²	#15689118	1	2	yes	—
228	C₂²	#15689130	1	2	yes	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	4	4	no	—
232	C₄	—	94	2	no	—
233	C₄	—	376	2	no	—
234	C₄	—	188	1	no	—
235	C₄	—	188	2	no	—
236	C₄	#15689343	1	2	yes	—
237	C₄	#15689347	1	2	yes	—
238	C₄	#15689428	1	2	yes	—
239	C₄	#15689432	1	2	yes	—
240	C₂	#20242049	1	1	yes	characteristic
241	C₂	#20242097	1	2	yes	—
242	C₂	#20242112	1	1	yes	characteristic
243	C₂	#20243378	1	1	yes	characteristic
244	C₂	#20243401	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊Q₈×Dic₄₇

C₂

yes

maximal, characteristic

#20243504

C₂

yes

maximal

C₂×#15688872

C₂

yes

maximal, characteristic

#20241272

C₂

yes

maximal

C₂×C₄₇×#333

C₂

yes

maximal, characteristic

C₂×Q₈×Dic₄₇

C₄

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

#15689030

C₄

yes

—

#15689022

—

#15688993

C₂²

yes

characteristic

C₄⋊C₄×Dic₄₇

—

C₄²×Dic₄₇

C₂²

yes

—

—

—

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₄₇×#333

—

C₂²×C₄₇⋊C₈

—

Q₈×Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₇

D₄

yes

—

C₂×C₄×Dic₄₇

D₄

yes

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄₇⋊#95

—

C₂²×Q₈×C₄₇

C₂×C₄

yes

—

C₂²×C₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

D₄

yes

—

C₄⋊Q₈×C₄₇

Q₈

yes

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₄⋊C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂²⋊C₄

yes

—

C₂²×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₂²×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×Q₈

yes

characteristic

C₄²×C₄₇

#41

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₄⋊C₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

#100

yes

—

C₈×C₄₇

—

100

C₄₇⋊C₈

—

101

#8594

—

maximal, Sylow

102

C₂²×C₄₇

#380

yes

characteristic

103

C₂²×C₄₇

C₂×#100

yes

characteristic

104

C₂²×C₄₇

#413

yes

characteristic

105

C₂²×C₄₇

#416

yes

—

106

C₂²×C₄₇

#419

yes

—

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

#464

yes

—

111

C₄×C₄₇

#464

yes

—

112

C₄×C₄₇

#479

yes

—

113

C₄×C₄₇

#479

yes

—

114

Dic₄₇

—

115

Dic₄₇

—

116

Dic₄₇

—

117

Dic₄₇

—

118

C₄×C₄⋊Q₈

—

119

#1831

—

120

C₂×#333

—

121

C₂×#333

D₄₇

yes

characteristic

122

#1296

—

123

C₂×C₄₇

#1543

yes

characteristic

124

C₂×C₄₇

#1554

yes

—

125

C₂×C₄₇

#1558

yes

characteristic

126

C₂×C₄₇

#1800

yes

characteristic

127

C₂×C₄₇

#1805

yes

—

128

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

129

C₂×C₄×Q₈

—

130

C₂×C₄⋊C₈

—

131

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

132

#391

—

133

#389

—

134

#384

—

135

C₄×C₄⋊C₄

—

136

C₄³

—

137

#336

—

138

#336

—

139

#333

—

140

#333

—

141

C₄₇

#8594

yes

characteristic, complemented, Sylow

142

C₂²×Q₈

C₄×D₄₇

yes

—

143

C₂²×C₈

—

144

C₂²×C₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

Dic₉₄

yes

—

147

C₄⋊Q₈

C₂²⋊D₄₇

yes

—

148

C₄×Q₈

—

188

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄²

—

154

C₂×C₄²

—

155

C₂×C₄²

—

156

C₂×C₄²

—

157

C₂×C₄²

—

158

C₂×C₄²

C₂²×D₄₇

yes

characteristic

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

#95

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

Dic₄₇⋊C₄

yes

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

174

C₂²×C₄

D₄×D₄₇

yes

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

188

—

179

C₂×C₈

—

188

—

180

C₂×C₈

—

188

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

188

—

184

C₄⋊C₄

—

188

—

185

C₄⋊C₄

—

188

—

186

C₄⋊C₄

—

188

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

188

—

193

C₄²

—

188

—

194

C₄²

C₂×Dic₉₄

yes

characteristic

195

C₄²

#10625352

yes

—

196

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

197

C₂³

C₂²⋊C₄×D₄₇

yes

characteristic

198

Q₈

—

199

Q₈

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

188

—

213

C₂×C₄

—

188

—

214

C₂×C₄

C₂×Dic₄₇⋊C₄

yes

characteristic

215

C₂×C₄

#13093980

yes

characteristic

216

C₂×C₄

#13093996

yes

—

217

C₂×C₄

#13094001

yes

—

218

C₂×C₄

#13094045

yes

—

219

C₂×C₄

#13094047

yes

—

220

C₂×C₄

#13094053

yes

—

221

C₂×C₄

#13094056

yes

—

222

C₈

—

223

C₈

—

376

—

224

C₂²

#15688981

yes

characteristic

225

C₂²

#100×D₄₇

yes

characteristic

226

C₂²

#15689104

yes

characteristic

227

C₂²

#15689118

yes

—

228

C₂²

#15689130

yes

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

376

—

234

C₄

—

188

—

235

C₄

—

188

—

236

C₄

#15689343

yes

—

237

C₄

#15689347

yes

—

238

C₄

#15689428

yes

—

239

C₄

#15689432

yes

—

240

C₂

#20242049

yes

characteristic

241

C₂

#20242097

yes

—

242

C₂

#20242112

yes

characteristic

243

C₂

#20243378

yes

characteristic

244

C₂

#20243401

yes

—

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#333	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#333	D₄₇
hypocenter	C₄₇	#8594
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

subgroup

G/H

center

C₂³

C₂²⋊C₄×D₄₇

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₂×C₄₇×#333

C₂

socle, prime radical

C₂³×C₄₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

N	H ≅ G/N	type
141. C₄₇	#8594	semidirect

H ≅ G/N

type

141. C₄₇

#8594

semidirect

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

subgroup	index
C₄⋊Q₈×Dic₄₇	2
#20243504	2
C₂×#15688872	2
#20241272	2
C₂×C₄₇×#333	2
#8594	47

subgroup

index

C₄⋊Q₈×Dic₄₇

C₂×C₄₇×#333

Subgroups — #26109107

Conjugacy classes of subgroups

Complements

Maximal subgroups