Group #20244465 — subgroups

Subgroups — #20244465

Order 6016.

426 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 91 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	C₂²×#10625336	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#10625334	C₂	1	1	yes	maximal, characteristic
3	C₂×#13093948	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13093945	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689025	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688878	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#124×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×#10625336	—	2	2	no	—
10	C₂×#10625336	—	2	2	no	—
11	C₂×#10625336	—	2	2	no	—
12	C₂×#10625334	—	2	2	no	—
13	C₂×#10625334	—	2	2	no	—
14	C₂×#10625334	—	2	2	no	—
15	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
18	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
19	#13093948	—	2	2	no	—
20	#13093945	—	2	2	no	—
21	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
23	#124×C₄₇	—	2	2	no	—
24	#124×C₄₇	—	2	2	no	—
25	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
26	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
27	C₂⁴×C₄₇	—	2	1	no	—
28	C₂³×D₄₇	—	2	1	no	—
29	C₂×Q₈×C₄₇	—	2	1	no	—
30	C₂×Q₈×C₄₇	—	2	1	no	—
31	C₂×Q₈×C₄₇	—	2	1	no	—
32	C₂×Q₈×C₄₇	—	2	1	no	—
33	C₂×Q₈×C₄₇	—	2	1	no	—
34	C₂×Q₈×C₄₇	D₄	1	2	yes	—
35	C₂×D₄×C₄₇	—	2	1	no	—
36	C₂×D₄×C₄₇	—	2	1	no	—
37	C₂×D₄×C₄₇	—	2	1	no	—
38	C₂×D₄×C₄₇	—	2	1	no	—
39	C₂×D₄×C₄₇	—	2	1	no	—
40	C₂×D₄×C₄₇	D₄	1	2	yes	—
41	C₂²×C₄×C₄₇	—	2	1	no	—
42	C₂²×C₄×C₄₇	D₄	1	2	yes	—
43	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×Dic₄₇	—	2	1	no	—
45	C₂×D₁₈₈	—	2	1	no	—
46	C₂×D₁₈₈	—	2	1	no	—
47	C₂×D₁₈₈	—	2	1	no	—
48	C₂×D₁₈₈	—	2	1	no	—
49	C₂×D₁₈₈	—	2	1	no	—
50	C₂×D₁₈₈	D₄	1	2	yes	—
51	C₂²⋊C₄×C₄₇	—	2	8	no	—
52	C₄²×C₄₇	—	2	1	no	—
53	C₄²×C₄₇	—	2	1	no	—
54	#10625336	—	2	8	no	—
55	#10625334	—	2	8	no	—
56	(C₂×D₄₇)⋊C₄	—	4	4	no	—
57	C₄⋊Dic₄₇	—	2	1	no	—
58	C₄⋊Dic₄₇	—	2	1	no	—
59	C₂×C₄₇⋊C₈	—	2	1	no	—
60	C₂×C₄₇⋊C₈	—	2	1	no	—
61	C₂×C₄₇⋊C₈	—	2	1	no	—
62	C₂×C₄₇⋊C₈	—	2	1	no	—
63	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
64	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
65	C₂³×C₄₇	—	2	2	no	—
66	C₂³×C₄₇	—	4	1	no	—
67	C₂³×C₄₇	—	4	1	no	—
68	C₂³×C₄₇	—	4	2	no	—
69	C₂³×C₄₇	—	4	2	no	—
70	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
71	C₂²×D₄₇	—	2	2	no	—
72	C₂²×D₄₇	—	4	1	no	—
73	C₂²×D₄₇	—	4	1	no	—
74	C₂²×D₄₇	—	4	2	no	—
75	C₂²×D₄₇	—	4	2	no	—
76	Q₈×C₄₇	—	2	2	no	—
77	Q₈×C₄₇	—	2	2	no	—
78	Q₈×C₄₇	—	4	1	no	—
79	Q₈×C₄₇	—	4	1	no	—
80	D₄×C₄₇	—	2	2	no	—
81	D₄×C₄₇	—	2	2	no	—
82	D₄×C₄₇	—	4	1	no	—
83	D₄×C₄₇	—	4	1	no	—
84	C₂×C₄×C₄₇	—	2	2	no	—
85	C₂×C₄×C₄₇	—	2	2	no	—
86	C₂×C₄×C₄₇	—	2	2	no	—
87	C₂×C₄×C₄₇	—	2	2	no	—
88	C₂×C₄×C₄₇	—	4	1	no	—
89	C₂×C₄×C₄₇	—	4	1	no	—
90	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
96	C₂×Dic₄₇	—	4	1	no	—
97	C₂×Dic₄₇	—	4	2	no	—
98	D₁₈₈	—	2	2	no	—
99	D₁₈₈	—	2	2	no	—
100	D₁₈₈	—	4	1	no	—
101	D₁₈₈	—	4	1	no	—
102	C₄₇⋊C₈	—	2	2	no	—
103	C₄₇⋊C₈	—	2	2	no	—
104	C₂²×C₄₇	—	4	2	no	—
105	C₂²×C₄₇	—	4	4	no	—
106	C₂²×C₄₇	—	8	2	no	—
107	C₂²×C₄₇	—	8	1	no	—
108	C₂²×C₄₇	—	8	1	no	—
109	C₂²×C₄₇	#120	1	1	yes	characteristic
110	C₂²×C₄₇	#121	1	1	yes	characteristic
111	C₂²×C₄₇	#127	1	1	yes	characteristic
112	C₂²×C₄₇	#135	1	2	yes	—
113	C₂²×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
114	C₂×D₄₇	—	4	2	no	—
115	C₂×D₄₇	—	4	4	no	—
116	C₂×D₄₇	—	8	2	no	—
117	C₂×D₄₇	—	8	1	no	—
118	C₂×D₄₇	—	8	1	no	—
119	C₄×C₄₇	—	4	2	no	—
120	C₄×C₄₇	—	4	2	no	—
121	C₄×C₄₇	#120	1	1	yes	characteristic
122	C₄×C₄₇	#120	1	1	yes	characteristic
123	C₄×C₄₇	#121	1	1	yes	characteristic
124	C₄×C₄₇	#121	1	1	yes	characteristic
125	Dic₄₇	—	8	1	no	—
126	#2012	—	47	1	no	maximal, Sylow
127	C₂×C₄₇	—	8	2	no	—
128	C₂×C₄₇	#392	1	1	yes	characteristic
129	C₂×C₄₇	#449	1	2	yes	—
130	C₂×C₄₇	#463	1	2	yes	—
131	C₂×C₄₇	#495	1	1	yes	characteristic
132	C₂×C₄₇	#496	1	1	yes	characteristic
133	D₄₇	—	8	2	no	—
134	C₂²×SD₁₆	—	47	1	no	—
135	C₂²×D₈	—	47	1	no	—
136	C₂×#124	D₄₇	1	1	yes	characteristic, complemented
137	C₂×#103	—	47	1	no	—
138	C₂×#102	—	47	1	no	—
139	#390	—	47	1	no	—
140	#336	—	47	1	no	—
141	C₄₇	#2012	1	1	yes	characteristic, complemented, Sylow
142	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
143	C₂²×D₄	—	47	1	no	—
144	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
145	C₂×SD₁₆	—	94	2	no	—
146	C₂×SD₁₆	—	94	2	no	—
147	C₂×SD₁₆	—	94	2	no	—
148	C₂×D₈	—	94	2	no	—
149	C₂×D₈	—	94	2	no	—
150	C₂×D₈	—	94	2	no	—
151	C₂²×C₈	—	47	1	no	—
152	C₂²×C₈	—	47	1	no	—
153	#124	—	2	2	no	—
154	#124	—	2	2	no	—
155	C₂×C₄⋊C₄	—	47	1	no	—
156	C₂×C₂²⋊C₄	—	2	2	no	—
157	C₂×C₂²⋊C₄	—	94	2	no	—
158	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
159	#103	—	94	2	no	—
160	#102	—	94	2	no	—
161	C₂⁴	—	2	1	no	—
162	C₂⁴	—	94	1	no	—
163	C₂×Q₈	—	2	1	no	—
164	C₂×Q₈	—	2	1	no	—
165	C₂×Q₈	—	2	1	no	—
166	C₂×Q₈	—	2	1	no	—
167	C₂×Q₈	—	2	1	no	—
168	C₂×Q₈	C₂²⋊D₄₇	1	2	yes	—
169	C₂×D₄	—	2	1	no	—
170	C₂×D₄	—	2	1	no	—
171	C₂×D₄	—	2	1	no	—
172	C₂×D₄	—	2	1	no	—
173	C₂×D₄	—	2	1	no	—
174	C₂×D₄	—	47	2	no	—
175	C₂×D₄	—	94	1	no	—
176	C₂×D₄	—	94	1	no	—
177	C₂×D₄	—	94	1	no	—
178	C₂×D₄	—	94	1	no	—
179	C₂×D₄	—	94	1	no	—
180	C₂×D₄	C₂²⋊D₄₇	1	2	yes	—
181	C₂²×C₄	—	2	1	no	—
182	C₂²×C₄	—	94	1	no	—
183	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
184	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
185	SD₁₆	—	94	8	no	—
186	D₈	—	94	8	no	—
187	C₂×C₈	—	47	2	no	—
188	C₂×C₈	—	47	2	no	—
189	C₂×C₈	—	94	1	no	—
190	C₂×C₈	—	94	1	no	—
191	C₂×C₈	—	94	1	no	—
192	C₂×C₈	—	94	1	no	—
193	C₄⋊C₄	—	94	1	no	—
194	C₄⋊C₄	—	94	1	no	—
195	C₂²⋊C₄	—	2	8	no	—
196	C₂²⋊C₄	—	188	4	no	—
197	C₄²	—	2	1	no	—
198	C₄²	—	2	1	no	—
199	C₂³	—	2	2	no	—
200	C₂³	—	4	1	no	—
201	C₂³	—	4	1	no	—
202	C₂³	—	4	2	no	—
203	C₂³	—	4	2	no	—
204	C₂³	—	94	2	no	—
205	C₂³	—	188	1	no	—
206	C₂³	—	188	1	no	—
207	C₂³	—	188	2	no	—
208	C₂³	—	188	2	no	—
209	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
210	Q₈	—	2	2	no	—
211	Q₈	—	2	2	no	—
212	Q₈	—	4	1	no	—
213	Q₈	—	4	1	no	—
214	D₄	—	2	2	no	—
215	D₄	—	2	2	no	—
216	D₄	—	4	1	no	—
217	D₄	—	4	1	no	—
218	D₄	—	94	2	no	—
219	D₄	—	94	2	no	—
220	D₄	—	188	1	no	—
221	D₄	—	188	1	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	1	no	—
228	C₂×C₄	—	188	1	no	—
229	C₂×C₄	—	188	2	no	—
230	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
231	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
232	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
233	C₂×C₄	#10625352	1	1	yes	characteristic
234	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
235	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
236	C₈	—	94	2	no	—
237	C₈	—	94	2	no	—
238	C₂²	—	4	4	no	—
239	C₂²	—	4	2	no	—
240	C₂²	—	8	1	no	—
241	C₂²	—	8	1	no	—
242	C₂²	—	8	2	no	—
243	C₂²	—	376	1	no	—
244	C₂²	—	376	1	no	—
245	C₂²	—	376	2	no	—
246	C₂²	—	188	2	no	—
247	C₂²	—	188	4	no	—
248	C₂²	#13093993	1	1	yes	characteristic
249	C₂²	#13093995	1	1	yes	characteristic
250	C₂²	#13094020	1	1	yes	characteristic
251	C₂²	#13094044	1	2	yes	—
252	C₂²	#13094049	1	2	yes	—
253	C₄	—	4	2	no	—
254	C₄	—	4	2	no	—
255	C₄	—	376	1	no	—
256	C₄	#13093992	1	1	yes	characteristic
257	C₄	#13093992	1	1	yes	characteristic
258	C₄	#13093996	1	1	yes	characteristic
259	C₄	#13093996	1	1	yes	characteristic
260	C₂	—	8	2	no	—
261	C₂	—	376	2	no	—
262	C₂	#15689031	1	1	yes	characteristic
263	C₂	#15689268	1	2	yes	—
264	C₂	#15689335	1	2	yes	—
265	C₂	#15689505	1	1	yes	characteristic
266	C₂	#15689513	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10625336

C₂

yes

maximal, characteristic, complemented

C₂²×#10625334

C₂

yes

maximal, characteristic

C₂×#13093948

C₂

yes

maximal, characteristic, complemented

C₂×#13093945

C₂

yes

maximal, characteristic, complemented

#15689025

C₂

yes

maximal, characteristic, complemented

#15688878

C₂

yes

maximal, characteristic, complemented

C₂×#124×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₈₈

C₂²

yes

—

—

—

—

—

—

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

characteristic

C₂×(C₂×D₄₇)⋊C₄

—

#13093948

—

#13093945

—

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

C₂²×D₄×C₄₇

C₂²

yes

characteristic

#124×C₄₇

—

#124×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂⁴×C₄₇

—

C₂³×D₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

D₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

D₄

yes

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

#10625336

—

#10625334

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

—

C₂×C₄₇⋊C₈

D₄

yes

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

100

D₁₈₈

—

101

D₁₈₈

—

102

C₄₇⋊C₈

—

103

C₄₇⋊C₈

—

104

C₂²×C₄₇

—

105

C₂²×C₄₇

—

106

C₂²×C₄₇

—

107

C₂²×C₄₇

—

108

C₂²×C₄₇

—

109

C₂²×C₄₇

#120

yes

characteristic

110

C₂²×C₄₇

#121

yes

characteristic

111

C₂²×C₄₇

#127

yes

characteristic

112

C₂²×C₄₇

#135

yes

—

113

C₂²×C₄₇

AGL(1,ℤ/8)

yes

—

114

C₂×D₄₇

—

115

C₂×D₄₇

—

116

C₂×D₄₇

—

117

C₂×D₄₇

—

118

C₂×D₄₇

—

119

C₄×C₄₇

—

120

C₄×C₄₇

—

121

C₄×C₄₇

#120

yes

characteristic

122

C₄×C₄₇

#120

yes

characteristic

123

C₄×C₄₇

#121

yes

characteristic

124

C₄×C₄₇

#121

yes

characteristic

125

Dic₄₇

—

126

#2012

—

maximal, Sylow

127

C₂×C₄₇

—

128

C₂×C₄₇

#392

yes

characteristic

129

C₂×C₄₇

#449

yes

—

130

C₂×C₄₇

#463

yes

—

131

C₂×C₄₇

#495

yes

characteristic

132

C₂×C₄₇

#496

yes

characteristic

133

D₄₇

—

134

C₂²×SD₁₆

—

135

C₂²×D₈

—

136

C₂×#124

D₄₇

yes

characteristic, complemented

137

C₂×#103

—

138

C₂×#102

—

139

#390

—

140

#336

—

141

C₄₇

#2012

yes

characteristic, complemented, Sylow

142

C₂²×Q₈

C₂×D₄₇

yes

characteristic

143

C₂²×D₄

—

144

C₂²×D₄

C₂×D₄₇

yes

characteristic

145

C₂×SD₁₆

—

146

C₂×SD₁₆

—

147

C₂×SD₁₆

—

148

C₂×D₈

—

149

C₂×D₈

—

150

C₂×D₈

—

151

C₂²×C₈

—

152

C₂²×C₈

—

153

#124

—

154

#124

—

155

C₂×C₄⋊C₄

—

156

C₂×C₂²⋊C₄

—

157

C₂×C₂²⋊C₄

—

158

C₂×C₄²

C₂×D₄₇

yes

characteristic

159

#103

—

160

#102

—

161

C₂⁴

—

162

C₂⁴

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

C₂²⋊D₄₇

yes

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂×D₄

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

C₂²⋊D₄₇

yes

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

C₂²⋊D₄₇

yes

—

184

C₂²×C₄

C₂²×D₄₇

yes

characteristic

185

SD₁₆

—

186

D₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₂²⋊C₄

—

196

C₂²⋊C₄

—

188

—

197

C₄²

—

198

C₄²

—

199

C₂³

—

200

C₂³

—

201

C₂³

—

202

C₂³

—

203

C₂³

—

204

C₂³

—

205

C₂³

—

188

—

206

C₂³

—

188

—

207

C₂³

—

188

—

208

C₂³

—

188

—

209

C₂³

C₂×C₂²⋊D₄₇

yes

characteristic

210

Q₈

—

211

Q₈

—

212

Q₈

—

213

Q₈

—

214

D₄

—

215

D₄

—

216

D₄

—

217

D₄

—

218

D₄

—

219

D₄

—

220

D₄

—

188

—

221

D₄

—

188

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

188

—

229

C₂×C₄

—

188

—

230

C₂×C₄

D₄×D₄₇

yes

characteristic

231

C₂×C₄

D₄×D₄₇

yes

characteristic

232

C₂×C₄

D₄×D₄₇

yes

characteristic

233

C₂×C₄

#10625352

yes

characteristic

234

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

235

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

236

C₈

—

237

C₈

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

376

—

244

C₂²

—

376

—

245

C₂²

—

376

—

246

C₂²

—

188

—

247

C₂²

—

188

—

248

C₂²

#13093993

yes

characteristic

249

C₂²

#13093995

yes

characteristic

250

C₂²

#13094020

yes

characteristic

251

C₂²

#13094044

yes

—

252

C₂²

#13094049

yes

—

253

C₄

—

254

C₄

—

255

C₄

—

376

—

256

C₄

#13093992

yes

characteristic

257

C₄

#13093992

yes

characteristic

258

C₄

#13093996

yes

characteristic

259

C₄

#13093996

yes

characteristic

260

C₂

—

261

C₂

—

376

—

262

C₂

#15689031

yes

characteristic

263

C₂

#15689268

yes

—

264

C₂

#15689335

yes

—

265

C₂

#15689505

yes

characteristic

266

C₂

#15689513

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₇
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#124×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂×#124	D₄₇
hypocenter	C₄₇	#2012
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#124

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₇

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#124×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#124

N	H ≅ G/N	type
1. C₂²×#10625336	C₂	semidirect
3. C₂×#13093948	C₂	semidirect
4. C₂×#13093945	C₂	semidirect
5. #15689025	C₂	semidirect
6. #15688878	C₂	semidirect
7. C₂×#124×C₄₇	C₂	semidirect
136. C₂×#124	D₄₇	semidirect
141. C₄₇	#2012	semidirect

H ≅ G/N

type

1. C₂²×#10625336

C₂

semidirect

3. C₂×#13093948

C₂

semidirect

4. C₂×#13093945

C₂

semidirect

5. #15689025

C₂

semidirect

6. #15688878

C₂

semidirect

7. C₂×#124×C₄₇

C₂

semidirect

136. C₂×#124

D₄₇

semidirect

141. C₄₇

#2012

semidirect

Subgroups — #20244465

Conjugacy classes of subgroups

Complements