Group #20253995 — subgroups

Subgroups — #20253995

Order 6016.

364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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	#15689680	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689533	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689518	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689493	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689482	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689379	C₂	1	2	yes	maximal, complemented
7	#15689367	C₂	1	2	yes	maximal
8	C₄×#10625337	C₂	1	2	yes	maximal, complemented
9	C₄×#10625335	C₂	1	2	yes	maximal, complemented
10	C₄×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#529	C₂	1	1	yes	maximal, characteristic
12	C₂×#10625337	C₂²	1	2	yes	—
13	C₂×#10625335	C₂²	1	2	yes	—
14	C₂×#10625329	C₂²	1	2	yes	—
15	#13094024	C₂²	1	1	yes	characteristic
16	#13094024	C₂²	1	1	yes	characteristic
17	#13094016	—	2	1	no	—
18	#13094003	—	2	1	no	—
19	#13094003	C₂²	1	2	yes	—
20	C₄×Dic₉₄	—	2	1	no	—
21	C₄×Dic₉₄	C₂²	1	2	yes	—
22	#13093983	—	2	1	no	—
23	#13093957	C₂²	1	2	yes	—
24	#13093955	C₂²	1	2	yes	—
25	#13093948	C₂²	1	2	yes	—
26	#13093947	C₂²	1	2	yes	—
27	#13093947	C₂²	1	2	yes	—
28	#13093945	C₂²	1	2	yes	—
29	#13093935	C₂²	1	1	yes	characteristic
30	#13093935	C₂²	1	1	yes	characteristic
31	C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
32	#126×C₄₇	—	2	1	no	—
33	#125×C₄₇	C₂²	1	1	yes	characteristic
34	#124×C₄₇	C₂²	1	1	yes	characteristic
35	#123×C₄₇	—	2	1	no	—
36	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	#121×C₄₇	C₂²	1	1	yes	characteristic
38	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₄₇	—	2	1	no	—
40	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
41	#117×C₄₇	—	2	1	no	—
42	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
44	C₂×D₄×C₄₇	—	2	1	no	—
45	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	—	2	1	no	—
47	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₂×Dic₉₄	—	2	1	no	—
51	C₂×Dic₉₄	C₂³	1	2	yes	—
52	C₄⋊C₄×C₄₇	—	2	1	no	—
53	C₄⋊C₄×C₄₇	—	2	1	no	—
54	C₄⋊C₄×C₄₇	—	2	1	no	—
55	C₄⋊C₄×C₄₇	—	2	1	no	—
56	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
58	C₂²⋊C₄×C₄₇	—	2	1	no	—
59	C₂²⋊C₄×C₄₇	—	2	1	no	—
60	C₂²⋊C₄×C₄₇	—	2	1	no	—
61	C₂²⋊C₄×C₄₇	—	2	1	no	—
62	C₂²⋊C₄×C₄₇	—	2	1	no	—
63	C₄²×C₄₇	—	2	1	no	—
64	C₄²×C₄₇	D₄	1	1	yes	characteristic
65	C₄²×C₄₇	D₄	1	1	yes	characteristic
66	C₄²×C₄₇	C₂³	1	1	yes	characteristic
67	C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₂²⋊Dic₄₇	—	2	2	no	—
69	#10625337	—	2	4	no	—
70	#10625335	—	2	4	no	—
71	C₄⋊Dic₄₇	—	2	1	no	—
72	C₄⋊Dic₄₇	—	2	1	no	—
73	C₄⋊Dic₄₇	—	2	1	no	—
74	C₄⋊Dic₄₇	C₂³	1	2	yes	—
75	Dic₄₇⋊C₄	—	2	2	no	—
76	Dic₄₇⋊C₄	—	2	2	no	—
77	C₄×Dic₄₇	—	2	2	no	—
78	#10625329	—	2	4	no	—
79	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
80	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
81	C₂³×C₄₇	—	2	1	no	—
82	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
83	Q₈×C₄₇	—	2	2	no	—
84	D₄×C₄₇	—	2	2	no	—
85	D₄×C₄₇	—	4	2	no	—
86	C₂×C₄×C₄₇	—	2	2	no	—
87	C₂×C₄×C₄₇	—	2	2	no	—
88	C₂×C₄×C₄₇	—	2	1	no	—
89	C₂×C₄×C₄₇	—	2	1	no	—
90	C₂×C₄×C₄₇	—	2	1	no	—
91	C₂×C₄×C₄₇	—	4	1	no	—
92	C₂×C₄×C₄₇	—	4	2	no	—
93	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
99	C₂×Dic₄₇	—	2	2	no	—
100	C₂×Dic₄₇	—	2	2	no	—
101	Dic₉₄	—	2	2	no	—
102	Dic₉₄	—	2	2	no	—
103	Dic₉₄	—	4	2	no	—
104	C₄₇⋊C₈	—	2	2	no	—
105	C₄₇⋊C₈	#41	1	4	yes	—
106	C₂²×C₄₇	—	2	1	no	—
107	C₂²×C₄₇	—	2	1	no	—
108	C₂²×C₄₇	—	2	1	no	—
109	C₂²×C₄₇	—	4	1	no	—
110	C₂²×C₄₇	—	4	1	no	—
111	C₂²×C₄₇	—	4	1	no	—
112	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
113	C₄×C₄₇	—	2	1	no	—
114	C₄×C₄₇	—	2	1	no	—
115	C₄×C₄₇	—	2	1	no	—
116	C₄×C₄₇	—	2	1	no	—
117	C₄×C₄₇	—	4	1	no	—
118	C₄×C₄₇	—	4	1	no	—
119	C₄×C₄₇	—	4	1	no	—
120	C₄×C₄₇	#137	1	2	yes	—
121	C₄×C₄₇	C₂×#41	1	2	yes	—
122	Dic₄₇	—	4	2	no	—
123	Dic₄₇	—	4	2	no	—
124	#3172	—	47	1	no	maximal, Sylow
125	C₂×C₄₇	—	4	1	no	—
126	C₂×C₄₇	—	8	1	no	—
127	C₂×C₄₇	#532	1	1	yes	characteristic
128	C₂×C₄₇	C₂×#137	1	1	yes	characteristic
129	C₂×C₄₇	#575	1	1	yes	characteristic
130	#533	—	47	1	no	—
131	#529	D₄₇	1	1	yes	characteristic
132	#501	—	47	1	no	—
133	#497	—	47	1	no	—
134	#491	—	47	1	no	—
135	#489	—	47	1	no	—
136	#470	—	47	2	no	—
137	#468	—	47	2	no	—
138	C₄×Q₁₆	—	47	2	no	—
139	C₄×SD₁₆	—	47	2	no	—
140	C₄×M₁₆	—	47	1	no	—
141	C₄₇	#3172	1	1	yes	characteristic, complemented, Sylow
142	C₂×Q₁₆	—	47	2	no	—
143	C₂×SD₁₆	—	47	2	no	—
144	C₂×M₁₆	—	47	2	no	—
145	C₄⋊Q₈	—	47	1	no	—
146	C₄⋊Q₈	—	47	1	no	—
147	#126	—	2	1	no	—
148	#125	—	94	1	no	—
149	#125	C₂×D₄₇	1	1	yes	characteristic
150	#124	C₂×D₄₇	1	1	yes	characteristic
151	#123	—	2	1	no	—
152	C₂²⋊Q₈	—	47	2	no	—
153	C₂²⋊Q₈	—	94	1	no	—
154	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
155	#121	C₂×D₄₇	1	1	yes	characteristic
156	C₄×Q₈	—	47	2	no	—
157	C₄×Q₈	—	94	1	no	—
158	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
159	C₄×D₄	—	2	1	no	—
160	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
161	#117	—	2	1	no	—
162	#117	—	94	1	no	—
163	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
164	#107	—	47	2	no	—
165	#106	—	47	2	no	—
166	#103	—	47	2	no	—
167	#103	—	47	2	no	—
168	#103	—	47	2	no	—
169	#102	—	47	2	no	—
170	#97	—	47	1	no	—
171	#97	—	47	1	no	—
172	C₄×C₈	—	47	2	no	—
173	C₂×Q₈	—	47	2	no	—
174	C₂×Q₈	—	94	1	no	—
175	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
176	C₂×D₄	—	2	1	no	—
177	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
178	C₂²×C₄	—	2	1	no	—
179	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
180	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
181	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
182	Q₁₆	—	94	4	no	—
183	SD₁₆	—	94	4	no	—
184	M₁₆	—	94	4	no	—
185	C₂×C₈	—	47	2	no	—
186	C₂×C₈	—	47	2	no	—
187	C₄⋊C₄	—	2	1	no	—
188	C₄⋊C₄	—	2	1	no	—
189	C₄⋊C₄	—	2	1	no	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	47	2	no	—
192	C₄⋊C₄	—	94	2	no	—
193	C₄⋊C₄	—	94	2	no	—
194	C₄⋊C₄	—	94	1	no	—
195	C₄⋊C₄	—	94	1	no	—
196	C₄⋊C₄	—	94	1	no	—
197	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
198	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
199	C₂²⋊C₄	—	2	1	no	—
200	C₂²⋊C₄	—	2	1	no	—
201	C₂²⋊C₄	—	2	1	no	—
202	C₂²⋊C₄	—	2	1	no	—
203	C₂²⋊C₄	—	2	1	no	—
204	C₂²⋊C₄	—	94	2	no	—
205	C₄²	—	2	1	no	—
206	C₄²	—	94	2	no	—
207	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
208	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
209	C₄²	C₂²×D₄₇	1	1	yes	characteristic
210	C₄²	C₂²×D₄₇	1	1	yes	characteristic
211	C₂³	—	2	1	no	—
212	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
213	Q₈	—	2	2	no	—
214	Q₈	—	94	2	no	—
215	Q₈	—	94	2	no	—
216	Q₈	—	188	2	no	—
217	D₄	—	2	2	no	—
218	D₄	—	4	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	4	1	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	94	2	no	—
227	C₂×C₄	—	94	2	no	—
228	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
229	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
230	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
231	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
232	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
233	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
234	C₈	—	47	4	no	—
235	C₈	—	94	2	no	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	—	4	1	no	—
240	C₂²	—	4	1	no	—
241	C₂²	—	4	1	no	—
242	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	2	1	no	—
247	C₄	—	4	1	no	—
248	C₄	—	4	1	no	—
249	C₄	—	4	1	no	—
250	C₄	—	188	2	no	—
251	C₄	—	188	2	no	—
252	C₄	#13094054	1	2	yes	—
253	C₄	#41×D₄₇	1	2	yes	—
254	C₂	—	4	1	no	—
255	C₂	—	8	1	no	—
256	C₂	#15689669	1	1	yes	characteristic
257	C₂	C₂×#13094054	1	1	yes	characteristic
258	C₂	#15689921	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689680

C₂

yes

maximal, characteristic, complemented

#15689533

C₂

yes

maximal, characteristic, complemented

#15689518

C₂

yes

maximal, characteristic, complemented

#15689493

C₂

yes

maximal, characteristic, complemented

#15689482

C₂

yes

maximal, characteristic, complemented

#15689379

C₂

yes

maximal, complemented

#15689367

C₂

yes

maximal

C₄×#10625337

C₂

yes

maximal, complemented

C₄×#10625335

C₂

yes

maximal, complemented

C₄×#10625329

C₂

yes

maximal, characteristic, complemented

C₄₇×#529

C₂

yes

maximal, characteristic

C₂×#10625337

C₂²

yes

—

C₂×#10625335

C₂²

yes

—

C₂×#10625329

C₂²

yes

—

#13094024

C₂²

yes

characteristic

#13094024

C₂²

yes

—

—

C₂²

yes

—

C₄×Dic₉₄

—

C₄×Dic₉₄

C₂²

yes

—

#13093983

—

#13093957

C₂²

yes

—

#13093955

C₂²

yes

—

#13093948

C₂²

yes

—

#13093947

C₂²

yes

—

#13093947

C₂²

yes

—

#13093945

C₂²

yes

—

#13093935

C₂²

yes

characteristic

#13093935

C₂²

yes

characteristic

C₄×C₄₇⋊C₈

C₂²

yes

—

#126×C₄₇

—

#125×C₄₇

C₂²

yes

characteristic

#124×C₄₇

C₂²

yes

characteristic

#123×C₄₇

—

C₂²⋊Q₈×C₄₇

C₂²

yes

characteristic

#121×C₄₇

C₂²

yes

characteristic

C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

C₂²

yes

characteristic

#117×C₄₇

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

C₂³

yes

characteristic

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

C₂³

yes

characteristic

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

C₂²⋊Dic₄₇

—

#10625337

—

#10625335

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

C₂³

yes

—

C₂×C₄₇⋊C₈

C₂³

yes

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

Q₈×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×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

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

100

C₂×Dic₄₇

—

101

Dic₉₄

—

102

Dic₉₄

—

103

Dic₉₄

—

104

C₄₇⋊C₈

—

105

C₄₇⋊C₈

#41

yes

—

106

C₂²×C₄₇

—

107

C₂²×C₄₇

—

108

C₂²×C₄₇

—

109

C₂²×C₄₇

—

110

C₂²×C₄₇

—

111

C₂²×C₄₇

—

112

C₂²×C₄₇

C₂²×D₄

yes

characteristic

113

C₄×C₄₇

—

114

C₄×C₄₇

—

115

C₄×C₄₇

—

116

C₄×C₄₇

—

117

C₄×C₄₇

—

118

C₄×C₄₇

—

119

C₄×C₄₇

—

120

C₄×C₄₇

#137

yes

—

121

C₄×C₄₇

C₂×#41

yes

—

122

Dic₄₇

—

123

Dic₄₇

—

124

#3172

—

maximal, Sylow

125

C₂×C₄₇

—

126

C₂×C₄₇

—

127

C₂×C₄₇

#532

yes

characteristic

128

C₂×C₄₇

C₂×#137

yes

characteristic

129

C₂×C₄₇

#575

yes

characteristic

130

#533

—

131

#529

D₄₇

yes

characteristic

132

#501

—

133

#497

—

134

#491

—

135

#489

—

136

#470

—

137

#468

—

138

C₄×Q₁₆

—

139

C₄×SD₁₆

—

140

C₄×M₁₆

—

141

C₄₇

#3172

yes

characteristic, complemented, Sylow

142

C₂×Q₁₆

—

143

C₂×SD₁₆

—

144

C₂×M₁₆

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

#126

—

148

#125

—

149

#125

C₂×D₄₇

yes

characteristic

150

#124

C₂×D₄₇

yes

characteristic

151

#123

—

152

C₂²⋊Q₈

—

153

C₂²⋊Q₈

—

154

C₂²⋊Q₈

C₂×D₄₇

yes

characteristic

155

#121

C₂×D₄₇

yes

characteristic

156

C₄×Q₈

—

157

C₄×Q₈

—

158

C₄×Q₈

C₂×D₄₇

yes

characteristic

159

C₄×D₄

—

160

C₄×D₄

C₂×D₄₇

yes

characteristic

161

#117

—

162

#117

—

163

C₂×C₄²

C₂×D₄₇

yes

characteristic

164

#107

—

165

#106

—

166

#103

—

167

#103

—

168

#103

—

169

#102

—

170

#97

—

171

#97

—

172

C₄×C₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

C₂²×D₄₇

yes

characteristic

176

C₂×D₄

—

177

C₂×D₄

C₂²×D₄₇

yes

characteristic

178

C₂²×C₄

—

179

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

180

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

181

C₂²×C₄

C₂²×D₄₇

yes

characteristic

182

Q₁₆

—

183

SD₁₆

—

184

M₁₆

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

C₂²×D₄₇

yes

characteristic

198

C₄⋊C₄

C₂²×D₄₇

yes

characteristic

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

202

C₂²⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₄²

—

206

C₄²

—

207

C₄²

C₂²⋊D₄₇

yes

characteristic

208

C₄²

C₂²⋊D₄₇

yes

characteristic

209

C₄²

C₂²×D₄₇

yes

characteristic

210

C₄²

C₂²×D₄₇

yes

characteristic

211

C₂³

—

212

C₂³

C₂×C₂²⋊D₄₇

yes

characteristic

213

Q₈

—

214

Q₈

—

215

Q₈

—

216

Q₈

—

188

—

217

D₄

—

218

D₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

229

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

230

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

231

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

232

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

233

C₂×C₄

C₂³×D₄₇

yes

characteristic

234

C₈

—

235

C₈

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

188

—

251

C₄

—

188

—

252

C₄

#13094054

yes

—

253

C₄

#41×D₄₇

yes

—

254

C₂

—

255

C₂

—

256

C₂

#15689669

yes

characteristic

257

C₂

C₂×#13094054

yes

characteristic

258

C₂

#15689921

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#529	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#529	D₄₇
hypocenter	C₄₇	#3172
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #529

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₄₇

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₄₇×#529

C₂

socle

C₂²×C₄₇

C₂²×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #529

N	H ≅ G/N	type
1. #15689680	C₂	semidirect
2. #15689533	C₂	semidirect
3. #15689518	C₂	semidirect
4. #15689493	C₂	semidirect
5. #15689482	C₂	semidirect
6. #15689379	C₂	semidirect
8. C₄×#10625337	C₂	semidirect
9. C₄×#10625335	C₂	semidirect
10. C₄×#10625329	C₂	semidirect
141. C₄₇	#3172	semidirect

H ≅ G/N

type

1. #15689680

C₂

semidirect

2. #15689533

C₂

semidirect

3. #15689518

C₂

semidirect

4. #15689493

C₂

semidirect

5. #15689482

C₂

semidirect

6. #15689379

C₂

semidirect

8. C₄×#10625337

C₂

semidirect

9. C₄×#10625335

C₂

semidirect

10. C₄×#10625329

C₂

semidirect

141. C₄₇

#3172

semidirect

Subgroups — #20253995

Conjugacy classes of subgroups

Complements