Group #20253171 — subgroups

Subgroups — #20253171

Order 6016.

388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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	#15689678	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#10625354	C₂	1	1	yes	maximal, characteristic
3	#15689428	C₂	1	2	yes	maximal, complemented
4	#15689422	C₂	1	2	yes	maximal, complemented
5	#15689418	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689414	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689400	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689158	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689118	C₂	1	2	yes	maximal
11	C₄₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10625354	C₂²	1	1	yes	characteristic
13	C₂×C₈×D₄₇	C₂²	1	2	yes	—
14	#13094024	C₂²	1	1	yes	characteristic
15	#13094015	C₂²	1	2	yes	—
16	#13094004	—	2	1	no	—
17	#13094000	—	2	1	no	—
18	Q₈×Dic₄₇	—	2	1	no	—
19	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
20	#13093989	—	2	1	no	—
21	C₄×D₁₈₈	—	2	1	no	—
22	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
23	#13093986	—	2	1	no	—
24	#13093986	C₂²	1	1	yes	characteristic
25	#13093982	—	2	1	no	—
26	#13093982	C₂²	1	1	yes	characteristic
27	#13093982	C₂²	1	2	yes	—
28	C₄²×D₄₇	—	2	1	no	—
29	C₄²×D₄₇	C₂²	1	1	yes	characteristic
30	#13093957	C₂²	1	2	yes	—
31	#13093957	C₂²	1	2	yes	—
32	#13093956	C₂²	1	2	yes	—
33	C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
34	Dic₄₇⋊C₈	C₂²	1	2	yes	—
35	#13093948	C₂²	1	2	yes	—
36	#13093946	C₂²	1	2	yes	—
37	#13093944	C₂²	1	2	yes	—
38	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
40	#106×C₄₇	C₂²	1	2	yes	—
41	C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
42	#103×C₄₇	C₂²	1	2	yes	—
43	C₂×Q₈×C₄₇	—	2	1	no	—
44	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
45	#10625354	—	2	2	no	—
46	#10625354	Q₈	1	4	yes	complemented
47	C₂×D₁₈₈	—	2	1	no	—
48	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
49	C₂×C₄×D₄₇	—	2	1	no	—
50	C₂×C₄×D₄₇	—	2	1	no	—
51	C₂×C₄×D₄₇	—	2	1	no	—
52	C₂×C₄×D₄₇	D₄	1	1	yes	characteristic
53	C₂×C₄×D₄₇	D₄	1	1	yes	characteristic
54	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
55	C₂×Dic₉₄	—	2	1	no	—
56	C₂×C₈×C₄₇	C₂³	1	2	yes	—
57	C₄⋊C₄×C₄₇	—	2	1	no	—
58	C₄⋊C₄×C₄₇	—	2	1	no	—
59	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
60	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
61	C₄²×C₄₇	—	2	1	no	—
62	C₄²×C₄₇	C₂³	1	1	yes	characteristic
63	(C₂×D₄₇)⋊C₄	—	2	1	no	—
64	(C₂×D₄₇)⋊C₄	—	2	2	no	—
65	(C₂×D₄₇)⋊C₄	—	2	1	no	—
66	(C₂×D₄₇)⋊C₄	—	2	1	no	—
67	C₄⋊Dic₄₇	—	2	1	no	—
68	C₄⋊Dic₄₇	—	2	1	no	—
69	C₄⋊Dic₄₇	—	2	2	no	—
70	C₄⋊Dic₄₇	C₂³	1	2	yes	—
71	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
72	Dic₄₇⋊C₄	—	2	2	no	—
73	C₄×Dic₄₇	—	2	1	no	—
74	C₄×Dic₄₇	—	2	1	no	—
75	C₄×Dic₄₇	—	2	2	no	—
76	C₄×Dic₄₇	D₄	1	1	yes	characteristic
77	C₄×Dic₄₇	D₄	1	1	yes	characteristic
78	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
80	C₈×D₄₇	—	2	4	no	—
81	C₂²×D₄₇	—	2	1	no	—
82	C₂²×D₄₇	C₂×D₄	1	1	yes	characteristic
83	Q₈×C₄₇	—	2	1	no	—
84	Q₈×C₄₇	—	4	2	no	—
85	Q₈×C₄₇	C₂×Q₈	1	2	yes	—
86	C₂×C₄×C₄₇	—	2	1	no	—
87	C₂×C₄×C₄₇	—	2	2	no	—
88	C₂×C₄×C₄₇	—	2	1	no	—
89	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
92	C₂×Dic₄₇	—	2	1	no	—
93	C₂×Dic₄₇	—	2	2	no	—
94	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
97	D₁₈₈	—	2	4	no	—
98	D₁₈₈	—	2	1	no	—
99	D₁₈₈	C₂×Q₈	1	2	yes	—
100	C₄×D₄₇	—	2	2	no	—
101	C₄×D₄₇	—	2	4	no	—
102	C₄×D₄₇	—	4	1	no	—
103	C₄×D₄₇	—	4	2	no	—
104	C₄×D₄₇	—	4	2	no	—
105	C₄×D₄₇	C₂×Q₈	1	2	yes	—
106	C₄×D₄₇	#41	1	2	yes	—
107	Dic₉₄	—	4	2	no	—
108	C₈×C₄₇	—	2	2	no	—
109	C₄₇⋊C₈	—	2	2	no	—
110	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
111	C₂×D₄₇	—	2	1	no	—
112	C₂×D₄₇	—	2	1	no	—
113	C₂×D₄₇	—	2	2	no	—
114	C₂×D₄₇	—	4	1	no	—
115	C₂×D₄₇	—	4	1	no	—
116	C₂×D₄₇	C₂²⋊Q₈	1	2	yes	—
117	C₄×C₄₇	—	2	2	no	—
118	C₄×C₄₇	—	2	1	no	—
119	C₄×C₄₇	—	4	2	no	—
120	C₄×C₄₇	—	4	1	no	—
121	C₄×C₄₇	#135	1	2	yes	—
122	C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
123	C₄×C₄₇	C₂×#41	1	1	yes	characteristic
124	Dic₄₇	—	2	1	no	—
125	Dic₄₇	—	2	1	no	—
126	Dic₄₇	—	4	1	no	—
127	Dic₄₇	—	4	2	no	—
128	Dic₄₇	C₂²⋊Q₈	1	2	yes	—
129	#3076	—	47	1	no	maximal, Sylow
130	C₂×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
131	C₂×C₄₇	C₂×#135	1	1	yes	characteristic
132	C₂×C₄₇	#575	1	1	yes	characteristic
133	D₄₇	—	2	2	no	—
134	D₄₇	—	4	2	no	—
135	#533	—	47	1	no	—
136	C₄×#41	—	47	1	no	—
137	#479	—	47	2	no	—
138	#478	—	47	2	no	—
139	#477	—	47	1	no	—
140	#476	—	47	1	no	—
141	#475	D₄₇	1	1	yes	characteristic, complemented
142	#474	—	47	1	no	—
143	#427	—	47	2	no	—
144	C₂×C₄⋊C₈	—	47	1	no	—
145	#416	—	47	2	no	—
146	C₄₇	#3076	1	1	yes	characteristic, complemented, Sylow
147	C₂×#41	—	47	1	no	—
148	C₂²×C₈	—	47	2	no	—
149	C₄⋊Q₈	—	47	1	no	—
150	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
151	#125	—	47	2	no	—
152	C₂²⋊Q₈	—	94	1	no	—
153	C₂²⋊Q₈	—	94	1	no	—
154	C₄×Q₈	—	47	1	no	—
155	C₄×Q₈	—	94	1	no	—
156	C₄×Q₈	—	94	1	no	—
157	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
158	C₄×D₄	—	47	1	no	—
159	C₄×D₄	—	47	1	no	—
160	C₄×D₄	—	94	1	no	—
161	C₄×D₄	—	94	1	no	—
162	#117	—	47	1	no	—
163	#117	—	47	2	no	—
164	#117	—	94	1	no	—
165	C₂×C₄²	—	47	1	no	—
166	C₂×C₄²	—	94	1	no	—
167	#107	—	47	2	no	—
168	#107	—	47	2	no	—
169	#106	—	47	2	no	—
170	#106	C₂×D₄₇	1	2	yes	—
171	C₄⋊C₈	—	47	2	no	—
172	C₄⋊C₈	—	47	1	no	—
173	C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
174	#103	—	47	2	no	—
175	#103	C₂×D₄₇	1	2	yes	—
176	#102	—	47	2	no	—
177	#102	—	47	2	no	—
178	#41	—	47	4	no	—
179	#41	—	94	2	no	—
180	C₂×Q₈	—	2	1	no	—
181	C₂×Q₈	—	94	1	no	—
182	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
183	C₂×D₄	—	47	1	no	—
184	C₂×D₄	—	94	1	no	—
185	C₂²×C₄	—	47	1	no	—
186	C₂²×C₄	—	47	1	no	—
187	C₂²×C₄	—	47	1	no	—
188	C₂²×C₄	—	94	1	no	—
189	C₂²×C₄	—	94	1	no	—
190	C₂²×C₄	—	94	1	no	—
191	C₂×C₈	—	47	2	no	—
192	C₂×C₈	—	94	4	no	—
193	C₂×C₈	C₂²×D₄₇	1	2	yes	—
194	C₄⋊C₄	—	2	1	no	—
195	C₄⋊C₄	—	2	1	no	—
196	C₄⋊C₄	—	47	2	no	—
197	C₄⋊C₄	—	47	1	no	—
198	C₄⋊C₄	—	94	2	no	—
199	C₄⋊C₄	—	94	1	no	—
200	C₄⋊C₄	—	94	2	no	—
201	C₄⋊C₄	—	94	1	no	—
202	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
203	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
204	C₂²⋊C₄	—	94	1	no	—
205	C₂²⋊C₄	—	94	1	no	—
206	C₂²⋊C₄	—	94	2	no	—
207	C₂²⋊C₄	—	94	1	no	—
208	C₄²	—	2	1	no	—
209	C₄²	—	47	1	no	—
210	C₄²	—	47	1	no	—
211	C₄²	—	47	1	no	—
212	C₄²	—	94	1	no	—
213	C₄²	—	94	1	no	—
214	C₄²	—	94	2	no	—
215	C₄²	C₂²×D₄₇	1	1	yes	characteristic
216	C₂³	—	47	1	no	—
217	C₂³	—	94	1	no	—
218	Q₈	—	2	1	no	—
219	Q₈	—	4	2	no	—
220	Q₈	—	188	2	no	—
221	Q₈	Q₈×D₄₇	1	2	yes	—
222	D₄	—	47	2	no	—
223	D₄	—	94	4	no	—
224	D₄	—	94	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	47	1	no	—
229	C₂×C₄	—	47	2	no	—
230	C₂×C₄	—	47	2	no	—
231	C₂×C₄	—	47	1	no	—
232	C₂×C₄	—	47	1	no	—
233	C₂×C₄	—	94	4	no	—
234	C₂×C₄	—	94	2	no	—
235	C₂×C₄	—	94	1	no	—
236	C₂×C₄	—	94	2	no	—
237	C₂×C₄	—	188	1	no	—
238	C₂×C₄	—	188	2	no	—
239	C₂×C₄	—	188	2	no	—
240	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
241	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
242	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
243	C₈	—	2	2	no	—
244	C₈	—	94	2	no	—
245	C₂²	—	47	2	no	—
246	C₂²	—	94	1	no	—
247	C₂²	—	94	1	no	—
248	C₂²	—	94	2	no	—
249	C₂²	—	188	1	no	—
250	C₂²	—	188	1	no	—
251	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
252	C₄	—	2	2	no	—
253	C₄	—	2	1	no	—
254	C₄	—	4	2	no	—
255	C₄	—	4	1	no	—
256	C₄	—	47	2	no	—
257	C₄	—	94	1	no	—
258	C₄	—	94	1	no	—
259	C₄	—	188	1	no	—
260	C₄	—	188	2	no	—
261	C₄	#13094045	1	2	yes	—
262	C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
263	C₄	#41×D₄₇	1	1	yes	characteristic
264	C₂	—	94	2	no	—
265	C₂	—	188	2	no	—
266	C₂	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
267	C₂	C₂×#13094045	1	1	yes	characteristic
268	C₂	#15689922	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689678

C₂

yes

maximal, characteristic, complemented

C₄×#10625354

C₂

yes

maximal, characteristic

#15689428

C₂

yes

maximal, complemented

#15689422

C₂

yes

maximal, complemented

#15689418

C₂

yes

maximal, characteristic, complemented

#15689414

C₂

yes

maximal, characteristic, complemented

#15689400

C₂

yes

maximal, characteristic, complemented

#15689158

C₂

yes

maximal, complemented

C₄⋊C₈×D₄₇

C₂

yes

maximal, characteristic, complemented

#15689118

C₂

yes

maximal

C₄₇×#475

C₂

yes

maximal, characteristic, complemented

C₂×#10625354

C₂²

yes

characteristic

C₂×C₈×D₄₇

C₂²

yes

—

#13094024

C₂²

yes

characteristic

#13094015

C₂²

yes

—

#13094004

—

#13094000

—

Q₈×Dic₄₇

—

Q₈×Dic₄₇

C₂²

yes

characteristic

#13093989

—

C₄×D₁₈₈

—

C₄×D₁₈₈

C₂²

yes

characteristic

#13093986

—

#13093986

C₂²

yes

characteristic

#13093982

—

#13093982

C₂²

yes

characteristic

#13093982

C₂²

yes

—

C₄²×D₄₇

—

C₄²×D₄₇

C₂²

yes

characteristic

#13093957

C₂²

yes

—

#13093957

C₂²

yes

—

#13093956

C₂²

yes

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

Dic₄₇⋊C₈

C₂²

yes

—

#13093948

C₂²

yes

—

#13093946

C₂²

yes

—

#13093944

C₂²

yes

—

C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₄×Q₈×C₄₇

C₂²

yes

characteristic

#106×C₄₇

C₂²

yes

—

C₄⋊C₈×C₄₇

C₂²

yes

characteristic

#103×C₄₇

C₂²

yes

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂³

yes

characteristic

#10625354

—

#10625354

Q₈

yes

complemented

C₂×D₁₈₈

—

C₂×D₁₈₈

C₂³

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

D₄

yes

characteristic

C₂×C₄×D₄₇

D₄

yes

characteristic

C₂×C₄×D₄₇

C₂³

yes

characteristic

C₂×Dic₉₄

—

C₂×C₈×C₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂³

yes

—

C₄⋊Dic₄₇

C₂³

yes

characteristic

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

D₄

yes

characteristic

C₄×Dic₄₇

D₄

yes

characteristic

C₄×Dic₄₇

C₂³

yes

characteristic

C₂×C₄₇⋊C₈

C₂³

yes

—

C₈×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₂×D₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

C₂×Q₈

yes

—

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

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

C₂×D₄

yes

characteristic

D₁₈₈

—

D₁₈₈

—

D₁₈₈

C₂×Q₈

yes

—

100

C₄×D₄₇

—

101

C₄×D₄₇

—

102

C₄×D₄₇

—

103

C₄×D₄₇

—

104

C₄×D₄₇

—

105

C₄×D₄₇

C₂×Q₈

yes

—

106

C₄×D₄₇

#41

yes

—

107

Dic₉₄

—

108

C₈×C₄₇

—

109

C₄₇⋊C₈

—

110

C₂²×C₄₇

C₂²×D₄

yes

characteristic

111

C₂×D₄₇

—

112

C₂×D₄₇

—

113

C₂×D₄₇

—

114

C₂×D₄₇

—

115

C₂×D₄₇

—

116

C₂×D₄₇

C₂²⋊Q₈

yes

—

117

C₄×C₄₇

—

118

C₄×C₄₇

—

119

C₄×C₄₇

—

120

C₄×C₄₇

—

121

C₄×C₄₇

#135

yes

—

122

C₄×C₄₇

C₂²×Q₈

yes

characteristic

123

C₄×C₄₇

C₂×#41

yes

characteristic

124

Dic₄₇

—

125

Dic₄₇

—

126

Dic₄₇

—

127

Dic₄₇

—

128

Dic₄₇

C₂²⋊Q₈

yes

—

129

#3076

—

maximal, Sylow

130

C₂×C₄₇

C₂×C₂²⋊Q₈

yes

characteristic

131

C₂×C₄₇

C₂×#135

yes

characteristic

132

C₂×C₄₇

#575

yes

characteristic

133

D₄₇

—

134

D₄₇

—

135

#533

—

136

C₄×#41

—

137

#479

—

138

#478

—

139

#477

—

140

#476

—

141

#475

D₄₇

yes

characteristic, complemented

142

#474

—

143

#427

—

144

C₂×C₄⋊C₈

—

145

#416

—

146

C₄₇

#3076

yes

characteristic, complemented, Sylow

147

C₂×#41

—

148

C₂²×C₈

—

149

C₄⋊Q₈

—

150

C₄⋊Q₈

C₂×D₄₇

yes

characteristic

151

#125

—

152

C₂²⋊Q₈

—

153

C₂²⋊Q₈

—

154

C₄×Q₈

—

155

C₄×Q₈

—

156

C₄×Q₈

—

157

C₄×Q₈

C₂×D₄₇

yes

characteristic

158

C₄×D₄

—

159

C₄×D₄

—

160

C₄×D₄

—

161

C₄×D₄

—

162

#117

—

163

#117

—

164

#117

—

165

C₂×C₄²

—

166

C₂×C₄²

—

167

#107

—

168

#107

—

169

#106

—

170

#106

C₂×D₄₇

yes

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

C₄⋊C₈

C₂×D₄₇

yes

characteristic

174

#103

—

175

#103

C₂×D₄₇

yes

—

176

#102

—

177

#102

—

178

#41

—

179

#41

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

C₂²×D₄₇

yes

characteristic

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

C₂²×D₄₇

yes

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

C₂²×D₄₇

yes

—

203

C₄⋊C₄

C₂²×D₄₇

yes

characteristic

204

C₂²⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₂²⋊C₄

—

208

C₄²

—

209

C₄²

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₄²

—

215

C₄²

C₂²×D₄₇

yes

characteristic

216

C₂³

—

217

C₂³

—

218

Q₈

—

219

Q₈

—

220

Q₈

—

188

—

221

Q₈

Q₈×D₄₇

yes

—

222

D₄

—

223

D₄

—

224

D₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

188

—

238

C₂×C₄

—

188

—

239

C₂×C₄

—

188

—

240

C₂×C₄

D₄×D₄₇

yes

characteristic

241

C₂×C₄

D₄×D₄₇

yes

characteristic

242

C₂×C₄

C₂³×D₄₇

yes

characteristic

243

C₈

—

244

C₈

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

188

—

250

C₂²

—

188

—

251

C₂²

C₂×D₄×D₄₇

yes

characteristic

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

188

—

260

C₄

—

188

—

261

C₄

#13094045

yes

—

262

C₄

C₂×Q₈×D₄₇

yes

characteristic

263

C₄

#41×D₄₇

yes

characteristic

264

C₂

—

265

C₂

—

188

—

266

C₂

C₂²⋊Q₈×D₄₇

yes

characteristic

267

C₂

C₂×#13094045

yes

characteristic

268

C₂

#15689922

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#475	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#475	D₄₇
hypocenter	C₄₇	#3076
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #475

subgroup

G/H

center

C₂²

C₂×D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₄₇×#475

C₂

socle

C₂²×C₄₇

C₂²×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #475

N	H ≅ G/N	type
1. #15689678	C₂	semidirect
3. #15689428	C₂	semidirect
4. #15689422	C₂	semidirect
5. #15689418	C₂	semidirect
6. #15689414	C₂	semidirect
7. #15689400	C₂	semidirect
8. #15689158	C₂	semidirect
9. C₄⋊C₈×D₄₇	C₂	semidirect
11. C₄₇×#475	C₂	semidirect
46. #10625354	Q₈	semidirect
141. #475	D₄₇	semidirect
146. C₄₇	#3076	semidirect

H ≅ G/N

type

1. #15689678

C₂

semidirect

3. #15689428

C₂

semidirect

4. #15689422

C₂

semidirect

5. #15689418

C₂

semidirect

6. #15689414

C₂

semidirect

7. #15689400

C₂

semidirect

8. #15689158

C₂

semidirect

9. C₄⋊C₈×D₄₇

C₂

semidirect

11. C₄₇×#475

C₂

semidirect

46. #10625354

Q₈

semidirect

141. #475

D₄₇

semidirect

146. C₄₇

#3076

semidirect

Subgroups — #20253171

Conjugacy classes of subgroups

Complements