Group #20251687 — subgroups

Subgroups — #20251687

Order 6016.

696 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 177 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	C₂×#13094011	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13094003	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689028	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689026	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689017	C₂	1	4	yes	maximal, complemented
7	#15689003	C₂	1	4	yes	maximal, complemented
8	#15688988	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#121×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
11	C₂³×Dic₄₇	C₂²	1	2	yes	—
12	#13094011	—	2	4	no	—
13	#13094003	—	2	4	no	—
14	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
16	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
17	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
18	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
19	C₂×C₄×Dic₄₇	—	2	4	no	—
20	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
21	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
23	C₄₇⋊#95	C₂²	1	4	yes	—
24	C₄₇⋊#95	C₂²	1	4	yes	—
25	C₂²×D₄×C₄₇	C₂²	1	2	yes	—
26	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
28	#121×C₄₇	—	2	4	no	—
29	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
31	C₂⁴×C₄₇	C₂³	1	2	yes	—
32	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
33	C₂×D₄×C₄₇	—	2	4	no	—
34	C₂×D₄×C₄₇	—	2	8	no	—
35	C₂×D₄×C₄₇	—	2	2	no	—
36	C₂×D₄×C₄₇	—	2	2	no	—
37	C₂×D₄×C₄₇	—	2	2	no	—
38	C₂²×C₄×C₄₇	—	2	2	no	—
39	C₂²×C₄×C₄₇	—	2	2	no	—
40	C₂²×C₄×C₄₇	D₄	1	4	yes	—
41	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
42	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×Dic₄₇	—	2	4	no	—
45	C₂²×Dic₄₇	—	2	4	no	—
46	C₂²×Dic₄₇	—	2	4	no	—
47	C₂²×Dic₄₇	C₂³	1	2	yes	—
48	C₂²×Dic₄₇	C₂³	1	2	yes	—
49	C₂²×Dic₄₇	C₂³	1	2	yes	—
50	C₂²×Dic₄₇	C₂³	1	2	yes	—
51	C₂×Dic₉₄	—	2	2	no	—
52	C₂×Dic₉₄	—	2	2	no	—
53	C₂×Dic₉₄	—	2	2	no	—
54	C₄⋊C₄×C₄₇	—	2	2	no	—
55	C₂²⋊C₄×C₄₇	—	2	4	no	—
56	C₂²⋊Dic₄₇	—	2	4	no	—
57	C₂²⋊Dic₄₇	—	2	8	no	—
58	C₂²⋊Dic₄₇	—	2	8	no	—
59	C₄⋊Dic₄₇	—	2	2	no	—
60	Dic₄₇⋊C₄	—	2	4	no	—
61	C₄×Dic₄₇	—	2	2	no	—
62	C₄×Dic₄₇	—	2	4	no	—
63	C₄×Dic₄₇	D₄	1	4	yes	complemented
64	C₂³×C₄₇	—	2	1	no	—
65	C₂³×C₄₇	—	2	2	no	—
66	C₂³×C₄₇	—	2	1	no	—
67	C₂³×C₄₇	—	2	2	no	—
68	C₂³×C₄₇	—	2	2	no	—
69	C₂³×C₄₇	—	2	4	no	—
70	C₂³×C₄₇	—	2	2	no	—
71	C₂³×C₄₇	—	2	4	no	—
72	C₂³×C₄₇	C₂×D₄	1	2	yes	—
73	C₂³×C₄₇	#41	1	4	yes	—
74	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
75	D₄×C₄₇	—	4	8	no	—
76	D₄×C₄₇	—	4	4	no	—
77	C₂×C₄×C₄₇	—	2	1	no	—
78	C₂×C₄×C₄₇	—	2	1	no	—
79	C₂×C₄×C₄₇	—	2	8	no	—
80	C₂×C₄×C₄₇	—	2	2	no	—
81	C₂×C₄×C₄₇	—	2	4	no	—
82	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
83	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
84	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
85	C₂×C₄×C₄₇	#41	1	2	yes	—
86	C₂×Dic₄₇	—	2	16	no	—
87	C₂×Dic₄₇	—	2	2	no	—
88	C₂×Dic₄₇	—	2	2	no	—
89	C₂×Dic₄₇	—	2	2	no	—
90	C₂×Dic₄₇	—	2	2	no	—
91	C₂×Dic₄₇	—	2	2	no	—
92	C₂×Dic₄₇	—	2	2	no	—
93	C₂×Dic₄₇	—	2	2	no	—
94	C₂×Dic₄₇	—	2	4	no	—
95	C₂×Dic₄₇	—	2	2	no	—
96	C₂×Dic₄₇	C₂×D₄	1	4	yes	—
97	C₂×Dic₄₇	#41	1	4	yes	—
98	Dic₉₄	—	4	4	no	—
99	C₂²×C₄₇	—	2	2	no	—
100	C₂²×C₄₇	—	2	4	no	—
101	C₂²×C₄₇	—	2	4	no	—
102	C₂²×C₄₇	—	2	2	no	—
103	C₂²×C₄₇	—	4	2	no	—
104	C₂²×C₄₇	—	4	4	no	—
105	C₂²×C₄₇	—	4	2	no	—
106	C₂²×C₄₇	—	4	4	no	—
107	C₂²×C₄₇	—	4	2	no	—
108	C₂²×C₄₇	#124	1	4	yes	complemented
109	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
110	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
111	C₂²×C₄₇	C₂×#41	1	2	yes	—
112	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
113	C₂²×C₄₇	C₂×#41	1	2	yes	—
114	C₄×C₄₇	—	2	2	no	—
115	C₄×C₄₇	—	4	2	no	—
116	C₄×C₄₇	#121	1	4	yes	—
117	Dic₄₇	—	2	4	no	—
118	Dic₄₇	—	2	4	no	—
119	Dic₄₇	—	4	2	no	—
120	Dic₄₇	—	4	2	no	—
121	#2850	—	47	1	no	maximal, Sylow
122	C₂×C₄₇	—	2	4	no	—
123	C₂×C₄₇	—	8	2	no	—
124	C₂×C₄₇	C₂×#121	1	1	yes	characteristic
125	C₂×C₄₇	#525	1	2	yes	—
126	C₂×C₄₇	C₂×#124	1	1	yes	characteristic
127	C₂×C₄₇	#529	1	2	yes	—
128	C₂×C₄₇	#532	1	1	yes	characteristic
129	C₂×#124	—	47	1	no	—
130	C₂×C₂²⋊Q₈	—	47	1	no	—
131	C₂×#121	D₄₇	1	1	yes	characteristic
132	C₂²×C₄²	—	47	1	no	—
133	#391	—	47	1	no	—
134	#390	—	47	1	no	—
135	#388	—	47	4	no	—
136	#386	—	47	4	no	—
137	#382	—	47	1	no	—
138	C₄₇	#2850	1	1	yes	characteristic, complemented, Sylow
139	C₂²×Q₈	—	47	1	no	—
140	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
141	C₂²×D₄	C₂×D₄₇	1	2	yes	—
142	C₂³×C₄	—	47	2	no	—
143	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
144	#124	—	94	4	no	—
145	C₂²⋊Q₈	—	94	4	no	—
146	#121	—	2	4	no	—
147	C₂×C₄⋊C₄	—	47	2	no	—
148	C₂×C₄⋊C₄	—	47	1	no	—
149	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
150	C₂×C₂²⋊C₄	—	47	2	no	—
151	C₂×C₂²⋊C₄	—	47	4	no	—
152	C₂×C₂²⋊C₄	—	47	4	no	—
153	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
154	C₂×C₄²	—	47	1	no	—
155	C₂×C₄²	—	47	2	no	—
156	C₂×C₄²	—	47	1	no	—
157	C₂×C₄²	—	94	4	no	—
158	#95	—	47	4	no	—
159	#95	—	47	4	no	—
160	C₂⁴	C₂²×D₄₇	1	2	yes	—
161	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
162	C₂×Q₈	—	94	2	no	—
163	C₂×Q₈	—	94	2	no	—
164	C₂×Q₈	—	94	2	no	—
165	C₂×D₄	—	2	8	no	—
166	C₂×D₄	—	2	4	no	—
167	C₂×D₄	—	2	2	no	—
168	C₂×D₄	—	2	2	no	—
169	C₂×D₄	—	2	2	no	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	47	2	no	—
173	C₂²×C₄	—	47	2	no	—
174	C₂²×C₄	—	47	2	no	—
175	C₂²×C₄	—	47	2	no	—
176	C₂²×C₄	—	94	4	no	—
177	C₂²×C₄	—	94	4	no	—
178	C₂²×C₄	—	94	4	no	—
179	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
180	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
181	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
182	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	94	4	no	—
185	C₄⋊C₄	—	94	2	no	—
186	C₂²⋊C₄	—	2	4	no	—
187	C₂²⋊C₄	—	94	8	no	—
188	C₂²⋊C₄	—	94	8	no	—
189	C₂²⋊C₄	—	94	4	no	—
190	C₄²	—	47	4	no	—
191	C₄²	—	94	4	no	—
192	C₄²	—	94	2	no	—
193	C₂³	—	2	1	no	—
194	C₂³	—	2	2	no	—
195	C₂³	—	2	1	no	—
196	C₂³	—	2	2	no	—
197	C₂³	—	2	2	no	—
198	C₂³	—	2	4	no	—
199	C₂³	—	2	2	no	—
200	C₂³	—	2	4	no	—
201	C₂³	#10625352	1	4	yes	—
202	C₂³	C₂×C₂²⋊D₄₇	1	2	yes	—
203	C₂³	C₂³×D₄₇	1	1	yes	characteristic
204	Q₈	—	188	4	no	—
205	D₄	—	4	8	no	—
206	D₄	—	4	4	no	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	8	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	4	no	—
212	C₂×C₄	—	47	4	no	—
213	C₂×C₄	—	47	4	no	—
214	C₂×C₄	—	94	16	no	—
215	C₂×C₄	—	94	2	no	—
216	C₂×C₄	—	94	2	no	—
217	C₂×C₄	—	94	2	no	—
218	C₂×C₄	—	94	2	no	—
219	C₂×C₄	—	94	2	no	—
220	C₂×C₄	—	94	2	no	—
221	C₂×C₄	—	94	2	no	—
222	C₂×C₄	—	94	4	no	—
223	C₂×C₄	—	94	2	no	—
224	C₂×C₄	D₄×D₄₇	1	2	yes	—
225	C₂×C₄	#10625352	1	2	yes	—
226	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
227	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
228	C₂²	—	2	2	no	—
229	C₂²	—	2	4	no	—
230	C₂²	—	2	4	no	—
231	C₂²	—	2	2	no	—
232	C₂²	—	4	2	no	—
233	C₂²	—	4	4	no	—
234	C₂²	—	4	2	no	—
235	C₂²	—	4	4	no	—
236	C₂²	—	4	2	no	—
237	C₂²	#13094011	1	4	yes	complemented
238	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
239	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
240	C₂²	#41×D₄₇	1	2	yes	—
241	C₂²	C₂×#10625352	1	1	yes	characteristic
242	C₂²	C₂×#10625352	1	2	yes	—
243	C₄	—	2	2	no	—
244	C₄	—	4	2	no	—
245	C₄	—	94	4	no	—
246	C₄	—	94	4	no	—
247	C₄	—	188	2	no	—
248	C₄	—	188	2	no	—
249	C₄	#13093996	1	4	yes	—
250	C₂	—	2	4	no	—
251	C₂	—	8	2	no	—
252	C₂	C₂×#13093996	1	1	yes	characteristic
253	C₂	#15689633	1	2	yes	—
254	C₂	C₂×#13094011	1	1	yes	characteristic
255	C₂	#15689654	1	2	yes	—
256	C₂	#15689669	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094011

C₂

yes

maximal, characteristic, complemented

C₂×#13094003

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×Dic₄₇

C₂

yes

maximal, characteristic, complemented

#15689028

C₂

yes

maximal, characteristic, complemented

#15689026

C₂

yes

maximal, characteristic, complemented

#15689017

C₂

yes

maximal, complemented

#15689003

C₂

yes

maximal, complemented

#15688988

C₂

yes

maximal, characteristic, complemented

C₂×#121×C₄₇

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

characteristic

C₂³×Dic₄₇

C₂²

yes

—

#13094011

—

#13094003

—

C₂×C₄⋊Dic₄₇

C₂²

yes

characteristic

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×D₄×C₄₇

C₂²

yes

—

C₂²×D₄×C₄₇

C₂²

yes

characteristic

C₂³×C₄×C₄₇

C₂²

yes

characteristic

#121×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

D₄

yes

complemented

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

#41

yes

—

Dic₉₄

—

C₂²×C₄₇

—

100

C₂²×C₄₇

—

101

C₂²×C₄₇

—

102

C₂²×C₄₇

—

103

C₂²×C₄₇

—

104

C₂²×C₄₇

—

105

C₂²×C₄₇

—

106

C₂²×C₄₇

—

107

C₂²×C₄₇

—

108

C₂²×C₄₇

#124

yes

complemented

109

C₂²×C₄₇

C₂²×D₄

yes

characteristic

110

C₂²×C₄₇

C₂²×D₄

yes

characteristic

111

C₂²×C₄₇

C₂×#41

yes

—

112

C₂²×C₄₇

C₂×#41

yes

characteristic

113

C₂²×C₄₇

C₂×#41

yes

—

114

C₄×C₄₇

—

115

C₄×C₄₇

—

116

C₄×C₄₇

#121

yes

—

117

Dic₄₇

—

118

Dic₄₇

—

119

Dic₄₇

—

120

Dic₄₇

—

121

#2850

—

maximal, Sylow

122

C₂×C₄₇

—

123

C₂×C₄₇

—

124

C₂×C₄₇

C₂×#121

yes

characteristic

125

C₂×C₄₇

#525

yes

—

126

C₂×C₄₇

C₂×#124

yes

characteristic

127

C₂×C₄₇

#529

yes

—

128

C₂×C₄₇

#532

yes

characteristic

129

C₂×#124

—

130

C₂×C₂²⋊Q₈

—

131

C₂×#121

D₄₇

yes

characteristic

132

C₂²×C₄²

—

133

#391

—

134

#390

—

135

#388

—

136

#386

—

137

#382

—

138

C₄₇

#2850

yes

characteristic, complemented, Sylow

139

C₂²×Q₈

—

140

C₂²×D₄

C₂×D₄₇

yes

characteristic

141

C₂²×D₄

C₂×D₄₇

yes

—

142

C₂³×C₄

—

143

C₂³×C₄

C₂×D₄₇

yes

characteristic

144

#124

—

145

C₂²⋊Q₈

—

146

#121

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

150

C₂×C₂²⋊C₄

—

151

C₂×C₂²⋊C₄

—

152

C₂×C₂²⋊C₄

—

153

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

154

C₂×C₄²

—

155

C₂×C₄²

—

156

C₂×C₄²

—

157

C₂×C₄²

—

158

#95

—

159

#95

—

160

C₂⁴

C₂²×D₄₇

yes

—

161

C₂⁴

C₂²×D₄₇

yes

characteristic

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

C₂²⋊D₄₇

yes

—

180

C₂²×C₄

C₂²×D₄₇

yes

—

181

C₂²×C₄

C₂²×D₄₇

yes

characteristic

182

C₂²×C₄

C₂²×D₄₇

yes

characteristic

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₂²⋊C₄

—

187

C₂²⋊C₄

—

188

C₂²⋊C₄

—

189

C₂²⋊C₄

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₂³

—

194

C₂³

—

195

C₂³

—

196

C₂³

—

197

C₂³

—

198

C₂³

—

199

C₂³

—

200

C₂³

—

201

C₂³

#10625352

yes

—

202

C₂³

C₂×C₂²⋊D₄₇

yes

—

203

C₂³

C₂³×D₄₇

yes

characteristic

204

Q₈

—

188

—

205

D₄

—

206

D₄

—

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

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

D₄×D₄₇

yes

—

225

C₂×C₄

#10625352

yes

—

226

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

227

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

#13094011

yes

complemented

238

C₂²

C₂×D₄×D₄₇

yes

characteristic

239

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

240

C₂²

#41×D₄₇

yes

—

241

C₂²

C₂×#10625352

yes

characteristic

242

C₂²

C₂×#10625352

yes

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

188

—

248

C₄

—

188

—

249

C₄

#13093996

yes

—

250

C₂

—

251

C₂

—

252

C₂

C₂×#13093996

yes

characteristic

253

C₂

#15689633

yes

—

254

C₂

C₂×#13094011

yes

characteristic

255

C₂

#15689654

yes

—

256

C₂

#15689669

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₂×#121×C₄₇	C₂
hypercenter	C₂×#121	D₄₇
hypocenter	C₄₇	#2850
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#121

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₂×#121×C₄₇

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₂×#121

N	H ≅ G/N	type
1. C₂×#13094011	C₂	semidirect
2. C₂×#13094003	C₂	semidirect
3. C₂²×C₄×Dic₄₇	C₂	semidirect
4. #15689028	C₂	semidirect
5. #15689026	C₂	semidirect
6. #15689017	C₂	semidirect
7. #15689003	C₂	semidirect
8. #15688988	C₂	semidirect
63. C₄×Dic₄₇	D₄	semidirect
108. C₂²×C₄₇	#124	semidirect
138. C₄₇	#2850	semidirect
237. C₂²	#13094011	semidirect

H ≅ G/N

type

1. C₂×#13094011

C₂

semidirect

2. C₂×#13094003

C₂

semidirect

3. C₂²×C₄×Dic₄₇

C₂

semidirect

4. #15689028

C₂

semidirect

5. #15689026

C₂

semidirect

6. #15689017

C₂

semidirect

7. #15689003

C₂

semidirect

8. #15688988

C₂

semidirect

63. C₄×Dic₄₇

D₄

semidirect

108. C₂²×C₄₇

#124

semidirect

138. C₄₇

#2850

semidirect

237. C₂²

#13094011

semidirect

Subgroups — #20251687

Conjugacy classes of subgroups

Complements