Group #26106848 — subgroups

Subgroups — #26106848

Order 12032.

518 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 161 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×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#20241709	C₂	1	1	yes	maximal, characteristic
3	#20241675	C₂	1	2	yes	maximal, complemented
4	#20241239	C₂	1	2	yes	maximal, complemented
5	C₄×#100×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₄	1	2	yes	—
7	D₄×C₄₇⋊C₈	—	2	2	no	—
8	D₄×C₄₇⋊C₈	—	2	2	no	—
9	#15689176	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊(C₄₇⋊C₈)	C₄	1	2	yes	—
12	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	#15688847	C₄	1	4	yes	—
14	#15688845	—	2	2	no	—
15	#15688845	—	2	2	no	—
16	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#100×C₄₇	C₄	1	2	yes	—
18	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#343	C₄	1	2	yes	—
20	C₂²×C₄₇⋊C₈	—	2	2	no	—
21	C₂²×C₄₇⋊C₈	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	4	4	no	—
23	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
25	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
27	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
28	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
29	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
30	C₄×C₄₇⋊C₈	—	2	2	no	—
31	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
32	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
33	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
35	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
36	C₄×D₄×C₄₇	—	2	2	no	—
37	C₄×D₄×C₄₇	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
40	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
41	#100×C₄₇	—	2	4	no	—
42	#97×C₄₇	—	2	2	no	—
43	C₄×C₈×C₄₇	—	2	2	no	—
44	C₂⁴×C₄₇	C₄²	1	2	yes	—
45	C₂×D₄×C₄₇	—	2	2	no	—
46	C₂×D₄×C₄₇	—	2	2	no	—
47	C₂×D₄×C₄₇	M₁₆	1	4	yes	—
48	C₂²×C₄×C₄₇	—	2	2	no	—
49	C₂²×C₄×C₄₇	—	2	2	no	—
50	C₂²×C₄×C₄₇	—	4	2	no	—
51	C₂²×C₄×C₄₇	—	4	2	no	—
52	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
53	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
56	M₁₆×C₄₇	—	2	4	no	—
57	M₁₆×C₄₇	—	2	4	no	—
58	C₂×C₈×C₄₇	—	2	4	no	—
59	C₄⋊C₄×C₄₇	—	2	2	no	—
60	C₂²⋊C₄×C₄₇	—	2	4	no	—
61	C₄²×C₄₇	C₂×D₄	1	2	yes	—
62	C₄²×C₄₇	#41	1	2	yes	—
63	C₂×C₄₇⋊C₈	—	2	2	no	—
64	C₂×C₄₇⋊C₈	—	2	2	no	—
65	C₂×C₄₇⋊C₈	—	2	4	no	—
66	C₂×C₄₇⋊C₈	—	4	1	no	—
67	C₂×C₄₇⋊C₈	—	4	4	no	—
68	C₂×C₄₇⋊C₈	—	4	4	no	—
69	C₂×C₄₇⋊C₈	—	4	2	no	—
70	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
71	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
73	C₂³×C₄₇	—	2	2	no	—
74	C₂³×C₄₇	—	2	2	no	—
75	C₂³×C₄₇	—	4	2	no	—
76	C₂³×C₄₇	—	4	2	no	—
77	C₂³×C₄₇	#97	1	4	yes	—
78	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
79	D₄×C₄₇	—	2	8	no	—
80	C₂×C₄×C₄₇	—	2	1	no	—
81	C₂×C₄×C₄₇	—	2	1	no	—
82	C₂×C₄×C₄₇	—	2	2	no	—
83	C₂×C₄×C₄₇	—	4	1	no	—
84	C₂×C₄×C₄₇	—	4	4	no	—
85	C₂×C₄×C₄₇	—	4	2	no	—
86	C₂×C₄×C₄₇	—	4	2	no	—
87	C₂×C₄×C₄₇	—	4	2	no	—
88	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
90	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
91	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
92	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
93	C₂×C₄×C₄₇	#131	1	2	yes	—
94	C₈×C₄₇	—	4	4	no	—
95	C₄₇⋊C₈	—	2	1	no	—
96	C₄₇⋊C₈	—	2	2	no	—
97	C₄₇⋊C₈	—	4	4	no	—
98	C₄₇⋊C₈	—	4	2	no	—
99	C₄₇⋊C₈	#100	1	2	yes	complemented
100	#8164	—	47	1	no	maximal, Sylow
101	C₂²×C₄₇	—	2	1	no	—
102	C₂²×C₄₇	—	2	1	no	—
103	C₂²×C₄₇	—	2	4	no	—
104	C₂²×C₄₇	—	4	4	no	—
105	C₂²×C₄₇	—	4	4	no	—
106	C₂²×C₄₇	—	4	2	no	—
107	C₂²×C₄₇	—	4	2	no	—
108	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄₇	C₂×#97	1	1	yes	characteristic
110	C₂²×C₄₇	#405	1	1	yes	characteristic
111	C₄×C₄₇	—	2	1	no	—
112	C₄×C₄₇	—	2	2	no	—
113	C₄×C₄₇	—	4	2	no	—
114	C₄×C₄₇	C₂×#100	1	1	yes	characteristic
115	C₄×C₄₇	#413	1	1	yes	characteristic
116	C₄×C₄₇	#435	1	4	yes	—
117	C₂×C₈×D₄	—	47	1	no	—
118	C₄×#100	D₄₇	1	1	yes	characteristic
119	#1460	—	47	1	no	—
120	#1451	—	47	2	no	—
121	#1283	—	47	2	no	—
122	C₂×C₄₇	—	2	1	no	—
123	C₂×C₄₇	—	2	1	no	—
124	C₂×C₄₇	—	4	4	no	—
125	C₂×C₄₇	#1752	1	1	yes	characteristic
126	C₂×C₄₇	C₄×#100	1	1	yes	characteristic
127	C₂×C₄₇	#1757	1	1	yes	characteristic
128	C₂³×C₈	—	47	2	no	—
129	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
130	C₈×D₄	—	94	2	no	—
131	C₈×D₄	—	94	2	no	—
132	#431	—	47	2	no	—
133	C₂×C₄⋊C₈	—	47	1	no	—
134	C₂×#100	Dic₄₇	1	2	yes	—
135	C₂×C₂²⋊C₈	—	47	2	no	—
136	C₄×M₁₆	C₂×D₄₇	1	2	yes	—
137	C₂×C₄×C₈	—	47	1	no	—
138	#343	Dic₄₇	1	2	yes	—
139	#323	—	47	4	no	—
140	#322	—	94	2	no	—
141	#322	—	94	2	no	—
142	C₄₇	#8164	1	1	yes	characteristic, complemented, Sylow
143	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
144	C₂³×C₄	C₄×D₄₇	1	2	yes	—
145	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
146	C₂²×C₈	—	47	1	no	—
147	C₂²×C₈	—	47	1	no	—
148	C₂²×C₈	—	47	2	no	—
149	C₂²×C₈	—	94	2	no	—
150	C₂²×C₈	—	94	2	no	—
151	C₂²×C₈	—	188	4	no	—
152	C₄×D₄	—	2	2	no	—
153	C₄×D₄	—	2	2	no	—
154	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
155	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
156	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
157	C₄⋊C₈	—	94	2	no	—
158	C₄⋊C₈	—	94	2	no	—
159	#100	—	2	4	no	—
160	C₂²⋊C₈	—	47	4	no	—
161	C₂²⋊C₈	—	94	4	no	—
162	#97	—	2	2	no	—
163	C₄×C₈	—	2	2	no	—
164	C₄×C₈	—	47	2	no	—
165	C₄×C₈	—	47	2	no	—
166	C₄×C₈	—	94	2	no	—
167	C₂⁴	C₄×Dic₄₇	1	2	yes	—
168	C₂×D₄	—	2	2	no	—
169	C₂×D₄	—	2	2	no	—
170	C₂×D₄	#10625329	1	4	yes	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	4	2	no	—
174	C₂²×C₄	—	4	2	no	—
175	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
176	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
178	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
179	M₁₆	—	2	4	no	—
180	M₁₆	—	2	4	no	—
181	C₂×C₈	—	2	4	no	—
182	C₂×C₈	—	47	1	no	—
183	C₂×C₈	—	47	2	no	—
184	C₂×C₈	—	47	1	no	—
185	C₂×C₈	—	94	2	no	—
186	C₂×C₈	—	94	2	no	—
187	C₂×C₈	—	94	4	no	—
188	C₂×C₈	—	188	4	no	—
189	C₂×C₈	—	188	1	no	—
190	C₂×C₈	—	188	4	no	—
191	C₂×C₈	—	188	2	no	—
192	C₄⋊C₄	—	2	2	no	—
193	C₂²⋊C₄	—	2	4	no	—
194	C₄²	D₄×D₄₇	1	2	yes	—
195	C₄²	#10625352	1	2	yes	—
196	C₂³	—	2	2	no	—
197	C₂³	—	2	2	no	—
198	C₂³	—	4	2	no	—
199	C₂³	—	4	2	no	—
200	C₂³	#13093935	1	4	yes	—
201	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
202	D₄	—	2	8	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
212	C₂×C₄	#13093980	1	1	yes	characteristic
213	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
214	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
215	C₂×C₄	C₂×#10625329	1	2	yes	—
216	C₂×C₄	#13094031	1	2	yes	—
217	C₈	—	4	4	no	—
218	C₈	—	47	2	no	—
219	C₈	—	94	1	no	—
220	C₈	—	94	2	no	—
221	C₈	—	188	4	no	—
222	C₈	—	188	2	no	—
223	C₂²	—	2	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	4	no	—
226	C₂²	—	4	4	no	—
227	C₂²	—	4	4	no	—
228	C₂²	—	4	2	no	—
229	C₂²	—	4	2	no	—
230	C₂²	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
231	C₂²	C₂×#13093935	1	1	yes	characteristic
232	C₂²	#15689079	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	2	no	—
235	C₄	—	4	2	no	—
236	C₄	#100×D₄₇	1	1	yes	characteristic
237	C₄	#15689104	1	1	yes	characteristic
238	C₄	#15689195	1	4	yes	—
239	C₂	—	2	1	no	—
240	C₂	—	2	1	no	—
241	C₂	—	4	4	no	—
242	C₂	#20243166	1	1	yes	characteristic
243	C₂	#100×Dic₄₇	1	1	yes	characteristic
244	C₂	#20243191	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₄×C₄₇⋊C₈

C₂

yes

maximal, characteristic

#20241709

C₂

yes

maximal, characteristic

#20241675

C₂

yes

maximal, complemented

#20241239

C₂

yes

maximal, complemented

C₄×#100×C₄₇

C₂

yes

maximal, characteristic

C₂³×C₄₇⋊C₈

C₄

yes

—

D₄×C₄₇⋊C₈

—

D₄×C₄₇⋊C₈

—

#15689176

C₂²

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

C₂×C₂²⋊(C₄₇⋊C₈)

C₄

yes

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

characteristic

#15688847

C₄

yes

—

#15688845

—

#15688845

—

C₂×C₄×D₄×C₄₇

C₂²

yes

characteristic

C₂×#100×C₄₇

C₄

yes

—

C₄×M₁₆×C₄₇

C₂²

yes

—

C₄₇×#343

C₄

yes

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₇⋊C₈

C₂×C₄

yes

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

C₂×C₄

yes

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₂²×D₄×C₄₇

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₇

C₂×C₄

yes

—

C₂×M₁₆×C₄₇

C₂×C₄

yes

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#100×C₄₇

—

#97×C₄₇

—

C₄×C₈×C₄₇

—

C₂⁴×C₄₇

C₄²

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

M₁₆

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₄²

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

—

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

characteristic

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#97

yes

—

C₂³×C₄₇

C₂×C₄²

yes

characteristic

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×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

#117

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₂×M₁₆

yes

—

C₂×C₄×C₄₇

#131

yes

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

yes

100

—

101

C₂²×C₄₇

—

102

C₂²×C₄₇

—

103

C₂²×C₄₇

—

104

C₂²×C₄₇

—

105

C₂²×C₄₇

—

106

C₂²×C₄₇

—

107

C₂²×C₄₇

—

108

C₂²×C₄₇

C₄×C₂²⋊C₄

yes

characteristic

109

C₂²×C₄₇

C₂×#97

yes

characteristic

110

C₂²×C₄₇

#405

yes

characteristic

111

C₄×C₄₇

—

112

C₄×C₄₇

—

113

C₄×C₄₇

—

114

C₄×C₄₇

C₂×#100

yes

characteristic

115

C₄×C₄₇

#413

yes

characteristic

116

C₄×C₄₇

#435

yes

—

117

C₂×C₈×D₄

—

118

C₄×#100

D₄₇

yes

characteristic

119

#1460

—

120

#1451

—

121

#1283

—

122

C₂×C₄₇

—

123

C₂×C₄₇

—

124

C₂×C₄₇

—

125

C₂×C₄₇

#1752

yes

characteristic

126

C₂×C₄₇

C₄×#100

yes

characteristic

127

C₂×C₄₇

#1757

yes

characteristic

128

C₂³×C₈

—

129

C₂×C₄×D₄

C₂×D₄₇

yes

characteristic

130

C₈×D₄

—

131

C₈×D₄

—

132

#431

—

133

C₂×C₄⋊C₈

—

134

C₂×#100

Dic₄₇

yes

—

135

C₂×C₂²⋊C₈

—

136

C₄×M₁₆

C₂×D₄₇

yes

—

137

C₂×C₄×C₈

—

138

#343

Dic₄₇

yes

—

139

#323

—

140

#322

—

141

#322

—

142

C₄₇

#8164

yes

characteristic, complemented, Sylow

143

C₂²×D₄

C₂×Dic₄₇

yes

characteristic

144

C₂³×C₄

C₄×D₄₇

yes

—

145

C₂×M₁₆

C₂×Dic₄₇

yes

—

146

C₂²×C₈

—

147

C₂²×C₈

—

148

C₂²×C₈

—

149

C₂²×C₈

—

150

C₂²×C₈

—

151

C₂²×C₈

—

188

—

152

C₄×D₄

—

153

C₄×D₄

—

154

C₂×C₄⋊C₄

C₂×Dic₄₇

yes

characteristic

155

C₂×C₂²⋊C₄

C₄×D₄₇

yes

—

156

C₂×C₄²

C₂²×D₄₇

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

#100

—

160

C₂²⋊C₈

—

161

C₂²⋊C₈

—

162

#97

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₄×C₈

—

166

C₄×C₈

—

167

C₂⁴

C₄×Dic₄₇

yes

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

#10625329

yes

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₄×Dic₄₇

yes

—

176

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

177

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

178

C₂²×C₄

C₂²×Dic₄₇

yes

characteristic

179

M₁₆

—

180

M₁₆

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

188

—

189

C₂×C₈

—

188

—

190

C₂×C₈

—

188

—

191

C₂×C₈

—

188

—

192

C₄⋊C₄

—

193

C₂²⋊C₄

—

194

C₄²

D₄×D₄₇

yes

—

195

C₄²

#10625352

yes

—

196

C₂³

—

197

C₂³

—

198

C₂³

—

199

C₂³

—

200

C₂³

#13093935

yes

—

201

C₂³

C₂×C₄×Dic₄₇

yes

characteristic

202

D₄

—

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

C₂²⋊C₄×D₄₇

yes

characteristic

212

C₂×C₄

#13093980

yes

characteristic

213

C₂×C₄

(C₂²⋊D₄₇)⋊C₄

yes

—

214

C₂×C₄

D₄×Dic₄₇

yes

—

215

C₂×C₄

C₂×#10625329

yes

—

216

C₂×C₄

#13094031

yes

—

217

C₈

—

218

C₈

—

219

C₈

—

220

C₈

—

221

C₈

—

188

—

222

C₈

—

188

—

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

C₂²⋊C₄×Dic₄₇

yes

characteristic

231

C₂²

C₂×#13093935

yes

characteristic

232

C₂²

#15689079

yes

characteristic

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

#100×D₄₇

yes

characteristic

237

C₄

#15689104

yes

characteristic

238

C₄

#15689195

yes

—

239

C₂

—

240

C₂

—

241

C₂

—

242

C₂

#20243166

yes

characteristic

243

C₂

#100×Dic₄₇

yes

characteristic

244

C₂

#20243191

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₇
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄×#100×C₄₇	C₂
socle	C₂²×C₄₇	C₄×C₂²⋊C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₄×#100	D₄₇
hypocenter	C₄₇	#8164
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#100

subgroup

G/H

center

C₂×C₄

C₂²⋊C₄×D₄₇

commutator

C₂³×C₄₇

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄×#100×C₄₇

C₂

socle

C₂²×C₄₇

C₄×C₂²⋊C₄

prime radical

C₂²×D₄×C₄₇

C₂×C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#100

N	H ≅ G/N	type
3. #20241675	C₂	semidirect
4. #20241239	C₂	semidirect
99. C₄₇⋊C₈	#100	semidirect
142. C₄₇	#8164	semidirect

H ≅ G/N

type

3. #20241675

C₂

semidirect

4. #20241239

C₂

semidirect

99. C₄₇⋊C₈

#100

semidirect

142. C₄₇

#8164

semidirect

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

subgroup	index
C₂×D₄×C₄₇⋊C₈	2
#20241709	2
#20241675	2
#20241239	2
C₄×#100×C₄₇	2
#8164	47

subgroup

index

C₂×D₄×C₄₇⋊C₈

C₄×#100×C₄₇

Subgroups — #26106848

Conjugacy classes of subgroups

Complements

Maximal subgroups