Group #26132210 — subgroups

Subgroups — #26132210

Order 12032.

454 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 135 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×#15689080	C₂	1	1	yes	maximal, characteristic
2	#20245143	C₂	1	2	yes	maximal, complemented
3	C₂×#15688904	C₂	1	2	yes	maximal
4	#20241472	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#10625324	C₂²	1	1	yes	characteristic
7	C₂²×C₈×D₄₇	C₄	1	1	yes	characteristic
8	C₂×#13093981	C₄	1	1	yes	characteristic
9	C₂×#13093964	C₂²	1	2	yes	—
10	#15689080	—	2	4	no	—
11	C₂×#13093934	C₄	1	1	yes	characteristic
12	C₂×C₄×C₄₇⋊C₈	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
14	Dic₄₇⋊C₁₆	—	2	4	no	—
15	#15688904	—	2	4	no	—
16	C₂×M₃₂×C₄₇	C₂²	1	2	yes	—
17	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×#10625324	—	2	2	no	—
20	C₂×#10625324	—	2	2	no	—
21	C₂×#10625324	D₄	1	2	yes	—
22	C₂×#10625324	Q₈	1	2	yes	—
23	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×D₄₇	—	2	2	no	—
26	C₂×C₈×D₄₇	—	2	2	no	—
27	C₂×C₈×D₄₇	—	2	2	no	—
28	#13093981	—	2	2	no	—
29	#13093981	—	2	2	no	—
30	C₂×Dic₄₇⋊C₄	C₈	1	2	yes	—
31	C₂×(C₂×D₄₇)⋊C₄	C₈	1	2	yes	—
32	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
33	#13093964	—	2	2	no	—
34	#13093964	—	2	2	no	—
35	C₂×C₄₇⋊C₁₆	—	2	2	no	—
36	#13093934	—	2	2	no	—
37	C₄×C₄₇⋊C₈	—	2	2	no	—
38	C₈×Dic₄₇	D₄	1	4	yes	—
39	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
41	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
42	M₃₂×C₄₇	—	2	2	no	—
43	M₃₂×C₄₇	—	2	2	no	—
44	C₂×C₁₆×C₄₇	—	2	2	no	—
45	#97×C₄₇	—	2	2	no	—
46	C₂³×D₄₇	C₂×C₈	1	1	yes	characteristic
47	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
48	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
49	C₂²×Dic₄₇	C₂×C₈	1	1	yes	characteristic
50	C₂²×Dic₄₇	C₂×C₈	1	2	yes	—
51	C₂×C₄×D₄₇	—	2	1	no	—
52	C₂×C₄×D₄₇	—	2	1	no	—
53	C₂×C₄×D₄₇	—	2	1	no	—
54	C₂×C₄×D₄₇	—	2	1	no	—
55	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
56	C₂×C₄×D₄₇	M₁₆	1	2	yes	—
57	C₂×C₈×C₄₇	—	2	1	no	—
58	C₂×C₈×C₄₇	—	2	1	no	—
59	C₂×C₈×C₄₇	M₁₆	1	2	yes	—
60	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
62	C₂×C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
63	C₂×C₈×C₄₇	#41	1	2	yes	—
64	C₄²×C₄₇	—	2	1	no	—
65	C₄²×C₄₇	—	2	1	no	—
66	(C₂×D₄₇)⋊C₄	—	2	4	no	—
67	Dic₄₇⋊C₄	—	2	4	no	—
68	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
69	C₄×Dic₄₇	M₁₆	1	2	yes	—
70	C₂×C₄₇⋊C₈	—	2	1	no	—
71	C₂×C₄₇⋊C₈	—	2	1	no	—
72	C₂×C₄₇⋊C₈	—	2	1	no	—
73	C₂×C₄₇⋊C₈	—	2	1	no	—
74	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
75	C₂×C₄₇⋊C₈	C₄⋊C₄	1	2	yes	—
76	#10625324	—	2	4	no	—
77	#10625324	—	2	4	no	—
78	C₈×D₄₇	—	2	8	no	—
79	C₁₆×C₄₇	—	4	2	no	—
80	C₄₇⋊C₁₆	—	4	2	no	—
81	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
82	C₂²×D₄₇	—	2	1	no	—
83	C₂²×D₄₇	—	2	1	no	—
84	C₂²×D₄₇	—	4	2	no	—
85	C₂²×D₄₇	C₄⋊C₈	1	2	yes	—
86	C₂×C₄×C₄₇	—	2	2	no	—
87	C₂×C₄×C₄₇	—	4	2	no	—
88	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
91	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
92	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
93	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
94	C₂×Dic₄₇	—	2	1	no	—
95	C₂×Dic₄₇	—	2	1	no	—
96	C₂×Dic₄₇	—	4	2	no	—
97	C₂×Dic₄₇	C₂²⋊C₈	1	4	yes	—
98	C₂×Dic₄₇	C₄⋊C₈	1	2	yes	—
99	C₄×D₄₇	—	2	2	no	—
100	C₄×D₄₇	—	2	2	no	—
101	C₄×D₄₇	—	2	2	no	—
102	C₄×D₄₇	—	2	2	no	—
103	C₈×C₄₇	—	2	2	no	—
104	C₈×C₄₇	#121	1	2	yes	—
105	C₈×C₄₇	C₂²⋊Q₈	1	2	yes	—
106	C₄₇⋊C₈	—	2	2	no	—
107	C₄₇⋊C₈	—	2	2	no	—
108	#12786	—	47	1	no	maximal, Sylow
109	C₂²×C₄₇	—	2	2	no	—
110	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
111	C₂²×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
112	C₂²×C₄₇	#431	1	1	yes	characteristic
113	C₂×D₄₇	—	2	2	no	—
114	C₂×D₄₇	—	4	2	no	—
115	C₂×D₄₇	—	4	2	no	—
116	C₂×D₄₇	—	4	2	no	—
117	C₄×C₄₇	—	4	2	no	—
118	C₄×C₄₇	#380	1	1	yes	characteristic
119	C₄×C₄₇	#407	1	1	yes	characteristic
120	C₄×C₄₇	#423	1	1	yes	characteristic
121	C₄×C₄₇	#432	1	1	yes	characteristic
122	Dic₄₇	—	2	2	no	—
123	Dic₄₇	—	2	4	no	—
124	C₂×#405	—	47	1	no	—
125	#2150	—	47	2	no	—
126	C₂×#349	—	47	2	no	—
127	#1377	—	47	1	no	—
128	#1377	D₄₇	1	1	yes	characteristic, complemented
129	C₂×C₄₇	—	2	1	no	—
130	C₂×C₄₇	—	2	1	no	—
131	C₂×C₄₇	#1797	1	1	yes	characteristic
132	C₂×C₄₇	#2115	1	2	yes	—
133	D₄₇	—	4	2	no	—
134	C₂²×M₁₆	—	47	1	no	—
135	C₂³×C₈	—	47	1	no	—
136	C₂×#117	—	47	1	no	—
137	C₂×M₃₂	—	47	2	no	—
138	C₂×M₃₂	C₂×D₄₇	1	2	yes	—
139	#405	—	94	4	no	—
140	C₂×#97	—	47	1	no	—
141	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
142	C₂×C₄×C₈	—	47	1	no	—
143	C₂×C₄×C₈	—	47	1	no	—
144	C₄⋊C₁₆	—	94	4	no	—
145	#349	—	94	4	no	—
146	C₄₇	#12786	1	1	yes	characteristic, complemented, Sylow
147	C₂³×C₄	—	47	1	no	—
148	C₂×M₁₆	—	47	2	no	—
149	C₂×M₁₆	—	47	2	no	—
150	C₂×M₁₆	—	94	2	no	—
151	C₂×M₁₆	—	94	2	no	—
152	C₂²×C₈	—	47	1	no	—
153	C₂²×C₈	—	47	1	no	—
154	C₂²×C₈	—	94	2	no	—
155	C₂²×C₈	—	94	2	no	—
156	C₂²×C₈	—	94	2	no	—
157	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
158	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
159	#117	—	94	2	no	—
160	#117	—	94	2	no	—
161	C₂×C₄⋊C₄	—	47	2	no	—
162	C₂×C₂²⋊C₄	—	47	2	no	—
163	C₂×C₄²	—	47	1	no	—
164	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
165	M₃₂	—	2	2	no	—
166	M₃₂	—	2	2	no	—
167	M₃₂	—	94	2	no	—
168	M₃₂	—	94	2	no	—
169	C₂×C₁₆	—	2	2	no	—
170	C₂×C₁₆	—	94	2	no	—
171	#97	—	2	2	no	—
172	#97	—	94	2	no	—
173	C₄×C₈	—	47	4	no	—
174	C₄×C₈	—	94	2	no	—
175	C₂⁴	—	47	1	no	—
176	C₂²×C₄	—	47	1	no	—
177	C₂²×C₄	—	47	2	no	—
178	C₂²×C₄	—	47	2	no	—
179	C₂²×C₄	—	47	2	no	—
180	C₂²×C₄	—	94	1	no	—
181	C₂²×C₄	—	94	1	no	—
182	C₂²×C₄	—	94	1	no	—
183	C₂²×C₄	—	94	1	no	—
184	C₂²×C₄	C₈×D₄₇	1	2	yes	—
185	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
186	M₁₆	—	94	4	no	—
187	M₁₆	—	94	4	no	—
188	C₂×C₈	—	2	1	no	—
189	C₂×C₈	—	2	1	no	—
190	C₂×C₈	—	47	2	no	—
191	C₂×C₈	—	47	2	no	—
192	C₂×C₈	—	94	8	no	—
193	C₂×C₈	—	94	1	no	—
194	C₂×C₈	—	94	1	no	—
195	C₂×C₈	—	94	1	no	—
196	C₂×C₈	—	94	1	no	—
197	C₂×C₈	#10625324	1	2	yes	—
198	C₂×C₈	#10625350	1	2	yes	—
199	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
200	C₂×C₈	D₄×D₄₇	1	2	yes	—
201	C₂×C₈	Q₈×D₄₇	1	1	yes	characteristic
202	C₄⋊C₄	—	94	4	no	—
203	C₂²⋊C₄	—	94	4	no	—
204	C₄²	—	2	1	no	—
205	C₄²	—	2	1	no	—
206	C₄²	—	47	2	no	—
207	C₄²	—	47	2	no	—
208	C₁₆	—	4	2	no	—
209	C₁₆	—	188	2	no	—
210	C₂³	—	47	2	no	—
211	C₂³	—	94	1	no	—
212	C₂³	—	94	1	no	—
213	C₂³	—	188	2	no	—
214	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	47	4	no	—
218	C₂×C₄	—	47	2	no	—
219	C₂×C₄	—	94	1	no	—
220	C₂×C₄	—	94	1	no	—
221	C₂×C₄	—	94	2	no	—
222	C₂×C₄	—	94	2	no	—
223	C₂×C₄	—	94	2	no	—
224	C₂×C₄	—	94	2	no	—
225	C₂×C₄	—	188	2	no	—
226	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
227	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
228	C₂×C₄	#13093981	1	1	yes	characteristic
229	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
230	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
231	C₂×C₄	C₂×#10625324	1	1	yes	characteristic
232	C₈	—	2	2	no	—
233	C₈	—	94	2	no	—
234	C₈	—	94	2	no	—
235	C₈	#13093997	1	2	yes	—
236	C₈	#13094002	1	2	yes	—
237	C₂²	—	2	2	no	—
238	C₂²	—	94	2	no	—
239	C₂²	—	188	2	no	—
240	C₂²	—	188	2	no	—
241	C₂²	—	188	2	no	—
242	C₂²	C₂²⋊C₈×D₄₇	1	1	yes	characteristic
243	C₂²	C₄⋊C₈×D₄₇	1	1	yes	characteristic
244	C₂²	#15689174	1	1	yes	characteristic
245	C₄	—	4	2	no	—
246	C₄	—	94	4	no	—
247	C₄	—	94	2	no	—
248	C₄	#15688982	1	1	yes	characteristic
249	C₄	#15689085	1	1	yes	characteristic
250	C₄	#15689145	1	1	yes	characteristic
251	C₄	#15689178	1	1	yes	characteristic
252	C₂	—	2	1	no	—
253	C₂	—	2	1	no	—
254	C₂	—	188	2	no	—
255	C₂	#20243367	1	1	yes	characteristic
256	C₂	#20245007	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689080

C₂

yes

maximal, characteristic

#20245143

C₂

yes

maximal, complemented

C₂×#15688904

C₂

yes

maximal

#20241472

C₂

yes

maximal, characteristic, complemented

C₄₇×#1377

C₂

yes

maximal, characteristic, complemented

C₂²×#10625324

C₂²

yes

characteristic

C₂²×C₈×D₄₇

C₄

yes

characteristic

C₂×#13093981

C₄

yes

characteristic

C₂×#13093964

C₂²

yes

—

#15689080

—

C₂×#13093934

C₄

yes

characteristic

C₂×C₄×C₄₇⋊C₈

C₄

yes

characteristic

C₂×C₈×Dic₄₇

C₂²

yes

characteristic

Dic₄₇⋊C₁₆

—

#15688904

—

C₂×M₃₂×C₄₇

C₂²

yes

—

C₂×#97×C₄₇

C₂²

yes

characteristic

C₂²×C₄×D₄₇

C₂×C₄

yes

—

—

D₄

yes

—

C₂×#10625324

Q₈

yes

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

—

#13093981

—

#13093981

—

C₂×Dic₄₇⋊C₄

C₈

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₈

yes

—

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

#13093964

—

#13093964

—

C₂×C₄₇⋊C₁₆

—

#13093934

—

C₄×C₄₇⋊C₈

—

C₈×Dic₄₇

D₄

yes

—

C₂²×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

M₃₂×C₄₇

—

M₃₂×C₄₇

—

C₂×C₁₆×C₄₇

—

#97×C₄₇

—

C₂³×D₄₇

C₂×C₈

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₈

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₈

yes

characteristic

C₂²×Dic₄₇

C₂×C₈

yes

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

C₄⋊C₄

yes

—

C₂×C₄×D₄₇

M₁₆

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

M₁₆

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₄₇

#41

yes

—

C₄²×C₄₇

—

C₄²×C₄₇

—

(C₂×D₄₇)⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

C₂²⋊C₄

yes

—

C₄×Dic₄₇

M₁₆

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

—

C₂×C₄₇⋊C₈

C₄⋊C₄

yes

—

#10625324

—

#10625324

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂²×C₈

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₄⋊C₈

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₇

#117

yes

characteristic

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²⋊C₈

yes

—

C₂×Dic₄₇

C₄⋊C₈

yes

—

C₄×D₄₇

—

100

C₄×D₄₇

—

101

C₄×D₄₇

—

102

C₄×D₄₇

—

103

C₈×C₄₇

—

104

C₈×C₄₇

#121

yes

—

105

C₈×C₄₇

C₂²⋊Q₈

yes

—

106

C₄₇⋊C₈

—

107

C₄₇⋊C₈

—

108

#12786

—

maximal, Sylow

109

C₂²×C₄₇

—

110

C₂²×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

111

C₂²×C₄₇

C₂×C₄⋊C₈

yes

characteristic

112

C₂²×C₄₇

#431

yes

characteristic

113

C₂×D₄₇

—

114

C₂×D₄₇

—

115

C₂×D₄₇

—

116

C₂×D₄₇

—

117

C₄×C₄₇

—

118

C₄×C₄₇

#380

yes

characteristic

119

C₄×C₄₇

#407

yes

characteristic

120

C₄×C₄₇

#423

yes

characteristic

121

C₄×C₄₇

#432

yes

characteristic

122

Dic₄₇

—

123

Dic₄₇

—

124

C₂×#405

—

125

#2150

—

126

C₂×#349

—

127

#1377

—

128

#1377

D₄₇

yes

characteristic, complemented

129

C₂×C₄₇

—

130

C₂×C₄₇

—

131

C₂×C₄₇

#1797

yes

characteristic

132

C₂×C₄₇

#2115

yes

—

133

D₄₇

—

134

C₂²×M₁₆

—

135

C₂³×C₈

—

136

C₂×#117

—

137

C₂×M₃₂

—

138

C₂×M₃₂

C₂×D₄₇

yes

—

139

#405

—

140

C₂×#97

—

141

C₂×#97

C₂×D₄₇

yes

characteristic

142

C₂×C₄×C₈

—

143

C₂×C₄×C₈

—

144

C₄⋊C₁₆

—

145

#349

—

146

C₄₇

#12786

yes

characteristic, complemented, Sylow

147

C₂³×C₄

—

148

C₂×M₁₆

—

149

C₂×M₁₆

—

150

C₂×M₁₆

—

151

C₂×M₁₆

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

—

156

C₂²×C₈

—

157

C₂²×C₈

C₄×D₄₇

yes

characteristic

158

C₂²×C₈

C₂²×D₄₇

yes

characteristic

159

#117

—

160

#117

—

161

C₂×C₄⋊C₄

—

162

C₂×C₂²⋊C₄

—

163

C₂×C₄²

—

164

C₂×C₄²

C₄×D₄₇

yes

characteristic

165

M₃₂

—

166

M₃₂

—

167

M₃₂

—

168

M₃₂

—

169

C₂×C₁₆

—

170

C₂×C₁₆

—

171

#97

—

172

#97

—

173

C₄×C₈

—

174

C₄×C₈

—

175

C₂⁴

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

C₈×D₄₇

yes

—

185

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

186

M₁₆

—

187

M₁₆

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

#10625324

yes

—

198

C₂×C₈

#10625350

yes

—

199

C₂×C₈

D₄×D₄₇

yes

characteristic

200

C₂×C₈

D₄×D₄₇

yes

—

201

C₂×C₈

Q₈×D₄₇

yes

characteristic

202

C₄⋊C₄

—

203

C₂²⋊C₄

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₁₆

—

209

C₁₆

—

188

—

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

—

188

—

214

C₂³

C₂×C₈×D₄₇

yes

characteristic

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

—

225

C₂×C₄

—

188

—

226

C₂×C₄

C₂²⋊C₄×D₄₇

yes

characteristic

227

C₂×C₄

C₄⋊C₄×D₄₇

yes

characteristic

228

C₂×C₄

#13093981

yes

characteristic

229

C₂×C₄

M₁₆×D₄₇

yes

characteristic

230

C₂×C₄

M₁₆×D₄₇

yes

characteristic

231

C₂×C₄

C₂×#10625324

yes

characteristic

232

C₈

—

233

C₈

—

234

C₈

—

235

C₈

#13093997

yes

—

236

C₈

#13094002

yes

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

188

—

240

C₂²

—

188

—

241

C₂²

—

188

—

242

C₂²

C₂²⋊C₈×D₄₇

yes

characteristic

243

C₂²

C₄⋊C₈×D₄₇

yes

characteristic

244

C₂²

#15689174

yes

characteristic

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

#15688982

yes

characteristic

249

C₄

#15689085

yes

characteristic

250

C₄

#15689145

yes

characteristic

251

C₄

#15689178

yes

characteristic

252

C₂

—

253

C₂

—

254

C₂

—

188

—

255

C₂

#20243367

yes

characteristic

256

C₂

#20245007

yes

—

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₇
commutator	C₂³×C₄₇	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#1377	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₈
prime radical	C₂³×D₄₇	C₂×C₈
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#1377	D₄₇
hypocenter	C₄₇	#12786
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1377

subgroup

G/H

center

C₂×C₄

C₂²⋊C₄×D₄₇

commutator

C₂³×C₄₇

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₄₇×#1377

C₂

socle

C₂²×C₄₇

C₂×C₂²⋊C₈

prime radical

C₂³×D₄₇

C₂×C₈

cosocle

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1377

N	H ≅ G/N	type
2. #20245143	C₂	semidirect
4. #20241472	C₂	semidirect
5. C₄₇×#1377	C₂	semidirect
128. #1377	D₄₇	semidirect
146. C₄₇	#12786	semidirect

H ≅ G/N

type

2. #20245143

C₂

semidirect

4. #20241472

C₂

semidirect

5. C₄₇×#1377

C₂

semidirect

128. #1377

D₄₇

semidirect

146. C₄₇

#12786

semidirect

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

subgroup	index
C₂×#15689080	2
#20245143	2
C₂×#15688904	2
#20241472	2
C₄₇×#1377	2
#12786	47

subgroup

index

C₄₇×#1377

Subgroups — #26132210

Conjugacy classes of subgroups

Complements

Maximal subgroups