Group #26143436 — subgroups

Subgroups — #26143436

Order 12032.

6494 conjugacy classes of subgroups; only the 651 normal subgroups are shown.

normal subgroups only

This group has 6494 conjugacy classes of subgroups — too many to draw. Only its 651 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×#15688986	C₂	1	2	yes	maximal, complemented
2	C₂×#15688979	C₂	1	4	yes	maximal, complemented
3	#20241629	C₂	1	8	yes	maximal, complemented
4	C₂⁴×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
6	C₂²×C₂²⋊Dic₄₇	C₂²	1	16	yes	complemented
7	#15688986	—	2	8	no	—
8	#15688979	—	2	16	no	—
9	C₂×C₄₇⋊#95	C₂²	1	8	yes	complemented
10	C₂⁶×C₄₇	C₂²	1	2	yes	—
11	C₂³×D₄×C₄₇	—	2	16	no	—
12	C₂³×D₄×C₄₇	—	2	8	no	—
13	C₂³×D₄×C₄₇	C₄	1	8	yes	complemented
14	C₂³×D₄×C₄₇	C₂²	1	4	yes	—
15	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂³×Dic₄₇	C₂³	1	8	yes	—
17	C₂×C₂²⋊Dic₄₇	—	2	16	no	—
18	C₂×C₂²⋊Dic₄₇	—	2	32	no	—
19	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
20	C₂×C₂²⋊Dic₄₇	—	4	32	no	—
21	C₄₇⋊#95	—	2	16	no	—
22	C₂⁵×C₄₇	—	2	8	no	—
23	C₂⁵×C₄₇	—	2	8	no	—
24	C₂⁵×C₄₇	—	4	16	no	—
25	C₂⁵×C₄₇	C₂×C₄	1	8	yes	—
26	C₂⁵×C₄₇	D₄	1	16	yes	—
27	C₂⁵×C₄₇	C₂³	1	4	yes	—
28	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
29	C₂²×D₄×C₄₇	—	2	128	no	—
30	C₂²×D₄×C₄₇	—	2	64	no	—
31	C₂²×D₄×C₄₇	—	2	32	no	—
32	C₂²×D₄×C₄₇	—	2	32	no	—
33	C₂²×D₄×C₄₇	—	2	16	no	—
34	C₂²×D₄×C₄₇	C₂×C₄	1	16	yes	—
35	C₂³×C₄×C₄₇	—	2	8	no	—
36	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₄₇	D₄	1	8	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
39	C₂⁴×C₄₇	—	2	8	no	—
40	C₂⁴×C₄₇	—	2	16	no	—
41	C₂⁴×C₄₇	—	2	16	no	—
42	C₂⁴×C₄₇	—	2	64	no	—
43	C₂⁴×C₄₇	—	2	8	no	—
44	C₂⁴×C₄₇	—	2	8	no	—
45	C₂⁴×C₄₇	—	2	32	no	—
46	C₂⁴×C₄₇	—	4	32	no	—
47	C₂⁴×C₄₇	—	4	64	no	—
48	C₂⁴×C₄₇	—	4	64	no	—
49	C₂⁴×C₄₇	—	4	64	no	—
50	C₂⁴×C₄₇	C₂²⋊C₄	1	32	yes	complemented
51	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
52	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
53	C₂⁴×C₄₇	C₂×D₄	1	16	yes	—
54	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
55	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
56	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
57	C₂×D₄×C₄₇	—	2	128	no	—
58	C₂×D₄×C₄₇	—	2	256	no	—
59	C₂×D₄×C₄₇	—	2	64	no	—
60	C₂×D₄×C₄₇	—	2	32	no	—
61	C₂²×C₄×C₄₇	—	2	16	no	—
62	C₂²×C₄×C₄₇	—	2	32	no	—
63	C₂²×C₄×C₄₇	—	2	8	no	—
64	C₂²×C₄×C₄₇	C₂²⋊C₄	1	16	yes	complemented
65	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
66	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
67	C₂²×Dic₄₇	—	2	8	no	—
68	C₂²×Dic₄₇	—	2	16	no	—
69	C₂²×Dic₄₇	—	2	32	no	—
70	C₂²⋊Dic₄₇	—	4	64	no	—
71	C₂²⋊Dic₄₇	—	4	16	no	—
72	C₂³×C₄₇	—	2	8	no	—
73	C₂³×C₄₇	—	2	32	no	—
74	C₂³×C₄₇	—	2	16	no	—
75	C₂³×C₄₇	—	2	8	no	—
76	C₂³×C₄₇	—	2	8	no	—
77	C₂³×C₄₇	—	2	32	no	—
78	C₂³×C₄₇	—	2	32	no	—
79	C₂³×C₄₇	—	2	32	no	—
80	C₂³×C₄₇	—	2	32	no	—
81	C₂³×C₄₇	—	2	64	no	—
82	C₂³×C₄₇	—	4	64	no	—
83	C₂³×C₄₇	—	4	64	no	—
84	C₂³×C₄₇	—	4	64	no	—
85	C₂³×C₄₇	—	4	256	no	—
86	C₂³×C₄₇	—	4	32	no	—
87	C₂³×C₄₇	—	4	32	no	—
88	C₂³×C₄₇	C₂×C₂²⋊C₄	1	16	yes	—
89	C₂³×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
90	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
91	C₂³×C₄₇	#120	1	16	yes	—
92	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
93	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
94	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
95	C₂³×C₄₇	H(5,𝔽₂)	1	8	yes	—
96	D₄×C₄₇	—	2	128	no	—
97	C₂×C₄×C₄₇	—	2	8	no	—
98	C₂×C₄×C₄₇	—	2	16	no	—
99	C₂×C₄×C₄₇	—	2	32	no	—
100	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
101	C₂×Dic₄₇	—	4	8	no	—
102	C₂×Dic₄₇	—	4	32	no	—
103	C₂×Dic₄₇	—	4	16	no	—
104	#14335	—	47	1	no	maximal, Sylow
105	C₂²×C₄₇	—	2	16	no	—
106	C₂²×C₄₇	—	2	8	no	—
107	C₂²×C₄₇	—	2	32	no	—
108	C₂²×C₄₇	—	2	32	no	—
109	C₂²×C₄₇	—	2	16	no	—
110	C₂²×C₄₇	—	4	128	no	—
111	C₂²×C₄₇	—	4	16	no	—
112	C₂²×C₄₇	—	4	16	no	—
113	C₂²×C₄₇	—	4	64	no	—
114	C₂²×C₄₇	#379	1	8	yes	—
115	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	2	yes	—
116	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄₇	#518	1	4	yes	—
118	C₂²×C₄₇	C₂×#120	1	4	yes	—
119	C₂²×C₄₇	#534	1	16	yes	—
120	C₂²×C₄₇	#535	1	8	yes	—
121	C₄×C₄₇	—	2	8	no	—
122	Dic₄₇	—	8	8	no	—
123	C₂⁴×D₄	D₄₇	1	1	yes	characteristic
124	C₂×#381	—	47	2	no	—
125	C₂×#379	—	47	4	no	—
126	#1438	—	47	8	no	—
127	C₂×C₄₇	—	2	8	no	—
128	C₂×C₄₇	—	4	16	no	—
129	C₂×C₄₇	C₂×#379	1	1	yes	characteristic
130	C₂×C₄₇	#2308	1	4	yes	—
131	C₂×C₄₇	#2309	1	2	yes	—
132	C₂×C₄₇	#2613	1	8	yes	—
133	C₂⁶	C₂×D₄₇	1	2	yes	—
134	C₂³×D₄	—	2	16	no	—
135	C₂³×D₄	—	2	8	no	—
136	C₂³×D₄	Dic₄₇	1	8	yes	complemented
137	C₂³×D₄	C₂×D₄₇	1	4	yes	—
138	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
139	C₂²×C₂²⋊C₄	—	47	4	no	—
140	C₂²×C₂²⋊C₄	—	47	16	no	—
141	#381	—	94	8	no	—
142	#379	—	94	16	no	—
143	C₂×#95	—	47	8	no	—
144	C₄₇	#14335	1	1	yes	characteristic, complemented, Sylow
145	C₂⁵	—	2	8	no	—
146	C₂⁵	—	2	8	no	—
147	C₂⁵	—	4	16	no	—
148	C₂⁵	C₂×Dic₄₇	1	8	yes	—
149	C₂⁵	C₂²⋊D₄₇	1	16	yes	—
150	C₂⁵	C₂²×D₄₇	1	4	yes	—
151	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
152	C₂²×D₄	—	2	128	no	—
153	C₂²×D₄	—	2	64	no	—
154	C₂²×D₄	—	2	32	no	—
155	C₂²×D₄	—	2	32	no	—
156	C₂²×D₄	—	2	16	no	—
157	C₂²×D₄	C₂×Dic₄₇	1	16	yes	—
158	C₂³×C₄	—	2	8	no	—
159	C₂³×C₄	—	47	8	no	—
160	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
161	C₂³×C₄	C₂²⋊D₄₇	1	8	yes	—
162	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
163	C₂×C₂²⋊C₄	—	94	32	no	—
164	C₂×C₂²⋊C₄	—	94	16	no	—
165	C₂×C₂²⋊C₄	—	94	8	no	—
166	C₂×C₂²⋊C₄	—	188	32	no	—
167	#95	—	94	16	no	—
168	C₂⁴	—	2	8	no	—
169	C₂⁴	—	2	16	no	—
170	C₂⁴	—	2	16	no	—
171	C₂⁴	—	2	64	no	—
172	C₂⁴	—	2	8	no	—
173	C₂⁴	—	2	8	no	—
174	C₂⁴	—	2	32	no	—
175	C₂⁴	—	4	32	no	—
176	C₂⁴	—	4	64	no	—
177	C₂⁴	—	4	64	no	—
178	C₂⁴	—	4	64	no	—
179	C₂⁴	C₂²⋊Dic₄₇	1	32	yes	complemented
180	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
181	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
182	C₂⁴	C₂×C₂²⋊D₄₇	1	16	yes	—
183	C₂⁴	C₂×C₂²⋊D₄₇	1	8	yes	—
184	C₂⁴	C₂×C₂²⋊D₄₇	1	4	yes	—
185	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
186	C₂×D₄	—	2	256	no	—
187	C₂×D₄	—	2	128	no	—
188	C₂×D₄	—	2	64	no	—
189	C₂×D₄	—	2	32	no	—
190	C₂²×C₄	—	2	16	no	—
191	C₂²×C₄	—	2	32	no	—
192	C₂²×C₄	—	2	8	no	—
193	C₂²×C₄	—	94	8	no	—
194	C₂²×C₄	—	94	16	no	—
195	C₂²×C₄	—	94	32	no	—
196	C₂²×C₄	C₂²⋊Dic₄₇	1	16	yes	complemented
197	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
198	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
199	C₂²⋊C₄	—	188	64	no	—
200	C₂²⋊C₄	—	188	16	no	—
201	C₂³	—	2	8	no	—
202	C₂³	—	2	32	no	—
203	C₂³	—	2	16	no	—
204	C₂³	—	2	64	no	—
205	C₂³	—	2	8	no	—
206	C₂³	—	2	8	no	—
207	C₂³	—	2	32	no	—
208	C₂³	—	2	32	no	—
209	C₂³	—	2	32	no	—
210	C₂³	—	2	32	no	—
211	C₂³	—	4	64	no	—
212	C₂³	—	4	256	no	—
213	C₂³	—	4	64	no	—
214	C₂³	—	4	64	no	—
215	C₂³	—	4	32	no	—
216	C₂³	—	4	32	no	—
217	C₂³	C₂×C₂²⋊Dic₄₇	1	16	yes	—
218	C₂³	C₂×C₂²⋊Dic₄₇	1	8	yes	—
219	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
220	C₂³	#13093993	1	16	yes	—
221	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
222	C₂³	C₂²×C₂²⋊D₄₇	1	4	yes	—
223	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
224	C₂³	#13094069	1	8	yes	—
225	D₄	—	2	128	no	—
226	C₂×C₄	—	2	32	no	—
227	C₂×C₄	—	2	8	no	—
228	C₂×C₄	—	2	16	no	—
229	C₂×C₄	—	188	8	no	—
230	C₂×C₄	—	188	32	no	—
231	C₂×C₄	—	188	16	no	—
232	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	8	yes	—
233	C₂²	—	2	32	no	—
234	C₂²	—	2	16	no	—
235	C₂²	—	2	8	no	—
236	C₂²	—	2	32	no	—
237	C₂²	—	2	16	no	—
238	C₂²	—	4	128	no	—
239	C₂²	—	4	64	no	—
240	C₂²	—	4	16	no	—
241	C₂²	—	4	16	no	—
242	C₂²	#15688979	1	8	yes	—
243	C₂²	C₂²×C₂²⋊Dic₄₇	1	2	yes	—
244	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
245	C₂²	#15689598	1	4	yes	—
246	C₂²	C₂×#13093993	1	4	yes	—
247	C₂²	#15689682	1	16	yes	—
248	C₂²	#15689690	1	8	yes	—
249	C₄	—	2	8	no	—
250	C₄	—	376	8	no	—
251	C₂	—	2	8	no	—
252	C₂	—	4	16	no	—
253	C₂	C₂×#15688979	1	1	yes	characteristic
254	C₂	#20245966	1	4	yes	—
255	C₂	#20245970	1	2	yes	—
256	C₂	#20249100	1	8	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15688986

C₂

yes

maximal, complemented

C₂×#15688979

C₂

yes

maximal, complemented

#20241629

C₂

yes

maximal, complemented

C₂⁴×D₄×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₂²⋊Dic₄₇

C₂²

yes

—

C₂²×C₂²⋊Dic₄₇

C₂²

yes

complemented

#15688986

—

#15688979

—

C₂×C₄₇⋊#95

C₂²

yes

complemented

C₂⁶×C₄₇

C₂²

yes

—

C₂³×D₄×C₄₇

—

C₂³×D₄×C₄₇

—

C₂³×D₄×C₄₇

C₄

yes

complemented

C₂³×D₄×C₄₇

C₂²

yes

—

C₂⁴×C₄×C₄₇

C₂²

yes

characteristic

C₂³×Dic₄₇

C₂³

yes

—

C₂×C₂²⋊Dic₄₇

—

C₂×C₂²⋊Dic₄₇

—

C₂×C₂²⋊Dic₄₇

—

C₂×C₂²⋊Dic₄₇

—

C₄₇⋊#95

—

C₂⁵×C₄₇

—

C₂⁵×C₄₇

—

C₂⁵×C₄₇

—

C₂⁵×C₄₇

C₂×C₄

yes

—

C₂⁵×C₄₇

D₄

yes

—

C₂⁵×C₄₇

C₂³

yes

—

C₂⁵×C₄₇

C₂³

yes

characteristic

C₂²×D₄×C₄₇

—

128

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

C₂×C₄

yes

—

C₂³×C₄×C₄₇

—

C₂³×C₄×C₄₇

C₂×C₄

yes

—

C₂³×C₄×C₄₇

D₄

yes

—

C₂³×C₄×C₄₇

C₂³

yes

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

C₂²⋊C₄

yes

complemented

C₂⁴×C₄₇

C₂²×C₄

yes

—

C₂⁴×C₄₇

C₂²×C₄

yes

—

C₂⁴×C₄₇

C₂×D₄

yes

—

C₂⁴×C₄₇

C₂×D₄

yes

—

C₂⁴×C₄₇

C₂×D₄

yes

—

C₂⁴×C₄₇

C₂⁴

yes

characteristic

C₂×D₄×C₄₇

—

128

—

C₂×D₄×C₄₇

—

256

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

complemented

C₂²×C₄×C₄₇

C₂²×C₄

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

256

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

—

C₂³×C₄₇

#120

yes

—

C₂³×C₄₇

C₂³×C₄

yes

characteristic

C₂³×C₄₇

C₂²×D₄

yes

—

C₂³×C₄₇

C₂²×D₄

yes

—

C₂³×C₄₇

H(5,𝔽₂)

yes

—

D₄×C₄₇

—

128

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

100

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

—

101

C₂×Dic₄₇

—

102

C₂×Dic₄₇

—

103

C₂×Dic₄₇

—

104

#14335

—

maximal, Sylow

105

C₂²×C₄₇

—

106

C₂²×C₄₇

—

107

C₂²×C₄₇

—

108

C₂²×C₄₇

—

109

C₂²×C₄₇

—

110

C₂²×C₄₇

—

128

—

111

C₂²×C₄₇

—

112

C₂²×C₄₇

—

113

C₂²×C₄₇

—

114

C₂²×C₄₇

#379

yes

—

115

C₂²×C₄₇

C₂²×C₂²⋊C₄

yes

—

116

C₂²×C₄₇

C₂²×C₂²⋊C₄

yes

characteristic

117

C₂²×C₄₇

#518

yes

—

118

C₂²×C₄₇

C₂×#120

yes

—

119

C₂²×C₄₇

#534

yes

—

120

C₂²×C₄₇

#535

yes

—

121

C₄×C₄₇

—

122

Dic₄₇

—

123

C₂⁴×D₄

D₄₇

yes

characteristic

124

C₂×#381

—

125

C₂×#379

—

126

#1438

—

127

C₂×C₄₇

—

128

C₂×C₄₇

—

129

C₂×C₄₇

C₂×#379

yes

characteristic

130

C₂×C₄₇

#2308

yes

—

131

C₂×C₄₇

#2309

yes

—

132

C₂×C₄₇

#2613

yes

—

133

C₂⁶

C₂×D₄₇

yes

—

134

C₂³×D₄

—

135

C₂³×D₄

—

136

C₂³×D₄

Dic₄₇

yes

complemented

137

C₂³×D₄

C₂×D₄₇

yes

—

138

C₂⁴×C₄

C₂×D₄₇

yes

characteristic

139

C₂²×C₂²⋊C₄

—

140

C₂²×C₂²⋊C₄

—

141

#381

—

142

#379

—

143

C₂×#95

—

144

C₄₇

#14335

yes

characteristic, complemented, Sylow

145

C₂⁵

—

146

C₂⁵

—

147

C₂⁵

—

148

C₂⁵

C₂×Dic₄₇

yes

—

149

C₂⁵

C₂²⋊D₄₇

yes

—

150

C₂⁵

C₂²×D₄₇

yes

—

151

C₂⁵

C₂²×D₄₇

yes

characteristic

152

C₂²×D₄

—

128

—

153

C₂²×D₄

—

154

C₂²×D₄

—

155

C₂²×D₄

—

156

C₂²×D₄

—

157

C₂²×D₄

C₂×Dic₄₇

yes

—

158

C₂³×C₄

—

159

C₂³×C₄

—

160

C₂³×C₄

C₂×Dic₄₇

yes

—

161

C₂³×C₄

C₂²⋊D₄₇

yes

—

162

C₂³×C₄

C₂²×D₄₇

yes

—

163

C₂×C₂²⋊C₄

—

164

C₂×C₂²⋊C₄

—

165

C₂×C₂²⋊C₄

—

166

C₂×C₂²⋊C₄

—

188

—

167

#95

—

168

C₂⁴

—

169

C₂⁴

—

170

C₂⁴

—

171

C₂⁴

—

172

C₂⁴

—

173

C₂⁴

—

174

C₂⁴

—

175

C₂⁴

—

176

C₂⁴

—

177

C₂⁴

—

178

C₂⁴

—

179

C₂⁴

C₂²⋊Dic₄₇

yes

complemented

180

C₂⁴

C₂²×Dic₄₇

yes

—

181

C₂⁴

C₂²×Dic₄₇

yes

—

182

C₂⁴

C₂×C₂²⋊D₄₇

yes

—

183

C₂⁴

C₂×C₂²⋊D₄₇

yes

—

184

C₂⁴

C₂×C₂²⋊D₄₇

yes

—

185

C₂⁴

C₂³×D₄₇

yes

characteristic

186

C₂×D₄

—

256

—

187

C₂×D₄

—

128

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

C₂²⋊Dic₄₇

yes

complemented

197

C₂²×C₄

C₂²×Dic₄₇

yes

—

198

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

—

199

C₂²⋊C₄

—

188

—

200

C₂²⋊C₄

—

188

—

201

C₂³

—

202

C₂³

—

203

C₂³

—

204

C₂³

—

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

—

256

—

213

C₂³

—

214

C₂³

—

215

C₂³

—

216

C₂³

—

217

C₂³

C₂×C₂²⋊Dic₄₇

yes

—

218

C₂³

C₂×C₂²⋊Dic₄₇

yes

—

219

C₂³

C₂×C₂²⋊Dic₄₇

yes

—

220

C₂³

#13093993

yes

—

221

C₂³

C₂³×Dic₄₇

yes

characteristic

222

C₂³

C₂²×C₂²⋊D₄₇

yes

—

223

C₂³

C₂²×C₂²⋊D₄₇

yes

—

224

C₂³

#13094069

yes

—

225

D₄

—

128

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

188

—

230

C₂×C₄

—

188

—

231

C₂×C₄

—

188

—

232

C₂×C₄

C₂×C₂²⋊Dic₄₇

yes

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

128

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

#15688979

yes

—

243

C₂²

C₂²×C₂²⋊Dic₄₇

yes

—

244

C₂²

C₂²×C₂²⋊Dic₄₇

yes

characteristic

245

C₂²

#15689598

yes

—

246

C₂²

C₂×#13093993

yes

—

247

C₂²

#15689682

yes

—

248

C₂²

#15689690

yes

—

249

C₄

—

250

C₄

—

376

—

251

C₂

—

252

C₂

—

253

C₂

C₂×#15688979

yes

characteristic

254

C₂

#20245966

yes

—

255

C₂

#20245970

yes

—

256

C₂

#20249100

yes

—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₄₇
commutator	C₂³×C₄₇	C₂³×C₄
Fitting, prime radical	C₂⁴×D₄×C₄₇	C₂
socle, cosocle	C₂⁴×C₄₇	C₂⁴
hypercenter	C₂⁴×D₄	D₄₇
hypocenter	C₄₇	#14335
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×D₄

subgroup

G/H

center, Frattini

C₂⁴

C₂³×D₄₇

commutator

C₂³×C₄₇

C₂³×C₄

Fitting, prime radical

C₂⁴×D₄×C₄₇

C₂

socle, cosocle

C₂⁴×C₄₇

C₂⁴

hypercenter

C₂⁴×D₄

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂⁴ ◁ C₂⁴×D₄

N	H ≅ G/N	type
1. C₂×#15688986	C₂	semidirect
2. C₂×#15688979	C₂	semidirect
3. #20241629	C₂	semidirect
6. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
9. C₂×C₄₇⋊#95	C₂²	semidirect
13. C₂³×D₄×C₄₇	C₄	semidirect
50. C₂⁴×C₄₇	C₂²⋊C₄	semidirect
64. C₂²×C₄×C₄₇	C₂²⋊C₄	semidirect
136. C₂³×D₄	Dic₄₇	semidirect
144. C₄₇	#14335	semidirect
179. C₂⁴	C₂²⋊Dic₄₇	semidirect
196. C₂²×C₄	C₂²⋊Dic₄₇	semidirect

H ≅ G/N

type

1. C₂×#15688986

C₂

semidirect

2. C₂×#15688979

C₂

semidirect

3. #20241629

C₂

semidirect

6. C₂²×C₂²⋊Dic₄₇

C₂²

semidirect

9. C₂×C₄₇⋊#95

C₂²

semidirect

13. C₂³×D₄×C₄₇

C₄

semidirect

50. C₂⁴×C₄₇

C₂²⋊C₄

semidirect

64. C₂²×C₄×C₄₇

C₂²⋊C₄

semidirect

136. C₂³×D₄

Dic₄₇

semidirect

144. C₄₇

#14335

semidirect

179. C₂⁴

C₂²⋊Dic₄₇

semidirect

196. C₂²×C₄

C₂²⋊Dic₄₇

semidirect

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

subgroup	index
C₂×#15688986	2
C₂×#15688979	2
#20241629	2
C₂⁴×D₄×C₄₇	2
#14335	47

subgroup

index

C₂⁴×D₄×C₄₇

Subgroups — #26143436

Conjugacy classes of subgroups

Complements

Maximal subgroups