Group #26110693 — subgroups

Subgroups — #26110693

Order 12032.

644 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 155 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	#20246453	C₂	1	1	yes	maximal, characteristic
2	#20244195	C₂	1	1	yes	maximal, characteristic
3	#20244147	C₂	1	2	yes	maximal, complemented
4	#20241227	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#331	C₂	1	1	yes	maximal, characteristic
6	C₂×D₄×Dic₄₇	—	2	2	no	—
7	C₂×#13093958	—	2	2	no	—
8	C₂×#13093945	—	2	2	no	—
9	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
10	#15689026	—	2	2	no	—
11	#15689003	—	2	2	no	—
12	#15688993	C₂²	1	1	yes	characteristic
13	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
14	#15688886	—	2	2	no	—
15	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
17	C₄₇×#331	C₄	1	4	yes	complemented
18	C₂³×Dic₄₇	—	2	2	no	—
19	C₂²×C₄₇⋊C₈	—	2	1	no	—
20	D₄×Dic₄₇	—	4	4	no	—
21	D₄×Dic₄₇	—	4	4	no	—
22	C₂×C₄⋊Dic₄₇	—	2	1	no	—
23	C₂×C₄⋊Dic₄₇	—	2	2	no	—
24	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
25	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
26	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
27	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
28	C₂×C₄×Dic₄₇	—	2	2	no	—
29	#13093958	—	4	4	no	—
30	#13093945	—	4	4	no	—
31	C₄×C₄₇⋊C₈	—	2	2	no	—
32	C₄₇⋊#95	—	2	2	no	—
33	C₂²×D₄×C₄₇	—	2	2	no	—
34	C₂²×D₄×C₄₇	D₄	1	2	yes	—
35	C₂²×C₈×C₄₇	—	2	2	no	—
36	#127×C₄₇	—	2	2	no	—
37	#127×C₄₇	C₂×C₄	1	2	yes	—
38	#127×C₄₇	Q₈	1	2	yes	—
39	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
40	C₄⋊C₈×C₄₇	—	2	2	no	—
41	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
42	C₂⁴×C₄₇	—	2	2	no	—
43	C₂×D₄×C₄₇	—	2	4	no	—
44	C₂×D₄×C₄₇	—	2	4	no	—
45	C₂×D₄×C₄₇	—	2	2	no	—
46	C₂×D₄×C₄₇	—	4	2	no	—
47	C₂×D₄×C₄₇	—	4	2	no	—
48	C₂×D₄×C₄₇	—	4	2	no	—
49	C₂×D₄×C₄₇	—	4	2	no	—
50	C₂×D₄×C₄₇	—	4	2	no	—
51	C₂×D₄×C₄₇	—	4	2	no	—
52	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
53	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
55	C₂²×Dic₄₇	—	2	2	no	—
56	C₂²×Dic₄₇	—	2	2	no	—
57	C₂²×Dic₄₇	—	4	8	no	—
58	C₂²×Dic₄₇	—	4	1	no	—
59	C₂²×Dic₄₇	—	8	2	no	—
60	C₂×C₈×C₄₇	—	2	4	no	—
61	C₂×C₈×C₄₇	—	4	2	no	—
62	C₂×C₈×C₄₇	—	4	2	no	—
63	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
64	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
65	C₄²×C₄₇	#41	1	2	yes	—
66	C₂²⋊Dic₄₇	—	4	8	no	—
67	C₂²⋊Dic₄₇	—	8	2	no	—
68	C₄⋊Dic₄₇	—	2	2	no	—
69	C₄⋊Dic₄₇	—	2	2	no	—
70	C₄⋊Dic₄₇	—	2	2	no	—
71	C₄⋊Dic₄₇	—	4	2	no	—
72	C₄⋊Dic₄₇	—	4	2	no	—
73	C₄⋊Dic₄₇	—	4	2	no	—
74	C₄⋊Dic₄₇	D₈	1	4	yes	—
75	C₄×Dic₄₇	—	4	2	no	—
76	C₄×Dic₄₇	—	4	2	no	—
77	C₂×C₄₇⋊C₈	—	2	2	no	—
78	C₂×C₄₇⋊C₈	—	4	1	no	—
79	C₂×C₄₇⋊C₈	—	4	1	no	—
80	C₂³×C₄₇	—	2	4	no	—
81	C₂³×C₄₇	—	4	4	no	—
82	C₂³×C₄₇	—	4	4	no	—
83	C₂³×C₄₇	—	4	2	no	—
84	C₂³×C₄₇	—	4	2	no	—
85	C₂³×C₄₇	#120	1	1	yes	characteristic
86	D₄×C₄₇	—	4	4	no	—
87	D₄×C₄₇	—	4	4	no	—
88	D₄×C₄₇	—	4	4	no	—
89	D₄×C₄₇	—	4	4	no	—
90	D₄×C₄₇	—	4	4	no	—
91	D₄×C₄₇	—	8	2	no	—
92	C₂×C₄×C₄₇	—	2	1	no	—
93	C₂×C₄×C₄₇	—	2	1	no	—
94	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
96	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
97	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
98	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
99	C₂×C₄×C₄₇	#135	1	2	yes	—
100	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
101	C₂×C₄×C₄₇	#137	1	2	yes	—
102	C₂×Dic₄₇	—	2	4	no	—
103	C₂×Dic₄₇	—	4	2	no	—
104	C₂×Dic₄₇	—	4	2	no	—
105	C₂×Dic₄₇	—	4	2	no	—
106	C₂×Dic₄₇	—	4	2	no	—
107	C₂×Dic₄₇	—	4	2	no	—
108	C₂×Dic₄₇	—	8	8	no	—
109	C₂×Dic₄₇	—	8	2	no	—
110	C₂×Dic₄₇	—	8	1	no	—
111	C₈×C₄₇	—	4	4	no	—
112	C₄₇⋊C₈	—	4	2	no	—
113	#8920	—	47	1	no	maximal, Sylow
114	C₂²×C₄₇	—	4	4	no	—
115	C₂²×C₄₇	—	4	8	no	—
116	C₂²×C₄₇	—	8	2	no	—
117	C₂²×C₄₇	—	8	2	no	—
118	C₂²×C₄₇	—	8	4	no	—
119	C₂²×C₄₇	#385	1	1	yes	characteristic
120	C₂²×C₄₇	#447	1	2	yes	—
121	C₂²×C₄₇	#452	1	2	yes	—
122	C₂²×C₄₇	#453	1	1	yes	characteristic
123	C₂²×C₄₇	#455	1	1	yes	characteristic
124	C₄×C₄₇	—	2	1	no	—
125	C₄×C₄₇	—	2	1	no	—
126	C₄×C₄₇	C₄×D₈	1	2	yes	—
127	C₄×C₄₇	#440	1	2	yes	—
128	C₄×C₄₇	#474	1	2	yes	—
129	C₄×C₄₇	#478	1	2	yes	—
130	Dic₄₇	—	4	4	no	—
131	Dic₄₇	—	8	2	no	—
132	Dic₄₇	—	16	1	no	—
133	#2366	—	47	1	no	—
134	#1957	—	47	1	no	—
135	#1947	—	47	2	no	—
136	C₂×#331	D₄₇	1	1	yes	characteristic
137	#1279	—	47	2	no	—
138	C₂×C₄₇	—	8	4	no	—
139	C₂×C₄₇	#1619	1	1	yes	characteristic
140	C₂×C₄₇	#1630	1	1	yes	characteristic
141	C₂×C₄₇	#1641	1	2	yes	—
142	C₂×C₄₇	#1856	1	1	yes	characteristic
143	C₂×C₄₇	#1862	1	2	yes	—
144	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
145	C₂×C₄×D₄	—	94	2	no	—
146	C₂×#107	—	94	2	no	—
147	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
148	C₂×#102	—	94	2	no	—
149	C₂×C₄×C₈	—	47	1	no	—
150	#390	—	94	2	no	—
151	#386	—	94	2	no	—
152	#384	—	47	1	no	—
153	C₄×C₄⋊C₄	—	47	2	no	—
154	#340	—	94	2	no	—
155	#331	Dic₄₇	1	4	yes	complemented
156	C₄₇	#8920	1	1	yes	characteristic, complemented, Sylow
157	C₂²×D₄	—	2	2	no	—
158	C₂²×D₄	D₁₈₈	1	2	yes	—
159	C₂³×C₄	—	94	2	no	—
160	C₂²×C₈	—	2	2	no	—
161	C₂²×C₈	—	94	1	no	—
162	#127	—	2	2	no	—
163	#127	Dic₉₄	1	2	yes	—
164	#127	C₂×Dic₄₇	1	2	yes	—
165	C₄×D₄	—	188	4	no	—
166	C₄×D₄	—	188	4	no	—
167	C₂×C₄⋊C₄	—	47	2	no	—
168	C₂×C₄⋊C₄	—	47	2	no	—
169	C₂×C₄⋊C₄	—	94	1	no	—
170	C₂×C₄⋊C₄	—	94	2	no	—
171	C₂×C₂²⋊C₄	—	94	2	no	—
172	C₂×C₂²⋊C₄	—	94	4	no	—
173	C₂×C₄²	—	94	2	no	—
174	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
175	#107	—	188	4	no	—
176	C₄⋊C₈	—	2	2	no	—
177	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	complemented
178	#102	—	188	4	no	—
179	C₄×C₈	—	94	2	no	—
180	#95	—	94	2	no	—
181	C₂⁴	—	2	2	no	—
182	C₂×D₄	—	2	4	no	—
183	C₂×D₄	—	2	4	no	—
184	C₂×D₄	—	2	2	no	—
185	C₂×D₄	—	4	2	no	—
186	C₂×D₄	—	4	2	no	—
187	C₂×D₄	—	4	2	no	—
188	C₂×D₄	—	4	2	no	—
189	C₂×D₄	—	4	2	no	—
190	C₂×D₄	—	4	2	no	—
191	C₂×D₄	C₄⋊Dic₄₇	1	4	yes	—
192	C₂²×C₄	—	94	2	no	—
193	C₂²×C₄	—	94	2	no	—
194	C₂²×C₄	—	376	2	no	—
195	C₂²×C₄	—	188	8	no	—
196	C₂²×C₄	—	188	1	no	—
197	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
198	C₂²×C₄	D₄×D₄₇	1	2	yes	—
199	C₂×C₈	—	2	4	no	—
200	C₂×C₈	—	4	2	no	—
201	C₂×C₈	—	4	2	no	—
202	C₂×C₈	—	94	2	no	—
203	C₂×C₈	—	188	1	no	—
204	C₂×C₈	—	188	1	no	—
205	C₄⋊C₄	—	47	4	no	—
206	C₄⋊C₄	—	94	2	no	—
207	C₄⋊C₄	—	94	2	no	—
208	C₄⋊C₄	—	94	2	no	—
209	C₄⋊C₄	—	188	2	no	—
210	C₄⋊C₄	—	188	2	no	—
211	C₄⋊C₄	—	188	2	no	—
212	C₂²⋊C₄	—	376	2	no	—
213	C₂²⋊C₄	—	188	8	no	—
214	C₄²	—	188	2	no	—
215	C₄²	—	188	2	no	—
216	C₄²	C₂×Dic₉₄	1	1	yes	characteristic
217	C₄²	#10625352	1	2	yes	—
218	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
219	C₂³	—	2	4	no	—
220	C₂³	—	4	4	no	—
221	C₂³	—	4	4	no	—
222	C₂³	—	4	2	no	—
223	C₂³	—	4	2	no	—
224	C₂³	#13093994	1	1	yes	characteristic
225	D₄	—	4	4	no	—
226	D₄	—	4	4	no	—
227	D₄	—	4	4	no	—
228	D₄	—	4	4	no	—
229	D₄	—	4	4	no	—
230	D₄	—	8	2	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	94	4	no	—
234	C₂×C₄	—	376	8	no	—
235	C₂×C₄	—	376	2	no	—
236	C₂×C₄	—	376	1	no	—
237	C₂×C₄	—	188	2	no	—
238	C₂×C₄	—	188	2	no	—
239	C₂×C₄	—	188	2	no	—
240	C₂×C₄	—	188	2	no	—
241	C₂×C₄	—	188	2	no	—
242	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
243	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
244	C₂×C₄	#13094001	1	2	yes	—
245	C₂×C₄	#13094008	1	1	yes	characteristic
246	C₂×C₄	D₈×D₄₇	1	2	yes	—
247	C₂×C₄	#13094043	1	2	yes	—
248	C₂×C₄	#13094051	1	2	yes	—
249	C₂×C₄	#13094053	1	2	yes	—
250	C₈	—	4	4	no	—
251	C₈	—	188	2	no	—
252	C₂²	—	4	4	no	—
253	C₂²	—	4	8	no	—
254	C₂²	—	8	2	no	—
255	C₂²	—	8	2	no	—
256	C₂²	—	8	4	no	—
257	C₂²	#15688998	1	1	yes	characteristic
258	C₂²	#15689258	1	2	yes	—
259	C₂²	#15689286	1	2	yes	—
260	C₂²	#15689293	1	1	yes	characteristic
261	C₂²	#15689303	1	1	yes	characteristic
262	C₄	—	2	1	no	—
263	C₄	—	2	1	no	—
264	C₄	—	376	2	no	—
265	C₄	—	188	4	no	—
266	C₄	—	752	1	no	—
267	C₄	D₈×Dic₄₇	1	2	yes	—
268	C₄	#15689224	1	2	yes	—
269	C₄	#15689401	1	2	yes	—
270	C₄	#15689421	1	2	yes	—
271	C₂	—	8	4	no	—
272	C₂	#20242443	1	1	yes	characteristic
273	C₂	#20242510	1	1	yes	characteristic
274	C₂	#20242582	1	2	yes	—
275	C₂	#20243600	1	1	yes	characteristic
276	C₂	#20243637	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20246453

C₂

yes

maximal, characteristic

#20244195

C₂

yes

maximal, characteristic

#20244147

C₂

yes

maximal, complemented

#20241227

C₂

yes

maximal, complemented

C₂×C₄₇×#331

C₂

yes

maximal, characteristic

C₂×D₄×Dic₄₇

—

C₂×#13093958

—

C₂×#13093945

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

—

C₂²

yes

characteristic

C₄×C₄⋊Dic₄₇

C₂²

yes

—

#15688886

—

C₂×#127×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₄₇×#331

C₄

yes

complemented

C₂³×Dic₄₇

—

C₂²×C₄₇⋊C₈

—

D₄×Dic₄₇

—

D₄×Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×C₂²⋊Dic₄₇

—

C₂×C₂²⋊Dic₄₇

—

C₂×C₄×Dic₄₇

—

#13093958

—

#13093945

—

C₄×C₄₇⋊C₈

—

C₄₇⋊#95

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

—

#127×C₄₇

—

#127×C₄₇

C₂×C₄

yes

—

#127×C₄₇

Q₈

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

C₂×C₄

yes

complemented

C₂⁴×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

C₄⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×Q₈

yes

characteristic

C₄²×C₄₇

#41

yes

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

D₈

yes

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#120

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₇

#123

yes

characteristic

C₂×C₄×C₄₇

C₂×D₈

yes

—

C₂×C₄×C₄₇

#135

yes

—

100

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

101

C₂×C₄×C₄₇

#137

yes

—

102

C₂×Dic₄₇

—

103

C₂×Dic₄₇

—

104

C₂×Dic₄₇

—

105

C₂×Dic₄₇

—

106

C₂×Dic₄₇

—

107

C₂×Dic₄₇

—

108

C₂×Dic₄₇

—

109

C₂×Dic₄₇

—

110

C₂×Dic₄₇

—

111

C₈×C₄₇

—

112

C₄₇⋊C₈

—

113

#8920

—

maximal, Sylow

114

C₂²×C₄₇

—

115

C₂²×C₄₇

—

116

C₂²×C₄₇

—

117

C₂²×C₄₇

—

118

C₂²×C₄₇

—

119

C₂²×C₄₇

#385

yes

characteristic

120

C₂²×C₄₇

#447

yes

—

121

C₂²×C₄₇

#452

yes

—

122

C₂²×C₄₇

#453

yes

characteristic

123

C₂²×C₄₇

#455

yes

characteristic

124

C₄×C₄₇

—

125

C₄×C₄₇

—

126

C₄×C₄₇

C₄×D₈

yes

—

127

C₄×C₄₇

#440

yes

—

128

C₄×C₄₇

#474

yes

—

129

C₄×C₄₇

#478

yes

—

130

Dic₄₇

—

131

Dic₄₇

—

132

Dic₄₇

—

133

#2366

—

134

#1957

—

135

#1947

—

136

C₂×#331

D₄₇

yes

characteristic

137

#1279

—

138

C₂×C₄₇

—

139

C₂×C₄₇

#1619

yes

characteristic

140

C₂×C₄₇

#1630

yes

characteristic

141

C₂×C₄₇

#1641

yes

—

142

C₂×C₄₇

#1856

yes

characteristic

143

C₂×C₄₇

#1862

yes

—

144

C₂×#127

C₂×D₄₇

yes

characteristic

145

C₂×C₄×D₄

—

146

C₂×#107

—

147

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

148

C₂×#102

—

149

C₂×C₄×C₈

—

150

#390

—

151

#386

—

152

#384

—

153

C₄×C₄⋊C₄

—

154

#340

—

155

#331

Dic₄₇

yes

complemented

156

C₄₇

#8920

yes

characteristic, complemented, Sylow

157

C₂²×D₄

—

158

C₂²×D₄

D₁₈₈

yes

—

159

C₂³×C₄

—

160

C₂²×C₈

—

161

C₂²×C₈

—

162

#127

—

163

#127

Dic₉₄

yes

—

164

#127

C₂×Dic₄₇

yes

—

165

C₄×D₄

—

188

—

166

C₄×D₄

—

188

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄⋊C₄

—

171

C₂×C₂²⋊C₄

—

172

C₂×C₂²⋊C₄

—

173

C₂×C₄²

—

174

C₂×C₄²

C₂²×D₄₇

yes

characteristic

175

#107

—

188

—

176

C₄⋊C₈

—

177

C₄⋊C₈

C₂×Dic₄₇

yes

complemented

178

#102

—

188

—

179

C₄×C₈

—

180

#95

—

181

C₂⁴

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

C₄⋊Dic₄₇

yes

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

376

—

195

C₂²×C₄

—

188

—

196

C₂²×C₄

—

188

—

197

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

198

C₂²×C₄

D₄×D₄₇

yes

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

188

—

204

C₂×C₈

—

188

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

188

—

210

C₄⋊C₄

—

188

—

211

C₄⋊C₄

—

188

—

212

C₂²⋊C₄

—

376

—

213

C₂²⋊C₄

—

188

—

214

C₄²

—

188

—

215

C₄²

—

188

—

216

C₄²

C₂×Dic₉₄

yes

characteristic

217

C₄²

#10625352

yes

—

218

C₄²

C₂²×Dic₄₇

yes

characteristic

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

#13093994

yes

characteristic

225

D₄

—

226

D₄

—

227

D₄

—

228

D₄

—

229

D₄

—

230

D₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

376

—

235

C₂×C₄

—

376

—

236

C₂×C₄

—

376

—

237

C₂×C₄

—

188

—

238

C₂×C₄

—

188

—

239

C₂×C₄

—

188

—

240

C₂×C₄

—

188

—

241

C₂×C₄

—

188

—

242

C₂×C₄

C₂×C₄⋊Dic₄₇

yes

characteristic

243

C₂×C₄

D₄×Dic₄₇

yes

—

244

C₂×C₄

#13094001

yes

—

245

C₂×C₄

#13094008

yes

characteristic

246

C₂×C₄

D₈×D₄₇

yes

—

247

C₂×C₄

#13094043

yes

—

248

C₂×C₄

#13094051

yes

—

249

C₂×C₄

#13094053

yes

—

250

C₈

—

251

C₈

—

188

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

—

257

C₂²

#15688998

yes

characteristic

258

C₂²

#15689258

yes

—

259

C₂²

#15689286

yes

—

260

C₂²

#15689293

yes

characteristic

261

C₂²

#15689303

yes

characteristic

262

C₄

—

263

C₄

—

264

C₄

—

376

—

265

C₄

—

188

—

266

C₄

—

752

—

267

C₄

D₈×Dic₄₇

yes

—

268

C₄

#15689224

yes

—

269

C₄

#15689401

yes

—

270

C₄

#15689421

yes

—

271

C₂

—

272

C₂

#20242443

yes

characteristic

273

C₂

#20242510

yes

characteristic

274

C₂

#20242582

yes

—

275

C₂

#20243600

yes

characteristic

276

C₂

#20243637

yes

—

	subgroup	G/H
center	C₂³	#13093994
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#331	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂×#127×C₄₇	C₂²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#331	D₄₇
hypocenter	C₄₇	#8920
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#331

subgroup

G/H

center

C₂³

#13093994

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₂×C₄₇×#331

C₂

socle

C₂³×C₄₇

#120

prime radical

C₂×#127×C₄₇

C₂²

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#331

N	H ≅ G/N	type
3. #20244147	C₂	semidirect
4. #20241227	C₂	semidirect
17. C₄₇×#331	C₄	semidirect
41. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
155. #331	Dic₄₇	semidirect
156. C₄₇	#8920	semidirect
177. C₄⋊C₈	C₂×Dic₄₇	semidirect

H ≅ G/N

type

3. #20244147

C₂

semidirect

4. #20241227

C₂

semidirect

17. C₄₇×#331

C₄

semidirect

41. C₄⋊C₈×C₄₇

C₂×C₄

semidirect

155. #331

Dic₄₇

semidirect

156. C₄₇

#8920

semidirect

177. C₄⋊C₈

C₂×Dic₄₇

semidirect

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

subgroup	index
#20246453	2
#20244195	2
#20244147	2
#20241227	2
C₂×C₄₇×#331	2
#8920	47

subgroup

index

C₂×C₄₇×#331

Subgroups — #26110693

Conjugacy classes of subgroups

Complements

Maximal subgroups