Group #26111585 — subgroups

Subgroups — #26111585

Order 12032.

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

normal subgroups only

This group has 570 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	#20246478	C₂	1	1	yes	maximal, characteristic
2	#20244337	C₂	1	2	yes	maximal
3	C₂×#15688872	C₂	1	1	yes	maximal, characteristic
4	#20241228	C₂	1	2	yes	maximal
5	C₂×C₄₇×#494	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
7	#15689030	—	2	2	no	—
8	#15689022	—	2	2	no	—
9	C₄⋊C₄×Dic₄₇	—	2	2	no	—
10	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
11	#15688885	—	2	2	no	—
12	#15688885	—	2	2	no	—
13	#15688872	—	2	2	no	—
14	C₂²×Q₁₆×C₄₇	—	2	2	no	—
15	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#494	—	2	2	no	—
18	C₄₇×#494	C₄	1	4	yes	complemented
19	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄₇⋊C₈	—	2	2	no	—
21	C₂×C₄⋊Dic₄₇	—	2	2	no	—
22	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
23	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
24	C₂×C₄×Dic₄₇	—	2	2	no	—
25	C₂×C₄×Dic₄₇	—	2	2	no	—
26	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
27	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
28	C₄₇⋊#95	—	2	4	no	—
29	C₄₇⋊#95	—	2	2	no	—
30	C₂²×Q₈×C₄₇	—	2	1	no	—
31	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
32	C₂×Q₁₆×C₄₇	—	2	8	no	—
33	C₂×Q₁₆×C₄₇	—	4	4	no	—
34	C₂×Q₁₆×C₄₇	—	4	4	no	—
35	C₂²×C₈×C₄₇	—	2	1	no	—
36	C₄⋊Q₈×C₄₇	—	2	1	no	—
37	C₄⋊Q₈×C₄₇	—	2	2	no	—
38	C₄⋊Q₈×C₄₇	—	2	2	no	—
39	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
40	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
41	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
42	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
45	C₄×C₈×C₄₇	—	2	1	no	—
46	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
47	C₂×Q₈×C₄₇	—	2	2	no	—
48	C₂×Q₈×C₄₇	—	2	2	no	—
49	C₂×Q₈×C₄₇	—	4	2	no	—
50	C₂×Q₈×C₄₇	—	4	2	no	—
51	C₂×Q₈×C₄₇	—	4	2	no	—
52	C₂×Q₈×C₄₇	—	4	2	no	—
53	C₂×Q₈×C₄₇	—	4	1	no	—
54	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
55	C₂²×C₄×C₄₇	—	2	2	no	—
56	C₂²×C₄×C₄₇	—	4	1	no	—
57	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
59	C₂²×Dic₄₇	—	2	2	no	—
60	C₂²×Dic₄₇	—	2	2	no	—
61	Q₁₆×C₄₇	—	4	16	no	—
62	C₂×C₈×C₄₇	—	2	2	no	—
63	C₂×C₈×C₄₇	—	2	2	no	—
64	C₂×C₈×C₄₇	—	2	2	no	—
65	C₄⋊C₄×C₄₇	—	2	4	no	—
66	C₄⋊C₄×C₄₇	—	2	4	no	—
67	C₄⋊C₄×C₄₇	—	2	4	no	—
68	C₄⋊C₄×C₄₇	—	4	2	no	—
69	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
70	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₄₇	#41	1	2	yes	—
72	C₄⋊Dic₄₇	—	2	2	no	—
73	C₄⋊Dic₄₇	—	2	2	no	—
74	C₄⋊Dic₄₇	—	2	2	no	—
75	C₄⋊Dic₄₇	—	8	2	no	—
76	C₄⋊Dic₄₇	Q₁₆	1	4	yes	complemented
77	C₄×Dic₄₇	—	4	2	no	—
78	C₄×Dic₄₇	—	4	2	no	—
79	C₄×Dic₄₇	—	8	2	no	—
80	C₂×C₄₇⋊C₈	—	4	2	no	—
81	C₂×C₄₇⋊C₈	—	4	2	no	—
82	C₂×C₄₇⋊C₈	—	4	2	no	—
83	C₂³×C₄₇	#120	1	1	yes	characteristic
84	Q₈×C₄₇	—	4	4	no	—
85	Q₈×C₄₇	—	4	4	no	—
86	Q₈×C₄₇	—	8	2	no	—
87	Q₈×C₄₇	—	8	2	no	—
88	C₂×C₄×C₄₇	—	2	1	no	—
89	C₂×C₄×C₄₇	—	2	1	no	—
90	C₂×C₄×C₄₇	—	2	4	no	—
91	C₂×C₄×C₄₇	—	4	2	no	—
92	C₂×C₄×C₄₇	—	4	2	no	—
93	C₂×C₄×C₄₇	—	4	2	no	—
94	C₂×C₄×C₄₇	—	8	1	no	—
95	C₂×C₄×C₄₇	—	8	1	no	—
96	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₄₇	#121	1	2	yes	—
99	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
100	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
101	C₂×C₄×C₄₇	#135	1	2	yes	—
102	C₂×C₄×C₄₇	#137	1	2	yes	—
103	C₂×C₄×C₄₇	#137	1	2	yes	—
104	C₂×Dic₄₇	—	2	4	no	—
105	C₂×Dic₄₇	—	4	2	no	—
106	C₂×Dic₄₇	—	4	2	no	—
107	C₂×Dic₄₇	—	4	2	no	—
108	C₂×Dic₄₇	—	4	2	no	—
109	C₂×Dic₄₇	—	4	2	no	—
110	C₈×C₄₇	—	2	4	no	—
111	C₄₇⋊C₈	—	8	2	no	—
112	#9066	—	47	1	no	maximal, Sylow
113	C₂²×C₄₇	#386	1	1	yes	characteristic
114	C₂²×C₄₇	#451	1	2	yes	—
115	C₂²×C₄₇	#452	1	2	yes	—
116	C₂²×C₄₇	#453	1	1	yes	characteristic
117	C₂²×C₄₇	#453	1	1	yes	characteristic
118	C₄×C₄₇	—	2	1	no	—
119	C₄×C₄₇	—	2	1	no	—
120	C₄×C₄₇	—	4	4	no	—
121	C₄×C₄₇	—	8	2	no	—
122	C₄×C₄₇	C₄×Q₁₆	1	2	yes	—
123	C₄×C₄₇	#441	1	2	yes	—
124	C₄×C₄₇	#462	1	2	yes	—
125	C₄×C₄₇	#464	1	2	yes	—
126	Dic₄₇	—	4	4	no	—
127	Dic₄₇	—	8	2	no	—
128	C₂×#494	D₄₇	1	1	yes	characteristic
129	#2369	—	47	1	no	—
130	#1987	—	47	2	no	—
131	C₂×#333	—	47	1	no	—
132	#1279	—	47	2	no	—
133	C₂×C₄₇	#1632	1	2	yes	—
134	C₂×C₄₇	#1633	1	1	yes	characteristic
135	C₂×C₄₇	#1634	1	1	yes	characteristic
136	C₂×C₄₇	#1878	1	2	yes	—
137	C₂×C₄₇	#1887	1	1	yes	characteristic
138	C₂²×Q₁₆	—	2	2	no	—
139	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
140	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
141	#494	—	2	2	no	—
142	#494	Dic₄₇	1	4	yes	complemented
143	C₂×C₄⋊C₈	—	47	2	no	—
144	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
145	#391	—	94	2	no	—
146	#389	—	94	2	no	—
147	C₄×C₄⋊C₄	—	47	2	no	—
148	C₄×C₄⋊C₄	—	94	2	no	—
149	#340	—	94	2	no	—
150	#340	—	94	2	no	—
151	#333	—	94	2	no	—
152	C₄₇	#9066	1	1	yes	characteristic, complemented, Sylow
153	C₂²×Q₈	—	2	1	no	—
154	C₂²×Q₈	C₂²⋊D₄₇	1	2	yes	—
155	C₂×Q₁₆	—	2	8	no	—
156	C₂×Q₁₆	—	4	4	no	—
157	C₂×Q₁₆	—	4	4	no	—
158	C₂²×C₈	—	2	1	no	—
159	C₂²×C₈	—	94	2	no	—
160	C₄⋊Q₈	—	2	2	no	—
161	C₄⋊Q₈	—	2	2	no	—
162	C₄⋊Q₈	—	2	1	no	—
163	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
164	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
165	C₄⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
166	C₂×C₄⋊C₄	—	2	2	no	—
167	C₂×C₄⋊C₄	—	2	2	no	—
168	C₂×C₄⋊C₄	—	47	2	no	—
169	C₂×C₄⋊C₄	—	47	2	no	—
170	C₂×C₄⋊C₄	—	94	2	no	—
171	C₂×C₄²	—	94	2	no	—
172	C₂×C₄²	—	94	2	no	—
173	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
174	C₄⋊C₈	—	94	2	no	—
175	C₄⋊C₈	—	94	2	no	—
176	C₄×C₈	—	2	1	no	—
177	C₄×C₈	C₂×Dic₄₇	1	2	yes	—
178	#95	—	94	4	no	—
179	#95	—	94	2	no	—
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	2	no	—
185	C₂×Q₈	—	4	2	no	—
186	C₂×Q₈	—	4	1	no	—
187	C₂×Q₈	C₂²⋊Dic₄₇	1	4	yes	—
188	C₂²×C₄	—	2	2	no	—
189	C₂²×C₄	—	4	1	no	—
190	C₂²×C₄	—	94	2	no	—
191	C₂²×C₄	—	94	2	no	—
192	C₂²×C₄	D₄×D₄₇	1	2	yes	—
193	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
194	Q₁₆	—	4	16	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	2	2	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	188	2	no	—
199	C₂×C₈	—	188	2	no	—
200	C₂×C₈	—	188	2	no	—
201	C₄⋊C₄	—	2	4	no	—
202	C₄⋊C₄	—	2	4	no	—
203	C₄⋊C₄	—	2	4	no	—
204	C₄⋊C₄	—	4	2	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	—	376	2	no	—
210	C₄²	—	376	2	no	—
211	C₄²	—	188	2	no	—
212	C₄²	—	188	2	no	—
213	C₄²	#10625352	1	2	yes	—
214	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
215	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
216	C₂³	#13093992	1	1	yes	characteristic
217	Q₈	—	4	4	no	—
218	Q₈	—	4	4	no	—
219	Q₈	—	8	2	no	—
220	Q₈	—	8	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	4	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	8	1	no	—
228	C₂×C₄	—	8	1	no	—
229	C₂×C₄	—	94	4	no	—
230	C₂×C₄	—	188	2	no	—
231	C₂×C₄	—	188	2	no	—
232	C₂×C₄	—	188	2	no	—
233	C₂×C₄	—	188	2	no	—
234	C₂×C₄	—	188	2	no	—
235	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
236	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
237	C₂×C₄	#13093996	1	2	yes	—
238	C₂×C₄	#13094005	1	1	yes	characteristic
239	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
240	C₂×C₄	#13094047	1	2	yes	—
241	C₂×C₄	#13094056	1	2	yes	—
242	C₂×C₄	#13094056	1	2	yes	—
243	C₈	—	2	4	no	—
244	C₈	—	376	2	no	—
245	C₂²	#15689003	1	1	yes	characteristic
246	C₂²	#15689277	1	2	yes	—
247	C₂²	#15689284	1	2	yes	—
248	C₂²	#15689290	1	1	yes	characteristic
249	C₂²	#15689290	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	4	4	no	—
253	C₄	—	8	2	no	—
254	C₄	—	376	2	no	—
255	C₄	—	188	4	no	—
256	C₄	Q₁₆×Dic₄₇	1	2	yes	—
257	C₄	#15689230	1	2	yes	—
258	C₄	#15689331	1	2	yes	—
259	C₄	#15689347	1	2	yes	—
260	C₂	#20242519	1	2	yes	—
261	C₂	#20242526	1	1	yes	characteristic
262	C₂	#20242531	1	1	yes	characteristic
263	C₂	#20243731	1	2	yes	—
264	C₂	#20243787	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20246478

C₂

yes

maximal, characteristic

#20244337

C₂

yes

maximal

C₂×#15688872

C₂

yes

maximal, characteristic

#20241228

C₂

yes

maximal

C₂×C₄₇×#494

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

#15689030

—

#15689022

—

C₄⋊C₄×Dic₄₇

—

C₄×C₄⋊Dic₄₇

C₂²

yes

—

#15688885

—

#15688885

—

#15688872

—

C₂²×Q₁₆×C₄₇

—

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₄₇×#494

—

C₄₇×#494

C₄

yes

complemented

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

D₄

yes

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂²×C₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

C₂×C₄

yes

—

C₄⋊Q₈×C₄₇

C₂×C₄

yes

—

C₄⋊Q₈×C₄₇

D₄

yes

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄×C₈×C₄₇

—

C₄×C₈×C₄₇

C₂×C₄

yes

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

Q₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

#41

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

Q₁₆

yes

complemented

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

#120

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×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

C₄×D₄

yes

—

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

#123

yes

characteristic

100

C₂×C₄×C₄₇

C₂×Q₁₆

yes

—

101

C₂×C₄×C₄₇

#135

yes

—

102

C₂×C₄×C₄₇

#137

yes

—

103

C₂×C₄×C₄₇

#137

yes

—

104

C₂×Dic₄₇

—

105

C₂×Dic₄₇

—

106

C₂×Dic₄₇

—

107

C₂×Dic₄₇

—

108

C₂×Dic₄₇

—

109

C₂×Dic₄₇

—

110

C₈×C₄₇

—

111

C₄₇⋊C₈

—

112

#9066

—

maximal, Sylow

113

C₂²×C₄₇

#386

yes

characteristic

114

C₂²×C₄₇

#451

yes

—

115

C₂²×C₄₇

#452

yes

—

116

C₂²×C₄₇

#453

yes

characteristic

117

C₂²×C₄₇

#453

yes

characteristic

118

C₄×C₄₇

—

119

C₄×C₄₇

—

120

C₄×C₄₇

—

121

C₄×C₄₇

—

122

C₄×C₄₇

C₄×Q₁₆

yes

—

123

C₄×C₄₇

#441

yes

—

124

C₄×C₄₇

#462

yes

—

125

C₄×C₄₇

#464

yes

—

126

Dic₄₇

—

127

Dic₄₇

—

128

C₂×#494

D₄₇

yes

characteristic

129

#2369

—

130

#1987

—

131

C₂×#333

—

132

#1279

—

133

C₂×C₄₇

#1632

yes

—

134

C₂×C₄₇

#1633

yes

characteristic

135

C₂×C₄₇

#1634

yes

characteristic

136

C₂×C₄₇

#1878

yes

—

137

C₂×C₄₇

#1887

yes

characteristic

138

C₂²×Q₁₆

—

139

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

140

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

141

#494

—

142

#494

Dic₄₇

yes

complemented

143

C₂×C₄⋊C₈

—

144

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

145

#391

—

146

#389

—

147

C₄×C₄⋊C₄

—

148

C₄×C₄⋊C₄

—

149

#340

—

150

#340

—

151

#333

—

152

C₄₇

#9066

yes

characteristic, complemented, Sylow

153

C₂²×Q₈

—

154

C₂²×Q₈

C₂²⋊D₄₇

yes

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

—

158

C₂²×C₈

—

159

C₂²×C₈

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

C₂×Dic₄₇

yes

—

164

C₄⋊Q₈

C₂×Dic₄₇

yes

—

165

C₄⋊Q₈

C₂²⋊D₄₇

yes

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄⋊C₄

—

171

C₂×C₄²

—

172

C₂×C₄²

—

173

C₂×C₄²

C₂²×D₄₇

yes

characteristic

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄×C₈

—

177

C₄×C₈

C₂×Dic₄₇

yes

—

178

#95

—

179

#95

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

C₂²⋊Dic₄₇

yes

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

D₄×D₄₇

yes

—

193

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

194

Q₁₆

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

188

—

199

C₂×C₈

—

188

—

200

C₂×C₈

—

188

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

376

—

210

C₄²

—

376

—

211

C₄²

—

188

—

212

C₄²

—

188

—

213

C₄²

#10625352

yes

—

214

C₄²

C₂²×Dic₄₇

yes

characteristic

215

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

216

C₂³

#13093992

yes

characteristic

217

Q₈

—

218

Q₈

—

219

Q₈

—

220

Q₈

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

188

—

231

C₂×C₄

—

188

—

232

C₂×C₄

—

188

—

233

C₂×C₄

—

188

—

234

C₂×C₄

—

188

—

235

C₂×C₄

C₂×C₂²⋊Dic₄₇

yes

characteristic

236

C₂×C₄

D₄×Dic₄₇

yes

—

237

C₂×C₄

#13093996

yes

—

238

C₂×C₄

#13094005

yes

characteristic

239

C₂×C₄

Q₁₆×D₄₇

yes

—

240

C₂×C₄

#13094047

yes

—

241

C₂×C₄

#13094056

yes

—

242

C₂×C₄

#13094056

yes

—

243

C₈

—

244

C₈

—

376

—

245

C₂²

#15689003

yes

characteristic

246

C₂²

#15689277

yes

—

247

C₂²

#15689284

yes

—

248

C₂²

#15689290

yes

characteristic

249

C₂²

#15689290

yes

characteristic

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

376

—

255

C₄

—

188

—

256

C₄

Q₁₆×Dic₄₇

yes

—

257

C₄

#15689230

yes

—

258

C₄

#15689331

yes

—

259

C₄

#15689347

yes

—

260

C₂

#20242519

yes

—

261

C₂

#20242526

yes

characteristic

262

C₂

#20242531

yes

characteristic

263

C₂

#20243731

yes

—

264

C₂

#20243787

yes

characteristic

	subgroup	G/H
center	C₂³	#13093992
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#494	C₂
socle, prime radical	C₂³×C₄₇	#120
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#494	D₄₇
hypocenter	C₄₇	#9066
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

subgroup

G/H

center

C₂³

#13093992

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₂×C₄₇×#494

C₂

socle, prime radical

C₂³×C₄₇

#120

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

N	H ≅ G/N	type
18. C₄₇×#494	C₄	semidirect
76. C₄⋊Dic₄₇	Q₁₆	semidirect
142. #494	Dic₄₇	semidirect
152. C₄₇	#9066	semidirect

H ≅ G/N

type

18. C₄₇×#494

C₄

semidirect

76. C₄⋊Dic₄₇

Q₁₆

semidirect

142. #494

Dic₄₇

semidirect

152. C₄₇

#9066

semidirect

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

subgroup	index
#20246478	2
#20244337	2
C₂×#15688872	2
#20241228	2
C₂×C₄₇×#494	2
#9066	47

subgroup

index

C₂×C₄₇×#494

Subgroups — #26111585

Conjugacy classes of subgroups

Complements

Maximal subgroups