Group #26113651 — subgroups

Subgroups — #26113651

Order 12032.

594 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 131 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	#20252412	C₂	1	1	yes	maximal, characteristic
2	#20248341	C₂	1	1	yes	maximal, characteristic
3	#20242074	C₂	1	2	yes	maximal, complemented
4	#20241289	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1800	C₂	1	1	yes	maximal, characteristic
6	C₂×#13094024	C₂²	1	1	yes	characteristic
7	C₂×#13094003	—	2	2	no	—
8	D₄×C₄₇⋊C₈	—	2	4	no	—
9	#15689176	C₂²	1	2	yes	—
10	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
11	#15689059	C₄	1	4	yes	—
12	#15689026	—	2	1	no	—
13	#15688992	—	2	1	no	—
14	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
15	#15688868	—	2	4	no	—
16	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#423	C₂²	1	2	yes	—
18	C₂×#100×C₄₇	—	2	1	no	—
19	C₄₇×#343	—	2	1	no	—
20	C₂²×Dic₉₄	—	2	1	no	—
21	C₂²×C₄₇⋊C₈	—	2	4	no	—
22	#13094024	—	2	2	no	—
23	#13094024	—	2	2	no	—
24	#13094003	—	4	8	no	—
25	C₂×C₄⋊Dic₄₇	—	2	1	no	—
26	C₂×C₄⋊Dic₄₇	—	2	1	no	—
27	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
28	C₂×Dic₄₇⋊C₄	—	2	4	no	—
29	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
30	C₂×C₄×Dic₄₇	—	2	1	no	—
31	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
32	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
33	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
34	C₄×C₄₇⋊C₈	—	2	2	no	—
35	C₄₇⋊#95	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	D₄	1	2	yes	—
38	C₂×M₁₆×C₄₇	—	2	2	no	—
39	C₄×D₄×C₄₇	—	2	2	no	—
40	C₄×D₄×C₄₇	—	2	2	no	—
41	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₄₇	—	2	2	no	—
45	C₄⋊C₈×C₄₇	—	2	2	no	—
46	#100×C₄₇	—	4	2	no	—
47	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
48	C₂×D₄×C₄₇	—	2	2	no	—
49	C₂×D₄×C₄₇	—	2	2	no	—
50	C₂×D₄×C₄₇	SD₁₆	1	2	yes	—
51	C₂×D₄×C₄₇	Q₁₆	1	2	yes	—
52	C₂²×C₄×C₄₇	—	2	2	no	—
53	C₂²×C₄×C₄₇	—	2	2	no	—
54	C₂²×C₄×C₄₇	—	4	4	no	—
55	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
59	C₂²×Dic₄₇	—	2	2	no	—
60	C₂²×Dic₄₇	—	2	2	no	—
61	C₂×Dic₉₄	—	4	4	no	—
62	C₂×Dic₉₄	—	4	1	no	—
63	C₂×Dic₉₄	—	4	1	no	—
64	M₁₆×C₄₇	—	4	2	no	—
65	M₁₆×C₄₇	—	4	2	no	—
66	C₂×C₈×C₄₇	—	4	2	no	—
67	C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂²⋊C₄×C₄₇	—	2	4	no	—
69	C₄²×C₄₇	C₂×D₄	1	2	yes	—
70	C₄²×C₄₇	#41	1	2	yes	—
71	C₂²⋊Dic₄₇	—	4	8	no	—
72	C₄⋊Dic₄₇	—	2	4	no	—
73	C₄⋊Dic₄₇	—	2	4	no	—
74	C₄⋊Dic₄₇	—	4	2	no	—
75	Dic₄₇⋊C₄	—	4	8	no	—
76	C₄×Dic₄₇	—	4	2	no	—
77	C₂×C₄₇⋊C₈	—	2	4	no	—
78	C₂×C₄₇⋊C₈	—	8	4	no	—
79	C₂³×C₄₇	—	2	2	no	—
80	C₂³×C₄₇	—	2	2	no	—
81	C₂³×C₄₇	—	4	2	no	—
82	C₂³×C₄₇	—	4	2	no	—
83	C₂³×C₄₇	#103	1	4	yes	—
84	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	D₄×C₄₇	—	2	4	no	—
86	D₄×C₄₇	—	2	4	no	—
87	C₂×C₄×C₄₇	—	2	2	no	—
88	C₂×C₄×C₄₇	—	2	2	no	—
89	C₂×C₄×C₄₇	—	4	1	no	—
90	C₂×C₄×C₄₇	—	4	4	no	—
91	C₂×C₄×C₄₇	—	4	2	no	—
92	C₂×C₄×C₄₇	—	8	2	no	—
93	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
94	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
95	C₂×C₄×C₄₇	#121	1	2	yes	—
96	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
97	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
99	C₂×C₄×C₄₇	#135	1	2	yes	—
100	C₂×Dic₄₇	—	2	4	no	—
101	C₂×Dic₄₇	—	4	2	no	—
102	C₂×Dic₄₇	—	4	2	no	—
103	C₂×Dic₄₇	—	4	4	no	—
104	C₂×Dic₄₇	—	4	2	no	—
105	Dic₉₄	—	8	2	no	—
106	Dic₉₄	—	8	2	no	—
107	C₈×C₄₇	—	8	2	no	—
108	C₄₇⋊C₈	—	4	4	no	—
109	#9395	—	47	1	no	maximal, Sylow
110	C₂²×C₄₇	—	2	1	no	—
111	C₂²×C₄₇	—	2	1	no	—
112	C₂²×C₄₇	—	2	4	no	—
113	C₂²×C₄₇	—	4	4	no	—
114	C₂²×C₄₇	—	4	2	no	—
115	C₂²×C₄₇	—	4	2	no	—
116	C₂²×C₄₇	—	8	2	no	—
117	C₂²×C₄₇	#386	1	1	yes	characteristic
118	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
119	C₂²×C₄₇	#416	1	1	yes	characteristic
120	C₄×C₄₇	—	2	1	no	—
121	C₄×C₄₇	—	2	2	no	—
122	C₄×C₄₇	—	4	2	no	—
123	C₄×C₄₇	#453	1	2	yes	—
124	C₄×C₄₇	#465	1	2	yes	—
125	C₄×C₄₇	#467	1	2	yes	—
126	Dic₄₇	—	4	4	no	—
127	Dic₄₇	—	8	2	no	—
128	#2972	—	47	1	no	—
129	#2542	—	47	1	no	—
130	#1800	D₄₇	1	1	yes	characteristic
131	#1549	—	47	2	no	—
132	#1303	—	47	2	no	—
133	C₂×C₄₇	—	2	1	no	—
134	C₂×C₄₇	—	2	1	no	—
135	C₂×C₄₇	—	4	4	no	—
136	C₂×C₄₇	#1887	1	1	yes	characteristic
137	C₂×C₄₇	#1892	1	1	yes	characteristic
138	C₂×C₄₇	#1915	1	1	yes	characteristic
139	C₂×C₄⋊Q₈	—	47	1	no	—
140	C₂×C₂²⋊Q₈	—	94	2	no	—
141	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
142	C₈×D₄	—	94	4	no	—
143	#431	—	47	2	no	—
144	#423	C₂×D₄₇	1	2	yes	—
145	C₂×#100	—	2	1	no	—
146	C₂×C₂²⋊C₈	—	94	2	no	—
147	#399	—	47	4	no	—
148	#390	—	94	1	no	—
149	#384	—	94	1	no	—
150	C₄×C₄⋊C₄	—	47	1	no	—
151	#343	—	2	1	no	—
152	#332	—	94	4	no	—
153	C₄₇	#9395	1	1	yes	characteristic, complemented, Sylow
154	C₂²×Q₈	—	94	1	no	—
155	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
156	C₂³×C₄	D₁₈₈	1	2	yes	—
157	C₂×M₁₆	—	2	2	no	—
158	C₂²×C₈	—	94	4	no	—
159	C₄⋊Q₈	—	94	2	no	—
160	C₄⋊Q₈	—	94	2	no	—
161	C₂²⋊Q₈	—	188	8	no	—
162	C₄×D₄	—	2	2	no	—
163	C₄×D₄	—	2	2	no	—
164	C₂×C₄⋊C₄	—	47	2	no	—
165	C₂×C₄⋊C₄	—	94	1	no	—
166	C₂×C₄⋊C₄	—	94	4	no	—
167	C₂×C₄⋊C₄	—	94	1	no	—
168	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
169	C₂×C₂²⋊C₄	—	94	4	no	—
170	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
171	C₂×C₄²	—	94	1	no	—
172	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
173	C₄⋊C₈	—	2	2	no	—
174	C₄⋊C₈	—	2	2	no	—
175	C₄⋊C₈	—	47	4	no	—
176	#100	—	4	2	no	—
177	C₂²⋊C₈	—	94	4	no	—
178	C₂²⋊C₈	—	94	2	no	—
179	C₄×C₈	—	94	2	no	—
180	#95	—	47	2	no	—
181	C₂⁴	(C₂×D₄₇)⋊C₄	1	2	yes	—
182	C₂×Q₈	—	188	4	no	—
183	C₂×Q₈	—	188	1	no	—
184	C₂×Q₈	—	188	1	no	—
185	C₂×D₄	—	2	2	no	—
186	C₂×D₄	—	2	2	no	—
187	C₂×D₄	#10625335	1	2	yes	—
188	C₂×D₄	#10625337	1	2	yes	—
189	C₂²×C₄	—	2	2	no	—
190	C₂²×C₄	—	2	2	no	—
191	C₂²×C₄	—	4	4	no	—
192	C₂²×C₄	—	94	2	no	—
193	C₂²×C₄	—	94	2	no	—
194	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
195	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
196	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
197	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
198	M₁₆	—	4	2	no	—
199	M₁₆	—	4	2	no	—
200	C₂×C₈	—	4	2	no	—
201	C₂×C₈	—	94	4	no	—
202	C₂×C₈	—	376	4	no	—
203	C₄⋊C₄	—	2	2	no	—
204	C₄⋊C₄	—	94	4	no	—
205	C₄⋊C₄	—	94	4	no	—
206	C₄⋊C₄	—	188	8	no	—
207	C₄⋊C₄	—	188	2	no	—
208	C₂²⋊C₄	—	2	4	no	—
209	C₂²⋊C₄	—	188	8	no	—
210	C₄²	—	188	2	no	—
211	C₄²	D₄×D₄₇	1	2	yes	—
212	C₄²	#10625352	1	2	yes	—
213	C₂³	—	2	2	no	—
214	C₂³	—	2	2	no	—
215	C₂³	—	4	2	no	—
216	C₂³	—	4	2	no	—
217	C₂³	#13093947	1	4	yes	—
218	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
219	Q₈	—	376	2	no	—
220	Q₈	—	376	2	no	—
221	D₄	—	2	4	no	—
222	D₄	—	2	4	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	4	1	no	—
226	C₂×C₄	—	4	4	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	8	2	no	—
229	C₂×C₄	—	94	4	no	—
230	C₂×C₄	—	188	4	no	—
231	C₂×C₄	—	188	2	no	—
232	C₂×C₄	—	188	2	no	—
233	C₂×C₄	—	188	2	no	—
234	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
235	C₂×C₄	#13093994	1	1	yes	characteristic
236	C₂×C₄	#13093996	1	2	yes	—
237	C₂×C₄	#13094008	1	1	yes	characteristic
238	C₂×C₄	C₂×#10625335	1	1	yes	characteristic
239	C₂×C₄	C₂×#10625337	1	1	yes	characteristic
240	C₂×C₄	#13094044	1	2	yes	—
241	C₈	—	8	2	no	—
242	C₈	—	188	4	no	—
243	C₂²	—	2	1	no	—
244	C₂²	—	2	1	no	—
245	C₂²	—	2	4	no	—
246	C₂²	—	4	4	no	—
247	C₂²	—	4	2	no	—
248	C₂²	—	4	2	no	—
249	C₂²	—	8	2	no	—
250	C₂²	#15689000	1	1	yes	characteristic
251	C₂²	C₂×#13093947	1	1	yes	characteristic
252	C₂²	#15689117	1	1	yes	characteristic
253	C₄	—	2	1	no	—
254	C₄	—	2	2	no	—
255	C₄	—	4	2	no	—
256	C₄	—	376	2	no	—
257	C₄	—	188	4	no	—
258	C₄	#15689293	1	2	yes	—
259	C₄	#15689350	1	2	yes	—
260	C₄	#15689362	1	2	yes	—
261	C₂	—	2	1	no	—
262	C₂	—	2	1	no	—
263	C₂	—	4	4	no	—
264	C₂	#20243784	1	1	yes	characteristic
265	C₂	#20243809	1	1	yes	characteristic
266	C₂	#20243938	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252412

C₂

yes

maximal, characteristic

#20248341

C₂

yes

maximal, characteristic

#20242074

C₂

yes

maximal, complemented

#20241289

C₂

yes

maximal, complemented

C₄₇×#1800

C₂

yes

maximal, characteristic

C₂×#13094024

C₂²

yes

characteristic

C₂×#13094003

—

D₄×C₄₇⋊C₈

—

#15689176

C₂²

yes

—

C₂×C₂²⋊(C₄₇⋊C₈)

—

#15689059

C₄

yes

—

#15689026

—

#15688992

—

C₄×C₄⋊Dic₄₇

C₂²

yes

characteristic

#15688868

—

C₂×C₄×D₄×C₄₇

C₂²

yes

characteristic

C₄₇×#423

C₂²

yes

—

C₂×#100×C₄₇

—

C₄₇×#343

—

C₂²×Dic₉₄

—

C₂²×C₄₇⋊C₈

—

#13094024

—

#13094024

—

#13094003

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

—

C₂×Dic₄₇⋊C₄

—

C₂×C₂²⋊Dic₄₇

—

C₂×C₄×Dic₄₇

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

—

C₄₇⋊#95

C₂×C₄

yes

—

C₂²×D₄×C₄₇

D₄

yes

characteristic

C₂³×C₄×C₄₇

D₄

yes

—

C₂×M₁₆×C₄₇

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

#100×C₄₇

—

C₂⁴×C₄₇

C₂²⋊C₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

SD₁₆

yes

—

C₂×D₄×C₄₇

Q₁₆

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#103

yes

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

#120

yes

characteristic

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

#123

yes

characteristic

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₄₇

#135

yes

—

100

C₂×Dic₄₇

—

101

C₂×Dic₄₇

—

102

C₂×Dic₄₇

—

103

C₂×Dic₄₇

—

104

C₂×Dic₄₇

—

105

Dic₉₄

—

106

Dic₉₄

—

107

C₈×C₄₇

—

108

C₄₇⋊C₈

—

109

#9395

—

maximal, Sylow

110

C₂²×C₄₇

—

111

C₂²×C₄₇

—

112

C₂²×C₄₇

—

113

C₂²×C₄₇

—

114

C₂²×C₄₇

—

115

C₂²×C₄₇

—

116

C₂²×C₄₇

—

117

C₂²×C₄₇

#386

yes

characteristic

118

C₂²×C₄₇

C₂×#103

yes

characteristic

119

C₂²×C₄₇

#416

yes

characteristic

120

C₄×C₄₇

—

121

C₄×C₄₇

—

122

C₄×C₄₇

—

123

C₄×C₄₇

#453

yes

—

124

C₄×C₄₇

#465

yes

—

125

C₄×C₄₇

#467

yes

—

126

Dic₄₇

—

127

Dic₄₇

—

128

#2972

—

129

#2542

—

130

#1800

D₄₇

yes

characteristic

131

#1549

—

132

#1303

—

133

C₂×C₄₇

—

134

C₂×C₄₇

—

135

C₂×C₄₇

—

136

C₂×C₄₇

#1887

yes

characteristic

137

C₂×C₄₇

#1892

yes

characteristic

138

C₂×C₄₇

#1915

yes

characteristic

139

C₂×C₄⋊Q₈

—

140

C₂×C₂²⋊Q₈

—

141

C₂×C₄×D₄

C₂×D₄₇

yes

characteristic

142

C₈×D₄

—

143

#431

—

144

#423

C₂×D₄₇

yes

—

145

C₂×#100

—

146

C₂×C₂²⋊C₈

—

147

#399

—

148

#390

—

149

#384

—

150

C₄×C₄⋊C₄

—

151

#343

—

152

#332

—

153

C₄₇

#9395

yes

characteristic, complemented, Sylow

154

C₂²×Q₈

—

155

C₂²×D₄

C₂²⋊D₄₇

yes

characteristic

156

C₂³×C₄

D₁₈₈

yes

—

157

C₂×M₁₆

—

158

C₂²×C₈

—

159

C₄⋊Q₈

—

160

C₄⋊Q₈

—

161

C₂²⋊Q₈

—

188

—

162

C₄×D₄

—

163

C₄×D₄

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

C₂²⋊D₄₇

yes

characteristic

169

C₂×C₂²⋊C₄

—

170

C₂×C₂²⋊C₄

C₄×D₄₇

yes

—

171

C₂×C₄²

—

172

C₂×C₄²

C₂²×D₄₇

yes

characteristic

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

#100

—

177

C₂²⋊C₈

—

178

C₂²⋊C₈

—

179

C₄×C₈

—

180

#95

—

181

C₂⁴

(C₂×D₄₇)⋊C₄

yes

—

182

C₂×Q₈

—

188

—

183

C₂×Q₈

—

188

—

184

C₂×Q₈

—

188

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

#10625335

yes

—

188

C₂×D₄

#10625337

yes

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

195

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

196

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

197

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

198

M₁₆

—

199

M₁₆

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

376

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

188

—

207

C₄⋊C₄

—

188

—

208

C₂²⋊C₄

—

209

C₂²⋊C₄

—

188

—

210

C₄²

—

188

—

211

C₄²

D₄×D₄₇

yes

—

212

C₄²

#10625352

yes

—

213

C₂³

—

214

C₂³

—

215

C₂³

—

216

C₂³

—

217

C₂³

#13093947

yes

—

218

C₂³

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

219

Q₈

—

376

—

220

Q₈

—

376

—

221

D₄

—

222

D₄

—

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

(C₂²⋊D₄₇)⋊C₄

yes

—

235

C₂×C₄

#13093994

yes

characteristic

236

C₂×C₄

#13093996

yes

—

237

C₂×C₄

#13094008

yes

characteristic

238

C₂×C₄

C₂×#10625335

yes

characteristic

239

C₂×C₄

C₂×#10625337

yes

characteristic

240

C₂×C₄

#13094044

yes

—

241

C₈

—

242

C₈

—

188

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

#15689000

yes

characteristic

251

C₂²

C₂×#13093947

yes

characteristic

252

C₂²

#15689117

yes

characteristic

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

376

—

257

C₄

—

188

—

258

C₄

#15689293

yes

—

259

C₄

#15689350

yes

—

260

C₄

#15689362

yes

—

261

C₂

—

262

C₂

—

263

C₂

—

264

C₂

#20243784

yes

characteristic

265

C₂

#20243809

yes

characteristic

266

C₂

#20243938

yes

characteristic

	subgroup	G/H
center	C₂²	#15689000
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1800	C₂
socle	C₂²×C₄₇	#386
prime radical	C₂²×D₄×C₄₇	D₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1800	D₄₇
hypocenter	C₄₇	#9395
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1800

subgroup

G/H

center

C₂²

#15689000

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1800

C₂

socle

C₂²×C₄₇

#386

prime radical

C₂²×D₄×C₄₇

D₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1800

N	H ≅ G/N	type
3. #20242074	C₂	semidirect
4. #20241289	C₂	semidirect
153. C₄₇	#9395	semidirect

H ≅ G/N

type

3. #20242074

C₂

semidirect

4. #20241289

C₂

semidirect

153. C₄₇

#9395

semidirect

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

subgroup	index
#20252412	2
#20248341	2
#20242074	2
#20241289	2
C₄₇×#1800	2
#9395	47

subgroup

index

C₄₇×#1800

Subgroups — #26113651

Conjugacy classes of subgroups

Complements

Maximal subgroups