Group #26113641 — subgroups

Subgroups — #26113641

Order 12032.

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

normal subgroups only

This group has 558 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	#20248380	C₂	1	1	yes	maximal, characteristic
3	#20242061	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×#13094011	—	2	1	no	—
8	D₄×C₄₇⋊C₈	—	2	4	no	—
9	#15689176	C₂²	1	2	yes	—
10	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
11	#15689048	C₄	1	4	yes	—
12	#15689028	—	2	1	no	—
13	#15688983	—	2	2	no	—
14	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
15	#15688870	—	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	#13094011	—	4	2	no	—
25	#13094011	—	4	2	no	—
26	C₂×C₄⋊Dic₄₇	—	2	1	no	—
27	C₂×C₄⋊Dic₄₇	—	2	1	no	—
28	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
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	—	2	4	no	—
36	C₄₇⋊#95	C₂×C₄	1	2	yes	—
37	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	D₄	1	2	yes	—
39	C₂×M₁₆×C₄₇	—	2	2	no	—
40	C₄×D₄×C₄₇	—	2	2	no	—
41	C₄×D₄×C₄₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
45	C₄⋊C₈×C₄₇	—	2	2	no	—
46	C₄⋊C₈×C₄₇	—	2	2	no	—
47	#100×C₄₇	—	4	2	no	—
48	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
49	C₂×D₄×C₄₇	—	2	2	no	—
50	C₂×D₄×C₄₇	—	2	2	no	—
51	C₂×D₄×C₄₇	D₈	1	2	yes	—
52	C₂×D₄×C₄₇	SD₁₆	1	2	yes	—
53	C₂²×C₄×C₄₇	—	2	2	no	—
54	C₂²×C₄×C₄₇	—	2	2	no	—
55	C₂²×C₄×C₄₇	—	4	4	no	—
56	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
60	C₂²×Dic₄₇	—	2	2	no	—
61	C₂²×Dic₄₇	—	2	2	no	—
62	C₂×Dic₉₄	—	4	2	no	—
63	C₂×Dic₉₄	—	4	1	no	—
64	C₂×Dic₉₄	—	4	1	no	—
65	C₂×Dic₉₄	—	4	2	no	—
66	M₁₆×C₄₇	—	4	2	no	—
67	M₁₆×C₄₇	—	4	2	no	—
68	C₂×C₈×C₄₇	—	4	2	no	—
69	C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂²⋊C₄×C₄₇	—	2	4	no	—
71	C₄²×C₄₇	C₂×D₄	1	2	yes	—
72	C₄²×C₄₇	#41	1	2	yes	—
73	C₂²⋊Dic₄₇	—	4	8	no	—
74	C₄⋊Dic₄₇	—	2	4	no	—
75	C₄⋊Dic₄₇	—	4	2	no	—
76	C₄⋊Dic₄₇	—	4	1	no	—
77	C₄⋊Dic₄₇	—	4	1	no	—
78	C₄×Dic₄₇	—	4	1	no	—
79	C₄×Dic₄₇	—	4	1	no	—
80	C₂×C₄₇⋊C₈	—	2	4	no	—
81	C₂×C₄₇⋊C₈	—	8	4	no	—
82	C₂³×C₄₇	—	2	2	no	—
83	C₂³×C₄₇	—	2	2	no	—
84	C₂³×C₄₇	—	4	2	no	—
85	C₂³×C₄₇	—	4	2	no	—
86	C₂³×C₄₇	#102	1	4	yes	—
87	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	D₄×C₄₇	—	2	4	no	—
89	D₄×C₄₇	—	2	4	no	—
90	C₂×C₄×C₄₇	—	2	2	no	—
91	C₂×C₄×C₄₇	—	2	2	no	—
92	C₂×C₄×C₄₇	—	4	1	no	—
93	C₂×C₄×C₄₇	—	4	4	no	—
94	C₂×C₄×C₄₇	—	4	2	no	—
95	C₂×C₄×C₄₇	—	8	2	no	—
96	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
97	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
98	C₂×C₄×C₄₇	#121	1	2	yes	—
99	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
100	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
101	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
102	C₂×C₄×C₄₇	#135	1	2	yes	—
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	—	4	2	no	—
109	Dic₉₄	—	8	2	no	—
110	Dic₉₄	—	8	2	no	—
111	C₈×C₄₇	—	8	2	no	—
112	C₄₇⋊C₈	—	4	4	no	—
113	#9393	—	47	1	no	maximal, Sylow
114	C₂²×C₄₇	—	2	1	no	—
115	C₂²×C₄₇	—	2	1	no	—
116	C₂²×C₄₇	—	2	4	no	—
117	C₂²×C₄₇	—	4	4	no	—
118	C₂²×C₄₇	—	4	2	no	—
119	C₂²×C₄₇	—	4	2	no	—
120	C₂²×C₄₇	—	8	2	no	—
121	C₂²×C₄₇	#386	1	1	yes	characteristic
122	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
123	C₂²×C₄₇	#416	1	1	yes	characteristic
124	C₄×C₄₇	—	2	1	no	—
125	C₄×C₄₇	—	2	2	no	—
126	C₄×C₄₇	—	4	2	no	—
127	C₄×C₄₇	#455	1	2	yes	—
128	C₄×C₄₇	#465	1	2	yes	—
129	C₄×C₄₇	#466	1	2	yes	—
130	Dic₄₇	—	8	2	no	—
131	Dic₄₇	—	8	2	no	—
132	#2972	—	47	1	no	—
133	#2547	—	47	1	no	—
134	#1800	D₄₇	1	1	yes	characteristic
135	#1546	—	47	2	no	—
136	#1303	—	47	2	no	—
137	C₂×C₄₇	—	2	1	no	—
138	C₂×C₄₇	—	2	1	no	—
139	C₂×C₄₇	—	4	4	no	—
140	C₂×C₄₇	#1885	1	1	yes	characteristic
141	C₂×C₄₇	#1893	1	1	yes	characteristic
142	C₂×C₄₇	#1915	1	1	yes	characteristic
143	C₂×C₄⋊Q₈	—	47	1	no	—
144	C₂×#124	—	94	1	no	—
145	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
146	C₈×D₄	—	94	4	no	—
147	#431	—	47	2	no	—
148	#423	C₂×D₄₇	1	2	yes	—
149	C₂×#100	—	2	1	no	—
150	C₂×C₂²⋊C₈	—	94	2	no	—
151	#397	—	47	4	no	—
152	#391	—	94	1	no	—
153	#380	—	94	2	no	—
154	C₄×C₄⋊C₄	—	47	1	no	—
155	#343	—	2	1	no	—
156	#332	—	94	4	no	—
157	C₄₇	#9393	1	1	yes	characteristic, complemented, Sylow
158	C₂²×Q₈	—	94	1	no	—
159	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
160	C₂³×C₄	D₁₈₈	1	2	yes	—
161	C₂×M₁₆	—	2	2	no	—
162	C₂²×C₈	—	94	4	no	—
163	C₄⋊Q₈	—	94	2	no	—
164	C₄⋊Q₈	—	94	2	no	—
165	#124	—	188	2	no	—
166	#124	—	188	2	no	—
167	C₄×D₄	—	2	2	no	—
168	C₄×D₄	—	2	2	no	—
169	C₂×C₄⋊C₄	—	47	2	no	—
170	C₂×C₄⋊C₄	—	94	1	no	—
171	C₂×C₄⋊C₄	—	94	1	no	—
172	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
173	C₂×C₂²⋊C₄	—	94	4	no	—
174	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
175	C₂×C₄²	—	94	1	no	—
176	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
177	C₄⋊C₈	—	2	2	no	—
178	C₄⋊C₈	—	2	2	no	—
179	C₄⋊C₈	—	47	4	no	—
180	#100	—	4	2	no	—
181	C₂²⋊C₈	—	94	4	no	—
182	C₂²⋊C₈	—	94	2	no	—
183	C₄×C₈	—	94	2	no	—
184	#95	—	47	2	no	—
185	#95	—	94	4	no	—
186	C₂⁴	(C₂×D₄₇)⋊C₄	1	2	yes	—
187	C₂×Q₈	—	188	2	no	—
188	C₂×Q₈	—	188	1	no	—
189	C₂×Q₈	—	188	1	no	—
190	C₂×Q₈	—	188	2	no	—
191	C₂×D₄	—	2	2	no	—
192	C₂×D₄	—	2	2	no	—
193	C₂×D₄	#10625334	1	2	yes	—
194	C₂×D₄	#10625336	1	2	yes	—
195	C₂²×C₄	—	2	2	no	—
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	—	4	4	no	—
198	C₂²×C₄	—	94	2	no	—
199	C₂²×C₄	—	94	2	no	—
200	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
201	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
202	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
203	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
204	M₁₆	—	4	2	no	—
205	M₁₆	—	4	2	no	—
206	C₂×C₈	—	4	2	no	—
207	C₂×C₈	—	94	4	no	—
208	C₂×C₈	—	376	4	no	—
209	C₄⋊C₄	—	2	2	no	—
210	C₄⋊C₄	—	94	4	no	—
211	C₄⋊C₄	—	188	2	no	—
212	C₄⋊C₄	—	188	1	no	—
213	C₄⋊C₄	—	188	1	no	—
214	C₂²⋊C₄	—	2	4	no	—
215	C₂²⋊C₄	—	188	8	no	—
216	C₄²	—	188	1	no	—
217	C₄²	—	188	1	no	—
218	C₄²	D₄×D₄₇	1	2	yes	—
219	C₄²	#10625352	1	2	yes	—
220	C₂³	—	2	2	no	—
221	C₂³	—	2	2	no	—
222	C₂³	—	4	2	no	—
223	C₂³	—	4	2	no	—
224	C₂³	#13093944	1	4	yes	—
225	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
226	Q₈	—	376	2	no	—
227	Q₈	—	376	2	no	—
228	D₄	—	2	4	no	—
229	D₄	—	2	4	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	4	1	no	—
233	C₂×C₄	—	4	4	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	8	2	no	—
236	C₂×C₄	—	188	2	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	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
243	C₂×C₄	#13093994	1	1	yes	characteristic
244	C₂×C₄	#13093996	1	2	yes	—
245	C₂×C₄	#13094008	1	1	yes	characteristic
246	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
247	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
248	C₂×C₄	#13094044	1	2	yes	—
249	C₈	—	8	2	no	—
250	C₈	—	188	4	no	—
251	C₂²	—	2	1	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	2	4	no	—
254	C₂²	—	4	4	no	—
255	C₂²	—	4	2	no	—
256	C₂²	—	4	2	no	—
257	C₂²	—	8	2	no	—
258	C₂²	#15689000	1	1	yes	characteristic
259	C₂²	C₂×#13093944	1	1	yes	characteristic
260	C₂²	#15689117	1	1	yes	characteristic
261	C₄	—	2	1	no	—
262	C₄	—	2	2	no	—
263	C₄	—	4	2	no	—
264	C₄	—	376	2	no	—
265	C₄	—	376	2	no	—
266	C₄	#15689303	1	2	yes	—
267	C₄	#15689354	1	2	yes	—
268	C₄	#15689357	1	2	yes	—
269	C₂	—	2	1	no	—
270	C₂	—	2	1	no	—
271	C₂	—	4	4	no	—
272	C₂	#20243774	1	1	yes	characteristic
273	C₂	#20243814	1	1	yes	characteristic
274	C₂	#20243938	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252412

C₂

yes

maximal, characteristic

#20248380

C₂

yes

maximal, characteristic

#20242061

C₂

yes

maximal, complemented

#20241289

C₂

yes

maximal, complemented

C₄₇×#1800

C₂

yes

maximal, characteristic

C₂×#13094024

C₂²

yes

characteristic

C₂×#13094011

—

D₄×C₄₇⋊C₈

—

#15689176

C₂²

yes

—

C₂×C₂²⋊(C₄₇⋊C₈)

—

#15689048

C₄

yes

—

#15689028

—

#15688983

—

C₄×C₄⋊Dic₄₇

C₂²

yes

characteristic

#15688870

—

C₂×C₄×D₄×C₄₇

C₂²

yes

characteristic

C₄₇×#423

C₂²

yes

—

C₂×#100×C₄₇

—

C₄₇×#343

—

C₂²×Dic₉₄

—

C₂²×C₄₇⋊C₈

—

—

—

—

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

—

C₂×C₂²⋊Dic₄₇

—

C₂×C₄×Dic₄₇

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

—

C₄₇⋊#95

—

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

D₈

yes

—

C₂×D₄×C₄₇

SD₁₆

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

—

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

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#102

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

100

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

101

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

102

C₂×C₄×C₄₇

#135

yes

—

103

C₂×Dic₄₇

—

104

C₂×Dic₄₇

—

105

C₂×Dic₄₇

—

106

C₂×Dic₄₇

—

107

C₂×Dic₄₇

—

108

C₂×Dic₄₇

—

109

Dic₉₄

—

110

Dic₉₄

—

111

C₈×C₄₇

—

112

C₄₇⋊C₈

—

113

#9393

—

maximal, Sylow

114

C₂²×C₄₇

—

115

C₂²×C₄₇

—

116

C₂²×C₄₇

—

117

C₂²×C₄₇

—

118

C₂²×C₄₇

—

119

C₂²×C₄₇

—

120

C₂²×C₄₇

—

121

C₂²×C₄₇

#386

yes

characteristic

122

C₂²×C₄₇

C₂×#102

yes

characteristic

123

C₂²×C₄₇

#416

yes

characteristic

124

C₄×C₄₇

—

125

C₄×C₄₇

—

126

C₄×C₄₇

—

127

C₄×C₄₇

#455

yes

—

128

C₄×C₄₇

#465

yes

—

129

C₄×C₄₇

#466

yes

—

130

Dic₄₇

—

131

Dic₄₇

—

132

#2972

—

133

#2547

—

134

#1800

D₄₇

yes

characteristic

135

#1546

—

136

#1303

—

137

C₂×C₄₇

—

138

C₂×C₄₇

—

139

C₂×C₄₇

—

140

C₂×C₄₇

#1885

yes

characteristic

141

C₂×C₄₇

#1893

yes

characteristic

142

C₂×C₄₇

#1915

yes

characteristic

143

C₂×C₄⋊Q₈

—

144

C₂×#124

—

145

C₂×C₄×D₄

C₂×D₄₇

yes

characteristic

146

C₈×D₄

—

147

#431

—

148

#423

C₂×D₄₇

yes

—

149

C₂×#100

—

150

C₂×C₂²⋊C₈

—

151

#397

—

152

#391

—

153

#380

—

154

C₄×C₄⋊C₄

—

155

#343

—

156

#332

—

157

C₄₇

#9393

yes

characteristic, complemented, Sylow

158

C₂²×Q₈

—

159

C₂²×D₄

C₂²⋊D₄₇

yes

characteristic

160

C₂³×C₄

D₁₈₈

yes

—

161

C₂×M₁₆

—

162

C₂²×C₈

—

163

C₄⋊Q₈

—

164

C₄⋊Q₈

—

165

#124

—

188

—

166

#124

—

188

—

167

C₄×D₄

—

168

C₄×D₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄⋊C₄

—

171

C₂×C₄⋊C₄

—

172

C₂×C₄⋊C₄

C₂²⋊D₄₇

yes

characteristic

173

C₂×C₂²⋊C₄

—

174

C₂×C₂²⋊C₄

C₄×D₄₇

yes

—

175

C₂×C₄²

—

176

C₂×C₄²

C₂²×D₄₇

yes

characteristic

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

#100

—

181

C₂²⋊C₈

—

182

C₂²⋊C₈

—

183

C₄×C₈

—

184

#95

—

185

#95

—

186

C₂⁴

(C₂×D₄₇)⋊C₄

yes

—

187

C₂×Q₈

—

188

—

188

C₂×Q₈

—

188

—

189

C₂×Q₈

—

188

—

190

C₂×Q₈

—

188

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

#10625334

yes

—

194

C₂×D₄

#10625336

yes

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

—

200

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

201

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

202

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

203

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

204

M₁₆

—

205

M₁₆

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

376

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

188

—

212

C₄⋊C₄

—

188

—

213

C₄⋊C₄

—

188

—

214

C₂²⋊C₄

—

215

C₂²⋊C₄

—

188

—

216

C₄²

—

188

—

217

C₄²

—

188

—

218

C₄²

D₄×D₄₇

yes

—

219

C₄²

#10625352

yes

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

#13093944

yes

—

225

C₂³

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

226

Q₈

—

376

—

227

Q₈

—

376

—

228

D₄

—

229

D₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

188

—

237

C₂×C₄

—

188

—

238

C₂×C₄

—

188

—

239

C₂×C₄

—

188

—

240

C₂×C₄

—

188

—

241

C₂×C₄

—

188

—

242

C₂×C₄

(C₂²⋊D₄₇)⋊C₄

yes

—

243

C₂×C₄

#13093994

yes

characteristic

244

C₂×C₄

#13093996

yes

—

245

C₂×C₄

#13094008

yes

characteristic

246

C₂×C₄

C₂×#10625334

yes

characteristic

247

C₂×C₄

C₂×#10625336

yes

characteristic

248

C₂×C₄

#13094044

yes

—

249

C₈

—

250

C₈

—

188

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

#15689000

yes

characteristic

259

C₂²

C₂×#13093944

yes

characteristic

260

C₂²

#15689117

yes

characteristic

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

376

—

265

C₄

—

376

—

266

C₄

#15689303

yes

—

267

C₄

#15689354

yes

—

268

C₄

#15689357

yes

—

269

C₂

—

270

C₂

—

271

C₂

—

272

C₂

#20243774

yes

characteristic

273

C₂

#20243814

yes

characteristic

274

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	#9393
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. #20242061	C₂	semidirect
4. #20241289	C₂	semidirect
157. C₄₇	#9393	semidirect

H ≅ G/N

type

3. #20242061

C₂

semidirect

4. #20241289

C₂

semidirect

157. C₄₇

#9393

semidirect

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

subgroup	index
#20252412	2
#20248380	2
#20242061	2
#20241289	2
C₄₇×#1800	2
#9393	47

subgroup

index

C₄₇×#1800

Subgroups — #26113641

Conjugacy classes of subgroups

Complements

Maximal subgroups