Group #26133653 — subgroups

Subgroups — #26133653

Order 12032.

506 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 143 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	C₂²×#13093964	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689364	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688926	C₂	1	2	yes	maximal, complemented
4	#20241479	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1808	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₈₈	C₂²	1	1	yes	characteristic
7	C₂×#13094003	—	2	1	no	—
8	C₂×#13093964	—	2	4	no	—
9	C₂×#13093964	—	2	2	no	—
10	C₂²×C₄₇⋊C₁₆	C₂²	1	2	yes	—
11	#15689364	—	2	2	no	—
12	#15689364	C₄	1	4	yes	complemented
13	C₂×#13093958	C₂²	1	1	yes	characteristic
14	C₂×#13093949	—	2	1	no	—
15	#15688926	—	2	4	no	—
16	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#107×C₄₇	C₂²	1	2	yes	—
18	C₄₇×#380	—	2	1	no	—
19	C₄₇×#340	—	2	1	no	—
20	C₂²×Dic₉₄	—	2	1	no	—
21	C₂×Dic₁₈₈	—	2	2	no	—
22	C₂×Dic₁₈₈	—	2	2	no	—
23	C₂×Dic₁₈₈	—	2	1	no	—
24	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
25	#13094003	—	2	4	no	—
26	#13094003	—	4	2	no	—
27	C₂×C₄⋊Dic₄₇	—	2	1	no	—
28	C₂×Dic₄₇⋊C₄	—	4	1	no	—
29	C₂×C₂²⋊Dic₄₇	—	4	1	no	—
30	#13093964	—	2	8	no	—
31	C₂×C₄₇⋊C₁₆	—	2	2	no	—
32	C₂×C₄₇⋊C₁₆	—	2	2	no	—
33	C₂×C₄₇⋊C₁₆	D₄	1	4	yes	—
34	#13093958	—	2	1	no	—
35	#13093958	C₂×C₄	1	2	yes	—
36	#13093949	—	2	4	no	—
37	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₄₇	—	2	2	no	—
39	C₂²×C₈×C₄₇	—	2	2	no	—
40	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₄₇	D₄	1	2	yes	—
43	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
45	C₂×C₂²⋊C₄×C₄₇	—	4	1	no	—
46	#107×C₄₇	—	2	2	no	—
47	#107×C₄₇	—	2	2	no	—
48	#95×C₄₇	—	4	1	no	—
49	C₂⁴×C₄₇	D₈	1	1	yes	characteristic
50	C₂²×C₄×C₄₇	—	2	2	no	—
51	C₂²×C₄×C₄₇	—	2	2	no	—
52	C₂²×C₄×C₄₇	—	4	2	no	—
53	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
54	C₂²×C₄×C₄₇	D₈	1	1	yes	characteristic
55	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
56	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
57	C₂²×Dic₄₇	—	4	1	no	—
58	C₂²×Dic₄₇	—	4	1	no	—
59	C₂×Dic₉₄	—	2	2	no	—
60	C₂×Dic₉₄	—	4	2	no	—
61	C₂×Dic₉₄	—	4	2	no	—
62	C₂×Dic₉₄	—	4	1	no	—
63	C₂×C₈×C₄₇	—	2	2	no	—
64	C₂×C₈×C₄₇	—	2	4	no	—
65	C₂×C₈×C₄₇	—	2	2	no	—
66	C₂×C₈×C₄₇	—	2	2	no	—
67	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
68	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
70	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₄₇	#41	1	2	yes	—
72	C₄⋊C₄×C₄₇	—	4	2	no	—
73	C₄⋊C₄×C₄₇	—	4	2	no	—
74	C₂²⋊C₄×C₄₇	—	8	2	no	—
75	C₂²⋊Dic₄₇	—	4	4	no	—
76	C₄⋊Dic₄₇	—	2	2	no	—
77	C₄⋊Dic₄₇	—	4	1	no	—
78	Dic₄₇⋊C₄	—	4	4	no	—
79	Dic₁₈₈	—	2	4	no	—
80	Dic₁₈₈	—	4	1	no	—
81	Dic₁₈₈	—	4	1	no	—
82	C₄₇⋊C₁₆	—	2	4	no	—
83	C₂³×C₄₇	—	2	2	no	—
84	C₂³×C₄₇	—	2	1	no	—
85	C₂³×C₄₇	—	2	2	no	—
86	C₂³×C₄₇	—	2	1	no	—
87	C₂³×C₄₇	#102	1	2	yes	—
88	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₄₇	—	2	2	no	—
90	C₂×C₄×C₄₇	—	2	2	no	—
91	C₂×C₄×C₄₇	—	2	2	no	—
92	C₂×C₄×C₄₇	—	2	4	no	—
93	C₂×C₄×C₄₇	—	8	2	no	—
94	C₂×C₄×C₄₇	—	8	2	no	—
95	C₂×C₄×C₄₇	—	8	2	no	—
96	C₂×C₄×C₄₇	#102	1	2	yes	—
97	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₄₇	#121	1	2	yes	—
99	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
100	C₂×C₄×C₄₇	#135	1	2	yes	—
101	C₂×Dic₄₇	—	4	2	no	—
102	C₂×Dic₄₇	—	4	2	no	—
103	C₂×Dic₄₇	—	8	2	no	—
104	C₂×Dic₄₇	—	8	1	no	—
105	C₂×Dic₄₇	—	8	1	no	—
106	Dic₉₄	—	4	2	no	—
107	Dic₉₄	—	4	2	no	—
108	Dic₉₄	—	8	2	no	—
109	C₈×C₄₇	—	2	2	no	—
110	C₈×C₄₇	C₄×D₄	1	2	yes	—
111	C₈×C₄₇	#120	1	1	yes	characteristic
112	C₈×C₄₇	#123	1	1	yes	characteristic
113	#13062	—	47	1	no	maximal, Sylow
114	C₂²×C₄₇	—	2	2	no	—
115	C₂²×C₄₇	—	2	2	no	—
116	C₂²×C₄₇	—	2	2	no	—
117	C₂²×C₄₇	—	4	2	no	—
118	C₂²×C₄₇	—	4	2	no	—
119	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
120	C₂²×C₄₇	#466	1	2	yes	—
121	C₂²×C₄₇	#509	1	1	yes	characteristic
122	C₂²×C₄₇	#510	1	2	yes	—
123	C₂²×C₄₇	#510	1	1	yes	characteristic
124	C₄×C₄₇	—	2	2	no	—
125	C₄×C₄₇	—	16	2	no	—
126	C₄×C₄₇	#386	1	1	yes	characteristic
127	C₄×C₄₇	#416	1	1	yes	characteristic
128	C₄×C₄₇	#465	1	2	yes	—
129	Dic₄₇	—	8	2	no	—
130	Dic₄₇	—	8	2	no	—
131	C₂²×M₃₂	—	47	1	no	—
132	C₂×#467	—	47	1	no	—
133	C₂×#358	—	47	2	no	—
134	#1808	D₄₇	1	1	yes	characteristic
135	#1380	—	47	2	no	—
136	C₂×C₄₇	—	4	2	no	—
137	C₂×C₄₇	#1893	1	1	yes	characteristic
138	C₂×C₄₇	#2139	1	1	yes	characteristic
139	C₂×C₄₇	#2141	1	1	yes	characteristic
140	C₂×C₄₇	#2219	1	2	yes	—
141	C₂×C₄₇	#2220	1	2	yes	—
142	C₂²×Q₁₆	—	47	1	no	—
143	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
144	C₂×C₂²⋊Q₈	—	94	1	no	—
145	C₂×M₃₂	—	94	4	no	—
146	C₂×M₃₂	—	94	2	no	—
147	C₂²×C₁₆	—	47	2	no	—
148	#467	—	47	4	no	—
149	#467	—	94	2	no	—
150	C₂×#107	—	47	1	no	—
151	C₂×#107	C₂×D₄₇	1	2	yes	—
152	C₂×#103	—	94	1	no	—
153	#380	—	2	1	no	—
154	#358	—	94	4	no	—
155	#340	—	2	1	no	—
156	C₄₇	#13062	1	1	yes	characteristic, complemented, Sylow
157	C₂²×Q₈	—	94	1	no	—
158	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
159	C₂×Q₁₆	—	47	2	no	—
160	C₂×Q₁₆	—	94	1	no	—
161	C₂×Q₁₆	—	94	2	no	—
162	C₂×Q₁₆	—	94	2	no	—
163	C₂²×C₈	—	2	2	no	—
164	C₂²×C₈	—	2	2	no	—
165	C₂²×C₈	C₄×D₄₇	1	2	yes	—
166	C₂²×C₈	D₁₈₈	1	2	yes	—
167	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
168	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
169	C₂²⋊Q₈	—	94	4	no	—
170	C₂²⋊Q₈	—	188	2	no	—
171	C₂×C₄⋊C₄	—	2	2	no	—
172	C₂×C₄⋊C₄	—	94	1	no	—
173	C₂×C₄⋊C₄	—	188	1	no	—
174	C₂×C₂²⋊C₄	—	4	1	no	—
175	C₂×C₂²⋊C₄	—	188	1	no	—
176	M₃₂	—	94	8	no	—
177	C₂×C₁₆	—	47	4	no	—
178	C₂×C₁₆	—	94	2	no	—
179	C₂×C₁₆	—	94	2	no	—
180	#107	—	2	2	no	—
181	#107	—	2	2	no	—
182	#107	—	47	2	no	—
183	#107	—	94	1	no	—
184	#103	—	94	4	no	—
185	#95	—	4	1	no	—
186	C₂⁴	#10625334	1	1	yes	characteristic
187	C₂×Q₈	—	94	2	no	—
188	C₂×Q₈	—	188	2	no	—
189	C₂×Q₈	—	188	2	no	—
190	C₂×Q₈	—	188	1	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	4	2	no	—
194	C₂²×C₄	—	188	1	no	—
195	C₂²×C₄	—	188	1	no	—
196	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
197	C₂²×C₄	#10625334	1	1	yes	characteristic
198	C₂²×C₄	#10625336	1	2	yes	—
199	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
200	Q₁₆	—	94	4	no	—
201	Q₁₆	—	188	1	no	—
202	Q₁₆	—	188	1	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	2	4	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	2	2	no	—
207	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
208	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
209	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
210	C₂×C₈	D₄×D₄₇	1	2	yes	—
211	C₂×C₈	#10625352	1	2	yes	—
212	C₄⋊C₄	—	4	2	no	—
213	C₄⋊C₄	—	4	2	no	—
214	C₄⋊C₄	—	94	2	no	—
215	C₄⋊C₄	—	188	4	no	—
216	C₄⋊C₄	—	188	1	no	—
217	C₂²⋊C₄	—	8	2	no	—
218	C₂²⋊C₄	—	188	4	no	—
219	C₁₆	—	94	4	no	—
220	C₂³	—	2	1	no	—
221	C₂³	—	2	2	no	—
222	C₂³	—	2	1	no	—
223	C₂³	—	2	2	no	—
224	C₂³	#13093944	1	2	yes	—
225	C₂³	C₂×#10625334	1	1	yes	characteristic
226	Q₈	—	376	2	no	—
227	Q₈	—	188	2	no	—
228	Q₈	—	188	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	4	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	8	2	no	—
234	C₂×C₄	—	8	2	no	—
235	C₂×C₄	—	8	2	no	—
236	C₂×C₄	—	376	1	no	—
237	C₂×C₄	—	376	1	no	—
238	C₂×C₄	—	376	2	no	—
239	C₂×C₄	—	188	2	no	—
240	C₂×C₄	—	188	2	no	—
241	C₂×C₄	#13093944	1	2	yes	—
242	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
243	C₂×C₄	#13093996	1	2	yes	—
244	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
245	C₂×C₄	#13094044	1	2	yes	—
246	C₈	—	2	2	no	—
247	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
248	C₈	#13093994	1	1	yes	characteristic
249	C₈	#13094008	1	1	yes	characteristic
250	C₂²	—	2	2	no	—
251	C₂²	—	2	2	no	—
252	C₂²	—	2	2	no	—
253	C₂²	—	4	2	no	—
254	C₂²	—	4	2	no	—
255	C₂²	C₂×#13093944	1	1	yes	characteristic
256	C₂²	#15689357	1	2	yes	—
257	C₂²	#15689559	1	1	yes	characteristic
258	C₂²	#15689563	1	2	yes	—
259	C₂²	#15689564	1	1	yes	characteristic
260	C₄	—	2	2	no	—
261	C₄	—	16	2	no	—
262	C₄	—	376	2	no	—
263	C₄	—	376	2	no	—
264	C₄	#15689000	1	1	yes	characteristic
265	C₄	#15689117	1	1	yes	characteristic
266	C₄	#15689354	1	2	yes	—
267	C₂	—	4	2	no	—
268	C₂	#20243814	1	1	yes	characteristic
269	C₂	#20245098	1	1	yes	characteristic
270	C₂	#20245107	1	1	yes	characteristic
271	C₂	#20245494	1	2	yes	—
272	C₂	#20245499	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#13093964

C₂

yes

maximal, characteristic

C₂×#15689364

C₂

yes

maximal, characteristic

C₂×#15688926

C₂

yes

maximal, complemented

#20241479

C₂

yes

maximal, complemented

C₄₇×#1808

C₂

yes

maximal, characteristic

C₂²×Dic₁₈₈

C₂²

yes

—

—

—

C₂²×C₄₇⋊C₁₆

C₂²

yes

—

#15689364

—

#15689364

C₄

yes

complemented

C₂×#13093958

C₂²

yes

characteristic

C₂×#13093949

—

#15688926

—

C₂³×C₈×C₄₇

C₂²

yes

characteristic

C₂×#107×C₄₇

C₂²

yes

—

C₄₇×#380

—

C₄₇×#340

—

C₂²×Dic₉₄

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

C₂×C₄

yes

—

#13094003

—

#13094003

—

C₂×C₄⋊Dic₄₇

—

C₂×Dic₄₇⋊C₄

—

C₂×C₂²⋊Dic₄₇

—

#13093964

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

D₄

yes

—

#13093958

—

#13093958

C₂×C₄

yes

—

#13093949

—

C₂³×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₂×C₄

yes

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

—

#107×C₄₇

—

#107×C₄₇

—

#95×C₄₇

—

C₂⁴×C₄₇

D₈

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

D₈

yes

characteristic

C₂²×C₄×C₄₇

SD₁₆

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

#41

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#102

yes

—

C₂³×C₄₇

C₂×D₈

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#102

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

100

C₂×C₄×C₄₇

#135

yes

—

101

C₂×Dic₄₇

—

102

C₂×Dic₄₇

—

103

C₂×Dic₄₇

—

104

C₂×Dic₄₇

—

105

C₂×Dic₄₇

—

106

Dic₉₄

—

107

Dic₉₄

—

108

Dic₉₄

—

109

C₈×C₄₇

—

110

C₈×C₄₇

C₄×D₄

yes

—

111

C₈×C₄₇

#120

yes

characteristic

112

C₈×C₄₇

yes

113

—

114

C₂²×C₄₇

—

115

C₂²×C₄₇

—

116

C₂²×C₄₇

—

117

C₂²×C₄₇

—

118

C₂²×C₄₇

—

119

C₂²×C₄₇

C₂×#102

yes

characteristic

120

C₂²×C₄₇

#466

yes

—

121

C₂²×C₄₇

#509

yes

characteristic

122

C₂²×C₄₇

#510

yes

—

123

C₂²×C₄₇

#510

yes

characteristic

124

C₄×C₄₇

—

125

C₄×C₄₇

—

126

C₄×C₄₇

#386

yes

characteristic

127

C₄×C₄₇

#416

yes

characteristic

128

C₄×C₄₇

#465

yes

—

129

Dic₄₇

—

130

Dic₄₇

—

131

C₂²×M₃₂

—

132

C₂×#467

—

133

C₂×#358

—

134

#1808

D₄₇

yes

characteristic

135

#1380

—

136

C₂×C₄₇

—

137

C₂×C₄₇

#1893

yes

characteristic

138

C₂×C₄₇

#2139

yes

characteristic

139

C₂×C₄₇

#2141

yes

characteristic

140

C₂×C₄₇

#2219

yes

—

141

C₂×C₄₇

#2220

yes

—

142

C₂²×Q₁₆

—

143

C₂³×C₈

C₂×D₄₇

yes

characteristic

144

C₂×C₂²⋊Q₈

—

145

C₂×M₃₂

—

146

C₂×M₃₂

—

147

C₂²×C₁₆

—

148

#467

—

149

#467

—

150

C₂×#107

—

151

C₂×#107

C₂×D₄₇

yes

—

152

C₂×#103

—

153

#380

—

154

#358

—

155

#340

—

156

C₄₇

#13062

yes

characteristic, complemented, Sylow

157

C₂²×Q₈

—

158

C₂³×C₄

C₂²⋊D₄₇

yes

characteristic

159

C₂×Q₁₆

—

160

C₂×Q₁₆

—

161

C₂×Q₁₆

—

162

C₂×Q₁₆

—

163

C₂²×C₈

—

164

C₂²×C₈

—

165

C₂²×C₈

C₄×D₄₇

yes

—

166

C₂²×C₈

D₁₈₈

yes

—

167

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

168

C₂²×C₈

C₂²×D₄₇

yes

characteristic

169

C₂²⋊Q₈

—

170

C₂²⋊Q₈

—

188

—

171

C₂×C₄⋊C₄

—

172

C₂×C₄⋊C₄

—

173

C₂×C₄⋊C₄

—

188

—

174

C₂×C₂²⋊C₄

—

175

C₂×C₂²⋊C₄

—

188

—

176

M₃₂

—

177

C₂×C₁₆

—

178

C₂×C₁₆

—

179

C₂×C₁₆

—

180

#107

—

181

#107

—

182

#107

—

183

#107

—

184

#103

—

185

#95

—

186

C₂⁴

#10625334

yes

characteristic

187

C₂×Q₈

—

188

C₂×Q₈

—

188

—

189

C₂×Q₈

—

188

—

190

C₂×Q₈

—

188

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

188

—

195

C₂²×C₄

—

188

—

196

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

197

C₂²×C₄

#10625334

yes

characteristic

198

C₂²×C₄

#10625336

yes

—

199

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

200

Q₁₆

—

201

Q₁₆

—

188

—

202

Q₁₆

—

188

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

208

C₂×C₈

C₂×C₄×D₄₇

yes

characteristic

209

C₂×C₈

C₂×D₁₈₈

yes

characteristic

210

C₂×C₈

D₄×D₄₇

yes

—

211

C₂×C₈

#10625352

yes

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

188

—

216

C₄⋊C₄

—

188

—

217

C₂²⋊C₄

—

218

C₂²⋊C₄

—

188

—

219

C₁₆

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

#13093944

yes

—

225

C₂³

C₂×#10625334

yes

characteristic

226

Q₈

—

376

—

227

Q₈

—

188

—

228

Q₈

—

188

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

376

—

237

C₂×C₄

—

376

—

238

C₂×C₄

—

376

—

239

C₂×C₄

—

188

—

240

C₂×C₄

—

188

—

241

C₂×C₄

#13093944

yes

—

242

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

243

C₂×C₄

#13093996

yes

—

244

C₂×C₄

C₂×#10625336

yes

characteristic

245

C₂×C₄

#13094044

yes

—

246

C₈

—

247

C₈

(C₂²⋊D₄₇)⋊C₄

yes

—

248

C₈

#13093994

yes

characteristic

249

C₈

#13094008

yes

characteristic

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

C₂×#13093944

yes

characteristic

256

C₂²

#15689357

yes

—

257

C₂²

#15689559

yes

characteristic

258

C₂²

#15689563

yes

—

259

C₂²

#15689564

yes

characteristic

260

C₄

—

261

C₄

—

262

C₄

—

376

—

263

C₄

—

376

—

264

C₄

#15689000

yes

characteristic

265

C₄

#15689117

yes

characteristic

266

C₄

#15689354

yes

—

267

C₂

—

268

C₂

#20243814

yes

characteristic

269

C₂

#20245098

yes

characteristic

270

C₂

#20245107

yes

characteristic

271

C₂

#20245494

yes

—

272

C₂

#20245499

yes

—

	subgroup	G/H
center	C₂³	C₂×#10625334
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#1808	C₂
socle	C₂³×C₄₇	C₂×D₈
prime radical	C₂⁴×C₄₇	D₈
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#1808	D₄₇
hypocenter	C₄₇	#13062
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1808

subgroup

G/H

center

C₂³

C₂×#10625334

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₄₇×#1808

C₂

socle

C₂³×C₄₇

C₂×D₈

prime radical

C₂⁴×C₄₇

D₈

cosocle

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1808

N	H ≅ G/N	type
3. C₂×#15688926	C₂	semidirect
4. #20241479	C₂	semidirect
12. #15689364	C₄	semidirect
156. C₄₇	#13062	semidirect

H ≅ G/N

type

3. C₂×#15688926

C₂

semidirect

4. #20241479

C₂

semidirect

12. #15689364

C₄

semidirect

156. C₄₇

#13062

semidirect

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

subgroup	index
C₂²×#13093964	2
C₂×#15689364	2
C₂×#15688926	2
#20241479	2
C₄₇×#1808	2
#13062	47

subgroup

index

C₄₇×#1808

Subgroups — #26133653

Conjugacy classes of subgroups

Complements

Maximal subgroups