Group #26113694 — subgroups

Subgroups — #26113694

Order 12032.

570 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 123 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	#20252429	C₂	1	1	yes	maximal, characteristic
2	#20243380	C₂	1	1	yes	maximal, characteristic
3	#20242073	C₂	1	2	yes	maximal, complemented
4	#20241291	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2542	C₂	1	1	yes	maximal, characteristic
6	#15689201	—	2	4	no	—
7	#15689176	C₂²	1	2	yes	—
8	#15689147	C₂²	1	2	yes	—
9	C₂×#13093941	—	2	1	no	—
10	#15689087	—	2	2	no	—
11	#15688892	—	2	1	no	—
12	#15688869	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
15	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#399	C₄	1	4	yes	—
17	C₄₇×#390	—	2	1	no	—
18	C₄₇×#384	—	2	1	no	—
19	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×#10625329	—	2	4	no	—
21	C₂×#10625329	—	2	2	no	—
22	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
23	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
24	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
25	#13093941	—	4	2	no	—
26	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
27	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
28	C₄×C₄₇⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₄₇	—	2	1	no	—
30	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₄₇	D₄	1	2	yes	—
32	C₄⋊Q₈×C₄₇	—	2	2	no	—
33	C₄⋊Q₈×C₄₇	—	2	2	no	—
34	C₂²⋊Q₈×C₄₇	—	4	8	no	—
35	C₄×D₄×C₄₇	—	2	2	no	—
36	C₄×D₄×C₄₇	—	2	2	no	—
37	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
38	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
39	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
40	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
41	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
43	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₄₇	—	2	1	no	—
45	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
46	#95×C₄₇	C₂×C₄	1	2	yes	—
47	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
48	C₂×Q₈×C₄₇	—	4	4	no	—
49	C₂×Q₈×C₄₇	—	4	1	no	—
50	C₂×Q₈×C₄₇	—	4	1	no	—
51	C₂×D₄×C₄₇	—	2	2	no	—
52	C₂×D₄×C₄₇	—	2	1	no	—
53	C₂×D₄×C₄₇	—	2	1	no	—
54	C₂×D₄×C₄₇	—	2	2	no	—
55	C₂²×C₄×C₄₇	—	2	2	no	—
56	C₂²×C₄×C₄₇	—	2	2	no	—
57	C₂²×C₄×C₄₇	—	2	2	no	—
58	C₂²×C₄×C₄₇	—	2	2	no	—
59	C₂²×C₄×C₄₇	—	4	4	no	—
60	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
64	C₄⋊C₄×C₄₇	—	2	4	no	—
65	C₄⋊C₄×C₄₇	—	2	2	no	—
66	C₄⋊C₄×C₄₇	—	2	4	no	—
67	C₄⋊C₄×C₄₇	—	4	8	no	—
68	C₄⋊C₄×C₄₇	—	4	2	no	—
69	C₂²⋊C₄×C₄₇	—	2	4	no	—
70	C₂²⋊C₄×C₄₇	—	4	8	no	—
71	C₄²×C₄₇	—	4	1	no	—
72	C₄²×C₄₇	—	4	1	no	—
73	C₄²×C₄₇	C₂×D₄	1	2	yes	—
74	C₄²×C₄₇	#41	1	2	yes	—
75	#10625329	—	4	2	no	—
76	#10625329	—	4	2	no	—
77	#10625329	—	8	4	no	—
78	C₂×C₄₇⋊C₈	—	2	4	no	—
79	C₂×C₄₇⋊C₈	—	4	2	no	—
80	C₂³×C₄₇	—	2	2	no	—
81	C₂³×C₄₇	—	2	2	no	—
82	C₂³×C₄₇	—	2	2	no	—
83	C₂³×C₄₇	—	4	2	no	—
84	C₂³×C₄₇	—	4	2	no	—
85	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	Q₈×C₄₇	—	8	2	no	—
87	Q₈×C₄₇	—	8	2	no	—
88	D₄×C₄₇	—	4	2	no	—
89	D₄×C₄₇	—	4	2	no	—
90	C₂×C₄×C₄₇	—	2	2	no	—
91	C₂×C₄×C₄₇	—	2	4	no	—
92	C₂×C₄×C₄₇	—	2	2	no	—
93	C₂×C₄×C₄₇	—	4	1	no	—
94	C₂×C₄×C₄₇	—	4	2	no	—
95	C₂×C₄×C₄₇	—	4	2	no	—
96	C₂×C₄×C₄₇	—	4	4	no	—
97	C₂×C₄×C₄₇	—	4	2	no	—
98	C₂×C₄×C₄₇	—	4	4	no	—
99	C₂×C₄×C₄₇	—	4	2	no	—
100	C₂×C₄×C₄₇	—	8	2	no	—
101	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
102	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
103	C₂×C₄×C₄₇	#121	1	2	yes	—
104	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
105	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
106	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
107	C₂×C₄×C₄₇	#137	1	2	yes	—
108	C₄₇⋊C₈	—	4	4	no	—
109	C₄₇⋊C₈	—	8	2	no	—
110	#9403	—	47	1	no	maximal, Sylow
111	C₂²×C₄₇	—	2	1	no	—
112	C₂²×C₄₇	—	2	1	no	—
113	C₂²×C₄₇	—	4	4	no	—
114	C₂²×C₄₇	—	4	2	no	—
115	C₂²×C₄₇	—	4	2	no	—
116	C₂²×C₄₇	—	4	2	no	—
117	C₂²×C₄₇	—	8	2	no	—
118	C₂²×C₄₇	#386	1	1	yes	characteristic
119	C₂²×C₄₇	#417	1	1	yes	characteristic
120	C₂²×C₄₇	#419	1	1	yes	characteristic
121	C₄×C₄₇	—	2	1	no	—
122	C₄×C₄₇	—	2	2	no	—
123	C₄×C₄₇	—	4	4	no	—
124	C₄×C₄₇	—	4	2	no	—
125	C₄×C₄₇	—	8	2	no	—
126	C₄×C₄₇	#453	1	2	yes	—
127	C₄×C₄₇	#468	1	2	yes	—
128	C₄×C₄₇	#470	1	2	yes	—
129	#2975	—	47	1	no	—
130	#2542	D₄₇	1	1	yes	characteristic
131	#1800	—	47	1	no	—
132	#1549	—	47	2	no	—
133	#1303	—	47	2	no	—
134	C₂×C₄₇	—	2	1	no	—
135	C₂×C₄₇	—	2	1	no	—
136	C₂×C₄₇	—	8	2	no	—
137	C₂×C₄₇	#1887	1	1	yes	characteristic
138	C₂×C₄₇	#1894	1	1	yes	characteristic
139	C₂×C₄₇	#1915	1	1	yes	characteristic
140	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
141	C₂×C₂²⋊Q₈	—	2	2	no	—
142	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
143	#436	—	94	4	no	—
144	#431	—	47	2	no	—
145	#423	—	47	2	no	—
146	C₂×#100	—	94	1	no	—
147	#407	—	94	2	no	—
148	#399	Dic₄₇	1	4	yes	—
149	#390	—	2	1	no	—
150	#384	—	2	1	no	—
151	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
152	#343	—	94	1	no	—
153	#332	—	94	4	no	—
154	C₄₇	#9403	1	1	yes	characteristic, complemented, Sylow
155	C₂²×Q₈	—	2	1	no	—
156	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
157	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
158	C₂×M₁₆	—	94	4	no	—
159	C₂×M₁₆	—	94	2	no	—
160	C₄⋊Q₈	—	2	2	no	—
161	C₄⋊Q₈	—	2	2	no	—
162	C₂²⋊Q₈	—	4	8	no	—
163	C₄×D₄	—	2	2	no	—
164	C₄×D₄	—	2	2	no	—
165	C₂×C₄⋊C₄	—	2	1	no	—
166	C₂×C₄⋊C₄	—	2	4	no	—
167	C₂×C₄⋊C₄	—	2	1	no	—
168	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
169	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
170	C₂×C₂²⋊C₄	—	2	4	no	—
171	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
172	C₂×C₄²	—	2	1	no	—
173	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
174	C₄⋊C₈	—	47	4	no	—
175	C₄⋊C₈	—	94	2	no	—
176	C₄⋊C₈	—	94	2	no	—
177	#100	—	188	2	no	—
178	C₂²⋊C₈	—	94	4	no	—
179	C₂²⋊C₈	—	94	2	no	—
180	C₄×C₈	—	94	2	no	—
181	#95	C₂×Dic₄₇	1	2	yes	—
182	C₂⁴	C₂²⋊Dic₄₇	1	2	yes	—
183	C₂×Q₈	—	4	4	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	—	4	1	no	—
186	C₂×D₄	—	2	2	no	—
187	C₂×D₄	—	2	1	no	—
188	C₂×D₄	—	2	1	no	—
189	C₂×D₄	—	2	2	no	—
190	C₂²×C₄	—	2	2	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	4	4	no	—
195	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
196	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
197	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
198	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
199	M₁₆	—	376	4	no	—
200	M₁₆	—	188	2	no	—
201	M₁₆	—	188	2	no	—
202	C₂×C₈	—	94	4	no	—
203	C₂×C₈	—	188	2	no	—
204	C₄⋊C₄	—	2	4	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	2	4	no	—
207	C₄⋊C₄	—	4	8	no	—
208	C₄⋊C₄	—	4	2	no	—
209	C₂²⋊C₄	—	2	4	no	—
210	C₂²⋊C₄	—	4	8	no	—
211	C₄²	—	4	1	no	—
212	C₄²	—	4	1	no	—
213	C₄²	D₄×D₄₇	1	2	yes	—
214	C₄²	#10625352	1	2	yes	—
215	C₂³	—	2	2	no	—
216	C₂³	—	2	2	no	—
217	C₂³	—	2	2	no	—
218	C₂³	—	4	2	no	—
219	C₂³	—	4	2	no	—
220	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
221	Q₈	—	8	2	no	—
222	Q₈	—	8	2	no	—
223	D₄	—	4	2	no	—
224	D₄	—	4	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	4	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	4	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	4	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	8	2	no	—
236	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
237	C₂×C₄	#13093992	1	1	yes	characteristic
238	C₂×C₄	#13093996	1	2	yes	—
239	C₂×C₄	#13094005	1	1	yes	characteristic
240	C₂×C₄	#13094049	1	1	yes	characteristic
241	C₂×C₄	#13094054	1	1	yes	characteristic
242	C₂×C₄	#13094055	1	2	yes	—
243	C₈	—	376	2	no	—
244	C₈	—	188	4	no	—
245	C₂²	—	2	1	no	—
246	C₂²	—	2	1	no	—
247	C₂²	—	4	4	no	—
248	C₂²	—	4	2	no	—
249	C₂²	—	4	2	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	8	2	no	—
252	C₂²	#15689003	1	1	yes	characteristic
253	C₂²	#15689124	1	1	yes	characteristic
254	C₂²	#15689132	1	1	yes	characteristic
255	C₄	—	2	1	no	—
256	C₄	—	2	2	no	—
257	C₄	—	4	4	no	—
258	C₄	—	4	2	no	—
259	C₄	—	8	2	no	—
260	C₄	#15689290	1	2	yes	—
261	C₄	#15689371	1	2	yes	—
262	C₄	#15689379	1	2	yes	—
263	C₂	—	2	1	no	—
264	C₂	—	2	1	no	—
265	C₂	—	8	2	no	—
266	C₂	#20243787	1	1	yes	characteristic
267	C₂	#20243822	1	1	yes	characteristic
268	C₂	#20243941	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252429

C₂

yes

maximal, characteristic

#20243380

C₂

yes

maximal, characteristic

#20242073

C₂

yes

maximal, complemented

#20241291

C₂

yes

maximal, complemented

C₄₇×#2542

C₂

yes

maximal, characteristic

#15689201

—

#15689176

C₂²

yes

—

#15689147

C₂²

yes

—

—

—

—

—

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊Q₈×C₄₇

—

C₂×C₄×D₄×C₄₇

C₂²

yes

characteristic

C₄₇×#399

C₄

yes

—

C₄₇×#390

—

C₄₇×#384

—

C₄×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×#10625329

—

C₂×#10625329

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

#13093941

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

—

C₂²×Q₈×C₄₇

—

C₂²×D₄×C₄₇

D₄

yes

characteristic

C₂³×C₄×C₄₇

D₄

yes

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₂²⋊Q₈×C₄₇

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#95×C₄₇

C₂×C₄

yes

—

C₂⁴×C₄₇

C₂²⋊C₄

yes

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

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

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

#10625329

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

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

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

100

C₂×C₄×C₄₇

—

101

C₂×C₄×C₄₇

C₄×D₄

yes

—

102

C₂×C₄×C₄₇

#120

yes

characteristic

103

C₂×C₄×C₄₇

#121

yes

—

104

C₂×C₄×C₄₇

#123

yes

characteristic

105

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

characteristic

106

C₂×C₄×C₄₇

#137

yes

characteristic

107

C₂×C₄×C₄₇

#137

yes

—

108

C₄₇⋊C₈

—

109

C₄₇⋊C₈

—

110

#9403

—

maximal, Sylow

111

C₂²×C₄₇

—

112

C₂²×C₄₇

—

113

C₂²×C₄₇

—

114

C₂²×C₄₇

—

115

C₂²×C₄₇

—

116

C₂²×C₄₇

—

117

C₂²×C₄₇

—

118

C₂²×C₄₇

#386

yes

characteristic

119

C₂²×C₄₇

#417

yes

characteristic

120

C₂²×C₄₇

#419

yes

characteristic

121

C₄×C₄₇

—

122

C₄×C₄₇

—

123

C₄×C₄₇

—

124

C₄×C₄₇

—

125

C₄×C₄₇

—

126

C₄×C₄₇

#453

yes

—

127

C₄×C₄₇

#468

yes

—

128

C₄×C₄₇

#470

yes

—

129

#2975

—

130

#2542

D₄₇

yes

characteristic

131

#1800

—

132

#1549

—

133

#1303

—

134

C₂×C₄₇

—

135

C₂×C₄₇

—

136

C₂×C₄₇

—

137

C₂×C₄₇

#1887

yes

characteristic

138

C₂×C₄₇

#1894

yes

characteristic

139

C₂×C₄₇

#1915

yes

characteristic

140

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

141

C₂×C₂²⋊Q₈

—

142

C₂×C₄×D₄

C₂×D₄₇

yes

characteristic

143

#436

—

144

#431

—

145

#423

—

146

C₂×#100

—

147

#407

—

148

#399

Dic₄₇

yes

—

149

#390

—

150

#384

—

151

C₄×C₄⋊C₄

C₂×D₄₇

yes

characteristic

152

#343

—

153

#332

—

154

C₄₇

#9403

yes

characteristic, complemented, Sylow

155

C₂²×Q₈

—

156

C₂²×D₄

C₂²⋊D₄₇

yes

characteristic

157

C₂³×C₄

C₂²⋊D₄₇

yes

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

C₂²⋊Q₈

—

163

C₄×D₄

—

164

C₄×D₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

C₂×Dic₄₇

yes

—

169

C₂×C₄⋊C₄

C₂²⋊D₄₇

yes

characteristic

170

C₂×C₂²⋊C₄

—

171

C₂×C₂²⋊C₄

C₂×Dic₄₇

yes

—

172

C₂×C₄²

—

173

C₂×C₄²

C₂²×D₄₇

yes

characteristic

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

#100

—

188

—

178

C₂²⋊C₈

—

179

C₂²⋊C₈

—

180

C₄×C₈

—

181

#95

C₂×Dic₄₇

yes

—

182

C₂⁴

C₂²⋊Dic₄₇

yes

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

196

C₂²×C₄

C₂²×Dic₄₇

yes

characteristic

197

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

198

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

199

M₁₆

—

376

—

200

M₁₆

—

188

—

201

M₁₆

—

188

—

202

C₂×C₈

—

203

C₂×C₈

—

188

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₂²⋊C₄

—

210

C₂²⋊C₄

—

211

C₄²

—

212

C₄²

—

213

C₄²

D₄×D₄₇

yes

—

214

C₄²

#10625352

yes

—

215

C₂³

—

216

C₂³

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

C₂×C₂²⋊Dic₄₇

yes

characteristic

221

Q₈

—

222

Q₈

—

223

D₄

—

224

D₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

D₄×Dic₄₇

yes

—

237

C₂×C₄

#13093992

yes

characteristic

238

C₂×C₄

#13093996

yes

—

239

C₂×C₄

#13094005

yes

characteristic

240

C₂×C₄

#13094049

yes

characteristic

241

C₂×C₄

#13094054

yes

characteristic

242

C₂×C₄

#13094055

yes

—

243

C₈

—

376

—

244

C₈

—

188

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

#15689003

yes

characteristic

253

C₂²

#15689124

yes

characteristic

254

C₂²

#15689132

yes

characteristic

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

#15689290

yes

—

261

C₄

#15689371

yes

—

262

C₄

#15689379

yes

—

263

C₂

—

264

C₂

—

265

C₂

—

266

C₂

#20243787

yes

characteristic

267

C₂

#20243822

yes

characteristic

268

C₂

#20243941

yes

characteristic

	subgroup	G/H
center	C₂²	#15689003
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#2542	C₂
socle	C₂²×C₄₇	#386
prime radical	C₂²×D₄×C₄₇	D₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#2542	D₄₇
hypocenter	C₄₇	#9403
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2542

subgroup

G/H

center

C₂²

#15689003

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#2542

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 ◁ #2542

N	H ≅ G/N	type
3. #20242073	C₂	semidirect
4. #20241291	C₂	semidirect
154. C₄₇	#9403	semidirect

H ≅ G/N

type

3. #20242073

C₂

semidirect

4. #20241291

C₂

semidirect

154. C₄₇

#9403

semidirect

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

subgroup	index
#20252429	2
#20243380	2
#20242073	2
#20241291	2
C₄₇×#2542	2
#9403	47

subgroup

index

C₄₇×#2542

Subgroups — #26113694

Conjugacy classes of subgroups

Complements

Maximal subgroups