Group #26115397 — subgroups

Subgroups — #26115397

Order 12032.

590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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	#20243505	C₂	1	1	yes	maximal, characteristic, complemented
2	#20243241	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15688869	C₂	1	2	yes	maximal, complemented
4	C₂×#15688867	C₂	1	2	yes	maximal
5	C₄₇×#2858	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
8	C₂×#13093935	—	2	1	no	—
9	#15688878	—	2	1	no	—
10	#15688878	—	2	2	no	—
11	#15688869	—	2	4	no	—
12	#15688867	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₇	—	2	2	no	—
16	C₄₇×#390	—	2	1	no	—
17	C₄₇×#390	—	2	1	no	—
18	C₄₇×#390	C₄	1	4	yes	—
19	C₄³×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄₇⋊C₈	—	2	2	no	—
21	C₂²×C₄₇⋊C₈	—	2	2	no	—
22	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
23	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
24	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
25	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
26	#13093935	—	4	2	no	—
27	C₂²×Q₈×C₄₇	—	2	1	no	—
28	C₂²×D₄×C₄₇	—	2	1	no	—
29	C₂²×D₄×C₄₇	—	2	1	no	—
30	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
31	C₄⋊Q₈×C₄₇	—	2	2	no	—
32	C₄⋊Q₈×C₄₇	—	2	2	no	—
33	#127×C₄₇	—	2	2	no	—
34	#127×C₄₇	—	2	2	no	—
35	#124×C₄₇	—	4	8	no	—
36	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
37	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
38	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
39	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
40	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₄₇	D₄	1	2	yes	—
42	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
45	C₂⁴×C₄₇	—	2	2	no	—
46	C₂×Q₈×C₄₇	—	4	1	no	—
47	C₂×Q₈×C₄₇	—	4	1	no	—
48	C₂×Q₈×C₄₇	—	4	4	no	—
49	C₂×D₄×C₄₇	—	2	4	no	—
50	C₂×D₄×C₄₇	—	4	4	no	—
51	C₂×D₄×C₄₇	—	4	2	no	—
52	C₂×D₄×C₄₇	—	4	1	no	—
53	C₂×D₄×C₄₇	—	4	1	no	—
54	C₂×D₄×C₄₇	—	4	2	no	—
55	C₂×D₄×C₄₇	—	4	4	no	—
56	C₂×D₄×C₄₇	—	4	1	no	—
57	C₂×D₄×C₄₇	—	4	1	no	—
58	C₂²×C₄×C₄₇	—	2	2	no	—
59	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
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	—	4	2	no	—
66	C₂²⋊C₄×C₄₇	—	4	8	no	—
67	C₂²⋊C₄×C₄₇	—	4	8	no	—
68	C₄²×C₄₇	—	2	2	no	—
69	C₄²×C₄₇	—	2	4	no	—
70	C₄²×C₄₇	—	2	1	no	—
71	C₄²×C₄₇	—	2	1	no	—
72	C₄²×C₄₇	—	4	2	no	—
73	C₄²×C₄₇	C₂×D₄	1	2	yes	—
74	C₄²×C₄₇	#41	1	2	yes	—
75	C₂×C₄₇⋊C₈	—	2	4	no	—
76	C₂×C₄₇⋊C₈	—	4	2	no	—
77	C₂×C₄₇⋊C₈	—	4	2	no	—
78	C₂×C₄₇⋊C₈	—	4	2	no	—
79	C₂×C₄₇⋊C₈	—	4	4	no	—
80	C₂³×C₄₇	—	4	2	no	—
81	C₂³×C₄₇	—	4	4	no	—
82	C₂³×C₄₇	—	4	2	no	—
83	C₂³×C₄₇	—	4	2	no	—
84	C₂³×C₄₇	—	4	4	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	—	8	4	no	—
89	D₄×C₄₇	—	8	2	no	—
90	D₄×C₄₇	—	8	2	no	—
91	D₄×C₄₇	—	8	2	no	—
92	D₄×C₄₇	—	8	2	no	—
93	C₂×C₄×C₄₇	—	2	2	no	—
94	C₂×C₄×C₄₇	—	2	2	no	—
95	C₂×C₄×C₄₇	—	2	2	no	—
96	C₂×C₄×C₄₇	—	2	2	no	—
97	C₂×C₄×C₄₇	—	2	2	no	—
98	C₂×C₄×C₄₇	—	2	2	no	—
99	C₂×C₄×C₄₇	—	2	2	no	—
100	C₂×C₄×C₄₇	—	4	2	no	—
101	C₂×C₄×C₄₇	—	4	4	no	—
102	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
103	C₂×C₄×C₄₇	#121	1	2	yes	—
104	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
105	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
106	C₂×C₄×C₄₇	#135	1	2	yes	—
107	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
108	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
109	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
110	C₄₇⋊C₈	—	4	4	no	—
111	C₄₇⋊C₈	—	8	2	no	—
112	#9710	—	47	1	no	maximal, Sylow
113	C₂²×C₄₇	—	8	4	no	—
114	C₂²×C₄₇	—	8	4	no	—
115	C₂²×C₄₇	—	8	2	no	—
116	C₂²×C₄₇	—	8	2	no	—
117	C₂²×C₄₇	—	8	2	no	—
118	C₂²×C₄₇	#390	1	1	yes	characteristic
119	C₂²×C₄₇	#413	1	2	yes	—
120	C₂²×C₄₇	#416	1	1	yes	characteristic
121	C₂²×C₄₇	#417	1	1	yes	characteristic
122	C₂²×C₄₇	#418	1	2	yes	—
123	C₄×C₄₇	—	2	2	no	—
124	C₄×C₄₇	—	4	2	no	—
125	C₄×C₄₇	—	4	2	no	—
126	C₄×C₄₇	—	8	2	no	—
127	C₄×C₄₇	#463	1	2	yes	—
128	C₄×C₄₇	#464	1	2	yes	—
129	C₄×C₄₇	#490	1	2	yes	—
130	C₄×C₄₇	#496	1	2	yes	—
131	#2858	D₄₇	1	1	yes	characteristic
132	#1831	—	47	1	no	—
133	#1767	—	47	1	no	—
134	C₂×#332	—	47	2	no	—
135	C₂×#331	—	47	2	no	—
136	C₂×C₄₇	—	16	2	no	—
137	C₂×C₄₇	#1553	1	2	yes	—
138	C₂×C₄₇	#1557	1	2	yes	—
139	C₂×C₄₇	#1961	1	1	yes	characteristic
140	C₂×C₄₇	#1967	1	1	yes	characteristic
141	C₂×C₄₇	#1983	1	1	yes	characteristic
142	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
143	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
144	C₂×#124	—	2	2	no	—
145	C₂×C₄⋊C₈	—	47	2	no	—
146	C₂×C₄⋊C₈	—	47	2	no	—
147	C₂×#97	—	94	1	no	—
148	#390	—	2	1	no	—
149	#390	—	2	1	no	—
150	#390	Dic₄₇	1	4	yes	—
151	C₄³	C₂×D₄₇	1	1	yes	characteristic
152	#336	—	94	2	no	—
153	#336	—	94	1	no	—
154	#332	—	94	4	no	—
155	#331	—	94	4	no	—
156	C₄₇	#9710	1	1	yes	characteristic, complemented, Sylow
157	C₂²×Q₈	—	2	1	no	—
158	C₂²×D₄	—	2	1	no	—
159	C₂²×D₄	—	2	1	no	—
160	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
161	C₂²×C₈	—	94	2	no	—
162	C₂²×C₈	—	94	2	no	—
163	C₄⋊Q₈	—	2	2	no	—
164	C₄⋊Q₈	—	2	2	no	—
165	#127	—	2	2	no	—
166	#127	—	2	2	no	—
167	#124	—	4	8	no	—
168	C₂×C₄⋊C₄	—	2	1	no	—
169	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
170	C₂×C₂²⋊C₄	—	2	4	no	—
171	C₂×C₂²⋊C₄	—	2	4	no	—
172	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
173	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
174	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
175	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
176	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
177	C₄⋊C₈	—	47	4	no	—
178	C₄⋊C₈	—	94	2	no	—
179	C₄⋊C₈	—	94	2	no	—
180	C₄⋊C₈	—	94	2	no	—
181	#97	—	188	2	no	—
182	C₂⁴	—	2	2	no	—
183	C₂×Q₈	—	4	1	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	—	4	4	no	—
186	C₂×D₄	—	2	4	no	—
187	C₂×D₄	—	4	4	no	—
188	C₂×D₄	—	4	2	no	—
189	C₂×D₄	—	4	1	no	—
190	C₂×D₄	—	4	1	no	—
191	C₂×D₄	—	4	2	no	—
192	C₂×D₄	—	4	1	no	—
193	C₂×D₄	—	4	4	no	—
194	C₂×D₄	—	4	1	no	—
195	C₂²×C₄	—	2	2	no	—
196	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
197	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
198	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
199	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
200	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
201	C₂×C₈	—	94	4	no	—
202	C₂×C₈	—	188	2	no	—
203	C₂×C₈	—	188	4	no	—
204	C₂×C₈	—	188	2	no	—
205	C₂×C₈	—	188	2	no	—
206	C₄⋊C₄	—	2	4	no	—
207	C₄⋊C₄	—	4	2	no	—
208	C₂²⋊C₄	—	4	8	no	—
209	C₂²⋊C₄	—	4	8	no	—
210	C₄²	—	2	2	no	—
211	C₄²	—	2	1	no	—
212	C₄²	—	2	4	no	—
213	C₄²	—	2	1	no	—
214	C₄²	—	4	2	no	—
215	C₄²	D₄×D₄₇	1	2	yes	—
216	C₄²	#10625352	1	2	yes	—
217	C₂³	—	4	2	no	—
218	C₂³	—	4	4	no	—
219	C₂³	—	4	2	no	—
220	C₂³	—	4	2	no	—
221	C₂³	—	4	4	no	—
222	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
223	Q₈	—	8	2	no	—
224	Q₈	—	8	2	no	—
225	D₄	—	8	4	no	—
226	D₄	—	8	2	no	—
227	D₄	—	8	2	no	—
228	D₄	—	8	2	no	—
229	D₄	—	8	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	4	4	no	—
239	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
240	C₂×C₄	#13093995	1	2	yes	—
241	C₂×C₄	#13094011	1	1	yes	characteristic
242	C₂×C₄	#13094020	1	1	yes	characteristic
243	C₂×C₄	#13094044	1	2	yes	—
244	C₂×C₄	#13094049	1	1	yes	characteristic
245	C₂×C₄	#13094050	1	4	yes	—
246	C₂×C₄	#13094054	1	1	yes	characteristic
247	C₈	—	376	2	no	—
248	C₈	—	188	4	no	—
249	C₂²	—	8	2	no	—
250	C₂²	—	8	2	no	—
251	C₂²	—	8	4	no	—
252	C₂²	—	8	4	no	—
253	C₂²	—	8	2	no	—
254	C₂²	#15689026	1	1	yes	characteristic
255	C₂²	#15689107	1	2	yes	—
256	C₂²	#15689119	1	1	yes	characteristic
257	C₂²	#15689124	1	1	yes	characteristic
258	C₂²	#15689128	1	2	yes	—
259	C₄	—	2	2	no	—
260	C₄	—	4	2	no	—
261	C₄	—	4	2	no	—
262	C₄	—	8	2	no	—
263	C₄	#15689335	1	2	yes	—
264	C₄	#15689342	1	2	yes	—
265	C₄	#15689487	1	2	yes	—
266	C₄	#15689510	1	2	yes	—
267	C₂	—	16	2	no	—
268	C₂	#20242093	1	2	yes	—
269	C₂	#20242110	1	2	yes	—
270	C₂	#20244213	1	1	yes	characteristic
271	C₂	#20244238	1	1	yes	characteristic
272	C₂	#20244321	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20243505

C₂

yes

maximal, characteristic, complemented

#20243241

C₂

yes

maximal, characteristic, complemented

C₂×#15688869

C₂

yes

maximal, complemented

C₂×#15688867

C₂

yes

maximal

C₄₇×#2858

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

—

—

—

—

—

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₂×#127×C₄₇

C₂²

yes

characteristic

C₂×#124×C₄₇

—

C₄₇×#390

—

C₄₇×#390

—

C₄₇×#390

C₄

yes

—

C₄³×C₄₇

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

#13093935

—

C₂²×Q₈×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

C₂×C₄

yes

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

#127×C₄₇

—

#127×C₄₇

—

#124×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₂⁴×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

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

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

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

—

D₄×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

—

100

C₂×C₄×C₄₇

—

101

C₂×C₄×C₄₇

—

102

C₂×C₄×C₄₇

C₄×D₄

yes

—

103

C₂×C₄×C₄₇

#121

yes

—

104

C₂×C₄×C₄₇

#124

yes

characteristic

105

C₂×C₄×C₄₇

#127

yes

characteristic

106

C₂×C₄×C₄₇

#135

yes

—

107

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

characteristic

108

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

109

C₂×C₄×C₄₇

#137

yes

characteristic

110

C₄₇⋊C₈

—

111

C₄₇⋊C₈

—

112

#9710

—

maximal, Sylow

113

C₂²×C₄₇

—

114

C₂²×C₄₇

—

115

C₂²×C₄₇

—

116

C₂²×C₄₇

—

117

C₂²×C₄₇

—

118

C₂²×C₄₇

#390

yes

characteristic

119

C₂²×C₄₇

#413

yes

—

120

C₂²×C₄₇

#416

yes

characteristic

121

C₂²×C₄₇

#417

yes

characteristic

122

C₂²×C₄₇

#418

yes

—

123

C₄×C₄₇

—

124

C₄×C₄₇

—

125

C₄×C₄₇

—

126

C₄×C₄₇

—

127

C₄×C₄₇

#463

yes

—

128

C₄×C₄₇

#464

yes

—

129

C₄×C₄₇

#490

yes

—

130

C₄×C₄₇

#496

yes

—

131

#2858

D₄₇

yes

characteristic

132

#1831

—

133

#1767

—

134

C₂×#332

—

135

C₂×#331

—

136

C₂×C₄₇

—

137

C₂×C₄₇

#1553

yes

—

138

C₂×C₄₇

#1557

yes

—

139

C₂×C₄₇

#1961

yes

characteristic

140

C₂×C₄₇

#1967

yes

characteristic

141

C₂×C₄₇

#1983

yes

characteristic

142

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

143

C₂×#127

C₂×D₄₇

yes

characteristic

144

C₂×#124

—

145

C₂×C₄⋊C₈

—

146

C₂×C₄⋊C₈

—

147

C₂×#97

—

148

#390

—

149

#390

—

150

#390

Dic₄₇

yes

—

151

C₄³

C₂×D₄₇

yes

characteristic

152

#336

—

153

#336

—

154

#332

—

155

#331

—

156

C₄₇

#9710

yes

characteristic, complemented, Sylow

157

C₂²×Q₈

—

158

C₂²×D₄

—

159

C₂²×D₄

—

160

C₂²×D₄

C₂×Dic₄₇

yes

—

161

C₂²×C₈

—

162

C₂²×C₈

—

163

C₄⋊Q₈

—

164

C₄⋊Q₈

—

165

#127

—

166

#127

—

167

#124

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

C₂×Dic₄₇

yes

—

170

C₂×C₂²⋊C₄

—

171

C₂×C₂²⋊C₄

—

172

C₂×C₄²

C₂×Dic₄₇

yes

—

173

C₂×C₄²

C₂²⋊D₄₇

yes

—

174

C₂×C₄²

C₂²⋊D₄₇

yes

characteristic

175

C₂×C₄²

C₂²⋊D₄₇

yes

characteristic

176

C₂×C₄²

C₂²×D₄₇

yes

characteristic

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

#97

—

188

—

182

C₂⁴

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂²×C₄

—

196

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

197

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

198

C₂²×C₄

C₂²×Dic₄₇

yes

characteristic

199

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

200

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

201

C₂×C₈

—

202

C₂×C₈

—

188

—

203

C₂×C₈

—

188

—

204

C₂×C₈

—

188

—

205

C₂×C₈

—

188

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₂²⋊C₄

—

209

C₂²⋊C₄

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₄²

—

215

C₄²

D₄×D₄₇

yes

—

216

C₄²

#10625352

yes

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

C₂×C₂²⋊Dic₄₇

yes

characteristic

223

Q₈

—

224

Q₈

—

225

D₄

—

226

D₄

—

227

D₄

—

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

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

D₄×Dic₄₇

yes

—

240

C₂×C₄

#13093995

yes

—

241

C₂×C₄

#13094011

yes

characteristic

242

C₂×C₄

#13094020

yes

characteristic

243

C₂×C₄

#13094044

yes

—

244

C₂×C₄

#13094049

yes

characteristic

245

C₂×C₄

#13094050

yes

—

246

C₂×C₄

#13094054

yes

characteristic

247

C₈

—

376

—

248

C₈

—

188

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

#15689026

yes

characteristic

255

C₂²

#15689107

yes

—

256

C₂²

#15689119

yes

characteristic

257

C₂²

#15689124

yes

characteristic

258

C₂²

#15689128

yes

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

#15689335

yes

—

264

C₄

#15689342

yes

—

265

C₄

#15689487

yes

—

266

C₄

#15689510

yes

—

267

C₂

—

268

C₂

#20242093

yes

—

269

C₂

#20242110

yes

—

270

C₂

#20244213

yes

characteristic

271

C₂

#20244238

yes

characteristic

272

C₂

#20244321

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#2858	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂×#127×C₄₇	C₂²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#2858	D₄₇
hypocenter	C₄₇	#9710
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2858

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₄₇

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#2858

C₂

socle

C₂³×C₄₇

C₂×C₂²⋊C₄

prime radical

C₂×#127×C₄₇

C₂²

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #2858

N	H ≅ G/N	type
1. #20243505	C₂	semidirect
2. #20243241	C₂	semidirect
3. C₂×#15688869	C₂	semidirect
156. C₄₇	#9710	semidirect

H ≅ G/N

type

1. #20243505

C₂

semidirect

2. #20243241

C₂

semidirect

3. C₂×#15688869

C₂

semidirect

156. C₄₇

#9710

semidirect

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

subgroup	index
#20243505	2
#20243241	2
C₂×#15688869	2
C₂×#15688867	2
C₄₇×#2858	2
#9710	47

subgroup

index

C₄₇×#2858

Subgroups — #26115397

Conjugacy classes of subgroups

Complements

Maximal subgroups