Group #26134754 — subgroups

Subgroups — #26134754

Order 12032.

514 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 147 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	C₂×#15689507	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15688926	C₂	1	2	yes	maximal, complemented
4	C₂×#15688923	C₂	1	2	yes	maximal
5	C₄×#107×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Dic₁₈₈	C₂²	1	1	yes	characteristic
7	C₂²×#10625325	—	2	1	no	—
8	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
9	C₂×#13094012	—	2	1	no	—
10	C₂²×C₄₇⋊C₁₆	C₂²	1	2	yes	—
11	#15689507	—	2	2	no	—
12	#15689507	C₄	1	4	yes	complemented
13	C₄⋊(C₄₇⋊C₁₆)	—	2	2	no	—
14	#15688926	—	2	4	no	—
15	#15688923	—	2	4	no	—
16	C₂×#107×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
19	C₄₇×#340	—	2	1	no	—
20	C₂²×Dic₉₄	—	2	1	no	—
21	C₂²×D₁₈₈	—	2	1	no	—
22	C₂×Dic₁₈₈	—	2	2	no	—
23	C₂×Dic₁₈₈	—	2	2	no	—
24	C₂×Dic₁₈₈	—	2	1	no	—
25	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
26	C₂×#10625325	—	2	4	no	—
27	C₂×#10625325	—	4	4	no	—
28	C₂×D₃₇₆	—	2	2	no	—
29	C₂×D₃₇₆	—	2	2	no	—
30	C₂×D₃₇₆	—	2	1	no	—
31	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
32	#13094012	—	2	4	no	—
33	#13094012	—	4	2	no	—
34	C₂×(C₂×D₄₇)⋊C₄	—	4	1	no	—
35	C₂×(C₂×D₄₇)⋊C₄	—	4	1	no	—
36	C₂×C₄₇⋊C₁₆	—	2	2	no	—
37	C₂×C₄₇⋊C₁₆	—	2	2	no	—
38	C₂×C₄₇⋊C₁₆	—	2	2	no	—
39	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
42	C₂×C₄²×C₄₇	—	4	1	no	—
43	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
44	#107×C₄₇	—	2	2	no	—
45	#107×C₄₇	D₄	1	4	yes	—
46	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
47	C₄×C₈×C₄₇	D₄	1	2	yes	—
48	#95×C₄₇	—	4	1	no	—
49	C₂³×D₄₇	—	4	1	no	—
50	C₂²×C₄×C₄₇	—	4	2	no	—
51	C₂²×C₄×C₄₇	D₈	1	1	yes	characteristic
52	C₂²×C₄×C₄₇	D₈	1	1	yes	characteristic
53	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
54	C₂²×Dic₄₇	—	4	1	no	—
55	C₂×D₁₈₈	—	2	2	no	—
56	C₂×D₁₈₈	—	4	2	no	—
57	C₂×D₁₈₈	—	4	2	no	—
58	C₂×D₁₈₈	—	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	C₂²⋊C₄	1	2	yes	—
65	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
67	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₂×C₈×C₄₇	#41	1	2	yes	—
69	C₄⋊C₄×C₄₇	—	2	4	no	—
70	C₄⋊C₄×C₄₇	—	4	2	no	—
71	C₄²×C₄₇	—	8	2	no	—
72	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
73	C₄²×C₄₇	SD₁₆	1	2	yes	—
74	(C₂×D₄₇)⋊C₄	—	4	4	no	—
75	(C₂×D₄₇)⋊C₄	—	4	4	no	—
76	Dic₁₈₈	—	2	4	no	—
77	Dic₁₈₈	—	4	1	no	—
78	Dic₁₈₈	—	4	1	no	—
79	D₃₇₆	—	2	4	no	—
80	D₃₇₆	—	4	1	no	—
81	D₃₇₆	—	4	1	no	—
82	#10625325	—	4	8	no	—
83	C₄₇⋊C₁₆	—	4	2	no	—
84	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
85	C₂²×D₄₇	—	4	2	no	—
86	C₂²×D₄₇	—	8	2	no	—
87	C₂²×D₄₇	—	8	2	no	—
88	C₂²×D₄₇	—	8	1	no	—
89	C₂²×D₄₇	—	8	1	no	—
90	C₂×C₄×C₄₇	—	2	2	no	—
91	C₂×C₄×C₄₇	—	2	1	no	—
92	C₂×C₄×C₄₇	—	2	1	no	—
93	C₂×C₄×C₄₇	—	4	4	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	#102	1	2	yes	—
98	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₄₇	#121	1	2	yes	—
100	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
101	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
102	C₂×Dic₄₇	—	4	2	no	—
103	C₂×Dic₄₇	—	8	2	no	—
104	D₁₈₈	—	4	2	no	—
105	D₁₈₈	—	4	2	no	—
106	D₁₈₈	—	8	2	no	—
107	Dic₉₄	—	4	2	no	—
108	Dic₉₄	—	4	2	no	—
109	Dic₉₄	—	8	2	no	—
110	C₈×C₄₇	—	2	2	no	—
111	C₈×C₄₇	C₄×D₄	1	2	yes	—
112	C₈×C₄₇	#124	1	1	yes	characteristic
113	C₈×C₄₇	#127	1	1	yes	characteristic
114	#13254	—	47	1	no	maximal, Sylow
115	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
116	C₂²×C₄₇	#459	1	2	yes	—
117	C₂²×C₄₇	#508	1	2	yes	—
118	C₂²×C₄₇	#509	1	1	yes	characteristic
119	C₂²×C₄₇	#510	1	1	yes	characteristic
120	C₂×D₄₇	—	8	2	no	—
121	C₂×D₄₇	—	8	2	no	—
122	C₂×D₄₇	—	8	2	no	—
123	C₂×D₄₇	—	16	2	no	—
124	C₂×D₄₇	—	16	2	no	—
125	C₄×C₄₇	—	2	2	no	—
126	C₄×C₄₇	—	2	2	no	—
127	C₄×C₄₇	—	8	4	no	—
128	C₄×C₄₇	#390	1	1	yes	characteristic
129	C₄×C₄₇	#418	1	1	yes	characteristic
130	C₄×C₄₇	#460	1	2	yes	—
131	Dic₄₇	—	8	2	no	—
132	C₂×#495	—	47	1	no	—
133	C₂×C₄⋊C₁₆	—	47	1	no	—
134	C₂×#358	—	47	2	no	—
135	C₂×#357	—	47	2	no	—
136	C₄×#107	D₄₇	1	1	yes	characteristic, complemented
137	C₂×C₄₇	#1982	1	1	yes	characteristic
138	C₂×C₄₇	#2138	1	1	yes	characteristic
139	C₂×C₄₇	#2139	1	1	yes	characteristic
140	C₂×C₄₇	#2210	1	2	yes	—
141	C₂×C₄₇	#2211	1	2	yes	—
142	D₄₇	—	16	2	no	—
143	C₂²×Q₁₆	—	47	1	no	—
144	C₂²×SD₁₆	—	94	1	no	—
145	C₂²×D₈	—	47	1	no	—
146	C₂×#124	—	94	1	no	—
147	C₂²×C₁₆	—	47	2	no	—
148	#495	—	47	4	no	—
149	#495	—	94	2	no	—
150	C₂×#107	C₂×D₄₇	1	2	yes	—
151	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
152	C₄×C₄⋊C₄	—	2	1	no	—
153	C₄⋊C₁₆	—	94	2	no	—
154	#358	—	94	4	no	—
155	#357	—	94	4	no	—
156	#340	—	2	1	no	—
157	C₄₇	#13254	1	1	yes	characteristic, complemented, Sylow
158	C₂²×Q₈	—	94	1	no	—
159	C₂²×D₄	—	94	1	no	—
160	C₂×Q₁₆	—	47	2	no	—
161	C₂×Q₁₆	—	94	2	no	—
162	C₂×Q₁₆	—	94	1	no	—
163	C₂×Q₁₆	—	94	2	no	—
164	C₂×SD₁₆	—	94	4	no	—
165	C₂×SD₁₆	—	188	4	no	—
166	C₂×D₈	—	47	2	no	—
167	C₂×D₈	—	94	2	no	—
168	C₂×D₈	—	94	1	no	—
169	C₂×D₈	—	94	2	no	—
170	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
171	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
172	#124	—	94	4	no	—
173	#124	—	188	2	no	—
174	C₂×C₄⋊C₄	—	2	2	no	—
175	C₂×C₂²⋊C₄	—	188	1	no	—
176	C₂×C₂²⋊C₄	—	188	1	no	—
177	C₂×C₄²	—	4	1	no	—
178	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
179	C₂×C₁₆	—	94	2	no	—
180	C₂×C₁₆	—	94	2	no	—
181	C₂×C₁₆	—	94	2	no	—
182	#107	—	2	2	no	—
183	#107	D₁₈₈	1	4	yes	—
184	C₄×C₈	C₄×D₄₇	1	2	yes	—
185	C₄×C₈	D₁₈₈	1	2	yes	—
186	#95	—	4	1	no	—
187	C₂⁴	—	188	1	no	—
188	C₂×Q₈	—	94	2	no	—
189	C₂×Q₈	—	188	2	no	—
190	C₂×Q₈	—	188	2	no	—
191	C₂×Q₈	—	188	1	no	—
192	C₂×D₄	—	94	2	no	—
193	C₂×D₄	—	188	2	no	—
194	C₂×D₄	—	188	1	no	—
195	C₂×D₄	—	188	2	no	—
196	C₂²×C₄	—	4	2	no	—
197	C₂²×C₄	—	188	1	no	—
198	C₂²×C₄	#10625334	1	1	yes	characteristic
199	C₂²×C₄	#10625334	1	1	yes	characteristic
200	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
201	Q₁₆	—	94	4	no	—
202	Q₁₆	—	188	1	no	—
203	Q₁₆	—	188	1	no	—
204	SD₁₆	—	188	8	no	—
205	D₈	—	94	4	no	—
206	D₈	—	188	1	no	—
207	D₈	—	188	1	no	—
208	C₂×C₈	—	2	2	no	—
209	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
210	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
211	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
212	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
213	C₂×C₈	#10625350	1	2	yes	—
214	C₄⋊C₄	—	2	4	no	—
215	C₄⋊C₄	—	4	2	no	—
216	C₂²⋊C₄	—	188	4	no	—
217	C₂²⋊C₄	—	188	4	no	—
218	C₄²	—	8	2	no	—
219	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
220	C₄²	#10625336	1	2	yes	—
221	C₁₆	—	188	2	no	—
222	C₂³	—	376	2	no	—
223	C₂³	—	376	1	no	—
224	C₂³	—	376	1	no	—
225	C₂³	—	376	2	no	—
226	C₂³	—	188	2	no	—
227	C₂³	C₂×#10625334	1	1	yes	characteristic
228	Q₈	—	376	2	no	—
229	Q₈	—	188	2	no	—
230	Q₈	—	188	2	no	—
231	D₄	—	376	2	no	—
232	D₄	—	188	2	no	—
233	D₄	—	188	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	4	4	no	—
238	C₂×C₄	—	8	2	no	—
239	C₂×C₄	—	8	2	no	—
240	C₂×C₄	—	376	2	no	—
241	C₂×C₄	—	188	2	no	—
242	C₂×C₄	#13093944	1	2	yes	—
243	C₂×C₄	#13093944	1	2	yes	—
244	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
245	C₂×C₄	#13093998	1	2	yes	—
246	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
247	C₂×C₄	#13094049	1	2	yes	—
248	C₈	—	2	2	no	—
249	C₈	C₄×D₁₈₈	1	2	yes	—
250	C₈	#13094012	1	1	yes	characteristic
251	C₈	#13094021	1	1	yes	characteristic
252	C₂²	—	376	2	no	—
253	C₂²	—	376	2	no	—
254	C₂²	—	376	2	no	—
255	C₂²	—	752	2	no	—
256	C₂²	—	752	2	no	—
257	C₂²	C₂×#13093944	1	1	yes	characteristic
258	C₂²	#15689318	1	2	yes	—
259	C₂²	#15689553	1	2	yes	—
260	C₂²	#15689559	1	1	yes	characteristic
261	C₂²	#15689564	1	1	yes	characteristic
262	C₄	—	2	2	no	—
263	C₄	—	2	2	no	—
264	C₄	—	8	4	no	—
265	C₄	—	376	2	no	—
266	C₄	#15689025	1	1	yes	characteristic
267	C₄	#15689127	1	1	yes	characteristic
268	C₄	#15689323	1	2	yes	—
269	C₂	—	752	2	no	—
270	C₂	#20244315	1	1	yes	characteristic
271	C₂	#20245093	1	1	yes	characteristic
272	C₂	#20245098	1	1	yes	characteristic
273	C₂	#20245443	1	2	yes	—
274	C₂	#20245450	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689507

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₇⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

C₂×#15688926

C₂

yes

maximal, complemented

C₂×#15688923

C₂

yes

maximal

C₄×#107×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₁₈₈

C₂²

yes

characteristic

C₂²×#10625325

—

C₂²×D₃₇₆

C₂²

yes

characteristic

C₂×#13094012

—

C₂²×C₄₇⋊C₁₆

C₂²

yes

—

#15689507

—

#15689507

C₄

yes

complemented

C₄⋊(C₄₇⋊C₁₆)

—

#15688926

—

#15688923

—

C₂×#107×C₄₇

C₂²

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₄₇

—

C₄₇×#340

—

C₂²×Dic₉₄

—

C₂²×D₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

C₂×C₄

yes

—

C₂×#10625325

—

C₂×#10625325

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

C₂×C₄

yes

—

#13094012

—

#13094012

—

C₂×(C₂×D₄₇)⋊C₄

—

C₂×(C₂×D₄₇)⋊C₄

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

D₄

yes

characteristic

#107×C₄₇

—

#107×C₄₇

D₄

yes

—

C₄×C₈×C₄₇

C₂×C₄

yes

—

C₄×C₈×C₄₇

D₄

yes

—

#95×C₄₇

—

C₂³×D₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₈

yes

characteristic

C₂²×C₄×C₄₇

D₈

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

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

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂²⋊C₄

yes

—

C₄²×C₄₇

SD₁₆

yes

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

D₃₇₆

—

D₃₇₆

—

D₃₇₆

—

#10625325

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂×D₈

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

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

#102

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

#121

yes

—

100

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

101

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

102

C₂×Dic₄₇

—

103

C₂×Dic₄₇

—

104

D₁₈₈

—

105

D₁₈₈

—

106

D₁₈₈

—

107

Dic₉₄

—

108

Dic₉₄

—

109

Dic₉₄

—

110

C₈×C₄₇

—

111

C₈×C₄₇

C₄×D₄

yes

—

112

C₈×C₄₇

#124

yes

characteristic

113

C₈×C₄₇

yes

114

—

115

C₂²×C₄₇

C₂×#102

yes

characteristic

116

C₂²×C₄₇

#459

yes

—

117

C₂²×C₄₇

#508

yes

—

118

C₂²×C₄₇

#509

yes

characteristic

119

C₂²×C₄₇

#510

yes

characteristic

120

C₂×D₄₇

—

121

C₂×D₄₇

—

122

C₂×D₄₇

—

123

C₂×D₄₇

—

124

C₂×D₄₇

—

125

C₄×C₄₇

—

126

C₄×C₄₇

—

127

C₄×C₄₇

—

128

C₄×C₄₇

#390

yes

characteristic

129

C₄×C₄₇

#418

yes

characteristic

130

C₄×C₄₇

#460

yes

—

131

Dic₄₇

—

132

C₂×#495

—

133

C₂×C₄⋊C₁₆

—

134

C₂×#358

—

135

C₂×#357

—

136

C₄×#107

D₄₇

yes

characteristic, complemented

137

C₂×C₄₇

#1982

yes

characteristic

138

C₂×C₄₇

#2138

yes

characteristic

139

C₂×C₄₇

#2139

yes

characteristic

140

C₂×C₄₇

#2210

yes

—

141

C₂×C₄₇

#2211

yes

—

142

D₄₇

—

143

C₂²×Q₁₆

—

144

C₂²×SD₁₆

—

145

C₂²×D₈

—

146

C₂×#124

—

147

C₂²×C₁₆

—

148

#495

—

149

#495

—

150

C₂×#107

C₂×D₄₇

yes

—

151

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

152

C₄×C₄⋊C₄

—

153

C₄⋊C₁₆

—

154

#358

—

155

#357

—

156

#340

—

157

C₄₇

#13254

yes

characteristic, complemented, Sylow

158

C₂²×Q₈

—

159

C₂²×D₄

—

160

C₂×Q₁₆

—

161

C₂×Q₁₆

—

162

C₂×Q₁₆

—

163

C₂×Q₁₆

—

164

C₂×SD₁₆

—

165

C₂×SD₁₆

—

188

—

166

C₂×D₈

—

167

C₂×D₈

—

168

C₂×D₈

—

169

C₂×D₈

—

170

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

171

C₂²×C₈

C₂²×D₄₇

yes

characteristic

172

#124

—

173

#124

—

188

—

174

C₂×C₄⋊C₄

—

175

C₂×C₂²⋊C₄

—

188

—

176

C₂×C₂²⋊C₄

—

188

—

177

C₂×C₄²

—

178

C₂×C₄²

C₂²⋊D₄₇

yes

characteristic

179

C₂×C₁₆

—

180

C₂×C₁₆

—

181

C₂×C₁₆

—

182

#107

—

183

#107

D₁₈₈

yes

—

184

C₄×C₈

C₄×D₄₇

yes

—

185

C₄×C₈

D₁₈₈

yes

—

186

#95

—

187

C₂⁴

—

188

—

188

C₂×Q₈

—

189

C₂×Q₈

—

188

—

190

C₂×Q₈

—

188

—

191

C₂×Q₈

—

188

—

192

C₂×D₄

—

193

C₂×D₄

—

188

—

194

C₂×D₄

—

188

—

195

C₂×D₄

—

188

—

196

C₂²×C₄

—

197

C₂²×C₄

—

188

—

198

C₂²×C₄

#10625334

yes

characteristic

199

C₂²×C₄

#10625334

yes

characteristic

200

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

201

Q₁₆

—

202

Q₁₆

—

188

—

203

Q₁₆

—

188

—

204

SD₁₆

—

188

—

205

D₈

—

206

D₈

—

188

—

207

D₈

—

188

—

208

C₂×C₈

—

209

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

210

C₂×C₈

C₂×C₄×D₄₇

yes

characteristic

211

C₂×C₈

C₂×D₁₈₈

yes

—

212

C₂×C₈

C₂×D₁₈₈

yes

characteristic

213

C₂×C₈

#10625350

yes

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₂²⋊C₄

—

188

—

217

C₂²⋊C₄

—

188

—

218

C₄²

—

219

C₄²

(C₂×D₄₇)⋊C₄

yes

—

220

C₄²

#10625336

yes

—

221

C₁₆

—

188

—

222

C₂³

—

376

—

223

C₂³

—

376

—

224

C₂³

—

376

—

225

C₂³

—

376

—

226

C₂³

—

188

—

227

C₂³

C₂×#10625334

yes

characteristic

228

Q₈

—

376

—

229

Q₈

—

188

—

230

Q₈

—

188

—

231

D₄

—

376

—

232

D₄

—

188

—

233

D₄

—

188

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

376

—

241

C₂×C₄

—

188

—

242

C₂×C₄

#13093944

yes

—

243

C₂×C₄

#13093944

yes

—

244

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

245

C₂×C₄

#13093998

yes

—

246

C₂×C₄

C₂×#10625336

yes

characteristic

247

C₂×C₄

#13094049

yes

—

248

C₈

—

249

C₈

C₄×D₁₈₈

yes

—

250

C₈

#13094012

yes

characteristic

251

C₈

#13094021

yes

characteristic

252

C₂²

—

376

—

253

C₂²

—

376

—

254

C₂²

—

376

—

255

C₂²

—

752

—

256

C₂²

—

752

—

257

C₂²

C₂×#13093944

yes

characteristic

258

C₂²

#15689318

yes

—

259

C₂²

#15689553

yes

—

260

C₂²

#15689559

yes

characteristic

261

C₂²

#15689564

yes

characteristic

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

—

376

—

266

C₄

#15689025

yes

characteristic

267

C₄

#15689127

yes

characteristic

268

C₄

#15689323

yes

—

269

C₂

—

752

—

270

C₂

#20244315

yes

characteristic

271

C₂

#20245093

yes

characteristic

272

C₂

#20245098

yes

characteristic

273

C₂

#20245443

yes

—

274

C₂

#20245450

yes

—

	subgroup	G/H
center	C₂³	C₂×#10625334
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄×#107×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₈
prime radical	C₂²×D₃₇₆	C₂²
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	C₄×#107	D₄₇
hypocenter	C₄₇	#13254
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#107

subgroup

G/H

center

C₂³

C₂×#10625334

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₄×#107×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₈

prime radical

C₂²×D₃₇₆

C₂²

cosocle

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#107

N	H ≅ G/N	type
2. C₂×C₄⋊(C₄₇⋊C₁₆)	C₂	semidirect
3. C₂×#15688926	C₂	semidirect
5. C₄×#107×C₄₇	C₂	semidirect
12. #15689507	C₄	semidirect
136. C₄×#107	D₄₇	semidirect
157. C₄₇	#13254	semidirect

H ≅ G/N

type

2. C₂×C₄⋊(C₄₇⋊C₁₆)

C₂

semidirect

3. C₂×#15688926

C₂

semidirect

5. C₄×#107×C₄₇

C₂

semidirect

12. #15689507

C₄

semidirect

136. C₄×#107

D₄₇

semidirect

157. C₄₇

#13254

semidirect

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

subgroup	index
C₂×#15689507	2
C₂×C₄⋊(C₄₇⋊C₁₆)	2
C₂×#15688926	2
C₂×#15688923	2
C₄×#107×C₄₇	2
#13254	47

subgroup

index

C₂×C₄⋊(C₄₇⋊C₁₆)

C₄×#107×C₄₇

Subgroups — #26134754

Conjugacy classes of subgroups

Complements

Maximal subgroups