Group #26135109 — subgroups

Subgroups — #26135109

Order 12032.

698 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13093965	C₂	1	2	yes	maximal, complemented
2	C₂×#15688924	C₂	1	2	yes	maximal, complemented
3	#20244254	C₂	1	1	yes	maximal, characteristic, complemented
4	#20241466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
7	C₂×#13093965	—	2	4	no	—
8	C₂×#13093965	—	2	4	no	—
9	C₂×#13093965	—	2	4	no	—
10	C₂²×C₄₇⋊C₁₆	C₂²	1	2	yes	—
11	C₂×#13093958	C₂²	1	1	yes	characteristic
12	C₂×#13093946	—	2	1	no	—
13	#15689025	—	2	1	no	—
14	#15688924	—	2	4	no	—
15	C₂²×D₈×C₄₇	—	2	1	no	—
16	C₂²×D₈×C₄₇	C₂²	1	2	yes	—
17	C₂×#127×C₄₇	—	2	1	no	—
18	C₄₇×#493	—	2	4	no	—
19	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×D₁₈₈	—	2	1	no	—
21	C₂×D₃₇₆	—	2	2	no	—
22	C₂×D₃₇₆	—	2	2	no	—
23	C₂×D₃₇₆	—	2	1	no	—
24	C₂×D₃₇₆	D₄	1	2	yes	complemented
25	C₂×C₄⋊Dic₄₇	—	2	1	no	—
26	C₂×(C₂×D₄₇)⋊C₄	—	4	2	no	—
27	#13093965	—	2	16	no	—
28	C₂×C₄₇⋊C₁₆	—	2	2	no	—
29	C₂×C₄₇⋊C₁₆	—	2	2	no	—
30	C₂×C₄₇⋊C₁₆	D₄	1	4	yes	complemented
31	#13093958	—	2	2	no	—
32	#13093946	—	4	2	no	—
33	C₂²×D₄×C₄₇	—	2	2	no	—
34	C₂²×D₄×C₄₇	—	4	2	no	—
35	C₂×D₈×C₄₇	—	2	4	no	—
36	C₂×D₈×C₄₇	—	2	2	no	—
37	C₂×D₈×C₄₇	—	2	2	no	—
38	C₂×D₈×C₄₇	—	2	2	no	—
39	C₂×D₈×C₄₇	—	2	2	no	—
40	C₂×D₈×C₄₇	—	2	2	no	—
41	C₂×D₈×C₄₇	—	4	2	no	—
42	C₂×D₈×C₄₇	—	4	2	no	—
43	C₂×D₈×C₄₇	D₄	1	4	yes	—
44	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
46	#127×C₄₇	—	2	4	no	—
47	#127×C₄₇	—	4	2	no	—
48	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
49	C₄×C₈×C₄₇	—	2	2	no	—
50	C₂⁴×C₄₇	—	4	2	no	—
51	C₂³×D₄₇	—	4	1	no	—
52	C₂×D₄×C₄₇	—	2	4	no	—
53	C₂×D₄×C₄₇	—	4	8	no	—
54	C₂×D₄×C₄₇	—	4	2	no	—
55	C₂×D₄×C₄₇	—	4	2	no	—
56	C₂×D₄×C₄₇	—	4	2	no	—
57	C₂×D₄×C₄₇	—	4	2	no	—
58	C₂×D₄×C₄₇	—	4	2	no	—
59	C₂×D₄×C₄₇	—	8	4	no	—
60	C₂×D₄×C₄₇	—	8	4	no	—
61	C₂²×C₄×C₄₇	D₈	1	2	yes	—
62	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
63	C₂²×Dic₄₇	—	4	1	no	—
64	C₂×D₁₈₈	—	2	2	no	—
65	C₂×D₁₈₈	—	4	1	no	—
66	C₂×D₁₈₈	—	4	1	no	—
67	C₂×D₁₈₈	—	4	1	no	—
68	C₂×D₁₈₈	—	4	1	no	—
69	C₂×D₁₈₈	—	4	1	no	—
70	D₈×C₄₇	—	2	4	no	—
71	D₈×C₄₇	—	2	4	no	—
72	D₈×C₄₇	—	4	8	no	—
73	D₈×C₄₇	—	4	2	no	—
74	D₈×C₄₇	—	4	2	no	—
75	C₂×C₈×C₄₇	—	2	1	no	—
76	C₂×C₈×C₄₇	—	2	1	no	—
77	C₂×C₈×C₄₇	D₈	1	2	yes	—
78	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
80	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
81	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
82	C₄²×C₄₇	—	2	1	no	—
83	C₄²×C₄₇	—	2	1	no	—
84	(C₂×D₄₇)⋊C₄	—	8	4	no	—
85	C₄⋊Dic₄₇	—	4	1	no	—
86	C₄⋊Dic₄₇	—	4	1	no	—
87	D₃₇₆	—	2	4	no	—
88	D₃₇₆	—	4	2	no	—
89	C₄₇⋊C₁₆	—	2	4	no	—
90	C₂³×C₄₇	—	4	4	no	—
91	C₂³×C₄₇	—	8	2	no	—
92	C₂³×C₄₇	—	8	2	no	—
93	C₂³×C₄₇	—	8	4	no	—
94	C₂³×C₄₇	—	8	4	no	—
95	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
96	C₂²×D₄₇	—	4	2	no	—
97	C₂²×D₄₇	—	8	1	no	—
98	C₂²×D₄₇	—	8	1	no	—
99	C₂²×D₄₇	—	8	2	no	—
100	C₂²×D₄₇	—	8	2	no	—
101	D₄×C₄₇	—	4	4	no	—
102	D₄×C₄₇	—	4	4	no	—
103	D₄×C₄₇	—	8	16	no	—
104	D₄×C₄₇	—	8	2	no	—
105	D₄×C₄₇	—	8	2	no	—
106	C₂×C₄×C₄₇	—	2	2	no	—
107	C₂×C₄×C₄₇	—	2	2	no	—
108	C₂×C₄×C₄₇	D₁₆	1	4	yes	complemented
109	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
110	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
111	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
112	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
113	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
114	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
115	C₂×Dic₄₇	—	8	1	no	—
116	C₂×Dic₄₇	—	8	2	no	—
117	D₁₈₈	—	4	2	no	—
118	D₁₈₈	—	4	2	no	—
119	D₁₈₈	—	8	1	no	—
120	D₁₈₈	—	8	1	no	—
121	C₈×C₄₇	—	2	2	no	—
122	C₈×C₄₇	#120	1	2	yes	—
123	C₈×C₄₇	#121	1	2	yes	—
124	#13325	—	47	1	no	maximal, Sylow
125	C₂²×C₄₇	—	8	8	no	—
126	C₂²×C₄₇	—	8	4	no	—
127	C₂²×C₄₇	—	16	4	no	—
128	C₂²×C₄₇	—	16	2	no	—
129	C₂²×C₄₇	—	16	2	no	—
130	C₂²×C₄₇	#447	1	1	yes	characteristic
131	C₂²×C₄₇	#459	1	1	yes	characteristic
132	C₂²×C₄₇	#493	1	1	yes	characteristic
133	C₂²×C₄₇	C₂×D₁₆	1	2	yes	—
134	C₂²×C₄₇	#509	1	2	yes	—
135	C₂×D₄₇	—	8	4	no	—
136	C₂×D₄₇	—	8	2	no	—
137	C₂×D₄₇	—	16	2	no	—
138	C₂×D₄₇	—	16	1	no	—
139	C₂×D₄₇	—	16	1	no	—
140	C₄×C₄₇	—	2	4	no	—
141	C₄×C₄₇	#392	1	1	yes	characteristic
142	C₄×C₄₇	#447	1	1	yes	characteristic
143	C₄×C₄₇	#459	1	1	yes	characteristic
144	C₄×C₄₇	#496	1	1	yes	characteristic
145	Dic₄₇	—	16	1	no	—
146	C₂²×D₁₆	—	47	2	no	—
147	C₂×#493	D₄₇	1	1	yes	characteristic, complemented
148	C₂×#357	—	47	2	no	—
149	#1970	—	47	1	no	—
150	#1374	—	47	1	no	—
151	C₂×C₄₇	—	16	4	no	—
152	C₂×C₄₇	#2011	1	1	yes	characteristic
153	C₂×C₄₇	#2184	1	2	yes	—
154	C₂×C₄₇	#2206	1	2	yes	—
155	C₂×C₄₇	#2246	1	1	yes	characteristic
156	C₂×C₄₇	#2250	1	1	yes	characteristic
157	D₄₇	—	16	2	no	—
158	C₂²×D₈	—	2	1	no	—
159	C₂²×D₈	—	47	1	no	—
160	C₂²×D₈	C₂×D₄₇	1	2	yes	—
161	C₂×#127	—	2	1	no	—
162	C₂×D₁₆	—	94	4	no	—
163	C₂×D₁₆	—	94	4	no	—
164	C₂×D₁₆	—	94	4	no	—
165	C₂²×C₁₆	—	47	2	no	—
166	#493	—	2	4	no	—
167	C₂×#107	—	47	1	no	—
168	C₂×#102	—	94	1	no	—
169	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
170	#390	—	94	1	no	—
171	#357	—	94	4	no	—
172	C₄₇	#13325	1	1	yes	characteristic, complemented, Sylow
173	C₂²×D₄	—	2	2	no	—
174	C₂²×D₄	—	4	2	no	—
175	C₂²×D₄	—	94	1	no	—
176	C₂×D₈	—	2	4	no	—
177	C₂×D₈	—	2	2	no	—
178	C₂×D₈	—	2	2	no	—
179	C₂×D₈	—	2	2	no	—
180	C₂×D₈	—	2	2	no	—
181	C₂×D₈	—	2	2	no	—
182	C₂×D₈	—	4	2	no	—
183	C₂×D₈	—	4	2	no	—
184	C₂×D₈	—	47	2	no	—
185	C₂×D₈	—	94	2	no	—
186	C₂×D₈	—	94	1	no	—
187	C₂×D₈	—	94	2	no	—
188	C₂×D₈	C₂²⋊D₄₇	1	4	yes	—
189	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
190	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
191	#127	—	2	4	no	—
192	#127	—	4	2	no	—
193	C₂×C₄⋊C₄	—	94	1	no	—
194	C₂×C₂²⋊C₄	—	188	2	no	—
195	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
196	D₁₆	—	94	16	no	—
197	C₂×C₁₆	—	47	4	no	—
198	C₂×C₁₆	—	94	2	no	—
199	C₂×C₁₆	—	94	2	no	—
200	#107	—	94	2	no	—
201	#102	—	188	2	no	—
202	C₄×C₈	—	2	2	no	—
203	C₂⁴	—	4	2	no	—
204	C₂⁴	—	188	1	no	—
205	C₂×D₄	—	2	4	no	—
206	C₂×D₄	—	4	8	no	—
207	C₂×D₄	—	4	2	no	—
208	C₂×D₄	—	4	2	no	—
209	C₂×D₄	—	4	2	no	—
210	C₂×D₄	—	4	2	no	—
211	C₂×D₄	—	4	2	no	—
212	C₂×D₄	—	8	4	no	—
213	C₂×D₄	—	8	4	no	—
214	C₂×D₄	—	94	2	no	—
215	C₂×D₄	—	188	1	no	—
216	C₂×D₄	—	188	1	no	—
217	C₂×D₄	—	188	1	no	—
218	C₂×D₄	—	188	1	no	—
219	C₂×D₄	—	188	1	no	—
220	C₂²×C₄	—	188	1	no	—
221	C₂²×C₄	#10625334	1	2	yes	—
222	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
223	D₈	—	2	4	no	—
224	D₈	—	2	4	no	—
225	D₈	—	4	8	no	—
226	D₈	—	4	2	no	—
227	D₈	—	4	2	no	—
228	D₈	—	94	4	no	—
229	D₈	—	188	2	no	—
230	C₂×C₈	—	2	1	no	—
231	C₂×C₈	—	2	1	no	—
232	C₂×C₈	#10625334	1	2	yes	—
233	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
234	C₂×C₈	D₄×D₄₇	1	2	yes	—
235	C₂×C₈	#10625352	1	1	yes	characteristic
236	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
237	C₄⋊C₄	—	188	1	no	—
238	C₄⋊C₄	—	188	1	no	—
239	C₂²⋊C₄	—	376	4	no	—
240	C₄²	—	2	1	no	—
241	C₄²	—	2	1	no	—
242	C₁₆	—	94	4	no	—
243	C₂³	—	4	4	no	—
244	C₂³	—	8	2	no	—
245	C₂³	—	8	4	no	—
246	C₂³	—	8	4	no	—
247	C₂³	—	8	2	no	—
248	C₂³	—	376	1	no	—
249	C₂³	—	376	1	no	—
250	C₂³	—	376	2	no	—
251	C₂³	—	376	2	no	—
252	C₂³	—	188	2	no	—
253	C₂³	C₂×#10625334	1	1	yes	characteristic
254	D₄	—	4	4	no	—
255	D₄	—	4	4	no	—
256	D₄	—	8	16	no	—
257	D₄	—	8	2	no	—
258	D₄	—	8	2	no	—
259	D₄	—	376	1	no	—
260	D₄	—	376	1	no	—
261	D₄	—	188	2	no	—
262	D₄	—	188	2	no	—
263	C₂×C₄	—	2	2	no	—
264	C₂×C₄	—	2	2	no	—
265	C₂×C₄	—	376	1	no	—
266	C₂×C₄	—	376	2	no	—
267	C₂×C₄	#13093965	1	4	yes	complemented
268	C₂×C₄	#13093993	1	1	yes	characteristic
269	C₂×C₄	#13093995	1	1	yes	characteristic
270	C₂×C₄	#13094020	1	1	yes	characteristic
271	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
272	C₂×C₄	#13094050	1	1	yes	characteristic
273	C₂×C₄	#13094050	1	1	yes	characteristic
274	C₈	—	2	2	no	—
275	C₈	#13093992	1	2	yes	—
276	C₈	#13093996	1	2	yes	—
277	C₂²	—	8	8	no	—
278	C₂²	—	8	4	no	—
279	C₂²	—	16	2	no	—
280	C₂²	—	16	2	no	—
281	C₂²	—	16	4	no	—
282	C₂²	—	376	4	no	—
283	C₂²	—	376	2	no	—
284	C₂²	—	752	2	no	—
285	C₂²	—	752	1	no	—
286	C₂²	—	752	1	no	—
287	C₂²	#15689257	1	1	yes	characteristic
288	C₂²	#15689315	1	1	yes	characteristic
289	C₂²	#15689499	1	1	yes	characteristic
290	C₂²	C₂×#13093965	1	2	yes	—
291	C₂²	#15689559	1	2	yes	—
292	C₄	—	2	4	no	—
293	C₄	—	752	1	no	—
294	C₄	#15689031	1	1	yes	characteristic
295	C₄	#15689257	1	1	yes	characteristic
296	C₄	#15689315	1	1	yes	characteristic
297	C₄	#15689510	1	1	yes	characteristic
298	C₂	—	16	4	no	—
299	C₂	—	752	2	no	—
300	C₂	#20244459	1	1	yes	characteristic
301	C₂	#20245300	1	2	yes	—
302	C₂	#20245420	1	2	yes	—
303	C₂	#20245637	1	1	yes	characteristic
304	C₂	#20245652	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#13093965

C₂

yes

maximal, complemented

C₂×#15688924

C₂

yes

maximal, complemented

#20244254

C₂

yes

maximal, characteristic, complemented

#20241466

C₂

yes

maximal, characteristic, complemented

C₂×C₄₇×#493

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₇₆

C₂²

yes

—

—

—

C₂²×C₄₇⋊C₁₆

C₂²

yes

—

C₂×#13093958

C₂²

yes

—

—

—

C₂²×D₈×C₄₇

—

C₂²×D₈×C₄₇

C₂²

yes

—

C₂×#127×C₄₇

—

C₄₇×#493

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂²×D₁₈₈

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

D₄

yes

complemented

C₂×C₄⋊Dic₄₇

—

C₂×(C₂×D₄₇)⋊C₄

—

#13093965

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

D₄

yes

complemented

#13093958

—

#13093946

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂×D₈×C₄₇

—

C₂×D₈×C₄₇

—

C₂×D₈×C₄₇

—

C₂×D₈×C₄₇

—

C₂×D₈×C₄₇

—

C₂×D₈×C₄₇

—

C₂×D₈×C₄₇

—

C₂×D₈×C₄₇

—

C₂×D₈×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

C₂³

yes

characteristic

#127×C₄₇

—

#127×C₄₇

—

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₄×C₈×C₄₇

—

C₂⁴×C₄₇

—

C₂³×D₄₇

—

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

D₈

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

D₈×C₄₇

—

D₈×C₄₇

—

D₈×C₄₇

—

D₈×C₄₇

—

D₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₈

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

#41

yes

characteristic

C₄²×C₄₇

—

C₄²×C₄₇

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

D₃₇₆

—

D₃₇₆

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₈

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

100

C₂²×D₄₇

—

101

D₄×C₄₇

—

102

D₄×C₄₇

—

103

D₄×C₄₇

—

104

D₄×C₄₇

—

105

D₄×C₄₇

—

106

C₂×C₄×C₄₇

—

107

C₂×C₄×C₄₇

—

108

C₂×C₄×C₄₇

D₁₆

yes

complemented

109

C₂×C₄×C₄₇

#120

yes

characteristic

110

C₂×C₄×C₄₇

#121

yes

characteristic

111

C₂×C₄×C₄₇

#127

yes

characteristic

112

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

113

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

characteristic

114

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

characteristic

115

C₂×Dic₄₇

—

116

C₂×Dic₄₇

—

117

D₁₈₈

—

118

D₁₈₈

—

119

D₁₈₈

—

120

D₁₈₈

—

121

C₈×C₄₇

—

122

C₈×C₄₇

#120

yes

—

123

C₈×C₄₇

#121

yes

—

124

#13325

—

maximal, Sylow

125

C₂²×C₄₇

—

126

C₂²×C₄₇

—

127

C₂²×C₄₇

—

128

C₂²×C₄₇

—

129

C₂²×C₄₇

—

130

C₂²×C₄₇

#447

yes

characteristic

131

C₂²×C₄₇

#459

yes

characteristic

132

C₂²×C₄₇

#493

yes

characteristic

133

C₂²×C₄₇

C₂×D₁₆

yes

—

134

C₂²×C₄₇

#509

yes

—

135

C₂×D₄₇

—

136

C₂×D₄₇

—

137

C₂×D₄₇

—

138

C₂×D₄₇

—

139

C₂×D₄₇

—

140

C₄×C₄₇

—

141

C₄×C₄₇

#392

yes

characteristic

142

C₄×C₄₇

#447

yes

characteristic

143

C₄×C₄₇

#459

yes

characteristic

144

C₄×C₄₇

#496

yes

characteristic

145

Dic₄₇

—

146

C₂²×D₁₆

—

147

C₂×#493

D₄₇

yes

characteristic, complemented

148

C₂×#357

—

149

#1970

—

150

#1374

—

151

C₂×C₄₇

—

152

C₂×C₄₇

#2011

yes

characteristic

153

C₂×C₄₇

#2184

yes

—

154

C₂×C₄₇

#2206

yes

—

155

C₂×C₄₇

#2246

yes

characteristic

156

C₂×C₄₇

#2250

yes

characteristic

157

D₄₇

—

158

C₂²×D₈

—

159

C₂²×D₈

—

160

C₂²×D₈

C₂×D₄₇

yes

—

161

C₂×#127

—

162

C₂×D₁₆

—

163

C₂×D₁₆

—

164

C₂×D₁₆

—

165

C₂²×C₁₆

—

166

#493

—

167

C₂×#107

—

168

C₂×#102

—

169

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

170

#390

—

171

#357

—

172

C₄₇

#13325

yes

characteristic, complemented, Sylow

173

C₂²×D₄

—

174

C₂²×D₄

—

175

C₂²×D₄

—

176

C₂×D₈

—

177

C₂×D₈

—

178

C₂×D₈

—

179

C₂×D₈

—

180

C₂×D₈

—

181

C₂×D₈

—

182

C₂×D₈

—

183

C₂×D₈

—

184

C₂×D₈

—

185

C₂×D₈

—

186

C₂×D₈

—

187

C₂×D₈

—

188

C₂×D₈

C₂²⋊D₄₇

yes

—

189

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

190

C₂²×C₈

C₂²×D₄₇

yes

characteristic

191

#127

—

192

#127

—

193

C₂×C₄⋊C₄

—

194

C₂×C₂²⋊C₄

—

188

—

195

C₂×C₄²

C₂²⋊D₄₇

yes

characteristic

196

D₁₆

—

197

C₂×C₁₆

—

198

C₂×C₁₆

—

199

C₂×C₁₆

—

200

#107

—

201

#102

—

188

—

202

C₄×C₈

—

203

C₂⁴

—

204

C₂⁴

—

188

—

205

C₂×D₄

—

206

C₂×D₄

—

207

C₂×D₄

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

—

213

C₂×D₄

—

214

C₂×D₄

—

215

C₂×D₄

—

188

—

216

C₂×D₄

—

188

—

217

C₂×D₄

—

188

—

218

C₂×D₄

—

188

—

219

C₂×D₄

—

188

—

220

C₂²×C₄

—

188

—

221

C₂²×C₄

#10625334

yes

—

222

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

223

D₈

—

224

D₈

—

225

D₈

—

226

D₈

—

227

D₈

—

228

D₈

—

229

D₈

—

188

—

230

C₂×C₈

—

231

C₂×C₈

—

232

C₂×C₈

#10625334

yes

—

233

C₂×C₈

D₄×D₄₇

yes

characteristic

234

C₂×C₈

D₄×D₄₇

yes

—

235

C₂×C₈

#10625352

yes

characteristic

236

C₂×C₈

C₂×C₂²⋊D₄₇

yes

—

237

C₄⋊C₄

—

188

—

238

C₄⋊C₄

—

188

—

239

C₂²⋊C₄

—

376

—

240

C₄²

—

241

C₄²

—

242

C₁₆

—

243

C₂³

—

244

C₂³

—

245

C₂³

—

246

C₂³

—

247

C₂³

—

248

C₂³

—

376

—

249

C₂³

—

376

—

250

C₂³

—

376

—

251

C₂³

—

376

—

252

C₂³

—

188

—

253

C₂³

C₂×#10625334

yes

characteristic

254

D₄

—

255

D₄

—

256

D₄

—

257

D₄

—

258

D₄

—

259

D₄

—

376

—

260

D₄

—

376

—

261

D₄

—

188

—

262

D₄

—

188

—

263

C₂×C₄

—

264

C₂×C₄

—

265

C₂×C₄

—

376

—

266

C₂×C₄

—

376

—

267

C₂×C₄

#13093965

yes

complemented

268

C₂×C₄

#13093993

yes

characteristic

269

C₂×C₄

#13093995

yes

characteristic

270

C₂×C₄

#13094020

yes

characteristic

271

C₂×C₄

C₂×#10625334

yes

characteristic

272

C₂×C₄

#13094050

yes

characteristic

273

C₂×C₄

#13094050

yes

characteristic

274

C₈

—

275

C₈

#13093992

yes

—

276

C₈

#13093996

yes

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

280

C₂²

—

281

C₂²

—

282

C₂²

—

376

—

283

C₂²

—

376

—

284

C₂²

—

752

—

285

C₂²

—

752

—

286

C₂²

—

752

—

287

C₂²

#15689257

yes

characteristic

288

C₂²

#15689315

yes

characteristic

289

C₂²

#15689499

yes

characteristic

290

C₂²

C₂×#13093965

yes

—

291

C₂²

#15689559

yes

—

292

C₄

—

293

C₄

—

752

—

294

C₄

#15689031

yes

characteristic

295

C₄

#15689257

yes

characteristic

296

C₄

#15689315

yes

characteristic

297

C₄

#15689510

yes

characteristic

298

C₂

—

299

C₂

—

752

—

300

C₂

#20244459

yes

characteristic

301

C₂

#20245300

yes

—

302

C₂

#20245420

yes

—

303

C₂

#20245637

yes

characteristic

304

C₂

#20245652

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×#10625334
commutator, cosocle	C₂²×C₈×C₄₇	C₂³
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₂×C₄₇×#493	C₂
socle	C₂³×C₄₇	C₂×D₈
hypercenter	C₂×#493	D₄₇
hypocenter	C₄₇	#13325
LCS	G ▷ C₂²×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#493

subgroup

G/H

center

C₂³

C₂×#10625334

commutator, cosocle

C₂²×C₈×C₄₇

C₂³

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₂×C₄₇×#493

C₂

socle

C₂³×C₄₇

C₂×D₈

D₄₇

C₄₇

G ▷ C₂²×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#493

N	H ≅ G/N	type
1. C₂²×#13093965	C₂	semidirect
2. C₂×#15688924	C₂	semidirect
3. #20244254	C₂	semidirect
4. #20241466	C₂	semidirect
5. C₂×C₄₇×#493	C₂	semidirect
24. C₂×D₃₇₆	D₄	semidirect
30. C₂×C₄₇⋊C₁₆	D₄	semidirect
108. C₂×C₄×C₄₇	D₁₆	semidirect
147. C₂×#493	D₄₇	semidirect
172. C₄₇	#13325	semidirect
267. C₂×C₄	#13093965	semidirect

H ≅ G/N

type

1. C₂²×#13093965

C₂

semidirect

2. C₂×#15688924

C₂

semidirect

3. #20244254

C₂

semidirect

4. #20241466

C₂

semidirect

5. C₂×C₄₇×#493

C₂

semidirect

24. C₂×D₃₇₆

D₄

semidirect

30. C₂×C₄₇⋊C₁₆

D₄

semidirect

108. C₂×C₄×C₄₇

D₁₆

semidirect

147. C₂×#493

D₄₇

semidirect

172. C₄₇

#13325

semidirect

267. C₂×C₄

#13093965

semidirect

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

subgroup	index
C₂²×#13093965	2
C₂×#15688924	2
#20244254	2
#20241466	2
C₂×C₄₇×#493	2
#13325	47

subgroup

index

C₂×C₄₇×#493

Subgroups — #26135109

Conjugacy classes of subgroups

Complements

Maximal subgroups