Group #26111573 — subgroups

Subgroups — #26111573

Order 12032.

738 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 155 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	#20246453	C₂	1	1	yes	maximal, characteristic
2	#20244337	C₂	1	2	yes	maximal, complemented
3	C₂×#15688867	C₂	1	1	yes	maximal, characteristic
4	#20241228	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#492	C₂	1	1	yes	maximal, characteristic
6	C₂×D₄×Dic₄₇	—	2	2	no	—
7	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
8	#15689026	—	2	2	no	—
9	#15689003	—	2	2	no	—
10	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
11	#15688885	—	2	2	no	—
12	#15688885	—	2	2	no	—
13	#15688867	—	2	2	no	—
14	C₂²×SD₁₆×C₄₇	—	2	2	no	—
15	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#492	—	2	2	no	—
18	C₄₇×#492	C₄	1	4	yes	complemented
19	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₂³×Dic₄₇	—	2	2	no	—
21	C₂²×C₄₇⋊C₈	—	2	2	no	—
22	D₄×Dic₄₇	—	4	4	no	—
23	D₄×Dic₄₇	—	4	4	no	—
24	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
25	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
26	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
27	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
28	C₂×C₄×Dic₄₇	—	2	2	no	—
29	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
30	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
31	C₄₇⋊#95	—	2	2	no	—
32	C₂²×Q₈×C₄₇	—	2	1	no	—
33	C₂²×D₄×C₄₇	—	2	2	no	—
34	C₂²×D₄×C₄₇	D₄	1	2	yes	—
35	C₂×SD₁₆×C₄₇	—	2	8	no	—
36	C₂×SD₁₆×C₄₇	—	4	4	no	—
37	C₂×SD₁₆×C₄₇	—	4	4	no	—
38	C₂²×C₈×C₄₇	—	2	1	no	—
39	C₄⋊Q₈×C₄₇	—	2	1	no	—
40	C₄⋊Q₈×C₄₇	—	2	2	no	—
41	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
42	#127×C₄₇	—	2	2	no	—
43	#127×C₄₇	C₂×C₄	1	2	yes	—
44	#127×C₄₇	D₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
46	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
47	C₄×C₈×C₄₇	—	2	1	no	—
48	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	complemented
49	C₂⁴×C₄₇	—	2	2	no	—
50	C₂×Q₈×C₄₇	—	2	2	no	—
51	C₂×Q₈×C₄₇	—	4	2	no	—
52	C₂×Q₈×C₄₇	—	4	2	no	—
53	C₂×Q₈×C₄₇	—	4	1	no	—
54	C₂×D₄×C₄₇	—	2	4	no	—
55	C₂×D₄×C₄₇	—	2	4	no	—
56	C₂×D₄×C₄₇	—	2	2	no	—
57	C₂×D₄×C₄₇	—	4	2	no	—
58	C₂×D₄×C₄₇	—	4	2	no	—
59	C₂×D₄×C₄₇	—	4	2	no	—
60	C₂×D₄×C₄₇	—	4	2	no	—
61	C₂×D₄×C₄₇	—	4	2	no	—
62	C₂×D₄×C₄₇	—	4	2	no	—
63	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
64	C₂²×C₄×C₄₇	—	4	1	no	—
65	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
67	C₂²×Dic₄₇	—	2	2	no	—
68	C₂²×Dic₄₇	—	2	2	no	—
69	C₂²×Dic₄₇	—	4	8	no	—
70	C₂²×Dic₄₇	—	8	2	no	—
71	SD₁₆×C₄₇	—	4	16	no	—
72	C₂×C₈×C₄₇	—	2	2	no	—
73	C₂×C₈×C₄₇	—	2	2	no	—
74	C₂×C₈×C₄₇	—	2	2	no	—
75	C₄⋊C₄×C₄₇	—	2	4	no	—
76	C₄⋊C₄×C₄₇	—	4	2	no	—
77	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₄₇	#41	1	2	yes	—
80	C₂²⋊Dic₄₇	—	4	8	no	—
81	C₂²⋊Dic₄₇	—	8	2	no	—
82	C₄⋊Dic₄₇	—	2	2	no	—
83	C₄⋊Dic₄₇	—	2	2	no	—
84	C₄⋊Dic₄₇	—	2	2	no	—
85	C₄⋊Dic₄₇	SD₁₆	1	4	yes	complemented
86	C₄×Dic₄₇	—	4	2	no	—
87	C₄×Dic₄₇	—	4	2	no	—
88	C₂×C₄₇⋊C₈	—	4	2	no	—
89	C₂×C₄₇⋊C₈	—	4	2	no	—
90	C₂×C₄₇⋊C₈	—	4	2	no	—
91	C₂³×C₄₇	—	2	4	no	—
92	C₂³×C₄₇	—	4	4	no	—
93	C₂³×C₄₇	—	4	4	no	—
94	C₂³×C₄₇	—	4	2	no	—
95	C₂³×C₄₇	—	4	2	no	—
96	C₂³×C₄₇	#120	1	1	yes	characteristic
97	Q₈×C₄₇	—	4	4	no	—
98	Q₈×C₄₇	—	8	2	no	—
99	D₄×C₄₇	—	4	4	no	—
100	D₄×C₄₇	—	4	4	no	—
101	D₄×C₄₇	—	4	4	no	—
102	D₄×C₄₇	—	4	4	no	—
103	D₄×C₄₇	—	4	4	no	—
104	D₄×C₄₇	—	8	2	no	—
105	C₂×C₄×C₄₇	—	2	1	no	—
106	C₂×C₄×C₄₇	—	2	1	no	—
107	C₂×C₄×C₄₇	—	4	2	no	—
108	C₂×C₄×C₄₇	—	8	1	no	—
109	C₂×C₄×C₄₇	—	8	1	no	—
110	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
112	C₂×C₄×C₄₇	#121	1	2	yes	—
113	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
114	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
115	C₂×C₄×C₄₇	#135	1	2	yes	—
116	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
117	C₂×C₄×C₄₇	#137	1	2	yes	—
118	C₂×Dic₄₇	—	2	4	no	—
119	C₂×Dic₄₇	—	4	2	no	—
120	C₂×Dic₄₇	—	4	2	no	—
121	C₂×Dic₄₇	—	4	2	no	—
122	C₂×Dic₄₇	—	4	2	no	—
123	C₂×Dic₄₇	—	4	2	no	—
124	C₂×Dic₄₇	—	8	8	no	—
125	C₈×C₄₇	—	2	4	no	—
126	C₄₇⋊C₈	—	8	2	no	—
127	#9064	—	47	1	no	maximal, Sylow
128	C₂²×C₄₇	—	4	8	no	—
129	C₂²×C₄₇	—	4	4	no	—
130	C₂²×C₄₇	—	8	2	no	—
131	C₂²×C₄₇	—	8	2	no	—
132	C₂²×C₄₇	—	8	4	no	—
133	C₂²×C₄₇	#386	1	1	yes	characteristic
134	C₂²×C₄₇	#450	1	2	yes	—
135	C₂²×C₄₇	#452	1	2	yes	—
136	C₂²×C₄₇	#453	1	1	yes	characteristic
137	C₂²×C₄₇	#453	1	1	yes	characteristic
138	C₄×C₄₇	—	2	1	no	—
139	C₄×C₄₇	—	2	1	no	—
140	C₄×C₄₇	—	8	2	no	—
141	C₄×C₄₇	C₄×SD₁₆	1	2	yes	—
142	C₄×C₄₇	#440	1	2	yes	—
143	C₄×C₄₇	#461	1	2	yes	—
144	C₄×C₄₇	#463	1	2	yes	—
145	Dic₄₇	—	4	4	no	—
146	Dic₄₇	—	8	2	no	—
147	C₂×#492	D₄₇	1	1	yes	characteristic
148	#2366	—	47	1	no	—
149	#1987	—	47	2	no	—
150	C₂×#331	—	47	1	no	—
151	#1279	—	47	2	no	—
152	C₂×C₄₇	—	8	4	no	—
153	C₂×C₄₇	#1629	1	1	yes	characteristic
154	C₂×C₄₇	#1630	1	1	yes	characteristic
155	C₂×C₄₇	#1631	1	2	yes	—
156	C₂×C₄₇	#1877	1	2	yes	—
157	C₂×C₄₇	#1887	1	1	yes	characteristic
158	C₂²×SD₁₆	—	2	2	no	—
159	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
160	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
161	C₂×C₄×D₄	—	94	2	no	—
162	#492	—	2	2	no	—
163	#492	Dic₄₇	1	4	yes	complemented
164	C₂×C₄⋊C₈	—	47	2	no	—
165	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
166	#390	—	94	2	no	—
167	#386	—	94	2	no	—
168	C₄×C₄⋊C₄	—	47	2	no	—
169	#340	—	94	2	no	—
170	#340	—	94	2	no	—
171	#331	—	94	2	no	—
172	C₄₇	#9064	1	1	yes	characteristic, complemented, Sylow
173	C₂²×Q₈	—	2	1	no	—
174	C₂²×D₄	—	2	2	no	—
175	C₂²×D₄	C₂²⋊D₄₇	1	2	yes	—
176	C₂³×C₄	—	94	2	no	—
177	C₂×SD₁₆	—	2	8	no	—
178	C₂×SD₁₆	—	4	4	no	—
179	C₂×SD₁₆	—	4	4	no	—
180	C₂²×C₈	—	2	1	no	—
181	C₂²×C₈	—	94	2	no	—
182	C₄⋊Q₈	—	2	2	no	—
183	C₄⋊Q₈	—	2	1	no	—
184	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	complemented
185	#127	—	2	2	no	—
186	#127	C₂×Dic₄₇	1	2	yes	—
187	#127	C₂²⋊D₄₇	1	2	yes	—
188	C₄×D₄	—	188	4	no	—
189	C₄×D₄	—	188	4	no	—
190	C₂×C₄⋊C₄	—	2	2	no	—
191	C₂×C₄⋊C₄	—	47	2	no	—
192	C₂×C₄⋊C₄	—	47	2	no	—
193	C₂×C₂²⋊C₄	—	94	2	no	—
194	C₂×C₂²⋊C₄	—	94	4	no	—
195	C₂×C₄²	—	94	2	no	—
196	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
197	C₄⋊C₈	—	94	2	no	—
198	C₄⋊C₈	—	94	2	no	—
199	C₄×C₈	—	2	1	no	—
200	C₄×C₈	C₂×Dic₄₇	1	2	yes	complemented
201	#95	—	94	2	no	—
202	C₂⁴	—	2	2	no	—
203	C₂×Q₈	—	2	2	no	—
204	C₂×Q₈	—	4	2	no	—
205	C₂×Q₈	—	4	2	no	—
206	C₂×Q₈	—	4	1	no	—
207	C₂×D₄	—	2	4	no	—
208	C₂×D₄	—	2	4	no	—
209	C₂×D₄	—	2	2	no	—
210	C₂×D₄	—	4	2	no	—
211	C₂×D₄	—	4	2	no	—
212	C₂×D₄	—	4	2	no	—
213	C₂×D₄	—	4	2	no	—
214	C₂×D₄	—	4	2	no	—
215	C₂×D₄	—	4	2	no	—
216	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
217	C₂²×C₄	—	4	1	no	—
218	C₂²×C₄	—	94	2	no	—
219	C₂²×C₄	—	94	2	no	—
220	C₂²×C₄	—	376	2	no	—
221	C₂²×C₄	—	188	8	no	—
222	C₂²×C₄	D₄×D₄₇	1	2	yes	—
223	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
224	SD₁₆	—	4	16	no	—
225	C₂×C₈	—	2	2	no	—
226	C₂×C₈	—	2	2	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	188	2	no	—
229	C₂×C₈	—	188	2	no	—
230	C₂×C₈	—	188	2	no	—
231	C₄⋊C₄	—	2	4	no	—
232	C₄⋊C₄	—	4	2	no	—
233	C₄⋊C₄	—	47	4	no	—
234	C₄⋊C₄	—	94	2	no	—
235	C₄⋊C₄	—	94	2	no	—
236	C₄⋊C₄	—	94	2	no	—
237	C₂²⋊C₄	—	376	2	no	—
238	C₂²⋊C₄	—	188	8	no	—
239	C₄²	—	188	2	no	—
240	C₄²	—	188	2	no	—
241	C₄²	#10625352	1	2	yes	—
242	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
243	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
244	C₂³	—	2	4	no	—
245	C₂³	—	4	4	no	—
246	C₂³	—	4	4	no	—
247	C₂³	—	4	2	no	—
248	C₂³	—	4	2	no	—
249	C₂³	#13093992	1	1	yes	characteristic
250	Q₈	—	4	4	no	—
251	Q₈	—	8	2	no	—
252	D₄	—	4	4	no	—
253	D₄	—	4	4	no	—
254	D₄	—	4	4	no	—
255	D₄	—	4	4	no	—
256	D₄	—	4	4	no	—
257	D₄	—	8	2	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	8	1	no	—
262	C₂×C₄	—	8	1	no	—
263	C₂×C₄	—	94	4	no	—
264	C₂×C₄	—	376	8	no	—
265	C₂×C₄	—	188	2	no	—
266	C₂×C₄	—	188	2	no	—
267	C₂×C₄	—	188	2	no	—
268	C₂×C₄	—	188	2	no	—
269	C₂×C₄	—	188	2	no	—
270	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
271	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
272	C₂×C₄	#13093996	1	2	yes	—
273	C₂×C₄	#13094005	1	1	yes	characteristic
274	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
275	C₂×C₄	#13094045	1	2	yes	—
276	C₂×C₄	#13094051	1	2	yes	—
277	C₂×C₄	#13094053	1	2	yes	—
278	C₈	—	2	4	no	—
279	C₈	—	376	2	no	—
280	C₂²	—	4	8	no	—
281	C₂²	—	4	4	no	—
282	C₂²	—	8	2	no	—
283	C₂²	—	8	2	no	—
284	C₂²	—	8	4	no	—
285	C₂²	#15689003	1	1	yes	characteristic
286	C₂²	#15689272	1	2	yes	—
287	C₂²	#15689282	1	2	yes	—
288	C₂²	#15689290	1	1	yes	characteristic
289	C₂²	#15689290	1	1	yes	characteristic
290	C₄	—	2	1	no	—
291	C₄	—	2	1	no	—
292	C₄	—	8	2	no	—
293	C₄	—	376	2	no	—
294	C₄	—	188	4	no	—
295	C₄	SD₁₆×Dic₄₇	1	2	yes	—
296	C₄	#15689224	1	2	yes	—
297	C₄	#15689326	1	2	yes	—
298	C₄	#15689340	1	2	yes	—
299	C₂	—	8	4	no	—
300	C₂	#20242502	1	1	yes	characteristic
301	C₂	#20242507	1	1	yes	characteristic
302	C₂	#20242512	1	2	yes	—
303	C₂	#20243724	1	2	yes	—
304	C₂	#20243787	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20246453

C₂

yes

maximal, characteristic

#20244337

C₂

yes

maximal, complemented

C₂×#15688867

C₂

yes

maximal, characteristic

#20241228

C₂

yes

maximal, complemented

C₂×C₄₇×#492

C₂

yes

maximal, characteristic

C₂×D₄×Dic₄₇

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

#15689026

—

#15689003

—

C₄×C₄⋊Dic₄₇

C₂²

yes

—

#15688885

—

#15688885

—

#15688867

—

C₂²×SD₁₆×C₄₇

—

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₂×#127×C₄₇

C₂²

yes

characteristic

C₄₇×#492

—

C₄₇×#492

C₄

yes

complemented

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂³×Dic₄₇

—

C₂²×C₄₇⋊C₈

—

D₄×Dic₄₇

—

D₄×Dic₄₇

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×C₂²⋊Dic₄₇

—

C₂×C₂²⋊Dic₄₇

—

C₂×C₄×Dic₄₇

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄₇⋊#95

—

C₂²×Q₈×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

D₄

yes

—

C₂×SD₁₆×C₄₇

—

C₂×SD₁₆×C₄₇

—

C₂×SD₁₆×C₄₇

—

C₂²×C₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

C₂×C₄

yes

complemented

#127×C₄₇

—

#127×C₄₇

C₂×C₄

yes

—

#127×C₄₇

D₄

yes

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄×C₈×C₄₇

—

C₄×C₈×C₄₇

C₂×C₄

yes

complemented

C₂⁴×C₄₇

—

C₂×Q₈×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

—

C₂×D₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

SD₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

#41

yes

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

SD₁₆

yes

complemented

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#120

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

100

D₄×C₄₇

—

101

D₄×C₄₇

—

102

D₄×C₄₇

—

103

D₄×C₄₇

—

104

D₄×C₄₇

—

105

C₂×C₄×C₄₇

—

106

C₂×C₄×C₄₇

—

107

C₂×C₄×C₄₇

—

108

C₂×C₄×C₄₇

—

109

C₂×C₄×C₄₇

—

110

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

111

C₂×C₄×C₄₇

C₄×D₄

yes

—

112

C₂×C₄×C₄₇

#121

yes

—

113

C₂×C₄×C₄₇

#123

yes

characteristic

114

C₂×C₄×C₄₇

C₂×SD₁₆

yes

—

115

C₂×C₄×C₄₇

#135

yes

—

116

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

117

C₂×C₄×C₄₇

#137

yes

—

118

C₂×Dic₄₇

—

119

C₂×Dic₄₇

—

120

C₂×Dic₄₇

—

121

C₂×Dic₄₇

—

122

C₂×Dic₄₇

—

123

C₂×Dic₄₇

—

124

C₂×Dic₄₇

—

125

C₈×C₄₇

—

126

C₄₇⋊C₈

—

127

#9064

—

maximal, Sylow

128

C₂²×C₄₇

—

129

C₂²×C₄₇

—

130

C₂²×C₄₇

—

131

C₂²×C₄₇

—

132

C₂²×C₄₇

—

133

C₂²×C₄₇

#386

yes

characteristic

134

C₂²×C₄₇

#450

yes

—

135

C₂²×C₄₇

#452

yes

—

136

C₂²×C₄₇

#453

yes

characteristic

137

C₂²×C₄₇

#453

yes

characteristic

138

C₄×C₄₇

—

139

C₄×C₄₇

—

140

C₄×C₄₇

—

141

C₄×C₄₇

C₄×SD₁₆

yes

—

142

C₄×C₄₇

#440

yes

—

143

C₄×C₄₇

#461

yes

—

144

C₄×C₄₇

#463

yes

—

145

Dic₄₇

—

146

Dic₄₇

—

147

C₂×#492

D₄₇

yes

characteristic

148

#2366

—

149

#1987

—

150

C₂×#331

—

151

#1279

—

152

C₂×C₄₇

—

153

C₂×C₄₇

#1629

yes

characteristic

154

C₂×C₄₇

#1630

yes

characteristic

155

C₂×C₄₇

#1631

yes

—

156

C₂×C₄₇

#1877

yes

—

157

C₂×C₄₇

#1887

yes

characteristic

158

C₂²×SD₁₆

—

159

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

160

C₂×#127

C₂×D₄₇

yes

characteristic

161

C₂×C₄×D₄

—

162

#492

—

163

#492

Dic₄₇

yes

complemented

164

C₂×C₄⋊C₈

—

165

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

166

#390

—

167

#386

—

168

C₄×C₄⋊C₄

—

169

#340

—

170

#340

—

171

#331

—

172

C₄₇

#9064

yes

characteristic, complemented, Sylow

173

C₂²×Q₈

—

174

C₂²×D₄

—

175

C₂²×D₄

C₂²⋊D₄₇

yes

—

176

C₂³×C₄

—

177

C₂×SD₁₆

—

178

C₂×SD₁₆

—

179

C₂×SD₁₆

—

180

C₂²×C₈

—

181

C₂²×C₈

—

182

C₄⋊Q₈

—

183

C₄⋊Q₈

—

184

C₄⋊Q₈

C₂×Dic₄₇

yes

complemented

185

#127

—

186

#127

C₂×Dic₄₇

yes

—

187

#127

C₂²⋊D₄₇

yes

—

188

C₄×D₄

—

188

—

189

C₄×D₄

—

188

—

190

C₂×C₄⋊C₄

—

191

C₂×C₄⋊C₄

—

192

C₂×C₄⋊C₄

—

193

C₂×C₂²⋊C₄

—

194

C₂×C₂²⋊C₄

—

195

C₂×C₄²

—

196

C₂×C₄²

C₂²×D₄₇

yes

characteristic

197

C₄⋊C₈

—

198

C₄⋊C₈

—

199

C₄×C₈

—

200

C₄×C₈

C₂×Dic₄₇

yes

complemented

201

#95

—

202

C₂⁴

—

203

C₂×Q₈

—

204

C₂×Q₈

—

205

C₂×Q₈

—

206

C₂×Q₈

—

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

—

216

C₂×D₄

C₂²⋊Dic₄₇

yes

—

217

C₂²×C₄

—

218

C₂²×C₄

—

219

C₂²×C₄

—

220

C₂²×C₄

—

376

—

221

C₂²×C₄

—

188

—

222

C₂²×C₄

D₄×D₄₇

yes

—

223

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

224

SD₁₆

—

225

C₂×C₈

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₂×C₈

—

188

—

229

C₂×C₈

—

188

—

230

C₂×C₈

—

188

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₂²⋊C₄

—

376

—

238

C₂²⋊C₄

—

188

—

239

C₄²

—

188

—

240

C₄²

—

188

—

241

C₄²

#10625352

yes

—

242

C₄²

C₂²×Dic₄₇

yes

characteristic

243

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

244

C₂³

—

245

C₂³

—

246

C₂³

—

247

C₂³

—

248

C₂³

—

249

C₂³

#13093992

yes

characteristic

250

Q₈

—

251

Q₈

—

252

D₄

—

253

D₄

—

254

D₄

—

255

D₄

—

256

D₄

—

257

D₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

—

264

C₂×C₄

—

376

—

265

C₂×C₄

—

188

—

266

C₂×C₄

—

188

—

267

C₂×C₄

—

188

—

268

C₂×C₄

—

188

—

269

C₂×C₄

—

188

—

270

C₂×C₄

C₂×C₂²⋊Dic₄₇

yes

characteristic

271

C₂×C₄

D₄×Dic₄₇

yes

—

272

C₂×C₄

#13093996

yes

—

273

C₂×C₄

#13094005

yes

characteristic

274

C₂×C₄

SD₁₆×D₄₇

yes

—

275

C₂×C₄

#13094045

yes

—

276

C₂×C₄

#13094051

yes

—

277

C₂×C₄

#13094053

yes

—

278

C₈

—

279

C₈

—

376

—

280

C₂²

—

281

C₂²

—

282

C₂²

—

283

C₂²

—

284

C₂²

—

285

C₂²

#15689003

yes

characteristic

286

C₂²

#15689272

yes

—

287

C₂²

#15689282

yes

—

288

C₂²

#15689290

yes

characteristic

289

C₂²

#15689290

yes

characteristic

290

C₄

—

291

C₄

—

292

C₄

—

293

C₄

—

376

—

294

C₄

—

188

—

295

C₄

SD₁₆×Dic₄₇

yes

—

296

C₄

#15689224

yes

—

297

C₄

#15689326

yes

—

298

C₄

#15689340

yes

—

299

C₂

—

300

C₂

#20242502

yes

characteristic

301

C₂

#20242507

yes

characteristic

302

C₂

#20242512

yes

—

303

C₂

#20243724

yes

—

304

C₂

#20243787

yes

characteristic

	subgroup	G/H
center	C₂³	#13093992
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#492	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂×#127×C₄₇	C₂²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#492	D₄₇
hypocenter	C₄₇	#9064
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#492

subgroup

G/H

center

C₂³

#13093992

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₂×C₄₇×#492

C₂

socle

C₂³×C₄₇

#120

prime radical

C₂×#127×C₄₇

C₂²

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#492

N	H ≅ G/N	type
2. #20244337	C₂	semidirect
4. #20241228	C₂	semidirect
18. C₄₇×#492	C₄	semidirect
41. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
48. C₄×C₈×C₄₇	C₂×C₄	semidirect
85. C₄⋊Dic₄₇	SD₁₆	semidirect
163. #492	Dic₄₇	semidirect
172. C₄₇	#9064	semidirect
184. C₄⋊Q₈	C₂×Dic₄₇	semidirect
200. C₄×C₈	C₂×Dic₄₇	semidirect

H ≅ G/N

type

2. #20244337

C₂

semidirect

4. #20241228

C₂

semidirect

18. C₄₇×#492

C₄

semidirect

41. C₄⋊Q₈×C₄₇

C₂×C₄

semidirect

48. C₄×C₈×C₄₇

C₂×C₄

semidirect

85. C₄⋊Dic₄₇

SD₁₆

semidirect

163. #492

Dic₄₇

semidirect

172. C₄₇

#9064

semidirect

184. C₄⋊Q₈

C₂×Dic₄₇

semidirect

200. C₄×C₈

C₂×Dic₄₇

semidirect

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

subgroup	index
#20246453	2
#20244337	2
C₂×#15688867	2
#20241228	2
C₂×C₄₇×#492	2
#9064	47

subgroup

index

C₂×C₄₇×#492

Subgroups — #26111573

Conjugacy classes of subgroups

Complements

Maximal subgroups