Group #26111568 — subgroups

Subgroups — #26111568

Order 12032.

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

normal subgroups only

This group has 654 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	#20246478	C₂	1	1	yes	maximal, characteristic, complemented
2	#20244316	C₂	1	2	yes	maximal
3	C₂×#15688872	C₂	1	1	yes	maximal, characteristic, complemented
4	#20241228	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#492	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
7	C₂×#13093945	—	2	2	no	—
8	C₂×#13093945	—	2	2	no	—
9	#15689030	—	2	2	no	—
10	#15689022	—	2	2	no	—
11	C₄⋊C₄×Dic₄₇	—	2	2	no	—
12	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
13	#15688872	—	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	C₂²×C₄₇⋊C₈	—	2	2	no	—
21	C₂×C₄⋊Dic₄₇	—	2	2	no	—
22	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
23	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
24	C₂×C₄×Dic₄₇	—	2	2	no	—
25	C₂×C₄×Dic₄₇	—	2	2	no	—
26	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
27	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
28	#13093945	—	4	4	no	—
29	#13093945	—	4	4	no	—
30	C₄₇⋊#95	—	2	4	no	—
31	C₄₇⋊#95	—	2	2	no	—
32	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
33	C₂²×D₄×C₄₇	—	2	1	no	—
34	C₂²×D₄×C₄₇	—	2	2	no	—
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	2	no	—
40	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
41	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
42	#127×C₄₇	—	2	1	no	—
43	#127×C₄₇	—	2	2	no	—
44	#127×C₄₇	C₂×C₄	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	—
49	C₂⁴×C₄₇	—	4	1	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	C₂²⋊C₄	1	4	yes	—
54	C₂×D₄×C₄₇	—	2	2	no	—
55	C₂×D₄×C₄₇	—	2	4	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	—	4	1	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	—	4	2	no	—
64	C₂²×C₄×C₄₇	—	2	2	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	SD₁₆×C₄₇	—	4	16	no	—
70	C₂×C₈×C₄₇	—	2	2	no	—
71	C₂×C₈×C₄₇	—	2	2	no	—
72	C₂×C₈×C₄₇	—	2	2	no	—
73	C₄⋊C₄×C₄₇	—	2	4	no	—
74	C₄⋊C₄×C₄₇	—	2	4	no	—
75	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₄₇	#41	1	2	yes	—
78	C₄⋊Dic₄₇	—	2	2	no	—
79	C₄⋊Dic₄₇	—	2	2	no	—
80	C₄⋊Dic₄₇	—	2	2	no	—
81	C₄⋊Dic₄₇	—	8	2	no	—
82	C₄⋊Dic₄₇	SD₁₆	1	4	yes	complemented
83	C₄×Dic₄₇	—	4	2	no	—
84	C₄×Dic₄₇	—	4	2	no	—
85	C₄×Dic₄₇	—	8	2	no	—
86	C₂×C₄₇⋊C₈	—	4	2	no	—
87	C₂×C₄₇⋊C₈	—	4	2	no	—
88	C₂×C₄₇⋊C₈	—	4	2	no	—
89	C₂³×C₄₇	—	4	2	no	—
90	C₂³×C₄₇	—	8	2	no	—
91	C₂³×C₄₇	—	8	2	no	—
92	C₂³×C₄₇	—	8	1	no	—
93	C₂³×C₄₇	—	8	1	no	—
94	C₂³×C₄₇	#120	1	1	yes	characteristic
95	Q₈×C₄₇	—	4	4	no	—
96	Q₈×C₄₇	—	8	2	no	—
97	D₄×C₄₇	—	4	4	no	—
98	D₄×C₄₇	—	4	4	no	—
99	D₄×C₄₇	—	4	4	no	—
100	D₄×C₄₇	—	8	2	no	—
101	D₄×C₄₇	—	8	2	no	—
102	D₄×C₄₇	—	8	2	no	—
103	C₂×C₄×C₄₇	—	2	1	no	—
104	C₂×C₄×C₄₇	—	2	1	no	—
105	C₂×C₄×C₄₇	—	2	4	no	—
106	C₂×C₄×C₄₇	—	4	2	no	—
107	C₂×C₄×C₄₇	—	4	2	no	—
108	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
110	C₂×C₄×C₄₇	#121	1	2	yes	—
111	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
112	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
113	C₂×C₄×C₄₇	#135	1	2	yes	—
114	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
115	C₂×C₄×C₄₇	#137	1	2	yes	—
116	C₂×Dic₄₇	—	2	4	no	—
117	C₂×Dic₄₇	—	4	2	no	—
118	C₂×Dic₄₇	—	4	2	no	—
119	C₂×Dic₄₇	—	4	2	no	—
120	C₂×Dic₄₇	—	4	2	no	—
121	C₂×Dic₄₇	—	4	2	no	—
122	C₈×C₄₇	—	2	4	no	—
123	C₄₇⋊C₈	—	8	2	no	—
124	#9063	—	47	1	no	maximal, Sylow
125	C₂²×C₄₇	—	8	4	no	—
126	C₂²×C₄₇	—	8	2	no	—
127	C₂²×C₄₇	—	16	2	no	—
128	C₂²×C₄₇	—	16	1	no	—
129	C₂²×C₄₇	—	16	1	no	—
130	C₂²×C₄₇	#386	1	1	yes	characteristic
131	C₂²×C₄₇	#448	1	2	yes	—
132	C₂²×C₄₇	#449	1	2	yes	—
133	C₂²×C₄₇	#453	1	1	yes	characteristic
134	C₂²×C₄₇	#453	1	1	yes	characteristic
135	C₄×C₄₇	—	2	1	no	—
136	C₄×C₄₇	—	2	1	no	—
137	C₄×C₄₇	—	4	4	no	—
138	C₄×C₄₇	C₄×SD₁₆	1	2	yes	—
139	C₄×C₄₇	#440	1	2	yes	—
140	C₄×C₄₇	#460	1	2	yes	—
141	C₄×C₄₇	#464	1	2	yes	—
142	Dic₄₇	—	4	4	no	—
143	Dic₄₇	—	8	2	no	—
144	C₂×#492	D₄₇	1	1	yes	characteristic
145	#2369	—	47	1	no	—
146	#1982	—	47	2	no	—
147	C₂×#333	—	47	1	no	—
148	#1279	—	47	2	no	—
149	C₂×C₄₇	—	16	2	no	—
150	C₂×C₄₇	#1622	1	2	yes	—
151	C₂×C₄₇	#1623	1	1	yes	characteristic
152	C₂×C₄₇	#1624	1	1	yes	characteristic
153	C₂×C₄₇	#1880	1	2	yes	—
154	C₂×C₄₇	#1887	1	1	yes	characteristic
155	C₂²×SD₁₆	—	2	2	no	—
156	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
157	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
158	#492	—	2	2	no	—
159	#492	Dic₄₇	1	4	yes	complemented
160	C₂×C₄⋊C₈	—	47	2	no	—
161	C₂×#102	—	94	2	no	—
162	C₂×#102	—	94	2	no	—
163	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
164	#391	—	94	2	no	—
165	#389	—	94	2	no	—
166	C₄×C₄⋊C₄	—	47	2	no	—
167	C₄×C₄⋊C₄	—	94	2	no	—
168	#333	—	94	2	no	—
169	C₄₇	#9063	1	1	yes	characteristic, complemented, Sylow
170	C₂²×Q₈	C₂²⋊D₄₇	1	2	yes	—
171	C₂²×D₄	—	2	2	no	—
172	C₂²×D₄	—	2	1	no	—
173	C₂×SD₁₆	—	2	8	no	—
174	C₂×SD₁₆	—	4	4	no	—
175	C₂×SD₁₆	—	4	4	no	—
176	C₂²×C₈	—	2	1	no	—
177	C₂²×C₈	—	94	2	no	—
178	C₄⋊Q₈	—	2	2	no	—
179	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
180	C₄⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
181	#127	—	2	2	no	—
182	#127	—	2	1	no	—
183	#127	C₂×Dic₄₇	1	2	yes	—
184	C₂×C₄⋊C₄	—	2	2	no	—
185	C₂×C₄⋊C₄	—	47	2	no	—
186	C₂×C₄⋊C₄	—	47	2	no	—
187	C₂×C₄⋊C₄	—	94	2	no	—
188	C₂×C₄²	—	94	2	no	—
189	C₂×C₄²	—	94	2	no	—
190	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
191	C₄⋊C₈	—	94	2	no	—
192	C₄⋊C₈	—	94	2	no	—
193	#102	—	188	4	no	—
194	#102	—	188	4	no	—
195	C₄×C₈	—	2	1	no	—
196	C₄×C₈	C₂×Dic₄₇	1	2	yes	—
197	#95	—	94	4	no	—
198	#95	—	94	2	no	—
199	C₂⁴	—	4	1	no	—
200	C₂×Q₈	—	2	2	no	—
201	C₂×Q₈	—	4	2	no	—
202	C₂×Q₈	—	4	2	no	—
203	C₂×Q₈	C₂²⋊Dic₄₇	1	4	yes	—
204	C₂×D₄	—	2	2	no	—
205	C₂×D₄	—	2	4	no	—
206	C₂×D₄	—	4	2	no	—
207	C₂×D₄	—	4	2	no	—
208	C₂×D₄	—	4	2	no	—
209	C₂×D₄	—	4	1	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	C₂²×C₄	—	2	2	no	—
215	C₂²×C₄	—	94	2	no	—
216	C₂²×C₄	—	94	2	no	—
217	C₂²×C₄	D₄×D₄₇	1	2	yes	—
218	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
219	SD₁₆	—	4	16	no	—
220	C₂×C₈	—	2	2	no	—
221	C₂×C₈	—	2	2	no	—
222	C₂×C₈	—	2	2	no	—
223	C₂×C₈	—	188	2	no	—
224	C₂×C₈	—	188	2	no	—
225	C₂×C₈	—	188	2	no	—
226	C₄⋊C₄	—	2	4	no	—
227	C₄⋊C₄	—	2	4	no	—
228	C₄⋊C₄	—	47	4	no	—
229	C₄⋊C₄	—	94	2	no	—
230	C₄⋊C₄	—	94	2	no	—
231	C₄⋊C₄	—	94	2	no	—
232	C₄⋊C₄	—	376	2	no	—
233	C₄²	—	376	2	no	—
234	C₄²	—	188	2	no	—
235	C₄²	—	188	2	no	—
236	C₄²	#10625352	1	2	yes	—
237	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
238	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
239	C₂³	—	4	2	no	—
240	C₂³	—	8	2	no	—
241	C₂³	—	8	2	no	—
242	C₂³	—	8	1	no	—
243	C₂³	—	8	1	no	—
244	C₂³	#13093992	1	1	yes	characteristic
245	Q₈	—	4	4	no	—
246	Q₈	—	8	2	no	—
247	D₄	—	4	4	no	—
248	D₄	—	4	4	no	—
249	D₄	—	4	4	no	—
250	D₄	—	8	2	no	—
251	D₄	—	8	2	no	—
252	D₄	—	8	2	no	—
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	2	1	no	—
255	C₂×C₄	—	2	4	no	—
256	C₂×C₄	—	4	2	no	—
257	C₂×C₄	—	4	2	no	—
258	C₂×C₄	—	94	4	no	—
259	C₂×C₄	—	188	2	no	—
260	C₂×C₄	—	188	2	no	—
261	C₂×C₄	—	188	2	no	—
262	C₂×C₄	—	188	2	no	—
263	C₂×C₄	—	188	2	no	—
264	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
265	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
266	C₂×C₄	#13093996	1	2	yes	—
267	C₂×C₄	#13094005	1	1	yes	characteristic
268	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
269	C₂×C₄	#13094045	1	2	yes	—
270	C₂×C₄	#13094051	1	2	yes	—
271	C₂×C₄	#13094053	1	2	yes	—
272	C₈	—	2	4	no	—
273	C₈	—	376	2	no	—
274	C₂²	—	8	4	no	—
275	C₂²	—	8	2	no	—
276	C₂²	—	16	2	no	—
277	C₂²	—	16	1	no	—
278	C₂²	—	16	1	no	—
279	C₂²	#15689003	1	1	yes	characteristic
280	C₂²	#15689260	1	2	yes	—
281	C₂²	#15689267	1	2	yes	—
282	C₂²	#15689290	1	1	yes	characteristic
283	C₂²	#15689290	1	1	yes	characteristic
284	C₄	—	2	1	no	—
285	C₄	—	2	1	no	—
286	C₄	—	4	4	no	—
287	C₄	—	376	2	no	—
288	C₄	—	188	4	no	—
289	C₄	SD₁₆×Dic₄₇	1	2	yes	—
290	C₄	#15689224	1	2	yes	—
291	C₄	#15689321	1	2	yes	—
292	C₄	#15689343	1	2	yes	—
293	C₂	—	16	2	no	—
294	C₂	#20242457	1	2	yes	—
295	C₂	#20242464	1	1	yes	characteristic
296	C₂	#20242469	1	1	yes	characteristic
297	C₂	#20243745	1	2	yes	—
298	C₂	#20243787	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20246478

C₂

yes

maximal, characteristic, complemented

#20244316

C₂

yes

maximal

C₂×#15688872

C₂

yes

maximal, characteristic, complemented

#20241228

C₂

yes

maximal, complemented

C₂×C₄₇×#492

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

—

—

—

—

C₄⋊C₄×Dic₄₇

—

C₄×C₄⋊Dic₄₇

C₂²

yes

—

#15688872

—

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

C₂²×C₄₇⋊C₈

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

#13093945

—

#13093945

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂²×Q₈×C₄₇

D₄

yes

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂×SD₁₆×C₄₇

—

C₂×SD₁₆×C₄₇

—

C₂×SD₁₆×C₄₇

—

C₂²×C₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

C₂×C₄

yes

—

C₄⋊Q₈×C₄₇

D₄

yes

—

#127×C₄₇

—

#127×C₄₇

—

#127×C₄₇

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄×C₈×C₄₇

—

C₄×C₈×C₄₇

C₂×C₄

yes

—

C₂⁴×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂²⋊C₄

yes

—

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×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

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

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

SD₁₆

yes

complemented

C₄×Dic₄₇

—

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

—

D₄×C₄₇

—

D₄×C₄₇

—

100

D₄×C₄₇

—

101

D₄×C₄₇

—

102

D₄×C₄₇

—

103

C₂×C₄×C₄₇

—

104

C₂×C₄×C₄₇

—

105

C₂×C₄×C₄₇

—

106

C₂×C₄×C₄₇

—

107

C₂×C₄×C₄₇

—

108

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

109

C₂×C₄×C₄₇

C₄×D₄

yes

—

110

C₂×C₄×C₄₇

#121

yes

—

111

C₂×C₄×C₄₇

#123

yes

characteristic

112

C₂×C₄×C₄₇

C₂×SD₁₆

yes

—

113

C₂×C₄×C₄₇

#135

yes

—

114

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

115

C₂×C₄×C₄₇

#137

yes

—

116

C₂×Dic₄₇

—

117

C₂×Dic₄₇

—

118

C₂×Dic₄₇

—

119

C₂×Dic₄₇

—

120

C₂×Dic₄₇

—

121

C₂×Dic₄₇

—

122

C₈×C₄₇

—

123

C₄₇⋊C₈

—

124

#9063

—

maximal, Sylow

125

C₂²×C₄₇

—

126

C₂²×C₄₇

—

127

C₂²×C₄₇

—

128

C₂²×C₄₇

—

129

C₂²×C₄₇

—

130

C₂²×C₄₇

#386

yes

characteristic

131

C₂²×C₄₇

#448

yes

—

132

C₂²×C₄₇

#449

yes

—

133

C₂²×C₄₇

#453

yes

characteristic

134

C₂²×C₄₇

#453

yes

characteristic

135

C₄×C₄₇

—

136

C₄×C₄₇

—

137

C₄×C₄₇

—

138

C₄×C₄₇

C₄×SD₁₆

yes

—

139

C₄×C₄₇

#440

yes

—

140

C₄×C₄₇

#460

yes

—

141

C₄×C₄₇

#464

yes

—

142

Dic₄₇

—

143

Dic₄₇

—

144

C₂×#492

D₄₇

yes

characteristic

145

#2369

—

146

#1982

—

147

C₂×#333

—

148

#1279

—

149

C₂×C₄₇

—

150

C₂×C₄₇

#1622

yes

—

151

C₂×C₄₇

#1623

yes

characteristic

152

C₂×C₄₇

#1624

yes

characteristic

153

C₂×C₄₇

#1880

yes

—

154

C₂×C₄₇

#1887

yes

characteristic

155

C₂²×SD₁₆

—

156

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

157

C₂×#127

C₂×D₄₇

yes

characteristic

158

#492

—

159

#492

Dic₄₇

yes

complemented

160

C₂×C₄⋊C₈

—

161

C₂×#102

—

162

C₂×#102

—

163

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

164

#391

—

165

#389

—

166

C₄×C₄⋊C₄

—

167

C₄×C₄⋊C₄

—

168

#333

—

169

C₄₇

#9063

yes

characteristic, complemented, Sylow

170

C₂²×Q₈

C₂²⋊D₄₇

yes

—

171

C₂²×D₄

—

172

C₂²×D₄

—

173

C₂×SD₁₆

—

174

C₂×SD₁₆

—

175

C₂×SD₁₆

—

176

C₂²×C₈

—

177

C₂²×C₈

—

178

C₄⋊Q₈

—

179

C₄⋊Q₈

C₂×Dic₄₇

yes

—

180

C₄⋊Q₈

C₂²⋊D₄₇

yes

—

181

#127

—

182

#127

—

183

#127

C₂×Dic₄₇

yes

—

184

C₂×C₄⋊C₄

—

185

C₂×C₄⋊C₄

—

186

C₂×C₄⋊C₄

—

187

C₂×C₄⋊C₄

—

188

C₂×C₄²

—

189

C₂×C₄²

—

190

C₂×C₄²

C₂²×D₄₇

yes

characteristic

191

C₄⋊C₈

—

192

C₄⋊C₈

—

193

#102

—

188

—

194

#102

—

188

—

195

C₄×C₈

—

196

C₄×C₈

C₂×Dic₄₇

yes

—

197

#95

—

198

#95

—

199

C₂⁴

—

200

C₂×Q₈

—

201

C₂×Q₈

—

202

C₂×Q₈

—

203

C₂×Q₈

C₂²⋊Dic₄₇

yes

—

204

C₂×D₄

—

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

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

D₄×D₄₇

yes

—

218

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

219

SD₁₆

—

220

C₂×C₈

—

221

C₂×C₈

—

222

C₂×C₈

—

223

C₂×C₈

—

188

—

224

C₂×C₈

—

188

—

225

C₂×C₈

—

188

—

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

376

—

233

C₄²

—

376

—

234

C₄²

—

188

—

235

C₄²

—

188

—

236

C₄²

#10625352

yes

—

237

C₄²

C₂²×Dic₄₇

yes

characteristic

238

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

239

C₂³

—

240

C₂³

—

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

#13093992

yes

characteristic

245

Q₈

—

246

Q₈

—

247

D₄

—

248

D₄

—

249

D₄

—

250

D₄

—

251

D₄

—

252

D₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

188

—

260

C₂×C₄

—

188

—

261

C₂×C₄

—

188

—

262

C₂×C₄

—

188

—

263

C₂×C₄

—

188

—

264

C₂×C₄

C₂×C₂²⋊Dic₄₇

yes

characteristic

265

C₂×C₄

D₄×Dic₄₇

yes

—

266

C₂×C₄

#13093996

yes

—

267

C₂×C₄

#13094005

yes

characteristic

268

C₂×C₄

SD₁₆×D₄₇

yes

—

269

C₂×C₄

#13094045

yes

—

270

C₂×C₄

#13094051

yes

—

271

C₂×C₄

#13094053

yes

—

272

C₈

—

273

C₈

—

376

—

274

C₂²

—

275

C₂²

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

#15689003

yes

characteristic

280

C₂²

#15689260

yes

—

281

C₂²

#15689267

yes

—

282

C₂²

#15689290

yes

characteristic

283

C₂²

#15689290

yes

characteristic

284

C₄

—

285

C₄

—

286

C₄

—

287

C₄

—

376

—

288

C₄

—

188

—

289

C₄

SD₁₆×Dic₄₇

yes

—

290

C₄

#15689224

yes

—

291

C₄

#15689321

yes

—

292

C₄

#15689343

yes

—

293

C₂

—

294

C₂

#20242457

yes

—

295

C₂

#20242464

yes

characteristic

296

C₂

#20242469

yes

characteristic

297

C₂

#20243745

yes

—

298

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	#9063
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
1. #20246478	C₂	semidirect
3. C₂×#15688872	C₂	semidirect
4. #20241228	C₂	semidirect
18. C₄₇×#492	C₄	semidirect
82. C₄⋊Dic₄₇	SD₁₆	semidirect
159. #492	Dic₄₇	semidirect
169. C₄₇	#9063	semidirect

H ≅ G/N

type

1. #20246478

C₂

semidirect

3. C₂×#15688872

C₂

semidirect

4. #20241228

C₂

semidirect

18. C₄₇×#492

C₄

semidirect

82. C₄⋊Dic₄₇

SD₁₆

semidirect

159. #492

Dic₄₇

semidirect

169. C₄₇

#9063

semidirect

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

subgroup	index
#20246478	2
#20244316	2
C₂×#15688872	2
#20241228	2
C₂×C₄₇×#492	2
#9063	47

subgroup

index

C₂×C₄₇×#492

Subgroups — #26111568

Conjugacy classes of subgroups

Complements

Maximal subgroups