Group #26049688 — subgroups

Subgroups — C₄₇×#9990 #26049688

Order 12032.

826 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 826 conjugacy classes of subgroups — too many to draw. Only its 106 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	C₄₇×#3195	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#450	C₂	1	2	yes	maximal
3	C₄₇×#1783	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1472	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1298	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×SD₁₆×C₄₇	—	2	2	no	—
8	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
9	C₄₇×#483	—	2	2	no	—
10	C₄₇×#470	—	2	2	no	—
11	C₄₇×#451	—	2	2	no	—
12	C₄₇×#450	—	2	4	no	—
13	C₄₇×#450	—	2	4	no	—
14	C₂×#102×C₄₇	—	2	2	no	—
15	C₂×#100×C₄₇	—	2	2	no	—
16	C₄₇×#407	C₂²	1	1	yes	characteristic
17	C₄₇×#407	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#324	—	2	4	no	—
20	C₂⁵×C₄₇	—	2	1	no	—
21	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
22	C₂²×D₄×C₄₇	—	2	2	no	—
23	C₂²×D₄×C₄₇	—	2	1	no	—
24	C₂²×D₄×C₄₇	—	2	2	no	—
25	C₂²×D₄×C₄₇	—	4	4	no	—
26	C₂²×D₄×C₄₇	D₄	1	2	yes	—
27	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
28	C₂×Q₁₆×C₄₇	—	2	2	no	—
29	C₂×SD₁₆×C₄₇	—	2	8	no	—
30	C₂×SD₁₆×C₄₇	—	4	8	no	—
31	C₂×M₁₆×C₄₇	—	2	1	no	—
32	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
33	C₂²×C₈×C₄₇	—	2	2	no	—
34	C₂²⋊Q₈×C₄₇	—	2	2	no	—
35	C₂²⋊Q₈×C₄₇	—	2	2	no	—
36	C₂²⋊Q₈×C₄₇	—	2	2	no	—
37	C₂²⋊Q₈×C₄₇	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
39	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
40	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
41	#106×C₄₇	—	2	2	no	—
42	#103×C₄₇	—	2	4	no	—
43	#102×C₄₇	—	2	8	no	—
44	#100×C₄₇	—	4	4	no	—
45	C₂²⋊C₈×C₄₇	—	2	2	no	—
46	C₂²⋊C₈×C₄₇	—	2	2	no	—
47	C₂²⋊C₈×C₄₇	—	2	2	no	—
48	C₂²⋊C₈×C₄₇	D₄	1	4	yes	—
49	C₂⁴×C₄₇	—	2	2	no	—
50	C₂⁴×C₄₇	—	4	4	no	—
51	C₂⁴×C₄₇	—	4	2	no	—
52	C₂⁴×C₄₇	—	8	4	no	—
53	C₂⁴×C₄₇	#41	1	1	yes	characteristic
54	C₂×Q₈×C₄₇	—	2	2	no	—
55	C₂×Q₈×C₄₇	—	2	2	no	—
56	C₂×Q₈×C₄₇	—	4	4	no	—
57	C₂×D₄×C₄₇	—	2	8	no	—
58	C₂×D₄×C₄₇	—	2	4	no	—
59	C₂×D₄×C₄₇	—	2	4	no	—
60	C₂×D₄×C₄₇	—	4	4	no	—
61	C₂×D₄×C₄₇	—	4	2	no	—
62	C₂×D₄×C₄₇	—	4	4	no	—
63	C₂×D₄×C₄₇	—	4	8	no	—
64	C₂×D₄×C₄₇	—	4	1	no	—
65	C₂×D₄×C₄₇	—	4	1	no	—
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	4	2	no	—
69	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
70	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
73	Q₁₆×C₄₇	—	8	2	no	—
74	SD₁₆×C₄₇	—	4	16	no	—
75	M₁₆×C₄₇	—	4	2	no	—
76	M₁₆×C₄₇	—	4	2	no	—
77	C₂×C₈×C₄₇	—	2	2	no	—
78	C₂×C₈×C₄₇	—	2	4	no	—
79	C₂×C₈×C₄₇	—	4	4	no	—
80	C₂×C₈×C₄₇	—	4	1	no	—
81	C₄⋊C₄×C₄₇	—	2	2	no	—
82	C₄⋊C₄×C₄₇	—	2	2	no	—
83	C₄⋊C₄×C₄₇	—	4	2	no	—
84	C₄⋊C₄×C₄₇	—	4	2	no	—
85	C₂²⋊C₄×C₄₇	—	4	2	no	—
86	C₂²⋊C₄×C₄₇	—	4	2	no	—
87	C₂³×C₄₇	—	2	4	no	—
88	C₂³×C₄₇	—	2	4	no	—
89	C₂³×C₄₇	—	4	1	no	—
90	C₂³×C₄₇	—	4	8	no	—
91	C₂³×C₄₇	—	4	2	no	—
92	C₂³×C₄₇	—	4	2	no	—
93	C₂³×C₄₇	—	8	4	no	—
94	C₂³×C₄₇	—	8	4	no	—
95	C₂³×C₄₇	—	8	16	no	—
96	C₂³×C₄₇	—	8	4	no	—
97	C₂³×C₄₇	#121	1	1	yes	characteristic
98	C₂³×C₄₇	#121	1	2	yes	—
99	Q₈×C₄₇	—	4	4	no	—
100	Q₈×C₄₇	—	4	4	no	—
101	D₄×C₄₇	—	2	8	no	—
102	D₄×C₄₇	—	4	4	no	—
103	D₄×C₄₇	—	4	4	no	—
104	D₄×C₄₇	—	4	4	no	—
105	C₂×C₄×C₄₇	—	2	4	no	—
106	C₂×C₄×C₄₇	—	2	2	no	—
107	C₂×C₄×C₄₇	—	4	1	no	—
108	C₂×C₄×C₄₇	—	4	2	no	—
109	C₂×C₄×C₄₇	—	4	2	no	—
110	C₂×C₄×C₄₇	—	4	2	no	—
111	C₂×C₄×C₄₇	—	4	4	no	—
112	C₂×C₄×C₄₇	—	8	2	no	—
113	C₂×C₄×C₄₇	#120	1	2	yes	—
114	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
115	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
116	C₈×C₄₇	—	4	4	no	—
117	C₈×C₄₇	—	4	2	no	—
118	C₈×C₄₇	—	8	1	no	—
119	#9990	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂²×C₄₇	—	2	2	no	—
121	C₂²×C₄₇	—	2	2	no	—
122	C₂²×C₄₇	—	2	2	no	—
123	C₂²×C₄₇	—	2	1	no	—
124	C₂²×C₄₇	—	4	4	no	—
125	C₂²×C₄₇	—	4	4	no	—
126	C₂²×C₄₇	—	8	16	no	—
127	C₂²×C₄₇	—	8	4	no	—
128	C₂²×C₄₇	—	8	4	no	—
129	C₂²×C₄₇	—	8	4	no	—
130	C₂²×C₄₇	#392	1	1	yes	characteristic
131	C₂²×C₄₇	#471	1	4	yes	—
132	C₄×C₄₇	—	2	2	no	—
133	C₄×C₄₇	—	2	1	no	—
134	C₄×C₄₇	—	8	2	no	—
135	C₄×C₄₇	—	8	2	no	—
136	C₄×C₄₇	B(4,𝔽₂)	1	2	yes	—
137	#3195	C₂×C₄₇	1	1	yes	characteristic, complemented
138	C₂×#450	C₂×C₄₇	1	2	yes	—
139	#1783	C₂×C₄₇	1	1	yes	characteristic
140	#1472	C₂×C₄₇	1	2	yes	complemented
141	#1298	C₂×C₄₇	1	1	yes	characteristic, complemented
142	C₂×C₄₇	—	2	4	no	—
143	C₂×C₄₇	—	4	1	no	—
144	C₂×C₄₇	—	8	4	no	—
145	C₂×C₄₇	#2019	1	2	yes	—
146	C₂×C₄₇	#2021	1	1	yes	characteristic
147	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
148	C₂²×SD₁₆	—	2	2	no	—
149	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
150	#483	—	2	2	no	—
151	#470	—	2	2	no	—
152	#451	—	2	2	no	—
153	#450	—	2	4	no	—
154	#450	—	2	4	no	—
155	C₂×#102	—	2	2	no	—
156	C₂×#100	—	2	2	no	—
157	#407	C₂²×C₄₇	1	1	yes	characteristic
158	#407	C₂²×C₄₇	1	1	yes	characteristic
159	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
160	#324	—	2	4	no	—
161	C₄₇	#9990	1	1	yes	characteristic, direct product factor, Sylow
162	C₂⁵	—	2	1	no	—
163	C₂²×Q₈	D₄×C₄₇	1	2	yes	—
164	C₂²×D₄	—	2	2	no	—
165	C₂²×D₄	—	2	1	no	—
166	C₂²×D₄	—	2	2	no	—
167	C₂²×D₄	—	4	4	no	—
168	C₂²×D₄	D₄×C₄₇	1	2	yes	—
169	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
170	C₂×Q₁₆	—	2	2	no	—
171	C₂×SD₁₆	—	2	8	no	—
172	C₂×SD₁₆	—	4	8	no	—
173	C₂×M₁₆	—	2	1	no	—
174	C₂×M₁₆	D₄×C₄₇	1	2	yes	—
175	C₂²×C₈	—	2	2	no	—
176	C₂²⋊Q₈	—	2	2	no	—
177	C₂²⋊Q₈	—	2	2	no	—
178	C₂²⋊Q₈	—	2	2	no	—
179	C₂²⋊Q₈	—	2	2	no	—
180	C₂×C₄⋊C₄	—	2	2	no	—
181	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
182	C₂×C₂²⋊C₄	—	2	2	no	—
183	#106	—	2	2	no	—
184	#103	—	2	4	no	—
185	#102	—	2	8	no	—
186	#100	—	4	4	no	—
187	C₂²⋊C₈	—	2	2	no	—
188	C₂²⋊C₈	—	2	2	no	—
189	C₂²⋊C₈	—	2	2	no	—
190	C₂²⋊C₈	D₄×C₄₇	1	4	yes	—
191	C₂⁴	—	2	2	no	—
192	C₂⁴	—	4	4	no	—
193	C₂⁴	—	4	2	no	—
194	C₂⁴	—	8	4	no	—
195	C₂⁴	#41×C₄₇	1	1	yes	characteristic
196	C₂×Q₈	—	2	2	no	—
197	C₂×Q₈	—	2	2	no	—
198	C₂×Q₈	—	4	4	no	—
199	C₂×D₄	—	2	8	no	—
200	C₂×D₄	—	2	4	no	—
201	C₂×D₄	—	2	4	no	—
202	C₂×D₄	—	4	4	no	—
203	C₂×D₄	—	4	2	no	—
204	C₂×D₄	—	4	4	no	—
205	C₂×D₄	—	4	8	no	—
206	C₂×D₄	—	4	1	no	—
207	C₂×D₄	—	4	1	no	—
208	C₂²×C₄	—	2	2	no	—
209	C₂²×C₄	—	2	2	no	—
210	C₂²×C₄	—	4	2	no	—
211	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
212	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
213	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
214	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
215	Q₁₆	—	8	2	no	—
216	SD₁₆	—	4	16	no	—
217	M₁₆	—	4	2	no	—
218	M₁₆	—	4	2	no	—
219	C₂×C₈	—	2	2	no	—
220	C₂×C₈	—	2	4	no	—
221	C₂×C₈	—	4	4	no	—
222	C₂×C₈	—	4	1	no	—
223	C₄⋊C₄	—	2	2	no	—
224	C₄⋊C₄	—	2	2	no	—
225	C₄⋊C₄	—	4	2	no	—
226	C₄⋊C₄	—	4	2	no	—
227	C₂²⋊C₄	—	4	2	no	—
228	C₂²⋊C₄	—	4	2	no	—
229	C₂³	—	2	4	no	—
230	C₂³	—	2	4	no	—
231	C₂³	—	4	1	no	—
232	C₂³	—	4	8	no	—
233	C₂³	—	4	2	no	—
234	C₂³	—	4	2	no	—
235	C₂³	—	8	4	no	—
236	C₂³	—	8	4	no	—
237	C₂³	—	8	16	no	—
238	C₂³	—	8	4	no	—
239	C₂³	#121×C₄₇	1	1	yes	characteristic
240	C₂³	#121×C₄₇	1	2	yes	—
241	Q₈	—	4	4	no	—
242	Q₈	—	4	4	no	—
243	D₄	—	2	8	no	—
244	D₄	—	4	4	no	—
245	D₄	—	4	4	no	—
246	D₄	—	4	4	no	—
247	C₂×C₄	—	2	4	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	4	1	no	—
250	C₂×C₄	—	4	2	no	—
251	C₂×C₄	—	4	4	no	—
252	C₂×C₄	—	4	2	no	—
253	C₂×C₄	—	4	2	no	—
254	C₂×C₄	—	8	2	no	—
255	C₂×C₄	#120×C₄₇	1	2	yes	—
256	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
257	C₂×C₄	#127×C₄₇	1	1	yes	characteristic
258	C₈	—	4	4	no	—
259	C₈	—	4	2	no	—
260	C₈	—	8	1	no	—
261	C₂²	—	2	2	no	—
262	C₂²	—	2	2	no	—
263	C₂²	—	2	2	no	—
264	C₂²	—	2	1	no	—
265	C₂²	—	4	4	no	—
266	C₂²	—	4	4	no	—
267	C₂²	—	8	16	no	—
268	C₂²	—	8	4	no	—
269	C₂²	—	8	4	no	—
270	C₂²	—	8	4	no	—
271	C₂²	C₄₇×#392	1	1	yes	characteristic
272	C₂²	C₄₇×#471	1	4	yes	—
273	C₄	—	2	2	no	—
274	C₄	—	2	1	no	—
275	C₄	—	8	2	no	—
276	C₄	—	8	2	no	—
277	C₄	C₄₇×B(4,𝔽₂)	1	2	yes	—
278	C₂	—	2	4	no	—
279	C₂	—	4	1	no	—
280	C₂	—	8	4	no	—
281	C₂	C₄₇×#2019	1	2	yes	—
282	C₂	C₄₇×#2021	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₇×#3195

C₂

yes

maximal, characteristic, complemented

C₂×C₄₇×#450

C₂

yes

maximal

C₄₇×#1783

C₂

yes

maximal, characteristic

C₄₇×#1472

C₂

yes

maximal, complemented

C₄₇×#1298

C₂

yes

maximal, characteristic, complemented

C₂³×D₄×C₄₇

C₂²

yes

characteristic

C₂²×SD₁₆×C₄₇

—

C₂×C₂²⋊Q₈×C₄₇

C₂²

yes

—

C₄₇×#483

—

C₄₇×#470

—

C₄₇×#451

—

C₄₇×#450

—

C₄₇×#450

—

C₂×#102×C₄₇

—

C₂×#100×C₄₇

—

C₄₇×#407

C₂²

yes

characteristic

C₄₇×#407

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₄₇

C₂²

yes

—

C₄₇×#324

—

C₂⁵×C₄₇

—

C₂²×Q₈×C₄₇

D₄

yes

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

D₄

yes

—

C₂³×C₄×C₄₇

C₂³

yes

characteristic

C₂×Q₁₆×C₄₇

—

C₂×SD₁₆×C₄₇

—

C₂×SD₁₆×C₄₇

—

C₂×M₁₆×C₄₇

—

C₂×M₁₆×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

—

C₂²⋊Q₈×C₄₇

—

C₂²⋊Q₈×C₄₇

—

C₂²⋊Q₈×C₄₇

—

C₂²⋊Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

—

C₂×C₂²⋊C₄×C₄₇

—

#106×C₄₇

—

#103×C₄₇

—

#102×C₄₇

—

#100×C₄₇

—

C₂²⋊C₈×C₄₇

—

C₂²⋊C₈×C₄₇

—

C₂²⋊C₈×C₄₇

—

C₂²⋊C₈×C₄₇

D₄

yes

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

#41

yes

characteristic

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×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

Q₁₆×C₄₇

—

SD₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#121

yes

characteristic

C₂³×C₄₇

#121

yes

—

Q₈×C₄₇

—

100

Q₈×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

—

111

C₂×C₄×C₄₇

—

112

C₂×C₄×C₄₇

—

113

C₂×C₄×C₄₇

#120

yes

—

114

C₂×C₄×C₄₇

#120

yes

characteristic

115

C₂×C₄×C₄₇

#127

yes

characteristic

116

C₈×C₄₇

—

117

C₈×C₄₇

—

118

C₈×C₄₇

—

119

#9990

C₄₇

yes

maximal, characteristic, direct product factor, Sylow

120

C₂²×C₄₇

—

121

C₂²×C₄₇

—

122

C₂²×C₄₇

—

123

C₂²×C₄₇

—

124

C₂²×C₄₇

—

125

C₂²×C₄₇

—

126

C₂²×C₄₇

—

127

C₂²×C₄₇

—

128

C₂²×C₄₇

—

129

C₂²×C₄₇

—

130

C₂²×C₄₇

#392

yes

characteristic

131

C₂²×C₄₇

#471

yes

—

132

C₄×C₄₇

—

133

C₄×C₄₇

—

134

C₄×C₄₇

—

135

C₄×C₄₇

—

136

C₄×C₄₇

B(4,𝔽₂)

yes

—

137

#3195

C₂×C₄₇

yes

characteristic, complemented

138

C₂×#450

C₂×C₄₇

yes

—

139

#1783

C₂×C₄₇

yes

characteristic

140

#1472

C₂×C₄₇

yes

complemented

141

#1298

C₂×C₄₇

yes

characteristic, complemented

142

C₂×C₄₇

—

143

C₂×C₄₇

—

144

C₂×C₄₇

—

145

C₂×C₄₇

#2019

yes

—

146

C₂×C₄₇

#2021

yes

characteristic

147

C₂³×D₄

C₂²×C₄₇

yes

characteristic

148

C₂²×SD₁₆

—

149

C₂×C₂²⋊Q₈

C₂²×C₄₇

yes

—

150

#483

—

151

#470

—

152

#451

—

153

#450

—

154

#450

—

155

C₂×#102

—

156

C₂×#100

—

157

#407

C₂²×C₄₇

yes

characteristic

158

#407

C₂²×C₄₇

yes

characteristic

159

C₂×C₂²⋊C₈

C₂²×C₄₇

yes

—

160

#324

—

161

C₄₇

#9990

yes

characteristic, direct product factor, Sylow

162

C₂⁵

—

163

C₂²×Q₈

D₄×C₄₇

yes

—

164

C₂²×D₄

—

165

C₂²×D₄

—

166

C₂²×D₄

—

167

C₂²×D₄

—

168

C₂²×D₄

D₄×C₄₇

yes

—

169

C₂³×C₄

C₂³×C₄₇

yes

characteristic

170

C₂×Q₁₆

—

171

C₂×SD₁₆

—

172

C₂×SD₁₆

—

173

C₂×M₁₆

—

174

C₂×M₁₆

D₄×C₄₇

yes

—

175

C₂²×C₈

—

176

C₂²⋊Q₈

—

177

C₂²⋊Q₈

—

178

C₂²⋊Q₈

—

179

C₂²⋊Q₈

—

180

C₂×C₄⋊C₄

—

181

C₂×C₄⋊C₄

D₄×C₄₇

yes

—

182

C₂×C₂²⋊C₄

—

183

#106

—

184

#103

—

185

#102

—

186

#100

—

187

C₂²⋊C₈

—

188

C₂²⋊C₈

—

189

C₂²⋊C₈

—

190

C₂²⋊C₈

D₄×C₄₇

yes

—

191

C₂⁴

—

192

C₂⁴

—

193

C₂⁴

—

194

C₂⁴

—

195

C₂⁴

#41×C₄₇

yes

characteristic

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂×Q₈

—

199

C₂×D₄

—

200

C₂×D₄

—

201

C₂×D₄

—

202

C₂×D₄

—

203

C₂×D₄

—

204

C₂×D₄

—

205

C₂×D₄

—

206

C₂×D₄

—

207

C₂×D₄

—

208

C₂²×C₄

—

209

C₂²×C₄

—

210

C₂²×C₄

—

211

C₂²×C₄

C₂×D₄×C₄₇

yes

—

212

C₂²×C₄

C₂×D₄×C₄₇

yes

characteristic

213

C₂²×C₄

C₂×D₄×C₄₇

yes

characteristic

214

C₂²×C₄

C₂×D₄×C₄₇

yes

—

215

Q₁₆

—

216

SD₁₆

—

217

M₁₆

—

218

M₁₆

—

219

C₂×C₈

—

220

C₂×C₈

—

221

C₂×C₈

—

222

C₂×C₈

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₄⋊C₄

—

226

C₄⋊C₄

—

227

C₂²⋊C₄

—

228

C₂²⋊C₄

—

229

C₂³

—

230

C₂³

—

231

C₂³

—

232

C₂³

—

233

C₂³

—

234

C₂³

—

235

C₂³

—

236

C₂³

—

237

C₂³

—

238

C₂³

—

239

C₂³

#121×C₄₇

yes

characteristic

240

C₂³

#121×C₄₇

yes

—

241

Q₈

—

242

Q₈

—

243

D₄

—

244

D₄

—

245

D₄

—

246

D₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

252

C₂×C₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

#120×C₄₇

yes

—

256

C₂×C₄

#120×C₄₇

yes

characteristic

257

C₂×C₄

#127×C₄₇

yes

characteristic

258

C₈

—

259

C₈

—

260

C₈

—

261

C₂²

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

266

C₂²

—

267

C₂²

—

268

C₂²

—

269

C₂²

—

270

C₂²

—

271

C₂²

C₄₇×#392

yes

characteristic

272

C₂²

C₄₇×#471

yes

—

273

C₄

—

274

C₄

—

275

C₄

—

276

C₄

—

277

C₄

C₄₇×B(4,𝔽₂)

yes

—

278

C₂

—

279

C₂

—

280

C₂

—

281

C₂

C₄₇×#2019

yes

—

282

C₂

C₄₇×#2021

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

subgroup

G/H

center, socle

C₂²×C₄₇

#392

commutator, Frattini, cosocle

C₂³×C₄

C₂³×C₄₇

prime radical

C₂³×D₄×C₄₇

C₂²

LCS

G ▷ C₂³×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

N	H ≅ G/N	type
1. C₄₇×#3195	C₂	semidirect
4. C₄₇×#1472	C₂	semidirect
5. C₄₇×#1298	C₂	semidirect
119. #9990	C₄₇	direct (N × H)
137. #3195	C₂×C₄₇	semidirect
140. #1472	C₂×C₄₇	semidirect
141. #1298	C₂×C₄₇	semidirect
161. C₄₇	#9990	direct (N × H)

H ≅ G/N

type

1. C₄₇×#3195

C₂

semidirect

4. C₄₇×#1472

C₂

semidirect

5. C₄₇×#1298

C₂

semidirect

119. #9990

C₄₇

direct (N × H)

137. #3195

C₂×C₄₇

semidirect

140. #1472

C₂×C₄₇

semidirect

141. #1298

C₂×C₄₇

semidirect

161. C₄₇

#9990

direct (N × H)

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

subgroup	index
C₄₇×#3195	2
C₂×C₄₇×#450	2
C₄₇×#1783	2
C₄₇×#1472	2
C₄₇×#1298	2
#9990	47

subgroup

index

C₄₇×#3195

C₂×C₄₇×#450

C₄₇×#1783

C₄₇×#1472

C₄₇×#1298

#9990

Subgroups — C₄₇×#9990 #26049688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C47×#9990 #26049688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#9990 #26049688