Group #26107840 — subgroups

Subgroups — #26107840

Order 12032.

686 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 143 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	#20257198	C₂	1	1	yes	maximal, characteristic
2	#20243384	C₂	1	1	yes	maximal, characteristic
3	#20242076	C₂	1	2	yes	maximal
4	#20241844	C₂	1	2	yes	maximal
5	C₄₇×#1984	C₂	1	1	yes	maximal, characteristic
6	Q₈×Dic₉₄	—	2	2	no	—
7	#15689852	—	2	2	no	—
8	#15689849	—	2	4	no	—
9	#15689754	—	2	1	no	—
10	#15689754	C₄	1	4	yes	—
11	#15689680	—	2	2	no	—
12	#15689680	C₂²	1	2	yes	—
13	#15689601	—	2	1	no	—
14	#15689147	C₂²	1	2	yes	—
15	C₂×#13093943	—	2	1	no	—
16	#15688892	—	2	1	no	—
17	#15688871	—	2	2	no	—
18	#15688870	—	2	2	no	—
19	#15688855	—	2	4	no	—
20	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#336	—	2	2	no	—
24	C₂×#10625329	—	2	2	no	—
25	#13094024	—	2	2	no	—
26	#13094024	—	2	2	no	—
27	#13094024	D₄	1	2	yes	—
28	#13094024	D₄	1	2	yes	—
29	#13094023	—	2	4	no	—
30	#13094023	—	2	8	no	—
31	#13094016	—	2	4	no	—
32	#13094016	—	2	2	no	—
33	#13094015	—	2	4	no	—
34	#13094015	—	2	8	no	—
35	#13094003	—	2	4	no	—
36	#13094003	—	2	2	no	—
37	#13094003	C₂×C₄	1	4	yes	—
38	Q₈×Dic₄₇	—	2	4	no	—
39	Q₈×Dic₄₇	—	2	4	no	—
40	C₄×Dic₉₄	—	2	4	no	—
41	C₄×Dic₉₄	—	2	4	no	—
42	C₄×Dic₉₄	—	2	2	no	—
43	C₄×Dic₉₄	D₄	1	4	yes	—
44	#13093983	—	2	4	no	—
45	#13093983	—	2	2	no	—
46	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
47	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
48	#13093943	—	4	2	no	—
49	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₄₇	—	2	1	no	—
51	C₂²×C₈×C₄₇	—	2	1	no	—
52	C₄×Q₈×C₄₇	—	2	2	no	—
53	C₄×Q₈×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₇	D₄	1	2	yes	—
57	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₄₇	—	2	2	no	—
59	C₄×C₈×C₄₇	—	2	2	no	—
60	C₂×Q₈×C₄₇	—	2	2	no	—
61	C₂×Q₈×C₄₇	—	2	2	no	—
62	C₂×Q₈×C₄₇	SD₁₆	1	2	yes	—
63	C₂×Q₈×C₄₇	Q₁₆	1	2	yes	—
64	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
66	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
69	C₂×Dic₉₄	—	2	2	no	—
70	C₂×Dic₉₄	—	2	4	no	—
71	C₂×Dic₉₄	C₂²⋊C₄	1	4	yes	—
72	C₂×C₈×C₄₇	—	2	2	no	—
73	C₂×C₈×C₄₇	—	4	1	no	—
74	C₂×C₈×C₄₇	—	4	1	no	—
75	C₂×C₈×C₄₇	—	4	2	no	—
76	C₂×C₈×C₄₇	—	4	1	no	—
77	C₄⋊C₄×C₄₇	—	2	4	no	—
78	C₄⋊C₄×C₄₇	—	2	2	no	—
79	C₄²×C₄₇	—	2	2	no	—
80	C₄²×C₄₇	—	2	2	no	—
81	C₄²×C₄₇	C₂×D₄	1	2	yes	—
82	C₄²×C₄₇	C₂×D₄	1	2	yes	—
83	C₂²⋊Dic₄₇	—	2	4	no	—
84	C₄⋊Dic₄₇	—	2	4	no	—
85	C₄⋊Dic₄₇	—	2	4	no	—
86	C₄⋊Dic₄₇	—	2	4	no	—
87	C₄⋊Dic₄₇	—	2	2	no	—
88	C₄⋊Dic₄₇	—	2	2	no	—
89	C₄⋊Dic₄₇	—	2	2	no	—
90	C₄⋊Dic₄₇	C₂²⋊C₄	1	4	yes	—
91	Dic₄₇⋊C₄	—	2	8	no	—
92	Dic₄₇⋊C₄	—	2	4	no	—
93	Dic₄₇⋊C₄	—	2	4	no	—
94	C₄×Dic₄₇	—	2	8	no	—
95	C₄×Dic₄₇	—	2	4	no	—
96	#10625329	—	4	2	no	—
97	#10625329	—	4	2	no	—
98	C₂×C₄₇⋊C₈	—	4	2	no	—
99	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	Q₈×C₄₇	—	2	4	no	—
101	Q₈×C₄₇	—	2	4	no	—
102	C₂×C₄×C₄₇	—	2	2	no	—
103	C₂×C₄×C₄₇	—	2	2	no	—
104	C₂×C₄×C₄₇	—	2	1	no	—
105	C₂×C₄×C₄₇	—	2	1	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	#103	1	4	yes	—
110	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
111	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
112	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
113	C₂×C₄×C₄₇	#120	1	2	yes	—
114	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
115	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
116	C₂×C₄×C₄₇	#137	1	2	yes	—
117	C₂×Dic₄₇	—	2	4	no	—
118	C₂×Dic₄₇	—	2	4	no	—
119	Dic₉₄	—	4	2	no	—
120	Dic₉₄	—	4	2	no	—
121	Dic₉₄	—	4	4	no	—
122	Dic₉₄	—	8	4	no	—
123	C₈×C₄₇	—	4	2	no	—
124	C₈×C₄₇	—	8	1	no	—
125	C₄₇⋊C₈	—	8	2	no	—
126	#8356	—	47	1	no	maximal, Sylow
127	C₂²×C₄₇	—	2	1	no	—
128	C₂²×C₄₇	—	2	1	no	—
129	C₂²×C₄₇	#379	1	1	yes	characteristic
130	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
131	C₂²×C₄₇	#419	1	1	yes	characteristic
132	C₄×C₄₇	—	2	1	no	—
133	C₄×C₄₇	—	2	4	no	—
134	C₄×C₄₇	—	2	2	no	—
135	C₄×C₄₇	—	4	2	no	—
136	C₄×C₄₇	#448	1	2	yes	—
137	C₄×C₄₇	#451	1	2	yes	—
138	C₄×C₄₇	#454	1	1	yes	characteristic
139	C₄×C₄₇	#456	1	1	yes	characteristic
140	Dic₄₇	—	4	4	no	—
141	Dic₄₇	—	4	4	no	—
142	#3502	—	47	1	no	—
143	#1984	D₄₇	1	1	yes	characteristic
144	#1801	—	47	1	no	—
145	#1550	—	47	2	no	—
146	#1493	—	47	2	no	—
147	C₂×C₄₇	—	2	1	no	—
148	C₂×C₄₇	—	2	1	no	—
149	C₂×C₄₇	#1787	1	1	yes	characteristic
150	C₂×C₄₇	#1791	1	1	yes	characteristic
151	C₂×C₄₇	#1793	1	1	yes	characteristic
152	Q₈²	—	94	2	no	—
153	#557	—	94	4	no	—
154	#557	—	94	2	no	—
155	#544	—	47	4	no	—
156	#544	—	94	1	no	—
157	#533	—	47	2	no	—
158	#533	—	94	2	no	—
159	#519	—	94	1	no	—
160	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
161	#423	—	47	2	no	—
162	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
163	C₂×#101	—	94	1	no	—
164	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
165	#343	—	94	1	no	—
166	#336	—	2	2	no	—
167	#333	—	94	2	no	—
168	#332	—	94	2	no	—
169	Q₈⋊C₈	—	94	4	no	—
170	C₄₇	#8356	1	1	yes	characteristic, complemented, Sylow
171	C₂²×Q₈	D₁₈₈	1	1	yes	characteristic
172	C₂×M₁₆	—	94	2	no	—
173	C₂²×C₈	—	2	1	no	—
174	C₂²×C₈	—	2	1	no	—
175	C₄⋊Q₈	—	47	2	no	—
176	C₄⋊Q₈	—	47	2	no	—
177	C₄⋊Q₈	—	94	2	no	—
178	C₄⋊Q₈	—	94	2	no	—
179	C₄⋊Q₈	—	94	8	no	—
180	C₄⋊Q₈	—	94	4	no	—
181	#125	—	94	4	no	—
182	#125	—	94	8	no	—
183	#125	—	94	4	no	—
184	#125	—	94	2	no	—
185	C₂²⋊Q₈	—	47	4	no	—
186	C₂²⋊Q₈	—	94	4	no	—
187	C₂²⋊Q₈	—	94	2	no	—
188	C₄×Q₈	—	2	2	no	—
189	C₄×Q₈	—	2	2	no	—
190	C₄×Q₈	—	47	4	no	—
191	C₄×Q₈	—	94	4	no	—
192	C₄×Q₈	—	94	4	no	—
193	C₄×Q₈	—	94	4	no	—
194	C₄×Q₈	—	94	4	no	—
195	C₄×Q₈	—	94	2	no	—
196	#117	—	94	4	no	—
197	#117	—	94	2	no	—
198	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
199	C₂×C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
200	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
201	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
202	C₄⋊C₈	—	2	2	no	—
203	C₄⋊C₈	—	94	2	no	—
204	C₄⋊C₈	—	94	2	no	—
205	#101	—	188	2	no	—
206	C₄×C₈	—	2	2	no	—
207	C₂×Q₈	—	2	2	no	—
208	C₂×Q₈	—	2	2	no	—
209	C₂×Q₈	—	47	4	no	—
210	C₂×Q₈	—	94	4	no	—
211	C₂×Q₈	—	94	2	no	—
212	C₂×Q₈	#10625325	1	2	yes	—
213	C₂×Q₈	Dic₁₈₈	1	2	yes	—
214	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
215	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
216	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
217	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
218	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
219	M₁₆	—	188	2	no	—
220	M₁₆	—	188	2	no	—
221	C₂×C₈	—	2	2	no	—
222	C₂×C₈	—	4	1	no	—
223	C₂×C₈	—	4	1	no	—
224	C₂×C₈	—	4	2	no	—
225	C₂×C₈	—	4	1	no	—
226	C₂×C₈	—	188	2	no	—
227	C₄⋊C₄	—	2	4	no	—
228	C₄⋊C₄	—	2	2	no	—
229	C₄⋊C₄	—	47	4	no	—
230	C₄⋊C₄	—	94	8	no	—
231	C₄⋊C₄	—	94	4	no	—
232	C₄⋊C₄	—	94	4	no	—
233	C₄⋊C₄	—	94	4	no	—
234	C₄⋊C₄	—	94	4	no	—
235	C₄⋊C₄	—	94	4	no	—
236	C₄⋊C₄	—	94	2	no	—
237	C₄⋊C₄	—	94	2	no	—
238	C₄⋊C₄	—	94	2	no	—
239	C₂²⋊C₄	—	94	4	no	—
240	C₄²	—	2	2	no	—
241	C₄²	—	2	2	no	—
242	C₄²	—	94	8	no	—
243	C₄²	—	94	4	no	—
244	C₄²	D₄×D₄₇	1	2	yes	—
245	C₄²	D₄×D₄₇	1	2	yes	—
246	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
247	Q₈	—	2	4	no	—
248	Q₈	—	2	4	no	—
249	Q₈	—	376	4	no	—
250	Q₈	—	188	4	no	—
251	Q₈	—	188	2	no	—
252	Q₈	—	188	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	4	1	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	94	4	no	—
261	C₂×C₄	—	94	4	no	—
262	C₂×C₄	#13093949	1	4	yes	—
263	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
264	C₂×C₄	#13093992	1	1	yes	characteristic
265	C₂×C₄	#13093992	1	1	yes	characteristic
266	C₂×C₄	#13093994	1	2	yes	—
267	C₂×C₄	C₂×#10625325	1	1	yes	characteristic
268	C₂×C₄	C₂×Dic₁₈₈	1	1	yes	characteristic
269	C₂×C₄	#13094057	1	2	yes	—
270	C₈	—	4	2	no	—
271	C₈	—	8	1	no	—
272	C₈	—	376	2	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	2	1	no	—
275	C₂²	#15688978	1	1	yes	characteristic
276	C₂²	C₂×#13093949	1	1	yes	characteristic
277	C₂²	#15689133	1	1	yes	characteristic
278	C₄	—	2	4	no	—
279	C₄	—	2	2	no	—
280	C₄	—	2	1	no	—
281	C₄	—	4	2	no	—
282	C₄	—	188	4	no	—
283	C₄	—	188	4	no	—
284	C₄	#15689264	1	2	yes	—
285	C₄	#15689281	1	2	yes	—
286	C₄	#15689295	1	1	yes	characteristic
287	C₄	#15689305	1	1	yes	characteristic
288	C₂	—	2	1	no	—
289	C₂	—	2	1	no	—
290	C₂	#20243324	1	1	yes	characteristic
291	C₂	#20243338	1	1	yes	characteristic
292	C₂	#20243346	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20257198

C₂

yes

maximal, characteristic

#20243384

C₂

yes

maximal, characteristic

#20242076

C₂

yes

maximal

#20241844

C₂

yes

maximal

C₄₇×#1984

C₂

yes

maximal, characteristic

Q₈×Dic₉₄

—

—

—

—

C₄

yes

—

#15689680

—

#15689680

C₂²

yes

—

#15689601

—

#15689147

C₂²

yes

—

—

—

—

—

—

C₂×C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#336

—

—

—

—

D₄

yes

—

#13094024

D₄

yes

—

—

—

—

—

—

—

—

—

C₂×C₄

yes

—

Q₈×Dic₄₇

—

Q₈×Dic₄₇

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₄×Dic₉₄

D₄

yes

—

#13093983

—

#13093983

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

#13093943

—

C₂²×Q₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

—

C₄×Q₈×C₄₇

—

C₄×Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄×C₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

SD₁₆

yes

—

C₂×Q₈×C₄₇

Q₁₆

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

C₂×D₄

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂²⋊C₄

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

100

Q₈×C₄₇

—

101

Q₈×C₄₇

—

102

C₂×C₄×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

—

109

C₂×C₄×C₄₇

#103

yes

—

110

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

—

111

C₂×C₄×C₄₇

#120

yes

characteristic

112

C₂×C₄×C₄₇

#120

yes

characteristic

113

C₂×C₄×C₄₇

#120

yes

—

114

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

115

C₂×C₄×C₄₇

C₂×Q₁₆

yes

characteristic

116

C₂×C₄×C₄₇

#137

yes

—

117

C₂×Dic₄₇

—

118

C₂×Dic₄₇

—

119

Dic₉₄

—

120

Dic₉₄

—

121

Dic₉₄

—

122

Dic₉₄

—

123

C₈×C₄₇

—

124

C₈×C₄₇

—

125

C₄₇⋊C₈

—

126

#8356

—

maximal, Sylow

127

C₂²×C₄₇

—

128

C₂²×C₄₇

—

129

C₂²×C₄₇

#379

yes

characteristic

130

C₂²×C₄₇

C₂×#103

yes

characteristic

131

C₂²×C₄₇

#419

yes

characteristic

132

C₄×C₄₇

—

133

C₄×C₄₇

—

134

C₄×C₄₇

—

135

C₄×C₄₇

—

136

C₄×C₄₇

#448

yes

—

137

C₄×C₄₇

#451

yes

—

138

C₄×C₄₇

#454

yes

characteristic

139

C₄×C₄₇

#456

yes

characteristic

140

Dic₄₇

—

141

Dic₄₇

—

142

#3502

—

143

#1984

D₄₇

yes

characteristic

144

#1801

—

145

#1550

—

146

#1493

—

147

C₂×C₄₇

—

148

C₂×C₄₇

—

149

C₂×C₄₇

#1787

yes

characteristic

150

C₂×C₄₇

#1791

yes

characteristic

151

C₂×C₄₇

#1793

yes

characteristic

152

Q₈²

—

153

#557

—

154

#557

—

155

#544

—

156

#544

—

157

#533

—

158

#533

—

159

#519

—

160

C₂×C₄×Q₈

C₂×D₄₇

yes

characteristic

161

#423

—

162

C₂×C₄⋊C₈

C₂×D₄₇

yes

characteristic

163

C₂×#101

—

164

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

165

#343

—

166

#336

—

167

#333

—

168

#332

—

169

Q₈⋊C₈

—

170

C₄₇

#8356

yes

characteristic, complemented, Sylow

171

C₂²×Q₈

D₁₈₈

yes

characteristic

172

C₂×M₁₆

—

173

C₂²×C₈

—

174

C₂²×C₈

—

175

C₄⋊Q₈

—

176

C₄⋊Q₈

—

177

C₄⋊Q₈

—

178

C₄⋊Q₈

—

179

C₄⋊Q₈

—

180

C₄⋊Q₈

—

181

#125

—

182

#125

—

183

#125

—

184

#125

—

185

C₂²⋊Q₈

—

186

C₂²⋊Q₈

—

187

C₂²⋊Q₈

—

188

C₄×Q₈

—

189

C₄×Q₈

—

190

C₄×Q₈

—

191

C₄×Q₈

—

192

C₄×Q₈

—

193

C₄×Q₈

—

194

C₄×Q₈

—

195

C₄×Q₈

—

196

#117

—

197

#117

—

198

C₂×C₄⋊C₄

C₄×D₄₇

yes

—

199

C₂×C₄⋊C₄

D₁₈₈

yes

characteristic

200

C₂×C₄²

C₂²⋊D₄₇

yes

—

201

C₂×C₄²

C₂²×D₄₇

yes

characteristic

202

C₄⋊C₈

—

203

C₄⋊C₈

—

204

C₄⋊C₈

—

205

#101

—

188

—

206

C₄×C₈

—

207

C₂×Q₈

—

208

C₂×Q₈

—

209

C₂×Q₈

—

210

C₂×Q₈

—

211

C₂×Q₈

—

212

C₂×Q₈

#10625325

yes

—

213

C₂×Q₈

Dic₁₈₈

yes

—

214

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

215

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

216

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

217

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

218

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

219

M₁₆

—

188

—

220

M₁₆

—

188

—

221

C₂×C₈

—

222

C₂×C₈

—

223

C₂×C₈

—

224

C₂×C₈

—

225

C₂×C₈

—

226

C₂×C₈

—

188

—

227

C₄⋊C₄

—

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₄⋊C₄

—

238

C₄⋊C₄

—

239

C₂²⋊C₄

—

240

C₄²

—

241

C₄²

—

242

C₄²

—

243

C₄²

—

244

C₄²

D₄×D₄₇

yes

—

245

C₄²

D₄×D₄₇

yes

—

246

C₂³

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

247

Q₈

—

248

Q₈

—

249

Q₈

—

376

—

250

Q₈

—

188

—

251

Q₈

—

188

—

252

Q₈

—

188

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

#13093949

yes

—

263

C₂×C₄

C₂²⋊C₄×D₄₇

yes

—

264

C₂×C₄

#13093992

yes

characteristic

265

C₂×C₄

#13093992

yes

characteristic

266

C₂×C₄

#13093994

yes

—

267

C₂×C₄

C₂×#10625325

yes

characteristic

268

C₂×C₄

C₂×Dic₁₈₈

yes

characteristic

269

C₂×C₄

#13094057

yes

—

270

C₈

—

271

C₈

—

272

C₈

—

376

—

273

C₂²

—

274

C₂²

—

275

C₂²

#15688978

yes

characteristic

276

C₂²

C₂×#13093949

yes

characteristic

277

C₂²

#15689133

yes

characteristic

278

C₄

—

279

C₄

—

280

C₄

—

281

C₄

—

282

C₄

—

188

—

283

C₄

—

188

—

284

C₄

#15689264

yes

—

285

C₄

#15689281

yes

—

286

C₄

#15689295

yes

characteristic

287

C₄

#15689305

yes

characteristic

288

C₂

—

289

C₂

—

290

C₂

#20243324

yes

characteristic

291

C₂

#20243338

yes

characteristic

292

C₂

#20243346

yes

characteristic

	subgroup	G/H
center	C₂²	#15688978
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1984	C₂
socle	C₂²×C₄₇	#379
prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1984	D₄₇
hypocenter	C₄₇	#8356
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1984

subgroup

G/H

center

C₂²

#15688978

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1984

C₂

socle

C₂²×C₄₇

#379

prime radical

C₂³×C₄₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1984

N	H ≅ G/N	type
170. C₄₇	#8356	semidirect

H ≅ G/N

type

170. C₄₇

#8356

semidirect

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

subgroup	index
#20257198	2
#20243384	2
#20242076	2
#20241844	2
C₄₇×#1984	2
#8356	47

subgroup

index

C₄₇×#1984

Subgroups — #26107840

Conjugacy classes of subgroups

Complements

Maximal subgroups