Group #26108027 — subgroups

Subgroups — #26108027

Order 12032.

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

normal subgroups only

This group has 706 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	C₂×#15689852	C₂	1	1	yes	maximal, characteristic
2	#20242070	C₂	1	2	yes	maximal
3	#20241816	C₂	1	2	yes	maximal
4	#20241712	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1801	C₂	1	1	yes	maximal, characteristic
6	#15689852	—	2	4	no	—
7	#15689852	—	2	4	no	—
8	C₂×#13094024	C₄	1	2	yes	—
9	C₂×#13094024	C₂²	1	1	yes	characteristic
10	C₂×#13094015	—	2	2	no	—
11	C₂×#13094015	—	2	1	no	—
12	C₂×Q₈×Dic₄₇	—	2	1	no	—
13	C₂×C₄×Dic₉₄	C₄	1	2	yes	—
14	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
15	#15689176	C₂²	1	2	yes	—
16	#15688871	—	2	4	no	—
17	#15688853	—	2	4	no	—
18	#15688849	—	2	2	no	—
19	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#423	C₂²	1	2	yes	—
21	C₂×#101×C₄₇	—	2	1	no	—
22	C₄₇×#343	—	2	1	no	—
23	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
24	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
25	#13094024	—	2	4	no	—
26	#13094024	—	2	4	no	—
27	#13094024	—	2	2	no	—
28	#13094024	D₄	1	4	yes	—
29	#13094015	—	2	16	no	—
30	#13094015	—	2	8	no	—
31	Q₈×Dic₄₇	—	2	8	no	—
32	C₄×Dic₉₄	—	2	4	no	—
33	C₄×Dic₉₄	—	2	2	no	—
34	C₄×Dic₉₄	—	2	4	no	—
35	C₄×Dic₉₄	D₄	1	4	yes	—
36	C₂×C₄⋊Dic₄₇	—	2	2	no	—
37	C₂×C₄⋊Dic₄₇	—	2	2	no	—
38	C₂×C₄⋊Dic₄₇	—	2	1	no	—
39	C₂×C₄⋊Dic₄₇	—	2	1	no	—
40	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂×Dic₄₇⋊C₄	—	2	2	no	—
42	C₂×Dic₄₇⋊C₄	—	2	1	no	—
43	C₂×C₄×Dic₄₇	—	2	2	no	—
44	C₂×C₄×Dic₄₇	—	2	1	no	—
45	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
46	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
47	C₄×C₄₇⋊C₈	—	2	2	no	—
48	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
49	C₂×M₁₆×C₄₇	—	2	2	no	—
50	C₄×Q₈×C₄₇	—	2	2	no	—
51	C₄×Q₈×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
56	C₄⋊C₈×C₄₇	—	2	2	no	—
57	C₄⋊C₈×C₄₇	—	2	2	no	—
58	#101×C₄₇	—	4	2	no	—
59	C₂×Q₈×C₄₇	—	2	2	no	—
60	C₂×Q₈×C₄₇	—	2	2	no	—
61	C₂×Q₈×C₄₇	SD₁₆	1	2	yes	—
62	C₂×Q₈×C₄₇	Q₁₆	1	2	yes	—
63	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₂²×Dic₄₇	—	2	1	no	—
69	C₂²×Dic₄₇	—	2	2	no	—
70	C₂²×Dic₄₇	—	2	1	no	—
71	C₂×Dic₉₄	—	2	1	no	—
72	C₂×Dic₉₄	—	2	2	no	—
73	C₂×Dic₉₄	—	4	2	no	—
74	C₂×Dic₉₄	—	4	4	no	—
75	C₂×Dic₉₄	C₂²⋊C₄	1	2	yes	—
76	C₂×Dic₉₄	C₂²⋊C₄	1	4	yes	—
77	M₁₆×C₄₇	—	4	2	no	—
78	M₁₆×C₄₇	—	4	2	no	—
79	C₂×C₈×C₄₇	—	4	2	no	—
80	C₄⋊C₄×C₄₇	—	2	4	no	—
81	C₄⋊C₄×C₄₇	—	2	2	no	—
82	C₄²×C₄₇	—	2	2	no	—
83	C₄²×C₄₇	—	2	2	no	—
84	C₄²×C₄₇	C₂×D₄	1	2	yes	—
85	C₄²×C₄₇	C₂×D₄	1	2	yes	—
86	C₄⋊Dic₄₇	—	2	8	no	—
87	C₄⋊Dic₄₇	—	2	8	no	—
88	C₄⋊Dic₄₇	—	2	1	no	—
89	C₄⋊Dic₄₇	—	2	4	no	—
90	C₄⋊Dic₄₇	—	2	4	no	—
91	C₄⋊Dic₄₇	C₂²⋊C₄	1	2	yes	—
92	Dic₄₇⋊C₄	—	2	8	no	—
93	Dic₄₇⋊C₄	—	2	4	no	—
94	C₄×Dic₄₇	—	2	8	no	—
95	C₄×Dic₄₇	—	2	4	no	—
96	C₂×C₄₇⋊C₈	—	4	2	no	—
97	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	Q₈×C₄₇	—	2	4	no	—
99	Q₈×C₄₇	—	2	4	no	—
100	C₂×C₄×C₄₇	—	2	2	no	—
101	C₂×C₄×C₄₇	—	2	2	no	—
102	C₂×C₄×C₄₇	—	2	2	no	—
103	C₂×C₄×C₄₇	—	2	2	no	—
104	C₂×C₄×C₄₇	—	4	1	no	—
105	C₂×C₄×C₄₇	—	4	2	no	—
106	C₂×C₄×C₄₇	#103	1	4	yes	—
107	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₄×C₄₇	#120	1	2	yes	—
110	C₂×C₄×C₄₇	#120	1	2	yes	—
111	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
112	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
113	C₂×C₄×C₄₇	#137	1	2	yes	—
114	C₂×Dic₄₇	—	2	2	no	—
115	C₂×Dic₄₇	—	2	2	no	—
116	C₂×Dic₄₇	—	2	4	no	—
117	C₂×Dic₄₇	—	4	2	no	—
118	C₂×Dic₄₇	—	4	4	no	—
119	C₂×Dic₄₇	—	4	2	no	—
120	Dic₉₄	—	2	4	no	—
121	Dic₉₄	—	4	2	no	—
122	Dic₉₄	—	4	4	no	—
123	Dic₉₄	—	4	4	no	—
124	C₈×C₄₇	—	8	2	no	—
125	C₄₇⋊C₈	—	8	2	no	—
126	#8392	—	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	2	no	—
133	C₄×C₄₇	—	2	1	no	—
134	C₄×C₄₇	—	2	4	no	—
135	C₄×C₄₇	—	4	2	no	—
136	C₄×C₄₇	#413	1	2	yes	—
137	C₄×C₄₇	#448	1	2	yes	—
138	C₄×C₄₇	#451	1	2	yes	—
139	Dic₄₇	—	4	2	no	—
140	Dic₄₇	—	4	2	no	—
141	Dic₄₇	—	4	4	no	—
142	C₂×#557	—	47	1	no	—
143	#1801	D₄₇	1	1	yes	characteristic
144	#1548	—	47	2	no	—
145	#1487	—	47	2	no	—
146	#1461	—	47	1	no	—
147	C₂×C₄₇	—	2	1	no	—
148	C₂×C₄₇	—	2	1	no	—
149	C₂×C₄₇	#1785	1	1	yes	characteristic
150	C₂×C₄₇	#1787	1	1	yes	characteristic
151	C₂×C₄₇	#1796	1	1	yes	characteristic
152	#557	—	94	4	no	—
153	#557	—	94	4	no	—
154	C₂×C₄⋊Q₈	—	47	2	no	—
155	C₂×C₄⋊Q₈	—	47	1	no	—
156	C₂×#125	—	94	2	no	—
157	C₂×#125	—	94	1	no	—
158	C₂×C₄×Q₈	—	47	2	no	—
159	C₂×C₄×Q₈	—	47	1	no	—
160	C₂×C₄×Q₈	—	94	1	no	—
161	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
162	#431	—	47	2	no	—
163	#423	C₂×D₄₇	1	2	yes	—
164	C₂×#101	—	2	1	no	—
165	#343	—	2	1	no	—
166	#333	—	94	4	no	—
167	Q₈⋊C₈	—	94	4	no	—
168	#324	—	94	2	no	—
169	C₄₇	#8392	1	1	yes	characteristic, complemented, Sylow
170	C₂²×Q₈	—	47	1	no	—
171	C₂²×Q₈	—	47	2	no	—
172	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
173	C₂×M₁₆	—	2	2	no	—
174	C₄⋊Q₈	—	47	4	no	—
175	C₄⋊Q₈	—	94	4	no	—
176	C₄⋊Q₈	—	94	4	no	—
177	C₄⋊Q₈	—	94	2	no	—
178	#125	—	94	16	no	—
179	#125	—	94	8	no	—
180	C₄×Q₈	—	2	2	no	—
181	C₄×Q₈	—	2	2	no	—
182	C₄×Q₈	—	47	4	no	—
183	C₄×Q₈	—	94	4	no	—
184	C₄×Q₈	—	94	4	no	—
185	C₄×Q₈	—	94	8	no	—
186	C₄×Q₈	—	94	2	no	—
187	C₂×C₄⋊C₄	—	47	1	no	—
188	C₂×C₄⋊C₄	—	94	2	no	—
189	C₂×C₄⋊C₄	—	94	2	no	—
190	C₂×C₄⋊C₄	—	94	2	no	—
191	C₂×C₄⋊C₄	—	94	1	no	—
192	C₂×C₄⋊C₄	—	94	1	no	—
193	C₂×C₄⋊C₄	—	94	1	no	—
194	C₂×C₄⋊C₄	D₁₈₈	1	2	yes	—
195	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
196	C₂×C₄²	—	94	2	no	—
197	C₂×C₄²	—	94	1	no	—
198	C₂×C₄²	C₄×D₄₇	1	2	yes	—
199	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
200	C₄⋊C₈	—	2	2	no	—
201	C₄⋊C₈	—	2	2	no	—
202	C₄⋊C₈	—	94	2	no	—
203	#101	—	4	2	no	—
204	C₂²⋊C₈	—	94	2	no	—
205	C₄×C₈	—	94	2	no	—
206	C₂×Q₈	—	2	2	no	—
207	C₂×Q₈	—	2	2	no	—
208	C₂×Q₈	—	47	2	no	—
209	C₂×Q₈	—	47	4	no	—
210	C₂×Q₈	—	94	1	no	—
211	C₂×Q₈	—	94	2	no	—
212	C₂×Q₈	—	188	2	no	—
213	C₂×Q₈	—	188	4	no	—
214	C₂×Q₈	#10625335	1	2	yes	—
215	C₂×Q₈	#10625337	1	2	yes	—
216	C₂²×C₄	—	94	1	no	—
217	C₂²×C₄	—	94	2	no	—
218	C₂²×C₄	—	94	1	no	—
219	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
220	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
221	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
222	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
223	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
224	M₁₆	—	4	2	no	—
225	M₁₆	—	4	2	no	—
226	C₂×C₈	—	4	2	no	—
227	C₂×C₈	—	188	2	no	—
228	C₄⋊C₄	—	2	2	no	—
229	C₄⋊C₄	—	2	4	no	—
230	C₄⋊C₄	—	47	2	no	—
231	C₄⋊C₄	—	94	8	no	—
232	C₄⋊C₄	—	94	8	no	—
233	C₄⋊C₄	—	94	8	no	—
234	C₄⋊C₄	—	94	1	no	—
235	C₄⋊C₄	—	94	4	no	—
236	C₄⋊C₄	—	94	4	no	—
237	C₄⋊C₄	—	94	4	no	—
238	C₄²	—	2	2	no	—
239	C₄²	—	2	2	no	—
240	C₄²	—	94	8	no	—
241	C₄²	—	94	4	no	—
242	C₄²	D₄×D₄₇	1	2	yes	—
243	C₄²	D₄×D₄₇	1	2	yes	—
244	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
245	Q₈	—	2	4	no	—
246	Q₈	—	2	4	no	—
247	Q₈	—	94	4	no	—
248	Q₈	—	188	4	no	—
249	Q₈	—	188	2	no	—
250	Q₈	—	188	4	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	4	1	no	—
256	C₂×C₄	—	4	2	no	—
257	C₂×C₄	—	94	2	no	—
258	C₂×C₄	—	94	2	no	—
259	C₂×C₄	—	94	4	no	—
260	C₂×C₄	—	188	2	no	—
261	C₂×C₄	—	188	2	no	—
262	C₂×C₄	—	188	4	no	—
263	C₂×C₄	#13093947	1	4	yes	—
264	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
265	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
266	C₂×C₄	#13093992	1	2	yes	—
267	C₂×C₄	#13093994	1	2	yes	—
268	C₂×C₄	C₂×#10625335	1	1	yes	characteristic
269	C₂×C₄	C₂×#10625337	1	1	yes	characteristic
270	C₂×C₄	#13094054	1	2	yes	—
271	C₈	—	8	2	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×#13093947	1	1	yes	characteristic
277	C₂²	#15689131	1	1	yes	characteristic
278	C₄	—	2	1	no	—
279	C₄	—	2	4	no	—
280	C₄	—	2	2	no	—
281	C₄	—	4	2	no	—
282	C₄	—	188	2	no	—
283	C₄	—	188	4	no	—
284	C₄	—	188	2	no	—
285	C₄	#15689106	1	2	yes	—
286	C₄	#15689261	1	2	yes	—
287	C₄	#15689278	1	2	yes	—
288	C₂	—	2	1	no	—
289	C₂	—	2	1	no	—
290	C₂	#20243315	1	1	yes	characteristic
291	C₂	#20243322	1	1	yes	characteristic
292	C₂	#20243364	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689852

C₂

yes

maximal, characteristic

#20242070

C₂

yes

maximal

#20241816

C₂

yes

maximal

#20241712

C₂

yes

maximal, characteristic

C₄₇×#1801

C₂

yes

maximal, characteristic

#15689852

—

#15689852

—

C₂×#13094024

C₄

yes

—

C₂×#13094024

C₂²

yes

characteristic

C₂×#13094015

—

C₂×#13094015

—

C₂×Q₈×Dic₄₇

—

C₂×C₄×Dic₉₄

C₄

yes

—

C₂×C₄×Dic₉₄

C₂²

yes

characteristic

#15689176

C₂²

yes

—

#15688871

—

#15688853

—

#15688849

—

C₂×C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₄₇×#423

C₂²

yes

—

C₂×#101×C₄₇

—

C₄₇×#343

—

C₂²×Dic₉₄

C₂×C₄

yes

—

C₂²×Dic₉₄

C₂×C₄

yes

—

—

—

D₄

yes

—

#13094015

—

#13094015

—

Q₈×Dic₄₇

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₄×Dic₉₄

D₄

yes

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

characteristic

C₂×Dic₄₇⋊C₄

—

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

—

C₄⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

—

C₂²×Q₈×C₄₇

D₄

yes

characteristic

C₂×M₁₆×C₄₇

—

C₄×Q₈×C₄₇

—

C₄×Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

#101×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

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

C₂²⋊C₄

yes

—

C₂×Dic₉₄

C₂²⋊C₄

yes

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂²⋊C₄

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

100

C₂×C₄×C₄₇

—

101

C₂×C₄×C₄₇

—

102

C₂×C₄×C₄₇

—

103

C₂×C₄×C₄₇

—

104

C₂×C₄×C₄₇

—

105

C₂×C₄×C₄₇

—

106

C₂×C₄×C₄₇

#103

yes

—

107

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

108

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

109

C₂×C₄×C₄₇

#120

yes

—

110

C₂×C₄×C₄₇

#120

yes

—

111

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

112

C₂×C₄×C₄₇

C₂×Q₁₆

yes

characteristic

113

C₂×C₄×C₄₇

#137

yes

—

114

C₂×Dic₄₇

—

115

C₂×Dic₄₇

—

116

C₂×Dic₄₇

—

117

C₂×Dic₄₇

—

118

C₂×Dic₄₇

—

119

C₂×Dic₄₇

—

120

Dic₉₄

—

121

Dic₉₄

—

122

Dic₉₄

—

123

Dic₉₄

—

124

C₈×C₄₇

—

125

C₄₇⋊C₈

—

126

#8392

—

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

#413

yes

—

137

C₄×C₄₇

#448

yes

—

138

C₄×C₄₇

#451

yes

—

139

Dic₄₇

—

140

Dic₄₇

—

141

Dic₄₇

—

142

C₂×#557

—

143

#1801

D₄₇

yes

characteristic

144

#1548

—

145

#1487

—

146

#1461

—

147

C₂×C₄₇

—

148

C₂×C₄₇

—

149

C₂×C₄₇

#1785

yes

characteristic

150

C₂×C₄₇

#1787

yes

characteristic

151

C₂×C₄₇

#1796

yes

characteristic

152

#557

—

153

#557

—

154

C₂×C₄⋊Q₈

—

155

C₂×C₄⋊Q₈

—

156

C₂×#125

—

157

C₂×#125

—

158

C₂×C₄×Q₈

—

159

C₂×C₄×Q₈

—

160

C₂×C₄×Q₈

—

161

C₂×C₄×Q₈

C₂×D₄₇

yes

characteristic

162

#431

—

163

#423

C₂×D₄₇

yes

—

164

C₂×#101

—

165

#343

—

166

#333

—

167

Q₈⋊C₈

—

168

#324

—

169

C₄₇

#8392

yes

characteristic, complemented, Sylow

170

C₂²×Q₈

—

171

C₂²×Q₈

—

172

C₂²×Q₈

C₂²⋊D₄₇

yes

characteristic

173

C₂×M₁₆

—

174

C₄⋊Q₈

—

175

C₄⋊Q₈

—

176

C₄⋊Q₈

—

177

C₄⋊Q₈

—

178

#125

—

179

#125

—

180

C₄×Q₈

—

181

C₄×Q₈

—

182

C₄×Q₈

—

183

C₄×Q₈

—

184

C₄×Q₈

—

185

C₄×Q₈

—

186

C₄×Q₈

—

187

C₂×C₄⋊C₄

—

188

C₂×C₄⋊C₄

—

189

C₂×C₄⋊C₄

—

190

C₂×C₄⋊C₄

—

191

C₂×C₄⋊C₄

—

192

C₂×C₄⋊C₄

—

193

C₂×C₄⋊C₄

—

194

C₂×C₄⋊C₄

D₁₈₈

yes

—

195

C₂×C₄⋊C₄

C₂²⋊D₄₇

yes

characteristic

196

C₂×C₄²

—

197

C₂×C₄²

—

198

C₂×C₄²

C₄×D₄₇

yes

—

199

C₂×C₄²

C₂²×D₄₇

yes

characteristic

200

C₄⋊C₈

—

201

C₄⋊C₈

—

202

C₄⋊C₈

—

203

#101

—

204

C₂²⋊C₈

—

205

C₄×C₈

—

206

C₂×Q₈

—

207

C₂×Q₈

—

208

C₂×Q₈

—

209

C₂×Q₈

—

210

C₂×Q₈

—

211

C₂×Q₈

—

212

C₂×Q₈

—

188

—

213

C₂×Q₈

—

188

—

214

C₂×Q₈

#10625335

yes

—

215

C₂×Q₈

#10625337

yes

—

216

C₂²×C₄

—

217

C₂²×C₄

—

218

C₂²×C₄

—

219

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

220

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

221

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

222

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

223

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

224

M₁₆

—

225

M₁₆

—

226

C₂×C₈

—

227

C₂×C₈

—

188

—

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

C₄²

—

239

C₄²

—

240

C₄²

—

241

C₄²

—

242

C₄²

D₄×D₄₇

yes

—

243

C₄²

D₄×D₄₇

yes

—

244

C₂³

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

245

Q₈

—

246

Q₈

—

247

Q₈

—

248

Q₈

—

188

—

249

Q₈

—

188

—

250

Q₈

—

188

—

251

C₂×C₄

—

252

C₂×C₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

188

—

261

C₂×C₄

—

188

—

262

C₂×C₄

—

188

—

263

C₂×C₄

#13093947

yes

—

264

C₂×C₄

C₂²⋊C₄×D₄₇

yes

characteristic

265

C₂×C₄

C₂²⋊C₄×D₄₇

yes

characteristic

266

C₂×C₄

#13093992

yes

—

267

C₂×C₄

#13093994

yes

—

268

C₂×C₄

C₂×#10625335

yes

characteristic

269

C₂×C₄

C₂×#10625337

yes

characteristic

270

C₂×C₄

#13094054

yes

—

271

C₈

—

272

C₈

—

376

—

273

C₂²

—

274

C₂²

—

275

C₂²

#15688978

yes

characteristic

276

C₂²

C₂×#13093947

yes

characteristic

277

C₂²

#15689131

yes

characteristic

278

C₄

—

279

C₄

—

280

C₄

—

281

C₄

—

282

C₄

—

188

—

283

C₄

—

188

—

284

C₄

—

188

—

285

C₄

#15689106

yes

—

286

C₄

#15689261

yes

—

287

C₄

#15689278

yes

—

288

C₂

—

289

C₂

—

290

C₂

#20243315

yes

characteristic

291

C₂

#20243322

yes

characteristic

292

C₂

#20243364

yes

characteristic

	subgroup	G/H
center	C₂²	#15688978
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1801	C₂
socle	C₂²×C₄₇	#379
prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1801	D₄₇
hypocenter	C₄₇	#8392
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

subgroup

G/H

center

C₂²

#15688978

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1801

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 ◁ #1801

N	H ≅ G/N	type
169. C₄₇	#8392	semidirect

H ≅ G/N

type

169. C₄₇

#8392

semidirect

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

subgroup	index
C₂×#15689852	2
#20242070	2
#20241816	2
#20241712	2
C₄₇×#1801	2
#8392	47

subgroup

index

C₄₇×#1801

Subgroups — #26108027

Conjugacy classes of subgroups

Complements

Maximal subgroups