Group #26104494 — subgroups

Subgroups — #26104494

Order 12032.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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	C₄×#13094024	C₂	1	1	yes	maximal, characteristic
2	#20243241	C₂	1	1	yes	maximal, characteristic
3	#20241213	C₂	1	4	yes	maximal
4	C₄₇×#1839	C₂	1	1	yes	maximal, characteristic
5	C₂×#13094024	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₉₄	C₄	1	2	yes	—
7	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
8	C₂×#13093935	—	2	1	no	—
9	#15689029	C₂²	1	2	yes	—
10	#15689021	—	2	1	no	—
11	#15689021	—	2	1	no	—
12	#15688993	C₄	1	1	yes	characteristic
13	C₄×C₄⋊Dic₄₇	—	2	1	no	—
14	C₄×C₄⋊Dic₄₇	—	2	1	no	—
15	#15688878	C₂²	1	2	yes	—
16	C₄³×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#336	—	2	1	no	—
18	C₄₇×#336	—	2	1	no	—
19	C₄₇×#336	C₂²	1	2	yes	—
20	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
21	C₂²×C₄₇⋊C₈	—	2	2	no	—
22	#13094024	—	2	4	no	—
23	C₄×Dic₉₄	—	4	4	no	—
24	C₂×C₄⋊Dic₄₇	—	2	1	no	—
25	C₂×C₄⋊Dic₄₇	—	2	1	no	—
26	C₂×C₄⋊Dic₄₇	—	2	1	no	—
27	C₂×C₄⋊Dic₄₇	—	2	1	no	—
28	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
29	C₂×Dic₄₇⋊C₄	—	2	2	no	—
30	C₂×C₄×Dic₄₇	—	2	2	no	—
31	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
32	#13093935	—	4	2	no	—
33	C₄₇⋊#95	—	2	2	no	—
34	C₄₇⋊#95	—	2	2	no	—
35	C₂²×C₈×C₄₇	—	2	2	no	—
36	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₄₇	—	2	2	no	—
51	C₂²×Dic₄₇	—	2	2	no	—
52	C₂×Dic₉₄	—	2	2	no	—
53	C₂×Dic₉₄	—	4	2	no	—
54	C₂×Dic₉₄	—	4	2	no	—
55	C₂×Dic₉₄	M₁₆	1	4	yes	—
56	C₂×C₈×C₄₇	—	4	2	no	—
57	C₂×C₈×C₄₇	—	4	2	no	—
58	C₂×C₈×C₄₇	—	4	2	no	—
59	C₄²×C₄₇	—	2	2	no	—
60	C₄²×C₄₇	—	2	2	no	—
61	C₄²×C₄₇	—	2	2	no	—
62	C₄²×C₄₇	—	2	2	no	—
63	C₄²×C₄₇	—	4	1	no	—
64	C₄²×C₄₇	—	4	1	no	—
65	C₄²×C₄₇	SD₁₆	1	2	yes	—
66	C₄²×C₄₇	Q₁₆	1	2	yes	—
67	C₄⋊Dic₄₇	—	2	4	no	—
68	C₄⋊Dic₄₇	—	2	4	no	—
69	C₄⋊Dic₄₇	—	4	2	no	—
70	C₄⋊Dic₄₇	—	4	2	no	—
71	C₄⋊Dic₄₇	—	4	2	no	—
72	Dic₄₇⋊C₄	—	4	4	no	—
73	C₄×Dic₄₇	—	4	4	no	—
74	C₂×C₄₇⋊C₈	—	2	4	no	—
75	C₂×C₄₇⋊C₈	—	4	2	no	—
76	C₂×C₄₇⋊C₈	—	4	2	no	—
77	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₄×C₄₇	—	2	1	no	—
79	C₂×C₄×C₄₇	—	2	1	no	—
80	C₂×C₄×C₄₇	—	2	1	no	—
81	C₂×C₄×C₄₇	—	2	1	no	—
82	C₂×C₄×C₄₇	—	2	1	no	—
83	C₂×C₄×C₄₇	—	2	1	no	—
84	C₂×C₄×C₄₇	—	2	1	no	—
85	C₂×C₄×C₄₇	—	2	1	no	—
86	C₂×C₄×C₄₇	—	2	1	no	—
87	C₂×C₄×C₄₇	—	2	1	no	—
88	C₂×C₄×C₄₇	—	2	1	no	—
89	C₂×C₄×C₄₇	—	2	1	no	—
90	C₂×C₄×C₄₇	—	2	1	no	—
91	C₂×C₄×C₄₇	—	2	1	no	—
92	C₂×C₄×C₄₇	#100	1	2	yes	—
93	C₂×C₄×C₄₇	#103	1	2	yes	—
94	C₂×C₄×C₄₇	#103	1	2	yes	—
95	C₂×C₄×C₄₇	#104	1	2	yes	—
96	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
97	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
99	C₂×C₄×C₄₇	#137	1	2	yes	—
100	C₂×Dic₄₇	—	2	4	no	—
101	C₂×Dic₄₇	—	4	2	no	—
102	C₂×Dic₄₇	—	4	2	no	—
103	C₂×Dic₄₇	—	4	2	no	—
104	C₂×Dic₄₇	—	4	2	no	—
105	C₂×Dic₄₇	—	4	2	no	—
106	Dic₉₄	—	4	4	no	—
107	Dic₉₄	—	4	4	no	—
108	C₈×C₄₇	—	8	2	no	—
109	C₄₇⋊C₈	—	4	4	no	—
110	#7624	—	47	1	no	maximal, Sylow
111	C₂²×C₄₇	#407	1	1	yes	characteristic
112	C₂²×C₄₇	#410	1	1	yes	characteristic
113	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
114	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
115	C₂²×C₄₇	#419	1	1	yes	characteristic
116	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
117	C₂²×C₄₇	#421	1	1	yes	characteristic
118	C₄×C₄₇	—	2	2	no	—
119	C₄×C₄₇	—	2	2	no	—
120	C₄×C₄₇	—	2	2	no	—
121	C₄×C₄₇	—	2	2	no	—
122	C₄×C₄₇	—	2	1	no	—
123	C₄×C₄₇	—	2	1	no	—
124	C₄×C₄₇	—	2	2	no	—
125	C₄×C₄₇	—	2	2	no	—
126	Dic₄₇	—	4	4	no	—
127	Dic₄₇	—	8	2	no	—
128	C₄×C₄⋊Q₈	—	47	1	no	—
129	#1839	D₄₇	1	1	yes	characteristic
130	#1767	—	47	1	no	—
131	#1272	—	47	4	no	—
132	C₂×C₄₇	#1466	1	1	yes	characteristic
133	C₂×C₄₇	#1487	1	1	yes	characteristic
134	C₂×C₄₇	#1491	1	1	yes	characteristic
135	C₂×C₄₇	#1503	1	1	yes	characteristic
136	C₂×C₄₇	#1515	1	1	yes	characteristic
137	C₂×C₄₇	#1530	1	1	yes	characteristic
138	C₂×C₄₇	#1548	1	1	yes	characteristic
139	C₂×C₄⋊Q₈	—	47	1	no	—
140	C₂×C₄×Q₈	—	47	2	no	—
141	C₂×C₄⋊C₈	—	94	1	no	—
142	C₂×#97	—	94	1	no	—
143	#391	—	47	2	no	—
144	#389	—	94	1	no	—
145	#389	—	94	1	no	—
146	#384	—	47	1	no	—
147	C₄×C₄⋊C₄	—	94	1	no	—
148	C₄×C₄⋊C₄	—	94	1	no	—
149	C₄³	C₂×D₄₇	1	1	yes	characteristic
150	#336	—	2	1	no	—
151	#336	—	2	1	no	—
152	#336	—	47	2	no	—
153	#336	C₂×D₄₇	1	2	yes	—
154	C₄₇	#7624	1	1	yes	characteristic, complemented, Sylow
155	C₂²×Q₈	—	47	2	no	—
156	C₂²×C₈	—	2	2	no	—
157	C₂²×C₈	—	94	2	no	—
158	C₄⋊Q₈	—	94	4	no	—
159	C₄×Q₈	—	188	4	no	—
160	C₂×C₄⋊C₄	—	47	2	no	—
161	C₂×C₄⋊C₄	—	94	1	no	—
162	C₂×C₄⋊C₄	—	94	1	no	—
163	C₂×C₄⋊C₄	—	94	2	no	—
164	C₂×C₄⋊C₄	—	94	1	no	—
165	C₂×C₄⋊C₄	—	94	1	no	—
166	C₂×C₄²	—	94	2	no	—
167	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
168	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
169	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
170	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
171	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
172	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
173	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
174	C₄⋊C₈	—	94	4	no	—
175	#97	—	188	2	no	—
176	#95	—	94	2	no	—
177	#95	—	94	2	no	—
178	C₂×Q₈	—	47	4	no	—
179	C₂×Q₈	—	94	2	no	—
180	C₂×Q₈	—	188	2	no	—
181	C₂×Q₈	—	188	2	no	—
182	C₂²×C₄	—	94	2	no	—
183	C₂²×C₄	—	94	2	no	—
184	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
185	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
186	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
187	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
189	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
190	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
191	C₂×C₈	—	4	2	no	—
192	C₂×C₈	—	4	2	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	94	4	no	—
195	C₂×C₈	—	188	2	no	—
196	C₂×C₈	—	188	2	no	—
197	C₄⋊C₄	—	94	4	no	—
198	C₄⋊C₄	—	94	4	no	—
199	C₄⋊C₄	—	188	2	no	—
200	C₄⋊C₄	—	188	2	no	—
201	C₄⋊C₄	—	188	4	no	—
202	C₄⋊C₄	—	188	2	no	—
203	C₄²	—	2	2	no	—
204	C₄²	—	2	2	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	2	2	no	—
207	C₄²	—	4	1	no	—
208	C₄²	—	4	1	no	—
209	C₄²	—	188	4	no	—
210	C₄²	#10625325	1	2	yes	—
211	C₄²	Dic₁₈₈	1	2	yes	—
212	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
213	Q₈	—	188	4	no	—
214	Q₈	—	188	4	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	94	4	no	—
230	C₂×C₄	—	188	2	no	—
231	C₂×C₄	—	188	2	no	—
232	C₂×C₄	—	188	2	no	—
233	C₂×C₄	—	188	2	no	—
234	C₂×C₄	—	188	2	no	—
235	C₂×C₄	#13093940	1	2	yes	—
236	C₂×C₄	#13093949	1	2	yes	—
237	C₂×C₄	#13093949	1	2	yes	—
238	C₂×C₄	#13093950	1	2	yes	—
239	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
240	C₂×C₄	C₂×#10625325	1	1	yes	characteristic
241	C₂×C₄	C₂×Dic₁₈₈	1	1	yes	characteristic
242	C₂×C₄	#13094054	1	2	yes	—
243	C₈	—	8	2	no	—
244	C₈	—	188	4	no	—
245	C₂²	#15689086	1	1	yes	characteristic
246	C₂²	#15689096	1	1	yes	characteristic
247	C₂²	C₂×#13093940	1	1	yes	characteristic
248	C₂²	C₂×#13093949	1	1	yes	characteristic
249	C₂²	#15689131	1	1	yes	characteristic
250	C₂²	C₂×#13093950	1	1	yes	characteristic
251	C₂²	#15689141	1	1	yes	characteristic
252	C₄	—	2	2	no	—
253	C₄	—	2	2	no	—
254	C₄	—	2	2	no	—
255	C₄	—	2	2	no	—
256	C₄	—	2	2	no	—
257	C₄	—	2	2	no	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	376	2	no	—
261	C₄	—	188	4	no	—
262	C₂	#20241728	1	1	yes	characteristic
263	C₂	#20241818	1	1	yes	characteristic
264	C₂	#20241834	1	1	yes	characteristic
265	C₂	#20241888	1	1	yes	characteristic
266	C₂	#20241938	1	1	yes	characteristic
267	C₂	#20242000	1	1	yes	characteristic
268	C₂	#20242068	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13094024

C₂

yes

maximal, characteristic

#20243241

C₂

yes

maximal, characteristic

#20241213

C₂

yes

maximal

C₄₇×#1839

C₂

yes

maximal, characteristic

C₂×#13094024

C₄

yes

characteristic

C₂×C₄×Dic₉₄

C₄

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

—

C₂×#13093935

—

#15689029

C₂²

yes

—

#15689021

—

#15689021

—

#15688993

C₄

yes

characteristic

C₄×C₄⋊Dic₄₇

—

C₄×C₄⋊Dic₄₇

—

#15688878

C₂²

yes

—

C₄³×C₄₇

C₂²

yes

characteristic

C₄₇×#336

—

C₄₇×#336

—

C₄₇×#336

C₂²

yes

—

C₂²×Dic₉₄

C₂×C₄

yes

—

C₂²×C₄₇⋊C₈

—

#13094024

—

C₄×Dic₉₄

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

—

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₄⋊(C₄₇⋊C₈)

—

#13093935

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

—

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

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

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

M₁₆

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

SD₁₆

yes

—

C₄²×C₄₇

Q₁₆

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#100

yes

—

C₂×C₄×C₄₇

#103

yes

—

C₂×C₄×C₄₇

#103

yes

—

C₂×C₄×C₄₇

#104

yes

—

C₂×C₄×C₄₇

C₂×M₁₆

yes

—

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₄₇

#137

yes

—

100

C₂×Dic₄₇

—

101

C₂×Dic₄₇

—

102

C₂×Dic₄₇

—

103

C₂×Dic₄₇

—

104

C₂×Dic₄₇

—

105

C₂×Dic₄₇

—

106

Dic₉₄

—

107

Dic₉₄

—

108

C₈×C₄₇

—

109

C₄₇⋊C₈

—

110

#7624

—

maximal, Sylow

111

C₂²×C₄₇

#407

yes

characteristic

112

C₂²×C₄₇

#410

yes

characteristic

113

C₂²×C₄₇

C₂×#100

yes

characteristic

114

C₂²×C₄₇

C₂×#103

yes

characteristic

115

C₂²×C₄₇

#419

yes

characteristic

116

C₂²×C₄₇

C₂×#104

yes

characteristic

117

C₂²×C₄₇

#421

yes

characteristic

118

C₄×C₄₇

—

119

C₄×C₄₇

—

120

C₄×C₄₇

—

121

C₄×C₄₇

—

122

C₄×C₄₇

—

123

C₄×C₄₇

—

124

C₄×C₄₇

—

125

C₄×C₄₇

—

126

Dic₄₇

—

127

Dic₄₇

—

128

C₄×C₄⋊Q₈

—

129

#1839

D₄₇

yes

characteristic

130

#1767

—

131

#1272

—

132

C₂×C₄₇

#1466

yes

characteristic

133

C₂×C₄₇

#1487

yes

characteristic

134

C₂×C₄₇

#1491

yes

characteristic

135

C₂×C₄₇

#1503

yes

characteristic

136

C₂×C₄₇

#1515

yes

characteristic

137

C₂×C₄₇

#1530

yes

characteristic

138

C₂×C₄₇

#1548

yes

characteristic

139

C₂×C₄⋊Q₈

—

140

C₂×C₄×Q₈

—

141

C₂×C₄⋊C₈

—

142

C₂×#97

—

143

#391

—

144

#389

—

145

#389

—

146

#384

—

147

C₄×C₄⋊C₄

—

148

C₄×C₄⋊C₄

—

149

C₄³

C₂×D₄₇

yes

characteristic

150

#336

—

151

#336

—

152

#336

—

153

#336

C₂×D₄₇

yes

—

154

C₄₇

#7624

yes

characteristic, complemented, Sylow

155

C₂²×Q₈

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

C₄⋊Q₈

—

159

C₄×Q₈

—

188

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄²

—

167

C₂×C₄²

C₄×D₄₇

yes

characteristic

168

C₂×C₄²

C₄×D₄₇

yes

characteristic

169

C₂×C₄²

D₁₈₈

yes

characteristic

170

C₂×C₄²

D₁₈₈

yes

characteristic

171

C₂×C₄²

C₂²⋊D₄₇

yes

characteristic

172

C₂×C₄²

C₂²⋊D₄₇

yes

characteristic

173

C₂×C₄²

C₂²×D₄₇

yes

characteristic

174

C₄⋊C₈

—

175

#97

—

188

—

176

#95

—

177

#95

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

—

188

—

181

C₂×Q₈

—

188

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

185

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

186

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

187

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

188

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

189

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

190

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

188

—

196

C₂×C₈

—

188

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

188

—

200

C₄⋊C₄

—

188

—

201

C₄⋊C₄

—

188

—

202

C₄⋊C₄

—

188

—

203

C₄²

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

—

209

C₄²

—

188

—

210

C₄²

#10625325

yes

—

211

C₄²

Dic₁₈₈

yes

—

212

C₂³

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

213

Q₈

—

188

—

214

Q₈

—

188

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

188

—

231

C₂×C₄

—

188

—

232

C₂×C₄

—

188

—

233

C₂×C₄

—

188

—

234

C₂×C₄

—

188

—

235

C₂×C₄

#13093940

yes

—

236

C₂×C₄

#13093949

yes

—

237

C₂×C₄

#13093949

yes

—

238

C₂×C₄

#13093950

yes

—

239

C₂×C₄

M₁₆×D₄₇

yes

—

240

C₂×C₄

C₂×#10625325

yes

characteristic

241

C₂×C₄

C₂×Dic₁₈₈

yes

characteristic

242

C₂×C₄

#13094054

yes

—

243

C₈

—

244

C₈

—

188

—

245

C₂²

#15689086

yes

characteristic

246

C₂²

#15689096

yes

characteristic

247

C₂²

C₂×#13093940

yes

characteristic

248

C₂²

C₂×#13093949

yes

characteristic

249

C₂²

#15689131

yes

characteristic

250

C₂²

C₂×#13093950

yes

characteristic

251

C₂²

#15689141

yes

characteristic

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

376

—

261

C₄

—

188

—

262

C₂

#20241728

yes

characteristic

263

C₂

#20241818

yes

characteristic

264

C₂

#20241834

yes

characteristic

265

C₂

#20241888

yes

characteristic

266

C₂

#20241938

yes

characteristic

267

C₂

#20242000

yes

characteristic

268

C₂

#20242068

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1839	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1839	D₄₇
hypocenter	C₄₇	#7624
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1839

subgroup

G/H

center

C₂³

C₂×(C₂×D₄₇)⋊C₄

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1839

C₂

socle, prime radical

C₂³×C₄₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1839

N	H ≅ G/N	type
154. C₄₇	#7624	semidirect

H ≅ G/N

type

154. C₄₇

#7624

semidirect

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

subgroup	index
C₄×#13094024	2
#20243241	2
#20241213	2
C₄₇×#1839	2
#7624	47

subgroup

index

C₄₇×#1839

Subgroups — #26104494

Conjugacy classes of subgroups

Complements

Maximal subgroups