Group #26372718 — subgroups

Subgroups — #26372718

Order 12032.

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

normal subgroups only

This group has 488 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	#20254028	C₂	1	2	yes	maximal, complemented
2	#20245538	C₂	1	2	yes	maximal, complemented
3	#20245524	C₂	1	2	yes	maximal, complemented
4	#20245503	C₂	1	2	yes	maximal, complemented
5	#20245474	C₂	1	1	yes	maximal, characteristic
6	#20245452	C₂	1	2	yes	maximal, complemented
7	#20245446	C₂	1	2	yes	maximal, complemented
8	#20245146	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#2216	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689746	—	2	2	no	—
11	C₂×#13093967	C₂²	1	2	yes	—
12	C₂×D₇₅₂	C₂²	1	1	yes	characteristic
13	C₂×#13093964	C₂²	1	1	yes	characteristic
14	#15689527	C₂²	1	2	yes	—
15	#15689508	C₂²	1	2	yes	—
16	#15689484	—	2	2	no	—
17	#15689371	—	2	2	no	—
18	#15689359	C₂²	1	2	yes	—
19	#15689226	—	2	2	no	—
20	Q₁₆×Dic₄₇	C₂²	1	2	yes	—
21	#15689205	C₂²	1	2	yes	—
22	#15689078	C₂²	1	1	yes	characteristic
23	#15688949	C₂²	1	1	yes	characteristic
24	#15688948	C₂²	1	2	yes	—
25	Dic₄₇⋊C₁₆	C₂²	1	2	yes	—
26	Dic₄₇⋊C₁₆	C₂²	1	2	yes	—
27	#15688927	C₂²	1	2	yes	—
28	#15688925	C₂²	1	2	yes	—
29	#15688923	C₂²	1	2	yes	—
30	C₂×Q₃₂×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#467	C₂²	1	2	yes	—
33	C₄₇×#366	C₂²	1	1	yes	characteristic
34	C₄₇×#358	C₂²	1	2	yes	—
35	C₂×#10625336	—	2	2	no	—
36	C₂×D₃₇₆	C₂³	1	2	yes	—
37	C₂×#10625329	D₄	1	1	yes	characteristic
38	#13094023	—	2	2	no	—
39	#13094019	—	4	2	no	—
40	#13094013	—	2	2	no	—
41	#13094010	—	4	2	no	—
42	#13094006	—	4	2	no	—
43	#13094004	—	4	2	no	—
44	#13093998	—	2	2	no	—
45	Q₈×Dic₄₇	—	2	2	no	—
46	#13093986	—	2	2	no	—
47	#13093983	D₄	1	1	yes	characteristic
48	#13093967	—	4	2	no	—
49	D₇₅₂	—	4	1	no	—
50	#13093964	—	4	1	no	—
51	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
52	#13093958	C₂³	1	2	yes	—
53	#13093957	—	2	2	no	—
54	#13093948	—	2	2	no	—
55	#13093946	—	2	2	no	—
56	#13093944	—	2	2	no	—
57	#13093934	D₄	1	2	yes	—
58	C₈×Dic₄₇	C₂³	1	2	yes	—
59	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
60	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
61	C₂²⋊Q₈×C₄₇	—	2	2	no	—
62	Q₃₂×C₄₇	—	4	1	no	—
63	C₂×C₁₆×C₄₇	—	4	1	no	—
64	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
66	#107×C₄₇	C₂³	1	2	yes	—
67	#103×C₄₇	—	2	2	no	—
68	C₂×Q₈×C₄₇	—	2	2	no	—
69	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
70	C₂×C₂²⋊D₄₇	—	4	2	no	—
71	C₂×D₁₈₈	—	2	2	no	—
72	C₂×C₄×D₄₇	—	4	2	no	—
73	C₂×Dic₉₄	—	4	2	no	—
74	Q₁₆×C₄₇	—	2	2	no	—
75	Q₁₆×C₄₇	—	2	2	no	—
76	C₂×C₈×C₄₇	—	2	1	no	—
77	C₂×C₈×C₄₇	—	2	1	no	—
78	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
80	C₄⋊C₄×C₄₇	—	2	2	no	—
81	C₄⋊C₄×C₄₇	—	4	2	no	—
82	C₂²⋊C₄×C₄₇	—	4	2	no	—
83	C₂²⋊Dic₄₇	D₈	1	2	yes	—
84	#10625336	—	4	4	no	—
85	(C₂×D₄₇)⋊C₄	—	4	2	no	—
86	(C₂×D₄₇)⋊C₄	—	4	2	no	—
87	(C₂×D₄₇)⋊C₄	—	4	2	no	—
88	(C₂×D₄₇)⋊C₄	—	4	2	no	—
89	C₄⋊Dic₄₇	—	2	2	no	—
90	C₄⋊Dic₄₇	—	4	2	no	—
91	C₄⋊Dic₄₇	D₈	1	1	yes	characteristic
92	C₄⋊Dic₄₇	D₈	1	1	yes	characteristic
93	Dic₄₇⋊C₄	—	4	2	no	—
94	C₄×Dic₄₇	—	4	2	no	—
95	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
96	#10625329	—	4	1	no	—
97	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
98	D₃₇₆	—	2	2	no	—
99	D₃₇₆	—	2	2	no	—
100	C₁₆×C₄₇	—	2	1	no	—
101	C₁₆×C₄₇	—	2	1	no	—
102	C₄₇⋊C₁₆	—	2	2	no	—
103	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
104	C₂²×D₄₇	—	4	2	no	—
105	Q₈×C₄₇	—	4	2	no	—
106	Q₈×C₄₇	—	4	2	no	—
107	C₂×C₄×C₄₇	—	2	1	no	—
108	C₂×C₄×C₄₇	—	2	1	no	—
109	C₂×C₄×C₄₇	—	4	2	no	—
110	C₂×C₄×C₄₇	—	4	2	no	—
111	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
112	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
113	C₂²⋊D₄₇	—	16	2	no	—
114	C₂×Dic₄₇	—	4	2	no	—
115	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
116	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
117	D₁₈₈	—	4	2	no	—
118	D₁₈₈	—	4	2	no	—
119	C₄×D₄₇	—	16	2	no	—
120	Dic₉₄	—	16	2	no	—
121	C₈×C₄₇	—	2	1	no	—
122	C₈×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
123	C₈×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
124	C₄₇⋊C₈	—	2	2	no	—
125	#33828	—	47	1	no	maximal, Sylow
126	C₂²×C₄₇	—	2	1	no	—
127	C₂²×C₄₇	—	2	1	no	—
128	C₂²×C₄₇	—	2	1	no	—
129	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
130	C₂×D₄₇	—	8	2	no	—
131	C₂×D₄₇	—	8	2	no	—
132	C₂×D₄₇	—	8	2	no	—
133	C₄×C₄₇	—	2	1	no	—
134	C₄×C₄₇	—	8	2	no	—
135	C₄×C₄₇	—	8	2	no	—
136	C₄×C₄₇	#537	1	1	yes	characteristic
137	C₄×C₄₇	#575	1	1	yes	characteristic
138	Dic₄₇	—	2	2	no	—
139	Dic₄₇	—	2	2	no	—
140	Dic₄₇	—	8	2	no	—
141	#3175	—	47	2	no	—
142	#2227	—	47	2	no	—
143	#2224	—	47	2	no	—
144	#2220	—	47	2	no	—
145	#2216	D₄₇	1	1	yes	characteristic, complemented
146	#2215	—	47	1	no	—
147	#2211	—	47	2	no	—
148	#2210	—	47	2	no	—
149	#2151	—	47	1	no	—
150	C₂×C₄₇	—	4	1	no	—
151	C₂×C₄₇	#3245	1	1	yes	characteristic
152	C₂×C₄₇	#3415	1	1	yes	characteristic
153	C₂×C₄₇	#3417	1	1	yes	characteristic
154	D₄₇	—	16	2	no	—
155	#542	—	94	2	no	—
156	C₂×Q₃₂	C₂×D₄₇	1	1	yes	characteristic
157	C₂×SD₃₂	—	47	2	no	—
158	C₂×D₁₆	—	47	1	no	—
159	C₂×M₃₂	—	47	1	no	—
160	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic
161	#500	—	47	2	no	—
162	#495	—	47	2	no	—
163	#489	—	94	2	no	—
164	#468	—	94	2	no	—
165	#467	C₂×D₄₇	1	2	yes	—
166	#466	—	47	2	no	—
167	#440	—	94	2	no	—
168	C₄×Q₁₆	—	47	2	no	—
169	C₄×D₈	—	47	2	no	—
170	#405	—	47	1	no	—
171	#366	—	47	1	no	—
172	#366	—	47	2	no	—
173	#366	C₂×D₄₇	1	1	yes	characteristic
174	C₄⋊C₁₆	—	47	2	no	—
175	C₄⋊C₁₆	—	47	2	no	—
176	#358	—	47	2	no	—
177	#358	C₂×D₄₇	1	2	yes	—
178	#357	—	47	2	no	—
179	#357	—	47	2	no	—
180	C₄₇	#33828	1	1	yes	characteristic, complemented, Sylow
181	C₂×Q₁₆	C₂²×D₄₇	1	2	yes	—
182	C₂×SD₁₆	—	94	2	no	—
183	C₂×D₈	—	47	2	no	—
184	C₂×M₁₆	—	47	1	no	—
185	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
186	C₄⋊Q₈	—	94	2	no	—
187	#126	—	188	2	no	—
188	#124	—	94	2	no	—
189	#124	—	188	2	no	—
190	#123	—	188	2	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	188	2	no	—
193	#121	—	94	2	no	—
194	C₄×Q₈	—	94	2	no	—
195	C₄×D₄	—	94	2	no	—
196	#117	—	47	1	no	—
197	Q₃₂	—	4	1	no	—
198	SD₃₂	—	188	2	no	—
199	D₁₆	—	188	1	no	—
200	M₃₂	—	188	1	no	—
201	C₂×C₁₆	—	4	1	no	—
202	C₂×C₁₆	—	47	2	no	—
203	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
204	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
205	#107	—	47	2	no	—
206	#107	—	94	2	no	—
207	#107	C₂²×D₄₇	1	2	yes	—
208	#103	—	2	2	no	—
209	#103	—	94	2	no	—
210	#102	—	94	2	no	—
211	#102	—	94	2	no	—
212	#97	—	47	2	no	—
213	C₄×C₈	—	47	2	no	—
214	C₂×Q₈	—	2	2	no	—
215	C₂×Q₈	—	188	2	no	—
216	C₂×D₄	—	94	2	no	—
217	C₂×D₄	—	188	2	no	—
218	C₂²×C₄	—	188	2	no	—
219	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
220	Q₁₆	—	2	2	no	—
221	Q₁₆	—	2	2	no	—
222	SD₁₆	—	188	4	no	—
223	D₈	—	94	2	no	—
224	D₈	—	94	2	no	—
225	M₁₆	—	188	1	no	—
226	C₂×C₈	—	2	1	no	—
227	C₂×C₈	—	2	1	no	—
228	C₂×C₈	—	47	2	no	—
229	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
230	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
231	C₄⋊C₄	—	2	2	no	—
232	C₄⋊C₄	—	4	2	no	—
233	C₄⋊C₄	—	47	1	no	—
234	C₄⋊C₄	—	47	1	no	—
235	C₄⋊C₄	—	94	2	no	—
236	C₄⋊C₄	—	188	2	no	—
237	C₄⋊C₄	—	188	2	no	—
238	C₂²⋊C₄	—	4	2	no	—
239	C₂²⋊C₄	—	47	2	no	—
240	C₂²⋊C₄	—	188	2	no	—
241	C₂²⋊C₄	—	188	2	no	—
242	C₂²⋊C₄	—	188	2	no	—
243	C₂²⋊C₄	—	188	2	no	—
244	C₄²	—	47	2	no	—
245	C₄²	—	188	2	no	—
246	C₁₆	—	2	1	no	—
247	C₁₆	—	2	1	no	—
248	C₁₆	—	94	2	no	—
249	C₂³	—	188	2	no	—
250	C₂³	D₈×D₄₇	1	1	yes	characteristic
251	Q₈	—	4	2	no	—
252	Q₈	—	4	2	no	—
253	Q₈	—	752	2	no	—
254	D₄	—	188	2	no	—
255	D₄	—	188	2	no	—
256	D₄	—	752	2	no	—
257	C₂×C₄	—	2	1	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	47	2	no	—
262	C₂×C₄	—	47	2	no	—
263	C₂×C₄	—	188	2	no	—
264	C₂×C₄	—	752	2	no	—
265	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
266	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
267	C₈	—	2	1	no	—
268	C₈	—	94	2	no	—
269	C₈	#13094069	1	1	yes	characteristic
270	C₈	#13094071	1	1	yes	characteristic
271	C₂²	—	2	1	no	—
272	C₂²	—	2	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	376	2	no	—
275	C₂²	—	376	2	no	—
276	C₂²	—	376	2	no	—
277	C₂²	C₂×D₈×D₄₇	1	1	yes	characteristic
278	C₄	—	2	1	no	—
279	C₄	—	8	2	no	—
280	C₄	—	8	2	no	—
281	C₄	—	94	2	no	—
282	C₄	—	94	2	no	—
283	C₄	—	376	2	no	—
284	C₄	#15689700	1	1	yes	characteristic
285	C₄	#15689920	1	1	yes	characteristic
286	C₂	—	4	1	no	—
287	C₂	—	752	2	no	—
288	C₂	#20254694	1	1	yes	characteristic
289	C₂	#20256526	1	1	yes	characteristic
290	C₂	#20256537	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20254028

C₂

yes

maximal, complemented

#20245538

C₂

yes

maximal, complemented

#20245524

C₂

yes

maximal, complemented

#20245503

C₂

yes

maximal, complemented

#20245474

C₂

yes

maximal, characteristic

#20245452

C₂

yes

maximal, complemented

#20245446

C₂

yes

maximal, complemented

#20245146

C₂

yes

maximal, characteristic, complemented

C₄₇×#2216

C₂

yes

maximal, characteristic, complemented

#15689746

—

C₂×#13093967

C₂²

yes

—

C₂×D₇₅₂

C₂²

yes

characteristic

C₂×#13093964

C₂²

yes

characteristic

#15689527

C₂²

yes

—

#15689508

C₂²

yes

—

#15689484

—

#15689371

—

#15689359

C₂²

yes

—

#15689226

—

Q₁₆×Dic₄₇

C₂²

yes

—

#15689205

C₂²

yes

—

#15689078

C₂²

yes

characteristic

#15688949

C₂²

yes

characteristic

#15688948

C₂²

yes

—

Dic₄₇⋊C₁₆

C₂²

yes

—

Dic₄₇⋊C₁₆

C₂²

yes

—

#15688927

C₂²

yes

—

#15688925

C₂²

yes

—

#15688923

C₂²

yes

—

C₂×Q₃₂×C₄₇

C₂²

yes

characteristic

C₂²×C₁₆×C₄₇

C₂²

yes

characteristic

C₄₇×#467

C₂²

yes

—

C₄₇×#366

C₂²

yes

characteristic

C₄₇×#358

C₂²

yes

—

C₂×#10625336

—

C₂×D₃₇₆

C₂³

yes

—

C₂×#10625329

D₄

yes

—

—

—

—

—

—

—

Q₈×Dic₄₇

—

#13093986

—

#13093983

D₄

yes

characteristic

#13093967

—

D₇₅₂

—

#13093964

—

C₂×C₄₇⋊C₁₆

C₂³

yes

—

#13093958

C₂³

yes

—

—

—

—

—

D₄

yes

—

C₈×Dic₄₇

C₂³

yes

—

C₂×Q₁₆×C₄₇

C₂³

yes

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

C₂²⋊Q₈×C₄₇

—

Q₃₂×C₄₇

—

C₂×C₁₆×C₄₇

—

C₂×C₁₆×C₄₇

C₂³

yes

characteristic

C₂×C₁₆×C₄₇

C₂³

yes

characteristic

#107×C₄₇

C₂³

yes

—

#103×C₄₇

—

C₂×Q₈×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₄₇

—

C₂×D₁₈₈

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂⁴

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

D₈

yes

—

#10625336

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

D₈

yes

characteristic

C₄⋊Dic₄₇

D₈

yes

characteristic

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₂×D₄

yes

—

#10625329

—

C₂×C₄₇⋊C₈

C₂×D₄

yes

—

D₃₇₆

—

D₃₇₆

—

100

C₁₆×C₄₇

—

101

C₁₆×C₄₇

—

102

C₄₇⋊C₁₆

—

103

C₂³×C₄₇

C₂×D₈

yes

characteristic

104

C₂²×D₄₇

—

105

Q₈×C₄₇

—

106

Q₈×C₄₇

—

107

C₂×C₄×C₄₇

—

108

C₂×C₄×C₄₇

—

109

C₂×C₄×C₄₇

—

110

C₂×C₄×C₄₇

—

111

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

112

C₂×C₄×C₄₇

C₂²×D₄

yes

characteristic

113

C₂²⋊D₄₇

—

114

C₂×Dic₄₇

—

115

C₂×Dic₄₇

C₂×D₈

yes

—

116

C₂×Dic₄₇

C₂×D₈

yes

—

117

D₁₈₈

—

118

D₁₈₈

—

119

C₄×D₄₇

—

120

Dic₉₄

—

121

C₈×C₄₇

—

122

C₈×C₄₇

H(5,𝔽₂)

yes

characteristic

123

C₈×C₄₇

2₋¹⁺⁴

yes

characteristic

124

C₄₇⋊C₈

—

125

#33828

—

maximal, Sylow

126

C₂²×C₄₇

—

127

C₂²×C₄₇

—

128

C₂²×C₄₇

—

129

C₂²×C₄₇

C₂²×D₈

yes

characteristic

130

C₂×D₄₇

—

131

C₂×D₄₇

—

132

C₂×D₄₇

—

133

C₄×C₄₇

—

134

C₄×C₄₇

—

135

C₄×C₄₇

—

136

C₄×C₄₇

#537

yes

characteristic

137

C₄×C₄₇

#575

yes

characteristic

138

Dic₄₇

—

139

Dic₄₇

—

140

Dic₄₇

—

141

#3175

—

142

#2227

—

143

#2224

—

144

#2220

—

145

#2216

D₄₇

yes

characteristic, complemented

146

#2215

—

147

#2211

—

148

#2210

—

149

#2151

—

150

C₂×C₄₇

—

151

C₂×C₄₇

#3245

yes

characteristic

152

C₂×C₄₇

#3415

yes

characteristic

153

C₂×C₄₇

#3417

yes

characteristic

154

D₄₇

—

155

#542

—

156

C₂×Q₃₂

C₂×D₄₇

yes

characteristic

157

C₂×SD₃₂

—

158

C₂×D₁₆

—

159

C₂×M₃₂

—

160

C₂²×C₁₆

C₂×D₄₇

yes

characteristic

161

#500

—

162

#495

—

163

#489

—

164

#468

—

165

#467

C₂×D₄₇

yes

—

166

#466

—

167

#440

—

168

C₄×Q₁₆

—

169

C₄×D₈

—

170

#405

—

171

#366

—

172

#366

—

173

#366

C₂×D₄₇

yes

characteristic

174

C₄⋊C₁₆

—

175

C₄⋊C₁₆

—

176

#358

—

177

#358

C₂×D₄₇

yes

—

178

#357

—

179

#357

—

180

C₄₇

#33828

yes

characteristic, complemented, Sylow

181

C₂×Q₁₆

C₂²×D₄₇

yes

—

182

C₂×SD₁₆

—

183

C₂×D₈

—

184

C₂×M₁₆

—

185

C₂²×C₈

C₂²×D₄₇

yes

characteristic

186

C₄⋊Q₈

—

187

#126

—

188

—

188

#124

—

189

#124

—

188

—

190

#123

—

188

—

191

C₂²⋊Q₈

—

192

C₂²⋊Q₈

—

188

—

193

#121

—

194

C₄×Q₈

—

195

C₄×D₄

—

196

#117

—

197

Q₃₂

—

198

SD₃₂

—

188

—

199

D₁₆

—

188

—

200

M₃₂

—

188

—

201

C₂×C₁₆

—

202

C₂×C₁₆

—

203

C₂×C₁₆

C₂²×D₄₇

yes

characteristic

204

C₂×C₁₆

C₂²×D₄₇

yes

characteristic

205

#107

—

206

#107

—

207

#107

C₂²×D₄₇

yes

—

208

#103

—

209

#103

—

210

#102

—

211

#102

—

212

#97

—

213

C₄×C₈

—

214

C₂×Q₈

—

215

C₂×Q₈

—

188

—

216

C₂×D₄

—

217

C₂×D₄

—

188

—

218

C₂²×C₄

—

188

—

219

C₂²×C₄

D₄×D₄₇

yes

characteristic

220

Q₁₆

—

221

Q₁₆

—

222

SD₁₆

—

188

—

223

D₈

—

224

D₈

—

225

M₁₆

—

188

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₂×C₈

—

229

C₂×C₈

D₄×D₄₇

yes

characteristic

230

C₂×C₈

C₂³×D₄₇

yes

characteristic

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

188

—

237

C₄⋊C₄

—

188

—

238

C₂²⋊C₄

—

239

C₂²⋊C₄

—

240

C₂²⋊C₄

—

188

—

241

C₂²⋊C₄

—

188

—

242

C₂²⋊C₄

—

188

—

243

C₂²⋊C₄

—

188

—

244

C₄²

—

245

C₄²

—

188

—

246

C₁₆

—

247

C₁₆

—

248

C₁₆

—

249

C₂³

—

188

—

250

C₂³

D₈×D₄₇

yes

characteristic

251

Q₈

—

252

Q₈

—

253

Q₈

—

752

—

254

D₄

—

188

—

255

D₄

—

188

—

256

D₄

—

752

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

—

188

—

264

C₂×C₄

—

752

—

265

C₂×C₄

D₈×D₄₇

yes

characteristic

266

C₂×C₄

C₂×D₄×D₄₇

yes

characteristic

267

C₈

—

268

C₈

—

269

C₈

#13094069

yes

characteristic

270

C₈

#13094071

yes

characteristic

271

C₂²

—

272

C₂²

—

273

C₂²

—

274

C₂²

—

376

—

275

C₂²

—

376

—

276

C₂²

—

376

—

277

C₂²

C₂×D₈×D₄₇

yes

characteristic

278

C₄

—

279

C₄

—

280

C₄

—

281

C₄

—

282

C₄

—

283

C₄

—

376

—

284

C₄

#15689700

yes

characteristic

285

C₄

#15689920

yes

characteristic

286

C₂

—

287

C₂

—

752

—

288

C₂

#20254694

yes

characteristic

289

C₂

#20256526

yes

characteristic

290

C₂

#20256537

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₄₇
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₄₇×#2216	C₂
socle	C₂²×C₄₇	C₂²×D₈
prime radical	#20245474	C₂
hypercenter	#2216	D₄₇
hypocenter	C₄₇	#33828
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2216

subgroup

G/H

center

C₂²

C₂×D₈×D₄₇

commutator, cosocle

C₂×C₈×C₄₇

C₂⁴

Frattini

C₂×C₈

C₂³×D₄₇

Fitting

C₄₇×#2216

C₂

socle

C₂²×C₄₇

C₂²×D₈

C₂

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2216

N	H ≅ G/N	type
1. #20254028	C₂	semidirect
2. #20245538	C₂	semidirect
3. #20245524	C₂	semidirect
4. #20245503	C₂	semidirect
6. #20245452	C₂	semidirect
7. #20245446	C₂	semidirect
8. #20245146	C₂	semidirect
9. C₄₇×#2216	C₂	semidirect
145. #2216	D₄₇	semidirect
180. C₄₇	#33828	semidirect

H ≅ G/N

type

1. #20254028

C₂

semidirect

2. #20245538

C₂

semidirect

3. #20245524

C₂

semidirect

4. #20245503

C₂

semidirect

6. #20245452

C₂

semidirect

7. #20245446

C₂

semidirect

8. #20245146

C₂

semidirect

9. C₄₇×#2216

C₂

semidirect

145. #2216

D₄₇

semidirect

180. C₄₇

#33828

semidirect

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

subgroup	index
#20254028	2
#20245538	2
#20245524	2
#20245503	2
#20245474	2
#20245452	2
#20245446	2
#20245146	2
C₄₇×#2216	2
#33828	47

subgroup

index

C₄₇×#2216

Subgroups — #26372718

Conjugacy classes of subgroups

Complements

Maximal subgroups