Group #26135635 — subgroups

Subgroups — #26135635

Order 12032.

462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 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×#15689503	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688928	C₂	1	2	yes	maximal
3	C₂×#15688928	C₂	1	2	yes	maximal
4	#20244121	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1374	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₈₈	—	2	1	no	—
7	C₂²×Dic₁₈₈	C₂²	1	2	yes	—
8	C₂×#13094024	—	2	1	no	—
9	#15689503	—	2	4	no	—
10	C₂×#13093958	C₂²	1	1	yes	characteristic
11	C₂×#13093958	C₂²	1	1	yes	characteristic
12	#15689021	—	2	1	no	—
13	#15688928	—	2	4	no	—
14	#15688928	—	2	4	no	—
15	#15688886	—	2	1	no	—
16	C₂²×C₁₆×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×Dic₉₄	—	2	2	no	—
19	C₂×Dic₁₈₈	—	2	2	no	—
20	C₂×Dic₁₈₈	—	2	2	no	—
21	C₂×Dic₁₈₈	—	2	2	no	—
22	C₂×Dic₁₈₈	—	2	2	no	—
23	C₂×Dic₁₈₈	—	2	4	no	—
24	C₂×Dic₁₈₈	—	2	2	no	—
25	C₂×Dic₁₈₈	—	4	2	no	—
26	C₂×Dic₁₈₈	—	4	2	no	—
27	C₂×Dic₁₈₈	D₄	1	4	yes	—
28	#13094024	—	2	4	no	—
29	#13094024	—	4	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	1	no	—
31	C₂×C₄⋊Dic₄₇	—	2	1	no	—
32	C₂×C₄⋊Dic₄₇	—	4	1	no	—
33	C₂×C₄⋊Dic₄₇	—	4	1	no	—
34	C₂×Dic₄₇⋊C₄	—	4	1	no	—
35	#13093958	—	2	1	no	—
36	#13093958	—	2	2	no	—
37	#13093958	D₄	1	2	yes	—
38	C₄₇⋊#95	—	4	1	no	—
39	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
41	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
42	C₂×C₁₆×C₄₇	—	2	2	no	—
43	C₂×C₁₆×C₄₇	—	2	2	no	—
44	C₂×C₁₆×C₄₇	—	2	2	no	—
45	C₄×C₈×C₄₇	—	2	2	no	—
46	C₂²×C₄×C₄₇	D₈	1	1	yes	characteristic
47	C₂²×C₄×C₄₇	D₈	1	1	yes	characteristic
48	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
49	C₂²×Dic₄₇	—	4	1	no	—
50	C₂²×Dic₄₇	—	4	2	no	—
51	C₂²×Dic₄₇	—	4	1	no	—
52	C₂×Dic₉₄	—	2	4	no	—
53	C₂×Dic₉₄	—	4	2	no	—
54	C₂×Dic₉₄	—	4	2	no	—
55	C₂×Dic₉₄	—	4	2	no	—
56	C₂×Dic₉₄	—	4	2	no	—
57	C₂×Dic₉₄	—	4	2	no	—
58	C₂×C₈×C₄₇	—	2	1	no	—
59	C₂×C₈×C₄₇	—	2	1	no	—
60	C₂×C₈×C₄₇	SD₁₆	1	2	yes	—
61	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₄₇	#41	1	2	yes	—
64	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
65	C₄²×C₄₇	—	2	1	no	—
66	C₄²×C₄₇	—	2	1	no	—
67	C₄⋊Dic₄₇	—	2	2	no	—
68	C₄⋊Dic₄₇	—	4	4	no	—
69	C₄⋊Dic₄₇	—	4	4	no	—
70	C₄⋊Dic₄₇	—	4	1	no	—
71	C₄⋊Dic₄₇	—	4	1	no	—
72	C₄⋊Dic₄₇	—	4	1	no	—
73	Dic₄₇⋊C₄	—	8	2	no	—
74	Dic₁₈₈	—	2	4	no	—
75	Dic₁₈₈	—	2	4	no	—
76	Dic₁₈₈	—	4	8	no	—
77	Dic₁₈₈	—	4	2	no	—
78	Dic₁₈₈	—	4	2	no	—
79	C₁₆×C₄₇	—	4	2	no	—
80	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
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	SD₃₂	1	2	yes	—
86	C₂×C₄×C₄₇	Q₃₂	1	2	yes	—
87	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
88	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
89	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
90	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
91	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
92	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
93	C₂×Dic₄₇	—	4	4	no	—
94	C₂×Dic₄₇	—	4	2	no	—
95	C₂×Dic₄₇	—	8	2	no	—
96	C₂×Dic₄₇	—	8	2	no	—
97	C₂×Dic₄₇	—	8	1	no	—
98	C₂×Dic₄₇	—	8	1	no	—
99	C₂×Dic₄₇	—	8	1	no	—
100	C₂×Dic₄₇	—	8	1	no	—
101	C₂×Dic₄₇	—	8	1	no	—
102	Dic₉₄	—	4	4	no	—
103	Dic₉₄	—	4	4	no	—
104	Dic₉₄	—	8	2	no	—
105	Dic₉₄	—	8	2	no	—
106	C₈×C₄₇	—	2	2	no	—
107	C₈×C₄₇	#121	1	2	yes	—
108	C₈×C₄₇	#123	1	2	yes	—
109	#13409	—	47	1	no	maximal, Sylow
110	C₂²×C₄₇	#447	1	1	yes	characteristic
111	C₂²×C₄₇	#459	1	1	yes	characteristic
112	C₂²×C₄₇	#486	1	1	yes	characteristic
113	C₂²×C₄₇	C₂×SD₃₂	1	1	yes	characteristic
114	C₂²×C₄₇	C₂×Q₃₂	1	1	yes	characteristic
115	C₂²×C₄₇	#510	1	1	yes	characteristic
116	C₂²×C₄₇	#510	1	1	yes	characteristic
117	C₄×C₄₇	—	2	2	no	—
118	C₄×C₄₇	—	2	2	no	—
119	C₄×C₄₇	#394	1	1	yes	characteristic
120	C₄×C₄₇	#450	1	1	yes	characteristic
121	C₄×C₄₇	#460	1	1	yes	characteristic
122	C₄×C₄₇	#490	1	1	yes	characteristic
123	Dic₄₇	—	8	2	no	—
124	Dic₄₇	—	8	4	no	—
125	Dic₄₇	—	16	1	no	—
126	C₂×#494	—	47	1	no	—
127	C₂×#358	—	47	2	no	—
128	C₂×#358	—	47	2	no	—
129	#1942	—	47	1	no	—
130	#1374	D₄₇	1	1	yes	characteristic
131	C₂×C₄₇	#2041	1	1	yes	characteristic
132	C₂×C₄₇	#2185	1	1	yes	characteristic
133	C₂×C₄₇	#2188	1	1	yes	characteristic
134	C₂×C₄₇	#2208	1	1	yes	characteristic
135	C₂×C₄₇	#2209	1	1	yes	characteristic
136	C₂×C₄₇	#2241	1	1	yes	characteristic
137	C₂×C₄₇	#2245	1	1	yes	characteristic
138	C₂²×Q₁₆	—	47	2	no	—
139	C₂²×Q₁₆	—	94	1	no	—
140	C₂×C₄⋊Q₈	—	94	1	no	—
141	C₂²×C₁₆	C₂×D₄₇	1	2	yes	—
142	#494	—	94	4	no	—
143	C₂×#107	—	47	1	no	—
144	C₂×#107	—	47	1	no	—
145	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
146	#389	—	94	1	no	—
147	#358	—	94	4	no	—
148	#358	—	94	4	no	—
149	#340	—	94	1	no	—
150	C₄₇	#13409	1	1	yes	characteristic, complemented, Sylow
151	C₂²×Q₈	—	94	2	no	—
152	C₂×Q₁₆	—	47	4	no	—
153	C₂×Q₁₆	—	94	4	no	—
154	C₂×Q₁₆	—	94	2	no	—
155	C₂×Q₁₆	—	94	2	no	—
156	C₂×Q₁₆	—	94	2	no	—
157	C₂×Q₁₆	—	94	2	no	—
158	C₂×Q₁₆	—	94	2	no	—
159	C₂×Q₁₆	—	188	2	no	—
160	C₂×Q₁₆	—	188	2	no	—
161	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
162	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
163	C₄⋊Q₈	—	94	4	no	—
164	C₄⋊Q₈	—	188	2	no	—
165	C₂×C₄⋊C₄	—	94	1	no	—
166	C₂×C₄⋊C₄	—	94	1	no	—
167	C₂×C₄⋊C₄	—	188	1	no	—
168	C₂×C₄⋊C₄	—	188	1	no	—
169	C₂×C₄⋊C₄	—	188	1	no	—
170	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
171	C₂×C₁₆	—	2	2	no	—
172	C₂×C₁₆	—	2	2	no	—
173	C₂×C₁₆	—	2	2	no	—
174	#107	—	47	2	no	—
175	#107	—	94	1	no	—
176	#107	—	94	2	no	—
177	C₄×C₈	—	2	2	no	—
178	#95	—	188	1	no	—
179	C₂×Q₈	—	94	4	no	—
180	C₂×Q₈	—	188	2	no	—
181	C₂×Q₈	—	188	2	no	—
182	C₂×Q₈	—	188	2	no	—
183	C₂×Q₈	—	188	2	no	—
184	C₂×Q₈	—	188	2	no	—
185	C₂²×C₄	—	188	1	no	—
186	C₂²×C₄	—	188	1	no	—
187	C₂²×C₄	—	188	2	no	—
188	C₂²×C₄	D₃₇₆	1	1	yes	characteristic
189	C₂²×C₄	D₃₇₆	1	1	yes	characteristic
190	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
191	Q₁₆	—	94	4	no	—
192	Q₁₆	—	94	4	no	—
193	Q₁₆	—	188	8	no	—
194	Q₁₆	—	188	2	no	—
195	Q₁₆	—	188	2	no	—
196	C₂×C₈	—	2	1	no	—
197	C₂×C₈	—	2	1	no	—
198	C₂×C₈	#10625325	1	2	yes	—
199	C₂×C₈	#10625350	1	2	yes	—
200	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
201	C₂×C₈	D₄×D₄₇	1	2	yes	—
202	C₂×C₈	#10625354	1	1	yes	characteristic
203	C₄⋊C₄	—	94	2	no	—
204	C₄⋊C₄	—	376	2	no	—
205	C₄⋊C₄	—	188	4	no	—
206	C₄⋊C₄	—	188	4	no	—
207	C₄⋊C₄	—	188	1	no	—
208	C₄⋊C₄	—	188	1	no	—
209	C₄⋊C₄	—	188	1	no	—
210	C₄²	—	2	1	no	—
211	C₄²	—	2	1	no	—
212	C₁₆	—	4	2	no	—
213	C₂³	C₂×D₃₇₆	1	1	yes	characteristic
214	Q₈	—	376	2	no	—
215	Q₈	—	376	2	no	—
216	Q₈	—	188	4	no	—
217	Q₈	—	188	4	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	—	376	1	no	—
223	C₂×C₄	—	376	1	no	—
224	C₂×C₄	—	376	2	no	—
225	C₂×C₄	—	376	2	no	—
226	C₂×C₄	—	376	1	no	—
227	C₂×C₄	—	376	1	no	—
228	C₂×C₄	—	376	1	no	—
229	C₂×C₄	—	188	4	no	—
230	C₂×C₄	—	188	2	no	—
231	C₂×C₄	#13093969	1	2	yes	—
232	C₂×C₄	Dic₃₇₆	1	2	yes	—
233	C₂×C₄	#13093994	1	1	yes	characteristic
234	C₂×C₄	#13093999	1	1	yes	characteristic
235	C₂×C₄	#13094012	1	1	yes	characteristic
236	C₂×C₄	C₂×#10625325	1	1	yes	characteristic
237	C₂×C₄	#13094052	1	1	yes	characteristic
238	C₂×C₄	#13094052	1	1	yes	characteristic
239	C₈	—	2	2	no	—
240	C₈	#13093997	1	2	yes	—
241	C₈	#13094009	1	2	yes	—
242	C₂²	#15689259	1	1	yes	characteristic
243	C₂²	#15689319	1	1	yes	characteristic
244	C₂²	#15689470	1	1	yes	characteristic
245	C₂²	C₂×#13093969	1	1	yes	characteristic
246	C₂²	C₂×Dic₃₇₆	1	1	yes	characteristic
247	C₂²	#15689566	1	1	yes	characteristic
248	C₂²	#15689566	1	1	yes	characteristic
249	C₄	—	2	2	no	—
250	C₄	—	2	2	no	—
251	C₄	—	376	4	no	—
252	C₄	—	376	2	no	—
253	C₄	—	752	1	no	—
254	C₄	#15689041	1	1	yes	characteristic
255	C₄	#15689276	1	1	yes	characteristic
256	C₄	#15689324	1	1	yes	characteristic
257	C₄	#15689488	1	1	yes	characteristic
258	C₂	#20244623	1	1	yes	characteristic
259	C₂	#20245307	1	1	yes	characteristic
260	C₂	#20245324	1	1	yes	characteristic
261	C₂	#20245434	1	1	yes	characteristic
262	C₂	#20245439	1	1	yes	characteristic
263	C₂	#20245616	1	1	yes	characteristic
264	C₂	#20245634	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689503

C₂

yes

maximal, characteristic

C₂×#15688928

C₂

yes

maximal

C₂×#15688928

C₂

yes

maximal

#20244121

C₂

yes

maximal, characteristic

C₄₇×#1374

C₂

yes

maximal, characteristic

C₂²×Dic₁₈₈

—

C₂²×Dic₁₈₈

C₂²

yes

—

C₂×#13094024

—

#15689503

—

C₂×#13093958

C₂²

yes

characteristic

C₂×#13093958

C₂²

yes

—

—

—

—

C₂²×C₁₆×C₄₇

C₂²

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂²×Dic₉₄

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

D₄

yes

—

#13094024

—

#13094024

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×Dic₄₇⋊C₄

—

#13093958

—

#13093958

—

#13093958

D₄

yes

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₁₆×C₄₇

—

C₂×C₁₆×C₄₇

—

C₂×C₁₆×C₄₇

—

C₄×C₈×C₄₇

—

C₂²×C₄×C₄₇

D₈

yes

characteristic

C₂²×C₄×C₄₇

D₈

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

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

SD₁₆

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

#41

yes

—

C₂×C₈×C₄₇

#41

yes

characteristic

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

C₁₆×C₄₇

—

C₂³×C₄₇

C₂×D₈

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

SD₃₂

yes

—

C₂×C₄×C₄₇

Q₃₂

yes

—

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₂×SD₁₆

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

100

C₂×Dic₄₇

—

101

C₂×Dic₄₇

—

102

Dic₉₄

—

103

Dic₉₄

—

104

Dic₉₄

—

105

Dic₉₄

—

106

C₈×C₄₇

—

107

C₈×C₄₇

#121

yes

—

108

C₈×C₄₇

#123

yes

—

109

#13409

—

maximal, Sylow

110

C₂²×C₄₇

#447

yes

characteristic

111

C₂²×C₄₇

#459

yes

characteristic

112

C₂²×C₄₇

#486

yes

characteristic

113

C₂²×C₄₇

C₂×SD₃₂

yes

characteristic

114

C₂²×C₄₇

C₂×Q₃₂

yes

characteristic

115

C₂²×C₄₇

#510

yes

characteristic

116

C₂²×C₄₇

#510

yes

characteristic

117

C₄×C₄₇

—

118

C₄×C₄₇

—

119

C₄×C₄₇

#394

yes

characteristic

120

C₄×C₄₇

#450

yes

characteristic

121

C₄×C₄₇

#460

yes

characteristic

122

C₄×C₄₇

#490

yes

characteristic

123

Dic₄₇

—

124

Dic₄₇

—

125

Dic₄₇

—

126

C₂×#494

—

127

C₂×#358

—

128

C₂×#358

—

129

#1942

—

130

#1374

D₄₇

yes

characteristic

131

C₂×C₄₇

#2041

yes

characteristic

132

C₂×C₄₇

#2185

yes

characteristic

133

C₂×C₄₇

#2188

yes

characteristic

134

C₂×C₄₇

#2208

yes

characteristic

135

C₂×C₄₇

#2209

yes

characteristic

136

C₂×C₄₇

#2241

yes

characteristic

137

C₂×C₄₇

#2245

yes

characteristic

138

C₂²×Q₁₆

—

139

C₂²×Q₁₆

—

140

C₂×C₄⋊Q₈

—

141

C₂²×C₁₆

C₂×D₄₇

yes

—

142

#494

—

143

C₂×#107

—

144

C₂×#107

—

145

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

146

#389

—

147

#358

—

148

#358

—

149

#340

—

150

C₄₇

#13409

yes

characteristic, complemented, Sylow

151

C₂²×Q₈

—

152

C₂×Q₁₆

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

—

158

C₂×Q₁₆

—

159

C₂×Q₁₆

—

188

—

160

C₂×Q₁₆

—

188

—

161

C₂²×C₈

D₁₈₈

yes

characteristic

162

C₂²×C₈

C₂²×D₄₇

yes

characteristic

163

C₄⋊Q₈

—

164

C₄⋊Q₈

—

188

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

188

—

168

C₂×C₄⋊C₄

—

188

—

169

C₂×C₄⋊C₄

—

188

—

170

C₂×C₄²

D₁₈₈

yes

characteristic

171

C₂×C₁₆

—

172

C₂×C₁₆

—

173

C₂×C₁₆

—

174

#107

—

175

#107

—

176

#107

—

177

C₄×C₈

—

178

#95

—

188

—

179

C₂×Q₈

—

180

C₂×Q₈

—

188

—

181

C₂×Q₈

—

188

—

182

C₂×Q₈

—

188

—

183

C₂×Q₈

—

188

—

184

C₂×Q₈

—

188

—

185

C₂²×C₄

—

188

—

186

C₂²×C₄

—

188

—

187

C₂²×C₄

—

188

—

188

C₂²×C₄

D₃₇₆

yes

characteristic

189

C₂²×C₄

D₃₇₆

yes

characteristic

190

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

191

Q₁₆

—

192

Q₁₆

—

193

Q₁₆

—

188

—

194

Q₁₆

—

188

—

195

Q₁₆

—

188

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

#10625325

yes

—

199

C₂×C₈

#10625350

yes

—

200

C₂×C₈

D₄×D₄₇

yes

characteristic

201

C₂×C₈

D₄×D₄₇

yes

—

202

C₂×C₈

#10625354

yes

characteristic

203

C₄⋊C₄

—

204

C₄⋊C₄

—

376

—

205

C₄⋊C₄

—

188

—

206

C₄⋊C₄

—

188

—

207

C₄⋊C₄

—

188

—

208

C₄⋊C₄

—

188

—

209

C₄⋊C₄

—

188

—

210

C₄²

—

211

C₄²

—

212

C₁₆

—

213

C₂³

C₂×D₃₇₆

yes

characteristic

214

Q₈

—

376

—

215

Q₈

—

376

—

216

Q₈

—

188

—

217

Q₈

—

188

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

376

—

223

C₂×C₄

—

376

—

224

C₂×C₄

—

376

—

225

C₂×C₄

—

376

—

226

C₂×C₄

—

376

—

227

C₂×C₄

—

376

—

228

C₂×C₄

—

376

—

229

C₂×C₄

—

188

—

230

C₂×C₄

—

188

—

231

C₂×C₄

#13093969

yes

—

232

C₂×C₄

Dic₃₇₆

yes

—

233

C₂×C₄

#13093994

yes

characteristic

234

C₂×C₄

#13093999

yes

characteristic

235

C₂×C₄

#13094012

yes

characteristic

236

C₂×C₄

C₂×#10625325

yes

characteristic

237

C₂×C₄

#13094052

yes

characteristic

238

C₂×C₄

#13094052

yes

characteristic

239

C₈

—

240

C₈

#13093997

yes

—

241

C₈

#13094009

yes

—

242

C₂²

#15689259

yes

characteristic

243

C₂²

#15689319

yes

characteristic

244

C₂²

#15689470

yes

characteristic

245

C₂²

C₂×#13093969

yes

characteristic

246

C₂²

C₂×Dic₃₇₆

yes

characteristic

247

C₂²

#15689566

yes

characteristic

248

C₂²

#15689566

yes

characteristic

249

C₄

—

250

C₄

—

251

C₄

—

376

—

252

C₄

—

376

—

253

C₄

—

752

—

254

C₄

#15689041

yes

characteristic

255

C₄

#15689276

yes

characteristic

256

C₄

#15689324

yes

characteristic

257

C₄

#15689488

yes

characteristic

258

C₂

#20244623

yes

characteristic

259

C₂

#20245307

yes

characteristic

260

C₂

#20245324

yes

characteristic

261

C₂

#20245434

yes

characteristic

262

C₂

#20245439

yes

characteristic

263

C₂

#20245616

yes

characteristic

264

C₂

#20245634

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₃₇₆
commutator, cosocle	C₂²×C₈×C₄₇	C₂³
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#1374	C₂
socle, prime radical	C₂³×C₄₇	C₂×D₈
hypercenter	#1374	D₄₇
hypocenter	C₄₇	#13409
LCS	G ▷ C₂²×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

subgroup

G/H

center

C₂³

C₂×D₃₇₆

commutator, cosocle

C₂²×C₈×C₄₇

C₂³

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₄₇×#1374

C₂

socle, prime radical

C₂³×C₄₇

C₂×D₈

D₄₇

C₄₇

G ▷ C₂²×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

N	H ≅ G/N	type
150. C₄₇	#13409	semidirect

H ≅ G/N

type

150. C₄₇

#13409

semidirect

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

subgroup	index
C₂×#15689503	2
C₂×#15688928	2
#20244121	2
C₄₇×#1374	2
#13409	47

subgroup

index

C₄₇×#1374

Subgroups — #26135635

Conjugacy classes of subgroups

Complements

Maximal subgroups