Group #26131945 — subgroups

Subgroups — #26131945

Order 12032.

906 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 906 conjugacy classes of subgroups — too many to draw. Only its 171 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×#15688939	C₂	1	4	yes	maximal, complemented
2	#20244999	C₂	1	1	yes	maximal, characteristic
3	#20243426	C₂	1	1	yes	maximal, characteristic
4	C₂³×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#13093964	C₂²	1	2	yes	—
6	C₂×#13093960	C₂²	1	2	yes	—
7	#15689087	—	2	1	no	—
8	#15688939	—	2	8	no	—
9	C₂²⋊(C₄₇⋊C₁₆)	—	2	2	no	—
10	#15688888	—	2	1	no	—
11	C₂³×Q₈×C₄₇	—	2	1	no	—
12	C₂²×Q₁₆×C₄₇	—	2	8	no	—
13	C₂²×Q₁₆×C₄₇	—	2	1	no	—
14	C₂²×Q₁₆×C₄₇	—	2	2	no	—
15	C₂²×Q₁₆×C₄₇	C₄	1	4	yes	—
16	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	—
17	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#10625329	—	2	2	no	—
19	#13093964	—	2	4	no	—
20	C₂×C₄₇⋊C₁₆	—	2	2	no	—
21	#13093960	—	2	4	no	—
22	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
23	C₂²×Q₈×C₄₇	—	2	8	no	—
24	C₂²×Q₈×C₄₇	—	2	4	no	—
25	C₂²×Q₈×C₄₇	—	2	2	no	—
26	C₂²×Q₈×C₄₇	—	4	4	no	—
27	C₂²×Q₈×C₄₇	—	4	2	no	—
28	C₂²×Q₈×C₄₇	—	4	1	no	—
29	C₂³×C₄×C₄₇	—	4	1	no	—
30	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
31	C₂×Q₁₆×C₄₇	—	2	8	no	—
32	C₂×Q₁₆×C₄₇	—	2	16	no	—
33	C₂×Q₁₆×C₄₇	—	2	16	no	—
34	C₂×Q₁₆×C₄₇	—	2	4	no	—
35	C₂×Q₁₆×C₄₇	—	2	4	no	—
36	C₂×Q₁₆×C₄₇	—	2	2	no	—
37	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
38	C₂×Q₁₆×C₄₇	D₄	1	8	yes	—
39	C₂²×C₈×C₄₇	—	2	4	no	—
40	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₄₇	D₄	1	2	yes	—
43	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
44	C₂⁴×C₄₇	SD₁₆	1	1	yes	characteristic
45	C₂×Q₈×C₄₇	—	2	16	no	—
46	C₂×Q₈×C₄₇	—	2	4	no	—
47	C₂×Q₈×C₄₇	—	2	8	no	—
48	C₂×Q₈×C₄₇	—	4	8	no	—
49	C₂×Q₈×C₄₇	—	4	8	no	—
50	C₂×Q₈×C₄₇	—	4	16	no	—
51	C₂×Q₈×C₄₇	—	4	4	no	—
52	C₂×Q₈×C₄₇	—	4	2	no	—
53	C₂×Q₈×C₄₇	—	4	4	no	—
54	C₂²×C₄×C₄₇	—	2	2	no	—
55	C₂²×C₄×C₄₇	—	2	2	no	—
56	C₂²×C₄×C₄₇	—	4	8	no	—
57	C₂²×C₄×C₄₇	—	4	4	no	—
58	C₂²×C₄×C₄₇	—	4	2	no	—
59	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₄₇	D₈	1	2	yes	—
61	C₂²×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
62	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
63	Q₁₆×C₄₇	—	2	16	no	—
64	Q₁₆×C₄₇	—	2	4	no	—
65	Q₁₆×C₄₇	—	2	8	no	—
66	Q₁₆×C₄₇	C₂²⋊C₄	1	8	yes	—
67	C₂×C₈×C₄₇	—	2	2	no	—
68	C₂×C₈×C₄₇	—	2	4	no	—
69	C₂×C₈×C₄₇	—	2	4	no	—
70	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
71	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
73	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
74	#10625329	—	4	2	no	—
75	#10625329	—	4	2	no	—
76	C₂×C₄₇⋊C₈	—	4	2	no	—
77	C₄₇⋊C₁₆	—	4	2	no	—
78	C₂³×C₄₇	—	2	4	no	—
79	C₂³×C₄₇	—	2	2	no	—
80	C₂³×C₄₇	#102	1	2	yes	—
81	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
82	Q₈×C₄₇	—	2	8	no	—
83	Q₈×C₄₇	—	4	16	no	—
84	Q₈×C₄₇	—	4	4	no	—
85	Q₈×C₄₇	—	4	8	no	—
86	C₂×C₄×C₄₇	—	2	2	no	—
87	C₂×C₄×C₄₇	—	2	2	no	—
88	C₂×C₄×C₄₇	—	2	2	no	—
89	C₂×C₄×C₄₇	—	2	4	no	—
90	C₂×C₄×C₄₇	—	4	16	no	—
91	C₂×C₄×C₄₇	—	4	4	no	—
92	C₂×C₄×C₄₇	—	4	8	no	—
93	C₂×C₄×C₄₇	#102	1	2	yes	—
94	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₄₇	#120	1	2	yes	—
96	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
97	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
98	C₈×C₄₇	—	2	2	no	—
99	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
100	C₈×C₄₇	#120	1	2	yes	—
101	C₄₇⋊C₈	—	8	2	no	—
102	#12737	—	47	1	no	maximal, Sylow
103	C₂²×C₄₇	—	2	8	no	—
104	C₂²×C₄₇	—	2	2	no	—
105	C₂²×C₄₇	—	2	2	no	—
106	C₂²×C₄₇	—	2	2	no	—
107	C₂²×C₄₇	#362	1	4	yes	complemented
108	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
109	C₂²×C₄₇	#450	1	2	yes	—
110	C₄×C₄₇	—	2	2	no	—
111	C₄×C₄₇	—	4	8	no	—
112	C₄×C₄₇	#379	1	1	yes	characteristic
113	C₄×C₄₇	#418	1	1	yes	characteristic
114	C₄×C₄₇	#447	1	2	yes	—
115	C₂³×Q₁₆	D₄₇	1	1	yes	characteristic
116	C₂×#362	—	47	4	no	—
117	#2112	—	47	1	no	—
118	#1810	—	47	1	no	—
119	C₂×C₄₇	—	2	4	no	—
120	C₂×C₄₇	—	2	2	no	—
121	C₂×C₄₇	#1786	1	1	yes	characteristic
122	C₂×C₄₇	C₂×#362	1	2	yes	—
123	C₂³×Q₈	—	2	1	no	—
124	C₂²×Q₁₆	—	2	8	no	—
125	C₂²×Q₁₆	—	2	1	no	—
126	C₂²×Q₁₆	—	2	2	no	—
127	C₂²×Q₁₆	Dic₄₇	1	4	yes	—
128	C₂²×Q₁₆	C₂×D₄₇	1	2	yes	—
129	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
130	C₂×M₃₂	—	47	2	no	—
131	C₂×#108	—	47	2	no	—
132	#407	—	94	1	no	—
133	#362	—	94	8	no	—
134	C₂²⋊C₁₆	—	94	2	no	—
135	#341	—	94	1	no	—
136	C₄₇	#12737	1	1	yes	characteristic, complemented, Sylow
137	C₂²×Q₈	—	2	8	no	—
138	C₂²×Q₈	—	2	4	no	—
139	C₂²×Q₈	—	2	2	no	—
140	C₂²×Q₈	—	4	4	no	—
141	C₂²×Q₈	—	4	2	no	—
142	C₂²×Q₈	—	4	1	no	—
143	C₂³×C₄	—	4	1	no	—
144	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
145	C₂×Q₁₆	—	2	8	no	—
146	C₂×Q₁₆	—	2	16	no	—
147	C₂×Q₁₆	—	2	16	no	—
148	C₂×Q₁₆	—	2	4	no	—
149	C₂×Q₁₆	—	2	4	no	—
150	C₂×Q₁₆	—	2	2	no	—
151	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	—
152	C₂×Q₁₆	C₂²⋊D₄₇	1	8	yes	—
153	C₂×M₁₆	—	94	2	no	—
154	C₂²×C₈	—	2	4	no	—
155	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
156	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
157	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
158	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
159	M₃₂	—	94	4	no	—
160	C₂×C₁₆	—	94	2	no	—
161	#108	—	94	4	no	—
162	C₂²⋊C₈	—	188	2	no	—
163	C₂⁴	#10625335	1	1	yes	characteristic
164	C₂×Q₈	—	2	16	no	—
165	C₂×Q₈	—	2	4	no	—
166	C₂×Q₈	—	2	8	no	—
167	C₂×Q₈	—	4	8	no	—
168	C₂×Q₈	—	4	16	no	—
169	C₂×Q₈	—	4	8	no	—
170	C₂×Q₈	—	4	4	no	—
171	C₂×Q₈	—	4	2	no	—
172	C₂×Q₈	—	4	4	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	—	4	8	no	—
176	C₂²×C₄	—	4	4	no	—
177	C₂²×C₄	—	4	2	no	—
178	C₂²×C₄	#10625334	1	2	yes	—
179	C₂²×C₄	#10625335	1	1	yes	characteristic
180	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
181	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
182	Q₁₆	—	2	16	no	—
183	Q₁₆	—	2	4	no	—
184	Q₁₆	—	2	8	no	—
185	Q₁₆	C₂²⋊Dic₄₇	1	8	yes	—
186	M₁₆	—	188	2	no	—
187	M₁₆	—	188	2	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	2	4	no	—
190	C₂×C₈	—	2	4	no	—
191	C₂×C₈	—	188	2	no	—
192	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
193	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
194	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
195	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
196	C₁₆	—	188	2	no	—
197	C₂³	—	2	2	no	—
198	C₂³	—	2	4	no	—
199	C₂³	#13093945	1	2	yes	—
200	C₂³	C₂×#10625335	1	1	yes	characteristic
201	Q₈	—	2	8	no	—
202	Q₈	—	4	16	no	—
203	Q₈	—	4	8	no	—
204	Q₈	—	4	4	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	4	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	4	16	no	—
210	C₂×C₄	—	4	8	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	#13093945	1	2	yes	—
213	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
214	C₂×C₄	#13093993	1	2	yes	—
215	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
216	C₂×C₄	#13094050	1	2	yes	—
217	C₈	—	2	2	no	—
218	C₈	—	376	2	no	—
219	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
220	C₈	#13093993	1	2	yes	—
221	C₂²	—	2	8	no	—
222	C₂²	—	2	2	no	—
223	C₂²	—	2	2	no	—
224	C₂²	—	2	2	no	—
225	C₂²	#15688939	1	4	yes	complemented
226	C₂²	C₂×#13093945	1	1	yes	characteristic
227	C₂²	#15689274	1	2	yes	—
228	C₄	—	2	2	no	—
229	C₄	—	4	8	no	—
230	C₄	#15688979	1	1	yes	characteristic
231	C₄	#15689128	1	1	yes	characteristic
232	C₄	#15689257	1	2	yes	—
233	C₂	—	2	2	no	—
234	C₂	—	2	4	no	—
235	C₂	#20243319	1	1	yes	characteristic
236	C₂	C₂×#15688939	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15688939

C₂

yes

maximal, complemented

#20244999

C₂

yes

maximal, characteristic

#20243426

C₂

yes

maximal, characteristic

C₂³×Q₁₆×C₄₇

C₂

yes

maximal, characteristic

C₂×#13093964

C₂²

yes

—

C₂×#13093960

C₂²

yes

—

#15689087

—

#15688939

—

C₂²⋊(C₄₇⋊C₁₆)

—

#15688888

—

C₂³×Q₈×C₄₇

—

C₂²×Q₁₆×C₄₇

—

C₂²×Q₁₆×C₄₇

—

C₂²×Q₁₆×C₄₇

—

C₂²×Q₁₆×C₄₇

C₄

yes

—

C₂²×Q₁₆×C₄₇

C₂²

yes

—

C₂³×C₈×C₄₇

C₂²

yes

characteristic

C₂×#10625329

—

#13093964

—

C₂×C₄₇⋊C₁₆

—

#13093960

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

—

C₂³×C₄×C₄₇

—

C₂³×C₄×C₄₇

D₄

yes

characteristic

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

C₂×C₄

yes

—

C₂×Q₁₆×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₂×C₄

yes

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

C₂⁴×C₄₇

SD₁₆

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

D₈

yes

—

C₂²×C₄×C₄₇

SD₁₆

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#102

yes

—

C₂³×C₄₇

C₂×SD₁₆

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×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

#102

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

#120

yes

—

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₈×C₄₇

—

C₈×C₄₇

C₂×C₂²⋊C₄

yes

—

100

C₈×C₄₇

#120

yes

—

101

C₄₇⋊C₈

—

102

#12737

—

maximal, Sylow

103

C₂²×C₄₇

—

104

C₂²×C₄₇

—

105

C₂²×C₄₇

—

106

C₂²×C₄₇

—

107

C₂²×C₄₇

#362

yes

complemented

108

C₂²×C₄₇

C₂×#102

yes

characteristic

109

C₂²×C₄₇

#450

yes

—

110

C₄×C₄₇

—

111

C₄×C₄₇

—

112

C₄×C₄₇

#379

yes

characteristic

113

C₄×C₄₇

#418

yes

characteristic

114

C₄×C₄₇

#447

yes

—

115

C₂³×Q₁₆

D₄₇

yes

characteristic

116

C₂×#362

—

117

#2112

—

118

#1810

—

119

C₂×C₄₇

—

120

C₂×C₄₇

—

121

C₂×C₄₇

#1786

yes

characteristic

122

C₂×C₄₇

C₂×#362

yes

—

123

C₂³×Q₈

—

124

C₂²×Q₁₆

—

125

C₂²×Q₁₆

—

126

C₂²×Q₁₆

—

127

C₂²×Q₁₆

Dic₄₇

yes

—

128

C₂²×Q₁₆

C₂×D₄₇

yes

—

129

C₂³×C₈

C₂×D₄₇

yes

characteristic

130

C₂×M₃₂

—

131

C₂×#108

—

132

#407

—

133

#362

—

134

C₂²⋊C₁₆

—

135

#341

—

136

C₄₇

#12737

yes

characteristic, complemented, Sylow

137

C₂²×Q₈

—

138

C₂²×Q₈

—

139

C₂²×Q₈

—

140

C₂²×Q₈

—

141

C₂²×Q₈

—

142

C₂²×Q₈

—

143

C₂³×C₄

—

144

C₂³×C₄

C₂²⋊D₄₇

yes

characteristic

145

C₂×Q₁₆

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

148

C₂×Q₁₆

—

149

C₂×Q₁₆

—

150

C₂×Q₁₆

—

151

C₂×Q₁₆

C₂×Dic₄₇

yes

—

152

C₂×Q₁₆

C₂²⋊D₄₇

yes

—

153

C₂×M₁₆

—

154

C₂²×C₈

—

155

C₂²×C₈

C₂×Dic₄₇

yes

—

156

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

157

C₂²×C₈

C₂²⋊D₄₇

yes

—

158

C₂²×C₈

C₂²×D₄₇

yes

characteristic

159

M₃₂

—

160

C₂×C₁₆

—

161

#108

—

162

C₂²⋊C₈

—

188

—

163

C₂⁴

#10625335

yes

characteristic

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

#10625334

yes

—

179

C₂²×C₄

#10625335

yes

characteristic

180

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

181

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

182

Q₁₆

—

183

Q₁₆

—

184

Q₁₆

—

185

Q₁₆

C₂²⋊Dic₄₇

yes

—

186

M₁₆

—

188

—

187

M₁₆

—

188

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

188

—

192

C₂×C₈

C₂²⋊Dic₄₇

yes

—

193

C₂×C₈

C₂²×Dic₄₇

yes

characteristic

194

C₂×C₈

C₂×C₂²⋊D₄₇

yes

—

195

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

196

C₁₆

—

188

—

197

C₂³

—

198

C₂³

—

199

C₂³

#13093945

yes

—

200

C₂³

C₂×#10625335

yes

characteristic

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

#13093945

yes

—

213

C₂×C₄

C₂×C₂²⋊Dic₄₇

yes

characteristic

214

C₂×C₄

#13093993

yes

—

215

C₂×C₄

C₂×#10625334

yes

characteristic

216

C₂×C₄

#13094050

yes

—

217

C₈

—

218

C₈

—

376

—

219

C₈

C₂×C₂²⋊Dic₄₇

yes

—

220

C₈

#13093993

yes

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

#15688939

yes

complemented

226

C₂²

C₂×#13093945

yes

characteristic

227

C₂²

#15689274

yes

—

228

C₄

—

229

C₄

—

230

C₄

#15688979

yes

characteristic

231

C₄

#15689128

yes

characteristic

232

C₄

#15689257

yes

—

233

C₂

—

234

C₂

—

235

C₂

#20243319

yes

characteristic

236

C₂

C₂×#15688939

yes

—

	subgroup	G/H
center	C₂²	C₂×#13093945
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₂³×Q₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×#102
prime radical	C₂⁴×C₄₇	SD₁₆
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	C₂³×Q₁₆	D₄₇
hypocenter	C₄₇	#12737
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂³×Q₁₆

subgroup

G/H

center

C₂²

C₂×#13093945

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₂³×Q₁₆×C₄₇

C₂

socle

C₂²×C₄₇

C₂×#102

prime radical

C₂⁴×C₄₇

SD₁₆

cosocle

C₂²×C₈×C₄₇

C₂³

hypercenter

C₂³×Q₁₆

D₄₇

hypocenter

C₄₇

#12737

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂³×Q₁₆

N	H ≅ G/N	type
1. C₂×#15688939	C₂	semidirect
107. C₂²×C₄₇	#362	semidirect
136. C₄₇	#12737	semidirect
225. C₂²	#15688939	semidirect

H ≅ G/N

type

1. C₂×#15688939

C₂

semidirect

107. C₂²×C₄₇

#362

semidirect

136. C₄₇

#12737

semidirect

225. C₂²

#15688939

semidirect

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

subgroup	index
C₂×#15688939	2
#20244999	2
#20243426	2
C₂³×Q₁₆×C₄₇	2
#12737	47

subgroup

index

C₂³×Q₁₆×C₄₇

Subgroups — #26131945

Conjugacy classes of subgroups

Complements

Maximal subgroups