Group #25015105 — subgroups

Subgroups — #25015105

Order 11008.

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

normal subgroups only

This group has 566 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	C₂×#14583276	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582713	C₂	1	2	yes	maximal, complemented
3	#19136312	C₂	1	2	yes	maximal, complemented
4	#19134474	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₃₄₄	—	2	1	no	—
7	C₂²×D₃₄₄	C₂²	1	2	yes	—
8	C₂×#13063322	—	2	1	no	—
9	#14583276	—	2	2	no	—
10	#14583276	C₄	1	4	yes	complemented
11	C₂×#13063261	C₂²	1	1	yes	characteristic
12	#14582937	C₂²	1	1	yes	characteristic
13	#14582854	—	2	1	no	—
14	#14582713	—	2	4	no	—
15	#14582701	—	2	4	no	—
16	#14582659	—	2	1	no	—
17	C₂×M₃₂×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#364	—	2	2	no	—
20	C₂²×D₁₇₂	—	2	2	no	—
21	C₂²×D₁₇₂	—	4	2	no	—
22	C₂×D₃₄₄	—	2	2	no	—
23	C₂×D₃₄₄	—	2	2	no	—
24	C₂×D₃₄₄	—	2	2	no	—
25	C₂×D₃₄₄	—	2	2	no	—
26	C₂×D₃₄₄	—	2	4	no	—
27	C₂×D₃₄₄	—	2	2	no	—
28	C₂×D₃₄₄	—	4	1	no	—
29	C₂×D₃₄₄	—	4	1	no	—
30	C₂×D₃₄₄	—	4	2	no	—
31	C₂×D₃₄₄	C₂×C₄	1	4	yes	—
32	C₂×#10621877	—	2	1	no	—
33	#13063322	—	2	4	no	—
34	#13063322	—	4	2	no	—
35	#13063284	—	2	1	no	—
36	#13063261	—	2	1	no	—
37	#13063261	D₄	1	2	yes	complemented
38	#13063259	D₄	1	2	yes	complemented
39	#13063257	—	2	1	no	—
40	#13063235	—	4	1	no	—
41	C₈×Dic₄₃	—	4	1	no	—
42	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
44	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
45	M₃₂×C₄₃	—	2	2	no	—
46	M₃₂×C₄₃	—	2	2	no	—
47	C₂×C₁₆×C₄₃	—	2	2	no	—
48	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
49	C₄×C₈×C₄₃	D₄	1	2	yes	—
50	C₂³×D₄₃	—	4	2	no	—
51	C₂²×C₄×C₄₃	—	2	1	no	—
52	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
53	C₂×D₁₇₂	—	2	4	no	—
54	C₂×D₁₇₂	—	4	8	no	—
55	C₂×D₁₇₂	—	4	2	no	—
56	C₂×D₁₇₂	—	4	2	no	—
57	C₂×D₁₇₂	—	4	2	no	—
58	C₂×D₁₇₂	—	4	2	no	—
59	C₂×D₁₇₂	—	4	2	no	—
60	C₂×D₁₇₂	—	8	8	no	—
61	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
62	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
63	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
64	C₂×C₈×C₄₃	SD₁₆	1	2	yes	—
65	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
68	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
70	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
71	C₄²×C₄₃	—	2	1	no	—
72	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
73	C₂²⋊Dic₄₃	—	4	1	no	—
74	C₄⋊Dic₄₃	—	2	2	no	—
75	C₄×Dic₄₃	—	4	1	no	—
76	#10621877	—	2	2	no	—
77	#10621877	—	4	1	no	—
78	C₂×C₄₃⋊C₈	—	4	1	no	—
79	D₃₄₄	—	2	4	no	—
80	D₃₄₄	—	2	4	no	—
81	D₃₄₄	—	4	4	no	—
82	D₃₄₄	—	4	4	no	—
83	D₃₄₄	—	4	2	no	—
84	D₃₄₄	—	4	2	no	—
85	C₁₆×C₄₃	—	4	2	no	—
86	C₂³×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
87	C₂²×D₄₃	—	4	4	no	—
88	C₂²×D₄₃	—	8	8	no	—
89	C₂²×D₄₃	—	8	2	no	—
90	C₂²×D₄₃	—	8	2	no	—
91	C₂×C₄×C₄₃	—	2	4	no	—
92	C₂×C₄×C₄₃	—	2	2	no	—
93	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
95	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
96	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
97	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
99	C₂×Dic₄₃	—	4	2	no	—
100	D₁₇₂	—	4	4	no	—
101	D₁₇₂	—	4	4	no	—
102	D₁₇₂	—	8	16	no	—
103	D₁₇₂	—	8	2	no	—
104	D₁₇₂	—	8	2	no	—
105	C₈×C₄₃	#102	1	2	yes	—
106	C₈×C₄₃	#102	1	2	yes	—
107	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
108	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
109	C₈×C₄₃	#124	1	1	yes	characteristic
110	C₈×C₄₃	#127	1	1	yes	characteristic
111	C₄₃⋊C₈	—	4	2	no	—
112	#13261	—	43	1	no	maximal, Sylow
113	C₂²×C₄₃	—	2	2	no	—
114	C₂²×C₄₃	#418	1	1	yes	characteristic
115	C₂²×C₄₃	#459	1	1	yes	characteristic
116	C₂²×C₄₃	#460	1	1	yes	characteristic
117	C₂×D₄₃	—	8	8	no	—
118	C₂×D₄₃	—	8	4	no	—
119	C₂×D₄₃	—	16	4	no	—
120	C₂×D₄₃	—	16	4	no	—
121	C₄×C₄₃	—	2	4	no	—
122	C₄×C₄₃	#390	1	1	yes	characteristic
123	C₄×C₄₃	C₂×#102	1	1	yes	characteristic
124	C₄×C₄₃	#459	1	1	yes	characteristic
125	C₄×C₄₃	#460	1	1	yes	characteristic
126	Dic₄₃	—	8	2	no	—
127	C₂×#493	—	43	1	no	—
128	C₂×#364	D₄₃	1	1	yes	characteristic, complemented
129	C₂×#361	—	43	2	no	—
130	#2140	—	43	2	no	—
131	#1772	—	43	1	no	—
132	C₂×C₄₃	—	2	1	no	—
133	C₂×C₄₃	—	2	1	no	—
134	C₂×C₄₃	#1982	1	1	yes	characteristic
135	C₂×C₄₃	#2213	1	2	yes	—
136	D₄₃	—	16	4	no	—
137	C₂²×D₈	—	43	2	no	—
138	C₂²×D₈	—	86	1	no	—
139	C₂×#127	—	86	1	no	—
140	C₂×M₃₂	C₂×D₄₃	1	2	yes	—
141	#493	—	43	4	no	—
142	#493	—	86	2	no	—
143	C₂×#108	—	43	1	no	—
144	#427	—	43	1	no	—
145	#405	—	86	1	no	—
146	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
147	#364	—	2	2	no	—
148	#361	—	86	4	no	—
149	#357	—	86	4	no	—
150	#339	—	86	1	no	—
151	C₄₃	#13261	1	1	yes	characteristic, complemented, Sylow
152	C₂²×D₄	—	86	2	no	—
153	C₂²×D₄	—	172	2	no	—
154	C₂×D₈	—	43	4	no	—
155	C₂×D₈	—	86	4	no	—
156	C₂×D₈	—	86	2	no	—
157	C₂×D₈	—	86	2	no	—
158	C₂×D₈	—	86	2	no	—
159	C₂×D₈	—	86	2	no	—
160	C₂×D₈	—	86	2	no	—
161	C₂×D₈	—	172	2	no	—
162	C₂×D₈	—	172	1	no	—
163	C₂×D₈	—	172	1	no	—
164	C₂×M₁₆	—	86	1	no	—
165	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
166	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
167	#127	—	86	4	no	—
168	#127	—	172	2	no	—
169	#117	—	86	1	no	—
170	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
171	M₃₂	—	2	2	no	—
172	M₃₂	—	2	2	no	—
173	C₂×C₁₆	—	2	2	no	—
174	#108	—	43	2	no	—
175	#108	—	86	1	no	—
176	#107	—	43	2	no	—
177	#106	—	86	1	no	—
178	#97	—	172	1	no	—
179	C₄×C₈	—	172	1	no	—
180	C₄×C₈	C₄×D₄₃	1	2	yes	—
181	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
182	C₂⁴	—	172	2	no	—
183	C₂×D₄	—	86	4	no	—
184	C₂×D₄	—	344	8	no	—
185	C₂×D₄	—	172	8	no	—
186	C₂×D₄	—	172	2	no	—
187	C₂×D₄	—	172	2	no	—
188	C₂×D₄	—	172	2	no	—
189	C₂×D₄	—	172	2	no	—
190	C₂×D₄	—	172	2	no	—
191	C₂²×C₄	—	2	1	no	—
192	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
193	D₈	—	86	4	no	—
194	D₈	—	86	4	no	—
195	D₈	—	172	4	no	—
196	D₈	—	172	4	no	—
197	D₈	—	172	2	no	—
198	D₈	—	172	2	no	—
199	M₁₆	—	86	2	no	—
200	M₁₆	—	172	1	no	—
201	C₂×C₈	—	172	1	no	—
202	C₂×C₈	#10621873	1	2	yes	—
203	C₂×C₈	D₃₄₄	1	1	yes	characteristic
204	C₂×C₈	D₃₄₄	1	1	yes	characteristic
205	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
206	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
207	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
208	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
209	C₂×C₈	#10621902	1	1	yes	characteristic
210	C₂×C₈	#10621902	1	1	yes	characteristic
211	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
212	C₄⋊C₄	—	86	2	no	—
213	C₂²⋊C₄	—	172	1	no	—
214	C₄²	—	2	1	no	—
215	C₄²	—	172	1	no	—
216	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
217	C₁₆	—	4	2	no	—
218	C₂³	—	344	8	no	—
219	C₂³	—	344	2	no	—
220	C₂³	—	344	2	no	—
221	C₂³	—	172	4	no	—
222	C₂³	#13063353	1	1	yes	characteristic
223	D₄	—	344	16	no	—
224	D₄	—	344	2	no	—
225	D₄	—	344	2	no	—
226	D₄	—	172	4	no	—
227	D₄	—	172	4	no	—
228	C₂×C₄	—	2	4	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	172	2	no	—
231	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
232	C₂×C₄	#13063300	1	1	yes	characteristic
233	C₂×C₄	#13063300	1	1	yes	characteristic
234	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
235	C₂×C₄	C₂×#10621873	1	1	yes	characteristic
236	C₂×C₄	#13063353	1	1	yes	characteristic
237	C₈	—	172	2	no	—
238	C₈	#13063247	1	2	yes	—
239	C₈	#13063247	1	2	yes	—
240	C₈	#13063287	1	1	yes	characteristic
241	C₈	#13063287	1	1	yes	characteristic
242	C₈	#13063314	1	1	yes	characteristic
243	C₈	#13063321	1	1	yes	characteristic
244	C₂²	—	2	2	no	—
245	C₂²	—	344	8	no	—
246	C₂²	—	344	4	no	—
247	C₂²	—	688	4	no	—
248	C₂²	—	688	4	no	—
249	C₂²	#14582905	1	1	yes	characteristic
250	C₂²	#14583095	1	1	yes	characteristic
251	C₂²	#14583100	1	1	yes	characteristic
252	C₄	—	2	4	no	—
253	C₄	—	344	2	no	—
254	C₄	#14582800	1	1	yes	characteristic
255	C₄	C₂×#13063247	1	1	yes	characteristic
256	C₄	#14583095	1	1	yes	characteristic
257	C₄	#14583100	1	1	yes	characteristic
258	C₂	—	2	1	no	—
259	C₂	—	2	1	no	—
260	C₂	—	688	4	no	—
261	C₂	#19135521	1	1	yes	characteristic
262	C₂	#19136672	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583276

C₂

yes

maximal, characteristic

C₂×#14582713

C₂

yes

maximal, complemented

#19136312

C₂

yes

maximal, complemented

#19134474

C₂

yes

maximal, characteristic, complemented

C₂×C₄₃×#364

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₄₄

—

C₂²×D₃₄₄

C₂²

yes

—

C₂×#13063322

—

#14583276

—

#14583276

C₄

yes

complemented

C₂×#13063261

C₂²

yes

characteristic

#14582937

C₂²

yes

—

—

—

—

C₂×M₃₂×C₄₃

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#364

—

C₂²×D₁₇₂

—

C₂²×D₁₇₂

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

C₂×C₄

yes

—

—

—

—

—

—

D₄

yes

complemented

#13063259

D₄

yes

complemented

#13063257

—

#13063235

—

C₈×Dic₄₃

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

M₃₂×C₄₃

—

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂³×D₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

D₈

yes

characteristic

C₂×C₈×C₄₃

D₈

yes

characteristic

C₂×C₈×C₄₃

SD₁₆

yes

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

C₂×C₈×C₄₃

yes

C₂×C₈×C₄₃

yes

C₄²×C₄₃

—

C₄²×C₄₃

C₂²⋊C₄

yes

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

C₁₆×C₄₃

—

C₂³×C₄₃

AGL(1,ℤ/8)

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

characteristic

C₂×Dic₄₃

—

100

D₁₇₂

—

101

D₁₇₂

—

102

D₁₇₂

—

103

D₁₇₂

—

104

D₁₇₂

—

105

C₈×C₄₃

#102

yes

—

106

C₈×C₄₃

#102

yes

—

107

C₈×C₄₃

C₄×D₄

yes

characteristic

108

C₈×C₄₃

C₄×D₄

yes

characteristic

109

C₈×C₄₃

#124

yes

characteristic

110

C₈×C₄₃

#127

yes

characteristic

111

C₄₃⋊C₈

—

112

#13261

—

maximal, Sylow

113

C₂²×C₄₃

—

114

C₂²×C₄₃

#418

yes

characteristic

115

C₂²×C₄₃

#459

yes

characteristic

116

C₂²×C₄₃

#460

yes

characteristic

117

C₂×D₄₃

—

118

C₂×D₄₃

—

119

C₂×D₄₃

—

120

C₂×D₄₃

—

121

C₄×C₄₃

—

122

C₄×C₄₃

#390

yes

characteristic

123

C₄×C₄₃

C₂×#102

yes

characteristic

124

C₄×C₄₃

#459

yes

characteristic

125

C₄×C₄₃

#460

yes

characteristic

126

Dic₄₃

—

127

C₂×#493

—

128

C₂×#364

D₄₃

yes

characteristic, complemented

129

C₂×#361

—

130

#2140

—

131

#1772

—

132

C₂×C₄₃

—

133

C₂×C₄₃

—

134

C₂×C₄₃

#1982

yes

characteristic

135

C₂×C₄₃

#2213

yes

—

136

D₄₃

—

137

C₂²×D₈

—

138

C₂²×D₈

—

139

C₂×#127

—

140

C₂×M₃₂

C₂×D₄₃

yes

—

141

#493

—

142

#493

—

143

C₂×#108

—

144

#427

—

145

#405

—

146

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

147

#364

—

148

#361

—

149

#357

—

150

#339

—

151

C₄₃

#13261

yes

characteristic, complemented, Sylow

152

C₂²×D₄

—

153

C₂²×D₄

—

172

—

154

C₂×D₈

—

155

C₂×D₈

—

156

C₂×D₈

—

157

C₂×D₈

—

158

C₂×D₈

—

159

C₂×D₈

—

160

C₂×D₈

—

161

C₂×D₈

—

172

—

162

C₂×D₈

—

172

—

163

C₂×D₈

—

172

—

164

C₂×M₁₆

—

165

C₂²×C₈

D₁₇₂

yes

characteristic

166

C₂²×C₈

C₂²×D₄₃

yes

characteristic

167

#127

—

168

#127

—

172

—

169

#117

—

170

C₂×C₄²

D₁₇₂

yes

characteristic

171

M₃₂

—

172

M₃₂

—

173

C₂×C₁₆

—

174

#108

—

175

#108

—

176

#107

—

177

#106

—

178

#97

—

172

—

179

C₄×C₈

—

172

—

180

C₄×C₈

C₄×D₄₃

yes

—

181

C₄×C₈

C₂²⋊D₄₃

yes

—

182

C₂⁴

—

172

—

183

C₂×D₄

—

184

C₂×D₄

—

344

—

185

C₂×D₄

—

172

—

186

C₂×D₄

—

172

—

187

C₂×D₄

—

172

—

188

C₂×D₄

—

172

—

189

C₂×D₄

—

172

—

190

C₂×D₄

—

172

—

191

C₂²×C₄

—

192

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

193

D₈

—

194

D₈

—

195

D₈

—

172

—

196

D₈

—

172

—

197

D₈

—

172

—

198

D₈

—

172

—

199

M₁₆

—

200

M₁₆

—

172

—

201

C₂×C₈

—

172

—

202

C₂×C₈

#10621873

yes

—

203

C₂×C₈

D₃₄₄

yes

characteristic

204

C₂×C₈

D₃₄₄

yes

characteristic

205

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

206

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

207

C₂×C₈

D₄×D₄₃

yes

characteristic

208

C₂×C₈

D₄×D₄₃

yes

characteristic

209

C₂×C₈

#10621902

yes

characteristic

210

C₂×C₈

#10621902

yes

characteristic

211

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

212

C₄⋊C₄

—

213

C₂²⋊C₄

—

172

—

214

C₄²

—

215

C₄²

—

172

—

216

C₄²

(C₂×D₄₃)⋊C₄

yes

—

217

C₁₆

—

218

C₂³

—

344

—

219

C₂³

—

344

—

220

C₂³

—

344

—

221

C₂³

—

172

—

222

C₂³

#13063353

yes

characteristic

223

D₄

—

344

—

224

D₄

—

344

—

225

D₄

—

344

—

226

D₄

—

172

—

227

D₄

—

172

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

172

—

231

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

232

C₂×C₄

#13063300

yes

characteristic

233

C₂×C₄

#13063300

yes

characteristic

234

C₂×C₄

C₂×D₃₄₄

yes

characteristic

235

C₂×C₄

C₂×#10621873

yes

characteristic

236

C₂×C₄

#13063353

yes

characteristic

237

C₈

—

172

—

238

C₈

#13063247

yes

—

239

C₈

#13063247

yes

—

240

C₈

#13063287

yes

characteristic

241

C₈

#13063287

yes

characteristic

242

C₈

#13063314

yes

characteristic

243

C₈

#13063321

yes

characteristic

244

C₂²

—

245

C₂²

—

344

—

246

C₂²

—

344

—

247

C₂²

—

688

—

248

C₂²

—

688

—

249

C₂²

#14582905

yes

characteristic

250

C₂²

#14583095

yes

characteristic

251

C₂²

#14583100

yes

characteristic

252

C₄

—

253

C₄

—

344

—

254

C₄

#14582800

yes

characteristic

255

C₄

C₂×#13063247

yes

characteristic

256

C₄

#14583095

yes

characteristic

257

C₄

#14583100

yes

characteristic

258

C₂

—

259

C₂

—

260

C₂

—

688

—

261

C₂

#19135521

yes

characteristic

262

C₂

#19136672

yes

—

	subgroup	G/H
center	C₂²	#14583095
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#364	C₂
socle	C₂²×C₄₃	#459
prime radical	C₂×#14583276	C₂
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#364	D₄₃
hypocenter	C₄₃	#13261
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

subgroup

G/H

center

C₂²

#14583095

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×#364

C₂

C₂²×C₄₃

C₂

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

N	H ≅ G/N	type
2. C₂×#14582713	C₂	semidirect
3. #19136312	C₂	semidirect
4. #19134474	C₂	semidirect
5. C₂×C₄₃×#364	C₂	semidirect
10. #14583276	C₄	semidirect
37. #13063261	D₄	semidirect
38. #13063259	D₄	semidirect
128. C₂×#364	D₄₃	semidirect
151. C₄₃	#13261	semidirect

H ≅ G/N

type

2. C₂×#14582713

C₂

semidirect

3. #19136312

C₂

semidirect

4. #19134474

C₂

semidirect

5. C₂×C₄₃×#364

C₂

semidirect

10. #14583276

C₄

semidirect

37. #13063261

D₄

semidirect

38. #13063259

D₄

semidirect

128. C₂×#364

D₄₃

semidirect

151. C₄₃

#13261

semidirect

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

subgroup	index
C₂×#14583276	2
C₂×#14582713	2
#19136312	2
#19134474	2
C₂×C₄₃×#364	2
#13261	43

subgroup

index

C₂×C₄₃×#364

Subgroups — #25015105

Conjugacy classes of subgroups

Complements

Maximal subgroups