Group #15761824 — subgroups

Subgroups — #15761824

Order 3328.

586 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 147 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×C₄×D₁₀₄	C₂	1	1	yes	maximal, characteristic
2	#13115629	C₂	1	2	yes	maximal, complemented
3	C₂×#11718075	C₂	1	2	yes	maximal, complemented
4	C₂×#11718046	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₀₄	C₄	1	1	yes	characteristic
7	C₂×C₄×D₅₂	C₂²	1	2	yes	—
8	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88061	C₄	1	2	yes	—
11	C₂×#88060	—	2	4	no	—
12	C₂×#88058	C₄	1	1	yes	characteristic
13	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
14	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
15	C₄×D₁₀₄	—	2	2	no	—
16	C₄×D₁₀₄	—	2	2	no	—
17	C₁₃×#334	—	2	2	no	—
18	#11718075	—	2	4	no	—
19	#11718046	—	2	2	no	—
20	C₂²×D₅₂	C₂×C₄	1	2	yes	—
21	C₂²×C₄×D₁₃	—	2	2	no	—
22	C₂²×C₈×C₁₃	—	2	2	no	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
26	C₂×#6103	—	2	2	no	—
27	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
28	C₂²×#1055	—	2	1	no	—
29	C₂²×#1055	D₄	1	2	yes	—
30	C₂×D₁₀₄	—	2	4	no	—
31	C₂×D₁₀₄	—	2	2	no	—
32	C₄×D₅₂	—	2	2	no	—
33	C₄×D₅₂	—	2	2	no	—
34	C₄×D₅₂	—	2	2	no	—
35	C₄×D₅₂	—	2	2	no	—
36	C₁₃×C₄⋊C₈	—	2	2	no	—
37	C₁₃×C₄⋊C₈	—	2	2	no	—
38	C₄×C₈×C₁₃	D₄	1	2	yes	—
39	C₄×C₈×C₁₃	D₄	1	2	yes	—
40	#88061	—	2	4	no	—
41	#88060	—	4	8	no	—
42	#88058	—	2	2	no	—
43	C₄×#1055	—	2	1	no	—
44	C₄×#1055	—	2	1	no	—
45	C₄×#1055	—	2	1	no	—
46	C₄×#1055	D₄	1	2	yes	—
47	#9665	—	13	1	no	maximal, Sylow
48	C₂³×D₁₃	—	2	2	no	—
49	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
52	C₂²×Dic₁₃	—	2	2	no	—
53	C₂×D₅₂	—	2	2	no	—
54	C₂×D₅₂	—	2	2	no	—
55	C₂×D₅₂	—	2	2	no	—
56	C₂×D₅₂	—	2	2	no	—
57	C₂×D₅₂	—	2	2	no	—
58	C₂×D₅₂	M₁₆	1	4	yes	—
59	C₂×C₄×D₁₃	—	4	2	no	—
60	C₂×C₄×D₁₃	—	4	2	no	—
61	C₂×C₄×D₁₃	—	4	4	no	—
62	C₂×C₄×D₁₃	—	4	4	no	—
63	C₂×C₈×C₁₃	—	2	2	no	—
64	C₂×C₈×C₁₃	—	2	2	no	—
65	C₂×C₈×C₁₃	—	4	2	no	—
66	C₂×C₈×C₁₃	—	4	4	no	—
67	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
68	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
69	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₃	#41	1	1	yes	characteristic
73	#6103	—	4	2	no	—
74	#6103	—	4	2	no	—
75	C₄⋊Dic₁₃	—	2	2	no	—
76	C₄⋊Dic₁₃	—	2	2	no	—
77	C₂×#1055	—	2	4	no	—
78	C₂×#1055	—	2	2	no	—
79	C₂×#1055	—	2	2	no	—
80	C₂×#1055	—	2	4	no	—
81	D₁₀₄	—	2	8	no	—
82	C₂×C₄×D₈	—	13	1	no	—
83	#1954	—	13	2	no	—
84	C₂×#334	D₁₃	1	1	yes	characteristic, complemented
85	C₂×D₄⋊C₈	—	13	2	no	—
86	C₂×#322	—	13	1	no	—
87	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
88	C₂²×D₁₃	—	2	4	no	—
89	C₂²×D₁₃	—	4	2	no	—
90	C₂²×D₁₃	—	4	2	no	—
91	C₂²×D₁₃	—	4	4	no	—
92	C₂²×D₁₃	—	4	4	no	—
93	C₂×C₄×C₁₃	—	2	2	no	—
94	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
96	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
97	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
98	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
99	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
101	C₂×C₄×C₁₃	#131	1	2	yes	—
102	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
103	C₂×Dic₁₃	—	4	2	no	—
104	C₂×Dic₁₃	—	4	4	no	—
105	D₅₂	—	2	4	no	—
106	D₅₂	—	2	4	no	—
107	D₅₂	—	4	2	no	—
108	D₅₂	—	4	2	no	—
109	C₄×D₁₃	—	8	4	no	—
110	C₄×D₁₃	—	8	2	no	—
111	C₄×D₁₃	—	8	2	no	—
112	C₈×C₁₃	—	2	2	no	—
113	C₈×C₁₃	—	2	2	no	—
114	C₈×C₁₃	—	8	2	no	—
115	#1055	—	2	4	no	—
116	#1055	—	4	2	no	—
117	C₂²×D₈	—	13	1	no	—
118	C₂×C₄×D₄	—	13	2	no	—
119	C₄×D₈	—	26	2	no	—
120	C₄×D₈	—	26	2	no	—
121	C₂×#107	—	13	1	no	—
122	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
123	C₂×#102	—	13	2	no	—
124	C₂×C₂²⋊C₈	—	26	4	no	—
125	C₂×C₄×C₈	—	13	1	no	—
126	C₂×C₄×C₈	—	13	1	no	—
127	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
128	#334	—	2	2	no	—
129	D₄⋊C₈	—	26	4	no	—
130	#322	—	26	2	no	—
131	C₂²×C₁₃	#390	1	1	yes	characteristic
132	C₂²×C₁₃	#435	1	2	yes	—
133	C₂²×C₁₃	#442	1	2	yes	—
134	C₂²×C₁₃	#443	1	2	yes	—
135	C₂×D₁₃	—	4	8	no	—
136	C₂×D₁₃	—	4	4	no	—
137	C₂×D₁₃	—	8	4	no	—
138	C₂×D₁₃	—	8	2	no	—
139	C₂×D₁₃	—	8	2	no	—
140	C₄×C₁₃	—	2	1	no	—
141	C₄×C₁₃	—	2	1	no	—
142	C₄×C₁₃	#407	1	1	yes	characteristic
143	C₄×C₁₃	#408	1	1	yes	characteristic
144	C₄×C₁₃	#435	1	2	yes	—
145	C₄×C₁₃	#469	1	2	yes	—
146	C₄×C₁₃	#496	1	2	yes	—
147	Dic₁₃	—	8	2	no	—
148	C₂²×D₄	—	13	2	no	—
149	C₂³×C₄	—	26	2	no	—
150	C₂×D₈	—	26	4	no	—
151	C₂×D₈	—	26	2	no	—
152	C₂²×C₈	—	2	2	no	—
153	C₂²×C₈	—	13	2	no	—
154	C₂²×C₈	—	26	1	no	—
155	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
156	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
157	C₄×D₄	—	26	2	no	—
158	C₄×D₄	—	26	2	no	—
159	C₄×D₄	—	26	2	no	—
160	C₄×D₄	—	26	2	no	—
161	C₂×C₄⋊C₄	—	13	2	no	—
162	C₂×C₂²⋊C₄	—	26	2	no	—
163	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
164	#107	—	26	2	no	—
165	C₄⋊C₈	—	2	2	no	—
166	C₄⋊C₈	—	2	2	no	—
167	#102	—	26	4	no	—
168	C₂²⋊C₈	—	52	8	no	—
169	C₄×C₈	—	13	2	no	—
170	C₄×C₈	—	26	1	no	—
171	C₄×C₈	—	26	1	no	—
172	C₄×C₈	—	26	1	no	—
173	C₄×C₈	D₅₂	1	2	yes	—
174	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
175	C₂×C₁₃	#1586	1	4	yes	—
176	C₂×C₁₃	#1955	1	1	yes	characteristic
177	C₂×C₁₃	#1972	1	1	yes	characteristic
178	C₂×C₁₃	#1974	1	1	yes	characteristic
179	D₁₃	—	8	4	no	—
180	C₂⁴	—	26	2	no	—
181	C₂×D₄	—	13	4	no	—
182	C₂×D₄	—	26	2	no	—
183	C₂×D₄	—	26	2	no	—
184	C₂×D₄	—	26	2	no	—
185	C₂×D₄	—	26	2	no	—
186	C₂×D₄	—	26	2	no	—
187	C₂²×C₄	—	26	2	no	—
188	C₂²×C₄	—	52	2	no	—
189	C₂²×C₄	—	52	4	no	—
190	C₂²×C₄	—	52	4	no	—
191	C₂²×C₄	—	52	2	no	—
192	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
193	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
194	C₂²×C₄	#6131	1	1	yes	characteristic
195	D₈	—	26	8	no	—
196	C₂×C₈	—	2	2	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	4	4	no	—
199	C₂×C₈	—	4	2	no	—
200	C₂×C₈	—	26	4	no	—
201	C₂×C₈	—	26	2	no	—
202	C₂×C₈	—	26	2	no	—
203	C₂×C₈	—	26	4	no	—
204	C₂×C₈	#6103	1	2	yes	—
205	C₂×C₈	#6103	1	2	yes	—
206	C₄⋊C₄	—	26	2	no	—
207	C₄⋊C₄	—	26	2	no	—
208	C₂²⋊C₄	—	52	2	no	—
209	C₂²⋊C₄	—	52	2	no	—
210	C₄²	C₂×D₅₂	1	1	yes	characteristic
211	C₄²	D₄×D₁₃	1	1	yes	characteristic
212	C₄²	#6131	1	1	yes	characteristic
213	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
214	C₁₃	#9665	1	1	yes	characteristic, complemented, Sylow
215	C₂³	—	26	4	no	—
216	C₂³	—	52	2	no	—
217	C₂³	—	52	4	no	—
218	C₂³	—	52	4	no	—
219	C₂³	—	52	2	no	—
220	C₂³	#88147	1	1	yes	characteristic
221	D₄	—	26	4	no	—
222	D₄	—	26	4	no	—
223	D₄	—	52	2	no	—
224	D₄	—	52	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	52	4	no	—
227	C₂×C₄	—	52	2	no	—
228	C₂×C₄	—	104	4	no	—
229	C₂×C₄	—	104	2	no	—
230	C₂×C₄	—	104	2	no	—
231	C₂×C₄	#88147	1	1	yes	characteristic
232	C₂×C₄	#88149	1	1	yes	characteristic
233	C₂×C₄	#88149	1	1	yes	characteristic
234	C₂×C₄	#88155	1	2	yes	—
235	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
236	C₂×C₄	#88168	1	4	yes	—
237	C₂×C₄	C₂×#6103	1	1	yes	characteristic
238	C₂×C₄	#88194	1	1	yes	characteristic
239	C₂×C₄	#88201	1	1	yes	characteristic
240	C₈	—	2	2	no	—
241	C₈	—	2	2	no	—
242	C₈	—	8	2	no	—
243	C₈	—	26	4	no	—
244	C₈	—	52	2	no	—
245	C₂²	—	52	8	no	—
246	C₂²	—	52	4	no	—
247	C₂²	—	104	2	no	—
248	C₂²	—	104	2	no	—
249	C₂²	—	104	4	no	—
250	C₂²	#11718497	1	2	yes	—
251	C₂²	#11718530	1	2	yes	—
252	C₂²	#11718556	1	2	yes	—
253	C₂²	#11718649	1	1	yes	characteristic
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	104	2	no	—
257	C₄	#11718497	1	2	yes	—
258	C₄	#11718526	1	2	yes	—
259	C₄	#11718771	1	1	yes	characteristic
260	C₄	#11718787	1	1	yes	characteristic
261	C₄	#11718837	1	2	yes	—
262	C₂	—	104	4	no	—
263	C₂	#13113699	1	4	yes	—
264	C₂	#13115633	1	1	yes	characteristic
265	C₂	#13115710	1	1	yes	characteristic
266	C₂	#13115722	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×D₁₀₄

C₂

yes

maximal, characteristic

#13115629

C₂

yes

maximal, complemented

C₂×#11718075

C₂

yes

maximal, complemented

C₂×#11718046

C₂

yes

maximal, characteristic, complemented

C₂×C₁₃×#334

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₀₄

C₄

yes

characteristic

C₂×C₄×D₅₂

C₂²

yes

—

C₂×C₁₃×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₂×#88061

C₄

yes

—

C₂×#88060

—

C₂×#88058

C₄

yes

characteristic

C₂×C₄×#1055

C₂²

yes

characteristic

C₂×C₄×#1055

C₂²

yes

characteristic

C₄×D₁₀₄

—

C₄×D₁₀₄

—

C₁₃×#334

—

#11718075

—

#11718046

—

C₂²×D₅₂

C₂×C₄

yes

—

C₂²×C₄×D₁₃

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×#6103

—

C₂×C₄⋊Dic₁₃

C₂×C₄

yes

—

C₂²×#1055

—

C₂²×#1055

D₄

yes

—

C₂×D₁₀₄

—

C₂×D₁₀₄

—

C₄×D₅₂

—

C₄×D₅₂

—

C₄×D₅₂

—

C₄×D₅₂

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

C₄×C₈×C₁₃

D₄

yes

—

C₄×C₈×C₁₃

D₄

yes

—

—

—

—

—

—

—

D₄

yes

—

#9665

—

maximal, Sylow

C₂³×D₁₃

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

#41

yes

characteristic

C₂²×Dic₁₃

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

M₁₆

yes

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

—

C₄²×C₁₃

C₂×D₄

yes

characteristic

C₄²×C₁₃

C₂×D₄

yes

characteristic

C₄²×C₁₃

C₂×D₄

yes

C₄²×C₁₃

yes

—

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

—

—

—

—

D₁₀₄

—

C₂×C₄×D₈

—

#1954

—

C₂×#334

D₁₃

yes

characteristic, complemented

C₂×D₄⋊C₈

—

C₂×#322

—

C₂³×C₁₃

C₄×D₄

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₄×D₄

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

100

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

101

C₂×C₄×C₁₃

#131

yes

—

102

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

103

C₂×Dic₁₃

—

104

C₂×Dic₁₃

—

105

D₅₂

—

106

D₅₂

—

107

D₅₂

—

108

D₅₂

—

109

C₄×D₁₃

—

110

C₄×D₁₃

—

111

C₄×D₁₃

—

112

C₈×C₁₃

—

113

C₈×C₁₃

—

114

C₈×C₁₃

—

115

#1055

—

116

#1055

—

117

C₂²×D₈

—

118

C₂×C₄×D₄

—

119

C₄×D₈

—

120

C₄×D₈

—

121

C₂×#107

—

122

C₂×C₄⋊C₈

C₂×D₁₃

yes

—

123

C₂×#102

—

124

C₂×C₂²⋊C₈

—

125

C₂×C₄×C₈

—

126

C₂×C₄×C₈

—

127

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

128

#334

—

129

D₄⋊C₈

—

130

#322

—

131

C₂²×C₁₃

#390

yes

characteristic

132

C₂²×C₁₃

#435

yes

—

133

C₂²×C₁₃

#442

yes

—

134

C₂²×C₁₃

#443

yes

—

135

C₂×D₁₃

—

136

C₂×D₁₃

—

137

C₂×D₁₃

—

138

C₂×D₁₃

—

139

C₂×D₁₃

—

140

C₄×C₁₃

—

141

C₄×C₁₃

—

142

C₄×C₁₃

#407

yes

characteristic

143

C₄×C₁₃

#408

yes

characteristic

144

C₄×C₁₃

#435

yes

—

145

C₄×C₁₃

#469

yes

—

146

C₄×C₁₃

#496

yes

—

147

Dic₁₃

—

148

C₂²×D₄

—

149

C₂³×C₄

—

150

C₂×D₈

—

151

C₂×D₈

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

C₄×D₁₃

yes

characteristic

156

C₂²×C₈

C₄×D₁₃

yes

characteristic

157

C₄×D₄

—

158

C₄×D₄

—

159

C₄×D₄

—

160

C₄×D₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₂²⋊C₄

—

163

C₂×C₄²

C₂²×D₁₃

yes

characteristic

164

#107

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

#102

—

168

C₂²⋊C₈

—

169

C₄×C₈

—

170

C₄×C₈

—

171

C₄×C₈

—

172

C₄×C₈

—

173

C₄×C₈

D₅₂

yes

—

174

C₄×C₈

C₂²⋊D₁₃

yes

—

175

C₂×C₁₃

#1586

yes

—

176

C₂×C₁₃

#1955

yes

characteristic

177

C₂×C₁₃

#1972

yes

characteristic

178

C₂×C₁₃

#1974

yes

characteristic

179

D₁₃

—

180

C₂⁴

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

C₂×C₄×D₁₃

yes

characteristic

193

C₂²×C₄

D₄×D₁₃

yes

characteristic

194

C₂²×C₄

#6131

yes

characteristic

195

D₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

#6103

yes

—

205

C₂×C₈

#6103

yes

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₂²⋊C₄

—

209

C₂²⋊C₄

—

210

C₄²

C₂×D₅₂

yes

characteristic

211

C₄²

D₄×D₁₃

yes

characteristic

212

C₄²

#6131

yes

characteristic

213

C₄²

C₂×C₂²⋊D₁₃

yes

characteristic

214

C₁₃

#9665

yes

characteristic, complemented, Sylow

215

C₂³

—

216

C₂³

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

#88147

yes

characteristic

221

D₄

—

222

D₄

—

223

D₄

—

224

D₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

104

—

229

C₂×C₄

—

104

—

230

C₂×C₄

—

104

—

231

C₂×C₄

#88147

yes

characteristic

232

C₂×C₄

#88149

yes

characteristic

233

C₂×C₄

#88149

yes

characteristic

234

C₂×C₄

#88155

yes

—

235

C₂×C₄

M₁₆×D₁₃

yes

—

236

C₂×C₄

#88168

yes

—

237

C₂×C₄

C₂×#6103

yes

characteristic

238

C₂×C₄

#88194

yes

characteristic

239

C₂×C₄

#88201

yes

characteristic

240

C₈

—

241

C₈

—

242

C₈

—

243

C₈

—

244

C₈

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

104

—

248

C₂²

—

104

—

249

C₂²

—

104

—

250

C₂²

#11718497

yes

—

251

C₂²

#11718530

yes

—

252

C₂²

#11718556

yes

—

253

C₂²

#11718649

yes

characteristic

254

C₄

—

255

C₄

—

256

C₄

—

104

—

257

C₄

#11718497

yes

—

258

C₄

#11718526

yes

—

259

C₄

#11718771

yes

characteristic

260

C₄

#11718787

yes

characteristic

261

C₄

#11718837

yes

—

262

C₂

—

104

—

263

C₂

#13113699

yes

—

264

C₂

#13115633

yes

characteristic

265

C₂

#13115710

yes

characteristic

266

C₂

#13115722

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×#334	C₂
socle	C₂³×C₁₃	C₄×D₄
prime radical	C₂²×D₁₀₄	C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×#334	D₁₃
hypocenter	C₁₃	#9665
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

subgroup

G/H

center

C₂²×C₄

D₄×D₁₃

commutator

C₂²×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₂×C₁₃×#334

C₂

socle

C₂³×C₁₃

C₄×D₄

prime radical

C₂²×D₁₀₄

C₄

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

N	H ≅ G/N	type
2. #13115629	C₂	semidirect
3. C₂×#11718075	C₂	semidirect
4. C₂×#11718046	C₂	semidirect
5. C₂×C₁₃×#334	C₂	semidirect
84. C₂×#334	D₁₃	semidirect
214. C₁₃	#9665	semidirect

H ≅ G/N

type

2. #13115629

C₂

semidirect

3. C₂×#11718075

C₂

semidirect

4. C₂×#11718046

C₂

semidirect

5. C₂×C₁₃×#334

C₂

semidirect

84. C₂×#334

D₁₃

semidirect

214. C₁₃

#9665

semidirect

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

subgroup	index
C₂×C₄×D₁₀₄	2
#13115629	2
C₂×#11718075	2
C₂×#11718046	2
C₂×C₁₃×#334	2
#9665	13

subgroup

index

C₂×C₄×D₁₀₄

C₂×C₁₃×#334

Subgroups — #15761824

Conjugacy classes of subgroups

Complements

Maximal subgroups