Group #15781781 — subgroups

Subgroups — #15781781

Order 3328.

558 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 129 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	C₂²×Dic₁₀₄	C₂	1	2	yes	maximal
2	C₂×#11718360	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718095	C₂	1	2	yes	maximal
4	#13115697	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1374	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₅₂	—	2	1	no	—
7	C₂²×Dic₅₂	C₂²	1	1	yes	characteristic
8	C₂²×Dic₅₂	C₂²	1	2	yes	—
9	C₂×#88123	—	2	1	no	—
10	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×#88058	C₂²	1	1	yes	characteristic
13	C₂×#88056	—	2	1	no	—
14	#11718590	—	2	1	no	—
15	C₂×Dic₁₀₄	—	2	4	no	—
16	C₂×Dic₁₀₄	—	2	4	no	—
17	C₂×Dic₁₀₄	—	2	4	no	—
18	#11718360	—	2	4	no	—
19	#11718095	—	2	4	no	—
20	C₂²×Dic₂₆	—	2	2	no	—
21	C₂²×Dic₂₆	—	2	1	no	—
22	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₃	—	2	1	no	—
26	C₂×C₄⋊Dic₁₃	—	4	2	no	—
27	C₂×Dic₅₂	—	2	2	no	—
28	C₂×Dic₅₂	—	2	2	no	—
29	C₂×Dic₅₂	—	2	2	no	—
30	C₂×Dic₅₂	—	2	2	no	—
31	C₂×Dic₅₂	—	2	2	no	—
32	C₂×Dic₅₂	—	2	2	no	—
33	C₂×Dic₅₂	—	2	4	no	—
34	C₂×Dic₅₂	—	2	2	no	—
35	C₂×Dic₅₂	—	2	1	no	—
36	C₂×Dic₅₂	—	4	2	no	—
37	C₂×Dic₅₂	—	4	2	no	—
38	C₂×Dic₅₂	D₄	1	2	yes	—
39	C₂×Dic₅₂	D₄	1	4	yes	—
40	#88123	—	2	4	no	—
41	#88123	—	4	2	no	—
42	C₂×C₁₃×C₁₆	—	2	2	no	—
43	C₂×C₁₃×C₁₆	—	2	2	no	—
44	C₂×C₁₃×C₁₆	D₄	1	4	yes	—
45	C₄×C₈×C₁₃	—	2	2	no	—
46	#88071	—	4	2	no	—
47	#88058	—	2	2	no	—
48	#88056	—	4	2	no	—
49	Dic₁₀₄	—	2	16	no	—
50	#13330	—	13	1	no	maximal, Sylow
51	C₂²×C₄×C₁₃	D₈	1	2	yes	—
52	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×Dic₁₃	—	4	1	no	—
54	C₂²×Dic₁₃	—	4	2	no	—
55	C₂²×Dic₁₃	—	4	1	no	—
56	C₂×Dic₂₆	—	2	4	no	—
57	C₂×Dic₂₆	—	2	2	no	—
58	C₂×Dic₂₆	—	4	1	no	—
59	C₂×Dic₂₆	—	4	2	no	—
60	C₂×Dic₂₆	—	4	1	no	—
61	C₂×Dic₂₆	—	4	2	no	—
62	C₂×Dic₂₆	—	4	2	no	—
63	C₂×Dic₂₆	—	4	1	no	—
64	C₂×Dic₂₆	—	4	2	no	—
65	C₂×Dic₂₆	—	4	1	no	—
66	C₂×Dic₂₆	—	4	2	no	—
67	C₂×Dic₂₆	—	4	1	no	—
68	C₂×C₈×C₁₃	—	2	1	no	—
69	C₂×C₈×C₁₃	—	2	1	no	—
70	C₂×C₈×C₁₃	D₈	1	2	yes	—
71	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
73	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
74	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
75	C₄²×C₁₃	—	2	1	no	—
76	C₄²×C₁₃	—	2	1	no	—
77	C₄⋊Dic₁₃	—	4	8	no	—
78	C₄⋊Dic₁₃	—	4	1	no	—
79	C₄⋊Dic₁₃	—	4	1	no	—
80	Dic₅₂	—	2	4	no	—
81	Dic₅₂	—	2	4	no	—
82	Dic₅₂	—	2	4	no	—
83	Dic₅₂	—	4	8	no	—
84	Dic₅₂	—	4	2	no	—
85	Dic₅₂	—	4	2	no	—
86	Dic₅₂	—	4	2	no	—
87	C₁₃×C₁₆	—	2	4	no	—
88	C₂²×Q₃₂	—	13	2	no	—
89	C₂×#494	—	13	1	no	—
90	C₂×#358	—	13	2	no	—
91	#1969	—	13	1	no	—
92	#1374	D₁₃	1	1	yes	characteristic
93	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
94	C₂×C₄×C₁₃	—	2	2	no	—
95	C₂×C₄×C₁₃	—	2	2	no	—
96	C₂×C₄×C₁₃	Q₃₂	1	4	yes	complemented
97	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
98	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
99	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
101	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
102	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×Dic₁₃	—	4	4	no	—
104	C₂×Dic₁₃	—	4	2	no	—
105	C₂×Dic₁₃	—	8	1	no	—
106	C₂×Dic₁₃	—	8	2	no	—
107	C₂×Dic₁₃	—	8	2	no	—
108	C₂×Dic₁₃	—	8	1	no	—
109	C₂×Dic₁₃	—	8	1	no	—
110	C₂×Dic₁₃	—	8	2	no	—
111	Dic₂₆	—	4	2	no	—
112	Dic₂₆	—	4	4	no	—
113	Dic₂₆	—	4	4	no	—
114	Dic₂₆	—	4	2	no	—
115	Dic₂₆	—	8	1	no	—
116	Dic₂₆	—	8	2	no	—
117	Dic₂₆	—	8	2	no	—
118	Dic₂₆	—	8	1	no	—
119	C₈×C₁₃	—	2	2	no	—
120	C₈×C₁₃	#120	1	2	yes	—
121	C₈×C₁₃	#121	1	2	yes	—
122	C₂²×Q₁₆	—	13	2	no	—
123	C₂²×Q₁₆	—	13	1	no	—
124	C₂²×Q₁₆	—	26	1	no	—
125	C₂×C₄⋊Q₈	—	26	1	no	—
126	C₂×Q₃₂	—	26	4	no	—
127	C₂×Q₃₂	—	26	4	no	—
128	C₂×Q₃₂	—	26	4	no	—
129	C₂²×C₁₆	C₂×D₁₃	1	2	yes	—
130	#494	—	26	4	no	—
131	C₂×#107	—	13	1	no	—
132	C₂×#103	—	26	1	no	—
133	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
134	#391	—	26	1	no	—
135	#358	—	26	4	no	—
136	C₂²×C₁₃	#447	1	1	yes	characteristic
137	C₂²×C₁₃	#459	1	1	yes	characteristic
138	C₂²×C₁₃	#493	1	1	yes	characteristic
139	C₂²×C₁₃	C₂×Q₃₂	1	2	yes	—
140	C₂²×C₁₃	#510	1	2	yes	—
141	C₄×C₁₃	—	2	4	no	—
142	C₄×C₁₃	#392	1	1	yes	characteristic
143	C₄×C₁₃	#447	1	1	yes	characteristic
144	C₄×C₁₃	#459	1	1	yes	characteristic
145	C₄×C₁₃	#496	1	1	yes	characteristic
146	Dic₁₃	—	8	4	no	—
147	Dic₁₃	—	8	2	no	—
148	Dic₁₃	—	16	1	no	—
149	C₂²×Q₈	—	26	2	no	—
150	C₂²×Q₈	—	26	1	no	—
151	C₂×Q₁₆	—	13	4	no	—
152	C₂×Q₁₆	—	13	2	no	—
153	C₂×Q₁₆	—	26	4	no	—
154	C₂×Q₁₆	—	26	2	no	—
155	C₂×Q₁₆	—	26	2	no	—
156	C₂×Q₁₆	—	26	2	no	—
157	C₂×Q₁₆	—	26	2	no	—
158	C₂×Q₁₆	—	26	2	no	—
159	C₂×Q₁₆	—	26	2	no	—
160	C₂×Q₁₆	—	26	2	no	—
161	C₂×Q₁₆	—	26	1	no	—
162	C₂×Q₁₆	—	52	2	no	—
163	C₂×Q₁₆	—	52	2	no	—
164	C₂²×C₈	D₅₂	1	1	yes	characteristic
165	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
166	C₄⋊Q₈	—	26	4	no	—
167	C₄⋊Q₈	—	52	2	no	—
168	C₂×C₄⋊C₄	—	26	1	no	—
169	C₂×C₄⋊C₄	—	52	2	no	—
170	C₂×C₄²	D₅₂	1	1	yes	characteristic
171	Q₃₂	—	26	16	no	—
172	C₂×C₁₆	—	2	2	no	—
173	C₂×C₁₆	—	2	2	no	—
174	C₂×C₁₆	D₅₂	1	4	yes	—
175	#107	—	26	2	no	—
176	#103	—	52	2	no	—
177	C₄×C₈	—	2	2	no	—
178	#95	—	52	2	no	—
179	C₂×C₁₃	#2011	1	1	yes	characteristic
180	C₂×C₁₃	#2188	1	2	yes	—
181	C₂×C₁₃	#2209	1	2	yes	—
182	C₂×C₁₃	#2247	1	1	yes	characteristic
183	C₂×C₁₃	#2251	1	1	yes	characteristic
184	C₂×Q₈	—	26	4	no	—
185	C₂×Q₈	—	26	2	no	—
186	C₂×Q₈	—	52	2	no	—
187	C₂×Q₈	—	52	1	no	—
188	C₂×Q₈	—	52	2	no	—
189	C₂×Q₈	—	52	1	no	—
190	C₂×Q₈	—	52	1	no	—
191	C₂×Q₈	—	52	2	no	—
192	C₂×Q₈	—	52	1	no	—
193	C₂×Q₈	—	52	2	no	—
194	C₂×Q₈	—	52	2	no	—
195	C₂×Q₈	—	52	1	no	—
196	C₂²×C₄	—	52	1	no	—
197	C₂²×C₄	—	52	2	no	—
198	C₂²×C₄	—	52	1	no	—
199	C₂²×C₄	D₁₀₄	1	2	yes	—
200	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
201	Q₁₆	—	26	4	no	—
202	Q₁₆	—	26	4	no	—
203	Q₁₆	—	26	4	no	—
204	Q₁₆	—	52	8	no	—
205	Q₁₆	—	52	2	no	—
206	Q₁₆	—	52	2	no	—
207	Q₁₆	—	52	2	no	—
208	C₂×C₈	—	2	1	no	—
209	C₂×C₈	—	2	1	no	—
210	C₂×C₈	D₁₀₄	1	2	yes	—
211	C₂×C₈	C₂×D₅₂	1	2	yes	—
212	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
213	C₂×C₈	D₄×D₁₃	1	2	yes	—
214	C₂×C₈	#6131	1	1	yes	characteristic
215	C₄⋊C₄	—	52	8	no	—
216	C₄⋊C₄	—	52	1	no	—
217	C₄⋊C₄	—	52	1	no	—
218	C₄²	—	2	1	no	—
219	C₄²	—	2	1	no	—
220	C₁₆	—	2	4	no	—
221	C₁₃	#13330	1	1	yes	characteristic, complemented, Sylow
222	C₂³	C₂×D₁₀₄	1	1	yes	characteristic
223	Q₈	—	52	2	no	—
224	Q₈	—	52	2	no	—
225	Q₈	—	52	4	no	—
226	Q₈	—	52	4	no	—
227	Q₈	—	104	2	no	—
228	Q₈	—	104	2	no	—
229	Q₈	—	104	1	no	—
230	Q₈	—	104	1	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	52	2	no	—
234	C₂×C₄	—	52	4	no	—
235	C₂×C₄	—	104	2	no	—
236	C₂×C₄	—	104	1	no	—
237	C₂×C₄	—	104	2	no	—
238	C₂×C₄	—	104	1	no	—
239	C₂×C₄	—	104	2	no	—
240	C₂×C₄	—	104	1	no	—
241	C₂×C₄	Dic₁₀₄	1	4	yes	complemented
242	C₂×C₄	#88128	1	1	yes	characteristic
243	C₂×C₄	#88136	1	1	yes	characteristic
244	C₂×C₄	#88149	1	1	yes	characteristic
245	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
246	C₂×C₄	#88162	1	1	yes	characteristic
247	C₂×C₄	#88162	1	1	yes	characteristic
248	C₈	—	2	2	no	—
249	C₈	#88136	1	2	yes	—
250	C₈	#88149	1	2	yes	—
251	C₂²	#11718356	1	1	yes	characteristic
252	C₂²	#11718393	1	1	yes	characteristic
253	C₂²	#11718504	1	1	yes	characteristic
254	C₂²	C₂×Dic₁₀₄	1	2	yes	—
255	C₂²	#11718570	1	2	yes	—
256	C₄	—	2	4	no	—
257	C₄	—	104	2	no	—
258	C₄	—	104	4	no	—
259	C₄	—	208	1	no	—
260	C₄	#11718332	1	1	yes	characteristic
261	C₄	#11718373	1	1	yes	characteristic
262	C₄	#11718393	1	1	yes	characteristic
263	C₄	#11718504	1	1	yes	characteristic
264	C₂	#13115909	1	1	yes	characteristic
265	C₂	#13116772	1	2	yes	—
266	C₂	#13116887	1	2	yes	—
267	C₂	#13117089	1	1	yes	characteristic
268	C₂	#13117107	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₁₀₄

C₂

yes

maximal

C₂×#11718360

C₂

yes

maximal, characteristic

C₂×#11718095

C₂

yes

maximal

#13115697

C₂

yes

maximal, characteristic

C₁₃×#1374

C₂

yes

maximal, characteristic

C₂²×Dic₅₂

—

C₂²×Dic₅₂

C₂²

yes

characteristic

C₂²×Dic₅₂

C₂²

yes

—

C₂×#88123

—

C₂²×C₁₃×C₁₆

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₂×#88058

C₂²

yes

characteristic

C₂×#88056

—

#11718590

—

C₂×Dic₁₀₄

—

C₂×Dic₁₀₄

—

C₂×Dic₁₀₄

—

#11718360

—

#11718095

—

C₂²×Dic₂₆

—

C₂²×Dic₂₆

—

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

D₄

yes

—

C₂×Dic₅₂

D₄

yes

—

#88123

—

#88123

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

D₄

yes

—

C₄×C₈×C₁₃

—

#88071

—

#88058

—

#88056

—

Dic₁₀₄

—

#13330

—

maximal, Sylow

C₂²×C₄×C₁₃

D₈

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₈

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

#41

yes

characteristic

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

Dic₅₂

—

Dic₅₂

—

Dic₅₂

—

Dic₅₂

—

Dic₅₂

—

Dic₅₂

—

Dic₅₂

—

C₁₃×C₁₆

—

C₂²×Q₃₂

—

—

—

—

D₁₃

yes

characteristic

C₂³×C₁₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

Q₃₂

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

100

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

101

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

characteristic

102

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

characteristic

103

C₂×Dic₁₃

—

104

C₂×Dic₁₃

—

105

C₂×Dic₁₃

—

106

C₂×Dic₁₃

—

107

C₂×Dic₁₃

—

108

C₂×Dic₁₃

—

109

C₂×Dic₁₃

—

110

C₂×Dic₁₃

—

111

Dic₂₆

—

112

Dic₂₆

—

113

Dic₂₆

—

114

Dic₂₆

—

115

Dic₂₆

—

116

Dic₂₆

—

117

Dic₂₆

—

118

Dic₂₆

—

119

C₈×C₁₃

—

120

C₈×C₁₃

#120

yes

—

121

C₈×C₁₃

#121

yes

—

122

C₂²×Q₁₆

—

123

C₂²×Q₁₆

—

124

C₂²×Q₁₆

—

125

C₂×C₄⋊Q₈

—

126

C₂×Q₃₂

—

127

C₂×Q₃₂

—

128

C₂×Q₃₂

—

129

C₂²×C₁₆

C₂×D₁₃

yes

—

130

#494

—

131

C₂×#107

—

132

C₂×#103

—

133

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

134

#391

—

135

#358

—

136

C₂²×C₁₃

#447

yes

characteristic

137

C₂²×C₁₃

#459

yes

characteristic

138

C₂²×C₁₃

#493

yes

characteristic

139

C₂²×C₁₃

C₂×Q₃₂

yes

—

140

C₂²×C₁₃

#510

yes

—

141

C₄×C₁₃

—

142

C₄×C₁₃

#392

yes

characteristic

143

C₄×C₁₃

#447

yes

characteristic

144

C₄×C₁₃

#459

yes

characteristic

145

C₄×C₁₃

#496

yes

characteristic

146

Dic₁₃

—

147

Dic₁₃

—

148

Dic₁₃

—

149

C₂²×Q₈

—

150

C₂²×Q₈

—

151

C₂×Q₁₆

—

152

C₂×Q₁₆

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

—

158

C₂×Q₁₆

—

159

C₂×Q₁₆

—

160

C₂×Q₁₆

—

161

C₂×Q₁₆

—

162

C₂×Q₁₆

—

163

C₂×Q₁₆

—

164

C₂²×C₈

D₅₂

yes

characteristic

165

C₂²×C₈

C₂²×D₁₃

yes

characteristic

166

C₄⋊Q₈

—

167

C₄⋊Q₈

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄²

D₅₂

yes

characteristic

171

Q₃₂

—

172

C₂×C₁₆

—

173

C₂×C₁₆

—

174

C₂×C₁₆

D₅₂

yes

—

175

#107

—

176

#103

—

177

C₄×C₈

—

178

#95

—

179

C₂×C₁₃

#2011

yes

characteristic

180

C₂×C₁₃

#2188

yes

—

181

C₂×C₁₃

#2209

yes

—

182

C₂×C₁₃

#2247

yes

characteristic

183

C₂×C₁₃

#2251

yes

characteristic

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂×Q₈

—

194

C₂×Q₈

—

195

C₂×Q₈

—

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

D₁₀₄

yes

—

200

C₂²×C₄

C₂×D₅₂

yes

characteristic

201

Q₁₆

—

202

Q₁₆

—

203

Q₁₆

—

204

Q₁₆

—

205

Q₁₆

—

206

Q₁₆

—

207

Q₁₆

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

D₁₀₄

yes

—

211

C₂×C₈

C₂×D₅₂

yes

—

212

C₂×C₈

D₄×D₁₃

yes

characteristic

213

C₂×C₈

D₄×D₁₃

yes

—

214

C₂×C₈

#6131

yes

characteristic

215

C₄⋊C₄

—

216

C₄⋊C₄

—

217

C₄⋊C₄

—

218

C₄²

—

219

C₄²

—

220

C₁₆

—

221

C₁₃

#13330

yes

characteristic, complemented, Sylow

222

C₂³

C₂×D₁₀₄

yes

characteristic

223

Q₈

—

224

Q₈

—

225

Q₈

—

226

Q₈

—

227

Q₈

—

104

—

228

Q₈

—

104

—

229

Q₈

—

104

—

230

Q₈

—

104

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

104

—

236

C₂×C₄

—

104

—

237

C₂×C₄

—

104

—

238

C₂×C₄

—

104

—

239

C₂×C₄

—

104

—

240

C₂×C₄

—

104

—

241

C₂×C₄

Dic₁₀₄

yes

complemented

242

C₂×C₄

#88128

yes

characteristic

243

C₂×C₄

#88136

yes

characteristic

244

C₂×C₄

#88149

yes

characteristic

245

C₂×C₄

C₂×D₁₀₄

yes

characteristic

246

C₂×C₄

#88162

yes

characteristic

247

C₂×C₄

#88162

yes

characteristic

248

C₈

—

249

C₈

#88136

yes

—

250

C₈

#88149

yes

—

251

C₂²

#11718356

yes

characteristic

252

C₂²

#11718393

yes

characteristic

253

C₂²

#11718504

yes

characteristic

254

C₂²

C₂×Dic₁₀₄

yes

—

255

C₂²

#11718570

yes

—

256

C₄

—

257

C₄

—

104

—

258

C₄

—

104

—

259

C₄

—

208

—

260

C₄

#11718332

yes

characteristic

261

C₄

#11718373

yes

characteristic

262

C₄

#11718393

yes

characteristic

263

C₄

#11718504

yes

characteristic

264

C₂

#13115909

yes

characteristic

265

C₂

#13116772

yes

—

266

C₂

#13116887

yes

—

267

C₂

#13117089

yes

characteristic

268

C₂

#13117107

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₁₀₄
commutator, cosocle	C₂²×C₈×C₁₃	C₂³
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1374	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₈
hypercenter	#1374	D₁₃
hypocenter	C₁₃	#13330
LCS	G ▷ C₂²×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

subgroup

G/H

center

C₂³

C₂×D₁₀₄

commutator, cosocle

C₂²×C₈×C₁₃

C₂³

Frattini

C₂²×C₈

C₂²×D₁₃

Fitting

C₁₃×#1374

C₂

socle, prime radical

C₂³×C₁₃

C₂×D₈

D₁₃

C₁₃

G ▷ C₂²×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

N	H ≅ G/N	type
96. C₂×C₄×C₁₃	Q₃₂	semidirect
221. C₁₃	#13330	semidirect
241. C₂×C₄	Dic₁₀₄	semidirect

H ≅ G/N

type

96. C₂×C₄×C₁₃

Q₃₂

semidirect

221. C₁₃

#13330

semidirect

241. C₂×C₄

Dic₁₀₄

semidirect

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

subgroup	index
C₂²×Dic₁₀₄	2
C₂×#11718360	2
C₂×#11718095	2
#13115697	2
C₁₃×#1374	2
#13330	13

subgroup

index

C₂²×Dic₁₀₄

C₁₃×#1374

Subgroups — #15781781

Conjugacy classes of subgroups

Complements

Maximal subgroups