Group #36447663 — subgroups

Subgroups — #36447663

Order 22784.

418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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	#26028965	C₂	1	1	yes	maximal, characteristic
2	#26020383	C₂	1	1	yes	maximal, characteristic, complemented
3	#26018813	C₂	1	2	yes	maximal
4	#26018111	C₂	1	2	yes	maximal, complemented
5	C₈₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15668018	—	2	1	no	—
7	#19152148	C₂²	1	1	yes	characteristic
8	#19151677	—	2	1	no	—
9	#19151677	C₄	1	2	yes	complemented
10	C₈×D₃₅₆	—	2	1	no	—
11	C₈×D₃₅₆	C₄	1	2	yes	complemented
12	#19151622	C₂²	1	1	yes	characteristic
13	#19151564	—	2	1	no	—
14	#19151464	C₂²	1	2	yes	—
15	#19151361	—	2	1	no	—
16	#19151361	—	2	1	no	—
17	#19151333	—	2	4	no	—
18	#431×C₈₉	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	#335×C₈₉	—	2	1	no	—
21	#334×C₈₉	—	2	1	no	—
22	C₂×#13083574	—	2	1	no	—
23	#15668018	—	4	4	no	—
24	C₂×#13083558	—	2	1	no	—
25	C₂×#13083557	—	2	2	no	—
26	C₂×C₈×D₈₉	—	2	2	no	—
27	#15668012	Q₈	1	1	yes	characteristic
28	#15668009	Q₈	1	1	yes	characteristic
29	#15668000	—	2	1	no	—
30	#15667986	—	2	1	no	—
31	#15667986	D₄	1	2	yes	—
32	C₄×D₃₅₆	—	2	1	no	—
33	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
34	C₂×C₄⋊Dic₈₉	—	2	2	no	—
35	C₄⋊#10623494	—	2	1	no	—
36	C₄⋊#10623494	C₂×C₄	1	2	yes	—
37	#15667924	—	2	2	no	—
38	#15667924	—	2	2	no	—
39	#15667919	—	2	2	no	—
40	#15667919	—	2	2	no	—
41	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₈₉	—	2	2	no	—
45	C₂²⋊C₈×C₈₉	—	2	2	no	—
46	C₄×C₈×C₈₉	—	2	2	no	—
47	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
49	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
50	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
51	#13083574	—	4	2	no	—
52	#13083574	—	4	2	no	—
53	C₂×Dic₁₇₈	—	2	1	no	—
54	C₂×D₃₅₆	—	2	1	no	—
55	C₂×D₃₅₆	—	2	1	no	—
56	C₂×D₃₅₆	C₄⋊C₄	1	2	yes	—
57	C₂×C₂²⋊D₈₉	—	2	2	no	—
58	C₂²×Dic₈₉	—	4	2	no	—
59	C₂×C₄×D₈₉	—	2	2	no	—
60	#13083558	—	4	2	no	—
61	#13083557	—	4	4	no	—
62	C₂×#10623494	—	2	2	no	—
63	C₈×D₈₉	—	4	4	no	—
64	C₄⋊Dic₈₉	—	2	1	no	—
65	C₄⋊Dic₈₉	—	4	2	no	—
66	C₄⋊Dic₈₉	—	4	2	no	—
67	C₄⋊Dic₈₉	C₄⋊C₄	1	2	yes	—
68	#13083551	—	2	2	no	—
69	#13083551	—	2	2	no	—
70	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
73	C₂×C₈×C₈₉	—	2	2	no	—
74	C₂×C₈×C₈₉	—	2	2	no	—
75	C₂×C₈×C₈₉	—	4	2	no	—
76	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
81	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
83	C₄²×C₈₉	#41	1	1	yes	characteristic
84	C₂³×C₈₉	#121	1	1	yes	characteristic
85	C₂²×D₈₉	—	2	2	no	—
86	C₂×C₄×C₈₉	—	4	1	no	—
87	C₂×C₄×C₈₉	—	4	1	no	—
88	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
91	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
92	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
93	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
94	C₂×C₄×C₈₉	#135	1	2	yes	—
95	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
96	C₂²⋊D₈₉	—	4	4	no	—
97	C₂×Dic₈₉	—	2	2	no	—
98	C₂×Dic₈₉	—	8	2	no	—
99	C₂×Dic₈₉	—	8	2	no	—
100	C₂×Dic₈₉	—	8	2	no	—
101	D₃₅₆	—	4	2	no	—
102	D₃₅₆	—	4	2	no	—
103	D₃₅₆	—	4	2	no	—
104	C₄×D₈₉	—	4	2	no	—
105	C₄×D₈₉	—	4	2	no	—
106	Dic₁₇₈	—	4	2	no	—
107	C₈×C₈₉	—	2	1	no	—
108	C₈×C₈₉	—	2	1	no	—
109	C₈×C₈₉	—	2	1	no	—
110	C₈×C₈₉	—	2	1	no	—
111	C₈×C₈₉	—	8	2	no	—
112	#10623494	—	4	2	no	—
113	C₂²×C₈₉	—	2	1	no	—
114	C₂²×C₈₉	—	2	1	no	—
115	C₂²×C₈₉	#380	1	1	yes	characteristic
116	C₂²×C₈₉	#463	1	2	yes	—
117	C₂×D₈₉	—	4	2	no	—
118	C₂×D₈₉	—	4	2	no	—
119	C₂×D₈₉	—	4	2	no	—
120	C₄×C₈₉	—	2	1	no	—
121	C₄×C₈₉	—	2	1	no	—
122	C₄×C₈₉	—	2	1	no	—
123	C₄×C₈₉	—	2	1	no	—
124	C₄×C₈₉	#416	1	1	yes	characteristic
125	C₄×C₈₉	#418	1	1	yes	characteristic
126	C₄×C₈₉	#478	1	2	yes	—
127	Dic₈₉	—	4	2	no	—
128	Dic₈₉	—	16	2	no	—
129	#8680	—	89	1	no	maximal, Sylow
130	C₂×C₈₉	—	2	2	no	—
131	C₂×C₈₉	#1804	1	1	yes	characteristic
132	C₂×C₈₉	#1812	1	1	yes	characteristic
133	C₂×C₈₉	#1814	1	1	yes	characteristic
134	D₈₉	—	8	2	no	—
135	#2931	—	89	1	no	—
136	#1835	—	89	1	no	—
137	#1564	D₈₉	1	1	yes	characteristic, complemented
138	#1517	—	89	2	no	—
139	#1286	—	89	2	no	—
140	C₈₉	#8680	1	1	yes	characteristic, complemented, Sylow
141	C₂×#131	—	178	1	no	—
142	#532	—	89	1	no	—
143	#436	—	89	2	no	—
144	#436	—	178	1	no	—
145	C₈×D₄	—	89	2	no	—
146	C₈×D₄	—	178	1	no	—
147	#431	C₂×D₈₉	1	2	yes	—
148	#423	—	89	1	no	—
149	#408	—	178	1	no	—
150	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
151	#382	—	89	2	no	—
152	#340	—	178	1	no	—
153	#340	—	178	1	no	—
154	#335	—	2	1	no	—
155	#334	—	2	1	no	—
156	#327	—	178	4	no	—
157	C₂×#41	—	178	1	no	—
158	#131	—	356	4	no	—
159	C₂×M₁₆	—	178	1	no	—
160	C₂×M₁₆	—	178	2	no	—
161	C₂²×C₈	—	178	2	no	—
162	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
163	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
164	C₄⋊Q₈	—	89	1	no	—
165	#127	—	89	1	no	—
166	#124	—	178	1	no	—
167	#121	—	89	2	no	—
168	#121	—	178	1	no	—
169	C₄×D₄	—	89	2	no	—
170	C₄×D₄	—	178	1	no	—
171	C₂×C₄⋊C₄	—	178	2	no	—
172	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
173	C₄⋊C₈	—	2	2	no	—
174	C₄⋊C₈	—	89	2	no	—
175	C₄⋊C₈	—	178	1	no	—
176	C₂²⋊C₈	—	2	2	no	—
177	C₂²⋊C₈	—	178	2	no	—
178	C₂²⋊C₈	—	178	2	no	—
179	C₄×C₈	—	2	2	no	—
180	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
181	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
182	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
183	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
184	#95	—	178	2	no	—
185	#95	—	178	2	no	—
186	#41	—	356	2	no	—
187	#41	—	356	2	no	—
188	C₂×Q₈	—	178	1	no	—
189	C₂×D₄	—	89	2	no	—
190	C₂×D₄	—	178	2	no	—
191	C₂×D₄	—	178	1	no	—
192	C₂×D₄	—	178	1	no	—
193	C₂²×C₄	—	356	2	no	—
194	C₂²×C₄	—	178	2	no	—
195	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
196	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
197	C₂²×C₄	#13083575	1	1	yes	characteristic
198	M₁₆	—	356	4	no	—
199	M₁₆	—	356	2	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	2	2	no	—
202	C₂×C₈	—	4	2	no	—
203	C₂×C₈	—	356	4	no	—
204	C₂×C₈	—	178	2	no	—
205	C₂×C₈	#13083551	1	1	yes	characteristic
206	C₂×C₈	#13083551	1	1	yes	characteristic
207	C₂×C₈	#13083551	1	1	yes	characteristic
208	C₂×C₈	#13083551	1	1	yes	characteristic
209	C₄⋊C₄	—	89	2	no	—
210	C₄⋊C₄	—	356	2	no	—
211	C₄⋊C₄	—	356	2	no	—
212	C₄⋊C₄	—	178	1	no	—
213	C₂²⋊C₄	—	178	2	no	—
214	C₂²⋊C₄	—	178	2	no	—
215	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
216	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
217	C₄²	Q₈×D₈₉	1	1	yes	characteristic
218	C₄²	#13083573	1	1	yes	characteristic
219	C₂³	—	178	2	no	—
220	C₂³	#15667987	1	1	yes	characteristic
221	Q₈	—	356	2	no	—
222	D₄	—	356	2	no	—
223	D₄	—	356	2	no	—
224	D₄	—	356	4	no	—
225	D₄	—	356	2	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	1	no	—
228	C₂×C₄	—	356	2	no	—
229	C₂×C₄	—	356	2	no	—
230	C₂×C₄	—	178	2	no	—
231	C₂×C₄	—	712	2	no	—
232	C₂×C₄	—	712	2	no	—
233	C₂×C₄	—	712	2	no	—
234	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
235	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
236	C₂×C₄	#15667970	1	1	yes	characteristic
237	C₂×C₄	#15667983	1	1	yes	characteristic
238	C₂×C₄	#15667988	1	1	yes	characteristic
239	C₂×C₄	#15667992	1	1	yes	characteristic
240	C₂×C₄	#15668034	1	2	yes	—
241	C₂×C₄	#15668040	1	2	yes	—
242	C₈	—	2	1	no	—
243	C₈	—	2	1	no	—
244	C₈	—	2	1	no	—
245	C₈	—	2	1	no	—
246	C₈	—	8	2	no	—
247	C₈	—	356	2	no	—
248	C₂²	—	2	1	no	—
249	C₂²	—	2	1	no	—
250	C₂²	—	356	2	no	—
251	C₂²	—	356	2	no	—
252	C₂²	—	356	2	no	—
253	C₂²	#19151455	1	1	yes	characteristic
254	C₂²	#19151814	1	2	yes	—
255	C₄	—	2	1	no	—
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	2	1	no	—
259	C₄	—	356	2	no	—
260	C₄	—	1424	2	no	—
261	C₄	#19151595	1	1	yes	characteristic
262	C₄	#19151604	1	1	yes	characteristic
263	C₄	#19151899	1	2	yes	—
264	C₂	—	2	2	no	—
265	C₂	—	712	2	no	—
266	C₂	#26020263	1	1	yes	characteristic
267	C₂	#26020295	1	1	yes	characteristic
268	C₂	#26020307	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26028965

C₂

yes

maximal, characteristic

#26020383

C₂

yes

maximal, characteristic, complemented

#26018813

C₂

yes

maximal

#26018111

C₂

yes

maximal, complemented

C₈₉×#1564

C₂

yes

maximal, characteristic, complemented

C₂×#15668018

—

#19152148

C₂²

yes

characteristic

#19151677

—

#19151677

C₄

yes

complemented

C₈×D₃₅₆

—

C₈×D₃₅₆

C₄

yes

complemented

#19151622

C₂²

yes

characteristic

#19151564

—

#19151464

C₂²

yes

—

#19151361

—

#19151361

—

#19151333

—

#431×C₈₉

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

#335×C₈₉

—

#334×C₈₉

—

—

—

—

—

C₂×C₈×D₈₉

—

#15668012

Q₈

yes

characteristic

#15668009

Q₈

yes

—

—

D₄

yes

—

C₄×D₃₅₆

—

C₄×D₃₅₆

C₂×C₄

yes

—

C₂×C₄⋊Dic₈₉

—

C₄⋊#10623494

—

C₄⋊#10623494

C₂×C₄

yes

—

—

—

—

—

C₂²×C₈×C₈₉

D₄

yes

characteristic

C₂²×C₈×C₈₉

D₄

yes

characteristic

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

C₂²⋊C₈×C₈₉

—

C₄×C₈×C₈₉

—

C₄×C₈×C₈₉

C₂×C₄

yes

characteristic

C₄×C₈×C₈₉

C₂×C₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

#13083574

—

#13083574

—

C₂×Dic₁₇₈

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

C₄⋊C₄

yes

—

C₂×C₂²⋊D₈₉

—

C₂²×Dic₈₉

—

C₂×C₄×D₈₉

—

#13083558

—

#13083557

—

C₂×#10623494

—

C₈×D₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

C₄⋊C₄

yes

—

#13083551

—

#13083551

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

#41

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₄²×C₈₉

C₂²×C₄

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

C₂×Q₈

yes

C₄²×C₈₉

yes

C₂³×C₈₉

yes

C₂²×D₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₉

#135

yes

—

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

—

C₂²⋊D₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

100

C₂×Dic₈₉

—

101

D₃₅₆

—

102

D₃₅₆

—

103

D₃₅₆

—

104

C₄×D₈₉

—

105

C₄×D₈₉

—

106

Dic₁₇₈

—

107

C₈×C₈₉

—

108

C₈×C₈₉

—

109

C₈×C₈₉

—

110

C₈×C₈₉

—

111

C₈×C₈₉

—

112

#10623494

—

113

C₂²×C₈₉

—

114

C₂²×C₈₉

—

115

C₂²×C₈₉

#380

yes

characteristic

116

C₂²×C₈₉

#463

yes

—

117

C₂×D₈₉

—

118

C₂×D₈₉

—

119

C₂×D₈₉

—

120

C₄×C₈₉

—

121

C₄×C₈₉

—

122

C₄×C₈₉

—

123

C₄×C₈₉

—

124

C₄×C₈₉

#416

yes

characteristic

125

C₄×C₈₉

#418

yes

characteristic

126

C₄×C₈₉

#478

yes

—

127

Dic₈₉

—

128

Dic₈₉

—

129

#8680

—

maximal, Sylow

130

C₂×C₈₉

—

131

C₂×C₈₉

#1804

yes

characteristic

132

C₂×C₈₉

#1812

yes

characteristic

133

C₂×C₈₉

#1814

yes

characteristic

134

D₈₉

—

135

#2931

—

136

#1835

—

137

#1564

D₈₉

yes

characteristic, complemented

138

#1517

—

139

#1286

—

140

C₈₉

#8680

yes

characteristic, complemented, Sylow

141

C₂×#131

—

178

—

142

#532

—

143

#436

—

144

#436

—

178

—

145

C₈×D₄

—

146

C₈×D₄

—

178

—

147

#431

C₂×D₈₉

yes

—

148

#423

—

149

#408

—

178

—

150

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

151

#382

—

152

#340

—

178

—

153

#340

—

178

—

154

#335

—

155

#334

—

156

#327

—

178

—

157

C₂×#41

—

178

—

158

#131

—

356

—

159

C₂×M₁₆

—

178

—

160

C₂×M₁₆

—

178

—

161

C₂²×C₈

—

178

—

162

C₂²×C₈

D₃₅₆

yes

characteristic

163

C₂²×C₈

D₃₅₆

yes

characteristic

164

C₄⋊Q₈

—

165

#127

—

166

#124

—

178

—

167

#121

—

168

#121

—

178

—

169

C₄×D₄

—

170

C₄×D₄

—

178

—

171

C₂×C₄⋊C₄

—

178

—

172

C₂×C₄²

C₂²×D₈₉

yes

characteristic

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

178

—

176

C₂²⋊C₈

—

177

C₂²⋊C₈

—

178

—

178

C₂²⋊C₈

—

178

—

179

C₄×C₈

—

180

C₄×C₈

C₄×D₈₉

yes

characteristic

181

C₄×C₈

C₄×D₈₉

yes

characteristic

182

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

183

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

184

#95

—

178

—

185

#95

—

178

—

186

#41

—

356

—

187

#41

—

356

—

188

C₂×Q₈

—

178

—

189

C₂×D₄

—

190

C₂×D₄

—

178

—

191

C₂×D₄

—

178

—

192

C₂×D₄

—

178

—

193

C₂²×C₄

—

356

—

194

C₂²×C₄

—

178

—

195

C₂²×C₄

D₄×D₈₉

yes

characteristic

196

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

197

C₂²×C₄

#13083575

yes

characteristic

198

M₁₆

—

356

—

199

M₁₆

—

356

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

356

—

204

C₂×C₈

—

178

—

205

C₂×C₈

#13083551

yes

characteristic

206

C₂×C₈

#13083551

yes

characteristic

207

C₂×C₈

#13083551

yes

characteristic

208

C₂×C₈

#13083551

yes

characteristic

209

C₄⋊C₄

—

210

C₄⋊C₄

—

356

—

211

C₄⋊C₄

—

356

—

212

C₄⋊C₄

—

178

—

213

C₂²⋊C₄

—

178

—

214

C₂²⋊C₄

—

178

—

215

C₄²

C₂×C₄×D₈₉

yes

characteristic

216

C₄²

C₂×C₂²⋊D₈₉

yes

characteristic

217

C₄²

Q₈×D₈₉

yes

characteristic

218

C₄²

#13083573

yes

characteristic

219

C₂³

—

178

—

220

C₂³

#15667987

yes

characteristic

221

Q₈

—

356

—

222

D₄

—

356

—

223

D₄

—

356

—

224

D₄

—

356

—

225

D₄

—

356

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

356

—

229

C₂×C₄

—

356

—

230

C₂×C₄

—

178

—

231

C₂×C₄

—

712

—

232

C₂×C₄

—

712

—

233

C₂×C₄

—

712

—

234

C₂×C₄

C₂×#13083551

yes

characteristic

235

C₂×C₄

C₄⋊C₄×D₈₉

yes

characteristic

236

C₂×C₄

#15667970

yes

characteristic

237

C₂×C₄

#15667983

yes

characteristic

238

C₂×C₄

#15667988

yes

characteristic

239

C₂×C₄

#15667992

yes

characteristic

240

C₂×C₄

#15668034

yes

—

241

C₂×C₄

#15668040

yes

—

242

C₈

—

243

C₈

—

244

C₈

—

245

C₈

—

246

C₈

—

247

C₈

—

356

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

356

—

251

C₂²

—

356

—

252

C₂²

—

356

—

253

C₂²

#19151455

yes

characteristic

254

C₂²

#19151814

yes

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

356

—

260

C₄

—

1424

—

261

C₄

#19151595

yes

characteristic

262

C₄

#19151604

yes

characteristic

263

C₄

#19151899

yes

—

264

C₂

—

265

C₂

—

712

—

266

C₂

#26020263

yes

characteristic

267

C₂

#26020295

yes

characteristic

268

C₂

#26020307

yes

characteristic

	subgroup	G/H
center	C₂²	#19151455
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1564	C₂
socle	C₂²×C₈₉	#380
prime radical	#19152148	C₂²
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1564	D₈₉
hypocenter	C₈₉	#8680
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

subgroup

G/H

center

C₂²

#19151455

commutator

C₄²×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1564

C₂

C₂²×C₈₉

C₂²

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

N	H ≅ G/N	type
2. #26020383	C₂	semidirect
4. #26018111	C₂	semidirect
5. C₈₉×#1564	C₂	semidirect
9. #19151677	C₄	semidirect
11. C₈×D₃₅₆	C₄	semidirect
137. #1564	D₈₉	semidirect
140. C₈₉	#8680	semidirect

H ≅ G/N

type

2. #26020383

C₂

semidirect

4. #26018111

C₂

semidirect

5. C₈₉×#1564

C₂

semidirect

9. #19151677

C₄

semidirect

11. C₈×D₃₅₆

C₄

semidirect

137. #1564

D₈₉

semidirect

140. C₈₉

#8680

semidirect

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

subgroup	index
#26028965	2
#26020383	2
#26018813	2
#26018111	2
C₈₉×#1564	2
#8680	89

subgroup

index

C₈₉×#1564

Subgroups — #36447663

Conjugacy classes of subgroups

Complements

Maximal subgroups