Group #36388200 — subgroups

Subgroups — C₈₉×#10352 #36388200

Order 22784.

416 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 138 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	C₈₉×#2571	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#1987	C₂	1	2	yes	maximal
3	C₈₉×#1956	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1296	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#1279	C₂	1	2	yes	maximal
6	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
8	C₂×#103×C₈₉	—	2	2	no	—
9	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
10	#400×C₈₉	—	2	2	no	—
11	#389×C₈₉	—	2	2	no	—
12	#384×C₈₉	C₂²	1	1	yes	characteristic
13	#382×C₈₉	—	2	2	no	—
14	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
15	#340×C₈₉	—	2	2	no	—
16	#340×C₈₉	—	2	2	no	—
17	C₂²×Q₈×C₈₉	—	2	1	no	—
18	C₂²×C₈×C₈₉	—	2	1	no	—
19	C₂²×C₈×C₈₉	—	2	2	no	—
20	C₄⋊Q₈×C₈₉	—	2	2	no	—
21	C₄⋊Q₈×C₈₉	—	2	1	no	—
22	C₄⋊Q₈×C₈₉	Q₈	1	2	yes	—
23	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
24	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
25	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
27	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
28	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
29	C₂×C₄²×C₈₉	—	2	2	no	—
30	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
31	C₄⋊C₈×C₈₉	—	2	2	no	—
32	C₄⋊C₈×C₈₉	—	2	2	no	—
33	#103×C₈₉	—	4	4	no	—
34	C₄×C₈×C₈₉	—	2	2	no	—
35	#95×C₈₉	—	2	2	no	—
36	#95×C₈₉	—	2	4	no	—
37	#95×C₈₉	—	2	2	no	—
38	C₂×Q₈×C₈₉	—	2	2	no	—
39	C₂×Q₈×C₈₉	—	4	2	no	—
40	C₂×Q₈×C₈₉	—	4	2	no	—
41	C₂×Q₈×C₈₉	—	4	1	no	—
42	C₂²×C₄×C₈₉	—	2	2	no	—
43	C₂²×C₄×C₈₉	—	2	2	no	—
44	C₂²×C₄×C₈₉	—	2	2	no	—
45	C₂²×C₄×C₈₉	—	4	1	no	—
46	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
48	C₂×C₈×C₈₉	—	2	2	no	—
49	C₂×C₈×C₈₉	—	4	1	no	—
50	C₂×C₈×C₈₉	—	4	1	no	—
51	C₂×C₈×C₈₉	—	4	2	no	—
52	C₂×C₈×C₈₉	—	4	2	no	—
53	C₂×C₈×C₈₉	—	4	2	no	—
54	C₄⋊C₄×C₈₉	—	2	4	no	—
55	C₄⋊C₄×C₈₉	—	2	2	no	—
56	C₄⋊C₄×C₈₉	—	2	2	no	—
57	C₄⋊C₄×C₈₉	—	2	2	no	—
58	C₄⋊C₄×C₈₉	—	2	2	no	—
59	C₄⋊C₄×C₈₉	—	4	2	no	—
60	C₄⋊C₄×C₈₉	—	4	2	no	—
61	C₄⋊C₄×C₈₉	—	4	2	no	—
62	C₄⋊C₄×C₈₉	—	4	2	no	—
63	C₄⋊C₄×C₈₉	—	8	2	no	—
64	C₄²×C₈₉	—	4	2	no	—
65	C₄²×C₈₉	—	4	2	no	—
66	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
67	C₄²×C₈₉	#41	1	2	yes	—
68	C₄²×C₈₉	#41	1	1	yes	characteristic
69	C₂³×C₈₉	#120	1	1	yes	characteristic
70	Q₈×C₈₉	—	4	4	no	—
71	Q₈×C₈₉	—	8	2	no	—
72	C₂×C₄×C₈₉	—	2	1	no	—
73	C₂×C₄×C₈₉	—	2	1	no	—
74	C₂×C₄×C₈₉	—	4	2	no	—
75	C₂×C₄×C₈₉	—	4	2	no	—
76	C₂×C₄×C₈₉	—	4	2	no	—
77	C₂×C₄×C₈₉	—	4	2	no	—
78	C₂×C₄×C₈₉	—	4	2	no	—
79	C₂×C₄×C₈₉	—	4	4	no	—
80	C₂×C₄×C₈₉	—	4	2	no	—
81	C₂×C₄×C₈₉	—	4	2	no	—
82	C₂×C₄×C₈₉	—	4	2	no	—
83	C₂×C₄×C₈₉	—	8	1	no	—
84	C₂×C₄×C₈₉	—	8	1	no	—
85	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
87	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
88	C₂×C₄×C₈₉	#124	1	2	yes	—
89	C₂×C₄×C₈₉	#135	1	2	yes	—
90	C₂×C₄×C₈₉	#135	1	2	yes	—
91	C₂×C₄×C₈₉	#137	1	2	yes	—
92	C₂×C₄×C₈₉	#137	1	2	yes	—
93	C₈×C₈₉	—	4	2	no	—
94	C₈×C₈₉	—	8	2	no	—
95	C₂²×C₈₉	#393	1	1	yes	characteristic
96	C₂²×C₈₉	#452	1	2	yes	—
97	C₂²×C₈₉	#452	1	2	yes	—
98	C₂²×C₈₉	#453	1	1	yes	characteristic
99	C₂²×C₈₉	#454	1	1	yes	characteristic
100	C₄×C₈₉	—	2	1	no	—
101	C₄×C₈₉	—	2	1	no	—
102	C₄×C₈₉	—	8	2	no	—
103	C₄×C₈₉	—	8	2	no	—
104	C₄×C₈₉	—	8	2	no	—
105	C₄×C₈₉	—	8	2	no	—
106	C₄×C₈₉	#479	1	2	yes	—
107	C₄×C₈₉	#479	1	2	yes	—
108	C₄×C₈₉	#488	1	2	yes	—
109	C₄×C₈₉	#491	1	2	yes	—
110	#10352	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂×C₈₉	#1630	1	1	yes	characteristic
112	C₂×C₈₉	#1634	1	1	yes	characteristic
113	C₂×C₈₉	#1638	1	2	yes	—
114	C₂×C₈₉	#2026	1	2	yes	—
115	C₂×C₈₉	#2027	1	1	yes	characteristic
116	#2571	C₂×C₈₉	1	1	yes	characteristic
117	#1987	C₂×C₈₉	1	2	yes	—
118	#1956	C₂×C₈₉	1	1	yes	characteristic
119	#1296	C₂×C₈₉	1	1	yes	characteristic
120	#1279	C₂×C₈₉	1	2	yes	—
121	C₈₉	#10352	1	1	yes	characteristic, direct product factor, Sylow
122	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
123	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
124	C₂×#103	—	2	2	no	—
125	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
126	#400	—	2	2	no	—
127	#389	—	2	2	no	—
128	#384	C₂²×C₈₉	1	1	yes	characteristic
129	#382	—	2	2	no	—
130	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
131	#340	—	2	2	no	—
132	#340	—	2	2	no	—
133	C₂²×Q₈	—	2	1	no	—
134	C₂²×C₈	—	2	1	no	—
135	C₂²×C₈	—	2	2	no	—
136	C₄⋊Q₈	—	2	2	no	—
137	C₄⋊Q₈	—	2	1	no	—
138	C₄⋊Q₈	Q₈×C₈₉	1	2	yes	—
139	C₂×C₄⋊C₄	—	2	2	no	—
140	C₂×C₄⋊C₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
143	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
144	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
145	C₂×C₄²	—	2	2	no	—
146	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	—	2	2	no	—
149	#103	—	4	4	no	—
150	C₄×C₈	—	2	2	no	—
151	#95	—	2	2	no	—
152	#95	—	2	4	no	—
153	#95	—	2	2	no	—
154	C₂×Q₈	—	2	2	no	—
155	C₂×Q₈	—	4	2	no	—
156	C₂×Q₈	—	4	2	no	—
157	C₂×Q₈	—	4	1	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	2	2	no	—
160	C₂²×C₄	—	2	2	no	—
161	C₂²×C₄	—	4	1	no	—
162	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
163	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
164	C₂×C₈	—	2	2	no	—
165	C₂×C₈	—	4	1	no	—
166	C₂×C₈	—	4	1	no	—
167	C₂×C₈	—	4	2	no	—
168	C₂×C₈	—	4	2	no	—
169	C₂×C₈	—	4	2	no	—
170	C₄⋊C₄	—	2	4	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	2	2	no	—
173	C₄⋊C₄	—	2	2	no	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	8	2	no	—
180	C₄²	—	4	2	no	—
181	C₄²	—	4	2	no	—
182	C₄²	C₂×Q₈×C₈₉	1	1	yes	characteristic
183	C₄²	#41×C₈₉	1	2	yes	—
184	C₄²	#41×C₈₉	1	1	yes	characteristic
185	C₂³	#120×C₈₉	1	1	yes	characteristic
186	Q₈	—	4	4	no	—
187	Q₈	—	8	2	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	4	2	no	—
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	4	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	8	1	no	—
200	C₂×C₄	—	8	1	no	—
201	C₂×C₄	C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
202	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
203	C₂×C₄	#124×C₈₉	1	1	yes	characteristic
204	C₂×C₄	#124×C₈₉	1	2	yes	—
205	C₂×C₄	#135×C₈₉	1	2	yes	—
206	C₂×C₄	#135×C₈₉	1	2	yes	—
207	C₂×C₄	#137×C₈₉	1	2	yes	—
208	C₂×C₄	#137×C₈₉	1	2	yes	—
209	C₈	—	4	2	no	—
210	C₈	—	8	2	no	—
211	C₂²	#393×C₈₉	1	1	yes	characteristic
212	C₂²	#452×C₈₉	1	2	yes	—
213	C₂²	#452×C₈₉	1	2	yes	—
214	C₂²	#453×C₈₉	1	1	yes	characteristic
215	C₂²	#454×C₈₉	1	1	yes	characteristic
216	C₄	—	2	1	no	—
217	C₄	—	2	1	no	—
218	C₄	—	8	2	no	—
219	C₄	—	8	2	no	—
220	C₄	—	8	2	no	—
221	C₄	—	8	2	no	—
222	C₄	#479×C₈₉	1	2	yes	—
223	C₄	#479×C₈₉	1	2	yes	—
224	C₄	#488×C₈₉	1	2	yes	—
225	C₄	#491×C₈₉	1	2	yes	—
226	C₂	C₈₉×#1630	1	1	yes	characteristic
227	C₂	C₈₉×#1634	1	1	yes	characteristic
228	C₂	C₈₉×#1638	1	2	yes	—
229	C₂	C₈₉×#2026	1	2	yes	—
230	C₂	C₈₉×#2027	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈₉×#2571

C₂

yes

maximal, characteristic

C₈₉×#1987

C₂

yes

maximal

C₈₉×#1956

C₂

yes

maximal, characteristic

C₈₉×#1296

C₂

yes

maximal, characteristic

C₈₉×#1279

C₂

yes

maximal

C₂×C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₈₉

C₂²

yes

—

C₂×#103×C₈₉

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

#400×C₈₉

—

#389×C₈₉

—

#384×C₈₉

C₂²

yes

characteristic

#382×C₈₉

—

C₄×C₄⋊C₄×C₈₉

C₂²

yes

—

#340×C₈₉

—

#340×C₈₉

—

C₂²×Q₈×C₈₉

—

C₂²×C₈×C₈₉

—

C₂²×C₈×C₈₉

—

C₄⋊Q₈×C₈₉

—

C₄⋊Q₈×C₈₉

—

C₄⋊Q₈×C₈₉

Q₈

yes

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

C₄⋊C₈×C₈₉

—

#103×C₈₉

—

C₄×C₈×C₈₉

—

#95×C₈₉

—

#95×C₈₉

—

#95×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂×Q₈

yes

characteristic

C₄²×C₈₉

#41

yes

—

C₄²×C₈₉

yes

C₂³×C₈₉

yes

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₈₉

#124

yes

characteristic

C₂×C₄×C₈₉

#124

yes

—

C₂×C₄×C₈₉

#135

yes

—

C₂×C₄×C₈₉

#135

yes

—

C₂×C₄×C₈₉

#137

yes

—

C₂×C₄×C₈₉

#137

yes

—

C₈×C₈₉

—

C₈×C₈₉

—

C₂²×C₈₉

#393

yes

characteristic

C₂²×C₈₉

#452

yes

—

C₂²×C₈₉

#452

yes

—

C₂²×C₈₉

yes

C₂²×C₈₉

yes

100

C₄×C₈₉

—

101

C₄×C₈₉

—

102

C₄×C₈₉

—

103

C₄×C₈₉

—

104

C₄×C₈₉

—

105

C₄×C₈₉

—

106

C₄×C₈₉

#479

yes

—

107

C₄×C₈₉

#479

yes

—

108

C₄×C₈₉

#488

yes

—

109

C₄×C₈₉

#491

yes

—

110

#10352

C₈₉

yes

maximal, characteristic, direct product factor, Sylow

111

C₂×C₈₉

#1630

yes

characteristic

112

C₂×C₈₉

#1634

yes

characteristic

113

C₂×C₈₉

#1638

yes

—

114

C₂×C₈₉

#2026

yes

—

115

C₂×C₈₉

#2027

yes

characteristic

116

#2571

C₂×C₈₉

yes

characteristic

117

#1987

C₂×C₈₉

yes

—

118

#1956

C₂×C₈₉

yes

characteristic

119

#1296

C₂×C₈₉

yes

characteristic

120

#1279

C₂×C₈₉

yes

—

121

C₈₉

#10352

yes

characteristic, direct product factor, Sylow

122

C₂×C₄⋊Q₈

C₂²×C₈₉

yes

characteristic

123

C₂×C₄⋊C₈

C₂²×C₈₉

yes

—

124

C₂×#103

—

125

C₂×C₄×C₈

C₂²×C₈₉

yes

characteristic

126

#400

—

127

#389

—

128

#384

C₂²×C₈₉

yes

characteristic

129

#382

—

130

C₄×C₄⋊C₄

C₂²×C₈₉

yes

—

131

#340

—

132

#340

—

133

C₂²×Q₈

—

134

C₂²×C₈

—

135

C₂²×C₈

—

136

C₄⋊Q₈

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

Q₈×C₈₉

yes

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

D₄×C₈₉

yes

—

143

C₂×C₄⋊C₄

D₄×C₈₉

yes

—

144

C₂×C₄⋊C₄

D₄×C₈₉

yes

—

145

C₂×C₄²

—

146

C₂×C₄²

C₂³×C₈₉

yes

characteristic

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

#103

—

150

C₄×C₈

—

151

#95

—

152

#95

—

153

#95

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

C₂×D₄×C₈₉

yes

characteristic

163

C₂²×C₄

C₂×D₄×C₈₉

yes

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄²

—

181

C₄²

—

182

C₄²

C₂×Q₈×C₈₉

yes

characteristic

183

C₄²

#41×C₈₉

yes

—

184

C₄²

#41×C₈₉

yes

characteristic

185

C₂³

#120×C₈₉

yes

characteristic

186

Q₈

—

187

Q₈

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

C₂²⋊Q₈×C₈₉

yes

characteristic

202

C₂×C₄

C₂²⋊Q₈×C₈₉

yes

—

203

C₂×C₄

#124×C₈₉

yes

characteristic

204

C₂×C₄

#124×C₈₉

yes

—

205

C₂×C₄

#135×C₈₉

yes

—

206

C₂×C₄

#135×C₈₉

yes

—

207

C₂×C₄

#137×C₈₉

yes

—

208

C₂×C₄

#137×C₈₉

yes

—

209

C₈

—

210

C₈

—

211

C₂²

#393×C₈₉

yes

characteristic

212

C₂²

#452×C₈₉

yes

—

213

C₂²

#452×C₈₉

yes

—

214

C₂²

#453×C₈₉

yes

characteristic

215

C₂²

#454×C₈₉

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

#479×C₈₉

yes

—

223

C₄

#479×C₈₉

yes

—

224

C₄

#488×C₈₉

yes

—

225

C₄

#491×C₈₉

yes

—

226

C₂

C₈₉×#1630

yes

characteristic

227

C₂

C₈₉×#1634

yes

characteristic

228

C₂

C₈₉×#1638

yes

—

229

C₂

C₈₉×#2026

yes

—

230

C₂

C₈₉×#2027

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₈₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₈₉

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₈₉

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

N	H ≅ G/N	type
110. #10352	C₈₉	direct (N × H)
121. C₈₉	#10352	direct (N × H)

H ≅ G/N

type

110. #10352

C₈₉

direct (N × H)

121. C₈₉

#10352

direct (N × H)

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

subgroup	index
C₈₉×#2571	2
C₈₉×#1987	2
C₈₉×#1956	2
C₈₉×#1296	2
C₈₉×#1279	2
#10352	89

subgroup

index

C₈₉×#2571

C₈₉×#1987

C₈₉×#1956

C₈₉×#1296

C₈₉×#1279

#10352

Subgroups — C₈₉×#10352 #36388200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C89×#10352 #36388200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#10352 #36388200