Group #36387239 — subgroups

Subgroups — C₈₉×#9391 #36387239

Order 22784.

538 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 154 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×#2972	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2563	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1800	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1548	C₂	1	2	yes	maximal, complemented
5	C₈₉×#1303	C₂	1	2	yes	maximal, complemented
6	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
8	C₈×D₄×C₈₉	—	2	4	no	—
9	#431×C₈₉	C₂²	1	2	yes	—
10	#423×C₈₉	C₂²	1	2	yes	—
11	C₂×#100×C₈₉	—	2	1	no	—
12	C₂×C₂²⋊C₈×C₈₉	—	2	2	no	—
13	#393×C₈₉	C₄	1	4	yes	—
14	#390×C₈₉	—	2	1	no	—
15	#382×C₈₉	—	2	1	no	—
16	#380×C₈₉	—	2	2	no	—
17	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
18	#343×C₈₉	—	2	1	no	—
19	#333×C₈₉	—	2	4	no	—
20	C₂²×Q₈×C₈₉	C₂×C₄	1	2	yes	—
21	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₈₉	D₄	1	2	yes	—
23	C₂×M₁₆×C₈₉	—	2	2	no	—
24	C₂²×C₈×C₈₉	—	2	4	no	—
25	C₄⋊Q₈×C₈₉	—	2	2	no	—
26	C₄⋊Q₈×C₈₉	—	2	2	no	—
27	C₄×D₄×C₈₉	—	2	2	no	—
28	C₄×D₄×C₈₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
34	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₈₉	—	2	1	no	—
36	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
37	C₄⋊C₈×C₈₉	—	2	2	no	—
38	C₄⋊C₈×C₈₉	—	2	2	no	—
39	C₄⋊C₈×C₈₉	D₄	1	4	yes	—
40	#100×C₈₉	—	4	2	no	—
41	C₂²⋊C₈×C₈₉	—	2	4	no	—
42	C₂²⋊C₈×C₈₉	—	2	2	no	—
43	C₄×C₈×C₈₉	—	2	2	no	—
44	#95×C₈₉	—	2	4	no	—
45	#95×C₈₉	C₂×C₄	1	2	yes	—
46	C₂⁴×C₈₉	C₂²⋊C₄	1	2	yes	—
47	C₂×Q₈×C₈₉	—	2	4	no	—
48	C₂×Q₈×C₈₉	—	8	2	no	—
49	C₂×D₄×C₈₉	—	2	2	no	—
50	C₂×D₄×C₈₉	—	2	2	no	—
51	C₂×D₄×C₈₉	SD₁₆	1	2	yes	—
52	C₂×D₄×C₈₉	Q₁₆	1	2	yes	—
53	C₂²×C₄×C₈₉	—	2	2	no	—
54	C₂²×C₄×C₈₉	—	2	2	no	—
55	C₂²×C₄×C₈₉	—	2	2	no	—
56	C₂²×C₄×C₈₉	—	2	2	no	—
57	C₂²×C₄×C₈₉	—	4	4	no	—
58	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
62	M₁₆×C₈₉	—	4	2	no	—
63	M₁₆×C₈₉	—	4	2	no	—
64	C₂×C₈×C₈₉	—	2	4	no	—
65	C₂×C₈×C₈₉	—	4	2	no	—
66	C₂×C₈×C₈₉	—	8	4	no	—
67	C₄⋊C₄×C₈₉	—	2	2	no	—
68	C₄⋊C₄×C₈₉	—	4	2	no	—
69	C₄⋊C₄×C₈₉	—	4	1	no	—
70	C₄⋊C₄×C₈₉	—	4	2	no	—
71	C₄⋊C₄×C₈₉	—	4	1	no	—
72	C₂²⋊C₄×C₈₉	—	2	4	no	—
73	C₂²⋊C₄×C₈₉	—	8	4	no	—
74	C₄²×C₈₉	—	4	2	no	—
75	C₄²×C₈₉	C₂×D₄	1	2	yes	—
76	C₄²×C₈₉	#41	1	2	yes	—
77	C₂³×C₈₉	—	2	2	no	—
78	C₂³×C₈₉	—	2	2	no	—
79	C₂³×C₈₉	—	4	2	no	—
80	C₂³×C₈₉	—	4	2	no	—
81	C₂³×C₈₉	#103	1	4	yes	—
82	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	Q₈×C₈₉	—	8	4	no	—
84	D₄×C₈₉	—	2	4	no	—
85	D₄×C₈₉	—	2	4	no	—
86	C₂×C₄×C₈₉	—	2	2	no	—
87	C₂×C₄×C₈₉	—	2	2	no	—
88	C₂×C₄×C₈₉	—	4	1	no	—
89	C₂×C₄×C₈₉	—	4	4	no	—
90	C₂×C₄×C₈₉	—	4	2	no	—
91	C₂×C₄×C₈₉	—	4	2	no	—
92	C₂×C₄×C₈₉	—	4	4	no	—
93	C₂×C₄×C₈₉	—	4	2	no	—
94	C₂×C₄×C₈₉	—	4	2	no	—
95	C₂×C₄×C₈₉	—	4	2	no	—
96	C₂×C₄×C₈₉	—	8	2	no	—
97	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
99	C₂×C₄×C₈₉	#121	1	2	yes	—
100	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
101	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
102	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
103	C₂×C₄×C₈₉	#135	1	2	yes	—
104	C₈×C₈₉	—	4	4	no	—
105	C₈×C₈₉	—	8	2	no	—
106	C₂²×C₈₉	—	2	1	no	—
107	C₂²×C₈₉	—	2	1	no	—
108	C₂²×C₈₉	—	2	4	no	—
109	C₂²×C₈₉	—	4	4	no	—
110	C₂²×C₈₉	—	4	2	no	—
111	C₂²×C₈₉	—	4	2	no	—
112	C₂²×C₈₉	—	8	2	no	—
113	C₂²×C₈₉	#386	1	1	yes	characteristic
114	C₂²×C₈₉	C₂×#103	1	1	yes	characteristic
115	C₂²×C₈₉	#416	1	1	yes	characteristic
116	C₄×C₈₉	—	2	1	no	—
117	C₄×C₈₉	—	2	2	no	—
118	C₄×C₈₉	—	4	2	no	—
119	C₄×C₈₉	—	8	2	no	—
120	C₄×C₈₉	—	8	2	no	—
121	C₄×C₈₉	#455	1	2	yes	—
122	C₄×C₈₉	#465	1	2	yes	—
123	C₄×C₈₉	#467	1	2	yes	—
124	#9391	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂×C₈₉	—	2	1	no	—
126	C₂×C₈₉	—	2	1	no	—
127	C₂×C₈₉	—	4	4	no	—
128	C₂×C₈₉	#1885	1	1	yes	characteristic
129	C₂×C₈₉	#1892	1	1	yes	characteristic
130	C₂×C₈₉	#1914	1	1	yes	characteristic
131	#2972	C₂×C₈₉	1	1	yes	characteristic
132	#2563	C₂×C₈₉	1	1	yes	characteristic
133	#1800	C₂×C₈₉	1	1	yes	characteristic
134	#1548	C₂×C₈₉	1	2	yes	complemented
135	#1303	C₂×C₈₉	1	2	yes	complemented
136	C₈₉	#9391	1	1	yes	characteristic, direct product factor, Sylow
137	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
138	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
139	C₈×D₄	—	2	4	no	—
140	#431	C₂²×C₈₉	1	2	yes	—
141	#423	C₂²×C₈₉	1	2	yes	—
142	C₂×#100	—	2	1	no	—
143	C₂×C₂²⋊C₈	—	2	2	no	—
144	#393	C₄×C₈₉	1	4	yes	—
145	#390	—	2	1	no	—
146	#382	—	2	1	no	—
147	#380	—	2	2	no	—
148	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
149	#343	—	2	1	no	—
150	#333	—	2	4	no	—
151	C₂²×Q₈	C₂×C₄×C₈₉	1	2	yes	—
152	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
153	C₂³×C₄	D₄×C₈₉	1	2	yes	—
154	C₂×M₁₆	—	2	2	no	—
155	C₂²×C₈	—	2	4	no	—
156	C₄⋊Q₈	—	2	2	no	—
157	C₄⋊Q₈	—	2	2	no	—
158	C₄×D₄	—	2	2	no	—
159	C₄×D₄	—	2	2	no	—
160	C₂×C₄⋊C₄	—	2	1	no	—
161	C₂×C₄⋊C₄	—	2	1	no	—
162	C₂×C₄⋊C₄	—	2	1	no	—
163	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
164	C₂×C₂²⋊C₄	—	2	4	no	—
165	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
166	C₂×C₄²	—	2	1	no	—
167	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
168	C₄⋊C₈	—	2	2	no	—
169	C₄⋊C₈	—	2	2	no	—
170	C₄⋊C₈	D₄×C₈₉	1	4	yes	—
171	#100	—	4	2	no	—
172	C₂²⋊C₈	—	2	4	no	—
173	C₂²⋊C₈	—	2	2	no	—
174	C₄×C₈	—	2	2	no	—
175	#95	—	2	4	no	—
176	#95	C₂×C₄×C₈₉	1	2	yes	—
177	C₂⁴	C₂²⋊C₄×C₈₉	1	2	yes	—
178	C₂×Q₈	—	2	4	no	—
179	C₂×Q₈	—	8	2	no	—
180	C₂×D₄	—	2	2	no	—
181	C₂×D₄	—	2	2	no	—
182	C₂×D₄	SD₁₆×C₈₉	1	2	yes	—
183	C₂×D₄	Q₁₆×C₈₉	1	2	yes	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	—	2	2	no	—
186	C₂²×C₄	—	2	2	no	—
187	C₂²×C₄	—	2	2	no	—
188	C₂²×C₄	—	4	4	no	—
189	C₂²×C₄	C₂²⋊C₄×C₈₉	1	2	yes	—
190	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
191	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
192	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
193	M₁₆	—	4	2	no	—
194	M₁₆	—	4	2	no	—
195	C₂×C₈	—	2	4	no	—
196	C₂×C₈	—	4	2	no	—
197	C₂×C₈	—	8	4	no	—
198	C₄⋊C₄	—	2	2	no	—
199	C₄⋊C₄	—	4	2	no	—
200	C₄⋊C₄	—	4	1	no	—
201	C₄⋊C₄	—	4	2	no	—
202	C₄⋊C₄	—	4	1	no	—
203	C₂²⋊C₄	—	2	4	no	—
204	C₂²⋊C₄	—	8	4	no	—
205	C₄²	—	4	2	no	—
206	C₄²	C₂×D₄×C₈₉	1	2	yes	—
207	C₄²	#41×C₈₉	1	2	yes	—
208	C₂³	—	2	2	no	—
209	C₂³	—	2	2	no	—
210	C₂³	—	4	2	no	—
211	C₂³	—	4	2	no	—
212	C₂³	#103×C₈₉	1	4	yes	—
213	C₂³	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
214	Q₈	—	8	4	no	—
215	D₄	—	2	4	no	—
216	D₄	—	2	4	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	4	1	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	4	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	8	2	no	—
228	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
229	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
230	C₂×C₄	#121×C₈₉	1	2	yes	—
231	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
232	C₂×C₄	C₂×SD₁₆×C₈₉	1	1	yes	characteristic
233	C₂×C₄	C₂×Q₁₆×C₈₉	1	1	yes	characteristic
234	C₂×C₄	#135×C₈₉	1	2	yes	—
235	C₈	—	4	4	no	—
236	C₈	—	8	2	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	—	2	4	no	—
240	C₂²	—	4	4	no	—
241	C₂²	—	4	2	no	—
242	C₂²	—	4	2	no	—
243	C₂²	—	8	2	no	—
244	C₂²	#386×C₈₉	1	1	yes	characteristic
245	C₂²	C₂×#103×C₈₉	1	1	yes	characteristic
246	C₂²	#416×C₈₉	1	1	yes	characteristic
247	C₄	—	2	1	no	—
248	C₄	—	2	2	no	—
249	C₄	—	4	2	no	—
250	C₄	—	8	2	no	—
251	C₄	—	8	2	no	—
252	C₄	#455×C₈₉	1	2	yes	—
253	C₄	#465×C₈₉	1	2	yes	—
254	C₄	#467×C₈₉	1	2	yes	—
255	C₂	—	2	1	no	—
256	C₂	—	2	1	no	—
257	C₂	—	4	4	no	—
258	C₂	C₈₉×#1885	1	1	yes	characteristic
259	C₂	C₈₉×#1892	1	1	yes	characteristic
260	C₂	C₈₉×#1914	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈₉×#2972

C₂

yes

maximal, characteristic

C₈₉×#2563

C₂

yes

maximal, characteristic

C₈₉×#1800

C₂

yes

maximal, characteristic

C₈₉×#1548

C₂

yes

maximal, complemented

C₈₉×#1303

C₂

yes

maximal, complemented

C₂×C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

C₂×C₄×D₄×C₈₉

C₂²

yes

characteristic

C₈×D₄×C₈₉

—

#431×C₈₉

C₂²

yes

—

#423×C₈₉

C₂²

yes

—

C₂×#100×C₈₉

—

C₂×C₂²⋊C₈×C₈₉

—

#393×C₈₉

C₄

yes

—

#390×C₈₉

—

#382×C₈₉

—

#380×C₈₉

—

C₄×C₄⋊C₄×C₈₉

C₂²

yes

characteristic

#343×C₈₉

—

#333×C₈₉

—

C₂²×Q₈×C₈₉

C₂×C₄

yes

—

C₂²×D₄×C₈₉

D₄

yes

characteristic

C₂³×C₄×C₈₉

D₄

yes

—

C₂×M₁₆×C₈₉

—

C₂²×C₈×C₈₉

—

C₄⋊Q₈×C₈₉

—

C₄⋊Q₈×C₈₉

—

C₄×D₄×C₈₉

—

C₄×D₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₈₉

—

C₂×C₂²⋊C₄×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

C₄⋊C₈×C₈₉

—

C₄⋊C₈×C₈₉

D₄

yes

—

#100×C₈₉

—

C₂²⋊C₈×C₈₉

—

C₂²⋊C₈×C₈₉

—

C₄×C₈×C₈₉

—

#95×C₈₉

—

#95×C₈₉

C₂×C₄

yes

—

C₂⁴×C₈₉

C₂²⋊C₄

yes

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

SD₁₆

yes

—

C₂×D₄×C₈₉

Q₁₆

yes

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

M₁₆×C₈₉

—

M₁₆×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

—

C₂²⋊C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

#103

yes

—

C₂³×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₈₉

—

D₄×C₈₉

—

D₄×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

C₄×D₄

yes

—

C₂×C₄×C₈₉

#120

yes

characteristic

C₂×C₄×C₈₉

#121

yes

—

100

C₂×C₄×C₈₉

#123

yes

characteristic

101

C₂×C₄×C₈₉

C₂×SD₁₆

yes

characteristic

102

C₂×C₄×C₈₉

C₂×Q₁₆

yes

characteristic

103

C₂×C₄×C₈₉

#135

yes

—

104

C₈×C₈₉

—

105

C₈×C₈₉

—

106

C₂²×C₈₉

—

107

C₂²×C₈₉

—

108

C₂²×C₈₉

—

109

C₂²×C₈₉

—

110

C₂²×C₈₉

—

111

C₂²×C₈₉

—

112

C₂²×C₈₉

—

113

C₂²×C₈₉

#386

yes

characteristic

114

C₂²×C₈₉

C₂×#103

yes

characteristic

115

C₂²×C₈₉

#416

yes

characteristic

116

C₄×C₈₉

—

117

C₄×C₈₉

—

118

C₄×C₈₉

—

119

C₄×C₈₉

—

120

C₄×C₈₉

—

121

C₄×C₈₉

#455

yes

—

122

C₄×C₈₉

#465

yes

—

123

C₄×C₈₉

#467

yes

—

124

#9391

C₈₉

yes

maximal, characteristic, direct product factor, Sylow

125

C₂×C₈₉

—

126

C₂×C₈₉

—

127

C₂×C₈₉

—

128

C₂×C₈₉

#1885

yes

characteristic

129

C₂×C₈₉

#1892

yes

characteristic

130

C₂×C₈₉

#1914

yes

characteristic

131

#2972

C₂×C₈₉

yes

characteristic

132

#2563

C₂×C₈₉

yes

characteristic

133

#1800

C₂×C₈₉

yes

characteristic

134

#1548

C₂×C₈₉

yes

complemented

135

#1303

C₂×C₈₉

yes

complemented

136

C₈₉

#9391

yes

characteristic, direct product factor, Sylow

137

C₂×C₄⋊Q₈

C₂²×C₈₉

yes

characteristic

138

C₂×C₄×D₄

C₂²×C₈₉

yes

characteristic

139

C₈×D₄

—

140

#431

C₂²×C₈₉

yes

—

141

#423

C₂²×C₈₉

yes

—

142

C₂×#100

—

143

C₂×C₂²⋊C₈

—

144

#393

C₄×C₈₉

yes

—

145

#390

—

146

#382

—

147

#380

—

148

C₄×C₄⋊C₄

C₂²×C₈₉

yes

characteristic

149

#343

—

150

#333

—

151

C₂²×Q₈

C₂×C₄×C₈₉

yes

—

152

C₂²×D₄

D₄×C₈₉

yes

characteristic

153

C₂³×C₄

D₄×C₈₉

yes

—

154

C₂×M₁₆

—

155

C₂²×C₈

—

156

C₄⋊Q₈

—

157

C₄⋊Q₈

—

158

C₄×D₄

—

159

C₄×D₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

D₄×C₈₉

yes

characteristic

164

C₂×C₂²⋊C₄

—

165

C₂×C₂²⋊C₄

C₂×C₄×C₈₉

yes

—

166

C₂×C₄²

—

167

C₂×C₄²

C₂³×C₈₉

yes

characteristic

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

C₄⋊C₈

D₄×C₈₉

yes

—

171

#100

—

172

C₂²⋊C₈

—

173

C₂²⋊C₈

—

174

C₄×C₈

—

175

#95

—

176

#95

C₂×C₄×C₈₉

yes

—

177

C₂⁴

C₂²⋊C₄×C₈₉

yes

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

SD₁₆×C₈₉

yes

—

183

C₂×D₄

Q₁₆×C₈₉

yes

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

C₂²⋊C₄×C₈₉

yes

—

190

C₂²×C₄

C₂²×C₄×C₈₉

yes

characteristic

191

C₂²×C₄

C₂×D₄×C₈₉

yes

characteristic

192

C₂²×C₄

C₂×D₄×C₈₉

yes

characteristic

193

M₁₆

—

194

M₁₆

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₄²

—

206

C₄²

C₂×D₄×C₈₉

yes

—

207

C₄²

#41×C₈₉

yes

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

#103×C₈₉

yes

—

213

C₂³

C₂×C₂²⋊C₄×C₈₉

yes

characteristic

214

Q₈

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

C₄×D₄×C₈₉

yes

—

229

C₂×C₄

#120×C₈₉

yes

characteristic

230

C₂×C₄

#121×C₈₉

yes

—

231

C₂×C₄

#123×C₈₉

yes

characteristic

232

C₂×C₄

C₂×SD₁₆×C₈₉

yes

characteristic

233

C₂×C₄

C₂×Q₁₆×C₈₉

yes

characteristic

234

C₂×C₄

#135×C₈₉

yes

—

235

C₈

—

236

C₈

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

#386×C₈₉

yes

characteristic

245

C₂²

C₂×#103×C₈₉

yes

characteristic

246

C₂²

#416×C₈₉

yes

characteristic

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

#455×C₈₉

yes

—

253

C₄

#465×C₈₉

yes

—

254

C₄

#467×C₈₉

yes

—

255

C₂

—

256

C₂

—

257

C₂

—

258

C₂

C₈₉×#1885

yes

characteristic

259

C₂

C₈₉×#1892

yes

characteristic

260

C₂

C₈₉×#1914

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₈₉
Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
prime radical	C₂²×D₄×C₈₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₈₉

#386

commutator

C₂²×C₄

C₂²×C₄×C₈₉

Frattini, cosocle

C₂×C₄²

C₂³×C₈₉

prime radical

C₂²×D₄×C₈₉

D₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

N	H ≅ G/N	type
4. C₈₉×#1548	C₂	semidirect
5. C₈₉×#1303	C₂	semidirect
124. #9391	C₈₉	direct (N × H)
134. #1548	C₂×C₈₉	semidirect
135. #1303	C₂×C₈₉	semidirect
136. C₈₉	#9391	direct (N × H)

H ≅ G/N

type

4. C₈₉×#1548

C₂

semidirect

5. C₈₉×#1303

C₂

semidirect

124. #9391

C₈₉

direct (N × H)

134. #1548

C₂×C₈₉

semidirect

135. #1303

C₂×C₈₉

semidirect

136. C₈₉

#9391

direct (N × H)

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

subgroup	index
C₈₉×#2972	2
C₈₉×#2563	2
C₈₉×#1800	2
C₈₉×#1548	2
C₈₉×#1303	2
#9391	89

subgroup

index

C₈₉×#2972

C₈₉×#2563

C₈₉×#1800

C₈₉×#1548

C₈₉×#1303

#9391

Subgroups — C₈₉×#9391 #36387239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C89×#9391 #36387239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#9391 #36387239