Group #36387251 — subgroups

Subgroups — C₈₉×#9403 #36387251

Order 22784.

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

normal subgroups only

This group has 570 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×#2975	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2542	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1800	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1549	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×C₂²⋊Q₈×C₈₉	—	2	2	no	—
8	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
9	#436×C₈₉	—	2	4	no	—
10	#431×C₈₉	C₂²	1	2	yes	—
11	#423×C₈₉	C₂²	1	2	yes	—
12	C₂×#100×C₈₉	—	2	1	no	—
13	#407×C₈₉	—	2	2	no	—
14	#399×C₈₉	C₄	1	4	yes	—
15	#390×C₈₉	—	2	1	no	—
16	#384×C₈₉	—	2	1	no	—
17	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
18	#343×C₈₉	—	2	1	no	—
19	#332×C₈₉	—	2	4	no	—
20	C₂²×Q₈×C₈₉	—	2	1	no	—
21	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₈₉	D₄	1	2	yes	—
23	C₂×M₁₆×C₈₉	—	2	4	no	—
24	C₂×M₁₆×C₈₉	—	2	2	no	—
25	C₄⋊Q₈×C₈₉	—	2	2	no	—
26	C₄⋊Q₈×C₈₉	—	2	2	no	—
27	C₂²⋊Q₈×C₈₉	—	4	8	no	—
28	C₄×D₄×C₈₉	—	2	2	no	—
29	C₄×D₄×C₈₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
32	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
34	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
36	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₈₉	—	2	1	no	—
38	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
39	C₄⋊C₈×C₈₉	—	2	2	no	—
40	C₄⋊C₈×C₈₉	—	2	2	no	—
41	C₄⋊C₈×C₈₉	D₄	1	4	yes	—
42	#100×C₈₉	—	4	2	no	—
43	C₂²⋊C₈×C₈₉	—	2	4	no	—
44	C₂²⋊C₈×C₈₉	—	2	2	no	—
45	C₄×C₈×C₈₉	—	2	2	no	—
46	#95×C₈₉	C₂×C₄	1	2	yes	—
47	C₂⁴×C₈₉	C₂²⋊C₄	1	2	yes	—
48	C₂×Q₈×C₈₉	—	4	4	no	—
49	C₂×Q₈×C₈₉	—	4	1	no	—
50	C₂×Q₈×C₈₉	—	4	1	no	—
51	C₂×D₄×C₈₉	—	2	2	no	—
52	C₂×D₄×C₈₉	—	2	1	no	—
53	C₂×D₄×C₈₉	—	2	2	no	—
54	C₂×D₄×C₈₉	—	2	1	no	—
55	C₂²×C₄×C₈₉	—	2	2	no	—
56	C₂²×C₄×C₈₉	—	2	2	no	—
57	C₂²×C₄×C₈₉	—	2	2	no	—
58	C₂²×C₄×C₈₉	—	2	2	no	—
59	C₂²×C₄×C₈₉	—	4	4	no	—
60	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
64	M₁₆×C₈₉	—	4	2	no	—
65	M₁₆×C₈₉	—	4	2	no	—
66	M₁₆×C₈₉	—	8	4	no	—
67	C₂×C₈×C₈₉	—	2	4	no	—
68	C₂×C₈×C₈₉	—	4	2	no	—
69	C₄⋊C₄×C₈₉	—	2	4	no	—
70	C₄⋊C₄×C₈₉	—	2	2	no	—
71	C₄⋊C₄×C₈₉	—	2	4	no	—
72	C₄⋊C₄×C₈₉	—	4	8	no	—
73	C₄⋊C₄×C₈₉	—	4	2	no	—
74	C₂²⋊C₄×C₈₉	—	2	4	no	—
75	C₂²⋊C₄×C₈₉	—	4	8	no	—
76	C₄²×C₈₉	—	4	1	no	—
77	C₄²×C₈₉	—	4	1	no	—
78	C₄²×C₈₉	C₂×D₄	1	2	yes	—
79	C₄²×C₈₉	#41	1	2	yes	—
80	C₂³×C₈₉	—	2	2	no	—
81	C₂³×C₈₉	—	2	2	no	—
82	C₂³×C₈₉	—	2	2	no	—
83	C₂³×C₈₉	—	4	2	no	—
84	C₂³×C₈₉	—	4	2	no	—
85	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	Q₈×C₈₉	—	8	2	no	—
87	Q₈×C₈₉	—	8	2	no	—
88	D₄×C₈₉	—	4	2	no	—
89	D₄×C₈₉	—	4	2	no	—
90	C₂×C₄×C₈₉	—	2	2	no	—
91	C₂×C₄×C₈₉	—	2	4	no	—
92	C₂×C₄×C₈₉	—	2	2	no	—
93	C₂×C₄×C₈₉	—	4	1	no	—
94	C₂×C₄×C₈₉	—	4	2	no	—
95	C₂×C₄×C₈₉	—	4	2	no	—
96	C₂×C₄×C₈₉	—	4	4	no	—
97	C₂×C₄×C₈₉	—	4	2	no	—
98	C₂×C₄×C₈₉	—	4	4	no	—
99	C₂×C₄×C₈₉	—	4	2	no	—
100	C₂×C₄×C₈₉	—	8	2	no	—
101	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
102	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
103	C₂×C₄×C₈₉	#121	1	2	yes	—
104	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
105	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
106	C₂×C₄×C₈₉	#137	1	2	yes	—
107	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
108	C₈×C₈₉	—	4	4	no	—
109	C₈×C₈₉	—	8	2	no	—
110	C₂²×C₈₉	—	2	1	no	—
111	C₂²×C₈₉	—	2	1	no	—
112	C₂²×C₈₉	—	4	4	no	—
113	C₂²×C₈₉	—	4	2	no	—
114	C₂²×C₈₉	—	4	2	no	—
115	C₂²×C₈₉	—	4	2	no	—
116	C₂²×C₈₉	—	8	2	no	—
117	C₂²×C₈₉	#386	1	1	yes	characteristic
118	C₂²×C₈₉	#417	1	1	yes	characteristic
119	C₂²×C₈₉	#419	1	1	yes	characteristic
120	C₄×C₈₉	—	2	1	no	—
121	C₄×C₈₉	—	2	2	no	—
122	C₄×C₈₉	—	4	4	no	—
123	C₄×C₈₉	—	4	2	no	—
124	C₄×C₈₉	—	8	2	no	—
125	C₄×C₈₉	#453	1	2	yes	—
126	C₄×C₈₉	#468	1	2	yes	—
127	C₄×C₈₉	#470	1	2	yes	—
128	#9403	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂×C₈₉	—	2	1	no	—
130	C₂×C₈₉	—	2	1	no	—
131	C₂×C₈₉	—	8	2	no	—
132	C₂×C₈₉	#1887	1	1	yes	characteristic
133	C₂×C₈₉	#1894	1	1	yes	characteristic
134	C₂×C₈₉	#1915	1	1	yes	characteristic
135	#2975	C₂×C₈₉	1	1	yes	characteristic
136	#2542	C₂×C₈₉	1	1	yes	characteristic
137	#1800	C₂×C₈₉	1	1	yes	characteristic
138	#1549	C₂×C₈₉	1	2	yes	complemented
139	#1303	C₂×C₈₉	1	2	yes	complemented
140	C₈₉	#9403	1	1	yes	characteristic, direct product factor, Sylow
141	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
142	C₂×C₂²⋊Q₈	—	2	2	no	—
143	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
144	#436	—	2	4	no	—
145	#431	C₂²×C₈₉	1	2	yes	—
146	#423	C₂²×C₈₉	1	2	yes	—
147	C₂×#100	—	2	1	no	—
148	#407	—	2	2	no	—
149	#399	C₄×C₈₉	1	4	yes	—
150	#390	—	2	1	no	—
151	#384	—	2	1	no	—
152	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
153	#343	—	2	1	no	—
154	#332	—	2	4	no	—
155	C₂²×Q₈	—	2	1	no	—
156	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
157	C₂³×C₄	D₄×C₈₉	1	2	yes	—
158	C₂×M₁₆	—	2	4	no	—
159	C₂×M₁₆	—	2	2	no	—
160	C₄⋊Q₈	—	2	2	no	—
161	C₄⋊Q₈	—	2	2	no	—
162	C₂²⋊Q₈	—	4	8	no	—
163	C₄×D₄	—	2	2	no	—
164	C₄×D₄	—	2	2	no	—
165	C₂×C₄⋊C₄	—	2	1	no	—
166	C₂×C₄⋊C₄	—	2	4	no	—
167	C₂×C₄⋊C₄	—	2	1	no	—
168	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
169	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
170	C₂×C₂²⋊C₄	—	2	4	no	—
171	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
172	C₂×C₄²	—	2	1	no	—
173	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
174	C₄⋊C₈	—	2	2	no	—
175	C₄⋊C₈	—	2	2	no	—
176	C₄⋊C₈	D₄×C₈₉	1	4	yes	—
177	#100	—	4	2	no	—
178	C₂²⋊C₈	—	2	4	no	—
179	C₂²⋊C₈	—	2	2	no	—
180	C₄×C₈	—	2	2	no	—
181	#95	C₂×C₄×C₈₉	1	2	yes	—
182	C₂⁴	C₂²⋊C₄×C₈₉	1	2	yes	—
183	C₂×Q₈	—	4	4	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	—	4	1	no	—
186	C₂×D₄	—	2	2	no	—
187	C₂×D₄	—	2	1	no	—
188	C₂×D₄	—	2	2	no	—
189	C₂×D₄	—	2	1	no	—
190	C₂²×C₄	—	2	2	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	4	4	no	—
195	C₂²×C₄	C₂²⋊C₄×C₈₉	1	2	yes	—
196	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
197	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
198	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
199	M₁₆	—	4	2	no	—
200	M₁₆	—	4	2	no	—
201	M₁₆	—	8	4	no	—
202	C₂×C₈	—	2	4	no	—
203	C₂×C₈	—	4	2	no	—
204	C₄⋊C₄	—	2	4	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	2	4	no	—
207	C₄⋊C₄	—	4	8	no	—
208	C₄⋊C₄	—	4	2	no	—
209	C₂²⋊C₄	—	2	4	no	—
210	C₂²⋊C₄	—	4	8	no	—
211	C₄²	—	4	1	no	—
212	C₄²	—	4	1	no	—
213	C₄²	C₂×D₄×C₈₉	1	2	yes	—
214	C₄²	#41×C₈₉	1	2	yes	—
215	C₂³	—	2	2	no	—
216	C₂³	—	2	2	no	—
217	C₂³	—	2	2	no	—
218	C₂³	—	4	2	no	—
219	C₂³	—	4	2	no	—
220	C₂³	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
221	Q₈	—	8	2	no	—
222	Q₈	—	8	2	no	—
223	D₄	—	4	2	no	—
224	D₄	—	4	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	4	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	4	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	4	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	8	2	no	—
236	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
237	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
238	C₂×C₄	#121×C₈₉	1	2	yes	—
239	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
240	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
241	C₂×C₄	#137×C₈₉	1	2	yes	—
242	C₂×C₄	#137×C₈₉	1	1	yes	characteristic
243	C₈	—	4	4	no	—
244	C₈	—	8	2	no	—
245	C₂²	—	2	1	no	—
246	C₂²	—	2	1	no	—
247	C₂²	—	4	4	no	—
248	C₂²	—	4	2	no	—
249	C₂²	—	4	2	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	8	2	no	—
252	C₂²	#386×C₈₉	1	1	yes	characteristic
253	C₂²	#417×C₈₉	1	1	yes	characteristic
254	C₂²	#419×C₈₉	1	1	yes	characteristic
255	C₄	—	2	1	no	—
256	C₄	—	2	2	no	—
257	C₄	—	4	4	no	—
258	C₄	—	4	2	no	—
259	C₄	—	8	2	no	—
260	C₄	#453×C₈₉	1	2	yes	—
261	C₄	#468×C₈₉	1	2	yes	—
262	C₄	#470×C₈₉	1	2	yes	—
263	C₂	—	2	1	no	—
264	C₂	—	2	1	no	—
265	C₂	—	8	2	no	—
266	C₂	C₈₉×#1887	1	1	yes	characteristic
267	C₂	C₈₉×#1894	1	1	yes	characteristic
268	C₂	C₈₉×#1915	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈₉×#2975

C₂

yes

maximal, characteristic

C₈₉×#2542

C₂

yes

maximal, characteristic

C₈₉×#1800

C₂

yes

maximal, characteristic

C₈₉×#1549

C₂

yes

maximal, complemented

C₈₉×#1303

C₂

yes

maximal, complemented

C₂×C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

C₂×C₂²⋊Q₈×C₈₉

—

C₂×C₄×D₄×C₈₉

C₂²

yes

characteristic

#436×C₈₉

—

#431×C₈₉

C₂²

yes

—

#423×C₈₉

C₂²

yes

—

C₂×#100×C₈₉

—

#407×C₈₉

—

#399×C₈₉

C₄

yes

—

#390×C₈₉

—

#384×C₈₉

—

C₄×C₄⋊C₄×C₈₉

C₂²

yes

characteristic

#343×C₈₉

—

#332×C₈₉

—

C₂²×Q₈×C₈₉

—

C₂²×D₄×C₈₉

D₄

yes

characteristic

C₂³×C₄×C₈₉

D₄

yes

—

C₂×M₁₆×C₈₉

—

C₂×M₁₆×C₈₉

—

C₄⋊Q₈×C₈₉

—

C₄⋊Q₈×C₈₉

—

C₂²⋊Q₈×C₈₉

—

C₄×D₄×C₈₉

—

C₄×D₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

C₂×C₄

yes

—

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

C₂×C₄

yes

—

C₂⁴×C₈₉

C₂²⋊C₄

yes

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

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

—

M₁₆×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

—

C₄²×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₈₉

—

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

—

100

C₂×C₄×C₈₉

—

101

C₂×C₄×C₈₉

C₄×D₄

yes

—

102

C₂×C₄×C₈₉

#120

yes

characteristic

103

C₂×C₄×C₈₉

#121

yes

—

104

C₂×C₄×C₈₉

#123

yes

characteristic

105

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

characteristic

106

C₂×C₄×C₈₉

#137

yes

—

107

C₂×C₄×C₈₉

#137

yes

characteristic

108

C₈×C₈₉

—

109

C₈×C₈₉

—

110

C₂²×C₈₉

—

111

C₂²×C₈₉

—

112

C₂²×C₈₉

—

113

C₂²×C₈₉

—

114

C₂²×C₈₉

—

115

C₂²×C₈₉

—

116

C₂²×C₈₉

—

117

C₂²×C₈₉

#386

yes

characteristic

118

C₂²×C₈₉

#417

yes

characteristic

119

C₂²×C₈₉

#419

yes

characteristic

120

C₄×C₈₉

—

121

C₄×C₈₉

—

122

C₄×C₈₉

—

123

C₄×C₈₉

—

124

C₄×C₈₉

—

125

C₄×C₈₉

#453

yes

—

126

C₄×C₈₉

#468

yes

—

127

C₄×C₈₉

#470

yes

—

128

#9403

C₈₉

yes

maximal, characteristic, direct product factor, Sylow

129

C₂×C₈₉

—

130

C₂×C₈₉

—

131

C₂×C₈₉

—

132

C₂×C₈₉

#1887

yes

characteristic

133

C₂×C₈₉

#1894

yes

characteristic

134

C₂×C₈₉

#1915

yes

characteristic

135

#2975

C₂×C₈₉

yes

characteristic

136

#2542

C₂×C₈₉

yes

characteristic

137

#1800

C₂×C₈₉

yes

characteristic

138

#1549

C₂×C₈₉

yes

complemented

139

#1303

C₂×C₈₉

yes

complemented

140

C₈₉

#9403

yes

characteristic, direct product factor, Sylow

141

C₂×C₄⋊Q₈

C₂²×C₈₉

yes

characteristic

142

C₂×C₂²⋊Q₈

—

143

C₂×C₄×D₄

C₂²×C₈₉

yes

characteristic

144

#436

—

145

#431

C₂²×C₈₉

yes

—

146

#423

C₂²×C₈₉

yes

—

147

C₂×#100

—

148

#407

—

149

#399

C₄×C₈₉

yes

—

150

#390

—

151

#384

—

152

C₄×C₄⋊C₄

C₂²×C₈₉

yes

characteristic

153

#343

—

154

#332

—

155

C₂²×Q₈

—

156

C₂²×D₄

D₄×C₈₉

yes

characteristic

157

C₂³×C₄

D₄×C₈₉

yes

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

C₂²⋊Q₈

—

163

C₄×D₄

—

164

C₄×D₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

C₂×C₄×C₈₉

yes

—

169

C₂×C₄⋊C₄

D₄×C₈₉

yes

characteristic

170

C₂×C₂²⋊C₄

—

171

C₂×C₂²⋊C₄

C₂×C₄×C₈₉

yes

—

172

C₂×C₄²

—

173

C₂×C₄²

C₂³×C₈₉

yes

characteristic

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

D₄×C₈₉

yes

—

177

#100

—

178

C₂²⋊C₈

—

179

C₂²⋊C₈

—

180

C₄×C₈

—

181

#95

C₂×C₄×C₈₉

yes

—

182

C₂⁴

C₂²⋊C₄×C₈₉

yes

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

C₂²⋊C₄×C₈₉

yes

—

196

C₂²×C₄

C₂²×C₄×C₈₉

yes

characteristic

197

C₂²×C₄

C₂×D₄×C₈₉

yes

characteristic

198

C₂²×C₄

C₂×D₄×C₈₉

yes

characteristic

199

M₁₆

—

200

M₁₆

—

201

M₁₆

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₂²⋊C₄

—

210

C₂²⋊C₄

—

211

C₄²

—

212

C₄²

—

213

C₄²

C₂×D₄×C₈₉

yes

—

214

C₄²

#41×C₈₉

yes

—

215

C₂³

—

216

C₂³

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

C₂×C₂²⋊C₄×C₈₉

yes

characteristic

221

Q₈

—

222

Q₈

—

223

D₄

—

224

D₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

C₄×D₄×C₈₉

yes

—

237

C₂×C₄

#120×C₈₉

yes

characteristic

238

C₂×C₄

#121×C₈₉

yes

—

239

C₂×C₄

#123×C₈₉

yes

characteristic

240

C₂×C₄

AGL(1,ℤ/8)×C₈₉

yes

characteristic

241

C₂×C₄

#137×C₈₉

yes

—

242

C₂×C₄

#137×C₈₉

yes

characteristic

243

C₈

—

244

C₈

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

#386×C₈₉

yes

characteristic

253

C₂²

#417×C₈₉

yes

characteristic

254

C₂²

#419×C₈₉

yes

characteristic

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

#453×C₈₉

yes

—

261

C₄

#468×C₈₉

yes

—

262

C₄

#470×C₈₉

yes

—

263

C₂

—

264

C₂

—

265

C₂

—

266

C₂

C₈₉×#1887

yes

characteristic

267

C₂

C₈₉×#1894

yes

characteristic

268

C₂

C₈₉×#1915

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×#1549	C₂	semidirect
5. C₈₉×#1303	C₂	semidirect
128. #9403	C₈₉	direct (N × H)
138. #1549	C₂×C₈₉	semidirect
139. #1303	C₂×C₈₉	semidirect
140. C₈₉	#9403	direct (N × H)

H ≅ G/N

type

4. C₈₉×#1549

C₂

semidirect

5. C₈₉×#1303

C₂

semidirect

128. #9403

C₈₉

direct (N × H)

138. #1549

C₂×C₈₉

semidirect

139. #1303

C₂×C₈₉

semidirect

140. C₈₉

#9403

direct (N × H)

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

subgroup	index
C₈₉×#2975	2
C₈₉×#2542	2
C₈₉×#1800	2
C₈₉×#1549	2
C₈₉×#1303	2
#9403	89

subgroup

index

C₈₉×#2975

C₈₉×#2542

C₈₉×#1800

C₈₉×#1549

C₈₉×#1303

#9403

Subgroups — C₈₉×#9403 #36387251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C89×#9403 #36387251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#9403 #36387251