Group #36388199 — subgroups

Subgroups — C₈₉×#10351 #36388199

Order 22784.

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

normal subgroups only

This group has 500 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, complemented
2	C₈₉×#1982	C₂	1	2	yes	maximal
3	C₈₉×#1957	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1279	C₂	1	2	yes	maximal, complemented
6	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
8	C₂×#102×C₈₉	—	2	2	no	—
9	C₂×#102×C₈₉	—	2	2	no	—
10	C₂×#102×C₈₉	—	2	2	no	—
11	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
12	#400×C₈₉	—	2	2	no	—
13	#389×C₈₉	—	2	2	no	—
14	#384×C₈₉	C₂²	1	1	yes	characteristic
15	#382×C₈₉	—	2	2	no	—
16	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
17	C₂²×D₄×C₈₉	—	2	1	no	—
18	C₂²×D₄×C₈₉	—	2	2	no	—
19	C₂²×C₈×C₈₉	—	2	1	no	—
20	C₂²×C₈×C₈₉	—	2	2	no	—
21	#127×C₈₉	—	2	2	no	—
22	#127×C₈₉	—	2	1	no	—
23	#127×C₈₉	Q₈	1	2	yes	—
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	#102×C₈₉	—	4	4	no	—
34	#102×C₈₉	—	4	4	no	—
35	#102×C₈₉	—	4	4	no	—
36	C₄×C₈×C₈₉	—	2	2	no	—
37	#95×C₈₉	—	2	2	no	—
38	#95×C₈₉	—	2	4	no	—
39	#95×C₈₉	—	2	2	no	—
40	C₂⁴×C₈₉	—	4	1	no	—
41	C₂×D₄×C₈₉	—	2	2	no	—
42	C₂×D₄×C₈₉	—	2	4	no	—
43	C₂×D₄×C₈₉	—	4	2	no	—
44	C₂×D₄×C₈₉	—	4	2	no	—
45	C₂×D₄×C₈₉	—	4	1	no	—
46	C₂×D₄×C₈₉	—	4	2	no	—
47	C₂×D₄×C₈₉	—	4	2	no	—
48	C₂×D₄×C₈₉	—	4	2	no	—
49	C₂×D₄×C₈₉	—	4	2	no	—
50	C₂×D₄×C₈₉	—	4	2	no	—
51	C₂²×C₄×C₈₉	—	2	2	no	—
52	C₂²×C₄×C₈₉	—	2	2	no	—
53	C₂²×C₄×C₈₉	—	2	2	no	—
54	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
56	C₂×C₈×C₈₉	—	2	2	no	—
57	C₂×C₈×C₈₉	—	4	1	no	—
58	C₂×C₈×C₈₉	—	4	1	no	—
59	C₂×C₈×C₈₉	—	4	2	no	—
60	C₂×C₈×C₈₉	—	4	2	no	—
61	C₂×C₈×C₈₉	—	4	2	no	—
62	C₄⋊C₄×C₈₉	—	2	2	no	—
63	C₄⋊C₄×C₈₉	—	2	2	no	—
64	C₄⋊C₄×C₈₉	—	2	2	no	—
65	C₄⋊C₄×C₈₉	—	2	2	no	—
66	C₄⋊C₄×C₈₉	—	4	2	no	—
67	C₄⋊C₄×C₈₉	—	4	2	no	—
68	C₄⋊C₄×C₈₉	—	4	2	no	—
69	C₄⋊C₄×C₈₉	—	8	2	no	—
70	C₄²×C₈₉	—	4	2	no	—
71	C₄²×C₈₉	—	4	2	no	—
72	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
73	C₄²×C₈₉	#41	1	2	yes	—
74	C₄²×C₈₉	#41	1	1	yes	characteristic
75	C₂³×C₈₉	—	4	2	no	—
76	C₂³×C₈₉	—	8	2	no	—
77	C₂³×C₈₉	—	8	2	no	—
78	C₂³×C₈₉	—	8	1	no	—
79	C₂³×C₈₉	—	8	1	no	—
80	C₂³×C₈₉	#120	1	1	yes	characteristic
81	D₄×C₈₉	—	4	4	no	—
82	D₄×C₈₉	—	4	4	no	—
83	D₄×C₈₉	—	4	4	no	—
84	D₄×C₈₉	—	8	2	no	—
85	D₄×C₈₉	—	8	2	no	—
86	D₄×C₈₉	—	8	2	no	—
87	C₂×C₄×C₈₉	—	2	1	no	—
88	C₂×C₄×C₈₉	—	2	1	no	—
89	C₂×C₄×C₈₉	—	4	2	no	—
90	C₂×C₄×C₈₉	—	4	2	no	—
91	C₂×C₄×C₈₉	—	4	2	no	—
92	C₂×C₄×C₈₉	—	4	2	no	—
93	C₂×C₄×C₈₉	—	4	4	no	—
94	C₂×C₄×C₈₉	—	4	2	no	—
95	C₂×C₄×C₈₉	—	4	2	no	—
96	C₂×C₄×C₈₉	—	4	2	no	—
97	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
98	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
99	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
100	C₂×C₄×C₈₉	#124	1	2	yes	—
101	C₂×C₄×C₈₉	#135	1	2	yes	—
102	C₂×C₄×C₈₉	#135	1	2	yes	—
103	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
104	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
105	C₈×C₈₉	—	4	2	no	—
106	C₈×C₈₉	—	8	2	no	—
107	C₂²×C₈₉	—	8	4	no	—
108	C₂²×C₈₉	—	8	2	no	—
109	C₂²×C₈₉	—	16	1	no	—
110	C₂²×C₈₉	—	16	1	no	—
111	C₂²×C₈₉	—	16	2	no	—
112	C₂²×C₈₉	#393	1	1	yes	characteristic
113	C₂²×C₈₉	#449	1	2	yes	—
114	C₂²×C₈₉	#449	1	2	yes	—
115	C₂²×C₈₉	#453	1	1	yes	characteristic
116	C₂²×C₈₉	#454	1	1	yes	characteristic
117	C₄×C₈₉	—	2	1	no	—
118	C₄×C₈₉	—	2	1	no	—
119	C₄×C₈₉	—	8	2	no	—
120	C₄×C₈₉	—	8	2	no	—
121	C₄×C₈₉	—	8	2	no	—
122	C₄×C₈₉	#478	1	2	yes	—
123	C₄×C₈₉	#478	1	2	yes	—
124	C₄×C₈₉	#488	1	2	yes	—
125	C₄×C₈₉	#490	1	2	yes	—
126	#10351	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂×C₈₉	—	16	2	no	—
128	C₂×C₈₉	#1620	1	1	yes	characteristic
129	C₂×C₈₉	#1624	1	1	yes	characteristic
130	C₂×C₈₉	#1628	1	2	yes	—
131	C₂×C₈₉	#2025	1	2	yes	—
132	C₂×C₈₉	#2027	1	1	yes	characteristic
133	#2571	C₂×C₈₉	1	1	yes	characteristic, complemented
134	#1982	C₂×C₈₉	1	2	yes	—
135	#1957	C₂×C₈₉	1	1	yes	characteristic
136	#1296	C₂×C₈₉	1	1	yes	characteristic, complemented
137	#1279	C₂×C₈₉	1	2	yes	complemented
138	C₈₉	#10351	1	1	yes	characteristic, direct product factor, Sylow
139	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
140	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
141	C₂×#102	—	2	2	no	—
142	C₂×#102	—	2	2	no	—
143	C₂×#102	—	2	2	no	—
144	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
145	#400	—	2	2	no	—
146	#389	—	2	2	no	—
147	#384	C₂²×C₈₉	1	1	yes	characteristic
148	#382	—	2	2	no	—
149	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
150	C₂²×D₄	—	2	1	no	—
151	C₂²×D₄	—	2	2	no	—
152	C₂²×C₈	—	2	1	no	—
153	C₂²×C₈	—	2	2	no	—
154	#127	—	2	2	no	—
155	#127	—	2	1	no	—
156	#127	Q₈×C₈₉	1	2	yes	—
157	C₂×C₄⋊C₄	—	2	2	no	—
158	C₂×C₄⋊C₄	—	2	2	no	—
159	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
160	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
161	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
162	C₂×C₄²	—	2	2	no	—
163	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	2	2	no	—
166	#102	—	4	4	no	—
167	#102	—	4	4	no	—
168	#102	—	4	4	no	—
169	C₄×C₈	—	2	2	no	—
170	#95	—	2	2	no	—
171	#95	—	2	4	no	—
172	#95	—	2	2	no	—
173	C₂⁴	—	4	1	no	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	—	2	4	no	—
176	C₂×D₄	—	4	2	no	—
177	C₂×D₄	—	4	2	no	—
178	C₂×D₄	—	4	1	no	—
179	C₂×D₄	—	4	2	no	—
180	C₂×D₄	—	4	2	no	—
181	C₂×D₄	—	4	2	no	—
182	C₂×D₄	—	4	2	no	—
183	C₂×D₄	—	4	2	no	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	—	2	2	no	—
186	C₂²×C₄	—	2	2	no	—
187	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
188	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	—	4	1	no	—
191	C₂×C₈	—	4	1	no	—
192	C₂×C₈	—	4	2	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	4	2	no	—
195	C₄⋊C₄	—	2	2	no	—
196	C₄⋊C₄	—	2	2	no	—
197	C₄⋊C₄	—	2	2	no	—
198	C₄⋊C₄	—	2	2	no	—
199	C₄⋊C₄	—	4	2	no	—
200	C₄⋊C₄	—	4	2	no	—
201	C₄⋊C₄	—	4	2	no	—
202	C₄⋊C₄	—	8	2	no	—
203	C₄²	—	4	2	no	—
204	C₄²	—	4	2	no	—
205	C₄²	C₂×Q₈×C₈₉	1	1	yes	characteristic
206	C₄²	#41×C₈₉	1	2	yes	—
207	C₄²	#41×C₈₉	1	1	yes	characteristic
208	C₂³	—	4	2	no	—
209	C₂³	—	8	2	no	—
210	C₂³	—	8	2	no	—
211	C₂³	—	8	1	no	—
212	C₂³	—	8	1	no	—
213	C₂³	#120×C₈₉	1	1	yes	characteristic
214	D₄	—	4	4	no	—
215	D₄	—	4	4	no	—
216	D₄	—	4	4	no	—
217	D₄	—	8	2	no	—
218	D₄	—	8	2	no	—
219	D₄	—	8	2	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	4	4	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
231	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
232	C₂×C₄	#124×C₈₉	1	1	yes	characteristic
233	C₂×C₄	#124×C₈₉	1	2	yes	—
234	C₂×C₄	#135×C₈₉	1	2	yes	—
235	C₂×C₄	#135×C₈₉	1	2	yes	—
236	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
237	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
238	C₈	—	4	2	no	—
239	C₈	—	8	2	no	—
240	C₂²	—	8	4	no	—
241	C₂²	—	8	2	no	—
242	C₂²	—	16	1	no	—
243	C₂²	—	16	1	no	—
244	C₂²	—	16	2	no	—
245	C₂²	#393×C₈₉	1	1	yes	characteristic
246	C₂²	#449×C₈₉	1	2	yes	—
247	C₂²	#449×C₈₉	1	2	yes	—
248	C₂²	#453×C₈₉	1	1	yes	characteristic
249	C₂²	#454×C₈₉	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	8	2	no	—
253	C₄	—	8	2	no	—
254	C₄	—	8	2	no	—
255	C₄	#478×C₈₉	1	2	yes	—
256	C₄	#478×C₈₉	1	2	yes	—
257	C₄	#488×C₈₉	1	2	yes	—
258	C₄	#490×C₈₉	1	2	yes	—
259	C₂	—	16	2	no	—
260	C₂	C₈₉×#1620	1	1	yes	characteristic
261	C₂	C₈₉×#1624	1	1	yes	characteristic
262	C₂	C₈₉×#1628	1	2	yes	—
263	C₂	C₈₉×#2025	1	2	yes	—
264	C₂	C₈₉×#2027	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈₉×#2571

C₂

yes

maximal, characteristic, complemented

C₈₉×#1982

C₂

yes

maximal

C₈₉×#1957

C₂

yes

maximal, characteristic

C₈₉×#1296

C₂

yes

maximal, characteristic, complemented

C₈₉×#1279

C₂

yes

maximal, complemented

C₂×#127×C₈₉

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₈₉

C₂²

yes

—

C₂×#102×C₈₉

—

C₂×#102×C₈₉

—

C₂×#102×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

—

C₂²×D₄×C₈₉

—

C₂²×D₄×C₈₉

—

C₂²×C₈×C₈₉

—

C₂²×C₈×C₈₉

—

#127×C₈₉

—

#127×C₈₉

—

#127×C₈₉

Q₈

yes

—

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

—

#102×C₈₉

—

#102×C₈₉

—

#102×C₈₉

—

C₄×C₈×C₈₉

—

#95×C₈₉

—

#95×C₈₉

—

#95×C₈₉

—

C₂⁴×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×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

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

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂×Q₈

yes

characteristic

C₄²×C₈₉

#41

yes

—

C₄²×C₈₉

#41

yes

characteristic

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

#120

yes

characteristic

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

D₄×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

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₈₉

#124

yes

characteristic

100

C₂×C₄×C₈₉

#124

yes

—

101

C₂×C₄×C₈₉

#135

yes

—

102

C₂×C₄×C₈₉

#135

yes

—

103

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

—

104

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

—

105

C₈×C₈₉

—

106

C₈×C₈₉

—

107

C₂²×C₈₉

—

108

C₂²×C₈₉

—

109

C₂²×C₈₉

—

110

C₂²×C₈₉

—

111

C₂²×C₈₉

—

112

C₂²×C₈₉

#393

yes

characteristic

113

C₂²×C₈₉

#449

yes

—

114

C₂²×C₈₉

#449

yes

—

115

C₂²×C₈₉

#453

yes

characteristic

116

C₂²×C₈₉

#454

yes

characteristic

117

C₄×C₈₉

—

118

C₄×C₈₉

—

119

C₄×C₈₉

—

120

C₄×C₈₉

—

121

C₄×C₈₉

—

122

C₄×C₈₉

#478

yes

—

123

C₄×C₈₉

#478

yes

—

124

C₄×C₈₉

#488

yes

—

125

C₄×C₈₉

#490

yes

—

126

#10351

C₈₉

yes

maximal, characteristic, direct product factor, Sylow

127

C₂×C₈₉

—

128

C₂×C₈₉

#1620

yes

characteristic

129

C₂×C₈₉

#1624

yes

characteristic

130

C₂×C₈₉

#1628

yes

—

131

C₂×C₈₉

#2025

yes

—

132

C₂×C₈₉

#2027

yes

characteristic

133

#2571

C₂×C₈₉

yes

characteristic, complemented

134

#1982

C₂×C₈₉

yes

—

135

#1957

C₂×C₈₉

yes

characteristic

136

#1296

C₂×C₈₉

yes

characteristic, complemented

137

#1279

C₂×C₈₉

yes

complemented

138

C₈₉

#10351

yes

characteristic, direct product factor, Sylow

139

C₂×#127

C₂²×C₈₉

yes

characteristic

140

C₂×C₄⋊C₈

C₂²×C₈₉

yes

—

141

C₂×#102

—

142

C₂×#102

—

143

C₂×#102

—

144

C₂×C₄×C₈

C₂²×C₈₉

yes

characteristic

145

#400

—

146

#389

—

147

#384

C₂²×C₈₉

yes

characteristic

148

#382

—

149

C₄×C₄⋊C₄

C₂²×C₈₉

yes

—

150

C₂²×D₄

—

151

C₂²×D₄

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

#127

—

155

#127

—

156

#127

Q₈×C₈₉

yes

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

D₄×C₈₉

yes

—

160

C₂×C₄⋊C₄

D₄×C₈₉

yes

—

161

C₂×C₄⋊C₄

D₄×C₈₉

yes

—

162

C₂×C₄²

—

163

C₂×C₄²

C₂³×C₈₉

yes

characteristic

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

#102

—

167

#102

—

168

#102

—

169

C₄×C₈

—

170

#95

—

171

#95

—

172

#95

—

173

C₂⁴

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

C₂×D₄×C₈₉

yes

characteristic

188

C₂²×C₄

C₂×D₄×C₈₉

yes

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄²

—

204

C₄²

—

205

C₄²

C₂×Q₈×C₈₉

yes

characteristic

206

C₄²

#41×C₈₉

yes

—

207

C₄²

#41×C₈₉

yes

characteristic

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

#120×C₈₉

yes

characteristic

214

D₄

—

215

D₄

—

216

D₄

—

217

D₄

—

218

D₄

—

219

D₄

—

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

—

229

C₂×C₄

—

230

C₂×C₄

C₂²⋊Q₈×C₈₉

yes

characteristic

231

C₂×C₄

C₂²⋊Q₈×C₈₉

yes

—

232

C₂×C₄

#124×C₈₉

yes

characteristic

233

C₂×C₄

#124×C₈₉

yes

—

234

C₂×C₄

#135×C₈₉

yes

—

235

C₂×C₄

#135×C₈₉

yes

—

236

C₂×C₄

AGL(1,ℤ/8)×C₈₉

yes

—

237

C₂×C₄

AGL(1,ℤ/8)×C₈₉

yes

—

238

C₈

—

239

C₈

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

#393×C₈₉

yes

characteristic

246

C₂²

#449×C₈₉

yes

—

247

C₂²

#449×C₈₉

yes

—

248

C₂²

#453×C₈₉

yes

characteristic

249

C₂²

#454×C₈₉

yes

characteristic

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

#478×C₈₉

yes

—

256

C₄

#478×C₈₉

yes

—

257

C₄

#488×C₈₉

yes

—

258

C₄

#490×C₈₉

yes

—

259

C₂

—

260

C₂

C₈₉×#1620

yes

characteristic

261

C₂

C₈₉×#1624

yes

characteristic

262

C₂

C₈₉×#1628

yes

—

263

C₂

C₈₉×#2025

yes

—

264

C₂

C₈₉×#2027

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
prime radical	C₂×#127×C₈₉	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₈₉

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₈₉

prime radical

C₂×#127×C₈₉

C₂²

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

N	H ≅ G/N	type
1. C₈₉×#2571	C₂	semidirect
4. C₈₉×#1296	C₂	semidirect
5. C₈₉×#1279	C₂	semidirect
126. #10351	C₈₉	direct (N × H)
133. #2571	C₂×C₈₉	semidirect
136. #1296	C₂×C₈₉	semidirect
137. #1279	C₂×C₈₉	semidirect
138. C₈₉	#10351	direct (N × H)

H ≅ G/N

type

1. C₈₉×#2571

C₂

semidirect

4. C₈₉×#1296

C₂

semidirect

5. C₈₉×#1279

C₂

semidirect

126. #10351

C₈₉

direct (N × H)

133. #2571

C₂×C₈₉

semidirect

136. #1296

C₂×C₈₉

semidirect

137. #1279

C₂×C₈₉

semidirect

138. C₈₉

#10351

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×#1982	2
C₈₉×#1957	2
C₈₉×#1296	2
C₈₉×#1279	2
#10351	89

subgroup

index

C₈₉×#2571

C₈₉×#1982

C₈₉×#1957

C₈₉×#1296

C₈₉×#1279

#10351

Subgroups — C₈₉×#10351 #36388199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C89×#10351 #36388199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#10351 #36388199