Group #36385674 — subgroups

Subgroups — C₈₉×#7826 #36385674

Order 22784.

462 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2683	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2100	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2094	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1271	C₂	1	2	yes	maximal, complemented
5	C₈₉×#1270	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂²⋊Q₈×C₈₉	—	2	2	no	—
7	C₂×#106×C₈₉	—	2	1	no	—
8	C₂×#102×C₈₉	—	2	1	no	—
9	#396×C₈₉	—	2	2	no	—
10	#395×C₈₉	—	2	1	no	—
11	#390×C₈₉	C₂²	1	1	yes	characteristic
12	#389×C₈₉	C₂²	1	2	yes	—
13	#386×C₈₉	—	2	1	no	—
14	#384×C₈₉	C₂²	1	1	yes	characteristic
15	#340×C₈₉	—	2	2	no	—
16	#340×C₈₉	—	2	2	no	—
17	#336×C₈₉	C₂²	1	2	yes	—
18	#336×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×Q₈×C₈₉	—	2	1	no	—
20	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
21	C₂³×C₄×C₈₉	—	2	1	no	—
22	C₂²×C₈×C₈₉	—	2	1	no	—
23	C₂²×C₈×C₈₉	—	2	2	no	—
24	C₂²⋊Q₈×C₈₉	—	4	4	no	—
25	C₂²⋊Q₈×C₈₉	—	4	4	no	—
26	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
31	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
34	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
35	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
36	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
37	#106×C₈₉	—	4	2	no	—
38	#102×C₈₉	—	4	2	no	—
39	#95×C₈₉	—	2	1	no	—
40	#95×C₈₉	—	2	2	no	—
41	C₂⁴×C₈₉	—	2	1	no	—
42	C₂×Q₈×C₈₉	—	4	4	no	—
43	C₂×Q₈×C₈₉	—	8	1	no	—
44	C₂×D₄×C₈₉	—	2	1	no	—
45	C₂×D₄×C₈₉	—	4	1	no	—
46	C₂×D₄×C₈₉	—	4	1	no	—
47	C₂×D₄×C₈₉	Q₁₆	1	2	yes	—
48	C₂²×C₄×C₈₉	—	2	2	no	—
49	C₂²×C₄×C₈₉	—	2	2	no	—
50	C₂²×C₄×C₈₉	—	2	1	no	—
51	C₂²×C₄×C₈₉	—	4	4	no	—
52	C₂²×C₄×C₈₉	—	4	1	no	—
53	C₂²×C₄×C₈₉	—	8	1	no	—
54	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
55	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
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	—	4	4	no	—
64	C₄⋊C₄×C₈₉	—	4	1	no	—
65	C₄⋊C₄×C₈₉	—	4	2	no	—
66	C₄⋊C₄×C₈₉	—	4	1	no	—
67	C₄⋊C₄×C₈₉	—	4	1	no	—
68	C₄⋊C₄×C₈₉	—	4	4	no	—
69	C₄⋊C₄×C₈₉	—	4	2	no	—
70	C₄⋊C₄×C₈₉	—	4	2	no	—
71	C₄⋊C₄×C₈₉	SD₁₆	1	4	yes	—
72	C₂²⋊C₄×C₈₉	—	4	4	no	—
73	C₂²⋊C₄×C₈₉	—	4	2	no	—
74	C₂²⋊C₄×C₈₉	—	4	2	no	—
75	C₂²⋊C₄×C₈₉	—	8	1	no	—
76	C₄²×C₈₉	—	4	1	no	—
77	C₂³×C₈₉	—	2	2	no	—
78	C₂³×C₈₉	—	4	2	no	—
79	C₂³×C₈₉	—	4	1	no	—
80	C₂³×C₈₉	—	4	2	no	—
81	C₂³×C₈₉	—	4	1	no	—
82	C₂³×C₈₉	#120	1	1	yes	characteristic
83	Q₈×C₈₉	—	8	4	no	—
84	D₄×C₈₉	—	4	2	no	—
85	D₄×C₈₉	—	8	1	no	—
86	C₂×C₄×C₈₉	—	2	1	no	—
87	C₂×C₄×C₈₉	—	2	2	no	—
88	C₂×C₄×C₈₉	—	2	2	no	—
89	C₂×C₄×C₈₉	—	2	1	no	—
90	C₂×C₄×C₈₉	—	2	4	no	—
91	C₂×C₄×C₈₉	—	4	2	no	—
92	C₂×C₄×C₈₉	—	4	2	no	—
93	C₂×C₄×C₈₉	—	4	2	no	—
94	C₂×C₄×C₈₉	—	4	2	no	—
95	C₂×C₄×C₈₉	—	4	1	no	—
96	C₂×C₄×C₈₉	—	4	2	no	—
97	C₂×C₄×C₈₉	—	4	2	no	—
98	C₂×C₄×C₈₉	—	8	4	no	—
99	C₂×C₄×C₈₉	—	8	1	no	—
100	C₂×C₄×C₈₉	—	8	2	no	—
101	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
102	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
103	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
104	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
105	C₈×C₈₉	—	4	2	no	—
106	C₈×C₈₉	—	8	2	no	—
107	C₂²×C₈₉	—	4	2	no	—
108	C₂²×C₈₉	—	4	4	no	—
109	C₂²×C₈₉	—	8	2	no	—
110	C₂²×C₈₉	—	8	1	no	—
111	C₂²×C₈₉	—	8	1	no	—
112	C₂²×C₈₉	#450	1	2	yes	—
113	C₂²×C₈₉	#451	1	1	yes	characteristic
114	C₂²×C₈₉	#453	1	1	yes	characteristic
115	C₂²×C₈₉	#454	1	2	yes	—
116	C₂²×C₈₉	#458	1	1	yes	characteristic
117	C₄×C₈₉	—	2	1	no	—
118	C₄×C₈₉	—	2	1	no	—
119	C₄×C₈₉	—	2	2	no	—
120	C₄×C₈₉	—	2	2	no	—
121	C₄×C₈₉	—	4	4	no	—
122	C₄×C₈₉	—	8	2	no	—
123	C₄×C₈₉	—	8	1	no	—
124	C₄×C₈₉	—	16	1	no	—
125	#7826	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂×C₈₉	—	8	2	no	—
127	C₂×C₈₉	#1614	1	1	yes	characteristic
128	C₂×C₈₉	#1616	1	2	yes	—
129	C₂×C₈₉	#1629	1	1	yes	characteristic
130	C₂×C₈₉	#1637	1	2	yes	—
131	C₂×C₈₉	#1657	1	1	yes	characteristic
132	#2683	C₂×C₈₉	1	1	yes	characteristic
133	#2100	C₂×C₈₉	1	2	yes	complemented
134	#2094	C₂×C₈₉	1	1	yes	characteristic
135	#1271	C₂×C₈₉	1	2	yes	complemented
136	#1270	C₂×C₈₉	1	1	yes	characteristic
137	C₈₉	#7826	1	1	yes	characteristic, direct product factor, Sylow
138	C₂×C₂²⋊Q₈	—	2	2	no	—
139	C₂×#106	—	2	1	no	—
140	C₂×#102	—	2	1	no	—
141	#396	—	2	2	no	—
142	#395	—	2	1	no	—
143	#390	C₂²×C₈₉	1	1	yes	characteristic
144	#389	C₂²×C₈₉	1	2	yes	—
145	#386	—	2	1	no	—
146	#384	C₂²×C₈₉	1	1	yes	characteristic
147	#340	—	2	2	no	—
148	#340	—	2	2	no	—
149	#336	C₂²×C₈₉	1	1	yes	characteristic
150	#336	C₂²×C₈₉	1	2	yes	—
151	C₂²×Q₈	—	2	1	no	—
152	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
153	C₂³×C₄	—	2	1	no	—
154	C₂²×C₈	—	2	1	no	—
155	C₂²×C₈	—	2	2	no	—
156	C₂²⋊Q₈	—	4	4	no	—
157	C₂²⋊Q₈	—	4	4	no	—
158	C₂×C₄⋊C₄	—	2	2	no	—
159	C₂×C₄⋊C₄	—	2	2	no	—
160	C₂×C₄⋊C₄	—	2	2	no	—
161	C₂×C₄⋊C₄	—	2	1	no	—
162	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
163	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
164	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
165	C₂×C₂²⋊C₄	—	2	2	no	—
166	C₂×C₂²⋊C₄	—	2	2	no	—
167	C₂×C₂²⋊C₄	—	2	1	no	—
168	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
169	#106	—	4	2	no	—
170	#102	—	4	2	no	—
171	#95	—	2	1	no	—
172	#95	—	2	2	no	—
173	C₂⁴	—	2	1	no	—
174	C₂×Q₈	—	4	4	no	—
175	C₂×Q₈	—	8	1	no	—
176	C₂×D₄	—	2	1	no	—
177	C₂×D₄	—	4	1	no	—
178	C₂×D₄	—	4	1	no	—
179	C₂×D₄	Q₁₆×C₈₉	1	2	yes	—
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	2	1	no	—
183	C₂²×C₄	—	4	4	no	—
184	C₂²×C₄	—	4	1	no	—
185	C₂²×C₄	—	8	1	no	—
186	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
187	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	4	1	no	—
190	C₂×C₈	—	4	1	no	—
191	C₂×C₈	—	4	2	no	—
192	C₂×C₈	—	4	2	no	—
193	C₂×C₈	—	4	2	no	—
194	C₄⋊C₄	—	2	2	no	—
195	C₄⋊C₄	—	4	1	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄⋊C₄	—	4	4	no	—
198	C₄⋊C₄	—	4	1	no	—
199	C₄⋊C₄	—	4	1	no	—
200	C₄⋊C₄	—	4	4	no	—
201	C₄⋊C₄	—	4	2	no	—
202	C₄⋊C₄	—	4	2	no	—
203	C₄⋊C₄	SD₁₆×C₈₉	1	4	yes	—
204	C₂²⋊C₄	—	4	4	no	—
205	C₂²⋊C₄	—	4	2	no	—
206	C₂²⋊C₄	—	4	2	no	—
207	C₂²⋊C₄	—	8	1	no	—
208	C₄²	—	4	1	no	—
209	C₂³	—	2	2	no	—
210	C₂³	—	4	2	no	—
211	C₂³	—	4	1	no	—
212	C₂³	—	4	2	no	—
213	C₂³	—	4	1	no	—
214	C₂³	#120×C₈₉	1	1	yes	characteristic
215	Q₈	—	8	4	no	—
216	D₄	—	4	2	no	—
217	D₄	—	8	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	4	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	4	1	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	8	4	no	—
231	C₂×C₄	—	8	1	no	—
232	C₂×C₄	—	8	2	no	—
233	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
234	C₂×C₄	C₂×Q₁₆×C₈₉	1	1	yes	characteristic
235	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
236	C₂×C₄	#137×C₈₉	1	1	yes	characteristic
237	C₈	—	4	2	no	—
238	C₈	—	8	2	no	—
239	C₂²	—	4	2	no	—
240	C₂²	—	4	4	no	—
241	C₂²	—	8	2	no	—
242	C₂²	—	8	1	no	—
243	C₂²	—	8	1	no	—
244	C₂²	#450×C₈₉	1	2	yes	—
245	C₂²	#451×C₈₉	1	1	yes	characteristic
246	C₂²	#453×C₈₉	1	1	yes	characteristic
247	C₂²	#454×C₈₉	1	2	yes	—
248	C₂²	#458×C₈₉	1	1	yes	characteristic
249	C₄	—	2	1	no	—
250	C₄	—	2	1	no	—
251	C₄	—	2	2	no	—
252	C₄	—	2	2	no	—
253	C₄	—	4	4	no	—
254	C₄	—	8	2	no	—
255	C₄	—	8	1	no	—
256	C₄	—	16	1	no	—
257	C₂	—	8	2	no	—
258	C₂	C₈₉×#1614	1	1	yes	characteristic
259	C₂	C₈₉×#1616	1	2	yes	—
260	C₂	C₈₉×#1629	1	1	yes	characteristic
261	C₂	C₈₉×#1637	1	2	yes	—
262	C₂	C₈₉×#1657	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈₉×#2683

C₂

yes

maximal, characteristic

C₈₉×#2100

C₂

yes

maximal, complemented

C₈₉×#2094

C₂

yes

maximal, characteristic

C₈₉×#1271

C₂

yes

maximal, complemented

C₈₉×#1270

C₂

yes

maximal, characteristic

C₂×C₂²⋊Q₈×C₈₉

—

C₂×#106×C₈₉

—

C₂×#102×C₈₉

—

#396×C₈₉

—

#395×C₈₉

—

#390×C₈₉

C₂²

yes

characteristic

#389×C₈₉

C₂²

yes

—

#386×C₈₉

—

#384×C₈₉

C₂²

yes

characteristic

#340×C₈₉

—

#340×C₈₉

—

#336×C₈₉

C₂²

yes

—

#336×C₈₉

C₂²

yes

characteristic

C₂²×Q₈×C₈₉

—

C₂²×D₄×C₈₉

D₄

yes

characteristic

C₂³×C₄×C₈₉

—

C₂²×C₈×C₈₉

—

C₂²×C₈×C₈₉

—

C₂²⋊Q₈×C₈₉

—

C₂²⋊Q₈×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

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

characteristic

C₂×C₂²⋊C₄×C₈₉

—

C₂×C₂²⋊C₄×C₈₉

—

C₂×C₂²⋊C₄×C₈₉

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

#106×C₈₉

—

#102×C₈₉

—

#95×C₈₉

—

#95×C₈₉

—

C₂⁴×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

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×C₈₉

C₂×D₄

yes

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

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

SD₁₆

yes

—

C₂²⋊C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

#120

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

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

100

C₂×C₄×C₈₉

—

101

C₂×C₄×C₈₉

C₂×SD₁₆

yes

—

102

C₂×C₄×C₈₉

C₂×Q₁₆

yes

characteristic

103

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

—

104

C₂×C₄×C₈₉

#137

yes

characteristic

105

C₈×C₈₉

—

106

C₈×C₈₉

—

107

C₂²×C₈₉

—

108

C₂²×C₈₉

—

109

C₂²×C₈₉

—

110

C₂²×C₈₉

—

111

C₂²×C₈₉

—

112

C₂²×C₈₉

#450

yes

—

113

C₂²×C₈₉

#451

yes

characteristic

114

C₂²×C₈₉

#453

yes

characteristic

115

C₂²×C₈₉

#454

yes

—

116

C₂²×C₈₉

#458

yes

characteristic

117

C₄×C₈₉

—

118

C₄×C₈₉

—

119

C₄×C₈₉

—

120

C₄×C₈₉

—

121

C₄×C₈₉

—

122

C₄×C₈₉

—

123

C₄×C₈₉

—

124

C₄×C₈₉

—

125

#7826

C₈₉

yes

maximal, characteristic, direct product factor, Sylow

126

C₂×C₈₉

—

127

C₂×C₈₉

#1614

yes

characteristic

128

C₂×C₈₉

#1616

yes

—

129

C₂×C₈₉

#1629

yes

characteristic

130

C₂×C₈₉

#1637

yes

—

131

C₂×C₈₉

#1657

yes

characteristic

132

#2683

C₂×C₈₉

yes

characteristic

133

#2100

C₂×C₈₉

yes

complemented

134

#2094

C₂×C₈₉

yes

characteristic

135

#1271

C₂×C₈₉

yes

complemented

136

#1270

C₂×C₈₉

yes

characteristic

137

C₈₉

#7826

yes

characteristic, direct product factor, Sylow

138

C₂×C₂²⋊Q₈

—

139

C₂×#106

—

140

C₂×#102

—

141

#396

—

142

#395

—

143

#390

C₂²×C₈₉

yes

characteristic

144

#389

C₂²×C₈₉

yes

—

145

#386

—

146

#384

C₂²×C₈₉

yes

characteristic

147

#340

—

148

#340

—

149

#336

C₂²×C₈₉

yes

characteristic

150

#336

C₂²×C₈₉

yes

—

151

C₂²×Q₈

—

152

C₂²×D₄

D₄×C₈₉

yes

characteristic

153

C₂³×C₄

—

154

C₂²×C₈

—

155

C₂²×C₈

—

156

C₂²⋊Q₈

—

157

C₂²⋊Q₈

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

D₄×C₈₉

yes

—

163

C₂×C₄⋊C₄

D₄×C₈₉

yes

—

164

C₂×C₄⋊C₄

D₄×C₈₉

yes

characteristic

165

C₂×C₂²⋊C₄

—

166

C₂×C₂²⋊C₄

—

167

C₂×C₂²⋊C₄

—

168

C₂×C₄²

C₂³×C₈₉

yes

characteristic

169

#106

—

170

#102

—

171

#95

—

172

#95

—

173

C₂⁴

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

Q₁₆×C₈₉

yes

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

C₂×D₄×C₈₉

yes

—

187

C₂²×C₄

C₂×D₄×C₈₉

yes

characteristic

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₄⋊C₄

—

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

C₄⋊C₄

SD₁₆×C₈₉

yes

—

204

C₂²⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₂²⋊C₄

—

208

C₄²

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

—

214

C₂³

#120×C₈₉

yes

characteristic

215

Q₈

—

216

D₄

—

217

D₄

—

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

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

C₂×SD₁₆×C₈₉

yes

—

234

C₂×C₄

C₂×Q₁₆×C₈₉

yes

characteristic

235

C₂×C₄

AGL(1,ℤ/8)×C₈₉

yes

—

236

C₂×C₄

#137×C₈₉

yes

characteristic

237

C₈

—

238

C₈

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

#450×C₈₉

yes

—

245

C₂²

#451×C₈₉

yes

characteristic

246

C₂²

#453×C₈₉

yes

characteristic

247

C₂²

#454×C₈₉

yes

—

248

C₂²

#458×C₈₉

yes

characteristic

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₂

—

258

C₂

C₈₉×#1614

yes

characteristic

259

C₂

C₈₉×#1616

yes

—

260

C₂

C₈₉×#1629

yes

characteristic

261

C₂

C₈₉×#1637

yes

—

262

C₂

C₈₉×#1657

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
prime radical	C₂²×D₄×C₈₉	D₄
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ 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

C₂²×D₄×C₈₉

D₄

LCS

G ▷ C₂×C₄² ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

N	H ≅ G/N	type
2. C₈₉×#2100	C₂	semidirect
4. C₈₉×#1271	C₂	semidirect
125. #7826	C₈₉	direct (N × H)
133. #2100	C₂×C₈₉	semidirect
135. #1271	C₂×C₈₉	semidirect
137. C₈₉	#7826	direct (N × H)

H ≅ G/N

type

2. C₈₉×#2100

C₂

semidirect

4. C₈₉×#1271

C₂

semidirect

125. #7826

C₈₉

direct (N × H)

133. #2100

C₂×C₈₉

semidirect

135. #1271

C₂×C₈₉

semidirect

137. C₈₉

#7826

direct (N × H)

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

subgroup	index
C₈₉×#2683	2
C₈₉×#2100	2
C₈₉×#2094	2
C₈₉×#1271	2
C₈₉×#1270	2
#7826	89

subgroup

index

C₈₉×#2683

C₈₉×#2100

C₈₉×#2094

C₈₉×#1271

C₈₉×#1270

#7826

Subgroups — C₈₉×#7826 #36385674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C89×#7826 #36385674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#7826 #36385674