Group #36470653 — subgroups

Subgroups — #36470653

Order 22784.

462 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 135 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	C₂×M₁₆×Dic₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151380	C₂	1	1	yes	maximal, characteristic
3	#26018333	C₂	1	2	yes	maximal, complemented
4	#26018331	C₂	1	2	yes	maximal, complemented
5	C₂×#349×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×#13083558	C₄	1	1	yes	characteristic
7	C₂²×C₄×Dic₈₉	C₄	1	1	yes	characteristic
8	C₂×#15667952	C₂²	1	2	yes	—
9	M₁₆×Dic₈₉	—	2	2	no	—
10	M₁₆×Dic₈₉	—	2	2	no	—
11	C₂×#15667922	C₄	1	1	yes	characteristic
12	C₂×#15667922	C₂²	1	1	yes	characteristic
13	C₂×C₈×Dic₈₉	C₄	1	1	yes	characteristic
14	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
15	#19151380	—	2	2	no	—
16	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×M₃₂×C₈₉	C₂²	1	2	yes	—
18	#349×C₈₉	—	2	2	no	—
19	C₂³×Dic₈₉	—	2	1	no	—
20	C₂×#13083558	—	2	2	no	—
21	C₂×#13083558	—	2	2	no	—
22	C₂×#13083558	—	2	2	no	—
23	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
24	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×Dic₈₉	—	2	2	no	—
26	C₂×C₄×Dic₈₉	—	2	1	no	—
27	C₂×C₄×Dic₈₉	C₈	1	4	yes	—
28	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
30	#15667952	—	2	2	no	—
31	#15667952	—	2	2	no	—
32	C₂×#13083549	—	2	2	no	—
33	#15667922	—	2	2	no	—
34	#15667922	—	2	1	no	—
35	#15667922	—	2	1	no	—
36	C₈×Dic₈₉	—	2	2	no	—
37	C₈×Dic₈₉	—	2	1	no	—
38	C₈×Dic₈₉	—	2	1	no	—
39	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₈₉	—	2	2	no	—
41	C₂×M₁₆×C₈₉	—	2	2	no	—
42	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
43	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
44	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
46	M₃₂×C₈₉	—	2	2	no	—
47	M₃₂×C₈₉	—	2	2	no	—
48	C₂×C₁₆×C₈₉	—	2	2	no	—
49	C₂²×Dic₈₉	—	2	1	no	—
50	C₂²×Dic₈₉	—	2	4	no	—
51	C₂²×Dic₈₉	—	2	1	no	—
52	C₂²×Dic₈₉	—	4	4	no	—
53	#13083558	—	2	8	no	—
54	C₂×#10623494	—	2	1	no	—
55	C₂×#10623494	—	2	1	no	—
56	C₂×#10623494	—	2	1	no	—
57	C₂×#10623494	—	2	1	no	—
58	C₂×#10623494	M₁₆	1	2	yes	—
59	C₂×#10623494	M₁₆	1	2	yes	—
60	C₄×Dic₈₉	—	2	4	no	—
61	C₄×Dic₈₉	—	2	1	no	—
62	C₄×Dic₈₉	—	2	1	no	—
63	C₄×Dic₈₉	C₂×C₈	1	2	yes	—
64	C₄×Dic₈₉	C₂×C₈	1	2	yes	—
65	#13083549	—	4	2	no	—
66	C₂⁴×C₈₉	M₁₆	1	1	yes	characteristic
67	C₂²×C₄×C₈₉	—	2	1	no	—
68	C₂²×C₄×C₈₉	—	2	1	no	—
69	C₂²×C₄×C₈₉	—	2	1	no	—
70	C₂²×C₄×C₈₉	—	2	1	no	—
71	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
72	C₂²×C₄×C₈₉	C₂×C₈	1	2	yes	—
73	C₂²×C₄×C₈₉	M₁₆	1	1	yes	characteristic
74	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
75	M₁₆×C₈₉	—	2	4	no	—
76	M₁₆×C₈₉	—	2	4	no	—
77	C₂×C₈×C₈₉	—	2	1	no	—
78	C₂×C₈×C₈₉	—	2	1	no	—
79	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
80	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₈×C₈₉	#41	1	2	yes	—
83	C₂×C₈×C₈₉	#41	1	2	yes	—
84	C₁₆×C₈₉	—	4	2	no	—
85	C₂³×C₈₉	—	2	1	no	—
86	C₂³×C₈₉	—	2	1	no	—
87	C₂³×C₈₉	—	4	2	no	—
88	C₂³×C₈₉	C₂²⋊C₈	1	2	yes	—
89	C₂³×C₈₉	C₂×M₁₆	1	1	yes	characteristic
90	C₂×C₄×C₈₉	—	2	1	no	—
91	C₂×C₄×C₈₉	—	2	1	no	—
92	C₂×C₄×C₈₉	—	2	2	no	—
93	C₂×C₄×C₈₉	—	2	2	no	—
94	C₂×C₄×C₈₉	—	2	2	no	—
95	C₂×C₄×C₈₉	—	2	2	no	—
96	C₂×C₄×C₈₉	C₂²⋊C₈	1	2	yes	—
97	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
99	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
100	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
101	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
102	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
103	C₂×Dic₈₉	—	2	4	no	—
104	C₂×Dic₈₉	—	2	2	no	—
105	C₂×Dic₈₉	—	2	2	no	—
106	C₂×Dic₈₉	—	4	8	no	—
107	C₂×Dic₈₉	—	4	2	no	—
108	C₈×C₈₉	—	2	2	no	—
109	C₈×C₈₉	#123	1	2	yes	—
110	C₈×C₈₉	#123	1	2	yes	—
111	#10623494	—	2	2	no	—
112	#10623494	—	2	2	no	—
113	C₂²×C₈₉	—	2	2	no	—
114	C₂²×C₈₉	—	2	2	no	—
115	C₂²×C₈₉	—	4	2	no	—
116	C₂²×C₈₉	—	4	2	no	—
117	C₂²×C₈₉	—	4	2	no	—
118	C₂²×C₈₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
119	C₂²×C₈₉	#432	1	1	yes	characteristic
120	C₂²×C₈₉	#432	1	1	yes	characteristic
121	C₄×C₈₉	—	2	2	no	—
122	C₄×C₈₉	#381	1	1	yes	characteristic
123	C₄×C₈₉	#407	1	1	yes	characteristic
124	C₄×C₈₉	#431	1	1	yes	characteristic
125	C₄×C₈₉	#431	1	1	yes	characteristic
126	Dic₈₉	—	2	4	no	—
127	Dic₈₉	—	4	2	no	—
128	#12849	—	89	1	no	maximal, Sylow
129	C₂×C₈₉	—	2	1	no	—
130	C₂×C₈₉	—	2	1	no	—
131	C₂×C₈₉	—	4	2	no	—
132	C₂×C₈₉	#1817	1	1	yes	characteristic
133	C₂×C₈₉	#2165	1	2	yes	—
134	C₂×C₄×M₁₆	—	89	1	no	—
135	C₂×#349	—	89	1	no	—
136	C₂×#349	D₈₉	1	1	yes	characteristic
137	#1376	—	89	2	no	—
138	#1375	—	89	2	no	—
139	C₈₉	#12849	1	1	yes	characteristic, complemented, Sylow
140	C₂²×M₁₆	—	89	1	no	—
141	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
142	C₂²×C₄²	—	89	1	no	—
143	C₂×M₃₂	—	89	2	no	—
144	C₂×M₃₂	C₂×D₈₉	1	2	yes	—
145	C₄×M₁₆	—	178	2	no	—
146	C₄×M₁₆	—	178	2	no	—
147	C₂×#97	—	89	1	no	—
148	C₂×#97	—	89	1	no	—
149	C₂×C₄×C₈	—	89	1	no	—
150	C₂×C₄×C₈	—	89	1	no	—
151	#349	—	2	2	no	—
152	#349	—	178	2	no	—
153	C₂³×C₄	—	178	1	no	—
154	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
155	C₂×M₁₆	—	2	2	no	—
156	C₂×M₁₆	—	2	2	no	—
157	C₂×M₁₆	—	178	2	no	—
158	C₂×M₁₆	—	178	2	no	—
159	C₂×M₁₆	—	178	2	no	—
160	C₂×M₁₆	D₃₅₆	1	2	yes	—
161	C₂×M₁₆	C₂²⋊D₈₉	1	2	yes	—
162	C₂²×C₈	—	89	1	no	—
163	C₂²×C₈	—	89	1	no	—
164	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
165	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
166	C₂×C₄²	—	89	4	no	—
167	C₂×C₄²	—	89	1	no	—
168	C₂×C₄²	—	89	1	no	—
169	C₂×C₄²	—	178	2	no	—
170	C₂×C₄²	—	178	1	no	—
171	M₃₂	—	2	2	no	—
172	M₃₂	—	2	2	no	—
173	M₃₂	—	178	2	no	—
174	M₃₂	—	178	2	no	—
175	C₂×C₁₆	—	2	2	no	—
176	C₂×C₁₆	—	178	2	no	—
177	#97	—	178	2	no	—
178	#97	—	178	1	no	—
179	#97	—	178	1	no	—
180	C₄×C₈	—	178	2	no	—
181	C₄×C₈	—	178	1	no	—
182	C₄×C₈	—	178	1	no	—
183	C₂⁴	#13083557	1	1	yes	characteristic
184	C₂²×C₄	—	2	1	no	—
185	C₂²×C₄	—	2	1	no	—
186	C₂²×C₄	—	2	1	no	—
187	C₂²×C₄	—	2	1	no	—
188	C₂²×C₄	—	356	4	no	—
189	C₂²×C₄	—	178	1	no	—
190	C₂²×C₄	—	178	4	no	—
191	C₂²×C₄	—	178	1	no	—
192	C₂²×C₄	#13083551	1	2	yes	—
193	C₂²×C₄	C₈×D₈₉	1	2	yes	—
194	C₂²×C₄	#13083557	1	1	yes	characteristic
195	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
196	M₁₆	—	2	4	no	—
197	M₁₆	—	2	4	no	—
198	M₁₆	—	178	8	no	—
199	C₂×C₈	—	2	1	no	—
200	C₂×C₈	—	2	1	no	—
201	C₂×C₈	—	89	2	no	—
202	C₂×C₈	—	89	2	no	—
203	C₂×C₈	—	178	1	no	—
204	C₂×C₈	—	178	1	no	—
205	C₂×C₈	—	178	1	no	—
206	C₂×C₈	—	178	1	no	—
207	C₂×C₈	#13083551	1	2	yes	—
208	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
209	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
210	C₂×C₈	#13083573	1	2	yes	—
211	C₂×C₈	#13083573	1	2	yes	—
212	C₄²	—	89	2	no	—
213	C₄²	—	89	2	no	—
214	C₄²	—	178	4	no	—
215	C₄²	—	178	1	no	—
216	C₄²	—	178	1	no	—
217	C₁₆	—	4	2	no	—
218	C₁₆	—	356	2	no	—
219	C₂³	—	2	1	no	—
220	C₂³	—	2	1	no	—
221	C₂³	—	4	2	no	—
222	C₂³	#15667924	1	2	yes	—
223	C₂³	C₂×#13083557	1	1	yes	characteristic
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	356	2	no	—
231	C₂×C₄	—	356	8	no	—
232	C₂×C₄	—	178	2	no	—
233	C₂×C₄	—	178	4	no	—
234	C₂×C₄	—	178	2	no	—
235	C₂×C₄	#15667924	1	2	yes	—
236	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
237	C₂×C₄	#15667968	1	1	yes	characteristic
238	C₂×C₄	#15667968	1	1	yes	characteristic
239	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
240	C₂×C₄	M₁₆×D₈₉	1	1	yes	characteristic
241	C₂×C₄	M₁₆×D₈₉	1	1	yes	characteristic
242	C₈	—	2	2	no	—
243	C₈	—	178	2	no	—
244	C₈	—	178	2	no	—
245	C₈	#15667993	1	2	yes	—
246	C₈	#15667996	1	2	yes	—
247	C₂²	—	2	2	no	—
248	C₂²	—	2	2	no	—
249	C₂²	—	4	2	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	4	2	no	—
252	C₂²	C₂×#15667924	1	1	yes	characteristic
253	C₂²	#19151652	1	1	yes	characteristic
254	C₂²	#19151652	1	1	yes	characteristic
255	C₄	—	2	2	no	—
256	C₄	—	356	2	no	—
257	C₄	—	178	4	no	—
258	C₄	#19151459	1	1	yes	characteristic
259	C₄	#19151561	1	1	yes	characteristic
260	C₄	#19151648	1	1	yes	characteristic
261	C₄	#19151648	1	1	yes	characteristic
262	C₂	—	2	1	no	—
263	C₂	—	2	1	no	—
264	C₂	—	4	2	no	—
265	C₂	#26020318	1	1	yes	characteristic
266	C₂	#26022061	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×M₁₆×Dic₈₉

C₂

yes

maximal, characteristic

C₂×#19151380

C₂

yes

maximal, characteristic

#26018333

C₂

yes

maximal, complemented

#26018331

C₂

yes

maximal, complemented

C₂×#349×C₈₉

C₂

yes

maximal, characteristic

C₂²×#13083558

C₄

yes

characteristic

C₂²×C₄×Dic₈₉

C₄

yes

characteristic

C₂×#15667952

C₂²

yes

—

M₁₆×Dic₈₉

—

M₁₆×Dic₈₉

—

C₂×#15667922

C₄

yes

characteristic

C₂×#15667922

C₂²

yes

characteristic

C₂×C₈×Dic₈₉

C₄

yes

characteristic

C₂×C₈×Dic₈₉

C₂²

yes

characteristic

#19151380

—

C₂²×M₁₆×C₈₉

C₂²

yes

characteristic

C₂×M₃₂×C₈₉

C₂²

yes

—

#349×C₈₉

—

C₂³×Dic₈₉

—

—

—

—

C₂×C₄

yes

characteristic

C₂²×#10623494

C₂×C₄

yes

characteristic

C₂×C₄×Dic₈₉

—

C₂×C₄×Dic₈₉

—

C₂×C₄×Dic₈₉

C₈

yes

—

C₂×C₄×Dic₈₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₈₉

C₂×C₄

yes

—

—

—

—

—

—

C₈×Dic₈₉

—

C₈×Dic₈₉

—

C₈×Dic₈₉

—

C₂³×C₄×C₈₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₈₉

—

C₂×M₁₆×C₈₉

—

C₂×M₁₆×C₈₉

D₄

yes

—

C₂×M₁₆×C₈₉

D₄

yes

—

C₂²×C₈×C₈₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₈₉

C₂³

yes

characteristic

M₃₂×C₈₉

—

M₃₂×C₈₉

—

C₂×C₁₆×C₈₉

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

—

—

—

—

—

M₁₆

yes

—

C₂×#10623494

M₁₆

yes

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

C₂×C₈

yes

—

C₄×Dic₈₉

C₂×C₈

yes

—

#13083549

—

C₂⁴×C₈₉

M₁₆

yes

characteristic

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₈₉

C₂×C₈

yes

—

C₂²×C₄×C₈₉

M₁₆

yes

characteristic

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

M₁₆×C₈₉

—

M₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

—

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

#41

yes

—

C₂×C₈×C₈₉

#41

yes

—

C₁₆×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

C₂²⋊C₈

yes

—

C₂³×C₈₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂²⋊C₈

yes

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

100

C₂×C₄×C₈₉

C₂²×C₈

yes

characteristic

101

C₂×C₄×C₈₉

C₂×M₁₆

yes

characteristic

102

C₂×C₄×C₈₉

C₂×M₁₆

yes

characteristic

103

C₂×Dic₈₉

—

104

C₂×Dic₈₉

—

105

C₂×Dic₈₉

—

106

C₂×Dic₈₉

—

107

C₂×Dic₈₉

—

108

C₈×C₈₉

—

109

C₈×C₈₉

#123

yes

—

110

C₈×C₈₉

#123

yes

—

111

#10623494

—

112

#10623494

—

113

C₂²×C₈₉

—

114

C₂²×C₈₉

—

115

C₂²×C₈₉

—

116

C₂²×C₈₉

—

117

C₂²×C₈₉

—

118

C₂²×C₈₉

C₂×C₂²⋊C₈

yes

characteristic

119

C₂²×C₈₉

#432

yes

characteristic

120

C₂²×C₈₉

#432

yes

characteristic

121

C₄×C₈₉

—

122

C₄×C₈₉

#381

yes

characteristic

123

C₄×C₈₉

#407

yes

characteristic

124

C₄×C₈₉

#431

yes

characteristic

125

C₄×C₈₉

#431

yes

characteristic

126

Dic₈₉

—

127

Dic₈₉

—

128

#12849

—

maximal, Sylow

129

C₂×C₈₉

—

130

C₂×C₈₉

—

131

C₂×C₈₉

—

132

C₂×C₈₉

#1817

yes

characteristic

133

C₂×C₈₉

#2165

yes

—

134

C₂×C₄×M₁₆

—

135

C₂×#349

—

136

C₂×#349

D₈₉

yes

characteristic

137

#1376

—

138

#1375

—

139

C₈₉

#12849

yes

characteristic, complemented, Sylow

140

C₂²×M₁₆

—

141

C₂²×M₁₆

C₂×D₈₉

yes

characteristic

142

C₂²×C₄²

—

143

C₂×M₃₂

—

144

C₂×M₃₂

C₂×D₈₉

yes

—

145

C₄×M₁₆

—

178

—

146

C₄×M₁₆

—

178

—

147

C₂×#97

—

148

C₂×#97

—

149

C₂×C₄×C₈

—

150

C₂×C₄×C₈

—

151

#349

—

152

#349

—

178

—

153

C₂³×C₄

—

178

—

154

C₂³×C₄

C₄×D₈₉

yes

characteristic

155

C₂×M₁₆

—

156

C₂×M₁₆

—

157

C₂×M₁₆

—

178

—

158

C₂×M₁₆

—

178

—

159

C₂×M₁₆

—

178

—

160

C₂×M₁₆

D₃₅₆

yes

—

161

C₂×M₁₆

C₂²⋊D₈₉

yes

—

162

C₂²×C₈

—

163

C₂²×C₈

—

164

C₂²×C₈

C₄×D₈₉

yes

characteristic

165

C₂²×C₈

C₂²×D₈₉

yes

characteristic

166

C₂×C₄²

—

167

C₂×C₄²

—

168

C₂×C₄²

—

169

C₂×C₄²

—

178

—

170

C₂×C₄²

—

178

—

171

M₃₂

—

172

M₃₂

—

173

M₃₂

—

178

—

174

M₃₂

—

178

—

175

C₂×C₁₆

—

176

C₂×C₁₆

—

178

—

177

#97

—

178

—

178

#97

—

178

—

179

#97

—

178

—

180

C₄×C₈

—

178

—

181

C₄×C₈

—

178

—

182

C₄×C₈

—

178

—

183

C₂⁴

#13083557

yes

characteristic

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

356

—

189

C₂²×C₄

—

178

—

190

C₂²×C₄

—

178

—

191

C₂²×C₄

—

178

—

192

C₂²×C₄

#13083551

yes

—

193

C₂²×C₄

C₈×D₈₉

yes

—

194

C₂²×C₄

#13083557

yes

characteristic

195

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

196

M₁₆

—

197

M₁₆

—

198

M₁₆

—

178

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

178

—

204

C₂×C₈

—

178

—

205

C₂×C₈

—

178

—

206

C₂×C₈

—

178

—

207

C₂×C₈

#13083551

yes

—

208

C₂×C₈

C₂×C₂²⋊D₈₉

yes

characteristic

209

C₂×C₈

C₂×D₃₅₆

yes

characteristic

210

C₂×C₈

#13083573

yes

—

211

C₂×C₈

#13083573

yes

—

212

C₄²

—

213

C₄²

—

214

C₄²

—

178

—

215

C₄²

—

178

—

216

C₄²

—

178

—

217

C₁₆

—

218

C₁₆

—

356

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

#15667924

yes

—

223

C₂³

C₂×#13083557

yes

characteristic

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

356

—

231

C₂×C₄

—

356

—

232

C₂×C₄

—

178

—

233

C₂×C₄

—

178

—

234

C₂×C₄

—

178

—

235

C₂×C₄

#15667924

yes

—

236

C₂×C₄

C₂×#13083551

yes

characteristic

237

C₂×C₄

#15667968

yes

characteristic

238

C₂×C₄

#15667968

yes

characteristic

239

C₂×C₄

C₂×C₈×D₈₉

yes

characteristic

240

C₂×C₄

M₁₆×D₈₉

yes

characteristic

241

C₂×C₄

M₁₆×D₈₉

yes

characteristic

242

C₈

—

243

C₈

—

178

—

244

C₈

—

178

—

245

C₈

#15667993

yes

—

246

C₈

#15667996

yes

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

C₂×#15667924

yes

characteristic

253

C₂²

#19151652

yes

characteristic

254

C₂²

#19151652

yes

characteristic

255

C₄

—

256

C₄

—

356

—

257

C₄

—

178

—

258

C₄

#19151459

yes

characteristic

259

C₄

#19151561

yes

characteristic

260

C₄

#19151648

yes

characteristic

261

C₄

#19151648

yes

characteristic

262

C₂

—

263

C₂

—

264

C₂

—

265

C₂

#26020318

yes

characteristic

266

C₂

#26022061

yes

—

	subgroup	G/H
center	C₂×C₄	#15667968
commutator	C₂×C₄×C₈₉	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₂×#349×C₈₉	C₂
socle	C₂²×C₈₉	#432
prime radical	C₂⁴×C₈₉	M₁₆
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	C₂×#349	D₈₉
hypocenter	C₈₉	#12849
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#349

subgroup

G/H

center

C₂×C₄

#15667968

commutator

C₂×C₄×C₈₉

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₈₉

Fitting

C₂×#349×C₈₉

C₂

socle

C₂²×C₈₉

#432

prime radical

C₂⁴×C₈₉

M₁₆

cosocle

C₂²×C₈×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#349

N	H ≅ G/N	type
3. #26018333	C₂	semidirect
4. #26018331	C₂	semidirect
139. C₈₉	#12849	semidirect

H ≅ G/N

type

3. #26018333

C₂

semidirect

4. #26018331

C₂

semidirect

139. C₈₉

#12849

semidirect

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

subgroup	index
C₂×M₁₆×Dic₈₉	2
C₂×#19151380	2
#26018333	2
#26018331	2
C₂×#349×C₈₉	2
#12849	89

subgroup

index

C₂×M₁₆×Dic₈₉

C₂×#349×C₈₉

Subgroups — #36470653

Conjugacy classes of subgroups

Complements

Maximal subgroups