Group #36710877 — subgroups

Subgroups — #36710877

Order 22784.

488 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 143 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	#26030891	C₂	1	2	yes	maximal, complemented
2	#26022400	C₂	1	2	yes	maximal, complemented
3	#26022395	C₂	1	2	yes	maximal, complemented
4	#26022360	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022355	C₂	1	1	yes	maximal, characteristic
6	#26022348	C₂	1	2	yes	maximal, complemented
7	#26022315	C₂	1	2	yes	maximal, complemented
8	#26022308	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2151	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152219	—	2	2	no	—
11	C₂×Dic₇₁₂	C₂²	1	1	yes	characteristic
12	C₂×#15667957	C₂²	1	2	yes	—
13	C₂×D₁₄₂₄	C₂²	1	1	yes	characteristic
14	#19152003	C₂²	1	2	yes	—
15	#19151982	C₂²	1	2	yes	—
16	#19151958	—	2	2	no	—
17	#19151844	—	2	2	no	—
18	#19151839	C₂²	1	2	yes	—
19	#19151834	C₂²	1	2	yes	—
20	#19151700	—	2	2	no	—
21	C₄×Dic₃₅₆	C₂²	1	2	yes	—
22	C₄×D₇₁₂	C₂²	1	2	yes	—
23	#19151426	C₂²	1	1	yes	characteristic
24	#19151426	C₂²	1	2	yes	—
25	#19151426	C₂²	1	1	yes	characteristic
26	#19151403	C₂²	1	2	yes	—
27	#19151403	C₂²	1	2	yes	—
28	#19151400	C₂²	1	2	yes	—
29	#19151400	C₂²	1	2	yes	—
30	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
31	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
32	#405×C₈₉	C₂²	1	1	yes	characteristic
33	C₄⋊C₁₆×C₈₉	C₂²	1	2	yes	—
34	C₄⋊C₁₆×C₈₉	C₂²	1	2	yes	—
35	C₂×Dic₃₅₆	C₂³	1	2	yes	—
36	C₂×#13083563	—	2	2	no	—
37	C₂×D₇₁₂	C₂³	1	2	yes	—
38	#15668012	—	2	2	no	—
39	#15668007	—	4	2	no	—
40	#15668000	—	2	2	no	—
41	#15667998	—	4	2	no	—
42	#15667994	—	4	2	no	—
43	#15667991	—	2	2	no	—
44	#15667990	—	4	2	no	—
45	#15667986	—	2	2	no	—
46	C₄×Dic₁₇₈	—	2	2	no	—
47	C₄×D₃₅₆	—	2	2	no	—
48	Dic₇₁₂	—	4	1	no	—
49	#15667957	—	4	2	no	—
50	D₁₄₂₄	—	4	1	no	—
51	#15667946	—	2	2	no	—
52	#15667946	C₂³	1	2	yes	—
53	#15667946	C₂³	1	2	yes	—
54	#15667937	—	2	2	no	—
55	#15667937	—	2	2	no	—
56	#15667934	—	2	2	no	—
57	#15667934	—	2	2	no	—
58	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
60	#117×C₈₉	D₄	1	1	yes	characteristic
61	M₃₂×C₈₉	—	4	1	no	—
62	C₂×C₁₆×C₈₉	—	4	1	no	—
63	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
64	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
65	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
66	#97×C₈₉	D₄	1	2	yes	—
67	C₄×C₈×C₈₉	C₂³	1	2	yes	—
68	C₂×Dic₁₇₈	—	2	2	no	—
69	C₂×Dic₁₇₈	—	4	2	no	—
70	C₂×D₃₅₆	—	2	2	no	—
71	C₂×C₂²⋊D₈₉	—	4	2	no	—
72	C₂×C₄×D₈₉	—	4	2	no	—
73	Dic₃₅₆	—	2	2	no	—
74	Dic₃₅₆	—	2	2	no	—
75	#13083563	—	4	4	no	—
76	D₇₁₂	—	2	2	no	—
77	D₇₁₂	—	2	2	no	—
78	C₄⋊Dic₈₉	—	2	2	no	—
79	C₄⋊Dic₈₉	—	2	2	no	—
80	C₄⋊Dic₈₉	—	4	2	no	—
81	#13083553	—	4	2	no	—
82	#13083553	—	4	2	no	—
83	C₂²⋊Dic₈₉	—	4	2	no	—
84	#13083551	—	4	2	no	—
85	#13083551	—	4	2	no	—
86	#13083551	—	4	2	no	—
87	#13083551	—	4	2	no	—
88	C₄×Dic₈₉	—	4	2	no	—
89	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
90	M₁₆×C₈₉	—	4	1	no	—
91	C₂×C₈×C₈₉	—	2	1	no	—
92	C₂×C₈×C₈₉	—	2	1	no	—
93	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
94	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
96	C₄⋊C₄×C₈₉	D₈	1	2	yes	—
97	C₂²⋊C₄×C₈₉	D₈	1	1	yes	characteristic
98	C₂²⋊C₄×C₈₉	D₈	1	1	yes	characteristic
99	C₄²×C₈₉	C₂×D₄	1	2	yes	—
100	C₁₆×C₈₉	—	2	2	no	—
101	C₁₆×C₈₉	—	2	1	no	—
102	C₁₆×C₈₉	—	2	1	no	—
103	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
104	C₂²×D₈₉	—	4	2	no	—
105	C₂×C₄×C₈₉	—	2	1	no	—
106	C₂×C₄×C₈₉	—	2	1	no	—
107	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
108	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
109	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
110	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
111	C₂²⋊D₈₉	—	16	2	no	—
112	C₂×Dic₈₉	—	4	2	no	—
113	C₂×Dic₈₉	—	4	2	no	—
114	C₂×Dic₈₉	—	4	2	no	—
115	D₃₅₆	—	4	2	no	—
116	D₃₅₆	—	4	2	no	—
117	C₄×D₈₉	—	16	2	no	—
118	Dic₁₇₈	—	4	2	no	—
119	Dic₁₇₈	—	4	2	no	—
120	Dic₁₇₈	—	16	2	no	—
121	C₈×C₈₉	—	2	1	no	—
122	C₈×C₈₉	—	2	2	no	—
123	C₈×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
124	C₈×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
125	C₂²×C₈₉	—	2	2	no	—
126	C₂²×C₈₉	—	2	1	no	—
127	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
128	C₂×D₈₉	—	8	2	no	—
129	C₂×D₈₉	—	8	2	no	—
130	C₂×D₈₉	—	8	2	no	—
131	C₄×C₈₉	—	2	2	no	—
132	C₄×C₈₉	—	2	2	no	—
133	C₄×C₈₉	—	2	1	no	—
134	C₄×C₈₉	#537	1	1	yes	characteristic
135	C₄×C₈₉	#575	1	1	yes	characteristic
136	Dic₈₉	—	8	2	no	—
137	Dic₈₉	—	8	2	no	—
138	Dic₈₉	—	8	2	no	—
139	#33829	—	89	1	no	maximal, Sylow
140	C₂×C₈₉	—	4	1	no	—
141	C₂×C₈₉	#3245	1	1	yes	characteristic
142	C₂×C₈₉	#3416	1	2	yes	—
143	D₈₉	—	16	2	no	—
144	#3175	—	89	2	no	—
145	#2226	—	89	2	no	—
146	#2225	—	89	2	no	—
147	#2219	—	89	1	no	—
148	#2218	—	89	1	no	—
149	#2217	—	89	2	no	—
150	#2211	—	89	2	no	—
151	#2210	—	89	2	no	—
152	#2151	D₈₉	1	1	yes	characteristic, complemented
153	C₈₉	#33829	1	1	yes	characteristic, complemented, Sylow
154	#542	—	178	2	no	—
155	C₂×Q₃₂	—	89	1	no	—
156	C₂×SD₃₂	—	89	2	no	—
157	C₂×D₁₆	—	89	1	no	—
158	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
159	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
160	#500	—	89	2	no	—
161	#495	—	89	2	no	—
162	#489	—	178	2	no	—
163	#468	—	178	2	no	—
164	#467	—	89	2	no	—
165	#466	—	89	2	no	—
166	#440	—	178	2	no	—
167	C₄×Q₁₆	—	89	2	no	—
168	C₄×D₈	—	89	2	no	—
169	#405	C₂×D₈₉	1	1	yes	characteristic
170	#367	—	89	2	no	—
171	#367	—	89	1	no	—
172	#367	—	89	1	no	—
173	C₄⋊C₁₆	C₂×D₈₉	1	2	yes	—
174	C₄⋊C₁₆	C₂×D₈₉	1	2	yes	—
175	#358	—	89	2	no	—
176	#358	—	89	2	no	—
177	#357	—	89	2	no	—
178	#357	—	89	2	no	—
179	C₂×Q₁₆	—	89	2	no	—
180	C₂×SD₁₆	—	178	2	no	—
181	C₂×D₈	—	89	2	no	—
182	C₂×M₁₆	D₃₅₆	1	1	yes	characteristic
183	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
184	C₄⋊Q₈	—	178	2	no	—
185	#126	—	356	2	no	—
186	#124	—	356	2	no	—
187	#124	—	178	2	no	—
188	#123	—	356	2	no	—
189	C₂²⋊Q₈	—	356	2	no	—
190	C₂²⋊Q₈	—	178	2	no	—
191	#121	—	178	2	no	—
192	C₄×Q₈	—	178	2	no	—
193	C₄×D₄	—	178	2	no	—
194	#117	D₃₅₆	1	1	yes	characteristic
195	Q₃₂	—	356	1	no	—
196	SD₃₂	—	356	2	no	—
197	D₁₆	—	356	1	no	—
198	M₃₂	—	4	1	no	—
199	C₂×C₁₆	—	4	1	no	—
200	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
201	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
202	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
203	#107	—	89	2	no	—
204	#107	—	89	2	no	—
205	#107	—	178	2	no	—
206	#103	—	178	2	no	—
207	#103	—	178	2	no	—
208	#102	—	178	2	no	—
209	#102	—	178	2	no	—
210	#97	D₃₅₆	1	2	yes	—
211	C₄×C₈	C₂²×D₈₉	1	2	yes	—
212	C₂×Q₈	—	356	2	no	—
213	C₂×Q₈	—	178	2	no	—
214	C₂×D₄	—	356	2	no	—
215	C₂×D₄	—	178	2	no	—
216	C₂²×C₄	—	356	2	no	—
217	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
218	Q₁₆	—	178	2	no	—
219	Q₁₆	—	178	2	no	—
220	SD₁₆	—	356	4	no	—
221	D₈	—	178	2	no	—
222	D₈	—	178	2	no	—
223	M₁₆	—	4	1	no	—
224	C₂×C₈	—	2	1	no	—
225	C₂×C₈	—	2	1	no	—
226	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
227	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
228	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
229	C₄⋊C₄	—	356	2	no	—
230	C₄⋊C₄	—	356	2	no	—
231	C₄⋊C₄	—	356	2	no	—
232	C₄⋊C₄	—	178	2	no	—
233	C₄⋊C₄	—	178	2	no	—
234	C₄⋊C₄	D₇₁₂	1	2	yes	—
235	C₂²⋊C₄	—	356	2	no	—
236	C₂²⋊C₄	—	356	2	no	—
237	C₂²⋊C₄	—	356	2	no	—
238	C₂²⋊C₄	—	356	2	no	—
239	C₂²⋊C₄	—	356	2	no	—
240	C₂²⋊C₄	D₇₁₂	1	1	yes	characteristic
241	C₂²⋊C₄	D₇₁₂	1	1	yes	characteristic
242	C₄²	—	356	2	no	—
243	C₄²	C₂×D₃₅₆	1	2	yes	—
244	C₁₆	—	2	2	no	—
245	C₁₆	—	2	1	no	—
246	C₁₆	—	2	1	no	—
247	C₂³	—	356	2	no	—
248	C₂³	C₂×D₇₁₂	1	1	yes	characteristic
249	Q₈	—	356	2	no	—
250	Q₈	—	356	2	no	—
251	Q₈	—	1424	2	no	—
252	D₄	—	356	2	no	—
253	D₄	—	356	2	no	—
254	D₄	—	1424	2	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	356	2	no	—
258	C₂×C₄	—	356	2	no	—
259	C₂×C₄	—	356	2	no	—
260	C₂×C₄	—	1424	2	no	—
261	C₂×C₄	C₂×D₇₁₂	1	2	yes	—
262	C₂×C₄	C₂×D₇₁₂	1	2	yes	—
263	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
264	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
265	C₈	—	2	2	no	—
266	C₈	—	2	1	no	—
267	C₈	#15668057	1	1	yes	characteristic
268	C₈	#15668060	1	1	yes	characteristic
269	C₂²	—	2	1	no	—
270	C₂²	—	2	2	no	—
271	C₂²	—	712	2	no	—
272	C₂²	—	712	2	no	—
273	C₂²	—	712	2	no	—
274	C₂²	C₂²×D₇₁₂	1	1	yes	characteristic
275	C₄	—	2	1	no	—
276	C₄	—	2	2	no	—
277	C₄	—	2	2	no	—
278	C₄	—	712	2	no	—
279	C₄	—	712	2	no	—
280	C₄	—	712	2	no	—
281	C₄	#19152179	1	1	yes	characteristic
282	C₄	#19152398	1	1	yes	characteristic
283	C₂	—	4	1	no	—
284	C₂	—	1424	2	no	—
285	C₂	#26031562	1	1	yes	characteristic
286	C₂	#26033400	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26030891

C₂

yes

maximal, complemented

#26022400

C₂

yes

maximal, complemented

#26022395

C₂

yes

maximal, complemented

#26022360

C₂

yes

maximal, characteristic, complemented

#26022355

C₂

yes

maximal, characteristic

#26022348

C₂

yes

maximal, complemented

#26022315

C₂

yes

maximal, complemented

#26022308

C₂

yes

maximal, complemented

C₈₉×#2151

C₂

yes

maximal, characteristic, complemented

#19152219

—

C₂×Dic₇₁₂

C₂²

yes

characteristic

C₂×#15667957

C₂²

yes

—

C₂×D₁₄₂₄

C₂²

yes

characteristic

#19152003

C₂²

yes

—

#19151982

C₂²

yes

—

#19151958

—

#19151844

—

#19151839

C₂²

yes

—

#19151834

C₂²

yes

—

#19151700

—

C₄×Dic₃₅₆

C₂²

yes

—

C₄×D₇₁₂

C₂²

yes

—

#19151426

C₂²

yes

characteristic

#19151426

C₂²

yes

—

#19151426

C₂²

yes

characteristic

#19151403

C₂²

yes

—

#19151403

C₂²

yes

—

#19151400

C₂²

yes

—

#19151400

C₂²

yes

—

C₂×M₃₂×C₈₉

C₂²

yes

characteristic

C₂²×C₁₆×C₈₉

C₂²

yes

characteristic

#405×C₈₉

C₂²

yes

characteristic

C₄⋊C₁₆×C₈₉

C₂²

yes

—

C₄⋊C₁₆×C₈₉

C₂²

yes

—

C₂×Dic₃₅₆

C₂³

yes

—

C₂×#13083563

—

C₂×D₇₁₂

C₂³

yes

—

—

—

—

—

—

—

—

—

C₄×Dic₁₇₈

—

C₄×D₃₅₆

—

Dic₇₁₂

—

#15667957

—

D₁₄₂₄

—

#15667946

—

#15667946

C₂³

yes

—

#15667946

C₂³

yes

—

—

—

—

—

C₂×M₁₆×C₈₉

D₄

yes

characteristic

C₂²×C₈×C₈₉

C₂³

yes

characteristic

#117×C₈₉

D₄

yes

characteristic

M₃₂×C₈₉

—

C₂×C₁₆×C₈₉

—

C₂×C₁₆×C₈₉

C₂³

yes

characteristic

C₂×C₁₆×C₈₉

C₂³

yes

—

C₂×C₁₆×C₈₉

C₂³

yes

characteristic

#97×C₈₉

D₄

yes

—

C₄×C₈×C₈₉

C₂³

yes

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×D₃₅₆

—

C₂×C₂²⋊D₈₉

—

C₂×C₄×D₈₉

—

Dic₃₅₆

—

Dic₃₅₆

—

#13083563

—

D₇₁₂

—

D₇₁₂

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

#13083553

—

#13083553

—

C₂²⋊Dic₈₉

—

—

—

—

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

M₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂×D₄

yes

—

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂⁴

yes

characteristic

C₄⋊C₄×C₈₉

D₈

yes

—

C₂²⋊C₄×C₈₉

D₈

yes

characteristic

C₂²⋊C₄×C₈₉

D₈

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

—

100

C₁₆×C₈₉

—

101

C₁₆×C₈₉

—

102

C₁₆×C₈₉

—

103

C₂³×C₈₉

C₂×D₈

yes

characteristic

104

C₂²×D₈₉

—

105

C₂×C₄×C₈₉

—

106

C₂×C₄×C₈₉

—

107

C₂×C₄×C₈₉

C₂×D₈

yes

—

108

C₂×C₄×C₈₉

C₂×D₈

yes

—

109

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

110

C₂×C₄×C₈₉

C₂²×D₄

yes

characteristic

111

C₂²⋊D₈₉

—

112

C₂×Dic₈₉

—

113

C₂×Dic₈₉

—

114

C₂×Dic₈₉

—

115

D₃₅₆

—

116

D₃₅₆

—

117

C₄×D₈₉

—

118

Dic₁₇₈

—

119

Dic₁₇₈

—

120

Dic₁₇₈

—

121

C₈×C₈₉

—

122

C₈×C₈₉

—

123

C₈×C₈₉

H(5,𝔽₂)

yes

characteristic

124

C₈×C₈₉

2₋¹⁺⁴

yes

characteristic

125

C₂²×C₈₉

—

126

C₂²×C₈₉

—

127

C₂²×C₈₉

C₂²×D₈

yes

characteristic

128

C₂×D₈₉

—

129

C₂×D₈₉

—

130

C₂×D₈₉

—

131

C₄×C₈₉

—

132

C₄×C₈₉

—

133

C₄×C₈₉

—

134

C₄×C₈₉

#537

yes

characteristic

135

C₄×C₈₉

#575

yes

characteristic

136

Dic₈₉

—

137

Dic₈₉

—

138

Dic₈₉

—

139

#33829

—

maximal, Sylow

140

C₂×C₈₉

—

141

C₂×C₈₉

#3245

yes

characteristic

142

C₂×C₈₉

#3416

yes

—

143

D₈₉

—

144

#3175

—

145

#2226

—

146

#2225

—

147

#2219

—

148

#2218

—

149

#2217

—

150

#2211

—

151

#2210

—

152

#2151

D₈₉

yes

characteristic, complemented

153

C₈₉

#33829

yes

characteristic, complemented, Sylow

154

#542

—

178

—

155

C₂×Q₃₂

—

156

C₂×SD₃₂

—

157

C₂×D₁₆

—

158

C₂×M₃₂

C₂×D₈₉

yes

characteristic

159

C₂²×C₁₆

C₂×D₈₉

yes

characteristic

160

#500

—

161

#495

—

162

#489

—

178

—

163

#468

—

178

—

164

#467

—

165

#466

—

166

#440

—

178

—

167

C₄×Q₁₆

—

168

C₄×D₈

—

169

#405

C₂×D₈₉

yes

characteristic

170

#367

—

171

#367

—

172

#367

—

173

C₄⋊C₁₆

C₂×D₈₉

yes

—

174

C₄⋊C₁₆

C₂×D₈₉

yes

—

175

#358

—

176

#358

—

177

#357

—

178

#357

—

179

C₂×Q₁₆

—

180

C₂×SD₁₆

—

178

—

181

C₂×D₈

—

182

C₂×M₁₆

D₃₅₆

yes

characteristic

183

C₂²×C₈

C₂²×D₈₉

yes

characteristic

184

C₄⋊Q₈

—

178

—

185

#126

—

356

—

186

#124

—

356

—

187

#124

—

178

—

188

#123

—

356

—

189

C₂²⋊Q₈

—

356

—

190

C₂²⋊Q₈

—

178

—

191

#121

—

178

—

192

C₄×Q₈

—

178

—

193

C₄×D₄

—

178

—

194

#117

D₃₅₆

yes

characteristic

195

Q₃₂

—

356

—

196

SD₃₂

—

356

—

197

D₁₆

—

356

—

198

M₃₂

—

199

C₂×C₁₆

—

200

C₂×C₁₆

C₂²×D₈₉

yes

characteristic

201

C₂×C₁₆

C₂²×D₈₉

yes

—

202

C₂×C₁₆

C₂²×D₈₉

yes

characteristic

203

#107

—

204

#107

—

205

#107

—

178

—

206

#103

—

178

—

207

#103

—

178

—

208

#102

—

178

—

209

#102

—

178

—

210

#97

D₃₅₆

yes

—

211

C₄×C₈

C₂²×D₈₉

yes

—

212

C₂×Q₈

—

356

—

213

C₂×Q₈

—

178

—

214

C₂×D₄

—

356

—

215

C₂×D₄

—

178

—

216

C₂²×C₄

—

356

—

217

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

218

Q₁₆

—

178

—

219

Q₁₆

—

178

—

220

SD₁₆

—

356

—

221

D₈

—

178

—

222

D₈

—

178

—

223

M₁₆

—

224

C₂×C₈

—

225

C₂×C₈

—

226

C₂×C₈

C₂×D₃₅₆

yes

—

227

C₂×C₈

C₂×D₃₅₆

yes

characteristic

228

C₂×C₈

C₂³×D₈₉

yes

characteristic

229

C₄⋊C₄

—

356

—

230

C₄⋊C₄

—

356

—

231

C₄⋊C₄

—

356

—

232

C₄⋊C₄

—

178

—

233

C₄⋊C₄

—

178

—

234

C₄⋊C₄

D₇₁₂

yes

—

235

C₂²⋊C₄

—

356

—

236

C₂²⋊C₄

—

356

—

237

C₂²⋊C₄

—

356

—

238

C₂²⋊C₄

—

356

—

239

C₂²⋊C₄

—

356

—

240

C₂²⋊C₄

D₇₁₂

yes

characteristic

241

C₂²⋊C₄

D₇₁₂

yes

characteristic

242

C₄²

—

356

—

243

C₄²

C₂×D₃₅₆

yes

—

244

C₁₆

—

245

C₁₆

—

246

C₁₆

—

247

C₂³

—

356

—

248

C₂³

C₂×D₇₁₂

yes

characteristic

249

Q₈

—

356

—

250

Q₈

—

356

—

251

Q₈

—

1424

—

252

D₄

—

356

—

253

D₄

—

356

—

254

D₄

—

1424

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

356

—

258

C₂×C₄

—

356

—

259

C₂×C₄

—

356

—

260

C₂×C₄

—

1424

—

261

C₂×C₄

C₂×D₇₁₂

yes

—

262

C₂×C₄

C₂×D₇₁₂

yes

—

263

C₂×C₄

C₂×D₇₁₂

yes

characteristic

264

C₂×C₄

C₂²×D₃₅₆

yes

characteristic

265

C₈

—

266

C₈

—

267

C₈

#15668057

yes

characteristic

268

C₈

#15668060

yes

characteristic

269

C₂²

—

270

C₂²

—

271

C₂²

—

712

—

272

C₂²

—

712

—

273

C₂²

—

712

—

274

C₂²

C₂²×D₇₁₂

yes

characteristic

275

C₄

—

276

C₄

—

277

C₄

—

278

C₄

—

712

—

279

C₄

—

712

—

280

C₄

—

712

—

281

C₄

#19152179

yes

characteristic

282

C₄

#19152398

yes

characteristic

283

C₂

—

284

C₂

—

1424

—

285

C₂

#26031562

yes

characteristic

286

C₂

#26033400

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₇₁₂
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#2151	C₂
socle	C₂²×C₈₉	C₂²×D₈
prime radical	#26022355	C₂
hypercenter	#2151	D₈₉
hypocenter	C₈₉	#33829
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405 ◁ #2151

subgroup

G/H

center

C₂²

C₂²×D₇₁₂

commutator, cosocle

C₂×C₈×C₈₉

C₂⁴

Frattini

C₂×C₈

C₂³×D₈₉

Fitting

C₈₉×#2151

C₂

socle

C₂²×C₈₉

C₂²×D₈

C₂

D₈₉

C₈₉

G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ #117 ◁ #405 ◁ #2151

N	H ≅ G/N	type
1. #26030891	C₂	semidirect
2. #26022400	C₂	semidirect
3. #26022395	C₂	semidirect
4. #26022360	C₂	semidirect
6. #26022348	C₂	semidirect
7. #26022315	C₂	semidirect
8. #26022308	C₂	semidirect
9. C₈₉×#2151	C₂	semidirect
152. #2151	D₈₉	semidirect
153. C₈₉	#33829	semidirect

H ≅ G/N

type

1. #26030891

C₂

semidirect

2. #26022400

C₂

semidirect

3. #26022395

C₂

semidirect

4. #26022360

C₂

semidirect

6. #26022348

C₂

semidirect

7. #26022315

C₂

semidirect

8. #26022308

C₂

semidirect

9. C₈₉×#2151

C₂

semidirect

152. #2151

D₈₉

semidirect

153. C₈₉

#33829

semidirect

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

subgroup	index
#26030891	2
#26022400	2
#26022395	2
#26022360	2
#26022355	2
#26022348	2
#26022315	2
#26022308	2
C₈₉×#2151	2
#33829	89

subgroup

index

C₈₉×#2151

Subgroups — #36710877

Conjugacy classes of subgroups

Complements

Maximal subgroups