Subgroups — #26034271

Order 11392.

1252 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152312	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152307	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152300	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152294	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152291	C₂	1	2	yes	maximal, complemented
6	#19152268	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152242	C₂	1	2	yes	maximal, complemented
8	#19152235	C₂	1	2	yes	maximal, complemented
9	#19152235	C₂	1	2	yes	maximal, complemented
10	D₄×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152202	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152201	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152185	C₂	1	2	yes	maximal, complemented
15	#19152183	C₂	1	2	yes	maximal, complemented
16	#19152143	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152128	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152104	C₂	1	2	yes	maximal, complemented
19	C₂×#15667984	C₂	1	2	yes	maximal, complemented
20	#19152073	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152070	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×D₄×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄²×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083573	C₂²	1	2	yes	complemented
25	C₂×#13083573	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
28	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
29	C₂³×Dic₈₉	C₂²	1	2	yes	complemented
30	#15668011	C₂²	1	1	yes	characteristic, complemented
31	#15668008	C₂²	1	1	yes	characteristic, complemented
32	#15668008	C₂²	1	1	yes	characteristic, complemented
33	#15668007	C₂²	1	1	yes	characteristic, complemented
34	#15668007	C₂²	1	2	yes	complemented
35	#15668005	C₂²	1	1	yes	characteristic, complemented
36	#15668005	C₂²	1	2	yes	complemented
37	#15668004	C₂²	1	1	yes	characteristic, complemented
38	#15668003	C₂²	1	1	yes	characteristic, complemented
39	#15668002	C₂²	1	1	yes	characteristic, complemented
40	#15667999	C₂²	1	2	yes	complemented
41	#15667998	C₂²	1	1	yes	characteristic, complemented
42	#15667998	C₂²	1	2	yes	complemented
43	#15667998	C₂²	1	2	yes	complemented
44	#15667996	C₂²	1	1	yes	characteristic, complemented
45	#15667996	C₂²	1	2	yes	complemented
46	#15667996	C₂²	1	2	yes	complemented
47	#15667994	C₂²	1	2	yes	complemented
48	#15667994	C₂²	1	2	yes	complemented
49	#15667993	C₂²	1	1	yes	characteristic, complemented
50	#15667993	C₂²	1	2	yes	complemented
51	#15667993	C₂²	1	2	yes	complemented
52	#15667991	C₂²	1	2	yes	complemented
53	#15667989	C₂²	1	1	yes	characteristic, complemented
54	#15667989	C₂²	1	2	yes	complemented
55	#15667989	C₂²	1	2	yes	complemented
56	#15667986	C₂²	1	1	yes	characteristic, complemented
57	#15667986	C₂²	1	1	yes	characteristic, complemented
58	#15667984	C₂²	1	1	yes	characteristic
59	#15667984	C₂²	1	2	yes	complemented
60	#15667984	C₂²	1	2	yes	complemented
61	#15667984	C₂²	1	2	yes	complemented
62	#15667984	C₂²	1	2	yes	complemented
63	#15667984	C₂²	1	2	yes	complemented
64	#15667984	C₂²	1	2	yes	complemented
65	#15667984	C₂²	1	2	yes	complemented
66	#15667984	C₂²	1	2	yes	complemented
67	#15667984	C₂²	1	2	yes	complemented
68	#15667984	C₂²	1	2	yes	complemented
69	#15667984	C₂²	1	2	yes	complemented
70	#15667983	C₂²	1	2	yes	complemented
71	#15667983	C₂²	1	2	yes	complemented
72	#15667983	C₂²	1	1	yes	characteristic, complemented
73	#15667983	C₂²	1	1	yes	characteristic, complemented
74	#15667981	C₂²	1	2	yes	complemented
75	#15667981	C₂²	1	2	yes	complemented
76	#15667980	C₂²	1	2	yes	complemented
77	#15667980	C₂²	1	2	yes	complemented
78	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
80	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
81	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
82	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
83	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
84	D₄×Dic₈₉	C₂²	1	2	yes	complemented
85	D₄×Dic₈₉	C₂²	1	2	yes	complemented
86	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
87	D₄×Dic₈₉	C₂²	1	2	yes	complemented
88	D₄×Dic₈₉	C₂²	1	2	yes	complemented
89	D₄×Dic₈₉	C₂²	1	2	yes	complemented
90	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
91	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
92	#15667974	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
96	#15667972	C₂²	1	2	yes	complemented
97	#15667972	C₂²	1	2	yes	complemented
98	#15667972	C₂²	1	2	yes	complemented
99	#15667971	C₂²	1	1	yes	characteristic, complemented
100	#15667971	C₂²	1	1	yes	characteristic, complemented
101	#15667970	C₂²	1	1	yes	characteristic, complemented
102	#15667969	C₂²	1	1	yes	characteristic, complemented
103	#15667968	C₂²	1	2	yes	complemented
104	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic, complemented
105	C₂×#13083553	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊Dic₈₉	C₂²	1	2	yes	complemented
107	C₂×C₂²⋊Dic₈₉	C₂²	1	2	yes	complemented
108	C₂×C₂²⋊Dic₈₉	C₂²	1	2	yes	complemented
109	C₂×#13083551	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
111	C₂×C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
112	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic
113	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic
114	C₂²×D₄×C₈₉	C₂²	1	2	yes	complemented
115	#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
116	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
117	#121×C₈₉	C₂²	1	2	yes	complemented
118	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	#120×C₈₉	C₂²	1	2	yes	complemented
120	#120×C₈₉	C₂²	1	2	yes	complemented
121	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
122	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₈₉	C₂³	1	2	yes	—
124	#13083573	—	4	4	no	—
125	#13083573	—	4	4	no	—
126	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₇₈	C₂³	1	2	yes	—
128	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₈₉	—	4	4	no	—
130	C₂×C₂²⋊D₈₉	—	4	4	no	—
131	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
142	D₄×D₈₉	—	2	4	no	—
143	C₂²×Dic₈₉	—	4	4	no	—
144	C₂²×Dic₈₉	C₂³	1	2	yes	—
145	C₂²×Dic₈₉	C₂³	1	2	yes	—
146	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
147	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
148	C₂²×Dic₈₉	C₂³	1	2	yes	—
149	C₂²×Dic₈₉	C₂³	1	2	yes	—
150	C₂²×Dic₈₉	C₂³	1	2	yes	—
151	C₂²×Dic₈₉	C₂³	1	2	yes	—
152	C₂²×Dic₈₉	C₂³	1	2	yes	—
153	C₂²×Dic₈₉	C₂³	1	2	yes	—
154	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₈₉	C₂³	1	2	yes	—
156	C₂×C₄×D₈₉	C₂³	1	2	yes	—
157	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₈₉	C₂³	1	2	yes	—
163	C₄⋊Dic₈₉	C₂³	1	2	yes	—
164	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
165	#13083553	C₂³	1	1	yes	characteristic
166	#13083553	C₂³	1	2	yes	—
167	#13083553	C₂³	1	1	yes	characteristic
168	#13083553	C₂³	1	1	yes	characteristic
169	#13083553	C₂³	1	2	yes	—
170	#13083553	C₂³	1	1	yes	characteristic
171	#13083553	C₂³	1	1	yes	characteristic
172	#13083553	C₂³	1	1	yes	characteristic
173	#13083553	C₂³	1	2	yes	—
174	#13083553	C₂³	1	2	yes	—
175	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
184	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
185	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
186	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
187	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
188	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
189	#13083551	C₂³	1	1	yes	characteristic
190	#13083551	C₂³	1	1	yes	characteristic
191	#13083551	C₂³	1	2	yes	—
192	#13083551	C₂³	1	2	yes	—
193	#13083551	C₂³	1	2	yes	—
194	#13083551	C₂³	1	2	yes	—
195	#13083551	C₂³	1	2	yes	—
196	#13083551	C₂³	1	1	yes	characteristic
197	#13083551	C₂³	1	1	yes	characteristic
198	C₄×Dic₈₉	C₂³	1	2	yes	—
199	C₄×Dic₈₉	C₂³	1	2	yes	—
200	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
203	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
204	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
205	C₂⁴×C₈₉	C₂³	1	2	yes	—
206	C₂⁴×C₈₉	C₂³	1	2	yes	—
207	C₂×D₄×C₈₉	—	2	4	no	—
208	C₂×D₄×C₈₉	—	2	4	no	—
209	C₂×D₄×C₈₉	—	4	4	no	—
210	C₂×D₄×C₈₉	C₂³	1	2	yes	—
211	C₂×D₄×C₈₉	C₂³	1	2	yes	—
212	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
213	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
214	C₂×D₄×C₈₉	C₂³	1	2	yes	—
215	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
216	C₂×D₄×C₈₉	C₂³	1	2	yes	—
217	C₂×D₄×C₈₉	C₂³	1	2	yes	—
218	C₂×D₄×C₈₉	C₂³	1	2	yes	—
219	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
220	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
221	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
222	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
223	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
224	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
227	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
229	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
230	C₄²×C₈₉	C₂³	1	1	yes	characteristic
231	C₂³×C₈₉	—	2	4	no	—
232	C₂³×C₈₉	—	2	4	no	—
233	C₂³×C₈₉	—	2	4	no	—
234	C₂³×C₈₉	—	4	2	no	—
235	C₂³×C₈₉	—	4	2	no	—
236	C₂³×C₈₉	—	4	2	no	—
237	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
238	C₂³×C₈₉	C₂⁴	1	2	yes	—
239	C₂³×C₈₉	C₂⁴	1	2	yes	—
240	C₂³×C₈₉	C₂⁴	1	2	yes	—
241	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₂²×D₈₉	—	2	4	no	—
243	C₂²×D₈₉	—	4	2	no	—
244	C₂²×D₈₉	—	4	2	no	—
245	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
246	C₂²×D₈₉	C₂⁴	1	2	yes	—
247	D₄×C₈₉	—	2	4	no	—
248	D₄×C₈₉	—	2	4	no	—
249	D₄×C₈₉	—	2	2	no	—
250	D₄×C₈₉	—	2	4	no	—
251	D₄×C₈₉	—	2	2	no	—
252	D₄×C₈₉	—	2	2	no	—
253	D₄×C₈₉	—	4	2	no	—
254	D₄×C₈₉	—	4	2	no	—
255	D₄×C₈₉	—	4	2	no	—
256	D₄×C₈₉	#41	1	4	yes	complemented
257	C₂×C₄×C₈₉	—	2	2	no	—
258	C₂×C₄×C₈₉	—	2	2	no	—
259	C₂×C₄×C₈₉	—	4	2	no	—
260	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
265	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
266	C₂²⋊D₈₉	—	2	4	no	—
267	C₂²⋊D₈₉	—	2	2	no	—
268	C₂²⋊D₈₉	—	2	4	no	—
269	C₂²⋊D₈₉	—	2	2	no	—
270	C₂²⋊D₈₉	—	2	4	no	—
271	C₂²⋊D₈₉	—	4	2	no	—
272	C₂²⋊D₈₉	—	4	2	no	—
273	C₂²⋊D₈₉	—	4	2	no	—
274	C₂²⋊D₈₉	—	4	2	no	—
275	C₂²⋊D₈₉	—	4	2	no	—
276	C₂²⋊D₈₉	—	4	2	no	—
277	C₂×Dic₈₉	—	2	2	no	—
278	C₂×Dic₈₉	—	2	2	no	—
279	C₂×Dic₈₉	—	2	4	no	—
280	C₂×Dic₈₉	—	2	4	no	—
281	C₂×Dic₈₉	—	4	2	no	—
282	C₂×Dic₈₉	—	4	2	no	—
283	C₂×Dic₈₉	—	4	2	no	—
284	C₂×Dic₈₉	—	4	2	no	—
285	C₂×Dic₈₉	—	4	2	no	—
286	C₂×Dic₈₉	—	4	2	no	—
287	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₈₉	C₂⁴	1	2	yes	—
289	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
290	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
292	C₂×Dic₈₉	C₂⁴	1	2	yes	—
293	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
294	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
295	C₂×Dic₈₉	C₂⁴	1	2	yes	—
296	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
297	D₃₅₆	—	2	2	no	—
298	C₄×D₈₉	—	2	2	no	—
299	C₄×D₈₉	—	4	2	no	—
300	C₄×D₈₉	—	4	2	no	—
301	Dic₁₇₈	—	2	2	no	—
302	Dic₁₇₈	—	4	2	no	—
303	C₂²×C₈₉	—	2	1	no	—
304	C₂²×C₈₉	—	2	1	no	—
305	C₂²×C₈₉	—	2	2	no	—
306	C₂²×C₈₉	—	2	2	no	—
307	C₂²×C₈₉	—	2	1	no	—
308	C₂²×C₈₉	—	2	2	no	—
309	C₂²×C₈₉	—	2	2	no	—
310	C₂²×C₈₉	—	2	2	no	—
311	C₂²×C₈₉	—	2	2	no	—
312	C₂²×C₈₉	—	2	2	no	—
313	C₂²×C₈₉	—	2	1	no	—
314	C₂²×C₈₉	—	2	2	no	—
315	C₂²×C₈₉	—	2	1	no	—
316	C₂²×C₈₉	—	4	8	no	—
317	C₂²×C₈₉	—	8	4	no	—
318	C₂²×C₈₉	C₂×#41	1	4	yes	—
319	C₂²×C₈₉	H(5,𝔽₂)	1	2	yes	—
320	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
321	C₂×D₈₉	—	2	1	no	—
322	C₂×D₈₉	—	2	2	no	—
323	C₂×D₈₉	—	2	2	no	—
324	C₂×D₈₉	—	2	2	no	—
325	C₂×D₈₉	—	2	1	no	—
326	C₂×D₈₉	—	2	1	no	—
327	C₂×D₈₉	—	8	4	no	—
328	C₄×C₈₉	—	2	1	no	—
329	C₄×C₈₉	—	2	1	no	—
330	C₄×C₈₉	—	2	1	no	—
331	C₄×C₈₉	—	2	2	no	—
332	C₄×C₈₉	—	2	1	no	—
333	C₄×C₈₉	C₂×#41	1	2	yes	—
334	Dic₈₉	—	2	1	no	—
335	Dic₈₉	—	2	1	no	—
336	Dic₈₉	—	2	1	no	—
337	Dic₈₉	—	2	2	no	—
338	Dic₈₉	—	2	1	no	—
339	Dic₈₉	—	2	2	no	—
340	Dic₈₉	—	2	1	no	—
341	Dic₈₉	—	2	2	no	—
342	Dic₈₉	—	2	1	no	—
343	Dic₈₉	H(5,𝔽₂)	1	2	yes	—
344	C₂×C₈₉	—	2	4	no	—
345	C₂×C₈₉	—	2	2	no	—
346	C₂×C₈₉	—	4	2	no	—
347	C₂×C₈₉	—	4	2	no	—
348	C₂×C₈₉	—	4	1	no	—
349	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
350	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
352	D₈₉	—	4	2	no	—
353	D₈₉	—	4	1	no	—
354	#3519	—	89	1	no	maximal, Sylow
355	C₈₉	#3519	1	1	yes	characteristic, complemented, Sylow
356	#555	—	89	1	no	—
357	#554	—	89	1	no	—
358	#553	—	89	2	no	—
359	#553	—	89	1	no	—
360	#553	—	89	1	no	—
361	#550	—	89	1	no	—
362	#546	—	89	2	no	—
363	#546	—	89	2	no	—
364	#546	—	89	2	no	—
365	D₄²	—	89	1	no	—
366	D₄²	—	89	1	no	—
367	D₄²	D₈₉	1	1	yes	characteristic, complemented
368	#540	—	89	1	no	—
369	#540	—	89	1	no	—
370	#538	—	89	2	no	—
371	#538	—	89	2	no	—
372	#532	—	89	1	no	—
373	#529	—	89	1	no	—
374	#525	—	89	2	no	—
375	C₂×#121	—	89	2	no	—
376	#518	—	89	1	no	—
377	#518	—	89	1	no	—
378	C₂×C₄×D₄	—	89	1	no	—
379	C₂×#41	—	89	2	no	—
380	C₂×#41	—	89	2	no	—
381	C₂²×D₄	—	89	2	no	—
382	C₂²×D₄	—	89	2	no	—
383	C₂²×D₄	—	89	1	no	—
384	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic
385	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic
386	C₂²×D₄	C₂×D₈₉	1	2	yes	complemented
387	C₂³×C₄	—	89	2	no	—
388	C₄⋊Q₈	—	89	1	no	—
389	#127	—	89	1	no	—
390	#127	—	89	1	no	—
391	#127	C₂×D₈₉	1	1	yes	characteristic, complemented
392	#126	—	89	1	no	—
393	#126	—	89	2	no	—
394	#126	—	89	1	no	—
395	#126	—	89	2	no	—
396	#125	—	89	1	no	—
397	#125	—	89	1	no	—
398	#125	—	89	1	no	—
399	#124	—	89	2	no	—
400	#124	—	89	1	no	—
401	#124	—	89	2	no	—
402	#124	—	89	2	no	—
403	#123	—	89	2	no	—
404	#123	—	89	1	no	—
405	#123	—	89	2	no	—
406	#123	—	89	2	no	—
407	#123	—	89	1	no	—
408	#123	—	89	2	no	—
409	#123	—	89	2	no	—
410	#123	—	89	2	no	—
411	C₂²⋊Q₈	—	89	2	no	—
412	C₂²⋊Q₈	—	89	1	no	—
413	C₂²⋊Q₈	—	89	2	no	—
414	C₂²⋊Q₈	—	89	2	no	—
415	#121	—	89	1	no	—
416	#121	—	89	2	no	—
417	#121	—	89	2	no	—
418	#121	—	89	2	no	—
419	#121	—	89	2	no	—
420	#121	—	89	2	no	—
421	#121	—	89	2	no	—
422	#121	—	89	2	no	—
423	#121	—	89	2	no	—
424	#121	—	89	2	no	—
425	#121	—	89	1	no	—
426	#121	—	89	1	no	—
427	#121	—	89	2	no	—
428	#121	—	89	2	no	—
429	#121	—	89	2	no	—
430	#121	—	89	2	no	—
431	#121	—	89	1	no	—
432	#121	—	89	1	no	—
433	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
434	#121	C₂×D₈₉	1	2	yes	complemented
435	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
436	#120	—	89	2	no	—
437	#120	—	89	2	no	—
438	#120	—	89	2	no	—
439	#120	—	89	2	no	—
440	#120	C₂×D₈₉	1	2	yes	complemented
441	#120	C₂×D₈₉	1	2	yes	complemented
442	C₄×Q₈	—	89	1	no	—
443	C₄×D₄	—	89	1	no	—
444	C₄×D₄	—	89	1	no	—
445	C₄×D₄	—	89	2	no	—
446	C₄×D₄	—	89	1	no	—
447	C₄×D₄	—	89	2	no	—
448	C₄×D₄	—	89	1	no	—
449	C₄×D₄	—	89	1	no	—
450	C₄×D₄	—	89	2	no	—
451	C₄×D₄	—	89	1	no	—
452	C₄×D₄	—	89	2	no	—
453	C₄×D₄	—	89	1	no	—
454	C₄×D₄	—	89	2	no	—
455	C₄×D₄	—	89	2	no	—
456	C₄×D₄	—	89	1	no	—
457	C₄×D₄	—	89	1	no	—
458	C₄×D₄	—	89	1	no	—
459	C₄×D₄	—	89	2	no	—
460	C₄×D₄	—	89	2	no	—
461	C₄×D₄	—	89	2	no	—
462	C₄×D₄	—	89	1	no	—
463	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
464	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
465	#117	—	89	1	no	—
466	#117	—	89	1	no	—
467	#117	—	89	1	no	—
468	#117	—	89	2	no	—
469	#117	—	89	1	no	—
470	C₂×C₄⋊C₄	—	89	1	no	—
471	C₂×C₄⋊C₄	—	89	2	no	—
472	C₂×C₂²⋊C₄	—	89	2	no	—
473	C₂×C₂²⋊C₄	—	89	2	no	—
474	C₂×C₂²⋊C₄	—	89	2	no	—
475	C₂×C₂²⋊C₄	—	89	2	no	—
476	C₂×C₂²⋊C₄	—	89	2	no	—
477	C₂×C₄²	—	89	1	no	—
478	C₂⁴	—	89	2	no	—
479	C₂⁴	C₂²×D₈₉	1	2	yes	—
480	C₂⁴	C₂²×D₈₉	1	2	yes	—
481	#41	—	356	4	no	—
482	#41	—	356	4	no	—
483	C₂×Q₈	—	89	2	no	—
484	C₂×Q₈	—	89	1	no	—
485	C₂×D₄	—	2	4	no	—
486	C₂×D₄	—	2	4	no	—
487	C₂×D₄	—	4	4	no	—
488	C₂×D₄	—	89	2	no	—
489	C₂×D₄	—	89	2	no	—
490	C₂×D₄	—	89	2	no	—
491	C₂×D₄	—	89	2	no	—
492	C₂×D₄	—	89	2	no	—
493	C₂×D₄	—	89	2	no	—
494	C₂×D₄	—	89	2	no	—
495	C₂×D₄	—	89	2	no	—
496	C₂×D₄	—	89	1	no	—
497	C₂×D₄	—	89	1	no	—
498	C₂×D₄	—	89	2	no	—
499	C₂×D₄	—	89	1	no	—
500	C₂×D₄	—	356	4	no	—
501	C₂×D₄	—	356	4	no	—
502	C₂×D₄	—	178	4	no	—
503	C₂×D₄	C₂²×D₈₉	1	2	yes	—
504	C₂×D₄	C₂²×D₈₉	1	2	yes	—
505	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
506	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
507	C₂×D₄	C₂²×D₈₉	1	2	yes	—
508	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
509	C₂×D₄	C₂²×D₈₉	1	2	yes	—
510	C₂×D₄	C₂²×D₈₉	1	2	yes	—
511	C₂×D₄	C₂²×D₈₉	1	2	yes	—
512	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
513	C₂²×C₄	—	89	2	no	—
514	C₂²×C₄	—	89	2	no	—
515	C₂²×C₄	—	89	2	no	—
516	C₂²×C₄	—	89	2	no	—
517	C₂²×C₄	—	89	2	no	—
518	C₂²×C₄	—	89	2	no	—
519	C₂²×C₄	—	89	1	no	—
520	C₂²×C₄	—	89	1	no	—
521	C₂²×C₄	—	89	2	no	—
522	C₂²×C₄	—	89	2	no	—
523	C₂²×C₄	—	89	2	no	—
524	C₂²×C₄	—	89	2	no	—
525	C₂²×C₄	—	89	1	no	—
526	C₂²×C₄	—	356	4	no	—
527	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
528	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
529	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
530	C₄⋊C₄	—	89	1	no	—
531	C₄⋊C₄	—	89	1	no	—
532	C₄⋊C₄	—	89	2	no	—
533	C₄⋊C₄	—	89	1	no	—
534	C₄⋊C₄	—	89	2	no	—
535	C₄⋊C₄	—	89	2	no	—
536	C₄⋊C₄	—	89	2	no	—
537	C₄⋊C₄	—	89	1	no	—
538	C₄⋊C₄	—	89	1	no	—
539	C₄⋊C₄	—	89	1	no	—
540	C₄⋊C₄	—	89	1	no	—
541	C₄⋊C₄	—	89	1	no	—
542	C₄⋊C₄	—	89	1	no	—
543	C₄⋊C₄	—	89	1	no	—
544	C₄⋊C₄	—	89	2	no	—
545	C₄⋊C₄	—	89	2	no	—
546	C₄⋊C₄	—	89	1	no	—
547	C₄⋊C₄	—	89	1	no	—
548	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
549	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
550	C₂²⋊C₄	—	89	2	no	—
551	C₂²⋊C₄	—	89	1	no	—
552	C₂²⋊C₄	—	89	2	no	—
553	C₂²⋊C₄	—	89	1	no	—
554	C₂²⋊C₄	—	89	2	no	—
555	C₂²⋊C₄	—	89	2	no	—
556	C₂²⋊C₄	—	89	2	no	—
557	C₂²⋊C₄	—	89	2	no	—
558	C₂²⋊C₄	—	89	2	no	—
559	C₂²⋊C₄	—	89	2	no	—
560	C₂²⋊C₄	—	89	2	no	—
561	C₂²⋊C₄	—	89	1	no	—
562	C₂²⋊C₄	—	89	1	no	—
563	C₂²⋊C₄	—	89	2	no	—
564	C₂²⋊C₄	—	89	1	no	—
565	C₂²⋊C₄	—	89	2	no	—
566	C₂²⋊C₄	—	89	1	no	—
567	C₂²⋊C₄	—	89	2	no	—
568	C₂²⋊C₄	—	89	2	no	—
569	C₂²⋊C₄	—	89	1	no	—
570	C₂²⋊C₄	—	89	1	no	—
571	C₂²⋊C₄	—	89	2	no	—
572	C₂²⋊C₄	—	89	2	no	—
573	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
576	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
577	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
578	C₄²	—	89	1	no	—
579	C₄²	—	89	1	no	—
580	C₄²	—	89	1	no	—
581	C₄²	—	89	1	no	—
582	C₄²	—	89	2	no	—
583	C₄²	—	89	2	no	—
584	C₄²	—	89	1	no	—
585	C₄²	C₂²×D₈₉	1	1	yes	characteristic
586	C₂³	—	2	4	no	—
587	C₂³	—	2	4	no	—
588	C₂³	—	2	4	no	—
589	C₂³	—	4	2	no	—
590	C₂³	—	4	2	no	—
591	C₂³	—	4	2	no	—
592	C₂³	—	89	1	no	—
593	C₂³	—	89	2	no	—
594	C₂³	—	356	2	no	—
595	C₂³	—	356	2	no	—
596	C₂³	—	178	4	no	—
597	C₂³	C₂³×D₈₉	1	1	yes	characteristic
598	C₂³	C₂³×D₈₉	1	2	yes	—
599	C₂³	C₂³×D₈₉	1	2	yes	—
600	C₂³	C₂³×D₈₉	1	2	yes	—
601	C₂³	C₂³×D₈₉	1	1	yes	characteristic
602	Q₈	—	356	2	no	—
603	Q₈	—	178	2	no	—
604	D₄	—	2	4	no	—
605	D₄	—	2	4	no	—
606	D₄	—	2	2	no	—
607	D₄	—	2	4	no	—
608	D₄	—	2	2	no	—
609	D₄	—	2	2	no	—
610	D₄	—	4	2	no	—
611	D₄	—	4	2	no	—
612	D₄	—	4	2	no	—
613	D₄	—	356	2	no	—
614	D₄	—	356	2	no	—
615	D₄	—	356	2	no	—
616	D₄	—	356	2	no	—
617	D₄	—	356	2	no	—
618	D₄	—	356	2	no	—
619	D₄	—	178	2	no	—
620	D₄	—	178	4	no	—
621	D₄	—	178	4	no	—
622	D₄	—	178	2	no	—
623	D₄	—	178	4	no	—
624	D₄	—	178	2	no	—
625	D₄	#13083573	1	4	yes	complemented
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	89	1	no	—
630	C₂×C₄	—	89	1	no	—
631	C₂×C₄	—	89	1	no	—
632	C₂×C₄	—	89	2	no	—
633	C₂×C₄	—	89	1	no	—
634	C₂×C₄	—	89	1	no	—
635	C₂×C₄	—	89	1	no	—
636	C₂×C₄	—	89	2	no	—
637	C₂×C₄	—	89	1	no	—
638	C₂×C₄	—	89	2	no	—
639	C₂×C₄	—	356	2	no	—
640	C₂×C₄	—	356	2	no	—
641	C₂×C₄	—	356	2	no	—
642	C₂×C₄	—	356	2	no	—
643	C₂×C₄	—	356	2	no	—
644	C₂×C₄	—	356	2	no	—
645	C₂×C₄	—	356	2	no	—
646	C₂×C₄	—	356	2	no	—
647	C₂×C₄	—	178	2	no	—
648	C₂×C₄	—	178	4	no	—
649	C₂×C₄	—	178	4	no	—
650	C₂×C₄	—	178	2	no	—
651	C₂×C₄	—	178	2	no	—
652	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
653	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₈₉	1	2	yes	—
655	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
656	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
657	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	4	8	no	—
672	C₂²	—	8	4	no	—
673	C₂²	—	178	1	no	—
674	C₂²	—	178	2	no	—
675	C₂²	—	178	2	no	—
676	C₂²	—	178	1	no	—
677	C₂²	—	178	2	no	—
678	C₂²	—	178	1	no	—
679	C₂²	—	712	4	no	—
680	C₂²	C₂×#13083573	1	4	yes	—
681	C₂²	#15668057	1	2	yes	—
682	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	2	no	—
688	C₄	—	89	2	no	—
689	C₄	—	178	1	no	—
690	C₄	—	178	2	no	—
691	C₄	—	178	1	no	—
692	C₄	—	178	2	no	—
693	C₄	—	178	1	no	—
694	C₄	—	178	1	no	—
695	C₄	—	178	1	no	—
696	C₄	—	178	2	no	—
697	C₄	—	178	1	no	—
698	C₄	C₂×#13083573	1	2	yes	—
699	C₂	—	2	2	no	—
700	C₂	—	2	4	no	—
701	C₂	—	4	2	no	—
702	C₂	—	4	2	no	—
703	C₂	—	4	1	no	—
704	C₂	—	356	2	no	—
705	C₂	—	356	1	no	—
706	C₂	C₂²×#13083573	1	1	yes	characteristic
707	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
708	C₂	C₂×#15668057	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	D₄²×C₈₉	C₂
hypercenter	D₄²	D₈₉
hypocenter	C₈₉	#3519
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #19152312	C₂	semidirect
2. #19152307	C₂	semidirect
3. #19152300	C₂	semidirect
4. #19152294	C₂	semidirect
5. #19152291	C₂	semidirect
6. #19152268	C₂	semidirect
7. #19152242	C₂	semidirect
8. #19152235	C₂	semidirect
9. #19152235	C₂	semidirect
10. D₄×C₂²⋊D₈₉	C₂	semidirect
11. D₄×C₂²⋊D₈₉	C₂	semidirect
12. #19152202	C₂	semidirect
13. #19152201	C₂	semidirect
14. #19152185	C₂	semidirect
15. #19152183	C₂	semidirect
16. #19152143	C₂	semidirect
17. #19152128	C₂	semidirect
18. #19152104	C₂	semidirect
19. C₂×#15667984	C₂	semidirect
20. #19152073	C₂	semidirect
21. #19152070	C₂	semidirect
22. C₂×D₄×Dic₈₉	C₂	semidirect
23. D₄²×C₈₉	C₂	semidirect
24. C₂×#13083573	C₂²	semidirect
25. C₂×#13083573	C₂²	semidirect
26. C₂²×C₂²⋊D₈₉	C₂²	semidirect
27. C₂²×C₂²⋊D₈₉	C₂²	semidirect
29. C₂³×Dic₈₉	C₂²	semidirect
30. #15668011	C₂²	semidirect
31. #15668008	C₂²	semidirect
32. #15668008	C₂²	semidirect
33. #15668007	C₂²	semidirect
34. #15668007	C₂²	semidirect
35. #15668005	C₂²	semidirect
36. #15668005	C₂²	semidirect
37. #15668004	C₂²	semidirect
38. #15668003	C₂²	semidirect
39. #15668002	C₂²	semidirect
40. #15667999	C₂²	semidirect
41. #15667998	C₂²	semidirect
42. #15667998	C₂²	semidirect
43. #15667998	C₂²	semidirect
44. #15667996	C₂²	semidirect
45. #15667996	C₂²	semidirect
46. #15667996	C₂²	semidirect
47. #15667994	C₂²	semidirect
48. #15667994	C₂²	semidirect
49. #15667993	C₂²	semidirect
50. #15667993	C₂²	semidirect
51. #15667993	C₂²	semidirect
52. #15667991	C₂²	semidirect
53. #15667989	C₂²	semidirect
54. #15667989	C₂²	semidirect
55. #15667989	C₂²	semidirect
56. #15667986	C₂²	semidirect
57. #15667986	C₂²	semidirect
59. #15667984	C₂²	semidirect
60. #15667984	C₂²	semidirect
61. #15667984	C₂²	semidirect
62. #15667984	C₂²	semidirect
63. #15667984	C₂²	semidirect
64. #15667984	C₂²	semidirect
65. #15667984	C₂²	semidirect
66. #15667984	C₂²	semidirect
67. #15667984	C₂²	semidirect
68. #15667984	C₂²	semidirect
69. #15667984	C₂²	semidirect
70. #15667983	C₂²	semidirect
71. #15667983	C₂²	semidirect
72. #15667983	C₂²	semidirect
73. #15667983	C₂²	semidirect
74. #15667981	C₂²	semidirect
75. #15667981	C₂²	semidirect
76. #15667980	C₂²	semidirect
77. #15667980	C₂²	semidirect
78. C₄×Dic₁₇₈	C₂²	semidirect
79. C₄×D₃₅₆	C₂²	semidirect
83. D₄×Dic₈₉	C₂²	semidirect
84. D₄×Dic₈₉	C₂²	semidirect
85. D₄×Dic₈₉	C₂²	semidirect
86. D₄×Dic₈₉	C₂²	semidirect
87. D₄×Dic₈₉	C₂²	semidirect
88. D₄×Dic₈₉	C₂²	semidirect
89. D₄×Dic₈₉	C₂²	semidirect
90. D₄×Dic₈₉	C₂²	semidirect
91. D₄×Dic₈₉	C₂²	semidirect
92. #15667974	C₂²	semidirect
93. C₄×C₂²⋊D₈₉	C₂²	semidirect
94. C₄×C₂²⋊D₈₉	C₂²	semidirect
95. C₄×C₂²⋊D₈₉	C₂²	semidirect
96. #15667972	C₂²	semidirect
97. #15667972	C₂²	semidirect
98. #15667972	C₂²	semidirect
99. #15667971	C₂²	semidirect
100. #15667971	C₂²	semidirect
101. #15667970	C₂²	semidirect
102. #15667969	C₂²	semidirect
103. #15667968	C₂²	semidirect
104. C₂×C₄⋊Dic₈₉	C₂²	semidirect
105. C₂×#13083553	C₂²	semidirect
106. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
107. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
108. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
109. C₂×#13083551	C₂²	semidirect
110. C₂²⋊C₄×D₈₉	C₂²	semidirect
111. C₂×C₄×Dic₈₉	C₂²	semidirect
114. C₂²×D₄×C₈₉	C₂²	semidirect
115. #127×C₈₉	C₂²	semidirect
116. #121×C₈₉	C₂²	semidirect
117. #121×C₈₉	C₂²	semidirect
118. #121×C₈₉	C₂²	semidirect
119. #120×C₈₉	C₂²	semidirect
120. #120×C₈₉	C₂²	semidirect
122. C₄×D₄×C₈₉	C₂²	semidirect
256. D₄×C₈₉	#41	semidirect
355. C₈₉	#3519	semidirect
367. D₄²	D₈₉	semidirect
386. C₂²×D₄	C₂×D₈₉	semidirect
391. #127	C₂×D₈₉	semidirect
433. #121	C₂×D₈₉	semidirect
434. #121	C₂×D₈₉	semidirect
435. #121	C₂×D₈₉	semidirect
440. #120	C₂×D₈₉	semidirect
441. #120	C₂×D₈₉	semidirect
464. C₄×D₄	C₂×D₈₉	semidirect
625. D₄	#13083573	semidirect

Maximal subgroups

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

subgroup	index
#19152312	2
#19152307	2
#19152300	2
#19152294	2
#19152291	2
#19152268	2
#19152242	2
#19152235	2
D₄×C₂²⋊D₈₉	2
#19152202	2
#19152201	2
#19152185	2
#19152183	2
#19152143	2
#19152128	2
#19152104	2
C₂×#15667984	2
#19152073	2
#19152070	2
C₂×D₄×Dic₈₉	2
D₄²×C₈₉	2
#3519	89