Subgroups — #36559335

Order 22784.

826 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151659	C₂	1	1	yes	maximal, characteristic
2	#26022861	C₂	1	1	yes	maximal, characteristic
3	#26021020	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021020	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021015	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021010	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020451	C₂	1	1	yes	maximal, characteristic
8	#26020451	C₂	1	1	yes	maximal, characteristic
9	#26020445	C₂	1	1	yes	maximal, characteristic
10	#26020440	C₂	1	1	yes	maximal, characteristic
11	#26020150	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020150	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#15667945	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#15667943	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2274	C₂	1	1	yes	maximal, characteristic
16	#19151659	C₄	1	8	yes	complemented
17	C₂×#15667945	C₂²	1	1	yes	characteristic
18	C₂×#15667945	C₂²	1	1	yes	characteristic
19	C₂×#15667945	C₂²	1	1	yes	characteristic
20	C₂×#15667945	C₂²	1	1	yes	characteristic
21	C₂×#15667943	C₂²	1	1	yes	characteristic
22	C₂×#15667943	C₂²	1	1	yes	characteristic
23	C₂×#15667943	C₂²	1	1	yes	characteristic
24	C₂×#15667943	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊#10623494	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊#10623494	C₂²	1	1	yes	characteristic
29	C₂×#15667923	C₂²	1	1	yes	characteristic
30	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
31	#19151491	—	2	1	no	—
32	#19151491	—	2	1	no	—
33	#19151484	—	2	1	no	—
34	#19151484	—	2	1	no	—
35	#19151468	C₂²	1	1	yes	characteristic
36	#19151464	C₂²	1	1	yes	characteristic
37	#19151458	C₂²	1	1	yes	characteristic
38	#19151458	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
41	#19151360	C₂²	1	1	yes	characteristic
42	#19151360	C₂²	1	1	yes	characteristic
43	#19151360	C₂²	1	1	yes	characteristic
44	#19151360	C₂²	1	1	yes	characteristic
45	#19151360	C₂²	1	1	yes	characteristic
46	#19151360	C₂²	1	1	yes	characteristic
47	#19151360	C₂²	1	1	yes	characteristic
48	#19151360	C₂²	1	1	yes	characteristic
49	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
51	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
53	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
54	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
55	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
59	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
60	C₂²×#10623494	C₂³	1	1	yes	characteristic
61	C₂²×#10623494	C₂³	1	1	yes	characteristic
62	C₂²×#10623494	C₂³	1	1	yes	characteristic
63	C₂²×#10623494	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊Dic₈₉	—	2	1	no	—
65	C₂×C₄⋊Dic₈₉	—	2	1	no	—
66	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊Dic₈₉	—	2	1	no	—
71	C₂×C₂²⋊Dic₈₉	—	2	1	no	—
72	C₂×C₄×Dic₈₉	—	2	1	no	—
73	C₂×C₄×Dic₈₉	—	2	1	no	—
74	#15667945	—	2	2	no	—
75	#15667945	—	2	2	no	—
76	#15667945	—	2	2	no	—
77	#15667945	—	2	2	no	—
78	#15667943	—	2	2	no	—
79	#15667943	—	2	2	no	—
80	#15667943	—	2	2	no	—
81	#15667943	—	2	2	no	—
82	C₄⋊#10623494	C₂×C₄	1	4	yes	complemented
83	C₄⋊#10623494	C₂×C₄	1	4	yes	complemented
84	C₂²⋊#10623494	C₂×C₄	1	4	yes	—
85	C₂²⋊#10623494	C₂×C₄	1	4	yes	—
86	#15667923	C₂×C₄	1	4	yes	complemented
87	C₄×#10623494	C₂×C₄	1	4	yes	complemented
88	#15667919	—	2	1	no	—
89	#15667919	—	2	1	no	—
90	#15667919	—	2	1	no	—
91	#15667919	—	2	1	no	—
92	#15667919	—	2	1	no	—
93	#15667919	—	2	1	no	—
94	C₂³×C₄×C₈₉	—	2	1	no	—
95	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
96	#117×C₈₉	—	2	2	no	—
97	#117×C₈₉	—	2	2	no	—
98	#117×C₈₉	C₂×C₄	1	4	yes	—
99	#117×C₈₉	Q₈	1	4	yes	—
100	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
102	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
103	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₈₉	—	2	1	no	—
113	C₂×C₄²×C₈₉	—	2	1	no	—
114	C₂×C₄²×C₈₉	—	2	1	no	—
115	C₂×C₄²×C₈₉	—	2	1	no	—
116	C₂×C₄²×C₈₉	—	2	1	no	—
117	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
119	#95×C₈₉	—	2	1	no	—
120	#95×C₈₉	—	2	1	no	—
121	#95×C₈₉	—	2	1	no	—
122	#95×C₈₉	—	2	1	no	—
123	C₂²×Dic₈₉	—	2	1	no	—
124	C₂²×Dic₈₉	—	2	1	no	—
125	C₂²×Dic₈₉	—	2	1	no	—
126	C₂²×Dic₈₉	—	2	1	no	—
127	C₂×#10623494	—	2	1	no	—
128	C₂×#10623494	—	2	1	no	—
129	C₂×#10623494	—	2	1	no	—
130	C₂×#10623494	—	2	1	no	—
131	C₂×#10623494	—	2	1	no	—
132	C₂×#10623494	—	2	1	no	—
133	C₂×#10623494	—	2	1	no	—
134	C₂×#10623494	—	2	1	no	—
135	C₂×#10623494	C₂²×C₄	1	2	yes	—
136	C₂×#10623494	C₂²×C₄	1	2	yes	—
137	C₂×#10623494	C₂²×C₄	1	2	yes	—
138	C₂×#10623494	C₂²×C₄	1	2	yes	—
139	C₄⋊Dic₈₉	—	2	1	no	—
140	C₄⋊Dic₈₉	—	2	1	no	—
141	C₄⋊Dic₈₉	—	2	1	no	—
142	C₄⋊Dic₈₉	—	2	1	no	—
143	C₄⋊Dic₈₉	—	2	1	no	—
144	C₄⋊Dic₈₉	—	2	1	no	—
145	C₄⋊Dic₈₉	—	2	1	no	—
146	C₄⋊Dic₈₉	—	2	1	no	—
147	C₄⋊Dic₈₉	—	8	1	no	—
148	C₄⋊Dic₈₉	—	8	1	no	—
149	C₂²⋊Dic₈₉	—	8	1	no	—
150	C₂²⋊Dic₈₉	—	8	1	no	—
151	C₄×Dic₈₉	—	8	1	no	—
152	C₄×Dic₈₉	—	8	1	no	—
153	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₈₉	—	2	1	no	—
155	C₂²×C₄×C₈₉	—	2	1	no	—
156	C₂²×C₄×C₈₉	—	2	1	no	—
157	C₂²×C₄×C₈₉	—	2	1	no	—
158	C₂²×C₄×C₈₉	—	2	1	no	—
159	C₂²×C₄×C₈₉	—	2	1	no	—
160	C₂²×C₄×C₈₉	—	2	1	no	—
161	C₂²×C₄×C₈₉	—	2	1	no	—
162	C₂²×C₄×C₈₉	—	2	4	no	—
163	C₂²×C₄×C₈₉	—	8	1	no	—
164	C₂²×C₄×C₈₉	—	8	1	no	—
165	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
172	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
173	C₄⋊C₄×C₈₉	—	2	4	no	—
174	C₄⋊C₄×C₈₉	—	2	1	no	—
175	C₄⋊C₄×C₈₉	—	2	1	no	—
176	C₄⋊C₄×C₈₉	—	2	1	no	—
177	C₄⋊C₄×C₈₉	—	2	1	no	—
178	C₄⋊C₄×C₈₉	C₄⋊C₄	1	4	yes	—
179	C₄⋊C₄×C₈₉	C₄⋊C₄	1	4	yes	—
180	C₄⋊C₄×C₈₉	#41	1	2	yes	—
181	C₄⋊C₄×C₈₉	#41	1	2	yes	—
182	C₄⋊C₄×C₈₉	#41	1	2	yes	—
183	C₄⋊C₄×C₈₉	#41	1	2	yes	—
184	C₂²⋊C₄×C₈₉	—	2	4	no	—
185	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	4	yes	—
186	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	4	yes	—
187	C₄²×C₈₉	—	2	4	no	—
188	C₄²×C₈₉	—	8	1	no	—
189	C₄²×C₈₉	—	8	1	no	—
190	C₄²×C₈₉	—	8	1	no	—
191	C₄²×C₈₉	—	8	1	no	—
192	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
193	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
194	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
195	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
196	C₂³×C₈₉	—	2	1	no	—
197	C₂³×C₈₉	—	2	1	no	—
198	C₂³×C₈₉	—	2	1	no	—
199	C₂³×C₈₉	—	2	1	no	—
200	C₂³×C₈₉	—	2	1	no	—
201	C₂³×C₈₉	—	2	1	no	—
202	C₂³×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
203	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₈₉	—	2	1	no	—
205	C₂×C₄×C₈₉	—	2	1	no	—
206	C₂×C₄×C₈₉	—	2	1	no	—
207	C₂×C₄×C₈₉	—	2	1	no	—
208	C₂×C₄×C₈₉	—	2	1	no	—
209	C₂×C₄×C₈₉	—	2	1	no	—
210	C₂×C₄×C₈₉	—	2	1	no	—
211	C₂×C₄×C₈₉	—	2	1	no	—
212	C₂×C₄×C₈₉	—	2	1	no	—
213	C₂×C₄×C₈₉	—	2	1	no	—
214	C₂×C₄×C₈₉	—	2	2	no	—
215	C₂×C₄×C₈₉	—	2	2	no	—
216	C₂×C₄×C₈₉	—	2	2	no	—
217	C₂×C₄×C₈₉	—	2	2	no	—
218	C₂×C₄×C₈₉	—	2	2	no	—
219	C₂×C₄×C₈₉	—	2	2	no	—
220	C₂×C₄×C₈₉	—	2	2	no	—
221	C₂×C₄×C₈₉	—	2	2	no	—
222	C₂×C₄×C₈₉	—	4	1	no	—
223	C₂×C₄×C₈₉	—	4	1	no	—
224	C₂×C₄×C₈₉	—	4	1	no	—
225	C₂×C₄×C₈₉	—	4	1	no	—
226	C₂×C₄×C₈₉	—	4	1	no	—
227	C₂×C₄×C₈₉	—	4	1	no	—
228	C₂×C₄×C₈₉	—	4	1	no	—
229	C₂×C₄×C₈₉	—	4	1	no	—
230	C₂×C₄×C₈₉	—	8	4	no	—
231	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
232	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
233	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
234	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
235	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
236	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
238	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
242	C₂×Dic₈₉	—	4	1	no	—
243	C₂×Dic₈₉	—	4	1	no	—
244	C₂×Dic₈₉	—	4	1	no	—
245	C₂×Dic₈₉	—	4	1	no	—
246	C₂×Dic₈₉	—	4	1	no	—
247	C₂×Dic₈₉	—	4	1	no	—
248	C₂×Dic₈₉	—	4	1	no	—
249	C₂×Dic₈₉	—	4	1	no	—
250	C₂×Dic₈₉	—	4	1	no	—
251	C₂×Dic₈₉	—	4	1	no	—
252	C₂×Dic₈₉	—	4	1	no	—
253	C₂×Dic₈₉	—	4	1	no	—
254	#10623494	—	2	2	no	—
255	#10623494	—	2	2	no	—
256	#10623494	—	2	2	no	—
257	#10623494	—	2	2	no	—
258	C₂²×C₈₉	—	2	2	no	—
259	C₂²×C₈₉	—	2	2	no	—
260	C₂²×C₈₉	—	2	2	no	—
261	C₂²×C₈₉	—	4	1	no	—
262	C₂²×C₈₉	—	4	1	no	—
263	C₂²×C₈₉	—	4	1	no	—
264	C₂²×C₈₉	—	4	1	no	—
265	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
266	C₂²×C₈₉	#525	1	1	yes	characteristic
267	C₂²×C₈₉	#525	1	1	yes	characteristic
268	C₂²×C₈₉	#576	1	1	yes	characteristic
269	C₂²×C₈₉	#577	1	1	yes	characteristic
270	C₂²×C₈₉	#577	1	1	yes	characteristic
271	C₂²×C₈₉	#578	1	1	yes	characteristic
272	C₄×C₈₉	—	2	2	no	—
273	C₄×C₈₉	—	2	2	no	—
274	C₄×C₈₉	—	2	2	no	—
275	C₄×C₈₉	—	2	2	no	—
276	C₄×C₈₉	—	2	2	no	—
277	C₄×C₈₉	—	4	2	no	—
278	C₄×C₈₉	—	4	2	no	—
279	C₄×C₈₉	—	4	2	no	—
280	C₄×C₈₉	—	4	2	no	—
281	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
282	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
283	C₄×C₈₉	#533	1	1	yes	characteristic
284	C₄×C₈₉	#533	1	1	yes	characteristic
285	Dic₈₉	—	8	1	no	—
286	Dic₈₉	—	8	1	no	—
287	Dic₈₉	—	8	1	no	—
288	Dic₈₉	—	8	1	no	—
289	#21367	—	89	1	no	maximal, Sylow
290	C₂×C₈₉	—	4	2	no	—
291	C₂×C₈₉	#2296	1	1	yes	characteristic
292	C₂×C₈₉	#2912	1	1	yes	characteristic
293	C₂×C₈₉	#2913	1	1	yes	characteristic
294	C₂×C₈₉	#3118	1	1	yes	characteristic
295	C₂×C₈₉	#3119	1	1	yes	characteristic
296	C₂×C₈₉	#3120	1	1	yes	characteristic
297	C₂×C₈₉	#3121	1	1	yes	characteristic
298	C₂×#433	—	89	1	no	—
299	#2314	—	89	1	no	—
300	#2274	D₈₉	1	1	yes	characteristic
301	#1949	—	89	1	no	—
302	#1949	—	89	1	no	—
303	#1948	—	89	1	no	—
304	#1947	—	89	1	no	—
305	#1854	—	89	1	no	—
306	#1854	—	89	1	no	—
307	#1853	—	89	1	no	—
308	#1852	—	89	1	no	—
309	#1776	—	89	1	no	—
310	#1776	—	89	1	no	—
311	C₄×#107	—	89	1	no	—
312	C₄×#106	—	89	1	no	—
313	C₈₉	#21367	1	1	yes	characteristic, complemented, Sylow
314	C₂×#117	C₂×D₈₉	1	1	yes	characteristic
315	C₂×#117	C₂×D₈₉	1	1	yes	characteristic
316	C₂²×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
317	#433	—	89	8	no	—
318	C₂×#107	—	89	1	no	—
319	C₂×#107	—	89	1	no	—
320	C₂×#107	—	89	1	no	—
321	C₂×#107	—	89	1	no	—
322	C₂×#106	—	89	1	no	—
323	C₂×#106	—	89	1	no	—
324	C₂×#106	—	89	1	no	—
325	C₂×#106	—	89	1	no	—
326	C₂×C₄⋊C₈	—	89	1	no	—
327	C₂×C₄⋊C₈	—	89	1	no	—
328	C₂×C₂²⋊C₈	—	89	1	no	—
329	C₂×C₂²⋊C₈	—	89	1	no	—
330	C₂×#97	—	89	1	no	—
331	C₂×C₄×C₈	—	89	1	no	—
332	#388	—	178	1	no	—
333	#388	—	178	1	no	—
334	#387	—	178	1	no	—
335	#387	—	178	1	no	—
336	#384	—	89	1	no	—
337	#382	—	89	1	no	—
338	#380	—	89	1	no	—
339	#380	—	89	1	no	—
340	C₄×C₄⋊C₄	—	2	1	no	—
341	C₄×C₄⋊C₄	—	2	1	no	—
342	C₄×C₄⋊C₄	—	89	1	no	—
343	C₄×C₄⋊C₄	—	89	1	no	—
344	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
345	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
347	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
348	C₄×C₂²⋊C₄	—	2	1	no	—
349	C₄×C₂²⋊C₄	—	2	1	no	—
350	#340	—	89	1	no	—
351	#340	—	89	1	no	—
352	#340	—	89	1	no	—
353	#340	—	89	1	no	—
354	#340	—	89	1	no	—
355	#340	—	89	1	no	—
356	#340	—	89	1	no	—
357	#340	—	89	1	no	—
358	C₂³×C₄	—	2	1	no	—
359	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
360	C₂²×C₈	—	89	1	no	—
361	C₂²×C₈	—	89	1	no	—
362	C₂²×C₈	—	89	1	no	—
363	C₂²×C₈	—	89	1	no	—
364	#117	—	2	2	no	—
365	#117	—	2	2	no	—
366	#117	Dic₁₇₈	1	4	yes	—
367	#117	C₄×D₈₉	1	4	yes	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	89	1	no	—
372	C₂×C₄⋊C₄	—	89	1	no	—
373	C₂×C₄⋊C₄	—	89	1	no	—
374	C₂×C₄⋊C₄	—	89	1	no	—
375	C₂×C₄⋊C₄	—	178	1	no	—
376	C₂×C₄⋊C₄	—	178	1	no	—
377	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	178	1	no	—
385	C₂×C₂²⋊C₄	—	178	1	no	—
386	C₂×C₂²⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	—	2	1	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	—	178	1	no	—
394	C₂×C₄²	—	178	1	no	—
395	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
396	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
397	#107	—	178	2	no	—
398	#107	—	178	2	no	—
399	#107	—	178	2	no	—
400	#107	—	178	2	no	—
401	#106	—	178	2	no	—
402	#106	—	178	2	no	—
403	#106	—	178	2	no	—
404	#106	—	178	2	no	—
405	C₄⋊C₈	—	89	4	no	—
406	C₄⋊C₈	—	89	4	no	—
407	C₂²⋊C₈	—	89	4	no	—
408	C₂²⋊C₈	—	89	4	no	—
409	#97	—	89	4	no	—
410	C₄×C₈	—	89	4	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	178	1	no	—
416	#95	—	178	1	no	—
417	#95	—	178	1	no	—
418	#95	—	178	1	no	—
419	#95	—	178	1	no	—
420	#95	—	178	1	no	—
421	C₂⁴	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	8	1	no	—
432	C₂²×C₄	—	8	1	no	—
433	C₂²×C₄	—	178	1	no	—
434	C₂²×C₄	—	178	1	no	—
435	C₂²×C₄	—	178	1	no	—
436	C₂²×C₄	—	178	1	no	—
437	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
438	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
443	C₂²×C₄	C₂×Dic₁₇₈	1	2	yes	—
444	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
445	C₂×C₈	—	89	2	no	—
446	C₂×C₈	—	89	2	no	—
447	C₂×C₈	—	89	2	no	—
448	C₂×C₈	—	89	2	no	—
449	C₂×C₈	—	178	1	no	—
450	C₂×C₈	—	178	1	no	—
451	C₂×C₈	—	178	1	no	—
452	C₂×C₈	—	178	1	no	—
453	C₂×C₈	—	178	1	no	—
454	C₂×C₈	—	178	1	no	—
455	C₂×C₈	—	178	1	no	—
456	C₂×C₈	—	178	1	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	178	1	no	—
463	C₄⋊C₄	—	178	1	no	—
464	C₄⋊C₄	—	178	1	no	—
465	C₄⋊C₄	—	178	1	no	—
466	C₄⋊C₄	—	178	1	no	—
467	C₄⋊C₄	—	178	1	no	—
468	C₄⋊C₄	—	178	1	no	—
469	C₄⋊C₄	—	178	1	no	—
470	C₄⋊C₄	—	712	1	no	—
471	C₄⋊C₄	—	712	1	no	—
472	C₄⋊C₄	#13083553	1	4	yes	—
473	C₄⋊C₄	#13083553	1	4	yes	—
474	C₄⋊C₄	#13083574	1	2	yes	—
475	C₄⋊C₄	#13083574	1	2	yes	—
476	C₄⋊C₄	#13083574	1	2	yes	—
477	C₄⋊C₄	#13083574	1	2	yes	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	712	1	no	—
480	C₂²⋊C₄	—	712	1	no	—
481	C₂²⋊C₄	#13083553	1	4	yes	—
482	C₂²⋊C₄	#13083553	1	4	yes	—
483	C₄²	—	2	4	no	—
484	C₄²	—	8	1	no	—
485	C₄²	—	8	1	no	—
486	C₄²	—	8	1	no	—
487	C₄²	—	8	1	no	—
488	C₄²	—	712	1	no	—
489	C₄²	—	712	1	no	—
490	C₄²	C₂×C₄×D₈₉	1	2	yes	—
491	C₄²	C₂×C₄×D₈₉	1	2	yes	—
492	C₄²	C₂×Dic₁₇₈	1	2	yes	—
493	C₄²	C₂×Dic₁₇₈	1	2	yes	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	C₂×#13083553	1	2	yes	—
501	C₂³	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	8	4	no	—
529	C₂×C₄	—	356	1	no	—
530	C₂×C₄	—	356	1	no	—
531	C₂×C₄	—	356	1	no	—
532	C₂×C₄	—	356	1	no	—
533	C₂×C₄	—	356	1	no	—
534	C₂×C₄	—	356	1	no	—
535	C₂×C₄	—	356	1	no	—
536	C₂×C₄	—	356	1	no	—
537	C₂×C₄	—	356	1	no	—
538	C₂×C₄	—	356	1	no	—
539	C₂×C₄	—	356	1	no	—
540	C₂×C₄	—	356	1	no	—
541	C₂×C₄	C₂×#13083553	1	2	yes	—
542	C₂×C₄	C₂×#13083553	1	2	yes	—
543	C₂×C₄	C₂×#13083553	1	2	yes	—
544	C₂×C₄	C₂×#13083553	1	2	yes	—
545	C₂×C₄	C₂×#13083553	1	2	yes	—
546	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
547	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
548	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
549	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
550	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
551	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
552	C₈	—	178	2	no	—
553	C₈	—	178	2	no	—
554	C₈	—	178	2	no	—
555	C₈	—	178	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	C₂²×#13083553	1	1	yes	characteristic
564	C₂²	#19152109	1	1	yes	characteristic
565	C₂²	#19152109	1	1	yes	characteristic
566	C₂²	#19152401	1	1	yes	characteristic
567	C₂²	#19152406	1	1	yes	characteristic
568	C₂²	#19152409	1	1	yes	characteristic
569	C₂²	#19152413	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	4	2	no	—
579	C₄	—	712	1	no	—
580	C₄	—	712	1	no	—
581	C₄	—	712	1	no	—
582	C₄	—	712	1	no	—
583	C₄	C₄×#13083574	1	1	yes	characteristic
584	C₄	C₄×#13083574	1	1	yes	characteristic
585	C₄	#19152155	1	1	yes	characteristic
586	C₄	#19152155	1	1	yes	characteristic
587	C₂	—	4	2	no	—
588	C₂	#26022735	1	1	yes	characteristic
589	C₂	#26028845	1	1	yes	characteristic
590	C₂	#26028850	1	1	yes	characteristic
591	C₂	#26030436	1	1	yes	characteristic
592	C₂	#26030451	1	1	yes	characteristic
593	C₂	#26030466	1	1	yes	characteristic
594	C₂	#26030481	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#2274	C₂
socle	C₂³×C₈₉	C₂²×D₄
prime radical	C₂⁴×C₈₉	C₂×D₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#2274	D₈₉
hypocenter	C₈₉	#21367
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×#117 ◁ #2274

Complements

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

N	H ≅ G/N	type
3. #26021020	C₂	semidirect
4. #26021020	C₂	semidirect
5. #26021015	C₂	semidirect
6. #26021010	C₂	semidirect
11. #26020150	C₂	semidirect
12. #26020150	C₂	semidirect
13. C₄×#15667945	C₂	semidirect
14. C₄×#15667943	C₂	semidirect
16. #19151659	C₄	semidirect
82. C₄⋊#10623494	C₂×C₄	semidirect
83. C₄⋊#10623494	C₂×C₄	semidirect
86. #15667923	C₂×C₄	semidirect
87. C₄×#10623494	C₂×C₄	semidirect
313. C₈₉	#21367	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151659	2
#26022861	2
#26021020	2
#26021015	2
#26021010	2
#26020451	2
#26020445	2
#26020440	2
#26020150	2
C₄×#15667945	2
C₄×#15667943	2
C₈₉×#2274	2
#21367	89