Subgroups — #36524340

Order 22784.

634 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030264	C₂	1	1	yes	maximal, characteristic
2	#26029228	C₂	1	1	yes	maximal, characteristic, complemented
3	#26029208	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019105	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019098	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019091	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019084	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019056	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019055	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019049	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019044	C₂	1	1	yes	maximal, characteristic, complemented
12	#26019030	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018687	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018536	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1482	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#13083574	C₂²	1	1	yes	characteristic
17	#19151936	C₄	1	1	yes	characteristic
18	#19151919	C₄	1	1	yes	characteristic
19	#19151902	C₄	1	1	yes	characteristic
20	#19151895	C₄	1	1	yes	characteristic
21	#19151817	C₄	1	1	yes	characteristic
22	#19151810	C₄	1	1	yes	characteristic
23	#19151758	C₄	1	1	yes	characteristic
24	#19151741	C₄	1	1	yes	characteristic
25	#19151729	C₂²	1	1	yes	characteristic
26	Q₈×#10623494	C₂²	1	1	yes	characteristic
27	#19151722	C₂²	1	1	yes	characteristic
28	#19151722	C₂²	1	1	yes	characteristic
29	C₄×#13083564	C₂²	1	1	yes	characteristic
30	C₄×#13083561	C₂²	1	1	yes	characteristic
31	C₄×#13083562	C₂²	1	1	yes	characteristic
32	C₄×#13083559	C₂²	1	1	yes	characteristic
33	#19151676	C₂²	1	1	yes	characteristic
34	#19151670	—	2	1	no	—
35	D₄×#10623494	—	2	1	no	—
36	D₄×#10623494	C₂²	1	1	yes	characteristic
37	#19151663	C₂²	1	1	yes	characteristic
38	#19151663	C₂²	1	1	yes	characteristic
39	#19151661	—	2	1	no	—
40	#19151661	—	2	1	no	—
41	#19151659	—	2	1	no	—
42	#19151655	C₂²	1	1	yes	characteristic
43	#19151651	C₂²	1	1	yes	characteristic
44	#19151649	—	2	1	no	—
45	#19151554	—	2	1	no	—
46	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₈₉	—	2	1	no	—
48	#19151350	C₂²	1	1	yes	characteristic
49	#19151350	C₂²	1	1	yes	characteristic
50	#19151348	C₂²	1	1	yes	characteristic
51	#19151348	C₂²	1	1	yes	characteristic
52	#19151330	C₂²	1	1	yes	characteristic
53	#19151330	C₂²	1	1	yes	characteristic
54	#19151327	C₂²	1	1	yes	characteristic
55	#19151327	C₂²	1	1	yes	characteristic
56	#19151320	C₂²	1	1	yes	characteristic
57	#19151320	C₂²	1	1	yes	characteristic
58	C₈×#10623494	C₂²	1	1	yes	characteristic
59	C₈×#10623494	C₂²	1	1	yes	characteristic
60	#529×C₈₉	C₂²	1	1	yes	characteristic
61	#431×C₈₉	C₂²	1	1	yes	characteristic
62	#431×C₈₉	C₂²	1	1	yes	characteristic
63	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
64	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
66	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
68	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
72	C₂×#13083558	—	2	1	no	—
73	C₂²×#10623494	—	2	1	no	—
74	C₂²×#10623494	D₄	1	1	yes	characteristic
75	C₂²×#10623494	D₄	1	1	yes	characteristic
76	C₂×C₈×D₈₉	—	2	1	no	—
77	C₂×C₈×D₈₉	—	2	1	no	—
78	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
80	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
81	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
82	C₄×C₂²⋊D₈₉	—	2	1	no	—
83	C₄×C₂²⋊D₈₉	—	2	1	no	—
84	#15667971	C₂×C₄	1	1	yes	characteristic
85	#15667969	—	2	1	no	—
86	C₄²×D₈₉	—	2	1	no	—
87	#15667945	C₂×C₄	1	1	yes	characteristic
88	#15667945	C₂×C₄	1	1	yes	characteristic
89	#15667943	C₂×C₄	1	1	yes	characteristic
90	#15667943	C₂×C₄	1	1	yes	characteristic
91	C₄⋊#10623494	—	2	1	no	—
92	C₄⋊#10623494	—	2	1	no	—
93	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
94	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
95	C₄⋊#10623494	C₂³	1	1	yes	characteristic
96	C₄⋊#10623494	C₂³	1	1	yes	characteristic
97	#15667941	—	2	1	no	—
98	#15667941	—	2	1	no	—
99	#15667936	C₂×C₄	1	1	yes	characteristic
100	#15667936	C₂×C₄	1	1	yes	characteristic
101	#15667935	C₂×C₄	1	1	yes	characteristic
102	#15667935	C₂×C₄	1	1	yes	characteristic
103	#15667933	C₂×C₄	1	1	yes	characteristic
104	#15667933	C₂×C₄	1	1	yes	characteristic
105	#15667932	C₂×C₄	1	1	yes	characteristic
106	#15667932	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊#10623494	—	2	1	no	—
108	C₂²⋊#10623494	—	2	1	no	—
109	C₂²⋊#10623494	—	2	1	no	—
110	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
112	#15667924	—	2	1	no	—
113	#15667924	—	2	1	no	—
114	#15667923	—	2	1	no	—
115	#15667923	—	2	1	no	—
116	C₄×#10623494	—	2	1	no	—
117	C₄×#10623494	D₄	1	1	yes	characteristic
118	C₄×#10623494	D₄	1	1	yes	characteristic
119	C₄×#10623494	C₂³	1	1	yes	characteristic
120	C₄×#10623494	C₂³	1	1	yes	characteristic
121	C₄×#10623494	C₂³	1	1	yes	characteristic
122	C₄×#10623494	C₂³	1	1	yes	characteristic
123	C₈×Dic₈₉	—	2	1	no	—
124	C₈×Dic₈₉	—	2	1	no	—
125	#126×C₈₉	—	2	1	no	—
126	#125×C₈₉	C₂×C₄	1	1	yes	characteristic
127	#124×C₈₉	C₂×C₄	1	1	yes	characteristic
128	#123×C₈₉	—	2	1	no	—
129	C₂²⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
130	#121×C₈₉	C₂×C₄	1	1	yes	characteristic
131	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₄×D₄×C₈₉	—	2	1	no	—
133	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
134	#117×C₈₉	—	2	1	no	—
135	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₈₉	—	2	1	no	—
137	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
139	C₂²⋊C₈×C₈₉	—	2	1	no	—
140	C₂²⋊C₈×C₈₉	—	2	1	no	—
141	C₄×C₈×C₈₉	—	2	1	no	—
142	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	#13083574	—	2	2	no	—
145	#13083574	—	2	2	no	—
146	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₂²⋊D₈₉	—	2	1	no	—
149	C₂×C₄×D₈₉	—	2	1	no	—
150	C₂×C₄×D₈₉	—	2	1	no	—
151	C₂×C₄×D₈₉	—	2	1	no	—
152	#13083564	—	2	2	no	—
153	#13083562	—	2	2	no	—
154	#13083561	—	2	2	no	—
155	#13083559	—	2	2	no	—
156	#13083558	—	4	2	no	—
157	C₂×#10623494	—	2	2	no	—
158	C₂×#10623494	—	2	2	no	—
159	C₂×#10623494	—	2	1	no	—
160	C₂×#10623494	—	2	1	no	—
161	C₂×#10623494	—	4	2	no	—
162	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
163	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
164	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
165	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
166	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
167	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
168	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
169	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
170	C₈×D₈₉	—	4	2	no	—
171	C₈×D₈₉	—	4	2	no	—
172	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
173	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
174	#13083553	—	2	1	no	—
175	#13083553	—	2	1	no	—
176	C₂²⋊Dic₈₉	—	2	1	no	—
177	#13083551	—	2	1	no	—
178	#13083551	—	2	1	no	—
179	C₄×Dic₈₉	—	2	1	no	—
180	C₄×Dic₈₉	—	2	1	no	—
181	C₄×Dic₈₉	—	2	1	no	—
182	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
183	C₂×D₄×C₈₉	—	2	1	no	—
184	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₈₉	—	2	1	no	—
186	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
189	C₂×C₈×C₈₉	—	2	1	no	—
190	C₂×C₈×C₈₉	—	2	1	no	—
191	C₂×C₈×C₈₉	—	2	1	no	—
192	C₂×C₈×C₈₉	—	2	1	no	—
193	C₄⋊C₄×C₈₉	—	2	1	no	—
194	C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₄⋊C₄×C₈₉	—	2	1	no	—
196	C₄⋊C₄×C₈₉	—	2	1	no	—
197	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
199	C₂²⋊C₄×C₈₉	—	2	1	no	—
200	C₂²⋊C₄×C₈₉	—	2	1	no	—
201	C₂²⋊C₄×C₈₉	—	2	1	no	—
202	C₂²⋊C₄×C₈₉	—	2	1	no	—
203	C₂²⋊C₄×C₈₉	—	2	1	no	—
204	C₄²×C₈₉	—	2	1	no	—
205	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₈₉	#41	1	1	yes	characteristic
208	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
209	C₂³×C₈₉	—	2	1	no	—
210	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
211	C₂²×D₈₉	—	2	1	no	—
212	Q₈×C₈₉	—	2	1	no	—
213	Q₈×C₈₉	—	2	1	no	—
214	D₄×C₈₉	—	2	1	no	—
215	D₄×C₈₉	—	2	1	no	—
216	D₄×C₈₉	—	4	2	no	—
217	C₂×C₄×C₈₉	—	2	1	no	—
218	C₂×C₄×C₈₉	—	2	1	no	—
219	C₂×C₄×C₈₉	—	2	1	no	—
220	C₂×C₄×C₈₉	—	2	1	no	—
221	C₂×C₄×C₈₉	—	2	1	no	—
222	C₂×C₄×C₈₉	—	2	1	no	—
223	C₂×C₄×C₈₉	—	2	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	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
233	C₂²⋊D₈₉	—	2	4	no	—
234	C₂×Dic₈₉	—	2	1	no	—
235	C₂×Dic₈₉	—	2	1	no	—
236	C₂×Dic₈₉	—	2	1	no	—
237	D₃₅₆	—	2	1	no	—
238	D₃₅₆	#131	1	2	yes	—
239	C₄×D₈₉	—	2	4	no	—
240	C₄×D₈₉	—	4	2	no	—
241	C₄×D₈₉	—	4	1	no	—
242	C₄×D₈₉	—	4	1	no	—
243	Dic₁₇₈	—	2	1	no	—
244	Dic₁₇₈	#131	1	2	yes	—
245	C₈×C₈₉	—	4	1	no	—
246	C₈×C₈₉	—	4	1	no	—
247	C₈×C₈₉	—	4	1	no	—
248	C₈×C₈₉	—	4	1	no	—
249	#10623494	—	2	1	no	—
250	#10623494	—	2	1	no	—
251	#10623494	—	2	1	no	—
252	#10623494	—	2	1	no	—
253	#10623494	—	2	1	no	—
254	#10623494	—	2	1	no	—
255	#10623494	—	4	1	no	—
256	#10623494	—	4	1	no	—
257	#10623494	#135	1	2	yes	—
258	#10623494	#135	1	2	yes	—
259	C₂²×C₈₉	—	2	1	no	—
260	C₂²×C₈₉	—	2	1	no	—
261	C₂²×C₈₉	—	2	1	no	—
262	C₂²×C₈₉	—	4	1	no	—
263	C₂²×C₈₉	—	4	1	no	—
264	C₂²×C₈₉	—	4	1	no	—
265	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
266	C₂×D₈₉	—	2	2	no	—
267	C₂×D₈₉	—	4	1	no	—
268	C₂×D₈₉	—	4	1	no	—
269	C₄×C₈₉	—	2	1	no	—
270	C₄×C₈₉	—	2	1	no	—
271	C₄×C₈₉	—	2	1	no	—
272	C₄×C₈₉	—	2	1	no	—
273	C₄×C₈₉	—	4	1	no	—
274	C₄×C₈₉	—	4	1	no	—
275	C₄×C₈₉	—	4	1	no	—
276	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
277	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
278	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
279	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
280	Dic₈₉	—	2	2	no	—
281	Dic₈₉	—	4	1	no	—
282	Dic₈₉	—	4	1	no	—
283	#17904	—	89	1	no	maximal, Sylow
284	C₂×C₈₉	—	4	1	no	—
285	C₂×C₈₉	—	8	1	no	—
286	C₂×C₈₉	#2929	1	1	yes	characteristic
287	C₂×C₈₉	C₄×#135	1	1	yes	characteristic
288	C₂×C₈₉	#2955	1	1	yes	characteristic
289	D₈₉	—	4	2	no	—
290	#3102	—	89	1	no	—
291	#2966	—	89	1	no	—
292	C₈×#41	—	89	1	no	—
293	#1584	—	89	1	no	—
294	#1583	—	89	1	no	—
295	#1582	—	89	1	no	—
296	#1581	—	89	1	no	—
297	C₈×Q₁₆	—	89	1	no	—
298	C₈×SD₁₆	—	89	1	no	—
299	C₈×SD₁₆	—	89	1	no	—
300	C₈×D₈	—	89	1	no	—
301	#1572	—	89	1	no	—
302	#1488	—	89	1	no	—
303	#1482	D₈₉	1	1	yes	characteristic, complemented
304	#1450	—	89	1	no	—
305	C₈₉	#17904	1	1	yes	characteristic, complemented, Sylow
306	#529	C₂×D₈₉	1	1	yes	characteristic
307	C₄×#41	—	89	1	no	—
308	#485	—	89	1	no	—
309	#482	—	89	1	no	—
310	#479	—	89	1	no	—
311	#478	—	89	1	no	—
312	#464	—	89	1	no	—
313	#463	—	89	1	no	—
314	#452	—	89	1	no	—
315	#449	—	89	1	no	—
316	#446	—	89	1	no	—
317	C₈×Q₈	—	89	1	no	—
318	C₈×Q₈	—	89	1	no	—
319	C₈×Q₈	—	89	1	no	—
320	C₄×Q₁₆	—	89	1	no	—
321	C₄×SD₁₆	—	89	1	no	—
322	C₄×SD₁₆	—	89	1	no	—
323	C₄×D₈	—	89	1	no	—
324	#436	—	89	1	no	—
325	#435	—	178	1	no	—
326	C₈×D₄	—	89	1	no	—
327	C₈×D₄	—	89	1	no	—
328	C₈×D₄	—	89	1	no	—
329	C₈×D₄	—	178	1	no	—
330	C₈×D₄	—	178	1	no	—
331	C₈×D₄	—	178	1	no	—
332	#433	—	178	1	no	—
333	#432	—	89	1	no	—
334	#431	—	89	1	no	—
335	#431	—	178	1	no	—
336	#431	C₂×D₈₉	1	1	yes	characteristic
337	#431	C₂×D₈₉	1	1	yes	characteristic
338	#405	—	178	1	no	—
339	C₂×C₄×C₈	—	89	1	no	—
340	C₂×C₄×C₈	—	178	1	no	—
341	#335	—	89	1	no	—
342	#335	—	89	1	no	—
343	#334	—	89	1	no	—
344	#334	—	89	1	no	—
345	Q₈⋊C₈	—	89	1	no	—
346	Q₈⋊C₈	—	89	1	no	—
347	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
348	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
349	D₄⋊C₈	—	89	1	no	—
350	D₄⋊C₈	—	89	1	no	—
351	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
352	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
353	#322	—	89	1	no	—
354	#322	—	89	1	no	—
355	C₈²	—	89	1	no	—
356	C₈²	—	89	1	no	—
357	C₂×#41	—	89	1	no	—
358	C₂×Q₁₆	—	89	1	no	—
359	C₂×SD₁₆	—	89	1	no	—
360	C₂×SD₁₆	—	89	1	no	—
361	C₂×D₈	—	89	1	no	—
362	C₂×M₁₆	—	178	1	no	—
363	C₂²×C₈	—	89	1	no	—
364	C₂²×C₈	—	89	1	no	—
365	C₂²×C₈	—	178	1	no	—
366	C₂²×C₈	—	178	1	no	—
367	C₂²×C₈	—	178	1	no	—
368	#126	—	2	1	no	—
369	#125	C₄×D₈₉	1	1	yes	characteristic
370	#124	C₄×D₈₉	1	1	yes	characteristic
371	#123	—	2	1	no	—
372	C₂²⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
373	#121	C₄×D₈₉	1	1	yes	characteristic
374	C₄×Q₈	—	89	1	no	—
375	C₄×Q₈	—	89	1	no	—
376	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	89	1	no	—
379	C₄×D₄	—	89	1	no	—
380	C₄×D₄	—	178	1	no	—
381	C₄×D₄	—	178	1	no	—
382	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
383	#117	—	2	1	no	—
384	#117	—	89	1	no	—
385	#117	—	178	1	no	—
386	C₂×C₄²	—	178	1	no	—
387	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
388	#107	—	89	1	no	—
389	#107	—	89	1	no	—
390	#106	—	89	1	no	—
391	#106	—	89	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	—	89	1	no	—
394	C₄⋊C₈	—	89	1	no	—
395	C₄⋊C₈	—	89	1	no	—
396	C₄⋊C₈	—	89	1	no	—
397	C₄⋊C₈	—	178	1	no	—
398	C₄⋊C₈	—	178	1	no	—
399	C₄⋊C₈	—	178	1	no	—
400	C₄⋊C₈	—	178	1	no	—
401	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
402	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
403	#103	—	89	1	no	—
404	#103	—	89	1	no	—
405	#103	—	89	1	no	—
406	#103	—	89	1	no	—
407	#102	—	89	1	no	—
408	#102	—	89	1	no	—
409	#102	—	89	1	no	—
410	#102	—	89	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	89	1	no	—
414	C₂²⋊C₈	—	89	1	no	—
415	C₂²⋊C₈	—	178	1	no	—
416	C₂²⋊C₈	—	178	1	no	—
417	C₂²⋊C₈	—	178	1	no	—
418	C₂²⋊C₈	—	178	1	no	—
419	C₂²⋊C₈	—	178	1	no	—
420	#97	—	178	1	no	—
421	#97	—	178	1	no	—
422	C₄×C₈	—	2	1	no	—
423	C₄×C₈	—	89	1	no	—
424	C₄×C₈	—	89	1	no	—
425	C₄×C₈	—	89	1	no	—
426	C₄×C₈	—	89	1	no	—
427	C₄×C₈	—	89	1	no	—
428	C₄×C₈	—	89	1	no	—
429	C₄×C₈	—	178	1	no	—
430	C₄×C₈	—	178	1	no	—
431	C₄×C₈	—	178	1	no	—
432	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
434	#41	—	178	2	no	—
435	#41	—	178	2	no	—
436	C₂×Q₈	—	89	1	no	—
437	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	89	1	no	—
440	C₂×D₄	—	178	1	no	—
441	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	178	1	no	—
444	C₂²×C₄	—	178	1	no	—
445	C₂²×C₄	—	178	1	no	—
446	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
447	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
448	C₂²×C₄	#13083573	1	1	yes	characteristic
449	Q₁₆	—	178	2	no	—
450	SD₁₆	—	178	2	no	—
451	SD₁₆	—	178	2	no	—
452	D₈	—	178	2	no	—
453	M₁₆	—	356	2	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	89	1	no	—
459	C₂×C₈	—	89	1	no	—
460	C₂×C₈	—	89	1	no	—
461	C₂×C₈	—	89	1	no	—
462	C₂×C₈	—	89	1	no	—
463	C₂×C₈	—	89	1	no	—
464	C₂×C₈	—	89	1	no	—
465	C₂×C₈	—	89	1	no	—
466	C₂×C₈	—	356	2	no	—
467	C₂×C₈	—	356	2	no	—
468	C₂×C₈	—	356	2	no	—
469	C₂×C₈	—	178	2	no	—
470	C₂×C₈	—	178	2	no	—
471	C₂×C₈	—	178	1	no	—
472	C₂×C₈	—	178	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	89	1	no	—
478	C₄⋊C₄	—	89	1	no	—
479	C₄⋊C₄	—	178	1	no	—
480	C₄⋊C₄	—	178	1	no	—
481	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
482	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	178	1	no	—
489	C₂²⋊C₄	—	178	1	no	—
490	C₂²⋊C₄	—	178	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	178	1	no	—
493	C₄²	—	178	1	no	—
494	C₄²	—	178	1	no	—
495	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
496	C₄²	D₄×D₈₉	1	1	yes	characteristic
497	C₄²	#13083573	1	1	yes	characteristic
498	C₄²	C₂³×D₈₉	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	178	1	no	—
501	C₂³	#15667972	1	1	yes	characteristic
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	89	2	no	—
505	Q₈	—	178	1	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	4	2	no	—
509	D₄	—	89	2	no	—
510	D₄	—	178	4	no	—
511	D₄	—	178	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	356	2	no	—
523	C₂×C₄	—	356	1	no	—
524	C₂×C₄	—	356	1	no	—
525	C₂×C₄	—	178	4	no	—
526	C₂×C₄	—	178	1	no	—
527	C₂×C₄	—	178	1	no	—
528	C₂×C₄	—	178	1	no	—
529	C₂×C₄	#15667972	1	1	yes	characteristic
530	C₂×C₄	#15667972	1	1	yes	characteristic
531	C₂×C₄	#15667972	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
533	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
534	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	89	2	no	—
540	C₈	—	89	2	no	—
541	C₈	—	356	1	no	—
542	C₈	—	356	1	no	—
543	C₈	—	178	1	no	—
544	C₈	—	178	1	no	—
545	C₈	—	178	1	no	—
546	C₈	—	178	1	no	—
547	C₈	—	178	1	no	—
548	C₈	—	178	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	356	1	no	—
556	C₂²	—	356	1	no	—
557	C₂²	—	178	2	no	—
558	C₂²	C₂×#15667972	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	356	1	no	—
567	C₄	—	356	1	no	—
568	C₄	—	178	2	no	—
569	C₄	#131×D₈₉	1	1	yes	characteristic
570	C₄	#131×D₈₉	1	1	yes	characteristic
571	C₄	#135×D₈₉	1	1	yes	characteristic
572	C₄	#135×D₈₉	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	8	1	no	—
575	C₂	—	356	2	no	—
576	C₂	#26028949	1	1	yes	characteristic
577	C₂	#26029020	1	1	yes	characteristic
578	C₂	#26029151	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1482	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#19151741	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1482	D₈₉
hypocenter	C₈₉	#17904
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1482

Complements

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

N	H ≅ G/N	type
2. #26029228	C₂	semidirect
3. #26029208	C₂	semidirect
4. #26019105	C₂	semidirect
5. #26019098	C₂	semidirect
6. #26019091	C₂	semidirect
7. #26019084	C₂	semidirect
8. #26019056	C₂	semidirect
9. #26019055	C₂	semidirect
10. #26019049	C₂	semidirect
11. #26019044	C₂	semidirect
12. #26019030	C₂	semidirect
13. #26018687	C₂	semidirect
14. #26018536	C₂	semidirect
15. C₈₉×#1482	C₂	semidirect
303. #1482	D₈₉	semidirect
305. C₈₉	#17904	semidirect

Maximal subgroups

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

subgroup	index
#26030264	2
#26029228	2
#26029208	2
#26019105	2
#26019098	2
#26019091	2
#26019084	2
#26019056	2
#26019055	2
#26019049	2
#26019044	2
#26019030	2
#26018687	2
#26018536	2
C₈₉×#1482	2
#17904	89