Subgroups — #36524503

Order 22784.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030332	C₂	1	1	yes	maximal, characteristic
2	#26029403	C₂	1	1	yes	maximal, characteristic
3	#26019130	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019123	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019102	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019095	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019069	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019062	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#13083564	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#13083561	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019040	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018681	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018658	C₂	1	1	yes	maximal, characteristic
14	#26018552	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2982	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152132	C₂²	1	1	yes	characteristic
17	#19151928	C₄	1	1	yes	characteristic
18	#19151911	C₄	1	1	yes	characteristic
19	#19151905	C₄	1	1	yes	characteristic
20	#19151905	C₄	1	1	yes	characteristic
21	#19151820	C₄	1	1	yes	characteristic
22	#19151820	C₄	1	1	yes	characteristic
23	#19151754	C₄	1	1	yes	characteristic
24	#19151737	C₄	1	1	yes	characteristic
25	#19151728	C₂²	1	1	yes	characteristic
26	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
27	C₄×#13083564	C₂²	1	1	yes	characteristic
28	C₄×#13083564	C₂²	1	1	yes	characteristic
29	C₄×#13083561	C₂²	1	1	yes	characteristic
30	C₄×#13083561	C₂²	1	1	yes	characteristic
31	#19151677	C₂²	1	1	yes	characteristic
32	#19151673	—	2	1	no	—
33	#19151672	—	2	1	no	—
34	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
35	#19151658	—	2	1	no	—
36	#19151651	C₂²	1	1	yes	characteristic
37	#19151651	C₂²	1	1	yes	characteristic
38	#19151623	—	2	1	no	—
39	#19151622	C₂²	1	1	yes	characteristic
40	#19151350	C₂²	1	1	yes	characteristic
41	#19151350	C₂²	1	1	yes	characteristic
42	#19151348	C₂²	1	1	yes	characteristic
43	#19151348	C₂²	1	1	yes	characteristic
44	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
45	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
46	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
47	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
48	#19151328	C₂²	1	1	yes	characteristic
49	#19151328	C₂²	1	1	yes	characteristic
50	#19151325	C₂²	1	1	yes	characteristic
51	#19151325	C₂²	1	1	yes	characteristic
52	#19151320	C₂²	1	1	yes	characteristic
53	#19151320	C₂²	1	1	yes	characteristic
54	#19151319	C₂²	1	1	yes	characteristic
55	C₈×#10623494	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
57	C₈×Q₈×C₈₉	—	2	1	no	—
58	C₈×Q₈×C₈₉	—	2	1	no	—
59	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
62	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
63	#431×C₈₉	—	2	1	no	—
64	#431×C₈₉	—	2	1	no	—
65	#431×C₈₉	C₂²	1	1	yes	characteristic
66	#431×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
68	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083558	—	2	1	no	—
72	C₂×#13083557	—	2	1	no	—
73	C₂×C₈×D₈₉	—	2	1	no	—
74	#15668006	—	2	1	no	—
75	#15668004	C₂×C₄	1	1	yes	characteristic
76	#15668000	C₂×C₄	1	1	yes	characteristic
77	#15667995	—	2	1	no	—
78	#15667991	C₂×C₄	1	1	yes	characteristic
79	#15667986	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
81	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
82	C₄×C₂²⋊D₈₉	—	2	1	no	—
83	#15667969	—	2	1	no	—
84	#15667945	C₂×C₄	1	1	yes	characteristic
85	#15667945	C₂×C₄	1	1	yes	characteristic
86	#15667943	C₂×C₄	1	1	yes	characteristic
87	#15667943	C₂×C₄	1	1	yes	characteristic
88	C₄⋊#10623494	—	2	1	no	—
89	C₄⋊#10623494	—	2	1	no	—
90	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
91	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
92	C₄⋊#10623494	C₂³	1	1	yes	characteristic
93	C₄⋊#10623494	C₂³	1	1	yes	characteristic
94	#15667941	—	2	1	no	—
95	#15667941	—	2	1	no	—
96	#15667936	C₂×C₄	1	1	yes	characteristic
97	#15667936	C₂×C₄	1	1	yes	characteristic
98	#15667936	C₂×C₄	1	1	yes	characteristic
99	#15667936	C₂×C₄	1	1	yes	characteristic
100	#15667935	C₂×C₄	1	1	yes	characteristic
101	#15667935	C₂×C₄	1	1	yes	characteristic
102	#15667932	C₂×C₄	1	1	yes	characteristic
103	#15667932	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊#10623494	—	2	1	no	—
105	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
107	#15667924	—	2	1	no	—
108	#15667924	—	2	1	no	—
109	#15667922	—	2	1	no	—
110	C₄×#10623494	C₂³	1	1	yes	characteristic
111	C₄×#10623494	C₂³	1	1	yes	characteristic
112	C₄×#10623494	C₂³	1	1	yes	characteristic
113	C₄×#10623494	C₂³	1	1	yes	characteristic
114	C₈×Dic₈₉	—	2	1	no	—
115	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
116	C₄×Q₈×C₈₉	—	2	1	no	—
117	C₄×Q₈×C₈₉	—	2	1	no	—
118	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
119	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
120	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
121	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
123	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄²×C₈₉	—	2	1	no	—
125	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
126	C₄⋊C₈×C₈₉	—	2	1	no	—
127	C₄⋊C₈×C₈₉	—	2	1	no	—
128	C₄⋊C₈×C₈₉	—	2	1	no	—
129	C₄⋊C₈×C₈₉	—	2	1	no	—
130	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
131	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
132	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
134	C₂²⋊C₈×C₈₉	—	2	1	no	—
135	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
136	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
137	C₄×C₈×C₈₉	—	2	1	no	—
138	C₄×C₈×C₈₉	—	2	1	no	—
139	C₄×C₈×C₈₉	—	2	1	no	—
140	C₄×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	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₂²⋊D₈₉	—	2	1	no	—
147	C₂×C₄×D₈₉	—	2	1	no	—
148	#13083564	—	2	2	no	—
149	#13083564	—	2	2	no	—
150	#13083561	—	2	2	no	—
151	#13083561	—	2	2	no	—
152	#13083558	—	8	1	no	—
153	#13083557	—	8	1	no	—
154	C₂×#10623494	—	2	1	no	—
155	C₂×#10623494	—	2	1	no	—
156	C₂×#10623494	—	2	1	no	—
157	C₂×#10623494	—	2	1	no	—
158	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
159	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
160	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
161	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
162	C₈×D₈₉	—	8	1	no	—
163	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
164	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
165	#13083553	—	2	1	no	—
166	#13083553	—	2	1	no	—
167	#13083553	—	2	1	no	—
168	#13083553	—	2	1	no	—
169	C₂²⋊Dic₈₉	—	2	1	no	—
170	#13083551	—	2	1	no	—
171	#13083551	—	2	1	no	—
172	#13083551	—	2	1	no	—
173	#13083551	—	2	1	no	—
174	C₄×Dic₈₉	—	2	1	no	—
175	C₂×Q₈×C₈₉	—	2	2	no	—
176	C₂×Q₈×C₈₉	—	2	2	no	—
177	C₂×Q₈×C₈₉	—	2	1	no	—
178	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
179	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₈₉	—	2	1	no	—
181	C₂²×C₄×C₈₉	—	2	1	no	—
182	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
185	C₂×C₈×C₈₉	—	2	1	no	—
186	C₂×C₈×C₈₉	—	2	1	no	—
187	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
191	C₄⋊C₄×C₈₉	—	2	1	no	—
192	C₄⋊C₄×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	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₄²×C₈₉	—	2	1	no	—
199	C₄²×C₈₉	—	2	1	no	—
200	C₄²×C₈₉	—	2	1	no	—
201	C₄²×C₈₉	—	2	1	no	—
202	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
203	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₈₉	#41	1	1	yes	characteristic
205	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
206	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
207	C₂²×D₈₉	—	2	1	no	—
208	Q₈×C₈₉	—	2	4	no	—
209	Q₈×C₈₉	—	2	1	no	—
210	Q₈×C₈₉	—	2	1	no	—
211	Q₈×C₈₉	#131	1	2	yes	—
212	Q₈×C₈₉	#131	1	2	yes	—
213	C₂×C₄×C₈₉	—	2	4	no	—
214	C₂×C₄×C₈₉	—	2	1	no	—
215	C₂×C₄×C₈₉	—	2	1	no	—
216	C₂×C₄×C₈₉	—	2	1	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	—	4	1	no	—
223	C₂×C₄×C₈₉	—	8	1	no	—
224	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
230	C₂²⋊D₈₉	—	8	1	no	—
231	C₂×Dic₈₉	—	2	1	no	—
232	C₂×Dic₈₉	—	2	1	no	—
233	C₂×Dic₈₉	—	2	1	no	—
234	D₃₅₆	—	2	1	no	—
235	D₃₅₆	—	2	1	no	—
236	C₄×D₈₉	—	4	1	no	—
237	C₄×D₈₉	—	4	1	no	—
238	Dic₁₇₈	—	2	1	no	—
239	Dic₁₇₈	—	2	1	no	—
240	C₈×C₈₉	—	2	1	no	—
241	C₈×C₈₉	—	2	1	no	—
242	C₈×C₈₉	—	2	1	no	—
243	C₈×C₈₉	—	2	1	no	—
244	C₈×C₈₉	—	4	1	no	—
245	C₈×C₈₉	—	4	1	no	—
246	#10623494	—	2	1	no	—
247	#10623494	—	2	1	no	—
248	#10623494	—	2	1	no	—
249	#10623494	—	2	1	no	—
250	#10623494	—	4	1	no	—
251	#10623494	—	4	1	no	—
252	#10623494	—	4	1	no	—
253	#10623494	—	4	1	no	—
254	C₂²×C₈₉	—	2	1	no	—
255	C₂²×C₈₉	—	2	1	no	—
256	C₂²×C₈₉	—	2	1	no	—
257	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂×D₈₉	—	4	1	no	—
259	C₂×D₈₉	—	4	1	no	—
260	C₂×D₈₉	—	4	1	no	—
261	C₄×C₈₉	—	2	2	no	—
262	C₄×C₈₉	—	2	2	no	—
263	C₄×C₈₉	—	2	1	no	—
264	C₄×C₈₉	—	2	1	no	—
265	C₄×C₈₉	—	2	1	no	—
266	C₄×C₈₉	—	2	1	no	—
267	C₄×C₈₉	—	4	1	no	—
268	C₄×C₈₉	—	4	1	no	—
269	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
270	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
271	C₄×C₈₉	#577	1	1	yes	characteristic
272	C₄×C₈₉	#578	1	1	yes	characteristic
273	Dic₈₉	—	4	1	no	—
274	Dic₈₉	—	4	1	no	—
275	Dic₈₉	—	4	1	no	—
276	#17919	—	89	1	no	maximal, Sylow
277	C₂×C₈₉	—	4	1	no	—
278	C₂×C₈₉	#2929	1	1	yes	characteristic
279	C₂×C₈₉	#2947	1	1	yes	characteristic
280	C₂×C₈₉	#2957	1	1	yes	characteristic
281	D₈₉	—	8	1	no	—
282	#3108	—	89	1	no	—
283	#2993	—	89	1	no	—
284	#2982	D₈₉	1	1	yes	characteristic, complemented
285	#1588	—	89	1	no	—
286	#1587	—	89	1	no	—
287	#1584	—	89	1	no	—
288	#1583	—	89	1	no	—
289	#1579	—	89	1	no	—
290	SD₁₆⋊C₈	—	89	1	no	—
291	C₈×Q₁₆	—	89	1	no	—
292	C₈×SD₁₆	—	89	1	no	—
293	#1574	—	89	1	no	—
294	#1487	—	89	1	no	—
295	#1482	—	89	1	no	—
296	#1454	—	89	1	no	—
297	C₈₉	#17919	1	1	yes	characteristic, complemented, Sylow
298	#529	—	89	1	no	—
299	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
300	#483	—	89	1	no	—
301	#480	—	89	1	no	—
302	#479	—	89	1	no	—
303	#479	—	89	1	no	—
304	#464	—	89	1	no	—
305	#464	—	89	1	no	—
306	#451	—	89	1	no	—
307	#448	—	89	1	no	—
308	#446	—	89	1	no	—
309	C₈×Q₈	—	2	1	no	—
310	C₈×Q₈	—	2	1	no	—
311	C₈×Q₈	—	89	1	no	—
312	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
313	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
314	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
315	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
316	C₄×Q₁₆	—	89	1	no	—
317	C₄×Q₁₆	—	89	1	no	—
318	C₄×SD₁₆	—	89	1	no	—
319	C₄×SD₁₆	—	89	1	no	—
320	#436	—	89	1	no	—
321	#436	—	178	1	no	—
322	#435	—	178	1	no	—
323	C₈×D₄	—	89	1	no	—
324	#433	—	178	1	no	—
325	#431	—	2	1	no	—
326	#431	—	2	1	no	—
327	#431	—	89	1	no	—
328	#431	—	89	1	no	—
329	#431	C₂×D₈₉	1	1	yes	characteristic
330	#431	C₂×D₈₉	1	1	yes	characteristic
331	#424	—	178	1	no	—
332	#423	—	89	1	no	—
333	#335	—	89	1	no	—
334	#335	—	89	1	no	—
335	#334	—	89	1	no	—
336	#334	—	89	1	no	—
337	Q₈⋊C₈	—	89	1	no	—
338	Q₈⋊C₈	—	89	1	no	—
339	Q₈⋊C₈	—	89	1	no	—
340	Q₈⋊C₈	—	89	1	no	—
341	Q₈⋊C₈	—	89	1	no	—
342	Q₈⋊C₈	—	89	1	no	—
343	D₄⋊C₈	—	89	1	no	—
344	D₄⋊C₈	—	89	1	no	—
345	#322	—	89	1	no	—
346	#322	—	89	1	no	—
347	#322	—	89	1	no	—
348	C₈²	—	89	1	no	—
349	C₂²×Q₈	C₄×D₈₉	1	1	yes	characteristic
350	C₂×Q₁₆	—	89	1	no	—
351	C₂×Q₁₆	—	89	1	no	—
352	C₂×SD₁₆	—	89	1	no	—
353	C₂×SD₁₆	—	89	1	no	—
354	C₂×M₁₆	—	178	1	no	—
355	C₂×M₁₆	—	178	1	no	—
356	C₂²×C₈	—	178	1	no	—
357	#126	—	178	1	no	—
358	#125	—	89	1	no	—
359	#124	—	89	1	no	—
360	#123	—	178	1	no	—
361	C₂²⋊Q₈	—	89	1	no	—
362	#121	—	89	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	89	1	no	—
366	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
367	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
368	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
369	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
370	C₄×D₄	—	89	1	no	—
371	C₄×D₄	—	178	1	no	—
372	#117	—	178	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
377	#107	—	89	1	no	—
378	#107	—	89	1	no	—
379	#106	—	89	1	no	—
380	#106	—	89	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	2	1	no	—
385	C₄⋊C₈	—	89	1	no	—
386	C₄⋊C₈	—	89	1	no	—
387	C₄⋊C₈	—	89	1	no	—
388	C₄⋊C₈	—	89	1	no	—
389	C₄⋊C₈	—	178	1	no	—
390	C₄⋊C₈	—	178	1	no	—
391	C₄⋊C₈	—	178	1	no	—
392	C₄⋊C₈	—	178	1	no	—
393	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
394	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
395	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
396	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
397	#103	—	89	1	no	—
398	#103	—	89	1	no	—
399	#103	—	89	1	no	—
400	#103	—	89	1	no	—
401	#103	—	89	1	no	—
402	#103	—	89	1	no	—
403	#102	—	89	1	no	—
404	#102	—	89	1	no	—
405	C₂²⋊C₈	—	2	1	no	—
406	C₂²⋊C₈	—	89	1	no	—
407	C₂²⋊C₈	—	89	1	no	—
408	C₂²⋊C₈	—	178	1	no	—
409	C₂²⋊C₈	—	178	1	no	—
410	C₂²⋊C₈	—	178	1	no	—
411	C₂²⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
412	C₂²⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
413	#97	—	178	1	no	—
414	C₄×C₈	—	2	1	no	—
415	C₄×C₈	—	2	1	no	—
416	C₄×C₈	—	2	1	no	—
417	C₄×C₈	—	2	1	no	—
418	C₄×C₈	—	2	1	no	—
419	C₄×C₈	—	89	1	no	—
420	C₄×C₈	—	89	1	no	—
421	C₄×C₈	—	89	1	no	—
422	C₄×C₈	—	89	1	no	—
423	C₄×C₈	—	178	1	no	—
424	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	89	1	no	—
430	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
431	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
432	C₂×D₄	—	89	1	no	—
433	C₂×D₄	—	178	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	178	1	no	—
437	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
439	C₂²×C₄	#13083574	1	1	yes	characteristic
440	Q₁₆	—	178	2	no	—
441	Q₁₆	—	178	2	no	—
442	SD₁₆	—	178	2	no	—
443	SD₁₆	—	178	2	no	—
444	M₁₆	—	712	1	no	—
445	M₁₆	—	712	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	89	1	no	—
449	C₂×C₈	—	89	1	no	—
450	C₂×C₈	—	89	1	no	—
451	C₂×C₈	—	89	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	—	712	1	no	—
457	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
458	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
459	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
460	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	89	1	no	—
467	C₄⋊C₄	—	89	1	no	—
468	C₄⋊C₄	—	178	1	no	—
469	C₄⋊C₄	—	178	1	no	—
470	C₄⋊C₄	—	178	1	no	—
471	C₄⋊C₄	—	178	1	no	—
472	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
473	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
474	C₂²⋊C₄	—	178	1	no	—
475	C₂²⋊C₄	—	178	1	no	—
476	C₂²⋊C₄	—	178	1	no	—
477	C₂²⋊C₄	—	178	1	no	—
478	C₂²⋊C₄	—	178	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	178	1	no	—
484	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
485	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
486	C₄²	#13083574	1	1	yes	characteristic
487	C₄²	C₂³×D₈₉	1	1	yes	characteristic
488	C₂³	—	178	1	no	—
489	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
490	Q₈	—	2	4	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	178	1	no	—
494	Q₈	—	178	1	no	—
495	Q₈	#15668018	1	2	yes	—
496	Q₈	#15668018	1	2	yes	—
497	D₄	—	178	1	no	—
498	D₄	—	178	1	no	—
499	D₄	—	712	1	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	1	no	—
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	—	4	1	no	—
510	C₂×C₄	—	8	1	no	—
511	C₂×C₄	—	356	1	no	—
512	C₂×C₄	—	356	1	no	—
513	C₂×C₄	—	178	1	no	—
514	C₂×C₄	—	178	1	no	—
515	C₂×C₄	—	178	1	no	—
516	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
517	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
518	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
519	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
520	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
521	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	356	1	no	—
529	C₈	—	356	1	no	—
530	C₈	—	356	1	no	—
531	C₈	—	356	1	no	—
532	C₈	—	178	1	no	—
533	C₈	—	178	1	no	—
534	C₈	—	178	1	no	—
535	C₈	—	178	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	356	1	no	—
540	C₂²	—	356	1	no	—
541	C₂²	—	356	1	no	—
542	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	356	1	no	—
552	C₄	—	356	1	no	—
553	C₄	—	356	1	no	—
554	C₄	C₂×#15668018	1	1	yes	characteristic
555	C₄	C₂×#15668018	1	1	yes	characteristic
556	C₄	#19152406	1	1	yes	characteristic
557	C₄	#19152413	1	1	yes	characteristic
558	C₂	—	4	1	no	—
559	C₂	—	712	1	no	—
560	C₂	#26028946	1	1	yes	characteristic
561	C₂	#26029095	1	1	yes	characteristic
562	C₂	#26029167	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2982	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#15667986	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2982	D₈₉
hypocenter	C₈₉	#17919
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2982

Complements

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

N	H ≅ G/N	type
3. #26019130	C₂	semidirect
4. #26019123	C₂	semidirect
5. #26019102	C₂	semidirect
6. #26019095	C₂	semidirect
7. #26019069	C₂	semidirect
8. #26019062	C₂	semidirect
9. C₈×#13083564	C₂	semidirect
10. C₈×#13083561	C₂	semidirect
11. #26019040	C₂	semidirect
12. #26018681	C₂	semidirect
14. #26018552	C₂	semidirect
15. C₈₉×#2982	C₂	semidirect
284. #2982	D₈₉	semidirect
297. C₈₉	#17919	semidirect

Maximal subgroups

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

subgroup	index
#26030332	2
#26029403	2
#26019130	2
#26019123	2
#26019102	2
#26019095	2
#26019069	2
#26019062	2
C₈×#13083564	2
C₈×#13083561	2
#26019040	2
#26018681	2
#26018658	2
#26018552	2
C₈₉×#2982	2
#17919	89