Subgroups — #36524334

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	#26030270	C₂	1	1	yes	maximal, characteristic
2	#26029227	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019102	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019095	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019088	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019081	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×#13083564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#13083561	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#13083562	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#13083559	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019030	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018686	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018658	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018535	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152132	C₂²	1	1	yes	characteristic
17	#19151939	C₄	1	1	yes	characteristic
18	#19151922	C₄	1	1	yes	characteristic
19	#19151905	C₄	1	1	yes	characteristic
20	#19151898	C₄	1	1	yes	characteristic
21	#19151820	C₄	1	1	yes	characteristic
22	#19151813	C₄	1	1	yes	characteristic
23	#19151760	C₄	1	1	yes	characteristic
24	#19151743	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×#13083561	C₂²	1	1	yes	characteristic
29	C₄×#13083562	C₂²	1	1	yes	characteristic
30	C₄×#13083559	C₂²	1	1	yes	characteristic
31	#19151677	C₂²	1	1	yes	characteristic
32	#19151669	—	2	1	no	—
33	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₈₉	—	2	1	no	—
35	#19151657	—	2	1	no	—
36	#19151655	C₂²	1	1	yes	characteristic
37	#19151651	C₂²	1	1	yes	characteristic
38	#19151651	C₂²	1	1	yes	characteristic
39	#19151552	—	2	1	no	—
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	#19151328	C₂²	1	1	yes	characteristic
47	#19151328	C₂²	1	1	yes	characteristic
48	D₄⋊#10623494	C₂²	1	1	yes	characteristic
49	D₄⋊#10623494	C₂²	1	1	yes	characteristic
50	#19151325	C₂²	1	1	yes	characteristic
51	#19151325	C₂²	1	1	yes	characteristic
52	#19151319	C₂²	1	1	yes	characteristic
53	#19151319	C₂²	1	1	yes	characteristic
54	C₈×#10623494	C₂²	1	1	yes	characteristic
55	C₈×#10623494	C₂²	1	1	yes	characteristic
56	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
57	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
58	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
59	C₈×D₄×C₈₉	—	2	1	no	—
60	C₈×D₄×C₈₉	—	2	1	no	—
61	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
63	#431×C₈₉	—	2	1	no	—
64	#431×C₈₉	C₂²	1	1	yes	characteristic
65	C₂×C₄×C₈×C₈₉	—	2	1	no	—
66	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
68	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083557	—	2	1	no	—
72	C₂×C₈×D₈₉	—	2	1	no	—
73	#15668006	—	2	1	no	—
74	#15668004	C₂×C₄	1	1	yes	characteristic
75	#15668000	C₂×C₄	1	1	yes	characteristic
76	#15667995	—	2	1	no	—
77	#15667991	C₂×C₄	1	1	yes	characteristic
78	#15667986	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
80	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
81	C₄×C₂²⋊D₈₉	—	2	1	no	—
82	#15667969	—	2	1	no	—
83	#15667945	C₂×C₄	1	1	yes	characteristic
84	#15667945	C₂×C₄	1	1	yes	characteristic
85	#15667943	C₂×C₄	1	1	yes	characteristic
86	#15667943	C₂×C₄	1	1	yes	characteristic
87	C₄⋊#10623494	—	2	1	no	—
88	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
89	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
90	C₄⋊#10623494	C₂³	1	1	yes	characteristic
91	C₄⋊#10623494	C₂³	1	1	yes	characteristic
92	#15667941	—	2	1	no	—
93	#15667941	—	2	1	no	—
94	#15667936	C₂×C₄	1	1	yes	characteristic
95	#15667936	C₂×C₄	1	1	yes	characteristic
96	#15667935	C₂×C₄	1	1	yes	characteristic
97	#15667935	C₂×C₄	1	1	yes	characteristic
98	#15667933	C₂×C₄	1	1	yes	characteristic
99	#15667933	C₂×C₄	1	1	yes	characteristic
100	#15667932	C₂×C₄	1	1	yes	characteristic
101	#15667932	C₂×C₄	1	1	yes	characteristic
102	C₂²⋊#10623494	—	2	1	no	—
103	C₂²⋊#10623494	—	2	1	no	—
104	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
105	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
106	#15667924	—	2	1	no	—
107	#15667924	—	2	1	no	—
108	#15667923	—	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	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
116	C₂²×C₈×C₈₉	—	2	1	no	—
117	C₂²×C₈×C₈₉	—	2	1	no	—
118	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
119	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
120	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
121	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₄×D₄×C₈₉	—	2	1	no	—
123	C₄×D₄×C₈₉	—	2	1	no	—
124	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
125	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
126	#117×C₈₉	—	2	1	no	—
127	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
128	C₂×C₄²×C₈₉	—	2	1	no	—
129	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
130	C₄⋊C₈×C₈₉	—	2	1	no	—
131	C₄⋊C₈×C₈₉	—	2	1	no	—
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	—	2	1	no	—
136	C₂²⋊C₈×C₈₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
141	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
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	#13083562	—	2	2	no	—
150	#13083561	—	2	2	no	—
151	#13083559	—	2	2	no	—
152	#13083557	—	4	2	no	—
153	C₂×#10623494	—	2	1	no	—
154	C₂×#10623494	—	2	1	no	—
155	C₂×#10623494	—	2	1	no	—
156	C₂×#10623494	—	2	1	no	—
157	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
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	C₈×D₈₉	—	4	2	no	—
162	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
163	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
164	#13083553	—	2	1	no	—
165	#13083553	—	2	1	no	—
166	#13083553	—	2	1	no	—
167	#13083553	—	2	1	no	—
168	C₂²⋊Dic₈₉	—	2	1	no	—
169	#13083551	—	2	1	no	—
170	#13083551	—	2	1	no	—
171	#13083551	—	2	1	no	—
172	#13083551	—	2	1	no	—
173	C₄×Dic₈₉	—	2	1	no	—
174	#41×C₈₉	—	2	2	no	—
175	#41×C₈₉	—	2	2	no	—
176	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
177	C₂×D₄×C₈₉	—	2	1	no	—
178	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₈₉	—	2	1	no	—
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	2	no	—
186	C₂×C₈×C₈₉	—	2	2	no	—
187	C₂×C₈×C₈₉	—	2	1	no	—
188	C₂×C₈×C₈₉	—	2	1	no	—
189	C₂×C₈×C₈₉	—	4	2	no	—
190	C₂×C₈×C₈₉	—	4	2	no	—
191	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
192	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
193	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₈₉	—	2	1	no	—
203	C₄²×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	#131	1	2	yes	—
214	D₄×C₈₉	—	2	4	no	—
215	D₄×C₈₉	—	2	1	no	—
216	D₄×C₈₉	#131	1	2	yes	—
217	C₂×C₄×C₈₉	—	2	4	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	—	2	1	no	—
225	C₂×C₄×C₈₉	—	4	1	no	—
226	C₂×C₄×C₈₉	—	4	2	no	—
227	C₂×C₄×C₈₉	—	4	1	no	—
228	C₂×C₄×C₈₉	—	4	1	no	—
229	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
235	C₂²⋊D₈₉	—	4	2	no	—
236	C₂×Dic₈₉	—	2	1	no	—
237	C₂×Dic₈₉	—	2	1	no	—
238	C₂×Dic₈₉	—	2	1	no	—
239	D₃₅₆	—	2	1	no	—
240	D₃₅₆	—	2	1	no	—
241	C₄×D₈₉	—	4	1	no	—
242	C₄×D₈₉	—	4	1	no	—
243	Dic₁₇₈	—	2	1	no	—
244	Dic₁₇₈	—	2	1	no	—
245	C₈×C₈₉	—	2	1	no	—
246	C₈×C₈₉	—	2	1	no	—
247	C₈×C₈₉	—	4	1	no	—
248	C₈×C₈₉	—	4	1	no	—
249	C₈×C₈₉	#135	1	2	yes	—
250	C₈×C₈₉	#135	1	2	yes	—
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	—	4	1	no	—
258	#10623494	—	4	1	no	—
259	C₂²×C₈₉	—	2	1	no	—
260	C₂²×C₈₉	—	2	2	no	—
261	C₂²×C₈₉	—	2	1	no	—
262	C₂²×C₈₉	—	2	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	—	4	1	no	—
267	C₂×D₈₉	—	4	1	no	—
268	C₂×D₈₉	—	4	1	no	—
269	C₄×C₈₉	—	2	1	no	—
270	C₄×C₈₉	—	2	2	no	—
271	C₄×C₈₉	—	2	1	no	—
272	C₄×C₈₉	—	2	1	no	—
273	C₄×C₈₉	—	2	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	—	4	1	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	—	4	2	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	—	8	1	no	—
290	#3102	—	89	1	no	—
291	#2966	—	89	1	no	—
292	C₈×#41	D₈₉	1	1	yes	characteristic, complemented
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	—	89	1	no	—
304	#1450	—	89	1	no	—
305	C₈₉	#17904	1	1	yes	characteristic, complemented, Sylow
306	#529	—	89	1	no	—
307	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
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	C₂×D₈₉	1	1	yes	characteristic
319	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
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	—	2	1	no	—
327	C₈×D₄	—	2	1	no	—
328	C₈×D₄	—	89	1	no	—
329	C₈×D₄	—	178	1	no	—
330	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
331	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
332	#433	—	178	1	no	—
333	#432	—	89	1	no	—
334	#431	—	2	1	no	—
335	#431	—	89	1	no	—
336	#431	—	89	1	no	—
337	#431	C₂×D₈₉	1	1	yes	characteristic
338	#405	—	178	1	no	—
339	C₂×C₄×C₈	—	2	1	no	—
340	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
348	Q₈⋊C₈	—	89	1	no	—
349	D₄⋊C₈	—	89	1	no	—
350	D₄⋊C₈	—	89	1	no	—
351	D₄⋊C₈	—	89	1	no	—
352	D₄⋊C₈	—	89	1	no	—
353	#322	—	89	1	no	—
354	#322	—	89	1	no	—
355	C₈²	—	89	1	no	—
356	C₈²	—	89	1	no	—
357	C₂×#41	C₄×D₈₉	1	1	yes	characteristic
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	—	2	1	no	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	—	178	1	no	—
366	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
367	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
368	#126	—	178	1	no	—
369	#125	—	89	1	no	—
370	#124	—	89	1	no	—
371	#123	—	178	1	no	—
372	C₂²⋊Q₈	—	89	1	no	—
373	#121	—	89	1	no	—
374	C₄×Q₈	—	89	1	no	—
375	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
376	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	89	1	no	—
380	C₄×D₄	—	178	1	no	—
381	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
382	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
383	#117	—	2	1	no	—
384	#117	—	178	1	no	—
385	#117	C₄×D₈₉	1	1	yes	characteristic
386	C₂×C₄²	—	2	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	—	2	1	no	—
394	C₄⋊C₈	—	89	1	no	—
395	C₄⋊C₈	—	89	1	no	—
396	C₄⋊C₈	—	89	1	no	—
397	C₄⋊C₈	—	89	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	—	2	1	no	—
414	C₂²⋊C₈	—	89	1	no	—
415	C₂²⋊C₈	—	89	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	—	2	1	no	—
424	C₄×C₈	—	2	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	C₂²⋊D₈₉	1	1	yes	characteristic
431	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
432	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
434	#41	—	2	2	no	—
435	#41	—	2	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	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	178	1	no	—
446	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
448	C₂²×C₄	#13083574	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	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	4	2	no	—
459	C₂×C₈	—	4	2	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	—	356	2	no	—
465	C₂×C₈	—	178	1	no	—
466	C₂×C₈	—	178	1	no	—
467	C₂×C₈	—	178	1	no	—
468	C₂×C₈	—	178	1	no	—
469	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
470	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
471	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
472	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	89	1	no	—
476	C₄⋊C₄	—	89	1	no	—
477	C₄⋊C₄	—	178	1	no	—
478	C₄⋊C₄	—	178	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	—	178	1	no	—
487	C₂²⋊C₄	—	178	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	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	178	1	no	—
495	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
496	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
497	C₄²	#13083574	1	1	yes	characteristic
498	C₄²	C₂³×D₈₉	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	178	1	no	—
501	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
502	Q₈	—	2	1	no	—
503	Q₈	—	178	1	no	—
504	Q₈	—	178	1	no	—
505	Q₈	#15668018	1	2	yes	—
506	D₄	—	2	4	no	—
507	D₄	—	2	1	no	—
508	D₄	—	356	2	no	—
509	D₄	—	178	1	no	—
510	D₄	—	178	1	no	—
511	D₄	#15668018	1	2	yes	—
512	C₂×C₄	—	2	4	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	—	2	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	356	1	no	—
525	C₂×C₄	—	356	1	no	—
526	C₂×C₄	—	178	1	no	—
527	C₂×C₄	—	178	1	no	—
528	C₂×C₄	—	178	1	no	—
529	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
530	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
531	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
533	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
534	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	356	1	no	—
540	C₈	—	356	1	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	#15668032	1	2	yes	—
548	C₈	#15668032	1	2	yes	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	356	1	no	—
556	C₂²	—	356	1	no	—
557	C₂²	—	356	1	no	—
558	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	356	1	no	—
567	C₄	—	356	1	no	—
568	C₄	—	356	1	no	—
569	C₄	C₂×#15668018	1	1	yes	characteristic
570	C₄	C₂×#15668018	1	1	yes	characteristic
571	C₄	C₂×#15668032	1	1	yes	characteristic
572	C₄	C₂×#15668032	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	712	1	no	—
576	C₂	#26028946	1	1	yes	characteristic
577	C₂	C₄×#15668032	1	1	yes	characteristic
578	C₂	#26029153	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×#41×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#19151743	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₈×#41	D₈₉
hypocenter	C₈₉	#17904
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
2. #26029227	C₂	semidirect
3. #26019102	C₂	semidirect
4. #26019095	C₂	semidirect
5. #26019088	C₂	semidirect
6. #26019081	C₂	semidirect
7. C₈×#13083564	C₂	semidirect
8. C₈×#13083561	C₂	semidirect
9. C₈×#13083562	C₂	semidirect
10. C₈×#13083559	C₂	semidirect
11. #26019030	C₂	semidirect
12. #26018686	C₂	semidirect
13. #26018658	C₂	semidirect
14. #26018535	C₂	semidirect
15. C₈×#41×C₈₉	C₂	semidirect
292. C₈×#41	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
#26030270	2
#26029227	2
#26019102	2
#26019095	2
#26019088	2
#26019081	2
C₈×#13083564	2
C₈×#13083561	2
C₈×#13083562	2
C₈×#13083559	2
#26019030	2
#26018686	2
#26018658	2
#26018535	2
C₈×#41×C₈₉	2
#17904	89