Subgroups — #36524392

Order 22784.

626 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	#26030276	C₂	1	1	yes	maximal, characteristic
2	#26029226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×#13083575	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019130	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019118	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019107	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019075	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019071	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019067	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019067	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019029	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018685	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018659	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018543	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1587	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152135	C₂²	1	1	yes	characteristic
17	C₄×#13083575	C₂²	1	1	yes	characteristic
18	#19151938	C₄	1	1	yes	characteristic
19	#19151925	C₄	1	1	yes	characteristic
20	#19151907	C₄	1	1	yes	characteristic
21	#19151901	C₄	1	1	yes	characteristic
22	#19151822	C₄	1	1	yes	characteristic
23	#19151816	C₄	1	1	yes	characteristic
24	#19151759	C₄	1	1	yes	characteristic
25	#19151746	C₄	1	1	yes	characteristic
26	Q₈×#10623494	C₂²	1	1	yes	characteristic
27	Q₈×#10623494	C₂²	1	1	yes	characteristic
28	C₄×#13083561	C₂²	1	1	yes	characteristic
29	C₄×#13083561	C₂²	1	1	yes	characteristic
30	C₄×D₇₁₂	C₂²	1	1	yes	characteristic
31	#19151677	C₂²	1	1	yes	characteristic
32	#19151671	—	2	1	no	—
33	C₈×D₃₅₆	—	2	1	no	—
34	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
35	#19151663	—	2	1	no	—
36	#19151663	—	2	1	no	—
37	#19151663	C₂²	1	1	yes	characteristic
38	#19151663	C₂²	1	1	yes	characteristic
39	#19151658	—	2	1	no	—
40	#19151654	C₂²	1	1	yes	characteristic
41	#19151650	—	2	1	no	—
42	#19151650	C₂²	1	1	yes	characteristic
43	#19151649	C₂²	1	1	yes	characteristic
44	#19151649	C₂²	1	1	yes	characteristic
45	#19151555	—	2	1	no	—
46	C₄×C₈×D₈₉	—	2	1	no	—
47	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
48	#19151350	C₂²	1	1	yes	characteristic
49	#19151350	C₂²	1	1	yes	characteristic
50	#19151349	C₂²	1	1	yes	characteristic
51	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
52	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
53	#19151327	C₂²	1	1	yes	characteristic
54	#19151327	C₂²	1	1	yes	characteristic
55	#19151325	C₂²	1	1	yes	characteristic
56	#19151325	C₂²	1	1	yes	characteristic
57	#19151320	C₂²	1	1	yes	characteristic
58	#19151320	C₂²	1	1	yes	characteristic
59	#19151319	C₂²	1	1	yes	characteristic
60	#446×C₈₉	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
63	#334×C₈₉	C₂²	1	1	yes	characteristic
64	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
66	#322×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#13083575	C₂×C₄	1	1	yes	characteristic
68	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
70	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083557	—	2	1	no	—
72	C₂×C₈×D₈₉	—	2	1	no	—
73	C₂×C₈×D₈₉	—	2	1	no	—
74	C₂×C₈×D₈₉	—	2	1	no	—
75	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
76	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
77	#15668007	—	2	1	no	—
78	#15668003	C₂×C₄	1	1	yes	characteristic
79	#15668001	C₂×C₄	1	1	yes	characteristic
80	#15667997	—	2	1	no	—
81	#15667988	C₂×C₄	1	1	yes	characteristic
82	#15667987	C₂×C₄	1	1	yes	characteristic
83	Q₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
84	C₄×D₃₅₆	—	2	1	no	—
85	C₄×D₃₅₆	—	2	1	no	—
86	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
87	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
88	#15667974	—	2	1	no	—
89	#15667974	C₂×C₄	1	1	yes	characteristic
90	#15667970	—	2	1	no	—
91	#15667970	C₂×C₄	1	1	yes	characteristic
92	#15667969	—	2	1	no	—
93	C₄²×D₈₉	—	2	1	no	—
94	C₄²×D₈₉	C₂³	1	1	yes	characteristic
95	#15667946	C₂×C₄	1	1	yes	characteristic
96	#15667943	C₂×C₄	1	1	yes	characteristic
97	#15667943	C₂×C₄	1	1	yes	characteristic
98	C₄⋊#10623494	—	2	1	no	—
99	C₄⋊#10623494	—	2	1	no	—
100	C₄⋊#10623494	C₂³	1	1	yes	characteristic
101	C₄⋊#10623494	C₂³	1	1	yes	characteristic
102	#15667941	—	2	1	no	—
103	#15667941	C₂×C₄	1	1	yes	characteristic
104	#15667941	C₂×C₄	1	1	yes	characteristic
105	#15667936	C₂×C₄	1	1	yes	characteristic
106	#15667936	C₂×C₄	1	1	yes	characteristic
107	#15667934	C₂×C₄	1	1	yes	characteristic
108	#15667934	C₂×C₄	1	1	yes	characteristic
109	#15667932	C₂×C₄	1	1	yes	characteristic
110	#15667932	C₂×C₄	1	1	yes	characteristic
111	#15667924	—	2	1	no	—
112	#15667924	—	2	1	no	—
113	#15667924	—	2	1	no	—
114	#15667924	—	2	1	no	—
115	#15667924	—	2	1	no	—
116	#15667924	—	2	1	no	—
117	#15667924	—	2	1	no	—
118	#15667924	C₂×C₄	1	1	yes	characteristic
119	#15667924	C₂×C₄	1	1	yes	characteristic
120	#15667922	—	2	1	no	—
121	C₄×#10623494	—	2	1	no	—
122	C₄×#10623494	—	2	1	no	—
123	C₄×#10623494	C₂³	1	1	yes	characteristic
124	C₄×#10623494	C₂³	1	1	yes	characteristic
125	C₄×#10623494	C₂³	1	1	yes	characteristic
126	C₈×Dic₈₉	—	2	1	no	—
127	C₈×Dic₈₉	D₄	1	1	yes	characteristic
128	C₈×Dic₈₉	D₄	1	1	yes	characteristic
129	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
130	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
131	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
132	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₈₉	—	2	1	no	—
134	C₄⋊C₈×C₈₉	—	2	1	no	—
135	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
137	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
138	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
139	#97×C₈₉	—	2	1	no	—
140	C₄×C₈×C₈₉	—	2	1	no	—
141	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	#13083575	—	2	2	no	—
145	#13083575	—	2	2	no	—
146	C₂×D₃₅₆	—	2	1	no	—
147	C₂×D₃₅₆	—	2	1	no	—
148	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
149	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₈₉	—	2	1	no	—
151	C₂×C₄×D₈₉	—	2	1	no	—
152	C₂×C₄×D₈₉	—	2	1	no	—
153	C₂×C₄×D₈₉	—	2	1	no	—
154	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
157	#13083561	—	2	2	no	—
158	#13083561	—	2	2	no	—
159	D₇₁₂	—	2	2	no	—
160	#13083557	—	4	2	no	—
161	C₂×#10623494	—	2	1	no	—
162	C₂×#10623494	—	2	1	no	—
163	C₂×#10623494	—	2	1	no	—
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	C₈×D₈₉	—	4	1	no	—
169	C₈×D₈₉	—	4	1	no	—
170	C₈×D₈₉	—	4	2	no	—
171	C₈×D₈₉	—	4	2	no	—
172	C₈×D₈₉	—	4	2	no	—
173	C₄⋊Dic₈₉	—	2	1	no	—
174	C₄⋊Dic₈₉	—	2	1	no	—
175	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
176	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
177	#13083553	—	2	1	no	—
178	#13083553	—	2	1	no	—
179	#13083551	—	2	1	no	—
180	#13083551	—	2	1	no	—
181	#13083551	—	2	1	no	—
182	#13083551	—	2	1	no	—
183	#13083551	—	2	1	no	—
184	#13083551	—	2	1	no	—
185	#13083551	—	2	1	no	—
186	#13083551	—	2	1	no	—
187	C₄×Dic₈₉	—	2	1	no	—
188	C₄×Dic₈₉	—	2	1	no	—
189	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
190	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
191	C₄×Dic₈₉	#41	1	1	yes	characteristic
192	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
193	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
194	Q₁₆×C₈₉	—	2	2	no	—
195	C₂×C₈×C₈₉	—	2	1	no	—
196	C₂×C₈×C₈₉	—	2	1	no	—
197	C₂×C₈×C₈₉	—	2	1	no	—
198	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
202	C₄⋊C₄×C₈₉	—	2	1	no	—
203	C₄⋊C₄×C₈₉	—	2	1	no	—
204	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
205	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₈₉	—	2	1	no	—
207	C₄²×C₈₉	—	2	1	no	—
208	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
209	C₂²×D₈₉	—	2	1	no	—
210	C₂²×D₈₉	—	2	1	no	—
211	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
212	Q₈×C₈₉	—	2	1	no	—
213	Q₈×C₈₉	—	2	1	no	—
214	Q₈×C₈₉	—	2	1	no	—
215	Q₈×C₈₉	#131	1	2	yes	—
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	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
223	C₂×Dic₈₉	—	2	1	no	—
224	C₂×Dic₈₉	—	2	1	no	—
225	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
226	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
227	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
228	D₃₅₆	—	2	4	no	—
229	D₃₅₆	—	2	1	no	—
230	D₃₅₆	—	2	1	no	—
231	D₃₅₆	—	2	1	no	—
232	D₃₅₆	—	4	2	no	—
233	D₃₅₆	#131	1	2	yes	—
234	C₄×D₈₉	—	2	4	no	—
235	C₄×D₈₉	—	2	1	no	—
236	C₄×D₈₉	—	2	1	no	—
237	C₄×D₈₉	—	2	1	no	—
238	C₄×D₈₉	—	2	1	no	—
239	C₄×D₈₉	—	4	1	no	—
240	C₄×D₈₉	—	4	2	no	—
241	C₄×D₈₉	—	4	1	no	—
242	C₄×D₈₉	—	4	1	no	—
243	C₄×D₈₉	—	4	1	no	—
244	C₄×D₈₉	—	4	1	no	—
245	C₈×C₈₉	—	2	1	no	—
246	C₈×C₈₉	—	2	1	no	—
247	C₈×C₈₉	—	2	1	no	—
248	C₈×C₈₉	—	2	1	no	—
249	C₈×C₈₉	—	4	1	no	—
250	C₈×C₈₉	—	4	1	no	—
251	C₈×C₈₉	—	4	1	no	—
252	#10623494	—	2	1	no	—
253	#10623494	—	2	1	no	—
254	#10623494	—	2	1	no	—
255	#10623494	—	2	1	no	—
256	#10623494	—	4	1	no	—
257	#10623494	—	4	1	no	—
258	#10623494	—	4	1	no	—
259	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
260	C₂×D₈₉	—	2	1	no	—
261	C₂×D₈₉	—	2	2	no	—
262	C₂×D₈₉	—	2	1	no	—
263	C₂×D₈₉	—	2	1	no	—
264	C₂×D₈₉	—	4	1	no	—
265	C₂×D₈₉	—	4	1	no	—
266	C₂×D₈₉	—	4	1	no	—
267	C₂×D₈₉	—	4	1	no	—
268	C₂×D₈₉	—	4	1	no	—
269	C₄×C₈₉	—	2	2	no	—
270	C₄×C₈₉	—	2	1	no	—
271	C₄×C₈₉	—	4	1	no	—
272	C₄×C₈₉	—	4	1	no	—
273	C₄×C₈₉	—	4	1	no	—
274	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
275	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
276	C₄×C₈₉	#575	1	1	yes	characteristic
277	C₄×C₈₉	#575	1	1	yes	characteristic
278	Dic₈₉	—	2	1	no	—
279	Dic₈₉	—	2	1	no	—
280	Dic₈₉	—	2	1	no	—
281	Dic₈₉	—	4	1	no	—
282	Dic₈₉	—	4	1	no	—
283	#17909	—	89	1	no	maximal, Sylow
284	C₂×C₈₉	#2929	1	1	yes	characteristic
285	C₂×C₈₉	#2943	1	1	yes	characteristic
286	C₂×C₈₉	#2955	1	1	yes	characteristic
287	D₈₉	—	4	1	no	—
288	D₈₉	—	4	2	no	—
289	D₈₉	—	8	1	no	—
290	#3102	—	89	1	no	—
291	#2966	—	89	1	no	—
292	C₈×#41	—	89	1	no	—
293	#1588	—	89	1	no	—
294	#1587	D₈₉	1	1	yes	characteristic, complemented
295	#1586	—	89	1	no	—
296	#1585	—	89	1	no	—
297	#1580	—	89	1	no	—
298	#1579	—	89	1	no	—
299	SD₁₆⋊C₈	—	89	1	no	—
300	SD₁₆⋊C₈	—	89	1	no	—
301	#1572	—	89	1	no	—
302	#1488	—	89	1	no	—
303	#1482	—	89	1	no	—
304	#1452	—	89	1	no	—
305	C₈₉	#17909	1	1	yes	characteristic, complemented, Sylow
306	#529	—	89	1	no	—
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	C₂×D₈₉	1	1	yes	characteristic
317	C₈×Q₈	—	89	1	no	—
318	C₈×Q₈	—	89	1	no	—
319	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
320	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
336	#431	—	89	1	no	—
337	#431	—	178	1	no	—
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	C₂×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
352	D₄⋊C₈	—	89	1	no	—
353	#322	—	89	1	no	—
354	#322	—	89	1	no	—
355	#322	—	89	1	no	—
356	#322	C₂×D₈₉	1	1	yes	characteristic
357	C₂×#41	—	89	1	no	—
358	C₂×Q₁₆	C₄×D₈₉	1	1	yes	characteristic
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	—	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	C₂²×D₈₉	1	1	yes	characteristic
376	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
377	C₄×D₄	—	89	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	—	178	1	no	—
383	#117	—	89	1	no	—
384	#117	—	178	1	no	—
385	#117	—	178	1	no	—
386	C₂×C₄²	—	89	1	no	—
387	C₂×C₄²	—	178	1	no	—
388	#107	—	89	1	no	—
389	#107	C₄×D₈₉	1	1	yes	characteristic
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	C₄×D₈₉	1	1	yes	characteristic
406	#103	C₄×D₈₉	1	1	yes	characteristic
407	#102	—	89	1	no	—
408	#102	—	89	1	no	—
409	#102	—	89	1	no	—
410	#102	—	89	1	no	—
411	C₂²⋊C₈	—	89	1	no	—
412	C₂²⋊C₈	—	89	1	no	—
413	C₂²⋊C₈	—	178	1	no	—
414	C₂²⋊C₈	—	178	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	—	2	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	—	178	1	no	—
429	C₄×C₈	—	178	1	no	—
430	C₄×C₈	—	178	1	no	—
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	—	178	2	no	—
435	#41	—	178	2	no	—
436	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
437	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
438	C₂×D₄	—	89	1	no	—
439	C₂×D₄	—	89	1	no	—
440	C₂×D₄	—	178	1	no	—
441	C₂×D₄	—	178	1	no	—
442	C₂²×C₄	—	89	1	no	—
443	C₂²×C₄	—	89	1	no	—
444	C₂²×C₄	—	89	1	no	—
445	C₂²×C₄	—	178	1	no	—
446	C₂²×C₄	—	178	1	no	—
447	C₂²×C₄	—	178	1	no	—
448	C₂²×C₄	—	178	1	no	—
449	Q₁₆	—	2	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	—	89	1	no	—
458	C₂×C₈	—	89	1	no	—
459	C₂×C₈	—	89	1	no	—
460	C₂×C₈	—	89	1	no	—
461	C₂×C₈	—	356	2	no	—
462	C₂×C₈	—	356	1	no	—
463	C₂×C₈	—	356	1	no	—
464	C₂×C₈	—	356	2	no	—
465	C₂×C₈	—	356	2	no	—
466	C₂×C₈	—	178	1	no	—
467	C₂×C₈	—	178	1	no	—
468	C₂×C₈	—	178	1	no	—
469	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
470	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
471	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
472	C₂×C₈	D₄×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	—	178	1	no	—
484	C₂²⋊C₄	—	178	1	no	—
485	C₂²⋊C₄	—	178	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	—	89	1	no	—
494	C₄²	—	89	1	no	—
495	C₄²	—	89	1	no	—
496	C₄²	—	178	1	no	—
497	C₄²	—	178	1	no	—
498	C₄²	C₂³×D₈₉	1	1	yes	characteristic
499	C₂³	—	89	1	no	—
500	C₂³	—	178	1	no	—
501	C₂³	—	178	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	#15668020	1	2	yes	—
506	D₄	—	89	2	no	—
507	D₄	—	356	2	no	—
508	D₄	—	178	4	no	—
509	D₄	—	178	1	no	—
510	D₄	—	178	1	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	—	89	1	no	—
517	C₂×C₄	—	89	1	no	—
518	C₂×C₄	—	89	1	no	—
519	C₂×C₄	—	356	1	no	—
520	C₂×C₄	—	356	2	no	—
521	C₂×C₄	—	356	1	no	—
522	C₂×C₄	—	356	1	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	—	178	1	no	—
530	C₂×C₄	—	178	1	no	—
531	C₂×C₄	—	178	1	no	—
532	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
533	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
534	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	356	1	no	—
543	C₈	—	356	1	no	—
544	C₈	—	356	1	no	—
545	C₈	—	178	1	no	—
546	C₈	—	178	1	no	—
547	C₈	—	178	1	no	—
548	C₈	—	178	1	no	—
549	C₂²	—	356	1	no	—
550	C₂²	—	356	1	no	—
551	C₂²	—	356	1	no	—
552	C₂²	—	356	1	no	—
553	C₂²	—	356	1	no	—
554	C₂²	—	178	1	no	—
555	C₂²	—	178	2	no	—
556	C₂²	—	178	1	no	—
557	C₂²	—	178	1	no	—
558	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	2	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	356	1	no	—
565	C₄	—	356	1	no	—
566	C₄	—	178	1	no	—
567	C₄	—	178	1	no	—
568	C₄	—	178	1	no	—
569	C₄	#131×D₈₉	1	1	yes	characteristic
570	C₄	C₂×#15668020	1	1	yes	characteristic
571	C₄	#19152397	1	1	yes	characteristic
572	C₄	#19152397	1	1	yes	characteristic
573	C₂	—	356	2	no	—
574	C₂	—	356	1	no	—
575	C₂	—	712	1	no	—
576	C₂	#26028943	1	1	yes	characteristic
577	C₂	#26029051	1	1	yes	characteristic
578	C₂	#26029150	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×#1587	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#19151746	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1587	D₈₉
hypocenter	C₈₉	#17909
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1587

Complements

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

N	H ≅ G/N	type
2. #26029226	C₂	semidirect
3. C₈×#13083575	C₂	semidirect
4. #26019130	C₂	semidirect
5. #26019118	C₂	semidirect
6. #26019107	C₂	semidirect
7. #26019075	C₂	semidirect
8. #26019071	C₂	semidirect
9. #26019067	C₂	semidirect
10. #26019067	C₂	semidirect
11. #26019029	C₂	semidirect
12. #26018685	C₂	semidirect
13. #26018659	C₂	semidirect
14. #26018543	C₂	semidirect
15. C₈₉×#1587	C₂	semidirect
294. #1587	D₈₉	semidirect
305. C₈₉	#17909	semidirect

Maximal subgroups

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

subgroup	index
#26030276	2
#26029226	2
C₈×#13083575	2
#26019130	2
#26019118	2
#26019107	2
#26019075	2
#26019071	2
#26019067	2
#26019029	2
#26018685	2
#26018659	2
#26018543	2
C₈₉×#1587	2
#17909	89