Subgroups — #36606545

Order 22784.

664 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030799	C₂	1	1	yes	maximal, characteristic, complemented
2	#26030045	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151889	C₂	1	1	yes	maximal, characteristic
4	#26021762	C₂	1	2	yes	maximal, complemented
5	#26021611	C₂	1	2	yes	maximal
6	#26021241	C₂	1	1	yes	maximal, characteristic, complemented
7	#26021032	C₂	1	2	yes	maximal, complemented
8	#26021028	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020914	C₂	1	2	yes	maximal
10	C₄×#15667928	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668012	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
14	#19152008	—	2	2	no	—
15	#19152001	—	2	1	no	—
16	#19151994	—	2	1	no	—
17	#19151895	—	2	2	no	—
18	#19151889	—	2	1	no	—
19	#19151889	—	2	1	no	—
20	#19151889	—	2	2	no	—
21	#19151885	—	2	1	no	—
22	#19151875	—	2	1	no	—
23	C₂×#15667948	C₂²	1	2	yes	—
24	#19151641	C₂²	1	2	yes	—
25	#19151641	C₂²	1	2	yes	—
26	#19151641	C₂²	1	2	yes	—
27	C₂×#15667944	C₂²	1	2	yes	—
28	#19151622	C₂²	1	1	yes	characteristic
29	#19151602	C₂²	1	2	yes	—
30	C₂×#15667934	C₂²	1	2	yes	—
31	C₂×#15667928	C₂²	1	1	yes	characteristic
32	C₂×#15667928	C₂²	1	1	yes	characteristic
33	C₄×#13083558	C₂²	1	1	yes	characteristic
34	#19151366	C₂²	1	2	yes	—
35	#19151366	C₂²	1	2	yes	—
36	#19151366	C₂²	1	1	yes	characteristic
37	#19151366	C₂²	1	1	yes	characteristic
38	#19151363	C₂²	1	2	yes	—
39	#533×C₈₉	C₂²	1	1	yes	characteristic
40	#446×C₈₉	—	2	2	no	—
41	#446×C₈₉	—	2	1	no	—
42	C₈×Q₈×C₈₉	—	2	1	no	—
43	#424×C₈₉	C₂²	1	2	yes	—
44	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#405×C₈₉	C₂²	1	2	yes	—
46	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
47	C₂²×Dic₁₇₈	—	2	1	no	—
48	C₂²×D₃₅₆	C₂³	1	1	yes	characteristic
49	C₂²×C₄×D₈₉	—	2	1	no	—
50	C₂×#13083558	C₂³	1	2	yes	—
51	C₂×#13083558	C₂³	1	1	yes	characteristic
52	C₂×#13083558	C₂³	1	1	yes	characteristic
53	#15668012	—	2	1	no	—
54	#15668012	—	2	1	no	—
55	#15668012	—	2	1	no	—
56	#15668012	—	2	1	no	—
57	C₄×D₃₅₆	—	2	1	no	—
58	C₄×D₃₅₆	—	2	1	no	—
59	C₄×D₃₅₆	—	2	1	no	—
60	C₄×D₃₅₆	—	2	1	no	—
61	C₂×C₄⋊Dic₈₉	—	2	1	no	—
62	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
64	C₂×#13083551	—	2	1	no	—
65	#15667948	—	2	4	no	—
66	#15667945	—	2	2	no	—
67	#15667945	—	2	2	no	—
68	#15667945	—	2	2	no	—
69	#15667944	—	2	2	no	—
70	#15667944	—	2	2	no	—
71	#15667943	—	2	2	no	—
72	#15667943	—	2	2	no	—
73	#15667943	—	2	2	no	—
74	C₄⋊#10623494	—	2	1	no	—
75	C₄⋊#10623494	—	2	1	no	—
76	#15667934	—	2	2	no	—
77	#15667934	—	2	2	no	—
78	#15667932	—	2	2	no	—
79	#15667932	—	2	2	no	—
80	#15667928	—	2	2	no	—
81	#15667928	Q₈	1	4	yes	complemented
82	#15667923	—	2	1	no	—
83	C₄×#10623494	—	2	1	no	—
84	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
87	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
88	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
89	#125×C₈₉	D₄	1	2	yes	—
90	C₂²⋊Q₈×C₈₉	—	2	1	no	—
91	C₂²⋊Q₈×C₈₉	—	2	1	no	—
92	C₄×Q₈×C₈₉	—	2	1	no	—
93	C₄×Q₈×C₈₉	—	2	1	no	—
94	#117×C₈₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₈₉	—	2	2	no	—
97	C₄⋊C₈×C₈₉	—	2	2	no	—
98	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
99	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
100	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
101	#97×C₈₉	—	2	2	no	—
102	#97×C₈₉	—	2	1	no	—
103	C₄×C₈×C₈₉	—	2	2	no	—
104	C₄×C₈×C₈₉	—	2	1	no	—
105	C₂³×D₈₉	—	2	1	no	—
106	C₂×Dic₁₇₈	—	4	1	no	—
107	C₂×Dic₁₇₈	—	4	1	no	—
108	C₂×Dic₁₇₈	—	8	2	no	—
109	C₂×D₃₅₆	—	2	1	no	—
110	C₂×D₃₅₆	—	2	1	no	—
111	C₂×D₃₅₆	—	2	1	no	—
112	C₂×D₃₅₆	—	2	1	no	—
113	C₂×D₃₅₆	—	2	1	no	—
114	C₂×D₃₅₆	C₂×Q₈	1	2	yes	—
115	C₂²×Dic₈₉	—	2	1	no	—
116	C₂²×Dic₈₉	—	2	2	no	—
117	C₂×C₄×D₈₉	—	4	1	no	—
118	C₂×C₄×D₈₉	—	4	1	no	—
119	C₂×C₄×D₈₉	—	8	2	no	—
120	#13083558	—	2	1	no	—
121	#13083558	—	2	1	no	—
122	#13083558	—	2	2	no	—
123	#13083558	—	2	2	no	—
124	#13083558	C₂×Q₈	1	2	yes	—
125	#13083558	#41	1	2	yes	—
126	C₂×#10623494	—	2	1	no	—
127	C₂×#10623494	—	2	1	no	—
128	C₂×#10623494	—	2	2	no	—
129	C₄⋊Dic₈₉	—	2	1	no	—
130	C₄⋊Dic₈₉	—	2	1	no	—
131	C₄⋊Dic₈₉	—	2	2	no	—
132	C₄⋊Dic₈₉	—	2	2	no	—
133	C₄⋊Dic₈₉	—	4	1	no	—
134	C₄⋊Dic₈₉	—	4	1	no	—
135	#13083551	—	4	1	no	—
136	#13083551	—	4	1	no	—
137	C₂×Q₈×C₈₉	—	2	1	no	—
138	C₂×Q₈×C₈₉	—	2	1	no	—
139	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
140	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
142	M₁₆×C₈₉	—	2	1	no	—
143	M₁₆×C₈₉	—	2	1	no	—
144	M₁₆×C₈₉	—	2	1	no	—
145	M₁₆×C₈₉	C₂×Q₈	1	2	yes	—
146	C₂×C₈×C₈₉	—	2	1	no	—
147	C₂×C₈×C₈₉	—	2	2	no	—
148	C₂×C₈×C₈₉	—	2	2	no	—
149	C₂×C₈×C₈₉	—	2	1	no	—
150	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₈₉	—	2	2	no	—
153	C₄⋊C₄×C₈₉	—	2	2	no	—
154	C₄⋊C₄×C₈₉	—	2	1	no	—
155	C₄⋊C₄×C₈₉	—	2	1	no	—
156	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
158	C₂²⋊C₄×C₈₉	—	2	2	no	—
159	C₄²×C₈₉	—	2	2	no	—
160	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
165	C₂²×D₈₉	—	2	2	no	—
166	C₂²×D₈₉	—	4	1	no	—
167	C₂²×D₈₉	—	4	1	no	—
168	C₂²×D₈₉	—	8	1	no	—
169	C₂²×D₈₉	—	8	1	no	—
170	Q₈×C₈₉	—	4	2	no	—
171	Q₈×C₈₉	—	8	1	no	—
172	C₂×C₄×C₈₉	—	2	2	no	—
173	C₂×C₄×C₈₉	—	2	2	no	—
174	C₂×C₄×C₈₉	—	2	2	no	—
175	C₂×C₄×C₈₉	—	4	1	no	—
176	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
185	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
186	C₂×Dic₈₉	—	4	1	no	—
187	C₂×Dic₈₉	—	4	2	no	—
188	C₂×Dic₈₉	—	8	1	no	—
189	C₂×Dic₈₉	—	8	2	no	—
190	D₃₅₆	—	2	2	no	—
191	D₃₅₆	—	2	2	no	—
192	D₃₅₆	—	4	1	no	—
193	D₃₅₆	—	4	1	no	—
194	C₄×D₈₉	—	8	2	no	—
195	C₄×D₈₉	—	8	2	no	—
196	Dic₁₇₈	—	8	2	no	—
197	Dic₁₇₈	—	8	2	no	—
198	C₈×C₈₉	—	2	2	no	—
199	C₈×C₈₉	—	2	2	no	—
200	C₈×C₈₉	—	2	2	no	—
201	C₈×C₈₉	—	4	1	no	—
202	#10623494	—	2	2	no	—
203	#10623494	—	2	2	no	—
204	#10623494	—	4	2	no	—
205	C₂²×C₈₉	—	2	1	no	—
206	C₂²×C₈₉	—	2	1	no	—
207	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
208	C₂²×C₈₉	#533	1	1	yes	characteristic
209	C₂²×C₈₉	#541	1	1	yes	characteristic
210	C₂×D₈₉	—	4	2	no	—
211	C₂×D₈₉	—	8	2	no	—
212	C₂×D₈₉	—	8	1	no	—
213	C₂×D₈₉	—	8	1	no	—
214	C₂×D₈₉	—	8	2	no	—
215	C₄×C₈₉	—	2	1	no	—
216	C₄×C₈₉	—	2	1	no	—
217	C₄×C₈₉	—	2	1	no	—
218	C₄×C₈₉	—	4	2	no	—
219	C₄×C₈₉	—	4	2	no	—
220	C₄×C₈₉	#471	1	2	yes	—
221	C₄×C₈₉	#547	1	1	yes	characteristic
222	C₄×C₈₉	#548	1	1	yes	characteristic
223	C₄×C₈₉	D₄×Q₈	1	1	yes	characteristic
224	C₄×C₈₉	D₄×Q₈	1	1	yes	characteristic
225	Dic₈₉	—	8	1	no	—
226	Dic₈₉	—	8	2	no	—
227	#25490	—	89	1	no	maximal, Sylow
228	C₂×C₈₉	—	2	1	no	—
229	C₂×C₈₉	—	2	1	no	—
230	C₂×C₈₉	#2429	1	1	yes	characteristic
231	C₂×C₈₉	C₂×#471	1	1	yes	characteristic
232	C₂×C₈₉	#3068	1	1	yes	characteristic
233	D₈₉	—	8	2	no	—
234	#3165	—	89	1	no	—
235	#3077	—	89	1	no	—
236	C₂×#476	—	89	1	no	—
237	#2962	D₈₉	1	1	yes	characteristic, complemented
238	#2090	—	89	2	no	—
239	#2063	—	89	2	no	—
240	#1997	—	89	1	no	—
241	#1951	—	89	2	no	—
242	#1950	—	89	1	no	—
243	#1931	—	89	2	no	—
244	C₄×#100	—	89	1	no	—
245	C₈₉	#25490	1	1	yes	characteristic, complemented, Sylow
246	#533	C₂×D₈₉	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	—	89	1	no	—
248	C₂×C₄×D₄	—	89	1	no	—
249	#501	—	178	2	no	—
250	#500	—	178	1	no	—
251	#498	—	178	1	no	—
252	#478	—	178	2	no	—
253	#476	—	178	1	no	—
254	#476	—	178	1	no	—
255	#476	—	178	2	no	—
256	#476	—	178	1	no	—
257	#474	—	178	1	no	—
258	#446	—	2	2	no	—
259	#446	—	2	1	no	—
260	C₈×Q₈	—	2	1	no	—
261	C₂×#108	—	89	2	no	—
262	#428	—	89	2	no	—
263	#428	—	89	2	no	—
264	#428	—	89	2	no	—
265	C₂×#106	—	89	2	no	—
266	#424	C₂×D₈₉	1	2	yes	—
267	#423	—	89	1	no	—
268	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
269	#418	—	89	2	no	—
270	C₂×#102	—	89	2	no	—
271	C₂×#100	—	89	1	no	—
272	C₂×#100	—	89	1	no	—
273	#405	C₂×D₈₉	1	2	yes	—
274	C₄×M₁₆	—	89	1	no	—
275	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
276	#343	—	89	2	no	—
277	#343	—	89	1	no	—
278	#343	—	89	2	no	—
279	#343	—	89	1	no	—
280	#341	—	89	2	no	—
281	C₂²×Q₈	—	178	1	no	—
282	C₂²×D₄	—	89	1	no	—
283	C₂³×C₄	—	178	1	no	—
284	C₂×M₁₆	—	89	1	no	—
285	C₂×M₁₆	—	89	1	no	—
286	C₂×M₁₆	—	89	2	no	—
287	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
288	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
289	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
290	C₄⋊Q₈	—	178	1	no	—
291	C₄⋊Q₈	—	178	1	no	—
292	C₄⋊Q₈	—	178	1	no	—
293	C₄⋊Q₈	—	178	1	no	—
294	C₄⋊Q₈	D₃₅₆	1	1	yes	characteristic
295	C₄⋊Q₈	D₃₅₆	1	1	yes	characteristic
296	#125	D₃₅₆	1	2	yes	—
297	C₂²⋊Q₈	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×D₄	—	178	1	no	—
302	C₄×D₄	—	178	1	no	—
303	C₄×D₄	—	178	1	no	—
304	C₄×D₄	—	178	1	no	—
305	#117	C₂²×D₈₉	1	2	yes	—
306	C₂×C₄⋊C₄	—	89	1	no	—
307	C₂×C₄⋊C₄	—	89	2	no	—
308	C₂×C₄⋊C₄	—	178	1	no	—
309	C₂×C₂²⋊C₄	—	178	1	no	—
310	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
311	#108	—	178	4	no	—
312	#107	—	178	2	no	—
313	#107	—	178	2	no	—
314	#107	—	178	2	no	—
315	#106	—	178	2	no	—
316	#106	—	178	2	no	—
317	#106	—	178	2	no	—
318	#106	—	178	2	no	—
319	#106	—	178	2	no	—
320	C₄⋊C₈	—	2	2	no	—
321	C₄⋊C₈	—	2	2	no	—
322	C₄⋊C₈	—	178	1	no	—
323	C₄⋊C₈	—	178	1	no	—
324	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
325	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
326	C₄⋊C₈	C₂²⋊D₈₉	1	2	yes	—
327	#102	—	178	2	no	—
328	#102	—	178	2	no	—
329	#102	—	178	2	no	—
330	#102	—	178	2	no	—
331	#100	—	89	4	no	—
332	#100	—	178	2	no	—
333	#97	—	2	2	no	—
334	#97	—	2	1	no	—
335	#97	—	178	1	no	—
336	C₄×C₈	—	2	2	no	—
337	C₄×C₈	—	2	1	no	—
338	C₄×C₈	—	178	1	no	—
339	C₂⁴	—	178	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	356	1	no	—
343	C₂×Q₈	—	356	1	no	—
344	C₂×Q₈	—	712	2	no	—
345	C₂×D₄	—	89	2	no	—
346	C₂×D₄	—	178	1	no	—
347	C₂×D₄	—	178	1	no	—
348	C₂×D₄	—	178	1	no	—
349	C₂×D₄	—	178	1	no	—
350	C₂×D₄	—	178	1	no	—
351	C₂²×C₄	—	356	1	no	—
352	C₂²×C₄	—	356	1	no	—
353	C₂²×C₄	—	178	1	no	—
354	C₂²×C₄	—	178	2	no	—
355	C₂²×C₄	—	712	2	no	—
356	C₂²×C₄	#13083574	1	1	yes	characteristic
357	C₂²×C₄	#13083574	1	1	yes	characteristic
358	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
359	M₁₆	—	2	1	no	—
360	M₁₆	—	2	1	no	—
361	M₁₆	—	2	1	no	—
362	M₁₆	—	89	2	no	—
363	M₁₆	—	89	2	no	—
364	M₁₆	—	178	2	no	—
365	M₁₆	—	178	2	no	—
366	M₁₆	—	178	1	no	—
367	M₁₆	—	178	1	no	—
368	M₁₆	Q₈×D₈₉	1	2	yes	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	178	2	no	—
374	C₂×C₈	—	178	1	no	—
375	C₂×C₈	—	178	1	no	—
376	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
377	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	356	1	no	—
383	C₄⋊C₄	—	356	1	no	—
384	C₄⋊C₄	—	178	2	no	—
385	C₄⋊C₄	—	178	1	no	—
386	C₄⋊C₄	—	178	1	no	—
387	C₄⋊C₄	—	178	2	no	—
388	C₄⋊C₄	C₂×D₃₅₆	1	2	yes	—
389	C₄⋊C₄	C₂×D₃₅₆	1	2	yes	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	356	1	no	—
392	C₂²⋊C₄	—	356	1	no	—
393	C₄²	—	2	2	no	—
394	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
395	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
396	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
397	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
398	C₂³	—	356	1	no	—
399	C₂³	—	356	1	no	—
400	C₂³	—	178	2	no	—
401	C₂³	—	712	1	no	—
402	C₂³	—	712	1	no	—
403	C₂³	C₂×#13083574	1	1	yes	characteristic
404	Q₈	—	4	2	no	—
405	Q₈	—	8	1	no	—
406	Q₈	—	712	2	no	—
407	Q₈	—	712	2	no	—
408	D₄	—	356	1	no	—
409	D₄	—	356	1	no	—
410	D₄	—	178	2	no	—
411	D₄	—	178	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	356	1	no	—
417	C₂×C₄	—	356	2	no	—
418	C₂×C₄	—	712	2	no	—
419	C₂×C₄	—	712	2	no	—
420	C₂×C₄	—	712	1	no	—
421	C₂×C₄	—	712	2	no	—
422	C₂×C₄	#15667986	1	1	yes	characteristic
423	C₂×C₄	#15667986	1	1	yes	characteristic
424	C₂×C₄	#15667986	1	1	yes	characteristic
425	C₂×C₄	#15667986	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
428	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
429	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
430	C₂×C₄	#15668059	1	1	yes	characteristic
431	C₂×C₄	#15668060	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	4	1	no	—
436	C₈	—	356	2	no	—
437	C₈	—	178	2	no	—
438	C₈	—	178	2	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	356	2	no	—
442	C₂²	—	712	2	no	—
443	C₂²	—	712	2	no	—
444	C₂²	—	712	1	no	—
445	C₂²	—	712	1	no	—
446	C₂²	C₂×#15667986	1	1	yes	characteristic
447	C₂²	#19152152	1	1	yes	characteristic
448	C₂²	#19152206	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	712	1	no	—
455	C₄	—	712	2	no	—
456	C₄	#19151861	1	2	yes	—
457	C₄	#19152247	1	1	yes	characteristic
458	C₄	#19152260	1	1	yes	characteristic
459	C₄	Q₈×C₂²⋊D₈₉	1	1	yes	characteristic
460	C₄	Q₈×D₃₅₆	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	712	2	no	—
464	C₂	#26023845	1	1	yes	characteristic
465	C₂	C₂×#19151861	1	1	yes	characteristic
466	C₂	#26029980	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667986
commutator, cosocle	C₂²×C₄×C₈₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#2962	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂²×D₃₅₆	C₂³
hypercenter	#2962	D₈₉
hypocenter	C₈₉	#25490
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2962

Complements

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

N	H ≅ G/N	type
1. #26030799	C₂	semidirect
4. #26021762	C₂	semidirect
6. #26021241	C₂	semidirect
7. #26021032	C₂	semidirect
8. #26021028	C₂	semidirect
11. C₈₉×#2962	C₂	semidirect
81. #15667928	Q₈	semidirect
237. #2962	D₈₉	semidirect
245. C₈₉	#25490	semidirect

Maximal subgroups

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

subgroup	index
#26030799	2
#26030045	2
C₂×#19151889	2
#26021762	2
#26021611	2
#26021241	2
#26021032	2
#26021028	2
#26020914	2
C₄×#15667928	2
C₈₉×#2962	2
#25490	89