Subgroups — #36536902

Order 22784.

664 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030831	C₂	1	1	yes	maximal, characteristic, complemented
2	#26030312	C₂	1	2	yes	maximal, complemented
3	#26019668	C₂	1	2	yes	maximal, complemented
4	#26019661	C₂	1	2	yes	maximal, complemented
5	#26019656	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019651	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019612	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019607	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019000	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018912	C₂	1	2	yes	maximal, complemented
11	C₈×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152148	C₂²	1	2	yes	—
13	#19152003	C₂²	1	1	yes	characteristic
14	#19151975	C₂²	1	1	yes	characteristic
15	#19151945	C₂²	1	2	yes	—
16	#19151922	—	2	2	no	—
17	#19151893	C₂²	1	2	yes	—
18	#19151888	C₂²	1	2	yes	—
19	#19151834	—	2	1	no	—
20	#19151834	—	2	1	no	—
21	#19151798	C₂²	1	2	yes	—
22	#19151793	C₂²	1	2	yes	—
23	#19151743	—	2	2	no	—
24	C₄×#13083561	—	2	2	no	—
25	C₄×D₇₁₂	—	2	1	no	—
26	C₄×D₇₁₂	—	2	1	no	—
27	C₄×#13083559	—	2	2	no	—
28	#19151651	C₂²	1	2	yes	—
29	#19151351	C₂²	1	1	yes	characteristic
30	#19151351	C₂²	1	1	yes	characteristic
31	#19151349	C₂²	1	2	yes	—
32	#19151346	C₂²	1	2	yes	—
33	#19151346	C₂²	1	2	yes	—
34	#19151341	C₂²	1	2	yes	—
35	#19151341	C₂²	1	2	yes	—
36	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
37	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₈₉	—	2	1	no	—
40	C₈×D₄×C₈₉	—	2	1	no	—
41	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
43	#431×C₈₉	—	2	1	no	—
44	#431×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₈₉	—	2	1	no	—
46	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	—	2	2	no	—
48	C₂×#13083561	—	2	2	no	—
49	C₂×D₇₁₂	—	2	1	no	—
50	C₂×D₇₁₂	—	2	1	no	—
51	C₂×#13083559	—	2	2	no	—
52	#15668012	C₂³	1	2	yes	—
53	#15668009	C₂³	1	2	yes	—
54	#15668000	—	2	2	no	—
55	#15667986	—	2	2	no	—
56	#15667986	—	2	2	no	—
57	C₄×D₃₅₆	—	2	2	no	—
58	C₄×D₃₅₆	—	2	2	no	—
59	#15667946	—	2	1	no	—
60	#15667946	—	2	1	no	—
61	#15667945	—	2	2	no	—
62	#15667943	—	2	2	no	—
63	C₄⋊#10623494	C₂³	1	2	yes	—
64	C₄⋊#10623494	C₂³	1	2	yes	—
65	#15667936	—	2	2	no	—
66	#15667934	—	2	2	no	—
67	#15667934	—	2	2	no	—
68	#15667933	—	2	2	no	—
69	#15667932	—	2	2	no	—
70	#15667932	—	2	2	no	—
71	C₂²⋊#10623494	—	2	2	no	—
72	C₄×#10623494	—	2	2	no	—
73	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₈₉	—	2	1	no	—
75	C₂²×C₈×C₈₉	—	2	1	no	—
76	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₈₉	—	2	1	no	—
81	C₄×D₄×C₈₉	—	2	1	no	—
82	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
83	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
84	#117×C₈₉	—	2	1	no	—
85	#117×C₈₉	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₈₉	—	2	1	no	—
87	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₈₉	—	2	1	no	—
89	C₄⋊C₈×C₈₉	—	2	1	no	—
90	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₈₉	—	2	1	no	—
93	C₂²⋊C₈×C₈₉	—	2	1	no	—
94	C₂²⋊C₈×C₈₉	—	2	1	no	—
95	C₄×C₈×C₈₉	—	2	1	no	—
96	C₄×C₈×C₈₉	—	2	1	no	—
97	C₄×C₈×C₈₉	—	2	1	no	—
98	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
99	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
100	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	#13083574	—	8	4	no	—
103	C₂×Dic₁₇₈	—	2	2	no	—
104	C₂×D₃₅₆	—	2	2	no	—
105	C₂×D₃₅₆	—	2	2	no	—
106	C₂×D₃₅₆	—	2	2	no	—
107	C₂×C₂²⋊D₈₉	—	4	2	no	—
108	C₂×C₄×D₈₉	—	4	2	no	—
109	#13083561	—	4	4	no	—
110	D₇₁₂	—	4	2	no	—
111	D₇₁₂	—	4	2	no	—
112	#13083559	—	4	4	no	—
113	C₂×#10623494	—	2	2	no	—
114	C₂×#10623494	—	2	2	no	—
115	C₄⋊Dic₈₉	—	2	2	no	—
116	C₄⋊Dic₈₉	—	2	2	no	—
117	#13083551	—	4	2	no	—
118	#13083551	—	4	2	no	—
119	#41×C₈₉	—	2	2	no	—
120	#41×C₈₉	—	2	2	no	—
121	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₂×D₄×C₈₉	—	2	1	no	—
123	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	—	2	1	no	—
125	C₂²×C₄×C₈₉	—	2	1	no	—
126	C₂²×C₄×C₈₉	—	2	1	no	—
127	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
130	C₂×C₈×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	—	2	1	no	—
132	C₂×C₈×C₈₉	—	2	1	no	—
133	C₂×C₈×C₈₉	—	4	1	no	—
134	C₂×C₈×C₈₉	—	4	2	no	—
135	C₂×C₈×C₈₉	—	4	2	no	—
136	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₈₉	—	2	1	no	—
141	C₄⋊C₄×C₈₉	—	2	1	no	—
142	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂²⋊C₄×C₈₉	—	2	1	no	—
145	C₂²⋊C₄×C₈₉	—	2	1	no	—
146	C₂²⋊C₄×C₈₉	—	2	1	no	—
147	C₄²×C₈₉	—	2	1	no	—
148	C₄²×C₈₉	—	2	1	no	—
149	C₄²×C₈₉	—	2	1	no	—
150	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₈₉	#41	1	1	yes	characteristic
153	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
154	C₂³×C₈₉	—	2	1	no	—
155	C₂³×C₈₉	#121	1	1	yes	characteristic
156	C₂²×D₈₉	—	4	2	no	—
157	Q₈×C₈₉	—	2	1	no	—
158	Q₈×C₈₉	#135	1	2	yes	—
159	D₄×C₈₉	—	2	4	no	—
160	D₄×C₈₉	—	2	1	no	—
161	D₄×C₈₉	#135	1	2	yes	—
162	C₂×C₄×C₈₉	—	2	4	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	2	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	2	1	no	—
171	C₂×C₄×C₈₉	—	4	1	no	—
172	C₂×C₄×C₈₉	—	4	1	no	—
173	C₂×C₄×C₈₉	—	4	2	no	—
174	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₈₉	—	8	4	no	—
181	C₂×Dic₈₉	—	4	2	no	—
182	D₃₅₆	—	4	2	no	—
183	D₃₅₆	—	4	2	no	—
184	D₃₅₆	—	4	2	no	—
185	D₃₅₆	—	4	2	no	—
186	D₃₅₆	—	8	2	no	—
187	C₄×D₈₉	—	8	4	no	—
188	Dic₁₇₈	—	8	2	no	—
189	C₈×C₈₉	—	2	1	no	—
190	C₈×C₈₉	—	2	1	no	—
191	C₈×C₈₉	—	2	1	no	—
192	C₈×C₈₉	—	4	1	no	—
193	C₈×C₈₉	—	4	1	no	—
194	C₈×C₈₉	#135	1	2	yes	—
195	#10623494	—	4	2	no	—
196	#10623494	—	4	2	no	—
197	C₂²×C₈₉	—	2	1	no	—
198	C₂²×C₈₉	—	2	1	no	—
199	C₂²×C₈₉	—	2	2	no	—
200	C₂²×C₈₉	—	2	1	no	—
201	C₂²×C₈₉	—	4	1	no	—
202	C₂²×C₈₉	—	4	1	no	—
203	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
204	C₂×D₈₉	—	8	2	no	—
205	C₂×D₈₉	—	8	2	no	—
206	C₂×D₈₉	—	8	2	no	—
207	C₄×C₈₉	—	2	1	no	—
208	C₄×C₈₉	—	2	1	no	—
209	C₄×C₈₉	—	2	2	no	—
210	C₄×C₈₉	—	2	1	no	—
211	C₄×C₈₉	—	4	1	no	—
212	C₄×C₈₉	—	4	1	no	—
213	C₄×C₈₉	#472	1	2	yes	—
214	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
215	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
216	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
217	C₄×C₈₉	#575	1	1	yes	characteristic
218	Dic₈₉	—	8	2	no	—
219	#19128	—	89	1	no	maximal, Sylow
220	C₂×C₈₉	—	4	1	no	—
221	C₂×C₈₉	—	4	2	no	—
222	C₂×C₈₉	#3035	1	1	yes	characteristic
223	C₂×C₈₉	#3050	1	1	yes	characteristic
224	C₂×C₈₉	C₂×#472	1	1	yes	characteristic
225	D₈₉	—	16	2	no	—
226	#3169	—	89	1	no	—
227	#3106	—	89	2	no	—
228	C₈×#41	D₈₉	1	1	yes	characteristic, complemented
229	#1678	—	89	2	no	—
230	#1677	—	89	2	no	—
231	#1676	—	89	1	no	—
232	#1675	—	89	1	no	—
233	#1668	—	89	1	no	—
234	#1667	—	89	1	no	—
235	#1564	—	89	1	no	—
236	#1543	—	89	2	no	—
237	C₈₉	#19128	1	1	yes	characteristic, complemented, Sylow
238	#532	—	89	2	no	—
239	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
240	#500	—	89	1	no	—
241	#493	—	89	1	no	—
242	#486	—	89	2	no	—
243	#482	—	178	2	no	—
244	#477	—	89	2	no	—
245	#476	—	89	2	no	—
246	#466	—	178	1	no	—
247	#466	—	178	1	no	—
248	#460	—	89	2	no	—
249	#459	—	89	2	no	—
250	#449	—	178	2	no	—
251	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
252	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
253	C₄×SD₁₆	—	178	2	no	—
254	C₄×D₈	—	178	2	no	—
255	C₄×D₈	—	178	1	no	—
256	C₄×D₈	—	178	1	no	—
257	C₈×D₄	—	2	1	no	—
258	C₈×D₄	—	2	1	no	—
259	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
260	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
261	#431	—	2	1	no	—
262	#431	—	89	2	no	—
263	#431	C₂×D₈₉	1	1	yes	characteristic
264	C₂×C₄×C₈	—	2	1	no	—
265	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
266	#335	—	89	1	no	—
267	#335	—	89	1	no	—
268	#334	—	89	2	no	—
269	#333	—	89	2	no	—
270	#333	—	89	2	no	—
271	#331	—	89	2	no	—
272	#331	—	89	2	no	—
273	C₂×#41	—	178	2	no	—
274	C₂×#41	D₃₅₆	1	1	yes	characteristic
275	C₂×SD₁₆	—	178	2	no	—
276	C₂×D₈	—	178	2	no	—
277	C₂×D₈	—	178	1	no	—
278	C₂×D₈	—	178	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
282	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
283	C₄⋊Q₈	—	89	2	no	—
284	#127	—	89	2	no	—
285	#124	—	178	2	no	—
286	#121	—	178	2	no	—
287	#121	—	178	2	no	—
288	C₄×Q₈	D₃₅₆	1	1	yes	characteristic
289	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	178	2	no	—
293	C₄×D₄	—	178	2	no	—
294	C₄×D₄	D₃₅₆	1	1	yes	characteristic
295	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
296	#117	—	2	1	no	—
297	#117	D₃₅₆	1	1	yes	characteristic
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
300	#107	—	178	1	no	—
301	#107	—	178	1	no	—
302	#107	—	178	2	no	—
303	#106	—	178	2	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	89	2	no	—
307	C₄⋊C₈	—	89	2	no	—
308	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
309	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
310	#103	—	178	2	no	—
311	#102	—	178	2	no	—
312	#102	—	178	2	no	—
313	#102	—	178	2	no	—
314	#102	—	178	2	no	—
315	#102	—	178	2	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	C₂²⋊C₈	—	178	2	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	178	2	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	1	yes	characteristic
327	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	—	712	4	no	—
331	C₂×Q₈	—	178	2	no	—
332	C₂×Q₈	C₂×D₃₅₆	1	1	yes	characteristic
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	356	2	no	—
335	C₂×D₄	—	178	2	no	—
336	C₂×D₄	—	178	2	no	—
337	C₂×D₄	—	178	2	no	—
338	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	356	2	no	—
343	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
345	C₂²×C₄	#13083574	1	1	yes	characteristic
346	SD₁₆	—	356	4	no	—
347	D₈	—	356	2	no	—
348	D₈	—	356	4	no	—
349	D₈	—	356	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	4	2	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	178	2	no	—
357	C₂×C₈	—	178	2	no	—
358	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
359	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
360	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
361	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	178	2	no	—
365	C₄⋊C₄	—	178	2	no	—
366	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
367	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	356	2	no	—
372	C₂²⋊C₄	—	356	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
377	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
378	C₄²	#13083574	1	1	yes	characteristic
379	C₄²	C₂³×D₈₉	1	1	yes	characteristic
380	C₂³	—	2	1	no	—
381	C₂³	—	356	2	no	—
382	C₂³	#15667986	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	—	712	2	no	—
385	Q₈	#15668034	1	2	yes	—
386	D₄	—	2	4	no	—
387	D₄	—	2	1	no	—
388	D₄	—	356	2	no	—
389	D₄	—	356	2	no	—
390	D₄	—	356	2	no	—
391	D₄	—	356	2	no	—
392	D₄	—	712	2	no	—
393	D₄	—	712	4	no	—
394	D₄	#15668034	1	2	yes	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	356	2	no	—
408	C₂×C₄	—	712	4	no	—
409	C₂×C₄	#15667986	1	1	yes	characteristic
410	C₂×C₄	#15667986	1	1	yes	characteristic
411	C₂×C₄	#15667986	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
414	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	—	2	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	356	2	no	—
421	C₈	—	356	2	no	—
422	C₈	#15668032	1	2	yes	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	712	2	no	—
430	C₂²	—	712	2	no	—
431	C₂²	—	712	2	no	—
432	C₂²	C₂×#15667986	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	712	2	no	—
440	C₄	#19151868	1	2	yes	—
441	C₄	C₂×#15668032	1	1	yes	characteristic
442	C₄	C₂×#15668034	1	1	yes	characteristic
443	C₄	C₂×#15668034	1	1	yes	characteristic
444	C₄	#19152396	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	4	2	no	—
447	C₂	—	1424	2	no	—
448	C₂	#26029707	1	1	yes	characteristic
449	C₂	#26029833	1	1	yes	characteristic
450	C₂	C₂×#19151868	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15667986
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×#41×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#121
hypercenter	C₈×#41	D₈₉
hypocenter	C₈₉	#19128
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #26030831	C₂	semidirect
2. #26030312	C₂	semidirect
3. #26019668	C₂	semidirect
4. #26019661	C₂	semidirect
5. #26019656	C₂	semidirect
6. #26019651	C₂	semidirect
7. #26019612	C₂	semidirect
8. #26019607	C₂	semidirect
9. #26019000	C₂	semidirect
10. #26018912	C₂	semidirect
11. C₈×#41×C₈₉	C₂	semidirect
228. C₈×#41	D₈₉	semidirect
237. C₈₉	#19128	semidirect

Maximal subgroups

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

subgroup	index
#26030831	2
#26030312	2
#26019668	2
#26019661	2
#26019656	2
#26019651	2
#26019612	2
#26019607	2
#26019000	2
#26018912	2
C₈×#41×C₈₉	2
#19128	89