Subgroups — #36526184

Order 22784.

722 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030827	C₂	1	1	yes	maximal, characteristic
2	#26028998	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019135	C₂	1	2	yes	maximal, complemented
4	#26019081	C₂	1	2	yes	maximal, complemented
5	#26019079	C₂	1	2	yes	maximal, complemented
6	C₈×#13083559	C₂	1	2	yes	maximal, complemented
7	C₂×#19151350	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018651	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018650	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668020	—	2	1	no	—
13	#19152148	C₂²	1	1	yes	characteristic
14	#19152001	C₄	1	1	yes	characteristic
15	#19151974	C₄	1	1	yes	characteristic
16	#19151946	C₄	1	1	yes	characteristic
17	#19151944	C₄	1	1	yes	characteristic
18	#19151832	C₄	1	2	yes	—
19	#19151832	C₄	1	2	yes	—
20	C₄×#13083559	C₂²	1	2	yes	—
21	C₄×#13083559	C₂²	1	2	yes	—
22	#19151677	C₂²	1	2	yes	—
23	#19151671	—	2	2	no	—
24	C₈×D₃₅₆	C₂²	1	2	yes	—
25	#19151651	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
27	#19151566	—	2	1	no	—
28	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
29	#19151350	C₂²	1	1	yes	characteristic
30	#19151350	C₂²	1	1	yes	characteristic
31	#19151350	C₂²	1	1	yes	characteristic
32	#19151350	C₂²	1	1	yes	characteristic
33	D₄⋊#10623494	C₂²	1	2	yes	—
34	D₄⋊#10623494	C₂²	1	2	yes	—
35	#19151325	C₂²	1	2	yes	—
36	#19151325	C₂²	1	2	yes	—
37	#19151319	C₂²	1	2	yes	—
38	C₈×#10623494	C₂²	1	2	yes	—
39	C₂×#131×C₈₉	—	2	1	no	—
40	#532×C₈₉	C₂²	1	1	yes	characteristic
41	#436×C₈₉	C₂²	1	2	yes	—
42	#435×C₈₉	—	2	2	no	—
43	C₈×D₄×C₈₉	C₂²	1	2	yes	—
44	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#408×C₈₉	—	2	1	no	—
46	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	—	2	1	no	—
48	C₂×#13083559	C₂×C₄	1	2	yes	—
49	C₂×#13083559	C₂×C₄	1	2	yes	—
50	#15668020	—	4	4	no	—
51	C₂×#13083557	—	2	2	no	—
52	C₂²×#10623494	—	2	1	no	—
53	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
54	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₈₉	—	2	2	no	—
56	#15668012	C₂×C₄	1	1	yes	characteristic
57	#15668009	C₂×C₄	1	1	yes	characteristic
58	#15668000	—	2	1	no	—
59	#15667986	—	2	1	no	—
60	#15667986	C₂×C₄	1	2	yes	—
61	C₄×D₃₅₆	—	2	1	no	—
62	C₄×D₃₅₆	C₂³	1	2	yes	—
63	#15667945	C₂×C₄	1	2	yes	—
64	#15667945	C₂×C₄	1	2	yes	—
65	C₄⋊#10623494	—	2	1	no	—
66	C₄⋊#10623494	—	2	1	no	—
67	C₄⋊#10623494	C₂³	1	1	yes	characteristic
68	C₄⋊#10623494	C₂³	1	1	yes	characteristic
69	#15667933	C₂×C₄	1	2	yes	—
70	#15667933	C₂×C₄	1	2	yes	—
71	#15667932	C₂×C₄	1	2	yes	—
72	#15667932	C₂×C₄	1	2	yes	—
73	C₂²⋊#10623494	—	2	1	no	—
74	#15667924	—	2	2	no	—
75	#15667924	—	2	2	no	—
76	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
77	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
78	C₄×#10623494	C₂³	1	2	yes	—
79	C₄×#10623494	C₂³	1	1	yes	characteristic
80	C₄×#10623494	C₂³	1	1	yes	characteristic
81	C₂×#41×C₈₉	—	2	1	no	—
82	#131×C₈₉	—	4	4	no	—
83	C₂×M₁₆×C₈₉	—	2	2	no	—
84	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
85	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
86	C₂²×C₈×C₈₉	—	2	1	no	—
87	C₂²×C₈×C₈₉	—	2	2	no	—
88	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
89	#127×C₈₉	C₂×C₄	1	1	yes	characteristic
90	#124×C₈₉	—	2	1	no	—
91	#121×C₈₉	—	2	1	no	—
92	#121×C₈₉	C₂×C₄	1	2	yes	—
93	C₄×D₄×C₈₉	—	2	1	no	—
94	C₄×D₄×C₈₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₈₉	—	2	1	no	—
97	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²⋊C₈×C₈₉	—	2	2	no	—
100	C₂²⋊C₈×C₈₉	—	2	2	no	—
101	#97×C₈₉	D₄	1	2	yes	—
102	C₄×C₈×C₈₉	C₂³	1	2	yes	—
103	#13083574	—	4	2	no	—
104	#13083574	—	4	2	no	—
105	C₂×Dic₁₇₈	—	2	1	no	—
106	C₂×D₃₅₆	—	2	1	no	—
107	C₂×D₃₅₆	—	2	1	no	—
108	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
109	C₂×C₂²⋊D₈₉	—	2	2	no	—
110	C₂×C₄×D₈₉	—	2	2	no	—
111	#13083559	—	2	4	no	—
112	#13083559	—	4	2	no	—
113	#13083557	—	4	4	no	—
114	C₂×#10623494	—	2	2	no	—
115	C₂×#10623494	—	2	1	no	—
116	C₂×#10623494	—	2	1	no	—
117	C₂×#10623494	—	2	2	no	—
118	C₂×#10623494	—	4	1	no	—
119	C₂×#10623494	—	4	2	no	—
120	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
121	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
122	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
123	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
124	C₈×D₈₉	—	4	4	no	—
125	C₄⋊Dic₈₉	—	2	1	no	—
126	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
127	#13083551	—	2	2	no	—
128	#13083551	—	2	2	no	—
129	#41×C₈₉	—	4	2	no	—
130	#41×C₈₉	—	4	2	no	—
131	C₂×Q₈×C₈₉	—	2	1	no	—
132	C₂×D₄×C₈₉	—	2	2	no	—
133	C₂×D₄×C₈₉	—	2	1	no	—
134	C₂×D₄×C₈₉	—	2	1	no	—
135	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₈₉	—	2	2	no	—
137	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
140	M₁₆×C₈₉	—	2	2	no	—
141	M₁₆×C₈₉	—	4	4	no	—
142	M₁₆×C₈₉	D₈	1	4	yes	complemented
143	C₂×C₈×C₈₉	—	2	1	no	—
144	C₂×C₈×C₈₉	—	2	1	no	—
145	C₂×C₈×C₈₉	—	4	2	no	—
146	C₂×C₈×C₈₉	—	4	4	no	—
147	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
149	C₄⋊C₄×C₈₉	—	2	1	no	—
150	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
151	C₂²⋊C₄×C₈₉	—	2	2	no	—
152	C₂²⋊C₄×C₈₉	—	2	2	no	—
153	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₈₉	#41	1	1	yes	characteristic
156	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
157	C₂³×C₈₉	—	2	2	no	—
158	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
159	C₂²×D₈₉	—	2	2	no	—
160	Q₈×C₈₉	—	4	2	no	—
161	D₄×C₈₉	—	2	2	no	—
162	D₄×C₈₉	—	2	2	no	—
163	D₄×C₈₉	—	4	4	no	—
164	D₄×C₈₉	—	4	2	no	—
165	D₄×C₈₉	—	8	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	—	4	1	no	—
170	C₂×C₄×C₈₉	—	4	2	no	—
171	C₂×C₄×C₈₉	—	4	2	no	—
172	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
176	C₂×C₄×C₈₉	#135	1	2	yes	—
177	C₂×C₄×C₈₉	C₂³×C₄	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	—	4	4	no	—
181	C₂×Dic₈₉	—	2	2	no	—
182	D₃₅₆	—	2	2	no	—
183	D₃₅₆	—	2	2	no	—
184	D₃₅₆	—	4	2	no	—
185	D₃₅₆	—	8	1	no	—
186	C₄×D₈₉	—	4	2	no	—
187	C₄×D₈₉	—	4	2	no	—
188	Dic₁₇₈	—	4	2	no	—
189	C₈×C₈₉	—	2	2	no	—
190	C₈×C₈₉	—	4	1	no	—
191	C₈×C₈₉	—	4	1	no	—
192	C₈×C₈₉	C₂×D₈	1	4	yes	—
193	#10623494	—	2	1	no	—
194	#10623494	—	2	1	no	—
195	#10623494	—	2	1	no	—
196	#10623494	—	4	2	no	—
197	#10623494	—	4	1	no	—
198	#10623494	—	4	1	no	—
199	#10623494	#131	1	2	yes	complemented
200	C₂²×C₈₉	—	2	1	no	—
201	C₂²×C₈₉	—	2	1	no	—
202	C₂²×C₈₉	—	4	2	no	—
203	C₂²×C₈₉	—	4	2	no	—
204	C₂²×C₈₉	—	4	2	no	—
205	C₂²×C₈₉	C₄×D₈	1	2	yes	—
206	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
207	C₂×D₈₉	—	4	2	no	—
208	C₂×D₈₉	—	4	2	no	—
209	C₂×D₈₉	—	4	2	no	—
210	C₄×C₈₉	—	2	1	no	—
211	C₄×C₈₉	—	2	1	no	—
212	C₄×C₈₉	—	2	1	no	—
213	C₄×C₈₉	—	4	2	no	—
214	C₄×C₈₉	C₄×D₈	1	2	yes	—
215	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
216	C₄×C₈₉	#568	1	1	yes	characteristic
217	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
218	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
219	Dic₈₉	—	4	2	no	—
220	#18066	—	89	1	no	maximal, Sylow
221	C₂×C₈₉	—	2	2	no	—
222	C₂×C₈₉	—	8	2	no	—
223	C₂×C₈₉	#2935	1	1	yes	characteristic
224	C₂×C₈₉	C₂×C₄×D₈	1	1	yes	characteristic
225	C₂×C₈₉	#2957	1	1	yes	characteristic
226	D₈₉	—	8	2	no	—
227	#3169	—	89	1	no	—
228	#2935	—	89	1	no	—
229	#2935	D₈₉	1	1	yes	characteristic, complemented
230	#1589	—	89	2	no	—
231	#1581	—	89	2	no	—
232	#1581	—	89	2	no	—
233	C₈×D₈	—	89	2	no	—
234	C₂×#335	—	89	1	no	—
235	#1480	—	89	1	no	—
236	#1480	—	89	1	no	—
237	C₈×M₁₆	—	89	1	no	—
238	C₈₉	#18066	1	1	yes	characteristic, complemented, Sylow
239	C₂×#131	—	2	1	no	—
240	C₂×#131	—	178	1	no	—
241	#532	—	89	1	no	—
242	#532	C₂×D₈₉	1	1	yes	characteristic
243	#500	—	89	1	no	—
244	#493	—	89	1	no	—
245	#486	—	89	1	no	—
246	#486	—	89	1	no	—
247	#466	—	89	2	no	—
248	#466	—	89	2	no	—
249	C₄×D₈	—	89	2	no	—
250	C₄×D₈	—	89	2	no	—
251	#436	—	89	2	no	—
252	#436	C₂×D₈₉	1	2	yes	—
253	#435	—	2	2	no	—
254	#435	—	178	2	no	—
255	C₈×D₄	—	89	2	no	—
256	C₈×D₄	C₂×D₈₉	1	2	yes	—
257	#431	—	89	1	no	—
258	C₂×C₄⋊C₈	—	89	1	no	—
259	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
260	#408	—	2	1	no	—
261	#408	—	178	1	no	—
262	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
263	C₂×C₄×C₈	—	89	1	no	—
264	#335	—	89	1	no	—
265	#335	—	89	1	no	—
266	#335	—	89	1	no	—
267	#335	—	89	1	no	—
268	D₄⋊C₈	—	89	2	no	—
269	D₄⋊C₈	—	89	2	no	—
270	D₄⋊C₈	—	89	2	no	—
271	D₄⋊C₈	—	89	2	no	—
272	#322	—	89	2	no	—
273	C₈²	—	89	2	no	—
274	C₂×#41	—	2	1	no	—
275	C₂×#41	—	178	1	no	—
276	C₂×D₈	—	89	2	no	—
277	C₂×D₈	—	89	2	no	—
278	#131	—	4	4	no	—
279	#131	—	356	4	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	178	2	no	—
282	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
283	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	—	89	1	no	—
287	C₂²×C₈	—	89	1	no	—
288	C₂²×C₈	—	178	1	no	—
289	C₂²×C₈	—	178	2	no	—
290	C₄⋊Q₈	—	89	1	no	—
291	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
292	#127	—	89	1	no	—
293	#127	C₄×D₈₉	1	1	yes	characteristic
294	#124	—	2	1	no	—
295	#124	—	178	1	no	—
296	#121	—	2	1	no	—
297	#121	—	89	2	no	—
298	#121	—	178	1	no	—
299	#121	C₄×D₈₉	1	2	yes	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	89	2	no	—
302	C₄×D₄	—	178	1	no	—
303	C₄×D₄	C₂²×D₈₉	1	2	yes	—
304	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
305	#107	—	89	2	no	—
306	#107	—	89	2	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	89	1	no	—
309	C₄⋊C₈	—	89	1	no	—
310	C₄⋊C₈	—	178	1	no	—
311	C₄⋊C₈	—	178	1	no	—
312	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
313	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
314	#102	—	89	2	no	—
315	#102	—	89	2	no	—
316	#102	—	89	2	no	—
317	#102	—	89	2	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₂²⋊C₈	—	178	1	no	—
321	C₂²⋊C₈	—	178	2	no	—
322	C₂²⋊C₈	—	178	2	no	—
323	#97	C₂²⋊D₈₉	1	2	yes	—
324	C₄×C₈	—	89	1	no	—
325	C₄×C₈	—	89	1	no	—
326	C₄×C₈	—	89	1	no	—
327	C₄×C₈	—	89	1	no	—
328	C₄×C₈	—	89	2	no	—
329	C₄×C₈	C₂²×D₈₉	1	2	yes	—
330	#41	—	4	2	no	—
331	#41	—	4	2	no	—
332	#41	—	356	2	no	—
333	#41	—	356	2	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	178	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	89	2	no	—
340	C₂×D₄	—	178	2	no	—
341	C₂×D₄	—	178	1	no	—
342	C₂×D₄	—	178	1	no	—
343	C₂×D₄	C₂×C₄×D₈₉	1	2	yes	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	178	2	no	—
346	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
348	C₂²×C₄	#13083574	1	1	yes	characteristic
349	D₈	—	356	2	no	—
350	D₈	—	178	4	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	4	4	no	—
353	M₁₆	—	356	4	no	—
354	M₁₆	#13083559	1	4	yes	complemented
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	4	4	no	—
359	C₂×C₈	—	89	1	no	—
360	C₂×C₈	—	89	1	no	—
361	C₂×C₈	—	89	1	no	—
362	C₂×C₈	—	89	1	no	—
363	C₂×C₈	—	356	2	no	—
364	C₂×C₈	—	356	4	no	—
365	C₂×C₈	—	356	1	no	—
366	C₂×C₈	—	178	2	no	—
367	C₂×C₈	—	178	1	no	—
368	C₂×C₈	—	178	1	no	—
369	C₂×C₈	—	178	2	no	—
370	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
371	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	89	2	no	—
374	C₄⋊C₄	—	178	1	no	—
375	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	178	2	no	—
379	C₂²⋊C₄	—	178	2	no	—
380	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
381	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
382	C₄²	#13083574	1	1	yes	characteristic
383	C₄²	C₂³×D₈₉	1	1	yes	characteristic
384	C₂³	—	2	2	no	—
385	C₂³	—	178	2	no	—
386	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
387	Q₈	—	4	2	no	—
388	Q₈	—	356	2	no	—
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	4	no	—
392	D₄	—	4	2	no	—
393	D₄	—	8	1	no	—
394	D₄	—	356	4	no	—
395	D₄	—	356	2	no	—
396	D₄	—	178	2	no	—
397	D₄	—	178	2	no	—
398	D₄	—	712	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	356	2	no	—
406	C₂×C₄	—	356	2	no	—
407	C₂×C₄	—	178	2	no	—
408	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
409	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
410	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
411	C₂×C₄	C₂×#13083559	1	2	yes	—
412	C₂×C₄	#15668032	1	2	yes	—
413	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
414	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
415	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	89	2	no	—
420	C₈	—	356	2	no	—
421	C₈	—	356	1	no	—
422	C₈	—	356	1	no	—
423	C₈	—	178	1	no	—
424	C₈	—	178	1	no	—
425	C₈	—	178	1	no	—
426	C₈	C₂×#13083559	1	4	yes	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	356	2	no	—
433	C₂²	—	356	2	no	—
434	C₂²	—	356	2	no	—
435	C₂²	C₄×#13083559	1	2	yes	—
436	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	4	2	no	—
441	C₄	—	356	2	no	—
442	C₄	C₄×#13083559	1	2	yes	—
443	C₄	#131×D₈₉	1	1	yes	characteristic
444	C₄	#19152363	1	1	yes	characteristic
445	C₄	C₂²×#13083559	1	1	yes	characteristic
446	C₄	C₂×#15668032	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	8	2	no	—
449	C₂	—	712	2	no	—
450	C₂	#26028994	1	1	yes	characteristic
451	C₂	C₂×C₄×#13083559	1	1	yes	characteristic
452	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×#2935	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#26030827	C₂
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2935	D₈₉
hypocenter	C₈₉	#18066
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2935

Complements

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

N	H ≅ G/N	type
2. #26028998	C₂	semidirect
3. #26019135	C₂	semidirect
4. #26019081	C₂	semidirect
5. #26019079	C₂	semidirect
6. C₈×#13083559	C₂	semidirect
7. C₂×#19151350	C₂	semidirect
8. #26018651	C₂	semidirect
9. #26018650	C₂	semidirect
10. M₁₆×#10623494	C₂	semidirect
11. C₈₉×#2935	C₂	semidirect
142. M₁₆×C₈₉	D₈	semidirect
199. #10623494	#131	semidirect
229. #2935	D₈₉	semidirect
238. C₈₉	#18066	semidirect
354. M₁₆	#13083559	semidirect

Maximal subgroups

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

subgroup	index
#26030827	2
#26028998	2
#26019135	2
#26019081	2
#26019079	2
C₈×#13083559	2
C₂×#19151350	2
#26018651	2
#26018650	2
M₁₆×#10623494	2
C₈₉×#2935	2
#18066	89