Subgroups — #36536867

Order 22784.

726 conjugacy classes of subgroups.

The subgroup lattice has 464 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	#26029709	C₂	1	2	yes	maximal, complemented
3	C₈×#13083574	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019697	C₂	1	2	yes	maximal, complemented
5	#26019690	C₂	1	2	yes	maximal, complemented
6	#26019647	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019642	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019613	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019608	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018902	C₂	1	2	yes	maximal, complemented
11	C₂×#335×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668034	—	2	2	no	—
13	#19152148	C₂²	1	2	yes	—
14	C₄×#13083574	C₂²	1	1	yes	characteristic
15	#19152003	C₂²	1	1	yes	characteristic
16	#19151975	C₂²	1	1	yes	characteristic
17	#19151945	C₂²	1	2	yes	—
18	#19151834	—	2	1	no	—
19	#19151834	—	2	1	no	—
20	#19151821	—	2	2	no	—
21	#19151814	—	2	2	no	—
22	#19151809	C₂²	1	2	yes	—
23	#19151804	C₂²	1	2	yes	—
24	#19151799	C₂²	1	2	yes	—
25	#19151794	C₂²	1	2	yes	—
26	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
27	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
28	C₄×D₇₁₂	—	2	1	no	—
29	C₄×D₇₁₂	—	2	1	no	—
30	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
31	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
32	C₈×C₂²⋊D₈₉	—	2	1	no	—
33	C₈×C₂²⋊D₈₉	—	2	1	no	—
34	#19151651	C₂²	1	1	yes	characteristic
35	#19151649	—	2	1	no	—
36	#19151595	—	2	2	no	—
37	C₄×C₈×D₈₉	—	2	1	no	—
38	#19151345	C₂²	1	2	yes	—
39	#19151345	C₂²	1	2	yes	—
40	#19151341	C₂²	1	2	yes	—
41	#19151341	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
44	#335×C₈₉	C₂²	1	1	yes	characteristic
45	#335×C₈₉	C₂²	1	1	yes	characteristic
46	#335×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083574	—	2	2	no	—
48	C₂×#13083574	D₄	1	1	yes	characteristic
49	#15668034	—	4	8	no	—
50	C₂×Dic₃₅₆	—	2	2	no	—
51	C₂×#13083563	—	2	2	no	—
52	C₂×#13083563	—	2	2	no	—
53	C₂×D₇₁₂	—	2	2	no	—
54	C₂×D₇₁₂	—	2	1	no	—
55	C₂×D₇₁₂	—	2	1	no	—
56	C₂×C₈×D₈₉	—	2	1	no	—
57	C₂×C₈×D₈₉	—	2	1	no	—
58	#15668012	C₂³	1	2	yes	—
59	#15668009	C₂³	1	2	yes	—
60	#15668000	—	2	2	no	—
61	#15667986	—	2	2	no	—
62	#15667986	—	2	2	no	—
63	C₄×Dic₁₇₈	D₄	1	1	yes	characteristic
64	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
65	C₄×D₃₅₆	—	2	2	no	—
66	C₄×D₃₅₆	—	2	2	no	—
67	C₄×D₃₅₆	D₄	1	1	yes	characteristic
68	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
69	C₄×C₂²⋊D₈₉	—	2	1	no	—
70	C₄×C₂²⋊D₈₉	—	2	1	no	—
71	#15667971	D₄	1	1	yes	characteristic
72	#15667969	—	2	1	no	—
73	C₄²×D₈₉	—	2	1	no	—
74	#15667946	—	2	1	no	—
75	#15667946	—	2	1	no	—
76	C₄⋊#10623494	C₂³	1	1	yes	characteristic
77	C₄⋊#10623494	C₂³	1	1	yes	characteristic
78	#15667941	—	2	1	no	—
79	#15667941	—	2	1	no	—
80	#15667937	—	2	2	no	—
81	#15667937	—	2	2	no	—
82	#15667934	—	2	2	no	—
83	#15667934	—	2	2	no	—
84	#15667934	—	2	2	no	—
85	#15667934	—	2	2	no	—
86	C₂²⋊#10623494	—	2	1	no	—
87	#15667924	—	2	1	no	—
88	#15667924	—	2	1	no	—
89	C₄×#10623494	—	2	1	no	—
90	C₈×Dic₈₉	—	2	1	no	—
91	C₈×Dic₈₉	—	2	1	no	—
92	C₂²×C₈×C₈₉	—	2	2	no	—
93	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
94	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₈₉	—	2	2	no	—
97	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
98	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
99	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
100	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
101	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
103	#13083574	—	2	2	no	—
104	#13083574	—	4	4	no	—
105	#13083574	—	4	4	no	—
106	#13083574	D₈	1	4	yes	complemented
107	C₂×Dic₁₇₈	—	2	2	no	—
108	C₂×Dic₁₇₈	C₂×D₄	1	1	yes	characteristic
109	C₂×D₃₅₆	—	2	2	no	—
110	C₂×D₃₅₆	—	2	2	no	—
111	C₂×D₃₅₆	—	2	2	no	—
112	C₂×D₃₅₆	C₂×D₄	1	1	yes	characteristic
113	C₂×C₂²⋊D₈₉	—	2	1	no	—
114	C₂×C₂²⋊D₈₉	—	4	2	no	—
115	C₂×C₄×D₈₉	—	2	1	no	—
116	C₂×C₄×D₈₉	—	2	1	no	—
117	C₂×C₄×D₈₉	—	2	1	no	—
118	C₂×C₄×D₈₉	—	4	2	no	—
119	Dic₃₅₆	—	4	4	no	—
120	#13083563	—	4	4	no	—
121	#13083563	—	4	4	no	—
122	D₇₁₂	—	4	2	no	—
123	D₇₁₂	—	4	4	no	—
124	D₇₁₂	—	4	2	no	—
125	C₂×#10623494	—	2	1	no	—
126	C₂×#10623494	—	2	1	no	—
127	C₈×D₈₉	—	4	2	no	—
128	C₈×D₈₉	—	4	2	no	—
129	C₄⋊Dic₈₉	—	2	2	no	—
130	C₄⋊Dic₈₉	—	2	2	no	—
131	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
132	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
133	#13083553	—	2	1	no	—
134	#13083553	—	2	1	no	—
135	C₂²⋊Dic₈₉	—	2	1	no	—
136	#13083551	—	2	1	no	—
137	#13083551	—	2	1	no	—
138	#13083551	—	4	2	no	—
139	#13083551	—	4	2	no	—
140	C₄×Dic₈₉	—	2	1	no	—
141	C₄×Dic₈₉	—	2	1	no	—
142	C₄×Dic₈₉	—	2	1	no	—
143	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
146	C₂×C₈×C₈₉	—	2	2	no	—
147	C₂×C₈×C₈₉	—	2	2	no	—
148	C₂×C₈×C₈₉	—	2	2	no	—
149	C₂×C₈×C₈₉	—	4	1	no	—
150	C₂×C₈×C₈₉	—	4	4	no	—
151	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₈₉	#41	1	1	yes	characteristic
158	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
159	C₂³×C₈₉	#121	1	1	yes	characteristic
160	C₂²×D₈₉	—	2	1	no	—
161	C₂²×D₈₉	—	4	2	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	4	1	no	—
165	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
169	C₂×C₄×C₈₉	#135	1	2	yes	—
170	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
173	C₂²⋊D₈₉	—	2	4	no	—
174	C₂²⋊D₈₉	—	8	4	no	—
175	C₂×Dic₈₉	—	2	1	no	—
176	C₂×Dic₈₉	—	2	1	no	—
177	C₂×Dic₈₉	—	2	1	no	—
178	C₂×Dic₈₉	—	4	2	no	—
179	D₃₅₆	—	2	1	no	—
180	D₃₅₆	—	4	2	no	—
181	D₃₅₆	—	4	2	no	—
182	D₃₅₆	—	4	2	no	—
183	D₃₅₆	—	4	2	no	—
184	D₃₅₆	—	8	2	no	—
185	D₃₅₆	C₂×D₈	1	2	yes	—
186	C₄×D₈₉	—	2	4	no	—
187	C₄×D₈₉	—	4	2	no	—
188	C₄×D₈₉	—	4	1	no	—
189	C₄×D₈₉	—	4	1	no	—
190	C₄×D₈₉	—	8	4	no	—
191	Dic₁₇₈	—	2	1	no	—
192	Dic₁₇₈	—	4	2	no	—
193	Dic₁₇₈	—	4	2	no	—
194	Dic₁₇₈	C₂×D₈	1	2	yes	—
195	C₈×C₈₉	—	2	1	no	—
196	C₈×C₈₉	—	2	1	no	—
197	C₈×C₈₉	—	2	1	no	—
198	C₈×C₈₉	—	4	2	no	—
199	C₈×C₈₉	—	4	2	no	—
200	C₈×C₈₉	#135	1	2	yes	complemented
201	#10623494	—	4	1	no	—
202	#10623494	—	4	1	no	—
203	C₂²×C₈₉	—	2	1	no	—
204	C₂²×C₈₉	—	2	1	no	—
205	C₂²×C₈₉	#466	1	2	yes	—
206	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
207	C₂×D₈₉	—	2	2	no	—
208	C₂×D₈₉	—	4	1	no	—
209	C₂×D₈₉	—	4	1	no	—
210	C₂×D₈₉	—	8	2	no	—
211	C₂×D₈₉	—	8	2	no	—
212	C₂×D₈₉	—	8	2	no	—
213	C₄×C₈₉	—	2	1	no	—
214	C₄×C₈₉	—	2	1	no	—
215	C₄×C₈₉	—	2	1	no	—
216	C₄×C₈₉	#466	1	2	yes	—
217	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
218	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
219	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
220	C₄×C₈₉	#575	1	1	yes	characteristic
221	Dic₈₉	—	2	2	no	—
222	Dic₈₉	—	4	1	no	—
223	Dic₈₉	—	4	1	no	—
224	Dic₈₉	—	8	2	no	—
225	#19125	—	89	1	no	maximal, Sylow
226	C₂×C₈₉	—	2	2	no	—
227	C₂×C₈₉	#3035	1	1	yes	characteristic
228	C₂×C₈₉	C₂×#466	1	1	yes	characteristic
229	C₂×C₈₉	#3067	1	1	yes	characteristic
230	D₈₉	—	4	2	no	—
231	D₈₉	—	16	2	no	—
232	#3169	—	89	1	no	—
233	#3035	—	89	2	no	—
234	C₈×#41	—	89	1	no	—
235	#1682	—	89	2	no	—
236	#1681	—	89	2	no	—
237	#1674	—	89	1	no	—
238	#1673	—	89	1	no	—
239	#1668	—	89	1	no	—
240	#1667	—	89	1	no	—
241	C₂×#335	D₈₉	1	1	yes	characteristic, complemented
242	#1540	—	89	2	no	—
243	C₈₉	#19125	1	1	yes	characteristic, complemented, Sylow
244	C₂×#135	—	178	2	no	—
245	#532	—	89	2	no	—
246	C₄×#41	—	89	1	no	—
247	#500	—	89	1	no	—
248	#493	—	89	1	no	—
249	#486	—	89	2	no	—
250	#466	—	178	1	no	—
251	#466	—	178	1	no	—
252	#464	—	178	2	no	—
253	#463	—	178	2	no	—
254	#462	—	89	2	no	—
255	#461	—	89	2	no	—
256	#460	—	89	2	no	—
257	#459	—	89	2	no	—
258	C₈×Q₈	—	89	1	no	—
259	C₈×Q₈	—	89	1	no	—
260	C₄×D₈	—	178	1	no	—
261	C₄×D₈	—	178	1	no	—
262	C₈×D₄	—	89	1	no	—
263	C₈×D₄	—	89	1	no	—
264	C₈×D₄	—	178	1	no	—
265	C₈×D₄	—	178	1	no	—
266	#431	—	89	1	no	—
267	#431	—	178	1	no	—
268	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
269	#416	—	178	2	no	—
270	C₂×C₄×C₈	—	178	1	no	—
271	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
272	#335	C₂×D₈₉	1	1	yes	characteristic
273	#335	C₂×D₈₉	1	1	yes	characteristic
274	#335	C₂×D₈₉	1	2	yes	—
275	#332	—	89	2	no	—
276	#332	—	89	2	no	—
277	#331	—	89	2	no	—
278	#331	—	89	2	no	—
279	C₂×#41	—	89	1	no	—
280	C₂×#41	—	178	2	no	—
281	#135	—	356	8	no	—
282	C₂×Q₁₆	—	178	2	no	—
283	C₂×SD₁₆	—	178	2	no	—
284	C₂×SD₁₆	—	178	2	no	—
285	C₂×D₈	—	178	2	no	—
286	C₂×D₈	—	178	1	no	—
287	C₂×D₈	—	178	1	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	178	1	no	—
290	C₂²×C₈	—	178	1	no	—
291	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
292	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
293	C₄⋊Q₈	—	89	2	no	—
294	#127	—	89	2	no	—
295	#124	—	178	2	no	—
296	#121	—	178	2	no	—
297	#121	—	178	2	no	—
298	C₄×Q₈	—	89	1	no	—
299	C₄×Q₈	—	89	1	no	—
300	C₄×D₄	—	89	1	no	—
301	C₄×D₄	—	89	1	no	—
302	C₄×D₄	—	178	1	no	—
303	C₄×D₄	—	178	1	no	—
304	C₄×D₄	—	178	2	no	—
305	C₄×D₄	—	178	2	no	—
306	#117	—	89	1	no	—
307	#117	—	178	1	no	—
308	C₂×C₄²	—	178	1	no	—
309	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
310	#107	—	178	1	no	—
311	#107	—	178	1	no	—
312	C₄⋊C₈	—	2	2	no	—
313	C₄⋊C₈	—	89	1	no	—
314	C₄⋊C₈	—	89	1	no	—
315	C₄⋊C₈	—	178	1	no	—
316	C₄⋊C₈	—	178	1	no	—
317	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
318	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
319	#103	—	178	2	no	—
320	#103	—	178	2	no	—
321	#102	—	178	2	no	—
322	#102	—	178	2	no	—
323	#102	—	178	2	no	—
324	#102	—	178	2	no	—
325	C₂²⋊C₈	—	178	1	no	—
326	C₂²⋊C₈	—	178	1	no	—
327	C₂²⋊C₈	—	178	1	no	—
328	C₄×C₈	—	178	1	no	—
329	C₄×C₈	—	178	1	no	—
330	C₄×C₈	—	178	1	no	—
331	C₄×C₈	D₃₅₆	1	1	yes	characteristic
332	C₄×C₈	D₃₅₆	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
334	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
335	#41	—	89	4	no	—
336	#41	—	356	4	no	—
337	#41	—	356	4	no	—
338	#41	—	178	2	no	—
339	C₂×Q₈	—	89	1	no	—
340	C₂×Q₈	—	178	2	no	—
341	C₂×D₄	—	89	1	no	—
342	C₂×D₄	—	356	2	no	—
343	C₂×D₄	—	178	1	no	—
344	C₂×D₄	—	178	2	no	—
345	C₂×D₄	—	178	2	no	—
346	C₂×D₄	—	178	2	no	—
347	C₂²×C₄	—	356	2	no	—
348	C₂²×C₄	—	178	1	no	—
349	C₂²×C₄	—	178	1	no	—
350	C₂²×C₄	—	178	1	no	—
351	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
353	C₂²×C₄	#13083575	1	1	yes	characteristic
354	Q₁₆	—	356	4	no	—
355	SD₁₆	—	356	4	no	—
356	SD₁₆	—	356	4	no	—
357	D₈	—	356	2	no	—
358	D₈	—	356	4	no	—
359	D₈	—	356	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	4	no	—
365	C₂×C₈	—	356	2	no	—
366	C₂×C₈	—	356	2	no	—
367	C₂×C₈	—	178	1	no	—
368	C₂×C₈	—	178	1	no	—
369	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
370	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
371	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
372	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
373	C₄⋊C₄	—	89	1	no	—
374	C₄⋊C₄	—	89	1	no	—
375	C₄⋊C₄	—	178	2	no	—
376	C₄⋊C₄	—	178	2	no	—
377	C₄⋊C₄	—	178	1	no	—
378	C₄⋊C₄	—	178	1	no	—
379	C₂²⋊C₄	—	356	2	no	—
380	C₂²⋊C₄	—	356	2	no	—
381	C₂²⋊C₄	—	178	1	no	—
382	C₂²⋊C₄	—	178	1	no	—
383	C₂²⋊C₄	—	178	1	no	—
384	C₄²	—	178	1	no	—
385	C₄²	—	178	1	no	—
386	C₄²	—	178	1	no	—
387	C₄²	D₄×D₈₉	1	1	yes	characteristic
388	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
389	C₄²	#13083575	1	1	yes	characteristic
390	C₄²	C₂³×D₈₉	1	1	yes	characteristic
391	C₂³	—	356	2	no	—
392	C₂³	—	178	1	no	—
393	C₂³	#15667987	1	1	yes	characteristic
394	Q₈	—	89	2	no	—
395	Q₈	—	356	2	no	—
396	Q₈	—	356	2	no	—
397	Q₈	—	178	1	no	—
398	D₄	—	89	2	no	—
399	D₄	—	356	2	no	—
400	D₄	—	356	2	no	—
401	D₄	—	356	2	no	—
402	D₄	—	356	2	no	—
403	D₄	—	178	4	no	—
404	D₄	—	178	1	no	—
405	D₄	—	712	2	no	—
406	D₄	—	712	4	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	356	2	no	—
411	C₂×C₄	—	356	1	no	—
412	C₂×C₄	—	356	1	no	—
413	C₂×C₄	—	356	2	no	—
414	C₂×C₄	—	178	1	no	—
415	C₂×C₄	—	178	1	no	—
416	C₂×C₄	—	178	1	no	—
417	C₂×C₄	—	178	4	no	—
418	C₂×C₄	—	712	4	no	—
419	C₂×C₄	#15667987	1	1	yes	characteristic
420	C₂×C₄	#15667987	1	1	yes	characteristic
421	C₂×C₄	#15667987	1	1	yes	characteristic
422	C₂×C₄	D₈×D₈₉	1	2	yes	—
423	C₂×C₄	#15668035	1	2	yes	—
424	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
426	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
427	C₈	—	2	1	no	—
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	4	2	no	—
431	C₈	—	4	2	no	—
432	C₈	—	356	1	no	—
433	C₈	—	356	1	no	—
434	C₈	#15668034	1	2	yes	complemented
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	356	1	no	—
438	C₂²	—	356	1	no	—
439	C₂²	—	178	2	no	—
440	C₂²	—	712	2	no	—
441	C₂²	—	712	2	no	—
442	C₂²	—	712	2	no	—
443	C₂²	#19151835	1	2	yes	—
444	C₂²	C₂×#15667987	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	356	1	no	—
449	C₄	—	356	1	no	—
450	C₄	—	178	2	no	—
451	C₄	—	712	2	no	—
452	C₄	#19151835	1	2	yes	—
453	C₄	C₂×D₈×D₈₉	1	1	yes	characteristic
454	C₄	C₂×#15668034	1	1	yes	characteristic
455	C₄	C₂×#15668035	1	1	yes	characteristic
456	C₄	#19152398	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	356	2	no	—
459	C₂	—	1424	2	no	—
460	C₂	#26029709	1	1	yes	characteristic
461	C₂	C₂×#19151835	1	1	yes	characteristic
462	C₂	#26029973	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15667987
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×#335×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#121
hypercenter	C₂×#335	D₈₉
hypocenter	C₈₉	#19125
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
1. #26030831	C₂	semidirect
2. #26029709	C₂	semidirect
3. C₈×#13083574	C₂	semidirect
4. #26019697	C₂	semidirect
5. #26019690	C₂	semidirect
6. #26019647	C₂	semidirect
7. #26019642	C₂	semidirect
8. #26019613	C₂	semidirect
9. #26019608	C₂	semidirect
10. #26018902	C₂	semidirect
11. C₂×#335×C₈₉	C₂	semidirect
106. #13083574	D₈	semidirect
200. C₈×C₈₉	#135	semidirect
241. C₂×#335	D₈₉	semidirect
243. C₈₉	#19125	semidirect
434. C₈	#15668034	semidirect

Maximal subgroups

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

subgroup	index
#26030831	2
#26029709	2
C₈×#13083574	2
#26019697	2
#26019690	2
#26019647	2
#26019642	2
#26019613	2
#26019608	2
#26018902	2
C₂×#335×C₈₉	2
#19125	89