Subgroups — #36538262

Order 22784.

656 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030811	C₂	1	1	yes	maximal, characteristic
2	#26030059	C₂	1	1	yes	maximal, characteristic, complemented
3	#26029726	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019683	C₂	1	2	yes	maximal, complemented
6	#26019669	C₂	1	2	yes	maximal, complemented
7	#26019635	C₂	1	2	yes	maximal, complemented
8	#26019601	C₂	1	2	yes	maximal, complemented
9	#26018943	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018930	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1566	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668045	—	2	1	no	—
13	#19152155	C₂²	1	1	yes	characteristic
14	#19152148	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
16	#19151996	C₂²	1	1	yes	characteristic
17	#19151971	C₂²	1	1	yes	characteristic
18	#19151949	C₂²	1	1	yes	characteristic
19	#19151945	C₂²	1	1	yes	characteristic
20	#19151906	—	2	2	no	—
21	#19151894	C₂²	1	2	yes	—
22	#19151884	C₂²	1	2	yes	—
23	#19151827	—	2	1	no	—
24	#19151827	—	2	1	no	—
25	#19151821	—	2	2	no	—
26	#19151809	C₂²	1	2	yes	—
27	#19151799	C₂²	1	2	yes	—
28	C₈×Dic₁₇₈	—	2	1	no	—
29	C₈×Dic₁₇₈	—	2	1	no	—
30	C₈×Dic₁₇₈	C₂²	1	2	yes	—
31	C₈×Dic₁₇₈	C₂²	1	2	yes	—
32	C₄×#13083563	—	2	1	no	—
33	C₄×#13083563	—	2	1	no	—
34	#19151640	—	2	1	no	—
35	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
36	C₂×#15667941	—	2	1	no	—
37	#19151608	—	2	1	no	—
38	#19151600	—	2	1	no	—
39	C₂×C₈×Dic₈₉	—	2	1	no	—
40	#19151346	C₂²	1	2	yes	—
41	#19151345	C₂²	1	2	yes	—
42	#19151343	C₂²	1	2	yes	—
43	#19151341	C₂²	1	2	yes	—
44	#423×C₈₉	C₂²	1	1	yes	characteristic
45	#423×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
47	#334×C₈₉	C₂²	1	2	yes	—
48	#334×C₈₉	C₂²	1	2	yes	—
49	C₂×#13083574	—	2	1	no	—
50	C₂²×Dic₁₇₈	D₄	1	1	yes	characteristic
51	#15668045	—	4	4	no	—
52	C₂×Dic₃₅₆	—	2	2	no	—
53	C₂×#13083563	—	2	2	no	—
54	C₂×#13083563	—	2	1	no	—
55	C₂×#13083563	—	2	1	no	—
56	C₂²×#10623494	—	2	1	no	—
57	#15668012	C₂³	1	1	yes	characteristic
58	#15668012	C₂³	1	1	yes	characteristic
59	#15668012	C₂³	1	1	yes	characteristic
60	#15668009	C₂³	1	1	yes	characteristic
61	#15668004	—	2	1	no	—
62	#15668000	—	2	1	no	—
63	#15667991	—	2	1	no	—
64	#15667991	—	2	1	no	—
65	#15667986	—	2	1	no	—
66	#15667986	—	2	1	no	—
67	C₄×Dic₁₇₈	—	2	1	no	—
68	C₄×Dic₁₇₈	—	2	1	no	—
69	C₄×Dic₁₇₈	—	2	1	no	—
70	C₄×Dic₁₇₈	—	2	1	no	—
71	C₄×Dic₁₇₈	D₄	1	2	yes	—
72	C₄×Dic₁₇₈	C₂³	1	2	yes	—
73	C₄×D₃₅₆	—	2	1	no	—
74	C₄×D₃₅₆	—	2	1	no	—
75	#15667971	—	2	1	no	—
76	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
77	C₂×#13083553	—	2	1	no	—
78	C₂×C₄×Dic₈₉	—	2	1	no	—
79	#15667946	—	2	2	no	—
80	#15667944	—	2	2	no	—
81	#15667944	—	2	1	no	—
82	#15667944	—	2	1	no	—
83	C₄⋊#10623494	—	2	1	no	—
84	C₄⋊#10623494	C₂³	1	2	yes	—
85	#15667941	—	2	2	no	—
86	#15667941	—	2	2	no	—
87	#15667937	—	2	2	no	—
88	#15667937	—	2	2	no	—
89	#15667937	—	2	2	no	—
90	#15667937	—	2	1	no	—
91	#15667937	—	2	1	no	—
92	#15667934	—	2	2	no	—
93	#15667934	—	2	1	no	—
94	#15667934	—	2	1	no	—
95	C₈×Dic₈₉	—	2	2	no	—
96	C₈×Dic₈₉	—	2	2	no	—
97	C₂×M₁₆×C₈₉	—	2	1	no	—
98	C₂×M₁₆×C₈₉	—	2	1	no	—
99	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
100	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₈₉	—	2	1	no	—
103	C₄⋊C₈×C₈₉	—	2	1	no	—
104	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
105	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
106	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
108	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	#13083574	—	4	2	no	—
111	#13083574	—	4	2	no	—
112	C₂×Dic₁₇₈	—	2	1	no	—
113	C₂×Dic₁₇₈	—	2	2	no	—
114	C₂×Dic₁₇₈	—	2	1	no	—
115	C₂×Dic₁₇₈	—	2	1	no	—
116	C₂×Dic₁₇₈	—	2	1	no	—
117	C₂×Dic₁₇₈	SD₁₆	1	4	yes	complemented
118	C₂×Dic₁₇₈	C₂×D₄	1	2	yes	—
119	C₂×D₃₅₆	—	2	1	no	—
120	C₂×D₃₅₆	—	2	1	no	—
121	C₂×D₃₅₆	—	2	1	no	—
122	C₂×C₂²⋊D₈₉	—	4	1	no	—
123	C₂²×Dic₈₉	—	2	1	no	—
124	C₂²×Dic₈₉	—	2	1	no	—
125	C₂×C₄×D₈₉	—	4	1	no	—
126	Dic₃₅₆	—	4	4	no	—
127	#13083563	—	4	2	no	—
128	#13083563	—	4	4	no	—
129	#13083563	—	4	2	no	—
130	C₂×#10623494	—	2	2	no	—
131	C₂×#10623494	—	4	2	no	—
132	C₄⋊Dic₈₉	—	2	1	no	—
133	C₄⋊Dic₈₉	—	2	1	no	—
134	C₄⋊Dic₈₉	—	2	1	no	—
135	C₄⋊Dic₈₉	—	2	1	no	—
136	C₄⋊Dic₈₉	—	2	1	no	—
137	C₄⋊Dic₈₉	—	2	1	no	—
138	C₄⋊Dic₈₉	—	2	1	no	—
139	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
140	#13083553	—	2	2	no	—
141	#13083553	—	2	2	no	—
142	#13083553	—	4	1	no	—
143	#13083553	—	4	1	no	—
144	C₂²⋊Dic₈₉	—	4	1	no	—
145	#13083551	—	4	1	no	—
146	#13083551	—	4	1	no	—
147	C₄×Dic₈₉	—	2	2	no	—
148	C₄×Dic₈₉	—	2	2	no	—
149	C₄×Dic₈₉	—	4	1	no	—
150	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
153	M₁₆×C₈₉	—	4	2	no	—
154	M₁₆×C₈₉	—	4	2	no	—
155	C₂×C₈×C₈₉	—	2	2	no	—
156	C₂×C₈×C₈₉	—	2	2	no	—
157	C₂×C₈×C₈₉	—	2	2	no	—
158	C₂×C₈×C₈₉	—	4	1	no	—
159	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₈₉	#41	1	1	yes	characteristic
166	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
167	C₂³×C₈₉	#121	1	1	yes	characteristic
168	C₂²×D₈₉	—	4	1	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	#121	1	1	yes	characteristic
173	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
176	C₂×C₄×C₈₉	#135	1	2	yes	—
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	2	no	—
181	C₂×Dic₈₉	—	2	2	no	—
182	C₂×Dic₈₉	—	2	4	no	—
183	C₂×Dic₈₉	—	2	2	no	—
184	C₂×Dic₈₉	—	4	2	no	—
185	C₂×Dic₈₉	—	4	1	no	—
186	C₂×Dic₈₉	—	4	1	no	—
187	C₂×Dic₈₉	—	4	1	no	—
188	D₃₅₆	—	4	1	no	—
189	D₃₅₆	—	4	1	no	—
190	D₃₅₆	—	4	1	no	—
191	D₃₅₆	—	4	1	no	—
192	D₃₅₆	—	8	1	no	—
193	C₄×D₈₉	—	8	2	no	—
194	Dic₁₇₈	—	2	2	no	—
195	Dic₁₇₈	—	2	4	no	—
196	Dic₁₇₈	—	4	1	no	—
197	Dic₁₇₈	—	4	1	no	—
198	Dic₁₇₈	—	4	1	no	—
199	Dic₁₇₈	—	4	1	no	—
200	Dic₁₇₈	—	8	1	no	—
201	Dic₁₇₈	C₂×SD₁₆	1	4	yes	—
202	C₈×C₈₉	—	2	1	no	—
203	C₈×C₈₉	—	2	1	no	—
204	C₈×C₈₉	—	2	1	no	—
205	C₈×C₈₉	—	4	2	no	—
206	C₈×C₈₉	—	4	2	no	—
207	C₈×C₈₉	#137	1	2	yes	complemented
208	#10623494	—	4	2	no	—
209	C₂²×C₈₉	—	2	1	no	—
210	C₂²×C₈₉	—	2	1	no	—
211	C₂²×C₈₉	#465	1	2	yes	—
212	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
213	C₂×D₈₉	—	8	1	no	—
214	C₂×D₈₉	—	8	1	no	—
215	C₂×D₈₉	—	8	1	no	—
216	C₄×C₈₉	—	2	1	no	—
217	C₄×C₈₉	—	2	1	no	—
218	C₄×C₈₉	—	2	1	no	—
219	C₄×C₈₉	#465	1	2	yes	—
220	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
221	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
222	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
223	C₄×C₈₉	#575	1	1	yes	characteristic
224	Dic₈₉	—	2	4	no	—
225	Dic₈₉	—	4	2	no	—
226	Dic₈₉	—	8	1	no	—
227	Dic₈₉	—	8	1	no	—
228	Dic₈₉	—	8	1	no	—
229	#19260	—	89	1	no	maximal, Sylow
230	C₂×C₈₉	—	2	2	no	—
231	C₂×C₈₉	#3037	1	1	yes	characteristic
232	C₂×C₈₉	C₂×#465	1	1	yes	characteristic
233	C₂×C₈₉	#3067	1	1	yes	characteristic
234	D₈₉	—	16	1	no	—
235	#3167	—	89	1	no	—
236	#3078	—	89	1	no	—
237	#3037	—	89	1	no	—
238	C₂×C₈×Q₈	—	89	1	no	—
239	#1680	—	89	2	no	—
240	#1678	—	89	2	no	—
241	#1672	—	89	2	no	—
242	#1666	—	89	2	no	—
243	#1566	D₈₉	1	1	yes	characteristic, complemented
244	#1550	—	89	1	no	—
245	#1547	—	89	1	no	—
246	C₈₉	#19260	1	1	yes	characteristic, complemented, Sylow
247	C₂×#137	—	178	1	no	—
248	#533	—	89	1	no	—
249	#532	—	89	1	no	—
250	C₂×C₄×Q₈	—	89	1	no	—
251	#498	—	89	1	no	—
252	#492	—	89	1	no	—
253	#487	—	89	1	no	—
254	#486	—	89	1	no	—
255	#479	—	178	2	no	—
256	#477	—	89	2	no	—
257	#475	—	89	2	no	—
258	#465	—	178	1	no	—
259	#465	—	178	1	no	—
260	#464	—	178	2	no	—
261	#462	—	89	2	no	—
262	#460	—	89	2	no	—
263	C₈×Q₈	—	89	2	no	—
264	C₈×Q₈	—	89	2	no	—
265	C₈×Q₈	—	178	1	no	—
266	C₈×Q₈	—	178	1	no	—
267	C₄×SD₁₆	—	178	1	no	—
268	C₄×SD₁₆	—	178	1	no	—
269	#428	—	178	1	no	—
270	#423	C₂×D₈₉	1	1	yes	characteristic
271	#423	C₂×D₈₉	1	1	yes	characteristic
272	C₂×C₄⋊C₈	—	89	1	no	—
273	C₂×C₄⋊C₈	—	178	1	no	—
274	#419	—	178	1	no	—
275	#417	—	178	1	no	—
276	C₂×C₄×C₈	—	178	1	no	—
277	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
278	#334	C₂×D₈₉	1	2	yes	—
279	#334	C₂×D₈₉	1	2	yes	—
280	#333	—	89	2	no	—
281	#332	—	89	2	no	—
282	#332	—	89	2	no	—
283	#331	—	89	2	no	—
284	C₂×#41	—	178	1	no	—
285	C₂²×Q₈	—	89	1	no	—
286	#137	—	356	4	no	—
287	C₂×Q₁₆	—	178	2	no	—
288	C₂×SD₁₆	—	178	2	no	—
289	C₂×SD₁₆	—	178	1	no	—
290	C₂×SD₁₆	—	178	1	no	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂×M₁₆	—	2	1	no	—
293	C₂²×C₈	—	178	1	no	—
294	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
295	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
296	C₄⋊Q₈	—	89	1	no	—
297	C₄⋊Q₈	—	89	1	no	—
298	C₄⋊Q₈	—	89	1	no	—
299	#127	—	89	1	no	—
300	#125	—	178	1	no	—
301	#124	—	178	1	no	—
302	C₂²⋊Q₈	—	178	1	no	—
303	C₂²⋊Q₈	—	178	1	no	—
304	#121	—	178	1	no	—
305	#121	—	178	1	no	—
306	C₄×Q₈	—	89	2	no	—
307	C₄×Q₈	—	89	2	no	—
308	C₄×Q₈	—	178	1	no	—
309	C₄×Q₈	—	178	1	no	—
310	C₄×Q₈	—	178	1	no	—
311	C₄×Q₈	—	178	1	no	—
312	C₄×D₄	—	178	1	no	—
313	C₄×D₄	—	178	1	no	—
314	#117	—	178	1	no	—
315	C₂×C₄⋊C₄	—	89	1	no	—
316	C₂×C₄⋊C₄	—	178	1	no	—
317	C₂×C₄²	—	178	1	no	—
318	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
319	#107	—	178	2	no	—
320	#106	—	178	2	no	—
321	#106	—	178	1	no	—
322	#106	—	178	1	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	—	89	2	no	—
326	C₄⋊C₈	—	178	2	no	—
327	C₄⋊C₈	—	178	2	no	—
328	C₄⋊C₈	—	178	1	no	—
329	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
330	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
331	#103	—	178	2	no	—
332	#103	—	178	2	no	—
333	#103	—	178	2	no	—
334	#103	—	178	1	no	—
335	#103	—	178	1	no	—
336	#102	—	178	2	no	—
337	#102	—	178	1	no	—
338	#102	—	178	1	no	—
339	C₄×C₈	—	178	2	no	—
340	C₄×C₈	—	178	2	no	—
341	C₄×C₈	D₃₅₆	1	1	yes	characteristic
342	C₄×C₈	D₃₅₆	1	1	yes	characteristic
343	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
344	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
345	#41	—	356	2	no	—
346	#41	—	356	2	no	—
347	C₂×Q₈	—	89	4	no	—
348	C₂×Q₈	—	89	2	no	—
349	C₂×Q₈	—	178	1	no	—
350	C₂×Q₈	—	178	1	no	—
351	C₂×Q₈	—	178	1	no	—
352	C₂×Q₈	—	178	1	no	—
353	C₂×Q₈	—	178	2	no	—
354	C₂×D₄	—	356	1	no	—
355	C₂×D₄	—	178	1	no	—
356	C₂×D₄	—	178	1	no	—
357	C₂×D₄	—	178	1	no	—
358	C₂²×C₄	—	356	1	no	—
359	C₂²×C₄	—	178	1	no	—
360	C₂²×C₄	—	178	1	no	—
361	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
363	C₂²×C₄	#13083575	1	1	yes	characteristic
364	Q₁₆	—	356	4	no	—
365	SD₁₆	—	356	2	no	—
366	SD₁₆	—	356	4	no	—
367	SD₁₆	—	356	2	no	—
368	M₁₆	—	4	2	no	—
369	M₁₆	—	4	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	—	356	2	no	—
375	C₂×C₈	—	178	2	no	—
376	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
377	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
378	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
379	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
380	C₄⋊C₄	—	89	2	no	—
381	C₄⋊C₄	—	356	1	no	—
382	C₄⋊C₄	—	356	1	no	—
383	C₄⋊C₄	—	178	1	no	—
384	C₄⋊C₄	—	178	1	no	—
385	C₄⋊C₄	—	178	1	no	—
386	C₄⋊C₄	—	178	1	no	—
387	C₄⋊C₄	—	178	1	no	—
388	C₄⋊C₄	—	178	1	no	—
389	C₄⋊C₄	—	178	1	no	—
390	C₄⋊C₄	—	178	2	no	—
391	C₄⋊C₄	—	178	2	no	—
392	C₂²⋊C₄	—	356	1	no	—
393	C₂²⋊C₄	—	356	1	no	—
394	C₂²⋊C₄	—	356	1	no	—
395	C₄²	—	356	1	no	—
396	C₄²	—	178	2	no	—
397	C₄²	—	178	2	no	—
398	C₄²	D₄×D₈₉	1	1	yes	characteristic
399	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
400	C₄²	#13083575	1	1	yes	characteristic
401	C₄²	C₂³×D₈₉	1	1	yes	characteristic
402	C₂³	—	356	1	no	—
403	C₂³	#15667987	1	1	yes	characteristic
404	Q₈	—	89	4	no	—
405	Q₈	—	356	1	no	—
406	Q₈	—	356	1	no	—
407	Q₈	—	356	1	no	—
408	Q₈	—	356	1	no	—
409	Q₈	—	178	4	no	—
410	Q₈	—	178	2	no	—
411	Q₈	—	712	1	no	—
412	D₄	—	356	1	no	—
413	D₄	—	356	1	no	—
414	D₄	—	356	1	no	—
415	D₄	—	356	1	no	—
416	D₄	—	712	1	no	—
417	D₄	—	712	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	356	2	no	—
422	C₂×C₄	—	356	1	no	—
423	C₂×C₄	—	356	1	no	—
424	C₂×C₄	—	356	1	no	—
425	C₂×C₄	—	178	2	no	—
426	C₂×C₄	—	178	4	no	—
427	C₂×C₄	—	178	2	no	—
428	C₂×C₄	—	712	2	no	—
429	C₂×C₄	#15667987	1	1	yes	characteristic
430	C₂×C₄	#15667987	1	1	yes	characteristic
431	C₂×C₄	#15667987	1	1	yes	characteristic
432	C₂×C₄	SD₁₆×D₈₉	1	2	yes	—
433	C₂×C₄	#15668033	1	2	yes	—
434	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
436	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	2	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	2	no	—
442	C₈	—	356	2	no	—
443	C₈	#15668045	1	2	yes	complemented
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	712	1	no	—
447	C₂²	—	712	1	no	—
448	C₂²	—	712	1	no	—
449	C₂²	#19151828	1	2	yes	—
450	C₂²	C₂×#15667987	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	356	2	no	—
455	C₄	—	178	4	no	—
456	C₄	—	712	1	no	—
457	C₄	—	712	1	no	—
458	C₄	—	712	1	no	—
459	C₄	#19151828	1	2	yes	—
460	C₄	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
461	C₄	C₂×#15668033	1	1	yes	characteristic
462	C₄	C₂×#15668045	1	1	yes	characteristic
463	C₄	#19152398	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	1424	1	no	—
466	C₂	#26029726	1	1	yes	characteristic
467	C₂	C₂×#19151828	1	1	yes	characteristic
468	C₂	#26029973	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667987
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1566	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#19152148	C₂²
hypercenter	#1566	D₈₉
hypocenter	C₈₉	#19260
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1566

Complements

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

N	H ≅ G/N	type
2. #26030059	C₂	semidirect
4. C₂×C₈×Dic₁₇₈	C₂	semidirect
5. #26019683	C₂	semidirect
6. #26019669	C₂	semidirect
7. #26019635	C₂	semidirect
8. #26019601	C₂	semidirect
9. #26018943	C₂	semidirect
11. C₈₉×#1566	C₂	semidirect
117. C₂×Dic₁₇₈	SD₁₆	semidirect
207. C₈×C₈₉	#137	semidirect
243. #1566	D₈₉	semidirect
246. C₈₉	#19260	semidirect
443. C₈	#15668045	semidirect

Maximal subgroups

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

subgroup	index
#26030811	2
#26030059	2
#26029726	2
C₂×C₈×Dic₁₇₈	2
#26019683	2
#26019669	2
#26019635	2
#26019601	2
#26018943	2
#26018930	2
C₈₉×#1566	2
#19260	89