Subgroups — #36538224

Order 22784.

690 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	#26030834	C₂	1	1	yes	maximal, characteristic, complemented
2	#26030051	C₂	1	1	yes	maximal, characteristic
3	#26030045	C₂	1	1	yes	maximal, characteristic
4	C₂×#19151663	C₂	1	1	yes	maximal, characteristic
5	#26019706	C₂	1	2	yes	maximal, complemented
6	#26019702	C₂	1	2	yes	maximal, complemented
7	#26019650	C₂	1	2	yes	maximal, complemented
8	#26019616	C₂	1	2	yes	maximal, complemented
9	#26019010	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018940	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₈₉	—	2	1	no	—
13	#19152155	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
15	#19152001	C₂²	1	1	yes	characteristic, complemented
16	#19151977	C₂²	1	1	yes	characteristic, complemented
17	#19151950	C₂²	1	1	yes	characteristic, complemented
18	#19151948	C₂²	1	1	yes	characteristic, complemented
19	#19151899	—	2	2	no	—
20	#19151895	—	2	2	no	—
21	#19151889	C₂²	1	2	yes	—
22	#19151885	C₂²	1	2	yes	—
23	#19151879	C₂²	1	2	yes	—
24	#19151875	C₂²	1	2	yes	—
25	#19151837	—	2	1	no	—
26	#19151837	—	2	1	no	—
27	C₄×#13083564	—	2	1	no	—
28	C₄×#13083564	—	2	1	no	—
29	#19151663	—	2	1	no	—
30	#19151663	—	2	1	no	—
31	#19151663	C₂²	1	2	yes	—
32	#19151663	C₂²	1	2	yes	—
33	#19151641	—	2	1	no	—
34	#19151640	—	2	1	no	—
35	#19151622	C₂²	1	1	yes	characteristic
36	#19151604	—	2	1	no	—
37	#19151602	—	2	1	no	—
38	C₂×#15667924	—	2	1	no	—
39	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
40	#19151350	C₂²	1	2	yes	complemented
41	#19151350	C₂²	1	2	yes	complemented
42	#19151346	C₂²	1	2	yes	complemented
43	#19151345	C₂²	1	2	yes	complemented
44	#533×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	#333×C₈₉	C₂²	1	2	yes	complemented
48	#332×C₈₉	C₂²	1	2	yes	complemented
49	C₂²×D₃₅₆	D₄	1	1	yes	characteristic
50	C₂²×C₄×D₈₉	—	2	1	no	—
51	C₂×#13083564	—	2	1	no	—
52	C₂×#13083564	—	2	1	no	—
53	C₂×#13083558	—	2	1	no	—
54	C₂²×#10623494	D₄	1	1	yes	characteristic
55	C₂²×#10623494	D₄	1	1	yes	characteristic
56	C₂×C₈×D₈₉	—	2	2	no	—
57	C₂×C₈×D₈₉	—	2	2	no	—
58	C₂×C₈×D₈₉	—	4	4	no	—
59	#15668012	C₂³	1	1	yes	characteristic
60	#15668012	C₂³	1	1	yes	characteristic
61	#15668004	—	2	1	no	—
62	#15667991	—	2	1	no	—
63	#15667991	—	2	1	no	—
64	C₄×Dic₁₇₈	—	2	1	no	—
65	C₄×Dic₁₇₈	—	2	1	no	—
66	C₄×D₃₅₆	—	2	1	no	—
67	C₄×D₃₅₆	—	2	1	no	—
68	C₄×D₃₅₆	D₄	1	2	yes	—
69	C₄×D₃₅₆	C₂³	1	2	yes	—
70	#15667971	—	2	1	no	—
71	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
72	C₂×#13083551	—	2	1	no	—
73	#15667946	—	2	2	no	—
74	#15667945	—	2	1	no	—
75	#15667945	—	2	1	no	—
76	#15667945	—	2	2	no	—
77	#15667944	—	2	2	no	—
78	#15667943	—	2	2	no	—
79	C₄⋊#10623494	—	2	1	no	—
80	C₄⋊#10623494	C₂³	1	2	yes	—
81	#15667936	—	2	1	no	—
82	#15667936	—	2	1	no	—
83	#15667935	—	2	1	no	—
84	#15667935	—	2	1	no	—
85	#15667934	—	2	2	no	—
86	#15667934	—	2	2	no	—
87	#15667932	—	2	2	no	—
88	#15667932	—	2	2	no	—
89	#15667924	—	2	2	no	—
90	#15667924	—	2	2	no	—
91	C₄×#10623494	D₄	1	1	yes	characteristic
92	C₄×#10623494	D₄	1	1	yes	characteristic
93	C₄×#10623494	C₂³	1	1	yes	characteristic
94	C₄×#10623494	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₈₉	—	2	1	no	—
96	C₂²×C₈×C₈₉	—	2	1	no	—
97	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
99	#125×C₈₉	—	2	1	no	—
100	C₂²⋊Q₈×C₈₉	—	2	1	no	—
101	C₂²⋊Q₈×C₈₉	—	2	1	no	—
102	C₄×Q₈×C₈₉	—	2	1	no	—
103	C₄×Q₈×C₈₉	—	2	1	no	—
104	#117×C₈₉	—	2	1	no	—
105	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
106	C₄⋊C₈×C₈₉	—	2	1	no	—
107	C₄⋊C₈×C₈₉	—	2	1	no	—
108	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
109	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
110	C₂³×D₈₉	—	2	1	no	—
111	C₂×Dic₁₇₈	—	2	1	no	—
112	C₂×Dic₁₇₈	—	2	1	no	—
113	C₂×D₃₅₆	—	2	1	no	—
114	C₂×D₃₅₆	—	2	2	no	—
115	C₂×D₃₅₆	Q₁₆	1	4	yes	complemented
116	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
117	C₂²×Dic₈₉	—	2	1	no	—
118	C₂×C₄×D₈₉	—	2	2	no	—
119	C₂×C₄×D₈₉	—	2	2	no	—
120	C₂×C₄×D₈₉	—	4	2	no	—
121	C₂×C₄×D₈₉	—	4	2	no	—
122	#13083564	—	4	2	no	—
123	#13083564	—	4	2	no	—
124	#13083558	—	4	2	no	—
125	C₂×#10623494	—	2	2	no	—
126	C₂×#10623494	—	2	2	no	—
127	C₂×#10623494	—	4	1	no	—
128	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
129	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
130	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
131	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
132	C₈×D₈₉	—	4	4	no	—
133	C₈×D₈₉	—	4	4	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	—	4	1	no	—
141	#13083553	—	4	1	no	—
142	C₂²⋊Dic₈₉	—	4	1	no	—
143	#13083551	—	2	2	no	—
144	#13083551	—	2	2	no	—
145	C₄×Dic₈₉	—	4	1	no	—
146	C₂×Q₈×C₈₉	—	2	1	no	—
147	C₂×Q₈×C₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
151	M₁₆×C₈₉	—	4	2	no	—
152	C₂×C₈×C₈₉	—	2	2	no	—
153	C₂×C₈×C₈₉	—	2	2	no	—
154	C₂×C₈×C₈₉	—	4	2	no	—
155	C₄⋊C₄×C₈₉	—	2	1	no	—
156	C₄⋊C₄×C₈₉	—	2	1	no	—
157	C₄⋊C₄×C₈₉	—	2	1	no	—
158	C₄⋊C₄×C₈₉	—	2	1	no	—
159	C₄⋊C₄×C₈₉	—	4	1	no	—
160	C₄⋊C₄×C₈₉	—	4	1	no	—
161	C₂²⋊C₄×C₈₉	—	4	1	no	—
162	C₄²×C₈₉	—	4	1	no	—
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	—	2	2	no	—
169	C₂²×D₈₉	—	2	4	no	—
170	C₂²×D₈₉	—	4	2	no	—
171	C₂²×D₈₉	—	4	2	no	—
172	Q₈×C₈₉	—	4	1	no	—
173	Q₈×C₈₉	—	4	1	no	—
174	Q₈×C₈₉	—	8	1	no	—
175	C₂×C₄×C₈₉	—	2	1	no	—
176	C₂×C₄×C₈₉	—	2	1	no	—
177	C₂×C₄×C₈₉	—	4	1	no	—
178	C₂×C₄×C₈₉	—	4	1	no	—
179	C₂×C₄×C₈₉	—	4	1	no	—
180	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
184	C₂×C₄×C₈₉	#135	1	2	yes	—
185	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
188	C₂×Dic₈₉	—	2	2	no	—
189	C₂×Dic₈₉	—	4	2	no	—
190	C₂×Dic₈₉	—	4	1	no	—
191	C₂×Dic₈₉	—	4	1	no	—
192	D₃₅₆	—	2	2	no	—
193	D₃₅₆	—	2	4	no	—
194	D₃₅₆	C₂×Q₁₆	1	4	yes	—
195	C₄×D₈₉	—	4	4	no	—
196	C₄×D₈₉	—	4	2	no	—
197	C₄×D₈₉	—	4	2	no	—
198	Dic₁₇₈	—	4	1	no	—
199	Dic₁₇₈	—	4	1	no	—
200	Dic₁₇₈	—	8	1	no	—
201	C₈×C₈₉	—	4	2	no	—
202	C₈×C₈₉	—	4	2	no	—
203	#10623494	—	2	1	no	—
204	#10623494	—	2	1	no	—
205	#10623494	—	2	1	no	—
206	#10623494	—	4	2	no	—
207	#10623494	AGL(1,ℤ/8)	1	2	yes	—
208	C₂²×C₈₉	—	2	1	no	—
209	C₂²×C₈₉	—	2	1	no	—
210	C₂²×C₈₉	#467	1	2	yes	—
211	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
212	C₂×D₈₉	—	2	4	no	—
213	C₂×D₈₉	—	4	8	no	—
214	C₂×D₈₉	—	4	2	no	—
215	C₂×D₈₉	—	4	2	no	—
216	C₄×C₈₉	—	2	1	no	—
217	C₄×C₈₉	—	2	1	no	—
218	C₄×C₈₉	—	2	1	no	—
219	C₄×C₈₉	—	8	1	no	—
220	C₄×C₈₉	—	8	1	no	—
221	C₄×C₈₉	#467	1	2	yes	—
222	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
223	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
224	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
225	C₄×C₈₉	#575	1	1	yes	characteristic
226	Dic₈₉	—	4	2	no	—
227	Dic₈₉	—	8	1	no	—
228	Dic₈₉	—	8	1	no	—
229	#19256	—	89	1	no	maximal, Sylow
230	C₂×C₈₉	—	2	2	no	—
231	C₂×C₈₉	#3036	1	1	yes	characteristic
232	C₂×C₈₉	C₂×#467	1	1	yes	characteristic
233	C₂×C₈₉	#3067	1	1	yes	characteristic
234	D₈₉	—	4	4	no	—
235	#3170	—	89	1	no	—
236	#3077	—	89	1	no	—
237	#3077	—	89	1	no	—
238	C₂×C₈×D₄	—	89	1	no	—
239	#1683	—	89	2	no	—
240	#1683	—	89	2	no	—
241	#1675	—	89	2	no	—
242	#1669	—	89	2	no	—
243	#1567	—	89	1	no	—
244	#1550	—	89	1	no	—
245	#1550	D₈₉	1	1	yes	characteristic, complemented
246	C₈₉	#19256	1	1	yes	characteristic, complemented, Sylow
247	C₂³×C₈	—	178	1	no	—
248	#533	—	89	1	no	—
249	#533	C₂×D₈₉	1	1	yes	characteristic
250	C₂×C₄×D₄	—	89	1	no	—
251	#500	—	89	1	no	—
252	#494	—	89	1	no	—
253	#487	—	89	1	no	—
254	#487	—	89	1	no	—
255	#478	—	178	2	no	—
256	#478	—	178	2	no	—
257	#476	—	89	2	no	—
258	#476	—	89	2	no	—
259	#474	—	89	2	no	—
260	#474	—	89	2	no	—
261	#467	—	178	1	no	—
262	#467	—	178	1	no	—
263	C₄×Q₁₆	—	178	1	no	—
264	C₄×Q₁₆	—	178	1	no	—
265	C₈×D₄	—	89	2	no	—
266	C₈×D₄	—	89	2	no	—
267	C₈×D₄	—	178	1	no	—
268	C₈×D₄	—	178	1	no	—
269	#428	—	178	1	no	—
270	#428	—	178	1	no	—
271	#423	—	89	1	no	—
272	#423	C₂×D₈₉	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
274	#418	—	178	1	no	—
275	#418	—	178	1	no	—
276	C₂×C₂²⋊C₈	—	178	1	no	—
277	C₂×C₄×C₈	—	89	1	no	—
278	#335	—	89	2	no	—
279	#335	—	89	2	no	—
280	#333	—	89	2	no	—
281	#333	C₂×D₈₉	1	2	yes	complemented
282	#332	—	89	2	no	—
283	#332	C₂×D₈₉	1	2	yes	complemented
284	C₂²×D₄	—	89	1	no	—
285	C₂³×C₄	—	178	1	no	—
286	C₂×Q₁₆	—	178	1	no	—
287	C₂×Q₁₆	—	178	1	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₂×M₁₆	—	178	1	no	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	—	89	1	no	—
292	C₂²×C₈	—	89	1	no	—
293	C₂²×C₈	—	356	4	no	—
294	C₂²×C₈	—	178	2	no	—
295	C₂²×C₈	—	178	2	no	—
296	C₄⋊Q₈	—	89	1	no	—
297	C₄⋊Q₈	—	89	1	no	—
298	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
299	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
300	#125	—	2	1	no	—
301	#125	—	178	1	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	—	2	1	no	—
304	C₂²⋊Q₈	—	178	1	no	—
305	C₂²⋊Q₈	—	178	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	178	1	no	—
309	C₄×Q₈	—	178	1	no	—
310	C₄×D₄	—	89	2	no	—
311	C₄×D₄	—	89	2	no	—
312	C₄×D₄	—	178	1	no	—
313	C₄×D₄	—	178	1	no	—
314	#117	—	2	1	no	—
315	#117	—	178	1	no	—
316	C₂×C₄⋊C₄	—	89	1	no	—
317	C₂×C₂²⋊C₄	—	178	1	no	—
318	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
319	#107	—	178	2	no	—
320	#107	—	178	1	no	—
321	#107	—	178	1	no	—
322	#107	—	178	2	no	—
323	#106	—	178	2	no	—
324	#106	—	178	2	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	—	89	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	1	no	—
332	#103	—	178	1	no	—
333	#103	—	178	1	no	—
334	#103	—	178	1	no	—
335	#102	—	178	2	no	—
336	#102	—	178	2	no	—
337	#102	—	178	2	no	—
338	#102	—	178	2	no	—
339	C₂²⋊C₈	—	178	2	no	—
340	C₂²⋊C₈	—	178	2	no	—
341	C₄×C₈	—	89	1	no	—
342	C₄×C₈	—	89	1	no	—
343	C₄×C₈	—	89	1	no	—
344	C₄×C₈	—	89	1	no	—
345	C₂⁴	—	178	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	178	1	no	—
349	C₂×Q₈	—	178	1	no	—
350	C₂×D₄	—	89	4	no	—
351	C₂×D₄	—	89	2	no	—
352	C₂×D₄	—	178	1	no	—
353	C₂×D₄	—	178	2	no	—
354	C₂²×C₄	—	356	2	no	—
355	C₂²×C₄	—	356	2	no	—
356	C₂²×C₄	—	178	1	no	—
357	C₂²×C₄	—	178	2	no	—
358	C₂²×C₄	—	178	2	no	—
359	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
360	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
361	C₂²×C₄	#13083574	1	1	yes	characteristic
362	Q₁₆	—	356	2	no	—
363	Q₁₆	—	356	2	no	—
364	M₁₆	—	4	2	no	—
365	M₁₆	—	356	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	89	1	no	—
370	C₂×C₈	—	89	1	no	—
371	C₂×C₈	—	89	1	no	—
372	C₂×C₈	—	89	1	no	—
373	C₂×C₈	—	356	4	no	—
374	C₂×C₈	—	356	4	no	—
375	C₂×C₈	—	356	1	no	—
376	C₂×C₈	—	178	2	no	—
377	C₂×C₈	—	178	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	—	89	2	no	—
385	C₄⋊C₄	—	356	1	no	—
386	C₄⋊C₄	—	356	1	no	—
387	C₄⋊C₄	—	178	1	no	—
388	C₄⋊C₄	—	178	1	no	—
389	C₄⋊C₄	—	178	1	no	—
390	C₄⋊C₄	—	178	1	no	—
391	C₄⋊C₄	—	178	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	356	1	no	—
394	C₂²⋊C₄	—	178	2	no	—
395	C₂²⋊C₄	—	178	2	no	—
396	C₄²	—	4	1	no	—
397	C₄²	—	356	1	no	—
398	C₄²	D₄×D₈₉	1	1	yes	characteristic
399	C₄²	D₄×D₈₉	1	1	yes	characteristic
400	C₄²	#13083574	1	1	yes	characteristic
401	C₄²	C₂³×D₈₉	1	1	yes	characteristic
402	C₂³	—	356	2	no	—
403	C₂³	—	356	2	no	—
404	C₂³	—	178	2	no	—
405	C₂³	—	178	4	no	—
406	C₂³	#15667985	1	1	yes	characteristic
407	Q₈	—	4	1	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	8	1	no	—
410	Q₈	—	356	1	no	—
411	Q₈	—	356	1	no	—
412	Q₈	—	712	1	no	—
413	D₄	—	89	4	no	—
414	D₄	—	178	4	no	—
415	D₄	—	178	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	356	4	no	—
422	C₂×C₄	—	356	2	no	—
423	C₂×C₄	—	356	2	no	—
424	C₂×C₄	—	356	2	no	—
425	C₂×C₄	—	356	1	no	—
426	C₂×C₄	—	356	1	no	—
427	C₂×C₄	—	178	2	no	—
428	C₂×C₄	#15667985	1	1	yes	characteristic
429	C₂×C₄	#15667985	1	1	yes	characteristic
430	C₂×C₄	#15667985	1	1	yes	characteristic
431	C₂×C₄	Q₁₆×D₈₉	1	2	yes	—
432	C₂×C₄	#15668033	1	2	yes	—
433	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
434	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
435	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
436	C₈	—	4	2	no	—
437	C₈	—	4	2	no	—
438	C₈	—	89	2	no	—
439	C₈	—	356	2	no	—
440	C₈	—	178	1	no	—
441	C₈	—	178	1	no	—
442	C₈	—	178	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	356	8	no	—
446	C₂²	—	356	2	no	—
447	C₂²	—	356	2	no	—
448	C₂²	—	178	4	no	—
449	C₂²	#19151838	1	2	yes	—
450	C₂²	C₂×#15667985	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	1	no	—
456	C₄	—	356	2	no	—
457	C₄	—	712	1	no	—
458	C₄	—	712	1	no	—
459	C₄	#19151838	1	2	yes	—
460	C₄	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
461	C₄	C₂×#15668033	1	1	yes	characteristic
462	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
463	C₄	#19152397	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	356	4	no	—
466	C₂	#26029715	1	1	yes	characteristic
467	C₂	C₂×#19151838	1	1	yes	characteristic
468	C₂	#26029971	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667985
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1550	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂²×D₃₅₆	D₄
hypercenter	#1550	D₈₉
hypocenter	C₈₉	#19256
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1550

Complements

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

N	H ≅ G/N	type
1. #26030834	C₂	semidirect
5. #26019706	C₂	semidirect
6. #26019702	C₂	semidirect
7. #26019650	C₂	semidirect
8. #26019616	C₂	semidirect
9. #26019010	C₂	semidirect
10. #26018940	C₂	semidirect
11. C₈₉×#1550	C₂	semidirect
15. #19152001	C₂²	semidirect
16. #19151977	C₂²	semidirect
17. #19151950	C₂²	semidirect
18. #19151948	C₂²	semidirect
40. #19151350	C₂²	semidirect
41. #19151350	C₂²	semidirect
42. #19151346	C₂²	semidirect
43. #19151345	C₂²	semidirect
47. #333×C₈₉	C₂²	semidirect
48. #332×C₈₉	C₂²	semidirect
115. C₂×D₃₅₆	Q₁₆	semidirect
245. #1550	D₈₉	semidirect
246. C₈₉	#19256	semidirect
281. #333	C₂×D₈₉	semidirect
283. #332	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26030834	2
#26030051	2
#26030045	2
C₂×#19151663	2
#26019706	2
#26019702	2
#26019650	2
#26019616	2
#26019010	2
#26018940	2
C₈₉×#1550	2
#19256	89