Subgroups — #36538263

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	#26030812	C₂	1	1	yes	maximal, characteristic
2	#26029724	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019680	C₂	1	2	yes	maximal, complemented
5	#26019670	C₂	1	2	yes	maximal, complemented
6	#26019636	C₂	1	2	yes	maximal, complemented
7	#26019602	C₂	1	2	yes	maximal, complemented
8	#26019007	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018942	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018930	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668043	—	2	1	no	—
13	#19152148	C₂²	1	1	yes	characteristic
14	#19151994	C₂²	1	1	yes	characteristic
15	#19151972	C₂²	1	1	yes	characteristic
16	#19151948	C₂²	1	1	yes	characteristic
17	#19151946	C₂²	1	1	yes	characteristic
18	#19151829	—	2	1	no	—
19	#19151829	—	2	1	no	—
20	#19151820	—	2	2	no	—
21	#19151808	C₂²	1	2	yes	—
22	#19151798	C₂²	1	2	yes	—
23	Q₈×#10623494	—	2	1	no	—
24	Q₈×#10623494	—	2	1	no	—
25	Q₈×#10623494	C₂²	1	2	yes	—
26	Q₈×#10623494	C₂²	1	2	yes	—
27	C₄×#13083561	—	2	1	no	—
28	C₄×#13083561	—	2	1	no	—
29	#19151622	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊#10623494	—	2	1	no	—
31	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
32	#19151597	—	2	1	no	—
33	C₂×C₄×#10623494	—	2	1	no	—
34	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
35	#19151348	C₂²	1	2	yes	—
36	#19151348	C₂²	1	2	yes	—
37	#19151347	C₂²	1	2	yes	—
38	#19151345	C₂²	1	2	yes	—
39	#19151344	C₂²	1	2	yes	—
40	#19151341	C₂²	1	2	yes	—
41	#533×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
43	#479×C₈₉	—	2	2	no	—
44	#477×C₈₉	C₂²	1	2	yes	—
45	#475×C₈₉	C₂²	1	2	yes	—
46	#428×C₈₉	—	2	1	no	—
47	#423×C₈₉	C₂²	1	1	yes	characteristic
48	#419×C₈₉	—	2	1	no	—
49	C₂×#13083574	—	2	1	no	—
50	#15668043	—	4	4	no	—
51	C₂×#13083564	—	2	2	no	—
52	C₂×#13083561	—	2	1	no	—
53	C₂×#13083561	—	2	1	no	—
54	C₂×#13083561	—	2	2	no	—
55	C₂×#13083558	—	2	1	no	—
56	C₂²×#10623494	—	2	1	no	—
57	C₂²×#10623494	D₄	1	1	yes	characteristic
58	C₂²×#10623494	D₄	1	1	yes	characteristic
59	#15668012	C₂³	1	1	yes	characteristic
60	#15668009	C₂³	1	1	yes	characteristic
61	#15668000	—	2	1	no	—
62	#15667986	—	2	1	no	—
63	#15667986	—	2	1	no	—
64	C₄×D₃₅₆	—	2	1	no	—
65	C₄×D₃₅₆	—	2	1	no	—
66	#15667943	—	2	1	no	—
67	#15667943	—	2	1	no	—
68	C₄⋊#10623494	—	2	2	no	—
69	C₄⋊#10623494	—	2	2	no	—
70	C₄⋊#10623494	—	2	1	no	—
71	C₄⋊#10623494	—	2	1	no	—
72	C₄⋊#10623494	C₂³	1	2	yes	—
73	C₄⋊#10623494	C₂³	1	2	yes	—
74	#15667936	—	2	1	no	—
75	#15667936	—	2	1	no	—
76	#15667935	—	2	2	no	—
77	#15667932	—	2	1	no	—
78	#15667932	—	2	1	no	—
79	#15667932	—	2	2	no	—
80	C₄×#10623494	—	2	2	no	—
81	C₄×#10623494	—	2	2	no	—
82	C₄×#10623494	D₄	1	1	yes	characteristic
83	C₄×#10623494	D₄	1	1	yes	characteristic
84	C₄×#10623494	C₂³	1	1	yes	characteristic
85	C₄×#10623494	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
87	C₂×M₁₆×C₈₉	—	2	1	no	—
88	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
90	#125×C₈₉	—	2	1	no	—
91	C₂²⋊Q₈×C₈₉	—	2	1	no	—
92	C₂²⋊Q₈×C₈₉	—	2	1	no	—
93	C₄×Q₈×C₈₉	—	2	1	no	—
94	C₄×Q₈×C₈₉	—	2	1	no	—
95	C₄×Q₈×C₈₉	—	2	1	no	—
96	C₄×Q₈×C₈₉	—	2	1	no	—
97	C₄×Q₈×C₈₉	D₄	1	2	yes	—
98	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
99	#117×C₈₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₈₉	—	2	1	no	—
103	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
104	#107×C₈₉	—	2	2	no	—
105	#106×C₈₉	—	2	2	no	—
106	C₄⋊C₈×C₈₉	—	2	1	no	—
107	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
108	#103×C₈₉	—	2	2	no	—
109	#103×C₈₉	—	2	2	no	—
110	#13083574	—	4	2	no	—
111	#13083574	—	4	2	no	—
112	C₂×Dic₁₇₈	—	2	1	no	—
113	C₂×D₃₅₆	—	2	1	no	—
114	C₂×D₃₅₆	—	2	1	no	—
115	C₂×D₃₅₆	—	2	1	no	—
116	C₂×C₂²⋊D₈₉	—	4	1	no	—
117	C₂×C₄×D₈₉	—	4	1	no	—
118	#13083564	—	4	4	no	—
119	#13083561	—	4	2	no	—
120	#13083561	—	4	4	no	—
121	#13083561	—	4	2	no	—
122	#13083558	—	4	2	no	—
123	C₂×#10623494	—	2	2	no	—
124	C₂×#10623494	—	2	2	no	—
125	C₂×#10623494	—	2	2	no	—
126	C₂×#10623494	—	4	1	no	—
127	C₂×#10623494	—	4	2	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	C₄⋊Dic₈₉	—	2	1	no	—
133	C₄⋊Dic₈₉	—	2	1	no	—
134	#13083551	—	4	1	no	—
135	#13083551	—	4	1	no	—
136	C₂×Q₈×C₈₉	—	2	1	no	—
137	C₂×Q₈×C₈₉	—	2	2	no	—
138	C₂×Q₈×C₈₉	—	2	1	no	—
139	C₂×Q₈×C₈₉	—	2	1	no	—
140	C₂×Q₈×C₈₉	SD₁₆	1	4	yes	complemented
141	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₈₉	—	2	1	no	—
143	C₂²×C₄×C₈₉	—	2	1	no	—
144	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
147	M₁₆×C₈₉	—	4	2	no	—
148	C₂×C₈×C₈₉	—	2	2	no	—
149	C₄⋊C₄×C₈₉	—	2	2	no	—
150	C₄⋊C₄×C₈₉	—	2	1	no	—
151	C₄⋊C₄×C₈₉	—	2	2	no	—
152	C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₄⋊C₄×C₈₉	—	2	1	no	—
155	C₄⋊C₄×C₈₉	—	2	1	no	—
156	C₄⋊C₄×C₈₉	—	4	1	no	—
157	C₄⋊C₄×C₈₉	—	4	1	no	—
158	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
159	C₂²⋊C₄×C₈₉	—	4	1	no	—
160	C₄²×C₈₉	—	2	2	no	—
161	C₄²×C₈₉	—	2	2	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	—	4	1	no	—
169	Q₈×C₈₉	—	2	2	no	—
170	Q₈×C₈₉	—	2	4	no	—
171	Q₈×C₈₉	—	4	1	no	—
172	Q₈×C₈₉	—	4	1	no	—
173	Q₈×C₈₉	—	8	1	no	—
174	Q₈×C₈₉	C₂×SD₁₆	1	4	yes	—
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	2	4	no	—
177	C₂×C₄×C₈₉	—	2	1	no	—
178	C₂×C₄×C₈₉	—	2	1	no	—
179	C₂×C₄×C₈₉	—	2	2	no	—
180	C₂×C₄×C₈₉	—	4	1	no	—
181	C₂×C₄×C₈₉	—	4	2	no	—
182	C₂×C₄×C₈₉	—	4	1	no	—
183	C₂×C₄×C₈₉	—	4	1	no	—
184	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
186	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
188	C₂×C₄×C₈₉	#135	1	2	yes	—
189	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
192	C₂²⋊D₈₉	—	8	2	no	—
193	C₂×Dic₈₉	—	4	1	no	—
194	D₃₅₆	—	4	1	no	—
195	D₃₅₆	—	4	1	no	—
196	D₃₅₆	—	4	1	no	—
197	D₃₅₆	—	4	1	no	—
198	D₃₅₆	—	8	1	no	—
199	C₄×D₈₉	—	8	2	no	—
200	Dic₁₇₈	—	4	1	no	—
201	Dic₁₇₈	—	4	1	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	—	4	2	no	—
208	#10623494	#137	1	2	yes	complemented
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	4	no	—
218	C₄×C₈₉	—	2	1	no	—
219	C₄×C₈₉	—	2	1	no	—
220	C₄×C₈₉	—	4	2	no	—
221	C₄×C₈₉	—	8	1	no	—
222	C₄×C₈₉	—	8	1	no	—
223	C₄×C₈₉	#465	1	2	yes	—
224	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
225	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
226	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
227	C₄×C₈₉	#575	1	1	yes	characteristic
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	D₈₉	1	1	yes	characteristic, complemented
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	—	89	1	no	—
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	C₂×D₈₉	1	1	yes	characteristic
249	#532	—	89	1	no	—
250	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
251	#498	—	89	1	no	—
252	#492	—	89	1	no	—
253	#487	—	89	1	no	—
254	#486	—	89	1	no	—
255	#479	—	2	2	no	—
256	#477	C₂×D₈₉	1	2	yes	—
257	#475	C₂×D₈₉	1	2	yes	—
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	—	2	1	no	—
270	#423	—	89	1	no	—
271	#423	C₂×D₈₉	1	1	yes	characteristic
272	C₂×C₄⋊C₈	—	89	1	no	—
273	C₂×C₄⋊C₈	—	178	1	no	—
274	#419	—	2	1	no	—
275	#417	—	178	1	no	—
276	C₂×C₄×C₈	—	89	1	no	—
277	C₂×C₄×C₈	—	178	1	no	—
278	#334	—	89	2	no	—
279	#334	—	89	2	no	—
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	C₂²⋊D₈₉	1	1	yes	characteristic
286	#137	—	356	4	no	—
287	C₂×Q₁₆	—	178	2	no	—
288	C₂×SD₁₆	—	178	1	no	—
289	C₂×SD₁₆	—	178	1	no	—
290	C₂×SD₁₆	—	178	2	no	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂×M₁₆	—	178	1	no	—
293	C₂²×C₈	—	89	1	no	—
294	C₂²×C₈	—	89	1	no	—
295	C₂²×C₈	—	178	1	no	—
296	C₄⋊Q₈	—	89	1	no	—
297	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
298	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
299	#127	—	89	1	no	—
300	#125	—	2	1	no	—
301	#124	—	178	1	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	—	2	1	no	—
304	#121	—	178	1	no	—
305	#121	—	178	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	2	1	no	—
309	C₄×Q₈	—	2	1	no	—
310	C₄×Q₈	C₂²⋊D₈₉	1	2	yes	—
311	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
312	C₄×D₄	—	178	1	no	—
313	C₄×D₄	—	178	1	no	—
314	#117	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
319	#107	—	2	2	no	—
320	#106	—	2	2	no	—
321	#106	—	178	1	no	—
322	#106	—	178	1	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	89	2	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	—	178	1	no	—
330	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
331	#103	—	2	2	no	—
332	#103	—	2	2	no	—
333	#103	—	178	1	no	—
334	#103	—	178	1	no	—
335	#103	—	178	2	no	—
336	#102	—	178	1	no	—
337	#102	—	178	1	no	—
338	#102	—	178	2	no	—
339	C₄×C₈	—	89	1	no	—
340	C₄×C₈	—	89	1	no	—
341	C₄×C₈	—	89	1	no	—
342	C₄×C₈	—	89	1	no	—
343	C₄×C₈	—	178	2	no	—
344	C₄×C₈	—	178	2	no	—
345	#41	—	356	2	no	—
346	#41	—	356	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	178	1	no	—
352	C₂×Q₈	#13083561	1	4	yes	complemented
353	C₂×Q₈	C₂×C₂²⋊D₈₉	1	2	yes	—
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	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	356	1	no	—
361	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
362	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
363	C₂²×C₄	#13083573	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	—	356	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	89	1	no	—
372	C₂×C₈	—	89	1	no	—
373	C₂×C₈	—	89	1	no	—
374	C₂×C₈	—	89	1	no	—
375	C₂×C₈	—	356	2	no	—
376	C₂×C₈	—	356	1	no	—
377	C₂×C₈	—	178	2	no	—
378	C₂×C₈	—	178	2	no	—
379	C₂×C₈	—	178	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	—	178	1	no	—
390	C₄⋊C₄	—	178	1	no	—
391	C₄⋊C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	356	1	no	—
394	C₂²⋊C₄	—	356	1	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	4	1	no	—
398	C₄²	D₄×D₈₉	1	1	yes	characteristic
399	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
400	C₄²	#13083573	1	1	yes	characteristic
401	C₄²	C₂³×D₈₉	1	1	yes	characteristic
402	C₂³	—	356	1	no	—
403	C₂³	#15667984	1	1	yes	characteristic
404	Q₈	—	2	4	no	—
405	Q₈	—	2	2	no	—
406	Q₈	—	4	1	no	—
407	Q₈	—	4	1	no	—
408	Q₈	—	8	1	no	—
409	Q₈	—	356	1	no	—
410	Q₈	—	356	1	no	—
411	Q₈	C₂×#13083561	1	4	yes	—
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	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	356	1	no	—
428	C₂×C₄	—	712	2	no	—
429	C₂×C₄	#15667984	1	1	yes	characteristic
430	C₂×C₄	#15667984	1	1	yes	characteristic
431	C₂×C₄	#15667984	1	1	yes	characteristic
432	C₂×C₄	C₂×#13083561	1	2	yes	—
433	C₂×C₄	#15668032	1	2	yes	—
434	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
435	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
436	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
437	C₈	—	4	2	no	—
438	C₈	—	89	2	no	—
439	C₈	—	356	2	no	—
440	C₈	—	356	2	no	—
441	C₈	—	178	1	no	—
442	C₈	—	178	1	no	—
443	C₈	—	178	1	no	—
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	#19151829	1	2	yes	—
450	C₂²	C₂×#15667984	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	4	no	—
455	C₄	—	4	2	no	—
456	C₄	—	8	1	no	—
457	C₄	—	8	1	no	—
458	C₄	—	712	1	no	—
459	C₄	#19151829	1	2	yes	—
460	C₄	C₂²×#13083561	1	1	yes	characteristic
461	C₄	C₂×#15668032	1	1	yes	characteristic
462	C₄	#137×D₈₉	1	1	yes	characteristic
463	C₄	#19152397	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	1424	1	no	—
466	C₂	#26029721	1	1	yes	characteristic
467	C₂	C₂×#19151829	1	1	yes	characteristic
468	C₂	#26029969	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667984
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#3078	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#19152148	C₂²
hypercenter	#3078	D₈₉
hypocenter	C₈₉	#19260
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3078

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈×#10623494	C₂	semidirect
4. #26019680	C₂	semidirect
5. #26019670	C₂	semidirect
6. #26019636	C₂	semidirect
7. #26019602	C₂	semidirect
8. #26019007	C₂	semidirect
9. #26018942	C₂	semidirect
11. C₈₉×#3078	C₂	semidirect
140. C₂×Q₈×C₈₉	SD₁₆	semidirect
208. #10623494	#137	semidirect
236. #3078	D₈₉	semidirect
246. C₈₉	#19260	semidirect
352. C₂×Q₈	#13083561	semidirect

Maximal subgroups

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

subgroup	index
#26030812	2
#26029724	2
C₂×Q₈×#10623494	2
#26019680	2
#26019670	2
#26019636	2
#26019602	2
#26019007	2
#26018942	2
#26018930	2
C₈₉×#3078	2
#19260	89