Subgroups — #36536865

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	#26029707	C₂	1	2	yes	maximal, complemented
3	#26019696	C₂	1	2	yes	maximal, complemented
4	#26019689	C₂	1	2	yes	maximal, complemented
5	#26019646	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019641	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019612	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019607	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#19151351	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018899	C₂	1	2	yes	maximal, complemented
11	C₈×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668032	—	2	2	no	—
13	#19152148	C₂²	1	2	yes	—
14	#19152003	C₂²	1	1	yes	characteristic
15	#19151975	C₂²	1	1	yes	characteristic
16	#19151945	C₂²	1	2	yes	—
17	#19151834	—	2	1	no	—
18	#19151834	—	2	1	no	—
19	#19151820	—	2	2	no	—
20	#19151813	—	2	2	no	—
21	#19151808	C₂²	1	2	yes	—
22	#19151803	C₂²	1	2	yes	—
23	#19151798	C₂²	1	2	yes	—
24	#19151793	C₂²	1	2	yes	—
25	C₄×D₇₁₂	—	2	1	no	—
26	C₄×D₇₁₂	—	2	1	no	—
27	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
28	#19151592	—	2	2	no	—
29	#19151351	C₂²	1	1	yes	characteristic
30	#19151351	C₂²	1	1	yes	characteristic
31	#19151351	C₂²	1	2	yes	—
32	#19151343	C₂²	1	2	yes	—
33	#19151343	C₂²	1	2	yes	—
34	#19151341	C₂²	1	2	yes	—
35	#19151341	C₂²	1	2	yes	—
36	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
37	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₈₉	—	2	1	no	—
40	C₈×D₄×C₈₉	—	2	1	no	—
41	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
43	#431×C₈₉	—	2	1	no	—
44	#431×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₈₉	—	2	1	no	—
46	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	—	2	2	no	—
48	#15668032	—	4	8	no	—
49	C₂×#13083564	—	2	2	no	—
50	C₂×#13083562	—	2	2	no	—
51	C₂×#13083561	—	2	2	no	—
52	C₂×D₇₁₂	—	2	1	no	—
53	C₂×D₇₁₂	—	2	1	no	—
54	C₂×#13083559	—	2	2	no	—
55	C₂²×#10623494	—	2	2	no	—
56	#15668012	C₂³	1	2	yes	—
57	#15668009	C₂³	1	2	yes	—
58	#15668000	—	2	2	no	—
59	#15667986	—	2	2	no	—
60	#15667986	—	2	2	no	—
61	C₄×D₃₅₆	—	2	2	no	—
62	C₄×D₃₅₆	—	2	2	no	—
63	#15667946	—	2	1	no	—
64	#15667946	—	2	1	no	—
65	C₄⋊#10623494	—	2	2	no	—
66	C₄⋊#10623494	C₂³	1	2	yes	—
67	C₄⋊#10623494	C₂³	1	2	yes	—
68	#15667935	—	2	2	no	—
69	#15667935	—	2	2	no	—
70	#15667934	—	2	2	no	—
71	#15667934	—	2	2	no	—
72	#15667932	—	2	2	no	—
73	#15667932	—	2	2	no	—
74	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₈₉	—	2	1	no	—
76	C₂²×C₈×C₈₉	—	2	1	no	—
77	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
80	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
81	C₄×D₄×C₈₉	—	2	1	no	—
82	C₄×D₄×C₈₉	—	2	1	no	—
83	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
84	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
85	#117×C₈₉	—	2	1	no	—
86	#117×C₈₉	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₈₉	—	2	1	no	—
88	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₈₉	—	2	1	no	—
90	C₄⋊C₈×C₈₉	—	2	1	no	—
91	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂²⋊C₈×C₈₉	—	2	1	no	—
94	C₂²⋊C₈×C₈₉	—	2	1	no	—
95	C₂²⋊C₈×C₈₉	—	2	1	no	—
96	C₄×C₈×C₈₉	—	2	1	no	—
97	C₄×C₈×C₈₉	—	2	1	no	—
98	C₄×C₈×C₈₉	—	2	1	no	—
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	—	4	4	no	—
104	#13083574	—	4	4	no	—
105	C₂×Dic₁₇₈	—	2	2	no	—
106	C₂×D₃₅₆	—	2	2	no	—
107	C₂×D₃₅₆	—	2	2	no	—
108	C₂×D₃₅₆	—	2	2	no	—
109	C₂×C₂²⋊D₈₉	—	4	2	no	—
110	C₂×C₄×D₈₉	—	4	2	no	—
111	#13083564	—	4	4	no	—
112	#13083562	—	4	4	no	—
113	#13083561	—	4	4	no	—
114	D₇₁₂	—	4	2	no	—
115	D₇₁₂	—	4	2	no	—
116	#13083559	—	4	4	no	—
117	C₂×#10623494	—	2	2	no	—
118	C₂×#10623494	—	2	2	no	—
119	C₂×#10623494	—	4	4	no	—
120	C₄⋊Dic₈₉	—	2	2	no	—
121	C₄⋊Dic₈₉	—	2	2	no	—
122	#13083551	—	4	2	no	—
123	#13083551	—	4	2	no	—
124	#41×C₈₉	—	2	2	no	—
125	#41×C₈₉	D₈	1	4	yes	complemented
126	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂×D₄×C₈₉	—	2	1	no	—
128	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	—	2	1	no	—
130	C₂²×C₄×C₈₉	—	2	1	no	—
131	C₂²×C₄×C₈₉	—	2	1	no	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
135	C₂×C₈×C₈₉	—	2	2	no	—
136	C₂×C₈×C₈₉	—	2	1	no	—
137	C₂×C₈×C₈₉	—	2	1	no	—
138	C₂×C₈×C₈₉	—	4	1	no	—
139	C₂×C₈×C₈₉	—	4	2	no	—
140	C₂×C₈×C₈₉	—	4	2	no	—
141	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₄⋊C₄×C₈₉	—	2	1	no	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂²⋊C₄×C₈₉	—	2	1	no	—
150	C₂²⋊C₄×C₈₉	—	2	1	no	—
151	C₂²⋊C₄×C₈₉	—	2	1	no	—
152	C₄²×C₈₉	—	2	1	no	—
153	C₄²×C₈₉	—	2	1	no	—
154	C₄²×C₈₉	—	2	1	no	—
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	—	2	1	no	—
160	C₂³×C₈₉	#121	1	1	yes	characteristic
161	C₂²×D₈₉	—	4	2	no	—
162	Q₈×C₈₉	—	2	1	no	—
163	Q₈×C₈₉	C₂×D₈	1	2	yes	—
164	D₄×C₈₉	—	2	4	no	—
165	D₄×C₈₉	—	2	1	no	—
166	D₄×C₈₉	C₂×D₈	1	2	yes	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	2	4	no	—
171	C₂×C₄×C₈₉	—	2	1	no	—
172	C₂×C₄×C₈₉	—	2	1	no	—
173	C₂×C₄×C₈₉	—	4	1	no	—
174	C₂×C₄×C₈₉	—	4	2	no	—
175	C₂×C₄×C₈₉	—	4	1	no	—
176	C₂×C₄×C₈₉	—	4	1	no	—
177	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
181	C₂×C₄×C₈₉	#135	1	2	yes	—
182	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
185	C₂²⋊D₈₉	—	8	4	no	—
186	C₂×Dic₈₉	—	4	2	no	—
187	D₃₅₆	—	4	2	no	—
188	D₃₅₆	—	4	2	no	—
189	D₃₅₆	—	4	2	no	—
190	D₃₅₆	—	4	2	no	—
191	D₃₅₆	—	8	2	no	—
192	C₄×D₈₉	—	8	4	no	—
193	Dic₁₇₈	—	4	2	no	—
194	Dic₁₇₈	—	4	2	no	—
195	C₈×C₈₉	—	2	1	no	—
196	C₈×C₈₉	—	2	1	no	—
197	C₈×C₈₉	—	2	1	no	—
198	C₈×C₈₉	—	4	1	no	—
199	C₈×C₈₉	—	4	1	no	—
200	C₈×C₈₉	#135	1	2	yes	complemented
201	#10623494	—	4	2	no	—
202	#10623494	—	4	2	no	—
203	C₂²×C₈₉	—	2	1	no	—
204	C₂²×C₈₉	—	2	1	no	—
205	C₂²×C₈₉	—	2	2	no	—
206	C₂²×C₈₉	—	4	1	no	—
207	C₂²×C₈₉	—	4	1	no	—
208	C₂²×C₈₉	#466	1	2	yes	—
209	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
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	2	no	—
215	C₄×C₈₉	—	2	1	no	—
216	C₄×C₈₉	—	2	1	no	—
217	C₄×C₈₉	—	4	1	no	—
218	C₄×C₈₉	—	4	1	no	—
219	C₄×C₈₉	#466	1	2	yes	—
220	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
221	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
222	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
223	C₄×C₈₉	#575	1	1	yes	characteristic
224	Dic₈₉	—	8	2	no	—
225	#19125	—	89	1	no	maximal, Sylow
226	C₂×C₈₉	—	2	2	no	—
227	C₂×C₈₉	—	4	2	no	—
228	C₂×C₈₉	#3035	1	1	yes	characteristic
229	C₂×C₈₉	C₂×#466	1	1	yes	characteristic
230	C₂×C₈₉	#3067	1	1	yes	characteristic
231	D₈₉	—	16	2	no	—
232	#3169	—	89	1	no	—
233	#3035	—	89	2	no	—
234	C₈×#41	D₈₉	1	1	yes	characteristic, complemented
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	—	89	1	no	—
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	C₂×D₈₉	1	1	yes	characteristic
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	C₂×D₈₉	1	1	yes	characteristic
259	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
260	C₄×D₈	—	178	1	no	—
261	C₄×D₈	—	178	1	no	—
262	C₈×D₄	—	2	1	no	—
263	C₈×D₄	—	2	1	no	—
264	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
265	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
266	#431	—	2	1	no	—
267	#431	C₂×D₈₉	1	1	yes	characteristic
268	C₂×C₄⋊C₈	—	89	2	no	—
269	#416	—	178	2	no	—
270	C₂×C₄×C₈	—	2	1	no	—
271	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
272	#335	—	89	1	no	—
273	#335	—	89	1	no	—
274	#335	—	89	2	no	—
275	#332	—	89	2	no	—
276	#332	—	89	2	no	—
277	#331	—	89	2	no	—
278	#331	—	89	2	no	—
279	C₂×#41	—	178	2	no	—
280	C₂×#41	D₃₅₆	1	1	yes	characteristic
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	1	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	178	2	no	—
291	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
292	C₂²×C₈	C₂²⋊D₈₉	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	D₃₅₆	1	1	yes	characteristic
299	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	178	2	no	—
303	C₄×D₄	—	178	2	no	—
304	C₄×D₄	D₃₅₆	1	1	yes	characteristic
305	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
306	#117	—	2	1	no	—
307	#117	D₃₅₆	1	1	yes	characteristic
308	C₂×C₄²	—	2	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	1	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	89	2	no	—
315	C₄⋊C₈	—	89	2	no	—
316	C₄⋊C₈	—	178	2	no	—
317	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
318	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
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	—	2	1	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	C₄×C₈	—	2	1	no	—
329	C₄×C₈	—	2	1	no	—
330	C₄×C₈	—	2	1	no	—
331	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
332	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
334	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
335	#41	—	2	2	no	—
336	#41	—	356	4	no	—
337	#41	—	356	4	no	—
338	#41	D₇₁₂	1	4	yes	complemented
339	C₂×Q₈	—	178	2	no	—
340	C₂×Q₈	C₂×D₃₅₆	1	1	yes	characteristic
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	356	2	no	—
343	C₂×D₄	—	178	2	no	—
344	C₂×D₄	—	178	2	no	—
345	C₂×D₄	—	178	2	no	—
346	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	356	2	no	—
351	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
353	C₂²×C₄	#13083574	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	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	2	no	—
365	C₂×C₈	—	4	2	no	—
366	C₂×C₈	—	356	4	no	—
367	C₂×C₈	—	178	2	no	—
368	C₂×C₈	—	178	2	no	—
369	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
370	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
371	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
372	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	178	2	no	—
376	C₄⋊C₄	—	178	2	no	—
377	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
378	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	356	2	no	—
383	C₂²⋊C₄	—	356	2	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
388	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
389	C₄²	#13083574	1	1	yes	characteristic
390	C₄²	C₂³×D₈₉	1	1	yes	characteristic
391	C₂³	—	2	1	no	—
392	C₂³	—	356	2	no	—
393	C₂³	#15667986	1	1	yes	characteristic
394	Q₈	—	2	1	no	—
395	Q₈	—	356	2	no	—
396	Q₈	—	356	2	no	—
397	Q₈	C₂×D₇₁₂	1	2	yes	—
398	D₄	—	2	4	no	—
399	D₄	—	2	1	no	—
400	D₄	—	356	2	no	—
401	D₄	—	356	2	no	—
402	D₄	—	356	2	no	—
403	D₄	—	356	2	no	—
404	D₄	—	712	2	no	—
405	D₄	—	712	4	no	—
406	D₄	C₂×D₇₁₂	1	2	yes	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	356	2	no	—
418	C₂×C₄	—	712	4	no	—
419	C₂×C₄	#15667986	1	1	yes	characteristic
420	C₂×C₄	#15667986	1	1	yes	characteristic
421	C₂×C₄	#15667986	1	1	yes	characteristic
422	C₂×C₄	C₂×D₇₁₂	1	2	yes	—
423	C₂×C₄	#15668034	1	2	yes	—
424	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
426	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
427	C₈	—	2	1	no	—
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	1	no	—
432	C₈	—	356	2	no	—
433	C₈	—	356	2	no	—
434	C₈	#15668032	1	2	yes	complemented
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	712	2	no	—
441	C₂²	—	712	2	no	—
442	C₂²	—	712	2	no	—
443	C₂²	#19151834	1	2	yes	—
444	C₂²	C₂×#15667986	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	712	2	no	—
452	C₄	#19151834	1	2	yes	—
453	C₄	C₂²×D₇₁₂	1	1	yes	characteristic
454	C₄	C₂×#15668032	1	1	yes	characteristic
455	C₄	C₂×#15668034	1	1	yes	characteristic
456	C₄	#19152396	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	4	2	no	—
459	C₂	—	1424	2	no	—
460	C₂	#26029707	1	1	yes	characteristic
461	C₂	C₂×#19151834	1	1	yes	characteristic
462	C₂	#26029972	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15667986
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×#41×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#121
hypercenter	C₈×#41	D₈₉
hypocenter	C₈₉	#19125
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #26030831	C₂	semidirect
2. #26029707	C₂	semidirect
3. #26019696	C₂	semidirect
4. #26019689	C₂	semidirect
5. #26019646	C₂	semidirect
6. #26019641	C₂	semidirect
7. #26019612	C₂	semidirect
8. #26019607	C₂	semidirect
9. C₂×#19151351	C₂	semidirect
10. #26018899	C₂	semidirect
11. C₈×#41×C₈₉	C₂	semidirect
125. #41×C₈₉	D₈	semidirect
200. C₈×C₈₉	#135	semidirect
234. C₈×#41	D₈₉	semidirect
243. C₈₉	#19125	semidirect
338. #41	D₇₁₂	semidirect
434. C₈	#15668032	semidirect

Maximal subgroups

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

subgroup	index
#26030831	2
#26029707	2
#26019696	2
#26019689	2
#26019646	2
#26019641	2
#26019612	2
#26019607	2
C₂×#19151351	2
#26018899	2
C₈×#41×C₈₉	2
#19125	89