Subgroups — #36538339

Order 22784.

716 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030680	C₂	1	1	yes	maximal, characteristic, complemented
2	#26030403	C₂	1	2	yes	maximal, complemented
3	#26019622	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019617	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019612	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019607	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019600	C₂	1	2	yes	maximal, complemented
8	#26019593	C₂	1	2	yes	maximal, complemented
9	#26019015	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018955	C₂	1	2	yes	maximal, complemented
11	C₈×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668034	—	2	1	no	—
13	C₂×#15668034	—	2	1	no	—
14	#19152148	C₂²	1	2	yes	—
15	#19151982	—	2	1	no	—
16	#19151982	—	2	1	no	—
17	#19151978	C₂²	1	1	yes	characteristic
18	#19151975	C₂²	1	1	yes	characteristic
19	#19151971	C₂²	1	2	yes	—
20	#19151922	—	2	2	no	—
21	#19151883	C₂²	1	2	yes	—
22	#19151878	C₂²	1	2	yes	—
23	#19151798	C₂²	1	2	yes	—
24	#19151793	C₂²	1	2	yes	—
25	#19151743	—	2	2	no	—
26	#19151708	—	2	2	no	—
27	#19151696	—	2	2	no	—
28	#19151655	C₂²	1	2	yes	—
29	#19151351	C₂²	1	1	yes	characteristic
30	#19151351	C₂²	1	1	yes	characteristic
31	#19151349	C₂²	1	2	yes	—
32	#19151345	C₂²	1	2	yes	—
33	#19151345	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	#15668034	—	4	4	no	—
49	#15668034	—	4	4	no	—
50	C₂×Dic₃₅₆	—	2	1	no	—
51	C₂×Dic₃₅₆	—	2	1	no	—
52	C₂×#13083563	—	2	2	no	—
53	C₂×#13083563	—	2	2	no	—
54	C₂×#13083561	—	2	2	no	—
55	C₂×D₇₁₂	—	2	1	no	—
56	C₂×D₇₁₂	—	2	1	no	—
57	C₂×#13083559	—	2	2	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×D₃₅₆	—	2	2	no	—
64	C₄×D₃₅₆	—	2	2	no	—
65	#15667945	—	2	2	no	—
66	#15667943	—	2	2	no	—
67	C₄⋊#10623494	C₂³	1	2	yes	—
68	C₄⋊#10623494	C₂³	1	2	yes	—
69	#15667936	—	2	2	no	—
70	#15667933	—	2	2	no	—
71	#15667932	—	2	2	no	—
72	#15667932	—	2	2	no	—
73	C₂²⋊#10623494	—	2	2	no	—
74	#15667923	—	2	2	no	—
75	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₈₉	—	2	1	no	—
77	C₂²×C₈×C₈₉	—	2	1	no	—
78	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
80	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
81	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
82	C₄×D₄×C₈₉	—	2	1	no	—
83	C₄×D₄×C₈₉	—	2	1	no	—
84	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
85	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
86	#117×C₈₉	—	2	1	no	—
87	#117×C₈₉	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₈₉	—	2	1	no	—
89	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₈₉	—	2	1	no	—
91	C₄⋊C₈×C₈₉	—	2	1	no	—
92	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂²⋊C₈×C₈₉	—	2	1	no	—
95	C₂²⋊C₈×C₈₉	—	2	1	no	—
96	C₂²⋊C₈×C₈₉	—	2	1	no	—
97	C₄×C₈×C₈₉	—	2	1	no	—
98	C₄×C₈×C₈₉	—	2	1	no	—
99	C₄×C₈×C₈₉	—	2	1	no	—
100	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
101	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
102	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	#13083574	—	4	4	no	—
105	#13083574	—	4	4	no	—
106	C₂×Dic₁₇₈	—	2	2	no	—
107	C₂×D₃₅₆	—	2	2	no	—
108	C₂×D₃₅₆	—	2	2	no	—
109	C₂×D₃₅₆	—	2	2	no	—
110	C₂×C₂²⋊D₈₉	—	4	2	no	—
111	C₂×C₄×D₈₉	—	4	2	no	—
112	Dic₃₅₆	—	4	2	no	—
113	Dic₃₅₆	—	4	2	no	—
114	#13083563	—	4	4	no	—
115	#13083563	—	4	4	no	—
116	#13083561	—	4	4	no	—
117	D₇₁₂	—	4	2	no	—
118	D₇₁₂	—	4	2	no	—
119	#13083559	—	4	4	no	—
120	C₂×#10623494	—	2	2	no	—
121	C₂×#10623494	—	2	2	no	—
122	C₄⋊Dic₈₉	—	2	2	no	—
123	C₄⋊Dic₈₉	—	2	2	no	—
124	#13083551	—	4	2	no	—
125	#13083551	—	4	2	no	—
126	#41×C₈₉	—	2	2	no	—
127	#41×C₈₉	—	2	2	no	—
128	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂×D₄×C₈₉	—	2	1	no	—
130	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	—	2	1	no	—
132	C₂²×C₄×C₈₉	—	2	1	no	—
133	C₂²×C₄×C₈₉	—	2	1	no	—
134	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
137	C₂×C₈×C₈₉	—	2	2	no	—
138	C₂×C₈×C₈₉	—	2	2	no	—
139	C₂×C₈×C₈₉	—	2	1	no	—
140	C₂×C₈×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	4	2	no	—
142	C₂×C₈×C₈₉	—	4	2	no	—
143	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₄⋊C₄×C₈₉	—	2	1	no	—
149	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂²⋊C₄×C₈₉	—	2	1	no	—
152	C₂²⋊C₄×C₈₉	—	2	1	no	—
153	C₂²⋊C₄×C₈₉	—	2	1	no	—
154	C₄²×C₈₉	—	2	1	no	—
155	C₄²×C₈₉	—	2	1	no	—
156	C₄²×C₈₉	—	2	1	no	—
157	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₈₉	#41	1	1	yes	characteristic
160	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
161	C₂³×C₈₉	—	2	1	no	—
162	C₂³×C₈₉	#121	1	1	yes	characteristic
163	C₂²×D₈₉	—	4	2	no	—
164	Q₈×C₈₉	—	2	1	no	—
165	Q₈×C₈₉	#135	1	2	yes	complemented
166	D₄×C₈₉	—	2	4	no	—
167	D₄×C₈₉	—	2	1	no	—
168	D₄×C₈₉	#135	1	2	yes	complemented
169	C₂×C₄×C₈₉	—	2	4	no	—
170	C₂×C₄×C₈₉	—	2	1	no	—
171	C₂×C₄×C₈₉	—	2	1	no	—
172	C₂×C₄×C₈₉	—	2	1	no	—
173	C₂×C₄×C₈₉	—	2	1	no	—
174	C₂×C₄×C₈₉	—	2	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	2	no	—
179	C₂×C₄×C₈₉	—	4	1	no	—
180	C₂×C₄×C₈₉	—	4	1	no	—
181	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
183	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
187	C₂²⋊D₈₉	—	8	4	no	—
188	C₂×Dic₈₉	—	4	2	no	—
189	D₃₅₆	—	4	2	no	—
190	D₃₅₆	—	4	2	no	—
191	D₃₅₆	—	4	2	no	—
192	D₃₅₆	—	4	2	no	—
193	D₃₅₆	—	8	2	no	—
194	C₄×D₈₉	—	8	4	no	—
195	Dic₁₇₈	—	4	2	no	—
196	Dic₁₇₈	—	4	2	no	—
197	C₈×C₈₉	—	2	1	no	—
198	C₈×C₈₉	—	2	1	no	—
199	C₈×C₈₉	—	4	1	no	—
200	C₈×C₈₉	—	4	1	no	—
201	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
202	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
203	#10623494	—	4	2	no	—
204	#10623494	—	4	2	no	—
205	C₂²×C₈₉	—	2	1	no	—
206	C₂²×C₈₉	—	2	1	no	—
207	C₂²×C₈₉	—	2	2	no	—
208	C₂²×C₈₉	—	2	1	no	—
209	C₂²×C₈₉	—	4	1	no	—
210	C₂²×C₈₉	—	4	1	no	—
211	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
212	C₂×D₈₉	—	8	2	no	—
213	C₂×D₈₉	—	8	2	no	—
214	C₂×D₈₉	—	8	2	no	—
215	C₄×C₈₉	—	2	1	no	—
216	C₄×C₈₉	—	2	1	no	—
217	C₄×C₈₉	—	2	2	no	—
218	C₄×C₈₉	—	2	1	no	—
219	C₄×C₈₉	—	2	1	no	—
220	C₄×C₈₉	—	4	1	no	—
221	C₄×C₈₉	—	4	1	no	—
222	C₄×C₈₉	C₂×#135	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	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
226	Dic₈₉	—	8	2	no	—
227	#19269	—	89	1	no	maximal, Sylow
228	C₂×C₈₉	—	4	1	no	—
229	C₂×C₈₉	—	4	2	no	—
230	C₂×C₈₉	#3038	1	1	yes	characteristic
231	C₂×C₈₉	#3050	1	1	yes	characteristic
232	C₂×C₈₉	#3067	1	1	yes	characteristic
233	D₈₉	—	16	2	no	—
234	#3147	—	89	1	no	—
235	#3115	—	89	2	no	—
236	C₈×#41	D₈₉	1	1	yes	characteristic, complemented
237	#1670	—	89	1	no	—
238	#1669	—	89	1	no	—
239	#1668	—	89	1	no	—
240	#1667	—	89	1	no	—
241	#1666	—	89	2	no	—
242	#1665	—	89	2	no	—
243	#1568	—	89	1	no	—
244	#1553	—	89	2	no	—
245	C₈₉	#19269	1	1	yes	characteristic, complemented, Sylow
246	C₂×#135	—	178	1	no	—
247	C₂×#135	—	178	1	no	—
248	#532	—	89	2	no	—
249	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
250	#495	—	178	1	no	—
251	#495	—	178	1	no	—
252	#494	—	89	1	no	—
253	#493	—	89	1	no	—
254	#492	—	89	2	no	—
255	#482	—	178	2	no	—
256	#475	—	89	2	no	—
257	#474	—	89	2	no	—
258	#460	—	89	2	no	—
259	#459	—	89	2	no	—
260	#449	—	178	2	no	—
261	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
262	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
263	#442	—	178	2	no	—
264	#440	—	178	2	no	—
265	C₈×D₄	—	2	1	no	—
266	C₈×D₄	—	2	1	no	—
267	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
268	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
269	#432	—	89	2	no	—
270	#431	—	2	1	no	—
271	#431	C₂×D₈₉	1	1	yes	characteristic
272	C₂×C₄×C₈	—	2	1	no	—
273	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
274	#335	—	89	1	no	—
275	#335	—	89	1	no	—
276	#334	—	89	2	no	—
277	#332	—	89	2	no	—
278	#332	—	89	2	no	—
279	#331	—	89	2	no	—
280	#331	—	89	2	no	—
281	C₂×#41	—	178	2	no	—
282	C₂×#41	D₃₅₆	1	1	yes	characteristic
283	#135	—	356	4	no	—
284	#135	—	356	4	no	—
285	C₂×Q₁₆	—	178	1	no	—
286	C₂×Q₁₆	—	178	1	no	—
287	C₂×SD₁₆	—	178	2	no	—
288	C₂×SD₁₆	—	178	2	no	—
289	C₂×SD₁₆	—	178	2	no	—
290	C₂×D₈	—	178	2	no	—
291	C₂×D₈	—	178	1	no	—
292	C₂×D₈	—	178	1	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
296	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
297	C₄⋊Q₈	—	89	2	no	—
298	#127	—	89	2	no	—
299	#124	—	178	2	no	—
300	#121	—	178	2	no	—
301	#121	—	178	2	no	—
302	C₄×Q₈	D₃₅₆	1	1	yes	characteristic
303	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	178	2	no	—
307	C₄×D₄	—	178	2	no	—
308	C₄×D₄	D₃₅₆	1	1	yes	characteristic
309	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
310	#117	—	2	1	no	—
311	#117	D₃₅₆	1	1	yes	characteristic
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
314	#107	—	178	2	no	—
315	#106	—	178	2	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	89	2	no	—
319	C₄⋊C₈	—	89	2	no	—
320	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
321	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
322	#103	—	178	2	no	—
323	#102	—	178	2	no	—
324	#102	—	178	2	no	—
325	#102	—	178	2	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	178	2	no	—
330	#97	—	178	2	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	2	1	no	—
333	C₄×C₈	—	2	1	no	—
334	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
335	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
336	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
337	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	#41	—	356	4	no	—
341	#41	—	356	4	no	—
342	C₂×Q₈	—	178	2	no	—
343	C₂×Q₈	C₂×D₃₅₆	1	1	yes	characteristic
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	356	2	no	—
346	C₂×D₄	—	178	2	no	—
347	C₂×D₄	—	178	2	no	—
348	C₂×D₄	—	178	2	no	—
349	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	356	2	no	—
354	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
356	C₂²×C₄	#13083574	1	1	yes	characteristic
357	Q₁₆	—	356	2	no	—
358	Q₁₆	—	356	2	no	—
359	SD₁₆	—	356	4	no	—
360	SD₁₆	—	356	4	no	—
361	SD₁₆	—	356	4	no	—
362	D₈	—	356	2	no	—
363	D₈	—	356	4	no	—
364	D₈	—	356	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	—	4	2	no	—
371	C₂×C₈	—	178	2	no	—
372	C₂×C₈	—	178	2	no	—
373	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
374	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
375	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
376	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	178	2	no	—
380	C₄⋊C₄	—	178	2	no	—
381	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
382	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	356	2	no	—
387	C₂²⋊C₄	—	356	2	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
392	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
393	C₄²	#13083574	1	1	yes	characteristic
394	C₄²	C₂³×D₈₉	1	1	yes	characteristic
395	C₂³	—	2	1	no	—
396	C₂³	—	356	2	no	—
397	C₂³	#15667986	1	1	yes	characteristic
398	Q₈	—	2	1	no	—
399	Q₈	—	356	2	no	—
400	Q₈	—	356	2	no	—
401	Q₈	#15668034	1	2	yes	complemented
402	D₄	—	2	4	no	—
403	D₄	—	2	1	no	—
404	D₄	—	356	2	no	—
405	D₄	—	356	2	no	—
406	D₄	—	356	2	no	—
407	D₄	—	356	2	no	—
408	D₄	—	712	2	no	—
409	D₄	—	712	4	no	—
410	D₄	#15668034	1	2	yes	complemented
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	356	2	no	—
424	C₂×C₄	—	712	4	no	—
425	C₂×C₄	#15667986	1	1	yes	characteristic
426	C₂×C₄	#15667986	1	1	yes	characteristic
427	C₂×C₄	#15667986	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
430	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	4	1	no	—
434	C₈	—	4	1	no	—
435	C₈	—	356	2	no	—
436	C₈	—	356	2	no	—
437	C₈	#15668037	1	2	yes	—
438	C₈	#15668037	1	2	yes	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	712	2	no	—
446	C₂²	—	712	2	no	—
447	C₂²	—	712	2	no	—
448	C₂²	C₂×#15667986	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	712	2	no	—
457	C₄	C₂×#15668034	1	1	yes	characteristic
458	C₄	C₂×#15668034	1	1	yes	characteristic
459	C₄	C₂×#15668037	1	1	yes	characteristic
460	C₄	C₂×#15668037	1	1	yes	characteristic
461	C₂	—	4	1	no	—
462	C₂	—	4	2	no	—
463	C₂	—	1424	2	no	—
464	C₂	#26029732	1	1	yes	characteristic
465	C₂	#26029833	1	1	yes	characteristic
466	C₂	#26029972	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#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	#19269
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #26030680	C₂	semidirect
2. #26030403	C₂	semidirect
3. #26019622	C₂	semidirect
4. #26019617	C₂	semidirect
5. #26019612	C₂	semidirect
6. #26019607	C₂	semidirect
7. #26019600	C₂	semidirect
8. #26019593	C₂	semidirect
9. #26019015	C₂	semidirect
10. #26018955	C₂	semidirect
11. C₈×#41×C₈₉	C₂	semidirect
165. Q₈×C₈₉	#135	semidirect
168. D₄×C₈₉	#135	semidirect
236. C₈×#41	D₈₉	semidirect
245. C₈₉	#19269	semidirect
401. Q₈	#15668034	semidirect
410. D₄	#15668034	semidirect

Maximal subgroups

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

subgroup	index
#26030680	2
#26030403	2
#26019622	2
#26019617	2
#26019612	2
#26019607	2
#26019600	2
#26019593	2
#26019015	2
#26018955	2
C₈×#41×C₈₉	2
#19269	89