Subgroups — #36576508

Order 22784.

708 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030042	C₂	1	1	yes	maximal, characteristic
2	#26029195	C₂	1	1	yes	maximal, characteristic, complemented
3	#26028817	C₂	1	1	yes	maximal, characteristic
4	#26021229	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021028	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021005	C₂	1	2	yes	maximal, complemented
7	#26020852	C₂	1	2	yes	maximal, complemented
8	#26020530	C₂	1	2	yes	maximal
9	#26020096	C₂	1	2	yes	maximal
10	C₄×#15667940	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	C₂²	1	2	yes	—
13	#19152155	C₂²	1	1	yes	characteristic
14	C₄×#13083574	C₂²	1	1	yes	characteristic
15	#19151906	C₄	1	2	yes	complemented
16	#19151899	C₄	1	2	yes	complemented
17	#19151894	C₄	1	1	yes	characteristic, complemented
18	#19151889	C₄	1	1	yes	characteristic, complemented
19	#19151884	C₄	1	1	yes	characteristic, complemented
20	#19151879	C₄	1	1	yes	characteristic, complemented
21	#19151727	—	2	2	no	—
22	#19151725	—	2	1	no	—
23	#19151722	—	2	1	no	—
24	C₂×#15667948	C₂²	1	2	yes	—
25	#19151636	C₂²	1	2	yes	—
26	#19151624	C₂²	1	2	yes	—
27	#19151624	C₂²	1	2	yes	—
28	#19151623	—	2	2	no	—
29	#19151622	C₂²	1	1	yes	characteristic
30	#19151620	—	2	1	no	—
31	C₄⋊C₈×D₈₉	—	2	1	no	—
32	C₂×#15667940	C₂²	1	1	yes	characteristic
33	C₂×#15667940	C₂²	1	1	yes	characteristic
34	#19151595	C₂²	1	2	yes	—
35	#19151553	C₂²	1	2	yes	—
36	C₄×#13083558	C₂²	1	1	yes	characteristic
37	#19151363	C₂²	1	2	yes	—
38	#19151358	C₂²	1	2	yes	—
39	#19151358	C₂²	1	2	yes	—
40	#19151358	C₂²	1	1	yes	characteristic
41	#19151358	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#97×C₈₉	C₂²	1	2	yes	—
45	C₄³×C₈₉	C₂²	1	1	yes	characteristic
46	#336×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083574	C₂³	1	1	yes	characteristic
48	#15668018	—	2	4	no	—
49	#15668018	—	4	2	no	—
50	C₂×#13083558	C₂³	1	2	yes	—
51	C₂×#13083558	C₂³	1	1	yes	characteristic
52	C₂×#13083558	C₂³	1	1	yes	characteristic
53	C₂×#13083557	—	2	2	no	—
54	C₂×C₈×D₈₉	—	2	2	no	—
55	#15668012	C₂×C₄	1	1	yes	characteristic
56	#15668012	C₂×C₄	1	1	yes	characteristic
57	#15668004	C₂×C₄	1	2	yes	—
58	#15667991	—	2	1	no	—
59	#15667991	—	2	1	no	—
60	C₄×Dic₁₇₈	—	2	1	no	—
61	C₄×Dic₁₇₈	—	2	1	no	—
62	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
64	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
65	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
66	C₄×C₂²⋊D₈₉	—	2	1	no	—
67	C₄×C₂²⋊D₈₉	—	2	1	no	—
68	#15667971	C₂³	1	1	yes	characteristic
69	#15667971	C₂³	1	2	yes	—
70	#15667969	—	2	1	no	—
71	C₄²×D₈₉	—	2	1	no	—
72	#15667948	—	4	2	no	—
73	#15667946	C₂×C₄	1	2	yes	—
74	#15667946	C₂×C₄	1	2	yes	—
75	#15667944	C₂×C₄	1	2	yes	—
76	#15667944	C₂×C₄	1	2	yes	—
77	C₄⋊#10623494	—	2	1	no	—
78	C₄⋊#10623494	—	2	1	no	—
79	#15667941	—	2	2	no	—
80	#15667941	—	2	2	no	—
81	#15667941	—	2	2	no	—
82	#15667941	—	2	2	no	—
83	#15667940	—	2	2	no	—
84	#15667940	Q₈	1	4	yes	complemented
85	#15667937	C₂×C₄	1	2	yes	—
86	#15667937	C₂×C₄	1	2	yes	—
87	#15667934	C₂×C₄	1	2	yes	—
88	#15667934	C₂×C₄	1	2	yes	—
89	#15667923	—	2	1	no	—
90	#15667922	—	2	2	no	—
91	C₄×#10623494	—	2	1	no	—
92	C₈×Dic₈₉	—	2	2	no	—
93	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
94	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₈₉	—	2	1	no	—
96	C₂×C₄²×C₈₉	—	2	1	no	—
97	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
101	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
102	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
103	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
104	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
105	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
106	#97×C₈₉	—	4	2	no	—
107	#13083574	—	2	1	no	—
108	#13083574	—	2	1	no	—
109	#13083574	C₂×Q₈	1	2	yes	—
110	#13083574	#41	1	2	yes	—
111	C₂×Dic₁₇₈	—	2	1	no	—
112	C₂×Dic₁₇₈	—	2	1	no	—
113	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₂²⋊D₈₉	—	2	1	no	—
116	C₂×C₄×D₈₉	—	2	1	no	—
117	C₂×C₄×D₈₉	—	2	1	no	—
118	C₂×C₄×D₈₉	—	2	1	no	—
119	#13083558	—	2	1	no	—
120	#13083558	—	2	2	no	—
121	#13083558	—	2	1	no	—
122	#13083558	—	2	2	no	—
123	#13083558	—	2	1	no	—
124	#13083558	C₂×Q₈	1	2	yes	—
125	#13083557	—	4	4	no	—
126	C₂×#10623494	—	2	1	no	—
127	C₂×#10623494	—	2	2	no	—
128	C₂×#10623494	—	2	1	no	—
129	C₈×D₈₉	—	4	4	no	—
130	C₄⋊Dic₈₉	—	2	1	no	—
131	C₄⋊Dic₈₉	—	2	1	no	—
132	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
133	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
135	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
136	#13083553	—	2	1	no	—
137	#13083553	—	2	1	no	—
138	#13083553	—	2	2	no	—
139	#13083553	—	2	2	no	—
140	C₂²⋊Dic₈₉	—	2	1	no	—
141	C₂²⋊Dic₈₉	—	2	2	no	—
142	#13083551	—	2	1	no	—
143	#13083551	—	2	1	no	—
144	C₄×Dic₈₉	—	2	1	no	—
145	C₄×Dic₈₉	—	2	1	no	—
146	C₄×Dic₈₉	—	2	1	no	—
147	C₄×Dic₈₉	—	2	2	no	—
148	C₂²×C₄×C₈₉	—	2	1	no	—
149	C₂²×C₄×C₈₉	—	2	1	no	—
150	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
152	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
153	C₂×C₈×C₈₉	—	2	2	no	—
154	C₂×C₈×C₈₉	—	2	2	no	—
155	C₂×C₈×C₈₉	—	2	2	no	—
156	C₂×C₈×C₈₉	—	2	2	no	—
157	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
158	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
159	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
161	C₄²×C₈₉	—	2	1	no	—
162	C₄²×C₈₉	—	2	1	no	—
163	C₄²×C₈₉	—	2	1	no	—
164	C₄²×C₈₉	—	4	2	no	—
165	C₄²×C₈₉	—	4	2	no	—
166	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
171	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
172	C₂²×D₈₉	—	2	1	no	—
173	C₂×C₄×C₈₉	—	2	2	no	—
174	C₂×C₄×C₈₉	—	2	2	no	—
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	4	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	—	4	1	no	—
181	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
191	C₂²⋊D₈₉	—	2	2	no	—
192	C₂²⋊D₈₉	—	2	2	no	—
193	C₂×Dic₈₉	—	2	1	no	—
194	C₂×Dic₈₉	—	2	1	no	—
195	C₂×Dic₈₉	—	2	1	no	—
196	C₂×Dic₈₉	—	2	2	no	—
197	C₂×Dic₈₉	—	2	2	no	—
198	D₃₅₆	—	2	1	no	—
199	D₃₅₆	C₄×Q₈	1	2	yes	—
200	C₄×D₈₉	—	2	2	no	—
201	C₄×D₈₉	—	2	2	no	—
202	C₄×D₈₉	—	4	2	no	—
203	C₄×D₈₉	—	8	1	no	—
204	Dic₁₇₈	—	2	1	no	—
205	Dic₁₇₈	—	4	2	no	—
206	Dic₁₇₈	—	8	1	no	—
207	Dic₁₇₈	C₄×Q₈	1	2	yes	—
208	C₈×C₈₉	—	2	2	no	—
209	C₈×C₈₉	—	2	2	no	—
210	C₈×C₈₉	—	2	2	no	—
211	C₈×C₈₉	—	2	2	no	—
212	#10623494	—	2	2	no	—
213	#10623494	—	4	2	no	—
214	#10623494	—	4	1	no	—
215	C₂²×C₈₉	—	2	1	no	—
216	C₂²×C₈₉	—	2	1	no	—
217	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂²×C₈₉	#552	1	1	yes	characteristic
219	C₂²×C₈₉	#554	1	1	yes	characteristic
220	C₂×D₈₉	—	2	2	no	—
221	C₂×D₈₉	—	4	1	no	—
222	C₂×D₈₉	—	4	1	no	—
223	C₄×C₈₉	—	2	1	no	—
224	C₄×C₈₉	—	2	1	no	—
225	C₄×C₈₉	—	2	1	no	—
226	C₄×C₈₉	—	4	2	no	—
227	C₄×C₈₉	—	4	2	no	—
228	C₄×C₈₉	#444	1	2	yes	—
229	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
230	C₄×C₈₉	#520	1	1	yes	characteristic
231	C₄×C₈₉	#546	1	1	yes	characteristic
232	C₄×C₈₉	D₄×Q₈	1	1	yes	characteristic
233	Dic₈₉	—	2	2	no	—
234	Dic₈₉	—	4	2	no	—
235	Dic₈₉	—	4	1	no	—
236	Dic₈₉	—	4	2	no	—
237	Dic₈₉	—	4	1	no	—
238	#22983	—	89	1	no	maximal, Sylow
239	C₂×C₈₉	—	2	1	no	—
240	C₂×C₈₉	—	2	1	no	—
241	C₂×C₈₉	#2360	1	1	yes	characteristic
242	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
243	C₂×C₈₉	#2956	1	1	yes	characteristic
244	D₈₉	—	4	2	no	—
245	#3076	—	89	1	no	—
246	#2962	—	89	1	no	—
247	#2906	—	89	1	no	—
248	#1994	—	89	1	no	—
249	#1950	—	89	1	no	—
250	#1946	—	89	2	no	—
251	#1922	—	89	2	no	—
252	#1866	—	89	2	no	—
253	#1767	D₈₉	1	1	yes	characteristic, complemented
254	#1765	—	89	2	no	—
255	C₄×#104	—	89	1	no	—
256	C₈₉	#22983	1	1	yes	characteristic, complemented, Sylow
257	C₂×#131	—	89	2	no	—
258	#533	—	89	1	no	—
259	C₄×#41	—	89	1	no	—
260	#479	—	89	2	no	—
261	#478	—	89	2	no	—
262	#477	—	89	1	no	—
263	#476	—	89	1	no	—
264	#475	—	89	1	no	—
265	#474	—	89	1	no	—
266	#446	—	178	1	no	—
267	#446	—	178	2	no	—
268	C₈×Q₈	—	178	1	no	—
269	C₂×#108	—	89	2	no	—
270	#427	—	89	2	no	—
271	#424	—	89	2	no	—
272	#424	—	89	2	no	—
273	#424	—	178	2	no	—
274	#423	—	89	1	no	—
275	#423	—	178	1	no	—
276	C₂×C₄⋊C₈	—	178	1	no	—
277	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
279	C₂×#104	—	89	1	no	—
280	C₂×#104	—	89	1	no	—
281	#416	—	89	2	no	—
282	#405	—	89	2	no	—
283	C₄×M₁₆	—	89	1	no	—
284	C₂×#97	C₂×D₈₉	1	2	yes	—
285	C₄³	C₂×D₈₉	1	1	yes	characteristic
286	#341	—	89	2	no	—
287	#339	—	89	2	no	—
288	#339	—	89	1	no	—
289	#339	—	89	1	no	—
290	#339	—	89	2	no	—
291	#336	C₂×D₈₉	1	2	yes	—
292	C₂×#41	—	89	1	no	—
293	#131	—	356	2	no	—
294	#131	—	178	4	no	—
295	C₂×M₁₆	—	89	1	no	—
296	C₂×M₁₆	—	89	2	no	—
297	C₂×M₁₆	—	89	1	no	—
298	C₂×M₁₆	—	178	2	no	—
299	C₂²×C₈	—	178	2	no	—
300	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
301	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
302	C₄⋊Q₈	—	89	1	no	—
303	C₄⋊Q₈	—	89	1	no	—
304	#125	—	89	2	no	—
305	C₂²⋊Q₈	—	178	1	no	—
306	C₂²⋊Q₈	—	178	1	no	—
307	C₄×Q₈	—	89	1	no	—
308	C₄×Q₈	—	89	1	no	—
309	C₄×Q₈	—	178	1	no	—
310	C₄×Q₈	—	178	1	no	—
311	C₄×D₄	—	89	1	no	—
312	C₄×D₄	—	89	1	no	—
313	C₄×D₄	—	178	1	no	—
314	C₄×D₄	—	178	1	no	—
315	#117	—	89	1	no	—
316	#117	—	89	2	no	—
317	#117	—	178	1	no	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	178	1	no	—
321	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
322	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
323	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
324	#108	—	356	2	no	—
325	#107	—	89	2	no	—
326	#107	—	89	2	no	—
327	#106	—	89	2	no	—
328	#106	—	89	2	no	—
329	C₄⋊C₈	—	178	2	no	—
330	C₄⋊C₈	—	178	2	no	—
331	C₄⋊C₈	—	178	2	no	—
332	C₄⋊C₈	—	178	2	no	—
333	C₄⋊C₈	—	178	1	no	—
334	C₄⋊C₈	—	178	1	no	—
335	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
336	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
337	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
338	C₄⋊C₈	D₃₅₆	1	1	yes	characteristic
339	C₄⋊C₈	D₃₅₆	1	1	yes	characteristic
340	C₄⋊C₈	D₃₅₆	1	2	yes	—
341	#104	—	89	4	no	—
342	#104	—	178	2	no	—
343	#103	—	89	2	no	—
344	#103	—	89	2	no	—
345	#102	—	89	2	no	—
346	#102	—	89	2	no	—
347	#97	—	4	2	no	—
348	#97	—	178	2	no	—
349	#97	—	178	1	no	—
350	C₄×C₈	—	178	2	no	—
351	C₄×C₈	—	178	1	no	—
352	#41	—	89	2	no	—
353	#41	—	89	2	no	—
354	#41	—	178	1	no	—
355	#41	—	178	1	no	—
356	C₂×Q₈	—	89	1	no	—
357	C₂×Q₈	—	178	1	no	—
358	C₂×Q₈	—	178	1	no	—
359	C₂×D₄	—	89	1	no	—
360	C₂×D₄	—	178	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	178	1	no	—
364	C₂²×C₄	—	178	1	no	—
365	C₂²×C₄	—	178	1	no	—
366	C₂²×C₄	#13083574	1	1	yes	characteristic
367	C₂²×C₄	#13083574	1	1	yes	characteristic
368	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
369	M₁₆	—	89	2	no	—
370	M₁₆	—	356	4	no	—
371	M₁₆	—	178	1	no	—
372	M₁₆	—	178	2	no	—
373	M₁₆	—	178	1	no	—
374	M₁₆	—	178	2	no	—
375	M₁₆	—	178	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	356	4	no	—
381	C₂×C₈	—	178	1	no	—
382	C₂×C₈	—	178	2	no	—
383	C₂×C₈	—	178	1	no	—
384	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
385	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
386	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
387	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
388	C₄⋊C₄	—	89	2	no	—
389	C₄⋊C₄	—	89	2	no	—
390	C₄⋊C₄	—	89	1	no	—
391	C₄⋊C₄	—	89	1	no	—
392	C₄⋊C₄	—	178	1	no	—
393	C₄⋊C₄	—	178	1	no	—
394	C₄⋊C₄	—	178	2	no	—
395	C₄⋊C₄	—	178	2	no	—
396	C₄⋊C₄	—	178	1	no	—
397	C₄⋊C₄	—	178	1	no	—
398	C₂²⋊C₄	—	178	1	no	—
399	C₂²⋊C₄	—	178	2	no	—
400	C₂²⋊C₄	—	178	1	no	—
401	C₂²⋊C₄	—	178	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	4	2	no	—
406	C₄²	—	4	2	no	—
407	C₄²	—	178	1	no	—
408	C₄²	—	178	1	no	—
409	C₄²	—	178	2	no	—
410	C₄²	—	178	1	no	—
411	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
412	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
413	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
414	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
415	C₄²	Q₈×D₈₉	1	2	yes	—
416	C₂³	—	178	1	no	—
417	C₂³	C₂×#13083574	1	1	yes	characteristic
418	Q₈	—	89	2	no	—
419	Q₈	—	356	2	no	—
420	Q₈	—	178	1	no	—
421	Q₈	—	712	1	no	—
422	D₄	—	89	2	no	—
423	D₄	—	178	2	no	—
424	D₄	—	178	2	no	—
425	D₄	—	178	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	356	2	no	—
435	C₂×C₄	—	178	1	no	—
436	C₂×C₄	—	178	1	no	—
437	C₂×C₄	—	178	2	no	—
438	C₂×C₄	—	178	2	no	—
439	C₂×C₄	—	178	1	no	—
440	C₂×C₄	—	178	2	no	—
441	C₂×C₄	—	178	2	no	—
442	C₂×C₄	—	712	1	no	—
443	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
444	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
445	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
446	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
447	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
449	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
450	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
451	C₂×C₄	#15668057	1	1	yes	characteristic
452	C₂×C₄	#15668059	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	2	2	no	—
457	C₈	—	356	2	no	—
458	C₈	—	356	1	no	—
459	C₈	—	178	2	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	356	1	no	—
463	C₂²	—	356	1	no	—
464	C₂²	—	178	2	no	—
465	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
466	C₂²	#19152287	1	1	yes	characteristic
467	C₂²	#19152303	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	356	1	no	—
474	C₄	—	356	2	no	—
475	C₄	—	356	1	no	—
476	C₄	—	356	2	no	—
477	C₄	—	178	2	no	—
478	C₄	#19151721	1	2	yes	—
479	C₄	C₄×Q₈×D₈₉	1	1	yes	characteristic
480	C₄	#19152077	1	1	yes	characteristic
481	C₄	#19152243	1	1	yes	characteristic
482	C₄	Q₈×D₃₅₆	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	356	2	no	—
486	C₂	#26023259	1	1	yes	characteristic
487	C₂	C₂×#19151721	1	1	yes	characteristic
488	C₂	#26029163	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1767	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#13083574	C₂³
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1767	D₈₉
hypocenter	C₈₉	#22983
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #1767

Complements

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

N	H ≅ G/N	type
2. #26029195	C₂	semidirect
4. #26021229	C₂	semidirect
5. #26021028	C₂	semidirect
6. #26021005	C₂	semidirect
7. #26020852	C₂	semidirect
11. C₈₉×#1767	C₂	semidirect
15. #19151906	C₄	semidirect
16. #19151899	C₄	semidirect
17. #19151894	C₄	semidirect
18. #19151889	C₄	semidirect
19. #19151884	C₄	semidirect
20. #19151879	C₄	semidirect
84. #15667940	Q₈	semidirect
253. #1767	D₈₉	semidirect
256. C₈₉	#22983	semidirect

Maximal subgroups

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

subgroup	index
#26030042	2
#26029195	2
#26028817	2
#26021229	2
#26021028	2
#26021005	2
#26020852	2
#26020530	2
#26020096	2
C₄×#15667940	2
C₈₉×#1767	2
#22983	89