Subgroups — #36708907

Order 22784.

738 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152033	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#15667952	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19151834	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022367	C₂	1	2	yes	maximal, complemented
5	#26022353	C₂	1	2	yes	maximal, complemented
6	#26022350	C₂	1	2	yes	maximal, complemented
7	#26022336	C₂	1	2	yes	maximal, complemented
8	#26022041	C₂	1	1	yes	maximal, characteristic, complemented
9	#26021967	C₂	1	1	yes	maximal, characteristic, complemented
10	#26021964	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3050	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₇₁₂	C₂²	1	1	yes	characteristic
13	C₂×#15667986	—	2	1	no	—
14	#19152033	—	2	4	no	—
15	C₂×#15667955	C₂²	1	2	yes	complemented
16	C₂×#15667953	C₂²	1	2	yes	complemented
17	C₂×#15667952	—	2	4	no	—
18	C₂×#15667952	C₂²	1	1	yes	characteristic
19	C₂×#15667952	C₂²	1	1	yes	characteristic
20	C₂×#15667952	C₂²	1	2	yes	complemented
21	C₂²×#13083549	C₂²	1	2	yes	complemented
22	#19151834	—	2	1	no	—
23	#19151834	—	2	1	no	—
24	#19151834	C₂²	1	2	yes	—
25	#19151834	C₂²	1	2	yes	—
26	C₂×#15667946	C₂²	1	1	yes	characteristic
27	C₂×#15667934	—	2	1	no	—
28	#19151425	C₂²	1	2	yes	complemented
29	#19151423	C₂²	1	2	yes	complemented
30	#19151402	C₂²	1	2	yes	complemented
31	#19151399	C₂²	1	2	yes	complemented
32	#19151398	C₂²	1	2	yes	complemented
33	#19151398	C₂²	1	2	yes	complemented
34	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
36	#525×C₈₉	—	2	1	no	—
37	#467×C₈₉	C₂²	1	1	yes	characteristic, complemented
38	#467×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	#466×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	#466×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	#465×C₈₉	—	2	1	no	—
42	#465×C₈₉	—	2	1	no	—
43	#427×C₈₉	C₂²	1	1	yes	characteristic
44	#416×C₈₉	—	2	1	no	—
45	C₂²×D₃₅₆	—	2	1	no	—
46	C₂²×C₂²⋊D₈₉	—	4	1	no	—
47	C₂×D₇₁₂	—	2	2	no	—
48	C₂×D₇₁₂	—	2	1	no	—
49	C₂×D₇₁₂	—	2	2	no	—
50	C₂×D₇₁₂	C₂³	1	2	yes	—
51	#15667986	—	2	2	no	—
52	#15667986	—	2	2	no	—
53	#15667986	—	4	1	no	—
54	#15667986	—	4	1	no	—
55	C₂×C₄⋊Dic₈₉	—	2	1	no	—
56	C₂×#13083551	—	4	1	no	—
57	#15667955	—	2	4	no	—
58	#15667953	—	2	4	no	—
59	#15667952	—	2	4	no	—
60	#15667952	—	2	2	no	—
61	#15667952	D₄	1	4	yes	complemented
62	C₂×#13083549	—	2	4	no	—
63	C₂×#13083549	C₂³	1	2	yes	—
64	C₂×#13083549	C₂³	1	2	yes	—
65	#15667946	—	2	1	no	—
66	#15667946	C₂³	1	2	yes	—
67	#15667934	—	2	2	no	—
68	#15667934	—	2	2	no	—
69	C₂×#41×C₈₉	—	2	1	no	—
70	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
71	#135×C₈₉	—	2	2	no	—
72	#135×C₈₉	—	2	2	no	—
73	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
74	C₂×SD₁₆×C₈₉	—	2	1	no	—
75	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₈₉	—	2	2	no	—
77	C₂²×C₈×C₈₉	—	2	2	no	—
78	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
84	#123×C₈₉	—	4	1	no	—
85	C₂²⋊Q₈×C₈₉	—	2	1	no	—
86	C₂²⋊Q₈×C₈₉	—	2	1	no	—
87	#121×C₈₉	—	2	1	no	—
88	#121×C₈₉	—	2	1	no	—
89	#120×C₈₉	—	4	1	no	—
90	C₄×D₄×C₈₉	—	4	1	no	—
91	C₄×D₄×C₈₉	—	4	1	no	—
92	#117×C₈₉	—	2	1	no	—
93	#107×C₈₉	C₂³	1	1	yes	characteristic
94	#107×C₈₉	C₂³	1	1	yes	characteristic
95	#106×C₈₉	—	2	1	no	—
96	#103×C₈₉	—	2	1	no	—
97	#103×C₈₉	—	2	1	no	—
98	#102×C₈₉	—	2	1	no	—
99	#102×C₈₉	—	2	1	no	—
100	C₂³×D₈₉	—	4	1	no	—
101	C₂×D₃₅₆	—	2	2	no	—
102	C₂×D₃₅₆	—	4	2	no	—
103	C₂×D₃₅₆	—	4	2	no	—
104	C₂×D₃₅₆	—	4	1	no	—
105	C₂×C₂²⋊D₈₉	—	4	2	no	—
106	C₂×C₂²⋊D₈₉	—	4	2	no	—
107	C₂×C₂²⋊D₈₉	—	8	4	no	—
108	C₂²×Dic₈₉	—	4	1	no	—
109	D₇₁₂	—	2	2	no	—
110	D₇₁₂	—	2	2	no	—
111	D₇₁₂	—	4	2	no	—
112	C₄⋊Dic₈₉	—	2	2	no	—
113	C₄⋊Dic₈₉	—	4	1	no	—
114	#13083551	—	4	2	no	—
115	#13083551	—	4	2	no	—
116	#13083549	—	2	2	no	—
117	#13083549	C₂×D₄	1	4	yes	complemented
118	C₂⁴×C₈₉	D₈	1	1	yes	characteristic
119	#41×C₈₉	—	4	2	no	—
120	#41×C₈₉	—	4	2	no	—
121	C₂×Q₈×C₈₉	—	2	1	no	—
122	C₂×D₄×C₈₉	—	2	1	no	—
123	C₂×D₄×C₈₉	—	4	1	no	—
124	C₂×D₄×C₈₉	—	4	1	no	—
125	C₂×D₄×C₈₉	—	4	1	no	—
126	C₂²×C₄×C₈₉	—	2	2	no	—
127	C₂²×C₄×C₈₉	—	2	2	no	—
128	C₂²×C₄×C₈₉	—	4	1	no	—
129	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
135	Q₁₆×C₈₉	—	2	1	no	—
136	Q₁₆×C₈₉	—	2	1	no	—
137	SD₁₆×C₈₉	—	4	2	no	—
138	D₈×C₈₉	—	2	1	no	—
139	D₈×C₈₉	—	2	1	no	—
140	C₂×C₈×C₈₉	—	2	2	no	—
141	C₂×C₈×C₈₉	—	2	2	no	—
142	C₂×C₈×C₈₉	—	2	2	no	—
143	C₂×C₈×C₈₉	—	2	1	no	—
144	C₂×C₈×C₈₉	—	2	1	no	—
145	C₂×C₈×C₈₉	—	2	1	no	—
146	C₂×C₈×C₈₉	—	2	1	no	—
147	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₈₉	#41	1	2	yes	—
152	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
153	C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₄⋊C₄×C₈₉	—	2	1	no	—
155	C₄⋊C₄×C₈₉	—	4	1	no	—
156	C₄⋊C₄×C₈₉	—	4	1	no	—
157	C₂²⋊C₄×C₈₉	—	4	1	no	—
158	C₂²⋊C₄×C₈₉	—	4	1	no	—
159	C₂²⋊C₄×C₈₉	—	4	1	no	—
160	C₂²⋊C₄×C₈₉	—	4	1	no	—
161	C₂²⋊C₄×C₈₉	—	4	1	no	—
162	C₄²×C₈₉	—	4	1	no	—
163	C₂³×C₈₉	—	2	2	no	—
164	C₂³×C₈₉	—	2	2	no	—
165	C₂³×C₈₉	—	4	1	no	—
166	C₂³×C₈₉	—	4	1	no	—
167	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
168	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
169	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
170	C₂²×D₈₉	—	4	2	no	—
171	C₂²×D₈₉	—	8	2	no	—
172	C₂²×D₈₉	—	8	2	no	—
173	C₂²×D₈₉	—	8	2	no	—
174	Q₈×C₈₉	—	4	1	no	—
175	Q₈×C₈₉	—	4	1	no	—
176	D₄×C₈₉	—	4	1	no	—
177	D₄×C₈₉	—	4	1	no	—
178	D₄×C₈₉	—	8	2	no	—
179	D₄×C₈₉	—	8	2	no	—
180	D₄×C₈₉	—	8	2	no	—
181	C₂×C₄×C₈₉	—	2	2	no	—
182	C₂×C₄×C₈₉	—	2	1	no	—
183	C₂×C₄×C₈₉	—	2	1	no	—
184	C₂×C₄×C₈₉	—	2	1	no	—
185	C₂×C₄×C₈₉	—	2	1	no	—
186	C₂×C₄×C₈₉	—	2	2	no	—
187	C₂×C₄×C₈₉	—	2	2	no	—
188	C₂×C₄×C₈₉	—	4	1	no	—
189	C₂×C₄×C₈₉	—	4	1	no	—
190	C₂×C₄×C₈₉	—	4	1	no	—
191	C₂×C₄×C₈₉	—	8	2	no	—
192	C₂×C₄×C₈₉	#121	1	2	yes	—
193	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₈₉	#135	1	2	yes	—
197	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	C₂²⋊D₈₉	—	8	4	no	—
199	C₂²⋊D₈₉	—	8	4	no	—
200	C₂×Dic₈₉	—	4	2	no	—
201	C₂×Dic₈₉	—	8	2	no	—
202	D₃₅₆	—	4	2	no	—
203	D₃₅₆	—	4	2	no	—
204	D₃₅₆	—	8	2	no	—
205	C₈×C₈₉	—	2	1	no	—
206	C₈×C₈₉	—	2	1	no	—
207	C₈×C₈₉	#121	1	2	yes	—
208	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
209	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
210	C₂²×C₈₉	—	2	1	no	—
211	C₂²×C₈₉	—	2	1	no	—
212	C₂²×C₈₉	—	2	1	no	—
213	C₂²×C₈₉	—	2	1	no	—
214	C₂²×C₈₉	—	2	1	no	—
215	C₂²×C₈₉	—	2	1	no	—
216	C₂²×C₈₉	—	2	1	no	—
217	C₂²×C₈₉	—	4	4	no	—
218	C₂²×C₈₉	—	8	1	no	—
219	C₂²×C₈₉	—	8	1	no	—
220	C₂²×C₈₉	—	8	1	no	—
221	C₂²×C₈₉	#466	1	2	yes	—
222	C₂²×C₈₉	#509	1	2	yes	complemented
223	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
224	C₂×D₈₉	—	8	2	no	—
225	C₂×D₈₉	—	8	2	no	—
226	C₂×D₈₉	—	8	2	no	—
227	C₂×D₈₉	—	16	4	no	—
228	C₄×C₈₉	—	2	1	no	—
229	C₄×C₈₉	—	2	1	no	—
230	C₄×C₈₉	—	8	1	no	—
231	C₄×C₈₉	—	8	1	no	—
232	C₄×C₈₉	—	8	1	no	—
233	C₄×C₈₉	#466	1	2	yes	—
234	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
235	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
236	Dic₈₉	—	8	2	no	—
237	#33605	—	89	1	no	maximal, Sylow
238	C₂×C₈₉	—	2	2	no	—
239	C₂×C₈₉	—	2	2	no	—
240	C₂×C₈₉	—	4	1	no	—
241	C₂×C₈₉	—	16	1	no	—
242	C₂×C₈₉	C₂×#466	1	1	yes	characteristic
243	C₂×C₈₉	C₂×#509	1	1	yes	characteristic
244	C₂×C₈₉	#3414	1	1	yes	characteristic
245	D₈₉	—	16	2	no	—
246	C₂×#509	—	89	1	no	—
247	C₂²×M₃₂	—	89	1	no	—
248	#3050	D₈₉	1	1	yes	characteristic, complemented
249	C₂×#466	—	89	1	no	—
250	#2220	—	89	2	no	—
251	#2218	—	89	2	no	—
252	#2217	—	89	2	no	—
253	#2215	—	89	2	no	—
254	#2159	—	89	1	no	—
255	#2140	—	89	1	no	—
256	#2139	—	89	1	no	—
257	C₈₉	#33605	1	1	yes	characteristic, complemented, Sylow
258	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
259	C₂²×D₈	—	89	1	no	—
260	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
261	#525	—	2	1	no	—
262	C₂×#121	—	178	1	no	—
263	#509	—	178	4	no	—
264	C₂×SD₃₂	—	89	2	no	—
265	C₂×D₁₆	—	89	2	no	—
266	C₂×M₃₂	—	89	1	no	—
267	C₂×M₃₂	—	89	1	no	—
268	C₂×M₃₂	—	89	2	no	—
269	C₂×M₃₂	—	178	4	no	—
270	C₂²×C₁₆	—	89	2	no	—
271	#467	C₂×D₈₉	1	1	yes	characteristic, complemented
272	#467	C₂×D₈₉	1	1	yes	characteristic, complemented
273	#466	—	89	2	no	—
274	#466	—	89	2	no	—
275	#466	—	178	1	no	—
276	#466	—	178	1	no	—
277	#466	C₂×D₈₉	1	1	yes	characteristic, complemented
278	#466	C₂×D₈₉	1	1	yes	characteristic, complemented
279	#465	—	2	1	no	—
280	#465	—	2	1	no	—
281	#427	C₂×D₈₉	1	1	yes	characteristic
282	C₂×#107	—	89	1	no	—
283	#416	—	2	1	no	—
284	C₂×#102	—	178	1	no	—
285	#367	—	89	2	no	—
286	#366	—	89	2	no	—
287	#358	—	89	2	no	—
288	#357	—	89	2	no	—
289	#357	—	89	2	no	—
290	#357	—	89	2	no	—
291	C₂×#41	—	2	1	no	—
292	C₂²×D₄	—	356	1	no	—
293	C₂²×D₄	—	178	1	no	—
294	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
295	#135	—	2	2	no	—
296	#135	—	2	2	no	—
297	C₂×Q₁₆	C₂²×D₈₉	1	1	yes	characteristic
298	C₂×SD₁₆	—	2	1	no	—
299	C₂×D₈	—	89	2	no	—
300	C₂×D₈	—	178	2	no	—
301	C₂×D₈	—	178	1	no	—
302	C₂×D₈	—	178	2	no	—
303	C₂×D₈	C₂²×D₈₉	1	1	yes	characteristic
304	C₂²×C₈	—	2	2	no	—
305	C₂²×C₈	—	2	2	no	—
306	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
307	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
308	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
309	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
310	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
311	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
312	#123	—	4	1	no	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₂²⋊Q₈	—	2	1	no	—
315	#121	—	2	1	no	—
316	#121	—	2	1	no	—
317	#121	—	356	1	no	—
318	#121	—	356	1	no	—
319	#121	—	178	2	no	—
320	#121	—	178	2	no	—
321	#120	—	4	1	no	—
322	C₄×D₄	—	4	1	no	—
323	C₄×D₄	—	4	1	no	—
324	#117	—	2	1	no	—
325	C₂×C₄⋊C₄	—	178	1	no	—
326	C₂×C₂²⋊C₄	—	356	1	no	—
327	SD₃₂	—	178	4	no	—
328	D₁₆	—	178	4	no	—
329	M₃₂	—	89	4	no	—
330	M₃₂	—	178	4	no	—
331	M₃₂	—	178	2	no	—
332	C₂×C₁₆	—	89	2	no	—
333	C₂×C₁₆	—	89	2	no	—
334	C₂×C₁₆	—	178	4	no	—
335	#107	—	89	2	no	—
336	#107	—	178	1	no	—
337	#107	C₂²×D₈₉	1	1	yes	characteristic
338	#107	C₂²×D₈₉	1	1	yes	characteristic
339	#106	—	2	1	no	—
340	#103	—	2	1	no	—
341	#103	—	2	1	no	—
342	#102	—	2	1	no	—
343	#102	—	2	1	no	—
344	#102	—	178	2	no	—
345	#102	—	178	2	no	—
346	C₂⁴	—	356	1	no	—
347	C₂⁴	#13083559	1	1	yes	characteristic
348	#41	—	4	2	no	—
349	#41	—	4	2	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂×D₄	—	356	2	no	—
356	C₂×D₄	—	356	2	no	—
357	C₂×D₄	—	356	2	no	—
358	C₂×D₄	—	356	1	no	—
359	C₂×D₄	—	356	2	no	—
360	C₂×D₄	—	178	2	no	—
361	C₂×D₄	—	712	4	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	356	1	no	—
366	C₂²×C₄	#13083559	1	1	yes	characteristic
367	C₂²×C₄	#13083559	1	1	yes	characteristic
368	C₂²×C₄	#13083559	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
372	Q₁₆	—	2	1	no	—
373	Q₁₆	—	2	1	no	—
374	SD₁₆	—	4	2	no	—
375	D₈	—	2	1	no	—
376	D₈	—	2	1	no	—
377	D₈	—	356	2	no	—
378	D₈	—	178	2	no	—
379	D₈	—	178	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	D₄×D₈₉	1	2	yes	—
388	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
389	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
390	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
391	C₂×C₈	#13083573	1	2	yes	—
392	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	—	356	1	no	—
398	C₄⋊C₄	—	178	2	no	—
399	C₂²⋊C₄	—	4	1	no	—
400	C₂²⋊C₄	—	4	1	no	—
401	C₂²⋊C₄	—	4	1	no	—
402	C₂²⋊C₄	—	4	1	no	—
403	C₂²⋊C₄	—	4	1	no	—
404	C₂²⋊C₄	—	356	2	no	—
405	C₂²⋊C₄	—	356	2	no	—
406	C₄²	—	4	1	no	—
407	C₁₆	—	89	4	no	—
408	C₁₆	—	178	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	356	2	no	—
414	C₂³	—	712	2	no	—
415	C₂³	—	712	2	no	—
416	C₂³	—	712	2	no	—
417	C₂³	C₂×#13083559	1	1	yes	characteristic
418	C₂³	C₂×#13083559	1	1	yes	characteristic
419	C₂³	C₂×#13083559	1	1	yes	characteristic
420	Q₈	—	4	1	no	—
421	Q₈	—	4	1	no	—
422	D₄	—	4	1	no	—
423	D₄	—	4	1	no	—
424	D₄	—	8	2	no	—
425	D₄	—	8	2	no	—
426	D₄	—	8	2	no	—
427	D₄	—	356	2	no	—
428	D₄	—	356	2	no	—
429	D₄	—	712	4	no	—
430	D₄	—	712	4	no	—
431	D₄	—	712	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	8	2	no	—
443	C₂×C₄	—	356	2	no	—
444	C₂×C₄	—	712	2	no	—
445	C₂×C₄	#15667984	1	2	yes	—
446	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
447	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
448	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
449	C₂×C₄	#15668032	1	2	yes	—
450	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
451	C₈	—	2	1	no	—
452	C₈	—	2	1	no	—
453	C₈	#15667984	1	2	yes	—
454	C₈	C₂×D₄×D₈₉	1	1	yes	characteristic
455	C₈	C₂×#13083573	1	1	yes	characteristic
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	8	1	no	—
466	C₂²	—	8	1	no	—
467	C₂²	—	1424	4	no	—
468	C₂²	—	712	2	no	—
469	C₂²	—	712	2	no	—
470	C₂²	—	712	2	no	—
471	C₂²	#19151832	1	2	yes	—
472	C₂²	#19152033	1	2	yes	complemented
473	C₂²	C₂²×#13083559	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	1	no	—
478	C₄	—	8	1	no	—
479	C₄	—	712	2	no	—
480	C₄	#19151832	1	2	yes	—
481	C₄	C₂×#15667984	1	1	yes	characteristic
482	C₄	C₂×#15668032	1	1	yes	characteristic
483	C₂	—	2	2	no	—
484	C₂	—	2	2	no	—
485	C₂	—	4	1	no	—
486	C₂	—	16	1	no	—
487	C₂	—	1424	2	no	—
488	C₂	C₂×#19151832	1	1	yes	characteristic
489	C₂	C₂×#19152033	1	1	yes	characteristic
490	C₂	#26033386	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#13083559
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#3050	C₂
socle	C₂²×C₈₉	C₂²×D₈
hypercenter	#3050	D₈₉
hypocenter	C₈₉	#33605
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #3050

Complements

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

N	H ≅ G/N	type
1. C₂×#19152033	C₂	semidirect
2. C₂²×#15667952	C₂	semidirect
3. C₂×#19151834	C₂	semidirect
4. #26022367	C₂	semidirect
5. #26022353	C₂	semidirect
6. #26022350	C₂	semidirect
7. #26022336	C₂	semidirect
8. #26022041	C₂	semidirect
9. #26021967	C₂	semidirect
10. #26021964	C₂	semidirect
11. C₈₉×#3050	C₂	semidirect
15. C₂×#15667955	C₂²	semidirect
16. C₂×#15667953	C₂²	semidirect
20. C₂×#15667952	C₂²	semidirect
21. C₂²×#13083549	C₂²	semidirect
28. #19151425	C₂²	semidirect
29. #19151423	C₂²	semidirect
30. #19151402	C₂²	semidirect
31. #19151399	C₂²	semidirect
32. #19151398	C₂²	semidirect
33. #19151398	C₂²	semidirect
37. #467×C₈₉	C₂²	semidirect
38. #467×C₈₉	C₂²	semidirect
39. #466×C₈₉	C₂²	semidirect
40. #466×C₈₉	C₂²	semidirect
61. #15667952	D₄	semidirect
117. #13083549	C₂×D₄	semidirect
222. C₂²×C₈₉	#509	semidirect
248. #3050	D₈₉	semidirect
257. C₈₉	#33605	semidirect
271. #467	C₂×D₈₉	semidirect
272. #467	C₂×D₈₉	semidirect
277. #466	C₂×D₈₉	semidirect
278. #466	C₂×D₈₉	semidirect
472. C₂²	#19152033	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152033	2
C₂²×#15667952	2
C₂×#19151834	2
#26022367	2
#26022353	2
#26022350	2
#26022336	2
#26022041	2
#26021967	2
#26021964	2
C₈₉×#3050	2
#33605	89