Subgroups — #36526039

Order 22784.

626 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029373	C₂	1	1	yes	maximal, characteristic
2	#26029339	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#15668045	C₂	1	1	yes	maximal, characteristic
4	#26019162	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019150	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019125	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019111	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019104	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019090	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019066	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#13083563	C₂	1	1	yes	maximal, characteristic, complemented
12	#26019019	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018687	C₂	1	1	yes	maximal, characteristic
14	#26018682	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668045	C₄	1	1	yes	characteristic
17	C₄×#13083574	C₂²	1	1	yes	characteristic
18	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
19	#19151728	C₂²	1	1	yes	characteristic
20	#19151728	C₂²	1	1	yes	characteristic
21	#19151728	C₂²	1	1	yes	characteristic
22	#19151728	C₂²	1	1	yes	characteristic
23	#19151727	—	2	1	no	—
24	#19151727	—	2	1	no	—
25	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
26	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
27	#19151706	C₄	1	1	yes	characteristic
28	#19151706	C₄	1	1	yes	characteristic
29	#19151700	C₄	1	1	yes	characteristic
30	#19151700	C₄	1	1	yes	characteristic
31	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
32	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
33	C₄×#13083563	C₂²	1	1	yes	characteristic
34	C₄×#13083563	C₂²	1	1	yes	characteristic
35	#19151672	—	2	1	no	—
36	#19151672	—	2	1	no	—
37	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
38	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
39	#19151655	C₂²	1	1	yes	characteristic
40	#19151654	—	2	1	no	—
41	#19151652	—	2	1	no	—
42	#19151648	—	2	1	no	—
43	#19151640	C₄	1	1	yes	characteristic
44	#19151622	C₂²	1	1	yes	characteristic
45	C₄⋊C₈×D₈₉	—	2	1	no	—
46	#19151608	C₄	1	1	yes	characteristic
47	#19151600	C₄	1	1	yes	characteristic
48	#19151351	C₂²	1	1	yes	characteristic
49	#19151351	C₂²	1	1	yes	characteristic
50	#19151349	C₂²	1	1	yes	characteristic
51	#19151349	C₂²	1	1	yes	characteristic
52	#19151330	C₂²	1	1	yes	characteristic
53	#19151330	C₂²	1	1	yes	characteristic
54	#19151330	C₂²	1	1	yes	characteristic
55	#19151330	C₂²	1	1	yes	characteristic
56	#19151330	C₂²	1	1	yes	characteristic
57	#19151330	C₂²	1	1	yes	characteristic
58	#19151327	C₂²	1	1	yes	characteristic
59	#19151327	C₂²	1	1	yes	characteristic
60	#431×C₈₉	C₂²	1	1	yes	characteristic
61	#431×C₈₉	C₂²	1	1	yes	characteristic
62	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
63	#322×C₈₉	C₂²	1	1	yes	characteristic
64	#322×C₈₉	C₂²	1	1	yes	characteristic
65	#322×C₈₉	C₂²	1	1	yes	characteristic
66	C₈²×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
68	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
69	#15668045	—	2	4	no	—
70	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
71	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
72	C₂×#13083563	C₂×C₄	1	1	yes	characteristic
73	C₂×#13083563	C₂×C₄	1	1	yes	characteristic
74	C₂×#13083558	—	2	1	no	—
75	C₂×C₈×D₈₉	—	2	1	no	—
76	C₂×C₈×D₈₉	—	2	1	no	—
77	C₄×Dic₁₇₈	—	2	1	no	—
78	C₄×Dic₁₇₈	—	2	1	no	—
79	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
83	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
84	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
85	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
86	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
87	C₄×C₂²⋊D₈₉	—	2	1	no	—
88	C₄×C₂²⋊D₈₉	—	2	1	no	—
89	#15667971	C₂×C₄	1	1	yes	characteristic
90	#15667969	—	2	1	no	—
91	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
92	C₂×#13083553	—	2	1	no	—
93	C₂×C₄×Dic₈₉	—	2	1	no	—
94	C₄²×D₈₉	—	2	1	no	—
95	#15667946	C₂×C₄	1	1	yes	characteristic
96	#15667946	C₂×C₄	1	1	yes	characteristic
97	#15667944	C₂×C₄	1	1	yes	characteristic
98	#15667944	C₂×C₄	1	1	yes	characteristic
99	C₄⋊#10623494	—	2	1	no	—
100	C₄⋊#10623494	C₂³	1	1	yes	characteristic
101	C₄⋊#10623494	C₂³	1	1	yes	characteristic
102	C₄⋊#10623494	C₂³	1	1	yes	characteristic
103	C₄⋊#10623494	C₂³	1	1	yes	characteristic
104	#15667941	—	2	1	no	—
105	#15667941	—	2	1	no	—
106	#15667941	—	2	1	no	—
107	#15667941	—	2	1	no	—
108	#15667941	—	2	1	no	—
109	#15667941	—	2	1	no	—
110	#15667937	C₂×C₄	1	1	yes	characteristic
111	#15667937	C₂×C₄	1	1	yes	characteristic
112	#15667937	C₂×C₄	1	1	yes	characteristic
113	#15667937	C₂×C₄	1	1	yes	characteristic
114	#15667937	C₂×C₄	1	1	yes	characteristic
115	#15667937	C₂×C₄	1	1	yes	characteristic
116	#15667934	C₂×C₄	1	1	yes	characteristic
117	#15667934	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊#10623494	—	2	1	no	—
119	#15667924	—	2	1	no	—
120	#15667924	—	2	1	no	—
121	#15667923	—	2	1	no	—
122	#15667922	—	2	1	no	—
123	#15667922	—	2	1	no	—
124	#15667922	—	2	1	no	—
125	#15667922	—	2	1	no	—
126	C₈×Dic₈₉	—	2	1	no	—
127	C₈×Dic₈₉	—	2	1	no	—
128	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
129	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
130	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
131	C₄⋊C₈×C₈₉	—	2	1	no	—
132	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
133	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
134	C₂²⋊C₈×C₈₉	—	2	1	no	—
135	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
136	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
137	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
138	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
139	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
145	#13083574	—	2	2	no	—
146	#13083574	—	4	1	no	—
147	C₂×Dic₁₇₈	—	2	2	no	—
148	C₂×Dic₁₇₈	—	2	1	no	—
149	C₂×Dic₁₇₈	—	4	1	no	—
150	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₂²⋊D₈₉	—	2	1	no	—
155	C₂²×Dic₈₉	—	2	1	no	—
156	C₂²×Dic₈₉	—	2	1	no	—
157	C₂×C₄×D₈₉	—	2	1	no	—
158	C₂×C₄×D₈₉	—	2	1	no	—
159	C₂×C₄×D₈₉	—	2	1	no	—
160	Dic₃₅₆	—	2	2	no	—
161	Dic₃₅₆	—	2	2	no	—
162	#13083563	—	2	2	no	—
163	#13083563	M₁₆	1	4	yes	complemented
164	#13083558	—	8	1	no	—
165	C₂×#10623494	—	2	1	no	—
166	C₂×#10623494	—	2	1	no	—
167	C₂×#10623494	—	2	1	no	—
168	C₂×#10623494	—	2	1	no	—
169	C₈×D₈₉	—	8	1	no	—
170	C₈×D₈₉	—	8	1	no	—
171	C₄⋊Dic₈₉	—	2	1	no	—
172	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
173	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
174	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
175	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
176	#13083553	—	2	1	no	—
177	#13083553	—	2	1	no	—
178	#13083553	—	2	1	no	—
179	#13083553	—	2	1	no	—
180	#13083553	—	2	1	no	—
181	#13083553	—	2	1	no	—
182	C₂²⋊Dic₈₉	—	2	1	no	—
183	#13083551	—	2	1	no	—
184	#13083551	—	2	1	no	—
185	C₄×Dic₈₉	—	2	1	no	—
186	C₄×Dic₈₉	—	2	1	no	—
187	C₄×Dic₈₉	—	2	1	no	—
188	C₄×Dic₈₉	—	2	1	no	—
189	C₄×Dic₈₉	—	2	1	no	—
190	C₄×Dic₈₉	—	2	1	no	—
191	C₄×Dic₈₉	—	2	1	no	—
192	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
195	M₁₆×C₈₉	—	2	2	no	—
196	M₁₆×C₈₉	—	4	1	no	—
197	C₂×C₈×C₈₉	—	2	1	no	—
198	C₂×C₈×C₈₉	—	2	1	no	—
199	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
204	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
205	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
206	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₈₉	#41	1	1	yes	characteristic
210	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
211	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
212	C₂²×D₈₉	—	2	1	no	—
213	C₂×C₄×C₈₉	—	2	1	no	—
214	C₂×C₄×C₈₉	—	2	1	no	—
215	C₂×C₄×C₈₉	—	2	1	no	—
216	C₂×C₄×C₈₉	—	2	1	no	—
217	C₂×C₄×C₈₉	—	4	1	no	—
218	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
224	C₂²⋊D₈₉	—	4	2	no	—
225	C₂×Dic₈₉	—	2	1	no	—
226	C₂×Dic₈₉	—	2	1	no	—
227	C₂×Dic₈₉	—	2	1	no	—
228	C₂×Dic₈₉	—	2	1	no	—
229	C₂×Dic₈₉	—	2	1	no	—
230	C₂×Dic₈₉	—	2	1	no	—
231	C₂×Dic₈₉	—	2	1	no	—
232	C₂×Dic₈₉	—	4	2	no	—
233	C₂×Dic₈₉	—	4	2	no	—
234	D₃₅₆	—	2	1	no	—
235	D₃₅₆	C₂×M₁₆	1	2	yes	—
236	C₄×D₈₉	—	4	2	no	—
237	C₄×D₈₉	—	4	2	no	—
238	C₄×D₈₉	—	4	1	no	—
239	C₄×D₈₉	—	4	1	no	—
240	Dic₁₇₈	—	2	1	no	—
241	Dic₁₇₈	—	2	1	no	—
242	Dic₁₇₈	—	2	1	no	—
243	Dic₁₇₈	—	2	1	no	—
244	Dic₁₇₈	—	2	1	no	—
245	Dic₁₇₈	—	4	2	no	—
246	Dic₁₇₈	C₂×M₁₆	1	2	yes	—
247	C₈×C₈₉	—	2	1	no	—
248	C₈×C₈₉	—	2	1	no	—
249	C₈×C₈₉	—	2	1	no	—
250	C₈×C₈₉	—	2	1	no	—
251	C₈×C₈₉	—	2	1	no	—
252	C₈×C₈₉	—	2	1	no	—
253	C₈×C₈₉	—	2	1	no	—
254	C₈×C₈₉	—	4	1	no	—
255	C₈×C₈₉	—	4	1	no	—
256	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
257	#10623494	—	4	1	no	—
258	#10623494	—	4	1	no	—
259	#10623494	—	4	1	no	—
260	#10623494	—	4	1	no	—
261	C₂²×C₈₉	—	2	1	no	—
262	C₂²×C₈₉	—	2	1	no	—
263	C₂²×C₈₉	—	2	1	no	—
264	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
265	C₂×D₈₉	—	2	2	no	—
266	C₂×D₈₉	—	4	1	no	—
267	C₂×D₈₉	—	4	1	no	—
268	C₄×C₈₉	—	2	1	no	—
269	C₄×C₈₉	—	2	1	no	—
270	C₄×C₈₉	—	2	1	no	—
271	C₄×C₈₉	—	2	1	no	—
272	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
273	C₄×C₈₉	#568	1	1	yes	characteristic
274	C₄×C₈₉	#577	1	1	yes	characteristic
275	C₄×C₈₉	#578	1	1	yes	characteristic
276	Dic₈₉	—	2	2	no	—
277	Dic₈₉	—	4	1	no	—
278	Dic₈₉	—	4	1	no	—
279	Dic₈₉	—	4	1	no	—
280	Dic₈₉	—	4	1	no	—
281	Dic₈₉	—	4	1	no	—
282	Dic₈₉	—	4	1	no	—
283	#18051	—	89	1	no	maximal, Sylow
284	C₂×C₈₉	—	4	1	no	—
285	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
286	C₂×C₈₉	#2947	1	1	yes	characteristic
287	C₂×C₈₉	#2955	1	1	yes	characteristic
288	D₈₉	—	4	2	no	—
289	#2990	—	89	1	no	—
290	#2984	—	89	1	no	—
291	C₄×#137	—	89	1	no	—
292	#1593	—	89	1	no	—
293	#1591	—	89	1	no	—
294	#1587	—	89	1	no	—
295	#1585	—	89	1	no	—
296	#1584	—	89	1	no	—
297	#1582	—	89	1	no	—
298	SD₁₆⋊C₈	—	89	1	no	—
299	C₈×SD₁₆	—	89	1	no	—
300	#1569	—	89	1	no	—
301	#1488	—	89	1	no	—
302	#1487	—	89	1	no	—
303	#1453	D₈₉	1	1	yes	characteristic, complemented
304	C₈₉	#18051	1	1	yes	characteristic, complemented, Sylow
305	C₂×#137	—	89	1	no	—
306	C₄×#41	—	89	1	no	—
307	C₂×C₄×Q₈	—	89	1	no	—
308	#446	—	89	1	no	—
309	#446	—	89	1	no	—
310	#446	—	89	1	no	—
311	#446	—	89	1	no	—
312	#446	—	178	1	no	—
313	#446	—	178	1	no	—
314	C₈×Q₈	—	89	1	no	—
315	C₈×Q₈	—	89	1	no	—
316	#441	—	89	1	no	—
317	#441	—	89	1	no	—
318	#440	—	89	1	no	—
319	#440	—	89	1	no	—
320	C₄×Q₁₆	—	89	1	no	—
321	C₄×Q₁₆	—	89	1	no	—
322	C₄×SD₁₆	—	89	1	no	—
323	C₄×SD₁₆	—	89	1	no	—
324	#435	—	178	1	no	—
325	#435	—	178	1	no	—
326	C₈×D₄	—	89	1	no	—
327	C₈×D₄	—	89	1	no	—
328	#432	—	89	1	no	—
329	#432	—	178	1	no	—
330	#432	—	178	1	no	—
331	#431	—	178	1	no	—
332	#431	C₂×D₈₉	1	1	yes	characteristic
333	#431	C₂×D₈₉	1	1	yes	characteristic
334	#428	—	89	1	no	—
335	#423	—	89	1	no	—
336	C₂×C₄⋊C₈	—	178	1	no	—
337	#419	—	89	1	no	—
338	#417	—	89	1	no	—
339	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
340	#335	—	89	1	no	—
341	#335	—	89	1	no	—
342	#334	—	89	1	no	—
343	#334	—	89	1	no	—
344	Q₈⋊C₈	—	89	1	no	—
345	Q₈⋊C₈	—	89	1	no	—
346	Q₈⋊C₈	—	89	1	no	—
347	Q₈⋊C₈	—	89	1	no	—
348	Q₈⋊C₈	—	89	1	no	—
349	Q₈⋊C₈	—	89	1	no	—
350	D₄⋊C₈	—	89	1	no	—
351	D₄⋊C₈	—	89	1	no	—
352	#322	C₂×D₈₉	1	1	yes	characteristic
353	#322	C₂×D₈₉	1	1	yes	characteristic
354	#322	C₂×D₈₉	1	1	yes	characteristic
355	C₈²	C₂×D₈₉	1	1	yes	characteristic
356	C₂×#41	—	89	1	no	—
357	C₂²×Q₈	—	89	1	no	—
358	#137	—	178	4	no	—
359	C₂×Q₁₆	—	89	1	no	—
360	C₂×Q₁₆	—	89	1	no	—
361	C₂×SD₁₆	—	89	1	no	—
362	C₂×SD₁₆	—	89	1	no	—
363	C₂×M₁₆	—	178	1	no	—
364	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
365	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
366	C₂²×C₈	—	178	1	no	—
367	C₂²×C₈	—	178	1	no	—
368	C₄×Q₈	—	89	1	no	—
369	C₄×Q₈	—	89	1	no	—
370	C₄×Q₈	—	89	1	no	—
371	C₄×Q₈	—	89	1	no	—
372	C₄×Q₈	—	89	1	no	—
373	C₄×Q₈	—	89	1	no	—
374	C₄×Q₈	—	178	1	no	—
375	C₄×Q₈	—	178	1	no	—
376	C₄×D₄	—	89	1	no	—
377	C₄×D₄	—	89	1	no	—
378	C₄×D₄	—	178	1	no	—
379	C₄×D₄	—	178	1	no	—
380	#117	—	89	1	no	—
381	#117	—	178	1	no	—
382	C₂×C₄⋊C₄	—	89	1	no	—
383	C₂×C₄⋊C₄	—	178	1	no	—
384	C₂×C₄²	—	178	1	no	—
385	C₂×C₄²	—	178	1	no	—
386	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
387	#107	—	89	1	no	—
388	#107	—	89	1	no	—
389	#106	—	89	1	no	—
390	#106	—	89	1	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	89	1	no	—
393	C₄⋊C₈	—	89	1	no	—
394	C₄⋊C₈	—	89	1	no	—
395	C₄⋊C₈	—	89	1	no	—
396	C₄⋊C₈	—	178	1	no	—
397	C₄⋊C₈	—	178	1	no	—
398	C₄⋊C₈	—	178	1	no	—
399	C₄⋊C₈	—	178	1	no	—
400	C₄⋊C₈	—	178	1	no	—
401	C₄⋊C₈	—	178	1	no	—
402	C₄⋊C₈	—	178	1	no	—
403	C₄⋊C₈	D₃₅₆	1	1	yes	characteristic
404	C₄⋊C₈	D₃₅₆	1	1	yes	characteristic
405	#103	—	89	1	no	—
406	#103	—	89	1	no	—
407	#103	—	89	1	no	—
408	#103	—	89	1	no	—
409	#103	—	89	1	no	—
410	#103	—	89	1	no	—
411	#102	—	89	1	no	—
412	#102	—	89	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	—	178	1	no	—
415	C₂²⋊C₈	—	178	1	no	—
416	C₂²⋊C₈	—	178	1	no	—
417	C₂²⋊C₈	D₃₅₆	1	1	yes	characteristic
418	C₂²⋊C₈	D₃₅₆	1	1	yes	characteristic
419	#97	—	178	1	no	—
420	#97	—	178	1	no	—
421	#97	—	178	1	no	—
422	#97	—	178	1	no	—
423	#97	—	178	1	no	—
424	#97	C₄×D₈₉	1	1	yes	characteristic
425	#97	C₄×D₈₉	1	1	yes	characteristic
426	C₄×C₈	—	178	1	no	—
427	C₄×C₈	—	178	1	no	—
428	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
429	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
430	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
431	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
432	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
434	#41	—	356	1	no	—
435	#41	—	178	2	no	—
436	C₂×Q₈	—	89	1	no	—
437	C₂×Q₈	—	89	1	no	—
438	C₂×Q₈	—	89	1	no	—
439	C₂×Q₈	—	356	1	no	—
440	C₂×Q₈	—	178	2	no	—
441	C₂×Q₈	—	178	1	no	—
442	C₂×D₄	—	89	1	no	—
443	C₂×D₄	—	178	1	no	—
444	C₂²×C₄	—	178	1	no	—
445	C₂²×C₄	—	178	1	no	—
446	C₂²×C₄	—	178	1	no	—
447	C₂²×C₄	—	178	1	no	—
448	C₂²×C₄	—	178	1	no	—
449	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
451	C₂²×C₄	#13083574	1	1	yes	characteristic
452	Q₁₆	—	178	2	no	—
453	Q₁₆	—	178	2	no	—
454	SD₁₆	—	89	4	no	—
455	SD₁₆	—	178	2	no	—
456	M₁₆	—	2	2	no	—
457	M₁₆	—	4	1	no	—
458	M₁₆	—	712	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	178	1	no	—
462	C₂×C₈	—	178	1	no	—
463	C₂×C₈	—	178	1	no	—
464	C₂×C₈	—	178	1	no	—
465	C₂×C₈	—	712	1	no	—
466	C₂×C₈	—	712	1	no	—
467	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
468	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
469	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
470	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
471	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
472	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
473	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
474	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
475	C₄⋊C₄	—	89	1	no	—
476	C₄⋊C₄	—	89	1	no	—
477	C₄⋊C₄	—	89	1	no	—
478	C₄⋊C₄	—	89	1	no	—
479	C₄⋊C₄	—	178	1	no	—
480	C₄⋊C₄	—	178	1	no	—
481	C₄⋊C₄	—	178	1	no	—
482	C₄⋊C₄	—	178	1	no	—
483	C₄⋊C₄	—	178	1	no	—
484	C₄⋊C₄	—	178	1	no	—
485	C₄⋊C₄	—	178	1	no	—
486	C₂²⋊C₄	—	178	1	no	—
487	C₂²⋊C₄	—	178	1	no	—
488	C₂²⋊C₄	—	178	1	no	—
489	C₄²	—	178	1	no	—
490	C₄²	—	178	1	no	—
491	C₄²	—	178	1	no	—
492	C₄²	—	178	1	no	—
493	C₄²	—	178	1	no	—
494	C₄²	—	178	1	no	—
495	C₄²	—	178	1	no	—
496	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
497	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
498	C₄²	#13083574	1	1	yes	characteristic
499	C₄²	C₂³×D₈₉	1	1	yes	characteristic
500	C₂³	—	178	1	no	—
501	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
502	Q₈	—	89	2	no	—
503	Q₈	—	356	2	no	—
504	Q₈	—	178	1	no	—
505	Q₈	—	178	1	no	—
506	Q₈	—	178	1	no	—
507	Q₈	—	178	1	no	—
508	Q₈	—	178	1	no	—
509	D₄	—	89	2	no	—
510	D₄	—	356	2	no	—
511	D₄	—	178	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	356	2	no	—
518	C₂×C₄	—	356	2	no	—
519	C₂×C₄	—	356	2	no	—
520	C₂×C₄	—	356	2	no	—
521	C₂×C₄	—	356	1	no	—
522	C₂×C₄	—	356	1	no	—
523	C₂×C₄	—	178	1	no	—
524	C₂×C₄	—	178	1	no	—
525	C₂×C₄	—	178	1	no	—
526	C₂×C₄	—	178	1	no	—
527	C₂×C₄	—	178	1	no	—
528	C₂×C₄	—	178	1	no	—
529	C₂×C₄	—	178	1	no	—
530	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
531	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
532	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
533	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
535	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	2	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	356	1	no	—
546	C₈	—	356	1	no	—
547	C₈	—	356	1	no	—
548	C₈	—	356	1	no	—
549	C₈	M₁₆×D₈₉	1	2	yes	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	356	1	no	—
554	C₂²	—	356	1	no	—
555	C₂²	—	178	2	no	—
556	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	356	1	no	—
562	C₄	—	356	1	no	—
563	C₄	—	356	1	no	—
564	C₄	—	356	1	no	—
565	C₄	—	356	1	no	—
566	C₄	—	356	1	no	—
567	C₄	—	178	2	no	—
568	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
569	C₄	#19152364	1	1	yes	characteristic
570	C₄	#19152410	1	1	yes	characteristic
571	C₄	#19152415	1	1	yes	characteristic
572	C₂	—	4	1	no	—
573	C₂	—	356	2	no	—
574	C₂	M₁₆×D₃₅₆	1	1	yes	characteristic
575	C₂	#26029097	1	1	yes	characteristic
576	C₂	#26029156	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1453	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#13083574	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1453	D₈₉
hypocenter	C₈₉	#18051
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #1453

Complements

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

N	H ≅ G/N	type
2. #26029339	C₂	semidirect
4. #26019162	C₂	semidirect
5. #26019150	C₂	semidirect
6. #26019125	C₂	semidirect
7. #26019111	C₂	semidirect
8. #26019104	C₂	semidirect
9. #26019090	C₂	semidirect
10. #26019066	C₂	semidirect
11. C₈×#13083563	C₂	semidirect
12. #26019019	C₂	semidirect
14. #26018682	C₂	semidirect
15. C₈₉×#1453	C₂	semidirect
163. #13083563	M₁₆	semidirect
303. #1453	D₈₉	semidirect
304. C₈₉	#18051	semidirect

Maximal subgroups

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

subgroup	index
#26029373	2
#26029339	2
C₄×#15668045	2
#26019162	2
#26019150	2
#26019125	2
#26019111	2
#26019104	2
#26019090	2
#26019066	2
C₈×#13083563	2
#26019019	2
#26018687	2
#26018682	2
C₈₉×#1453	2
#18051	89