Subgroups — #36707999

Order 22784.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#13083574	C₂	1	1	yes	maximal, characteristic
2	#26022158	C₂	1	2	yes	maximal, complemented
3	#26022079	C₂	1	2	yes	maximal, complemented
4	#26022077	C₂	1	2	yes	maximal, complemented
5	C₁₆×C₂²⋊D₈₉	C₂	1	2	yes	maximal, complemented
6	#26022055	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022053	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022053	C₂	1	1	yes	maximal, characteristic, complemented
9	#26021845	C₂	1	1	yes	maximal, characteristic, complemented
10	#346×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#346×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#13083574	C₄	1	1	yes	characteristic
13	C₂×#15667951	C₂²	1	2	yes	—
14	C₂×C₁₆×D₈₉	C₂²	1	2	yes	—
15	C₈×Dic₁₇₈	C₄	1	1	yes	characteristic
16	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
17	C₈×D₃₅₆	C₄	1	1	yes	characteristic
18	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
19	C₈×C₂²⋊D₈₉	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₈₉	C₄	1	1	yes	characteristic
21	C₈×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
22	C₈×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
23	#19151651	C₄	1	1	yes	characteristic
24	#19151649	C₄	1	1	yes	characteristic
25	#19151649	C₄	1	1	yes	characteristic
26	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
28	C₄⋊#13083549	C₂²	1	2	yes	—
29	#19151416	C₂²	1	2	yes	—
30	#19151416	C₂²	1	2	yes	—
31	C₂²⋊#13083549	C₂²	1	2	yes	—
32	#19151377	C₂²	1	2	yes	—
33	#19151377	C₂²	1	2	yes	—
34	#19151374	C₂²	1	1	yes	characteristic
35	#19151374	C₂²	1	1	yes	characteristic
36	#19151373	C₂²	1	2	yes	—
37	C₁₆×Dic₈₉	C₂²	1	2	yes	—
38	C₂²×C₁₆×C₈₉	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
40	#346×C₈₉	C₂²	1	2	yes	—
41	#346×C₈₉	C₂²	1	1	yes	characteristic
42	#346×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#13083574	C₈	1	1	yes	characteristic
44	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
47	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
48	C₄×Dic₁₇₈	C₈	1	1	yes	characteristic
49	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
50	C₄×D₃₅₆	C₈	1	1	yes	characteristic
51	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
52	C₄×C₂²⋊D₈₉	C₈	1	1	yes	characteristic
53	C₄×C₂²⋊D₈₉	C₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
55	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
56	#15667971	C₈	1	1	yes	characteristic
57	#15667969	C₈	1	1	yes	characteristic
58	#15667969	C₈	1	1	yes	characteristic
59	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
61	#15667951	—	2	4	no	—
62	C₂×#13083549	C₂³	1	2	yes	—
63	C₂×#13083549	C₂³	1	2	yes	—
64	C₁₆×D₈₉	—	2	4	no	—
65	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
66	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
67	#15667941	C₂×C₄	1	1	yes	characteristic
68	#15667941	C₂×C₄	1	1	yes	characteristic
69	#15667941	C₂×C₄	1	1	yes	characteristic
70	#15667941	C₂×C₄	1	1	yes	characteristic
71	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
72	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
73	#15667924	C₂×C₄	1	1	yes	characteristic
74	#15667924	C₂×C₄	1	1	yes	characteristic
75	#15667924	C₂×C₄	1	1	yes	characteristic
76	#15667924	C₂×C₄	1	1	yes	characteristic
77	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
78	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
82	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₁₆×C₈₉	—	2	4	no	—
87	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
88	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
89	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	#13083574	—	2	4	no	—
94	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
95	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
96	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
97	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
98	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
99	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
104	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
105	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
106	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
107	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
108	C₈×D₈₉	—	2	2	no	—
109	C₈×D₈₉	—	2	2	no	—
110	C₈×D₈₉	—	2	2	no	—
111	C₈×D₈₉	—	2	2	no	—
112	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
113	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
114	#13083553	C₂×C₈	1	1	yes	characteristic
115	#13083553	C₂×C₈	1	1	yes	characteristic
116	#13083553	C₂×C₈	1	1	yes	characteristic
117	#13083553	C₂×C₈	1	1	yes	characteristic
118	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
119	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
120	#13083551	C₂×C₈	1	1	yes	characteristic
121	#13083551	C₂×C₈	1	1	yes	characteristic
122	#13083551	C₂×C₈	1	1	yes	characteristic
123	#13083551	C₂×C₈	1	1	yes	characteristic
124	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
125	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
126	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
127	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
128	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
130	#13083549	—	2	2	no	—
131	#13083549	—	2	2	no	—
132	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₈₉	—	2	2	no	—
136	C₂×C₈×C₈₉	—	2	2	no	—
137	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
141	C₄²×C₈₉	C₂×C₈	1	1	yes	characteristic
142	C₄²×C₈₉	C₂×C₈	1	1	yes	characteristic
143	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
145	C₁₆×C₈₉	—	2	2	no	—
146	C₁₆×C₈₉	#41	1	4	yes	complemented
147	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
148	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₈₉	—	2	2	no	—
151	C₂×C₄×C₈₉	—	2	1	no	—
152	C₂×C₄×C₈₉	—	2	1	no	—
153	C₂×C₄×C₈₉	—	4	1	no	—
154	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
160	C₂²⋊D₈₉	—	2	2	no	—
161	C₂²⋊D₈₉	M₃₂	1	4	yes	complemented
162	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
163	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
164	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
165	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
166	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
167	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
168	D₃₅₆	—	2	2	no	—
169	C₄×D₈₉	—	2	2	no	—
170	C₄×D₈₉	—	2	1	no	—
171	C₄×D₈₉	—	2	1	no	—
172	C₄×D₈₉	—	2	1	no	—
173	C₄×D₈₉	—	2	1	no	—
174	C₄×D₈₉	—	2	2	no	—
175	C₄×D₈₉	—	4	1	no	—
176	C₄×D₈₉	—	4	1	no	—
177	Dic₁₇₈	—	2	2	no	—
178	C₈×C₈₉	—	2	1	no	—
179	C₈×C₈₉	—	2	1	no	—
180	C₈×C₈₉	#131	1	2	yes	—
181	C₈×C₈₉	C₂×#41	1	2	yes	—
182	#10623494	—	2	1	no	—
183	#10623494	—	2	1	no	—
184	#10623494	—	2	1	no	—
185	#10623494	—	2	1	no	—
186	C₂²×C₈₉	—	2	1	no	—
187	C₂²×C₈₉	—	2	1	no	—
188	C₂²×C₈₉	C₂×M₃₂	1	2	yes	—
189	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
190	C₂×D₈₉	—	2	1	no	—
191	C₂×D₈₉	—	2	1	no	—
192	C₂×D₈₉	—	2	1	no	—
193	C₂×D₈₉	—	2	1	no	—
194	C₂×D₈₉	—	2	1	no	—
195	C₂×D₈₉	C₂×M₃₂	1	2	yes	—
196	C₄×C₈₉	—	2	1	no	—
197	C₄×C₈₉	—	2	1	no	—
198	C₄×C₈₉	—	2	1	no	—
199	C₄×C₈₉	—	2	1	no	—
200	C₄×C₈₉	—	2	1	no	—
201	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
202	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
203	Dic₈₉	—	2	1	no	—
204	Dic₈₉	—	2	1	no	—
205	Dic₈₉	—	2	1	no	—
206	Dic₈₉	—	2	1	no	—
207	Dic₈₉	—	2	1	no	—
208	Dic₈₉	C₂×M₃₂	1	2	yes	—
209	#33484	—	89	1	no	maximal, Sylow
210	C₂×C₈₉	—	2	2	no	—
211	C₂×C₈₉	C₈×#41	1	1	yes	characteristic
212	C₂×C₈₉	C₂²×M₃₂	1	1	yes	characteristic
213	C₂×C₈₉	#3407	1	1	yes	characteristic
214	D₈₉	—	2	2	no	—
215	D₈₉	—	4	1	no	—
216	C₈×#41	—	89	1	no	—
217	#2183	—	89	2	no	—
218	#2168	—	89	2	no	—
219	#2168	—	89	2	no	—
220	D₄×C₁₆	—	89	2	no	—
221	#2163	—	89	1	no	—
222	#2163	—	89	1	no	—
223	#2163	—	89	1	no	—
224	C₄×M₃₂	—	89	1	no	—
225	C₂×#346	—	89	1	no	—
226	C₂×#346	D₈₉	1	1	yes	characteristic, complemented
227	C₈₉	#33484	1	1	yes	characteristic, complemented, Sylow
228	C₄×#41	—	89	1	no	—
229	C₂×M₃₂	—	89	2	no	—
230	C₂²×C₁₆	—	89	2	no	—
231	C₂²×C₁₆	C₂×D₈₉	1	2	yes	—
232	C₈×Q₈	—	89	1	no	—
233	C₈×Q₈	—	89	1	no	—
234	C₈×D₄	—	89	1	no	—
235	C₈×D₄	—	89	1	no	—
236	C₈×D₄	—	89	1	no	—
237	C₈×D₄	—	89	1	no	—
238	C₈×D₄	—	89	1	no	—
239	C₈×D₄	—	89	1	no	—
240	#431	—	89	1	no	—
241	#431	—	89	1	no	—
242	#431	—	89	1	no	—
243	C₂×C₄×C₈	—	89	1	no	—
244	C₂×C₄×C₈	—	89	1	no	—
245	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
246	C₄⋊C₁₆	—	89	2	no	—
247	C₄⋊C₁₆	—	89	2	no	—
248	C₄⋊C₁₆	—	89	2	no	—
249	C₂²⋊C₁₆	—	89	2	no	—
250	C₂²⋊C₁₆	—	89	2	no	—
251	C₂²⋊C₁₆	—	89	2	no	—
252	#346	—	89	2	no	—
253	#346	—	89	1	no	—
254	#346	—	89	1	no	—
255	#346	C₂×D₈₉	1	1	yes	characteristic
256	#346	C₂×D₈₉	1	1	yes	characteristic
257	#346	C₂×D₈₉	1	2	yes	—
258	C₄×C₁₆	—	89	2	no	—
259	C₂×#41	—	89	1	no	—
260	C₂²×C₈	—	89	1	no	—
261	C₂²×C₈	—	89	1	no	—
262	C₂²×C₈	—	89	1	no	—
263	C₂²×C₈	—	89	1	no	—
264	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
266	C₄×Q₈	—	89	1	no	—
267	C₄×Q₈	—	89	1	no	—
268	C₄×D₄	—	89	1	no	—
269	C₄×D₄	—	89	1	no	—
270	C₄×D₄	—	89	1	no	—
271	C₄×D₄	—	89	1	no	—
272	C₄×D₄	—	89	1	no	—
273	C₄×D₄	—	89	1	no	—
274	#117	—	89	1	no	—
275	#117	—	89	1	no	—
276	#117	—	89	1	no	—
277	C₂×C₄²	—	89	1	no	—
278	C₂×C₄²	—	89	1	no	—
279	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
280	M₃₂	—	178	4	no	—
281	C₂×C₁₆	—	2	4	no	—
282	C₂×C₁₆	—	89	2	no	—
283	C₂×C₁₆	—	89	2	no	—
284	C₂×C₁₆	—	178	4	no	—
285	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
286	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
287	C₄⋊C₈	—	89	1	no	—
288	C₄⋊C₈	—	89	1	no	—
289	C₄⋊C₈	—	89	1	no	—
290	C₄⋊C₈	—	89	1	no	—
291	C₄⋊C₈	—	89	1	no	—
292	C₄⋊C₈	—	89	1	no	—
293	C₂²⋊C₈	—	89	1	no	—
294	C₂²⋊C₈	—	89	1	no	—
295	C₂²⋊C₈	—	89	1	no	—
296	C₂²⋊C₈	—	89	1	no	—
297	C₂²⋊C₈	—	89	1	no	—
298	C₂²⋊C₈	—	89	1	no	—
299	C₄×C₈	—	89	1	no	—
300	C₄×C₈	—	89	1	no	—
301	C₄×C₈	—	89	1	no	—
302	C₄×C₈	—	89	1	no	—
303	C₄×C₈	—	89	1	no	—
304	C₄×C₈	—	89	1	no	—
305	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
306	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
307	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
308	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
309	#41	—	178	4	no	—
310	C₂×Q₈	—	89	1	no	—
311	C₂×D₄	—	89	1	no	—
312	C₂×D₄	—	89	1	no	—
313	C₂×D₄	—	89	1	no	—
314	C₂²×C₄	—	89	1	no	—
315	C₂²×C₄	—	89	1	no	—
316	C₂²×C₄	—	89	1	no	—
317	C₂²×C₄	—	89	1	no	—
318	C₂²×C₄	—	89	1	no	—
319	C₂²×C₄	—	89	1	no	—
320	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
321	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	89	1	no	—
326	C₂×C₈	—	89	1	no	—
327	C₂×C₈	—	89	1	no	—
328	C₂×C₈	—	89	1	no	—
329	C₂×C₈	—	178	2	no	—
330	C₂×C₈	—	178	2	no	—
331	C₂×C₈	—	178	2	no	—
332	C₂×C₈	—	178	2	no	—
333	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
336	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
337	C₄⋊C₄	—	89	1	no	—
338	C₄⋊C₄	—	89	1	no	—
339	C₄⋊C₄	—	89	1	no	—
340	C₄⋊C₄	—	89	1	no	—
341	C₄⋊C₄	—	89	1	no	—
342	C₄⋊C₄	—	89	1	no	—
343	C₂²⋊C₄	—	89	1	no	—
344	C₂²⋊C₄	—	89	1	no	—
345	C₂²⋊C₄	—	89	1	no	—
346	C₂²⋊C₄	—	89	1	no	—
347	C₂²⋊C₄	—	89	1	no	—
348	C₂²⋊C₄	—	89	1	no	—
349	C₄²	—	89	1	no	—
350	C₄²	—	89	1	no	—
351	C₄²	—	89	1	no	—
352	C₄²	—	89	1	no	—
353	C₄²	—	89	1	no	—
354	C₄²	—	89	1	no	—
355	C₄²	C₈×D₈₉	1	1	yes	characteristic
356	C₄²	C₈×D₈₉	1	1	yes	characteristic
357	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
358	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
359	C₁₆	—	2	2	no	—
360	C₁₆	—	178	2	no	—
361	C₁₆	—	178	2	no	—
362	C₁₆	#13083574	1	4	yes	complemented
363	C₂³	—	89	1	no	—
364	C₂³	—	89	1	no	—
365	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
366	Q₈	—	178	2	no	—
367	D₄	—	89	4	no	—
368	D₄	—	178	2	no	—
369	D₄	—	178	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	89	1	no	—
375	C₂×C₄	—	89	1	no	—
376	C₂×C₄	—	89	1	no	—
377	C₂×C₄	—	89	1	no	—
378	C₂×C₄	—	89	1	no	—
379	C₂×C₄	—	89	1	no	—
380	C₂×C₄	—	356	1	no	—
381	C₂×C₄	—	356	1	no	—
382	C₂×C₄	—	178	2	no	—
383	C₂×C₄	—	178	2	no	—
384	C₂×C₄	—	178	1	no	—
385	C₂×C₄	—	178	1	no	—
386	C₂×C₄	—	178	1	no	—
387	C₂×C₄	—	178	1	no	—
388	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
389	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
390	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
391	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
392	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	178	1	no	—
397	C₈	—	178	1	no	—
398	C₈	—	178	1	no	—
399	C₈	—	178	1	no	—
400	C₈	#15668018	1	2	yes	—
401	C₈	C₂×#13083574	1	2	yes	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	89	2	no	—
405	C₂²	—	178	1	no	—
406	C₂²	—	178	1	no	—
407	C₂²	—	178	1	no	—
408	C₂²	—	178	1	no	—
409	C₂²	—	178	1	no	—
410	C₂²	M₃₂×D₈₉	1	2	yes	—
411	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	89	2	no	—
418	C₄	—	178	1	no	—
419	C₄	—	178	1	no	—
420	C₄	—	178	1	no	—
421	C₄	—	178	1	no	—
422	C₄	—	178	1	no	—
423	C₄	C₄×#13083574	1	1	yes	characteristic
424	C₄	C₂×#15668018	1	1	yes	characteristic
425	C₂	—	2	2	no	—
426	C₂	—	356	1	no	—
427	C₂	—	178	2	no	—
428	C₂	C₈×#13083574	1	1	yes	characteristic
429	C₂	C₂×M₃₂×D₈₉	1	1	yes	characteristic
430	C₂	#26033354	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂³×C₈
Fitting	C₂×#346×C₈₉	C₂
prime radical	C₂×#13083574	C₈
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	C₂×#346	D₈₉
hypocenter	C₈₉	#33484
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#346

Complements

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

N	H ≅ G/N	type
2. #26022158	C₂	semidirect
3. #26022079	C₂	semidirect
4. #26022077	C₂	semidirect
5. C₁₆×C₂²⋊D₈₉	C₂	semidirect
6. #26022055	C₂	semidirect
7. #26022053	C₂	semidirect
8. #26022053	C₂	semidirect
9. #26021845	C₂	semidirect
10. #346×D₈₉	C₂	semidirect
11. C₂×#346×C₈₉	C₂	semidirect
146. C₁₆×C₈₉	#41	semidirect
161. C₂²⋊D₈₉	M₃₂	semidirect
226. C₂×#346	D₈₉	semidirect
227. C₈₉	#33484	semidirect
362. C₁₆	#13083574	semidirect

Maximal subgroups

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

subgroup	index
C₈×#13083574	2
#26022158	2
#26022079	2
#26022077	2
C₁₆×C₂²⋊D₈₉	2
#26022055	2
#26022053	2
#26021845	2
#346×D₈₉	2
C₂×#346×C₈₉	2
#33484	89