Subgroups — #36573338

Order 22784.

740 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151728	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic
3	#26022729	C₂	1	1	yes	maximal, characteristic
4	#26020972	C₂	1	2	yes	maximal
5	#26020970	C₂	1	1	yes	maximal, characteristic
6	#26020970	C₂	1	1	yes	maximal, characteristic
7	#26020967	C₂	1	2	yes	maximal
8	#26020370	C₂	1	2	yes	maximal
9	#26020369	C₂	1	1	yes	maximal, characteristic
10	#26020108	C₂	1	2	yes	maximal
11	C₄×C₄⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
13	#19151728	—	2	4	no	—
14	C₈×Dic₁₇₈	—	2	4	no	—
15	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
17	C₂×#15667941	C₂²	1	2	yes	—
18	C₂×#15667941	C₂²	1	2	yes	—
19	C₂×#15667941	C₂²	1	2	yes	—
20	C₂×#15667941	C₂²	1	2	yes	—
21	C₂×#15667922	C₂²	1	2	yes	—
22	C₂×C₈×Dic₈₉	C₂²	1	2	yes	—
23	#19151504	C₄	1	1	yes	characteristic
24	#19151504	C₄	1	1	yes	characteristic
25	#19151496	C₄	1	1	yes	characteristic
26	#19151496	C₄	1	1	yes	characteristic
27	#19151482	C₄	1	2	yes	—
28	#19151482	C₄	1	2	yes	—
29	C₄×#13083553	C₂²	1	2	yes	—
30	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
31	#19151444	C₂²	1	2	yes	—
32	#19151353	C₂²	1	2	yes	—
33	#19151353	C₂²	1	2	yes	—
34	#19151352	C₂²	1	2	yes	—
35	#19151352	C₂²	1	2	yes	—
36	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₄³×C₈₉	C₂²	1	1	yes	characteristic
41	#336×C₈₉	C₂²	1	1	yes	characteristic
42	#336×C₈₉	C₂²	1	1	yes	characteristic
43	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
44	C₂²×#10623494	C₂³	1	2	yes	—
45	C₂²×#10623494	C₂³	1	2	yes	—
46	C₄×Dic₁₇₈	D₄	1	4	yes	—
47	C₄×Dic₁₇₈	Q₈	1	4	yes	—
48	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
51	C₂×#13083553	C₂×C₄	1	2	yes	—
52	C₂×#13083553	C₂×C₄	1	2	yes	—
53	C₂×#13083553	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
55	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
56	C₄⋊#10623494	—	2	2	no	—
57	C₄⋊#10623494	—	2	2	no	—
58	#15667941	—	2	4	no	—
59	#15667941	—	2	4	no	—
60	#15667941	—	2	4	no	—
61	#15667941	—	2	4	no	—
62	#15667922	—	2	4	no	—
63	C₈×Dic₈₉	—	2	4	no	—
64	#15667919	C₂×C₄	1	2	yes	—
65	#15667919	C₂×C₄	1	2	yes	—
66	#15667919	C₂×C₄	1	2	yes	—
67	#15667919	C₂×C₄	1	2	yes	—
68	#15667919	C₂×C₄	1	2	yes	—
69	#15667919	C₂×C₄	1	2	yes	—
70	#15667919	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₈₉	—	2	2	no	—
83	C₄⋊C₈×C₈₉	—	2	2	no	—
84	C₄×C₈×C₈₉	—	2	2	no	—
85	C₄×C₈×C₈₉	—	2	2	no	—
86	C₂×Dic₁₇₈	—	2	2	no	—
87	C₂×Dic₁₇₈	—	2	2	no	—
88	C₂×Dic₁₇₈	C₄⋊C₄	1	4	yes	—
89	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
90	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
91	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
92	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
93	C₂×#10623494	—	2	2	no	—
94	C₂×#10623494	—	2	2	no	—
95	C₂×#10623494	—	2	2	no	—
96	C₂×#10623494	—	2	2	no	—
97	C₂×#10623494	—	2	2	no	—
98	C₂×#10623494	—	2	2	no	—
99	C₄⋊Dic₈₉	—	2	2	no	—
100	C₄⋊Dic₈₉	—	2	2	no	—
101	C₄⋊Dic₈₉	C₄⋊C₄	1	4	yes	—
102	#13083553	—	2	4	no	—
103	#13083553	—	4	2	no	—
104	#13083553	C₄⋊C₄	1	8	yes	—
105	C₄×Dic₈₉	—	2	2	no	—
106	C₄×Dic₈₉	—	2	2	no	—
107	C₄×Dic₈₉	C₂×D₄	1	4	yes	—
108	C₄×Dic₈₉	C₂×Q₈	1	4	yes	—
109	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₈₉	—	2	1	no	—
117	C₂×C₈×C₈₉	—	2	1	no	—
118	C₂×C₈×C₈₉	—	2	1	no	—
119	C₂×C₈×C₈₉	—	2	1	no	—
120	C₂×C₈×C₈₉	—	2	1	no	—
121	C₂×C₈×C₈₉	—	2	1	no	—
122	C₂×C₈×C₈₉	—	2	1	no	—
123	C₂×C₈×C₈₉	—	2	1	no	—
124	C₂×C₈×C₈₉	—	2	1	no	—
125	C₂×C₈×C₈₉	—	2	1	no	—
126	C₂×C₈×C₈₉	#41	1	2	yes	—
127	C₂×C₈×C₈₉	#41	1	2	yes	—
128	C₄²×C₈₉	—	2	2	no	—
129	C₄²×C₈₉	—	2	2	no	—
130	C₄²×C₈₉	—	2	2	no	—
131	C₄²×C₈₉	—	2	1	no	—
132	C₄²×C₈₉	—	2	1	no	—
133	C₄²×C₈₉	—	2	1	no	—
134	C₄²×C₈₉	—	2	1	no	—
135	C₄²×C₈₉	—	4	1	no	—
136	C₄²×C₈₉	C₂×D₄	1	2	yes	—
137	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
138	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
139	C₂×C₄×C₈₉	—	2	1	no	—
140	C₂×C₄×C₈₉	—	2	1	no	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	2	1	no	—
143	C₂×C₄×C₈₉	—	2	1	no	—
144	C₂×C₄×C₈₉	—	2	1	no	—
145	C₂×C₄×C₈₉	—	2	1	no	—
146	C₂×C₄×C₈₉	—	2	1	no	—
147	C₂×C₄×C₈₉	—	2	1	no	—
148	C₂×C₄×C₈₉	—	2	1	no	—
149	C₂×C₄×C₈₉	—	2	1	no	—
150	C₂×C₄×C₈₉	—	2	1	no	—
151	C₂×C₄×C₈₉	—	2	1	no	—
152	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
153	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₈₉	#131	1	2	yes	—
155	C₂×C₄×C₈₉	#131	1	2	yes	—
156	C₂×C₄×C₈₉	#131	1	2	yes	—
157	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
162	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
163	C₂×Dic₈₉	—	2	2	no	—
164	C₂×Dic₈₉	—	2	2	no	—
165	C₂×Dic₈₉	—	2	2	no	—
166	C₂×Dic₈₉	—	2	2	no	—
167	C₂×Dic₈₉	—	2	2	no	—
168	C₂×Dic₈₉	—	2	2	no	—
169	C₂×Dic₈₉	—	2	2	no	—
170	C₂×Dic₈₉	—	2	2	no	—
171	C₂×Dic₈₉	—	2	2	no	—
172	C₂×Dic₈₉	—	2	2	no	—
173	C₂×Dic₈₉	C₂×C₄⋊C₄	1	4	yes	—
174	C₂×Dic₈₉	C₂×C₄⋊C₄	1	4	yes	—
175	Dic₁₇₈	—	2	8	no	—
176	C₈×C₈₉	—	2	2	no	—
177	C₈×C₈₉	—	2	2	no	—
178	C₈×C₈₉	—	4	1	no	—
179	C₈×C₈₉	—	4	1	no	—
180	#10623494	—	4	2	no	—
181	#10623494	—	4	2	no	—
182	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
184	C₂²×C₈₉	#519	1	1	yes	characteristic
185	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
186	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
187	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
188	C₂²×C₈₉	#568	1	1	yes	characteristic
189	C₄×C₈₉	—	2	2	no	—
190	C₄×C₈₉	—	2	2	no	—
191	C₄×C₈₉	—	4	1	no	—
192	C₄×C₈₉	—	4	1	no	—
193	C₄×C₈₉	—	4	1	no	—
194	C₄×C₈₉	#424	1	4	yes	—
195	C₄×C₈₉	#548	1	1	yes	characteristic
196	C₄×C₈₉	#548	1	1	yes	characteristic
197	C₄×C₈₉	#557	1	1	yes	characteristic
198	C₄×C₈₉	#557	1	1	yes	characteristic
199	Dic₈₉	—	2	4	no	—
200	Dic₈₉	—	2	4	no	—
201	Dic₈₉	—	4	2	no	—
202	Dic₈₉	—	4	2	no	—
203	#22735	—	89	1	no	maximal, Sylow
204	C₂×C₈₉	#2351	1	1	yes	characteristic
205	C₂×C₈₉	C₂×#424	1	1	yes	characteristic
206	C₂×C₈₉	#2906	1	1	yes	characteristic
207	C₂×C₈₉	#2966	1	1	yes	characteristic
208	C₂×C₈₉	#2969	1	1	yes	characteristic
209	C₂×C₈₉	#2985	1	1	yes	characteristic
210	C₂×C₈₉	#2986	1	1	yes	characteristic
211	C₂×#446	—	89	1	no	—
212	C₂×C₈×Q₈	—	89	1	no	—
213	#2295	—	89	1	no	—
214	#1940	—	89	2	no	—
215	#1939	—	89	2	no	—
216	#1939	—	89	1	no	—
217	#1939	—	89	1	no	—
218	#1832	—	89	2	no	—
219	#1831	—	89	1	no	—
220	#1768	—	89	2	no	—
221	C₄×C₄⋊C₈	D₈₉	1	1	yes	characteristic
222	C₈₉	#22735	1	1	yes	characteristic, complemented, Sylow
223	C₂×C₄×Q₈	—	89	1	no	—
224	#446	—	178	4	no	—
225	C₈×Q₈	—	178	4	no	—
226	C₂×C₄⋊C₈	—	89	2	no	—
227	C₂×C₄⋊C₈	—	89	2	no	—
228	C₂×C₄⋊C₈	—	89	2	no	—
229	C₂×C₄⋊C₈	—	89	2	no	—
230	C₂×C₄⋊C₈	—	89	1	no	—
231	C₂×C₄⋊C₈	—	89	1	no	—
232	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
234	C₂×#97	—	89	2	no	—
235	C₂×C₄×C₈	—	89	2	no	—
236	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
238	#391	—	89	1	no	—
239	#391	—	89	1	no	—
240	#389	—	89	1	no	—
241	#389	—	89	1	no	—
242	#387	—	89	2	no	—
243	#387	—	89	2	no	—
244	C₄×C₄⋊C₄	—	89	1	no	—
245	C₄×C₄⋊C₄	—	89	2	no	—
246	#376	—	89	2	no	—
247	C₄³	C₂×D₈₉	1	1	yes	characteristic
248	#336	—	89	2	no	—
249	#336	—	89	2	no	—
250	#336	—	89	2	no	—
251	#336	—	89	2	no	—
252	#336	C₂×D₈₉	1	1	yes	characteristic
253	#336	C₂×D₈₉	1	1	yes	characteristic
254	C₂²×Q₈	—	89	1	no	—
255	C₂²×C₈	—	89	2	no	—
256	C₂²×C₈	—	89	2	no	—
257	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
258	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
259	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
260	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
261	C₄×Q₈	—	89	4	no	—
262	C₄×Q₈	—	89	4	no	—
263	C₂×C₄⋊C₄	—	89	2	no	—
264	C₂×C₄⋊C₄	—	89	1	no	—
265	C₂×C₄⋊C₄	—	89	2	no	—
266	C₂×C₄⋊C₄	—	89	2	no	—
267	C₂×C₄⋊C₄	—	89	1	no	—
268	C₂×C₄⋊C₄	—	89	1	no	—
269	C₂×C₄²	—	89	2	no	—
270	C₂×C₄²	—	89	2	no	—
271	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
272	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
273	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
274	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
275	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
276	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
277	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	2	no	—
280	C₄⋊C₈	—	178	4	no	—
281	C₄⋊C₈	—	178	4	no	—
282	C₄⋊C₈	—	178	4	no	—
283	C₄⋊C₈	—	178	4	no	—
284	C₄⋊C₈	—	178	2	no	—
285	C₄⋊C₈	—	178	2	no	—
286	#97	—	178	4	no	—
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	—	2	2	no	—
289	C₄×C₈	—	178	4	no	—
290	#95	—	89	2	no	—
291	#95	—	89	2	no	—
292	#95	—	89	2	no	—
293	#95	—	89	2	no	—
294	#95	—	89	2	no	—
295	#95	—	89	2	no	—
296	#95	—	89	2	no	—
297	C₂×Q₈	—	89	4	no	—
298	C₂×Q₈	—	178	2	no	—
299	C₂×Q₈	—	178	2	no	—
300	C₂²×C₄	—	89	2	no	—
301	C₂²×C₄	—	89	2	no	—
302	C₂²×C₄	—	89	2	no	—
303	C₂²×C₄	—	89	2	no	—
304	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
310	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	178	2	no	—
322	C₂×C₈	—	178	2	no	—
323	C₂×C₈	—	178	2	no	—
324	C₂×C₈	—	178	2	no	—
325	C₂×C₈	—	178	2	no	—
326	C₂×C₈	—	178	2	no	—
327	C₂×C₈	#13083574	1	2	yes	—
328	C₂×C₈	#13083574	1	2	yes	—
329	C₄⋊C₄	—	89	8	no	—
330	C₄⋊C₄	—	89	4	no	—
331	C₄⋊C₄	—	356	2	no	—
332	C₄⋊C₄	—	178	4	no	—
333	C₄⋊C₄	—	178	2	no	—
334	C₄⋊C₄	—	178	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	89	4	no	—
344	C₄²	—	89	4	no	—
345	C₄²	—	178	2	no	—
346	C₄²	—	178	2	no	—
347	C₄²	D₄×D₈₉	1	2	yes	—
348	C₄²	Q₈×D₈₉	1	2	yes	—
349	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
350	Q₈	—	178	8	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	89	4	no	—
365	C₂×C₄	—	89	4	no	—
366	C₂×C₄	—	178	2	no	—
367	C₂×C₄	—	178	2	no	—
368	C₂×C₄	—	178	2	no	—
369	C₂×C₄	—	178	2	no	—
370	C₂×C₄	—	178	2	no	—
371	C₂×C₄	—	178	2	no	—
372	C₂×C₄	—	178	2	no	—
373	C₂×C₄	—	178	2	no	—
374	C₂×C₄	—	178	2	no	—
375	C₂×C₄	—	178	2	no	—
376	C₂×C₄	C₄⋊C₄×D₈₉	1	2	yes	—
377	C₂×C₄	C₄⋊C₄×D₈₉	1	2	yes	—
378	C₂×C₄	#15668018	1	2	yes	—
379	C₂×C₄	#15668018	1	2	yes	—
380	C₂×C₄	#15668020	1	2	yes	—
381	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
382	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
383	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
384	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
385	C₂×C₄	#15668059	1	1	yes	characteristic
386	C₂×C₄	#15668059	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₈	—	4	1	no	—
390	C₈	—	4	1	no	—
391	C₈	—	356	2	no	—
392	C₈	—	356	2	no	—
393	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
394	C₂²	C₄×#13083574	1	1	yes	characteristic
395	C₂²	#19152075	1	1	yes	characteristic
396	C₂²	C₂×#15668018	1	1	yes	characteristic
397	C₂²	C₂×#15668018	1	1	yes	characteristic
398	C₂²	C₂×#15668020	1	1	yes	characteristic
399	C₂²	#19152364	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	356	2	no	—
406	C₄	—	356	2	no	—
407	C₄	—	178	4	no	—
408	C₄	—	178	4	no	—
409	C₄	#19151623	1	4	yes	—
410	C₄	#19152257	1	1	yes	characteristic
411	C₄	#19152257	1	1	yes	characteristic
412	C₄	#19152326	1	1	yes	characteristic
413	C₄	#19152326	1	1	yes	characteristic
414	C₂	#26023172	1	1	yes	characteristic
415	C₂	C₂×#19151623	1	1	yes	characteristic
416	C₂	#26028817	1	1	yes	characteristic
417	C₂	#26029227	1	1	yes	characteristic
418	C₂	#26029256	1	1	yes	characteristic
419	C₂	#26029346	1	1	yes	characteristic
420	C₂	#26029353	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator, socle, prime radical	C₂³×C₈₉	C₂³×C₄
Fitting	C₄×C₄⋊C₈×C₈₉	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄×C₄⋊C₈	D₈₉
hypocenter	C₈₉	#22735
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
222. C₈₉	#22735	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151728	2
C₂×C₈×Dic₁₇₈	2
#26022729	2
#26020972	2
#26020970	2
#26020967	2
#26020370	2
#26020369	2
#26020108	2
C₄×C₄⋊C₈×C₈₉	2
#22735	89