Subgroups — #36573232

Order 22784.

760 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151725	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151722	C₂	1	1	yes	maximal, characteristic
3	#26022729	C₂	1	1	yes	maximal, characteristic
4	#26020972	C₂	1	2	yes	maximal
5	#26020968	C₂	1	1	yes	maximal, characteristic
6	#26020968	C₂	1	1	yes	maximal, characteristic
7	#26020967	C₂	1	2	yes	maximal
8	#26020405	C₂	1	2	yes	maximal
9	#26020111	C₂	1	2	yes	maximal
10	C₄×C₄⋊#10623494	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1842	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
13	#19151725	—	2	4	no	—
14	#19151722	—	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×C₄×#10623494	C₂²	1	1	yes	characteristic
23	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₈₉	C₂²	1	2	yes	—
25	#19151504	C₄	1	1	yes	characteristic
26	#19151504	C₄	1	1	yes	characteristic
27	#19151496	C₄	1	1	yes	characteristic
28	#19151496	C₄	1	1	yes	characteristic
29	#19151482	C₄	1	2	yes	—
30	#19151482	C₄	1	2	yes	—
31	C₄×#13083553	C₂²	1	2	yes	—
32	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
33	#19151444	C₂²	1	2	yes	—
34	#19151353	C₂²	1	1	yes	characteristic
35	#19151353	C₂²	1	1	yes	characteristic
36	#19151352	C₂²	1	2	yes	—
37	#19151352	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
42	C₄³×C₈₉	C₂²	1	1	yes	characteristic
43	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
44	C₂²×#10623494	C₂³	1	1	yes	characteristic
45	C₂²×#10623494	C₂³	1	1	yes	characteristic
46	C₂²×#10623494	C₂³	1	1	yes	characteristic
47	C₂²×#10623494	C₂³	1	1	yes	characteristic
48	C₄×Dic₁₇₈	D₄	1	4	yes	—
49	C₄×Dic₁₇₈	Q₈	1	4	yes	—
50	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂×#13083553	C₂×C₄	1	2	yes	—
54	C₂×#13083553	C₂×C₄	1	2	yes	—
55	C₂×#13083553	C₂×C₄	1	2	yes	—
56	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
57	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
58	C₄⋊#10623494	—	2	2	no	—
59	C₄⋊#10623494	Q₈	1	4	yes	complemented
60	#15667941	—	2	4	no	—
61	#15667941	—	2	4	no	—
62	#15667941	—	4	2	no	—
63	#15667941	—	4	2	no	—
64	#15667922	—	2	4	no	—
65	C₄×#10623494	—	2	2	no	—
66	C₄×#10623494	—	2	2	no	—
67	C₈×Dic₈₉	—	2	4	no	—
68	#15667919	C₂×C₄	1	2	yes	—
69	#15667919	C₂×C₄	1	2	yes	—
70	#15667919	C₂×C₄	1	2	yes	—
71	#15667919	C₂×C₄	1	2	yes	—
72	#15667919	C₂×C₄	1	2	yes	—
73	#15667919	C₂×C₄	1	2	yes	—
74	#15667919	C₂×C₄	1	2	yes	—
75	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
76	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
77	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₈₉	—	2	2	no	—
85	C₄⋊C₈×C₈₉	—	2	2	no	—
86	C₄⋊C₈×C₈₉	—	2	4	no	—
87	C₄⋊C₈×C₈₉	—	4	2	no	—
88	C₂×Dic₁₇₈	—	2	2	no	—
89	C₂×Dic₁₇₈	—	2	2	no	—
90	C₂×Dic₁₇₈	C₄⋊C₄	1	4	yes	—
91	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
92	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
93	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
94	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
95	C₂×#10623494	—	2	1	no	—
96	C₂×#10623494	—	2	1	no	—
97	C₂×#10623494	—	2	1	no	—
98	C₂×#10623494	—	2	1	no	—
99	C₂×#10623494	—	2	1	no	—
100	C₂×#10623494	—	2	1	no	—
101	C₂×#10623494	—	2	1	no	—
102	C₂×#10623494	—	2	1	no	—
103	C₂×#10623494	—	2	1	no	—
104	C₂×#10623494	—	2	1	no	—
105	C₂×#10623494	C₂×Q₈	1	2	yes	—
106	C₂×#10623494	C₂×Q₈	1	2	yes	—
107	C₄⋊Dic₈₉	—	2	2	no	—
108	C₄⋊Dic₈₉	—	2	2	no	—
109	C₄⋊Dic₈₉	C₄⋊C₄	1	4	yes	—
110	#13083553	—	2	4	no	—
111	#13083553	—	4	2	no	—
112	#13083553	C₄⋊C₄	1	8	yes	—
113	C₄×Dic₈₉	—	2	2	no	—
114	C₄×Dic₈₉	—	2	2	no	—
115	C₄×Dic₈₉	C₂×D₄	1	4	yes	—
116	C₄×Dic₈₉	C₂×Q₈	1	4	yes	—
117	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
124	C₂×C₈×C₈₉	—	2	2	no	—
125	C₂×C₈×C₈₉	—	2	2	no	—
126	C₂×C₈×C₈₉	—	2	2	no	—
127	C₂×C₈×C₈₉	—	2	2	no	—
128	C₂×C₈×C₈₉	—	2	2	no	—
129	C₂×C₈×C₈₉	—	2	2	no	—
130	C₄²×C₈₉	—	2	2	no	—
131	C₄²×C₈₉	—	2	2	no	—
132	C₄²×C₈₉	—	2	2	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	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
139	C₄²×C₈₉	#41	1	2	yes	—
140	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
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	C₄×Q₈	1	2	yes	—
155	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
156	C₂×C₄×C₈₉	#131	1	2	yes	—
157	C₂×C₄×C₈₉	#131	1	2	yes	—
158	C₂×C₄×C₈₉	#131	1	2	yes	—
159	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
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	—	2	2	no	—
174	C₂×Dic₈₉	—	2	2	no	—
175	C₂×Dic₈₉	C₂×C₄⋊C₄	1	4	yes	—
176	C₂×Dic₈₉	C₂×C₄⋊C₄	1	4	yes	—
177	Dic₁₇₈	—	2	8	no	—
178	C₈×C₈₉	—	4	2	no	—
179	C₈×C₈₉	—	4	2	no	—
180	#10623494	—	2	2	no	—
181	#10623494	—	2	2	no	—
182	#10623494	—	4	1	no	—
183	#10623494	—	4	1	no	—
184	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
186	C₂²×C₈₉	#520	1	1	yes	characteristic
187	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
188	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
189	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
190	C₂²×C₈₉	#568	1	1	yes	characteristic
191	C₄×C₈₉	—	2	2	no	—
192	C₄×C₈₉	—	2	2	no	—
193	C₄×C₈₉	—	2	2	no	—
194	C₄×C₈₉	—	2	2	no	—
195	C₄×C₈₉	—	4	1	no	—
196	C₄×C₈₉	#424	1	4	yes	—
197	C₄×C₈₉	D₄×Q₈	1	1	yes	characteristic
198	C₄×C₈₉	#550	1	1	yes	characteristic
199	C₄×C₈₉	#557	1	1	yes	characteristic
200	C₄×C₈₉	Q₈²	1	1	yes	characteristic
201	Dic₈₉	—	2	4	no	—
202	Dic₈₉	—	2	4	no	—
203	Dic₈₉	—	4	2	no	—
204	Dic₈₉	—	4	2	no	—
205	#22721	—	89	1	no	maximal, Sylow
206	C₂×C₈₉	Q₈×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₈₉	C₂×#424	1	1	yes	characteristic
208	C₂×C₈₉	#2906	1	1	yes	characteristic
209	C₂×C₈₉	#2960	1	1	yes	characteristic
210	C₂×C₈₉	#2962	1	1	yes	characteristic
211	C₂×C₈₉	#2993	1	1	yes	characteristic
212	C₂×C₈₉	#2994	1	1	yes	characteristic
213	C₂×#446	—	89	1	no	—
214	C₂×C₈×Q₈	—	89	1	no	—
215	#2295	—	89	1	no	—
216	#1940	—	89	2	no	—
217	#1939	—	89	2	no	—
218	#1939	—	89	1	no	—
219	#1939	—	89	1	no	—
220	#1843	—	89	2	no	—
221	#1842	D₈₉	1	1	yes	characteristic
222	#1768	—	89	2	no	—
223	C₄×C₄⋊C₈	—	89	1	no	—
224	C₈₉	#22721	1	1	yes	characteristic, complemented, Sylow
225	C₂×C₄×Q₈	—	89	1	no	—
226	#446	—	178	4	no	—
227	C₈×Q₈	—	178	4	no	—
228	C₂×C₄⋊C₈	—	89	1	no	—
229	C₂×C₄⋊C₈	—	89	2	no	—
230	C₂×C₄⋊C₈	—	89	2	no	—
231	C₂×C₄⋊C₈	—	89	2	no	—
232	C₂×C₄⋊C₈	—	89	2	no	—
233	C₂×C₄⋊C₈	—	89	1	no	—
234	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
235	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
236	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
238	C₂×#97	—	89	2	no	—
239	C₂×C₄×C₈	—	89	2	no	—
240	C₂×C₄×C₈	—	89	1	no	—
241	C₂×C₄×C₈	—	89	1	no	—
242	#391	—	89	1	no	—
243	#391	—	89	1	no	—
244	#389	—	89	1	no	—
245	#389	—	89	1	no	—
246	#387	—	89	2	no	—
247	#387	—	89	2	no	—
248	C₄×C₄⋊C₄	—	89	1	no	—
249	C₄×C₄⋊C₄	—	89	2	no	—
250	#376	—	89	2	no	—
251	C₄³	C₂×D₈₉	1	1	yes	characteristic
252	#336	—	89	2	no	—
253	#336	—	89	2	no	—
254	#336	—	89	1	no	—
255	#336	—	89	1	no	—
256	C₂²×Q₈	—	89	1	no	—
257	C₂²×C₈	—	89	1	no	—
258	C₂²×C₈	—	89	1	no	—
259	C₂²×C₈	—	89	1	no	—
260	C₂²×C₈	—	89	1	no	—
261	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
262	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
263	C₄×Q₈	—	89	4	no	—
264	C₄×Q₈	—	89	4	no	—
265	C₂×C₄⋊C₄	—	89	2	no	—
266	C₂×C₄⋊C₄	—	89	1	no	—
267	C₂×C₄⋊C₄	—	89	2	no	—
268	C₂×C₄⋊C₄	—	89	2	no	—
269	C₂×C₄⋊C₄	—	89	1	no	—
270	C₂×C₄⋊C₄	—	89	1	no	—
271	C₂×C₄²	—	89	2	no	—
272	C₂×C₄²	—	89	2	no	—
273	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
274	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
275	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
276	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
277	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
278	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
279	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
280	C₄⋊C₈	—	2	2	no	—
281	C₄⋊C₈	—	2	2	no	—
282	C₄⋊C₈	—	2	4	no	—
283	C₄⋊C₈	—	4	2	no	—
284	C₄⋊C₈	—	89	4	no	—
285	C₄⋊C₈	—	356	2	no	—
286	C₄⋊C₈	—	356	2	no	—
287	C₄⋊C₈	—	178	4	no	—
288	C₄⋊C₈	—	178	4	no	—
289	C₄⋊C₈	—	178	2	no	—
290	#97	—	178	4	no	—
291	C₄×C₈	—	178	4	no	—
292	C₄×C₈	—	178	2	no	—
293	C₄×C₈	—	178	2	no	—
294	#95	—	89	2	no	—
295	#95	—	89	2	no	—
296	#95	—	89	2	no	—
297	#95	—	89	2	no	—
298	#95	—	89	2	no	—
299	#95	—	89	2	no	—
300	#95	—	89	2	no	—
301	C₂×Q₈	—	89	4	no	—
302	C₂×Q₈	—	178	2	no	—
303	C₂×Q₈	—	178	2	no	—
304	C₂²×C₄	—	89	2	no	—
305	C₂²×C₄	—	89	2	no	—
306	C₂²×C₄	—	89	2	no	—
307	C₂²×C₄	—	89	2	no	—
308	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
314	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	89	2	no	—
322	C₂×C₈	—	89	2	no	—
323	C₂×C₈	—	178	1	no	—
324	C₂×C₈	—	178	1	no	—
325	C₂×C₈	—	178	1	no	—
326	C₂×C₈	—	178	1	no	—
327	C₂×C₈	—	178	1	no	—
328	C₂×C₈	—	178	1	no	—
329	C₂×C₈	—	178	1	no	—
330	C₂×C₈	—	178	1	no	—
331	C₂×C₈	—	178	1	no	—
332	C₂×C₈	—	178	1	no	—
333	C₄⋊C₄	—	89	8	no	—
334	C₄⋊C₄	—	89	4	no	—
335	C₄⋊C₄	—	356	2	no	—
336	C₄⋊C₄	—	178	2	no	—
337	C₄⋊C₄	—	178	4	no	—
338	C₄⋊C₄	—	178	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	4	1	no	—
345	C₄²	—	89	4	no	—
346	C₄²	—	89	4	no	—
347	C₄²	—	178	2	no	—
348	C₄²	—	178	2	no	—
349	C₄²	D₄×D₈₉	1	2	yes	—
350	C₄²	Q₈×D₈₉	1	2	yes	—
351	C₄²	Q₈×D₈₉	1	2	yes	—
352	C₄²	#13083573	1	2	yes	—
353	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
354	Q₈	—	178	8	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	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	89	4	no	—
367	C₂×C₄	—	89	4	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	—	178	2	no	—
377	C₂×C₄	—	178	2	no	—
378	C₂×C₄	C₄⋊C₄×D₈₉	1	2	yes	—
379	C₂×C₄	C₄⋊C₄×D₈₉	1	2	yes	—
380	C₂×C₄	#15667977	1	2	yes	—
381	C₂×C₄	#15667977	1	2	yes	—
382	C₂×C₄	#15668018	1	2	yes	—
383	C₂×C₄	#15668020	1	2	yes	—
384	C₂×C₄	#15668020	1	2	yes	—
385	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
386	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
387	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
388	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
389	C₂×C₄	#15668057	1	1	yes	characteristic
390	C₂×C₄	#15668060	1	1	yes	characteristic
391	C₈	—	4	2	no	—
392	C₈	—	4	2	no	—
393	C₈	—	356	1	no	—
394	C₈	—	356	1	no	—
395	C₈	—	178	2	no	—
396	C₈	—	178	2	no	—
397	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
398	C₂²	C₂×#15667977	1	1	yes	characteristic
399	C₂²	#19152079	1	1	yes	characteristic
400	C₂²	C₂×#15668018	1	1	yes	characteristic
401	C₂²	C₂×#15668020	1	1	yes	characteristic
402	C₂²	C₂×#15668020	1	1	yes	characteristic
403	C₂²	#19152364	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	4	1	no	—
409	C₄	—	356	2	no	—
410	C₄	—	356	2	no	—
411	C₄	—	178	4	no	—
412	C₄	—	178	4	no	—
413	C₄	#19151623	1	4	yes	—
414	C₄	#19152263	1	1	yes	characteristic
415	C₄	#19152268	1	1	yes	characteristic
416	C₄	#19152323	1	1	yes	characteristic
417	C₄	#19152328	1	1	yes	characteristic
418	C₂	#26023164	1	1	yes	characteristic
419	C₂	C₂×#19151623	1	1	yes	characteristic
420	C₂	#26028821	1	1	yes	characteristic
421	C₂	#26029182	1	1	yes	characteristic
422	C₂	#26029195	1	1	yes	characteristic
423	C₂	#26029397	1	1	yes	characteristic
424	C₂	#26029408	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator, socle, prime radical	C₂³×C₈₉	C₂³×C₄
Fitting	C₈₉×#1842	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1842	D₈₉
hypocenter	C₈₉	#22721
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1842

Complements

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

N	H ≅ G/N	type
59. C₄⋊#10623494	Q₈	semidirect
224. C₈₉	#22721	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151725	2
C₂×#19151722	2
#26022729	2
#26020972	2
#26020968	2
#26020967	2
#26020405	2
#26020111	2
C₄×C₄⋊#10623494	2
C₈₉×#1842	2
#22721	89