Subgroups — #36460407

Order 22784.

1062 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26022736	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×Dic₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151359	C₂	1	1	yes	maximal, characteristic
4	C₂×#19151358	C₂	1	1	yes	maximal, characteristic
5	C₂×#19151357	C₂	1	1	yes	maximal, characteristic
6	#26019945	C₂	1	1	yes	maximal, characteristic
7	C₂×#339×C₈₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×#13083558	C₂²	1	1	yes	characteristic
9	C₂×#15667971	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₈₉	—	2	2	no	—
11	C₂²×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
13	#19151497	C₄	1	4	yes	complemented
14	#19151473	—	2	2	no	—
15	C₄×C₄⋊Dic₈₉	—	2	2	no	—
16	C₄²×Dic₈₉	—	2	2	no	—
17	C₄²×Dic₈₉	—	2	2	no	—
18	#19151359	—	2	2	no	—
19	#19151358	—	2	2	no	—
20	#19151357	C₄	1	4	yes	complemented
21	#19151352	—	2	2	no	—
22	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
25	#339×C₈₉	C₄	1	4	yes	complemented
26	C₂³×Dic₈₉	—	2	1	no	—
27	C₂³×Dic₈₉	D₄	1	2	yes	—
28	C₂×#13083558	—	2	1	no	—
29	C₂×#13083558	—	2	1	no	—
30	C₂×#13083558	—	2	1	no	—
31	C₂×#13083558	—	2	1	no	—
32	C₂×#13083558	—	2	1	no	—
33	C₂×#13083558	C₂×C₄	1	2	yes	—
34	C₂²×#10623494	—	2	1	no	—
35	#15667971	—	2	1	no	—
36	#15667971	—	2	1	no	—
37	#15667971	—	2	1	no	—
38	#15667971	—	2	1	no	—
39	C₂×C₄⋊Dic₈₉	—	2	4	no	—
40	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
41	C₂×C₂²⋊Dic₈₉	—	2	1	no	—
42	C₂×C₄×Dic₈₉	—	2	8	no	—
43	C₂×C₄×Dic₈₉	—	2	16	no	—
44	C₂×C₄×Dic₈₉	—	2	1	no	—
45	C₂×C₄×Dic₈₉	—	2	1	no	—
46	C₂×C₄×Dic₈₉	—	2	1	no	—
47	C₂×C₄×Dic₈₉	—	2	1	no	—
48	C₂×C₄×Dic₈₉	—	2	1	no	—
49	C₂×C₄×Dic₈₉	—	2	1	no	—
50	C₂×C₄×Dic₈₉	—	2	1	no	—
51	C₂×C₄×Dic₈₉	—	2	1	no	—
52	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₈₉	D₄	1	2	yes	—
55	C₂×C₄×Dic₈₉	D₄	1	2	yes	—
56	C₂×C₄×Dic₈₉	Q₈	1	2	yes	—
57	#15667919	—	2	4	no	—
58	C₂³×C₄×C₈₉	—	2	1	no	—
59	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₈₉	—	2	1	no	—
61	C₂×M₁₆×C₈₉	—	2	1	no	—
62	C₂×M₁₆×C₈₉	—	2	1	no	—
63	C₂×M₁₆×C₈₉	—	2	1	no	—
64	C₂×M₁₆×C₈₉	—	2	1	no	—
65	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
66	C₂²×C₈×C₈₉	—	2	1	no	—
67	#117×C₈₉	—	2	1	no	—
68	#117×C₈₉	—	2	1	no	—
69	#117×C₈₉	C₂×C₄	1	2	yes	—
70	#117×C₈₉	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
73	C₂×C₄²×C₈₉	—	2	1	no	—
74	C₂×C₄²×C₈₉	—	2	1	no	—
75	C₂×C₄²×C₈₉	—	2	1	no	—
76	C₂×C₄²×C₈₉	—	2	1	no	—
77	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₈₉	D₄	1	2	yes	—
79	C₂×C₄²×C₈₉	Q₈	1	2	yes	—
80	C₂²×Dic₈₉	—	2	8	no	—
81	C₂²×Dic₈₉	—	2	2	no	—
82	C₂²×Dic₈₉	—	2	2	no	—
83	C₂²×Dic₈₉	—	2	2	no	—
84	C₂²×Dic₈₉	—	2	2	no	—
85	C₂²×Dic₈₉	—	2	2	no	—
86	C₂²×Dic₈₉	—	2	8	no	—
87	C₂²×Dic₈₉	—	2	2	no	—
88	C₂²×Dic₈₉	C₂²⋊C₄	1	4	yes	—
89	#13083558	—	2	2	no	—
90	#13083558	—	2	2	no	—
91	#13083558	—	4	1	no	—
92	#13083558	—	4	1	no	—
93	C₂×#10623494	—	2	2	no	—
94	C₂×#10623494	—	4	1	no	—
95	C₂×#10623494	—	4	1	no	—
96	C₄⋊Dic₈₉	—	2	2	no	—
97	C₄⋊Dic₈₉	—	2	2	no	—
98	C₄⋊Dic₈₉	—	4	8	no	—
99	C₂²⋊Dic₈₉	—	4	1	no	—
100	C₂²⋊Dic₈₉	—	4	1	no	—
101	C₄×Dic₈₉	—	2	32	no	—
102	C₄×Dic₈₉	—	2	2	no	—
103	C₄×Dic₈₉	—	2	2	no	—
104	C₄×Dic₈₉	—	2	2	no	—
105	C₄×Dic₈₉	—	2	2	no	—
106	C₄×Dic₈₉	—	2	2	no	—
107	C₄×Dic₈₉	—	2	2	no	—
108	C₄×Dic₈₉	—	2	2	no	—
109	C₄×Dic₈₉	—	4	1	no	—
110	C₄×Dic₈₉	—	4	1	no	—
111	C₄×Dic₈₉	C₄⋊C₄	1	4	yes	complemented
112	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	—	2	8	no	—
114	C₂²×C₄×C₈₉	—	2	2	no	—
115	C₂²×C₄×C₈₉	—	2	2	no	—
116	C₂²×C₄×C₈₉	—	2	2	no	—
117	C₂²×C₄×C₈₉	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
132	M₁₆×C₈₉	—	2	2	no	—
133	M₁₆×C₈₉	—	2	2	no	—
134	M₁₆×C₈₉	—	4	1	no	—
135	M₁₆×C₈₉	—	4	1	no	—
136	C₂×C₈×C₈₉	—	2	2	no	—
137	C₂×C₈×C₈₉	—	4	1	no	—
138	C₂×C₈×C₈₉	—	4	1	no	—
139	C₄⋊C₄×C₈₉	—	2	2	no	—
140	C₄⋊C₄×C₈₉	C₄²	1	4	yes	complemented
141	C₂²⋊C₄×C₈₉	—	2	2	no	—
142	C₂²⋊C₄×C₈₉	—	2	2	no	—
143	C₄²×C₈₉	—	2	2	no	—
144	C₄²×C₈₉	—	2	2	no	—
145	C₄²×C₈₉	—	2	2	no	—
146	C₄²×C₈₉	—	2	2	no	—
147	C₄²×C₈₉	—	2	2	no	—
148	C₄²×C₈₉	C₄⋊C₄	1	4	yes	complemented
149	C₂³×C₈₉	—	2	4	no	—
150	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
152	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
153	C₂³×C₈₉	#120	1	1	yes	characteristic
154	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂³×C₈₉	#123	1	1	yes	characteristic
157	C₂×C₄×C₈₉	—	2	8	no	—
158	C₂×C₄×C₈₉	—	2	8	no	—
159	C₂×C₄×C₈₉	—	2	8	no	—
160	C₂×C₄×C₈₉	—	2	4	no	—
161	C₂×C₄×C₈₉	—	2	4	no	—
162	C₂×C₄×C₈₉	—	4	4	no	—
163	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
167	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
168	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
183	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
184	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
185	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
186	C₂×C₄×C₈₉	#125	1	1	yes	characteristic
187	C₂×C₄×C₈₉	#125	1	1	yes	characteristic
188	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
189	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₄⋊Q₈	1	1	yes	characteristic
191	C₂×Dic₈₉	—	2	8	no	—
192	C₂×Dic₈₉	—	2	8	no	—
193	C₂×Dic₈₉	—	2	8	no	—
194	C₂×Dic₈₉	—	2	8	no	—
195	C₂×Dic₈₉	—	2	8	no	—
196	C₂×Dic₈₉	—	2	4	no	—
197	C₂×Dic₈₉	—	2	4	no	—
198	C₂×Dic₈₉	—	2	4	no	—
199	C₂×Dic₈₉	—	4	2	no	—
200	C₂×Dic₈₉	—	4	4	no	—
201	C₂×Dic₈₉	#104	1	8	yes	—
202	C₈×C₈₉	—	4	2	no	—
203	#10623494	—	4	2	no	—
204	C₂²×C₈₉	—	2	2	no	—
205	C₂²×C₈₉	—	2	2	no	—
206	C₂²×C₈₉	—	2	2	no	—
207	C₂²×C₈₉	—	2	2	no	—
208	C₂²×C₈₉	—	2	2	no	—
209	C₂²×C₈₉	—	2	2	no	—
210	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₈₉	#385	1	1	yes	characteristic
212	C₂²×C₈₉	#385	1	1	yes	characteristic
213	C₂²×C₈₉	#386	1	1	yes	characteristic
214	C₂²×C₈₉	#387	1	1	yes	characteristic
215	C₂²×C₈₉	#387	1	1	yes	characteristic
216	C₂²×C₈₉	#391	1	1	yes	characteristic
217	C₂²×C₈₉	C₂×#104	1	4	yes	—
218	C₄×C₈₉	—	2	8	no	—
219	C₄×C₈₉	—	4	4	no	—
220	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
221	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
222	C₄×C₈₉	#387	1	1	yes	characteristic
223	C₄×C₈₉	#387	1	1	yes	characteristic
224	C₄×C₈₉	#388	1	1	yes	characteristic
225	C₄×C₈₉	#388	1	1	yes	characteristic
226	C₄×C₈₉	#389	1	1	yes	characteristic
227	C₄×C₈₉	#389	1	1	yes	characteristic
228	Dic₈₉	—	2	8	no	—
229	Dic₈₉	—	2	8	no	—
230	Dic₈₉	—	8	2	no	—
231	#10878	—	89	1	no	maximal, Sylow
232	C₂×C₈₉	—	2	1	no	—
233	C₂×C₈₉	—	2	1	no	—
234	C₂×C₈₉	—	2	1	no	—
235	C₂×C₈₉	—	2	1	no	—
236	C₂×C₈₉	#1436	1	1	yes	characteristic
237	C₂×C₈₉	C₄×#104	1	2	yes	—
238	C₂×C₈₉	#1896	1	2	yes	—
239	C₂×C₈₉	#1994	1	2	yes	—
240	#2296	—	89	1	no	—
241	C₂×C₄³	—	89	1	no	—
242	C₂×#339	—	89	1	no	—
243	C₂×#339	—	89	1	no	—
244	C₂×#339	—	89	1	no	—
245	C₂×#339	D₈₉	1	1	yes	characteristic
246	#1728	—	89	1	no	—
247	C₈₉	#10878	1	1	yes	characteristic, complemented, Sylow
248	C₂²×M₁₆	—	89	1	no	—
249	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
250	C₂×#117	—	89	1	no	—
251	C₂×#117	C₂×D₈₉	1	1	yes	characteristic
252	C₂²×C₄²	—	89	1	no	—
253	C₂²×C₄²	—	89	1	no	—
254	C₂²×C₄²	—	178	2	no	—
255	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
256	#389	—	89	4	no	—
257	#385	—	178	2	no	—
258	C₄×C₄⋊C₄	—	178	2	no	—
259	C₄³	—	178	2	no	—
260	C₄³	—	178	2	no	—
261	#339	—	89	4	no	—
262	#339	—	178	2	no	—
263	#339	—	178	2	no	—
264	#339	Dic₈₉	1	4	yes	complemented
265	#336	—	178	2	no	—
266	C₂³×C₄	—	2	1	no	—
267	C₂³×C₄	—	89	2	no	—
268	C₂³×C₄	—	178	1	no	—
269	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	89	2	no	—
276	C₂×M₁₆	—	178	1	no	—
277	C₂×M₁₆	—	178	1	no	—
278	C₂×M₁₆	—	178	1	no	—
279	C₂×M₁₆	—	178	1	no	—
280	C₂×M₁₆	—	178	1	no	—
281	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	178	1	no	—
284	#117	—	2	1	no	—
285	#117	—	2	1	no	—
286	#117	—	178	1	no	—
287	#117	—	178	1	no	—
288	#117	—	178	1	no	—
289	#117	—	178	1	no	—
290	#117	C₄×D₈₉	1	2	yes	—
291	#117	C₂×Dic₈₉	1	2	yes	—
292	C₂×C₄⋊C₄	—	89	2	no	—
293	C₂×C₄⋊C₄	—	178	4	no	—
294	C₂×C₄⋊C₄	C₄×D₈₉	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	178	1	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	89	2	no	—
302	C₂×C₄²	—	89	2	no	—
303	C₂×C₄²	—	89	2	no	—
304	C₂×C₄²	—	89	2	no	—
305	C₂×C₄²	—	89	2	no	—
306	C₂×C₄²	—	178	1	no	—
307	C₂×C₄²	—	178	8	no	—
308	C₂×C₄²	—	178	16	no	—
309	C₂×C₄²	—	178	1	no	—
310	C₂×C₄²	—	178	1	no	—
311	C₂×C₄²	—	178	1	no	—
312	C₂×C₄²	—	178	1	no	—
313	C₂×C₄²	—	178	1	no	—
314	C₂×C₄²	—	178	1	no	—
315	C₂×C₄²	—	178	1	no	—
316	C₂×C₄²	Dic₁₇₈	1	2	yes	—
317	C₂×C₄²	D₃₅₆	1	2	yes	—
318	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
319	#95	—	178	4	no	—
320	C₂⁴	D₄×D₈₉	1	1	yes	characteristic
321	C₂²×C₄	—	2	8	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	89	4	no	—
327	C₂²×C₄	—	178	8	no	—
328	C₂²×C₄	—	178	2	no	—
329	C₂²×C₄	—	178	8	no	—
330	C₂²×C₄	—	178	2	no	—
331	C₂²×C₄	—	178	2	no	—
332	C₂²×C₄	—	178	2	no	—
333	C₂²×C₄	—	178	2	no	—
334	C₂²×C₄	—	178	2	no	—
335	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
337	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
338	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
339	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
341	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
343	C₂²×C₄	#13083573	1	1	yes	characteristic
344	C₂²×C₄	#13083573	1	1	yes	characteristic
345	C₂²×C₄	#13083573	1	1	yes	characteristic
346	C₂²×C₄	#13083574	1	1	yes	characteristic
347	C₂²×C₄	#13083574	1	1	yes	characteristic
348	C₂²×C₄	#13083575	1	1	yes	characteristic
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	4	1	no	—
352	M₁₆	—	4	1	no	—
353	M₁₆	—	356	1	no	—
354	M₁₆	—	356	1	no	—
355	M₁₆	—	178	2	no	—
356	M₁₆	—	178	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	356	1	no	—
361	C₂×C₈	—	356	1	no	—
362	C₂×C₈	—	178	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	356	8	no	—
365	C₄⋊C₄	—	178	2	no	—
366	C₄⋊C₄	—	178	2	no	—
367	C₄⋊C₄	C₄×Dic₈₉	1	4	yes	complemented
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	356	1	no	—
371	C₂²⋊C₄	—	356	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	89	4	no	—
378	C₄²	—	356	1	no	—
379	C₄²	—	356	1	no	—
380	C₄²	—	178	32	no	—
381	C₄²	—	178	2	no	—
382	C₄²	—	178	2	no	—
383	C₄²	—	178	2	no	—
384	C₄²	—	178	2	no	—
385	C₄²	—	178	2	no	—
386	C₄²	—	178	2	no	—
387	C₄²	—	178	2	no	—
388	C₄²	C₄⋊Dic₈₉	1	4	yes	complemented
389	C₂³	—	2	4	no	—
390	C₂³	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
391	C₂³	#15667972	1	1	yes	characteristic
392	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
393	C₂³	#15667982	1	1	yes	characteristic
394	C₂³	#15667989	1	1	yes	characteristic
395	C₂³	#15667990	1	1	yes	characteristic
396	C₂³	#15667997	1	1	yes	characteristic
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	89	8	no	—
404	C₂×C₄	—	356	2	no	—
405	C₂×C₄	—	356	4	no	—
406	C₂×C₄	—	178	8	no	—
407	C₂×C₄	—	178	8	no	—
408	C₂×C₄	—	178	8	no	—
409	C₂×C₄	—	178	8	no	—
410	C₂×C₄	—	178	8	no	—
411	C₂×C₄	—	178	4	no	—
412	C₂×C₄	—	178	4	no	—
413	C₂×C₄	—	178	4	no	—
414	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
415	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
416	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
417	C₂×C₄	#15667968	1	1	yes	characteristic
418	C₂×C₄	#15667970	1	1	yes	characteristic
419	C₂×C₄	#15667971	1	1	yes	characteristic
420	C₂×C₄	#15667972	1	1	yes	characteristic
421	C₂×C₄	#15667974	1	1	yes	characteristic
422	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
423	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
424	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
425	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
426	C₂×C₄	#15667977	1	1	yes	characteristic
427	C₂×C₄	C₄×Dic₁₇₈	1	1	yes	characteristic
428	C₂×C₄	C₄×Dic₁₇₈	1	1	yes	characteristic
429	C₂×C₄	Q₈×Dic₈₉	1	1	yes	characteristic
430	C₂×C₄	#15667985	1	1	yes	characteristic
431	C₂×C₄	#15667987	1	1	yes	characteristic
432	C₂×C₄	#15667989	1	1	yes	characteristic
433	C₂×C₄	#15667992	1	1	yes	characteristic
434	C₂×C₄	#15667994	1	1	yes	characteristic
435	C₂×C₄	#15667996	1	1	yes	characteristic
436	C₂×C₄	#15667998	1	1	yes	characteristic
437	C₂×C₄	#15668002	1	1	yes	characteristic
438	C₂×C₄	#15668003	1	1	yes	characteristic
439	C₂×C₄	#15668005	1	1	yes	characteristic
440	C₂×C₄	#15668007	1	1	yes	characteristic
441	C₂×C₄	#15668011	1	1	yes	characteristic
442	C₈	—	4	2	no	—
443	C₈	—	356	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	C₂²⋊C₄×Dic₈₉	1	1	yes	characteristic
451	C₂²	#19151472	1	1	yes	characteristic
452	C₂²	#19151473	1	1	yes	characteristic
453	C₂²	#19151476	1	1	yes	characteristic
454	C₂²	#19151484	1	1	yes	characteristic
455	C₂²	#19151485	1	1	yes	characteristic
456	C₂²	#19151502	1	1	yes	characteristic
457	C₂²	#104×D₈₉	1	4	yes	—
458	C₄	—	2	8	no	—
459	C₄	—	4	4	no	—
460	C₄	—	178	8	no	—
461	C₄	—	178	8	no	—
462	C₄	—	712	2	no	—
463	C₄	C₄×C₄⋊Dic₈₉	1	1	yes	characteristic
464	C₄	C₄⋊C₄×Dic₈₉	1	1	yes	characteristic
465	C₄	#19151481	1	1	yes	characteristic
466	C₄	#19151483	1	1	yes	characteristic
467	C₄	#19151490	1	1	yes	characteristic
468	C₄	#19151491	1	1	yes	characteristic
469	C₄	#19151495	1	1	yes	characteristic
470	C₄	#19151497	1	1	yes	characteristic
471	C₂	—	2	1	no	—
472	C₂	—	2	1	no	—
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	#26018486	1	1	yes	characteristic
476	C₂	#104×Dic₈₉	1	2	yes	—
477	C₂	#26020694	1	2	yes	—
478	C₂	#26021227	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₈₉
Fitting	C₂×#339×C₈₉	C₂
socle	C₂³×C₈₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₈₉	C₂×D₄
cosocle	C₂³×C₄×C₈₉	C₂³
hypercenter	C₂×#339	D₈₉
hypocenter	C₈₉	#10878
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
13. #19151497	C₄	semidirect
20. #19151357	C₄	semidirect
25. #339×C₈₉	C₄	semidirect
111. C₄×Dic₈₉	C₄⋊C₄	semidirect
140. C₄⋊C₄×C₈₉	C₄²	semidirect
148. C₄²×C₈₉	C₄⋊C₄	semidirect
247. C₈₉	#10878	semidirect
264. #339	Dic₈₉	semidirect
367. C₄⋊C₄	C₄×Dic₈₉	semidirect
388. C₄²	C₄⋊Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26022736	2
C₂×C₄²×Dic₈₉	2
C₂×#19151359	2
C₂×#19151358	2
C₂×#19151357	2
#26019945	2
C₂×#339×C₈₉	2
#10878	89