Subgroups — #36553087

Order 22784.

866 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151726	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic
3	#26022724	C₂	1	1	yes	maximal, characteristic
4	#26020126	C₂	1	1	yes	maximal, characteristic
5	#26020124	C₂	1	1	yes	maximal, characteristic
6	#26020120	C₂	1	1	yes	maximal, characteristic
7	#26020120	C₂	1	1	yes	maximal, characteristic
8	#26020119	C₂	1	1	yes	maximal, characteristic
9	C₈×#13083553	C₂	1	1	yes	maximal, characteristic
10	#26020110	C₂	1	1	yes	maximal, characteristic
11	#26020109	C₂	1	1	yes	maximal, characteristic
12	C₄×#15667941	C₂	1	1	yes	maximal, characteristic
13	#26019940	C₂	1	1	yes	maximal, characteristic
14	#97×Dic₈₉	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1726	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
17	#19151726	C₄	1	8	yes	complemented
18	C₈×Dic₁₇₈	C₄	1	8	yes	complemented
19	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
21	C₂×#15667941	C₂²	1	1	yes	characteristic
22	C₂×#15667941	C₂²	1	1	yes	characteristic
23	C₂×#15667941	C₂²	1	1	yes	characteristic
24	C₂×#15667941	C₂²	1	1	yes	characteristic
25	C₂×#15667923	C₂²	1	1	yes	characteristic
26	C₂×#15667922	C₂²	1	1	yes	characteristic
27	C₂×#15667922	C₂²	1	1	yes	characteristic
28	C₂×#15667922	C₂²	1	1	yes	characteristic
29	C₂×#15667922	C₂²	1	1	yes	characteristic
30	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
35	#19151502	C₄	1	2	yes	—
36	#19151495	C₄	1	2	yes	—
37	#19151485	C₄	1	2	yes	—
38	#19151481	C₄	1	2	yes	—
39	C₄×#13083553	C₂²	1	1	yes	characteristic
40	C₄×#13083553	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
42	#19151444	C₂²	1	1	yes	characteristic
43	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
44	#19151353	C₂²	1	1	yes	characteristic
45	#19151353	C₂²	1	1	yes	characteristic
46	#19151352	C₂²	1	1	yes	characteristic
47	#19151352	C₂²	1	1	yes	characteristic
48	#19151352	C₂²	1	1	yes	characteristic
49	#19151352	C₂²	1	1	yes	characteristic
50	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
56	#376×C₈₉	C₂²	1	1	yes	characteristic
57	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
58	C₂²×#10623494	C₂³	1	1	yes	characteristic
59	C₂²×#10623494	C₂³	1	1	yes	characteristic
60	C₂²×#10623494	C₂³	1	1	yes	characteristic
61	C₂²×#10623494	C₂³	1	1	yes	characteristic
62	C₄×Dic₁₇₈	C₂×C₄	1	4	yes	—
63	C₄×Dic₁₇₈	C₂×C₄	1	4	yes	—
64	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
65	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
66	C₂×#13083553	C₂×C₄	1	2	yes	—
67	C₂×#13083553	C₂×C₄	1	2	yes	—
68	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
73	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
74	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
75	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
76	C₄⋊#10623494	C₂×C₄	1	4	yes	—
77	C₄⋊#10623494	C₂×C₄	1	4	yes	—
78	#15667941	C₂×C₄	1	4	yes	—
79	#15667941	C₂×C₄	1	4	yes	—
80	#15667941	C₂×C₄	1	4	yes	—
81	#15667941	C₂×C₄	1	4	yes	—
82	#15667923	—	2	2	no	—
83	#15667922	—	2	2	no	—
84	#15667922	—	2	2	no	—
85	#15667922	—	2	2	no	—
86	#15667922	C₂×C₄	1	4	yes	—
87	C₄×#10623494	—	2	2	no	—
88	C₈×Dic₈₉	—	2	2	no	—
89	C₈×Dic₈₉	C₂×C₄	1	4	yes	—
90	C₈×Dic₈₉	C₂×C₄	1	4	yes	—
91	C₈×Dic₈₉	C₂×C₄	1	4	yes	—
92	#15667919	C₂×C₄	1	2	yes	—
93	#15667919	C₂×C₄	1	2	yes	—
94	#15667919	C₂×C₄	1	2	yes	—
95	#15667919	C₂×C₄	1	2	yes	—
96	#15667919	C₂×C₄	1	2	yes	—
97	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
104	#97×C₈₉	—	2	2	no	—
105	#97×C₈₉	C₂×C₄	1	4	yes	—
106	#97×C₈₉	Q₈	1	4	yes	complemented
107	C₄×C₈×C₈₉	—	2	2	no	—
108	C₄×C₈×C₈₉	—	2	2	no	—
109	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	—
110	#95×C₈₉	C₂×C₄	1	2	yes	—
111	#95×C₈₉	C₂×C₄	1	2	yes	—
112	C₂×Dic₁₇₈	—	2	4	no	—
113	C₂×Dic₁₇₈	C₄²	1	4	yes	—
114	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
115	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
116	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×#10623494	—	2	1	no	—
121	C₂×#10623494	—	2	1	no	—
122	C₂×#10623494	—	2	1	no	—
123	C₂×#10623494	—	2	1	no	—
124	C₂×#10623494	—	2	1	no	—
125	C₂×#10623494	—	2	1	no	—
126	C₂×#10623494	—	2	1	no	—
127	C₂×#10623494	—	2	1	no	—
128	C₂×#10623494	C₂²×C₄	1	2	yes	—
129	C₂×#10623494	C₂²×C₄	1	2	yes	—
130	C₂×#10623494	C₂²×C₄	1	2	yes	—
131	C₂×#10623494	C₂²×C₄	1	2	yes	—
132	C₄⋊Dic₈₉	—	4	2	no	—
133	C₄⋊Dic₈₉	C₄²	1	4	yes	—
134	#13083553	—	2	4	no	—
135	#13083553	—	4	2	no	—
136	#13083553	C₄²	1	4	yes	—
137	#13083553	C₄²	1	4	yes	—
138	C₄×Dic₈₉	—	2	1	no	—
139	C₄×Dic₈₉	—	2	1	no	—
140	C₄×Dic₈₉	—	2	1	no	—
141	C₄×Dic₈₉	—	2	1	no	—
142	C₄×Dic₈₉	—	2	4	no	—
143	C₄×Dic₈₉	—	4	2	no	—
144	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
145	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
146	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
147	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
153	C₂×C₈×C₈₉	—	2	1	no	—
154	C₂×C₈×C₈₉	—	2	1	no	—
155	C₂×C₈×C₈₉	—	2	1	no	—
156	C₂×C₈×C₈₉	—	2	1	no	—
157	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
158	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
159	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
160	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
162	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
163	C₂×C₈×C₈₉	#41	1	2	yes	—
164	C₂×C₈×C₈₉	#41	1	2	yes	—
165	C₄²×C₈₉	—	2	1	no	—
166	C₄²×C₈₉	—	2	1	no	—
167	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
168	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
169	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
170	C₄²×C₈₉	#41	1	2	yes	—
171	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	—	2	2	no	—
173	C₂×C₄×C₈₉	—	2	2	no	—
174	C₂×C₄×C₈₉	—	2	2	no	—
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	2	2	no	—
177	C₂×C₄×C₈₉	—	2	2	no	—
178	C₂×C₄×C₈₉	—	2	2	no	—
179	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
180	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
181	C₂×C₄×C₈₉	C₄×Q₈	1	4	yes	—
182	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
188	C₂×Dic₈₉	—	2	2	no	—
189	C₂×Dic₈₉	—	2	2	no	—
190	C₂×Dic₈₉	—	2	2	no	—
191	C₂×Dic₈₉	—	2	2	no	—
192	C₂×Dic₈₉	—	2	2	no	—
193	C₂×Dic₈₉	—	2	2	no	—
194	C₂×Dic₈₉	—	2	2	no	—
195	C₂×Dic₈₉	—	2	2	no	—
196	C₂×Dic₈₉	—	2	2	no	—
197	C₂×Dic₈₉	C₂×C₄²	1	2	yes	—
198	C₂×Dic₈₉	C₂×C₄²	1	2	yes	—
199	C₂×Dic₈₉	C₂×C₄²	1	2	yes	—
200	C₂×Dic₈₉	C₂×C₄²	1	2	yes	—
201	C₂×Dic₈₉	#131	1	4	yes	—
202	Dic₁₇₈	—	2	8	no	—
203	C₈×C₈₉	—	2	2	no	—
204	C₈×C₈₉	—	2	2	no	—
205	C₈×C₈₉	C₄×Q₈	1	4	yes	—
206	C₈×C₈₉	C₄×Q₈	1	4	yes	—
207	#10623494	—	2	2	no	—
208	#10623494	—	2	2	no	—
209	#10623494	—	2	2	no	—
210	#10623494	—	2	2	no	—
211	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
212	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
213	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
214	C₂²×C₈₉	C₂×#131	1	2	yes	—
215	C₂²×C₈₉	#568	1	2	yes	—
216	C₄×C₈₉	—	2	2	no	—
217	C₄×C₈₉	—	2	2	no	—
218	C₄×C₈₉	—	2	4	no	—
219	C₄×C₈₉	—	4	2	no	—
220	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
221	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
222	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
223	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
224	Dic₈₉	—	2	2	no	—
225	Dic₈₉	—	2	2	no	—
226	Dic₈₉	—	2	2	no	—
227	Dic₈₉	—	4	2	no	—
228	Dic₈₉	—	4	2	no	—
229	Dic₈₉	#405	1	4	yes	—
230	#20521	—	89	1	no	maximal, Sylow
231	C₂×C₈₉	C₄²×Q₈	1	1	yes	characteristic
232	C₂×C₈₉	C₂×#405	1	1	yes	characteristic
233	C₂×C₈₉	#2875	1	1	yes	characteristic
234	C₂×C₈₉	#2962	1	2	yes	—
235	C₂×C₈₉	#2969	1	2	yes	—
236	C₂×#446	—	89	1	no	—
237	C₂×C₈×Q₈	—	89	1	no	—
238	#2295	—	89	1	no	—
239	#1771	—	89	1	no	—
240	#1771	—	89	1	no	—
241	#1770	—	89	1	no	—
242	#1770	—	89	1	no	—
243	#1770	—	89	1	no	—
244	C₈×C₄⋊C₄	—	89	1	no	—
245	#1768	—	89	1	no	—
246	#1768	—	89	1	no	—
247	C₄×C₄⋊C₈	—	89	1	no	—
248	#1726	—	89	1	no	—
249	#1726	D₈₉	1	1	yes	characteristic
250	C₄×#97	—	89	1	no	—
251	C₈₉	#20521	1	1	yes	characteristic, complemented, Sylow
252	C₂×C₄×Q₈	—	89	1	no	—
253	#446	—	89	8	no	—
254	C₈×Q₈	—	89	8	no	—
255	C₂×C₄⋊C₈	—	89	1	no	—
256	C₂×C₄⋊C₈	—	89	1	no	—
257	C₂×C₄⋊C₈	—	89	1	no	—
258	C₂×C₄⋊C₈	—	89	1	no	—
259	C₂×C₄⋊C₈	—	89	1	no	—
260	C₂×C₄⋊C₈	—	89	1	no	—
261	C₂×#97	—	89	1	no	—
262	C₂×#97	—	89	1	no	—
263	C₂×#97	—	89	1	no	—
264	C₂×#97	—	89	1	no	—
265	C₂×#97	—	89	1	no	—
266	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
267	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
268	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
269	C₂×C₄×C₈	—	89	1	no	—
270	C₂×C₄×C₈	—	89	1	no	—
271	C₂×C₄×C₈	—	89	1	no	—
272	C₂×C₄×C₈	—	89	1	no	—
273	C₂×C₄×C₈	—	89	1	no	—
274	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
275	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
277	#391	—	89	2	no	—
278	#389	—	89	2	no	—
279	#387	—	89	2	no	—
280	#387	—	89	2	no	—
281	C₄×C₄⋊C₄	—	89	1	no	—
282	C₄×C₄⋊C₄	—	89	1	no	—
283	C₄×C₄⋊C₄	—	89	1	no	—
284	#376	—	89	1	no	—
285	#376	C₂×D₈₉	1	1	yes	characteristic
286	C₄³	—	89	1	no	—
287	#336	—	89	1	no	—
288	#336	—	89	1	no	—
289	#336	—	89	1	no	—
290	#336	—	89	1	no	—
291	#336	—	89	1	no	—
292	#336	—	89	1	no	—
293	C₂²×Q₈	—	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	C₂²×D₈₉	1	1	yes	characteristic
299	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
300	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
301	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
302	C₄×Q₈	—	89	4	no	—
303	C₄×Q₈	—	89	4	no	—
304	C₂×C₄⋊C₄	—	89	1	no	—
305	C₂×C₄⋊C₄	—	89	1	no	—
306	C₂×C₄⋊C₄	—	89	1	no	—
307	C₂×C₄⋊C₄	—	89	2	no	—
308	C₂×C₄⋊C₄	—	89	2	no	—
309	C₂×C₄⋊C₄	—	89	2	no	—
310	C₂×C₄²	—	89	1	no	—
311	C₂×C₄²	—	89	1	no	—
312	C₂×C₄²	—	89	2	no	—
313	C₂×C₄²	—	89	2	no	—
314	C₂×C₄²	—	89	1	no	—
315	C₂×C₄²	—	89	1	no	—
316	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
317	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
318	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
319	C₄⋊C₈	—	89	4	no	—
320	C₄⋊C₈	—	89	4	no	—
321	C₄⋊C₈	—	89	4	no	—
322	C₄⋊C₈	—	89	4	no	—
323	C₄⋊C₈	—	89	4	no	—
324	C₄⋊C₈	—	89	4	no	—
325	#97	—	2	2	no	—
326	#97	—	89	4	no	—
327	#97	—	178	2	no	—
328	#97	—	178	2	no	—
329	#97	—	178	2	no	—
330	#97	—	178	2	no	—
331	#97	Dic₁₇₈	1	4	yes	complemented
332	#97	C₄×D₈₉	1	4	yes	—
333	C₄×C₈	—	2	2	no	—
334	C₄×C₈	—	2	2	no	—
335	C₄×C₈	—	89	4	no	—
336	C₄×C₈	—	89	4	no	—
337	C₄×C₈	—	89	4	no	—
338	C₄×C₈	—	178	2	no	—
339	C₄×C₈	—	178	2	no	—
340	C₄×C₈	C₄×D₈₉	1	4	yes	—
341	#95	—	89	2	no	—
342	#95	—	89	2	no	—
343	#95	—	89	2	no	—
344	#95	—	89	2	no	—
345	#95	—	89	2	no	—
346	#95	C₄×D₈₉	1	2	yes	—
347	#95	C₄×D₈₉	1	2	yes	—
348	C₂×Q₈	—	89	4	no	—
349	C₂×Q₈	—	178	4	no	—
350	C₂²×C₄	—	89	1	no	—
351	C₂²×C₄	—	89	1	no	—
352	C₂²×C₄	—	89	1	no	—
353	C₂²×C₄	—	89	1	no	—
354	C₂²×C₄	—	89	2	no	—
355	C₂²×C₄	—	89	2	no	—
356	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
357	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
358	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
360	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	89	2	no	—
366	C₂×C₈	—	89	2	no	—
367	C₂×C₈	—	89	2	no	—
368	C₂×C₈	—	89	2	no	—
369	C₂×C₈	—	178	1	no	—
370	C₂×C₈	—	178	1	no	—
371	C₂×C₈	—	178	1	no	—
372	C₂×C₈	—	178	1	no	—
373	C₂×C₈	—	178	1	no	—
374	C₂×C₈	—	178	1	no	—
375	C₂×C₈	—	178	1	no	—
376	C₂×C₈	—	178	1	no	—
377	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
378	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
379	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
380	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
381	C₂×C₈	C₂×Dic₁₇₈	1	2	yes	—
382	C₂×C₈	C₂×Dic₁₇₈	1	2	yes	—
383	C₂×C₈	#13083574	1	2	yes	—
384	C₂×C₈	#13083574	1	2	yes	—
385	C₄⋊C₄	—	89	4	no	—
386	C₄⋊C₄	—	89	4	no	—
387	C₄⋊C₄	—	89	4	no	—
388	C₄⋊C₄	—	356	2	no	—
389	C₄⋊C₄	—	356	2	no	—
390	C₄⋊C₄	—	178	4	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	89	2	no	—
394	C₄²	—	89	2	no	—
395	C₄²	—	89	2	no	—
396	C₄²	—	89	2	no	—
397	C₄²	—	356	2	no	—
398	C₄²	—	178	4	no	—
399	C₄²	—	178	1	no	—
400	C₄²	—	178	1	no	—
401	C₄²	—	178	1	no	—
402	C₄²	—	178	1	no	—
403	C₄²	C₂×C₄×D₈₉	1	2	yes	—
404	C₄²	C₂×C₄×D₈₉	1	2	yes	—
405	C₄²	C₂×Dic₁₇₈	1	2	yes	—
406	C₄²	#13083574	1	2	yes	—
407	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
408	Q₈	—	178	8	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	89	2	no	—
417	C₂×C₄	—	89	4	no	—
418	C₂×C₄	—	89	2	no	—
419	C₂×C₄	—	89	2	no	—
420	C₂×C₄	—	89	2	no	—
421	C₂×C₄	—	178	2	no	—
422	C₂×C₄	—	178	2	no	—
423	C₂×C₄	—	178	2	no	—
424	C₂×C₄	—	178	2	no	—
425	C₂×C₄	—	178	2	no	—
426	C₂×C₄	—	178	2	no	—
427	C₂×C₄	—	178	2	no	—
428	C₂×C₄	—	178	2	no	—
429	C₂×C₄	—	178	2	no	—
430	C₂×C₄	C₄²×D₈₉	1	2	yes	—
431	C₂×C₄	C₄²×D₈₉	1	2	yes	—
432	C₂×C₄	C₄×Dic₁₇₈	1	4	yes	—
433	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
435	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
436	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
437	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
438	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
439	C₈	—	2	2	no	—
440	C₈	—	2	2	no	—
441	C₈	—	178	2	no	—
442	C₈	—	178	2	no	—
443	C₈	—	178	2	no	—
444	C₈	—	178	2	no	—
445	C₈	C₄×Dic₁₇₈	1	4	yes	—
446	C₈	C₄×Dic₁₇₈	1	4	yes	—
447	C₂²	C₂×C₄²×D₈₉	1	1	yes	characteristic
448	C₂²	C₂×C₄×Dic₁₇₈	1	1	yes	characteristic
449	C₂²	C₄×#13083574	1	1	yes	characteristic
450	C₂²	#131×D₈₉	1	2	yes	—
451	C₂²	#19152363	1	2	yes	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	4	no	—
455	C₄	—	4	2	no	—
456	C₄	—	89	4	no	—
457	C₄	—	356	2	no	—
458	C₄	—	356	2	no	—
459	C₄	—	178	2	no	—
460	C₄	—	178	2	no	—
461	C₄	—	178	2	no	—
462	C₄	C₂×C₄×Dic₁₇₈	1	1	yes	characteristic
463	C₄	C₂×C₄×Dic₁₇₈	1	1	yes	characteristic
464	C₄	C₄×#13083574	1	1	yes	characteristic
465	C₄	C₄×#13083574	1	1	yes	characteristic
466	C₂	C₄²×Dic₁₇₈	1	1	yes	characteristic
467	C₂	#405×D₈₉	1	1	yes	characteristic
468	C₂	#26028679	1	1	yes	characteristic
469	C₂	#26029196	1	2	yes	—
470	C₂	#26029252	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator	C₂²×C₈₉	C₂²×C₄²
Fitting	C₈₉×#1726	C₂
socle, prime radical	C₂³×C₈₉	C₂³×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1726	D₈₉
hypocenter	C₈₉	#20521
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1726

Complements

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

N	H ≅ G/N	type
17. #19151726	C₄	semidirect
18. C₈×Dic₁₇₈	C₄	semidirect
106. #97×C₈₉	Q₈	semidirect
251. C₈₉	#20521	semidirect
331. #97	Dic₁₇₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151726	2
C₂×C₈×Dic₁₇₈	2
#26022724	2
#26020126	2
#26020124	2
#26020120	2
#26020119	2
C₈×#13083553	2
#26020110	2
#26020109	2
C₄×#15667941	2
#26019940	2
#97×Dic₈₉	2
C₈₉×#1726	2
#20521	89