Subgroups — #36559109

Order 22784.

814 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	C₄²×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic
2	#26021186	C₂	1	2	yes	maximal
3	#26020969	C₂	1	2	yes	maximal
4	#26020812	C₂	1	2	yes	maximal
5	#26020808	C₂	1	2	yes	maximal
6	C₄×#15667941	C₂	1	1	yes	maximal, characteristic
7	C₄×#15667941	C₂	1	1	yes	maximal, characteristic
8	C₄×C₄⋊#10623494	C₂	1	1	yes	maximal, characteristic
9	#26019997	C₂	1	1	yes	maximal, characteristic
10	C₄×C₈×Dic₈₉	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1744	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₁₇₈	C₄	1	1	yes	characteristic
13	C₂×C₄×Dic₁₇₈	C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
16	C₂×#15667941	C₂²	1	2	yes	—
17	C₂×#15667941	C₂²	1	2	yes	—
18	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
19	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₈₉	C₂²	1	2	yes	—
21	C₂×C₈×Dic₈₉	C₂²	1	2	yes	—
22	C₄×#13083553	C₄	1	1	yes	characteristic
23	C₄×#13083553	C₄	1	1	yes	characteristic
24	C₄×#13083553	C₄	1	1	yes	characteristic
25	C₄×#13083553	C₄	1	1	yes	characteristic
26	C₄×#13083553	C₂²	1	1	yes	characteristic
27	C₄×#13083553	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊Dic₈₉	C₄	1	1	yes	characteristic
29	C₄×C₄⋊Dic₈₉	C₄	1	1	yes	characteristic
30	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
31	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
32	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
33	#19151353	C₂²	1	2	yes	—
34	#19151352	C₂²	1	2	yes	—
35	#19151352	C₂²	1	2	yes	—
36	#19151352	C₂²	1	2	yes	—
37	#19151352	C₂²	1	2	yes	—
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	2	yes	—
42	#336×C₈₉	C₂²	1	2	yes	—
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	—	2	4	no	—
47	C₄×Dic₁₇₈	—	2	4	no	—
48	C₄×Dic₁₇₈	C₈	1	8	yes	complemented
49	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
52	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
53	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
54	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
55	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
56	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
57	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
68	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
69	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
70	C₄⋊#10623494	—	2	4	no	—
71	#15667941	—	2	4	no	—
72	#15667941	—	2	4	no	—
73	C₄×#10623494	—	2	2	no	—
74	C₄×#10623494	—	2	2	no	—
75	C₈×Dic₈₉	—	2	4	no	—
76	C₈×Dic₈₉	—	2	4	no	—
77	#15667919	C₂×C₄	1	1	yes	characteristic
78	#15667919	C₂×C₄	1	1	yes	characteristic
79	#15667919	C₂×C₄	1	1	yes	characteristic
80	#15667919	C₂×C₄	1	1	yes	characteristic
81	#15667919	C₂×C₄	1	1	yes	characteristic
82	#15667919	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
84	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
85	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₈₉	—	2	2	no	—
93	C₄×C₈×C₈₉	Q₈	1	4	yes	complemented
94	C₂×Dic₁₇₈	—	2	2	no	—
95	C₂×Dic₁₇₈	—	2	2	no	—
96	C₂×Dic₁₇₈	C₂×C₈	1	4	yes	—
97	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
105	C₂×#10623494	—	2	2	no	—
106	C₂×#10623494	—	2	2	no	—
107	C₂×#10623494	—	2	2	no	—
108	C₂×#10623494	—	2	2	no	—
109	C₂×#10623494	—	2	2	no	—
110	C₂×#10623494	#41	1	4	yes	—
111	C₄⋊Dic₈₉	—	2	2	no	—
112	C₄⋊Dic₈₉	—	2	2	no	—
113	C₄⋊Dic₈₉	C₂×C₈	1	4	yes	—
114	#13083553	—	2	2	no	—
115	#13083553	—	2	2	no	—
116	#13083553	—	2	2	no	—
117	#13083553	—	2	2	no	—
118	#13083553	C₂×C₈	1	4	yes	—
119	#13083553	C₂×C₈	1	4	yes	—
120	C₄×Dic₈₉	—	2	2	no	—
121	C₄×Dic₈₉	—	2	2	no	—
122	C₄×Dic₈₉	—	2	2	no	—
123	C₄×Dic₈₉	—	2	2	no	—
124	C₄×Dic₈₉	—	2	2	no	—
125	C₄×Dic₈₉	—	2	2	no	—
126	C₄×Dic₈₉	—	2	2	no	—
127	C₄×Dic₈₉	—	2	2	no	—
128	C₄×Dic₈₉	C₂×C₈	1	4	yes	—
129	C₄×Dic₈₉	C₂×C₈	1	4	yes	—
130	C₄×Dic₈₉	M₁₆	1	4	yes	—
131	C₄×Dic₈₉	#41	1	4	yes	—
132	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
139	C₂×C₈×C₈₉	—	2	2	no	—
140	C₂×C₈×C₈₉	—	2	2	no	—
141	C₂×C₈×C₈₉	—	2	2	no	—
142	C₂×C₈×C₈₉	—	2	2	no	—
143	C₂×C₈×C₈₉	—	2	2	no	—
144	C₂×C₈×C₈₉	C₂×Q₈	1	4	yes	—
145	C₄²×C₈₉	—	2	2	no	—
146	C₄²×C₈₉	—	2	2	no	—
147	C₄²×C₈₉	—	2	2	no	—
148	C₄²×C₈₉	—	2	2	no	—
149	C₄²×C₈₉	—	2	2	no	—
150	C₄²×C₈₉	C₂×C₈	1	4	yes	—
151	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
152	C₄²×C₈₉	#41	1	2	yes	—
153	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	—	2	1	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	2	1	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
165	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
166	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
167	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
168	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
169	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
170	C₂×C₄×C₈₉	#131	1	2	yes	—
171	C₂×C₄×C₈₉	#131	1	2	yes	—
172	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
174	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
175	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
176	C₂×Dic₈₉	—	2	1	no	—
177	C₂×Dic₈₉	—	2	1	no	—
178	C₂×Dic₈₉	—	2	1	no	—
179	C₂×Dic₈₉	—	2	1	no	—
180	C₂×Dic₈₉	—	2	1	no	—
181	C₂×Dic₈₉	—	2	1	no	—
182	C₂×Dic₈₉	—	2	1	no	—
183	C₂×Dic₈₉	—	2	1	no	—
184	C₂×Dic₈₉	—	2	1	no	—
185	C₂×Dic₈₉	—	2	1	no	—
186	C₂×Dic₈₉	—	2	1	no	—
187	C₂×Dic₈₉	—	2	1	no	—
188	C₂×Dic₈₉	—	2	1	no	—
189	C₂×Dic₈₉	—	2	1	no	—
190	C₂×Dic₈₉	—	2	1	no	—
191	C₂×Dic₈₉	—	2	1	no	—
192	C₂×Dic₈₉	#117	1	2	yes	—
193	C₂×Dic₈₉	#117	1	2	yes	—
194	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
195	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
196	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
197	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
198	C₂×Dic₈₉	C₂×M₁₆	1	2	yes	—
199	C₂×Dic₈₉	C₂×M₁₆	1	2	yes	—
200	Dic₁₇₈	—	2	8	no	—
201	C₈×C₈₉	—	2	4	no	—
202	C₈×C₈₉	—	4	2	no	—
203	#10623494	—	2	4	no	—
204	#10623494	—	4	2	no	—
205	C₂²×C₈₉	C₂×#117	1	1	yes	characteristic
206	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
207	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
208	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
209	C₂²×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
210	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
211	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
212	C₄×C₈₉	—	2	2	no	—
213	C₄×C₈₉	—	2	2	no	—
214	C₄×C₈₉	—	4	1	no	—
215	C₄×C₈₉	—	4	1	no	—
216	C₄×C₈₉	C₈×Q₈	1	4	yes	—
217	C₄×C₈₉	#446	1	4	yes	—
218	C₄×C₈₉	#529	1	2	yes	—
219	C₄×C₈₉	#533	1	2	yes	—
220	Dic₈₉	—	2	2	no	—
221	Dic₈₉	—	2	2	no	—
222	Dic₈₉	—	2	2	no	—
223	Dic₈₉	—	2	2	no	—
224	Dic₈₉	—	2	2	no	—
225	Dic₈₉	—	4	1	no	—
226	Dic₈₉	—	4	1	no	—
227	Dic₈₉	#431	1	4	yes	—
228	#21339	—	89	1	no	maximal, Sylow
229	C₂×C₈₉	#2295	1	1	yes	characteristic
230	C₂×C₈₉	C₂×#431	1	1	yes	characteristic
231	C₂×C₈₉	#2922	1	1	yes	characteristic
232	C₂×C₈₉	C₂×C₈×Q₈	1	1	yes	characteristic
233	C₂×C₈₉	C₂×#446	1	1	yes	characteristic
234	C₂×C₈₉	C₈×#41	1	1	yes	characteristic
235	C₂×C₈₉	#2965	1	1	yes	characteristic
236	C₄²×Q₈	—	89	1	no	—
237	#1984	—	89	2	no	—
238	#1939	—	89	2	no	—
239	#1916	—	89	2	no	—
240	#1916	—	89	2	no	—
241	C₄×C₄⋊C₈	—	89	1	no	—
242	C₄×C₄⋊C₈	—	89	1	no	—
243	C₄×C₄⋊C₈	—	89	1	no	—
244	#1744	—	89	1	no	—
245	#1744	D₈₉	1	1	yes	characteristic
246	C₄²×C₈	—	89	1	no	—
247	C₈₉	#21339	1	1	yes	characteristic, complemented, Sylow
248	C₂×C₄×Q₈	—	89	1	no	—
249	C₂×C₄×Q₈	—	89	1	no	—
250	C₂×C₄×Q₈	—	89	1	no	—
251	C₂×C₄⋊C₈	—	89	2	no	—
252	C₂×C₄⋊C₈	—	89	2	no	—
253	C₂×C₄⋊C₈	—	89	2	no	—
254	C₂×C₄×C₈	—	89	2	no	—
255	C₂×C₄×C₈	—	89	2	no	—
256	C₂×C₄×C₈	—	89	1	no	—
257	C₂×C₄×C₈	—	89	1	no	—
258	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
260	C₄×C₄⋊C₄	—	89	1	no	—
261	C₄×C₄⋊C₄	—	89	1	no	—
262	C₄×C₄⋊C₄	—	89	1	no	—
263	C₄×C₄⋊C₄	—	89	1	no	—
264	C₄×C₄⋊C₄	—	89	1	no	—
265	C₄×C₄⋊C₄	—	89	1	no	—
266	C₄×C₄⋊C₄	—	89	1	no	—
267	C₄×C₄⋊C₄	—	89	1	no	—
268	C₄×C₄⋊C₄	—	89	1	no	—
269	C₄³	—	89	1	no	—
270	C₄³	—	89	1	no	—
271	C₄³	C₂×D₈₉	1	1	yes	characteristic
272	#336	—	89	2	no	—
273	#336	—	89	2	no	—
274	#336	—	89	2	no	—
275	#336	—	89	2	no	—
276	#336	—	89	2	no	—
277	#336	C₂×D₈₉	1	2	yes	—
278	#336	C₂×D₈₉	1	2	yes	—
279	C₂²×Q₈	—	89	1	no	—
280	C₂²×C₈	—	89	2	no	—
281	C₂²×C₈	—	89	2	no	—
282	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
283	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
284	C₄×Q₈	—	89	8	no	—
285	C₄×Q₈	—	178	4	no	—
286	C₄×Q₈	—	178	4	no	—
287	C₂×C₄⋊C₄	—	89	1	no	—
288	C₂×C₄⋊C₄	—	89	1	no	—
289	C₂×C₄⋊C₄	—	89	1	no	—
290	C₂×C₄⋊C₄	—	89	1	no	—
291	C₂×C₄⋊C₄	—	89	1	no	—
292	C₂×C₄⋊C₄	—	89	1	no	—
293	C₂×C₄⋊C₄	—	89	1	no	—
294	C₂×C₄⋊C₄	—	89	1	no	—
295	C₂×C₄⋊C₄	—	89	1	no	—
296	C₂×C₄²	—	89	1	no	—
297	C₂×C₄²	—	89	1	no	—
298	C₂×C₄²	—	89	1	no	—
299	C₂×C₄²	—	89	1	no	—
300	C₂×C₄²	—	89	1	no	—
301	C₂×C₄²	—	89	1	no	—
302	C₂×C₄²	—	89	1	no	—
303	C₂×C₄²	—	89	1	no	—
304	C₂×C₄²	—	89	1	no	—
305	C₂×C₄²	—	89	1	no	—
306	C₂×C₄²	—	89	1	no	—
307	C₂×C₄²	—	89	1	no	—
308	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
309	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
310	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
311	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
312	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
313	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
314	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
315	C₄⋊C₈	—	178	4	no	—
316	C₄⋊C₈	—	178	4	no	—
317	C₄⋊C₈	—	178	4	no	—
318	C₄×C₈	—	2	2	no	—
319	C₄×C₈	—	178	4	no	—
320	C₄×C₈	—	178	4	no	—
321	C₄×C₈	—	178	2	no	—
322	C₄×C₈	—	178	2	no	—
323	C₄×C₈	Dic₁₇₈	1	4	yes	complemented
324	#95	—	89	1	no	—
325	#95	—	89	1	no	—
326	#95	—	89	1	no	—
327	#95	—	89	1	no	—
328	#95	—	89	1	no	—
329	#95	—	89	1	no	—
330	C₂×Q₈	—	89	4	no	—
331	C₂×Q₈	—	178	2	no	—
332	C₂×Q₈	—	178	2	no	—
333	C₂²×C₄	—	89	1	no	—
334	C₂²×C₄	—	89	1	no	—
335	C₂²×C₄	—	89	1	no	—
336	C₂²×C₄	—	89	1	no	—
337	C₂²×C₄	—	89	1	no	—
338	C₂²×C₄	—	89	1	no	—
339	C₂²×C₄	—	89	1	no	—
340	C₂²×C₄	—	89	1	no	—
341	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
347	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	89	4	no	—
354	C₂×C₈	—	178	2	no	—
355	C₂×C₈	—	178	2	no	—
356	C₂×C₈	—	178	2	no	—
357	C₂×C₈	—	178	2	no	—
358	C₂×C₈	—	178	2	no	—
359	C₂×C₈	C₂×Dic₁₇₈	1	4	yes	—
360	C₄⋊C₄	—	89	4	no	—
361	C₄⋊C₄	—	89	4	no	—
362	C₄⋊C₄	—	89	4	no	—
363	C₄⋊C₄	—	178	2	no	—
364	C₄⋊C₄	—	178	2	no	—
365	C₄⋊C₄	—	178	2	no	—
366	C₄⋊C₄	—	178	2	no	—
367	C₄⋊C₄	—	178	2	no	—
368	C₄⋊C₄	—	178	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	89	4	no	—
375	C₄²	—	89	4	no	—
376	C₄²	—	89	4	no	—
377	C₄²	—	89	4	no	—
378	C₄²	—	178	2	no	—
379	C₄²	—	178	2	no	—
380	C₄²	—	178	2	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	C₈×D₈₉	1	4	yes	—
387	C₄²	C₂×Dic₁₇₈	1	2	yes	—
388	C₄²	#13083574	1	2	yes	—
389	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
390	Q₈	—	178	8	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	89	2	no	—
402	C₂×C₄	—	89	2	no	—
403	C₂×C₄	—	89	2	no	—
404	C₂×C₄	—	89	2	no	—
405	C₂×C₄	—	89	2	no	—
406	C₂×C₄	—	89	2	no	—
407	C₂×C₄	—	89	2	no	—
408	C₂×C₄	—	89	2	no	—
409	C₂×C₄	—	178	1	no	—
410	C₂×C₄	—	178	1	no	—
411	C₂×C₄	—	178	1	no	—
412	C₂×C₄	—	178	1	no	—
413	C₂×C₄	—	178	1	no	—
414	C₂×C₄	—	178	1	no	—
415	C₂×C₄	—	178	1	no	—
416	C₂×C₄	—	178	1	no	—
417	C₂×C₄	—	178	1	no	—
418	C₂×C₄	—	178	1	no	—
419	C₂×C₄	—	178	1	no	—
420	C₂×C₄	—	178	1	no	—
421	C₂×C₄	—	178	1	no	—
422	C₂×C₄	—	178	1	no	—
423	C₂×C₄	—	178	1	no	—
424	C₂×C₄	—	178	1	no	—
425	C₂×C₄	C₄×Dic₁₇₈	1	2	yes	—
426	C₂×C₄	C₄×Dic₁₇₈	1	2	yes	—
427	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
428	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
429	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
430	C₂×C₄	M₁₆×D₈₉	1	2	yes	—
431	C₂×C₄	#15668018	1	2	yes	—
432	C₂×C₄	#15668020	1	2	yes	—
433	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
434	C₂×C₄	#41×D₈₉	1	2	yes	—
435	C₂×C₄	#41×D₈₉	1	2	yes	—
436	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
437	C₈	—	2	4	no	—
438	C₈	—	4	2	no	—
439	C₈	—	356	2	no	—
440	C₈	—	178	4	no	—
441	C₂²	#117×D₈₉	1	1	yes	characteristic
442	C₂²	C₂×C₄×Dic₁₇₈	1	1	yes	characteristic
443	C₂²	#19152066	1	1	yes	characteristic
444	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
445	C₂²	C₂×M₁₆×D₈₉	1	1	yes	characteristic
446	C₂²	C₂×#15668018	1	1	yes	characteristic
447	C₂²	C₂×#15668020	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	89	4	no	—
453	C₄	—	356	1	no	—
454	C₄	—	356	1	no	—
455	C₄	—	178	2	no	—
456	C₄	—	178	2	no	—
457	C₄	—	178	2	no	—
458	C₄	—	178	2	no	—
459	C₄	—	178	2	no	—
460	C₄	C₈×Dic₁₇₈	1	4	yes	—
461	C₄	#19151726	1	4	yes	—
462	C₄	#19152126	1	2	yes	—
463	C₄	#19152151	1	2	yes	—
464	C₂	#26022724	1	1	yes	characteristic
465	C₂	#431×D₈₉	1	1	yes	characteristic
466	C₂	#26028891	1	1	yes	characteristic
467	C₂	C₂×C₈×Dic₁₇₈	1	1	yes	characteristic
468	C₂	C₂×#19151726	1	1	yes	characteristic
469	C₂	#26029208	1	1	yes	characteristic
470	C₂	#26029216	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂²×D₈₉
commutator	C₂²×C₈₉	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1744	C₂
socle, prime radical	C₂³×C₈₉	C₂³×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1744	D₈₉
hypocenter	C₈₉	#21339
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄² ◁ #1744

Complements

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

N	H ≅ G/N	type
48. C₄×Dic₁₇₈	C₈	semidirect
93. C₄×C₈×C₈₉	Q₈	semidirect
247. C₈₉	#21339	semidirect
323. C₄×C₈	Dic₁₇₈	semidirect

Maximal subgroups

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

subgroup	index
C₄²×Dic₁₇₈	2
#26021186	2
#26020969	2
#26020812	2
#26020808	2
C₄×#15667941	2
C₄×C₄⋊#10623494	2
#26019997	2
C₄×C₈×Dic₈₉	2
C₈₉×#1744	2
#21339	89