Subgroups — #36574315

Order 22784.

784 conjugacy classes of subgroups.

The subgroup lattice has 494 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	#26020810	C₂	1	2	yes	maximal
4	#26020807	C₂	1	2	yes	maximal
5	#26020403	C₂	1	1	yes	maximal, characteristic
6	#26020368	C₂	1	1	yes	maximal, characteristic
7	#26020113	C₂	1	2	yes	maximal
8	C₄⋊C₈×Dic₈₉	C₂	1	1	yes	maximal, characteristic
9	C₄⋊C₈×Dic₈₉	C₂	1	1	yes	maximal, characteristic
10	C₄×C₄⋊#10623494	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1831	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	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×C₄×#10623494	C₂²	1	2	yes	—
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	2	no	—
48	C₄×Dic₁₇₈	—	2	2	no	—
49	C₄×Dic₁₇₈	C₈	1	8	yes	complemented
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	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×#13083553	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	C₂×C₄	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	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
71	C₄⋊#10623494	—	2	2	no	—
72	C₄⋊#10623494	Q₈	1	4	yes	complemented
73	#15667941	—	2	4	no	—
74	#15667941	—	4	2	no	—
75	C₄×#10623494	—	4	2	no	—
76	C₈×Dic₈₉	—	2	4	no	—
77	C₈×Dic₈₉	—	4	2	no	—
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	#15667919	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
85	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
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	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₈₉	—	2	2	no	—
94	C₄⋊C₈×C₈₉	—	2	2	no	—
95	C₂×Dic₁₇₈	—	2	2	no	—
96	C₂×Dic₁₇₈	—	2	2	no	—
97	C₂×Dic₁₇₈	C₂×C₈	1	4	yes	—
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	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
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	—	2	2	no	—
111	C₂×#10623494	C₂×Q₈	1	4	yes	—
112	C₄⋊Dic₈₉	—	2	2	no	—
113	C₄⋊Dic₈₉	—	2	2	no	—
114	C₄⋊Dic₈₉	C₂×C₈	1	4	yes	—
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	#13083553	M₁₆	1	4	yes	—
121	C₄×Dic₈₉	—	2	2	no	—
122	C₄×Dic₈₉	—	2	2	no	—
123	C₄×Dic₈₉	—	2	1	no	—
124	C₄×Dic₈₉	—	2	1	no	—
125	C₄×Dic₈₉	—	2	1	no	—
126	C₄×Dic₈₉	—	2	1	no	—
127	C₄×Dic₈₉	—	2	1	no	—
128	C₄×Dic₈₉	—	2	1	no	—
129	C₄×Dic₈₉	—	2	2	no	—
130	C₄×Dic₈₉	—	2	2	no	—
131	C₄×Dic₈₉	—	4	1	no	—
132	C₄×Dic₈₉	—	4	1	no	—
133	C₄×Dic₈₉	C₂×C₈	1	4	yes	—
134	C₄×Dic₈₉	C₂×C₈	1	4	yes	—
135	C₄×Dic₈₉	#41	1	2	yes	—
136	C₄×Dic₈₉	#41	1	2	yes	—
137	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₈₉	—	2	2	no	—
145	C₂×C₈×C₈₉	—	2	2	no	—
146	C₂×C₈×C₈₉	—	2	2	no	—
147	C₂×C₈×C₈₉	—	2	2	no	—
148	C₂×C₈×C₈₉	—	2	2	no	—
149	C₂×C₈×C₈₉	—	2	2	no	—
150	C₄²×C₈₉	—	2	2	no	—
151	C₄²×C₈₉	—	2	2	no	—
152	C₄²×C₈₉	—	2	1	no	—
153	C₄²×C₈₉	—	2	1	no	—
154	C₄²×C₈₉	—	2	1	no	—
155	C₄²×C₈₉	—	2	1	no	—
156	C₄²×C₈₉	—	4	1	no	—
157	C₄²×C₈₉	C₂×C₈	1	4	yes	—
158	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
159	C₄²×C₈₉	#41	1	2	yes	—
160	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
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	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	2	1	no	—
171	C₂×C₄×C₈₉	—	2	1	no	—
172	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
173	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
174	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
175	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
176	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
177	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
178	C₂×C₄×C₈₉	#131	1	2	yes	—
179	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
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	—	2	1	no	—
193	C₂×Dic₈₉	—	2	1	no	—
194	C₂×Dic₈₉	—	2	1	no	—
195	C₂×Dic₈₉	—	2	1	no	—
196	C₂×Dic₈₉	—	2	1	no	—
197	C₂×Dic₈₉	—	2	1	no	—
198	C₂×Dic₈₉	—	2	1	no	—
199	C₂×Dic₈₉	—	2	1	no	—
200	C₂×Dic₈₉	—	2	1	no	—
201	C₂×Dic₈₉	#117	1	2	yes	—
202	C₂×Dic₈₉	#117	1	2	yes	—
203	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
204	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
205	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
206	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
207	C₂×Dic₈₉	C₂×M₁₆	1	2	yes	—
208	C₂×Dic₈₉	C₂×M₁₆	1	2	yes	—
209	Dic₁₇₈	—	2	8	no	—
210	C₈×C₈₉	—	4	2	no	—
211	C₈×C₈₉	—	4	2	no	—
212	#10623494	—	2	4	no	—
213	#10623494	—	4	2	no	—
214	C₂²×C₈₉	C₂×#117	1	1	yes	characteristic
215	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
216	C₂²×C₈₉	#520	1	1	yes	characteristic
217	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
218	C₂²×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
219	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
220	C₂²×C₈₉	#568	1	1	yes	characteristic
221	C₄×C₈₉	—	2	2	no	—
222	C₄×C₈₉	—	2	2	no	—
223	C₄×C₈₉	—	2	2	no	—
224	C₄×C₈₉	—	2	2	no	—
225	C₄×C₈₉	—	4	1	no	—
226	C₄×C₈₉	C₈×Q₈	1	4	yes	—
227	C₄×C₈₉	#554	1	1	yes	characteristic
228	C₄×C₈₉	#556	1	1	yes	characteristic
229	C₄×C₈₉	#557	1	1	yes	characteristic
230	C₄×C₈₉	#559	1	1	yes	characteristic
231	Dic₈₉	—	2	2	no	—
232	Dic₈₉	—	2	2	no	—
233	Dic₈₉	—	2	2	no	—
234	Dic₈₉	—	2	2	no	—
235	Dic₈₉	—	2	2	no	—
236	Dic₈₉	—	4	1	no	—
237	Dic₈₉	—	4	1	no	—
238	Dic₈₉	#431	1	4	yes	—
239	#22821	—	89	1	no	maximal, Sylow
240	C₂×C₈₉	#2355	1	1	yes	characteristic
241	C₂×C₈₉	C₂×#431	1	1	yes	characteristic
242	C₂×C₈₉	#2925	1	1	yes	characteristic
243	C₂×C₈₉	C₂×C₈×Q₈	1	1	yes	characteristic
244	C₂×C₈₉	Q₈×M₁₆	1	1	yes	characteristic
245	C₂×C₈₉	#2988	1	1	yes	characteristic
246	C₂×C₈₉	#2990	1	1	yes	characteristic
247	C₄²×Q₈	—	89	1	no	—
248	#1984	—	89	2	no	—
249	#1916	—	89	2	no	—
250	#1916	—	89	2	no	—
251	#1842	—	89	1	no	—
252	#1831	—	89	1	no	—
253	#1831	D₈₉	1	1	yes	characteristic
254	C₈×C₄⋊C₄	—	89	2	no	—
255	C₄×C₄⋊C₈	—	89	1	no	—
256	C₄×C₄⋊C₈	—	89	1	no	—
257	C₄×C₄⋊C₈	—	89	1	no	—
258	C₈₉	#22821	1	1	yes	characteristic, complemented, Sylow
259	C₂×C₄×Q₈	—	89	1	no	—
260	C₂×C₄×Q₈	—	89	1	no	—
261	C₂×C₄×Q₈	—	89	1	no	—
262	C₂×C₄⋊C₈	—	89	1	no	—
263	C₂×C₄⋊C₈	—	89	2	no	—
264	C₂×C₄⋊C₈	—	89	2	no	—
265	C₂×C₄⋊C₈	—	89	1	no	—
266	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
268	C₂×C₄×C₈	—	89	2	no	—
269	C₂×C₄×C₈	—	89	2	no	—
270	C₂×C₄×C₈	—	89	2	no	—
271	C₄×C₄⋊C₄	—	89	1	no	—
272	C₄×C₄⋊C₄	—	89	1	no	—
273	C₄×C₄⋊C₄	—	89	1	no	—
274	C₄×C₄⋊C₄	—	89	1	no	—
275	C₄×C₄⋊C₄	—	89	1	no	—
276	C₄×C₄⋊C₄	—	89	1	no	—
277	C₄×C₄⋊C₄	—	89	1	no	—
278	C₄×C₄⋊C₄	—	89	1	no	—
279	C₄×C₄⋊C₄	—	89	1	no	—
280	C₄³	—	89	1	no	—
281	C₄³	—	89	1	no	—
282	C₄³	C₂×D₈₉	1	1	yes	characteristic
283	#336	—	89	2	no	—
284	#336	—	89	2	no	—
285	#336	—	89	2	no	—
286	#336	—	89	2	no	—
287	#336	—	89	2	no	—
288	#336	C₂×D₈₉	1	2	yes	—
289	#336	C₂×D₈₉	1	2	yes	—
290	C₂²×Q₈	—	89	1	no	—
291	C₂²×C₈	—	89	2	no	—
292	C₂²×C₈	—	89	2	no	—
293	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
294	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
295	C₄×Q₈	—	89	8	no	—
296	C₄×Q₈	—	178	2	no	—
297	C₄×Q₈	—	178	2	no	—
298	C₄×Q₈	—	178	4	no	—
299	C₂×C₄⋊C₄	—	89	1	no	—
300	C₂×C₄⋊C₄	—	89	1	no	—
301	C₂×C₄⋊C₄	—	89	1	no	—
302	C₂×C₄⋊C₄	—	89	1	no	—
303	C₂×C₄⋊C₄	—	89	1	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	1	no	—
308	C₂×C₄²	—	89	1	no	—
309	C₂×C₄²	—	89	1	no	—
310	C₂×C₄²	—	89	1	no	—
311	C₂×C₄²	—	89	1	no	—
312	C₂×C₄²	—	89	1	no	—
313	C₂×C₄²	—	89	1	no	—
314	C₂×C₄²	—	89	1	no	—
315	C₂×C₄²	—	89	1	no	—
316	C₂×C₄²	—	89	1	no	—
317	C₂×C₄²	—	89	1	no	—
318	C₂×C₄²	—	89	1	no	—
319	C₂×C₄²	—	89	1	no	—
320	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
321	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
322	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
323	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
324	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
325	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
326	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
327	C₄⋊C₈	—	2	2	no	—
328	C₄⋊C₈	—	2	2	no	—
329	C₄⋊C₈	—	89	4	no	—
330	C₄⋊C₈	—	356	2	no	—
331	C₄⋊C₈	—	178	4	no	—
332	C₄⋊C₈	—	178	2	no	—
333	C₄×C₈	—	356	2	no	—
334	C₄×C₈	—	356	2	no	—
335	C₄×C₈	—	178	4	no	—
336	#95	—	89	1	no	—
337	#95	—	89	1	no	—
338	#95	—	89	1	no	—
339	#95	—	89	1	no	—
340	#95	—	89	1	no	—
341	#95	—	89	1	no	—
342	C₂×Q₈	—	89	4	no	—
343	C₂×Q₈	—	178	2	no	—
344	C₂×Q₈	—	178	2	no	—
345	C₂²×C₄	—	89	1	no	—
346	C₂²×C₄	—	89	1	no	—
347	C₂²×C₄	—	89	1	no	—
348	C₂²×C₄	—	89	1	no	—
349	C₂²×C₄	—	89	1	no	—
350	C₂²×C₄	—	89	1	no	—
351	C₂²×C₄	—	89	1	no	—
352	C₂²×C₄	—	89	1	no	—
353	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
359	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	89	4	no	—
367	C₂×C₈	—	178	2	no	—
368	C₂×C₈	—	178	2	no	—
369	C₂×C₈	—	178	2	no	—
370	C₂×C₈	—	178	2	no	—
371	C₂×C₈	—	178	2	no	—
372	C₄⋊C₄	—	89	4	no	—
373	C₄⋊C₄	—	89	4	no	—
374	C₄⋊C₄	—	89	4	no	—
375	C₄⋊C₄	—	89	4	no	—
376	C₄⋊C₄	—	178	2	no	—
377	C₄⋊C₄	—	178	2	no	—
378	C₄⋊C₄	—	178	2	no	—
379	C₄⋊C₄	—	178	2	no	—
380	C₄⋊C₄	—	178	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	4	1	no	—
388	C₄²	—	89	4	no	—
389	C₄²	—	89	4	no	—
390	C₄²	—	89	2	no	—
391	C₄²	—	89	2	no	—
392	C₄²	—	356	1	no	—
393	C₄²	—	356	1	no	—
394	C₄²	—	178	2	no	—
395	C₄²	—	178	2	no	—
396	C₄²	—	178	2	no	—
397	C₄²	—	178	2	no	—
398	C₄²	—	178	1	no	—
399	C₄²	—	178	1	no	—
400	C₄²	—	178	1	no	—
401	C₄²	—	178	1	no	—
402	C₄²	—	178	1	no	—
403	C₄²	—	178	1	no	—
404	C₄²	C₈×D₈₉	1	4	yes	—
405	C₄²	Q₈×D₈₉	1	2	yes	—
406	C₄²	#13083573	1	2	yes	—
407	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
408	Q₈	—	178	8	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	89	2	no	—
421	C₂×C₄	—	89	2	no	—
422	C₂×C₄	—	89	2	no	—
423	C₂×C₄	—	89	2	no	—
424	C₂×C₄	—	89	2	no	—
425	C₂×C₄	—	89	2	no	—
426	C₂×C₄	—	89	2	no	—
427	C₂×C₄	—	89	2	no	—
428	C₂×C₄	—	178	1	no	—
429	C₂×C₄	—	178	1	no	—
430	C₂×C₄	—	178	1	no	—
431	C₂×C₄	—	178	1	no	—
432	C₂×C₄	—	178	1	no	—
433	C₂×C₄	—	178	1	no	—
434	C₂×C₄	—	178	1	no	—
435	C₂×C₄	—	178	1	no	—
436	C₂×C₄	—	178	1	no	—
437	C₂×C₄	—	178	1	no	—
438	C₂×C₄	—	178	1	no	—
439	C₂×C₄	—	178	1	no	—
440	C₂×C₄	—	178	1	no	—
441	C₂×C₄	—	178	1	no	—
442	C₂×C₄	—	178	1	no	—
443	C₂×C₄	—	178	1	no	—
444	C₂×C₄	#15667977	1	2	yes	—
445	C₂×C₄	#15667977	1	2	yes	—
446	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
447	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
448	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
449	C₂×C₄	M₁₆×D₈₉	1	2	yes	—
450	C₂×C₄	#15668020	1	2	yes	—
451	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
452	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
453	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
454	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
455	C₂×C₄	#15668058	1	1	yes	characteristic
456	C₂×C₄	#15668059	1	1	yes	characteristic
457	C₈	—	4	2	no	—
458	C₈	—	4	2	no	—
459	C₈	—	356	2	no	—
460	C₈	—	178	4	no	—
461	C₂²	#117×D₈₉	1	1	yes	characteristic
462	C₂²	C₂×#15667977	1	1	yes	characteristic
463	C₂²	#19152078	1	1	yes	characteristic
464	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
465	C₂²	C₂×M₁₆×D₈₉	1	1	yes	characteristic
466	C₂²	C₂×#15668020	1	1	yes	characteristic
467	C₂²	#19152364	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	4	1	no	—
473	C₄	—	89	4	no	—
474	C₄	—	356	1	no	—
475	C₄	—	356	1	no	—
476	C₄	—	178	2	no	—
477	C₄	—	178	2	no	—
478	C₄	—	178	2	no	—
479	C₄	—	178	2	no	—
480	C₄	—	178	2	no	—
481	C₄	#19151722	1	4	yes	—
482	C₄	#19152304	1	1	yes	characteristic
483	C₄	#19152317	1	1	yes	characteristic
484	C₄	#19152325	1	1	yes	characteristic
485	C₄	#19152330	1	1	yes	characteristic
486	C₂	#26023204	1	1	yes	characteristic
487	C₂	#431×D₈₉	1	1	yes	characteristic
488	C₂	#26028919	1	1	yes	characteristic
489	C₂	C₂×#19151722	1	1	yes	characteristic
490	C₂	#26029203	1	1	yes	characteristic
491	C₂	#26029360	1	1	yes	characteristic
492	C₂	#26029379	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator	C₂²×C₈₉	C₂³×C₈
Fitting	C₈₉×#1831	C₂
socle, prime radical	C₂³×C₈₉	C₂³×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1831	D₈₉
hypocenter	C₈₉	#22821
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1831

Complements

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

N	H ≅ G/N	type
49. C₄×Dic₁₇₈	C₈	semidirect
72. C₄⋊#10623494	Q₈	semidirect
258. C₈₉	#22821	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
#26020810	2
#26020807	2
#26020403	2
#26020368	2
#26020113	2
C₄⋊C₈×Dic₈₉	2
C₄×C₄⋊#10623494	2
C₈₉×#1831	2
#22821	89