Subgroups — #36520182

Order 22784.

704 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029219	C₂	1	1	yes	maximal, characteristic
2	#26029219	C₂	1	1	yes	maximal, characteristic
3	#26018555	C₂	1	1	yes	maximal, characteristic, complemented
4	#26018552	C₂	1	1	yes	maximal, characteristic, complemented
5	#26018552	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018549	C₂	1	1	yes	maximal, characteristic, complemented
7	#26018547	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018547	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018545	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018542	C₂	1	1	yes	maximal, characteristic, complemented
11	#26018541	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018536	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018533	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#13083558	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2922	C₂	1	1	yes	maximal, characteristic
16	#19151729	C₄	1	2	yes	—
17	#19151729	C₄	1	2	yes	—
18	#19151676	C₄	1	2	yes	—
19	#19151676	C₄	1	2	yes	—
20	#19151670	C₄	1	2	yes	—
21	#19151670	C₄	1	2	yes	—
22	#19151670	C₄	1	2	yes	—
23	#19151670	C₄	1	2	yes	—
24	#19151651	C₂²	1	1	yes	characteristic
25	#19151651	C₂²	1	1	yes	characteristic
26	#19151651	C₂²	1	1	yes	characteristic
27	#19151651	C₂²	1	1	yes	characteristic
28	#19151651	C₂²	1	1	yes	characteristic
29	#19151651	C₂²	1	1	yes	characteristic
30	C₄×#13083558	C₂²	1	1	yes	characteristic
31	C₄×#13083558	C₂²	1	1	yes	characteristic
32	C₄×#13083558	C₂²	1	1	yes	characteristic
33	C₄×#13083558	C₂²	1	1	yes	characteristic
34	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
35	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
36	#19151320	C₂²	1	1	yes	characteristic
37	#19151320	C₂²	1	1	yes	characteristic
38	#19151320	C₂²	1	1	yes	characteristic
39	#19151320	C₂²	1	1	yes	characteristic
40	#19151320	C₂²	1	1	yes	characteristic
41	#19151320	C₂²	1	1	yes	characteristic
42	#19151320	C₂²	1	1	yes	characteristic
43	#19151320	C₂²	1	1	yes	characteristic
44	#19151319	C₂²	1	1	yes	characteristic
45	#19151319	C₂²	1	1	yes	characteristic
46	#19151319	C₂²	1	1	yes	characteristic
47	#19151319	C₂²	1	1	yes	characteristic
48	C₈×#10623494	C₂²	1	1	yes	characteristic
49	C₈×#10623494	C₂²	1	1	yes	characteristic
50	C₈×#10623494	C₂²	1	1	yes	characteristic
51	C₈×#10623494	C₂²	1	1	yes	characteristic
52	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
53	#433×C₈₉	C₄	1	2	yes	—
54	#433×C₈₉	C₄	1	2	yes	—
55	#431×C₈₉	C₂²	1	1	yes	characteristic
56	#431×C₈₉	C₂²	1	1	yes	characteristic
57	#431×C₈₉	C₂²	1	1	yes	characteristic
58	#431×C₈₉	C₂²	1	1	yes	characteristic
59	#424×C₈₉	C₄	1	2	yes	—
60	#408×C₈₉	C₄	1	2	yes	—
61	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
62	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
63	C₂×#13083558	C₂×C₄	1	2	yes	—
64	C₂×#13083558	C₂×C₄	1	2	yes	—
65	C₂×#13083558	C₂×C₄	1	2	yes	—
66	C₂×#13083558	C₂×C₄	1	2	yes	—
67	C₂²×#10623494	C₂×C₄	1	2	yes	—
68	C₂²×#10623494	C₂×C₄	1	2	yes	—
69	C₄⋊#10623494	C₂×C₄	1	2	yes	—
70	C₄⋊#10623494	C₂×C₄	1	2	yes	—
71	C₄⋊#10623494	C₂×C₄	1	2	yes	—
72	C₄⋊#10623494	C₂×C₄	1	2	yes	—
73	C₄⋊#10623494	C₂×C₄	1	2	yes	—
74	C₄⋊#10623494	C₂×C₄	1	2	yes	—
75	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
76	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
77	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
78	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
79	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
80	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
81	#15667923	C₂×C₄	1	2	yes	—
82	#15667923	C₂×C₄	1	2	yes	—
83	#15667923	C₂×C₄	1	2	yes	—
84	#15667923	C₂×C₄	1	2	yes	—
85	C₄×#10623494	C₂×C₄	1	2	yes	—
86	C₄×#10623494	C₂×C₄	1	2	yes	—
87	C₄×#10623494	C₂³	1	1	yes	characteristic
88	C₄×#10623494	C₂³	1	1	yes	characteristic
89	C₄×#10623494	C₂³	1	1	yes	characteristic
90	C₄×#10623494	C₂³	1	1	yes	characteristic
91	C₄×#10623494	C₂³	1	1	yes	characteristic
92	C₄×#10623494	C₂³	1	1	yes	characteristic
93	C₄×#10623494	C₂³	1	1	yes	characteristic
94	C₄×#10623494	C₂³	1	1	yes	characteristic
95	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
96	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
97	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
98	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
99	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
100	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
101	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
102	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
103	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
106	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
107	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
108	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
113	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
114	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
115	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
116	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
117	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
118	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
119	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
120	#97×C₈₉	C₂×C₄	1	2	yes	—
121	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
122	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
126	#13083558	—	2	4	no	—
127	#13083558	—	2	4	no	—
128	#13083558	—	4	2	no	—
129	#13083558	—	4	2	no	—
130	C₂×#10623494	—	2	4	no	—
131	C₂×#10623494	—	4	2	no	—
132	C₂×#10623494	C₂²×C₄	1	2	yes	—
133	C₂×#10623494	C₂²×C₄	1	2	yes	—
134	C₂×#10623494	C₂²×C₄	1	2	yes	—
135	C₂×#10623494	C₂²×C₄	1	2	yes	—
136	C₂×#10623494	C₂²×C₄	1	2	yes	—
137	C₂×#10623494	C₂²×C₄	1	2	yes	—
138	C₂×#10623494	C₂²×C₄	1	2	yes	—
139	C₂×#10623494	C₂²×C₄	1	2	yes	—
140	#41×C₈₉	—	4	2	no	—
141	C₂×Q₈×C₈₉	C₄²	1	1	yes	characteristic
142	C₂×D₄×C₈₉	C₄²	1	1	yes	characteristic
143	C₂×D₄×C₈₉	C₄²	1	1	yes	characteristic
144	C₂×D₄×C₈₉	C₄²	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
152	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
154	M₁₆×C₈₉	—	4	2	no	—
155	C₂×C₈×C₈₉	—	4	2	no	—
156	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
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	C₄⋊C₄×C₈₉	C₄²	1	1	yes	characteristic
161	C₄⋊C₄×C₈₉	C₄²	1	1	yes	characteristic
162	C₄⋊C₄×C₈₉	C₄²	1	1	yes	characteristic
163	C₄⋊C₄×C₈₉	C₄²	1	1	yes	characteristic
164	C₄⋊C₄×C₈₉	C₄²	1	1	yes	characteristic
165	C₄⋊C₄×C₈₉	C₄²	1	1	yes	characteristic
166	C₂²⋊C₄×C₈₉	C₄²	1	1	yes	characteristic
167	C₂²⋊C₄×C₈₉	C₄²	1	1	yes	characteristic
168	C₂²⋊C₄×C₈₉	C₄²	1	1	yes	characteristic
169	C₂²⋊C₄×C₈₉	C₄²	1	1	yes	characteristic
170	C₂²⋊C₄×C₈₉	C₄²	1	1	yes	characteristic
171	C₂²⋊C₄×C₈₉	C₄²	1	1	yes	characteristic
172	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
180	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
182	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
183	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
184	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
185	Q₈×C₈₉	—	4	1	no	—
186	D₄×C₈₉	—	4	1	no	—
187	D₄×C₈₉	—	4	1	no	—
188	D₄×C₈₉	—	4	1	no	—
189	C₂×C₄×C₈₉	—	2	2	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	2	no	—
192	C₂×C₄×C₈₉	—	2	2	no	—
193	C₂×C₄×C₈₉	—	2	2	no	—
194	C₂×C₄×C₈₉	—	2	2	no	—
195	C₂×C₄×C₈₉	—	2	2	no	—
196	C₂×C₄×C₈₉	—	2	2	no	—
197	C₂×C₄×C₈₉	—	2	2	no	—
198	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
199	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
200	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
203	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
204	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
205	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
206	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
207	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
210	C₈×C₈₉	—	2	2	no	—
211	C₈×C₈₉	—	2	2	no	—
212	C₈×C₈₉	—	2	2	no	—
213	C₈×C₈₉	—	2	2	no	—
214	#10623494	—	2	2	no	—
215	#10623494	—	2	2	no	—
216	#10623494	—	2	2	no	—
217	#10623494	—	2	2	no	—
218	#10623494	—	2	2	no	—
219	#10623494	—	2	2	no	—
220	#10623494	—	2	2	no	—
221	#10623494	#131	1	4	yes	—
222	C₂²×C₈₉	—	2	1	no	—
223	C₂²×C₈₉	—	2	1	no	—
224	C₂²×C₈₉	—	2	1	no	—
225	C₂²×C₈₉	—	2	1	no	—
226	C₂²×C₈₉	—	2	1	no	—
227	C₂²×C₈₉	—	2	1	no	—
228	C₂²×C₈₉	—	2	1	no	—
229	C₂²×C₈₉	—	2	1	no	—
230	C₂²×C₈₉	—	2	1	no	—
231	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
232	C₄×C₈₉	—	2	1	no	—
233	C₄×C₈₉	—	2	1	no	—
234	C₄×C₈₉	—	2	1	no	—
235	C₄×C₈₉	—	2	1	no	—
236	C₄×C₈₉	—	2	1	no	—
237	C₄×C₈₉	—	2	1	no	—
238	C₄×C₈₉	—	2	1	no	—
239	C₄×C₈₉	—	2	1	no	—
240	C₄×C₈₉	—	2	1	no	—
241	C₄×C₈₉	C₂×#131	1	2	yes	—
242	C₄×C₈₉	#568	1	2	yes	—
243	C₄×C₈₉	#568	1	2	yes	—
244	#17340	—	89	1	no	maximal, Sylow
245	C₂×C₈₉	—	4	1	no	—
246	C₂×C₈₉	—	4	1	no	—
247	C₂×C₈₉	—	4	1	no	—
248	C₂×C₈₉	#2873	1	1	yes	characteristic
249	C₂×C₈₉	C₄×#131	1	1	yes	characteristic
250	C₂×C₈₉	#2875	1	1	yes	characteristic
251	#2965	—	89	1	no	—
252	#2965	—	89	1	no	—
253	#2922	D₈₉	1	1	yes	characteristic
254	#1455	—	89	1	no	—
255	#1454	—	89	1	no	—
256	#1454	—	89	1	no	—
257	#1453	—	89	1	no	—
258	#1453	—	89	1	no	—
259	#1453	—	89	1	no	—
260	#1452	—	89	1	no	—
261	#1451	—	89	1	no	—
262	#1451	—	89	1	no	—
263	#1450	—	89	1	no	—
264	C₈×M₁₆	—	89	1	no	—
265	C₈×M₁₆	—	89	1	no	—
266	C₈₉	#17340	1	1	yes	characteristic, complemented, Sylow
267	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
268	#446	—	89	2	no	—
269	#446	—	89	2	no	—
270	#436	—	89	2	no	—
271	#436	—	89	2	no	—
272	#435	—	89	2	no	—
273	#435	—	89	2	no	—
274	#435	—	89	2	no	—
275	#435	—	89	2	no	—
276	#433	Dic₈₉	1	2	yes	—
277	#433	Dic₈₉	1	2	yes	—
278	#431	—	89	1	no	—
279	#431	—	89	1	no	—
280	#431	—	89	1	no	—
281	#431	—	89	1	no	—
282	#431	—	89	1	no	—
283	#431	—	89	1	no	—
284	#431	C₂×D₈₉	1	1	yes	characteristic
285	#431	C₂×D₈₉	1	1	yes	characteristic
286	#431	C₂×D₈₉	1	1	yes	characteristic
287	#431	C₂×D₈₉	1	1	yes	characteristic
288	#424	Dic₈₉	1	2	yes	—
289	#408	Dic₈₉	1	2	yes	—
290	C₄×M₁₆	—	89	1	no	—
291	C₄×M₁₆	—	89	1	no	—
292	C₄×M₁₆	—	89	1	no	—
293	C₄×M₁₆	—	89	1	no	—
294	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
295	C₂×C₄×C₈	—	89	1	no	—
296	C₂×C₄×C₈	—	89	1	no	—
297	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
298	#322	—	89	1	no	—
299	#322	—	89	1	no	—
300	#322	—	89	1	no	—
301	#322	—	89	1	no	—
302	#322	—	89	1	no	—
303	#322	—	89	1	no	—
304	#322	—	89	1	no	—
305	#322	—	89	1	no	—
306	#322	—	89	1	no	—
307	#322	—	89	1	no	—
308	#322	—	89	1	no	—
309	#322	—	89	1	no	—
310	C₈²	—	89	1	no	—
311	C₈²	—	89	1	no	—
312	C₈²	—	89	1	no	—
313	C₈²	—	89	1	no	—
314	C₂×#41	C₂×Dic₈₉	1	1	yes	characteristic
315	C₂×M₁₆	—	89	2	no	—
316	C₂×M₁₆	—	89	2	no	—
317	C₂×M₁₆	—	89	2	no	—
318	C₂×M₁₆	—	89	2	no	—
319	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
320	C₂²×C₈	—	89	2	no	—
321	C₂²×C₈	—	89	2	no	—
322	C₂²×C₈	C₂×Dic₈₉	1	2	yes	—
323	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
324	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
325	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
326	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
327	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
328	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
329	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
330	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
331	#117	C₂×Dic₈₉	1	1	yes	characteristic
332	#117	C₂×Dic₈₉	1	1	yes	characteristic
333	#117	C₂×Dic₈₉	1	1	yes	characteristic
334	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
335	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
336	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
337	C₄⋊C₈	—	89	2	no	—
338	C₄⋊C₈	—	89	2	no	—
339	C₄⋊C₈	—	89	2	no	—
340	C₄⋊C₈	—	89	2	no	—
341	C₄⋊C₈	—	89	2	no	—
342	C₄⋊C₈	—	89	2	no	—
343	C₄⋊C₈	C₂×Dic₈₉	1	2	yes	—
344	C₄⋊C₈	C₂×Dic₈₉	1	2	yes	—
345	C₄⋊C₈	C₂×Dic₈₉	1	2	yes	—
346	C₄⋊C₈	C₂×Dic₈₉	1	2	yes	—
347	C₂²⋊C₈	—	89	2	no	—
348	C₂²⋊C₈	—	89	2	no	—
349	C₂²⋊C₈	—	89	2	no	—
350	C₂²⋊C₈	—	89	2	no	—
351	C₂²⋊C₈	—	89	2	no	—
352	C₂²⋊C₈	—	89	2	no	—
353	C₂²⋊C₈	C₂×Dic₈₉	1	2	yes	—
354	C₂²⋊C₈	C₂×Dic₈₉	1	2	yes	—
355	C₂²⋊C₈	C₂×Dic₈₉	1	2	yes	—
356	C₂²⋊C₈	C₂×Dic₈₉	1	2	yes	—
357	#97	—	89	2	no	—
358	#97	—	89	2	no	—
359	#97	—	89	2	no	—
360	#97	—	89	2	no	—
361	#97	C₂×Dic₈₉	1	2	yes	—
362	C₄×C₈	—	89	2	no	—
363	C₄×C₈	—	89	2	no	—
364	C₄×C₈	—	89	1	no	—
365	C₄×C₈	—	89	1	no	—
366	C₄×C₈	—	89	1	no	—
367	C₄×C₈	—	89	1	no	—
368	C₄×C₈	—	89	1	no	—
369	C₄×C₈	—	89	1	no	—
370	C₄×C₈	—	89	1	no	—
371	C₄×C₈	—	89	1	no	—
372	C₄×C₈	C₂×Dic₈₉	1	2	yes	—
373	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
374	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
375	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
376	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
377	#41	—	4	2	no	—
378	C₂×Q₈	C₄×Dic₈₉	1	1	yes	characteristic
379	C₂×D₄	C₄×Dic₈₉	1	1	yes	characteristic
380	C₂×D₄	C₄×Dic₈₉	1	1	yes	characteristic
381	C₂×D₄	C₄×Dic₈₉	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
388	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
389	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
390	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
391	M₁₆	—	4	2	no	—
392	M₁₆	—	356	2	no	—
393	M₁₆	—	356	2	no	—
394	M₁₆	—	178	4	no	—
395	M₁₆	—	178	4	no	—
396	C₂×C₈	—	4	2	no	—
397	C₂×C₈	—	89	2	no	—
398	C₂×C₈	—	89	2	no	—
399	C₂×C₈	—	89	2	no	—
400	C₂×C₈	—	89	2	no	—
401	C₂×C₈	—	89	2	no	—
402	C₂×C₈	—	89	2	no	—
403	C₂×C₈	—	89	2	no	—
404	C₂×C₈	—	89	2	no	—
405	C₂×C₈	—	356	2	no	—
406	C₂×C₈	—	178	4	no	—
407	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
408	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
409	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
410	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
411	C₄⋊C₄	C₄×Dic₈₉	1	1	yes	characteristic
412	C₄⋊C₄	C₄×Dic₈₉	1	1	yes	characteristic
413	C₄⋊C₄	C₄×Dic₈₉	1	1	yes	characteristic
414	C₄⋊C₄	C₄×Dic₈₉	1	1	yes	characteristic
415	C₄⋊C₄	C₄×Dic₈₉	1	1	yes	characteristic
416	C₄⋊C₄	C₄×Dic₈₉	1	1	yes	characteristic
417	C₂²⋊C₄	C₄×Dic₈₉	1	1	yes	characteristic
418	C₂²⋊C₄	C₄×Dic₈₉	1	1	yes	characteristic
419	C₂²⋊C₄	C₄×Dic₈₉	1	1	yes	characteristic
420	C₂²⋊C₄	C₄×Dic₈₉	1	1	yes	characteristic
421	C₂²⋊C₄	C₄×Dic₈₉	1	1	yes	characteristic
422	C₂²⋊C₄	C₄×Dic₈₉	1	1	yes	characteristic
423	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
424	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
425	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
426	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
427	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
428	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
429	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
430	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
431	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
432	C₄²	C₂³×D₈₉	1	1	yes	characteristic
433	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
434	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
435	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
436	Q₈	—	4	1	no	—
437	D₄	—	4	1	no	—
438	D₄	—	4	1	no	—
439	D₄	—	4	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
450	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
451	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
453	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
454	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
455	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
456	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
457	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
460	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	89	4	no	—
466	C₈	—	178	2	no	—
467	C₈	—	178	2	no	—
468	C₈	—	178	2	no	—
469	C₈	—	178	2	no	—
470	C₈	—	178	2	no	—
471	C₈	—	178	2	no	—
472	C₈	—	178	2	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	C₂²×C₄×Dic₈₉	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	#131×D₈₉	1	2	yes	—
493	C₄	#19152363	1	2	yes	—
494	C₄	#19152365	1	2	yes	—
495	C₂	—	4	1	no	—
496	C₂	—	4	1	no	—
497	C₂	—	4	1	no	—
498	C₂	#26028671	1	1	yes	characteristic
499	C₂	#131×Dic₈₉	1	1	yes	characteristic
500	C₂	#26028678	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂²×C₄²
Fitting	C₈₉×#2922	C₂
prime radical	C₂×#41×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2922	D₈₉
hypocenter	C₈₉	#17340
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄² ◁ #2922

Complements

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

N	H ≅ G/N	type
3. #26018555	C₂	semidirect
4. #26018552	C₂	semidirect
5. #26018552	C₂	semidirect
6. #26018549	C₂	semidirect
7. #26018547	C₂	semidirect
8. #26018547	C₂	semidirect
9. #26018545	C₂	semidirect
10. #26018542	C₂	semidirect
11. #26018541	C₂	semidirect
12. #26018536	C₂	semidirect
13. #26018533	C₂	semidirect
14. C₈×#13083558	C₂	semidirect
266. C₈₉	#17340	semidirect

Maximal subgroups

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

subgroup	index
#26029219	2
#26018555	2
#26018552	2
#26018549	2
#26018547	2
#26018545	2
#26018542	2
#26018541	2
#26018536	2
#26018533	2
C₈×#13083558	2
C₈₉×#2922	2
#17340	89