Subgroups — #36525340

Order 22784.

618 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029266	C₂	1	1	yes	maximal, characteristic, complemented
2	#26029257	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019149	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019143	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019103	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019089	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019089	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019082	C₂	1	1	yes	maximal, characteristic, complemented
9	SD₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
10	D₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019032	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018712	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018634	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018533	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3102	C₂	1	1	yes	maximal, characteristic
16	#19151729	C₂²	1	1	yes	characteristic
17	#19151729	C₂²	1	1	yes	characteristic
18	#19151729	C₂²	1	1	yes	characteristic
19	Q₈×#10623494	C₂²	1	1	yes	characteristic
20	#19151676	—	2	1	no	—
21	#19151676	C₂²	1	1	yes	characteristic
22	#19151670	—	2	1	no	—
23	#19151670	—	2	1	no	—
24	#19151670	—	2	1	no	—
25	D₄×#10623494	C₂²	1	1	yes	characteristic
26	D₄×#10623494	C₂²	1	1	yes	characteristic
27	D₄×#10623494	C₂²	1	1	yes	characteristic
28	#19151659	—	2	1	no	—
29	#19151655	—	2	1	no	—
30	#19151655	C₂²	1	1	yes	characteristic
31	#19151651	C₂²	1	1	yes	characteristic
32	#19151554	—	2	1	no	—
33	C₄×#13083558	C₂²	1	1	yes	characteristic
34	C₂×#15667923	—	2	1	no	—
35	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
36	#19151351	C₂²	1	1	yes	characteristic
37	#19151351	C₂²	1	1	yes	characteristic
38	#19151349	C₂²	1	1	yes	characteristic
39	#19151349	C₂²	1	1	yes	characteristic
40	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
41	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
42	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
43	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
44	D₄⋊#10623494	C₂²	1	1	yes	characteristic
45	D₄⋊#10623494	C₂²	1	1	yes	characteristic
46	D₄⋊#10623494	C₂²	1	1	yes	characteristic
47	D₄⋊#10623494	C₂²	1	1	yes	characteristic
48	#19151320	C₂²	1	1	yes	characteristic
49	#19151320	C₂²	1	1	yes	characteristic
50	C₈×#10623494	C₂²	1	1	yes	characteristic
51	C₈×#10623494	C₂²	1	1	yes	characteristic
52	#529×C₈₉	C₂²	1	1	yes	characteristic
53	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
54	#485×C₈₉	C₄	1	1	yes	characteristic
55	#482×C₈₉	C₄	1	1	yes	characteristic
56	#479×C₈₉	C₄	1	1	yes	characteristic
57	#478×C₈₉	C₄	1	1	yes	characteristic
58	#464×C₈₉	C₄	1	1	yes	characteristic
59	#463×C₈₉	C₄	1	1	yes	characteristic
60	#452×C₈₉	C₄	1	1	yes	characteristic
61	#449×C₈₉	C₄	1	1	yes	characteristic
62	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
63	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
64	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
65	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
66	#431×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#13083558	—	2	1	no	—
68	C₂×#13083558	D₄	1	1	yes	characteristic
69	C₂×#13083558	D₄	1	1	yes	characteristic
70	C₂²×#10623494	—	2	1	no	—
71	C₂²×#10623494	—	2	1	no	—
72	C₂²×#10623494	—	2	1	no	—
73	C₂²×#10623494	—	2	1	no	—
74	C₄⋊#10623494	—	2	1	no	—
75	C₄⋊#10623494	—	2	1	no	—
76	C₄⋊#10623494	—	2	1	no	—
77	C₄⋊#10623494	—	2	1	no	—
78	C₄⋊#10623494	C₂³	1	1	yes	characteristic
79	C₄⋊#10623494	C₂³	1	1	yes	characteristic
80	C₄⋊#10623494	C₂³	1	1	yes	characteristic
81	C₄⋊#10623494	C₂³	1	1	yes	characteristic
82	C₂²⋊#10623494	—	2	1	no	—
83	C₂²⋊#10623494	—	2	1	no	—
84	C₂²⋊#10623494	—	2	1	no	—
85	C₂²⋊#10623494	—	2	1	no	—
86	C₂²⋊#10623494	—	2	1	no	—
87	C₂²⋊#10623494	—	2	1	no	—
88	#15667923	—	2	1	no	—
89	#15667923	—	2	1	no	—
90	#15667923	—	2	1	no	—
91	#15667923	—	2	1	no	—
92	#15667923	D₄	1	1	yes	characteristic
93	#15667923	D₄	1	1	yes	characteristic
94	C₄×#10623494	—	2	1	no	—
95	C₄×#10623494	—	2	1	no	—
96	C₄×#10623494	—	2	1	no	—
97	C₄×#10623494	C₂³	1	1	yes	characteristic
98	C₄×#10623494	C₂³	1	1	yes	characteristic
99	C₄×#10623494	C₂³	1	1	yes	characteristic
100	C₄×#10623494	C₂³	1	1	yes	characteristic
101	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
102	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
103	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
104	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
105	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
106	#126×C₈₉	—	2	1	no	—
107	#125×C₈₉	C₂×C₄	1	1	yes	characteristic
108	#124×C₈₉	C₂×C₄	1	1	yes	characteristic
109	#123×C₈₉	—	2	1	no	—
110	C₂²⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
111	#121×C₈₉	C₂×C₄	1	1	yes	characteristic
112	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
113	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
115	C₄×D₄×C₈₉	—	2	1	no	—
116	C₄×D₄×C₈₉	—	2	1	no	—
117	C₄×D₄×C₈₉	—	2	1	no	—
118	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
120	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
121	#117×C₈₉	—	2	1	no	—
122	#117×C₈₉	—	2	1	no	—
123	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄²×C₈₉	—	2	1	no	—
125	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
126	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
127	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
128	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
129	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
130	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
131	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
132	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
133	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
134	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
135	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
136	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
137	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
138	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
139	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
142	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	#13083558	—	2	2	no	—
145	#13083558	—	2	2	no	—
146	#13083558	—	4	2	no	—
147	C₂×#10623494	—	2	1	no	—
148	C₂×#10623494	—	2	1	no	—
149	C₂×#10623494	—	2	1	no	—
150	C₂×#10623494	—	2	1	no	—
151	C₂×#10623494	—	2	1	no	—
152	C₂×#10623494	—	2	1	no	—
153	C₂×#10623494	—	4	2	no	—
154	C₂×#10623494	—	4	2	no	—
155	C₂×#10623494	—	4	2	no	—
156	C₂×#10623494	—	4	2	no	—
157	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
158	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
159	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
160	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
161	#41×C₈₉	—	2	2	no	—
162	#41×C₈₉	—	4	1	no	—
163	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×D₄×C₈₉	—	2	1	no	—
166	C₂×D₄×C₈₉	—	2	1	no	—
167	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₈₉	—	2	1	no	—
170	C₂²×C₄×C₈₉	—	2	1	no	—
171	C₂²×C₄×C₈₉	—	2	1	no	—
172	C₂²×C₄×C₈₉	—	2	1	no	—
173	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
176	Q₁₆×C₈₉	—	4	1	no	—
177	SD₁₆×C₈₉	—	2	2	no	—
178	SD₁₆×C₈₉	—	4	1	no	—
179	D₈×C₈₉	—	2	2	no	—
180	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
184	C₄⋊C₄×C₈₉	—	2	1	no	—
185	C₄⋊C₄×C₈₉	—	2	1	no	—
186	C₄⋊C₄×C₈₉	—	2	1	no	—
187	C₄⋊C₄×C₈₉	—	2	1	no	—
188	C₄⋊C₄×C₈₉	—	2	1	no	—
189	C₄⋊C₄×C₈₉	—	2	1	no	—
190	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
191	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
192	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
193	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
194	C₂²⋊C₄×C₈₉	—	2	1	no	—
195	C₂²⋊C₄×C₈₉	—	2	1	no	—
196	C₂²⋊C₄×C₈₉	—	2	1	no	—
197	C₂²⋊C₄×C₈₉	—	2	1	no	—
198	C₂²⋊C₄×C₈₉	—	2	1	no	—
199	C₂²⋊C₄×C₈₉	—	2	1	no	—
200	C₂²⋊C₄×C₈₉	—	2	1	no	—
201	C₂²⋊C₄×C₈₉	—	2	1	no	—
202	C₄²×C₈₉	—	2	1	no	—
203	C₄²×C₈₉	—	2	1	no	—
204	C₄²×C₈₉	—	2	1	no	—
205	C₄²×C₈₉	—	2	1	no	—
206	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₈₉	#41	1	1	yes	characteristic
209	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
210	C₂³×C₈₉	—	2	1	no	—
211	C₂³×C₈₉	—	2	1	no	—
212	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
213	Q₈×C₈₉	—	2	1	no	—
214	Q₈×C₈₉	—	2	1	no	—
215	Q₈×C₈₉	—	2	1	no	—
216	Q₈×C₈₉	—	2	1	no	—
217	D₄×C₈₉	—	2	1	no	—
218	D₄×C₈₉	—	2	1	no	—
219	D₄×C₈₉	—	2	1	no	—
220	D₄×C₈₉	—	4	2	no	—
221	D₄×C₈₉	—	8	1	no	—
222	D₄×C₈₉	#131	1	2	yes	—
223	C₂×C₄×C₈₉	—	2	1	no	—
224	C₂×C₄×C₈₉	—	2	1	no	—
225	C₂×C₄×C₈₉	—	2	1	no	—
226	C₂×C₄×C₈₉	—	2	1	no	—
227	C₂×C₄×C₈₉	—	2	1	no	—
228	C₂×C₄×C₈₉	—	2	1	no	—
229	C₂×C₄×C₈₉	—	2	1	no	—
230	C₂×C₄×C₈₉	—	2	1	no	—
231	C₂×C₄×C₈₉	—	2	1	no	—
232	C₂×C₄×C₈₉	—	2	1	no	—
233	C₂×C₄×C₈₉	—	4	1	no	—
234	C₂×C₄×C₈₉	—	4	2	no	—
235	C₂×C₄×C₈₉	—	4	1	no	—
236	C₂×C₄×C₈₉	—	4	1	no	—
237	C₂×C₄×C₈₉	—	4	1	no	—
238	C₂×C₄×C₈₉	—	4	1	no	—
239	C₂×C₄×C₈₉	—	8	1	no	—
240	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
246	C₈×C₈₉	—	2	1	no	—
247	C₈×C₈₉	—	2	1	no	—
248	C₈×C₈₉	—	2	1	no	—
249	C₈×C₈₉	—	2	1	no	—
250	#10623494	—	2	2	no	—
251	#10623494	—	2	1	no	—
252	#10623494	—	2	1	no	—
253	#10623494	—	4	1	no	—
254	#10623494	—	4	1	no	—
255	#10623494	—	4	1	no	—
256	#10623494	—	4	1	no	—
257	#10623494	—	4	1	no	—
258	#10623494	#135	1	2	yes	—
259	#10623494	#135	1	2	yes	—
260	C₂²×C₈₉	—	2	1	no	—
261	C₂²×C₈₉	—	2	2	no	—
262	C₂²×C₈₉	—	2	1	no	—
263	C₂²×C₈₉	—	2	1	no	—
264	C₂²×C₈₉	—	4	1	no	—
265	C₂²×C₈₉	—	4	1	no	—
266	C₂²×C₈₉	—	4	1	no	—
267	C₂²×C₈₉	—	4	1	no	—
268	C₂²×C₈₉	—	4	1	no	—
269	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₈₉	—	2	1	no	—
271	C₄×C₈₉	—	2	1	no	—
272	C₄×C₈₉	—	2	1	no	—
273	C₄×C₈₉	—	2	1	no	—
274	C₄×C₈₉	—	4	1	no	—
275	C₄×C₈₉	—	4	1	no	—
276	C₄×C₈₉	—	4	1	no	—
277	C₄×C₈₉	—	4	1	no	—
278	C₄×C₈₉	—	4	1	no	—
279	C₄×C₈₉	—	4	1	no	—
280	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
281	C₄×C₈₉	#568	1	1	yes	characteristic
282	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
283	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
284	#17996	—	89	1	no	maximal, Sylow
285	C₂×C₈₉	—	4	1	no	—
286	C₂×C₈₉	—	4	2	no	—
287	C₂×C₈₉	—	8	1	no	—
288	C₂×C₈₉	#2933	1	1	yes	characteristic
289	C₂×C₈₉	C₄×#135	1	1	yes	characteristic
290	C₂×C₈₉	#2956	1	1	yes	characteristic
291	#3102	D₈₉	1	1	yes	characteristic
292	#2970	—	89	1	no	—
293	#2969	—	89	1	no	—
294	#1591	—	89	1	no	—
295	#1590	—	89	1	no	—
296	#1584	—	89	1	no	—
297	#1582	—	89	1	no	—
298	#1582	—	89	1	no	—
299	#1581	—	89	1	no	—
300	C₈×SD₁₆	—	89	1	no	—
301	C₈×D₈	—	89	1	no	—
302	#1572	—	89	1	no	—
303	#1494	—	89	1	no	—
304	#1476	—	89	1	no	—
305	C₈×M₁₆	—	89	1	no	—
306	C₈₉	#17996	1	1	yes	characteristic, complemented, Sylow
307	#529	C₂×D₈₉	1	1	yes	characteristic
308	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
309	#485	Dic₈₉	1	1	yes	characteristic
310	#482	Dic₈₉	1	1	yes	characteristic
311	#479	Dic₈₉	1	1	yes	characteristic
312	#478	Dic₈₉	1	1	yes	characteristic
313	#464	Dic₈₉	1	1	yes	characteristic
314	#463	Dic₈₉	1	1	yes	characteristic
315	#452	Dic₈₉	1	1	yes	characteristic
316	#449	Dic₈₉	1	1	yes	characteristic
317	#446	—	89	1	no	—
318	#446	—	89	1	no	—
319	#446	—	89	1	no	—
320	C₈×Q₈	—	89	1	no	—
321	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
322	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
323	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
324	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
325	#436	—	89	1	no	—
326	#436	—	178	1	no	—
327	#435	—	178	1	no	—
328	#435	—	178	1	no	—
329	#435	—	178	1	no	—
330	C₈×D₄	—	89	1	no	—
331	C₈×D₄	—	89	1	no	—
332	C₈×D₄	—	89	1	no	—
333	#433	—	178	1	no	—
334	#432	—	89	1	no	—
335	#432	—	178	1	no	—
336	#431	—	89	1	no	—
337	#431	C₂×D₈₉	1	1	yes	characteristic
338	#405	—	178	1	no	—
339	C₄×M₁₆	—	89	1	no	—
340	C₂×#97	—	178	1	no	—
341	C₂×C₄×C₈	—	89	1	no	—
342	#335	—	89	1	no	—
343	#335	—	89	1	no	—
344	#334	—	89	1	no	—
345	#334	—	89	1	no	—
346	Q₈⋊C₈	—	89	1	no	—
347	Q₈⋊C₈	—	89	1	no	—
348	Q₈⋊C₈	—	89	1	no	—
349	Q₈⋊C₈	—	89	1	no	—
350	D₄⋊C₈	—	89	1	no	—
351	D₄⋊C₈	—	89	1	no	—
352	D₄⋊C₈	—	89	1	no	—
353	D₄⋊C₈	—	89	1	no	—
354	#322	—	89	1	no	—
355	#322	—	89	1	no	—
356	C₈²	—	89	1	no	—
357	C₈²	—	89	1	no	—
358	C₂×#41	C₂×Dic₈₉	1	1	yes	characteristic
359	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic
360	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
361	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
362	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
363	C₂×M₁₆	—	89	1	no	—
364	C₂×M₁₆	—	89	1	no	—
365	C₂×M₁₆	—	178	1	no	—
366	C₂²×C₈	—	178	1	no	—
367	C₂²×C₈	—	178	1	no	—
368	C₂²×C₈	—	178	1	no	—
369	C₂²×C₈	—	178	1	no	—
370	#126	—	2	1	no	—
371	#125	C₂×Dic₈₉	1	1	yes	characteristic
372	#124	C₂×Dic₈₉	1	1	yes	characteristic
373	#123	—	2	1	no	—
374	C₂²⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
375	#121	C₂×Dic₈₉	1	1	yes	characteristic
376	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
377	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
378	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
383	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
384	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	C₂×Dic₈₉	1	1	yes	characteristic
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
390	#107	C₂×Dic₈₉	1	1	yes	characteristic
391	#107	C₂×Dic₈₉	1	1	yes	characteristic
392	#106	C₂×Dic₈₉	1	1	yes	characteristic
393	#106	C₂×Dic₈₉	1	1	yes	characteristic
394	C₄⋊C₈	—	89	1	no	—
395	C₄⋊C₈	—	89	1	no	—
396	C₄⋊C₈	—	89	1	no	—
397	C₄⋊C₈	—	89	1	no	—
398	C₄⋊C₈	—	178	1	no	—
399	C₄⋊C₈	—	178	1	no	—
400	C₄⋊C₈	—	178	1	no	—
401	C₄⋊C₈	—	178	1	no	—
402	C₄⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
403	C₄⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
404	#103	C₂×Dic₈₉	1	1	yes	characteristic
405	#103	C₂×Dic₈₉	1	1	yes	characteristic
406	#103	C₂×Dic₈₉	1	1	yes	characteristic
407	#103	C₂×Dic₈₉	1	1	yes	characteristic
408	#102	C₂×Dic₈₉	1	1	yes	characteristic
409	#102	C₂×Dic₈₉	1	1	yes	characteristic
410	#102	C₂×Dic₈₉	1	1	yes	characteristic
411	#102	C₂×Dic₈₉	1	1	yes	characteristic
412	C₂²⋊C₈	—	178	1	no	—
413	C₂²⋊C₈	—	178	1	no	—
414	C₂²⋊C₈	—	178	1	no	—
415	C₂²⋊C₈	—	178	1	no	—
416	C₂²⋊C₈	—	178	1	no	—
417	C₂²⋊C₈	—	178	1	no	—
418	C₂²⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
419	C₂²⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
420	#97	—	89	1	no	—
421	#97	—	89	1	no	—
422	#97	—	178	1	no	—
423	#97	—	178	1	no	—
424	#97	—	178	1	no	—
425	#97	—	178	1	no	—
426	C₄×C₈	—	89	1	no	—
427	C₄×C₈	—	89	1	no	—
428	C₄×C₈	—	89	1	no	—
429	C₄×C₈	—	89	1	no	—
430	C₄×C₈	—	178	1	no	—
431	C₄×C₈	—	178	1	no	—
432	C₄×C₈	—	178	1	no	—
433	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
434	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
435	#41	—	2	2	no	—
436	#41	—	4	1	no	—
437	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
438	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
442	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
448	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
449	C₂²×C₄	#13083573	1	1	yes	characteristic
450	Q₁₆	—	4	1	no	—
451	SD₁₆	—	2	2	no	—
452	SD₁₆	—	4	1	no	—
453	D₈	—	2	2	no	—
454	M₁₆	—	356	2	no	—
455	M₁₆	—	178	2	no	—
456	M₁₆	—	178	2	no	—
457	C₂×C₈	—	89	1	no	—
458	C₂×C₈	—	89	1	no	—
459	C₂×C₈	—	89	1	no	—
460	C₂×C₈	—	89	1	no	—
461	C₂×C₈	—	356	2	no	—
462	C₂×C₈	—	356	2	no	—
463	C₂×C₈	—	356	2	no	—
464	C₂×C₈	—	356	2	no	—
465	C₂×C₈	—	178	1	no	—
466	C₂×C₈	—	178	1	no	—
467	C₂×C₈	—	178	1	no	—
468	C₂×C₈	—	178	1	no	—
469	C₂×C₈	—	178	1	no	—
470	C₂×C₈	—	178	1	no	—
471	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
472	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
473	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
474	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
498	C₄²	D₄×D₈₉	1	1	yes	characteristic
499	C₄²	#13083573	1	1	yes	characteristic
500	C₄²	C₂³×D₈₉	1	1	yes	characteristic
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
504	Q₈	—	2	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	1	no	—
510	D₄	—	2	1	no	—
511	D₄	—	4	2	no	—
512	D₄	—	8	1	no	—
513	D₄	#15668019	1	2	yes	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	8	1	no	—
531	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
532	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
533	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
534	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
535	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
536	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	89	2	no	—
542	C₈	—	89	2	no	—
543	C₈	—	356	1	no	—
544	C₈	—	356	1	no	—
545	C₈	—	356	1	no	—
546	C₈	—	356	1	no	—
547	C₈	—	356	1	no	—
548	C₈	—	178	2	no	—
549	C₈	—	178	1	no	—
550	C₈	—	178	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	C₂×#15668019	1	1	yes	characteristic
572	C₄	#19152365	1	1	yes	characteristic
573	C₄	#135×D₈₉	1	1	yes	characteristic
574	C₄	#135×D₈₉	1	1	yes	characteristic
575	C₂	—	4	1	no	—
576	C₂	—	4	2	no	—
577	C₂	—	8	1	no	—
578	C₂	#26028979	1	1	yes	characteristic
579	C₂	#135×Dic₈₉	1	1	yes	characteristic
580	C₂	#26029162	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#3102	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#449×C₈₉	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#3102	D₈₉
hypocenter	C₈₉	#17996
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3102

Complements

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

N	H ≅ G/N	type
1. #26029266	C₂	semidirect
2. #26029257	C₂	semidirect
3. #26019149	C₂	semidirect
4. #26019143	C₂	semidirect
5. #26019103	C₂	semidirect
6. #26019089	C₂	semidirect
7. #26019089	C₂	semidirect
8. #26019082	C₂	semidirect
9. SD₁₆×#10623494	C₂	semidirect
10. D₈×#10623494	C₂	semidirect
11. #26019032	C₂	semidirect
12. #26018712	C₂	semidirect
13. #26018634	C₂	semidirect
14. #26018533	C₂	semidirect
306. C₈₉	#17996	semidirect

Maximal subgroups

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

subgroup	index
#26029266	2
#26029257	2
#26019149	2
#26019143	2
#26019103	2
#26019089	2
#26019082	2
SD₁₆×#10623494	2
D₈×#10623494	2
#26019032	2
#26018712	2
#26018634	2
#26018533	2
C₈₉×#3102	2
#17996	89