Subgroups — #36552989

Order 22784.

1006 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151718	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151713	C₂	1	1	yes	maximal, characteristic
3	#26029050	C₂	1	1	yes	maximal, characteristic
4	C₄×#15668018	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020159	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020137	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020132	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020098	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020094	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020091	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020087	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020065	C₂	1	1	yes	maximal, characteristic, complemented
13	#26020062	C₂	1	1	yes	maximal, characteristic, complemented
14	#26019938	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#131×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668032	C₂²	1	1	yes	characteristic
17	C₂×#15668018	C₂²	1	1	yes	characteristic
18	C₂×#15668018	C₂²	1	1	yes	characteristic
19	C₄×#13083574	C₂²	1	1	yes	characteristic
20	#19151718	C₄	1	8	yes	complemented
21	#19151713	C₄	1	8	yes	complemented
22	#19151708	C₄	1	2	yes	complemented
23	#19151703	C₄	1	2	yes	complemented
24	#19151698	C₄	1	2	yes	complemented
25	#19151696	C₄	1	2	yes	complemented
26	C₂×#15667947	C₂²	1	1	yes	characteristic
27	C₂×#15667947	C₂²	1	1	yes	characteristic
28	#19151634	C₂²	1	1	yes	characteristic
29	C₂×#15667939	C₂²	1	1	yes	characteristic
30	C₂×#15667939	C₂²	1	1	yes	characteristic
31	C₂×#15667938	C₂²	1	1	yes	characteristic
32	C₂×#15667938	C₂²	1	1	yes	characteristic
33	#19151594	C₂²	1	1	yes	characteristic
34	#19151592	C₂²	1	1	yes	characteristic
35	#19151553	C₂²	1	1	yes	characteristic
36	#19151553	C₂²	1	1	yes	characteristic
37	#19151552	—	2	1	no	—
38	#19151552	—	2	1	no	—
39	C₄×#13083558	C₂²	1	1	yes	characteristic
40	C₄×#13083557	—	2	1	no	—
41	C₂×#15667923	C₂²	1	1	yes	characteristic
42	C₂×#15667922	C₂²	1	1	yes	characteristic
43	C₂×#15667922	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₈₉	—	2	1	no	—
47	#19151444	C₂²	1	1	yes	characteristic
48	#19151362	C₂²	1	1	yes	characteristic
49	#19151362	C₂²	1	1	yes	characteristic
50	#19151359	C₂²	1	1	yes	characteristic
51	#19151359	C₂²	1	1	yes	characteristic
52	#19151357	C₂²	1	1	yes	characteristic
53	#19151357	C₂²	1	1	yes	characteristic
54	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
56	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
57	#405×C₈₉	—	2	1	no	—
58	#405×C₈₉	—	2	1	no	—
59	#405×C₈₉	C₂²	1	1	yes	characteristic
60	#405×C₈₉	C₂²	1	1	yes	characteristic
61	C₄×M₁₆×C₈₉	—	2	1	no	—
62	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
63	C₂×C₄×C₈×C₈₉	—	2	1	no	—
64	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
65	C₂×#13083574	C₂³	1	1	yes	characteristic
66	#15668032	C₂×C₄	1	4	yes	—
67	#15668032	C₂×C₄	1	4	yes	—
68	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
72	#15668018	—	2	2	no	—
73	#15668018	—	2	2	no	—
74	#15668018	C₂×C₄	1	4	yes	complemented
75	#15668018	C₂×C₄	1	4	yes	complemented
76	C₂×#13083558	C₂³	1	1	yes	characteristic
77	C₂×#13083558	C₂³	1	1	yes	characteristic
78	C₂×#13083557	—	2	1	no	—
79	C₂×#13083557	—	2	1	no	—
80	C₂²×#10623494	C₂³	1	1	yes	characteristic
81	C₂²×#10623494	C₂³	1	1	yes	characteristic
82	C₂×C₈×D₈₉	—	2	1	no	—
83	C₂×C₈×D₈₉	—	2	1	no	—
84	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
85	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
86	C₄×C₂²⋊D₈₉	—	2	2	no	—
87	#15667971	C₂³	1	1	yes	characteristic
88	#15667969	—	2	1	no	—
89	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
90	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
91	C₄²×D₈₉	—	2	1	no	—
92	#15667947	C₂×C₄	1	4	yes	complemented
93	#15667947	C₂×C₄	1	4	yes	complemented
94	#15667945	C₂×C₄	1	2	yes	—
95	#15667943	C₂×C₄	1	2	yes	—
96	#15667939	C₂×C₄	1	4	yes	complemented
97	#15667939	C₂×C₄	1	4	yes	complemented
98	#15667938	C₂×C₄	1	4	yes	complemented
99	#15667938	C₂×C₄	1	4	yes	complemented
100	#15667936	C₂×C₄	1	2	yes	—
101	#15667935	C₂×C₄	1	2	yes	—
102	#15667933	C₂×C₄	1	2	yes	—
103	#15667932	C₂×C₄	1	2	yes	—
104	#15667923	—	2	1	no	—
105	#15667923	C₂×C₄	1	2	yes	—
106	#15667923	C₂×C₄	1	2	yes	—
107	#15667922	—	2	1	no	—
108	#15667922	—	2	1	no	—
109	#15667922	—	2	2	no	—
110	#15667922	C₂×C₄	1	4	yes	complemented
111	C₄×#10623494	—	2	1	no	—
112	C₈×Dic₈₉	—	2	1	no	—
113	C₈×Dic₈₉	—	2	1	no	—
114	C₈×Dic₈₉	—	2	2	no	—
115	C₈×Dic₈₉	C₂×C₄	1	4	yes	complemented
116	#15667919	—	2	2	no	—
117	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
118	#131×C₈₉	—	2	2	no	—
119	#131×C₈₉	—	2	2	no	—
120	#131×C₈₉	C₂×C₄	1	4	yes	complemented
121	#131×C₈₉	C₂×C₄	1	4	yes	complemented
122	C₂×M₁₆×C₈₉	—	2	1	no	—
123	C₂×M₁₆×C₈₉	—	2	1	no	—
124	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₈₉	—	2	1	no	—
127	C₂²×C₈×C₈₉	—	2	1	no	—
128	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
130	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
131	C₄×D₄×C₈₉	—	2	2	no	—
132	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
133	#117×C₈₉	—	2	1	no	—
134	#117×C₈₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₈₉	—	2	1	no	—
136	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
137	#97×C₈₉	—	2	1	no	—
138	#97×C₈₉	—	2	1	no	—
139	#97×C₈₉	—	2	1	no	—
140	C₄×C₈×C₈₉	—	2	1	no	—
141	C₄×C₈×C₈₉	—	2	1	no	—
142	C₄×C₈×C₈₉	—	2	1	no	—
143	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
144	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
145	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
146	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
147	#13083574	—	2	1	no	—
148	#13083574	—	2	1	no	—
149	#13083574	C₂²×C₄	1	2	yes	—
150	#13083574	C₂²×C₄	1	2	yes	—
151	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₂²⋊D₈₉	—	2	1	no	—
154	C₂²×Dic₈₉	—	2	1	no	—
155	C₂²×Dic₈₉	—	2	1	no	—
156	C₂×C₄×D₈₉	—	2	1	no	—
157	C₂×C₄×D₈₉	—	2	2	no	—
158	#13083564	C₄²	1	4	yes	—
159	#13083562	C₄²	1	4	yes	—
160	#13083561	C₄²	1	4	yes	—
161	#13083559	C₄²	1	4	yes	—
162	#13083558	—	2	1	no	—
163	#13083558	—	2	1	no	—
164	#13083558	C₂²×C₄	1	2	yes	—
165	#13083558	C₂²×C₄	1	2	yes	—
166	#13083557	—	2	4	no	—
167	#13083557	—	2	4	no	—
168	C₂×#10623494	—	2	1	no	—
169	C₂×#10623494	—	2	1	no	—
170	C₂×#10623494	—	2	1	no	—
171	C₂×#10623494	—	2	1	no	—
172	C₂×#10623494	C₂²×C₄	1	2	yes	—
173	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
174	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
175	C₂×#10623494	C₂²×C₄	1	2	yes	—
176	C₂×#10623494	C₂²×C₄	1	2	yes	—
177	C₈×D₈₉	—	2	4	no	—
178	C₈×D₈₉	—	2	4	no	—
179	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
180	#13083553	—	2	2	no	—
181	C₂²⋊Dic₈₉	—	2	1	no	—
182	#13083551	—	2	2	no	—
183	C₄×Dic₈₉	—	2	2	no	—
184	C₄×Dic₈₉	—	2	1	no	—
185	C₄×Dic₈₉	—	2	1	no	—
186	C₄×Dic₈₉	—	2	1	no	—
187	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
188	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
189	#41×C₈₉	—	2	1	no	—
190	#41×C₈₉	—	2	1	no	—
191	#41×C₈₉	C₂²×C₄	1	2	yes	—
192	#41×C₈₉	C₂²×C₄	1	2	yes	—
193	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
194	C₂×D₄×C₈₉	—	2	1	no	—
195	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₈₉	—	2	1	no	—
197	C₂²×C₄×C₈₉	—	2	2	no	—
198	C₂²×C₄×C₈₉	#41	1	2	yes	—
199	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
200	M₁₆×C₈₉	—	2	1	no	—
201	M₁₆×C₈₉	—	2	1	no	—
202	M₁₆×C₈₉	—	2	4	no	—
203	M₁₆×C₈₉	—	2	4	no	—
204	M₁₆×C₈₉	C₂²×C₄	1	2	yes	—
205	M₁₆×C₈₉	C₂²×C₄	1	2	yes	—
206	C₂×C₈×C₈₉	—	2	1	no	—
207	C₂×C₈×C₈₉	—	2	1	no	—
208	C₂×C₈×C₈₉	—	2	4	no	—
209	C₂×C₈×C₈₉	—	2	4	no	—
210	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
211	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
212	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
213	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
214	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
215	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
216	C₂×C₈×C₈₉	#41	1	2	yes	—
217	C₂×C₈×C₈₉	#41	1	2	yes	—
218	C₄⋊C₄×C₈₉	—	2	2	no	—
219	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
220	C₂²⋊C₄×C₈₉	—	2	1	no	—
221	C₂²⋊C₄×C₈₉	—	2	2	no	—
222	C₄²×C₈₉	—	2	2	no	—
223	C₄²×C₈₉	—	2	1	no	—
224	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
225	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₈₉	—	2	1	no	—
228	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
229	C₂²×D₈₉	—	2	1	no	—
230	Q₈×C₈₉	—	2	1	no	—
231	Q₈×C₈₉	C₂×C₄²	1	2	yes	—
232	D₄×C₈₉	—	2	2	no	—
233	D₄×C₈₉	—	2	2	no	—
234	D₄×C₈₉	—	2	1	no	—
235	D₄×C₈₉	C₂×C₄²	1	2	yes	—
236	C₂×C₄×C₈₉	—	2	1	no	—
237	C₂×C₄×C₈₉	—	2	2	no	—
238	C₂×C₄×C₈₉	—	2	2	no	—
239	C₂×C₄×C₈₉	—	2	2	no	—
240	C₂×C₄×C₈₉	—	4	2	no	—
241	C₂×C₄×C₈₉	—	4	4	no	—
242	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
243	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
244	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
250	C₂²⋊D₈₉	—	2	2	no	—
251	C₂²⋊D₈₉	—	2	2	no	—
252	C₂×Dic₈₉	—	2	1	no	—
253	C₂×Dic₈₉	—	2	2	no	—
254	C₂×Dic₈₉	—	2	2	no	—
255	C₂×Dic₈₉	—	2	2	no	—
256	C₂×Dic₈₉	—	4	2	no	—
257	C₂×Dic₈₉	—	4	2	no	—
258	D₃₅₆	—	2	1	no	—
259	D₃₅₆	C₂×C₄²	1	2	yes	—
260	C₄×D₈₉	—	2	2	no	—
261	C₄×D₈₉	—	2	2	no	—
262	C₄×D₈₉	—	4	4	no	—
263	Dic₁₇₈	—	2	1	no	—
264	Dic₁₇₈	C₂×C₄²	1	2	yes	—
265	C₈×C₈₉	—	2	2	no	—
266	C₈×C₈₉	—	2	2	no	—
267	C₈×C₈₉	C₄×D₄	1	2	yes	—
268	C₈×C₈₉	C₄×D₄	1	2	yes	—
269	C₈×C₈₉	C₄×D₄	1	2	yes	—
270	C₈×C₈₉	C₄×D₄	1	2	yes	—
271	#10623494	—	2	2	no	—
272	#10623494	—	2	2	no	—
273	#10623494	—	2	2	no	—
274	#10623494	C₂×C₄²	1	2	yes	—
275	#10623494	C₂×C₄²	1	2	yes	—
276	C₂²×C₈₉	—	2	2	no	—
277	C₂²×C₈₉	—	2	2	no	—
278	C₂²×C₈₉	—	4	2	no	—
279	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
280	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
281	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
282	C₂×D₈₉	—	2	2	no	—
283	C₂×D₈₉	—	4	2	no	—
284	C₄×C₈₉	—	2	2	no	—
285	C₄×C₈₉	—	2	2	no	—
286	C₄×C₈₉	—	2	2	no	—
287	C₄×C₈₉	—	4	2	no	—
288	C₄×C₈₉	C₂²×C₄²	1	1	yes	characteristic
289	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
290	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
291	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
292	Dic₈₉	—	2	2	no	—
293	Dic₈₉	—	4	2	no	—
294	Dic₈₉	—	4	2	no	—
295	Dic₈₉	—	4	2	no	—
296	#20510	—	89	1	no	maximal, Sylow
297	C₂×C₈₉	—	2	1	no	—
298	C₂×C₈₉	—	2	1	no	—
299	C₂×C₈₉	—	4	2	no	—
300	C₂×C₈₉	C₄²×D₄	1	1	yes	characteristic
301	C₂×C₈₉	#2955	1	2	yes	—
302	D₈₉	—	4	2	no	—
303	C₂×#444	—	89	1	no	—
304	C₂×#443	—	89	1	no	—
305	#2943	—	89	1	no	—
306	C₄×#131	—	89	1	no	—
307	C₄×#131	D₈₉	1	1	yes	characteristic, complemented
308	#1778	—	89	1	no	—
309	#1773	—	89	1	no	—
310	#1772	—	89	1	no	—
311	#1765	—	89	1	no	—
312	#1765	—	89	1	no	—
313	#1764	—	89	1	no	—
314	#1764	—	89	1	no	—
315	#1759	—	89	1	no	—
316	#1759	—	89	1	no	—
317	#1726	—	89	1	no	—
318	C₈₉	#20510	1	1	yes	characteristic, complemented, Sylow
319	C₂×#135	—	89	1	no	—
320	C₂×#131	—	89	1	no	—
321	C₂×#131	—	89	1	no	—
322	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
323	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
324	C₄×#41	—	89	1	no	—
325	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
326	#444	—	89	8	no	—
327	#443	—	89	8	no	—
328	#442	—	89	2	no	—
329	#441	—	89	2	no	—
330	#440	—	89	2	no	—
331	#440	—	89	2	no	—
332	C₂×#108	—	89	1	no	—
333	C₂×#108	—	89	1	no	—
334	#427	—	89	1	no	—
335	C₂×#104	—	89	1	no	—
336	C₂×#104	—	89	1	no	—
337	C₂×#104	—	89	1	no	—
338	C₂×#104	—	89	1	no	—
339	#416	—	89	1	no	—
340	#416	—	89	1	no	—
341	#405	—	2	1	no	—
342	#405	—	2	1	no	—
343	#405	—	89	1	no	—
344	#405	—	89	1	no	—
345	#405	—	178	1	no	—
346	#405	—	178	1	no	—
347	#405	C₂×D₈₉	1	1	yes	characteristic
348	#405	C₂×D₈₉	1	1	yes	characteristic
349	C₄×M₁₆	—	2	1	no	—
350	C₄×M₁₆	—	89	1	no	—
351	C₄×M₁₆	—	178	1	no	—
352	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
353	C₂×#97	—	89	1	no	—
354	C₂×#97	—	89	1	no	—
355	C₂×#97	—	89	1	no	—
356	C₂×C₄×C₈	—	2	1	no	—
357	C₂×C₄×C₈	—	89	1	no	—
358	C₂×C₄×C₈	—	89	1	no	—
359	C₂×C₄×C₈	—	178	1	no	—
360	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
361	#376	—	89	1	no	—
362	#341	—	89	1	no	—
363	#341	—	89	1	no	—
364	#339	—	89	1	no	—
365	#339	—	89	1	no	—
366	#339	—	89	1	no	—
367	#339	—	89	1	no	—
368	C₂×#41	—	89	1	no	—
369	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
370	#135	—	89	4	no	—
371	#135	—	89	4	no	—
372	C₂×Q₁₆	—	89	1	no	—
373	C₂×SD₁₆	—	89	1	no	—
374	C₂×SD₁₆	—	89	1	no	—
375	C₂×D₈	—	89	1	no	—
376	#131	—	2	2	no	—
377	#131	—	2	2	no	—
378	#131	—	89	4	no	—
379	#131	—	89	4	no	—
380	#131	—	178	2	no	—
381	#131	—	178	2	no	—
382	#131	C₄×D₈₉	1	4	yes	complemented
383	#131	C₄×D₈₉	1	4	yes	complemented
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	89	1	no	—
387	C₂×M₁₆	—	89	1	no	—
388	C₂×M₁₆	—	178	1	no	—
389	C₂×M₁₆	—	178	1	no	—
390	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
391	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	—	89	1	no	—
395	C₂²×C₈	—	89	1	no	—
396	C₂²×C₈	—	178	1	no	—
397	C₂²×C₈	—	178	1	no	—
398	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
399	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
400	C₄×Q₈	—	89	2	no	—
401	C₄×Q₈	C₄×D₈₉	1	2	yes	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	89	2	no	—
404	C₄×D₄	—	178	2	no	—
405	C₄×D₄	C₄×D₈₉	1	2	yes	—
406	#117	—	2	1	no	—
407	#117	—	89	1	no	—
408	#117	—	178	1	no	—
409	#117	C₂²×D₈₉	1	1	yes	characteristic
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	—	89	1	no	—
412	C₂×C₄²	—	89	1	no	—
413	C₂×C₄²	—	178	1	no	—
414	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
415	#108	—	89	4	no	—
416	#108	—	89	4	no	—
417	#107	—	89	2	no	—
418	#106	—	89	2	no	—
419	#104	—	89	4	no	—
420	#104	—	89	4	no	—
421	#104	—	89	4	no	—
422	#104	—	89	4	no	—
423	#103	—	89	2	no	—
424	#103	—	89	2	no	—
425	#102	—	89	2	no	—
426	#102	—	89	2	no	—
427	#97	—	2	1	no	—
428	#97	—	2	1	no	—
429	#97	—	2	1	no	—
430	#97	—	89	4	no	—
431	#97	—	89	2	no	—
432	#97	—	89	2	no	—
433	#97	—	178	1	no	—
434	#97	—	178	1	no	—
435	#97	—	178	2	no	—
436	#97	—	178	1	no	—
437	C₄×C₈	—	2	1	no	—
438	C₄×C₈	—	2	1	no	—
439	C₄×C₈	—	2	1	no	—
440	C₄×C₈	—	89	4	no	—
441	C₄×C₈	—	178	1	no	—
442	C₄×C₈	—	178	1	no	—
443	C₄×C₈	—	178	2	no	—
444	C₄×C₈	—	178	1	no	—
445	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
446	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
447	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
448	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
449	#95	—	178	2	no	—
450	#41	—	2	1	no	—
451	#41	—	2	1	no	—
452	#41	—	89	2	no	—
453	#41	—	89	2	no	—
454	#41	—	178	1	no	—
455	#41	—	178	1	no	—
456	#41	C₂×C₄×D₈₉	1	2	yes	—
457	#41	C₂×C₄×D₈₉	1	2	yes	—
458	C₂×Q₈	—	89	1	no	—
459	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	89	1	no	—
462	C₂×D₄	—	178	1	no	—
463	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	178	1	no	—
467	C₂²×C₄	—	178	1	no	—
468	C₂²×C₄	—	178	2	no	—
469	C₂²×C₄	—	178	1	no	—
470	C₂²×C₄	#13083574	1	2	yes	—
471	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
472	Q₁₆	—	89	4	no	—
473	SD₁₆	—	89	4	no	—
474	SD₁₆	—	89	4	no	—
475	D₈	—	89	4	no	—
476	M₁₆	—	2	1	no	—
477	M₁₆	—	2	1	no	—
478	M₁₆	—	2	4	no	—
479	M₁₆	—	2	4	no	—
480	M₁₆	—	89	2	no	—
481	M₁₆	—	89	2	no	—
482	M₁₆	—	178	1	no	—
483	M₁₆	—	178	1	no	—
484	M₁₆	—	178	4	no	—
485	M₁₆	—	178	4	no	—
486	M₁₆	C₂×C₄×D₈₉	1	2	yes	—
487	M₁₆	C₂×C₄×D₈₉	1	2	yes	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	4	no	—
491	C₂×C₈	—	2	4	no	—
492	C₂×C₈	—	89	2	no	—
493	C₂×C₈	—	89	1	no	—
494	C₂×C₈	—	89	1	no	—
495	C₂×C₈	—	89	2	no	—
496	C₂×C₈	—	89	2	no	—
497	C₂×C₈	—	178	1	no	—
498	C₂×C₈	—	178	1	no	—
499	C₂×C₈	—	178	1	no	—
500	C₂×C₈	—	178	1	no	—
501	C₂×C₈	—	178	4	no	—
502	C₂×C₈	—	178	4	no	—
503	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
504	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
505	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
506	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
507	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
508	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
509	C₂×C₈	#13083574	1	2	yes	—
510	C₂×C₈	#13083574	1	2	yes	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	89	2	no	—
513	C₄⋊C₄	—	178	2	no	—
514	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	178	1	no	—
518	C₂²⋊C₄	—	178	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	89	2	no	—
522	C₄²	—	89	2	no	—
523	C₄²	—	178	2	no	—
524	C₄²	—	178	1	no	—
525	C₄²	—	178	1	no	—
526	C₄²	—	178	1	no	—
527	C₄²	C₂×C₄×D₈₉	1	2	yes	—
528	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
529	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
530	C₂³	—	2	1	no	—
531	C₂³	—	178	1	no	—
532	C₂³	C₂×#13083574	1	1	yes	characteristic
533	Q₈	—	2	1	no	—
534	Q₈	—	89	2	no	—
535	Q₈	—	178	1	no	—
536	Q₈	C₄²×D₈₉	1	2	yes	—
537	D₄	—	2	2	no	—
538	D₄	—	2	2	no	—
539	D₄	—	2	1	no	—
540	D₄	—	89	2	no	—
541	D₄	—	178	2	no	—
542	D₄	—	178	2	no	—
543	D₄	—	178	1	no	—
544	D₄	C₄²×D₈₉	1	2	yes	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	356	4	no	—
552	C₂×C₄	—	356	2	no	—
553	C₂×C₄	—	356	2	no	—
554	C₂×C₄	—	178	2	no	—
555	C₂×C₄	—	178	2	no	—
556	C₂×C₄	—	178	2	no	—
557	C₂×C₄	—	178	1	no	—
558	C₂×C₄	—	178	2	no	—
559	C₂×C₄	—	178	2	no	—
560	C₂×C₄	C₄×C₂²⋊D₈₉	1	2	yes	—
561	C₂×C₄	C₄×C₂²⋊D₈₉	1	2	yes	—
562	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
563	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
564	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
565	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
566	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
567	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
568	C₈	—	2	2	no	—
569	C₈	—	2	2	no	—
570	C₈	—	89	2	no	—
571	C₈	—	89	2	no	—
572	C₈	—	178	2	no	—
573	C₈	—	178	2	no	—
574	C₈	—	178	2	no	—
575	C₈	C₄×C₂²⋊D₈₉	1	2	yes	—
576	C₈	C₄×C₂²⋊D₈₉	1	2	yes	—
577	C₈	C₄×C₂²⋊D₈₉	1	2	yes	—
578	C₈	C₄×C₂²⋊D₈₉	1	2	yes	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	356	2	no	—
583	C₂²	—	178	2	no	—
584	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
585	C₂²	C₄×#13083574	1	1	yes	characteristic
586	C₂²	C₄×#13083574	1	1	yes	characteristic
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	4	2	no	—
591	C₄	—	356	2	no	—
592	C₄	—	356	2	no	—
593	C₄	—	356	2	no	—
594	C₄	—	178	2	no	—
595	C₄	C₂×C₄²×D₈₉	1	1	yes	characteristic
596	C₄	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
597	C₄	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
598	C₄	C₄×#13083574	1	1	yes	characteristic
599	C₂	—	2	1	no	—
600	C₂	—	2	1	no	—
601	C₂	—	4	2	no	—
602	C₂	—	356	2	no	—
603	C₂	C₄²×C₂²⋊D₈₉	1	1	yes	characteristic
604	C₂	#26029153	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₈₉
commutator	C₄×C₈₉	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₄×#131×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668032	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄×#131	D₈₉
hypocenter	C₈₉	#20510
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
4. C₄×#15668018	C₂	semidirect
5. #26020159	C₂	semidirect
6. #26020137	C₂	semidirect
7. #26020132	C₂	semidirect
8. #26020098	C₂	semidirect
9. #26020094	C₂	semidirect
10. #26020091	C₂	semidirect
11. #26020087	C₂	semidirect
12. #26020065	C₂	semidirect
13. #26020062	C₂	semidirect
14. #26019938	C₂	semidirect
15. C₄×#131×C₈₉	C₂	semidirect
20. #19151718	C₄	semidirect
21. #19151713	C₄	semidirect
22. #19151708	C₄	semidirect
23. #19151703	C₄	semidirect
24. #19151698	C₄	semidirect
25. #19151696	C₄	semidirect
74. #15668018	C₂×C₄	semidirect
75. #15668018	C₂×C₄	semidirect
92. #15667947	C₂×C₄	semidirect
93. #15667947	C₂×C₄	semidirect
96. #15667939	C₂×C₄	semidirect
97. #15667939	C₂×C₄	semidirect
98. #15667938	C₂×C₄	semidirect
99. #15667938	C₂×C₄	semidirect
110. #15667922	C₂×C₄	semidirect
115. C₈×Dic₈₉	C₂×C₄	semidirect
120. #131×C₈₉	C₂×C₄	semidirect
121. #131×C₈₉	C₂×C₄	semidirect
307. C₄×#131	D₈₉	semidirect
318. C₈₉	#20510	semidirect
382. #131	C₄×D₈₉	semidirect
383. #131	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151718	2
C₂×#19151713	2
#26029050	2
C₄×#15668018	2
#26020159	2
#26020137	2
#26020132	2
#26020098	2
#26020094	2
#26020091	2
#26020087	2
#26020065	2
#26020062	2
#26019938	2
C₄×#131×C₈₉	2
#20510	89