Subgroups — #36572946

Order 22784.

812 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029167	C₂	1	1	yes	maximal, characteristic
2	#26029165	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151712	C₂	1	1	yes	maximal, characteristic
4	#26028862	C₂	1	1	yes	maximal, characteristic, complemented
5	#26028861	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021041	C₂	1	1	yes	maximal, characteristic, complemented
7	#26021039	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020494	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020493	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020491	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020423	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020305	C₂	1	1	yes	maximal, characteristic, complemented
13	#26020304	C₂	1	1	yes	maximal, characteristic, complemented
14	#26020130	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1861	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668032	C₂²	1	1	yes	characteristic
17	#19152365	C₂²	1	1	yes	characteristic
18	#19152364	C₂²	1	1	yes	characteristic
19	#19152364	C₂²	1	1	yes	characteristic
20	C₂×#15668020	C₂²	1	1	yes	characteristic
21	C₂×#15668019	C₂²	1	1	yes	characteristic
22	#19151718	—	2	2	no	—
23	#19151717	—	2	2	no	—
24	#19151713	—	2	2	no	—
25	#19151712	—	2	2	no	—
26	#19151712	C₄	1	2	yes	complemented
27	#19151712	C₄	1	2	yes	complemented
28	#19151712	C₄	1	2	yes	complemented
29	#19151712	C₄	1	2	yes	complemented
30	#19151647	C₂²	1	1	yes	characteristic
31	#19151646	—	2	2	no	—
32	#19151646	C₂²	1	1	yes	characteristic
33	#19151646	C₂²	1	1	yes	characteristic
34	#19151645	—	2	2	no	—
35	C₂×#15667947	—	2	2	no	—
36	C₂×#15667947	C₂²	1	1	yes	characteristic
37	C₂×#15667947	C₂²	1	1	yes	characteristic
38	C₂×#15667947	C₂²	1	1	yes	characteristic
39	C₂×#15667947	C₂²	1	1	yes	characteristic
40	C₂×#15667947	C₂²	1	1	yes	characteristic
41	C₂×#15667947	C₂²	1	1	yes	characteristic
42	#108×D₈₉	—	2	2	no	—
43	#19151634	C₂²	1	1	yes	characteristic
44	#19151622	C₂²	1	1	yes	characteristic
45	#19151616	C₂²	1	1	yes	characteristic
46	#19151615	C₂²	1	1	yes	characteristic
47	#19151614	C₂²	1	1	yes	characteristic
48	C₂×#15667940	C₂²	1	1	yes	characteristic
49	#19151556	C₂²	1	1	yes	characteristic
50	#19151554	C₂²	1	1	yes	characteristic
51	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
52	#19151370	C₂²	1	1	yes	characteristic
53	#19151369	C₂²	1	1	yes	characteristic
54	#19151368	C₂²	1	1	yes	characteristic
55	#19151358	C₂²	1	1	yes	characteristic
56	#568×C₈₉	C₂²	1	1	yes	characteristic
57	#430×C₈₉	C₂²	1	1	yes	characteristic
58	#423×C₈₉	C₂²	1	1	yes	characteristic
59	#421×C₈₉	C₂²	1	1	yes	characteristic
60	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
61	#344×C₈₉	C₂²	1	1	yes	characteristic
62	#339×C₈₉	C₂²	1	1	yes	characteristic
63	C₂×#13083574	C₂³	1	1	yes	characteristic
64	#15668032	C₂×C₄	1	2	yes	—
65	#15668032	C₂×C₄	1	2	yes	—
66	#15668032	D₄	1	2	yes	—
67	#15668032	D₄	1	2	yes	—
68	C₂×#13083564	Q₈	1	1	yes	characteristic
69	C₂×#13083562	Q₈	1	1	yes	characteristic
70	C₂×#13083561	Q₈	1	1	yes	characteristic
71	C₂×#13083559	Q₈	1	1	yes	characteristic
72	#15668020	—	2	1	no	—
73	#15668020	—	2	1	no	—
74	#15668020	—	2	2	no	—
75	#15668020	—	4	1	no	—
76	#15668020	C₂×C₄	1	2	yes	—
77	#15668020	C₂×C₄	1	2	yes	—
78	#15668019	—	2	1	no	—
79	#15668019	—	2	1	no	—
80	#15668019	—	2	2	no	—
81	#15668019	—	4	1	no	—
82	#15668019	C₂×C₄	1	2	yes	—
83	#15668019	C₂×C₄	1	2	yes	—
84	#15668018	—	2	2	no	—
85	#15668018	—	4	1	no	—
86	C₂×#13083558	—	2	1	no	—
87	C₂×#13083558	—	2	2	no	—
88	C₂×#13083558	C₂³	1	1	yes	characteristic
89	C₂×#13083558	C₂³	1	1	yes	characteristic
90	C₂×#13083558	C₂³	1	1	yes	characteristic
91	C₂×#13083558	C₂³	1	1	yes	characteristic
92	C₂×#13083557	—	2	1	no	—
93	M₁₆×D₈₉	—	2	2	no	—
94	M₁₆×D₈₉	—	2	2	no	—
95	C₂²×#10623494	—	2	1	no	—
96	C₂²×#10623494	C₂³	1	1	yes	characteristic
97	C₂²×#10623494	C₂³	1	1	yes	characteristic
98	C₂×C₈×D₈₉	—	2	1	no	—
99	#15667971	C₂³	1	1	yes	characteristic
100	#15667948	—	2	2	no	—
101	#15667947	—	2	2	no	—
102	#15667947	—	2	1	no	—
103	#15667947	—	2	1	no	—
104	#15667947	—	2	1	no	—
105	#15667947	—	2	1	no	—
106	#15667947	—	2	1	no	—
107	#15667947	—	2	1	no	—
108	#15667947	—	2	1	no	—
109	#15667947	—	2	1	no	—
110	#15667947	—	2	2	no	—
111	#15667947	C₂×C₄	1	2	yes	—
112	#15667947	C₂×C₄	1	2	yes	—
113	#15667947	D₄	1	2	yes	—
114	#15667947	D₄	1	2	yes	—
115	#15667945	—	2	1	no	—
116	#15667943	—	2	1	no	—
117	C₄⋊#10623494	—	4	1	no	—
118	#15667940	—	2	2	no	—
119	#15667940	C₂×C₄	1	2	yes	—
120	#15667940	C₂×C₄	1	2	yes	—
121	#15667939	—	2	2	no	—
122	#15667938	—	2	2	no	—
123	#15667923	—	2	1	no	—
124	#15667922	—	2	1	no	—
125	C₄×#10623494	—	2	1	no	—
126	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
127	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
128	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
129	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
130	C₈×Dic₈₉	—	2	1	no	—
131	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
132	#131×C₈₉	—	2	2	no	—
133	#131×C₈₉	—	4	1	no	—
134	C₂×M₁₆×C₈₉	—	2	2	no	—
135	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
139	#117×C₈₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
141	#108×C₈₉	—	2	2	no	—
142	C₄⋊C₈×C₈₉	—	4	1	no	—
143	#104×C₈₉	—	2	2	no	—
144	#104×C₈₉	C₂×C₄	1	2	yes	—
145	#104×C₈₉	C₂×C₄	1	2	yes	—
146	#13083574	—	2	1	no	—
147	#13083574	—	2	1	no	—
148	#13083574	C₂²×C₄	1	2	yes	—
149	#13083574	C₂×D₄	1	2	yes	—
150	C₂×Dic₁₇₈	C₂×Q₈	1	1	yes	characteristic
151	C₂×D₃₅₆	C₂×Q₈	1	1	yes	characteristic
152	C₂×C₂²⋊D₈₉	—	2	1	no	—
153	C₂×C₄×D₈₉	—	2	1	no	—
154	#13083564	C₄⋊C₄	1	2	yes	—
155	#13083564	C₄⋊C₄	1	2	yes	—
156	#13083562	C₄⋊C₄	1	2	yes	—
157	#13083562	C₄⋊C₄	1	2	yes	—
158	#13083561	C₄⋊C₄	1	2	yes	—
159	#13083561	C₄⋊C₄	1	2	yes	—
160	#13083559	C₄⋊C₄	1	2	yes	—
161	#13083559	C₄⋊C₄	1	2	yes	—
162	#13083558	—	2	1	no	—
163	#13083558	—	2	1	no	—
164	#13083558	—	2	2	no	—
165	#13083558	—	2	2	no	—
166	#13083558	—	2	1	no	—
167	#13083558	—	2	1	no	—
168	#13083558	—	2	1	no	—
169	#13083558	—	2	1	no	—
170	#13083558	—	4	2	no	—
171	#13083558	C₂²×C₄	1	2	yes	—
172	#13083558	C₂×D₄	1	2	yes	—
173	#13083557	—	2	2	no	—
174	#13083557	—	2	2	no	—
175	#13083557	—	4	2	no	—
176	#13083557	—	4	2	no	—
177	C₂×#10623494	—	2	1	no	—
178	C₂×#10623494	—	2	1	no	—
179	C₂×#10623494	—	2	2	no	—
180	C₂×#10623494	—	2	2	no	—
181	C₂×#10623494	—	2	1	no	—
182	C₂×#10623494	—	2	1	no	—
183	C₂×#10623494	—	4	2	no	—
184	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
185	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
186	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
187	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
188	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
189	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
190	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
191	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
192	C₂×#10623494	C₂×Q₈	1	1	yes	characteristic
193	C₂×#10623494	C₂×Q₈	1	1	yes	characteristic
194	C₂×#10623494	#41	1	1	yes	characteristic
195	C₂×#10623494	#41	1	1	yes	characteristic
196	C₈×D₈₉	—	2	2	no	—
197	C₈×D₈₉	—	2	2	no	—
198	C₈×D₈₉	—	4	2	no	—
199	C₈×D₈₉	—	4	2	no	—
200	C₄⋊Dic₈₉	—	2	1	no	—
201	C₂²⋊Dic₈₉	—	2	1	no	—
202	C₄×Dic₈₉	—	2	1	no	—
203	#41×C₈₉	—	2	1	no	—
204	#41×C₈₉	—	2	1	no	—
205	#41×C₈₉	C₂²×C₄	1	2	yes	—
206	#41×C₈₉	C₂×D₄	1	2	yes	—
207	C₂×Q₈×C₈₉	C₂×Q₈	1	1	yes	characteristic
208	C₂×D₄×C₈₉	—	2	1	no	—
209	C₂×D₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
210	C₂²×C₄×C₈₉	—	2	1	no	—
211	C₂²×C₄×C₈₉	—	2	1	no	—
212	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
213	M₁₆×C₈₉	—	2	1	no	—
214	M₁₆×C₈₉	—	2	1	no	—
215	M₁₆×C₈₉	—	2	1	no	—
216	M₁₆×C₈₉	—	2	1	no	—
217	M₁₆×C₈₉	—	2	1	no	—
218	M₁₆×C₈₉	—	2	1	no	—
219	M₁₆×C₈₉	—	4	2	no	—
220	M₁₆×C₈₉	C₂²×C₄	1	2	yes	—
221	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
222	C₂×C₈×C₈₉	—	2	1	no	—
223	C₂×C₈×C₈₉	—	2	1	no	—
224	C₂×C₈×C₈₉	—	2	1	no	—
225	C₂×C₈×C₈₉	—	2	1	no	—
226	C₂×C₈×C₈₉	—	4	2	no	—
227	C₄⋊C₄×C₈₉	—	2	1	no	—
228	C₂²⋊C₄×C₈₉	—	2	1	no	—
229	C₄²×C₈₉	—	2	1	no	—
230	C₄²×C₈₉	—	2	1	no	—
231	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
232	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
233	C₂³×C₈₉	—	2	1	no	—
234	C₂³×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
235	C₂²×D₈₉	—	2	1	no	—
236	Q₈×C₈₉	—	2	1	no	—
237	Q₈×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
238	D₄×C₈₉	—	2	2	no	—
239	D₄×C₈₉	—	2	2	no	—
240	D₄×C₈₉	—	2	1	no	—
241	D₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
242	C₂×C₄×C₈₉	—	2	1	no	—
243	C₂×C₄×C₈₉	—	2	1	no	—
244	C₂×C₄×C₈₉	—	2	2	no	—
245	C₂×C₄×C₈₉	—	2	2	no	—
246	C₂×C₄×C₈₉	—	2	1	no	—
247	C₂×C₄×C₈₉	—	4	2	no	—
248	C₂×C₄×C₈₉	—	4	1	no	—
249	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
250	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
253	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
255	C₂²⋊D₈₉	—	2	2	no	—
256	C₂²⋊D₈₉	—	2	2	no	—
257	C₂×Dic₈₉	—	2	1	no	—
258	C₂×Dic₈₉	—	4	1	no	—
259	D₃₅₆	—	2	1	no	—
260	D₃₅₆	C₂×C₄⋊C₄	1	2	yes	—
261	C₄×D₈₉	—	2	2	no	—
262	C₄×D₈₉	—	2	2	no	—
263	Dic₁₇₈	—	2	1	no	—
264	Dic₁₇₈	C₂×C₄⋊C₄	1	2	yes	—
265	C₈×C₈₉	—	2	2	no	—
266	C₈×C₈₉	—	2	2	no	—
267	C₈×C₈₉	—	4	1	no	—
268	C₈×C₈₉	—	4	1	no	—
269	#10623494	—	2	2	no	—
270	#10623494	—	2	2	no	—
271	#10623494	—	4	1	no	—
272	#10623494	—	4	1	no	—
273	#10623494	C₂×C₄⋊C₄	1	1	yes	characteristic
274	#10623494	C₂×C₄⋊C₄	1	1	yes	characteristic
275	#10623494	C₂×C₄⋊C₄	1	1	yes	characteristic
276	#10623494	C₂×C₄⋊C₄	1	1	yes	characteristic
277	#10623494	C₄×D₄	1	1	yes	characteristic
278	#10623494	C₄×D₄	1	1	yes	characteristic
279	#10623494	C₄×D₄	1	1	yes	characteristic
280	#10623494	C₄×D₄	1	1	yes	characteristic
281	C₂²×C₈₉	—	2	2	no	—
282	C₂²×C₈₉	—	4	1	no	—
283	C₂²×C₈₉	—	8	1	no	—
284	C₂²×C₈₉	#520	1	1	yes	characteristic
285	C₂²×C₈₉	#547	1	1	yes	characteristic
286	C₂²×C₈₉	D₄×Q₈	1	1	yes	characteristic
287	C₂×D₈₉	—	2	2	no	—
288	C₂×D₈₉	—	8	1	no	—
289	C₄×C₈₉	—	2	2	no	—
290	C₄×C₈₉	—	2	2	no	—
291	C₄×C₈₉	—	4	1	no	—
292	C₄×C₈₉	—	8	1	no	—
293	C₄×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
294	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
295	C₄×C₈₉	D₄²	1	1	yes	characteristic
296	C₄×C₈₉	#554	1	1	yes	characteristic
297	Dic₈₉	—	2	2	no	—
298	Dic₈₉	—	8	1	no	—
299	#22694	—	89	1	no	maximal, Sylow
300	C₂×C₈₉	—	2	1	no	—
301	C₂×C₈₉	—	2	1	no	—
302	C₂×C₈₉	—	2	1	no	—
303	C₂×C₈₉	—	4	2	no	—
304	C₂×C₈₉	D₄×C₄⋊C₄	1	1	yes	characteristic
305	D₈₉	—	4	2	no	—
306	#2957	—	89	1	no	—
307	#2957	—	89	1	no	—
308	C₂×#443	—	89	1	no	—
309	#2916	—	89	1	no	—
310	#2916	—	89	1	no	—
311	#1953	—	89	1	no	—
312	#1953	—	89	1	no	—
313	#1861	—	89	1	no	—
314	#1861	—	89	1	no	—
315	#1861	—	89	1	no	—
316	#1861	D₈₉	1	1	yes	characteristic, complemented
317	#1848	—	89	1	no	—
318	#1814	—	89	1	no	—
319	#1814	—	89	1	no	—
320	#1772	—	89	1	no	—
321	C₈₉	#22694	1	1	yes	characteristic, complemented, Sylow
322	C₂×#135	—	89	1	no	—
323	#568	—	89	1	no	—
324	#568	—	89	1	no	—
325	#568	—	89	1	no	—
326	#568	C₂×D₈₉	1	1	yes	characteristic
327	C₂×#131	—	89	1	no	—
328	C₂×#131	—	89	1	no	—
329	#444	—	178	2	no	—
330	#444	—	178	2	no	—
331	#443	—	89	2	no	—
332	#443	—	89	2	no	—
333	#443	—	89	2	no	—
334	#443	—	89	2	no	—
335	#443	—	178	2	no	—
336	#443	—	178	2	no	—
337	#430	—	89	1	no	—
338	#430	—	89	1	no	—
339	#430	—	89	1	no	—
340	#430	—	178	2	no	—
341	#430	—	178	2	no	—
342	#430	C₂×D₈₉	1	1	yes	characteristic
343	C₂×#108	—	89	1	no	—
344	C₂×#108	—	89	1	no	—
345	C₂×#108	—	89	1	no	—
346	C₂×#108	—	89	1	no	—
347	C₂×#108	—	89	1	no	—
348	C₂×#108	—	89	1	no	—
349	C₂×#108	—	178	2	no	—
350	C₂×#108	—	178	2	no	—
351	#427	—	89	1	no	—
352	#423	—	89	1	no	—
353	#423	C₂×D₈₉	1	1	yes	characteristic
354	#421	—	89	1	no	—
355	#421	—	89	1	no	—
356	#421	—	89	1	no	—
357	#421	C₂×D₈₉	1	1	yes	characteristic
358	C₂×#104	—	89	1	no	—
359	C₂×#104	C₂×D₈₉	1	1	yes	characteristic
360	#405	—	89	1	no	—
361	#405	—	89	1	no	—
362	C₂×C₄×C₈	—	89	1	no	—
363	#344	—	89	1	no	—
364	#344	—	89	1	no	—
365	#344	—	89	1	no	—
366	#344	C₂×D₈₉	1	1	yes	characteristic
367	#339	—	89	1	no	—
368	#339	C₂×D₈₉	1	1	yes	characteristic
369	C₂×#41	—	89	1	no	—
370	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
371	#135	—	89	2	no	—
372	#135	—	89	2	no	—
373	#135	—	89	2	no	—
374	#135	—	89	2	no	—
375	C₂×Q₁₆	—	89	1	no	—
376	C₂×SD₁₆	—	89	1	no	—
377	C₂×SD₁₆	—	89	1	no	—
378	C₂×D₈	—	89	1	no	—
379	#131	—	2	2	no	—
380	#131	—	4	1	no	—
381	#131	—	89	2	no	—
382	#131	—	89	2	no	—
383	#131	—	89	2	no	—
384	#131	—	89	2	no	—
385	#131	—	356	1	no	—
386	#131	—	356	1	no	—
387	#131	—	356	1	no	—
388	#131	—	178	2	no	—
389	#131	—	178	1	no	—
390	#131	—	178	1	no	—
391	#131	—	178	1	no	—
392	#131	—	178	1	no	—
393	#131	—	178	2	no	—
394	#131	—	178	2	no	—
395	C₂×M₁₆	—	2	2	no	—
396	C₂×M₁₆	—	89	1	no	—
397	C₂×M₁₆	—	89	1	no	—
398	C₂×M₁₆	—	89	1	no	—
399	C₂×M₁₆	—	89	1	no	—
400	C₂×M₁₆	—	178	1	no	—
401	C₂×M₁₆	—	178	1	no	—
402	C₂×M₁₆	—	178	2	no	—
403	C₂×M₁₆	—	178	2	no	—
404	C₂×M₁₆	—	178	2	no	—
405	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
406	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
407	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
408	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
409	C₂²×C₈	—	89	1	no	—
410	C₂²×C₈	—	89	1	no	—
411	C₂²×C₈	—	178	1	no	—
412	C₂²×C₈	—	178	1	no	—
413	#117	—	89	1	no	—
414	#117	C₂²×D₈₉	1	1	yes	characteristic
415	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
416	#108	—	2	2	no	—
417	#108	—	89	2	no	—
418	#108	—	89	2	no	—
419	#108	—	89	2	no	—
420	#108	—	89	2	no	—
421	#108	—	178	2	no	—
422	#108	—	178	1	no	—
423	#108	—	178	1	no	—
424	#108	—	178	1	no	—
425	#108	—	178	1	no	—
426	#108	—	178	1	no	—
427	#108	—	178	1	no	—
428	#108	—	178	1	no	—
429	#108	—	178	1	no	—
430	#108	—	178	2	no	—
431	#108	—	178	2	no	—
432	#107	—	178	1	no	—
433	#106	—	178	1	no	—
434	C₄⋊C₈	—	4	1	no	—
435	C₄⋊C₈	—	356	1	no	—
436	#104	—	2	2	no	—
437	#104	—	89	2	no	—
438	#104	—	89	2	no	—
439	#104	—	178	2	no	—
440	#104	—	178	2	no	—
441	#104	—	178	2	no	—
442	#104	C₄×D₈₉	1	2	yes	—
443	#104	C₄×D₈₉	1	2	yes	—
444	#97	—	178	1	no	—
445	#97	—	178	1	no	—
446	C₄×C₈	—	89	1	no	—
447	C₄×C₈	—	89	1	no	—
448	C₄×C₈	—	89	1	no	—
449	C₄×C₈	—	89	1	no	—
450	C₄×C₈	—	178	1	no	—
451	C₄×C₈	—	178	1	no	—
452	#41	—	2	1	no	—
453	#41	—	2	1	no	—
454	#41	—	89	2	no	—
455	#41	—	89	2	no	—
456	#41	—	178	1	no	—
457	#41	—	178	1	no	—
458	#41	C₂×C₄×D₈₉	1	2	yes	—
459	#41	D₄×D₈₉	1	2	yes	—
460	C₂×Q₈	—	89	1	no	—
461	C₂×Q₈	Q₈×D₈₉	1	1	yes	characteristic
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	89	1	no	—
464	C₂×D₄	—	178	1	no	—
465	C₂×D₄	Q₈×D₈₉	1	1	yes	characteristic
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	178	1	no	—
469	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
470	Q₁₆	—	89	2	no	—
471	Q₁₆	—	89	2	no	—
472	SD₁₆	—	89	2	no	—
473	SD₁₆	—	89	2	no	—
474	SD₁₆	—	89	2	no	—
475	SD₁₆	—	89	2	no	—
476	D₈	—	89	2	no	—
477	D₈	—	89	2	no	—
478	M₁₆	—	2	1	no	—
479	M₁₆	—	2	1	no	—
480	M₁₆	—	2	1	no	—
481	M₁₆	—	2	1	no	—
482	M₁₆	—	2	1	no	—
483	M₁₆	—	2	1	no	—
484	M₁₆	—	4	2	no	—
485	M₁₆	—	89	2	no	—
486	M₁₆	—	89	2	no	—
487	M₁₆	—	356	2	no	—
488	M₁₆	—	356	2	no	—
489	M₁₆	—	356	2	no	—
490	M₁₆	—	178	2	no	—
491	M₁₆	—	178	2	no	—
492	M₁₆	—	178	2	no	—
493	M₁₆	—	178	2	no	—
494	M₁₆	—	178	1	no	—
495	M₁₆	—	178	1	no	—
496	M₁₆	—	178	1	no	—
497	M₁₆	—	178	1	no	—
498	M₁₆	—	178	1	no	—
499	M₁₆	—	178	1	no	—
500	M₁₆	C₂×C₄×D₈₉	1	2	yes	—
501	M₁₆	D₄×D₈₉	1	2	yes	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	4	2	no	—
507	C₂×C₈	—	89	1	no	—
508	C₂×C₈	—	89	1	no	—
509	C₂×C₈	—	89	1	no	—
510	C₂×C₈	—	89	1	no	—
511	C₂×C₈	—	89	1	no	—
512	C₂×C₈	—	89	1	no	—
513	C₂×C₈	—	89	1	no	—
514	C₂×C₈	—	89	1	no	—
515	C₂×C₈	—	89	1	no	—
516	C₂×C₈	—	89	1	no	—
517	C₂×C₈	—	89	1	no	—
518	C₂×C₈	—	89	1	no	—
519	C₂×C₈	—	356	2	no	—
520	C₂×C₈	—	356	2	no	—
521	C₂×C₈	—	356	2	no	—
522	C₂×C₈	—	178	2	no	—
523	C₂×C₈	—	178	2	no	—
524	C₂×C₈	—	178	2	no	—
525	C₂×C₈	—	178	2	no	—
526	C₂×C₈	—	178	1	no	—
527	C₂×C₈	—	178	1	no	—
528	C₂×C₈	—	178	1	no	—
529	C₂×C₈	—	178	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	178	1	no	—
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	178	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	178	1	no	—
537	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
538	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
539	C₂³	—	2	1	no	—
540	C₂³	—	178	1	no	—
541	C₂³	#15668059	1	1	yes	characteristic
542	Q₈	—	2	1	no	—
543	Q₈	—	89	2	no	—
544	Q₈	—	178	1	no	—
545	Q₈	C₄⋊C₄×D₈₉	1	2	yes	—
546	D₄	—	2	2	no	—
547	D₄	—	2	2	no	—
548	D₄	—	2	1	no	—
549	D₄	—	89	2	no	—
550	D₄	—	178	2	no	—
551	D₄	—	178	2	no	—
552	D₄	—	178	1	no	—
553	D₄	C₄⋊C₄×D₈₉	1	2	yes	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	356	1	no	—
562	C₂×C₄	—	178	1	no	—
563	C₂×C₄	—	178	2	no	—
564	C₂×C₄	—	178	2	no	—
565	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
566	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
567	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
568	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
569	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
570	C₂×C₄	#15668057	1	1	yes	characteristic
571	C₈	—	2	2	no	—
572	C₈	—	2	2	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	89	1	no	—
576	C₈	—	89	1	no	—
577	C₈	—	89	1	no	—
578	C₈	—	89	1	no	—
579	C₈	—	89	1	no	—
580	C₈	—	89	1	no	—
581	C₈	—	89	1	no	—
582	C₈	—	89	1	no	—
583	C₈	—	356	1	no	—
584	C₈	—	356	1	no	—
585	C₈	—	178	2	no	—
586	C₈	—	178	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	8	1	no	—
590	C₂²	—	178	2	no	—
591	C₂²	—	712	1	no	—
592	C₂²	#19152077	1	1	yes	characteristic
593	C₂²	#19152246	1	1	yes	characteristic
594	C₂²	#19152261	1	1	yes	characteristic
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	4	1	no	—
598	C₄	—	8	1	no	—
599	C₄	—	178	2	no	—
600	C₄	—	712	1	no	—
601	C₄	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
602	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
603	C₄	#19152230	1	1	yes	characteristic
604	C₄	#19152302	1	1	yes	characteristic
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	—	4	2	no	—
609	C₂	—	356	2	no	—
610	C₂	#26023150	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19152230
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1861	C₂
socle	C₂×C₈₉	D₄×C₄⋊C₄
prime radical	C₂×#15668032	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1861	D₈₉
hypocenter	C₈₉	#22694
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1861

Complements

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

N	H ≅ G/N	type
4. #26028862	C₂	semidirect
5. #26028861	C₂	semidirect
6. #26021041	C₂	semidirect
7. #26021039	C₂	semidirect
8. #26020494	C₂	semidirect
9. #26020493	C₂	semidirect
10. #26020491	C₂	semidirect
11. #26020423	C₂	semidirect
12. #26020305	C₂	semidirect
13. #26020304	C₂	semidirect
14. #26020130	C₂	semidirect
15. C₈₉×#1861	C₂	semidirect
26. #19151712	C₄	semidirect
27. #19151712	C₄	semidirect
28. #19151712	C₄	semidirect
29. #19151712	C₄	semidirect
316. #1861	D₈₉	semidirect
321. C₈₉	#22694	semidirect

Maximal subgroups

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

subgroup	index
#26029167	2
#26029165	2
C₂×#19151712	2
#26028862	2
#26028861	2
#26021041	2
#26021039	2
#26020494	2
#26020493	2
#26020491	2
#26020423	2
#26020305	2
#26020304	2
#26020130	2
C₈₉×#1861	2
#22694	89