Subgroups — #36561362

Order 22784.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029973	C₂	1	1	yes	maximal, characteristic
2	#26029154	C₂	1	2	yes	maximal, complemented
3	C₂×#19151714	C₂	1	1	yes	maximal, characteristic, complemented
4	#26028674	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021150	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020920	C₂	1	2	yes	maximal, complemented
7	#26020754	C₂	1	2	yes	maximal, complemented
8	#26020307	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020134	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020051	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1953	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152398	C₂²	1	2	yes	—
13	C₂×#15668034	C₂²	1	1	yes	characteristic
14	C₂×#15668020	C₂²	1	2	yes	—
15	C₂×#15668020	C₂²	1	1	yes	characteristic
16	C₂×#15668018	C₂²	1	1	yes	characteristic
17	#19152066	C₂²	1	1	yes	characteristic
18	#19151874	C₄	1	2	yes	complemented
19	#19151869	C₄	1	2	yes	complemented
20	#19151862	C₄	1	4	yes	complemented
21	#19151719	—	2	4	no	—
22	#19151714	—	2	1	no	—
23	#19151714	—	2	1	no	—
24	#19151714	—	2	1	no	—
25	#19151714	—	2	1	no	—
26	#19151714	—	2	4	no	—
27	#19151636	C₂²	1	1	yes	characteristic
28	#19151614	C₂²	1	2	yes	—
29	#19151614	C₂²	1	2	yes	—
30	C₂×#15667938	C₂²	1	2	yes	—
31	#19151580	C₂²	1	2	yes	—
32	#19151571	C₂²	1	2	yes	—
33	#19151556	C₂²	1	2	yes	—
34	#19151555	—	2	1	no	—
35	#19151554	C₂²	1	1	yes	characteristic
36	#19151552	—	2	1	no	—
37	#19151550	—	2	1	no	—
38	M₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₈₉	—	2	1	no	—
41	#19151369	C₂²	1	2	yes	—
42	#19151359	C₂²	1	2	yes	—
43	#430×C₈₉	C₂²	1	2	yes	—
44	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
46	#405×C₈₉	C₂²	1	1	yes	characteristic
47	#344×C₈₉	C₂²	1	2	yes	—
48	C₂×#13083574	C₂³	1	2	yes	—
49	C₂×#13083574	C₂³	1	1	yes	characteristic
50	#15668045	—	2	2	no	—
51	#15668045	C₂×C₄	1	4	yes	—
52	#15668040	—	2	2	no	—
53	#15668040	C₂×C₄	1	4	yes	—
54	#15668034	—	2	4	no	—
55	#15668034	—	2	1	no	—
56	#15668034	—	2	1	no	—
57	#15668034	—	2	1	no	—
58	#15668034	—	2	1	no	—
59	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×#13083563	C₂×C₄	1	2	yes	complemented
61	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic, complemented
62	#15668020	—	2	1	no	—
63	#15668020	—	2	1	no	—
64	#15668020	—	2	2	no	—
65	#15668020	—	2	2	no	—
66	#15668020	—	2	2	no	—
67	#15668020	—	2	2	no	—
68	#15668020	D₄	1	2	yes	—
69	#15668020	D₄	1	2	yes	—
70	#15668018	—	2	1	no	—
71	#15668018	—	2	1	no	—
72	#15668018	C₂×C₄	1	2	yes	—
73	#15668018	C₂×C₄	1	2	yes	—
74	C₂×#13083558	C₂³	1	1	yes	characteristic
75	C₂×#13083557	—	2	1	no	—
76	C₂×#13083557	—	2	2	no	—
77	C₂×#13083557	—	2	1	no	—
78	C₂²×#10623494	C₂³	1	1	yes	characteristic
79	C₂×C₈×D₈₉	—	2	1	no	—
80	C₂×C₈×D₈₉	—	2	2	no	—
81	C₂×C₈×D₈₉	—	2	1	no	—
82	#15667977	—	2	1	no	—
83	#15667974	—	2	1	no	—
84	#15667972	—	2	2	no	—
85	#15667971	C₂³	1	2	yes	—
86	#15667969	—	2	1	no	—
87	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
88	C₄²×D₈₉	—	2	1	no	—
89	#15667946	—	2	1	no	—
90	#15667944	—	2	1	no	—
91	#15667938	—	2	4	no	—
92	#15667938	—	2	2	no	—
93	#15667938	—	2	2	no	—
94	#15667938	—	2	4	no	—
95	#15667930	C₂×C₄	1	4	yes	complemented
96	#15667928	C₂×C₄	1	4	yes	complemented
97	#15667926	—	2	4	no	—
98	#15667923	—	2	1	no	—
99	#15667922	—	2	2	no	—
100	#15667922	—	2	1	no	—
101	C₄×#10623494	—	2	1	no	—
102	C₈×Dic₈₉	—	2	2	no	—
103	C₈×Dic₈₉	—	2	1	no	—
104	C₈×Dic₈₉	D₄	1	1	yes	characteristic
105	C₈×Dic₈₉	D₄	1	1	yes	characteristic
106	C₈×Dic₈₉	D₄	1	1	yes	characteristic
107	C₈×Dic₈₉	D₄	1	1	yes	characteristic
108	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
109	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
110	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
112	#117×C₈₉	C₂³	1	1	yes	characteristic
113	#108×C₈₉	—	2	4	no	—
114	#108×C₈₉	—	2	1	no	—
115	#108×C₈₉	—	2	1	no	—
116	#108×C₈₉	C₂×C₄	1	2	yes	complemented
117	#108×C₈₉	C₂×C₄	1	2	yes	complemented
118	#97×C₈₉	—	2	1	no	—
119	C₄×C₈×C₈₉	—	2	1	no	—
120	#13083574	—	2	1	no	—
121	#13083574	—	2	1	no	—
122	#13083574	—	2	2	no	—
123	#13083574	—	2	2	no	—
124	#13083574	—	2	2	no	—
125	#13083574	—	2	2	no	—
126	#13083574	C₂²×C₄	1	2	yes	—
127	#13083574	C₂×D₄	1	2	yes	—
128	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
129	C₂×Dic₁₇₈	#41	1	1	yes	characteristic
130	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
131	C₂×D₃₅₆	#41	1	1	yes	characteristic
132	C₂×C₂²⋊D₈₉	—	2	1	no	—
133	C₂×C₂²⋊D₈₉	—	2	2	no	—
134	C₂²×Dic₈₉	—	2	1	no	—
135	C₂×C₄×D₈₉	—	2	1	no	—
136	C₂×C₄×D₈₉	—	2	2	no	—
137	C₂×C₄×D₈₉	—	2	2	no	—
138	Dic₃₅₆	—	2	4	no	—
139	Dic₃₅₆	—	2	1	no	—
140	Dic₃₅₆	—	2	1	no	—
141	#13083563	—	2	4	no	—
142	#13083563	—	2	4	no	—
143	#13083563	—	2	2	no	—
144	#13083563	—	2	2	no	—
145	D₇₁₂	—	2	4	no	—
146	D₇₁₂	—	2	1	no	—
147	D₇₁₂	—	2	1	no	—
148	#13083558	—	2	1	no	—
149	#13083558	C₂²×C₄	1	2	yes	—
150	#13083557	—	2	2	no	—
151	#13083557	—	2	2	no	—
152	#13083557	—	2	2	no	—
153	#13083557	—	2	2	no	—
154	#13083557	—	4	2	no	—
155	#13083557	—	4	2	no	—
156	C₂×#10623494	—	2	1	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	C₂×#10623494	#41	1	1	yes	characteristic
162	C₂×#10623494	#41	1	1	yes	characteristic
163	C₈×D₈₉	—	2	2	no	—
164	C₈×D₈₉	—	2	2	no	—
165	C₈×D₈₉	—	2	2	no	—
166	C₈×D₈₉	—	2	2	no	—
167	C₈×D₈₉	—	4	2	no	—
168	C₈×D₈₉	—	4	2	no	—
169	C₄⋊Dic₈₉	—	2	2	no	—
170	#13083553	—	2	2	no	—
171	C₂²⋊Dic₈₉	—	2	2	no	—
172	#13083551	—	2	2	no	—
173	C₄×Dic₈₉	—	2	2	no	—
174	C₄×Dic₈₉	—	2	1	no	—
175	C₄×Dic₈₉	—	2	2	no	—
176	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
177	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
179	M₁₆×C₈₉	—	2	1	no	—
180	M₁₆×C₈₉	—	2	2	no	—
181	M₁₆×C₈₉	—	2	2	no	—
182	M₁₆×C₈₉	—	2	2	no	—
183	M₁₆×C₈₉	C₂²×C₄	1	4	yes	—
184	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
185	C₂×C₈×C₈₉	—	2	1	no	—
186	C₂×C₈×C₈₉	—	2	2	no	—
187	C₂×C₈×C₈₉	—	2	2	no	—
188	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
191	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
192	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
193	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
194	C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₂²⋊C₄×C₈₉	#41	1	2	yes	—
196	C₄²×C₈₉	—	2	1	no	—
197	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
198	C₂²×D₈₉	—	2	1	no	—
199	C₂²×D₈₉	—	2	2	no	—
200	C₂×C₄×C₈₉	—	2	2	no	—
201	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
207	C₂²⋊D₈₉	—	2	2	no	—
208	C₂²⋊D₈₉	—	2	2	no	—
209	C₂²⋊D₈₉	—	4	2	no	—
210	C₂²⋊D₈₉	—	4	2	no	—
211	C₂×Dic₈₉	—	2	1	no	—
212	C₂×Dic₈₉	—	2	1	no	—
213	C₂×Dic₈₉	—	2	2	no	—
214	C₂×Dic₈₉	—	2	1	no	—
215	C₂×Dic₈₉	—	4	2	no	—
216	C₂×Dic₈₉	—	4	2	no	—
217	D₃₅₆	—	2	2	no	—
218	D₃₅₆	—	2	2	no	—
219	D₃₅₆	—	2	1	no	—
220	D₃₅₆	C₄×D₄	1	2	yes	—
221	C₄×D₈₉	—	2	2	no	—
222	C₄×D₈₉	—	2	2	no	—
223	C₄×D₈₉	—	4	4	no	—
224	C₄×D₈₉	—	4	2	no	—
225	C₄×D₈₉	—	4	2	no	—
226	Dic₁₇₈	—	2	1	no	—
227	Dic₁₇₈	—	2	2	no	—
228	Dic₁₇₈	—	2	2	no	—
229	Dic₁₇₈	C₄×D₄	1	2	yes	—
230	C₈×C₈₉	—	2	4	no	—
231	C₈×C₈₉	—	2	2	no	—
232	C₈×C₈₉	—	4	2	no	—
233	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
234	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
235	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
236	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
237	#10623494	—	2	2	no	—
238	#10623494	#121	1	1	yes	characteristic
239	#10623494	#121	1	1	yes	characteristic
240	#10623494	#121	1	1	yes	characteristic
241	#10623494	#121	1	1	yes	characteristic
242	C₂²×C₈₉	—	4	1	no	—
243	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
244	C₂²×C₈₉	#525	1	1	yes	characteristic
245	C₂²×C₈₉	#532	1	1	yes	characteristic
246	C₂×D₈₉	—	2	2	no	—
247	C₂×D₈₉	—	4	2	no	—
248	C₂×D₈₉	—	4	2	no	—
249	C₂×D₈₉	—	8	2	no	—
250	C₄×C₈₉	—	4	2	no	—
251	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
252	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
253	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
254	C₄×C₈₉	#529	1	1	yes	characteristic
255	Dic₈₉	—	2	2	no	—
256	Dic₈₉	—	2	2	no	—
257	Dic₈₉	—	4	1	no	—
258	Dic₈₉	—	4	2	no	—
259	Dic₈₉	—	8	2	no	—
260	#21558	—	89	1	no	maximal, Sylow
261	C₂×C₈₉	—	2	1	no	—
262	C₂×C₈₉	—	2	1	no	—
263	C₂×C₈₉	—	2	1	no	—
264	C₂×C₈₉	C₄×#121	1	1	yes	characteristic
265	D₈₉	—	4	2	no	—
266	D₈₉	—	8	2	no	—
267	#3067	—	89	1	no	—
268	#2955	—	89	2	no	—
269	C₂×#443	—	89	1	no	—
270	C₄×#131	—	89	1	no	—
271	#1976	—	89	1	no	—
272	#1953	D₈₉	1	1	yes	characteristic, complemented
273	#1932	—	89	2	no	—
274	#1906	—	89	2	no	—
275	#1814	—	89	1	no	—
276	#1772	—	89	1	no	—
277	#1757	—	89	2	no	—
278	C₈₉	#21558	1	1	yes	characteristic, complemented, Sylow
279	#575	—	89	2	no	—
280	C₂×#135	—	89	1	no	—
281	C₂×#131	—	89	1	no	—
282	C₂×#131	—	89	2	no	—
283	C₂×#131	—	89	1	no	—
284	C₄×#41	—	89	1	no	—
285	#473	—	89	2	no	—
286	#472	—	89	2	no	—
287	#471	—	89	4	no	—
288	#444	—	178	4	no	—
289	#443	—	178	1	no	—
290	#443	—	178	1	no	—
291	#443	—	178	1	no	—
292	#443	—	178	1	no	—
293	#443	—	178	4	no	—
294	#430	C₂×D₈₉	1	2	yes	—
295	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
296	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
297	#427	—	89	1	no	—
298	#421	—	89	2	no	—
299	#421	—	89	2	no	—
300	C₂×#104	—	89	2	no	—
301	#413	—	89	2	no	—
302	#410	—	89	2	no	—
303	#405	—	89	2	no	—
304	#405	—	89	1	no	—
305	#405	—	178	1	no	—
306	#405	—	178	1	no	—
307	#405	C₂×D₈₉	1	1	yes	characteristic
308	C₄×M₁₆	—	89	1	no	—
309	C₄×M₁₆	—	178	1	no	—
310	C₂×C₄×C₈	—	89	1	no	—
311	C₂×C₄×C₈	—	178	1	no	—
312	#344	—	89	2	no	—
313	#344	C₂×D₈₉	1	2	yes	—
314	#339	—	89	2	no	—
315	C₂×#41	—	89	1	no	—
316	C₂×#41	—	89	2	no	—
317	#137	—	89	4	no	—
318	#137	—	178	2	no	—
319	AGL(1,ℤ/8)	—	89	4	no	—
320	AGL(1,ℤ/8)	—	178	2	no	—
321	#135	—	178	4	no	—
322	#135	—	178	1	no	—
323	#135	—	178	1	no	—
324	#135	—	178	1	no	—
325	#135	—	178	1	no	—
326	C₂×Q₁₆	—	89	1	no	—
327	C₂×SD₁₆	—	89	2	no	—
328	C₂×D₈	—	89	1	no	—
329	#131	—	89	2	no	—
330	#131	—	89	2	no	—
331	#131	—	89	2	no	—
332	#131	—	89	2	no	—
333	#131	—	178	2	no	—
334	#131	—	178	2	no	—
335	#131	—	178	2	no	—
336	#131	—	178	2	no	—
337	#131	—	178	1	no	—
338	#131	—	178	1	no	—
339	#131	—	178	1	no	—
340	#131	—	178	1	no	—
341	C₂×M₁₆	—	89	1	no	—
342	C₂×M₁₆	—	178	2	no	—
343	C₂×M₁₆	—	178	1	no	—
344	C₂×M₁₆	—	178	1	no	—
345	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
346	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
347	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
348	C₂²×C₈	—	89	1	no	—
349	C₂²×C₈	—	178	2	no	—
350	C₂²×C₈	—	178	1	no	—
351	C₂²×C₈	—	178	1	no	—
352	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
353	C₄×Q₈	—	178	1	no	—
354	C₄×D₄	—	178	1	no	—
355	C₄×D₄	—	178	2	no	—
356	#117	—	89	2	no	—
357	#117	—	178	1	no	—
358	#117	C₂²×D₈₉	1	1	yes	characteristic
359	C₂×C₄²	—	89	1	no	—
360	C₂×C₄²	—	178	1	no	—
361	#108	—	2	4	no	—
362	#108	—	2	1	no	—
363	#108	—	2	1	no	—
364	#108	C₄×D₈₉	1	2	yes	complemented
365	#108	C₄×D₈₉	1	2	yes	complemented
366	#107	—	178	1	no	—
367	#106	—	178	1	no	—
368	#104	—	178	2	no	—
369	#104	—	178	2	no	—
370	#104	—	178	4	no	—
371	#104	—	178	4	no	—
372	#101	—	89	4	no	—
373	#100	—	89	4	no	—
374	#99	—	178	4	no	—
375	#97	—	2	1	no	—
376	#97	—	178	1	no	—
377	#97	—	178	1	no	—
378	#97	—	178	2	no	—
379	C₄×C₈	—	2	1	no	—
380	C₄×C₈	—	89	1	no	—
381	C₄×C₈	—	89	1	no	—
382	C₄×C₈	—	89	1	no	—
383	C₄×C₈	—	89	1	no	—
384	C₄×C₈	—	178	1	no	—
385	C₄×C₈	—	178	1	no	—
386	C₄×C₈	—	178	2	no	—
387	#41	—	89	2	no	—
388	#41	—	89	2	no	—
389	#41	—	178	2	no	—
390	#41	—	178	2	no	—
391	#41	—	178	2	no	—
392	#41	—	178	2	no	—
393	#41	—	178	1	no	—
394	#41	—	178	1	no	—
395	C₂×Q₈	—	89	2	no	—
396	C₂×Q₈	—	89	1	no	—
397	C₂×D₄	—	89	2	no	—
398	C₂×D₄	—	89	1	no	—
399	C₂×D₄	—	178	2	no	—
400	C₂×D₄	—	178	1	no	—
401	C₂²×C₄	—	178	2	no	—
402	C₂²×C₄	—	178	1	no	—
403	C₂²×C₄	—	178	2	no	—
404	C₂²×C₄	—	178	1	no	—
405	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
406	Q₁₆	—	178	4	no	—
407	Q₁₆	—	178	1	no	—
408	Q₁₆	—	178	1	no	—
409	SD₁₆	—	178	4	no	—
410	SD₁₆	—	178	4	no	—
411	SD₁₆	—	178	2	no	—
412	SD₁₆	—	178	2	no	—
413	D₈	—	178	4	no	—
414	D₈	—	178	1	no	—
415	D₈	—	178	1	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	2	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	89	2	no	—
421	M₁₆	—	356	2	no	—
422	M₁₆	—	356	2	no	—
423	M₁₆	—	178	2	no	—
424	M₁₆	—	178	2	no	—
425	M₁₆	—	178	1	no	—
426	M₁₆	—	178	2	no	—
427	M₁₆	—	178	2	no	—
428	M₁₆	C₂×C₄×D₈₉	1	4	yes	—
429	M₁₆	D₄×D₈₉	1	2	yes	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	89	1	no	—
434	C₂×C₈	—	89	1	no	—
435	C₂×C₈	—	89	1	no	—
436	C₂×C₈	—	89	1	no	—
437	C₂×C₈	—	89	1	no	—
438	C₂×C₈	—	89	1	no	—
439	C₂×C₈	—	356	2	no	—
440	C₂×C₈	—	356	2	no	—
441	C₂×C₈	—	178	2	no	—
442	C₂×C₈	—	178	2	no	—
443	C₂×C₈	—	178	1	no	—
444	C₂×C₈	—	178	2	no	—
445	C₂×C₈	—	178	2	no	—
446	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
447	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
448	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
449	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
450	C₂×C₈	#13083575	1	1	yes	characteristic
451	C₂×C₈	#13083575	1	1	yes	characteristic
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	178	2	no	—
454	C₄⋊C₄	—	178	2	no	—
455	C₂²⋊C₄	—	178	2	no	—
456	C₂²⋊C₄	—	178	2	no	—
457	C₂²⋊C₄	#13083575	1	2	yes	—
458	C₄²	—	2	1	no	—
459	C₄²	—	89	1	no	—
460	C₄²	—	89	1	no	—
461	C₄²	—	178	2	no	—
462	C₄²	—	178	2	no	—
463	C₄²	—	178	1	no	—
464	C₂³	—	178	1	no	—
465	C₂³	—	178	2	no	—
466	C₂³	C₂×#13083575	1	1	yes	characteristic
467	Q₈	—	89	2	no	—
468	Q₈	—	178	2	no	—
469	Q₈	—	178	2	no	—
470	Q₈	—	178	1	no	—
471	D₄	—	89	2	no	—
472	D₄	—	356	2	no	—
473	D₄	—	356	2	no	—
474	D₄	—	178	2	no	—
475	D₄	—	178	2	no	—
476	D₄	—	178	1	no	—
477	D₄	—	178	2	no	—
478	D₄	—	178	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	356	4	no	—
481	C₂×C₄	—	356	2	no	—
482	C₂×C₄	—	356	2	no	—
483	C₂×C₄	—	356	2	no	—
484	C₂×C₄	—	356	2	no	—
485	C₂×C₄	—	178	2	no	—
486	C₂×C₄	—	178	1	no	—
487	C₂×C₄	—	178	1	no	—
488	C₂×C₄	—	178	1	no	—
489	C₂×C₄	—	178	2	no	—
490	C₂×C₄	—	178	2	no	—
491	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
493	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
494	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
495	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
496	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
497	C₈	—	2	4	no	—
498	C₈	—	2	2	no	—
499	C₈	—	4	2	no	—
500	C₈	—	89	1	no	—
501	C₈	—	89	1	no	—
502	C₈	—	89	1	no	—
503	C₈	—	89	1	no	—
504	C₈	—	178	2	no	—
505	C₈	#15667974	1	1	yes	characteristic
506	C₈	#15667974	1	1	yes	characteristic
507	C₈	#15667974	1	1	yes	characteristic
508	C₈	#15667974	1	1	yes	characteristic
509	C₂²	—	4	1	no	—
510	C₂²	—	356	2	no	—
511	C₂²	—	356	2	no	—
512	C₂²	—	178	2	no	—
513	C₂²	—	712	2	no	—
514	C₂²	C₄×#13083575	1	1	yes	characteristic
515	C₂²	#19152111	1	1	yes	characteristic
516	C₂²	#19152149	1	1	yes	characteristic
517	C₄	—	4	2	no	—
518	C₄	—	356	1	no	—
519	C₄	—	356	2	no	—
520	C₄	—	178	2	no	—
521	C₄	—	178	2	no	—
522	C₄	—	712	2	no	—
523	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
524	C₄	C₂×#15667974	1	1	yes	characteristic
525	C₄	#121×D₈₉	1	1	yes	characteristic
526	C₄	#19152133	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	356	2	no	—
531	C₂	—	712	2	no	—
532	C₂	#26022760	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#121×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1953	C₂
socle	C₂×C₈₉	C₄×#121
prime radical	#26029973	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1953	D₈₉
hypocenter	C₈₉	#21558
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1953

Complements

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

N	H ≅ G/N	type
2. #26029154	C₂	semidirect
3. C₂×#19151714	C₂	semidirect
4. #26028674	C₂	semidirect
5. #26021150	C₂	semidirect
6. #26020920	C₂	semidirect
7. #26020754	C₂	semidirect
8. #26020307	C₂	semidirect
9. #26020134	C₂	semidirect
10. #26020051	C₂	semidirect
11. C₈₉×#1953	C₂	semidirect
18. #19151874	C₄	semidirect
19. #19151869	C₄	semidirect
20. #19151862	C₄	semidirect
59. C₂×Dic₃₅₆	C₂×C₄	semidirect
60. C₂×#13083563	C₂×C₄	semidirect
61. C₂×D₇₁₂	C₂×C₄	semidirect
95. #15667930	C₂×C₄	semidirect
96. #15667928	C₂×C₄	semidirect
116. #108×C₈₉	C₂×C₄	semidirect
117. #108×C₈₉	C₂×C₄	semidirect
272. #1953	D₈₉	semidirect
278. C₈₉	#21558	semidirect
364. #108	C₄×D₈₉	semidirect
365. #108	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029973	2
#26029154	2
C₂×#19151714	2
#26028674	2
#26021150	2
#26020920	2
#26020754	2
#26020307	2
#26020134	2
#26020051	2
C₈₉×#1953	2
#21558	89