Subgroups — #36448839

Order 22784.

644 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26023316	C₂	1	1	yes	maximal, characteristic
2	#26021057	C₂	1	1	yes	maximal, characteristic
3	#26021008	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19151341	C₂	1	1	yes	maximal, characteristic
5	#26018093	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018091	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1947	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15668009	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₃₅₆	—	2	1	no	—
10	C₂×#15667974	—	2	1	no	—
11	C₂×#15667945	—	2	1	no	—
12	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
13	C₂×#15667932	—	2	2	no	—
14	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
15	#19151500	—	2	1	no	—
16	#19151499	—	2	1	no	—
17	#19151476	—	2	2	no	—
18	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
19	#19151360	—	2	1	no	—
20	#19151341	C₄	1	4	yes	complemented
21	C₂×#107×C₈₉	—	2	1	no	—
22	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
23	#384×C₈₉	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
25	#340×C₈₉	—	2	1	no	—
26	C₂²×D₃₅₆	—	2	1	no	—
27	C₂²×D₃₅₆	—	2	1	no	—
28	C₂²×D₃₅₆	D₄	1	2	yes	—
29	C₂²×C₄×D₈₉	—	2	2	no	—
30	C₂²×#10623494	—	2	1	no	—
31	C₂²×#10623494	—	2	1	no	—
32	#15668009	—	2	1	no	—
33	#15668009	—	2	1	no	—
34	#15668009	C₂×C₄	1	2	yes	—
35	#15668009	Q₈	1	2	yes	—
36	C₄×D₃₅₆	—	4	2	no	—
37	C₄×D₃₅₆	—	4	2	no	—
38	#15667974	—	4	2	no	—
39	#15667974	—	4	2	no	—
40	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
41	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
42	C₂×#13083551	—	2	2	no	—
43	C₂×#13083551	—	2	2	no	—
44	C₂×#13083551	—	2	2	no	—
45	C₂×C₄×Dic₈₉	—	2	1	no	—
46	#15667945	—	4	2	no	—
47	C₄⋊#10623494	—	2	1	no	—
48	C₄⋊#10623494	C₂×C₄	1	2	yes	complemented
49	#15667932	—	4	4	no	—
50	C₄×#10623494	—	2	1	no	—
51	C₄×#10623494	—	2	1	no	—
52	#15667919	—	2	1	no	—
53	C₂²×C₈×C₈₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₈₉	—	2	1	no	—
60	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
61	#107×C₈₉	—	4	2	no	—
62	C₄⋊C₈×C₈₉	—	2	1	no	—
63	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	complemented
64	#95×C₈₉	—	2	1	no	—
65	C₂³×D₈₉	—	2	2	no	—
66	C₂×D₃₅₆	—	2	2	no	—
67	C₂×D₃₅₆	—	2	2	no	—
68	C₂×D₃₅₆	—	2	2	no	—
69	C₂×D₃₅₆	—	2	2	no	—
70	C₂×D₃₅₆	—	2	2	no	—
71	C₂×D₃₅₆	—	4	1	no	—
72	C₂×D₃₅₆	—	4	1	no	—
73	C₂×D₃₅₆	—	4	1	no	—
74	C₂×D₃₅₆	—	4	1	no	—
75	C₂×D₃₅₆	—	4	1	no	—
76	C₂×D₃₅₆	—	4	1	no	—
77	C₂×D₃₅₆	—	4	1	no	—
78	C₂×D₃₅₆	—	4	1	no	—
79	C₂×D₃₅₆	—	4	2	no	—
80	C₂×D₃₅₆	—	4	2	no	—
81	C₂×D₃₅₆	C₄⋊C₄	1	4	yes	—
82	C₂²×Dic₈₉	—	2	1	no	—
83	C₂²×Dic₈₉	—	2	1	no	—
84	C₂×C₄×D₈₉	—	4	4	no	—
85	C₂×C₄×D₈₉	—	4	4	no	—
86	C₂×C₄×D₈₉	—	8	2	no	—
87	C₂×#10623494	—	2	2	no	—
88	C₂×#10623494	—	2	2	no	—
89	C₂×#10623494	—	4	1	no	—
90	C₂×#10623494	—	4	1	no	—
91	C₂×#10623494	—	4	1	no	—
92	C₂×#10623494	—	4	1	no	—
93	C₄⋊Dic₈₉	—	2	1	no	—
94	C₄⋊Dic₈₉	—	2	1	no	—
95	C₄⋊Dic₈₉	—	2	1	no	—
96	C₄⋊Dic₈₉	D₈	1	2	yes	—
97	#13083551	—	4	4	no	—
98	#13083551	—	4	4	no	—
99	#13083551	—	8	2	no	—
100	C₄×Dic₈₉	—	4	1	no	—
101	C₄×Dic₈₉	—	4	1	no	—
102	C₂²×C₄×C₈₉	—	2	1	no	—
103	C₂²×C₄×C₈₉	—	2	1	no	—
104	C₂²×C₄×C₈₉	—	4	1	no	—
105	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₈₉	—	2	2	no	—
109	C₂×C₈×C₈₉	—	4	1	no	—
110	C₂×C₈×C₈₉	—	4	1	no	—
111	C₄⋊C₄×C₈₉	—	2	1	no	—
112	C₄⋊C₄×C₈₉	—	2	1	no	—
113	C₄⋊C₄×C₈₉	—	2	1	no	—
114	C₄⋊C₄×C₈₉	—	4	2	no	—
115	C₄⋊C₄×C₈₉	—	4	1	no	—
116	C₄⋊C₄×C₈₉	—	4	1	no	—
117	C₄⋊C₄×C₈₉	—	4	1	no	—
118	C₄⋊C₄×C₈₉	—	4	1	no	—
119	C₄⋊C₄×C₈₉	D₈	1	2	yes	—
120	C₄²×C₈₉	—	4	1	no	—
121	C₄²×C₈₉	—	4	1	no	—
122	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
124	C₄²×C₈₉	#41	1	1	yes	characteristic
125	C₄²×C₈₉	#41	1	1	yes	characteristic
126	C₂³×C₈₉	#120	1	1	yes	characteristic
127	C₂²×D₈₉	—	2	4	no	—
128	C₂²×D₈₉	—	4	2	no	—
129	C₂²×D₈₉	—	4	2	no	—
130	C₂²×D₈₉	—	4	2	no	—
131	C₂²×D₈₉	—	4	2	no	—
132	C₂²×D₈₉	—	4	2	no	—
133	C₂²×D₈₉	—	4	2	no	—
134	C₂×C₄×C₈₉	—	2	1	no	—
135	C₂×C₄×C₈₉	—	2	1	no	—
136	C₂×C₄×C₈₉	—	2	2	no	—
137	C₂×C₄×C₈₉	—	4	1	no	—
138	C₂×C₄×C₈₉	—	4	1	no	—
139	C₂×C₄×C₈₉	—	4	1	no	—
140	C₂×C₄×C₈₉	—	4	1	no	—
141	C₂×C₄×C₈₉	—	4	1	no	—
142	C₂×C₄×C₈₉	—	8	1	no	—
143	C₂×C₄×C₈₉	—	8	1	no	—
144	C₂×C₄×C₈₉	—	8	1	no	—
145	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
153	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
154	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
155	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
156	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
158	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
159	C₂×Dic₈₉	—	2	2	no	—
160	C₂×Dic₈₉	—	4	1	no	—
161	C₂×Dic₈₉	—	4	1	no	—
162	C₂×Dic₈₉	—	4	1	no	—
163	C₂×Dic₈₉	—	4	1	no	—
164	C₂×Dic₈₉	—	4	1	no	—
165	D₃₅₆	—	4	4	no	—
166	D₃₅₆	—	4	2	no	—
167	D₃₅₆	—	4	2	no	—
168	D₃₅₆	—	4	2	no	—
169	D₃₅₆	—	4	2	no	—
170	D₃₅₆	—	4	2	no	—
171	D₃₅₆	—	4	2	no	—
172	D₃₅₆	—	4	2	no	—
173	D₃₅₆	—	4	2	no	—
174	D₃₅₆	—	8	2	no	—
175	C₄×D₈₉	—	8	8	no	—
176	C₈×C₈₉	—	4	2	no	—
177	#10623494	—	4	2	no	—
178	#10623494	—	4	2	no	—
179	C₂²×C₈₉	#385	1	1	yes	characteristic
180	C₂²×C₈₉	#447	1	1	yes	characteristic
181	C₂²×C₈₉	#447	1	1	yes	characteristic
182	C₂²×C₈₉	#452	1	1	yes	characteristic
183	C₂²×C₈₉	#452	1	1	yes	characteristic
184	C₂²×C₈₉	#453	1	1	yes	characteristic
185	C₂²×C₈₉	#455	1	1	yes	characteristic
186	C₂×D₈₉	—	4	4	no	—
187	C₂×D₈₉	—	4	4	no	—
188	C₂×D₈₉	—	4	4	no	—
189	C₂×D₈₉	—	8	2	no	—
190	C₂×D₈₉	—	8	2	no	—
191	C₂×D₈₉	—	8	2	no	—
192	C₂×D₈₉	—	8	2	no	—
193	C₄×C₈₉	—	2	1	no	—
194	C₄×C₈₉	—	2	1	no	—
195	C₄×C₈₉	—	4	2	no	—
196	C₄×C₈₉	—	8	1	no	—
197	C₄×C₈₉	—	16	1	no	—
198	C₄×C₈₉	C₄×D₈	1	1	yes	characteristic
199	C₄×C₈₉	C₄×D₈	1	1	yes	characteristic
200	C₄×C₈₉	#440	1	1	yes	characteristic
201	C₄×C₈₉	#440	1	1	yes	characteristic
202	C₄×C₈₉	#474	1	1	yes	characteristic
203	C₄×C₈₉	#474	1	1	yes	characteristic
204	C₄×C₈₉	#478	1	1	yes	characteristic
205	C₄×C₈₉	#478	1	1	yes	characteristic
206	Dic₈₉	—	4	2	no	—
207	Dic₈₉	—	8	1	no	—
208	#8920	—	89	1	no	maximal, Sylow
209	C₂×C₈₉	#1619	1	1	yes	characteristic
210	C₂×C₈₉	#1630	1	1	yes	characteristic
211	C₂×C₈₉	#1641	1	1	yes	characteristic
212	C₂×C₈₉	#1641	1	1	yes	characteristic
213	C₂×C₈₉	#1856	1	1	yes	characteristic
214	C₂×C₈₉	#1862	1	1	yes	characteristic
215	C₂×C₈₉	#1862	1	1	yes	characteristic
216	D₈₉	—	8	4	no	—
217	#2366	—	89	1	no	—
218	#1957	—	89	1	no	—
219	#1947	—	89	1	no	—
220	#1947	D₈₉	1	1	yes	characteristic, complemented
221	C₂×#331	—	89	1	no	—
222	#1279	—	89	1	no	—
223	#1279	—	89	1	no	—
224	C₈₉	#8920	1	1	yes	characteristic, complemented, Sylow
225	C₂×#127	—	89	1	no	—
226	C₂×C₄×D₄	—	178	1	no	—
227	C₂×C₄×D₄	—	178	1	no	—
228	C₂×#107	—	2	1	no	—
229	C₂×#107	—	178	1	no	—
230	C₂×C₄⋊C₈	—	89	1	no	—
231	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
232	C₂×#102	—	178	2	no	—
233	C₂×C₄×C₈	—	89	1	no	—
234	#390	—	178	1	no	—
235	#390	—	178	1	no	—
236	#386	—	178	2	no	—
237	#384	C₂×D₈₉	1	1	yes	characteristic
238	C₄×C₄⋊C₄	—	89	1	no	—
239	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
240	#340	—	2	1	no	—
241	#340	—	178	1	no	—
242	#331	—	89	4	no	—
243	C₂²×D₄	—	89	2	no	—
244	C₂²×D₄	—	178	1	no	—
245	C₂²×D₄	—	178	1	no	—
246	C₂³×C₄	—	178	2	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	178	1	no	—
249	C₂²×C₈	—	178	1	no	—
250	#127	—	89	2	no	—
251	#127	—	89	2	no	—
252	#127	—	178	1	no	—
253	#127	—	178	1	no	—
254	C₄×D₄	—	356	2	no	—
255	C₄×D₄	—	356	2	no	—
256	C₄×D₄	—	356	2	no	—
257	C₄×D₄	—	356	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	89	1	no	—
262	C₂×C₄⋊C₄	—	89	1	no	—
263	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	178	2	no	—
266	C₂×C₂²⋊C₄	—	178	2	no	—
267	C₂×C₂²⋊C₄	—	178	2	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	—	178	1	no	—
270	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
271	#107	—	4	2	no	—
272	#107	—	356	2	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	89	2	no	—
275	C₄⋊C₈	—	178	1	no	—
276	C₄⋊C₈	C₄×D₈₉	1	2	yes	complemented
277	#102	—	356	4	no	—
278	C₄×C₈	—	178	1	no	—
279	C₄×C₈	—	178	1	no	—
280	#95	—	2	1	no	—
281	#95	—	178	1	no	—
282	C₂⁴	—	178	2	no	—
283	C₂×D₄	—	89	4	no	—
284	C₂×D₄	—	356	2	no	—
285	C₂×D₄	—	356	2	no	—
286	C₂×D₄	—	356	1	no	—
287	C₂×D₄	—	356	1	no	—
288	C₂×D₄	—	356	1	no	—
289	C₂×D₄	—	356	1	no	—
290	C₂×D₄	—	356	1	no	—
291	C₂×D₄	—	356	1	no	—
292	C₂×D₄	—	356	1	no	—
293	C₂×D₄	—	356	1	no	—
294	C₂×D₄	—	178	2	no	—
295	C₂×D₄	—	178	2	no	—
296	C₂×D₄	—	178	2	no	—
297	C₂×D₄	—	178	2	no	—
298	C₂×D₄	—	178	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	356	4	no	—
303	C₂²×C₄	—	356	4	no	—
304	C₂²×C₄	—	178	1	no	—
305	C₂²×C₄	—	178	1	no	—
306	C₂²×C₄	—	712	2	no	—
307	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	356	1	no	—
314	C₂×C₈	—	356	1	no	—
315	C₂×C₈	—	356	1	no	—
316	C₂×C₈	—	356	1	no	—
317	C₂×C₈	—	178	2	no	—
318	C₂×C₈	—	178	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	89	2	no	—
328	C₄⋊C₄	—	178	1	no	—
329	C₄⋊C₄	—	178	1	no	—
330	C₄⋊C₄	—	178	1	no	—
331	C₄⋊C₄	#13083559	1	2	yes	—
332	C₂²⋊C₄	—	356	4	no	—
333	C₂²⋊C₄	—	356	4	no	—
334	C₂²⋊C₄	—	712	2	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	—	356	1	no	—
338	C₄²	—	356	1	no	—
339	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
340	C₄²	Q₈×D₈₉	1	1	yes	characteristic
341	C₄²	#13083574	1	1	yes	characteristic
342	C₄²	#13083575	1	1	yes	characteristic
343	C₂³	—	356	2	no	—
344	C₂³	—	356	2	no	—
345	C₂³	—	356	2	no	—
346	C₂³	—	356	2	no	—
347	C₂³	—	356	2	no	—
348	C₂³	—	356	2	no	—
349	C₂³	—	178	4	no	—
350	C₂³	#15667980	1	1	yes	characteristic
351	D₄	—	356	4	no	—
352	D₄	—	356	2	no	—
353	D₄	—	356	2	no	—
354	D₄	—	356	2	no	—
355	D₄	—	356	2	no	—
356	D₄	—	356	2	no	—
357	D₄	—	356	2	no	—
358	D₄	—	356	2	no	—
359	D₄	—	356	2	no	—
360	D₄	—	712	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	8	1	no	—
370	C₂×C₄	—	8	1	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	—	356	1	no	—
373	C₂×C₄	—	356	1	no	—
374	C₂×C₄	—	356	1	no	—
375	C₂×C₄	—	356	1	no	—
376	C₂×C₄	—	356	1	no	—
377	C₂×C₄	—	178	2	no	—
378	C₂×C₄	—	712	8	no	—
379	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
380	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
381	C₂×C₄	#15667974	1	1	yes	characteristic
382	C₂×C₄	#15667988	1	1	yes	characteristic
383	C₂×C₄	#15667990	1	1	yes	characteristic
384	C₂×C₄	#15667997	1	1	yes	characteristic
385	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
386	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
387	C₂×C₄	#15668032	1	1	yes	characteristic
388	C₂×C₄	#15668035	1	1	yes	characteristic
389	C₂×C₄	#15668036	1	1	yes	characteristic
390	C₂×C₄	#15668037	1	1	yes	characteristic
391	C₂×C₄	#15668043	1	1	yes	characteristic
392	C₂×C₄	#15668044	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	—	356	2	no	—
395	C₈	—	356	2	no	—
396	C₂²	—	356	4	no	—
397	C₂²	—	356	4	no	—
398	C₂²	—	356	4	no	—
399	C₂²	—	712	2	no	—
400	C₂²	—	712	2	no	—
401	C₂²	—	712	2	no	—
402	C₂²	—	712	2	no	—
403	C₂²	#19151469	1	1	yes	characteristic
404	C₂²	#19151730	1	1	yes	characteristic
405	C₂²	#19151731	1	1	yes	characteristic
406	C₂²	#19151758	1	1	yes	characteristic
407	C₂²	#19151759	1	1	yes	characteristic
408	C₂²	#19151764	1	1	yes	characteristic
409	C₂²	#19151774	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	8	1	no	—
414	C₄	—	16	1	no	—
415	C₄	—	356	2	no	—
416	C₄	—	712	1	no	—
417	C₄	C₄×#13083559	1	1	yes	characteristic
418	C₄	#19151680	1	1	yes	characteristic
419	C₄	#19151696	1	1	yes	characteristic
420	C₄	#19151697	1	1	yes	characteristic
421	C₄	#19151875	1	1	yes	characteristic
422	C₄	#19151877	1	1	yes	characteristic
423	C₄	#19151895	1	1	yes	characteristic
424	C₄	#19151901	1	1	yes	characteristic
425	C₂	—	712	4	no	—
426	C₂	#26019305	1	1	yes	characteristic
427	C₂	#26019372	1	1	yes	characteristic
428	C₂	#26019443	1	1	yes	characteristic
429	C₂	#26019444	1	1	yes	characteristic
430	C₂	#26020460	1	1	yes	characteristic
431	C₂	#26020496	1	1	yes	characteristic
432	C₂	#26020498	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#15667980
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1947	C₂
socle	C₂³×C₈₉	#120
prime radical	C₂×#15668009	C₂²
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1947	D₈₉
hypocenter	C₈₉	#8920
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1947

Complements

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

N	H ≅ G/N	type
3. #26021008	C₂	semidirect
5. #26018093	C₂	semidirect
6. #26018091	C₂	semidirect
7. C₈₉×#1947	C₂	semidirect
20. #19151341	C₄	semidirect
48. C₄⋊#10623494	C₂×C₄	semidirect
63. C₄⋊C₈×C₈₉	C₂×C₄	semidirect
220. #1947	D₈₉	semidirect
224. C₈₉	#8920	semidirect
276. C₄⋊C₈	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26023316	2
#26021057	2
#26021008	2
C₂×#19151341	2
#26018093	2
#26018091	2
C₈₉×#1947	2
#8920	89