Subgroups — #36448848

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	#26021058	C₂	1	1	yes	maximal, characteristic
3	#26021015	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021011	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#19151341	C₂	1	1	yes	maximal, characteristic
6	#26018092	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1279	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×#15667946	—	2	1	no	—
12	C₂×#15667943	—	2	1	no	—
13	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
14	C₂×#15667934	—	2	2	no	—
15	#19151500	—	2	1	no	—
16	#19151499	—	2	1	no	—
17	#19151476	—	2	2	no	—
18	#19151468	C₂²	1	1	yes	characteristic
19	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
20	#19151361	—	2	1	no	—
21	#19151360	—	2	1	no	—
22	#19151341	C₄	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
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	#15668009	—	2	1	no	—
32	#15668009	—	2	1	no	—
33	#15668009	C₂×C₄	1	2	yes	—
34	#15668009	Q₈	1	2	yes	—
35	C₄×D₃₅₆	—	4	2	no	—
36	C₄×D₃₅₆	—	4	2	no	—
37	#15667974	—	4	2	no	—
38	#15667974	—	4	2	no	—
39	C₂×C₄⋊Dic₈₉	—	2	1	no	—
40	C₂×C₄⋊Dic₈₉	—	2	1	no	—
41	C₂×C₄⋊Dic₈₉	—	2	1	no	—
42	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
43	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
44	C₂×#13083551	—	2	2	no	—
45	C₂×#13083551	—	2	2	no	—
46	C₂×#13083551	—	2	2	no	—
47	C₂×C₄×Dic₈₉	—	2	1	no	—
48	#15667946	—	4	2	no	—
49	#15667943	—	4	2	no	—
50	C₄⋊#10623494	—	2	1	no	—
51	C₄⋊#10623494	C₂×C₄	1	2	yes	complemented
52	#15667934	—	4	4	no	—
53	#15667919	—	2	1	no	—
54	C₂²×C₈×C₈₉	—	2	1	no	—
55	C₂²×C₈×C₈₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₈₉	—	2	1	no	—
59	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
60	C₄⋊C₈×C₈₉	—	2	1	no	—
61	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	complemented
62	C₄×C₈×C₈₉	—	2	1	no	—
63	C₄×C₈×C₈₉	—	2	1	no	—
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	C₂²×Dic₈₉	—	4	1	no	—
85	C₂×C₄×D₈₉	—	4	4	no	—
86	C₂×C₄×D₈₉	—	4	4	no	—
87	C₂×C₄×D₈₉	—	8	2	no	—
88	C₂×#10623494	—	2	2	no	—
89	C₂×#10623494	—	4	1	no	—
90	C₂×#10623494	—	4	1	no	—
91	C₄⋊Dic₈₉	—	2	1	no	—
92	C₄⋊Dic₈₉	—	2	1	no	—
93	C₄⋊Dic₈₉	—	2	1	no	—
94	C₄⋊Dic₈₉	—	4	2	no	—
95	C₄⋊Dic₈₉	—	4	1	no	—
96	C₄⋊Dic₈₉	—	4	1	no	—
97	C₄⋊Dic₈₉	—	4	1	no	—
98	C₄⋊Dic₈₉	—	4	1	no	—
99	C₄⋊Dic₈₉	SD₁₆	1	2	yes	—
100	#13083551	—	4	4	no	—
101	#13083551	—	4	4	no	—
102	#13083551	—	8	2	no	—
103	C₄×Dic₈₉	—	4	1	no	—
104	C₄×Dic₈₉	—	4	1	no	—
105	C₂²×C₄×C₈₉	—	2	1	no	—
106	C₂²×C₄×C₈₉	—	2	1	no	—
107	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₈₉	—	2	2	no	—
111	C₂×C₈×C₈₉	—	2	2	no	—
112	C₂×C₈×C₈₉	—	4	1	no	—
113	C₂×C₈×C₈₉	—	4	1	no	—
114	C₂×C₈×C₈₉	—	4	1	no	—
115	C₂×C₈×C₈₉	—	4	1	no	—
116	C₄⋊C₄×C₈₉	—	2	1	no	—
117	C₄⋊C₄×C₈₉	—	2	1	no	—
118	C₄⋊C₄×C₈₉	—	2	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	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
147	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
150	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
151	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
152	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
156	C₂×Dic₈₉	—	2	2	no	—
157	C₂×Dic₈₉	—	4	1	no	—
158	C₂×Dic₈₉	—	4	1	no	—
159	C₂×Dic₈₉	—	4	1	no	—
160	C₂×Dic₈₉	—	4	1	no	—
161	C₂×Dic₈₉	—	4	1	no	—
162	C₂×Dic₈₉	—	8	1	no	—
163	C₂×Dic₈₉	—	8	1	no	—
164	C₂×Dic₈₉	—	8	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	C₈×C₈₉	—	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	#449	1	1	yes	characteristic
182	C₂²×C₈₉	#450	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	C₄×D₈	1	1	yes	characteristic
198	C₄×C₈₉	C₄×SD₁₆	1	1	yes	characteristic
199	C₄×C₈₉	#440	1	1	yes	characteristic
200	C₄×C₈₉	#442	1	1	yes	characteristic
201	C₄×C₈₉	#474	1	1	yes	characteristic
202	C₄×C₈₉	#476	1	1	yes	characteristic
203	C₄×C₈₉	#478	1	1	yes	characteristic
204	C₄×C₈₉	#478	1	1	yes	characteristic
205	Dic₈₉	—	4	2	no	—
206	Dic₈₉	—	8	1	no	—
207	Dic₈₉	—	16	1	no	—
208	#8921	—	89	1	no	maximal, Sylow
209	C₂×C₈₉	#1621	1	1	yes	characteristic
210	C₂×C₈₉	#1631	1	1	yes	characteristic
211	C₂×C₈₉	#1639	1	1	yes	characteristic
212	C₂×C₈₉	#1640	1	1	yes	characteristic
213	C₂×C₈₉	#1856	1	1	yes	characteristic
214	C₂×C₈₉	#1862	1	1	yes	characteristic
215	C₂×C₈₉	#1864	1	1	yes	characteristic
216	D₈₉	—	8	4	no	—
217	#2366	—	89	1	no	—
218	#1957	—	89	1	no	—
219	#1948	—	89	1	no	—
220	#1947	—	89	1	no	—
221	C₂×#331	—	89	1	no	—
222	#1279	—	89	1	no	—
223	#1279	D₈₉	1	1	yes	characteristic, complemented
224	C₈₉	#8921	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	—	178	1	no	—
229	C₂×#106	—	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	C₂×D₈₉	1	1	yes	characteristic
234	#390	—	178	1	no	—
235	#390	—	178	1	no	—
236	#386	—	178	2	no	—
237	#384	—	89	1	no	—
238	C₄×C₄⋊C₄	—	89	1	no	—
239	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
240	#340	—	178	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	—	2	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	—	89	1	no	—
259	C₂×C₄⋊C₄	—	89	1	no	—
260	C₂×C₄⋊C₄	—	178	1	no	—
261	C₂×C₄⋊C₄	—	178	1	no	—
262	C₂×C₄⋊C₄	—	178	1	no	—
263	C₂×C₄⋊C₄	D₃₅₆	1	1	yes	characteristic
264	C₂×C₄⋊C₄	D₃₅₆	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	—	356	2	no	—
272	#106	—	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	—	2	1	no	—
279	C₄×C₈	—	2	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	—	356	4	no	—
302	C₂²×C₄	—	356	4	no	—
303	C₂²×C₄	—	356	1	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×D₃₅₆	1	1	yes	characteristic
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	356	1	no	—
317	C₂×C₈	—	356	1	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	—	89	2	no	—
323	C₄⋊C₄	—	356	2	no	—
324	C₄⋊C₄	—	356	1	no	—
325	C₄⋊C₄	—	356	1	no	—
326	C₄⋊C₄	—	356	1	no	—
327	C₄⋊C₄	—	356	1	no	—
328	C₄⋊C₄	—	178	1	no	—
329	C₄⋊C₄	—	178	1	no	—
330	C₄⋊C₄	—	178	1	no	—
331	C₄⋊C₄	D₇₁₂	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	#13083573	1	1	yes	characteristic
342	C₄²	#13083574	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	#15667982	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	—	356	1	no	—
370	C₂×C₄	—	356	1	no	—
371	C₂×C₄	—	356	1	no	—
372	C₂×C₄	—	356	1	no	—
373	C₂×C₄	—	356	1	no	—
374	C₂×C₄	—	178	2	no	—
375	C₂×C₄	—	712	8	no	—
376	C₂×C₄	—	712	1	no	—
377	C₂×C₄	—	712	1	no	—
378	C₂×C₄	—	712	1	no	—
379	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
380	C₂×C₄	#15667972	1	1	yes	characteristic
381	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
382	C₂×C₄	#15667990	1	1	yes	characteristic
383	C₂×C₄	#15667992	1	1	yes	characteristic
384	C₂×C₄	#15667994	1	1	yes	characteristic
385	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
386	C₂×C₄	SD₁₆×D₈₉	1	1	yes	characteristic
387	C₂×C₄	#15668034	1	1	yes	characteristic
388	C₂×C₄	#15668035	1	1	yes	characteristic
389	C₂×C₄	#15668036	1	1	yes	characteristic
390	C₂×C₄	#15668039	1	1	yes	characteristic
391	C₂×C₄	#15668040	1	1	yes	characteristic
392	C₂×C₄	#15668045	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	—	4	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	#19151472	1	1	yes	characteristic
404	C₂²	#19151734	1	1	yes	characteristic
405	C₂²	#19151746	1	1	yes	characteristic
406	C₂²	#19151750	1	1	yes	characteristic
407	C₂²	#19151762	1	1	yes	characteristic
408	C₂²	#19151767	1	1	yes	characteristic
409	C₂²	#19151777	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	—	356	2	no	—
415	C₄	—	1424	1	no	—
416	C₄	—	712	1	no	—
417	C₄	C₄×D₇₁₂	1	1	yes	characteristic
418	C₄	#19151683	1	1	yes	characteristic
419	C₄	#19151700	1	1	yes	characteristic
420	C₄	#19151707	1	1	yes	characteristic
421	C₄	#19151879	1	1	yes	characteristic
422	C₄	#19151887	1	1	yes	characteristic
423	C₄	#19151899	1	1	yes	characteristic
424	C₄	#19151901	1	1	yes	characteristic
425	C₂	—	712	4	no	—
426	C₂	#26019319	1	1	yes	characteristic
427	C₂	#26019382	1	1	yes	characteristic
428	C₂	#26019433	1	1	yes	characteristic
429	C₂	#26019441	1	1	yes	characteristic
430	C₂	#26020463	1	1	yes	characteristic
431	C₂	#26020502	1	1	yes	characteristic
432	C₂	#26020514	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#15667982
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1279	C₂
socle	C₂³×C₈₉	#120
prime radical	C₂×#15668009	C₂²
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1279	D₈₉
hypocenter	C₈₉	#8921
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
3. #26021015	C₂	semidirect
4. #26021011	C₂	semidirect
6. #26018092	C₂	semidirect
7. C₈₉×#1279	C₂	semidirect
22. #19151341	C₄	semidirect
51. C₄⋊#10623494	C₂×C₄	semidirect
61. C₄⋊C₈×C₈₉	C₂×C₄	semidirect
223. #1279	D₈₉	semidirect
224. C₈₉	#8921	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
#26021058	2
#26021015	2
#26021011	2
C₂×#19151341	2
#26018092	2
C₈₉×#1279	2
#8921	89