Subgroups — #36449183

Order 22784.

592 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151889	C₂	1	1	yes	maximal, characteristic
2	#26023203	C₂	1	1	yes	maximal, characteristic
3	#26021199	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021053	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#19151325	C₂	1	1	yes	maximal, characteristic
6	#26018091	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15668012	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
10	C₂×#15667970	—	2	1	no	—
11	#19151889	—	2	2	no	—
12	#19151889	C₄	1	4	yes	complemented
13	C₂×#15667944	—	2	1	no	—
14	C₂×#15667935	—	2	2	no	—
15	C₂×#15667934	—	2	1	no	—
16	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
17	#19151499	—	2	1	no	—
18	#19151488	—	2	2	no	—
19	#19151455	—	2	1	no	—
20	C₄⋊C₄×Dic₈₉	—	2	1	no	—
21	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
22	#19151361	—	2	1	no	—
23	#19151361	—	2	1	no	—
24	#19151325	—	2	2	no	—
25	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
27	#384×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×Dic₁₇₈	—	2	1	no	—
29	C₂²×D₃₅₆	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₈₉	—	2	1	no	—
31	C₂²×#10623494	—	2	1	no	—
32	#15668012	—	2	1	no	—
33	#15668012	—	2	1	no	—
34	#15668012	—	2	1	no	—
35	#15668012	C₂×C₄	1	2	yes	—
36	C₄×D₃₅₆	—	2	1	no	—
37	C₄×D₃₅₆	—	2	1	no	—
38	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
39	C₄×D₃₅₆	D₄	1	2	yes	—
40	#15667970	—	4	2	no	—
41	#15667970	—	4	2	no	—
42	C₂×C₄⋊Dic₈₉	—	2	1	no	—
43	C₂×C₄⋊Dic₈₉	—	2	1	no	—
44	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
45	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
46	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
47	C₂×#13083551	—	2	2	no	—
48	C₂×#13083551	—	2	2	no	—
49	C₂×#13083551	—	2	1	no	—
50	C₂×C₄×Dic₈₉	—	2	2	no	—
51	C₂×C₄×Dic₈₉	—	2	1	no	—
52	#15667944	—	2	4	no	—
53	#15667935	—	4	4	no	—
54	#15667934	—	2	4	no	—
55	C₄×#10623494	—	2	1	no	—
56	C₄×#10623494	—	2	1	no	—
57	#15667919	—	2	2	no	—
58	#15667919	—	2	1	no	—
59	C₂²×C₈×C₈₉	—	2	1	no	—
60	C₂²×C₈×C₈₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
64	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
65	C₄⋊C₈×C₈₉	—	2	1	no	—
66	C₄⋊C₈×C₈₉	—	2	1	no	—
67	C₄⋊C₈×C₈₉	—	2	1	no	—
68	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
69	C₂³×D₈₉	—	2	1	no	—
70	C₂×Dic₁₇₈	—	2	2	no	—
71	C₂×Dic₁₇₈	—	4	2	no	—
72	C₂×Dic₁₇₈	—	4	2	no	—
73	C₂×Dic₁₇₈	—	4	1	no	—
74	C₂×D₃₅₆	—	2	1	no	—
75	C₂×D₃₅₆	—	2	1	no	—
76	C₂×D₃₅₆	—	2	1	no	—
77	C₂×D₃₅₆	—	2	1	no	—
78	C₂×D₃₅₆	—	2	1	no	—
79	C₂×D₃₅₆	C₂²⋊C₄	1	2	yes	—
80	C₂²×Dic₈₉	—	2	1	no	—
81	C₂²×Dic₈₉	—	2	1	no	—
82	C₂²×Dic₈₉	—	2	1	no	—
83	C₂²×Dic₈₉	—	4	1	no	—
84	C₂×C₄×D₈₉	—	2	2	no	—
85	C₂×C₄×D₈₉	—	2	2	no	—
86	C₂×C₄×D₈₉	—	4	1	no	—
87	C₂×C₄×D₈₉	—	4	1	no	—
88	C₂×C₄×D₈₉	—	4	1	no	—
89	C₂×C₄×D₈₉	—	4	1	no	—
90	C₂×#10623494	—	2	2	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	2	no	—
96	C₄⋊Dic₈₉	—	2	2	no	—
97	C₄⋊Dic₈₉	—	2	1	no	—
98	C₄⋊Dic₈₉	—	2	1	no	—
99	C₄⋊Dic₈₉	—	4	1	no	—
100	C₄⋊Dic₈₉	—	4	1	no	—
101	C₄⋊Dic₈₉	C₂²⋊C₄	1	2	yes	—
102	C₄⋊Dic₈₉	SD₁₆	1	2	yes	—
103	#13083551	—	2	2	no	—
104	#13083551	—	2	2	no	—
105	#13083551	—	4	4	no	—
106	#13083551	—	8	2	no	—
107	C₄×Dic₈₉	—	4	4	no	—
108	C₄×Dic₈₉	—	4	1	no	—
109	C₄×Dic₈₉	—	4	1	no	—
110	C₂²×C₄×C₈₉	—	2	2	no	—
111	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₈₉	—	2	2	no	—
115	C₂×C₈×C₈₉	—	4	1	no	—
116	C₂×C₈×C₈₉	—	4	1	no	—
117	C₂×C₈×C₈₉	—	4	1	no	—
118	C₂×C₈×C₈₉	—	4	1	no	—
119	C₂×C₈×C₈₉	—	4	1	no	—
120	C₄⋊C₄×C₈₉	—	4	2	no	—
121	C₄⋊C₄×C₈₉	—	4	1	no	—
122	C₄⋊C₄×C₈₉	—	4	1	no	—
123	C₄⋊C₄×C₈₉	—	4	1	no	—
124	C₄⋊C₄×C₈₉	—	4	1	no	—
125	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₈₉	#41	1	1	yes	characteristic
128	C₄²×C₈₉	#41	1	1	yes	characteristic
129	C₂³×C₈₉	#120	1	1	yes	characteristic
130	C₂²×D₈₉	—	2	2	no	—
131	C₂²×D₈₉	—	4	1	no	—
132	C₂²×D₈₉	—	4	1	no	—
133	C₂²×D₈₉	—	4	1	no	—
134	C₂²×D₈₉	—	4	1	no	—
135	C₂²×D₈₉	—	4	1	no	—
136	C₂²×D₈₉	—	4	1	no	—
137	C₂×C₄×C₈₉	—	2	1	no	—
138	C₂×C₄×C₈₉	—	2	1	no	—
139	C₂×C₄×C₈₉	—	4	2	no	—
140	C₂×C₄×C₈₉	—	4	2	no	—
141	C₂×C₄×C₈₉	—	4	2	no	—
142	C₂×C₄×C₈₉	C₂×C₂²⋊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	#121	1	1	yes	characteristic
146	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
147	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
149	C₂×C₄×C₈₉	#135	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	#137	1	1	yes	characteristic
154	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
155	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
156	C₂×Dic₈₉	—	2	2	no	—
157	C₂×Dic₈₉	—	2	2	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	—	4	2	no	—
163	C₂×Dic₈₉	—	4	1	no	—
164	C₂×Dic₈₉	—	4	1	no	—
165	C₂×Dic₈₉	—	4	1	no	—
166	C₂×Dic₈₉	—	8	1	no	—
167	C₂×Dic₈₉	—	8	1	no	—
168	D₃₅₆	—	2	2	no	—
169	D₃₅₆	—	2	2	no	—
170	D₃₅₆	—	4	1	no	—
171	D₃₅₆	—	4	1	no	—
172	C₄×D₈₉	—	4	2	no	—
173	C₄×D₈₉	—	4	2	no	—
174	C₄×D₈₉	—	4	2	no	—
175	C₄×D₈₉	—	4	2	no	—
176	Dic₁₇₈	—	4	4	no	—
177	Dic₁₇₈	—	8	2	no	—
178	C₈×C₈₉	—	4	2	no	—
179	C₈×C₈₉	—	8	1	no	—
180	#10623494	—	4	2	no	—
181	C₂²×C₈₉	#386	1	1	yes	characteristic
182	C₂²×C₈₉	#450	1	1	yes	characteristic
183	C₂²×C₈₉	#452	1	1	yes	characteristic
184	C₂²×C₈₉	#452	1	1	yes	characteristic
185	C₂²×C₈₉	#452	1	1	yes	characteristic
186	C₂²×C₈₉	#453	1	1	yes	characteristic
187	C₂²×C₈₉	#454	1	1	yes	characteristic
188	C₂×D₈₉	—	4	2	no	—
189	C₂×D₈₉	—	4	2	no	—
190	C₂×D₈₉	—	4	2	no	—
191	C₂×D₈₉	—	8	1	no	—
192	C₂×D₈₉	—	8	1	no	—
193	C₂×D₈₉	—	8	1	no	—
194	C₂×D₈₉	—	8	1	no	—
195	C₄×C₈₉	—	2	1	no	—
196	C₄×C₈₉	—	2	1	no	—
197	C₄×C₈₉	—	8	2	no	—
198	C₄×C₈₉	#416	1	1	yes	characteristic
199	C₄×C₈₉	#419	1	1	yes	characteristic
200	C₄×C₈₉	C₄×SD₁₆	1	1	yes	characteristic
201	C₄×C₈₉	#440	1	1	yes	characteristic
202	C₄×C₈₉	#461	1	1	yes	characteristic
203	C₄×C₈₉	#463	1	1	yes	characteristic
204	C₄×C₈₉	#485	1	1	yes	characteristic
205	C₄×C₈₉	#485	1	1	yes	characteristic
206	Dic₈₉	—	4	2	no	—
207	Dic₈₉	—	4	2	no	—
208	Dic₈₉	—	8	2	no	—
209	Dic₈₉	—	8	1	no	—
210	#8976	—	89	1	no	maximal, Sylow
211	C₂×C₈₉	#1631	1	1	yes	characteristic
212	C₂×C₈₉	#1634	1	1	yes	characteristic
213	C₂×C₈₉	#1635	1	1	yes	characteristic
214	C₂×C₈₉	#1638	1	1	yes	characteristic
215	C₂×C₈₉	#1873	1	1	yes	characteristic
216	C₂×C₈₉	#1877	1	1	yes	characteristic
217	C₂×C₈₉	#1883	1	1	yes	characteristic
218	D₈₉	—	8	2	no	—
219	C₂×#476	—	89	1	no	—
220	#2354	—	89	1	no	—
221	#1987	—	89	1	no	—
222	#1956	—	89	1	no	—
223	C₂×D₄⋊C₈	—	89	1	no	—
224	#1296	D₈₉	1	1	yes	characteristic, complemented
225	#1279	—	89	1	no	—
226	C₈₉	#8976	1	1	yes	characteristic, complemented, Sylow
227	C₂×C₄⋊Q₈	—	89	1	no	—
228	C₂×C₄×D₄	—	89	1	no	—
229	C₂×#117	—	178	1	no	—
230	#476	—	89	4	no	—
231	#476	—	178	2	no	—
232	C₂×#106	—	178	1	no	—
233	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
235	C₂×#103	—	178	2	no	—
236	C₂×#102	—	178	1	no	—
237	C₂×C₄×C₈	—	89	1	no	—
238	#390	—	178	1	no	—
239	#388	—	178	2	no	—
240	#384	C₂×D₈₉	1	1	yes	characteristic
241	#380	—	178	1	no	—
242	C₄×C₄⋊C₄	—	89	1	no	—
243	C₄×C₄⋊C₄	—	178	1	no	—
244	#340	—	178	1	no	—
245	#340	—	178	1	no	—
246	D₄⋊C₈	—	178	2	no	—
247	C₂²×Q₈	—	178	1	no	—
248	C₂²×D₄	—	89	1	no	—
249	C₂³×C₄	—	178	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	178	1	no	—
253	C₄⋊Q₈	—	89	2	no	—
254	C₄⋊Q₈	—	178	1	no	—
255	C₄⋊Q₈	—	178	1	no	—
256	C₄⋊Q₈	—	178	1	no	—
257	C₄×D₄	—	89	2	no	—
258	C₄×D₄	—	89	2	no	—
259	C₄×D₄	—	178	1	no	—
260	C₄×D₄	—	178	1	no	—
261	#117	—	356	2	no	—
262	#117	—	356	2	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	89	1	no	—
266	C₂×C₄⋊C₄	—	89	1	no	—
267	C₂×C₄⋊C₄	—	89	1	no	—
268	C₂×C₄⋊C₄	—	178	1	no	—
269	C₂×C₄⋊C₄	—	178	1	no	—
270	C₂×C₄⋊C₄	D₃₅₆	1	2	yes	—
271	C₂×C₂²⋊C₄	—	178	2	no	—
272	C₂×C₂²⋊C₄	—	178	1	no	—
273	C₂×C₂²⋊C₄	—	178	2	no	—
274	C₂×C₄²	—	178	2	no	—
275	C₂×C₄²	—	178	1	no	—
276	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
277	#106	—	178	4	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
282	#103	—	356	4	no	—
283	#102	—	178	4	no	—
284	C₄×C₈	—	178	1	no	—
285	C₄×C₈	—	178	1	no	—
286	#95	—	178	2	no	—
287	#95	—	178	1	no	—
288	C₂⁴	—	178	1	no	—
289	C₂×Q₈	—	356	2	no	—
290	C₂×Q₈	—	356	2	no	—
291	C₂×Q₈	—	356	1	no	—
292	C₂×Q₈	—	178	2	no	—
293	C₂×D₄	—	89	2	no	—
294	C₂×D₄	—	178	1	no	—
295	C₂×D₄	—	178	1	no	—
296	C₂×D₄	—	178	1	no	—
297	C₂×D₄	—	178	1	no	—
298	C₂×D₄	—	178	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	356	1	no	—
301	C₂²×C₄	—	356	1	no	—
302	C₂²×C₄	—	356	1	no	—
303	C₂²×C₄	—	356	1	no	—
304	C₂²×C₄	—	356	1	no	—
305	C₂²×C₄	—	178	1	no	—
306	C₂²×C₄	—	178	1	no	—
307	C₂²×C₄	—	178	1	no	—
308	C₂²×C₄	—	178	2	no	—
309	C₂²×C₄	—	178	2	no	—
310	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
311	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	356	1	no	—
320	C₂×C₈	—	356	1	no	—
321	C₂×C₈	—	178	2	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	—	89	2	no	—
329	C₄⋊C₄	—	356	1	no	—
330	C₄⋊C₄	—	356	1	no	—
331	C₄⋊C₄	—	178	2	no	—
332	C₄⋊C₄	—	178	1	no	—
333	C₄⋊C₄	—	178	1	no	—
334	C₄⋊C₄	—	178	2	no	—
335	C₄⋊C₄	—	178	1	no	—
336	C₄⋊C₄	—	178	1	no	—
337	C₂²⋊C₄	—	356	4	no	—
338	C₂²⋊C₄	—	178	2	no	—
339	C₂²⋊C₄	—	178	2	no	—
340	C₂²⋊C₄	—	712	2	no	—
341	C₄²	—	356	4	no	—
342	C₄²	—	356	1	no	—
343	C₄²	—	356	1	no	—
344	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
345	C₄²	D₄×D₈₉	1	1	yes	characteristic
346	C₄²	#13083574	1	1	yes	characteristic
347	C₄²	#13083575	1	1	yes	characteristic
348	C₂³	—	356	1	no	—
349	C₂³	—	356	1	no	—
350	C₂³	—	356	1	no	—
351	C₂³	—	356	1	no	—
352	C₂³	—	356	1	no	—
353	C₂³	—	356	1	no	—
354	C₂³	—	178	2	no	—
355	C₂³	#15667982	1	1	yes	characteristic
356	Q₈	—	356	4	no	—
357	Q₈	—	712	2	no	—
358	D₄	—	356	1	no	—
359	D₄	—	356	1	no	—
360	D₄	—	178	2	no	—
361	D₄	—	178	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	356	1	no	—
368	C₂×C₄	—	356	1	no	—
369	C₂×C₄	—	356	1	no	—
370	C₂×C₄	—	356	1	no	—
371	C₂×C₄	—	356	2	no	—
372	C₂×C₄	—	356	2	no	—
373	C₂×C₄	—	356	2	no	—
374	C₂×C₄	—	356	2	no	—
375	C₂×C₄	—	356	2	no	—
376	C₂×C₄	—	356	1	no	—
377	C₂×C₄	—	356	1	no	—
378	C₂×C₄	—	356	1	no	—
379	C₂×C₄	—	178	2	no	—
380	C₂×C₄	—	178	2	no	—
381	C₂×C₄	—	712	1	no	—
382	C₂×C₄	—	712	1	no	—
383	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
384	C₂×C₄	#15667974	1	1	yes	characteristic
385	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
386	C₂×C₄	#15667985	1	1	yes	characteristic
387	C₂×C₄	#15667987	1	1	yes	characteristic
388	C₂×C₄	#15667997	1	1	yes	characteristic
389	C₂×C₄	SD₁₆×D₈₉	1	1	yes	characteristic
390	C₂×C₄	#15668031	1	1	yes	characteristic
391	C₂×C₄	#15668033	1	1	yes	characteristic
392	C₂×C₄	#15668033	1	1	yes	characteristic
393	C₂×C₄	#15668036	1	1	yes	characteristic
394	C₂×C₄	#15668041	1	1	yes	characteristic
395	C₂×C₄	#15668044	1	1	yes	characteristic
396	C₂×C₄	#15668044	1	1	yes	characteristic
397	C₈	—	4	2	no	—
398	C₈	—	8	1	no	—
399	C₈	—	356	2	no	—
400	C₂²	—	356	2	no	—
401	C₂²	—	356	2	no	—
402	C₂²	—	356	2	no	—
403	C₂²	—	712	1	no	—
404	C₂²	—	712	1	no	—
405	C₂²	—	712	1	no	—
406	C₂²	—	712	1	no	—
407	C₂²	#19151476	1	1	yes	characteristic
408	C₂²	#19151750	1	1	yes	characteristic
409	C₂²	#19151761	1	1	yes	characteristic
410	C₂²	#19151763	1	1	yes	characteristic
411	C₂²	#19151763	1	1	yes	characteristic
412	C₂²	#19151768	1	1	yes	characteristic
413	C₂²	#19151773	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	8	2	no	—
417	C₄	—	356	2	no	—
418	C₄	—	356	2	no	—
419	C₄	—	712	2	no	—
420	C₄	—	712	1	no	—
421	C₄	#19151591	1	1	yes	characteristic
422	C₄	#19151605	1	1	yes	characteristic
423	C₄	#19151685	1	1	yes	characteristic
424	C₄	#19151697	1	1	yes	characteristic
425	C₄	#19151802	1	1	yes	characteristic
426	C₄	#19151812	1	1	yes	characteristic
427	C₄	#19151941	1	1	yes	characteristic
428	C₄	#19151942	1	1	yes	characteristic
429	C₂	—	712	2	no	—
430	C₂	#26019380	1	1	yes	characteristic
431	C₂	#26019398	1	1	yes	characteristic
432	C₂	#26019404	1	1	yes	characteristic
433	C₂	#26019425	1	1	yes	characteristic
434	C₂	#26020563	1	1	yes	characteristic
435	C₂	#26020587	1	1	yes	characteristic
436	C₂	#26020627	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#15667982
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1296	C₂
socle	C₂³×C₈₉	#120
prime radical	C₂²×D₃₅₆	D₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1296	D₈₉
hypocenter	C₈₉	#8976
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
3. #26021199	C₂	semidirect
4. #26021053	C₂	semidirect
6. #26018091	C₂	semidirect
7. C₈₉×#1296	C₂	semidirect
12. #19151889	C₄	semidirect
224. #1296	D₈₉	semidirect
226. C₈₉	#8976	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151889	2
#26023203	2
#26021199	2
#26021053	2
C₂×#19151325	2
#26018091	2
C₈₉×#1296	2
#8976	89