Subgroups — #36525645

Order 22784.

598 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030323	C₂	1	1	yes	maximal, characteristic
2	#26029353	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019140	C₂	1	2	yes	maximal, complemented
4	#26019128	C₂	1	2	yes	maximal, complemented
5	#26019123	C₂	1	2	yes	maximal, complemented
6	C₈×#13083564	C₂	1	2	yes	maximal, complemented
7	#26019043	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018706	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018634	C₂	1	1	yes	maximal, characteristic
10	#26018536	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2991	C₂	1	1	yes	maximal, characteristic
12	#19152155	C₂²	1	1	yes	characteristic
13	#19151939	C₄	1	2	yes	—
14	#19151883	C₄	1	1	yes	characteristic
15	#19151878	C₄	1	1	yes	characteristic
16	#19151808	C₄	1	1	yes	characteristic
17	#19151803	C₄	1	1	yes	characteristic
18	#19151760	C₄	1	2	yes	—
19	#19151728	C₂²	1	2	yes	—
20	#19151725	—	2	1	no	—
21	C₈×Dic₁₇₈	C₂²	1	2	yes	—
22	#19151722	—	2	1	no	—
23	C₄×#13083564	C₂²	1	2	yes	—
24	C₄×#13083562	C₂²	1	2	yes	—
25	#19151656	—	2	2	no	—
26	#19151651	C₂²	1	1	yes	characteristic
27	#19151651	C₂²	1	1	yes	characteristic
28	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
29	#19151350	C₂²	1	2	yes	—
30	#19151348	C₂²	1	2	yes	—
31	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
32	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
33	#19151328	C₂²	1	2	yes	—
34	#19151328	C₂²	1	2	yes	—
35	D₄⋊#10623494	C₂²	1	1	yes	characteristic
36	D₄⋊#10623494	C₂²	1	1	yes	characteristic
37	#19151320	C₂²	1	2	yes	—
38	C₈×#10623494	C₂²	1	2	yes	—
39	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₈₉	C₂²	1	2	yes	—
41	#436×C₈₉	—	2	2	no	—
42	#436×C₈₉	C₂²	1	2	yes	—
43	#431×C₈₉	—	2	1	no	—
44	#431×C₈₉	C₂²	1	1	yes	characteristic
45	#423×C₈₉	—	2	1	no	—
46	#423×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083564	C₂×C₄	1	2	yes	—
48	C₂×#13083562	C₂×C₄	1	2	yes	—
49	C₂²×#10623494	—	2	1	no	—
50	#15668012	C₂×C₄	1	1	yes	characteristic
51	#15668012	C₂×C₄	1	1	yes	characteristic
52	#15668004	—	2	1	no	—
53	#15667991	—	2	1	no	—
54	#15667991	C₂×C₄	1	2	yes	—
55	C₄×Dic₁₇₈	—	2	1	no	—
56	C₄×Dic₁₇₈	C₂³	1	2	yes	—
57	#15667971	—	2	1	no	—
58	#15667945	C₂×C₄	1	2	yes	—
59	#15667943	C₂×C₄	1	2	yes	—
60	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
61	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
62	C₄⋊#10623494	C₂³	1	1	yes	characteristic
63	C₄⋊#10623494	C₂³	1	1	yes	characteristic
64	#15667941	—	2	2	no	—
65	#15667941	—	2	2	no	—
66	#15667936	C₂×C₄	1	2	yes	—
67	#15667935	C₂×C₄	1	2	yes	—
68	#15667935	C₂×C₄	1	2	yes	—
69	#15667933	C₂×C₄	1	2	yes	—
70	C₂²⋊#10623494	—	2	1	no	—
71	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
72	#15667922	—	2	2	no	—
73	C₄×#10623494	—	2	1	no	—
74	C₄×#10623494	—	2	1	no	—
75	C₄×#10623494	C₂³	1	1	yes	characteristic
76	C₄×#10623494	C₂³	1	1	yes	characteristic
77	C₄×#10623494	C₂³	1	2	yes	—
78	C₈×Dic₈₉	—	2	2	no	—
79	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₂×M₁₆×C₈₉	—	2	1	no	—
81	C₂×M₁₆×C₈₉	—	2	2	no	—
82	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₈₉	—	2	1	no	—
85	C₄×D₄×C₈₉	—	2	1	no	—
86	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
87	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
88	#117×C₈₉	—	2	1	no	—
89	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₈₉	—	2	1	no	—
91	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₈₉	—	2	2	no	—
93	C₄⋊C₈×C₈₉	—	2	1	no	—
94	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
95	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
96	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
97	C₂²⋊C₈×C₈₉	—	2	2	no	—
98	C₂²⋊C₈×C₈₉	D₄	1	2	yes	—
99	C₄×C₈×C₈₉	—	2	2	no	—
100	C₄×C₈×C₈₉	C₂³	1	2	yes	—
101	C₂×Dic₁₇₈	—	2	1	no	—
102	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
103	#13083564	—	2	4	no	—
104	#13083562	—	4	2	no	—
105	C₂×#10623494	—	2	4	no	—
106	C₂×#10623494	—	2	1	no	—
107	C₂×#10623494	—	2	1	no	—
108	C₂×#10623494	—	2	1	no	—
109	C₂×#10623494	—	2	1	no	—
110	C₂×#10623494	C₂²×C₄	1	2	yes	—
111	C₂×#10623494	C₂²×C₄	1	2	yes	—
112	C₄⋊Dic₈₉	—	2	1	no	—
113	C₄⋊Dic₈₉	—	2	1	no	—
114	C₄⋊Dic₈₉	—	2	1	no	—
115	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
116	#13083553	—	2	2	no	—
117	#13083553	—	2	2	no	—
118	C₂²⋊Dic₈₉	—	2	2	no	—
119	C₄×Dic₈₉	—	2	2	no	—
120	#41×C₈₉	—	2	2	no	—
121	#41×C₈₉	—	4	1	no	—
122	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂×D₄×C₈₉	—	2	1	no	—
124	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	—	2	1	no	—
126	C₂²×C₄×C₈₉	—	2	1	no	—
127	C₂²×C₄×C₈₉	—	2	1	no	—
128	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
131	M₁₆×C₈₉	—	8	2	no	—
132	M₁₆×C₈₉	—	8	1	no	—
133	C₂×C₈×C₈₉	—	2	2	no	—
134	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₈₉	—	2	1	no	—
137	C₄⋊C₄×C₈₉	—	2	1	no	—
138	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²⋊C₄×C₈₉	—	2	1	no	—
141	C₂²⋊C₄×C₈₉	—	2	1	no	—
142	C₂²⋊C₄×C₈₉	—	2	1	no	—
143	C₄²×C₈₉	—	2	1	no	—
144	C₄²×C₈₉	—	2	1	no	—
145	C₄²×C₈₉	—	2	1	no	—
146	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₈₉	#41	1	1	yes	characteristic
149	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
150	C₂³×C₈₉	—	2	1	no	—
151	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
152	Q₈×C₈₉	—	2	1	no	—
153	Q₈×C₈₉	#131	1	2	yes	—
154	D₄×C₈₉	—	2	1	no	—
155	D₄×C₈₉	—	2	1	no	—
156	D₄×C₈₉	—	4	2	no	—
157	C₂×C₄×C₈₉	—	2	1	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	4	2	no	—
166	C₂×C₄×C₈₉	—	4	1	no	—
167	C₂×C₄×C₈₉	—	4	1	no	—
168	C₂×C₄×C₈₉	—	4	2	no	—
169	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
175	C₂×Dic₈₉	—	2	2	no	—
176	C₂×Dic₈₉	—	2	2	no	—
177	Dic₁₇₈	—	2	2	no	—
178	Dic₁₇₈	—	2	2	no	—
179	Dic₁₇₈	—	4	2	no	—
180	C₈×C₈₉	—	2	2	no	—
181	C₈×C₈₉	—	2	2	no	—
182	C₈×C₈₉	—	4	2	no	—
183	#10623494	—	2	2	no	—
184	#10623494	—	2	2	no	—
185	#10623494	—	2	2	no	—
186	#10623494	—	2	2	no	—
187	#10623494	—	4	1	no	—
188	#10623494	—	4	1	no	—
189	C₂²×C₈₉	—	2	1	no	—
190	C₂²×C₈₉	—	2	1	no	—
191	C₂²×C₈₉	—	2	1	no	—
192	C₂²×C₈₉	—	4	1	no	—
193	C₂²×C₈₉	—	4	1	no	—
194	C₂²×C₈₉	—	4	1	no	—
195	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
196	C₄×C₈₉	—	2	1	no	—
197	C₄×C₈₉	—	2	2	no	—
198	C₄×C₈₉	—	2	1	no	—
199	C₄×C₈₉	—	2	1	no	—
200	C₄×C₈₉	—	4	1	no	—
201	C₄×C₈₉	—	4	1	no	—
202	C₄×C₈₉	#443	1	2	yes	—
203	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
204	C₄×C₈₉	#568	1	1	yes	characteristic
205	C₄×C₈₉	#577	1	1	yes	characteristic
206	C₄×C₈₉	#578	1	1	yes	characteristic
207	Dic₈₉	—	4	2	no	—
208	Dic₈₉	—	4	2	no	—
209	#18019	—	89	1	no	maximal, Sylow
210	C₂×C₈₉	—	4	1	no	—
211	C₂×C₈₉	—	8	1	no	—
212	C₂×C₈₉	#2933	1	1	yes	characteristic
213	C₂×C₈₉	#2947	1	1	yes	characteristic
214	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
215	#3107	—	89	1	no	—
216	#2991	D₈₉	1	1	yes	characteristic
217	#2986	—	89	1	no	—
218	#1590	—	89	2	no	—
219	#1588	—	89	2	no	—
220	#1587	—	89	2	no	—
221	C₈×Q₁₆	—	89	2	no	—
222	#1574	—	89	1	no	—
223	#1493	—	89	1	no	—
224	#1476	—	89	1	no	—
225	#1450	—	89	1	no	—
226	C₈₉	#18019	1	1	yes	characteristic, complemented, Sylow
227	#533	—	89	1	no	—
228	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
229	#485	—	89	2	no	—
230	#475	—	89	1	no	—
231	#474	—	89	1	no	—
232	#462	—	89	1	no	—
233	#461	—	89	1	no	—
234	#452	—	89	2	no	—
235	#446	—	89	2	no	—
236	#446	—	178	1	no	—
237	C₈×Q₈	—	89	2	no	—
238	C₈×Q₈	—	178	1	no	—
239	C₈×Q₈	C₂×D₈₉	1	2	yes	—
240	C₄×Q₁₆	—	89	2	no	—
241	C₄×SD₁₆	—	89	2	no	—
242	#436	—	2	2	no	—
243	#436	C₂×D₈₉	1	2	yes	—
244	#433	—	178	2	no	—
245	#431	—	2	1	no	—
246	#431	—	89	1	no	—
247	#431	—	89	1	no	—
248	#431	C₂×D₈₉	1	1	yes	characteristic
249	#423	—	2	1	no	—
250	#423	C₂×D₈₉	1	1	yes	characteristic
251	C₂×C₄×C₈	—	89	1	no	—
252	#335	—	89	2	no	—
253	#334	—	89	2	no	—
254	Q₈⋊C₈	—	89	1	no	—
255	Q₈⋊C₈	—	89	1	no	—
256	Q₈⋊C₈	—	89	2	no	—
257	Q₈⋊C₈	—	89	2	no	—
258	D₄⋊C₈	—	89	1	no	—
259	D₄⋊C₈	—	89	1	no	—
260	#322	—	89	2	no	—
261	C₈²	—	89	2	no	—
262	C₂×#41	C₄×D₈₉	1	1	yes	characteristic
263	C₂×Q₁₆	—	89	2	no	—
264	C₂×SD₁₆	—	89	2	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	2	no	—
267	C₂²×C₈	—	178	1	no	—
268	C₄⋊Q₈	—	89	1	no	—
269	C₄⋊Q₈	—	89	1	no	—
270	#125	—	178	1	no	—
271	C₂²⋊Q₈	—	89	2	no	—
272	C₂²⋊Q₈	—	178	1	no	—
273	C₄×Q₈	—	89	2	no	—
274	C₄×Q₈	—	178	1	no	—
275	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
276	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
280	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
281	#117	—	2	1	no	—
282	#117	—	178	1	no	—
283	#117	C₄×D₈₉	1	1	yes	characteristic
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
286	#107	—	89	2	no	—
287	#106	—	89	2	no	—
288	C₄⋊C₈	—	2	2	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	89	1	no	—
291	C₄⋊C₈	—	89	1	no	—
292	C₄⋊C₈	—	89	1	no	—
293	C₄⋊C₈	—	89	1	no	—
294	C₄⋊C₈	—	178	2	no	—
295	C₄⋊C₈	—	178	2	no	—
296	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
297	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
298	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
299	#103	—	89	2	no	—
300	#103	—	89	2	no	—
301	#103	—	89	2	no	—
302	#102	—	89	2	no	—
303	C₂²⋊C₈	—	2	2	no	—
304	C₂²⋊C₈	—	89	2	no	—
305	C₂²⋊C₈	—	178	1	no	—
306	C₂²⋊C₈	C₂²⋊D₈₉	1	2	yes	—
307	#97	—	178	2	no	—
308	C₄×C₈	—	2	2	no	—
309	C₄×C₈	—	89	2	no	—
310	C₄×C₈	—	89	1	no	—
311	C₄×C₈	—	89	1	no	—
312	C₄×C₈	—	178	2	no	—
313	C₄×C₈	—	178	1	no	—
314	C₄×C₈	—	178	1	no	—
315	C₄×C₈	C₂²×D₈₉	1	2	yes	—
316	#41	—	2	2	no	—
317	#41	—	4	1	no	—
318	C₂×Q₈	—	89	2	no	—
319	C₂×Q₈	—	178	1	no	—
320	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
328	C₂²×C₄	#13083574	1	1	yes	characteristic
329	Q₁₆	—	178	4	no	—
330	SD₁₆	—	356	2	no	—
331	M₁₆	—	8	2	no	—
332	M₁₆	—	8	1	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	89	2	no	—
335	C₂×C₈	—	89	2	no	—
336	C₂×C₈	—	178	1	no	—
337	C₂×C₈	—	178	1	no	—
338	C₂×C₈	—	178	4	no	—
339	C₂×C₈	—	178	1	no	—
340	C₂×C₈	—	178	1	no	—
341	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
342	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	89	2	no	—
346	C₄⋊C₄	—	178	1	no	—
347	C₄⋊C₄	—	178	1	no	—
348	C₄⋊C₄	—	178	2	no	—
349	C₄⋊C₄	—	178	1	no	—
350	C₄⋊C₄	—	178	2	no	—
351	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
352	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	178	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	178	2	no	—
361	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
362	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
363	C₄²	#13083574	1	1	yes	characteristic
364	C₄²	C₂³×D₈₉	1	1	yes	characteristic
365	C₂³	—	2	1	no	—
366	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
367	Q₈	—	2	1	no	—
368	Q₈	—	356	2	no	—
369	Q₈	—	178	2	no	—
370	Q₈	—	178	2	no	—
371	Q₈	#15668020	1	2	yes	—
372	D₄	—	2	1	no	—
373	D₄	—	2	1	no	—
374	D₄	—	4	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	178	2	no	—
388	C₂×C₄	—	178	2	no	—
389	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
390	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
391	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
394	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	356	1	no	—
399	C₈	—	356	1	no	—
400	C₈	—	178	2	no	—
401	C₈	—	178	2	no	—
402	C₈	—	178	2	no	—
403	C₈	—	178	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	356	2	no	—
418	C₄	—	356	2	no	—
419	C₄	#19151713	1	2	yes	—
420	C₄	C₂×#15668020	1	1	yes	characteristic
421	C₄	#19152364	1	1	yes	characteristic
422	C₄	#19152409	1	1	yes	characteristic
423	C₄	#19152413	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	8	1	no	—
426	C₂	#26028977	1	1	yes	characteristic
427	C₂	#26029091	1	1	yes	characteristic
428	C₂	C₂×#19151713	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2991	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#41×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2991	D₈₉
hypocenter	C₈₉	#18019
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2991

Complements

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

N	H ≅ G/N	type
2. #26029353	C₂	semidirect
3. #26019140	C₂	semidirect
4. #26019128	C₂	semidirect
5. #26019123	C₂	semidirect
6. C₈×#13083564	C₂	semidirect
7. #26019043	C₂	semidirect
8. #26018706	C₂	semidirect
10. #26018536	C₂	semidirect
226. C₈₉	#18019	semidirect

Maximal subgroups

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

subgroup	index
#26030323	2
#26029353	2
#26019140	2
#26019128	2
#26019123	2
C₈×#13083564	2
#26019043	2
#26018706	2
#26018634	2
#26018536	2
C₈₉×#2991	2
#18019	89