Subgroups — #36523677

Order 22784.

634 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029219	C₂	1	1	yes	maximal, characteristic
2	#26028918	C₂	1	1	yes	maximal, characteristic
3	#26019043	C₂	1	2	yes	maximal, complemented
4	#26019035	C₂	1	2	yes	maximal, complemented
5	#26019026	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019024	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019017	C₂	1	2	yes	maximal, complemented
8	#26019010	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019002	C₂	1	2	yes	maximal, complemented
10	C₂×#19151348	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2906	C₂	1	1	yes	maximal, characteristic
12	#19151729	C₄	1	1	yes	characteristic
13	#19151729	C₄	1	1	yes	characteristic
14	#19151676	C₄	1	1	yes	characteristic
15	#19151676	C₄	1	1	yes	characteristic
16	#19151670	C₄	1	2	yes	—
17	#19151670	C₄	1	2	yes	—
18	#19151659	—	2	2	no	—
19	#19151655	C₂²	1	2	yes	—
20	#19151651	C₂²	1	2	yes	—
21	#19151651	C₂²	1	1	yes	characteristic
22	#19151651	C₂²	1	2	yes	—
23	#19151622	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
25	#19151565	—	2	1	no	—
26	#19151554	—	2	1	no	—
27	C₄×#13083558	C₂²	1	2	yes	—
28	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
29	#19151350	C₂²	1	2	yes	—
30	#19151350	C₂²	1	2	yes	—
31	#19151350	C₂²	1	2	yes	—
32	#19151350	C₂²	1	2	yes	—
33	#19151348	C₂²	1	1	yes	characteristic
34	#19151348	C₂²	1	1	yes	characteristic
35	#19151348	C₂²	1	1	yes	characteristic
36	#19151348	C₂²	1	1	yes	characteristic
37	#19151348	C₂²	1	2	yes	—
38	#19151348	C₂²	1	2	yes	—
39	C₂×#131×C₈₉	—	2	1	no	—
40	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
41	#424×C₈₉	—	2	2	no	—
42	#424×C₈₉	—	2	1	no	—
43	#423×C₈₉	C₂²	1	1	yes	characteristic
44	#423×C₈₉	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083558	—	2	1	no	—
48	C₂×#13083558	C₂×C₄	1	2	yes	—
49	C₂×#13083558	C₂×C₄	1	2	yes	—
50	C₂²×#10623494	—	2	1	no	—
51	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
52	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
53	C₄⋊#10623494	—	2	1	no	—
54	C₄⋊#10623494	—	2	1	no	—
55	C₄⋊#10623494	C₂×C₄	1	2	yes	—
56	C₄⋊#10623494	C₂×C₄	1	2	yes	—
57	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
58	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
59	C₄⋊#10623494	C₂³	1	1	yes	characteristic
60	C₄⋊#10623494	C₂³	1	1	yes	characteristic
61	C₄⋊#10623494	C₂³	1	2	yes	—
62	C₂²⋊#10623494	—	2	2	no	—
63	C₂²⋊#10623494	—	2	2	no	—
64	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
65	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
66	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
67	#15667923	—	2	2	no	—
68	#15667923	C₂×C₄	1	2	yes	—
69	#15667923	C₂×C₄	1	2	yes	—
70	C₄×#10623494	—	2	2	no	—
71	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
72	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
73	C₄×#10623494	C₂³	1	1	yes	characteristic
74	C₄×#10623494	C₂³	1	2	yes	—
75	C₄×#10623494	C₂³	1	1	yes	characteristic
76	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
77	#131×C₈₉	—	4	4	no	—
78	C₂×M₁₆×C₈₉	—	2	2	no	—
79	C₂×M₁₆×C₈₉	—	2	1	no	—
80	C₂²×C₈×C₈₉	—	2	2	no	—
81	C₂²×C₈×C₈₉	—	2	1	no	—
82	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₈₉	Q₈	1	1	yes	characteristic
84	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
85	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
86	C₄×D₄×C₈₉	Q₈	1	2	yes	—
87	C₄×D₄×C₈₉	Q₈	1	1	yes	characteristic
88	#117×C₈₉	D₄	1	2	yes	—
89	#117×C₈₉	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
92	C₄⋊C₈×C₈₉	—	2	2	no	—
93	C₄⋊C₈×C₈₉	—	2	1	no	—
94	C₄⋊C₈×C₈₉	—	2	2	no	—
95	C₄⋊C₈×C₈₉	—	2	1	no	—
96	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
99	#13083558	—	2	4	no	—
100	#13083558	—	4	2	no	—
101	#13083558	—	4	2	no	—
102	C₂×#10623494	—	2	2	no	—
103	C₂×#10623494	—	2	1	no	—
104	C₂×#10623494	—	2	1	no	—
105	C₂×#10623494	—	2	2	no	—
106	C₂×#10623494	—	4	1	no	—
107	C₂×#10623494	—	4	2	no	—
108	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
109	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
110	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
111	C₂×#10623494	C₂²×C₄	1	2	yes	—
112	C₂×#10623494	C₂²×C₄	1	2	yes	—
113	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
114	#41×C₈₉	—	2	2	no	—
115	#41×C₈₉	—	2	2	no	—
116	C₂×Q₈×C₈₉	C₄⋊C₄	1	1	yes	characteristic
117	C₂×D₄×C₈₉	C₄⋊C₄	1	2	yes	—
118	C₂×D₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
124	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
125	M₁₆×C₈₉	—	4	4	no	—
126	M₁₆×C₈₉	—	4	2	no	—
127	C₂×C₈×C₈₉	—	2	1	no	—
128	C₂×C₈×C₈₉	—	2	2	no	—
129	C₂×C₈×C₈₉	—	2	1	no	—
130	C₂×C₈×C₈₉	—	4	4	no	—
131	C₂×C₈×C₈₉	—	4	2	no	—
132	C₄⋊C₄×C₈₉	C₄⋊C₄	1	2	yes	—
133	C₄⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
134	C₄⋊C₄×C₈₉	C₄⋊C₄	1	2	yes	—
135	C₄⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
136	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	2	yes	—
137	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	2	yes	—
138	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	2	yes	—
139	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
141	C₄²×C₈₉	C₂×D₄	1	2	yes	—
142	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
144	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
145	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
146	C₂³×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
147	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
148	Q₈×C₈₉	—	2	2	no	—
149	D₄×C₈₉	—	2	4	no	—
150	D₄×C₈₉	—	2	2	no	—
151	C₂×C₄×C₈₉	—	2	1	no	—
152	C₂×C₄×C₈₉	—	2	2	no	—
153	C₂×C₄×C₈₉	—	2	1	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	—	4	1	no	—
158	C₂×C₄×C₈₉	—	4	2	no	—
159	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₈₉	#137	1	2	yes	—
167	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
170	C₈×C₈₉	—	4	1	no	—
171	C₈×C₈₉	—	4	2	no	—
172	C₈×C₈₉	—	4	1	no	—
173	#10623494	—	2	1	no	—
174	#10623494	—	2	2	no	—
175	#10623494	—	2	1	no	—
176	#10623494	—	2	1	no	—
177	#10623494	—	2	2	no	—
178	#10623494	—	4	2	no	—
179	#10623494	—	4	1	no	—
180	#10623494	—	4	1	no	—
181	#10623494	#131	1	2	yes	complemented
182	C₂²×C₈₉	—	2	1	no	—
183	C₂²×C₈₉	—	2	1	no	—
184	C₂²×C₈₉	—	2	2	no	—
185	C₂²×C₈₉	—	2	2	no	—
186	C₂²×C₈₉	—	2	2	no	—
187	C₂²×C₈₉	#428	1	2	yes	—
188	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
189	C₄×C₈₉	—	2	1	no	—
190	C₄×C₈₉	—	2	2	no	—
191	C₄×C₈₉	—	2	2	no	—
192	C₄×C₈₉	—	2	1	no	—
193	C₄×C₈₉	—	2	1	no	—
194	C₄×C₈₉	—	2	2	no	—
195	C₄×C₈₉	#428	1	2	yes	—
196	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
197	C₄×C₈₉	#568	1	1	yes	characteristic
198	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
200	#17830	—	89	1	no	maximal, Sylow
201	C₂×C₈₉	—	2	2	no	—
202	C₂×C₈₉	—	4	2	no	—
203	C₂×C₈₉	#2906	1	1	yes	characteristic
204	C₂×C₈₉	C₂×#428	1	1	yes	characteristic
205	C₂×C₈₉	#2916	1	1	yes	characteristic
206	#2965	—	89	1	no	—
207	#2925	—	89	1	no	—
208	#2906	D₈₉	1	1	yes	characteristic
209	#1574	—	89	2	no	—
210	#1573	—	89	2	no	—
211	#1571	—	89	1	no	—
212	#1570	—	89	1	no	—
213	#1569	—	89	2	no	—
214	#1567	—	89	1	no	—
215	#1565	—	89	2	no	—
216	C₂×#334	—	89	1	no	—
217	C₈₉	#17830	1	1	yes	characteristic, complemented, Sylow
218	C₂×#131	—	2	1	no	—
219	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
220	#446	—	89	1	no	—
221	#446	—	89	1	no	—
222	#436	—	89	1	no	—
223	#436	—	89	1	no	—
224	#435	—	89	2	no	—
225	#435	—	89	2	no	—
226	#433	—	178	2	no	—
227	#432	—	89	2	no	—
228	#431	—	89	1	no	—
229	#431	—	89	2	no	—
230	#431	—	89	2	no	—
231	#424	—	2	1	no	—
232	#424	—	2	2	no	—
233	#423	—	89	1	no	—
234	#423	C₂×D₈₉	1	1	yes	characteristic
235	#423	C₂×D₈₉	1	2	yes	—
236	C₂×C₄⋊C₈	—	89	1	no	—
237	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
239	#408	—	178	1	no	—
240	#405	—	178	1	no	—
241	C₄×M₁₆	—	89	2	no	—
242	C₂×C₄×C₈	—	89	1	no	—
243	#335	—	89	2	no	—
244	#335	—	89	2	no	—
245	#335	—	89	2	no	—
246	#335	—	89	2	no	—
247	#334	—	89	1	no	—
248	#334	—	89	1	no	—
249	#334	—	89	1	no	—
250	#334	—	89	1	no	—
251	#334	—	89	2	no	—
252	#334	—	89	2	no	—
253	C₂×#41	C₂²⋊D₈₉	1	1	yes	characteristic
254	#131	—	4	4	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	89	2	no	—
258	C₂×M₁₆	—	89	2	no	—
259	C₂×M₁₆	—	178	1	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	89	1	no	—
263	C₂²×C₈	—	89	1	no	—
264	C₂²×C₈	—	178	1	no	—
265	C₄×Q₈	Dic₁₇₈	1	1	yes	characteristic
266	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
267	C₄×D₄	Dic₁₇₈	1	2	yes	—
268	C₄×D₄	Dic₁₇₈	1	1	yes	characteristic
269	C₄×D₄	C₄×D₈₉	1	2	yes	—
270	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
271	#117	C₂²⋊D₈₉	1	1	yes	characteristic
272	#117	C₂²⋊D₈₉	1	2	yes	—
273	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	89	2	no	—
280	C₄⋊C₈	—	89	2	no	—
281	C₄⋊C₈	—	89	1	no	—
282	C₄⋊C₈	—	89	1	no	—
283	C₄⋊C₈	—	89	1	no	—
284	C₄⋊C₈	—	89	1	no	—
285	C₄⋊C₈	—	89	2	no	—
286	C₄⋊C₈	—	178	1	no	—
287	C₄⋊C₈	—	178	1	no	—
288	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
289	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
291	C₂²⋊C₈	—	89	2	no	—
292	C₂²⋊C₈	—	89	2	no	—
293	C₂²⋊C₈	—	89	2	no	—
294	C₂²⋊C₈	—	178	2	no	—
295	C₂²⋊C₈	—	178	2	no	—
296	#97	—	89	2	no	—
297	#97	—	89	2	no	—
298	#97	—	178	2	no	—
299	C₄×C₈	—	89	1	no	—
300	C₄×C₈	—	89	1	no	—
301	C₄×C₈	—	89	1	no	—
302	C₄×C₈	—	89	1	no	—
303	C₄×C₈	—	89	2	no	—
304	C₄×C₈	—	178	2	no	—
305	#41	—	2	2	no	—
306	#41	—	2	2	no	—
307	C₂×Q₈	#13083553	1	1	yes	characteristic
308	C₂×D₄	#13083553	1	2	yes	—
309	C₂×D₄	#13083553	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
312	C₂²×C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
313	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
314	C₂²×C₄	C₂×Dic₁₇₈	1	2	yes	—
315	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
316	M₁₆	—	4	4	no	—
317	M₁₆	—	4	2	no	—
318	M₁₆	—	356	2	no	—
319	M₁₆	—	356	2	no	—
320	M₁₆	—	178	4	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	4	4	no	—
325	C₂×C₈	—	4	2	no	—
326	C₂×C₈	—	89	1	no	—
327	C₂×C₈	—	89	1	no	—
328	C₂×C₈	—	89	1	no	—
329	C₂×C₈	—	89	1	no	—
330	C₂×C₈	—	89	2	no	—
331	C₂×C₈	—	89	2	no	—
332	C₂×C₈	—	356	2	no	—
333	C₂×C₈	—	356	1	no	—
334	C₂×C₈	—	178	2	no	—
335	C₂×C₈	—	178	1	no	—
336	C₂×C₈	—	178	2	no	—
337	C₂×C₈	—	178	1	no	—
338	C₄⋊C₄	#13083553	1	2	yes	—
339	C₄⋊C₄	#13083553	1	1	yes	characteristic
340	C₄⋊C₄	#13083553	1	2	yes	—
341	C₄⋊C₄	#13083553	1	1	yes	characteristic
342	C₂²⋊C₄	#13083553	1	2	yes	—
343	C₂²⋊C₄	#13083553	1	2	yes	—
344	C₂²⋊C₄	#13083553	1	2	yes	—
345	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
346	C₄²	C₂×C₄×D₈₉	1	2	yes	—
347	C₄²	C₂×C₂²⋊D₈₉	1	2	yes	—
348	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
349	C₄²	C₂×Dic₁₇₈	1	2	yes	—
350	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
351	C₄²	C₂³×D₈₉	1	1	yes	characteristic
352	C₂³	C₂×#13083553	1	2	yes	—
353	C₂³	C₂×#13083553	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
366	C₂×C₄	C₂×#13083553	1	2	yes	—
367	C₂×C₄	C₂×#13083553	1	2	yes	—
368	C₂×C₄	C₂×#13083553	1	2	yes	—
369	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
370	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
371	C₂×C₄	#15668038	1	2	yes	—
372	C₂×C₄	#15668043	1	2	yes	—
373	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
375	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
376	C₈	—	4	1	no	—
377	C₈	—	4	2	no	—
378	C₈	—	4	1	no	—
379	C₈	—	89	2	no	—
380	C₈	—	356	2	no	—
381	C₈	—	356	1	no	—
382	C₈	—	356	1	no	—
383	C₈	—	178	1	no	—
384	C₈	—	178	2	no	—
385	C₈	—	178	1	no	—
386	C₈	—	178	1	no	—
387	C₈	—	178	2	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	#19151638	1	2	yes	—
394	C₂²	C₂²×#13083553	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	#19151638	1	2	yes	—
402	C₄	#131×D₈₉	1	1	yes	characteristic
403	C₄	#19152363	1	1	yes	characteristic
404	C₄	C₂×#15668038	1	1	yes	characteristic
405	C₄	C₂×#15668043	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	4	2	no	—
408	C₂	#26028818	1	1	yes	characteristic
409	C₂	C₂×#19151638	1	1	yes	characteristic
410	C₂	#26028861	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×#2906	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₈₉	D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2906	D₈₉
hypocenter	C₈₉	#17830
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2906

Complements

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

N	H ≅ G/N	type
3. #26019043	C₂	semidirect
4. #26019035	C₂	semidirect
5. #26019026	C₂	semidirect
6. #26019024	C₂	semidirect
7. #26019017	C₂	semidirect
8. #26019010	C₂	semidirect
9. #26019002	C₂	semidirect
10. C₂×#19151348	C₂	semidirect
181. #10623494	#131	semidirect
217. C₈₉	#17830	semidirect

Maximal subgroups

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

subgroup	index
#26029219	2
#26028918	2
#26019043	2
#26019035	2
#26019026	2
#26019024	2
#26019017	2
#26019010	2
#26019002	2
C₂×#19151348	2
C₈₉×#2906	2
#17830	89