Subgroups — #36537486

Order 22784.

778 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26031373	C₂	1	1	yes	maximal, characteristic, complemented
2	#26031170	C₂	1	1	yes	maximal, characteristic
3	#26028965	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019714	C₂	1	4	yes	maximal, complemented
5	#26019590	C₂	1	4	yes	maximal, complemented
6	#26019000	C₂	1	1	yes	maximal, characteristic, complemented
7	#26018924	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018920	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#492×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15668018	—	2	1	no	—
11	#19152148	C₂²	1	1	yes	characteristic
12	#19152001	—	2	1	no	—
13	#19151974	—	2	1	no	—
14	#19151946	—	2	1	no	—
15	#19151944	—	2	1	no	—
16	#19151911	—	2	2	no	—
17	#19151875	C₂²	1	4	yes	complemented
18	#19151790	C₂²	1	4	yes	—
19	#19151732	—	2	2	no	—
20	#19151677	—	2	1	no	—
21	#19151677	C₂²	1	2	yes	complemented
22	C₈×D₃₅₆	—	2	1	no	—
23	C₈×D₃₅₆	C₂²	1	2	yes	complemented
24	#19151651	C₂²	1	1	yes	characteristic
25	#19151651	C₂²	1	1	yes	characteristic
26	#19151622	C₂²	1	1	yes	characteristic
27	#19151564	—	2	1	no	—
28	#19151351	C₂²	1	2	yes	complemented
29	#19151349	C₂²	1	2	yes	complemented
30	#19151344	C₂²	1	4	yes	complemented
31	#19151342	C₂²	1	4	yes	—
32	C₂²×SD₁₆×C₈₉	—	2	1	no	—
33	C₂²×SD₁₆×C₈₉	—	2	1	no	—
34	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
36	#492×C₈₉	—	2	1	no	—
37	#492×C₈₉	—	2	1	no	—
38	#492×C₈₉	C₂²	1	2	yes	—
39	#492×C₈₉	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#13083574	—	2	1	no	—
42	C₂×#13083559	—	2	4	no	—
43	#15668018	—	4	4	no	—
44	C₂×#13083558	—	2	1	no	—
45	C₂×#13083557	—	2	2	no	—
46	C₂×C₈×D₈₉	—	2	2	no	—
47	#15668012	D₄	1	1	yes	characteristic
48	#15668009	D₄	1	1	yes	characteristic
49	#15668000	—	2	1	no	—
50	#15667986	—	2	1	no	—
51	#15667986	D₄	1	2	yes	—
52	C₄×D₃₅₆	—	2	1	no	—
53	C₄×D₃₅₆	C₂³	1	2	yes	—
54	#15667945	—	2	4	no	—
55	C₄⋊#10623494	—	2	1	no	—
56	C₄⋊#10623494	C₂³	1	2	yes	—
57	C₄⋊#10623494	C₂³	1	2	yes	—
58	C₄⋊#10623494	C₂³	1	2	yes	—
59	#15667933	—	2	4	no	—
60	#15667932	—	2	4	no	—
61	C₂²⋊#10623494	—	2	1	no	—
62	C₂²⋊#10623494	—	2	1	no	—
63	#15667924	—	2	2	no	—
64	#15667924	—	2	2	no	—
65	C₄×#10623494	—	2	1	no	—
66	C₄×#10623494	—	2	1	no	—
67	C₂²×Q₈×C₈₉	—	2	1	no	—
68	C₂²×D₄×C₈₉	—	2	1	no	—
69	C₂²×D₄×C₈₉	—	2	1	no	—
70	C₂²×D₄×C₈₉	—	2	1	no	—
71	C₂×SD₁₆×C₈₉	—	2	2	no	—
72	C₂×SD₁₆×C₈₉	—	2	2	no	—
73	C₂×SD₁₆×C₈₉	—	2	2	no	—
74	C₂×SD₁₆×C₈₉	—	2	2	no	—
75	C₂×SD₁₆×C₈₉	—	4	4	no	—
76	C₂×SD₁₆×C₈₉	—	4	4	no	—
77	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
79	C₄⋊Q₈×C₈₉	—	2	1	no	—
80	C₄⋊Q₈×C₈₉	—	2	1	no	—
81	C₄⋊Q₈×C₈₉	—	2	1	no	—
82	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
83	#127×C₈₉	—	2	1	no	—
84	#127×C₈₉	—	2	1	no	—
85	#127×C₈₉	—	2	1	no	—
86	#127×C₈₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
89	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
91	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	#13083574	—	4	2	no	—
95	#13083574	—	4	2	no	—
96	C₂×Dic₁₇₈	—	2	1	no	—
97	C₂×D₃₅₆	—	2	1	no	—
98	C₂×D₃₅₆	—	2	1	no	—
99	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
100	C₂×C₂²⋊D₈₉	—	2	2	no	—
101	C₂×C₄×D₈₉	—	2	2	no	—
102	#13083559	—	8	4	no	—
103	#13083558	—	4	2	no	—
104	#13083557	—	4	4	no	—
105	C₂×#10623494	—	2	2	no	—
106	C₂×#10623494	—	2	2	no	—
107	C₂×#10623494	—	2	2	no	—
108	C₈×D₈₉	—	4	4	no	—
109	C₄⋊Dic₈₉	—	2	1	no	—
110	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
111	#13083551	—	2	2	no	—
112	#13083551	—	2	2	no	—
113	C₂⁴×C₈₉	—	4	1	no	—
114	C₂×Q₈×C₈₉	—	2	2	no	—
115	C₂×Q₈×C₈₉	—	4	1	no	—
116	C₂×Q₈×C₈₉	—	4	2	no	—
117	C₂×Q₈×C₈₉	—	4	2	no	—
118	C₂×D₄×C₈₉	—	2	2	no	—
119	C₂×D₄×C₈₉	—	2	2	no	—
120	C₂×D₄×C₈₉	—	2	2	no	—
121	C₂×D₄×C₈₉	—	4	1	no	—
122	C₂×D₄×C₈₉	—	4	1	no	—
123	C₂×D₄×C₈₉	—	4	1	no	—
124	C₂×D₄×C₈₉	—	4	2	no	—
125	C₂×D₄×C₈₉	—	4	2	no	—
126	C₂×D₄×C₈₉	—	8	2	no	—
127	C₂×D₄×C₈₉	—	8	2	no	—
128	C₂²×C₄×C₈₉	—	4	1	no	—
129	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
132	SD₁₆×C₈₉	—	4	4	no	—
133	SD₁₆×C₈₉	—	4	4	no	—
134	SD₁₆×C₈₉	—	4	4	no	—
135	SD₁₆×C₈₉	—	4	4	no	—
136	C₂×C₈×C₈₉	—	2	2	no	—
137	C₂×C₈×C₈₉	D₈	1	4	yes	complemented
138	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₄⋊C₄×C₈₉	—	2	2	no	—
143	C₄⋊C₄×C₈₉	—	2	2	no	—
144	C₄⋊C₄×C₈₉	—	4	1	no	—
145	C₄⋊C₄×C₈₉	—	4	1	no	—
146	C₄²×C₈₉	C₂×D₄	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	—	4	2	no	—
151	C₂³×C₈₉	—	8	2	no	—
152	C₂³×C₈₉	—	8	2	no	—
153	C₂³×C₈₉	—	8	2	no	—
154	C₂³×C₈₉	#121	1	1	yes	characteristic
155	C₂²×D₈₉	—	2	2	no	—
156	Q₈×C₈₉	—	4	2	no	—
157	Q₈×C₈₉	—	4	2	no	—
158	Q₈×C₈₉	—	8	2	no	—
159	D₄×C₈₉	—	4	2	no	—
160	D₄×C₈₉	—	4	2	no	—
161	D₄×C₈₉	—	4	4	no	—
162	D₄×C₈₉	—	8	2	no	—
163	D₄×C₈₉	—	8	2	no	—
164	D₄×C₈₉	—	8	2	no	—
165	D₄×C₈₉	—	8	2	no	—
166	C₂×C₄×C₈₉	—	2	2	no	—
167	C₂×C₄×C₈₉	—	2	2	no	—
168	C₂×C₄×C₈₉	—	4	2	no	—
169	C₂×C₄×C₈₉	—	8	2	no	—
170	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
174	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
175	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
178	C₂²⋊D₈₉	—	4	4	no	—
179	C₂×Dic₈₉	—	2	2	no	—
180	D₃₅₆	—	2	4	no	—
181	D₃₅₆	—	4	2	no	—
182	D₃₅₆	—	4	2	no	—
183	C₄×D₈₉	—	4	2	no	—
184	C₄×D₈₉	—	4	2	no	—
185	Dic₁₇₈	—	4	2	no	—
186	C₈×C₈₉	—	2	1	no	—
187	C₈×C₈₉	—	2	1	no	—
188	C₈×C₈₉	C₂×D₈	1	2	yes	—
189	C₈×C₈₉	C₂×D₈	1	2	yes	—
190	#10623494	—	4	2	no	—
191	#10623494	—	4	2	no	—
192	#10623494	—	4	2	no	—
193	C₂²×C₈₉	—	2	1	no	—
194	C₂²×C₈₉	—	2	1	no	—
195	C₂²×C₈₉	—	8	2	no	—
196	C₂²×C₈₉	—	8	2	no	—
197	C₂²×C₈₉	—	8	2	no	—
198	C₂²×C₈₉	—	16	4	no	—
199	C₂²×C₈₉	#459	1	2	yes	—
200	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
201	C₂×D₈₉	—	4	2	no	—
202	C₂×D₈₉	—	4	2	no	—
203	C₂×D₈₉	—	4	2	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	8	2	no	—
207	C₄×C₈₉	#459	1	2	yes	—
208	C₄×C₈₉	#471	1	2	yes	—
209	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
210	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₄×C₈₉	#577	1	2	yes	—
212	Dic₈₉	—	4	2	no	—
213	#19186	—	89	1	no	maximal, Sylow
214	C₂×C₈₉	—	2	2	no	—
215	C₂×C₈₉	—	16	2	no	—
216	C₂×C₈₉	C₂×#459	1	1	yes	characteristic
217	C₂×C₈₉	#3057	1	1	yes	characteristic
218	C₂×C₈₉	C₂×#471	1	1	yes	characteristic
219	D₈₉	—	8	2	no	—
220	#3226	—	89	1	no	—
221	#3205	—	89	1	no	—
222	C₂×#492	D₈₉	1	1	yes	characteristic, complemented
223	#2931	—	89	1	no	—
224	#1685	—	89	4	no	—
225	#1665	—	89	4	no	—
226	#1564	—	89	1	no	—
227	#1546	—	89	1	no	—
228	#1545	—	89	1	no	—
229	C₈₉	#19186	1	1	yes	characteristic, complemented, Sylow
230	C₂²×SD₁₆	—	2	1	no	—
231	C₂²×SD₁₆	—	2	1	no	—
232	C₂×#131	—	178	1	no	—
233	#532	—	89	1	no	—
234	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
235	C₂×#127	C₂×D₈₉	1	1	yes	characteristic
236	#500	—	178	1	no	—
237	#493	—	178	1	no	—
238	#492	—	2	1	no	—
239	#492	—	2	1	no	—
240	#492	C₂×D₈₉	1	2	yes	—
241	#492	C₂×D₈₉	1	2	yes	—
242	#486	—	178	1	no	—
243	#486	—	178	1	no	—
244	#480	—	178	2	no	—
245	#474	—	89	4	no	—
246	#459	—	89	4	no	—
247	#447	—	178	2	no	—
248	#436	—	89	2	no	—
249	#436	—	178	1	no	—
250	C₈×D₄	—	89	2	no	—
251	C₈×D₄	—	178	1	no	—
252	#431	—	89	1	no	—
253	#431	—	89	1	no	—
254	#423	—	89	1	no	—
255	#408	—	178	1	no	—
256	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
257	#335	—	89	2	no	—
258	#334	—	89	2	no	—
259	#332	—	89	4	no	—
260	#331	—	89	4	no	—
261	C₂×#41	—	178	1	no	—
262	C₂²×Q₈	—	2	1	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂×SD₁₆	—	2	2	no	—
267	C₂×SD₁₆	—	2	2	no	—
268	C₂×SD₁₆	—	2	2	no	—
269	C₂×SD₁₆	—	2	2	no	—
270	C₂×SD₁₆	—	4	4	no	—
271	C₂×SD₁₆	—	4	4	no	—
272	C₂×D₈	—	178	4	no	—
273	#131	—	356	4	no	—
274	C₂×M₁₆	—	178	1	no	—
275	C₂×M₁₆	—	178	2	no	—
276	C₂²×C₈	—	178	2	no	—
277	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
278	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
279	C₄⋊Q₈	—	2	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	89	1	no	—
283	C₄⋊Q₈	C₂²×D₈₉	1	2	yes	—
284	#127	—	2	1	no	—
285	#127	—	2	1	no	—
286	#127	—	2	1	no	—
287	#127	—	89	1	no	—
288	#127	C₂²×D₈₉	1	2	yes	—
289	#124	—	178	1	no	—
290	#121	—	89	2	no	—
291	#121	—	178	1	no	—
292	C₄×D₄	—	89	2	no	—
293	C₄×D₄	—	178	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
297	#107	—	178	4	no	—
298	C₄⋊C₈	—	89	2	no	—
299	C₄⋊C₈	—	89	2	no	—
300	C₄⋊C₈	—	89	2	no	—
301	C₄⋊C₈	—	178	1	no	—
302	#102	—	178	4	no	—
303	#102	—	178	4	no	—
304	C₂²⋊C₈	—	178	1	no	—
305	C₂²⋊C₈	—	178	1	no	—
306	C₂²⋊C₈	—	178	2	no	—
307	C₂²⋊C₈	—	178	2	no	—
308	C₄×C₈	—	178	1	no	—
309	C₄×C₈	—	178	1	no	—
310	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
311	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
314	C₂⁴	—	4	1	no	—
315	#41	—	356	2	no	—
316	#41	—	356	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	4	1	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	178	1	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	2	no	—
330	C₂×D₄	—	8	2	no	—
331	C₂×D₄	—	8	2	no	—
332	C₂×D₄	—	89	2	no	—
333	C₂×D₄	—	178	2	no	—
334	C₂×D₄	—	178	1	no	—
335	C₂×D₄	—	178	1	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	—	178	2	no	—
338	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
340	C₂²×C₄	#13083573	1	1	yes	characteristic
341	SD₁₆	—	4	4	no	—
342	SD₁₆	—	4	4	no	—
343	SD₁₆	—	4	4	no	—
344	SD₁₆	—	4	4	no	—
345	D₈	—	712	4	no	—
346	M₁₆	—	356	2	no	—
347	M₁₆	—	356	4	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	356	4	no	—
350	C₂×C₈	—	178	2	no	—
351	C₂×C₈	—	178	2	no	—
352	C₂×C₈	—	178	2	no	—
353	C₂×C₈	#13083559	1	4	yes	complemented
354	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
355	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
356	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
357	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	89	2	no	—
363	C₄⋊C₄	—	178	1	no	—
364	C₂²⋊C₄	—	178	2	no	—
365	C₂²⋊C₄	—	178	2	no	—
366	C₄²	D₄×D₈₉	1	1	yes	characteristic
367	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
368	C₄²	#13083573	1	1	yes	characteristic
369	C₄²	C₂³×D₈₉	1	1	yes	characteristic
370	C₂³	—	4	2	no	—
371	C₂³	—	8	2	no	—
372	C₂³	—	8	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	178	2	no	—
375	C₂³	#15667983	1	1	yes	characteristic
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	8	2	no	—
379	Q₈	—	356	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	4	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	2	no	—
384	D₄	—	8	2	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	2	no	—
387	D₄	—	356	4	no	—
388	D₄	—	356	2	no	—
389	D₄	—	356	2	no	—
390	D₄	—	178	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	—	356	2	no	—
396	C₂×C₄	—	356	2	no	—
397	C₂×C₄	—	178	2	no	—
398	C₂×C₄	#15667983	1	1	yes	characteristic
399	C₂×C₄	#15667983	1	1	yes	characteristic
400	C₂×C₄	#15667983	1	1	yes	characteristic
401	C₂×C₄	C₂×#13083559	1	2	yes	—
402	C₂×C₄	#15668038	1	2	yes	—
403	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
404	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
405	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
406	C₈	—	2	1	no	—
407	C₈	—	2	1	no	—
408	C₈	—	356	2	no	—
409	C₈	—	356	2	no	—
410	C₈	—	356	2	no	—
411	C₈	C₂×#13083559	1	2	yes	—
412	C₈	C₂×#13083559	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	16	4	no	—
419	C₂²	—	356	2	no	—
420	C₂²	—	356	2	no	—
421	C₂²	—	356	2	no	—
422	C₂²	#19151790	1	2	yes	—
423	C₂²	C₂×#15667983	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	8	2	no	—
427	C₄	—	356	2	no	—
428	C₄	#19151790	1	2	yes	—
429	C₄	#19151858	1	2	yes	—
430	C₄	C₂²×#13083559	1	1	yes	characteristic
431	C₄	C₂×#15668038	1	1	yes	characteristic
432	C₄	#19152404	1	2	yes	—
433	C₂	—	2	2	no	—
434	C₂	—	16	2	no	—
435	C₂	—	712	2	no	—
436	C₂	C₂×#19151790	1	1	yes	characteristic
437	C₂	#26029887	1	1	yes	characteristic
438	C₂	C₂×#19151858	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667983
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×#492×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#26031170	C₂
hypercenter	C₂×#492	D₈₉
hypocenter	C₈₉	#19186
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#492

Complements

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

N	H ≅ G/N	type
1. #26031373	C₂	semidirect
3. #26028965	C₂	semidirect
4. #26019714	C₂	semidirect
5. #26019590	C₂	semidirect
6. #26019000	C₂	semidirect
7. #26018924	C₂	semidirect
8. #26018920	C₂	semidirect
9. C₂×#492×C₈₉	C₂	semidirect
17. #19151875	C₂²	semidirect
21. #19151677	C₂²	semidirect
23. C₈×D₃₅₆	C₂²	semidirect
28. #19151351	C₂²	semidirect
29. #19151349	C₂²	semidirect
30. #19151344	C₂²	semidirect
137. C₂×C₈×C₈₉	D₈	semidirect
222. C₂×#492	D₈₉	semidirect
229. C₈₉	#19186	semidirect
353. C₂×C₈	#13083559	semidirect

Maximal subgroups

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

subgroup	index
#26031373	2
#26031170	2
#26028965	2
#26019714	2
#26019590	2
#26019000	2
#26018924	2
#26018920	2
C₂×#492×C₈₉	2
#19186	89