Subgroups — #36537139

Order 22784.

704 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030831	C₂	1	1	yes	maximal, characteristic, complemented
2	#26029709	C₂	1	2	yes	maximal, complemented
3	#26029218	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019821	C₂	1	2	yes	maximal, complemented
5	#26019814	C₂	1	2	yes	maximal, complemented
6	#26019771	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019766	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019737	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019732	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018902	C₂	1	2	yes	maximal, complemented
11	C₂×#334×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668034	—	2	2	no	—
13	#19152148	C₂²	1	2	yes	—
14	C₄×#13083574	C₂²	1	1	yes	characteristic
15	#19152003	C₂²	1	1	yes	characteristic
16	#19151975	C₂²	1	1	yes	characteristic
17	#19151945	C₂²	1	2	yes	—
18	#19151834	—	2	1	no	—
19	#19151834	—	2	1	no	—
20	#19151821	—	2	2	no	—
21	#19151814	—	2	2	no	—
22	#19151809	C₂²	1	2	yes	—
23	#19151804	C₂²	1	2	yes	—
24	#19151799	C₂²	1	2	yes	—
25	#19151794	C₂²	1	2	yes	—
26	#19151728	C₂²	1	1	yes	characteristic
27	#19151728	C₂²	1	1	yes	characteristic
28	C₄×D₇₁₂	—	2	1	no	—
29	C₄×D₇₁₂	—	2	1	no	—
30	#19151677	C₂²	1	1	yes	characteristic
31	#19151677	C₂²	1	1	yes	characteristic
32	#19151669	—	2	1	no	—
33	#19151669	—	2	1	no	—
34	#19151651	C₂²	1	1	yes	characteristic
35	#19151649	—	2	1	no	—
36	#19151595	—	2	2	no	—
37	C₄×#13083557	—	2	1	no	—
38	#19151345	C₂²	1	2	yes	—
39	#19151345	C₂²	1	2	yes	—
40	#19151341	C₂²	1	2	yes	—
41	#19151341	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
44	#334×C₈₉	C₂²	1	1	yes	characteristic
45	#334×C₈₉	C₂²	1	1	yes	characteristic
46	#334×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083574	—	2	2	no	—
48	C₂×#13083574	D₄	1	1	yes	characteristic
49	#15668034	—	4	8	no	—
50	C₂×Dic₃₅₆	—	2	2	no	—
51	C₂×#13083563	—	2	2	no	—
52	C₂×#13083563	—	2	2	no	—
53	C₂×D₇₁₂	—	2	2	no	—
54	C₂×D₇₁₂	—	2	1	no	—
55	C₂×D₇₁₂	—	2	1	no	—
56	C₂×#13083557	—	2	1	no	—
57	C₂×#13083557	—	2	1	no	—
58	#15668012	C₂³	1	2	yes	—
59	#15668009	C₂³	1	2	yes	—
60	#15668000	—	2	2	no	—
61	#15667986	—	2	2	no	—
62	#15667986	—	2	2	no	—
63	C₄×Dic₁₇₈	D₄	1	1	yes	characteristic
64	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
65	C₄×D₃₅₆	—	2	2	no	—
66	C₄×D₃₅₆	—	2	2	no	—
67	C₄×D₃₅₆	D₄	1	1	yes	characteristic
68	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
69	C₄×C₂²⋊D₈₉	—	2	1	no	—
70	C₄×C₂²⋊D₈₉	—	2	1	no	—
71	#15667971	D₄	1	1	yes	characteristic
72	#15667969	—	2	1	no	—
73	C₄²×D₈₉	—	2	1	no	—
74	#15667946	—	2	1	no	—
75	#15667946	—	2	1	no	—
76	C₄⋊#10623494	C₂³	1	1	yes	characteristic
77	C₄⋊#10623494	C₂³	1	1	yes	characteristic
78	#15667941	—	2	1	no	—
79	#15667941	—	2	1	no	—
80	#15667937	—	2	2	no	—
81	#15667937	—	2	2	no	—
82	#15667934	—	2	2	no	—
83	#15667934	—	2	2	no	—
84	#15667934	—	2	2	no	—
85	#15667934	—	2	2	no	—
86	C₂²⋊#10623494	—	2	1	no	—
87	#15667924	—	2	1	no	—
88	#15667924	—	2	1	no	—
89	#15667922	—	2	1	no	—
90	#15667922	—	2	1	no	—
91	C₄×#10623494	—	2	1	no	—
92	C₂²×C₈×C₈₉	—	2	2	no	—
93	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
94	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₈₉	—	2	2	no	—
97	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
98	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
99	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
100	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
101	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
103	#13083574	—	2	4	no	—
104	#13083574	—	4	4	no	—
105	#13083574	—	4	4	no	—
106	C₂×Dic₁₇₈	—	2	2	no	—
107	C₂×Dic₁₇₈	C₂×D₄	1	1	yes	characteristic
108	C₂×D₃₅₆	—	2	2	no	—
109	C₂×D₃₅₆	—	2	2	no	—
110	C₂×D₃₅₆	—	2	2	no	—
111	C₂×D₃₅₆	C₂×D₄	1	1	yes	characteristic
112	C₂×C₂²⋊D₈₉	—	2	1	no	—
113	C₂×C₂²⋊D₈₉	—	4	2	no	—
114	C₂×C₄×D₈₉	—	2	1	no	—
115	C₂×C₄×D₈₉	—	2	1	no	—
116	C₂×C₄×D₈₉	—	2	1	no	—
117	C₂×C₄×D₈₉	—	4	2	no	—
118	Dic₃₅₆	—	4	4	no	—
119	#13083563	—	4	4	no	—
120	#13083563	—	4	4	no	—
121	D₇₁₂	—	4	2	no	—
122	D₇₁₂	—	4	4	no	—
123	D₇₁₂	—	4	2	no	—
124	#13083557	—	4	2	no	—
125	#13083557	—	4	2	no	—
126	C₂×#10623494	—	2	1	no	—
127	C₂×#10623494	—	2	1	no	—
128	C₄⋊Dic₈₉	—	2	2	no	—
129	C₄⋊Dic₈₉	—	2	2	no	—
130	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
131	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
132	#13083553	—	2	1	no	—
133	#13083553	—	2	1	no	—
134	C₂²⋊Dic₈₉	—	2	1	no	—
135	#13083551	—	2	1	no	—
136	#13083551	—	2	1	no	—
137	#13083551	—	4	2	no	—
138	#13083551	—	4	2	no	—
139	C₄×Dic₈₉	—	2	1	no	—
140	C₄×Dic₈₉	—	2	1	no	—
141	C₄×Dic₈₉	—	2	1	no	—
142	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
145	C₂×C₈×C₈₉	—	2	2	no	—
146	C₂×C₈×C₈₉	—	2	2	no	—
147	C₂×C₈×C₈₉	—	2	2	no	—
148	C₂×C₈×C₈₉	—	4	1	no	—
149	C₂×C₈×C₈₉	—	4	4	no	—
150	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₈₉	#41	1	1	yes	characteristic
157	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
158	C₂³×C₈₉	#121	1	1	yes	characteristic
159	C₂²×D₈₉	—	2	1	no	—
160	C₂²×D₈₉	—	4	2	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	4	1	no	—
164	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
165	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	4	yes	—
168	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
171	C₂²⋊D₈₉	—	4	2	no	—
172	C₂²⋊D₈₉	—	8	4	no	—
173	C₂×Dic₈₉	—	2	1	no	—
174	C₂×Dic₈₉	—	2	1	no	—
175	C₂×Dic₈₉	—	2	1	no	—
176	C₂×Dic₈₉	—	4	2	no	—
177	D₃₅₆	—	2	2	no	—
178	D₃₅₆	—	4	2	no	—
179	D₃₅₆	—	4	2	no	—
180	D₃₅₆	—	4	2	no	—
181	D₃₅₆	—	4	2	no	—
182	D₃₅₆	—	8	2	no	—
183	C₄×D₈₉	—	4	2	no	—
184	C₄×D₈₉	—	4	1	no	—
185	C₄×D₈₉	—	4	1	no	—
186	C₄×D₈₉	—	4	2	no	—
187	C₄×D₈₉	—	8	4	no	—
188	Dic₁₇₈	—	2	2	no	—
189	Dic₁₇₈	—	4	2	no	—
190	Dic₁₇₈	—	4	2	no	—
191	C₈×C₈₉	—	2	1	no	—
192	C₈×C₈₉	—	2	1	no	—
193	C₈×C₈₉	—	2	1	no	—
194	C₈×C₈₉	—	4	2	no	—
195	C₈×C₈₉	—	4	2	no	—
196	C₈×C₈₉	#135	1	2	yes	complemented
197	#10623494	—	4	1	no	—
198	#10623494	—	4	1	no	—
199	C₂²×C₈₉	—	2	1	no	—
200	C₂²×C₈₉	—	2	1	no	—
201	C₂²×C₈₉	#469	1	2	yes	—
202	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
203	C₂×D₈₉	—	4	1	no	—
204	C₂×D₈₉	—	4	1	no	—
205	C₂×D₈₉	—	4	1	no	—
206	C₂×D₈₉	—	8	2	no	—
207	C₂×D₈₉	—	8	2	no	—
208	C₂×D₈₉	—	8	2	no	—
209	C₄×C₈₉	—	2	1	no	—
210	C₄×C₈₉	—	2	1	no	—
211	C₄×C₈₉	—	2	1	no	—
212	C₄×C₈₉	#469	1	2	yes	—
213	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
214	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
215	C₄×C₈₉	#575	1	1	yes	characteristic
216	Dic₈₉	—	4	1	no	—
217	Dic₈₉	—	4	1	no	—
218	Dic₈₉	—	4	1	no	—
219	Dic₈₉	—	8	2	no	—
220	#19157	—	89	1	no	maximal, Sylow
221	C₂×C₈₉	—	2	2	no	—
222	C₂×C₈₉	#3035	1	1	yes	characteristic
223	C₂×C₈₉	C₂×#469	1	1	yes	characteristic
224	C₂×C₈₉	#3067	1	1	yes	characteristic
225	D₈₉	—	8	1	no	—
226	D₈₉	—	16	2	no	—
227	#3169	—	89	1	no	—
228	#3035	—	89	2	no	—
229	#2965	—	89	1	no	—
230	#1702	—	89	2	no	—
231	#1701	—	89	2	no	—
232	#1694	—	89	1	no	—
233	#1693	—	89	1	no	—
234	#1688	—	89	1	no	—
235	#1687	—	89	1	no	—
236	C₂×#334	D₈₉	1	1	yes	characteristic, complemented
237	#1540	—	89	2	no	—
238	C₈₉	#19157	1	1	yes	characteristic, complemented, Sylow
239	C₂×#135	—	178	2	no	—
240	#532	—	89	2	no	—
241	C₄×#41	—	89	1	no	—
242	#500	—	89	1	no	—
243	#493	—	89	1	no	—
244	#486	—	89	2	no	—
245	#466	—	178	1	no	—
246	#466	—	178	1	no	—
247	#464	—	178	2	no	—
248	#463	—	178	2	no	—
249	#462	—	89	2	no	—
250	#461	—	89	2	no	—
251	#460	—	89	2	no	—
252	#459	—	89	2	no	—
253	#446	—	89	1	no	—
254	#446	—	89	1	no	—
255	C₄×D₈	—	178	1	no	—
256	C₄×D₈	—	178	1	no	—
257	#436	—	89	1	no	—
258	#436	—	89	1	no	—
259	#435	—	178	1	no	—
260	#435	—	178	1	no	—
261	#431	—	89	1	no	—
262	#431	—	178	1	no	—
263	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
264	#416	—	178	2	no	—
265	C₄×M₁₆	—	178	1	no	—
266	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
267	#334	C₂×D₈₉	1	1	yes	characteristic
268	#334	C₂×D₈₉	1	1	yes	characteristic
269	#334	C₂×D₈₉	1	2	yes	—
270	#332	—	89	2	no	—
271	#332	—	89	2	no	—
272	#331	—	89	2	no	—
273	#331	—	89	2	no	—
274	C₂×#41	—	89	1	no	—
275	C₂×#41	—	178	2	no	—
276	#135	—	356	8	no	—
277	C₂×Q₁₆	—	178	2	no	—
278	C₂×SD₁₆	—	178	2	no	—
279	C₂×SD₁₆	—	178	2	no	—
280	C₂×D₈	—	178	2	no	—
281	C₂×D₈	—	178	1	no	—
282	C₂×D₈	—	178	1	no	—
283	C₂×M₁₆	—	178	1	no	—
284	C₂×M₁₆	—	178	1	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
287	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
288	C₄⋊Q₈	—	89	2	no	—
289	#127	—	89	2	no	—
290	#124	—	178	2	no	—
291	#121	—	178	2	no	—
292	#121	—	178	2	no	—
293	C₄×Q₈	—	89	1	no	—
294	C₄×Q₈	—	89	1	no	—
295	C₄×D₄	—	89	1	no	—
296	C₄×D₄	—	89	1	no	—
297	C₄×D₄	—	178	1	no	—
298	C₄×D₄	—	178	1	no	—
299	C₄×D₄	—	178	2	no	—
300	C₄×D₄	—	178	2	no	—
301	#117	—	89	1	no	—
302	#117	—	178	1	no	—
303	C₂×C₄²	—	178	1	no	—
304	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
305	#107	—	178	1	no	—
306	#107	—	178	1	no	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	89	1	no	—
309	C₄⋊C₈	—	89	1	no	—
310	C₄⋊C₈	—	178	1	no	—
311	C₄⋊C₈	—	178	1	no	—
312	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
313	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
314	#103	—	178	2	no	—
315	#103	—	178	2	no	—
316	#102	—	178	2	no	—
317	#102	—	178	2	no	—
318	#102	—	178	2	no	—
319	#102	—	178	2	no	—
320	C₂²⋊C₈	—	178	1	no	—
321	C₂²⋊C₈	—	178	1	no	—
322	C₂²⋊C₈	—	178	1	no	—
323	#97	—	178	1	no	—
324	#97	—	178	1	no	—
325	C₄×C₈	—	178	1	no	—
326	C₄×C₈	D₃₅₆	1	1	yes	characteristic
327	C₄×C₈	D₃₅₆	1	1	yes	characteristic
328	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
330	#41	—	356	4	no	—
331	#41	—	356	4	no	—
332	#41	—	178	4	no	—
333	C₂×Q₈	—	89	1	no	—
334	C₂×Q₈	—	178	2	no	—
335	C₂×D₄	—	89	1	no	—
336	C₂×D₄	—	356	2	no	—
337	C₂×D₄	—	178	1	no	—
338	C₂×D₄	—	178	2	no	—
339	C₂×D₄	—	178	2	no	—
340	C₂×D₄	—	178	2	no	—
341	C₂²×C₄	—	356	2	no	—
342	C₂²×C₄	—	178	1	no	—
343	C₂²×C₄	—	178	1	no	—
344	C₂²×C₄	—	178	1	no	—
345	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
347	C₂²×C₄	#13083575	1	1	yes	characteristic
348	Q₁₆	—	356	4	no	—
349	SD₁₆	—	356	4	no	—
350	SD₁₆	—	356	4	no	—
351	D₈	—	356	2	no	—
352	D₈	—	356	4	no	—
353	D₈	—	356	2	no	—
354	M₁₆	—	356	2	no	—
355	M₁₆	—	356	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	4	4	no	—
361	C₂×C₈	—	178	1	no	—
362	C₂×C₈	—	178	1	no	—
363	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
364	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
365	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
366	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
367	C₄⋊C₄	—	89	1	no	—
368	C₄⋊C₄	—	89	1	no	—
369	C₄⋊C₄	—	178	2	no	—
370	C₄⋊C₄	—	178	2	no	—
371	C₄⋊C₄	—	178	1	no	—
372	C₄⋊C₄	—	178	1	no	—
373	C₂²⋊C₄	—	356	2	no	—
374	C₂²⋊C₄	—	356	2	no	—
375	C₂²⋊C₄	—	178	1	no	—
376	C₂²⋊C₄	—	178	1	no	—
377	C₂²⋊C₄	—	178	1	no	—
378	C₄²	—	178	1	no	—
379	C₄²	—	178	1	no	—
380	C₄²	—	178	1	no	—
381	C₄²	D₄×D₈₉	1	1	yes	characteristic
382	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
383	C₄²	#13083575	1	1	yes	characteristic
384	C₄²	C₂³×D₈₉	1	1	yes	characteristic
385	C₂³	—	356	2	no	—
386	C₂³	—	178	1	no	—
387	C₂³	#15667987	1	1	yes	characteristic
388	Q₈	—	356	2	no	—
389	Q₈	—	356	2	no	—
390	Q₈	—	178	2	no	—
391	D₄	—	356	2	no	—
392	D₄	—	356	2	no	—
393	D₄	—	356	2	no	—
394	D₄	—	356	2	no	—
395	D₄	—	356	2	no	—
396	D₄	—	178	2	no	—
397	D₄	—	712	2	no	—
398	D₄	—	712	4	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	356	2	no	—
403	C₂×C₄	—	356	1	no	—
404	C₂×C₄	—	356	2	no	—
405	C₂×C₄	—	356	1	no	—
406	C₂×C₄	—	356	2	no	—
407	C₂×C₄	—	178	1	no	—
408	C₂×C₄	—	178	1	no	—
409	C₂×C₄	—	178	1	no	—
410	C₂×C₄	—	712	4	no	—
411	C₂×C₄	#15667987	1	1	yes	characteristic
412	C₂×C₄	#15667987	1	1	yes	characteristic
413	C₂×C₄	#15667987	1	1	yes	characteristic
414	C₂×C₄	#15668039	1	4	yes	—
415	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
417	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	2	no	—
423	C₈	—	356	1	no	—
424	C₈	—	356	1	no	—
425	C₈	#15668034	1	2	yes	complemented
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	356	1	no	—
429	C₂²	—	356	1	no	—
430	C₂²	—	356	1	no	—
431	C₂²	—	712	2	no	—
432	C₂²	—	712	2	no	—
433	C₂²	—	712	2	no	—
434	C₂²	#19151852	1	2	yes	—
435	C₂²	C₂×#15667987	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	356	1	no	—
440	C₄	—	356	1	no	—
441	C₄	—	356	1	no	—
442	C₄	—	712	2	no	—
443	C₄	#19151852	1	2	yes	—
444	C₄	C₂×#15668034	1	1	yes	characteristic
445	C₄	C₂×#15668039	1	2	yes	—
446	C₄	#19152398	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	1424	2	no	—
449	C₂	—	712	1	no	—
450	C₂	#26029709	1	1	yes	characteristic
451	C₂	C₂×#19151852	1	1	yes	characteristic
452	C₂	#26029973	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15667987
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×#334×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#121
hypercenter	C₂×#334	D₈₉
hypocenter	C₈₉	#19157
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
1. #26030831	C₂	semidirect
2. #26029709	C₂	semidirect
3. #26029218	C₂	semidirect
4. #26019821	C₂	semidirect
5. #26019814	C₂	semidirect
6. #26019771	C₂	semidirect
7. #26019766	C₂	semidirect
8. #26019737	C₂	semidirect
9. #26019732	C₂	semidirect
10. #26018902	C₂	semidirect
11. C₂×#334×C₈₉	C₂	semidirect
196. C₈×C₈₉	#135	semidirect
236. C₂×#334	D₈₉	semidirect
238. C₈₉	#19157	semidirect
425. C₈	#15668034	semidirect

Maximal subgroups

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

subgroup	index
#26030831	2
#26029709	2
#26029218	2
#26019821	2
#26019814	2
#26019771	2
#26019766	2
#26019737	2
#26019732	2
#26018902	2
C₂×#334×C₈₉	2
#19157	89