Subgroups — #36523567

Order 22784.

602 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029365	C₂	1	1	yes	maximal, characteristic
2	#26029360	C₂	1	1	yes	maximal, characteristic
3	#26028894	C₂	1	1	yes	maximal, characteristic
4	#26019039	C₂	1	2	yes	maximal, complemented
5	#26019034	C₂	1	2	yes	maximal, complemented
6	#26019031	C₂	1	2	yes	maximal, complemented
7	#26019025	C₂	1	2	yes	maximal, complemented
8	#26019005	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019005	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19151351	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#13083574	C₂²	1	1	yes	characteristic
13	#19151728	—	2	1	no	—
14	C₈×Dic₁₇₈	—	2	1	no	—
15	#19151677	—	2	1	no	—
16	#19151666	—	2	2	no	—
17	C₈×D₃₅₆	—	2	1	no	—
18	#19151661	—	2	2	no	—
19	#19151657	C₄	1	2	yes	—
20	#19151657	C₄	1	2	yes	—
21	#19151654	C₂²	1	2	yes	—
22	#19151650	C₂²	1	2	yes	—
23	#19151649	C₂²	1	2	yes	—
24	#19151649	C₂²	1	2	yes	—
25	#19151624	C₄	1	1	yes	characteristic
26	#19151624	C₄	1	1	yes	characteristic
27	#19151620	C₂²	1	2	yes	—
28	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
30	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
31	#19151564	C₄	1	1	yes	characteristic
32	#19151564	C₄	1	1	yes	characteristic
33	C₄×#13083558	C₂²	1	1	yes	characteristic
34	#19151351	C₂²	1	2	yes	—
35	#19151351	C₂²	1	2	yes	—
36	#19151350	C₂²	1	2	yes	—
37	#19151350	C₂²	1	2	yes	—
38	#19151348	C₂²	1	2	yes	—
39	#19151348	C₂²	1	2	yes	—
40	#431×C₈₉	C₂²	1	1	yes	characteristic
41	#431×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
43	#335×C₈₉	C₂²	1	1	yes	characteristic
44	#335×C₈₉	C₂²	1	1	yes	characteristic
45	#334×C₈₉	C₂²	1	1	yes	characteristic
46	#334×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
48	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
49	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
50	C₂×#13083557	—	2	2	no	—
51	C₂²×#10623494	—	2	1	no	—
52	C₂²×#10623494	—	2	1	no	—
53	C₂×C₈×D₈₉	—	2	2	no	—
54	C₄×Dic₁₇₈	D₄	1	1	yes	characteristic
55	C₄×Dic₁₇₈	Q₈	1	1	yes	characteristic
56	C₄×D₃₅₆	D₄	1	1	yes	characteristic
57	C₄×D₃₅₆	Q₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₈₉	D₄	1	2	yes	—
59	C₄×C₂²⋊D₈₉	Q₈	1	2	yes	—
60	#15667971	C₂×C₄	1	1	yes	characteristic
61	#15667969	C₂×C₄	1	2	yes	—
62	C₄²×D₈₉	C₂³	1	2	yes	—
63	C₄⋊#10623494	—	2	1	no	—
64	C₄⋊#10623494	—	2	1	no	—
65	C₄⋊#10623494	C₂³	1	2	yes	—
66	C₄⋊#10623494	C₂³	1	2	yes	—
67	#15667941	—	2	2	no	—
68	#15667941	—	2	2	no	—
69	#15667941	C₂×C₄	1	2	yes	—
70	#15667941	C₂×C₄	1	2	yes	—
71	#15667941	C₂×C₄	1	2	yes	—
72	#15667941	C₂×C₄	1	2	yes	—
73	#15667924	—	2	2	no	—
74	#15667924	—	2	2	no	—
75	#15667924	C₂×C₄	1	2	yes	—
76	#15667924	C₂×C₄	1	2	yes	—
77	#15667924	C₂×C₄	1	2	yes	—
78	#15667924	C₂×C₄	1	2	yes	—
79	#15667923	C₂×C₄	1	2	yes	—
80	#15667922	—	2	2	no	—
81	C₄×#10623494	C₂³	1	2	yes	—
82	C₈×Dic₈₉	—	2	2	no	—
83	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₂²⋊C₈×C₈₉	—	2	1	no	—
91	C₂²⋊C₈×C₈₉	—	2	1	no	—
92	C₄×C₈×C₈₉	—	2	1	no	—
93	C₄×C₈×C₈₉	—	2	1	no	—
94	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	#13083574	—	2	2	no	—
99	#13083574	—	2	2	no	—
100	C₂×Dic₁₇₈	C₄⋊C₄	1	1	yes	characteristic
101	C₂×D₃₅₆	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₂²⋊D₈₉	C₄⋊C₄	1	2	yes	—
103	C₂×C₄×D₈₉	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₈₉	C₂×D₄	1	2	yes	—
105	C₂×C₄×D₈₉	C₂×Q₈	1	2	yes	—
106	#13083558	—	2	2	no	—
107	#13083558	—	2	2	no	—
108	#13083557	—	8	2	no	—
109	C₂×#10623494	—	2	2	no	—
110	C₂×#10623494	—	2	2	no	—
111	C₂×#10623494	—	8	1	no	—
112	C₂×#10623494	—	8	1	no	—
113	C₂×#10623494	C₂²×C₄	1	2	yes	—
114	C₂×#10623494	C₂²×C₄	1	2	yes	—
115	C₈×D₈₉	—	8	2	no	—
116	C₄⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
117	C₄⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
118	#13083553	C₄⋊C₄	1	2	yes	—
119	#13083553	C₄⋊C₄	1	2	yes	—
120	C₂²⋊Dic₈₉	C₄⋊C₄	1	2	yes	—
121	#13083551	C₄⋊C₄	1	2	yes	—
122	#13083551	C₄⋊C₄	1	2	yes	—
123	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
124	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
125	C₄×Dic₈₉	C₂×Q₈	1	2	yes	—
126	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
129	C₂×C₈×C₈₉	—	2	2	no	—
130	C₂×C₈×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	—	2	1	no	—
132	C₂×C₈×C₈₉	—	2	1	no	—
133	C₂×C₈×C₈₉	—	2	1	no	—
134	C₂×C₈×C₈₉	—	2	1	no	—
135	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
142	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
143	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂²×D₈₉	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₈₉	—	2	1	no	—
146	C₂×C₄×C₈₉	—	2	1	no	—
147	C₂×C₄×C₈₉	—	4	1	no	—
148	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₈₉	#131	1	2	yes	—
152	C₂×C₄×C₈₉	#131	1	2	yes	—
153	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
156	C₂²⋊D₈₉	—	2	4	no	—
157	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
160	D₃₅₆	—	2	2	no	—
161	C₄×D₈₉	—	2	2	no	—
162	C₄×D₈₉	—	2	2	no	—
163	C₄×D₈₉	—	2	2	no	—
164	C₄×D₈₉	—	2	2	no	—
165	C₄×D₈₉	—	4	2	no	—
166	Dic₁₇₈	—	2	2	no	—
167	C₈×C₈₉	—	2	1	no	—
168	C₈×C₈₉	—	2	1	no	—
169	C₈×C₈₉	—	2	1	no	—
170	C₈×C₈₉	—	2	1	no	—
171	C₈×C₈₉	—	4	1	no	—
172	C₈×C₈₉	—	4	1	no	—
173	C₈×C₈₉	—	4	1	no	—
174	C₈×C₈₉	—	4	1	no	—
175	#10623494	—	2	2	no	—
176	#10623494	—	2	2	no	—
177	#10623494	—	4	2	no	—
178	#10623494	—	4	2	no	—
179	C₂²×C₈₉	—	2	1	no	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	#424	1	2	yes	—
182	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₂×D₈₉	—	2	2	no	—
184	C₂×D₈₉	—	2	2	no	—
185	C₂×D₈₉	—	2	2	no	—
186	C₄×C₈₉	—	2	1	no	—
187	C₄×C₈₉	—	2	1	no	—
188	C₄×C₈₉	—	2	1	no	—
189	C₄×C₈₉	#424	1	2	yes	—
190	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
191	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
192	C₄×C₈₉	#576	1	1	yes	characteristic
193	C₄×C₈₉	#578	1	1	yes	characteristic
194	Dic₈₉	—	2	2	no	—
195	Dic₈₉	—	2	2	no	—
196	Dic₈₉	—	2	2	no	—
197	#17812	—	89	1	no	maximal, Sylow
198	C₂×C₈₉	—	2	2	no	—
199	C₂×C₈₉	C₂×#424	1	1	yes	characteristic
200	C₂×C₈₉	#2913	1	1	yes	characteristic
201	C₂×C₈₉	#2916	1	1	yes	characteristic
202	D₈₉	—	4	2	no	—
203	#2989	—	89	1	no	—
204	#2988	—	89	1	no	—
205	#2922	—	89	1	no	—
206	#1574	—	89	2	no	—
207	#1573	—	89	2	no	—
208	#1572	—	89	2	no	—
209	#1571	—	89	2	no	—
210	#1565	—	89	1	no	—
211	#1565	—	89	1	no	—
212	#1564	D₈₉	1	1	yes	characteristic, complemented
213	C₂×#335	—	89	1	no	—
214	C₈₉	#17812	1	1	yes	characteristic, complemented, Sylow
215	C₄×#41	—	89	1	no	—
216	#446	—	178	1	no	—
217	C₈×Q₈	—	178	1	no	—
218	#436	—	178	1	no	—
219	#435	—	178	2	no	—
220	C₈×D₄	—	178	1	no	—
221	C₈×D₄	—	178	2	no	—
222	#433	—	89	2	no	—
223	#433	—	89	2	no	—
224	#432	—	89	2	no	—
225	#431	—	89	2	no	—
226	#431	—	89	2	no	—
227	#431	—	89	2	no	—
228	#431	C₂×D₈₉	1	1	yes	characteristic
229	#431	C₂×D₈₉	1	1	yes	characteristic
230	#424	—	89	1	no	—
231	#424	—	89	1	no	—
232	#423	—	89	2	no	—
233	C₂×C₄⋊C₈	—	89	1	no	—
234	C₂×C₄⋊C₈	—	89	1	no	—
235	C₂×C₄⋊C₈	—	89	2	no	—
236	#408	—	89	1	no	—
237	#408	—	89	1	no	—
238	C₄×M₁₆	—	89	1	no	—
239	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
240	#335	—	89	2	no	—
241	#335	—	89	2	no	—
242	#335	—	89	2	no	—
243	#335	—	89	2	no	—
244	#335	C₂×D₈₉	1	1	yes	characteristic
245	#335	C₂×D₈₉	1	1	yes	characteristic
246	#334	—	89	2	no	—
247	#334	—	89	2	no	—
248	#334	C₂×D₈₉	1	1	yes	characteristic
249	#334	C₂×D₈₉	1	1	yes	characteristic
250	C₂×#41	—	89	1	no	—
251	C₂×M₁₆	—	89	1	no	—
252	C₂×M₁₆	—	89	1	no	—
253	C₂×M₁₆	—	178	2	no	—
254	C₂²×C₈	—	178	2	no	—
255	C₂²×C₈	—	178	1	no	—
256	C₂²×C₈	—	178	1	no	—
257	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
258	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
259	C₄×Q₈	—	89	1	no	—
260	C₄×Q₈	—	89	1	no	—
261	C₄×D₄	—	89	2	no	—
262	C₄×D₄	—	89	2	no	—
263	C₄×D₄	—	89	1	no	—
264	C₄×D₄	—	89	1	no	—
265	#117	—	89	1	no	—
266	#117	—	89	2	no	—
267	C₂×C₄²	—	89	2	no	—
268	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
269	C₄⋊C₈	—	89	2	no	—
270	C₄⋊C₈	—	89	2	no	—
271	C₄⋊C₈	—	89	2	no	—
272	C₄⋊C₈	—	89	2	no	—
273	C₄⋊C₈	—	89	2	no	—
274	C₄⋊C₈	—	89	2	no	—
275	C₄⋊C₈	—	178	2	no	—
276	C₄⋊C₈	—	178	2	no	—
277	C₄⋊C₈	—	178	1	no	—
278	C₄⋊C₈	—	178	1	no	—
279	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
280	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
281	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
282	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	2	1	no	—
285	C₂²⋊C₈	—	89	2	no	—
286	C₂²⋊C₈	—	89	2	no	—
287	C₂²⋊C₈	—	89	2	no	—
288	C₂²⋊C₈	—	89	2	no	—
289	C₂²⋊C₈	—	178	2	no	—
290	C₂²⋊C₈	—	178	2	no	—
291	#97	—	89	2	no	—
292	#97	—	178	2	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	89	2	no	—
296	C₄×C₈	—	178	2	no	—
297	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
298	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
300	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
301	#41	—	178	2	no	—
302	#41	—	178	2	no	—
303	C₂×Q₈	—	89	1	no	—
304	C₂×D₄	—	89	2	no	—
305	C₂×D₄	—	89	1	no	—
306	C₂²×C₄	—	89	2	no	—
307	C₂²×C₄	—	89	2	no	—
308	C₂²×C₄	—	89	2	no	—
309	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
310	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
311	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
312	M₁₆	—	178	2	no	—
313	M₁₆	—	178	2	no	—
314	M₁₆	—	712	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	89	2	no	—
322	C₂×C₈	—	89	2	no	—
323	C₂×C₈	—	178	2	no	—
324	C₂×C₈	—	178	2	no	—
325	C₂×C₈	—	712	2	no	—
326	C₂×C₈	—	712	1	no	—
327	C₂×C₈	—	712	1	no	—
328	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
329	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
330	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
331	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
332	C₄⋊C₄	—	89	2	no	—
333	C₄⋊C₄	—	89	2	no	—
334	C₄⋊C₄	—	89	1	no	—
335	C₄⋊C₄	—	89	1	no	—
336	C₂²⋊C₄	—	89	2	no	—
337	C₂²⋊C₄	—	89	2	no	—
338	C₂²⋊C₄	—	89	2	no	—
339	C₄²	—	89	2	no	—
340	C₄²	—	89	2	no	—
341	C₄²	—	89	2	no	—
342	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
343	C₄²	D₄×D₈₉	1	1	yes	characteristic
344	C₄²	Q₈×D₈₉	1	1	yes	characteristic
345	C₄²	C₂³×D₈₉	1	1	yes	characteristic
346	C₂³	—	89	2	no	—
347	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
348	Q₈	—	178	2	no	—
349	D₄	—	178	4	no	—
350	D₄	—	178	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	89	2	no	—
355	C₂×C₄	—	89	2	no	—
356	C₂×C₄	—	89	2	no	—
357	C₂×C₄	—	356	2	no	—
358	C₂×C₄	—	178	2	no	—
359	C₂×C₄	—	178	2	no	—
360	C₂×C₄	—	178	2	no	—
361	C₂×C₄	—	178	2	no	—
362	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
363	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
364	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
365	C₂×C₄	#15668018	1	2	yes	—
366	C₂×C₄	#15668020	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
369	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	2	1	no	—
374	C₈	—	4	1	no	—
375	C₈	—	4	1	no	—
376	C₈	—	4	1	no	—
377	C₈	—	4	1	no	—
378	C₈	—	356	2	no	—
379	C₈	—	356	2	no	—
380	C₈	—	178	2	no	—
381	C₈	—	178	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	178	2	no	—
385	C₂²	—	178	2	no	—
386	C₂²	—	178	2	no	—
387	C₂²	#19151623	1	2	yes	—
388	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	178	2	no	—
393	C₄	—	178	2	no	—
394	C₄	—	178	2	no	—
395	C₄	#19151623	1	2	yes	—
396	C₄	C₂×#15668018	1	1	yes	characteristic
397	C₄	C₂×#15668020	1	1	yes	characteristic
398	C₄	#19152400	1	1	yes	characteristic
399	C₄	#19152412	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	356	2	no	—
402	C₂	C₂×#19151623	1	1	yes	characteristic
403	C₂	#26028849	1	1	yes	characteristic
404	C₂	#26028860	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1564	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂×#13083574	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1564	D₈₉
hypocenter	C₈₉	#17812
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
4. #26019039	C₂	semidirect
5. #26019034	C₂	semidirect
6. #26019031	C₂	semidirect
7. #26019025	C₂	semidirect
8. #26019005	C₂	semidirect
9. #26019005	C₂	semidirect
10. C₂×#19151351	C₂	semidirect
11. C₈₉×#1564	C₂	semidirect
212. #1564	D₈₉	semidirect
214. C₈₉	#17812	semidirect

Maximal subgroups

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

subgroup	index
#26029365	2
#26029360	2
#26028894	2
#26019039	2
#26019034	2
#26019031	2
#26019025	2
#26019005	2
C₂×#19151351	2
C₈₉×#1564	2
#17812	89