Subgroups — #36708009

Order 22784.

662 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic
2	C₁₆×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#13083549	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022071	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₆×C₂²⋊D₈₉	C₂	1	2	yes	maximal, complemented
6	#26022069	C₂	1	2	yes	maximal, complemented
7	#26022050	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022049	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#19151377	C₂	1	2	yes	maximal, complemented
10	C₂²⋊C₁₆×D₈₉	C₂	1	2	yes	maximal, complemented
11	D₄×C₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₈₉	C₂²	1	2	yes	—
13	C₄×D₄×D₈₉	C₄	1	1	yes	characteristic
14	C₂²×#13083549	C₂²	1	2	yes	complemented
15	C₂×C₁₆×D₈₉	C₂²	1	2	yes	complemented
16	C₂×C₁₆×D₈₉	C₂²	1	2	yes	complemented
17	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
18	D₄×#10623494	C₄	1	1	yes	characteristic
19	#19151663	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₈₉	C₂²	1	2	yes	—
21	#19151661	C₄	1	2	yes	—
22	C₄⋊C₈×D₈₉	C₄	1	1	yes	characteristic
23	C₂²⋊C₈×D₈₉	C₄	1	2	yes	—
24	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
25	C₄⋊#13083549	C₂²	1	1	yes	characteristic, complemented
26	#19151416	C₂²	1	1	yes	characteristic, complemented
27	#19151416	C₂²	1	1	yes	characteristic, complemented
28	C₂²⋊#13083549	C₂²	1	2	yes	complemented
29	#19151377	C₂²	1	1	yes	characteristic
30	#19151377	C₂²	1	1	yes	characteristic
31	#19151377	C₂²	1	2	yes	—
32	#19151377	C₂²	1	2	yes	complemented
33	#19151377	C₂²	1	2	yes	complemented
34	C₄×#13083549	C₂²	1	1	yes	characteristic, complemented
35	C₁₆×Dic₈₉	C₂²	1	2	yes	complemented
36	C₂²×C₁₆×C₈₉	C₂²	1	2	yes	complemented
37	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
38	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₂²⋊C₁₆×C₈₉	C₂²	1	2	yes	complemented
40	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₄×D₈₉	C₈	1	1	yes	characteristic
42	C₂²×C₄×D₈₉	C₂×C₄	1	2	yes	—
43	C₂²×#10623494	C₂×C₄	1	2	yes	—
44	C₂×C₈×D₈₉	—	4	2	no	—
45	C₂×C₈×D₈₉	—	4	2	no	—
46	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
47	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
48	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
50	C₂×C₈×D₈₉	C₂³	1	2	yes	—
51	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
52	D₄×Dic₈₉	C₈	1	1	yes	characteristic
53	#15667974	C₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₈₉	C₂×C₄	1	2	yes	—
55	#15667972	C₈	1	2	yes	—
56	C₄⋊C₄×D₈₉	C₈	1	1	yes	characteristic
57	C₂²⋊C₄×D₈₉	C₈	1	2	yes	—
58	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
59	C₂×#13083549	—	4	2	no	—
60	C₂×#13083549	C₂³	1	2	yes	—
61	C₂×#13083549	C₂³	1	1	yes	characteristic
62	C₂×#13083549	C₂³	1	1	yes	characteristic
63	C₁₆×D₈₉	—	4	2	no	—
64	C₁₆×D₈₉	—	4	2	no	—
65	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
66	#15667941	C₂×C₄	1	2	yes	—
67	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
68	#15667924	C₂×C₄	1	2	yes	—
69	#15667924	C₂×C₄	1	2	yes	—
70	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
74	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₆×C₈₉	—	4	2	no	—
76	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
77	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
82	C₂³×D₈₉	C₂×C₈	1	2	yes	—
83	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
84	C₂×C₂²⋊D₈₉	C₂×C₈	1	2	yes	—
85	D₄×D₈₉	C₁₆	1	8	yes	complemented
86	C₂²×Dic₈₉	C₂×C₈	1	2	yes	—
87	C₂×C₄×D₈₉	—	4	2	no	—
88	C₂×C₄×D₈₉	—	4	2	no	—
89	C₂×C₄×D₈₉	C₂×C₈	1	2	yes	—
90	C₂×C₄×D₈₉	C₂×C₈	1	2	yes	—
91	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
92	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
93	C₂×C₄×D₈₉	C₂²×C₄	1	2	yes	—
94	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
95	C₂×#10623494	—	4	2	no	—
96	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
97	C₂×#10623494	C₂²×C₄	1	2	yes	—
98	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
99	C₈×D₈₉	—	2	1	no	—
100	C₈×D₈₉	—	2	1	no	—
101	C₈×D₈₉	—	2	2	no	—
102	C₈×D₈₉	—	2	2	no	—
103	C₈×D₈₉	—	4	2	no	—
104	C₈×D₈₉	—	4	2	no	—
105	C₈×D₈₉	—	4	1	no	—
106	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
107	#13083553	C₂×C₈	1	2	yes	—
108	C₂²⋊Dic₈₉	C₂×C₈	1	2	yes	—
109	#13083551	C₂×C₈	1	2	yes	—
110	#13083551	C₂×C₈	1	2	yes	—
111	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
112	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
113	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
114	#13083549	—	2	1	no	—
115	#13083549	—	2	2	no	—
116	#13083549	—	2	1	no	—
117	C₂×D₄×C₈₉	C₂×C₈	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₈₉	—	2	2	no	—
120	C₂×C₈×C₈₉	—	2	2	no	—
121	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
124	C₄⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
125	C₂²⋊C₄×C₈₉	C₂×C₈	1	2	yes	—
126	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₁₆×C₈₉	—	2	1	no	—
128	C₁₆×C₈₉	—	2	2	no	—
129	C₁₆×C₈₉	—	2	1	no	—
130	C₂³×C₈₉	C₂²×C₈	1	2	yes	—
131	C₂²×D₈₉	—	4	2	no	—
132	C₂²×D₈₉	—	4	2	no	—
133	C₂²×D₈₉	C₂×C₁₆	1	8	yes	complemented
134	C₂²×D₈₉	C₂²×C₈	1	2	yes	—
135	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
136	D₄×C₈₉	C₂×C₁₆	1	4	yes	complemented
137	C₂×C₄×C₈₉	—	2	2	no	—
138	C₂×C₄×C₈₉	—	2	2	no	—
139	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
140	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
143	C₂²⋊D₈₉	C₂×C₁₆	1	8	yes	complemented
144	C₂×Dic₈₉	—	4	2	no	—
145	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
146	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
147	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
148	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
149	D₃₅₆	C₂×C₁₆	1	4	yes	complemented
150	C₄×D₈₉	—	2	1	no	—
151	C₄×D₈₉	—	2	2	no	—
152	C₄×D₈₉	—	2	1	no	—
153	C₄×D₈₉	—	2	2	no	—
154	C₄×D₈₉	—	4	2	no	—
155	C₄×D₈₉	—	4	2	no	—
156	C₄×D₈₉	—	4	1	no	—
157	C₄×D₈₉	C₂×C₁₆	1	4	yes	complemented
158	C₈×C₈₉	—	2	2	no	—
159	C₈×C₈₉	—	2	1	no	—
160	C₈×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
161	C₈×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
162	#10623494	—	2	1	no	—
163	#10623494	—	2	2	no	—
164	#10623494	—	2	1	no	—
165	C₂²×C₈₉	—	2	2	no	—
166	C₂²×C₈₉	—	2	2	no	—
167	C₂²×C₈₉	C₂²×C₁₆	1	4	yes	—
168	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
169	C₂×D₈₉	—	2	1	no	—
170	C₂×D₈₉	—	2	2	no	—
171	C₂×D₈₉	—	2	1	no	—
172	C₂×D₈₉	—	2	2	no	—
173	C₂×D₈₉	—	4	8	no	—
174	C₂×D₈₉	C₂²×C₁₆	1	2	yes	—
175	C₂×D₈₉	C₂²×C₁₆	1	4	yes	—
176	C₄×C₈₉	—	2	1	no	—
177	C₄×C₈₉	—	2	2	no	—
178	C₄×C₈₉	C₂²×C₁₆	1	2	yes	—
179	C₄×C₈₉	#518	1	1	yes	characteristic
180	C₄×C₈₉	#568	1	1	yes	characteristic
181	Dic₈₉	—	2	1	no	—
182	Dic₈₉	—	2	1	no	—
183	Dic₈₉	—	2	2	no	—
184	Dic₈₉	C₂²×C₁₆	1	2	yes	—
185	#33486	—	89	1	no	maximal, Sylow
186	C₂×C₈₉	—	2	4	no	—
187	C₂×C₈₉	#2972	1	1	yes	characteristic
188	C₂×C₈₉	C₂³×C₁₆	1	1	yes	characteristic
189	C₂×C₈₉	#3407	1	1	yes	characteristic
190	D₈₉	—	2	2	no	—
191	D₈₉	—	2	4	no	—
192	C₂×C₈×D₄	—	89	1	no	—
193	D₄×C₁₆	—	89	2	no	—
194	D₄×C₁₆	—	89	1	no	—
195	D₄×C₁₆	—	89	1	no	—
196	D₄×C₁₆	—	89	2	no	—
197	D₄×C₁₆	—	89	1	no	—
198	D₄×C₁₆	D₈₉	1	1	yes	characteristic, complemented
199	#2162	—	89	1	no	—
200	#2162	—	89	1	no	—
201	C₂×C₂²⋊C₁₆	—	89	2	no	—
202	C₂×C₂²⋊C₁₆	—	89	2	no	—
203	C₈₉	#33486	1	1	yes	characteristic, complemented, Sylow
204	C₂³×C₈	—	89	2	no	—
205	C₂×C₄×D₄	—	89	1	no	—
206	C₂²×C₁₆	—	89	2	no	—
207	C₂²×C₁₆	—	89	2	no	—
208	C₂²×C₁₆	—	89	2	no	—
209	C₂²×C₁₆	C₂×D₈₉	1	2	yes	complemented
210	C₈×D₄	—	89	2	no	—
211	C₈×D₄	—	89	1	no	—
212	C₈×D₄	—	89	1	no	—
213	C₈×D₄	—	89	2	no	—
214	C₈×D₄	—	89	1	no	—
215	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
216	C₂×C₄⋊C₈	—	89	1	no	—
217	C₂×C₂²⋊C₈	—	89	2	no	—
218	C₂×C₄×C₈	—	89	1	no	—
219	C₄⋊C₁₆	—	89	1	no	—
220	C₄⋊C₁₆	—	89	1	no	—
221	C₄⋊C₁₆	—	89	1	no	—
222	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
223	C₂²⋊C₁₆	—	89	2	no	—
224	C₂²⋊C₁₆	—	89	2	no	—
225	C₂²⋊C₁₆	—	89	1	no	—
226	C₂²⋊C₁₆	—	89	1	no	—
227	C₂²⋊C₁₆	—	89	2	no	—
228	C₂²⋊C₁₆	—	89	2	no	—
229	C₂²⋊C₁₆	C₂×D₈₉	1	2	yes	complemented
230	C₄×C₁₆	—	89	2	no	—
231	C₄×C₁₆	—	89	1	no	—
232	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
233	C₂²×D₄	—	89	1	no	—
234	C₂³×C₄	—	89	2	no	—
235	C₂²×C₈	—	89	2	no	—
236	C₂²×C₈	—	89	2	no	—
237	C₂²×C₈	—	89	2	no	—
238	C₂²×C₈	—	89	1	no	—
239	C₂²×C₈	—	89	1	no	—
240	C₂²×C₈	—	89	2	no	—
241	C₂²×C₈	—	356	2	no	—
242	C₂²×C₈	—	356	2	no	—
243	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
244	C₄×D₄	—	89	1	no	—
245	C₄×D₄	—	89	2	no	—
246	C₄×D₄	—	89	1	no	—
247	C₄×D₄	—	89	2	no	—
248	C₄×D₄	—	89	1	no	—
249	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
250	C₂×C₄⋊C₄	—	89	1	no	—
251	C₂×C₂²⋊C₄	—	89	2	no	—
252	C₂×C₄²	—	89	1	no	—
253	C₂×C₁₆	—	4	2	no	—
254	C₂×C₁₆	—	89	1	no	—
255	C₂×C₁₆	—	89	2	no	—
256	C₂×C₁₆	—	89	1	no	—
257	C₂×C₁₆	—	356	2	no	—
258	C₂×C₁₆	—	356	2	no	—
259	C₂×C₁₆	—	356	2	no	—
260	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
261	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
262	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
263	C₄⋊C₈	—	89	2	no	—
264	C₄⋊C₈	—	89	1	no	—
265	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
266	C₂²⋊C₈	—	89	2	no	—
267	C₂²⋊C₈	—	89	2	no	—
268	C₂²⋊C₈	—	89	2	no	—
269	C₂²⋊C₈	C₄×D₈₉	1	2	yes	—
270	C₄×C₈	—	89	1	no	—
271	C₄×C₈	—	89	1	no	—
272	C₄×C₈	—	89	1	no	—
273	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
274	C₂⁴	—	89	2	no	—
275	C₂×D₄	—	89	2	no	—
276	C₂×D₄	—	89	8	no	—
277	C₂×D₄	—	89	1	no	—
278	C₂×D₄	C₈×D₈₉	1	1	yes	characteristic
279	C₂²×C₄	—	89	1	no	—
280	C₂²×C₄	—	89	2	no	—
281	C₂²×C₄	—	89	1	no	—
282	C₂²×C₄	—	89	2	no	—
283	C₂²×C₄	—	89	2	no	—
284	C₂²×C₄	—	89	2	no	—
285	C₂²×C₄	—	89	1	no	—
286	C₂²×C₄	—	356	2	no	—
287	C₂²×C₄	—	356	2	no	—
288	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	89	1	no	—
292	C₂×C₈	—	89	1	no	—
293	C₂×C₈	—	89	2	no	—
294	C₂×C₈	—	356	2	no	—
295	C₂×C₈	—	356	2	no	—
296	C₂×C₈	—	356	1	no	—
297	C₂×C₈	—	356	2	no	—
298	C₂×C₈	—	178	2	no	—
299	C₂×C₈	—	178	1	no	—
300	C₂×C₈	—	178	2	no	—
301	C₂×C₈	—	178	1	no	—
302	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
303	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
304	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
305	C₄⋊C₄	—	89	2	no	—
306	C₄⋊C₄	—	89	1	no	—
307	C₄⋊C₄	C₈×D₈₉	1	1	yes	characteristic
308	C₂²⋊C₄	—	89	2	no	—
309	C₂²⋊C₄	—	89	2	no	—
310	C₂²⋊C₄	—	89	2	no	—
311	C₂²⋊C₄	C₈×D₈₉	1	2	yes	—
312	C₄²	—	89	1	no	—
313	C₄²	—	89	1	no	—
314	C₄²	—	89	1	no	—
315	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
316	C₁₆	—	2	1	no	—
317	C₁₆	—	2	2	no	—
318	C₁₆	—	2	1	no	—
319	C₁₆	—	178	1	no	—
320	C₁₆	—	178	2	no	—
321	C₁₆	—	178	1	no	—
322	C₂³	—	89	8	no	—
323	C₂³	—	89	2	no	—
324	C₂³	—	89	1	no	—
325	C₂³	—	356	2	no	—
326	C₂³	—	356	2	no	—
327	C₂³	C₂×C₈×D₈₉	1	2	yes	—
328	D₄	—	89	8	no	—
329	D₄	—	89	4	no	—
330	D₄	C₁₆×D₈₉	1	4	yes	complemented
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	89	1	no	—
334	C₂×C₄	—	89	4	no	—
335	C₂×C₄	—	89	1	no	—
336	C₂×C₄	—	89	1	no	—
337	C₂×C₄	—	89	2	no	—
338	C₂×C₄	—	356	1	no	—
339	C₂×C₄	—	356	2	no	—
340	C₂×C₄	—	356	2	no	—
341	C₂×C₄	—	356	2	no	—
342	C₂×C₄	—	178	1	no	—
343	C₂×C₄	—	178	2	no	—
344	C₂×C₄	—	178	1	no	—
345	C₂×C₄	—	178	2	no	—
346	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
347	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
348	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
349	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
350	C₈	—	2	2	no	—
351	C₈	—	2	1	no	—
352	C₈	—	178	1	no	—
353	C₈	—	178	2	no	—
354	C₈	—	178	1	no	—
355	C₈	#15668057	1	1	yes	characteristic
356	C₈	#15668058	1	1	yes	characteristic
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	89	2	no	—
360	C₂²	—	89	4	no	—
361	C₂²	—	356	8	no	—
362	C₂²	—	178	1	no	—
363	C₂²	—	178	2	no	—
364	C₂²	—	178	1	no	—
365	C₂²	—	178	2	no	—
366	C₂²	C₂×C₁₆×D₈₉	1	4	yes	—
367	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	2	2	no	—
370	C₄	—	89	2	no	—
371	C₄	—	178	1	no	—
372	C₄	—	178	1	no	—
373	C₄	—	178	2	no	—
374	C₄	C₂×C₁₆×D₈₉	1	2	yes	—
375	C₄	#19152070	1	1	yes	characteristic
376	C₄	#19152363	1	1	yes	characteristic
377	C₂	—	2	4	no	—
378	C₂	—	178	2	no	—
379	C₂	—	178	4	no	—
380	C₂	#26029273	1	1	yes	characteristic
381	C₂	C₂²×C₁₆×D₈₉	1	1	yes	characteristic
382	C₂	#26033353	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₈₉
commutator	C₂×C₈₉	C₂³×C₁₆
Fitting	D₄×C₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂³×C₈
prime radical	C₂×D₄×D₈₉	C₈
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	D₄×C₁₆	D₈₉
hypocenter	C₈₉	#33486
LCS	G ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₁₆×D₃₅₆	C₂	semidirect
3. D₄×#13083549	C₂	semidirect
4. #26022071	C₂	semidirect
5. C₁₆×C₂²⋊D₈₉	C₂	semidirect
6. #26022069	C₂	semidirect
7. #26022050	C₂	semidirect
8. #26022049	C₂	semidirect
9. C₂×#19151377	C₂	semidirect
10. C₂²⋊C₁₆×D₈₉	C₂	semidirect
11. D₄×C₁₆×C₈₉	C₂	semidirect
14. C₂²×#13083549	C₂²	semidirect
15. C₂×C₁₆×D₈₉	C₂²	semidirect
16. C₂×C₁₆×D₈₉	C₂²	semidirect
25. C₄⋊#13083549	C₂²	semidirect
26. #19151416	C₂²	semidirect
27. #19151416	C₂²	semidirect
28. C₂²⋊#13083549	C₂²	semidirect
32. #19151377	C₂²	semidirect
33. #19151377	C₂²	semidirect
34. C₄×#13083549	C₂²	semidirect
35. C₁₆×Dic₈₉	C₂²	semidirect
36. C₂²×C₁₆×C₈₉	C₂²	semidirect
38. C₄⋊C₁₆×C₈₉	C₂²	semidirect
39. C₂²⋊C₁₆×C₈₉	C₂²	semidirect
40. C₄×C₁₆×C₈₉	C₂²	semidirect
85. D₄×D₈₉	C₁₆	semidirect
133. C₂²×D₈₉	C₂×C₁₆	semidirect
136. D₄×C₈₉	C₂×C₁₆	semidirect
143. C₂²⋊D₈₉	C₂×C₁₆	semidirect
149. D₃₅₆	C₂×C₁₆	semidirect
157. C₄×D₈₉	C₂×C₁₆	semidirect
198. D₄×C₁₆	D₈₉	semidirect
203. C₈₉	#33486	semidirect
209. C₂²×C₁₆	C₂×D₈₉	semidirect
222. C₄⋊C₁₆	C₂×D₈₉	semidirect
229. C₂²⋊C₁₆	C₂×D₈₉	semidirect
232. C₄×C₁₆	C₂×D₈₉	semidirect
330. D₄	C₁₆×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈×D₄×D₈₉	2
C₁₆×D₃₅₆	2
D₄×#13083549	2
#26022071	2
C₁₆×C₂²⋊D₈₉	2
#26022069	2
#26022050	2
#26022049	2
C₂×#19151377	2
C₂²⋊C₁₆×D₈₉	2
D₄×C₁₆×C₈₉	2
#33486	89