Subgroups — SD₁₆×C₂²⋊D₈₉ #26031942

Order 11392.

546 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic
4	#19151969	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151827	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151824	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151801	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151796	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151749	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151747	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151737	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151735	C₂	1	1	yes	maximal, characteristic, complemented
13	SD₁₆×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₈₉	—	2	1	no	—
18	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
19	C₂×#13083563	C₂²	1	1	yes	characteristic, complemented
20	C₂×#13083562	C₂²	1	1	yes	characteristic
21	C₂×#13083562	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
24	SD₁₆×D₈₉	—	2	4	no	—
25	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
26	#15668010	—	2	1	no	—
27	#15668010	C₂²	1	1	yes	characteristic, complemented
28	#15668008	C₂²	1	1	yes	characteristic
29	#15667991	—	2	1	no	—
30	#15667991	C₂²	1	1	yes	characteristic, complemented
31	#15667988	—	2	1	no	—
32	#15667988	C₂²	1	1	yes	characteristic, complemented
33	#15667986	C₂²	1	1	yes	characteristic
34	#15667984	—	2	1	no	—
35	#15667983	C₂²	1	1	yes	characteristic
36	#15667981	—	2	1	no	—
37	#15667980	—	2	1	no	—
38	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
39	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₈₉	—	2	1	no	—
41	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
42	#15667944	C₂²	1	1	yes	characteristic, complemented
43	#15667941	C₂²	1	1	yes	characteristic, complemented
44	#15667937	C₂²	1	1	yes	characteristic, complemented
45	#15667936	C₂²	1	1	yes	characteristic, complemented
46	#15667936	C₂²	1	1	yes	characteristic, complemented
47	#15667934	C₂²	1	1	yes	characteristic, complemented
48	#15667933	C₂²	1	1	yes	characteristic
49	#15667933	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊#10623494	C₂²	1	1	yes	characteristic, complemented
51	#15667924	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
53	C₂²×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×SD₁₆×C₈₉	—	2	4	no	—
56	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
58	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	C₂²×C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₈₉	—	2	1	no	—
62	C₂×Dic₁₇₈	—	2	1	no	—
63	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
64	Q₈×D₈₉	—	2	2	no	—
65	Q₈×D₈₉	—	4	1	no	—
66	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊D₈₉	—	2	1	no	—
68	C₂×C₂²⋊D₈₉	—	2	1	no	—
69	C₂×C₂²⋊D₈₉	—	2	1	no	—
70	C₂×C₂²⋊D₈₉	—	2	1	no	—
71	C₂×C₂²⋊D₈₉	—	2	1	no	—
72	C₂×C₂²⋊D₈₉	—	4	4	no	—
73	C₂×C₂²⋊D₈₉	D₄	1	1	yes	characteristic
74	D₄×D₈₉	—	2	2	no	—
75	D₄×D₈₉	—	4	1	no	—
76	C₂²×Dic₈₉	—	2	1	no	—
77	C₂×C₄×D₈₉	—	2	1	no	—
78	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
79	#13083563	—	2	2	no	—
80	#13083562	—	2	2	no	—
81	#13083562	—	4	1	no	—
82	#13083561	—	2	2	no	—
83	#13083561	—	4	1	no	—
84	C₂×#10623494	C₂³	1	1	yes	characteristic
85	C₂×#10623494	C₂³	1	1	yes	characteristic
86	C₈×D₈₉	—	2	2	no	—
87	C₄⋊Dic₈₉	—	2	1	no	—
88	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
89	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
90	#13083553	—	2	1	no	—
91	#13083553	—	2	1	no	—
92	#13083553	—	2	1	no	—
93	#13083553	—	2	1	no	—
94	#13083553	D₄	1	1	yes	characteristic
95	C₂²⋊Dic₈₉	—	2	1	no	—
96	C₂²⋊Dic₈₉	—	2	1	no	—
97	C₂²⋊Dic₈₉	—	2	1	no	—
98	C₂²⋊Dic₈₉	D₄	1	1	yes	characteristic
99	#13083551	—	2	1	no	—
100	#13083551	—	2	1	no	—
101	#13083551	D₄	1	1	yes	characteristic
102	C₄×Dic₈₉	—	2	1	no	—
103	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
104	C₂⁴×C₈₉	—	2	1	no	—
105	C₂×Q₈×C₈₉	—	2	1	no	—
106	C₂×Q₈×C₈₉	—	2	2	no	—
107	C₂×Q₈×C₈₉	—	4	1	no	—
108	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₈₉	—	2	2	no	—
111	C₂×D₄×C₈₉	—	2	1	no	—
112	C₂×D₄×C₈₉	—	4	1	no	—
113	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	—	2	1	no	—
116	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
117	SD₁₆×C₈₉	—	2	2	no	—
118	SD₁₆×C₈₉	—	2	2	no	—
119	SD₁₆×C₈₉	—	2	2	no	—
120	SD₁₆×C₈₉	D₄	1	4	yes	complemented
121	C₂×C₈×C₈₉	—	2	2	no	—
122	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₂³×C₈₉	—	2	1	no	—
125	C₂³×C₈₉	—	2	1	no	—
126	C₂³×C₈₉	—	4	2	no	—
127	C₂³×C₈₉	—	4	2	no	—
128	C₂³×C₈₉	—	8	1	no	—
129	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×D₈₉	—	2	1	no	—
131	C₂²×D₈₉	—	4	2	no	—
132	C₂²×D₈₉	—	4	2	no	—
133	C₂²×D₈₉	—	8	1	no	—
134	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
135	Q₈×C₈₉	—	2	1	no	—
136	Q₈×C₈₉	—	2	1	no	—
137	Q₈×C₈₉	—	2	1	no	—
138	Q₈×C₈₉	—	4	2	no	—
139	Q₈×C₈₉	C₂×D₄	1	2	yes	complemented
140	D₄×C₈₉	—	2	1	no	—
141	D₄×C₈₉	—	2	1	no	—
142	D₄×C₈₉	—	2	1	no	—
143	D₄×C₈₉	—	4	2	no	—
144	D₄×C₈₉	C₂×D₄	1	2	yes	—
145	C₂×C₄×C₈₉	—	2	1	no	—
146	C₂×C₄×C₈₉	—	2	1	no	—
147	C₂×C₄×C₈₉	—	2	1	no	—
148	C₂×C₄×C₈₉	—	2	1	no	—
149	C₂×C₄×C₈₉	—	4	2	no	—
150	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₂²⋊D₈₉	—	4	2	no	—
153	C₂²⋊D₈₉	—	4	2	no	—
154	C₂²⋊D₈₉	—	4	2	no	—
155	C₂²⋊D₈₉	—	4	2	no	—
156	C₂²⋊D₈₉	—	8	1	no	—
157	C₂²⋊D₈₉	SD₁₆	1	4	yes	direct product factor
158	C₂×Dic₈₉	—	2	1	no	—
159	C₂×Dic₈₉	—	2	1	no	—
160	C₂×Dic₈₉	—	2	1	no	—
161	C₂×Dic₈₉	—	4	2	no	—
162	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
163	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
164	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
165	D₃₅₆	—	2	1	no	—
166	D₃₅₆	—	2	1	no	—
167	C₄×D₈₉	—	2	1	no	—
168	C₄×D₈₉	—	2	1	no	—
169	C₄×D₈₉	—	4	2	no	—
170	Dic₁₇₈	—	2	1	no	—
171	Dic₁₇₈	—	2	1	no	—
172	Dic₁₇₈	—	4	2	no	—
173	C₈×C₈₉	—	2	1	no	—
174	C₈×C₈₉	C₂×D₄	1	2	yes	complemented
175	#10623494	—	2	1	no	—
176	#10623494	—	2	1	no	—
177	C₂²×C₈₉	—	2	1	no	—
178	C₂²×C₈₉	—	2	1	no	—
179	C₂²×C₈₉	—	2	2	no	—
180	C₂²×C₈₉	—	4	1	no	—
181	C₂²×C₈₉	—	4	1	no	—
182	C₂²×C₈₉	—	4	1	no	—
183	C₂²×C₈₉	—	4	1	no	—
184	C₂²×C₈₉	—	4	1	no	—
185	C₂²×C₈₉	—	8	4	no	—
186	C₂²×C₈₉	C₂×SD₁₆	1	2	yes	complemented
187	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×D₈₉	—	2	1	no	—
189	C₂×D₈₉	—	2	1	no	—
190	C₂×D₈₉	—	4	1	no	—
191	C₂×D₈₉	—	4	1	no	—
192	C₂×D₈₉	—	4	1	no	—
193	C₂×D₈₉	—	8	4	no	—
194	C₂×D₈₉	C₂×SD₁₆	1	2	yes	complemented
195	C₄×C₈₉	—	2	2	no	—
196	C₄×C₈₉	—	2	1	no	—
197	C₄×C₈₉	—	4	1	no	—
198	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
199	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
200	Dic₈₉	—	2	1	no	—
201	Dic₈₉	—	2	1	no	—
202	Dic₈₉	—	4	1	no	—
203	Dic₈₉	—	4	1	no	—
204	Dic₈₉	—	4	1	no	—
205	Dic₈₉	C₂×SD₁₆	1	2	yes	complemented
206	C₂×C₈₉	—	2	2	no	—
207	C₂×C₈₉	—	4	2	no	—
208	C₂×C₈₉	—	8	1	no	—
209	C₂×C₈₉	D₄²	1	1	yes	characteristic
210	C₂×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
211	C₂×C₈₉	#577	1	1	yes	characteristic
212	D₈₉	—	2	2	no	—
213	D₈₉	—	8	1	no	—
214	D₄×SD₁₆	—	89	1	no	maximal, Sylow
215	C₈₉	D₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
216	C₂²×SD₁₆	—	89	1	no	—
217	C₂²×SD₁₆	D₈₉	1	1	yes	characteristic, complemented
218	D₄×Q₈	—	89	1	no	—
219	D₄²	—	89	1	no	—
220	#492	—	89	1	no	—
221	#465	—	89	1	no	—
222	#465	—	89	1	no	—
223	#461	—	89	1	no	—
224	#460	—	89	1	no	—
225	#450	—	89	1	no	—
226	#450	—	89	1	no	—
227	#448	—	89	1	no	—
228	#448	—	89	1	no	—
229	C₄×SD₁₆	—	89	1	no	—
230	C₈×D₄	—	89	1	no	—
231	C₂²×Q₈	—	89	1	no	—
232	C₂²×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
233	C₂²×D₄	—	89	1	no	—
234	C₂²×D₄	—	178	1	no	—
235	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic
236	C₂×SD₁₆	—	2	4	no	—
237	C₂×SD₁₆	—	89	1	no	—
238	C₂×SD₁₆	—	89	1	no	—
239	C₂×SD₁₆	—	89	1	no	—
240	C₂×SD₁₆	—	89	1	no	—
241	C₂×SD₁₆	—	89	1	no	—
242	C₂×SD₁₆	—	178	4	no	—
243	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
244	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
245	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
246	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
247	C₂²×C₈	—	89	1	no	—
248	C₂²×C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
249	C₄⋊Q₈	—	89	1	no	—
250	C₄⋊Q₈	—	178	1	no	—
251	#127	—	89	1	no	—
252	C₂²⋊Q₈	—	89	1	no	—
253	C₂²⋊Q₈	—	89	1	no	—
254	C₂²⋊Q₈	—	178	1	no	—
255	C₂²⋊Q₈	—	178	1	no	—
256	#121	—	89	1	no	—
257	#121	—	89	1	no	—
258	#121	—	178	1	no	—
259	#120	—	178	1	no	—
260	#120	—	178	1	no	—
261	C₄×Q₈	—	89	1	no	—
262	C₄×D₄	—	89	1	no	—
263	C₄×D₄	—	89	1	no	—
264	C₄×D₄	—	178	1	no	—
265	#106	—	89	1	no	—
266	C₄⋊C₈	—	89	1	no	—
267	#103	—	89	1	no	—
268	#103	—	89	1	no	—
269	#103	—	89	1	no	—
270	#102	—	89	1	no	—
271	#102	—	89	1	no	—
272	#102	—	89	1	no	—
273	C₂²⋊C₈	—	89	1	no	—
274	C₂²⋊C₈	—	89	1	no	—
275	C₄×C₈	—	89	1	no	—
276	C₂⁴	—	2	1	no	—
277	C₂⁴	—	178	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	—	89	1	no	—
282	C₂×Q₈	—	356	1	no	—
283	C₂×Q₈	—	178	1	no	—
284	C₂×Q₈	—	178	2	no	—
285	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
286	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	89	1	no	—
291	C₂×D₄	—	89	1	no	—
292	C₂×D₄	—	356	4	no	—
293	C₂×D₄	—	356	1	no	—
294	C₂×D₄	—	178	1	no	—
295	C₂×D₄	—	178	1	no	—
296	C₂×D₄	—	178	1	no	—
297	C₂×D₄	—	178	1	no	—
298	C₂×D₄	—	178	1	no	—
299	C₂×D₄	—	178	2	no	—
300	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
301	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	89	1	no	—
304	C₂²×C₄	—	178	1	no	—
305	C₂²×C₄	—	178	1	no	—
306	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
307	SD₁₆	—	2	2	no	—
308	SD₁₆	—	2	2	no	—
309	SD₁₆	—	2	2	no	—
310	SD₁₆	—	356	1	no	—
311	SD₁₆	—	356	1	no	—
312	SD₁₆	—	178	2	no	—
313	SD₁₆	—	178	2	no	—
314	SD₁₆	—	178	2	no	—
315	SD₁₆	C₂²⋊D₈₉	1	4	yes	direct product factor
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	89	1	no	—
318	C₂×C₈	—	89	1	no	—
319	C₂×C₈	—	178	2	no	—
320	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
321	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
322	C₄⋊C₄	—	89	1	no	—
323	C₄⋊C₄	—	89	1	no	—
324	C₄⋊C₄	—	89	1	no	—
325	C₄⋊C₄	—	178	1	no	—
326	C₄⋊C₄	—	178	1	no	—
327	C₄⋊C₄	—	178	1	no	—
328	C₄⋊C₄	—	178	1	no	—
329	C₄⋊C₄	—	178	1	no	—
330	C₂²⋊C₄	—	89	1	no	—
331	C₂²⋊C₄	—	89	1	no	—
332	C₂²⋊C₄	—	178	1	no	—
333	C₂²⋊C₄	—	178	1	no	—
334	C₂²⋊C₄	—	178	1	no	—
335	C₂²⋊C₄	—	178	1	no	—
336	C₂²⋊C₄	—	178	1	no	—
337	C₄²	—	89	1	no	—
338	C₄²	—	178	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	8	1	no	—
344	C₂³	—	89	1	no	—
345	C₂³	—	356	2	no	—
346	C₂³	—	356	2	no	—
347	C₂³	—	178	1	no	—
348	C₂³	—	712	1	no	—
349	C₂³	D₄×D₈₉	1	1	yes	characteristic
350	Q₈	—	2	1	no	—
351	Q₈	—	2	1	no	—
352	Q₈	—	2	1	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	356	2	no	—
355	Q₈	—	178	1	no	—
356	Q₈	—	178	1	no	—
357	Q₈	C₂×C₂²⋊D₈₉	1	2	yes	complemented
358	D₄	—	2	1	no	—
359	D₄	—	2	1	no	—
360	D₄	—	2	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	89	4	no	—
363	D₄	—	356	2	no	—
364	D₄	—	356	2	no	—
365	D₄	—	356	2	no	—
366	D₄	—	356	2	no	—
367	D₄	—	178	1	no	—
368	D₄	—	178	1	no	—
369	D₄	—	712	1	no	—
370	D₄	C₂×C₂²⋊D₈₉	1	2	yes	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	89	1	no	—
377	C₂×C₄	—	89	1	no	—
378	C₂×C₄	—	89	1	no	—
379	C₂×C₄	—	356	2	no	—
380	C₂×C₄	—	356	2	no	—
381	C₂×C₄	—	178	1	no	—
382	C₂×C₄	—	178	1	no	—
383	C₂×C₄	—	178	1	no	—
384	C₂×C₄	—	178	1	no	—
385	C₂×C₄	—	178	1	no	—
386	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
387	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	178	1	no	—
390	C₈	—	178	1	no	—
391	C₈	C₂×C₂²⋊D₈₉	1	2	yes	complemented
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	8	4	no	—
401	C₂²	—	89	2	no	—
402	C₂²	—	356	1	no	—
403	C₂²	—	356	1	no	—
404	C₂²	—	356	1	no	—
405	C₂²	—	178	1	no	—
406	C₂²	—	178	1	no	—
407	C₂²	—	712	4	no	—
408	C₂²	SD₁₆×D₈₉	1	2	yes	complemented
409	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	1	no	—
413	C₄	—	89	2	no	—
414	C₄	—	356	1	no	—
415	C₄	—	356	1	no	—
416	C₄	—	356	1	no	—
417	C₄	—	178	1	no	—
418	C₄	—	178	1	no	—
419	C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
420	C₄	#15668057	1	1	yes	characteristic
421	C₂	—	2	2	no	—
422	C₂	—	4	2	no	—
423	C₂	—	8	1	no	—
424	C₂	—	178	2	no	—
425	C₂	—	712	1	no	—
426	C₂	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
427	C₂	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
428	C₂	#19152404	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	C₂²×SD₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	D₄×C₂²⋊D₈₉	C₂
hypercenter	C₂²×SD₁₆	D₈₉
hypocenter	C₈₉	D₄×SD₁₆
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×D₈₉	C₂	semidirect
2. Q₈×C₂²⋊D₈₉	C₂	semidirect
4. #19151969	C₂	semidirect
5. #19151827	C₂	semidirect
6. #19151824	C₂	semidirect
7. #19151801	C₂	semidirect
8. #19151796	C₂	semidirect
9. #19151749	C₂	semidirect
10. #19151747	C₂	semidirect
11. #19151737	C₂	semidirect
12. #19151735	C₂	semidirect
13. SD₁₆×Dic₈₉	C₂	semidirect
14. C₈×C₂²⋊D₈₉	C₂	semidirect
15. C₂²×SD₁₆×C₈₉	C₂	semidirect
16. C₂×Q₈×D₈₉	C₂²	semidirect
19. C₂×#13083563	C₂²	semidirect
21. C₂×#13083562	C₂²	semidirect
22. C₂×#13083561	C₂²	semidirect
23. C₂×#13083561	C₂²	semidirect
25. C₂×C₈×D₈₉	C₂²	semidirect
27. #15668010	C₂²	semidirect
30. #15667991	C₂²	semidirect
32. #15667988	C₂²	semidirect
38. Q₈×Dic₈₉	C₂²	semidirect
42. #15667944	C₂²	semidirect
43. #15667941	C₂²	semidirect
44. #15667937	C₂²	semidirect
45. #15667936	C₂²	semidirect
46. #15667936	C₂²	semidirect
47. #15667934	C₂²	semidirect
49. #15667933	C₂²	semidirect
50. C₂²⋊#10623494	C₂²	semidirect
51. #15667924	C₂²	semidirect
52. C₈×Dic₈₉	C₂²	semidirect
53. C₂²×Q₈×C₈₉	C₂²	semidirect
58. C₂×SD₁₆×C₈₉	C₂²	semidirect
59. C₂×SD₁₆×C₈₉	C₂²	semidirect
60. C₂²×C₈×C₈₉	C₂²	semidirect
120. SD₁₆×C₈₉	D₄	semidirect
139. Q₈×C₈₉	C₂×D₄	semidirect
157. C₂²⋊D₈₉	SD₁₆	direct (N × H)
174. C₈×C₈₉	C₂×D₄	semidirect
186. C₂²×C₈₉	C₂×SD₁₆	semidirect
194. C₂×D₈₉	C₂×SD₁₆	semidirect
205. Dic₈₉	C₂×SD₁₆	semidirect
215. C₈₉	D₄×SD₁₆	semidirect
217. C₂²×SD₁₆	D₈₉	semidirect
232. C₂²×Q₈	C₂×D₈₉	semidirect
245. C₂×SD₁₆	C₂×D₈₉	semidirect
246. C₂×SD₁₆	C₂×D₈₉	semidirect
248. C₂²×C₈	C₂×D₈₉	semidirect
315. SD₁₆	C₂²⋊D₈₉	direct (N × H)
357. Q₈	C₂×C₂²⋊D₈₉	semidirect
391. C₈	C₂×C₂²⋊D₈₉	semidirect
408. C₂²	SD₁₆×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×D₈₉	2
Q₈×C₂²⋊D₈₉	2
D₄×C₂²⋊D₈₉	2
#19151969	2
#19151827	2
#19151824	2
#19151801	2
#19151796	2
#19151749	2
#19151747	2
#19151737	2
#19151735	2
SD₁₆×Dic₈₉	2
C₈×C₂²⋊D₈₉	2
C₂²×SD₁₆×C₈₉	2
D₄×SD₁₆	89

Subgroups — SD16×C22⋊D89 #26031942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×C₂²⋊D₈₉ #26031942