Subgroups — #2230×D₈₉ #36709154

Order 22784.

558 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#498×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#443×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#26022424	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022423	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022422	C₂	1	2	yes	maximal, complemented
6	#26022421	C₂	1	2	yes	maximal, complemented
7	#26022420	C₂	1	1	yes	maximal, characteristic, complemented
8	#365×D₈₉	C₂	1	2	yes	maximal, complemented
9	#364×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#360×D₈₉	C₂	1	2	yes	maximal
11	C₈₉×#2230	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₈₉	C₂²	1	1	yes	characteristic
13	#131×D₈₉	—	2	1	no	—
14	C₄⋊Q₈×D₈₉	—	2	1	no	—
15	M₃₂×D₈₉	C₂²	1	2	yes	—
16	#19151996	C₂²	1	1	yes	characteristic, complemented
17	#19151995	—	2	1	no	—
18	#19151995	C₂²	1	2	yes	complemented
19	#19151994	—	2	1	no	—
20	#19151716	C₂²	1	1	yes	characteristic
21	#19151715	C₂²	1	1	yes	characteristic
22	#19151714	C₂²	1	1	yes	characteristic
23	#19151713	—	2	1	no	—
24	#19151712	—	2	1	no	—
25	#108×D₈₉	C₂²	1	1	yes	characteristic
26	#106×D₈₉	—	2	1	no	—
27	#106×D₈₉	C₂²	1	2	yes	—
28	#104×D₈₉	—	2	1	no	—
29	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
30	#19151422	C₂²	1	2	yes	complemented
31	#19151421	C₂²	1	2	yes	complemented
32	#19151420	C₂²	1	2	yes	complemented
33	#19151419	C₂²	1	1	yes	characteristic, complemented
34	#19151418	C₂²	1	2	yes	complemented
35	#19151409	C₂²	1	2	yes	—
36	#19151408	C₂²	1	2	yes	—
37	#19151407	C₂²	1	2	yes	—
38	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	#443×C₈₉	C₂²	1	1	yes	characteristic
40	#365×C₈₉	C₂²	1	2	yes	complemented
41	#364×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	#360×C₈₉	C₂²	1	2	yes	—
43	#41×D₈₉	—	2	1	no	—
44	C₂×Q₈×D₈₉	—	4	1	no	—
45	#15668035	Q₈	1	1	yes	characteristic, complemented
46	#15668034	C₂³	1	1	yes	characteristic
47	#15668033	—	2	1	no	—
48	#15668032	—	2	1	no	—
49	#15668031	Q₈	1	1	yes	characteristic, complemented
50	Q₁₆×D₈₉	Q₈	1	1	yes	characteristic, complemented
51	SD₁₆×D₈₉	—	2	1	no	—
52	D₈×D₈₉	Q₈	1	1	yes	characteristic, complemented
53	#15668020	—	2	1	no	—
54	#15668020	—	4	1	no	—
55	#15668019	—	2	1	no	—
56	#15668018	—	2	1	no	—
57	#15668018	—	4	1	no	—
58	M₁₆×D₈₉	—	2	1	no	—
59	M₁₆×D₈₉	—	4	1	no	—
60	C₂×C₈×D₈₉	—	4	1	no	—
61	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
62	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
63	#15668012	—	2	1	no	—
64	#15668011	—	2	2	no	—
65	#15668011	—	4	1	no	—
66	#15668010	—	4	1	no	—
67	C₄⋊C₄×D₈₉	—	2	2	no	—
68	C₄⋊C₄×D₈₉	—	4	1	no	—
69	C₄²×D₈₉	D₄	1	1	yes	characteristic
70	#15667952	C₂³	1	2	yes	—
71	#15667951	—	2	2	no	—
72	C₁₆×D₈₉	—	2	2	no	—
73	#15667948	C₂³	1	1	yes	characteristic
74	#15667947	—	2	1	no	—
75	#15667944	—	2	1	no	—
76	#15667944	C₂³	1	2	yes	—
77	#15667943	—	2	2	no	—
78	#15667943	—	2	2	no	—
79	#15667940	—	2	1	no	—
80	#15667939	—	2	1	no	—
81	#15667938	—	2	1	no	—
82	C₄×#10623494	D₄	1	1	yes	characteristic
83	C₈×Dic₈₉	D₄	1	1	yes	characteristic
84	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
85	#135×C₈₉	C₂³	1	1	yes	characteristic
86	#131×C₈₉	—	2	1	no	—
87	C₄⋊Q₈×C₈₉	—	2	1	no	—
88	M₃₂×C₈₉	C₂³	1	2	yes	—
89	#108×C₈₉	C₂³	1	1	yes	characteristic
90	#106×C₈₉	—	2	1	no	—
91	#106×C₈₉	C₂³	1	2	yes	—
92	#104×C₈₉	—	2	1	no	—
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	#13083575	—	2	1	no	—
95	#13083574	—	2	1	no	—
96	#13083574	—	4	1	no	—
97	#13083573	—	2	1	no	—
98	#13083573	—	4	1	no	—
99	C₂×Dic₁₇₈	—	4	2	no	—
100	C₂×Dic₁₇₈	—	4	1	no	—
101	Q₈×D₈₉	—	2	1	no	—
102	Q₈×D₈₉	—	8	4	no	—
103	D₄×D₈₉	—	2	1	no	—
104	D₄×D₈₉	—	4	1	no	—
105	C₂×C₄×D₈₉	—	2	1	no	—
106	C₂×C₄×D₈₉	—	4	1	no	—
107	C₂×C₄×D₈₉	—	4	2	no	—
108	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
109	Dic₃₅₆	C₂×Q₈	1	1	yes	characteristic, complemented
110	#13083564	—	2	1	no	—
111	#13083563	—	2	1	no	—
112	#13083562	—	2	1	no	—
113	#13083561	—	2	1	no	—
114	D₇₁₂	C₂×Q₈	1	1	yes	characteristic, complemented
115	#13083559	—	2	1	no	—
116	#13083558	—	2	1	no	—
117	#13083558	—	4	1	no	—
118	#13083557	—	4	1	no	—
119	#13083557	—	4	1	no	—
120	#13083557	—	4	1	no	—
121	C₂×#10623494	—	4	1	no	—
122	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
123	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
124	C₈×D₈₉	—	4	1	no	—
125	C₈×D₈₉	—	4	1	no	—
126	C₈×D₈₉	—	4	1	no	—
127	C₈×D₈₉	SD₁₆	1	1	yes	characteristic
128	C₈×D₈₉	SD₁₆	1	1	yes	characteristic
129	C₈×D₈₉	SD₁₆	1	1	yes	characteristic
130	C₈×D₈₉	SD₁₆	1	1	yes	characteristic
131	C₈×D₈₉	C₂×Q₈	1	1	yes	characteristic
132	C₈×D₈₉	C₂×Q₈	1	1	yes	characteristic
133	C₈×D₈₉	#41	1	1	yes	characteristic
134	C₈×D₈₉	#41	1	1	yes	characteristic
135	C₄⋊Dic₈₉	—	2	2	no	—
136	C₄⋊Dic₈₉	—	4	1	no	—
137	#13083553	—	4	2	no	—
138	#13083553	—	4	2	no	—
139	C₄×Dic₈₉	—	2	1	no	—
140	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
141	#13083549	—	2	2	no	—
142	#41×C₈₉	—	2	1	no	—
143	C₂×Q₈×C₈₉	—	4	1	no	—
144	Q₁₆×C₈₉	C₂×Q₈	1	1	yes	characteristic, complemented
145	SD₁₆×C₈₉	—	2	1	no	—
146	D₈×C₈₉	C₂×Q₈	1	1	yes	characteristic, complemented
147	M₁₆×C₈₉	—	2	1	no	—
148	M₁₆×C₈₉	—	4	1	no	—
149	C₂×C₈×C₈₉	—	4	1	no	—
150	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₄⋊C₄×C₈₉	—	2	2	no	—
153	C₄⋊C₄×C₈₉	—	4	1	no	—
154	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₁₆×C₈₉	—	2	2	no	—
156	C₂²×D₈₉	—	4	1	no	—
157	C₂²×D₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
158	Q₈×C₈₉	—	2	1	no	—
159	Q₈×C₈₉	—	8	2	no	—
160	D₄×C₈₉	—	2	1	no	—
161	D₄×C₈₉	—	4	1	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	4	1	no	—
164	C₂×C₄×C₈₉	—	4	2	no	—
165	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
166	C₂²⋊D₈₉	—	4	1	no	—
167	C₂²⋊D₈₉	—	4	1	no	—
168	C₂²⋊D₈₉	—	4	1	no	—
169	C₂×Dic₈₉	—	2	1	no	—
170	C₂×Dic₈₉	—	4	1	no	—
171	C₂×Dic₈₉	—	4	2	no	—
172	C₂×Dic₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
173	D₃₅₆	—	2	1	no	—
174	D₃₅₆	—	4	1	no	—
175	C₄×D₈₉	—	2	4	no	—
176	C₄×D₈₉	—	4	1	no	—
177	C₄×D₈₉	—	4	1	no	—
178	C₄×D₈₉	—	4	1	no	—
179	C₄×D₈₉	—	8	4	no	—
180	C₄×D₈₉	C₂²⋊Q₈	1	1	yes	characteristic
181	C₄×D₈₉	C₂²⋊Q₈	1	1	yes	characteristic
182	C₄×D₈₉	C₂×SD₁₆	1	1	yes	characteristic
183	C₄×D₈₉	C₂×SD₁₆	1	1	yes	characteristic
184	Dic₁₇₈	—	2	1	no	—
185	Dic₁₇₈	—	4	1	no	—
186	Dic₁₇₈	—	8	4	no	—
187	Dic₁₇₈	—	8	2	no	—
188	C₈×C₈₉	—	4	1	no	—
189	C₈×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
190	C₈×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
191	C₈×C₈₉	C₂²×Q₈	1	1	yes	characteristic
192	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
193	#10623494	—	4	1	no	—
194	#10623494	C₂²⋊Q₈	1	1	yes	characteristic
195	#10623494	C₂²⋊Q₈	1	1	yes	characteristic
196	#10623494	C₂×SD₁₆	1	1	yes	characteristic
197	#10623494	C₂×SD₁₆	1	1	yes	characteristic
198	C₂²×C₈₉	—	4	1	no	—
199	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₂×D₈₉	—	2	2	no	—
201	C₂×D₈₉	—	4	1	no	—
202	C₂×D₈₉	—	8	2	no	—
203	C₂×D₈₉	#476	1	1	yes	characteristic
204	C₂×D₈₉	#476	1	1	yes	characteristic
205	C₄×C₈₉	—	2	2	no	—
206	C₄×C₈₉	—	4	1	no	—
207	C₄×C₈₉	—	8	2	no	—
208	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
209	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
210	Dic₈₉	—	2	2	no	—
211	Dic₈₉	—	4	1	no	—
212	Dic₈₉	—	8	2	no	—
213	Dic₈₉	#476	1	1	yes	characteristic
214	Dic₈₉	#476	1	1	yes	characteristic
215	C₂×#2230	—	89	1	no	maximal, Sylow
216	C₂×C₈₉	—	2	1	no	—
217	C₂×C₈₉	—	8	1	no	—
218	C₂×C₈₉	C₂×#476	1	1	yes	characteristic
219	D₈₉	—	2	1	no	—
220	D₈₉	—	8	1	no	—
221	D₈₉	#2230	1	2	yes	direct product factor
222	C₂×#498	—	89	1	no	—
223	C₂×#443	—	89	1	no	—
224	#2230	—	89	1	no	—
225	#2230	—	89	1	no	—
226	#2230	—	89	2	no	—
227	#2230	—	89	1	no	—
228	#2230	—	89	2	no	—
229	#2230	D₈₉	1	1	yes	characteristic, direct product factor
230	C₂×#365	—	89	2	no	—
231	C₂×#364	—	89	1	no	—
232	C₂×#360	—	89	2	no	—
233	C₈₉	C₂×#2230	1	1	yes	characteristic, complemented, Sylow
234	C₂×#135	—	89	1	no	—
235	C₂×#131	—	178	1	no	—
236	C₂×C₄⋊Q₈	—	178	1	no	—
237	C₂×M₃₂	—	89	2	no	—
238	#498	—	89	2	no	—
239	#498	—	89	1	no	—
240	#498	—	178	1	no	—
241	#498	—	178	1	no	—
242	#498	C₂×D₈₉	1	1	yes	characteristic, complemented
243	#443	—	89	1	no	—
244	#443	—	89	1	no	—
245	#443	—	89	1	no	—
246	#443	—	178	1	no	—
247	#443	—	178	1	no	—
248	#443	C₂×D₈₉	1	1	yes	characteristic
249	C₂×#108	—	89	1	no	—
250	C₂×#106	—	89	2	no	—
251	C₂×#106	—	178	1	no	—
252	C₂×#104	—	178	1	no	—
253	C₂×C₄×C₈	—	89	1	no	—
254	#365	—	89	2	no	—
255	#365	—	89	2	no	—
256	#365	—	89	2	no	—
257	#365	C₂×D₈₉	1	2	yes	complemented
258	#364	—	89	2	no	—
259	#364	—	89	1	no	—
260	#364	C₂×D₈₉	1	1	yes	characteristic, complemented
261	#360	—	89	2	no	—
262	#360	—	89	2	no	—
263	#360	—	89	2	no	—
264	#360	C₂×D₈₉	1	2	yes	—
265	C₂×#41	—	178	1	no	—
266	C₂²×Q₈	—	356	1	no	—
267	#135	—	89	1	no	—
268	#135	—	89	1	no	—
269	#135	—	89	1	no	—
270	#135	—	178	1	no	—
271	#135	—	178	1	no	—
272	#135	C₂²×D₈₉	1	1	yes	characteristic
273	C₂×Q₁₆	—	89	1	no	—
274	C₂×SD₁₆	—	178	1	no	—
275	C₂×D₈	—	89	1	no	—
276	#131	—	2	1	no	—
277	#131	—	356	1	no	—
278	#131	—	356	1	no	—
279	#131	—	178	1	no	—
280	#131	—	178	1	no	—
281	#131	—	178	1	no	—
282	C₂×M₁₆	—	356	1	no	—
283	C₂×M₁₆	—	178	1	no	—
284	C₂²×C₈	—	89	1	no	—
285	C₂²×C₈	—	89	1	no	—
286	C₂²×C₈	—	356	1	no	—
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	356	1	no	—
289	C₄⋊Q₈	—	356	1	no	—
290	C₄⋊Q₈	—	178	2	no	—
291	C₄⋊Q₈	—	178	1	no	—
292	C₂×C₄⋊C₄	—	356	1	no	—
293	C₂×C₄⋊C₄	—	178	2	no	—
294	C₂×C₄²	—	89	1	no	—
295	M₃₂	—	89	2	no	—
296	M₃₂	—	178	2	no	—
297	M₃₂	C₂²×D₈₉	1	2	yes	—
298	C₂×C₁₆	—	178	2	no	—
299	#108	—	89	1	no	—
300	#108	—	178	1	no	—
301	#108	C₂²×D₈₉	1	1	yes	characteristic
302	#106	—	2	1	no	—
303	#106	—	89	2	no	—
304	#106	—	178	2	no	—
305	#106	—	178	2	no	—
306	#106	—	178	1	no	—
307	#106	C₂²×D₈₉	1	2	yes	—
308	#104	—	2	1	no	—
309	#104	—	178	1	no	—
310	#104	—	178	1	no	—
311	#104	—	178	1	no	—
312	C₄×C₈	—	89	1	no	—
313	C₄×C₈	—	89	1	no	—
314	C₄×C₈	—	89	1	no	—
315	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
316	#41	—	2	1	no	—
317	#41	—	356	1	no	—
318	#41	—	356	1	no	—
319	#41	—	178	1	no	—
320	#41	—	178	1	no	—
321	#41	—	178	1	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	356	1	no	—
324	C₂×Q₈	—	356	2	no	—
325	C₂×Q₈	—	178	1	no	—
326	C₂×Q₈	—	712	4	no	—
327	C₂×D₄	—	356	1	no	—
328	C₂×D₄	—	178	1	no	—
329	C₂²×C₄	—	89	1	no	—
330	C₂²×C₄	—	356	1	no	—
331	C₂²×C₄	—	356	2	no	—
332	C₂²×C₄	—	178	1	no	—
333	Q₁₆	—	89	1	no	—
334	Q₁₆	—	178	1	no	—
335	Q₁₆	Q₈×D₈₉	1	1	yes	characteristic, complemented
336	SD₁₆	—	2	1	no	—
337	SD₁₆	—	178	1	no	—
338	SD₁₆	—	178	1	no	—
339	SD₁₆	—	178	1	no	—
340	D₈	—	89	1	no	—
341	D₈	—	178	1	no	—
342	D₈	Q₈×D₈₉	1	1	yes	characteristic, complemented
343	M₁₆	—	2	1	no	—
344	M₁₆	—	4	1	no	—
345	M₁₆	—	356	1	no	—
346	M₁₆	—	356	1	no	—
347	M₁₆	—	356	1	no	—
348	M₁₆	—	356	1	no	—
349	M₁₆	—	178	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	89	1	no	—
352	C₂×C₈	—	89	1	no	—
353	C₂×C₈	—	89	1	no	—
354	C₂×C₈	—	89	1	no	—
355	C₂×C₈	—	89	1	no	—
356	C₂×C₈	—	89	1	no	—
357	C₂×C₈	—	89	1	no	—
358	C₂×C₈	—	89	1	no	—
359	C₂×C₈	—	89	1	no	—
360	C₂×C₈	—	89	1	no	—
361	C₂×C₈	—	356	1	no	—
362	C₂×C₈	—	356	1	no	—
363	C₂×C₈	—	356	1	no	—
364	C₂×C₈	—	356	1	no	—
365	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
366	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	356	1	no	—
370	C₄⋊C₄	—	356	2	no	—
371	C₄⋊C₄	—	356	2	no	—
372	C₄⋊C₄	—	178	2	no	—
373	C₄²	—	89	1	no	—
374	C₄²	—	178	1	no	—
375	C₄²	D₄×D₈₉	1	1	yes	characteristic
376	C₁₆	—	2	2	no	—
377	C₁₆	—	178	2	no	—
378	C₂³	—	89	1	no	—
379	C₂³	—	356	1	no	—
380	Q₈	—	2	1	no	—
381	Q₈	—	8	2	no	—
382	Q₈	—	356	1	no	—
383	Q₈	—	178	1	no	—
384	Q₈	—	712	2	no	—
385	Q₈	—	712	4	no	—
386	D₄	—	2	1	no	—
387	D₄	—	4	1	no	—
388	D₄	—	356	1	no	—
389	D₄	—	356	1	no	—
390	D₄	—	356	1	no	—
391	D₄	—	356	1	no	—
392	D₄	—	178	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	89	1	no	—
397	C₂×C₄	—	89	1	no	—
398	C₂×C₄	—	89	1	no	—
399	C₂×C₄	—	89	1	no	—
400	C₂×C₄	—	89	1	no	—
401	C₂×C₄	—	356	1	no	—
402	C₂×C₄	—	356	1	no	—
403	C₂×C₄	—	356	1	no	—
404	C₂×C₄	—	356	1	no	—
405	C₂×C₄	—	356	2	no	—
406	C₂×C₄	—	178	4	no	—
407	C₂×C₄	—	178	1	no	—
408	C₂×C₄	—	712	4	no	—
409	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
410	C₈	—	4	1	no	—
411	C₈	—	89	1	no	—
412	C₈	—	89	1	no	—
413	C₈	—	89	1	no	—
414	C₈	—	89	1	no	—
415	C₈	—	356	1	no	—
416	C₈	SD₁₆×D₈₉	1	1	yes	characteristic
417	C₈	SD₁₆×D₈₉	1	1	yes	characteristic
418	C₈	C₂×Q₈×D₈₉	1	1	yes	characteristic
419	C₈	#41×D₈₉	1	1	yes	characteristic
420	C₂²	—	4	1	no	—
421	C₂²	—	89	1	no	—
422	C₂²	—	89	1	no	—
423	C₂²	—	356	1	no	—
424	C₂²	—	178	2	no	—
425	C₂²	—	712	2	no	—
426	C₂²	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	89	1	no	—
431	C₄	—	89	1	no	—
432	C₄	—	356	1	no	—
433	C₄	—	178	2	no	—
434	C₄	—	712	2	no	—
435	C₄	C₂²⋊Q₈×D₈₉	1	1	yes	characteristic
436	C₄	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
437	C₂	—	2	1	no	—
438	C₂	—	8	1	no	—
439	C₂	—	89	2	no	—
440	C₂	—	178	1	no	—
441	C₂	—	712	1	no	—
442	C₂	#476×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#476×D₈₉
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#2230	C₂
socle	C₂×C₈₉	C₂×#476
prime radical	#135×D₈₉	C₂²
hypercenter	#2230	D₈₉
hypocenter	C₈₉	C₂×#2230
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2230

Complements

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

N	H ≅ G/N	type
1. #498×D₈₉	C₂	semidirect
3. #26022424	C₂	semidirect
4. #26022423	C₂	semidirect
5. #26022422	C₂	semidirect
6. #26022421	C₂	semidirect
7. #26022420	C₂	semidirect
8. #365×D₈₉	C₂	semidirect
9. #364×D₈₉	C₂	semidirect
11. C₈₉×#2230	C₂	semidirect
16. #19151996	C₂²	semidirect
18. #19151995	C₂²	semidirect
30. #19151422	C₂²	semidirect
31. #19151421	C₂²	semidirect
32. #19151420	C₂²	semidirect
33. #19151419	C₂²	semidirect
34. #19151418	C₂²	semidirect
38. #498×C₈₉	C₂²	semidirect
40. #365×C₈₉	C₂²	semidirect
41. #364×C₈₉	C₂²	semidirect
45. #15668035	Q₈	semidirect
49. #15668031	Q₈	semidirect
50. Q₁₆×D₈₉	Q₈	semidirect
52. D₈×D₈₉	Q₈	semidirect
109. Dic₃₅₆	C₂×Q₈	semidirect
114. D₇₁₂	C₂×Q₈	semidirect
144. Q₁₆×C₈₉	C₂×Q₈	semidirect
146. D₈×C₈₉	C₂×Q₈	semidirect
221. D₈₉	#2230	direct (N × H)
229. #2230	D₈₉	direct (N × H)
233. C₈₉	C₂×#2230	semidirect
242. #498	C₂×D₈₉	semidirect
257. #365	C₂×D₈₉	semidirect
260. #364	C₂×D₈₉	semidirect
335. Q₁₆	Q₈×D₈₉	semidirect
342. D₈	Q₈×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#498×D₈₉	2
#443×D₈₉	2
#26022424	2
#26022423	2
#26022422	2
#26022421	2
#26022420	2
#365×D₈₉	2
#364×D₈₉	2
#360×D₈₉	2
C₈₉×#2230	2
C₂×#2230	89

Subgroups — #2230×D89 #36709154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2230×D₈₉ #36709154