Subgroups — #26031749

Order 11392.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668039	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×SD₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152260	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151987	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151845	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151835	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151813	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151798	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151750	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151746	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151738	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151733	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151671	C₂	1	1	yes	maximal, characteristic, complemented
15	#440×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083575	C₂²	1	1	yes	characteristic, complemented
17	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₃₅₆	—	2	1	no	—
19	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
20	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
21	#15668039	—	2	4	no	—
22	C₂×#13083563	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13083563	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13083562	C₂²	1	1	yes	characteristic
25	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
26	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
27	SD₁₆×D₈₉	—	2	4	no	—
28	C₂×D₇₁₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₇₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₂×#13083559	C₂²	1	1	yes	characteristic
31	C₂×#13083557	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
33	#15668009	C₂²	1	1	yes	characteristic
34	#15668000	—	2	1	no	—
35	#15668000	C₂²	1	1	yes	characteristic, complemented
36	#15667992	—	2	1	no	—
37	#15667992	C₂²	1	1	yes	characteristic, complemented
38	#15667987	—	2	1	no	—
39	#15667987	C₂²	1	1	yes	characteristic
40	#15667987	C₂²	1	1	yes	characteristic
41	#15667987	C₂²	1	1	yes	characteristic, complemented
42	#15667986	—	2	1	no	—
43	#15667982	—	2	1	no	—
44	#15667982	—	2	1	no	—
45	C₄×D₃₅₆	—	2	1	no	—
46	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
47	C₄⋊#10623494	C₂²	1	1	yes	characteristic, complemented
48	#15667935	C₂²	1	1	yes	characteristic, complemented
49	#15667932	C₂²	1	1	yes	characteristic, complemented
50	#15667932	C₂²	1	1	yes	characteristic, complemented
51	#15667932	C₂²	1	1	yes	characteristic, complemented
52	#15667924	C₂²	1	1	yes	characteristic, complemented
53	#15667924	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
55	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
57	#107×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#102×C₈₉	C₂²	1	1	yes	characteristic
60	#97×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₈₉	—	2	1	no	—
62	C₂³×D₈₉	—	2	1	no	—
63	#13083575	—	2	2	no	—
64	#13083575	—	4	1	no	—
65	C₂×Dic₁₇₈	—	2	1	no	—
66	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
67	Q₈×D₈₉	—	2	2	no	—
68	Q₈×D₈₉	—	4	1	no	—
69	C₂×D₃₅₆	—	2	1	no	—
70	C₂×D₃₅₆	—	2	1	no	—
71	C₂×D₃₅₆	—	2	1	no	—
72	C₂×D₃₅₆	—	2	1	no	—
73	C₂×D₃₅₆	—	2	1	no	—
74	C₂×D₃₅₆	—	2	1	no	—
75	C₂×D₃₅₆	—	4	4	no	—
76	C₂×D₃₅₆	D₄	1	1	yes	characteristic
77	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
78	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
79	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
80	C₂×C₂²⋊D₈₉	—	2	1	no	—
81	C₂×C₂²⋊D₈₉	—	2	1	no	—
82	D₄×D₈₉	—	2	2	no	—
83	D₄×D₈₉	—	2	2	no	—
84	D₄×D₈₉	—	4	1	no	—
85	D₄×D₈₉	—	4	1	no	—
86	C₂×C₄×D₈₉	—	2	1	no	—
87	C₂×C₄×D₈₉	—	2	1	no	—
88	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
90	#13083563	—	2	2	no	—
91	#13083563	—	4	1	no	—
92	#13083562	—	2	2	no	—
93	#13083561	—	2	2	no	—
94	#13083561	—	2	2	no	—
95	D₇₁₂	—	2	2	no	—
96	D₇₁₂	—	4	1	no	—
97	#13083559	—	2	2	no	—
98	#13083557	—	2	2	no	—
99	C₂×#10623494	C₂³	1	1	yes	characteristic
100	C₂×#10623494	C₂³	1	1	yes	characteristic
101	C₈×D₈₉	—	2	2	no	—
102	C₄⋊Dic₈₉	—	2	1	no	—
103	C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
104	#13083551	—	2	1	no	—
105	#13083551	—	2	1	no	—
106	#13083551	—	2	1	no	—
107	#13083551	—	2	1	no	—
108	#13083551	—	2	1	no	—
109	#13083551	—	2	1	no	—
110	#13083551	D₄	1	1	yes	characteristic
111	#13083551	D₄	1	1	yes	characteristic
112	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	—	2	1	no	—
115	SD₁₆×C₈₉	D₄	1	4	yes	complemented
116	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
118	C₄⋊C₄×C₈₉	—	2	1	no	—
119	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
120	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
121	C₂²⋊C₄×C₈₉	—	2	1	no	—
122	C₄²×C₈₉	—	2	1	no	—
123	C₄²×C₈₉	C₂³	1	1	yes	characteristic
124	C₂³×C₈₉	—	2	1	no	—
125	C₂²×D₈₉	—	2	1	no	—
126	C₂²×D₈₉	—	2	1	no	—
127	C₂²×D₈₉	—	2	1	no	—
128	C₂²×D₈₉	—	4	2	no	—
129	C₂²×D₈₉	—	4	2	no	—
130	C₂²×D₈₉	—	4	2	no	—
131	C₂²×D₈₉	—	4	2	no	—
132	C₂²×D₈₉	—	8	1	no	—
133	C₂²×D₈₉	—	8	1	no	—
134	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₈₉	—	2	1	no	—
137	Q₈×C₈₉	C₂×D₄	1	2	yes	complemented
138	D₄×C₈₉	—	2	1	no	—
139	D₄×C₈₉	C₂×D₄	1	2	yes	—
140	C₂×C₄×C₈₉	—	2	1	no	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	2	1	no	—
143	C₂×C₄×C₈₉	—	4	2	no	—
144	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
147	C₂²⋊D₈₉	—	4	2	no	—
148	C₂²⋊D₈₉	—	4	2	no	—
149	C₂×Dic₈₉	—	2	1	no	—
150	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
152	D₃₅₆	—	2	2	no	—
153	D₃₅₆	—	2	1	no	—
154	D₃₅₆	—	2	1	no	—
155	D₃₅₆	—	2	1	no	—
156	D₃₅₆	—	2	1	no	—
157	D₃₅₆	—	2	1	no	—
158	D₃₅₆	—	2	1	no	—
159	D₃₅₆	—	4	2	no	—
160	D₃₅₆	—	4	2	no	—
161	D₃₅₆	—	4	2	no	—
162	D₃₅₆	—	4	2	no	—
163	D₃₅₆	—	4	2	no	—
164	D₃₅₆	—	8	1	no	—
165	C₄×D₈₉	—	2	1	no	—
166	C₄×D₈₉	—	2	1	no	—
167	C₄×D₈₉	—	2	1	no	—
168	C₄×D₈₉	—	2	1	no	—
169	C₄×D₈₉	—	4	2	no	—
170	C₄×D₈₉	—	4	2	no	—
171	Dic₁₇₈	—	2	1	no	—
172	Dic₁₇₈	—	2	1	no	—
173	Dic₁₇₈	—	4	2	no	—
174	C₈×C₈₉	—	2	1	no	—
175	C₈×C₈₉	C₂×D₄	1	2	yes	complemented
176	#10623494	—	2	1	no	—
177	#10623494	—	2	1	no	—
178	C₂²×C₈₉	—	2	2	no	—
179	C₂²×C₈₉	—	4	1	no	—
180	C₂²×C₈₉	—	4	1	no	—
181	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×D₈₉	—	2	1	no	—
183	C₂×D₈₉	—	2	1	no	—
184	C₂×D₈₉	—	2	1	no	—
185	C₂×D₈₉	—	2	1	no	—
186	C₂×D₈₉	—	2	1	no	—
187	C₂×D₈₉	—	4	1	no	—
188	C₂×D₈₉	—	4	1	no	—
189	C₂×D₈₉	—	4	1	no	—
190	C₂×D₈₉	—	4	1	no	—
191	C₂×D₈₉	—	4	1	no	—
192	C₂×D₈₉	—	4	1	no	—
193	C₂×D₈₉	—	4	1	no	—
194	C₂×D₈₉	—	4	1	no	—
195	C₂×D₈₉	—	4	1	no	—
196	C₂×D₈₉	—	8	4	no	—
197	C₂×D₈₉	—	8	4	no	—
198	C₂×D₈₉	AGL(1,ℤ/8)	1	2	yes	complemented
199	C₄×C₈₉	—	2	2	no	—
200	C₄×C₈₉	—	2	1	no	—
201	C₄×C₈₉	—	2	1	no	—
202	C₄×C₈₉	—	4	1	no	—
203	C₄×C₈₉	—	4	1	no	—
204	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
205	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
206	Dic₈₉	—	2	1	no	—
207	Dic₈₉	—	2	1	no	—
208	Dic₈₉	—	4	1	no	—
209	C₂×C₈₉	—	4	2	no	—
210	C₂×C₈₉	D₄²	1	1	yes	characteristic
211	C₂×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂×C₈₉	#577	1	1	yes	characteristic
213	D₈₉	—	2	2	no	—
214	D₈₉	—	4	1	no	—
215	D₈₉	—	8	1	no	—
216	D₈₉	—	8	1	no	—
217	D₈₉	—	8	1	no	—
218	#3265	—	89	1	no	maximal, Sylow
219	C₈₉	#3265	1	1	yes	characteristic, complemented, Sylow
220	C₂×AGL(1,ℤ/8)	—	89	1	no	—
221	C₂²×SD₁₆	—	89	1	no	—
222	#548	—	89	1	no	—
223	D₄²	—	89	1	no	—
224	#496	—	89	1	no	—
225	#468	—	89	1	no	—
226	#466	—	89	1	no	—
227	#463	—	89	1	no	—
228	#460	—	89	1	no	—
229	#450	—	89	1	no	—
230	#449	—	89	1	no	—
231	#448	—	89	1	no	—
232	#447	—	89	1	no	—
233	#440	D₈₉	1	1	yes	characteristic, complemented
234	#435	—	89	1	no	—
235	C₂×#41	—	89	1	no	—
236	C₂²×Q₈	—	89	1	no	—
237	C₂²×D₄	—	89	1	no	—
238	C₂²×D₄	—	89	1	no	—
239	C₂²×D₄	—	178	1	no	—
240	AGL(1,ℤ/8)	—	178	4	no	—
241	C₂×SD₁₆	—	89	1	no	—
242	C₂×SD₁₆	—	89	1	no	—
243	C₂×SD₁₆	—	89	1	no	—
244	C₂×SD₁₆	—	89	1	no	—
245	C₂×SD₁₆	—	89	1	no	—
246	C₂×SD₁₆	—	178	4	no	—
247	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
248	C₂×D₈	—	89	1	no	—
249	C₂×D₈	—	89	1	no	—
250	C₂×D₈	—	89	1	no	—
251	C₂×M₁₆	—	89	1	no	—
252	C₂²×C₈	—	89	1	no	—
253	#127	—	89	1	no	—
254	#124	—	89	1	no	—
255	#124	—	178	1	no	—
256	C₂²⋊Q₈	—	89	1	no	—
257	C₂²⋊Q₈	—	178	1	no	—
258	#121	—	89	1	no	—
259	#121	—	89	1	no	—
260	#121	—	89	1	no	—
261	#121	—	178	1	no	—
262	#121	—	178	1	no	—
263	#120	—	178	1	no	—
264	#120	—	178	1	no	—
265	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
266	C₄×D₄	—	89	1	no	—
267	C₄×D₄	—	178	1	no	—
268	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
269	#107	C₂×D₈₉	1	1	yes	characteristic, complemented
270	C₄⋊C₈	—	89	1	no	—
271	#103	—	89	1	no	—
272	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
273	#102	—	89	1	no	—
274	#102	—	89	1	no	—
275	#102	—	89	1	no	—
276	#102	C₂×D₈₉	1	1	yes	characteristic
277	C₂²⋊C₈	—	89	1	no	—
278	C₂²⋊C₈	—	89	1	no	—
279	#97	C₂×D₈₉	1	1	yes	characteristic, complemented
280	C₂⁴	—	178	1	no	—
281	C₂⁴	—	178	1	no	—
282	#41	—	356	1	no	—
283	#41	—	178	2	no	—
284	C₂×Q₈	—	89	1	no	—
285	C₂×Q₈	—	356	1	no	—
286	C₂×Q₈	—	178	1	no	—
287	C₂×Q₈	—	178	2	no	—
288	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
289	C₂×D₄	—	89	1	no	—
290	C₂×D₄	—	89	1	no	—
291	C₂×D₄	—	89	1	no	—
292	C₂×D₄	—	89	1	no	—
293	C₂×D₄	—	356	4	no	—
294	C₂×D₄	—	356	1	no	—
295	C₂×D₄	—	356	1	no	—
296	C₂×D₄	—	178	1	no	—
297	C₂×D₄	—	178	1	no	—
298	C₂×D₄	—	178	1	no	—
299	C₂×D₄	—	178	1	no	—
300	C₂×D₄	—	178	1	no	—
301	C₂×D₄	—	178	1	no	—
302	C₂×D₄	—	178	2	no	—
303	C₂×D₄	—	178	2	no	—
304	C₂×D₄	—	178	1	no	—
305	C₂×D₄	—	178	1	no	—
306	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	89	1	no	—
309	C₂²×C₄	—	89	1	no	—
310	C₂²×C₄	—	178	1	no	—
311	C₂²×C₄	—	178	1	no	—
312	SD₁₆	—	356	1	no	—
313	SD₁₆	—	178	2	no	—
314	SD₁₆	—	178	2	no	—
315	SD₁₆	—	178	2	no	—
316	SD₁₆	—	178	2	no	—
317	SD₁₆	D₃₅₆	1	4	yes	complemented
318	D₈	—	356	1	no	—
319	D₈	—	178	2	no	—
320	D₈	—	178	2	no	—
321	M₁₆	—	178	2	no	—
322	C₂×C₈	—	89	1	no	—
323	C₂×C₈	—	89	1	no	—
324	C₂×C₈	—	178	2	no	—
325	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	89	1	no	—
329	C₄⋊C₄	—	178	1	no	—
330	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
331	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	89	1	no	—
334	C₂²⋊C₄	—	89	1	no	—
335	C₂²⋊C₄	—	178	1	no	—
336	C₂²⋊C₄	—	178	1	no	—
337	C₂²⋊C₄	—	178	1	no	—
338	C₂²⋊C₄	—	178	1	no	—
339	C₂²⋊C₄	—	178	1	no	—
340	C₂²⋊C₄	—	178	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	C₂²×D₈₉	1	1	yes	characteristic
343	C₂³	—	2	1	no	—
344	C₂³	—	89	1	no	—
345	C₂³	—	89	1	no	—
346	C₂³	—	356	2	no	—
347	C₂³	—	356	2	no	—
348	C₂³	—	356	2	no	—
349	C₂³	—	356	2	no	—
350	C₂³	—	178	1	no	—
351	C₂³	—	178	1	no	—
352	C₂³	—	178	1	no	—
353	C₂³	—	712	1	no	—
354	C₂³	—	712	1	no	—
355	Q₈	—	2	1	no	—
356	Q₈	—	356	2	no	—
357	Q₈	—	178	1	no	—
358	Q₈	—	178	1	no	—
359	Q₈	C₂×D₃₅₆	1	2	yes	complemented
360	D₄	—	2	1	no	—
361	D₄	—	356	2	no	—
362	D₄	—	356	2	no	—
363	D₄	—	356	2	no	—
364	D₄	—	356	2	no	—
365	D₄	—	356	2	no	—
366	D₄	—	356	2	no	—
367	D₄	—	356	2	no	—
368	D₄	—	178	2	no	—
369	D₄	—	178	1	no	—
370	D₄	—	178	1	no	—
371	D₄	—	178	1	no	—
372	D₄	—	178	1	no	—
373	D₄	—	178	1	no	—
374	D₄	—	178	1	no	—
375	D₄	—	712	1	no	—
376	D₄	C₂×D₃₅₆	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	89	1	no	—
382	C₂×C₄	—	89	1	no	—
383	C₂×C₄	—	356	2	no	—
384	C₂×C₄	—	356	2	no	—
385	C₂×C₄	—	178	1	no	—
386	C₂×C₄	—	178	1	no	—
387	C₂×C₄	—	178	1	no	—
388	C₂×C₄	—	178	1	no	—
389	C₂×C₄	—	178	1	no	—
390	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
391	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	178	1	no	—
395	C₈	—	178	1	no	—
396	C₈	C₂×D₃₅₆	1	2	yes	complemented
397	C₂²	—	2	2	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	89	2	no	—
401	C₂²	—	356	1	no	—
402	C₂²	—	356	1	no	—
403	C₂²	—	356	1	no	—
404	C₂²	—	356	1	no	—
405	C₂²	—	356	1	no	—
406	C₂²	—	356	1	no	—
407	C₂²	—	356	1	no	—
408	C₂²	—	356	1	no	—
409	C₂²	—	356	1	no	—
410	C₂²	—	178	1	no	—
411	C₂²	—	178	1	no	—
412	C₂²	—	178	1	no	—
413	C₂²	—	178	1	no	—
414	C₂²	—	178	1	no	—
415	C₂²	—	712	4	no	—
416	C₂²	—	712	4	no	—
417	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	356	1	no	—
424	C₄	—	178	1	no	—
425	C₄	—	178	1	no	—
426	C₄	C₂²×D₃₅₆	1	1	yes	characteristic
427	C₄	#15668058	1	1	yes	characteristic
428	C₂	—	4	2	no	—
429	C₂	—	356	1	no	—
430	C₂	—	178	2	no	—
431	C₂	—	712	1	no	—
432	C₂	—	712	1	no	—
433	C₂	—	712	1	no	—
434	C₂	D₄×D₃₅₆	1	1	yes	characteristic
435	C₂	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
436	C₂	#19152407	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#440×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	#440	D₈₉
hypocenter	C₈₉	#3265
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #440

Complements

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

N	H ≅ G/N	type
1. C₂×#15668039	C₂	semidirect
2. C₂×SD₁₆×D₈₉	C₂	semidirect
3. #19152260	C₂	semidirect
4. D₄×D₃₅₆	C₂	semidirect
5. #19151987	C₂	semidirect
6. #19151845	C₂	semidirect
7. #19151835	C₂	semidirect
8. #19151813	C₂	semidirect
9. #19151798	C₂	semidirect
10. #19151750	C₂	semidirect
11. #19151746	C₂	semidirect
12. #19151738	C₂	semidirect
13. #19151733	C₂	semidirect
14. #19151671	C₂	semidirect
15. #440×C₈₉	C₂	semidirect
16. C₂×#13083575	C₂²	semidirect
17. C₂×Q₈×D₈₉	C₂²	semidirect
22. C₂×#13083563	C₂²	semidirect
23. C₂×#13083563	C₂²	semidirect
25. C₂×#13083561	C₂²	semidirect
26. C₂×#13083561	C₂²	semidirect
28. C₂×D₇₁₂	C₂²	semidirect
29. C₂×D₇₁₂	C₂²	semidirect
31. C₂×#13083557	C₂²	semidirect
32. C₂×C₈×D₈₉	C₂²	semidirect
35. #15668000	C₂²	semidirect
37. #15667992	C₂²	semidirect
41. #15667987	C₂²	semidirect
47. C₄⋊#10623494	C₂²	semidirect
48. #15667935	C₂²	semidirect
49. #15667932	C₂²	semidirect
50. #15667932	C₂²	semidirect
51. #15667932	C₂²	semidirect
52. #15667924	C₂²	semidirect
53. #15667924	C₂²	semidirect
55. C₄×Q₈×C₈₉	C₂²	semidirect
57. #107×C₈₉	C₂²	semidirect
58. #103×C₈₉	C₂²	semidirect
60. #97×C₈₉	C₂²	semidirect
115. SD₁₆×C₈₉	D₄	semidirect
137. Q₈×C₈₉	C₂×D₄	semidirect
175. C₈×C₈₉	C₂×D₄	semidirect
198. C₂×D₈₉	AGL(1,ℤ/8)	semidirect
219. C₈₉	#3265	semidirect
233. #440	D₈₉	semidirect
265. C₄×Q₈	C₂×D₈₉	semidirect
269. #107	C₂×D₈₉	semidirect
272. #103	C₂×D₈₉	semidirect
279. #97	C₂×D₈₉	semidirect
317. SD₁₆	D₃₅₆	semidirect
359. Q₈	C₂×D₃₅₆	semidirect
396. C₈	C₂×D₃₅₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15668039	2
C₂×SD₁₆×D₈₉	2
#19152260	2
D₄×D₃₅₆	2
#19151987	2
#19151845	2
#19151835	2
#19151813	2
#19151798	2
#19151750	2
#19151746	2
#19151738	2
#19151733	2
#19151671	2
#440×C₈₉	2
#3265	89