Subgroups — #26031859

Order 11392.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668038	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15668037	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152244	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151980	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151846	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151842	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151813	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151810	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151760	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151758	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151732	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151731	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#13083559	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151676	C₂	1	1	yes	maximal, characteristic, complemented
15	#546×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083574	C₂²	1	1	yes	characteristic
17	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
18	#15668038	—	2	4	no	—
19	#15668037	—	2	4	no	—
20	C₂×#13083564	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13083562	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13083562	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13083559	C₂²	1	1	yes	characteristic
26	C₂×#13083559	C₂²	1	1	yes	characteristic
27	C₂×#13083559	C₂²	1	1	yes	characteristic
28	C₂×#13083559	C₂²	1	1	yes	characteristic
29	C₂×#13083558	C₂²	1	1	yes	characteristic, complemented
30	C₂×#13083558	C₂²	1	1	yes	characteristic, complemented
31	#15668000	C₂²	1	1	yes	characteristic, complemented
32	#15667997	—	2	1	no	—
33	#15667991	C₂²	1	1	yes	characteristic, complemented
34	#15667986	C₂²	1	1	yes	characteristic
35	#15667985	—	2	1	no	—
36	#15667980	—	2	1	no	—
37	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
38	C₂²⋊C₄×D₈₉	—	2	1	no	—
39	#15667945	C₂²	1	1	yes	characteristic, complemented
40	C₄⋊#10623494	C₂²	1	1	yes	characteristic, complemented
41	#15667936	C₂²	1	1	yes	characteristic, complemented
42	#15667935	C₂²	1	1	yes	characteristic, complemented
43	#15667933	C₂²	1	1	yes	characteristic, complemented
44	#15667933	C₂²	1	1	yes	characteristic, complemented
45	#15667932	C₂²	1	1	yes	characteristic, complemented
46	#15667932	C₂²	1	1	yes	characteristic, complemented
47	C₂²⋊#10623494	C₂²	1	1	yes	characteristic, complemented
48	C₂²⋊#10623494	C₂²	1	1	yes	characteristic, complemented
49	C₄×#10623494	C₂²	1	1	yes	characteristic, complemented
50	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic
51	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#123×C₈₉	—	2	1	no	—
54	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	#121×C₈₉	—	2	1	no	—
56	#121×C₈₉	C₂²	1	1	yes	characteristic
57	#120×C₈₉	—	2	1	no	—
58	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
59	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
61	C₂³×D₈₉	—	2	1	no	—
62	#13083574	—	2	2	no	—
63	#13083574	—	4	1	no	—
64	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
65	C₂×D₃₅₆	—	2	2	no	—
66	C₂×D₃₅₆	—	2	1	no	—
67	C₂×D₃₅₆	—	4	1	no	—
68	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
69	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₈₉	—	2	1	no	—
71	C₂×C₂²⋊D₈₉	—	2	1	no	—
72	C₂×C₄×D₈₉	—	2	1	no	—
73	C₂×C₄×D₈₉	—	2	1	no	—
74	#13083564	—	4	1	no	—
75	#13083562	—	2	2	no	—
76	#13083562	—	2	2	no	—
77	#13083561	—	2	2	no	—
78	#13083561	—	2	2	no	—
79	#13083559	—	2	2	no	—
80	#13083559	—	2	2	no	—
81	#13083559	—	4	1	no	—
82	#13083559	D₄	1	4	yes	complemented
83	#13083558	—	2	2	no	—
84	#13083558	—	2	2	no	—
85	C₂×#10623494	C₂³	1	1	yes	characteristic
86	C₂×#10623494	C₂³	1	1	yes	characteristic
87	C₂×#10623494	C₂³	1	1	yes	characteristic
88	C₂×#10623494	C₂³	1	1	yes	characteristic
89	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
90	#13083553	—	2	1	no	—
91	C₂²⋊Dic₈₉	—	2	1	no	—
92	#13083551	—	2	1	no	—
93	#13083551	—	2	1	no	—
94	#13083551	—	2	1	no	—
95	#13083551	—	2	1	no	—
96	C₂⁴×C₈₉	—	2	1	no	—
97	#41×C₈₉	—	2	2	no	—
98	#41×C₈₉	—	4	1	no	—
99	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₂×D₄×C₈₉	—	2	2	no	—
101	C₂×D₄×C₈₉	—	2	1	no	—
102	C₂×D₄×C₈₉	—	2	1	no	—
103	C₂×D₄×C₈₉	—	2	1	no	—
104	C₂×D₄×C₈₉	—	4	1	no	—
105	C₂×D₄×C₈₉	D₄	1	1	yes	characteristic
106	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×C₄×C₈₉	—	2	1	no	—
109	C₂²×C₄×C₈₉	—	2	1	no	—
110	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₄⋊C₄×C₈₉	—	2	1	no	—
113	C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
114	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂²⋊C₄×C₈₉	—	2	1	no	—
116	C₂²⋊C₄×C₈₉	—	2	1	no	—
117	C₂²⋊C₄×C₈₉	—	2	1	no	—
118	C₂²⋊C₄×C₈₉	—	2	1	no	—
119	C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
121	C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
122	C₄²×C₈₉	C₂³	1	1	yes	characteristic
123	C₂³×C₈₉	—	2	1	no	—
124	C₂³×C₈₉	—	2	1	no	—
125	C₂³×C₈₉	—	4	2	no	—
126	C₂³×C₈₉	—	4	2	no	—
127	C₂³×C₈₉	—	8	1	no	—
128	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×D₈₉	—	2	1	no	—
131	C₂²×D₈₉	—	2	1	no	—
132	C₂²×D₈₉	—	4	2	no	—
133	C₂²×D₈₉	—	4	2	no	—
134	C₂²×D₈₉	—	8	1	no	—
135	Q₈×C₈₉	—	2	1	no	—
136	Q₈×C₈₉	—	2	1	no	—
137	D₄×C₈₉	—	2	1	no	—
138	D₄×C₈₉	—	2	1	no	—
139	D₄×C₈₉	—	2	1	no	—
140	D₄×C₈₉	—	4	1	no	—
141	D₄×C₈₉	—	4	2	no	—
142	D₄×C₈₉	—	4	2	no	—
143	D₄×C₈₉	—	8	1	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	—	2	1	no	—
150	C₂×C₄×C₈₉	—	2	1	no	—
151	C₂×C₄×C₈₉	—	4	2	no	—
152	C₂×C₄×C₈₉	—	8	1	no	—
153	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
158	C₂²⋊D₈₉	—	4	2	no	—
159	C₂²⋊D₈₉	—	8	1	no	—
160	C₂×Dic₈₉	—	2	1	no	—
161	C₂×Dic₈₉	—	2	1	no	—
162	D₃₅₆	—	2	1	no	—
163	D₃₅₆	—	2	1	no	—
164	D₃₅₆	—	2	1	no	—
165	D₃₅₆	—	4	2	no	—
166	D₃₅₆	C₂×D₄	1	2	yes	—
167	C₄×D₈₉	—	4	2	no	—
168	C₄×D₈₉	—	8	1	no	—
169	Dic₁₇₈	—	2	1	no	—
170	Dic₁₇₈	—	2	1	no	—
171	#10623494	—	2	1	no	—
172	#10623494	—	2	1	no	—
173	#10623494	—	2	1	no	—
174	#10623494	C₂×D₄	1	2	yes	—
175	C₂²×C₈₉	—	2	1	no	—
176	C₂²×C₈₉	—	2	1	no	—
177	C₂²×C₈₉	—	2	2	no	—
178	C₂²×C₈₉	—	2	1	no	—
179	C₂²×C₈₉	—	2	1	no	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	—	2	1	no	—
182	C₂²×C₈₉	—	4	1	no	—
183	C₂²×C₈₉	—	4	1	no	—
184	C₂²×C₈₉	—	4	1	no	—
185	C₂²×C₈₉	—	4	1	no	—
186	C₂²×C₈₉	—	4	1	no	—
187	C₂²×C₈₉	—	8	4	no	—
188	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×D₈₉	—	2	2	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	—	8	4	no	—
196	C₄×C₈₉	—	2	1	no	—
197	C₄×C₈₉	—	2	1	no	—
198	C₄×C₈₉	—	2	1	no	—
199	C₄×C₈₉	—	2	1	no	—
200	C₄×C₈₉	—	4	1	no	—
201	C₄×C₈₉	—	4	1	no	—
202	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
203	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
204	Dic₈₉	—	4	1	no	—
205	Dic₈₉	—	4	1	no	—
206	C₂×C₈₉	—	4	1	no	—
207	C₂×C₈₉	—	4	1	no	—
208	C₂×C₈₉	—	4	2	no	—
209	C₂×C₈₉	—	8	1	no	—
210	C₂×C₈₉	D₄²	1	1	yes	characteristic
211	C₂×C₈₉	#575	1	1	yes	characteristic
212	C₂×C₈₉	#576	1	1	yes	characteristic
213	D₈₉	—	4	2	no	—
214	D₈₉	—	8	1	no	—
215	#3273	—	89	1	no	maximal, Sylow
216	C₈₉	#3273	1	1	yes	characteristic, complemented, Sylow
217	C₂×AGL(1,ℤ/8)	—	89	1	no	—
218	C₂×AGL(1,ℤ/8)	—	89	1	no	—
219	#546	—	89	1	no	—
220	#546	D₈₉	1	1	yes	characteristic, complemented
221	#495	—	89	1	no	—
222	#468	—	89	1	no	—
223	#468	—	89	1	no	—
224	#463	—	89	1	no	—
225	#463	—	89	1	no	—
226	#452	—	89	1	no	—
227	#452	—	89	1	no	—
228	#447	—	89	1	no	—
229	#447	—	89	1	no	—
230	C₄×D₈	—	89	1	no	—
231	#436	—	89	1	no	—
232	C₂×#41	—	89	1	no	—
233	C₂×#41	C₂×D₈₉	1	1	yes	characteristic
234	C₂²×D₄	—	89	1	no	—
235	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
236	AGL(1,ℤ/8)	—	178	4	no	—
237	AGL(1,ℤ/8)	—	178	4	no	—
238	C₂×Q₁₆	—	89	1	no	—
239	C₂×SD₁₆	—	89	1	no	—
240	C₂×SD₁₆	—	89	1	no	—
241	C₂×SD₁₆	—	89	1	no	—
242	C₂×SD₁₆	—	89	1	no	—
243	C₂×D₈	—	89	1	no	—
244	C₂×D₈	—	89	1	no	—
245	C₂×D₈	—	89	1	no	—
246	C₂×D₈	—	89	1	no	—
247	C₂×M₁₆	—	89	1	no	—
248	C₂×M₁₆	—	89	1	no	—
249	#124	—	89	1	no	—
250	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
251	#123	—	2	1	no	—
252	#123	—	178	1	no	—
253	C₂²⋊Q₈	—	89	1	no	—
254	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
255	#121	—	2	1	no	—
256	#121	—	89	1	no	—
257	#121	—	178	1	no	—
258	#121	C₂×D₈₉	1	1	yes	characteristic
259	#120	—	2	1	no	—
260	#120	—	178	1	no	—
261	C₄×D₄	—	89	1	no	—
262	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
263	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	178	1	no	—
266	#107	—	89	1	no	—
267	C₄⋊C₈	—	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	#102	—	89	1	no	—
274	C₂²⋊C₈	—	89	1	no	—
275	C₂²⋊C₈	—	89	1	no	—
276	C₄×C₈	—	89	1	no	—
277	C₂⁴	—	2	1	no	—
278	C₂⁴	—	178	1	no	—
279	#41	—	2	2	no	—
280	#41	—	4	1	no	—
281	#41	—	356	1	no	—
282	#41	—	178	2	no	—
283	C₂×Q₈	—	89	1	no	—
284	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	1	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	1	no	—
293	C₂×D₄	—	178	2	no	—
294	C₂×D₄	—	178	1	no	—
295	C₂×D₄	—	178	1	no	—
296	C₂×D₄	—	178	1	no	—
297	C₂×D₄	C₂²⋊D₈₉	1	1	yes	characteristic
298	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
299	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	178	1	no	—
303	C₂²×C₄	—	178	1	no	—
304	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
306	Q₁₆	—	356	1	no	—
307	SD₁₆	—	178	2	no	—
308	SD₁₆	—	178	2	no	—
309	SD₁₆	—	178	2	no	—
310	SD₁₆	—	178	2	no	—
311	D₈	—	89	4	no	—
312	D₈	—	356	1	no	—
313	D₈	—	178	2	no	—
314	D₈	—	178	2	no	—
315	M₁₆	—	178	2	no	—
316	M₁₆	—	178	2	no	—
317	C₂×C₈	—	89	1	no	—
318	C₂×C₈	—	89	1	no	—
319	C₂×C₈	—	89	1	no	—
320	C₂×C₈	—	89	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	89	1	no	—
323	C₄⋊C₄	—	178	1	no	—
324	C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
325	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
326	C₂²⋊C₄	—	2	1	no	—
327	C₂²⋊C₄	—	2	1	no	—
328	C₂²⋊C₄	—	2	1	no	—
329	C₂²⋊C₄	—	2	1	no	—
330	C₂²⋊C₄	—	2	1	no	—
331	C₂²⋊C₄	—	178	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	C₂²⋊D₈₉	1	1	yes	characteristic
337	C₂²⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
338	C₄²	C₂²×D₈₉	1	1	yes	characteristic
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	—	356	2	no	—
345	C₂³	—	356	2	no	—
346	C₂³	—	178	1	no	—
347	C₂³	—	178	1	no	—
348	C₂³	—	712	1	no	—
349	C₂³	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
350	C₂³	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
351	Q₈	—	2	1	no	—
352	Q₈	—	2	1	no	—
353	Q₈	—	178	1	no	—
354	Q₈	—	178	1	no	—
355	D₄	—	2	1	no	—
356	D₄	—	2	1	no	—
357	D₄	—	2	1	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	8	1	no	—
362	D₄	—	89	2	no	—
363	D₄	—	356	2	no	—
364	D₄	—	356	2	no	—
365	D₄	—	178	1	no	—
366	D₄	—	178	1	no	—
367	D₄	—	178	1	no	—
368	D₄	—	712	1	no	—
369	D₄	D₄×D₈₉	1	2	yes	—
370	C₂×C₄	—	2	1	no	—
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	—	2	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	8	1	no	—
378	C₂×C₄	—	356	2	no	—
379	C₂×C₄	—	178	1	no	—
380	C₂×C₄	—	178	1	no	—
381	C₂×C₄	—	712	1	no	—
382	C₂×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
383	C₂×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
384	C₂×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
385	C₂×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
386	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
387	C₈	—	89	2	no	—
388	C₈	—	178	1	no	—
389	C₈	—	178	1	no	—
390	C₈	—	178	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	8	4	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	—	178	2	no	—
410	C₂²	—	712	4	no	—
411	C₂²	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	356	1	no	—
419	C₄	—	356	1	no	—
420	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
421	C₄	#15668057	1	1	yes	characteristic
422	C₂	—	4	1	no	—
423	C₂	—	4	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	8	1	no	—
426	C₂	—	356	2	no	—
427	C₂	—	712	1	no	—
428	C₂	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
429	C₂	#19152396	1	1	yes	characteristic
430	C₂	#19152401	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#546×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	#546	D₈₉
hypocenter	C₈₉	#3273
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₂×#15668038	C₂	semidirect
2. C₂×#15668037	C₂	semidirect
3. #19152244	C₂	semidirect
4. #19151980	C₂	semidirect
5. #19151846	C₂	semidirect
6. #19151842	C₂	semidirect
7. #19151813	C₂	semidirect
8. #19151810	C₂	semidirect
9. #19151760	C₂	semidirect
10. #19151758	C₂	semidirect
11. #19151732	C₂	semidirect
12. #19151731	C₂	semidirect
13. C₄×#13083559	C₂	semidirect
14. #19151676	C₂	semidirect
15. #546×C₈₉	C₂	semidirect
17. C₂²×D₃₅₆	C₂²	semidirect
20. C₂×#13083564	C₂²	semidirect
21. C₂×#13083562	C₂²	semidirect
22. C₂×#13083562	C₂²	semidirect
23. C₂×#13083561	C₂²	semidirect
24. C₂×#13083561	C₂²	semidirect
29. C₂×#13083558	C₂²	semidirect
30. C₂×#13083558	C₂²	semidirect
31. #15668000	C₂²	semidirect
33. #15667991	C₂²	semidirect
37. C₄×D₃₅₆	C₂²	semidirect
39. #15667945	C₂²	semidirect
40. C₄⋊#10623494	C₂²	semidirect
41. #15667936	C₂²	semidirect
42. #15667935	C₂²	semidirect
43. #15667933	C₂²	semidirect
44. #15667933	C₂²	semidirect
45. #15667932	C₂²	semidirect
46. #15667932	C₂²	semidirect
47. C₂²⋊#10623494	C₂²	semidirect
48. C₂²⋊#10623494	C₂²	semidirect
49. C₄×#10623494	C₂²	semidirect
51. C₂²×D₄×C₈₉	C₂²	semidirect
52. #124×C₈₉	C₂²	semidirect
54. C₂²⋊Q₈×C₈₉	C₂²	semidirect
59. C₄×D₄×C₈₉	C₂²	semidirect
82. #13083559	D₄	semidirect
216. C₈₉	#3273	semidirect
220. #546	D₈₉	semidirect
235. C₂²×D₄	C₂×D₈₉	semidirect
250. #124	C₂×D₈₉	semidirect
254. C₂²⋊Q₈	C₂×D₈₉	semidirect
263. C₄×D₄	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15668038	2
C₂×#15668037	2
#19152244	2
#19151980	2
#19151846	2
#19151842	2
#19151813	2
#19151810	2
#19151760	2
#19151758	2
#19151732	2
#19151731	2
C₄×#13083559	2
#19151676	2
#546×C₈₉	2
#3273	89