Subgroups — #36455519

Order 22784.

670 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151946	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151798	C₂	1	1	yes	maximal, characteristic
3	#26021179	C₂	1	1	yes	maximal, characteristic
4	C₂×#19151344	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈⋊#10623494	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018093	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13083561	—	2	1	no	—
9	C₂×#15668009	C₂²	1	1	yes	characteristic
10	#19151946	—	2	2	no	—
11	#19151946	—	2	2	no	—
12	#19151798	—	2	2	no	—
13	#19151798	—	2	2	no	—
14	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
16	C₂×#15667932	—	2	1	no	—
17	C₂×#15667932	—	2	2	no	—
18	C₂×#15667932	—	2	2	no	—
19	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
20	#19151344	—	2	2	no	—
21	Q₈⋊#10623494	—	2	2	no	—
22	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
23	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	#398×C₈₉	—	2	2	no	—
26	#391×C₈₉	—	2	1	no	—
27	#389×C₈₉	—	2	2	no	—
28	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×D₃₅₆	—	2	1	no	—
30	C₂²×D₃₅₆	—	2	1	no	—
31	C₂²×D₃₅₆	—	2	1	no	—
32	C₂×#13083561	—	2	4	no	—
33	C₂×#13083561	—	4	2	no	—
34	C₂×#13083561	—	4	2	no	—
35	C₂²×#10623494	—	2	1	no	—
36	C₂²×#10623494	—	2	1	no	—
37	C₂²×#10623494	—	2	1	no	—
38	#15668009	—	2	1	no	—
39	#15668009	—	2	1	no	—
40	#15668009	—	2	1	no	—
41	#15668009	D₄	1	2	yes	—
42	C₄⋊#10623494	—	2	1	no	—
43	C₄⋊#10623494	—	2	1	no	—
44	C₄⋊#10623494	—	2	1	no	—
45	C₄⋊#10623494	D₄	1	2	yes	—
46	#15667932	—	2	8	no	—
47	#15667932	—	2	4	no	—
48	#15667932	—	4	4	no	—
49	C₄×#10623494	—	2	1	no	—
50	C₄×#10623494	D₄	1	2	yes	—
51	C₂²×Q₈×C₈₉	—	2	1	no	—
52	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
53	C₄⋊Q₈×C₈₉	—	2	1	no	—
54	C₄⋊Q₈×C₈₉	—	2	1	no	—
55	C₄⋊Q₈×C₈₉	—	2	1	no	—
56	C₄⋊Q₈×C₈₉	—	2	1	no	—
57	C₄⋊Q₈×C₈₉	—	4	2	no	—
58	C₄⋊Q₈×C₈₉	—	4	2	no	—
59	C₄×Q₈×C₈₉	—	2	1	no	—
60	C₄×Q₈×C₈₉	—	2	1	no	—
61	C₄×Q₈×C₈₉	—	2	1	no	—
62	C₄×Q₈×C₈₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
64	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
69	C₂×C₄²×C₈₉	—	2	1	no	—
70	C₂×C₄²×C₈₉	—	2	1	no	—
71	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
72	#95×C₈₉	—	2	4	no	—
73	#95×C₈₉	—	2	1	no	—
74	C₂³×D₈₉	—	4	1	no	—
75	C₂×D₃₅₆	—	2	2	no	—
76	C₂×D₃₅₆	—	2	2	no	—
77	C₂×D₃₅₆	—	2	2	no	—
78	C₂×D₃₅₆	—	4	4	no	—
79	C₂×D₃₅₆	—	4	1	no	—
80	C₂×D₃₅₆	—	4	2	no	—
81	C₂×D₃₅₆	—	4	1	no	—
82	C₂×D₃₅₆	—	4	1	no	—
83	C₂×D₃₅₆	—	4	1	no	—
84	C₂×D₃₅₆	—	4	2	no	—
85	C₂×D₃₅₆	—	4	1	no	—
86	C₂×D₃₅₆	—	4	1	no	—
87	C₂×D₃₅₆	—	4	1	no	—
88	#13083561	—	4	8	no	—
89	C₂×#10623494	—	2	2	no	—
90	C₂×#10623494	—	2	2	no	—
91	C₂×#10623494	—	4	2	no	—
92	C₂×#10623494	—	4	1	no	—
93	C₂×#10623494	—	4	1	no	—
94	C₂×#10623494	—	4	1	no	—
95	C₂×#10623494	—	4	2	no	—
96	C₂×Q₈×C₈₉	—	2	1	no	—
97	C₂×Q₈×C₈₉	—	2	1	no	—
98	C₂×Q₈×C₈₉	—	2	1	no	—
99	C₂×Q₈×C₈₉	—	2	1	no	—
100	C₂×Q₈×C₈₉	—	2	1	no	—
101	C₂×Q₈×C₈₉	—	4	1	no	—
102	C₂×Q₈×C₈₉	—	4	1	no	—
103	C₂×Q₈×C₈₉	—	4	1	no	—
104	C₂×Q₈×C₈₉	—	4	1	no	—
105	C₂×Q₈×C₈₉	—	4	1	no	—
106	C₂×Q₈×C₈₉	—	4	1	no	—
107	C₂×Q₈×C₈₉	D₈	1	2	yes	—
108	C₂²×C₄×C₈₉	—	2	2	no	—
109	C₂²×C₄×C₈₉	—	2	1	no	—
110	C₂²×C₄×C₈₉	—	2	1	no	—
111	C₂²×C₄×C₈₉	—	2	2	no	—
112	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
115	C₄⋊C₄×C₈₉	—	2	2	no	—
116	C₄⋊C₄×C₈₉	—	2	1	no	—
117	C₄⋊C₄×C₈₉	—	2	2	no	—
118	C₄⋊C₄×C₈₉	—	2	1	no	—
119	C₄⋊C₄×C₈₉	—	2	2	no	—
120	C₄⋊C₄×C₈₉	—	4	8	no	—
121	C₄⋊C₄×C₈₉	—	4	1	no	—
122	C₄⋊C₄×C₈₉	—	4	1	no	—
123	C₄⋊C₄×C₈₉	—	4	1	no	—
124	C₄⋊C₄×C₈₉	—	4	1	no	—
125	C₄⋊C₄×C₈₉	SD₁₆	1	4	yes	complemented
126	C₄²×C₈₉	—	4	1	no	—
127	C₄²×C₈₉	—	4	1	no	—
128	C₄²×C₈₉	—	4	1	no	—
129	C₄²×C₈₉	—	4	1	no	—
130	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₈₉	#41	1	1	yes	characteristic
134	C₂³×C₈₉	#120	1	1	yes	characteristic
135	C₂²×D₈₉	—	4	2	no	—
136	C₂²×D₈₉	—	8	1	no	—
137	C₂²×D₈₉	—	8	2	no	—
138	C₂²×D₈₉	—	8	1	no	—
139	C₂²×D₈₉	—	8	2	no	—
140	Q₈×C₈₉	—	2	2	no	—
141	Q₈×C₈₉	—	2	2	no	—
142	Q₈×C₈₉	—	4	1	no	—
143	Q₈×C₈₉	—	4	1	no	—
144	Q₈×C₈₉	—	8	1	no	—
145	Q₈×C₈₉	—	8	1	no	—
146	Q₈×C₈₉	—	8	1	no	—
147	Q₈×C₈₉	—	8	1	no	—
148	C₂×C₄×C₈₉	—	2	2	no	—
149	C₂×C₄×C₈₉	—	2	2	no	—
150	C₂×C₄×C₈₉	—	2	4	no	—
151	C₂×C₄×C₈₉	—	4	1	no	—
152	C₂×C₄×C₈₉	—	4	2	no	—
153	C₂×C₄×C₈₉	—	4	1	no	—
154	C₂×C₄×C₈₉	—	4	2	no	—
155	C₂×C₄×C₈₉	—	4	1	no	—
156	C₂×C₄×C₈₉	—	4	2	no	—
157	C₂×C₄×C₈₉	—	4	2	no	—
158	C₂×C₄×C₈₉	—	4	2	no	—
159	C₂×C₄×C₈₉	—	4	2	no	—
160	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
161	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
162	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
164	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
165	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
168	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
169	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂×C₄×C₈₉	#137	1	2	yes	—
172	D₃₅₆	—	4	4	no	—
173	D₃₅₆	—	4	2	no	—
174	D₃₅₆	—	4	2	no	—
175	D₃₅₆	—	4	4	no	—
176	D₃₅₆	—	8	2	no	—
177	D₃₅₆	—	8	1	no	—
178	D₃₅₆	—	8	1	no	—
179	D₃₅₆	—	8	1	no	—
180	D₃₅₆	—	8	1	no	—
181	#10623494	—	4	2	no	—
182	#10623494	—	4	2	no	—
183	#10623494	—	8	1	no	—
184	C₂²×C₈₉	#392	1	1	yes	characteristic
185	C₂²×C₈₉	#447	1	1	yes	characteristic
186	C₂²×C₈₉	#448	1	2	yes	—
187	C₂²×C₈₉	#449	1	1	yes	characteristic
188	C₂²×C₈₉	#454	1	2	yes	—
189	C₂×D₈₉	—	8	2	no	—
190	C₂×D₈₉	—	8	2	no	—
191	C₂×D₈₉	—	8	2	no	—
192	C₂×D₈₉	—	16	2	no	—
193	C₂×D₈₉	—	16	2	no	—
194	C₄×C₈₉	—	2	1	no	—
195	C₄×C₈₉	—	2	1	no	—
196	C₄×C₈₉	—	4	4	no	—
197	C₄×C₈₉	—	4	2	no	—
198	C₄×C₈₉	—	8	2	no	—
199	C₄×C₈₉	—	8	1	no	—
200	C₄×C₈₉	#447	1	1	yes	characteristic
201	C₄×C₈₉	#449	1	1	yes	characteristic
202	C₄×C₈₉	#461	1	2	yes	—
203	C₄×C₈₉	#466	1	1	yes	characteristic
204	C₄×C₈₉	#469	1	1	yes	characteristic
205	C₄×C₈₉	#492	1	1	yes	characteristic
206	C₄×C₈₉	#497	1	1	yes	characteristic
207	#10051	—	89	1	no	maximal, Sylow
208	C₂×C₈₉	#1626	1	2	yes	—
209	C₂×C₈₉	#1627	1	2	yes	—
210	C₂×C₈₉	#1999	1	1	yes	characteristic
211	C₂×C₈₉	#2003	1	1	yes	characteristic
212	C₂×C₈₉	#2013	1	1	yes	characteristic
213	D₈₉	—	16	2	no	—
214	C₂×#486	—	89	1	no	—
215	C₂×#460	—	89	1	no	—
216	#2546	D₈₉	1	1	yes	characteristic, complemented
217	#1982	—	89	1	no	—
218	C₂×#332	—	89	1	no	—
219	C₂×Q₈⋊C₈	—	89	1	no	—
220	#1279	—	89	1	no	—
221	C₈₉	#10051	1	1	yes	characteristic, complemented, Sylow
222	C₂²×SD₁₆	—	178	1	no	—
223	C₂×C₄⋊Q₈	—	2	1	no	—
224	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
225	C₂×#127	—	89	1	no	—
226	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
227	#486	—	178	2	no	—
228	#486	—	178	2	no	—
229	#460	—	178	2	no	—
230	#460	—	178	2	no	—
231	C₂×C₄⋊C₈	—	89	1	no	—
232	C₂×C₄⋊C₈	—	89	1	no	—
233	C₂×#102	—	178	2	no	—
234	C₂×#102	—	178	2	no	—
235	C₂×#102	—	178	1	no	—
236	C₂×C₄×C₈	—	89	1	no	—
237	#398	—	2	2	no	—
238	#391	—	2	1	no	—
239	#389	—	2	2	no	—
240	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
241	#332	—	178	2	no	—
242	Q₈⋊C₈	—	178	2	no	—
243	C₂²×Q₈	—	2	1	no	—
244	C₂²×Q₈	C₂²⋊D₈₉	1	1	yes	characteristic
245	C₂²×D₄	—	178	1	no	—
246	C₂²×D₄	—	178	1	no	—
247	C₂²×D₄	—	178	1	no	—
248	C₂×SD₁₆	—	356	2	no	—
249	C₂×SD₁₆	—	356	2	no	—
250	C₂×SD₁₆	—	178	4	no	—
251	C₂²×C₈	—	178	1	no	—
252	C₂²×C₈	—	178	1	no	—
253	C₂²×C₈	—	178	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	—	4	2	no	—
259	C₄⋊Q₈	—	4	2	no	—
260	#127	—	89	2	no	—
261	#127	—	178	1	no	—
262	#127	—	178	1	no	—
263	#127	—	178	1	no	—
264	C₄×Q₈	—	2	1	no	—
265	C₄×Q₈	—	2	1	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	4	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	2	yes	—
273	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	2	yes	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
277	C₄⋊C₈	—	89	2	no	—
278	C₄⋊C₈	—	178	1	no	—
279	C₄⋊C₈	—	178	1	no	—
280	C₄⋊C₈	—	178	1	no	—
281	#102	—	356	4	no	—
282	#102	—	178	4	no	—
283	#102	—	178	8	no	—
284	C₄×C₈	—	89	2	no	—
285	C₄×C₈	—	178	1	no	—
286	#95	—	2	4	no	—
287	#95	—	2	1	no	—
288	C₂⁴	—	356	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×Q₈	#13083559	1	2	yes	—
301	C₂×D₄	—	356	4	no	—
302	C₂×D₄	—	356	1	no	—
303	C₂×D₄	—	356	1	no	—
304	C₂×D₄	—	356	1	no	—
305	C₂×D₄	—	356	1	no	—
306	C₂×D₄	—	356	2	no	—
307	C₂×D₄	—	356	1	no	—
308	C₂×D₄	—	356	1	no	—
309	C₂×D₄	—	356	1	no	—
310	C₂×D₄	—	356	2	no	—
311	C₂×D₄	—	178	2	no	—
312	C₂×D₄	—	178	2	no	—
313	C₂×D₄	—	178	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
321	SD₁₆	—	356	8	no	—
322	C₂×C₈	—	356	2	no	—
323	C₂×C₈	—	356	1	no	—
324	C₂×C₈	—	356	1	no	—
325	C₂×C₈	—	356	1	no	—
326	C₂×C₈	—	356	2	no	—
327	C₂×C₈	—	178	2	no	—
328	C₂×C₈	—	178	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	8	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	#13083561	1	4	yes	complemented
340	C₄²	—	4	1	no	—
341	C₄²	—	4	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	4	1	no	—
344	C₄²	D₄×D₈₉	1	1	yes	characteristic
345	C₄²	D₄×D₈₉	1	1	yes	characteristic
346	C₄²	D₄×D₈₉	1	1	yes	characteristic
347	C₄²	#13083573	1	1	yes	characteristic
348	C₂³	—	356	2	no	—
349	C₂³	—	712	1	no	—
350	C₂³	—	712	2	no	—
351	C₂³	—	712	1	no	—
352	C₂³	—	712	2	no	—
353	C₂³	#15667981	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	2	2	no	—
356	Q₈	—	4	1	no	—
357	Q₈	—	4	1	no	—
358	Q₈	—	8	1	no	—
359	Q₈	—	8	1	no	—
360	Q₈	—	8	1	no	—
361	Q₈	—	8	1	no	—
362	D₄	—	356	4	no	—
363	D₄	—	356	2	no	—
364	D₄	—	356	2	no	—
365	D₄	—	356	4	no	—
366	D₄	—	712	2	no	—
367	D₄	—	712	1	no	—
368	D₄	—	712	1	no	—
369	D₄	—	712	1	no	—
370	D₄	—	712	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	#15667980	1	1	yes	characteristic
384	C₂×C₄	#15667980	1	1	yes	characteristic
385	C₂×C₄	#15667983	1	1	yes	characteristic
386	C₂×C₄	#15667984	1	1	yes	characteristic
387	C₂×C₄	#15667984	1	1	yes	characteristic
388	C₂×C₄	#15668008	1	1	yes	characteristic
389	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
390	C₂×C₄	C₂×#13083561	1	2	yes	—
391	C₂×C₄	#15668032	1	1	yes	characteristic
392	C₂×C₄	#15668037	1	1	yes	characteristic
393	C₂×C₄	#15668038	1	1	yes	characteristic
394	C₂×C₄	#15668043	1	2	yes	—
395	C₈	—	356	2	no	—
396	C₈	—	356	2	no	—
397	C₈	—	712	1	no	—
398	C₂²	—	1424	2	no	—
399	C₂²	—	1424	2	no	—
400	C₂²	—	712	2	no	—
401	C₂²	—	712	2	no	—
402	C₂²	—	712	2	no	—
403	C₂²	#19151506	1	1	yes	characteristic
404	C₂²	#19151732	1	1	yes	characteristic
405	C₂²	#19151737	1	2	yes	—
406	C₂²	#19151743	1	1	yes	characteristic
407	C₂²	#19151771	1	2	yes	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	2	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	1	no	—
414	C₄	#19151731	1	1	yes	characteristic
415	C₄	#19151741	1	1	yes	characteristic
416	C₄	#19151800	1	2	yes	—
417	C₄	#19151832	1	1	yes	characteristic
418	C₄	#19151849	1	1	yes	characteristic
419	C₄	#19151972	1	1	yes	characteristic
420	C₄	#19151990	1	1	yes	characteristic
421	C₂	—	1424	2	no	—
422	C₂	#26019348	1	2	yes	—
423	C₂	#26019355	1	2	yes	—
424	C₂	#26021248	1	1	yes	characteristic
425	C₂	#26021272	1	1	yes	characteristic
426	C₂	#26021335	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#15667981
commutator, cosocle	C₂×C₄²×C₈₉	C₂³
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#2546	C₂
socle	C₂³×C₈₉	#120
prime radical	C₂×#15668009	C₂²
hypercenter	#2546	D₈₉
hypocenter	C₈₉	#10051
LCS	G ▷ C₂×C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2546

Complements

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

N	H ≅ G/N	type
4. C₂×#19151344	C₂	semidirect
5. C₂×Q₈⋊#10623494	C₂	semidirect
6. #26018093	C₂	semidirect
7. C₈₉×#2546	C₂	semidirect
125. C₄⋊C₄×C₈₉	SD₁₆	semidirect
216. #2546	D₈₉	semidirect
221. C₈₉	#10051	semidirect
339. C₄⋊C₄	#13083561	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151946	2
C₂×#19151798	2
#26021179	2
C₂×#19151344	2
C₂×Q₈⋊#10623494	2
#26018093	2
C₈₉×#2546	2
#10051	89