Subgroups — #36523669

Order 22784.

610 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×#10623494	C₂	1	1	yes	maximal, characteristic
2	#26028918	C₂	1	1	yes	maximal, characteristic
3	#26019033	C₂	1	2	yes	maximal, complemented
4	#26019030	C₂	1	2	yes	maximal, complemented
5	#26019024	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019022	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019013	C₂	1	2	yes	maximal, complemented
8	#26019010	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018998	C₂	1	2	yes	maximal, complemented
10	C₂×#19151350	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2925	C₂	1	1	yes	maximal, characteristic
12	Q₈×#10623494	C₄	1	1	yes	characteristic
13	Q₈×#10623494	C₄	1	1	yes	characteristic
14	D₄×#10623494	C₄	1	2	yes	—
15	D₄×#10623494	C₄	1	1	yes	characteristic
16	D₄×#10623494	C₄	1	2	yes	—
17	D₄×#10623494	C₄	1	1	yes	characteristic
18	#19151659	—	2	2	no	—
19	#19151655	C₂²	1	2	yes	—
20	#19151651	C₂²	1	2	yes	—
21	#19151651	C₂²	1	1	yes	characteristic
22	#19151651	C₂²	1	2	yes	—
23	#19151622	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
25	#19151565	—	2	1	no	—
26	#19151554	—	2	1	no	—
27	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
28	C₂×C₄×#10623494	C₂²	1	2	yes	—
29	#19151350	C₂²	1	1	yes	characteristic
30	#19151350	C₂²	1	1	yes	characteristic
31	#19151350	C₂²	1	1	yes	characteristic
32	#19151350	C₂²	1	1	yes	characteristic
33	#19151350	C₂²	1	2	yes	—
34	#19151350	C₂²	1	2	yes	—
35	#19151348	C₂²	1	2	yes	—
36	#19151348	C₂²	1	2	yes	—
37	#19151348	C₂²	1	2	yes	—
38	#19151348	C₂²	1	2	yes	—
39	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
40	#433×C₈₉	—	2	2	no	—
41	#432×C₈₉	C₂²	1	2	yes	—
42	#431×C₈₉	C₂²	1	2	yes	—
43	#423×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#408×C₈₉	—	2	1	no	—
46	#405×C₈₉	—	2	1	no	—
47	C₂×#13083558	—	2	1	no	—
48	C₂²×#10623494	—	2	1	no	—
49	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
50	C₂²×#10623494	C₂×C₄	1	2	yes	—
51	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
52	C₂²×#10623494	C₂×C₄	1	2	yes	—
53	C₄⋊#10623494	—	2	1	no	—
54	C₄⋊#10623494	—	2	1	no	—
55	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
56	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
57	C₄⋊#10623494	C₂×C₄	1	2	yes	—
58	C₄⋊#10623494	C₂×C₄	1	2	yes	—
59	C₄⋊#10623494	C₂³	1	1	yes	characteristic
60	C₄⋊#10623494	C₂³	1	1	yes	characteristic
61	C₄⋊#10623494	C₂³	1	2	yes	—
62	C₂²⋊#10623494	—	2	2	no	—
63	C₂²⋊#10623494	—	2	2	no	—
64	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
65	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
66	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
67	#15667923	—	2	2	no	—
68	C₄×#10623494	—	2	2	no	—
69	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
70	C₄×#10623494	C₂×C₄	1	2	yes	—
71	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
72	C₄×#10623494	C₂×C₄	1	2	yes	—
73	C₄×#10623494	C₂³	1	2	yes	—
74	C₄×#10623494	C₂³	1	1	yes	characteristic
75	C₄×#10623494	C₂³	1	1	yes	characteristic
76	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
77	C₂×M₁₆×C₈₉	—	2	1	no	—
78	C₂²×C₈×C₈₉	—	2	1	no	—
79	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₄×Q₈×C₈₉	Q₈	1	1	yes	characteristic
81	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
82	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
83	C₄×D₄×C₈₉	Q₈	1	2	yes	—
84	C₄×D₄×C₈₉	Q₈	1	1	yes	characteristic
85	#117×C₈₉	D₄	1	1	yes	characteristic
86	#117×C₈₉	D₄	1	2	yes	—
87	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
89	C₄⋊C₈×C₈₉	—	2	1	no	—
90	C₄⋊C₈×C₈₉	—	2	1	no	—
91	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
94	C₂²⋊C₈×C₈₉	—	2	2	no	—
95	C₂²⋊C₈×C₈₉	—	2	2	no	—
96	#97×C₈₉	—	2	2	no	—
97	C₄×C₈×C₈₉	—	2	2	no	—
98	#13083558	—	4	2	no	—
99	C₂×#10623494	—	2	2	no	—
100	C₂×#10623494	—	2	4	no	—
101	C₂×#10623494	—	2	1	no	—
102	C₂×#10623494	—	2	1	no	—
103	C₂×#10623494	—	2	2	no	—
104	C₂×#10623494	—	4	1	no	—
105	C₂×#10623494	—	4	2	no	—
106	C₂×#10623494	—	4	2	no	—
107	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
108	C₂×#10623494	C₂²×C₄	1	2	yes	—
109	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
110	C₂×#10623494	C₂²×C₄	1	2	yes	—
111	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
112	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
113	#41×C₈₉	—	2	2	no	—
114	#41×C₈₉	—	2	2	no	—
115	C₂×Q₈×C₈₉	C₄⋊C₄	1	1	yes	characteristic
116	C₂×D₄×C₈₉	C₄⋊C₄	1	2	yes	—
117	C₂×D₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
123	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
124	M₁₆×C₈₉	—	4	2	no	—
125	C₂×C₈×C₈₉	—	2	1	no	—
126	C₂×C₈×C₈₉	—	2	2	no	—
127	C₂×C₈×C₈₉	—	2	1	no	—
128	C₂×C₈×C₈₉	—	4	2	no	—
129	C₄⋊C₄×C₈₉	C₄⋊C₄	1	2	yes	—
130	C₄⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
131	C₄⋊C₄×C₈₉	C₄⋊C₄	1	2	yes	—
132	C₄⋊C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
133	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	2	yes	—
134	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	2	yes	—
135	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	2	yes	—
136	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
137	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₈₉	C₂×D₄	1	2	yes	—
139	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
141	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
142	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
143	C₂³×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
144	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
145	Q₈×C₈₉	—	2	2	no	—
146	D₄×C₈₉	—	2	4	no	—
147	D₄×C₈₉	—	2	2	no	—
148	C₂×C₄×C₈₉	—	2	1	no	—
149	C₂×C₄×C₈₉	—	2	2	no	—
150	C₂×C₄×C₈₉	—	2	1	no	—
151	C₂×C₄×C₈₉	—	2	2	no	—
152	C₂×C₄×C₈₉	—	2	2	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	4	1	no	—
155	C₂×C₄×C₈₉	—	4	2	no	—
156	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	#135	1	2	yes	—
163	C₂×C₄×C₈₉	#135	1	2	yes	—
164	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
167	C₈×C₈₉	—	4	1	no	—
168	C₈×C₈₉	—	4	1	no	—
169	C₈×C₈₉	—	4	2	no	—
170	#10623494	—	2	2	no	—
171	#10623494	—	2	1	no	—
172	#10623494	—	2	1	no	—
173	#10623494	—	2	2	no	—
174	#10623494	—	2	1	no	—
175	#10623494	—	4	1	no	—
176	#10623494	—	4	1	no	—
177	#10623494	—	4	2	no	—
178	#10623494	#131	1	2	yes	—
179	C₂²×C₈₉	—	2	1	no	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	—	2	2	no	—
182	C₂²×C₈₉	—	2	2	no	—
183	C₂²×C₈₉	—	2	2	no	—
184	C₂²×C₈₉	#427	1	2	yes	—
185	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
186	C₄×C₈₉	—	2	1	no	—
187	C₄×C₈₉	—	2	2	no	—
188	C₄×C₈₉	—	2	2	no	—
189	C₄×C₈₉	—	2	1	no	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	—	2	2	no	—
192	C₄×C₈₉	#427	1	2	yes	—
193	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
194	C₄×C₈₉	#568	1	1	yes	characteristic
195	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
196	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
197	#17829	—	89	1	no	maximal, Sylow
198	C₂×C₈₉	—	2	2	no	—
199	C₂×C₈₉	—	4	2	no	—
200	C₂×C₈₉	#2906	1	1	yes	characteristic
201	C₂×C₈₉	C₂×#427	1	1	yes	characteristic
202	C₂×C₈₉	#2916	1	1	yes	characteristic
203	C₈×#41	—	89	1	no	—
204	#2925	—	89	1	no	—
205	#2925	D₈₉	1	1	yes	characteristic
206	#1572	—	89	2	no	—
207	#1572	—	89	2	no	—
208	#1570	—	89	1	no	—
209	#1570	—	89	1	no	—
210	#1568	—	89	2	no	—
211	#1567	—	89	1	no	—
212	#1564	—	89	2	no	—
213	C₂×#335	—	89	1	no	—
214	C₈₉	#17829	1	1	yes	characteristic, complemented, Sylow
215	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
216	C₈×Q₈	—	89	1	no	—
217	C₈×Q₈	—	89	1	no	—
218	C₈×D₄	—	89	1	no	—
219	C₈×D₄	—	89	2	no	—
220	C₈×D₄	—	89	1	no	—
221	C₈×D₄	—	89	2	no	—
222	#433	—	2	2	no	—
223	#433	—	178	2	no	—
224	#432	—	89	2	no	—
225	#432	C₂×D₈₉	1	2	yes	—
226	#431	—	89	1	no	—
227	#431	—	89	2	no	—
228	#431	—	89	2	no	—
229	#431	C₂×D₈₉	1	2	yes	—
230	#423	—	89	1	no	—
231	#423	C₂×D₈₉	1	1	yes	characteristic
232	C₂×C₄⋊C₈	—	89	1	no	—
233	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
234	#408	—	2	1	no	—
235	#408	—	178	1	no	—
236	#405	—	2	1	no	—
237	#405	—	178	1	no	—
238	C₂×C₄×C₈	—	89	1	no	—
239	C₂×C₄×C₈	—	89	2	no	—
240	#335	—	89	1	no	—
241	#335	—	89	1	no	—
242	#335	—	89	1	no	—
243	#335	—	89	1	no	—
244	#335	—	89	2	no	—
245	#335	—	89	2	no	—
246	#334	—	89	2	no	—
247	#334	—	89	2	no	—
248	#334	—	89	2	no	—
249	#334	—	89	2	no	—
250	C₂×#41	C₂²⋊D₈₉	1	1	yes	characteristic
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	178	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	89	1	no	—
255	C₂²×C₈	—	89	2	no	—
256	C₂²×C₈	—	89	1	no	—
257	C₂²×C₈	—	89	2	no	—
258	C₂²×C₈	—	178	1	no	—
259	C₄×Q₈	Dic₁₇₈	1	1	yes	characteristic
260	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
261	C₄×D₄	Dic₁₇₈	1	2	yes	—
262	C₄×D₄	Dic₁₇₈	1	1	yes	characteristic
263	C₄×D₄	C₄×D₈₉	1	2	yes	—
264	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
265	#117	C₂²⋊D₈₉	1	1	yes	characteristic
266	#117	C₂²⋊D₈₉	1	2	yes	—
267	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
268	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	89	1	no	—
272	C₄⋊C₈	—	89	1	no	—
273	C₄⋊C₈	—	89	2	no	—
274	C₄⋊C₈	—	89	2	no	—
275	C₄⋊C₈	—	89	1	no	—
276	C₄⋊C₈	—	89	1	no	—
277	C₄⋊C₈	—	89	2	no	—
278	C₄⋊C₈	—	178	1	no	—
279	C₄⋊C₈	—	178	1	no	—
280	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
281	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
282	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	C₂²⋊C₈	—	89	2	no	—
286	C₂²⋊C₈	—	89	2	no	—
287	C₂²⋊C₈	—	89	2	no	—
288	C₂²⋊C₈	—	178	2	no	—
289	C₂²⋊C₈	—	178	2	no	—
290	#97	—	2	2	no	—
291	#97	—	178	2	no	—
292	C₄×C₈	—	2	2	no	—
293	C₄×C₈	—	89	1	no	—
294	C₄×C₈	—	89	2	no	—
295	C₄×C₈	—	89	1	no	—
296	C₄×C₈	—	89	2	no	—
297	C₄×C₈	—	89	2	no	—
298	C₄×C₈	—	89	1	no	—
299	C₄×C₈	—	89	1	no	—
300	C₄×C₈	—	178	2	no	—
301	#41	—	2	2	no	—
302	#41	—	2	2	no	—
303	C₂×Q₈	#13083553	1	1	yes	characteristic
304	C₂×D₄	#13083553	1	2	yes	—
305	C₂×D₄	#13083553	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
307	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
309	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
310	C₂²×C₄	C₂×Dic₁₇₈	1	2	yes	—
311	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
312	M₁₆	—	4	2	no	—
313	M₁₆	—	356	2	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	89	1	no	—
319	C₂×C₈	—	89	1	no	—
320	C₂×C₈	—	89	2	no	—
321	C₂×C₈	—	89	1	no	—
322	C₂×C₈	—	89	2	no	—
323	C₂×C₈	—	89	1	no	—
324	C₂×C₈	—	356	2	no	—
325	C₂×C₈	—	356	1	no	—
326	C₂×C₈	—	356	2	no	—
327	C₂×C₈	—	178	2	no	—
328	C₂×C₈	—	178	4	no	—
329	C₂×C₈	—	178	1	no	—
330	C₂×C₈	—	178	2	no	—
331	C₂×C₈	—	178	1	no	—
332	C₄⋊C₄	#13083553	1	2	yes	—
333	C₄⋊C₄	#13083553	1	1	yes	characteristic
334	C₄⋊C₄	#13083553	1	2	yes	—
335	C₄⋊C₄	#13083553	1	1	yes	characteristic
336	C₂²⋊C₄	#13083553	1	2	yes	—
337	C₂²⋊C₄	#13083553	1	2	yes	—
338	C₂²⋊C₄	#13083553	1	2	yes	—
339	C₄²	C₂×C₄×D₈₉	1	2	yes	—
340	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
341	C₄²	C₂×C₂²⋊D₈₉	1	2	yes	—
342	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
343	C₄²	C₂×Dic₁₇₈	1	2	yes	—
344	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
345	C₄²	C₂³×D₈₉	1	1	yes	characteristic
346	C₂³	C₂×#13083553	1	2	yes	—
347	C₂³	C₂×#13083553	1	1	yes	characteristic
348	Q₈	—	2	2	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₂×#13083553	1	2	yes	—
360	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
361	C₂×C₄	C₂×#13083553	1	2	yes	—
362	C₂×C₄	C₂×#13083553	1	2	yes	—
363	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
364	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
365	C₂×C₄	#15668032	1	2	yes	—
366	C₂×C₄	#15668032	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
369	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
370	C₈	—	4	1	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	2	no	—
373	C₈	—	89	2	no	—
374	C₈	—	356	1	no	—
375	C₈	—	356	1	no	—
376	C₈	—	356	2	no	—
377	C₈	—	178	2	no	—
378	C₈	—	178	1	no	—
379	C₈	—	178	2	no	—
380	C₈	—	178	1	no	—
381	C₈	—	178	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	#19151634	1	2	yes	—
388	C₂²	C₂²×#13083553	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	#19151634	1	2	yes	—
396	C₄	#131×D₈₉	1	1	yes	characteristic
397	C₄	#19152363	1	1	yes	characteristic
398	C₄	C₂×#15668032	1	1	yes	characteristic
399	C₄	C₂×#15668032	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	4	2	no	—
402	C₂	#26028818	1	1	yes	characteristic
403	C₂	C₂×#19151634	1	1	yes	characteristic
404	C₂	#26028861	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2925	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₈₉	D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2925	D₈₉
hypocenter	C₈₉	#17829
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2925

Complements

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

N	H ≅ G/N	type
3. #26019033	C₂	semidirect
4. #26019030	C₂	semidirect
5. #26019024	C₂	semidirect
6. #26019022	C₂	semidirect
7. #26019013	C₂	semidirect
8. #26019010	C₂	semidirect
9. #26018998	C₂	semidirect
10. C₂×#19151350	C₂	semidirect
214. C₈₉	#17829	semidirect

Maximal subgroups

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

subgroup	index
#41×#10623494	2
#26028918	2
#26019033	2
#26019030	2
#26019024	2
#26019022	2
#26019013	2
#26019010	2
#26018998	2
C₂×#19151350	2
C₈₉×#2925	2
#17829	89