Subgroups — #36524242

Order 22784.

636 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	#26029370	C₂	1	1	yes	maximal, characteristic
2	#26029337	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#15668043	C₂	1	1	yes	maximal, characteristic
4	#26019158	C₂	1	2	yes	maximal, complemented
5	#26019157	C₂	1	2	yes	maximal, complemented
6	#26019146	C₂	1	2	yes	maximal, complemented
7	#26019139	C₂	1	2	yes	maximal, complemented
8	#26019002	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018635	C₂	1	1	yes	maximal, characteristic
10	C₈×#13083558	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×Q₈⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668043	C₄	1	1	yes	characteristic
13	C₄×#13083574	C₂²	1	1	yes	characteristic
14	#19151729	—	2	1	no	—
15	#19151729	—	2	1	no	—
16	#19151729	C₂²	1	2	yes	—
17	#19151729	C₂²	1	2	yes	—
18	#19151725	C₂²	1	2	yes	—
19	#19151703	C₄	1	2	yes	—
20	#19151696	C₄	1	2	yes	—
21	C₄×#13083564	C₂²	1	2	yes	—
22	C₄×#13083561	C₂²	1	2	yes	—
23	#19151675	C₂²	1	2	yes	—
24	#19151669	—	2	2	no	—
25	#19151655	—	2	2	no	—
26	#19151654	—	2	1	no	—
27	#19151651	C₂²	1	1	yes	characteristic
28	#19151651	C₂²	1	1	yes	characteristic
29	#19151638	C₄	1	1	yes	characteristic
30	#19151620	—	2	1	no	—
31	#19151607	C₄	1	1	yes	characteristic
32	#19151597	C₄	1	1	yes	characteristic
33	C₄×#13083558	C₂²	1	1	yes	characteristic
34	#19151350	C₂²	1	2	yes	—
35	#19151348	C₂²	1	2	yes	—
36	#19151330	C₂²	1	1	yes	characteristic
37	#19151330	C₂²	1	1	yes	characteristic
38	#19151327	C₂²	1	1	yes	characteristic
39	#19151327	C₂²	1	1	yes	characteristic
40	#19151320	C₂²	1	2	yes	—
41	C₈×#10623494	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
45	Q₈⋊C₈×C₈₉	C₂²	1	2	yes	—
46	Q₈⋊C₈×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
48	#15668043	—	2	4	no	—
49	C₂×#13083564	C₂×C₄	1	2	yes	—
50	C₂×#13083561	C₂×C₄	1	2	yes	—
51	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
52	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
53	C₂×#13083557	—	2	2	no	—
54	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
55	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
56	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
57	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
58	C₄×C₂²⋊D₈₉	—	2	1	no	—
59	C₄×C₂²⋊D₈₉	—	2	1	no	—
60	#15667971	C₂×C₄	1	1	yes	characteristic
61	#15667969	—	2	1	no	—
62	C₄²×D₈₉	—	2	1	no	—
63	#15667945	C₂×C₄	1	2	yes	—
64	#15667943	C₂×C₄	1	2	yes	—
65	C₄⋊#10623494	—	2	2	no	—
66	C₄⋊#10623494	—	2	2	no	—
67	C₄⋊#10623494	D₄	1	1	yes	characteristic
68	C₄⋊#10623494	D₄	1	1	yes	characteristic
69	C₄⋊#10623494	C₂³	1	1	yes	characteristic
70	C₄⋊#10623494	C₂³	1	1	yes	characteristic
71	#15667941	—	2	2	no	—
72	#15667936	C₂×C₄	1	2	yes	—
73	#15667936	C₂×C₄	1	2	yes	—
74	#15667935	C₂×C₄	1	2	yes	—
75	#15667932	C₂×C₄	1	2	yes	—
76	C₂²⋊#10623494	—	2	1	no	—
77	C₂²⋊#10623494	D₄	1	2	yes	—
78	#15667924	—	2	2	no	—
79	#15667923	—	2	2	no	—
80	#15667923	—	2	2	no	—
81	#15667923	C₂×C₄	1	2	yes	—
82	#15667922	—	2	2	no	—
83	C₄×#10623494	—	2	1	no	—
84	C₄×#10623494	C₂³	1	2	yes	—
85	C₄×#10623494	C₂³	1	2	yes	—
86	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₈₉	—	2	1	no	—
88	C₂²×C₈×C₈₉	—	2	1	no	—
89	C₄×Q₈×C₈₉	—	2	1	no	—
90	C₄×Q₈×C₈₉	—	2	1	no	—
91	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
92	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₈₉	—	2	1	no	—
96	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₈₉	—	2	1	no	—
98	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
99	C₄×C₈×C₈₉	—	2	1	no	—
100	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	#13083574	—	2	2	no	—
103	#13083574	—	2	2	no	—
104	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
105	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₈₉	—	2	1	no	—
107	C₂×C₄×D₈₉	—	2	1	no	—
108	C₂×C₄×D₈₉	—	2	1	no	—
109	C₂×C₄×D₈₉	—	2	1	no	—
110	#13083564	—	2	4	no	—
111	#13083561	—	2	4	no	—
112	#13083558	—	2	2	no	—
113	#13083558	M₁₆	1	4	yes	complemented
114	#13083557	—	8	2	no	—
115	C₂×#10623494	—	2	1	no	—
116	C₂×#10623494	—	2	1	no	—
117	C₂×#10623494	C₂²×C₄	1	2	yes	—
118	C₂×#10623494	C₂²×C₄	1	2	yes	—
119	C₂×#10623494	C₂×D₄	1	2	yes	—
120	C₂×#10623494	C₂×D₄	1	2	yes	—
121	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
123	#13083553	—	2	1	no	—
124	#13083553	—	2	1	no	—
125	C₂²⋊Dic₈₉	—	2	1	no	—
126	#13083551	—	2	1	no	—
127	#13083551	—	2	1	no	—
128	C₄×Dic₈₉	—	2	1	no	—
129	C₄×Dic₈₉	—	2	1	no	—
130	C₄×Dic₈₉	—	2	1	no	—
131	C₂×Q₈×C₈₉	—	2	1	no	—
132	C₂×Q₈×C₈₉	—	2	2	no	—
133	C₂×Q₈×C₈₉	—	2	2	no	—
134	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₈₉	—	2	1	no	—
136	C₂²×C₄×C₈₉	—	2	1	no	—
137	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
140	C₂×C₈×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	2	2	no	—
142	C₂×C₈×C₈₉	—	2	1	no	—
143	C₂×C₈×C₈₉	—	4	2	no	—
144	C₂×C₈×C₈₉	—	8	1	no	—
145	C₄⋊C₄×C₈₉	—	2	2	no	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	—	2	2	no	—
148	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
149	C₄²×C₈₉	—	2	2	no	—
150	C₄²×C₈₉	—	2	2	no	—
151	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₈₉	#41	1	1	yes	characteristic
154	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
155	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
156	C₂²×D₈₉	—	2	1	no	—
157	Q₈×C₈₉	—	2	2	no	—
158	Q₈×C₈₉	—	2	2	no	—
159	Q₈×C₈₉	—	4	2	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	4	1	no	—
165	C₂×C₄×C₈₉	—	4	2	no	—
166	C₂×C₄×C₈₉	—	8	1	no	—
167	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
171	C₂×C₄×C₈₉	#131	1	2	yes	—
172	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
175	C₂²⋊D₈₉	—	4	2	no	—
176	C₂×Dic₈₉	—	2	1	no	—
177	C₂×Dic₈₉	—	2	1	no	—
178	C₂×Dic₈₉	—	2	1	no	—
179	D₃₅₆	—	2	1	no	—
180	D₃₅₆	—	2	1	no	—
181	C₄×D₈₉	—	4	1	no	—
182	C₄×D₈₉	—	4	1	no	—
183	C₄×D₈₉	—	4	2	no	—
184	C₄×D₈₉	—	8	1	no	—
185	Dic₁₇₈	—	2	1	no	—
186	Dic₁₇₈	—	2	1	no	—
187	C₈×C₈₉	—	2	2	no	—
188	C₈×C₈₉	—	4	1	no	—
189	C₈×C₈₉	—	4	2	no	—
190	#10623494	—	2	2	no	—
191	#10623494	—	2	2	no	—
192	#10623494	—	2	2	no	—
193	#10623494	—	4	1	no	—
194	#10623494	—	4	1	no	—
195	#10623494	C₂×M₁₆	1	4	yes	—
196	C₂²×C₈₉	—	2	1	no	—
197	C₂²×C₈₉	—	2	1	no	—
198	C₂²×C₈₉	#436	1	2	yes	—
199	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
200	C₂×D₈₉	—	4	1	no	—
201	C₂×D₈₉	—	4	1	no	—
202	C₂×D₈₉	—	4	1	no	—
203	C₄×C₈₉	—	2	1	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	4	2	no	—
207	C₄×C₈₉	—	4	2	no	—
208	C₄×C₈₉	#436	1	2	yes	—
209	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
210	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
211	C₄×C₈₉	#577	1	1	yes	characteristic
212	C₄×C₈₉	#578	1	1	yes	characteristic
213	Dic₈₉	—	4	1	no	—
214	Dic₈₉	—	4	1	no	—
215	Dic₈₉	—	4	1	no	—
216	#17894	—	89	1	no	maximal, Sylow
217	C₂×C₈₉	—	2	2	no	—
218	C₂×C₈₉	C₂×#436	1	1	yes	characteristic
219	C₂×C₈₉	#2947	1	1	yes	characteristic
220	C₂×C₈₉	#2956	1	1	yes	characteristic
221	D₈₉	—	8	1	no	—
222	#2989	—	89	1	no	—
223	#2983	—	89	1	no	—
224	C₄×#137	—	89	1	no	—
225	#1593	—	89	2	no	—
226	#1592	—	89	2	no	—
227	#1591	—	89	2	no	—
228	#1590	—	89	2	no	—
229	#1565	—	89	1	no	—
230	#1476	—	89	1	no	—
231	C₂×Q₈⋊C₈	D₈₉	1	1	yes	characteristic, complemented
232	C₈×M₁₆	—	89	1	no	—
233	C₈₉	#17894	1	1	yes	characteristic, complemented, Sylow
234	C₂×#137	—	89	1	no	—
235	C₄×#41	—	89	1	no	—
236	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
237	#446	—	89	2	no	—
238	#446	—	89	2	no	—
239	#446	—	89	2	no	—
240	#446	—	178	1	no	—
241	#446	—	178	1	no	—
242	#441	—	89	2	no	—
243	#440	—	89	2	no	—
244	C₄×Q₁₆	—	89	2	no	—
245	C₄×SD₁₆	—	89	2	no	—
246	#436	—	89	2	no	—
247	#435	—	178	2	no	—
248	#432	—	178	2	no	—
249	#432	—	178	1	no	—
250	#431	—	89	1	no	—
251	#431	—	89	1	no	—
252	#428	—	89	1	no	—
253	#423	—	178	1	no	—
254	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
255	#419	—	89	1	no	—
256	#417	—	89	1	no	—
257	C₄×M₁₆	—	89	1	no	—
258	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
259	#335	—	89	2	no	—
260	#334	—	89	2	no	—
261	Q₈⋊C₈	—	89	1	no	—
262	Q₈⋊C₈	—	89	1	no	—
263	Q₈⋊C₈	C₂×D₈₉	1	2	yes	—
264	Q₈⋊C₈	C₂×D₈₉	1	2	yes	—
265	D₄⋊C₈	—	89	1	no	—
266	D₄⋊C₈	—	89	1	no	—
267	#322	—	89	2	no	—
268	C₈²	—	89	2	no	—
269	C₂×#41	—	89	1	no	—
270	C₂²×Q₈	C₄×D₈₉	1	1	yes	characteristic
271	#137	—	178	4	no	—
272	C₂×Q₁₆	—	89	2	no	—
273	C₂×SD₁₆	—	89	2	no	—
274	C₂×M₁₆	—	89	1	no	—
275	C₂×M₁₆	—	89	1	no	—
276	C₂×M₁₆	—	178	2	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₄×Q₈	—	2	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	89	1	no	—
282	C₄×Q₈	—	89	1	no	—
283	C₄×Q₈	C₄×D₈₉	1	2	yes	—
284	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
285	C₄×D₄	—	89	1	no	—
286	C₄×D₄	—	89	1	no	—
287	C₄×D₄	—	178	1	no	—
288	C₄×D₄	—	178	1	no	—
289	#117	—	89	1	no	—
290	#117	—	178	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	178	1	no	—
295	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
296	#107	—	89	2	no	—
297	#106	—	89	2	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	89	1	no	—
300	C₄⋊C₈	—	89	1	no	—
301	C₄⋊C₈	—	89	1	no	—
302	C₄⋊C₈	—	89	1	no	—
303	C₄⋊C₈	—	178	2	no	—
304	C₄⋊C₈	—	178	2	no	—
305	C₄⋊C₈	—	178	2	no	—
306	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
307	#103	—	89	2	no	—
308	#103	—	89	2	no	—
309	#103	—	89	2	no	—
310	#102	—	89	2	no	—
311	C₂²⋊C₈	—	89	2	no	—
312	C₂²⋊C₈	—	178	2	no	—
313	C₂²⋊C₈	—	178	1	no	—
314	#97	—	89	2	no	—
315	#97	—	178	2	no	—
316	#97	—	178	2	no	—
317	#97	—	178	2	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	89	2	no	—
320	C₄×C₈	—	89	2	no	—
321	C₄×C₈	—	178	1	no	—
322	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
323	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
324	#41	—	178	2	no	—
325	#41	—	178	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	89	1	no	—
330	C₂×Q₈	C₂×C₄×D₈₉	1	2	yes	—
331	C₂×D₄	—	89	1	no	—
332	C₂×D₄	—	178	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	178	1	no	—
336	C₂²×C₄	—	178	1	no	—
337	C₂²×C₄	—	178	1	no	—
338	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
339	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
340	C₂²×C₄	#13083573	1	1	yes	characteristic
341	Q₁₆	—	178	4	no	—
342	SD₁₆	—	178	4	no	—
343	M₁₆	—	89	4	no	—
344	M₁₆	—	178	2	no	—
345	M₁₆	—	712	2	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	—	8	1	no	—
351	C₂×C₈	—	89	2	no	—
352	C₂×C₈	—	89	2	no	—
353	C₂×C₈	—	89	2	no	—
354	C₂×C₈	—	89	2	no	—
355	C₂×C₈	—	178	1	no	—
356	C₂×C₈	—	178	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	89	1	no	—
361	C₄⋊C₄	—	89	1	no	—
362	C₄⋊C₄	—	178	1	no	—
363	C₄⋊C₄	—	178	1	no	—
364	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
365	C₂²⋊C₄	—	178	1	no	—
366	C₂²⋊C₄	—	178	1	no	—
367	C₂²⋊C₄	—	178	1	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	178	1	no	—
371	C₄²	—	178	1	no	—
372	C₄²	—	178	1	no	—
373	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
374	C₄²	D₄×D₈₉	1	1	yes	characteristic
375	C₄²	#13083573	1	1	yes	characteristic
376	C₄²	C₂³×D₈₉	1	1	yes	characteristic
377	C₂³	—	178	1	no	—
378	C₂³	#15667972	1	1	yes	characteristic
379	Q₈	—	2	2	no	—
380	Q₈	—	2	2	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	178	1	no	—
383	Q₈	—	178	1	no	—
384	D₄	—	356	2	no	—
385	D₄	—	178	1	no	—
386	D₄	—	178	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	356	1	no	—
395	C₂×C₄	—	356	1	no	—
396	C₂×C₄	—	356	2	no	—
397	C₂×C₄	—	178	1	no	—
398	C₂×C₄	—	178	1	no	—
399	C₂×C₄	—	178	1	no	—
400	C₂×C₄	—	712	1	no	—
401	C₂×C₄	#15667972	1	1	yes	characteristic
402	C₂×C₄	#15667972	1	1	yes	characteristic
403	C₂×C₄	#15667972	1	1	yes	characteristic
404	C₂×C₄	M₁₆×D₈₉	1	2	yes	—
405	C₂×C₄	#15668018	1	2	yes	—
406	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
407	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
408	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	2	no	—
412	C₈	—	89	4	no	—
413	C₈	—	356	1	no	—
414	C₈	—	356	1	no	—
415	C₈	—	178	2	no	—
416	C₈	—	178	2	no	—
417	C₈	—	178	2	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	356	1	no	—
421	C₂²	—	356	1	no	—
422	C₂²	—	356	1	no	—
423	C₂²	#19151673	1	2	yes	—
424	C₂²	C₂×#15667972	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	356	1	no	—
431	C₄	—	356	1	no	—
432	C₄	—	356	1	no	—
433	C₄	#19151673	1	2	yes	—
434	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
435	C₄	C₂×#15668018	1	1	yes	characteristic
436	C₄	#19152404	1	1	yes	characteristic
437	C₄	#19152411	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	712	1	no	—
440	C₂	C₂×#19151673	1	1	yes	characteristic
441	C₂	#26029089	1	1	yes	characteristic
442	C₂	#26029158	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×Q₈⋊C₈×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#13083574	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×Q₈⋊C₈	D₈₉
hypocenter	C₈₉	#17894
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. #26029337	C₂	semidirect
4. #26019158	C₂	semidirect
5. #26019157	C₂	semidirect
6. #26019146	C₂	semidirect
7. #26019139	C₂	semidirect
8. #26019002	C₂	semidirect
10. C₈×#13083558	C₂	semidirect
11. C₂×Q₈⋊C₈×C₈₉	C₂	semidirect
113. #13083558	M₁₆	semidirect
231. C₂×Q₈⋊C₈	D₈₉	semidirect
233. C₈₉	#17894	semidirect

Maximal subgroups

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

subgroup	index
#26029370	2
#26029337	2
C₄×#15668043	2
#26019158	2
#26019157	2
#26019146	2
#26019139	2
#26019002	2
#26018635	2
C₈×#13083558	2
C₂×Q₈⋊C₈×C₈₉	2
#17894	89