Subgroups — #36526464

Order 22784.

644 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	#26030827	C₂	1	1	yes	maximal, characteristic
2	#26029318	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019164	C₂	1	2	yes	maximal, complemented
4	#26019081	C₂	1	2	yes	maximal, complemented
5	#26019079	C₂	1	2	yes	maximal, complemented
6	#26019074	C₂	1	2	yes	maximal, complemented
7	#26018998	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018669	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018668	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2979	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152148	C₂²	1	1	yes	characteristic
13	#19152001	C₄	1	1	yes	characteristic
14	#19151974	C₄	1	1	yes	characteristic
15	#19151946	C₄	1	1	yes	characteristic
16	#19151944	C₄	1	1	yes	characteristic
17	#19151832	C₄	1	2	yes	—
18	#19151832	C₄	1	2	yes	—
19	C₄×#13083559	C₂²	1	2	yes	—
20	C₄×#13083559	C₂²	1	2	yes	—
21	#19151677	C₂²	1	2	yes	—
22	#19151675	—	2	1	no	—
23	C₈×D₃₅₆	C₂²	1	2	yes	—
24	#19151663	—	2	1	no	—
25	#19151651	C₂²	1	1	yes	characteristic
26	#19151563	—	2	2	no	—
27	C₄×#13083558	C₂²	1	1	yes	characteristic
28	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
29	#19151350	C₂²	1	1	yes	characteristic
30	#19151350	C₂²	1	1	yes	characteristic
31	#19151348	C₂²	1	1	yes	characteristic
32	#19151348	C₂²	1	1	yes	characteristic
33	D₄⋊#10623494	C₂²	1	2	yes	—
34	D₄⋊#10623494	C₂²	1	2	yes	—
35	#19151325	C₂²	1	2	yes	—
36	#19151325	C₂²	1	2	yes	—
37	#19151320	C₂²	1	2	yes	—
38	#19151319	C₂²	1	2	yes	—
39	#532×C₈₉	C₂²	1	1	yes	characteristic
40	#436×C₈₉	—	2	1	no	—
41	#436×C₈₉	C₂²	1	2	yes	—
42	C₈×D₄×C₈₉	—	2	1	no	—
43	C₈×D₄×C₈₉	C₂²	1	2	yes	—
44	#431×C₈₉	C₂²	1	1	yes	characteristic
45	#431×C₈₉	C₂²	1	1	yes	characteristic
46	#408×C₈₉	—	2	2	no	—
47	C₂×#13083574	—	2	1	no	—
48	C₂×#13083559	C₂×C₄	1	2	yes	—
49	C₂×#13083559	C₂×C₄	1	2	yes	—
50	C₂×#13083558	—	2	1	no	—
51	C₂×#13083557	—	2	2	no	—
52	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
53	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₈₉	—	2	2	no	—
55	#15668012	C₂×C₄	1	1	yes	characteristic
56	#15668009	C₂×C₄	1	1	yes	characteristic
57	#15668000	—	2	1	no	—
58	#15667986	—	2	1	no	—
59	#15667986	C₂×C₄	1	2	yes	—
60	C₄×D₃₅₆	—	2	1	no	—
61	C₄×D₃₅₆	C₂³	1	2	yes	—
62	#15667945	C₂×C₄	1	2	yes	—
63	#15667945	C₂×C₄	1	2	yes	—
64	C₄⋊#10623494	C₂³	1	1	yes	characteristic
65	C₄⋊#10623494	C₂³	1	1	yes	characteristic
66	#15667933	C₂×C₄	1	2	yes	—
67	#15667933	C₂×C₄	1	2	yes	—
68	#15667932	C₂×C₄	1	2	yes	—
69	#15667932	C₂×C₄	1	2	yes	—
70	C₂²⋊#10623494	—	2	1	no	—
71	#15667924	—	2	2	no	—
72	#15667924	—	2	2	no	—
73	#15667923	—	2	1	no	—
74	C₄×#10623494	—	2	1	no	—
75	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
76	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
77	C₄×#10623494	C₂³	1	2	yes	—
78	C₄×#10623494	C₂³	1	1	yes	characteristic
79	C₄×#10623494	C₂³	1	1	yes	characteristic
80	C₂×#41×C₈₉	—	2	1	no	—
81	C₂×M₁₆×C₈₉	—	2	2	no	—
82	C₂²×C₈×C₈₉	—	2	2	no	—
83	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
84	#127×C₈₉	C₂×C₄	1	1	yes	characteristic
85	#124×C₈₉	—	2	1	no	—
86	#121×C₈₉	—	2	1	no	—
87	#121×C₈₉	C₂×C₄	1	2	yes	—
88	C₄×D₄×C₈₉	—	2	1	no	—
89	C₄×D₄×C₈₉	C₂³	1	2	yes	—
90	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
92	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
93	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂²⋊C₈×C₈₉	—	2	1	no	—
96	C₂²⋊C₈×C₈₉	—	2	2	no	—
97	C₂²⋊C₈×C₈₉	—	2	2	no	—
98	C₂²⋊C₈×C₈₉	D₄	1	2	yes	—
99	C₄×C₈×C₈₉	—	2	1	no	—
100	C₄×C₈×C₈₉	C₂³	1	2	yes	—
101	#13083574	—	8	1	no	—
102	#13083574	—	8	1	no	—
103	C₂×Dic₁₇₈	—	2	1	no	—
104	C₂×D₃₅₆	—	2	1	no	—
105	C₂×D₃₅₆	—	2	1	no	—
106	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
107	C₂×C₂²⋊D₈₉	—	2	2	no	—
108	C₂×C₄×D₈₉	—	2	2	no	—
109	#13083559	—	2	4	no	—
110	#13083559	—	4	2	no	—
111	#13083558	—	4	2	no	—
112	#13083557	—	8	2	no	—
113	C₂×#10623494	—	2	2	no	—
114	C₂×#10623494	—	2	1	no	—
115	C₂×#10623494	—	2	1	no	—
116	C₂×#10623494	—	2	2	no	—
117	C₂×#10623494	—	4	1	no	—
118	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
119	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
120	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
121	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
122	C₈×D₈₉	—	8	2	no	—
123	C₄⋊Dic₈₉	—	2	1	no	—
124	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
125	#13083551	—	2	2	no	—
126	#13083551	—	2	2	no	—
127	#41×C₈₉	—	8	1	no	—
128	#41×C₈₉	—	8	1	no	—
129	C₂×Q₈×C₈₉	—	2	1	no	—
130	C₂×D₄×C₈₉	—	2	2	no	—
131	C₂×D₄×C₈₉	—	2	1	no	—
132	C₂×D₄×C₈₉	—	2	1	no	—
133	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₈₉	—	2	2	no	—
135	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
138	M₁₆×C₈₉	—	8	2	no	—
139	C₂×C₈×C₈₉	—	2	1	no	—
140	C₂×C₈×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	8	2	no	—
142	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
144	C₄⋊C₄×C₈₉	—	2	1	no	—
145	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
146	C₂²⋊C₄×C₈₉	—	2	2	no	—
147	C₂²⋊C₄×C₈₉	—	2	2	no	—
148	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₈₉	#41	1	1	yes	characteristic
151	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₂³×C₈₉	—	2	2	no	—
153	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
154	C₂²×D₈₉	—	2	2	no	—
155	Q₈×C₈₉	—	8	1	no	—
156	D₄×C₈₉	—	2	2	no	—
157	D₄×C₈₉	—	2	2	no	—
158	D₄×C₈₉	—	4	2	no	—
159	D₄×C₈₉	—	8	1	no	—
160	D₄×C₈₉	—	8	2	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	2	no	—
166	C₂×C₄×C₈₉	—	2	2	no	—
167	C₂×C₄×C₈₉	—	4	2	no	—
168	C₂×C₄×C₈₉	—	4	2	no	—
169	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
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	—	8	2	no	—
176	C₂×Dic₈₉	—	2	2	no	—
177	D₃₅₆	—	2	2	no	—
178	D₃₅₆	—	2	2	no	—
179	D₃₅₆	—	4	2	no	—
180	D₃₅₆	—	8	1	no	—
181	C₄×D₈₉	—	4	2	no	—
182	C₄×D₈₉	—	4	2	no	—
183	Dic₁₇₈	—	8	1	no	—
184	C₈×C₈₉	—	2	2	no	—
185	C₈×C₈₉	—	2	2	no	—
186	C₈×C₈₉	—	4	1	no	—
187	C₈×C₈₉	—	4	1	no	—
188	#10623494	—	2	1	no	—
189	#10623494	—	2	1	no	—
190	#10623494	—	2	1	no	—
191	#10623494	—	4	2	no	—
192	#10623494	—	4	1	no	—
193	#10623494	—	4	1	no	—
194	#10623494	#131	1	2	yes	—
195	C₂²×C₈₉	—	2	1	no	—
196	C₂²×C₈₉	—	2	1	no	—
197	C₂²×C₈₉	—	2	1	no	—
198	C₂²×C₈₉	—	4	2	no	—
199	C₂²×C₈₉	—	4	2	no	—
200	C₂²×C₈₉	—	4	2	no	—
201	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂×D₈₉	—	4	2	no	—
203	C₂×D₈₉	—	4	2	no	—
204	C₂×D₈₉	—	4	2	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	—	2	1	no	—
208	C₄×C₈₉	—	4	2	no	—
209	C₄×C₈₉	#444	1	2	yes	—
210	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
211	C₄×C₈₉	#568	1	1	yes	characteristic
212	C₄×C₈₉	#576	1	1	yes	characteristic
213	C₄×C₈₉	#576	1	1	yes	characteristic
214	Dic₈₉	—	4	2	no	—
215	#18091	—	89	1	no	maximal, Sylow
216	C₂×C₈₉	—	4	1	no	—
217	C₂×C₈₉	—	8	2	no	—
218	C₂×C₈₉	#2935	1	1	yes	characteristic
219	C₂×C₈₉	#2948	1	1	yes	characteristic
220	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
221	D₈₉	—	8	2	no	—
222	#3169	—	89	1	no	—
223	#2979	—	89	1	no	—
224	#2979	D₈₉	1	1	yes	characteristic, complemented
225	#1594	—	89	2	no	—
226	#1581	—	89	2	no	—
227	#1581	—	89	2	no	—
228	#1580	—	89	2	no	—
229	#1564	—	89	1	no	—
230	#1484	—	89	1	no	—
231	#1484	—	89	1	no	—
232	#1451	—	89	1	no	—
233	C₈₉	#18091	1	1	yes	characteristic, complemented, Sylow
234	#532	—	89	1	no	—
235	#532	C₂×D₈₉	1	1	yes	characteristic
236	#500	—	89	1	no	—
237	#493	—	89	1	no	—
238	#486	—	89	1	no	—
239	#486	—	89	1	no	—
240	#466	—	89	2	no	—
241	#466	—	89	2	no	—
242	C₄×D₈	—	89	2	no	—
243	C₄×D₈	—	89	2	no	—
244	#436	—	2	1	no	—
245	#436	—	89	2	no	—
246	#436	—	178	1	no	—
247	#436	C₂×D₈₉	1	2	yes	—
248	C₈×D₄	—	2	1	no	—
249	C₈×D₄	—	89	2	no	—
250	C₈×D₄	—	178	1	no	—
251	C₈×D₄	C₂×D₈₉	1	2	yes	—
252	#431	—	89	1	no	—
253	#431	C₂×D₈₉	1	1	yes	characteristic
254	#431	C₂×D₈₉	1	1	yes	characteristic
255	#408	—	2	2	no	—
256	#408	—	178	2	no	—
257	C₄×M₁₆	—	89	1	no	—
258	C₂×C₄×C₈	—	89	1	no	—
259	#335	—	89	1	no	—
260	#335	—	89	1	no	—
261	#334	—	89	1	no	—
262	#334	—	89	1	no	—
263	D₄⋊C₈	—	89	2	no	—
264	D₄⋊C₈	—	89	2	no	—
265	D₄⋊C₈	—	89	2	no	—
266	D₄⋊C₈	—	89	2	no	—
267	#322	—	89	2	no	—
268	#322	—	89	2	no	—
269	C₂×#41	—	2	1	no	—
270	C₂×#41	—	178	1	no	—
271	C₂×D₈	—	89	2	no	—
272	C₂×D₈	—	89	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	178	1	no	—
275	C₂×M₁₆	—	178	2	no	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	—	89	1	no	—
278	C₂²×C₈	—	89	1	no	—
279	C₂²×C₈	—	178	2	no	—
280	C₄⋊Q₈	—	89	1	no	—
281	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
282	#127	—	89	1	no	—
283	#127	C₄×D₈₉	1	1	yes	characteristic
284	#124	—	2	1	no	—
285	#124	—	178	1	no	—
286	#121	—	2	1	no	—
287	#121	—	89	2	no	—
288	#121	—	178	1	no	—
289	#121	C₄×D₈₉	1	2	yes	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	89	2	no	—
292	C₄×D₄	—	178	1	no	—
293	C₄×D₄	C₂²×D₈₉	1	2	yes	—
294	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
295	#107	—	89	2	no	—
296	#107	—	89	2	no	—
297	C₄⋊C₈	—	89	1	no	—
298	C₄⋊C₈	—	89	1	no	—
299	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
300	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
301	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
302	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
303	#102	—	89	2	no	—
304	#102	—	89	2	no	—
305	#102	—	89	2	no	—
306	#102	—	89	2	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	C₂²⋊C₈	—	178	1	no	—
311	C₂²⋊C₈	—	178	2	no	—
312	C₂²⋊C₈	—	178	2	no	—
313	C₂²⋊C₈	C₂²⋊D₈₉	1	2	yes	—
314	#97	—	178	1	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	—	89	1	no	—
317	C₄×C₈	—	89	1	no	—
318	C₄×C₈	—	89	1	no	—
319	C₄×C₈	—	89	1	no	—
320	C₄×C₈	—	89	2	no	—
321	C₄×C₈	—	178	1	no	—
322	C₄×C₈	C₂²×D₈₉	1	2	yes	—
323	#41	—	8	1	no	—
324	#41	—	8	1	no	—
325	#41	—	712	1	no	—
326	#41	—	712	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	178	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	89	2	no	—
333	C₂×D₄	—	178	2	no	—
334	C₂×D₄	—	178	1	no	—
335	C₂×D₄	—	178	1	no	—
336	C₂×D₄	C₂×C₄×D₈₉	1	2	yes	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	178	2	no	—
339	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
341	C₂²×C₄	#13083574	1	1	yes	characteristic
342	D₈	—	356	2	no	—
343	D₈	—	178	4	no	—
344	M₁₆	—	8	2	no	—
345	M₁₆	—	356	2	no	—
346	M₁₆	—	712	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	8	2	no	—
350	C₂×C₈	—	89	1	no	—
351	C₂×C₈	—	89	1	no	—
352	C₂×C₈	—	89	1	no	—
353	C₂×C₈	—	89	1	no	—
354	C₂×C₈	—	356	1	no	—
355	C₂×C₈	—	178	2	no	—
356	C₂×C₈	—	178	1	no	—
357	C₂×C₈	—	178	1	no	—
358	C₂×C₈	—	178	2	no	—
359	C₂×C₈	—	712	2	no	—
360	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
361	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	89	2	no	—
364	C₄⋊C₄	—	178	1	no	—
365	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	178	2	no	—
369	C₂²⋊C₄	—	178	2	no	—
370	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
371	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
372	C₄²	#13083574	1	1	yes	characteristic
373	C₄²	C₂³×D₈₉	1	1	yes	characteristic
374	C₂³	—	2	2	no	—
375	C₂³	—	178	2	no	—
376	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
377	Q₈	—	8	1	no	—
378	Q₈	—	712	1	no	—
379	D₄	—	2	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	8	1	no	—
383	D₄	—	8	2	no	—
384	D₄	—	356	2	no	—
385	D₄	—	178	2	no	—
386	D₄	—	178	2	no	—
387	D₄	—	712	1	no	—
388	D₄	—	712	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	356	2	no	—
398	C₂×C₄	—	356	2	no	—
399	C₂×C₄	—	178	2	no	—
400	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
401	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
402	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
404	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
405	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	89	2	no	—
411	C₈	—	356	2	no	—
412	C₈	—	356	1	no	—
413	C₈	—	356	1	no	—
414	C₈	—	178	1	no	—
415	C₈	—	178	1	no	—
416	C₈	—	178	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	356	2	no	—
424	C₂²	—	356	2	no	—
425	C₂²	—	356	2	no	—
426	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	4	2	no	—
431	C₄	—	356	2	no	—
432	C₄	#19151718	1	2	yes	—
433	C₄	#131×D₈₉	1	1	yes	characteristic
434	C₄	#19152363	1	1	yes	characteristic
435	C₄	#19152401	1	1	yes	characteristic
436	C₄	#19152401	1	1	yes	characteristic
437	C₂	—	4	1	no	—
438	C₂	—	8	2	no	—
439	C₂	—	712	2	no	—
440	C₂	#26028994	1	1	yes	characteristic
441	C₂	#26029102	1	1	yes	characteristic
442	C₂	C₂×#19151718	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×#2979	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#26030827	C₂
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2979	D₈₉
hypocenter	C₈₉	#18091
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2979

Complements

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

N	H ≅ G/N	type
2. #26029318	C₂	semidirect
3. #26019164	C₂	semidirect
4. #26019081	C₂	semidirect
5. #26019079	C₂	semidirect
6. #26019074	C₂	semidirect
7. #26018998	C₂	semidirect
8. #26018669	C₂	semidirect
9. #26018668	C₂	semidirect
10. #26018542	C₂	semidirect
11. C₈₉×#2979	C₂	semidirect
224. #2979	D₈₉	semidirect
233. C₈₉	#18091	semidirect

Maximal subgroups

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

subgroup	index
#26030827	2
#26029318	2
#26019164	2
#26019081	2
#26019079	2
#26019074	2
#26018998	2
#26018669	2
#26018668	2
#26018542	2
C₈₉×#2979	2
#18091	89