Subgroups — #36524405

Order 22784.

632 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	#26030332	C₂	1	1	yes	maximal, characteristic
2	#26029221	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019127	C₂	1	2	yes	maximal, complemented
5	#26019120	C₂	1	2	yes	maximal, complemented
6	#26019056	C₂	1	2	yes	maximal, complemented
7	#26019049	C₂	1	2	yes	maximal, complemented
8	#26019038	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018666	C₂	1	1	yes	maximal, characteristic
10	M₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152132	C₂²	1	1	yes	characteristic
13	#19151928	C₄	1	1	yes	characteristic
14	#19151911	C₄	1	1	yes	characteristic
15	#19151905	C₄	1	2	yes	—
16	#19151820	C₄	1	2	yes	—
17	#19151754	C₄	1	1	yes	characteristic
18	#19151737	C₄	1	1	yes	characteristic
19	#19151725	C₂²	1	1	yes	characteristic
20	Q₈×#10623494	—	2	1	no	—
21	Q₈×#10623494	—	2	1	no	—
22	Q₈×#10623494	C₂²	1	2	yes	—
23	Q₈×#10623494	C₂²	1	2	yes	—
24	#19151722	C₂²	1	1	yes	characteristic
25	C₄×#13083564	C₂²	1	2	yes	—
26	C₄×#13083561	C₂²	1	2	yes	—
27	#19151675	C₂²	1	1	yes	characteristic
28	#19151666	—	2	1	no	—
29	#19151663	C₂²	1	1	yes	characteristic
30	#19151661	—	2	1	no	—
31	#19151660	—	2	1	no	—
32	#19151651	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊#10623494	—	2	1	no	—
34	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
35	#19151555	—	2	1	no	—
36	C₂×C₄×#10623494	—	2	1	no	—
37	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
38	#19151350	C₂²	1	2	yes	—
39	#19151348	C₂²	1	2	yes	—
40	#19151330	C₂²	1	2	yes	—
41	#19151327	C₂²	1	2	yes	—
42	#19151319	C₂²	1	2	yes	—
43	C₈×#10623494	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
45	#432×C₈₉	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
47	Q₈⋊C₈×C₈₉	C₂²	1	2	yes	—
48	Q₈⋊C₈×C₈₉	C₂²	1	2	yes	—
49	C₂×#13083564	C₂×C₄	1	2	yes	—
50	C₂×#13083561	C₂×C₄	1	2	yes	—
51	C₂×#13083557	—	2	1	no	—
52	C₂²×#10623494	—	2	1	no	—
53	C₂²×#10623494	D₄	1	1	yes	characteristic
54	C₂²×#10623494	D₄	1	1	yes	characteristic
55	C₂×C₈×D₈₉	—	2	1	no	—
56	#15668006	—	2	1	no	—
57	#15668004	C₂×C₄	1	1	yes	characteristic
58	#15668000	C₂×C₄	1	1	yes	characteristic
59	#15667995	—	2	1	no	—
60	#15667991	C₂×C₄	1	1	yes	characteristic
61	#15667986	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
63	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
64	C₄×C₂²⋊D₈₉	—	2	1	no	—
65	#15667969	—	2	1	no	—
66	#15667945	C₂×C₄	1	2	yes	—
67	#15667943	C₂×C₄	1	2	yes	—
68	C₄⋊#10623494	—	2	2	no	—
69	C₄⋊#10623494	—	2	2	no	—
70	C₄⋊#10623494	—	2	1	no	—
71	C₄⋊#10623494	C₂×C₄	1	2	yes	—
72	C₄⋊#10623494	C₂³	1	2	yes	—
73	#15667941	—	2	1	no	—
74	#15667941	—	2	1	no	—
75	#15667936	C₂×C₄	1	2	yes	—
76	#15667936	C₂×C₄	1	2	yes	—
77	#15667935	C₂×C₄	1	2	yes	—
78	#15667932	C₂×C₄	1	2	yes	—
79	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
81	#15667924	—	2	1	no	—
82	#15667924	—	2	1	no	—
83	#15667922	—	2	1	no	—
84	C₄×#10623494	—	2	2	no	—
85	C₄×#10623494	—	2	2	no	—
86	C₄×#10623494	D₄	1	1	yes	characteristic
87	C₄×#10623494	D₄	1	1	yes	characteristic
88	C₄×#10623494	C₂³	1	2	yes	—
89	C₄×#10623494	C₂³	1	1	yes	characteristic
90	C₄×#10623494	C₂³	1	1	yes	characteristic
91	C₈×Dic₈₉	—	2	1	no	—
92	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
93	C₂×M₁₆×C₈₉	—	2	1	no	—
94	C₄×Q₈×C₈₉	—	2	1	no	—
95	C₄×Q₈×C₈₉	—	2	1	no	—
96	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
97	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₈₉	—	2	1	no	—
101	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²⋊C₈×C₈₉	—	2	1	no	—
105	#97×C₈₉	—	2	1	no	—
106	#97×C₈₉	—	2	1	no	—
107	C₄×C₈×C₈₉	C₂³	1	2	yes	—
108	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
109	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₈₉	—	2	1	no	—
111	C₂×C₄×D₈₉	—	2	1	no	—
112	#13083564	—	2	4	no	—
113	#13083561	—	2	4	no	—
114	#13083557	—	4	2	no	—
115	C₂×#10623494	—	2	2	no	—
116	C₂×#10623494	—	2	2	no	—
117	C₂×#10623494	—	4	1	no	—
118	C₂×#10623494	—	4	2	no	—
119	C₂×#10623494	C₂²×C₄	1	2	yes	—
120	C₂×#10623494	C₂²×C₄	1	2	yes	—
121	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
122	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
123	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
124	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
125	C₈×D₈₉	—	4	2	no	—
126	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
128	#13083553	—	2	1	no	—
129	#13083553	—	2	1	no	—
130	#13083553	—	2	1	no	—
131	#13083553	—	2	1	no	—
132	C₂²⋊Dic₈₉	—	2	1	no	—
133	#13083551	—	2	1	no	—
134	#13083551	—	2	1	no	—
135	#13083551	—	2	1	no	—
136	#13083551	—	2	1	no	—
137	C₄×Dic₈₉	—	2	1	no	—
138	C₂×Q₈×C₈₉	—	2	4	no	—
139	C₂×Q₈×C₈₉	—	2	1	no	—
140	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₈₉	—	2	1	no	—
142	C₂²×C₄×C₈₉	—	2	1	no	—
143	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
146	M₁₆×C₈₉	—	2	4	no	—
147	C₂×C₈×C₈₉	—	2	2	no	—
148	C₂×C₈×C₈₉	—	2	1	no	—
149	C₂×C₈×C₈₉	—	2	1	no	—
150	C₄⋊C₄×C₈₉	—	2	2	no	—
151	C₄⋊C₄×C₈₉	—	2	1	no	—
152	C₄⋊C₄×C₈₉	—	2	2	no	—
153	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
154	C₄²×C₈₉	—	2	2	no	—
155	C₄²×C₈₉	—	2	2	no	—
156	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₈₉	#41	1	1	yes	characteristic
159	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
160	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₈₉	—	2	1	no	—
162	Q₈×C₈₉	—	2	4	no	—
163	Q₈×C₈₉	—	2	2	no	—
164	Q₈×C₈₉	#131	1	4	yes	—
165	C₂×C₄×C₈₉	—	2	4	no	—
166	C₂×C₄×C₈₉	—	2	2	no	—
167	C₂×C₄×C₈₉	—	2	2	no	—
168	C₂×C₄×C₈₉	—	2	2	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	2	1	no	—
171	C₂×C₄×C₈₉	—	2	2	no	—
172	C₂×C₄×C₈₉	—	4	2	no	—
173	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
179	C₂²⋊D₈₉	—	4	2	no	—
180	C₂×Dic₈₉	—	2	1	no	—
181	C₂×Dic₈₉	—	2	1	no	—
182	C₂×Dic₈₉	—	2	1	no	—
183	D₃₅₆	—	2	2	no	—
184	C₄×D₈₉	—	4	1	no	—
185	C₄×D₈₉	—	4	1	no	—
186	Dic₁₇₈	—	2	2	no	—
187	C₈×C₈₉	—	2	4	no	—
188	C₈×C₈₉	—	4	1	no	—
189	C₈×C₈₉	—	4	1	no	—
190	#10623494	—	2	2	no	—
191	#10623494	—	2	2	no	—
192	#10623494	—	2	1	no	—
193	#10623494	—	2	1	no	—
194	#10623494	—	2	1	no	—
195	#10623494	—	4	2	no	—
196	#10623494	#137	1	2	yes	—
197	C₂²×C₈₉	—	2	1	no	—
198	C₂²×C₈₉	—	2	1	no	—
199	C₂²×C₈₉	#443	1	2	yes	—
200	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂×D₈₉	—	4	1	no	—
202	C₂×D₈₉	—	4	1	no	—
203	C₂×D₈₉	—	4	1	no	—
204	C₄×C₈₉	—	2	4	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	—	2	1	no	—
208	C₄×C₈₉	—	2	1	no	—
209	C₄×C₈₉	—	4	2	no	—
210	C₄×C₈₉	C₂×#131	1	2	yes	—
211	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
212	C₄×C₈₉	#575	1	1	yes	characteristic
213	Dic₈₉	—	4	1	no	—
214	Dic₈₉	—	4	1	no	—
215	Dic₈₉	—	4	1	no	—
216	#17911	—	89	1	no	maximal, Sylow
217	C₂×C₈₉	—	2	2	no	—
218	C₂×C₈₉	#2929	1	1	yes	characteristic
219	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
220	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
221	D₈₉	—	8	1	no	—
222	#3108	—	89	1	no	—
223	#2966	—	89	1	no	—
224	C₂×C₈×Q₈	—	89	1	no	—
225	#1588	—	89	2	no	—
226	#1587	—	89	2	no	—
227	C₈×Q₁₆	—	89	2	no	—
228	C₈×SD₁₆	—	89	2	no	—
229	#1573	—	89	1	no	—
230	#1491	D₈₉	1	1	yes	characteristic, complemented
231	#1483	—	89	1	no	—
232	C₈×M₁₆	—	89	1	no	—
233	C₈₉	#17911	1	1	yes	characteristic, complemented, Sylow
234	#529	—	89	1	no	—
235	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
236	#483	—	89	1	no	—
237	#480	—	89	1	no	—
238	#479	—	89	2	no	—
239	#464	—	89	2	no	—
240	#451	—	89	1	no	—
241	#448	—	89	1	no	—
242	#446	—	89	1	no	—
243	C₈×Q₈	—	89	2	no	—
244	C₈×Q₈	—	89	2	no	—
245	C₈×Q₈	—	89	1	no	—
246	C₈×Q₈	—	178	1	no	—
247	C₈×Q₈	—	178	1	no	—
248	C₄×Q₁₆	—	89	2	no	—
249	C₄×SD₁₆	—	89	2	no	—
250	#436	—	89	1	no	—
251	#435	—	178	1	no	—
252	C₈×D₄	—	89	1	no	—
253	C₈×D₄	—	178	1	no	—
254	#433	—	178	1	no	—
255	#432	C₂×D₈₉	1	1	yes	characteristic
256	#431	—	89	1	no	—
257	C₂×C₄⋊C₈	—	89	1	no	—
258	C₂×C₄⋊C₈	—	178	1	no	—
259	#405	—	178	1	no	—
260	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
261	C₂×C₄×C₈	—	89	1	no	—
262	C₂×C₄×C₈	—	178	1	no	—
263	#335	—	89	2	no	—
264	#334	—	89	2	no	—
265	Q₈⋊C₈	—	89	2	no	—
266	Q₈⋊C₈	C₂×D₈₉	1	2	yes	—
267	Q₈⋊C₈	C₂×D₈₉	1	2	yes	—
268	D₄⋊C₈	—	89	2	no	—
269	#322	—	89	2	no	—
270	C₈²	—	89	2	no	—
271	C₂²×Q₈	C₄×D₈₉	1	1	yes	characteristic
272	C₂×Q₁₆	—	89	2	no	—
273	C₂×SD₁₆	—	89	2	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	178	1	no	—
276	C₂²×C₈	—	89	1	no	—
277	C₂²×C₈	—	89	1	no	—
278	C₂²×C₈	—	178	1	no	—
279	C₂²×C₈	—	178	1	no	—
280	#126	—	178	1	no	—
281	#125	—	89	1	no	—
282	#124	—	89	1	no	—
283	#123	—	178	1	no	—
284	C₂²⋊Q₈	—	89	1	no	—
285	#121	—	89	1	no	—
286	C₄×Q₈	—	2	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	89	1	no	—
289	C₄×Q₈	C₄×D₈₉	1	2	yes	—
290	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
291	C₄×D₄	—	89	1	no	—
292	C₄×D₄	—	178	1	no	—
293	#117	—	178	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
298	#107	—	89	2	no	—
299	#106	—	89	2	no	—
300	C₄⋊C₈	—	89	2	no	—
301	C₄⋊C₈	—	89	2	no	—
302	C₄⋊C₈	—	178	2	no	—
303	C₄⋊C₈	—	178	2	no	—
304	C₄⋊C₈	—	178	1	no	—
305	C₄⋊C₈	—	178	1	no	—
306	C₄⋊C₈	—	178	1	no	—
307	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
308	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
309	#103	—	89	2	no	—
310	#103	—	89	2	no	—
311	#103	—	89	2	no	—
312	#102	—	89	2	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	89	1	no	—
315	C₂²⋊C₈	—	89	1	no	—
316	C₂²⋊C₈	—	178	1	no	—
317	C₂²⋊C₈	—	178	1	no	—
318	#97	—	2	1	no	—
319	#97	—	2	1	no	—
320	#97	—	178	1	no	—
321	C₄×C₈	—	89	1	no	—
322	C₄×C₈	—	89	1	no	—
323	C₄×C₈	—	89	1	no	—
324	C₄×C₈	—	89	2	no	—
325	C₄×C₈	—	89	1	no	—
326	C₄×C₈	—	178	2	no	—
327	C₄×C₈	—	178	2	no	—
328	C₄×C₈	—	178	1	no	—
329	C₄×C₈	C₂²×D₈₉	1	2	yes	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	89	1	no	—
333	C₂×Q₈	C₂×C₄×D₈₉	1	2	yes	—
334	C₂×D₄	—	89	1	no	—
335	C₂×D₄	—	178	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	178	1	no	—
339	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
340	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
341	C₂²×C₄	#13083573	1	1	yes	characteristic
342	Q₁₆	—	178	4	no	—
343	SD₁₆	—	178	4	no	—
344	M₁₆	—	2	4	no	—
345	M₁₆	—	356	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	89	1	no	—
350	C₂×C₈	—	89	2	no	—
351	C₂×C₈	—	89	2	no	—
352	C₂×C₈	—	89	1	no	—
353	C₂×C₈	—	89	1	no	—
354	C₂×C₈	—	89	1	no	—
355	C₂×C₈	—	356	2	no	—
356	C₂×C₈	—	356	2	no	—
357	C₂×C₈	—	356	1	no	—
358	C₂×C₈	—	178	2	no	—
359	C₂×C₈	—	178	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	89	1	no	—
364	C₄⋊C₄	—	89	1	no	—
365	C₄⋊C₄	—	178	1	no	—
366	C₄⋊C₄	—	178	1	no	—
367	C₄⋊C₄	—	178	1	no	—
368	C₄⋊C₄	—	178	1	no	—
369	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
370	C₂²⋊C₄	—	178	1	no	—
371	C₂²⋊C₄	—	178	1	no	—
372	C₂²⋊C₄	—	178	1	no	—
373	C₂²⋊C₄	—	178	1	no	—
374	C₂²⋊C₄	—	178	1	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	178	1	no	—
378	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
379	C₄²	D₄×D₈₉	1	1	yes	characteristic
380	C₄²	#13083573	1	1	yes	characteristic
381	C₄²	C₂³×D₈₉	1	1	yes	characteristic
382	C₂³	—	178	1	no	—
383	C₂³	#15667972	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	178	2	no	—
387	Q₈	#15668020	1	4	yes	—
388	D₄	—	356	2	no	—
389	D₄	—	178	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	356	1	no	—
399	C₂×C₄	—	356	1	no	—
400	C₂×C₄	—	178	1	no	—
401	C₂×C₄	—	178	1	no	—
402	C₂×C₄	—	178	1	no	—
403	C₂×C₄	#15667972	1	1	yes	characteristic
404	C₂×C₄	#15667972	1	1	yes	characteristic
405	C₂×C₄	#15667972	1	1	yes	characteristic
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	4	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	89	2	no	—
413	C₈	—	356	2	no	—
414	C₈	—	178	1	no	—
415	C₈	—	178	1	no	—
416	C₈	—	178	1	no	—
417	C₈	—	178	2	no	—
418	C₈	—	178	2	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	356	1	no	—
422	C₂²	—	356	1	no	—
423	C₂²	—	356	1	no	—
424	C₂²	#19151712	1	2	yes	—
425	C₂²	C₂×#15667972	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	4	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	2	no	—
432	C₄	—	356	1	no	—
433	C₄	—	356	1	no	—
434	C₄	—	356	1	no	—
435	C₄	C₂×#15668020	1	2	yes	—
436	C₄	#137×D₈₉	1	1	yes	characteristic
437	C₄	#19152397	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	712	1	no	—
440	C₂	#26028942	1	1	yes	characteristic
441	C₂	#26029067	1	1	yes	characteristic
442	C₂	C₂×#19151712	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1491	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#15667986	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1491	D₈₉
hypocenter	C₈₉	#17911
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1491

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈×#10623494	C₂	semidirect
4. #26019127	C₂	semidirect
5. #26019120	C₂	semidirect
6. #26019056	C₂	semidirect
7. #26019049	C₂	semidirect
8. #26019038	C₂	semidirect
10. M₁₆×#10623494	C₂	semidirect
11. C₈₉×#1491	C₂	semidirect
230. #1491	D₈₉	semidirect
233. C₈₉	#17911	semidirect

Maximal subgroups

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

subgroup	index
#26030332	2
#26029221	2
C₂×Q₈×#10623494	2
#26019127	2
#26019120	2
#26019056	2
#26019049	2
#26019038	2
#26018666	2
M₁₆×#10623494	2
C₈₉×#1491	2
#17911	89