Subgroups — #36524435

Order 22784.

632 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030324	C₂	1	1	yes	maximal, characteristic
2	C₈×#13083574	C₂	1	1	yes	maximal, characteristic
3	#26029186	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019125	C₂	1	2	yes	maximal, complemented
5	#26019111	C₂	1	2	yes	maximal, complemented
6	C₈×Dic₃₅₆	C₂	1	2	yes	maximal, complemented
7	C₈×#13083563	C₂	1	2	yes	maximal, complemented
8	#26019041	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018692	C₂	1	1	yes	maximal, characteristic
10	#26018674	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152155	C₂²	1	1	yes	characteristic
13	C₄×#13083574	C₂²	1	1	yes	characteristic
14	#19151940	C₄	1	2	yes	—
15	#19151884	C₄	1	1	yes	characteristic
16	#19151879	C₄	1	1	yes	characteristic
17	#19151809	C₄	1	1	yes	characteristic
18	#19151804	C₄	1	1	yes	characteristic
19	#19151762	C₄	1	2	yes	—
20	#19151728	—	2	1	no	—
21	#19151728	C₂²	1	2	yes	—
22	C₈×Dic₁₇₈	—	2	1	no	—
23	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
24	C₈×Dic₁₇₈	C₂²	1	2	yes	—
25	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
26	C₄×Dic₃₅₆	C₂²	1	2	yes	—
27	C₄×#13083563	C₂²	1	2	yes	—
28	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
29	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
30	C₈×C₂²⋊D₈₉	—	2	1	no	—
31	C₈×C₂²⋊D₈₉	—	2	1	no	—
32	#19151651	C₂²	1	1	yes	characteristic
33	#19151649	—	2	1	no	—
34	#19151624	—	2	1	no	—
35	#19151622	C₂²	1	1	yes	characteristic
36	#19151553	—	2	1	no	—
37	C₄×C₈×D₈₉	—	2	1	no	—
38	#19151351	C₂²	1	2	yes	—
39	#19151349	C₂²	1	2	yes	—
40	#19151330	C₂²	1	2	yes	—
41	#19151330	C₂²	1	2	yes	—
42	#19151330	C₂²	1	2	yes	—
43	#19151327	C₂²	1	2	yes	—
44	#431×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
47	#322×C₈₉	C₂²	1	2	yes	—
48	C₈²×C₈₉	C₂²	1	2	yes	—
49	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
50	C₂×Dic₃₅₆	C₂×C₄	1	2	yes	—
51	C₂×#13083563	C₂×C₄	1	2	yes	—
52	C₂×#13083558	—	2	1	no	—
53	C₂×C₈×D₈₉	—	2	1	no	—
54	C₂×C₈×D₈₉	—	2	1	no	—
55	#15668012	C₂×C₄	1	1	yes	characteristic
56	#15668012	C₂×C₄	1	1	yes	characteristic
57	#15668004	—	2	1	no	—
58	#15667991	—	2	1	no	—
59	#15667991	C₂×C₄	1	2	yes	—
60	C₄×Dic₁₇₈	—	2	1	no	—
61	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₁₇₈	C₂³	1	2	yes	—
63	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
64	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
65	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
66	C₄×C₂²⋊D₈₉	—	2	1	no	—
67	C₄×C₂²⋊D₈₉	—	2	1	no	—
68	#15667971	—	2	1	no	—
69	#15667971	C₂×C₄	1	1	yes	characteristic
70	#15667969	—	2	1	no	—
71	C₄²×D₈₉	—	2	1	no	—
72	#15667946	C₂×C₄	1	2	yes	—
73	#15667944	C₂×C₄	1	2	yes	—
74	C₄⋊#10623494	—	2	1	no	—
75	C₄⋊#10623494	C₂³	1	2	yes	—
76	C₄⋊#10623494	C₂³	1	1	yes	characteristic
77	C₄⋊#10623494	C₂³	1	1	yes	characteristic
78	#15667941	—	2	2	no	—
79	#15667941	—	2	2	no	—
80	#15667941	—	2	1	no	—
81	#15667941	—	2	1	no	—
82	#15667937	C₂×C₄	1	2	yes	—
83	#15667937	C₂×C₄	1	2	yes	—
84	#15667937	C₂×C₄	1	2	yes	—
85	#15667934	C₂×C₄	1	2	yes	—
86	C₂²⋊#10623494	—	2	1	no	—
87	#15667924	—	2	1	no	—
88	#15667924	—	2	1	no	—
89	#15667922	—	2	2	no	—
90	C₄×#10623494	—	2	1	no	—
91	C₈×Dic₈₉	—	2	1	no	—
92	C₈×Dic₈₉	—	2	1	no	—
93	C₈×Dic₈₉	—	2	2	no	—
94	C₂×M₁₆×C₈₉	—	2	1	no	—
95	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
96	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
99	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
101	#97×C₈₉	—	2	1	no	—
102	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
103	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
104	C₄×C₈×C₈₉	C₂³	1	2	yes	—
105	C₄×C₈×C₈₉	C₂³	1	2	yes	—
106	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	#13083574	—	2	2	no	—
109	#13083574	—	2	2	no	—
110	C₂×Dic₁₇₈	—	2	1	no	—
111	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
112	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊D₈₉	—	2	1	no	—
115	C₂×C₄×D₈₉	—	2	1	no	—
116	C₂×C₄×D₈₉	—	2	1	no	—
117	C₂×C₄×D₈₉	—	2	1	no	—
118	Dic₃₅₆	—	2	4	no	—
119	#13083563	—	2	4	no	—
120	#13083558	—	4	2	no	—
121	C₂×#10623494	—	2	1	no	—
122	C₂×#10623494	—	2	1	no	—
123	C₂×#10623494	—	2	2	no	—
124	C₈×D₈₉	—	4	2	no	—
125	C₈×D₈₉	—	4	2	no	—
126	C₄⋊Dic₈₉	—	2	1	no	—
127	C₄⋊Dic₈₉	—	2	1	no	—
128	C₄⋊Dic₈₉	—	2	1	no	—
129	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
130	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
132	#13083553	—	2	1	no	—
133	#13083553	—	2	2	no	—
134	#13083553	—	2	1	no	—
135	#13083553	—	2	2	no	—
136	C₂²⋊Dic₈₉	—	2	2	no	—
137	C₂²⋊Dic₈₉	—	2	1	no	—
138	#13083551	—	2	1	no	—
139	#13083551	—	2	1	no	—
140	C₄×Dic₈₉	—	2	1	no	—
141	C₄×Dic₈₉	—	2	1	no	—
142	C₄×Dic₈₉	—	2	2	no	—
143	C₄×Dic₈₉	—	2	1	no	—
144	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
147	M₁₆×C₈₉	—	2	4	no	—
148	C₂×C₈×C₈₉	—	2	2	no	—
149	C₂×C₈×C₈₉	—	2	2	no	—
150	C₂×C₈×C₈₉	—	4	1	no	—
151	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₈₉	#41	1	1	yes	characteristic
160	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
161	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
162	C₂²×D₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	2	no	—
168	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
174	C₂²⋊D₈₉	—	2	4	no	—
175	C₂×Dic₈₉	—	2	1	no	—
176	C₂×Dic₈₉	—	2	1	no	—
177	C₂×Dic₈₉	—	2	1	no	—
178	C₂×Dic₈₉	—	2	2	no	—
179	C₂×Dic₈₉	—	2	2	no	—
180	D₃₅₆	—	2	1	no	—
181	D₃₅₆	#131	1	2	yes	—
182	C₄×D₈₉	—	2	4	no	—
183	C₄×D₈₉	—	4	1	no	—
184	C₄×D₈₉	—	4	1	no	—
185	C₄×D₈₉	—	4	2	no	—
186	Dic₁₇₈	—	2	1	no	—
187	Dic₁₇₈	—	2	2	no	—
188	Dic₁₇₈	—	2	2	no	—
189	Dic₁₇₈	—	4	2	no	—
190	Dic₁₇₈	#131	1	2	yes	—
191	C₈×C₈₉	—	2	4	no	—
192	C₈×C₈₉	—	2	2	no	—
193	C₈×C₈₉	—	2	2	no	—
194	C₈×C₈₉	—	2	1	no	—
195	C₈×C₈₉	—	2	1	no	—
196	C₈×C₈₉	—	2	1	no	—
197	C₈×C₈₉	#137	1	2	yes	—
198	#10623494	—	4	1	no	—
199	#10623494	—	4	1	no	—
200	#10623494	—	4	2	no	—
201	C₂²×C₈₉	—	2	1	no	—
202	C₂²×C₈₉	—	2	1	no	—
203	C₂²×C₈₉	—	2	1	no	—
204	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂×D₈₉	—	2	2	no	—
206	C₂×D₈₉	—	4	1	no	—
207	C₂×D₈₉	—	4	1	no	—
208	C₄×C₈₉	—	2	1	no	—
209	C₄×C₈₉	—	2	1	no	—
210	C₄×C₈₉	—	2	1	no	—
211	C₄×C₈₉	#443	1	2	yes	—
212	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
213	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
214	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
215	C₄×C₈₉	#575	1	1	yes	characteristic
216	Dic₈₉	—	2	2	no	—
217	Dic₈₉	—	4	2	no	—
218	Dic₈₉	—	4	1	no	—
219	Dic₈₉	—	4	2	no	—
220	Dic₈₉	—	4	1	no	—
221	#17913	—	89	1	no	maximal, Sylow
222	C₂×C₈₉	—	4	1	no	—
223	C₂×C₈₉	#2929	1	1	yes	characteristic
224	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
225	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
226	D₈₉	—	4	2	no	—
227	#3107	—	89	1	no	—
228	C₈×#41	—	89	1	no	—
229	#2960	—	89	1	no	—
230	#1587	—	89	2	no	—
231	#1585	—	89	2	no	—
232	C₈×Q₁₆	—	89	2	no	—
233	C₈×SD₁₆	—	89	2	no	—
234	#1574	—	89	1	no	—
235	#1489	—	89	1	no	—
236	#1485	—	89	1	no	—
237	C₈×M₁₆	D₈₉	1	1	yes	characteristic, complemented
238	C₈₉	#17913	1	1	yes	characteristic, complemented, Sylow
239	#533	—	89	1	no	—
240	C₄×#41	—	89	1	no	—
241	#485	—	89	2	no	—
242	#475	—	89	1	no	—
243	#474	—	89	1	no	—
244	#462	—	89	1	no	—
245	#461	—	89	1	no	—
246	#452	—	89	2	no	—
247	#446	—	89	2	no	—
248	#446	—	178	1	no	—
249	C₈×Q₈	—	89	2	no	—
250	C₈×Q₈	—	89	1	no	—
251	C₈×Q₈	—	89	1	no	—
252	C₈×Q₈	—	178	1	no	—
253	C₄×Q₁₆	—	89	2	no	—
254	C₄×SD₁₆	—	89	2	no	—
255	C₈×D₄	—	89	1	no	—
256	C₈×D₄	—	89	1	no	—
257	C₈×D₄	—	178	1	no	—
258	C₈×D₄	—	178	1	no	—
259	#431	—	89	1	no	—
260	#431	—	178	1	no	—
261	#431	C₂×D₈₉	1	1	yes	characteristic
262	#424	—	178	1	no	—
263	#423	—	89	1	no	—
264	#405	—	178	1	no	—
265	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
266	C₂×C₄×C₈	—	178	1	no	—
267	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
268	#335	—	89	2	no	—
269	#334	—	89	2	no	—
270	Q₈⋊C₈	—	89	2	no	—
271	Q₈⋊C₈	—	89	2	no	—
272	Q₈⋊C₈	—	89	2	no	—
273	D₄⋊C₈	—	89	2	no	—
274	#322	C₂×D₈₉	1	2	yes	—
275	C₈²	C₂×D₈₉	1	2	yes	—
276	C₂×#41	—	89	1	no	—
277	C₂×Q₁₆	—	89	2	no	—
278	C₂×SD₁₆	—	89	2	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	178	1	no	—
281	C₂²×C₈	—	178	1	no	—
282	C₂²×C₈	—	178	1	no	—
283	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
284	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
285	C₄⋊Q₈	—	89	1	no	—
286	C₄⋊Q₈	—	89	1	no	—
287	#125	—	178	1	no	—
288	C₂²⋊Q₈	—	89	2	no	—
289	C₂²⋊Q₈	—	178	1	no	—
290	C₄×Q₈	—	89	1	no	—
291	C₄×Q₈	—	89	1	no	—
292	C₄×Q₈	—	89	2	no	—
293	C₄×Q₈	—	178	1	no	—
294	C₄×D₄	—	89	1	no	—
295	C₄×D₄	—	89	1	no	—
296	C₄×D₄	—	178	1	no	—
297	C₄×D₄	—	178	1	no	—
298	#117	—	89	1	no	—
299	#117	—	178	1	no	—
300	#117	—	178	1	no	—
301	C₂×C₄²	—	178	1	no	—
302	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
303	#107	—	89	2	no	—
304	#106	—	89	2	no	—
305	C₄⋊C₈	—	89	2	no	—
306	C₄⋊C₈	—	89	1	no	—
307	C₄⋊C₈	—	89	1	no	—
308	C₄⋊C₈	—	178	2	no	—
309	C₄⋊C₈	—	178	2	no	—
310	C₄⋊C₈	—	178	1	no	—
311	C₄⋊C₈	—	178	1	no	—
312	C₄⋊C₈	—	178	1	no	—
313	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
314	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
315	#103	—	89	2	no	—
316	#103	—	89	2	no	—
317	#103	—	89	2	no	—
318	#102	—	89	2	no	—
319	C₂²⋊C₈	—	178	1	no	—
320	C₂²⋊C₈	—	178	1	no	—
321	C₂²⋊C₈	—	178	1	no	—
322	C₂²⋊C₈	C₄×D₈₉	1	2	yes	—
323	#97	—	2	1	no	—
324	#97	—	178	2	no	—
325	C₄×C₈	—	178	1	no	—
326	C₄×C₈	—	178	1	no	—
327	C₄×C₈	—	178	2	no	—
328	C₄×C₈	—	178	1	no	—
329	C₄×C₈	D₃₅₆	1	1	yes	characteristic
330	C₄×C₈	D₃₅₆	1	1	yes	characteristic
331	C₄×C₈	C₂²×D₈₉	1	2	yes	—
332	C₄×C₈	C₂²×D₈₉	1	2	yes	—
333	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
334	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
335	#41	—	178	2	no	—
336	#41	—	178	2	no	—
337	C₂×Q₈	—	89	1	no	—
338	C₂×Q₈	—	89	2	no	—
339	C₂×Q₈	—	178	1	no	—
340	C₂×D₄	—	89	1	no	—
341	C₂×D₄	—	178	1	no	—
342	C₂²×C₄	—	178	1	no	—
343	C₂²×C₄	—	178	1	no	—
344	C₂²×C₄	—	178	1	no	—
345	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
347	C₂²×C₄	#13083574	1	1	yes	characteristic
348	Q₁₆	—	178	4	no	—
349	SD₁₆	—	178	4	no	—
350	M₁₆	—	2	4	no	—
351	M₁₆	—	356	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	356	2	no	—
356	C₂×C₈	—	356	2	no	—
357	C₂×C₈	—	178	1	no	—
358	C₂×C₈	—	178	1	no	—
359	C₂×C₈	—	178	2	no	—
360	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
361	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
362	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
363	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
364	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
365	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
366	C₄⋊C₄	—	89	2	no	—
367	C₄⋊C₄	—	89	1	no	—
368	C₄⋊C₄	—	89	1	no	—
369	C₄⋊C₄	—	178	1	no	—
370	C₄⋊C₄	—	178	1	no	—
371	C₄⋊C₄	—	178	1	no	—
372	C₄⋊C₄	—	178	2	no	—
373	C₄⋊C₄	—	178	1	no	—
374	C₄⋊C₄	—	178	1	no	—
375	C₄⋊C₄	—	178	2	no	—
376	C₂²⋊C₄	—	178	1	no	—
377	C₂²⋊C₄	—	178	2	no	—
378	C₂²⋊C₄	—	178	1	no	—
379	C₂²⋊C₄	—	178	1	no	—
380	C₄²	—	178	1	no	—
381	C₄²	—	178	1	no	—
382	C₄²	—	178	1	no	—
383	C₄²	—	178	2	no	—
384	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
385	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
386	C₄²	#13083574	1	1	yes	characteristic
387	C₄²	C₂³×D₈₉	1	1	yes	characteristic
388	C₂³	—	178	1	no	—
389	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
390	Q₈	—	89	2	no	—
391	Q₈	—	356	2	no	—
392	Q₈	—	178	2	no	—
393	Q₈	—	178	2	no	—
394	Q₈	—	178	1	no	—
395	D₄	—	89	2	no	—
396	D₄	—	178	4	no	—
397	D₄	—	178	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	356	1	no	—
404	C₂×C₄	—	356	1	no	—
405	C₂×C₄	—	356	2	no	—
406	C₂×C₄	—	178	4	no	—
407	C₂×C₄	—	178	1	no	—
408	C₂×C₄	—	178	1	no	—
409	C₂×C₄	—	178	2	no	—
410	C₂×C₄	—	178	2	no	—
411	C₂×C₄	—	178	1	no	—
412	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
413	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
414	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
417	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	2	no	—
423	C₈	—	2	2	no	—
424	C₈	—	356	1	no	—
425	C₈	—	356	1	no	—
426	C₈	—	356	2	no	—
427	C₈	#15668045	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	356	1	no	—
432	C₂²	—	356	1	no	—
433	C₂²	—	178	2	no	—
434	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	356	1	no	—
439	C₄	—	356	1	no	—
440	C₄	—	356	2	no	—
441	C₄	—	356	2	no	—
442	C₄	—	178	2	no	—
443	C₄	#19151716	1	2	yes	—
444	C₄	#131×D₈₉	1	1	yes	characteristic
445	C₄	#131×D₈₉	1	1	yes	characteristic
446	C₄	C₂×#15668045	1	1	yes	characteristic
447	C₄	#19152398	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	356	2	no	—
450	C₂	#26028948	1	1	yes	characteristic
451	C₂	C₄×#15668045	1	1	yes	characteristic
452	C₂	C₂×#19151716	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×M₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#13083574	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₈×M₁₆	D₈₉
hypocenter	C₈₉	#17913
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
3. #26029186	C₂	semidirect
4. #26019125	C₂	semidirect
5. #26019111	C₂	semidirect
6. C₈×Dic₃₅₆	C₂	semidirect
7. C₈×#13083563	C₂	semidirect
8. #26019041	C₂	semidirect
10. #26018674	C₂	semidirect
11. C₈×M₁₆×C₈₉	C₂	semidirect
237. C₈×M₁₆	D₈₉	semidirect
238. C₈₉	#17913	semidirect

Maximal subgroups

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

subgroup	index
#26030324	2
C₈×#13083574	2
#26029186	2
#26019125	2
#26019111	2
C₈×Dic₃₅₆	2
C₈×#13083563	2
#26019041	2
#26018692	2
#26018674	2
C₈×M₁₆×C₈₉	2
#17913	89