Subgroups — #36524233

Order 22784.

684 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029292	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#15668037	C₂	1	1	yes	maximal, characteristic
3	#26019164	C₂	1	2	yes	maximal, complemented
4	#26019152	C₂	1	2	yes	maximal, complemented
5	#26019142	C₂	1	2	yes	maximal, complemented
6	#26019135	C₂	1	2	yes	maximal, complemented
7	#26019002	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018634	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#19151325	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2989	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668037	C₄	1	1	yes	characteristic
13	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
14	#19151708	C₄	1	2	yes	—
15	#19151696	C₄	1	2	yes	—
16	C₄×#13083561	C₂²	1	2	yes	—
17	C₄×#13083559	C₂²	1	2	yes	—
18	#19151677	C₂²	1	2	yes	—
19	#19151677	C₂²	1	2	yes	—
20	#19151675	—	2	1	no	—
21	#19151675	—	2	1	no	—
22	#19151651	C₂²	1	1	yes	characteristic
23	#19151641	C₄	1	1	yes	characteristic
24	#19151602	C₄	1	1	yes	characteristic
25	#19151599	C₄	1	1	yes	characteristic
26	#19151560	—	2	2	no	—
27	C₄×#13083558	C₂²	1	1	yes	characteristic
28	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
29	#19151350	C₂²	1	2	yes	complemented
30	#19151348	C₂²	1	2	yes	complemented
31	Q₈⋊#10623494	C₂²	1	1	yes	characteristic, complemented
32	Q₈⋊#10623494	C₂²	1	1	yes	characteristic, complemented
33	D₄⋊#10623494	C₂²	1	1	yes	characteristic, complemented
34	D₄⋊#10623494	C₂²	1	1	yes	characteristic, complemented
35	#19151325	C₂²	1	2	yes	—
36	#19151325	C₂²	1	2	yes	—
37	#19151320	C₂²	1	2	yes	complemented
38	C₈×#10623494	C₂²	1	2	yes	complemented
39	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
40	#446×C₈₉	C₂²	1	2	yes	complemented
41	#436×C₈₉	C₂²	1	2	yes	complemented
42	#435×C₈₉	—	2	2	no	—
43	#432×C₈₉	—	2	1	no	—
44	#431×C₈₉	C₂²	1	1	yes	characteristic
45	#423×C₈₉	—	2	1	no	—
46	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂²×D₃₅₆	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₈₉	—	2	1	no	—
49	#15668037	—	2	4	no	—
50	C₂×#13083561	C₂×C₄	1	2	yes	—
51	C₂×#13083559	C₂×C₄	1	2	yes	—
52	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
53	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
54	C₂×#13083557	—	2	2	no	—
55	C₂×#13083557	—	2	2	no	—
56	C₂²×#10623494	—	2	1	no	—
57	C₄×D₃₅₆	—	2	1	no	—
58	C₄×D₃₅₆	—	2	1	no	—
59	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
60	C₄×D₃₅₆	C₂³	1	2	yes	—
61	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
62	C₂×#13083551	—	2	1	no	—
63	#15667945	C₂×C₄	1	2	yes	—
64	#15667943	C₂×C₄	1	2	yes	—
65	C₄⋊#10623494	C₂³	1	1	yes	characteristic
66	C₄⋊#10623494	C₂³	1	1	yes	characteristic
67	#15667936	C₂×C₄	1	2	yes	—
68	#15667933	C₂×C₄	1	2	yes	—
69	#15667932	C₂×C₄	1	2	yes	—
70	#15667932	C₂×C₄	1	2	yes	—
71	C₂²⋊#10623494	—	2	1	no	—
72	#15667924	—	2	2	no	—
73	#15667924	—	2	2	no	—
74	#15667923	C₂×C₄	1	2	yes	—
75	C₄×#10623494	—	2	1	no	—
76	C₄×#10623494	—	2	1	no	—
77	C₄×#10623494	C₂³	1	1	yes	characteristic
78	C₄×#10623494	C₂³	1	1	yes	characteristic
79	C₄×#10623494	C₂³	1	2	yes	—
80	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₂×M₁₆×C₈₉	—	2	2	no	—
82	C₂²×C₈×C₈₉	—	2	1	no	—
83	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
84	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
85	C₄×D₄×C₈₉	—	2	1	no	—
86	C₄×D₄×C₈₉	—	2	1	no	—
87	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
89	#117×C₈₉	—	2	1	no	—
90	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₈₉	—	2	1	no	—
92	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₈₉	—	2	2	no	—
94	C₄⋊C₈×C₈₉	—	2	1	no	—
95	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
96	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
97	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
98	C₂²⋊C₈×C₈₉	—	2	2	no	—
99	C₂²⋊C₈×C₈₉	D₄	1	2	yes	—
100	#97×C₈₉	—	2	2	no	—
101	C₄×C₈×C₈₉	C₂³	1	2	yes	—
102	C₂³×D₈₉	—	2	1	no	—
103	C₂×D₃₅₆	—	2	2	no	—
104	C₂×D₃₅₆	—	2	2	no	—
105	C₂×D₃₅₆	—	2	1	no	—
106	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
107	C₂²×Dic₈₉	—	2	1	no	—
108	C₂×C₄×D₈₉	—	2	2	no	—
109	C₂×C₄×D₈₉	—	2	2	no	—
110	C₂×C₄×D₈₉	—	8	1	no	—
111	C₂×C₄×D₈₉	—	8	1	no	—
112	#13083561	—	2	4	no	—
113	#13083559	—	2	4	no	—
114	#13083558	—	2	2	no	—
115	#13083558	M₁₆	1	4	yes	complemented
116	#13083557	—	8	2	no	—
117	#13083557	—	8	2	no	—
118	C₂×#10623494	—	2	1	no	—
119	C₂×#10623494	—	2	1	no	—
120	C₂×#10623494	—	2	1	no	—
121	C₂×#10623494	—	2	1	no	—
122	C₂×#10623494	—	4	2	no	—
123	C₂×#10623494	C₂²×C₄	1	2	yes	—
124	C₂×#10623494	C₂²×C₄	1	2	yes	—
125	C₄⋊Dic₈₉	—	2	1	no	—
126	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
127	#13083551	—	2	2	no	—
128	#13083551	—	2	2	no	—
129	#41×C₈₉	—	2	2	no	—
130	#41×C₈₉	—	2	2	no	—
131	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×D₄×C₈₉	—	2	1	no	—
133	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	—	2	1	no	—
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	M₁₆×C₈₉	—	8	2	no	—
141	C₂×C₈×C₈₉	—	2	2	no	—
142	C₂×C₈×C₈₉	—	8	1	no	—
143	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
145	C₄⋊C₄×C₈₉	—	2	1	no	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²⋊C₄×C₈₉	—	2	1	no	—
150	C₂²⋊C₄×C₈₉	—	2	1	no	—
151	C₂²⋊C₄×C₈₉	—	2	1	no	—
152	C₄²×C₈₉	—	2	1	no	—
153	C₄²×C₈₉	—	2	1	no	—
154	C₄²×C₈₉	—	2	1	no	—
155	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₈₉	#41	1	1	yes	characteristic
158	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
159	C₂³×C₈₉	—	2	1	no	—
160	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₈₉	—	2	2	no	—
162	C₂²×D₈₉	—	4	2	no	—
163	C₂²×D₈₉	—	8	1	no	—
164	C₂²×D₈₉	—	8	1	no	—
165	Q₈×C₈₉	—	2	1	no	—
166	Q₈×C₈₉	—	2	1	no	—
167	D₄×C₈₉	—	2	1	no	—
168	D₄×C₈₉	—	2	1	no	—
169	D₄×C₈₉	—	4	2	no	—
170	C₂×C₄×C₈₉	—	2	1	no	—
171	C₂×C₄×C₈₉	—	2	1	no	—
172	C₂×C₄×C₈₉	—	2	1	no	—
173	C₂×C₄×C₈₉	—	2	1	no	—
174	C₂×C₄×C₈₉	—	2	1	no	—
175	C₂×C₄×C₈₉	—	4	1	no	—
176	C₂×C₄×C₈₉	—	4	1	no	—
177	C₂×C₄×C₈₉	—	4	1	no	—
178	C₂×C₄×C₈₉	—	4	2	no	—
179	C₂×C₄×C₈₉	—	8	1	no	—
180	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
184	C₂×C₄×C₈₉	#131	1	2	yes	—
185	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
188	C₂×Dic₈₉	—	2	2	no	—
189	C₂×Dic₈₉	—	8	1	no	—
190	D₃₅₆	—	2	2	no	—
191	D₃₅₆	—	2	2	no	—
192	D₃₅₆	—	4	2	no	—
193	C₄×D₈₉	—	4	2	no	—
194	C₄×D₈₉	—	4	2	no	—
195	C₄×D₈₉	—	8	2	no	—
196	C₈×C₈₉	—	2	2	no	—
197	C₈×C₈₉	—	2	2	no	—
198	C₈×C₈₉	—	4	2	no	—
199	#10623494	—	2	2	no	—
200	#10623494	—	2	2	no	—
201	#10623494	—	4	1	no	—
202	#10623494	—	4	1	no	—
203	#10623494	—	4	1	no	—
204	#10623494	C₂×M₁₆	1	4	yes	—
205	C₂²×C₈₉	—	2	1	no	—
206	C₂²×C₈₉	—	2	1	no	—
207	C₂²×C₈₉	—	4	1	no	—
208	C₂²×C₈₉	—	4	1	no	—
209	C₂²×C₈₉	—	4	1	no	—
210	C₂²×C₈₉	#436	1	2	yes	—
211	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂×D₈₉	—	4	2	no	—
213	C₂×D₈₉	—	4	2	no	—
214	C₂×D₈₉	—	4	2	no	—
215	C₂×D₈₉	—	8	4	no	—
216	C₄×C₈₉	—	2	1	no	—
217	C₄×C₈₉	—	2	1	no	—
218	C₄×C₈₉	—	2	1	no	—
219	C₄×C₈₉	—	4	1	no	—
220	C₄×C₈₉	—	4	1	no	—
221	C₄×C₈₉	—	4	1	no	—
222	C₄×C₈₉	#436	1	2	yes	—
223	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
224	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
225	C₄×C₈₉	#576	1	1	yes	characteristic
226	C₄×C₈₉	#577	1	1	yes	characteristic
227	Dic₈₉	—	4	2	no	—
228	#17893	—	89	1	no	maximal, Sylow
229	C₂×C₈₉	—	2	2	no	—
230	C₂×C₈₉	—	8	1	no	—
231	C₂×C₈₉	C₂×#436	1	1	yes	characteristic
232	C₂×C₈₉	#2946	1	1	yes	characteristic
233	C₂×C₈₉	#2956	1	1	yes	characteristic
234	D₈₉	—	8	2	no	—
235	#2989	D₈₉	1	1	yes	characteristic, complemented
236	#2975	—	89	1	no	—
237	C₄×AGL(1,ℤ/8)	—	89	1	no	—
238	#1594	—	89	2	no	—
239	#1592	—	89	2	no	—
240	#1590	—	89	2	no	—
241	#1589	—	89	2	no	—
242	#1565	—	89	1	no	—
243	#1476	—	89	1	no	—
244	C₂×D₄⋊C₈	—	89	1	no	—
245	C₈×M₁₆	—	89	1	no	—
246	C₈₉	#17893	1	1	yes	characteristic, complemented, Sylow
247	C₂×AGL(1,ℤ/8)	—	89	1	no	—
248	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
249	C₂×C₄×D₄	—	89	1	no	—
250	#446	C₂×D₈₉	1	2	yes	complemented
251	#442	—	89	2	no	—
252	#440	—	89	2	no	—
253	C₄×SD₁₆	—	89	2	no	—
254	C₄×D₈	—	89	2	no	—
255	#436	—	89	2	no	—
256	#436	—	89	2	no	—
257	#436	—	178	1	no	—
258	#436	—	178	1	no	—
259	#436	C₂×D₈₉	1	2	yes	complemented
260	#435	—	2	2	no	—
261	#432	—	2	1	no	—
262	#431	—	89	1	no	—
263	#431	C₂×D₈₉	1	1	yes	characteristic
264	#428	—	89	1	no	—
265	#423	—	2	1	no	—
266	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
267	#418	—	89	1	no	—
268	#417	—	89	1	no	—
269	#407	—	178	2	no	—
270	C₄×M₁₆	—	89	1	no	—
271	C₂×C₄×C₈	—	89	1	no	—
272	#335	—	89	2	no	—
273	#334	—	89	2	no	—
274	Q₈⋊C₈	—	89	1	no	—
275	Q₈⋊C₈	—	89	1	no	—
276	D₄⋊C₈	—	89	1	no	—
277	D₄⋊C₈	—	89	1	no	—
278	D₄⋊C₈	—	89	2	no	—
279	D₄⋊C₈	—	89	2	no	—
280	#322	—	89	2	no	—
281	C₈²	—	89	2	no	—
282	C₂×#41	C₄×D₈₉	1	1	yes	characteristic
283	C₂²×D₄	—	89	1	no	—
284	C₂³×C₄	—	178	1	no	—
285	AGL(1,ℤ/8)	—	178	4	no	—
286	C₂×SD₁₆	—	89	2	no	—
287	C₂×D₈	—	89	2	no	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	89	1	no	—
290	C₂×M₁₆	—	89	1	no	—
291	C₂×M₁₆	—	178	2	no	—
292	C₂×M₁₆	—	178	2	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	178	1	no	—
295	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
296	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	89	2	no	—
300	C₄×D₄	—	89	2	no	—
301	C₄×D₄	—	178	1	no	—
302	C₄×D₄	—	178	1	no	—
303	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
304	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
305	#117	—	2	1	no	—
306	#117	C₄×D₈₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	—	89	1	no	—
308	C₂×C₂²⋊C₄	—	178	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
311	#107	—	89	2	no	—
312	#106	—	89	2	no	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	89	1	no	—
316	C₄⋊C₈	—	89	1	no	—
317	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
318	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
319	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
320	#103	—	89	2	no	—
321	#102	—	89	2	no	—
322	#102	—	89	2	no	—
323	#102	—	89	2	no	—
324	C₂²⋊C₈	—	2	2	no	—
325	C₂²⋊C₈	—	178	1	no	—
326	C₂²⋊C₈	—	178	2	no	—
327	C₂²⋊C₈	—	178	2	no	—
328	C₂²⋊C₈	C₂²⋊D₈₉	1	2	yes	—
329	#97	—	2	2	no	—
330	#97	—	89	2	no	—
331	C₄×C₈	—	89	2	no	—
332	C₄×C₈	—	89	1	no	—
333	C₄×C₈	—	89	1	no	—
334	C₄×C₈	—	178	1	no	—
335	C₄×C₈	—	178	1	no	—
336	C₄×C₈	C₂²×D₈₉	1	2	yes	—
337	C₂⁴	—	178	1	no	—
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	89	2	no	—
343	C₂×D₄	—	178	1	no	—
344	C₂×D₄	—	178	2	no	—
345	C₂×D₄	—	178	2	no	—
346	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	178	2	no	—
351	C₂²×C₄	—	178	1	no	—
352	C₂²×C₄	—	178	2	no	—
353	C₂²×C₄	—	712	1	no	—
354	C₂²×C₄	—	712	1	no	—
355	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
357	C₂²×C₄	#13083574	1	1	yes	characteristic
358	SD₁₆	—	178	4	no	—
359	D₈	—	178	4	no	—
360	M₁₆	—	8	2	no	—
361	M₁₆	—	89	4	no	—
362	M₁₆	—	178	2	no	—
363	M₁₆	—	712	2	no	—
364	M₁₆	—	712	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	8	1	no	—
367	C₂×C₈	—	89	2	no	—
368	C₂×C₈	—	89	2	no	—
369	C₂×C₈	—	356	2	no	—
370	C₂×C₈	—	178	1	no	—
371	C₂×C₈	—	178	1	no	—
372	C₂×C₈	—	178	1	no	—
373	C₂×C₈	—	178	1	no	—
374	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
375	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	89	2	no	—
379	C₄⋊C₄	—	178	1	no	—
380	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
381	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	178	2	no	—
386	C₂²⋊C₄	—	178	2	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
391	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
392	C₄²	#13083574	1	1	yes	characteristic
393	C₄²	C₂³×D₈₉	1	1	yes	characteristic
394	C₂³	—	2	1	no	—
395	C₂³	—	356	2	no	—
396	C₂³	—	178	2	no	—
397	C₂³	—	712	1	no	—
398	C₂³	—	712	1	no	—
399	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	—	2	1	no	—
402	D₄	—	2	1	no	—
403	D₄	—	2	1	no	—
404	D₄	—	4	2	no	—
405	D₄	—	356	2	no	—
406	D₄	—	178	2	no	—
407	D₄	—	178	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	8	1	no	—
418	C₂×C₄	—	356	2	no	—
419	C₂×C₄	—	356	2	no	—
420	C₂×C₄	—	178	2	no	—
421	C₂×C₄	—	712	2	no	—
422	C₂×C₄	—	712	1	no	—
423	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
424	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
425	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
426	C₂×C₄	M₁₆×D₈₉	1	2	yes	—
427	C₂×C₄	#15668020	1	2	yes	—
428	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
429	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
430	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	4	2	no	—
434	C₈	—	89	4	no	—
435	C₈	—	356	1	no	—
436	C₈	—	356	1	no	—
437	C₈	—	356	1	no	—
438	C₈	—	178	2	no	—
439	C₈	—	178	2	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	356	2	no	—
446	C₂²	—	356	2	no	—
447	C₂²	—	356	2	no	—
448	C₂²	—	712	4	no	—
449	C₂²	#19151674	1	2	yes	—
450	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	356	2	no	—
458	C₄	#19151674	1	2	yes	—
459	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
460	C₄	C₂×#15668020	1	1	yes	characteristic
461	C₄	#19152401	1	1	yes	characteristic
462	C₄	#19152406	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	8	1	no	—
465	C₂	—	712	2	no	—
466	C₂	C₂×#19151674	1	1	yes	characteristic
467	C₂	#26029080	1	1	yes	characteristic
468	C₂	#26029159	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×#2989	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668037	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2989	D₈₉
hypocenter	C₈₉	#17893
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2989

Complements

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

N	H ≅ G/N	type
1. #26029292	C₂	semidirect
3. #26019164	C₂	semidirect
4. #26019152	C₂	semidirect
5. #26019142	C₂	semidirect
6. #26019135	C₂	semidirect
7. #26019002	C₂	semidirect
8. #26018634	C₂	semidirect
9. C₂×#19151325	C₂	semidirect
10. #26018533	C₂	semidirect
11. C₈₉×#2989	C₂	semidirect
29. #19151350	C₂²	semidirect
30. #19151348	C₂²	semidirect
31. Q₈⋊#10623494	C₂²	semidirect
32. Q₈⋊#10623494	C₂²	semidirect
33. D₄⋊#10623494	C₂²	semidirect
34. D₄⋊#10623494	C₂²	semidirect
37. #19151320	C₂²	semidirect
38. C₈×#10623494	C₂²	semidirect
40. #446×C₈₉	C₂²	semidirect
41. #436×C₈₉	C₂²	semidirect
115. #13083558	M₁₆	semidirect
235. #2989	D₈₉	semidirect
246. C₈₉	#17893	semidirect
250. #446	C₂×D₈₉	semidirect
259. #436	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029292	2
C₄×#15668037	2
#26019164	2
#26019152	2
#26019142	2
#26019135	2
#26019002	2
#26018634	2
C₂×#19151325	2
#26018533	2
C₈₉×#2989	2
#17893	89