Subgroups — C₄×#19152037 #36707752

Order 22784.

674 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152037	C₂	1	1	yes	maximal, characteristic
2	C₄×#15668031	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022122	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022120	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022117	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022113	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×Dic₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#15667958	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#15667956	C₂	1	1	yes	maximal, characteristic, complemented
11	#26022039	C₂	1	1	yes	maximal, characteristic, complemented
12	#26021970	C₂	1	1	yes	maximal, characteristic, complemented
13	#26021961	C₂	1	1	yes	maximal, characteristic
14	C₄×#15667951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668031	C₂²	1	1	yes	characteristic
17	C₂×Q₁₆×D₈₉	C₂²	1	1	yes	characteristic
18	C₄×#13083573	—	2	1	no	—
19	C₄×Q₈×D₈₉	—	2	1	no	—
20	#19152037	C₄	1	8	yes	direct product factor
21	C₂×Dic₇₁₂	C₂²	1	1	yes	characteristic
22	C₂×#15667958	C₂²	1	1	yes	characteristic
23	C₂×#15667956	C₂²	1	1	yes	characteristic
24	C₂×#15667951	C₂²	1	1	yes	characteristic
25	C₂×#15667951	C₂²	1	1	yes	characteristic
26	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
27	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
28	Q₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
29	#19151692	C₂²	1	1	yes	characteristic
30	#19151692	C₂²	1	1	yes	characteristic
31	C₄×#13083564	—	2	1	no	—
32	#19151690	—	2	1	no	—
33	#19151689	—	2	1	no	—
34	C₄×#13083562	—	2	1	no	—
35	D₈×Dic₈₉	C₂²	1	1	yes	characteristic
36	#19151635	C₂²	1	1	yes	characteristic
37	#107×D₈₉	C₂²	1	1	yes	characteristic
38	#19151591	—	2	1	no	—
39	#103×D₈₉	—	2	1	no	—
40	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
41	#19151425	C₂²	1	1	yes	characteristic
42	#19151424	C₂²	1	1	yes	characteristic
43	#19151423	C₂²	1	1	yes	characteristic
44	#19151403	C₂²	1	1	yes	characteristic
45	#19151403	C₂²	1	1	yes	characteristic
46	#19151402	C₂²	1	1	yes	characteristic
47	#19151401	C₂²	1	1	yes	characteristic
48	#19151401	C₂²	1	1	yes	characteristic
49	#19151399	C₂²	1	1	yes	characteristic
50	#19151373	C₂²	1	1	yes	characteristic
51	#19151373	C₂²	1	1	yes	characteristic
52	C₄×#13083549	C₂²	1	1	yes	characteristic
53	C₂×SD₃₂×C₈₉	C₂²	1	1	yes	characteristic
54	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
55	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
56	#367×C₈₉	C₂²	1	1	yes	characteristic
57	#358×C₈₉	C₂²	1	1	yes	characteristic
58	#357×C₈₉	C₂²	1	1	yes	characteristic
59	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
60	C₂×#13083573	—	2	1	no	—
61	C₂×Q₈×D₈₉	—	2	1	no	—
62	#15668031	—	2	2	no	—
63	#15668031	C₂×C₄	1	4	yes	—
64	C₂×Dic₃₅₆	C₂³	1	1	yes	characteristic
65	C₂×Dic₃₅₆	C₂³	1	1	yes	characteristic
66	C₂×#13083564	—	2	1	no	—
67	Q₁₆×D₈₉	—	2	2	no	—
68	Q₁₆×D₈₉	C₂×C₄	1	4	yes	complemented
69	C₂×#13083562	—	2	1	no	—
70	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
71	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
72	Q₈×Dic₈₉	—	2	1	no	—
73	C₄×Dic₁₇₈	—	2	1	no	—
74	C₄×Dic₁₇₈	—	2	1	no	—
75	C₄×Dic₁₇₈	—	4	1	no	—
76	#15667977	—	2	1	no	—
77	#15667977	—	2	1	no	—
78	#15667977	—	4	1	no	—
79	D₄×Dic₈₉	—	2	1	no	—
80	C₄×C₂²⋊D₈₉	—	4	1	no	—
81	#15667972	—	4	1	no	—
82	#15667970	—	2	1	no	—
83	#15667968	—	4	1	no	—
84	C₄⋊C₄×D₈₉	—	2	1	no	—
85	C₄⋊C₄×D₈₉	—	4	1	no	—
86	C₂×C₄×Dic₈₉	—	4	1	no	—
87	C₄²×D₈₉	—	4	1	no	—
88	C₄²×D₈₉	D₄	1	1	yes	characteristic
89	Dic₇₁₂	C₂×C₄	1	4	yes	complemented
90	#15667958	C₂×C₄	1	4	yes	complemented
91	#15667956	C₂×C₄	1	4	yes	complemented
92	#15667951	—	2	2	no	—
93	#15667951	C₂×C₄	1	4	yes	complemented
94	C₂×#13083549	C₂³	1	1	yes	characteristic
95	C₂×#13083549	C₂³	1	1	yes	characteristic
96	#15667946	C₂³	1	1	yes	characteristic
97	#15667946	C₂³	1	1	yes	characteristic
98	#15667945	—	2	1	no	—
99	#15667943	—	2	1	no	—
100	#15667937	—	2	1	no	—
101	#15667937	—	2	1	no	—
102	#15667936	—	2	1	no	—
103	#15667935	—	2	1	no	—
104	#15667935	—	2	1	no	—
105	#15667933	—	2	1	no	—
106	C₄×#10623494	D₄	1	1	yes	characteristic
107	C₈×Dic₈₉	D₄	1	1	yes	characteristic
108	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
109	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₄×Q₈×C₈₉	—	2	1	no	—
112	C₄×D₄×C₈₉	—	2	1	no	—
113	SD₃₂×C₈₉	C₂×C₄	1	4	yes	complemented
114	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
116	#107×C₈₉	C₂³	1	1	yes	characteristic
117	#107×C₈₉	C₂³	1	1	yes	characteristic
118	#103×C₈₉	—	2	1	no	—
119	#102×C₈₉	—	2	1	no	—
120	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
121	#13083573	—	2	4	no	—
122	#13083573	—	4	2	no	—
123	C₂×Dic₁₇₈	—	2	1	no	—
124	C₂×Dic₁₇₈	—	2	1	no	—
125	C₂×Dic₁₇₈	—	4	1	no	—
126	Q₈×D₈₉	—	2	4	no	—
127	Q₈×D₈₉	—	4	2	no	—
128	C₂×C₂²⋊D₈₉	—	4	1	no	—
129	C₂²×Dic₈₉	—	4	1	no	—
130	C₂²×Dic₈₉	—	4	1	no	—
131	C₂×C₄×D₈₉	—	4	1	no	—
132	C₂×C₄×D₈₉	—	4	1	no	—
133	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
134	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
135	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
136	Dic₃₅₆	—	2	1	no	—
137	Dic₃₅₆	—	2	1	no	—
138	Dic₃₅₆	C₂²×C₄	1	2	yes	—
139	Dic₃₅₆	C₂²×C₄	1	2	yes	—
140	#13083564	—	2	4	no	—
141	#13083562	—	2	4	no	—
142	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
143	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
144	C₈×D₈₉	—	2	2	no	—
145	C₈×D₈₉	C₂²×C₄	1	2	yes	—
146	C₈×D₈₉	#41	1	2	yes	—
147	C₄⋊Dic₈₉	—	2	1	no	—
148	C₄⋊Dic₈₉	—	2	1	no	—
149	C₄⋊Dic₈₉	—	4	1	no	—
150	#13083553	—	4	1	no	—
151	#13083553	—	4	1	no	—
152	#13083553	—	4	1	no	—
153	#13083553	—	4	1	no	—
154	#13083553	—	4	1	no	—
155	C₂²⋊Dic₈₉	—	4	1	no	—
156	#13083551	—	4	1	no	—
157	C₄×Dic₈₉	—	4	1	no	—
158	C₄×Dic₈₉	—	4	1	no	—
159	C₄×Dic₈₉	—	4	1	no	—
160	C₄×Dic₈₉	—	4	1	no	—
161	C₄×Dic₈₉	—	4	1	no	—
162	C₄×Dic₈₉	—	4	1	no	—
163	C₄×Dic₈₉	D₈	1	1	yes	characteristic
164	C₄×Dic₈₉	D₈	1	1	yes	characteristic
165	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
166	#13083549	—	2	1	no	—
167	#13083549	C₂²×C₄	1	2	yes	—
168	C₂×Q₈×C₈₉	—	2	1	no	—
169	C₂×D₄×C₈₉	—	2	1	no	—
170	C₂²×C₄×C₈₉	—	4	1	no	—
171	Q₁₆×C₈₉	—	2	1	no	—
172	Q₁₆×C₈₉	C₂²×C₄	1	2	yes	—
173	D₈×C₈₉	—	2	1	no	—
174	D₈×C₈₉	C₂²×C₄	1	2	yes	—
175	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
177	C₄⋊C₄×C₈₉	—	2	1	no	—
178	C₄⋊C₄×C₈₉	—	2	1	no	—
179	C₄⋊C₄×C₈₉	—	4	1	no	—
180	C₂²⋊C₄×C₈₉	—	4	1	no	—
181	C₄²×C₈₉	—	4	1	no	—
182	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
183	C₁₆×C₈₉	—	2	1	no	—
184	C₁₆×C₈₉	C₂²×C₄	1	2	yes	—
185	C₂³×C₈₉	—	4	1	no	—
186	C₂²×D₈₉	C₂×D₈	1	1	yes	characteristic
187	Q₈×C₈₉	—	2	2	no	—
188	Q₈×C₈₉	—	4	1	no	—
189	D₄×C₈₉	—	2	2	no	—
190	D₄×C₈₉	—	4	1	no	—
191	C₂×C₄×C₈₉	—	4	1	no	—
192	C₂×C₄×C₈₉	—	4	1	no	—
193	C₂×C₄×C₈₉	—	4	1	no	—
194	C₂×C₄×C₈₉	—	8	2	no	—
195	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	C₂²⋊D₈₉	—	4	4	no	—
199	C₂×Dic₈₉	—	4	1	no	—
200	C₂×Dic₈₉	—	4	1	no	—
201	C₂×Dic₈₉	—	4	4	no	—
202	C₂×Dic₈₉	—	4	1	no	—
203	C₂×Dic₈₉	—	4	1	no	—
204	C₂×Dic₈₉	—	8	2	no	—
205	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
206	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
207	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
208	C₄×D₈₉	—	2	2	no	—
209	C₄×D₈₉	—	4	1	no	—
210	C₄×D₈₉	—	4	4	no	—
211	C₄×D₈₉	—	8	2	no	—
212	C₄×D₈₉	C₄×D₄	1	2	yes	—
213	C₄×D₈₉	#135	1	2	yes	—
214	Dic₁₇₈	—	2	2	no	—
215	Dic₁₇₈	—	2	2	no	—
216	Dic₁₇₈	—	4	1	no	—
217	Dic₁₇₈	—	4	1	no	—
218	Dic₁₇₈	—	4	4	no	—
219	C₈×C₈₉	—	2	1	no	—
220	C₈×C₈₉	C₂³×C₄	1	1	yes	characteristic
221	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
222	#10623494	—	2	1	no	—
223	#10623494	C₄×D₄	1	2	yes	—
224	C₂²×C₈₉	—	4	2	no	—
225	C₂²×C₈₉	—	8	1	no	—
226	C₂²×C₈₉	—	8	1	no	—
227	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
228	C₂×D₈₉	—	2	1	no	—
229	C₂×D₈₉	—	2	1	no	—
230	C₂×D₈₉	C₄×D₈	1	2	yes	—
231	C₄×C₈₉	—	2	1	no	—
232	C₄×C₈₉	—	4	2	no	—
233	C₄×C₈₉	—	8	1	no	—
234	C₄×C₈₉	—	8	1	no	—
235	C₄×C₈₉	#510	1	2	yes	complemented
236	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
237	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
238	Dic₈₉	—	2	1	no	—
239	Dic₈₉	—	2	1	no	—
240	Dic₈₉	—	4	2	no	—
241	Dic₈₉	—	4	2	no	—
242	Dic₈₉	—	8	1	no	—
243	Dic₈₉	—	8	1	no	—
244	Dic₈₉	C₄×D₈	1	2	yes	—
245	C₄×#510	—	89	1	no	maximal, Sylow
246	C₂×C₈₉	—	8	2	no	—
247	C₂×C₈₉	C₂×C₄×D₈	1	1	yes	characteristic
248	C₂×C₈₉	C₂×#510	1	1	yes	characteristic
249	C₂×C₈₉	#3414	1	1	yes	characteristic
250	D₈₉	—	2	2	no	—
251	C₂×#510	—	89	1	no	—
252	C₄×#135	—	89	1	no	—
253	C₂×C₄×Q₁₆	—	89	1	no	—
254	#2176	—	89	1	no	—
255	#2176	—	89	1	no	—
256	#2175	—	89	1	no	—
257	#2175	—	89	1	no	—
258	C₄×Q₃₂	—	89	1	no	—
259	C₄×Q₃₂	—	89	1	no	—
260	C₄×SD₃₂	—	89	1	no	—
261	C₄×SD₃₂	D₈₉	1	1	yes	characteristic, complemented
262	#2159	—	89	1	no	—
263	#2141	—	89	1	no	—
264	#2139	—	89	1	no	—
265	C₄×M₃₂	—	89	1	no	—
266	C₈₉	C₄×#510	1	1	yes	characteristic, complemented, Sylow
267	C₂×#135	—	89	1	no	—
268	C₂²×Q₁₆	—	89	1	no	—
269	C₄×#41	—	178	1	no	—
270	C₂×C₄×Q₈	—	178	1	no	—
271	#510	—	89	8	no	—
272	C₂×Q₃₂	—	89	1	no	—
273	C₂×Q₃₂	—	89	1	no	—
274	C₂×SD₃₂	—	89	1	no	—
275	C₂×SD₃₂	C₂×D₈₉	1	1	yes	characteristic
276	C₂×M₃₂	—	89	1	no	—
277	C₂×M₃₂	—	89	1	no	—
278	C₄×Q₁₆	—	89	1	no	—
279	C₄×Q₁₆	—	89	1	no	—
280	C₄×Q₁₆	—	89	1	no	—
281	C₄×Q₁₆	—	89	1	no	—
282	C₄×Q₁₆	—	89	1	no	—
283	C₄×Q₁₆	—	178	1	no	—
284	C₄×Q₁₆	—	178	1	no	—
285	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
286	C₄×SD₁₆	—	178	1	no	—
287	C₄×SD₁₆	—	178	1	no	—
288	C₄×D₈	—	89	1	no	—
289	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
290	#427	—	89	1	no	—
291	C₂×#107	—	89	1	no	—
292	#416	—	178	1	no	—
293	C₂×#103	—	178	1	no	—
294	C₂×C₄×C₈	—	89	1	no	—
295	#367	—	89	1	no	—
296	#367	C₂×D₈₉	1	1	yes	characteristic
297	#366	—	89	1	no	—
298	#366	—	89	1	no	—
299	#358	—	89	1	no	—
300	#358	—	89	1	no	—
301	#358	—	89	1	no	—
302	#358	—	89	1	no	—
303	#358	—	89	1	no	—
304	#358	C₂×D₈₉	1	1	yes	characteristic
305	#357	—	89	1	no	—
306	#357	C₂×D₈₉	1	1	yes	characteristic
307	#346	—	89	1	no	—
308	#346	—	89	1	no	—
309	C₄×C₁₆	—	89	1	no	—
310	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
311	C₂×#41	—	178	1	no	—
312	C₂²×Q₈	—	178	1	no	—
313	#135	—	89	4	no	—
314	#135	—	178	2	no	—
315	C₂×Q₁₆	—	89	4	no	—
316	C₂×Q₁₆	—	89	1	no	—
317	C₂×Q₁₆	—	89	1	no	—
318	C₂×Q₁₆	—	178	2	no	—
319	C₂×Q₁₆	—	178	1	no	—
320	C₂×Q₁₆	C₂²×D₈₉	1	1	yes	characteristic
321	C₂×SD₁₆	—	178	1	no	—
322	C₂×D₈	C₂²×D₈₉	1	1	yes	characteristic
323	C₂²×C₈	—	89	1	no	—
324	C₂²×C₈	—	89	1	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×Q₈	—	356	1	no	—
327	C₄×Q₈	—	356	1	no	—
328	C₄×Q₈	—	178	1	no	—
329	C₄×Q₈	—	178	1	no	—
330	C₄×Q₈	—	178	1	no	—
331	C₄×Q₈	—	178	1	no	—
332	C₄×Q₈	—	178	1	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	356	1	no	—
335	C₄×D₄	—	356	1	no	—
336	C₄×D₄	—	178	1	no	—
337	#117	—	356	1	no	—
338	#117	—	178	1	no	—
339	C₂×C₄⋊C₄	—	356	1	no	—
340	C₂×C₄⋊C₄	—	178	1	no	—
341	C₂×C₄²	—	89	1	no	—
342	C₂×C₄²	—	356	1	no	—
343	C₂×C₄²	—	356	1	no	—
344	Q₃₂	—	89	4	no	—
345	Q₃₂	—	89	4	no	—
346	SD₃₂	—	89	4	no	—
347	SD₃₂	C₄×D₈₉	1	4	yes	complemented
348	M₃₂	—	89	4	no	—
349	M₃₂	—	178	2	no	—
350	C₂×C₁₆	—	89	1	no	—
351	C₂×C₁₆	—	89	1	no	—
352	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
353	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
354	#107	—	89	1	no	—
355	#107	—	89	1	no	—
356	#107	—	178	1	no	—
357	#107	C₂²×D₈₉	1	1	yes	characteristic
358	#107	C₂²×D₈₉	1	1	yes	characteristic
359	#106	—	178	1	no	—
360	#103	—	2	1	no	—
361	#103	—	178	1	no	—
362	#103	—	178	1	no	—
363	#103	—	178	1	no	—
364	#103	—	178	1	no	—
365	#103	—	178	1	no	—
366	#102	—	2	1	no	—
367	#102	—	178	1	no	—
368	C₄×C₈	—	89	1	no	—
369	C₄×C₈	—	89	1	no	—
370	C₄×C₈	—	89	1	no	—
371	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
372	#41	—	356	2	no	—
373	#41	—	178	4	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	356	1	no	—
376	C₂×Q₈	—	356	2	no	—
377	C₂×Q₈	—	178	4	no	—
378	C₂×Q₈	—	178	1	no	—
379	C₂×Q₈	—	178	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	356	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	89	1	no	—
384	C₂²×C₄	—	89	1	no	—
385	C₂²×C₄	—	89	1	no	—
386	C₂²×C₄	—	356	1	no	—
387	C₂²×C₄	—	356	1	no	—
388	C₂²×C₄	—	356	1	no	—
389	C₂²×C₄	—	356	1	no	—
390	Q₁₆	—	2	1	no	—
391	Q₁₆	—	89	2	no	—
392	Q₁₆	—	89	2	no	—
393	Q₁₆	—	178	4	no	—
394	Q₁₆	—	178	1	no	—
395	Q₁₆	—	178	1	no	—
396	Q₁₆	C₂×C₄×D₈₉	1	2	yes	—
397	SD₁₆	—	178	4	no	—
398	D₈	—	2	1	no	—
399	D₈	C₂×C₄×D₈₉	1	2	yes	—
400	C₂×C₈	—	89	1	no	—
401	C₂×C₈	—	89	2	no	—
402	C₂×C₈	—	89	2	no	—
403	C₂×C₈	—	89	1	no	—
404	C₂×C₈	—	178	2	no	—
405	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
406	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	—	356	1	no	—
411	C₄⋊C₄	—	356	1	no	—
412	C₄⋊C₄	—	356	1	no	—
413	C₄⋊C₄	—	356	1	no	—
414	C₄⋊C₄	—	356	1	no	—
415	C₄⋊C₄	—	356	1	no	—
416	C₄⋊C₄	—	178	1	no	—
417	C₄⋊C₄	—	178	1	no	—
418	C₂²⋊C₄	—	4	1	no	—
419	C₂²⋊C₄	—	356	1	no	—
420	C₂²⋊C₄	—	356	1	no	—
421	C₄²	—	4	1	no	—
422	C₄²	—	89	1	no	—
423	C₄²	—	89	1	no	—
424	C₄²	—	89	1	no	—
425	C₄²	—	356	1	no	—
426	C₄²	—	356	1	no	—
427	C₄²	—	356	1	no	—
428	C₄²	—	356	1	no	—
429	C₄²	—	356	1	no	—
430	C₄²	—	356	1	no	—
431	C₄²	D₄×D₈₉	1	1	yes	characteristic
432	C₁₆	—	2	1	no	—
433	C₁₆	—	89	2	no	—
434	C₁₆	—	178	1	no	—
435	C₁₆	C₂×C₄×D₈₉	1	2	yes	—
436	C₂³	—	4	1	no	—
437	C₂³	—	89	1	no	—
438	Q₈	—	2	2	no	—
439	Q₈	—	4	1	no	—
440	Q₈	—	356	4	no	—
441	Q₈	—	356	1	no	—
442	Q₈	—	356	1	no	—
443	Q₈	—	178	2	no	—
444	Q₈	—	178	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	4	1	no	—
447	D₄	—	356	4	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	8	2	no	—
452	C₂×C₄	—	89	1	no	—
453	C₂×C₄	—	89	2	no	—
454	C₂×C₄	—	89	2	no	—
455	C₂×C₄	—	89	1	no	—
456	C₂×C₄	—	89	1	no	—
457	C₂×C₄	—	356	1	no	—
458	C₂×C₄	—	356	4	no	—
459	C₂×C₄	—	356	4	no	—
460	C₂×C₄	—	356	1	no	—
461	C₂×C₄	—	356	1	no	—
462	C₂×C₄	—	356	1	no	—
463	C₂×C₄	—	356	1	no	—
464	C₂×C₄	—	178	2	no	—
465	C₂×C₄	—	712	2	no	—
466	C₂×C₄	—	712	2	no	—
467	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
468	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
469	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
470	C₈	—	2	1	no	—
471	C₈	—	89	2	no	—
472	C₈	—	178	1	no	—
473	C₈	C₂²×C₄×D₈₉	1	1	yes	characteristic
474	C₈	#41×D₈₉	1	1	yes	characteristic
475	C₂²	—	4	2	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	—	89	2	no	—
479	C₂²	—	178	1	no	—
480	C₂²	—	178	1	no	—
481	C₂²	C₂×D₈×D₈₉	1	1	yes	characteristic
482	C₄	—	2	1	no	—
483	C₄	—	4	2	no	—
484	C₄	—	8	1	no	—
485	C₄	—	8	1	no	—
486	C₄	—	89	2	no	—
487	C₄	—	356	2	no	—
488	C₄	—	356	2	no	—
489	C₄	—	178	1	no	—
490	C₄	—	178	1	no	—
491	C₄	—	712	1	no	—
492	C₄	—	712	1	no	—
493	C₄	#19152037	1	2	yes	direct product factor
494	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
495	C₄	#135×D₈₉	1	1	yes	characteristic
496	C₂	—	8	2	no	—
497	C₂	—	178	2	no	—
498	C₂	C₄×D₈×D₈₉	1	1	yes	characteristic
499	C₂	C₂×#19152037	1	1	yes	characteristic
500	C₂	#26033385	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₈×D₈₉
commutator	C₈×C₈₉	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₄×SD₃₂×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₈
prime radical	C₂×#15668031	C₂²
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	C₄×SD₃₂	D₈₉
hypocenter	C₈₉	C₄×#510
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×SD₃₂

Complements

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

N	H ≅ G/N	type
3. C₄×Q₁₆×D₈₉	C₂	semidirect
4. #26022122	C₂	semidirect
5. #26022120	C₂	semidirect
6. #26022117	C₂	semidirect
7. #26022113	C₂	semidirect
8. C₄×Dic₇₁₂	C₂	semidirect
9. C₄×#15667958	C₂	semidirect
10. C₄×#15667956	C₂	semidirect
11. #26022039	C₂	semidirect
12. #26021970	C₂	semidirect
14. C₄×#15667951	C₂	semidirect
15. C₄×SD₃₂×C₈₉	C₂	semidirect
20. #19152037	C₄	direct (N × H)
68. Q₁₆×D₈₉	C₂×C₄	semidirect
89. Dic₇₁₂	C₂×C₄	semidirect
90. #15667958	C₂×C₄	semidirect
91. #15667956	C₂×C₄	semidirect
93. #15667951	C₂×C₄	semidirect
113. SD₃₂×C₈₉	C₂×C₄	semidirect
235. C₄×C₈₉	#510	semidirect
261. C₄×SD₃₂	D₈₉	semidirect
266. C₈₉	C₄×#510	semidirect
347. SD₃₂	C₄×D₈₉	semidirect
493. C₄	#19152037	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19152037	2
C₄×#15668031	2
C₄×Q₁₆×D₈₉	2
#26022122	2
#26022120	2
#26022117	2
#26022113	2
C₄×Dic₇₁₂	2
C₄×#15667958	2
C₄×#15667956	2
#26022039	2
#26021970	2
#26021961	2
C₄×#15667951	2
C₄×SD₃₂×C₈₉	2
C₄×#510	89

Subgroups — C4×#19152037 #36707752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19152037 #36707752