Subgroups — C₄×#19151870 #36561313

Order 22784.

882 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151870	C₂	1	1	yes	maximal, characteristic
2	C₄×#15668043	C₂	1	2	yes	maximal
3	C₄×#15668018	C₂	1	1	yes	maximal, characteristic
4	#26021168	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021035	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020904	C₂	1	2	yes	maximal, complemented
7	#26020770	C₂	1	2	yes	maximal
8	#26020317	C₂	1	1	yes	maximal, characteristic
9	C₄×#15667948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#15667931	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×Q₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668043	C₂²	1	2	yes	—
13	C₂×#15668018	C₂²	1	1	yes	characteristic
14	C₂×#15668018	C₂²	1	1	yes	characteristic
15	C₄×#13083574	C₂²	1	1	yes	characteristic
16	#19151870	C₄	1	8	yes	direct product factor
17	#19151703	—	2	2	no	—
18	#19151696	—	2	2	no	—
19	C₄×#13083564	—	2	2	no	—
20	C₄×#13083561	—	2	2	no	—
21	C₂×#15667948	C₂²	1	1	yes	characteristic
22	C₂×#15667948	C₂²	1	1	yes	characteristic
23	#19151638	C₂²	1	2	yes	—
24	#19151607	C₂²	1	2	yes	—
25	#19151597	C₂²	1	2	yes	—
26	C₂×#15667931	C₂²	1	2	yes	—
27	C₂×#15667931	C₂²	1	2	yes	—
28	#19151553	C₂²	1	1	yes	characteristic
29	#19151553	C₂²	1	1	yes	characteristic
30	#19151552	—	2	1	no	—
31	#19151552	—	2	1	no	—
32	C₄×#13083558	C₂²	1	2	yes	—
33	C₄×#13083558	C₂²	1	1	yes	characteristic
34	C₄×#13083557	—	2	1	no	—
35	C₄×C₈×D₈₉	—	2	1	no	—
36	#19151367	C₂²	1	2	yes	—
37	#19151367	C₂²	1	2	yes	—
38	#19151363	C₂²	1	2	yes	—
39	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
41	C₄×Q₁₆×C₈₉	—	2	1	no	—
42	C₄×Q₁₆×C₈₉	—	2	1	no	—
43	C₄×Q₁₆×C₈₉	—	2	1	no	—
44	C₄×Q₁₆×C₈₉	—	2	1	no	—
45	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#103×C₈₉	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×#13083574	C₂³	1	1	yes	characteristic
49	#15668043	—	2	4	no	—
50	#15668043	C₂×C₄	1	8	yes	—
51	C₂×#13083564	—	2	2	no	—
52	C₂×#13083561	—	2	2	no	—
53	#15668018	—	2	2	no	—
54	#15668018	—	2	2	no	—
55	#15668018	—	2	2	no	—
56	#15668018	C₂×C₄	1	4	yes	—
57	C₂×#13083558	C₂³	1	2	yes	—
58	C₂×#13083558	C₂³	1	2	yes	—
59	C₂×#13083558	C₂³	1	1	yes	characteristic
60	C₂×#13083558	C₂³	1	1	yes	characteristic
61	C₂×#13083557	—	2	1	no	—
62	C₂×#13083557	—	2	1	no	—
63	C₂×C₈×D₈₉	—	2	1	no	—
64	C₂×C₈×D₈₉	—	2	1	no	—
65	C₄×Dic₁₇₈	D₄	1	1	yes	characteristic
66	C₄×Dic₁₇₈	D₄	1	1	yes	characteristic
67	C₄×D₃₅₆	D₄	1	1	yes	characteristic
68	C₄×D₃₅₆	D₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₈₉	—	2	1	no	—
70	C₄×C₂²⋊D₈₉	—	2	1	no	—
71	#15667971	C₂³	1	1	yes	characteristic
72	#15667969	—	2	1	no	—
73	C₄²×D₈₉	—	2	1	no	—
74	#15667948	—	2	2	no	—
75	#15667948	C₂×C₄	1	4	yes	complemented
76	#15667945	—	2	2	no	—
77	#15667943	—	2	2	no	—
78	#15667936	—	2	2	no	—
79	#15667936	—	2	2	no	—
80	#15667935	—	2	2	no	—
81	#15667932	—	2	2	no	—
82	#15667931	—	2	4	no	—
83	#15667931	C₂×C₄	1	8	yes	complemented
84	#15667923	—	2	2	no	—
85	#15667923	—	2	1	no	—
86	#15667922	—	2	1	no	—
87	#15667922	—	2	1	no	—
88	C₄×#10623494	—	2	2	no	—
89	C₄×#10623494	—	2	1	no	—
90	C₈×Dic₈₉	—	2	1	no	—
91	C₈×Dic₈₉	—	2	1	no	—
92	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
93	C₂×Q₁₆×C₈₉	—	2	1	no	—
94	C₂×Q₁₆×C₈₉	—	2	1	no	—
95	C₂×Q₁₆×C₈₉	—	2	2	no	—
96	C₂×Q₁₆×C₈₉	C₂×C₄	1	4	yes	complemented
97	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₈₉	—	2	2	no	—
100	C₄×Q₈×C₈₉	—	2	2	no	—
101	C₄×Q₈×C₈₉	—	2	2	no	—
102	C₄×Q₈×C₈₉	—	2	2	no	—
103	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
105	C₂×C₄²×C₈₉	—	2	2	no	—
106	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
107	#107×C₈₉	—	2	1	no	—
108	#107×C₈₉	—	2	1	no	—
109	#103×C₈₉	—	2	2	no	—
110	#103×C₈₉	—	2	2	no	—
111	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
112	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
113	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
114	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
115	#13083574	—	2	1	no	—
116	#13083574	—	2	1	no	—
117	#13083574	C₂²×C₄	1	2	yes	—
118	#13083574	#41	1	2	yes	—
119	C₂×Dic₁₇₈	C₂×D₄	1	1	yes	characteristic
120	C₂×D₃₅₆	C₂×D₄	1	1	yes	characteristic
121	C₂×C₂²⋊D₈₉	—	2	1	no	—
122	C₂×C₄×D₈₉	—	2	1	no	—
123	C₂×C₄×D₈₉	—	2	1	no	—
124	C₂×C₄×D₈₉	—	2	1	no	—
125	#13083564	—	2	8	no	—
126	#13083561	—	2	8	no	—
127	#13083558	—	2	1	no	—
128	#13083558	—	2	1	no	—
129	#13083558	—	2	2	no	—
130	#13083558	—	2	2	no	—
131	#13083558	—	2	2	no	—
132	#13083558	C₂²×C₄	1	2	yes	—
133	#13083558	C₂²×C₄	1	4	yes	—
134	#13083558	#41	1	2	yes	—
135	#13083557	—	2	4	no	—
136	#13083557	—	2	4	no	—
137	C₂×#10623494	—	2	1	no	—
138	C₂×#10623494	—	2	1	no	—
139	C₂×#10623494	—	2	2	no	—
140	C₂×#10623494	—	2	2	no	—
141	C₈×D₈₉	—	2	4	no	—
142	C₈×D₈₉	—	2	4	no	—
143	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
144	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
145	#13083553	—	2	1	no	—
146	#13083553	—	2	1	no	—
147	C₂²⋊Dic₈₉	—	2	1	no	—
148	#13083551	—	2	1	no	—
149	#13083551	—	2	1	no	—
150	C₄×Dic₈₉	—	2	1	no	—
151	C₄×Dic₈₉	—	2	1	no	—
152	C₄×Dic₈₉	—	2	1	no	—
153	C₂×Q₈×C₈₉	—	2	2	no	—
154	C₂×Q₈×C₈₉	—	2	2	no	—
155	C₂×Q₈×C₈₉	—	2	2	no	—
156	C₂×Q₈×C₈₉	—	2	2	no	—
157	C₂×Q₈×C₈₉	—	2	2	no	—
158	C₂×Q₈×C₈₉	C₂²×C₄	1	4	yes	—
159	C₂²×C₄×C₈₉	—	2	2	no	—
160	C₂²×C₄×C₈₉	—	2	2	no	—
161	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
162	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
163	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
164	Q₁₆×C₈₉	—	2	4	no	—
165	Q₁₆×C₈₉	—	2	4	no	—
166	C₂×C₈×C₈₉	—	2	1	no	—
167	C₂×C₈×C₈₉	—	2	1	no	—
168	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
169	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
171	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₈₉	#41	1	2	yes	—
174	C₄⋊C₄×C₈₉	—	2	2	no	—
175	C₄⋊C₄×C₈₉	—	2	2	no	—
176	C₄⋊C₄×C₈₉	—	4	2	no	—
177	C₄⋊C₄×C₈₉	—	4	2	no	—
178	C₄²×C₈₉	—	4	2	no	—
179	C₄²×C₈₉	—	4	2	no	—
180	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
184	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
185	C₂²×D₈₉	—	2	1	no	—
186	Q₈×C₈₉	—	2	4	no	—
187	Q₈×C₈₉	—	2	4	no	—
188	Q₈×C₈₉	—	4	2	no	—
189	Q₈×C₈₉	—	4	2	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	4	no	—
192	C₂×C₄×C₈₉	—	4	1	no	—
193	C₂×C₄×C₈₉	—	4	2	no	—
194	C₂×C₄×C₈₉	—	4	2	no	—
195	C₂×C₄×C₈₉	—	4	2	no	—
196	C₂×C₄×C₈₉	—	8	2	no	—
197	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
198	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
199	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
200	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
207	C₂²⋊D₈₉	—	2	2	no	—
208	C₂²⋊D₈₉	—	2	2	no	—
209	C₂×Dic₈₉	—	2	1	no	—
210	C₂×Dic₈₉	—	2	1	no	—
211	C₂×Dic₈₉	—	2	1	no	—
212	D₃₅₆	—	2	1	no	—
213	D₃₅₆	C₄×D₄	1	2	yes	—
214	C₄×D₈₉	—	2	2	no	—
215	C₄×D₈₉	—	2	2	no	—
216	C₄×D₈₉	—	4	2	no	—
217	C₄×D₈₉	—	4	2	no	—
218	Dic₁₇₈	—	2	1	no	—
219	Dic₁₇₈	C₄×D₄	1	2	yes	—
220	C₈×C₈₉	—	2	1	no	—
221	C₈×C₈₉	—	2	1	no	—
222	C₈×C₈₉	C₄×D₄	1	2	yes	—
223	C₈×C₈₉	C₄×D₄	1	2	yes	—
224	#10623494	—	2	2	no	—
225	#10623494	—	2	4	no	—
226	#10623494	—	2	2	no	—
227	#10623494	—	4	2	no	—
228	C₂²×C₈₉	—	2	1	no	—
229	C₂²×C₈₉	—	2	1	no	—
230	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
231	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
232	C₂²×C₈₉	#529	1	1	yes	characteristic
233	C₂×D₈₉	—	2	2	no	—
234	C₂×D₈₉	—	4	1	no	—
235	C₂×D₈₉	—	4	1	no	—
236	C₄×C₈₉	—	2	1	no	—
237	C₄×C₈₉	—	2	1	no	—
238	C₄×C₈₉	—	2	1	no	—
239	C₄×C₈₉	—	4	4	no	—
240	C₄×C₈₉	—	8	2	no	—
241	C₄×C₈₉	#473	1	2	yes	complemented
242	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
243	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₈₉	#525	1	1	yes	characteristic
245	C₄×C₈₉	#532	1	1	yes	characteristic
246	Dic₈₉	—	2	2	no	—
247	Dic₈₉	—	4	1	no	—
248	Dic₈₉	—	4	1	no	—
249	C₄×#473	—	89	1	no	maximal, Sylow
250	C₂×C₈₉	—	2	1	no	—
251	C₂×C₈₉	—	2	1	no	—
252	C₂×C₈₉	C₄×#121	1	1	yes	characteristic
253	C₂×C₈₉	C₂×#473	1	1	yes	characteristic
254	C₂×C₈₉	#3067	1	1	yes	characteristic
255	D₈₉	—	4	2	no	—
256	C₂×#473	—	89	1	no	—
257	C₄×#137	—	89	2	no	—
258	C₂×C₄×Q₁₆	D₈₉	1	1	yes	characteristic, complemented
259	C₄×#131	—	89	1	no	—
260	#1979	—	89	1	no	—
261	#1952	—	89	1	no	—
262	#1930	—	89	2	no	—
263	#1908	—	89	2	no	—
264	#1816	—	89	1	no	—
265	C₄×#108	—	89	1	no	—
266	C₄×#101	—	89	2	no	—
267	C₈₉	C₄×#473	1	1	yes	characteristic, complemented, Sylow
268	C₂×#137	—	89	2	no	—
269	C₂²×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
270	C₂×#131	—	89	1	no	—
271	C₂×#131	—	89	1	no	—
272	C₄×#41	—	89	1	no	—
273	C₂×C₄×Q₈	C₂×D₈₉	1	2	yes	—
274	#473	—	89	8	no	—
275	#441	—	178	2	no	—
276	#440	—	178	2	no	—
277	C₄×Q₁₆	—	2	1	no	—
278	C₄×Q₁₆	—	2	1	no	—
279	C₄×Q₁₆	—	2	1	no	—
280	C₄×Q₁₆	—	2	1	no	—
281	C₄×Q₁₆	—	178	2	no	—
282	C₄×SD₁₆	—	178	2	no	—
283	C₂×#108	—	89	1	no	—
284	C₂×#108	—	89	1	no	—
285	#428	—	89	2	no	—
286	C₂×#107	C₂×D₈₉	1	1	yes	characteristic
287	#419	—	89	2	no	—
288	#417	—	89	2	no	—
289	C₂×#103	C₂×D₈₉	1	2	yes	—
290	C₂×#101	—	89	2	no	—
291	C₂×#101	—	89	2	no	—
292	#405	—	89	1	no	—
293	#405	—	89	1	no	—
294	#405	—	178	1	no	—
295	#405	—	178	1	no	—
296	C₄×M₁₆	—	89	1	no	—
297	C₄×M₁₆	—	89	2	no	—
298	C₄×M₁₆	—	178	1	no	—
299	C₂×C₄×C₈	—	178	1	no	—
300	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
301	#343	—	89	2	no	—
302	#343	—	89	2	no	—
303	#341	—	89	2	no	—
304	C₂×#41	—	89	1	no	—
305	C₂²×Q₈	C₂²×D₈₉	1	2	yes	—
306	#137	—	89	8	no	—
307	#137	—	178	4	no	—
308	C₂×Q₁₆	—	2	1	no	—
309	C₂×Q₁₆	—	2	1	no	—
310	C₂×Q₁₆	—	2	2	no	—
311	C₂×Q₁₆	—	178	2	no	—
312	C₂×Q₁₆	C₄×D₈₉	1	4	yes	complemented
313	C₂×SD₁₆	—	178	2	no	—
314	#131	—	89	4	no	—
315	#131	—	178	2	no	—
316	#131	—	178	2	no	—
317	#131	—	178	2	no	—
318	C₂×M₁₆	—	89	1	no	—
319	C₂×M₁₆	—	89	1	no	—
320	C₂×M₁₆	—	89	2	no	—
321	C₂×M₁₆	—	89	2	no	—
322	C₂×M₁₆	—	178	1	no	—
323	C₂×M₁₆	—	178	1	no	—
324	C₂²×C₈	—	178	1	no	—
325	C₂²×C₈	—	178	1	no	—
326	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
327	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	89	1	no	—
333	C₄×Q₈	—	89	1	no	—
334	C₄×D₄	—	89	1	no	—
335	C₄×D₄	—	89	1	no	—
336	C₄×D₄	—	178	1	no	—
337	C₄×D₄	—	178	1	no	—
338	#117	—	89	1	no	—
339	#117	—	178	1	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	178	1	no	—
344	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
345	#108	—	89	4	no	—
346	#108	—	178	2	no	—
347	#107	—	2	1	no	—
348	#107	—	2	1	no	—
349	#107	—	178	2	no	—
350	#106	—	178	2	no	—
351	#103	—	2	2	no	—
352	#103	—	2	2	no	—
353	#103	—	178	2	no	—
354	#103	—	178	2	no	—
355	#103	—	178	2	no	—
356	#102	—	178	2	no	—
357	#101	—	89	8	no	—
358	#101	—	178	4	no	—
359	#97	—	178	1	no	—
360	#97	—	178	1	no	—
361	#97	—	178	2	no	—
362	#97	—	178	1	no	—
363	C₄×C₈	—	178	1	no	—
364	C₄×C₈	—	178	1	no	—
365	C₄×C₈	—	178	2	no	—
366	C₄×C₈	—	178	1	no	—
367	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
368	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
369	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
370	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
371	#41	—	89	2	no	—
372	#41	—	89	2	no	—
373	#41	—	178	1	no	—
374	#41	—	178	1	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	89	1	no	—
381	C₂×Q₈	C₂×C₄×D₈₉	1	4	yes	—
382	C₂×D₄	—	89	1	no	—
383	C₂×D₄	—	178	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	178	1	no	—
387	C₂²×C₄	—	178	1	no	—
388	C₂²×C₄	—	178	1	no	—
389	C₂²×C₄	#13083573	1	1	yes	characteristic
390	C₂²×C₄	#13083573	1	1	yes	characteristic
391	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
392	Q₁₆	—	2	4	no	—
393	Q₁₆	—	2	4	no	—
394	Q₁₆	—	178	8	no	—
395	SD₁₆	—	178	8	no	—
396	M₁₆	—	89	2	no	—
397	M₁₆	—	89	4	no	—
398	M₁₆	—	89	2	no	—
399	M₁₆	—	178	4	no	—
400	M₁₆	—	178	2	no	—
401	M₁₆	—	178	2	no	—
402	M₁₆	—	178	1	no	—
403	M₁₆	—	178	2	no	—
404	M₁₆	—	178	1	no	—
405	M₁₆	—	178	4	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	178	4	no	—
409	C₂×C₈	—	178	2	no	—
410	C₂×C₈	—	178	2	no	—
411	C₂×C₈	—	178	1	no	—
412	C₂×C₈	—	178	1	no	—
413	C₂×C₈	—	178	4	no	—
414	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
415	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
416	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
417	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
418	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
419	C₂×C₈	#13083574	1	2	yes	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	4	2	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	—	89	1	no	—
425	C₄⋊C₄	—	89	1	no	—
426	C₄⋊C₄	—	178	1	no	—
427	C₄⋊C₄	—	178	1	no	—
428	C₂²⋊C₄	—	178	1	no	—
429	C₂²⋊C₄	—	178	1	no	—
430	C₂²⋊C₄	—	178	1	no	—
431	C₄²	—	4	2	no	—
432	C₄²	—	4	2	no	—
433	C₄²	—	178	1	no	—
434	C₄²	—	178	1	no	—
435	C₄²	—	178	1	no	—
436	C₄²	D₄×D₈₉	1	1	yes	characteristic
437	C₄²	D₄×D₈₉	1	1	yes	characteristic
438	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
439	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
440	C₂³	—	178	1	no	—
441	C₂³	C₂×#13083573	1	1	yes	characteristic
442	Q₈	—	2	4	no	—
443	Q₈	—	2	4	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	89	2	no	—
447	Q₈	—	178	1	no	—
448	D₄	—	89	2	no	—
449	D₄	—	178	2	no	—
450	D₄	—	178	2	no	—
451	D₄	—	178	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	—	356	2	no	—
460	C₂×C₄	—	356	2	no	—
461	C₂×C₄	—	178	1	no	—
462	C₂×C₄	—	178	1	no	—
463	C₂×C₄	—	178	1	no	—
464	C₂×C₄	—	178	2	no	—
465	C₂×C₄	—	178	2	no	—
466	C₂×C₄	#15667983	1	1	yes	characteristic
467	C₂×C₄	#15667983	1	1	yes	characteristic
468	C₂×C₄	#15667983	1	1	yes	characteristic
469	C₂×C₄	#15667983	1	1	yes	characteristic
470	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
471	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
473	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
474	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
475	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
476	C₈	—	2	1	no	—
477	C₈	—	2	1	no	—
478	C₈	—	356	2	no	—
479	C₈	—	178	4	no	—
480	C₈	—	178	2	no	—
481	C₈	—	178	2	no	—
482	C₈	C₄×C₂²⋊D₈₉	1	2	yes	—
483	C₈	C₄×C₂²⋊D₈₉	1	2	yes	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	356	1	no	—
487	C₂²	—	356	1	no	—
488	C₂²	—	178	2	no	—
489	C₂²	C₄×#13083573	1	1	yes	characteristic
490	C₂²	C₂×#15667983	1	1	yes	characteristic
491	C₂²	#19152130	1	1	yes	characteristic
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	4	4	no	—
496	C₄	—	8	2	no	—
497	C₄	—	356	1	no	—
498	C₄	—	356	1	no	—
499	C₄	—	178	2	no	—
500	C₄	#19151870	1	2	yes	direct product factor
501	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
502	C₄	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
503	C₄	#19152105	1	1	yes	characteristic
504	C₄	#19152145	1	1	yes	characteristic
505	C₂	—	2	1	no	—
506	C₂	—	2	1	no	—
507	C₂	—	356	2	no	—
508	C₂	C₄×#15667983	1	1	yes	characteristic
509	C₂	C₂×#19151870	1	1	yes	characteristic
510	C₂	#26029968	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15667983
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₂×C₄×Q₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂×#13083574	C₂³
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₂×C₄×Q₁₆	D₈₉
hypocenter	C₈₉	C₄×#473
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
4. #26021168	C₂	semidirect
5. #26021035	C₂	semidirect
6. #26020904	C₂	semidirect
9. C₄×#15667948	C₂	semidirect
10. C₄×#15667931	C₂	semidirect
11. C₂×C₄×Q₁₆×C₈₉	C₂	semidirect
16. #19151870	C₄	direct (N × H)
75. #15667948	C₂×C₄	semidirect
83. #15667931	C₂×C₄	semidirect
96. C₂×Q₁₆×C₈₉	C₂×C₄	semidirect
241. C₄×C₈₉	#473	semidirect
258. C₂×C₄×Q₁₆	D₈₉	semidirect
267. C₈₉	C₄×#473	semidirect
312. C₂×Q₁₆	C₄×D₈₉	semidirect
500. C₄	#19151870	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×#19151870	2
C₄×#15668043	2
C₄×#15668018	2
#26021168	2
#26021035	2
#26020904	2
#26020770	2
#26020317	2
C₄×#15667948	2
C₄×#15667931	2
C₂×C₄×Q₁₆×C₈₉	2
C₄×#473	89

Subgroups — C4×#19151870 #36561313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19151870 #36561313