Subgroups — #36522788

Order 22784.

1018 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152155	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151651	C₂	1	1	yes	maximal, characteristic
3	#26018943	C₂	1	4	yes	maximal, complemented
4	#26018938	C₂	1	2	yes	maximal, complemented
5	#26018934	C₂	1	2	yes	maximal, complemented
6	#26018910	C₂	1	4	yes	maximal, complemented
7	C₂×#423×C₈₉	C₂	1	1	yes	maximal, characteristic
8	#19152155	—	2	1	no	—
9	#19152155	—	2	1	no	—
10	#19152155	—	2	1	no	—
11	#19152155	—	2	1	no	—
12	#19152155	C₄	1	2	yes	—
13	#19152155	C₄	1	2	yes	—
14	#19152155	C₂²	1	2	yes	—
15	#19152155	C₂²	1	2	yes	—
16	C₂×#15668012	C₂²	1	1	yes	characteristic
17	C₂×#15668012	C₂²	1	1	yes	characteristic
18	C₂×#15668004	—	2	1	no	—
19	C₂×#15667991	—	2	1	no	—
20	C₂×#15667991	C₄	1	2	yes	—
21	C₂×C₄×Dic₁₇₈	—	2	1	no	—
22	C₂×C₄×Dic₁₇₈	C₄	1	2	yes	—
23	C₂×#15667971	—	2	1	no	—
24	#19151651	—	2	1	no	—
25	#19151651	—	2	1	no	—
26	#19151651	C₂²	1	2	yes	—
27	#19151651	C₂²	1	2	yes	—
28	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
29	C₂×C₂²⋊#10623494	—	2	1	no	—
30	C₂×C₄×#10623494	—	2	1	no	—
31	#19151346	C₂²	1	8	yes	complemented
32	#19151343	C₂²	1	8	yes	complemented
33	C₂²×M₁₆×C₈₉	—	2	1	no	—
34	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
35	#423×C₈₉	—	2	1	no	—
36	#423×C₈₉	—	2	1	no	—
37	#423×C₈₉	C₂²	1	2	yes	—
38	#423×C₈₉	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
40	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
41	C₂²×Dic₁₇₈	—	2	1	no	—
42	C₂²×Dic₁₇₈	C₂×C₄	1	2	yes	—
43	C₂²×#10623494	—	2	2	no	—
44	#15668012	—	2	1	no	—
45	#15668012	—	2	1	no	—
46	#15668012	—	2	1	no	—
47	#15668012	—	2	1	no	—
48	#15668012	C₂×C₄	1	2	yes	—
49	#15668012	C₂×C₄	1	2	yes	—
50	#15668012	C₂³	1	2	yes	—
51	#15668012	C₂³	1	2	yes	—
52	#15668004	—	2	2	no	—
53	#15668004	—	2	2	no	—
54	#15668004	—	2	2	no	—
55	#15668004	—	2	2	no	—
56	#15667991	—	2	2	no	—
57	#15667991	—	2	2	no	—
58	#15667991	—	2	2	no	—
59	#15667991	—	2	2	no	—
60	#15667991	—	2	2	no	—
61	#15667991	—	2	2	no	—
62	#15667991	C₂×C₄	1	4	yes	—
63	#15667991	C₂×C₄	1	4	yes	—
64	C₄×Dic₁₇₈	—	2	2	no	—
65	C₄×Dic₁₇₈	—	2	2	no	—
66	C₄×Dic₁₇₈	—	2	2	no	—
67	C₄×Dic₁₇₈	—	2	2	no	—
68	C₄×Dic₁₇₈	—	2	2	no	—
69	C₄×Dic₁₇₈	—	2	2	no	—
70	C₄×Dic₁₇₈	C₂×C₄	1	4	yes	—
71	C₄×Dic₁₇₈	C₂×C₄	1	4	yes	—
72	#15667971	—	2	2	no	—
73	#15667971	—	2	2	no	—
74	#15667971	—	2	2	no	—
75	#15667971	—	2	2	no	—
76	C₂×C₄⋊Dic₈₉	—	2	1	no	—
77	C₂×C₄⋊Dic₈₉	—	2	1	no	—
78	C₂×C₄⋊Dic₈₉	—	2	1	no	—
79	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
80	C₂×#13083553	—	2	2	no	—
81	C₂×#13083553	—	2	2	no	—
82	C₂×C₂²⋊Dic₈₉	—	2	2	no	—
83	C₂×C₄×Dic₈₉	—	2	2	no	—
84	C₄⋊#10623494	—	2	2	no	—
85	C₄⋊#10623494	C₂³	1	4	yes	—
86	C₂²⋊#10623494	—	2	2	no	—
87	C₂²⋊#10623494	—	2	2	no	—
88	C₄×#10623494	—	2	2	no	—
89	C₄×#10623494	—	2	2	no	—
90	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
91	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
92	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
93	C₂×M₁₆×C₈₉	—	2	2	no	—
94	C₂×M₁₆×C₈₉	—	2	2	no	—
95	C₂×M₁₆×C₈₉	—	4	4	no	—
96	C₂²×C₈×C₈₉	—	2	2	no	—
97	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
109	C₄⋊C₈×C₈₉	—	2	2	no	—
110	C₄⋊C₈×C₈₉	—	2	2	no	—
111	C₄⋊C₈×C₈₉	—	2	2	no	—
112	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
113	C₂×Dic₁₇₈	—	2	2	no	—
114	C₂×Dic₁₇₈	—	2	2	no	—
115	C₂×Dic₁₇₈	—	2	2	no	—
116	C₂×Dic₁₇₈	—	4	4	no	—
117	C₂×Dic₁₇₈	—	4	4	no	—
118	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
119	C₂²×Dic₈₉	—	2	2	no	—
120	C₂²×Dic₈₉	—	2	2	no	—
121	C₂×#10623494	—	2	4	no	—
122	C₂×#10623494	—	4	4	no	—
123	C₄⋊Dic₈₉	—	2	2	no	—
124	C₄⋊Dic₈₉	—	2	2	no	—
125	C₄⋊Dic₈₉	—	2	2	no	—
126	C₄⋊Dic₈₉	—	2	2	no	—
127	C₄⋊Dic₈₉	—	2	2	no	—
128	C₄⋊Dic₈₉	—	2	2	no	—
129	C₄⋊Dic₈₉	—	2	2	no	—
130	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
131	#13083553	—	2	4	no	—
132	#13083553	—	2	4	no	—
133	#13083553	—	2	4	no	—
134	#13083553	—	2	4	no	—
135	C₂²⋊Dic₈₉	—	2	4	no	—
136	C₂²⋊Dic₈₉	—	2	4	no	—
137	C₄×Dic₈₉	—	2	4	no	—
138	C₄×Dic₈₉	—	2	4	no	—
139	C₂⁴×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×C₄×C₈₉	—	4	2	no	—
141	C₂²×C₄×C₈₉	—	4	2	no	—
142	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	SD₁₆	1	4	yes	—
152	C₂²×C₄×C₈₉	Q₁₆	1	4	yes	—
153	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
162	M₁₆×C₈₉	—	4	4	no	—
163	M₁₆×C₈₉	—	4	4	no	—
164	C₂×C₈×C₈₉	—	2	4	no	—
165	C₂×C₈×C₈₉	—	4	4	no	—
166	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
182	C₂³×C₈₉	—	4	1	no	—
183	C₂³×C₈₉	—	4	1	no	—
184	C₂³×C₈₉	#103	1	4	yes	—
185	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₈₉	—	2	2	no	—
189	C₂×C₄×C₈₉	—	2	2	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	2	no	—
192	C₂×C₄×C₈₉	—	2	2	no	—
193	C₂×C₄×C₈₉	—	2	2	no	—
194	C₂×C₄×C₈₉	—	4	1	no	—
195	C₂×C₄×C₈₉	—	4	1	no	—
196	C₂×C₄×C₈₉	—	4	1	no	—
197	C₂×C₄×C₈₉	—	4	1	no	—
198	C₂×C₄×C₈₉	—	4	1	no	—
199	C₂×C₄×C₈₉	—	4	1	no	—
200	C₂×C₄×C₈₉	#103	1	4	yes	—
201	C₂×C₄×C₈₉	#103	1	4	yes	—
202	C₂×C₄×C₈₉	#103	1	4	yes	—
203	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
213	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
214	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
215	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
216	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
217	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
218	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
221	C₂×Dic₈₉	—	2	4	no	—
222	C₂×Dic₈₉	—	2	4	no	—
223	C₂×Dic₈₉	—	4	4	no	—
224	C₂×Dic₈₉	—	4	4	no	—
225	Dic₁₇₈	—	4	4	no	—
226	Dic₁₇₈	—	4	4	no	—
227	Dic₁₇₈	—	4	4	no	—
228	Dic₁₇₈	—	4	4	no	—
229	C₈×C₈₉	—	4	4	no	—
230	#10623494	—	4	4	no	—
231	C₂²×C₈₉	—	2	1	no	—
232	C₂²×C₈₉	—	2	1	no	—
233	C₂²×C₈₉	—	2	1	no	—
234	C₂²×C₈₉	—	2	1	no	—
235	C₂²×C₈₉	—	2	1	no	—
236	C₂²×C₈₉	—	2	1	no	—
237	C₂²×C₈₉	—	4	4	no	—
238	C₂²×C₈₉	C₂×#103	1	2	yes	—
239	C₂²×C₈₉	C₂×#103	1	2	yes	—
240	C₂²×C₈₉	C₂×#103	1	2	yes	—
241	C₂²×C₈₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
242	C₄×C₈₉	—	2	1	no	—
243	C₄×C₈₉	—	2	1	no	—
244	C₄×C₈₉	—	2	1	no	—
245	C₄×C₈₉	—	2	1	no	—
246	C₄×C₈₉	—	2	1	no	—
247	C₄×C₈₉	—	2	1	no	—
248	C₄×C₈₉	#413	1	2	yes	—
249	C₄×C₈₉	C₂×#103	1	2	yes	—
250	C₄×C₈₉	C₂×#103	1	2	yes	—
251	C₄×C₈₉	C₂×#103	1	2	yes	—
252	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
253	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
254	C₄×C₈₉	#575	1	2	yes	—
255	Dic₈₉	—	4	4	no	—
256	Dic₈₉	—	4	4	no	—
257	#17708	—	89	1	no	maximal, Sylow
258	C₂×C₈₉	—	2	2	no	—
259	C₂×C₈₉	—	2	2	no	—
260	C₂×C₈₉	—	2	2	no	—
261	C₂×C₈₉	C₂×#413	1	1	yes	characteristic
262	C₂×C₈₉	C₂²×#103	1	1	yes	characteristic
263	C₂×C₈₉	#2896	1	1	yes	characteristic
264	C₂×#533	—	89	1	no	—
265	C₂×#431	—	89	1	no	—
266	C₂×#423	D₈₉	1	1	yes	characteristic
267	#1550	—	89	4	no	—
268	#1549	—	89	2	no	—
269	#1548	—	89	2	no	—
270	#1542	—	89	4	no	—
271	C₈₉	#17708	1	1	yes	characteristic, complemented, Sylow
272	C₂²×M₁₆	—	2	1	no	—
273	#533	—	89	2	no	—
274	#533	—	89	2	no	—
275	#533	—	89	2	no	—
276	#533	—	89	2	no	—
277	#533	—	178	1	no	—
278	#533	—	178	1	no	—
279	#533	—	178	1	no	—
280	#533	—	178	1	no	—
281	C₂×C₄⋊Q₈	—	89	1	no	—
282	C₂×C₄⋊Q₈	—	89	1	no	—
283	C₂×#125	—	178	1	no	—
284	C₂×C₂²⋊Q₈	—	89	2	no	—
285	C₂×C₂²⋊Q₈	—	178	1	no	—
286	C₂×C₄×Q₈	—	89	2	no	—
287	C₂×C₄×Q₈	—	178	1	no	—
288	C₂×#117	—	178	1	no	—
289	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
290	#431	—	89	2	no	—
291	#431	—	89	2	no	—
292	#431	—	178	1	no	—
293	#431	—	178	1	no	—
294	#423	—	2	1	no	—
295	#423	—	2	1	no	—
296	#423	C₂×D₈₉	1	2	yes	—
297	#423	C₂×D₈₉	1	2	yes	—
298	C₂×C₄⋊C₈	—	2	1	no	—
299	C₂×C₄⋊C₈	—	89	2	no	—
300	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
301	C₂×C₂²⋊C₈	—	178	1	no	—
302	C₂×C₄×C₈	—	178	1	no	—
303	#333	—	89	8	no	—
304	#332	—	89	8	no	—
305	C₂²×Q₈	—	89	2	no	—
306	C₂²×Q₈	—	178	1	no	—
307	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
308	C₂³×C₄	D₃₅₆	1	1	yes	characteristic
309	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	—	2	2	no	—
312	C₂×M₁₆	—	4	4	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	—	178	2	no	—
315	C₄⋊Q₈	—	89	2	no	—
316	C₄⋊Q₈	—	89	2	no	—
317	C₄⋊Q₈	—	89	2	no	—
318	C₄⋊Q₈	—	89	2	no	—
319	C₄⋊Q₈	—	178	1	no	—
320	C₄⋊Q₈	—	178	1	no	—
321	C₄⋊Q₈	—	178	1	no	—
322	C₄⋊Q₈	—	178	1	no	—
323	#125	—	178	2	no	—
324	#125	—	178	2	no	—
325	#125	—	178	2	no	—
326	#125	—	178	2	no	—
327	C₂²⋊Q₈	—	89	4	no	—
328	C₂²⋊Q₈	—	89	4	no	—
329	C₂²⋊Q₈	—	178	2	no	—
330	C₂²⋊Q₈	—	178	2	no	—
331	C₂²⋊Q₈	—	178	2	no	—
332	C₂²⋊Q₈	—	178	2	no	—
333	C₂²⋊Q₈	—	178	2	no	—
334	C₂²⋊Q₈	—	178	2	no	—
335	C₄×Q₈	—	89	4	no	—
336	C₄×Q₈	—	89	4	no	—
337	C₄×Q₈	—	178	2	no	—
338	C₄×Q₈	—	178	2	no	—
339	C₄×Q₈	—	178	2	no	—
340	C₄×Q₈	—	178	2	no	—
341	C₄×Q₈	—	178	2	no	—
342	C₄×Q₈	—	178	2	no	—
343	#117	—	178	2	no	—
344	#117	—	178	2	no	—
345	#117	—	178	2	no	—
346	#117	—	178	2	no	—
347	C₂×C₄⋊C₄	—	89	2	no	—
348	C₂×C₄⋊C₄	—	178	2	no	—
349	C₂×C₄⋊C₄	—	178	2	no	—
350	C₂×C₄⋊C₄	—	178	1	no	—
351	C₂×C₄⋊C₄	—	178	1	no	—
352	C₂×C₄⋊C₄	—	178	1	no	—
353	C₂×C₂²⋊C₄	—	178	2	no	—
354	C₂×C₄²	—	178	2	no	—
355	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
356	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
357	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
358	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
359	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
360	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
361	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
362	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
363	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
364	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
365	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
366	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
367	C₄⋊C₈	—	2	2	no	—
368	C₄⋊C₈	—	2	2	no	—
369	C₄⋊C₈	—	2	2	no	—
370	C₄⋊C₈	—	89	4	no	—
371	C₄⋊C₈	—	178	2	no	—
372	C₄⋊C₈	C₂²×D₈₉	1	4	yes	—
373	C₂²⋊C₈	—	178	2	no	—
374	C₂²⋊C₈	—	178	2	no	—
375	C₄×C₈	—	178	2	no	—
376	C₄×C₈	—	178	2	no	—
377	C₂⁴	#13083551	1	1	yes	characteristic
378	C₂×Q₈	—	89	4	no	—
379	C₂×Q₈	—	356	4	no	—
380	C₂×Q₈	—	356	4	no	—
381	C₂×Q₈	—	178	2	no	—
382	C₂×Q₈	—	178	2	no	—
383	C₂×Q₈	—	178	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	178	2	no	—
387	C₂²×C₄	—	178	2	no	—
388	C₂²×C₄	#13083551	1	1	yes	characteristic
389	C₂²×C₄	#13083551	1	1	yes	characteristic
390	C₂²×C₄	#13083551	1	1	yes	characteristic
391	C₂²×C₄	#13083551	1	1	yes	characteristic
392	C₂²×C₄	#13083551	1	1	yes	characteristic
393	C₂²×C₄	#13083551	1	1	yes	characteristic
394	C₂²×C₄	#13083551	1	1	yes	characteristic
395	C₂²×C₄	#13083551	1	1	yes	characteristic
396	C₂²×C₄	#13083551	1	1	yes	characteristic
397	C₂²×C₄	#13083562	1	4	yes	—
398	C₂²×C₄	#13083564	1	4	yes	—
399	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
400	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
401	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
404	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
408	M₁₆	—	4	4	no	—
409	M₁₆	—	4	4	no	—
410	C₂×C₈	—	2	4	no	—
411	C₂×C₈	—	4	4	no	—
412	C₂×C₈	—	356	4	no	—
413	C₂×C₈	—	178	4	no	—
414	C₄⋊C₄	—	89	4	no	—
415	C₄⋊C₄	—	178	2	no	—
416	C₄⋊C₄	—	178	2	no	—
417	C₄⋊C₄	—	178	2	no	—
418	C₄⋊C₄	—	178	2	no	—
419	C₄⋊C₄	—	178	2	no	—
420	C₄⋊C₄	—	178	2	no	—
421	C₄⋊C₄	—	178	4	no	—
422	C₄⋊C₄	—	178	4	no	—
423	C₄⋊C₄	—	178	4	no	—
424	C₄⋊C₄	—	178	4	no	—
425	C₄⋊C₄	—	178	2	no	—
426	C₂²⋊C₄	—	178	4	no	—
427	C₂²⋊C₄	—	178	4	no	—
428	C₄²	—	178	4	no	—
429	C₄²	—	178	4	no	—
430	C₄²	#13083551	1	1	yes	characteristic
431	C₄²	#13083551	1	1	yes	characteristic
432	C₄²	#13083551	1	1	yes	characteristic
433	C₄²	#13083551	1	1	yes	characteristic
434	C₄²	#13083551	1	1	yes	characteristic
435	C₄²	#13083551	1	1	yes	characteristic
436	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
437	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
438	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
439	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
440	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
441	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
442	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
443	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
444	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
445	C₄²	C₂³×D₈₉	1	1	yes	characteristic
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	#15667935	1	4	yes	—
449	C₂³	C₂×#13083551	1	1	yes	characteristic
450	C₂³	C₂×#13083551	1	1	yes	characteristic
451	C₂³	C₂×#13083551	1	1	yes	characteristic
452	Q₈	—	356	4	no	—
453	Q₈	—	356	4	no	—
454	Q₈	—	356	4	no	—
455	Q₈	—	356	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	356	4	no	—
469	C₂×C₄	—	356	4	no	—
470	C₂×C₄	—	178	4	no	—
471	C₂×C₄	—	178	4	no	—
472	C₂×C₄	#15667935	1	4	yes	—
473	C₂×C₄	#15667935	1	4	yes	—
474	C₂×C₄	#15667935	1	4	yes	—
475	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
476	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
477	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
478	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
479	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
480	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
481	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
482	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
483	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
484	C₂×C₄	C₂×#13083562	1	2	yes	—
485	C₂×C₄	C₂×#13083562	1	2	yes	—
486	C₂×C₄	C₂×#13083562	1	2	yes	—
487	C₂×C₄	C₂×#13083564	1	2	yes	—
488	C₂×C₄	C₂×#13083564	1	2	yes	—
489	C₂×C₄	C₂×#13083564	1	2	yes	—
490	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
491	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
493	C₈	—	4	4	no	—
494	C₈	—	356	4	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	4	4	no	—
502	C₂²	C₂×#15667935	1	2	yes	—
503	C₂²	C₂×#15667935	1	2	yes	—
504	C₂²	C₂×#15667935	1	2	yes	—
505	C₂²	C₂²×#13083551	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	356	4	no	—
513	C₄	—	356	4	no	—
514	C₄	#19151580	1	2	yes	—
515	C₄	C₂×#15667935	1	2	yes	—
516	C₄	C₂×#15667935	1	2	yes	—
517	C₄	C₂×#15667935	1	2	yes	—
518	C₄	C₂²×#13083562	1	1	yes	characteristic
519	C₄	C₂²×#13083564	1	1	yes	characteristic
520	C₄	#19152398	1	2	yes	—
521	C₂	—	2	2	no	—
522	C₂	—	2	2	no	—
523	C₂	—	2	2	no	—
524	C₂	C₂×#19151580	1	1	yes	characteristic
525	C₂	C₂²×#15667935	1	1	yes	characteristic
526	C₂	#26028772	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#13083551
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×#423×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₈₉	C₂²⋊C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×#423	D₈₉
hypocenter	C₈₉	#17708
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
3. #26018943	C₂	semidirect
4. #26018938	C₂	semidirect
5. #26018934	C₂	semidirect
6. #26018910	C₂	semidirect
31. #19151346	C₂²	semidirect
32. #19151343	C₂²	semidirect
271. C₈₉	#17708	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152155	2
C₂×#19151651	2
#26018943	2
#26018938	2
#26018934	2
#26018910	2
C₂×#423×C₈₉	2
#17708	89