Subgroups — #36444731

Order 22784.

674 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151651	C₂	1	1	yes	maximal, characteristic
2	#26022659	C₂	1	1	yes	maximal, characteristic
3	#26018153	C₂	1	4	yes	maximal, complemented
4	C₂×#423×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#15667971	—	2	1	no	—
6	#19151651	—	2	1	no	—
7	#19151651	—	2	1	no	—
8	#19151651	C₄	1	2	yes	complemented
9	#19151651	C₂²	1	2	yes	—
10	C₂×C₄⋊#10623494	C₄	1	2	yes	complemented
11	C₂×C₂²⋊#10623494	—	2	1	no	—
12	C₂×C₄×#10623494	—	2	1	no	—
13	#19151468	—	2	1	no	—
14	#19151464	C₄	1	2	yes	—
15	#19151458	—	2	1	no	—
16	#19151458	C₄	1	2	yes	—
17	C₄×C₄⋊Dic₈₉	—	2	1	no	—
18	C₄×C₄⋊Dic₈₉	C₂²	1	2	yes	—
19	C₂²×M₁₆×C₈₉	—	2	1	no	—
20	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
21	#423×C₈₉	—	2	1	no	—
22	#423×C₈₉	—	2	1	no	—
23	#423×C₈₉	C₄	1	2	yes	complemented
24	#423×C₈₉	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
26	C₂×C₄⋊C₈×C₈₉	C₄	1	2	yes	complemented
27	C₂²×#10623494	—	2	2	no	—
28	#15667971	—	4	2	no	—
29	#15667971	—	4	2	no	—
30	C₂×C₄⋊Dic₈₉	—	2	2	no	—
31	C₂×C₄⋊Dic₈₉	—	2	2	no	—
32	C₂×C₄⋊Dic₈₉	—	2	2	no	—
33	C₂×C₂²⋊Dic₈₉	—	2	2	no	—
34	C₂×C₄×Dic₈₉	—	2	2	no	—
35	C₄⋊#10623494	—	2	2	no	—
36	C₄⋊#10623494	C₂×C₄	1	4	yes	—
37	C₂²⋊#10623494	—	2	2	no	—
38	C₂²⋊#10623494	—	2	2	no	—
39	C₄×#10623494	—	2	2	no	—
40	C₄×#10623494	—	2	2	no	—
41	#15667919	—	2	2	no	—
42	#15667919	C₂×C₄	1	4	yes	—
43	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
46	C₂×M₁₆×C₈₉	—	2	2	no	—
47	C₂×M₁₆×C₈₉	—	2	2	no	—
48	C₂×M₁₆×C₈₉	—	4	2	no	—
49	C₂×M₁₆×C₈₉	—	4	2	no	—
50	C₂²×C₈×C₈₉	—	2	2	no	—
51	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₈₉	Q₈	1	1	yes	characteristic
61	C₂×C₄²×C₈₉	Q₈	1	1	yes	characteristic
62	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₈₉	—	2	2	no	—
64	C₄⋊C₈×C₈₉	—	2	2	no	—
65	C₄⋊C₈×C₈₉	—	2	2	no	—
66	C₄⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
67	C₂²×Dic₈₉	—	2	4	no	—
68	C₂×#10623494	—	2	4	no	—
69	C₂×#10623494	—	4	4	no	—
70	C₄⋊Dic₈₉	—	4	4	no	—
71	C₄⋊Dic₈₉	—	4	4	no	—
72	C₄⋊Dic₈₉	—	4	4	no	—
73	C₂²⋊Dic₈₉	—	4	4	no	—
74	C₄×Dic₈₉	—	4	2	no	—
75	C₄×Dic₈₉	—	4	2	no	—
76	C₂⁴×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₈₉	—	4	2	no	—
78	C₂²×C₄×C₈₉	—	4	2	no	—
79	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
80	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
81	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	D₈	1	2	yes	—
95	C₂²×C₄×C₈₉	SD₁₆	1	2	yes	—
96	C₂²×C₄×C₈₉	SD₁₆	1	2	yes	—
97	C₂²×C₄×C₈₉	Q₁₆	1	2	yes	—
98	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
101	M₁₆×C₈₉	—	4	4	no	—
102	M₁₆×C₈₉	—	4	2	no	—
103	M₁₆×C₈₉	—	4	2	no	—
104	C₂×C₈×C₈₉	—	2	4	no	—
105	C₂×C₈×C₈₉	—	4	4	no	—
106	C₄²×C₈₉	C₄²	1	1	yes	characteristic
107	C₄²×C₈₉	C₄²	1	1	yes	characteristic
108	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
118	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
122	C₂³×C₈₉	—	4	1	no	—
123	C₂³×C₈₉	—	4	1	no	—
124	C₂³×C₈₉	#95	1	1	yes	characteristic
125	C₂³×C₈₉	#95	1	1	yes	characteristic
126	C₂³×C₈₉	#102	1	2	yes	—
127	C₂³×C₈₉	#103	1	2	yes	—
128	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₈₉	—	2	2	no	—
130	C₂×C₄×C₈₉	—	2	2	no	—
131	C₂×C₄×C₈₉	—	2	2	no	—
132	C₂×C₄×C₈₉	—	2	2	no	—
133	C₂×C₄×C₈₉	—	2	2	no	—
134	C₂×C₄×C₈₉	—	2	2	no	—
135	C₂×C₄×C₈₉	—	4	1	no	—
136	C₂×C₄×C₈₉	—	4	1	no	—
137	C₂×C₄×C₈₉	—	4	1	no	—
138	C₂×C₄×C₈₉	—	4	1	no	—
139	C₂×C₄×C₈₉	—	4	1	no	—
140	C₂×C₄×C₈₉	—	4	1	no	—
141	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
142	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
143	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
144	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
145	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
146	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
147	C₂×C₄×C₈₉	#102	1	2	yes	—
148	C₂×C₄×C₈₉	#102	1	2	yes	—
149	C₂×C₄×C₈₉	#102	1	2	yes	—
150	C₂×C₄×C₈₉	#103	1	2	yes	—
151	C₂×C₄×C₈₉	#103	1	2	yes	—
152	C₂×C₄×C₈₉	#103	1	2	yes	—
153	C₂×C₄×C₈₉	#106	1	2	yes	—
154	C₂×C₄×C₈₉	#106	1	2	yes	—
155	C₂×C₄×C₈₉	#107	1	2	yes	—
156	C₂×C₄×C₈₉	#107	1	2	yes	—
157	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
167	C₂×Dic₈₉	—	4	4	no	—
168	C₂×Dic₈₉	—	4	4	no	—
169	C₂×Dic₈₉	—	4	4	no	—
170	C₈×C₈₉	—	4	4	no	—
171	#10623494	—	4	4	no	—
172	C₂²×C₈₉	—	2	1	no	—
173	C₂²×C₈₉	—	2	1	no	—
174	C₂²×C₈₉	—	2	1	no	—
175	C₂²×C₈₉	—	2	1	no	—
176	C₂²×C₈₉	—	2	1	no	—
177	C₂²×C₈₉	—	2	1	no	—
178	C₂²×C₈₉	—	4	2	no	—
179	C₂²×C₈₉	—	4	2	no	—
180	C₂²×C₈₉	#340	1	2	yes	—
181	C₂²×C₈₉	#340	1	2	yes	—
182	C₂²×C₈₉	C₂×#95	1	1	yes	characteristic
183	C₂²×C₈₉	C₂×#102	1	1	yes	characteristic
184	C₂²×C₈₉	C₂×#103	1	1	yes	characteristic
185	C₄×C₈₉	—	2	1	no	—
186	C₄×C₈₉	—	2	1	no	—
187	C₄×C₈₉	—	2	1	no	—
188	C₄×C₈₉	—	2	1	no	—
189	C₄×C₈₉	—	2	1	no	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	#340	1	2	yes	—
192	C₄×C₈₉	#340	1	2	yes	—
193	C₄×C₈₉	#344	1	2	yes	—
194	C₄×C₈₉	C₂×#102	1	1	yes	characteristic
195	C₄×C₈₉	C₂×#103	1	1	yes	characteristic
196	C₄×C₈₉	#421	1	2	yes	—
197	C₄×C₈₉	C₂×#106	1	1	yes	characteristic
198	C₄×C₈₉	C₂×#107	1	1	yes	characteristic
199	Dic₈₉	—	8	4	no	—
200	#8095	—	89	1	no	maximal, Sylow
201	C₂×C₈₉	—	2	1	no	—
202	C₂×C₈₉	—	2	2	no	—
203	C₂×C₈₉	—	2	2	no	—
204	C₂×C₈₉	—	2	1	no	—
205	C₂×C₈₉	#1733	1	1	yes	characteristic
206	C₂×C₈₉	C₂×#340	1	1	yes	characteristic
207	C₂×C₈₉	C₂×#344	1	1	yes	characteristic
208	C₂×#431	—	89	1	no	—
209	C₂×#423	D₈₉	1	1	yes	characteristic
210	#2285	—	89	1	no	—
211	#1303	—	89	4	no	—
212	C₈₉	#8095	1	1	yes	characteristic, complemented, Sylow
213	C₂²×M₁₆	—	2	1	no	—
214	C₂×#117	—	178	1	no	—
215	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
216	#431	—	89	2	no	—
217	#431	—	89	2	no	—
218	#431	—	178	1	no	—
219	#431	—	178	1	no	—
220	#423	—	2	1	no	—
221	#423	—	2	1	no	—
222	#423	Dic₈₉	1	2	yes	complemented
223	#423	C₂×D₈₉	1	2	yes	—
224	C₂×C₄⋊C₈	—	2	1	no	—
225	C₂×C₄⋊C₈	—	89	2	no	—
226	C₂×C₄⋊C₈	Dic₈₉	1	2	yes	complemented
227	C₂×C₂²⋊C₈	—	178	1	no	—
228	C₂×C₄×C₈	—	178	1	no	—
229	#384	—	178	1	no	—
230	#382	—	89	2	no	—
231	#380	—	89	2	no	—
232	#380	—	178	1	no	—
233	C₄×C₄⋊C₄	—	89	2	no	—
234	C₄×C₄⋊C₄	—	178	1	no	—
235	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
236	C₂³×C₄	D₃₅₆	1	1	yes	characteristic
237	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	4	2	no	—
241	C₂×M₁₆	—	4	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	178	2	no	—
244	#117	—	356	2	no	—
245	#117	—	356	2	no	—
246	C₂×C₄⋊C₄	—	178	2	no	—
247	C₂×C₄⋊C₄	—	178	2	no	—
248	C₂×C₄⋊C₄	—	178	2	no	—
249	C₂×C₂²⋊C₄	—	178	2	no	—
250	C₂×C₄²	—	178	2	no	—
251	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
252	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
253	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
254	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
255	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
256	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
257	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
258	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
259	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
260	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
261	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	—	89	4	no	—
267	C₄⋊C₈	—	178	2	no	—
268	C₄⋊C₈	C₂×Dic₈₉	1	4	yes	—
269	C₂²⋊C₈	—	178	2	no	—
270	C₂²⋊C₈	—	178	2	no	—
271	C₄×C₈	—	178	2	no	—
272	C₄×C₈	—	178	2	no	—
273	#95	—	89	4	no	—
274	#95	—	178	2	no	—
275	C₂⁴	#13083551	1	1	yes	characteristic
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	178	4	no	—
279	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
280	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
281	C₂²×C₄	#13083551	1	1	yes	characteristic
282	C₂²×C₄	#13083551	1	1	yes	characteristic
283	C₂²×C₄	#13083551	1	1	yes	characteristic
284	C₂²×C₄	#13083551	1	1	yes	characteristic
285	C₂²×C₄	#13083551	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
287	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
288	C₂²×C₄	#13083553	1	1	yes	characteristic
289	C₂²×C₄	#13083553	1	1	yes	characteristic
290	C₂²×C₄	#13083553	1	1	yes	characteristic
291	C₂²×C₄	#13083553	1	1	yes	characteristic
292	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
293	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
294	C₂²×C₄	#13083559	1	2	yes	—
295	C₂²×C₄	#13083561	1	2	yes	—
296	C₂²×C₄	#13083562	1	2	yes	—
297	C₂²×C₄	#13083564	1	2	yes	—
298	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
301	M₁₆	—	4	2	no	—
302	M₁₆	—	4	2	no	—
303	M₁₆	—	4	4	no	—
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	4	4	no	—
306	C₂×C₈	—	356	4	no	—
307	C₂×C₈	—	178	4	no	—
308	C₄⋊C₄	—	356	4	no	—
309	C₄⋊C₄	—	356	4	no	—
310	C₄⋊C₄	—	356	4	no	—
311	C₂²⋊C₄	—	356	4	no	—
312	C₄²	—	356	2	no	—
313	C₄²	—	356	2	no	—
314	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
315	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
316	C₄²	#13083551	1	1	yes	characteristic
317	C₄²	#13083551	1	1	yes	characteristic
318	C₄²	C₂²⋊Dic₈₉	1	1	yes	characteristic
319	C₄²	C₂²⋊Dic₈₉	1	1	yes	characteristic
320	C₄²	#13083553	1	1	yes	characteristic
321	C₄²	#13083553	1	1	yes	characteristic
322	C₄²	#13083553	1	1	yes	characteristic
323	C₄²	#13083553	1	1	yes	characteristic
324	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
325	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
326	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
327	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
328	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
329	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
330	C₂³	—	4	1	no	—
331	C₂³	—	4	1	no	—
332	C₂³	#15667919	1	1	yes	characteristic
333	C₂³	#15667919	1	1	yes	characteristic
334	C₂³	#15667932	1	2	yes	—
335	C₂³	#15667935	1	2	yes	—
336	C₂³	C₂×#13083551	1	1	yes	characteristic
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	356	4	no	—
350	C₂×C₄	—	356	4	no	—
351	C₂×C₄	—	356	4	no	—
352	C₂×C₄	#15667919	1	1	yes	characteristic
353	C₂×C₄	#15667919	1	1	yes	characteristic
354	C₂×C₄	#15667919	1	1	yes	characteristic
355	C₂×C₄	#15667919	1	1	yes	characteristic
356	C₂×C₄	#15667919	1	1	yes	characteristic
357	C₂×C₄	#15667919	1	1	yes	characteristic
358	C₂×C₄	#15667932	1	2	yes	—
359	C₂×C₄	#15667933	1	2	yes	—
360	C₂×C₄	#15667933	1	2	yes	—
361	C₂×C₄	#15667935	1	2	yes	—
362	C₂×C₄	#15667936	1	2	yes	—
363	C₂×C₄	#15667936	1	2	yes	—
364	C₂×C₄	#15667943	1	2	yes	—
365	C₂×C₄	#15667943	1	2	yes	—
366	C₂×C₄	#15667945	1	2	yes	—
367	C₂×C₄	#15667945	1	2	yes	—
368	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
369	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
370	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
371	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
372	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
374	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
375	C₂×C₄	C₂×#13083561	1	1	yes	characteristic
376	C₂×C₄	C₂×#13083562	1	1	yes	characteristic
377	C₂×C₄	C₂×#13083564	1	1	yes	characteristic
378	C₈	—	4	4	no	—
379	C₈	—	356	4	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	#19151360	1	2	yes	—
389	C₂²	#19151360	1	2	yes	—
390	C₂²	C₂×#15667919	1	1	yes	characteristic
391	C₂²	C₂×#15667932	1	1	yes	characteristic
392	C₂²	C₂×#15667935	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	712	4	no	—
400	C₄	#19151360	1	2	yes	—
401	C₄	#19151360	1	2	yes	—
402	C₄	#19151369	1	2	yes	—
403	C₄	C₂×#15667933	1	1	yes	characteristic
404	C₄	C₂×#15667936	1	1	yes	characteristic
405	C₄	#19151614	1	2	yes	—
406	C₄	C₂×#15667943	1	1	yes	characteristic
407	C₄	C₂×#15667945	1	1	yes	characteristic
408	C₂	—	2	1	no	—
409	C₂	—	2	2	no	—
410	C₂	—	2	2	no	—
411	C₂	—	2	1	no	—
412	C₂	#26019963	1	1	yes	characteristic
413	C₂	C₂×#19151360	1	1	yes	characteristic
414	C₂	C₂×#19151369	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₈₉
commutator	C₂×C₄×C₈₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₂×#423×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#95
prime radical	C₂⁴×C₈₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₂×#423	D₈₉
hypocenter	C₈₉	#8095
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. #26018153	C₂	semidirect
8. #19151651	C₄	semidirect
10. C₂×C₄⋊#10623494	C₄	semidirect
23. #423×C₈₉	C₄	semidirect
26. C₂×C₄⋊C₈×C₈₉	C₄	semidirect
212. C₈₉	#8095	semidirect
222. #423	Dic₈₉	semidirect
226. C₂×C₄⋊C₈	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151651	2
#26022659	2
#26018153	2
C₂×#423×C₈₉	2
#8095	89