Subgroups — #36444305

Order 22784.

714 conjugacy classes of subgroups.

The subgroup lattice has 434 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	#26018119	C₂	1	4	yes	maximal
4	C₈₉×#2285	C₂	1	1	yes	maximal, characteristic
5	C₂×#15667971	—	2	1	no	—
6	#19151651	—	2	1	no	—
7	#19151651	—	2	1	no	—
8	#19151651	—	2	1	no	—
9	#19151651	—	2	1	no	—
10	C₂×C₄⋊#10623494	C₄	1	2	yes	complemented
11	C₂×C₂²⋊#10623494	C₂²	1	2	yes	—
12	C₂×C₄×#10623494	C₄	1	2	yes	complemented
13	#19151468	—	2	1	no	—
14	#19151464	C₄	1	2	yes	complemented
15	#19151458	—	2	1	no	—
16	#19151458	C₂²	1	2	yes	—
17	C₄×C₄⋊Dic₈₉	—	2	1	no	—
18	C₄×C₄⋊Dic₈₉	C₄	1	2	yes	complemented
19	C₂×#117×C₈₉	—	2	1	no	—
20	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
21	#384×C₈₉	—	2	1	no	—
22	#382×C₈₉	C₄	1	2	yes	complemented
23	#380×C₈₉	—	2	1	no	—
24	#380×C₈₉	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
26	C₄×C₄⋊C₄×C₈₉	C₄	1	2	yes	complemented
27	C₂²×#10623494	C₂×C₄	1	4	yes	—
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	—	2	2	no	—
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	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
46	#117×C₈₉	—	4	2	no	—
47	#117×C₈₉	—	4	2	no	—
48	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
51	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
52	C₂×C₄²×C₈₉	—	2	2	no	—
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	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₈₉	Q₈	1	1	yes	characteristic
64	C₂×C₄²×C₈₉	Q₈	1	1	yes	characteristic
65	#95×C₈₉	—	2	2	no	—
66	#95×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	2	no	—
74	C₂²⋊Dic₈₉	—	4	2	no	—
75	C₄×Dic₈₉	—	4	4	no	—
76	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₈₉	—	2	4	no	—
78	C₂²×C₄×C₈₉	—	4	2	no	—
79	C₂²×C₄×C₈₉	—	4	2	no	—
80	C₂²×C₄×C₈₉	C₂²⋊C₄	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	D₈	1	2	yes	—
93	C₂²×C₄×C₈₉	SD₁₆	1	2	yes	—
94	C₂²×C₄×C₈₉	SD₁₆	1	2	yes	—
95	C₂²×C₄×C₈₉	Q₁₆	1	2	yes	—
96	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
102	C₄⋊C₄×C₈₉	—	4	4	no	—
103	C₄⋊C₄×C₈₉	—	4	4	no	—
104	C₄⋊C₄×C₈₉	—	4	4	no	—
105	C₂²⋊C₄×C₈₉	—	4	2	no	—
106	C₂²⋊C₄×C₈₉	—	4	2	no	—
107	C₄²×C₈₉	—	4	4	no	—
108	C₄²×C₈₉	C₄²	1	1	yes	characteristic
109	C₄²×C₈₉	C₄²	1	1	yes	characteristic
110	C₄²×C₈₉	C₄²	1	1	yes	characteristic
111	C₄²×C₈₉	C₄²	1	1	yes	characteristic
112	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₄²×C₈₉	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
119	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
120	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
121	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
122	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
123	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
124	C₂³×C₈₉	—	4	1	no	—
125	C₂³×C₈₉	—	4	1	no	—
126	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
130	C₂³×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
131	C₂³×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
132	C₂³×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
133	C₂×C₄×C₈₉	—	2	2	no	—
134	C₂×C₄×C₈₉	—	2	2	no	—
135	C₂×C₄×C₈₉	—	2	2	no	—
136	C₂×C₄×C₈₉	—	2	2	no	—
137	C₂×C₄×C₈₉	—	2	2	no	—
138	C₂×C₄×C₈₉	—	2	2	no	—
139	C₂×C₄×C₈₉	—	4	1	no	—
140	C₂×C₄×C₈₉	—	4	1	no	—
141	C₂×C₄×C₈₉	—	4	1	no	—
142	C₂×C₄×C₈₉	—	4	1	no	—
143	C₂×C₄×C₈₉	—	4	1	no	—
144	C₂×C₄×C₈₉	—	4	1	no	—
145	C₂×C₄×C₈₉	—	4	4	no	—
146	C₂×C₄×C₈₉	—	4	4	no	—
147	C₂×C₄×C₈₉	—	4	4	no	—
148	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
149	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
150	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
151	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
152	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
153	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
154	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
155	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
156	C₂×C₄×C₈₉	#102	1	2	yes	—
157	C₂×C₄×C₈₉	#102	1	2	yes	—
158	C₂×C₄×C₈₉	#102	1	2	yes	—
159	C₂×C₄×C₈₉	#102	1	2	yes	—
160	C₂×C₄×C₈₉	#103	1	2	yes	—
161	C₂×C₄×C₈₉	#103	1	2	yes	—
162	C₂×C₄×C₈₉	#103	1	2	yes	—
163	C₂×C₄×C₈₉	#103	1	2	yes	—
164	C₂×C₄×C₈₉	#106	1	2	yes	—
165	C₂×C₄×C₈₉	#106	1	2	yes	—
166	C₂×C₄×C₈₉	#107	1	2	yes	—
167	C₂×C₄×C₈₉	#107	1	2	yes	—
168	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×Dic₈₉	—	4	4	no	—
173	C₂×Dic₈₉	—	4	4	no	—
174	C₂×Dic₈₉	—	4	4	no	—
175	#10623494	—	4	4	no	—
176	C₂²×C₈₉	—	2	1	no	—
177	C₂²×C₈₉	—	2	1	no	—
178	C₂²×C₈₉	—	2	1	no	—
179	C₂²×C₈₉	—	2	1	no	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	—	2	1	no	—
182	C₂²×C₈₉	—	4	1	no	—
183	C₂²×C₈₉	—	4	1	no	—
184	C₂²×C₈₉	—	4	1	no	—
185	C₂²×C₈₉	—	4	1	no	—
186	C₂²×C₈₉	C₂×#95	1	1	yes	characteristic
187	C₂²×C₈₉	C₂×#102	1	1	yes	characteristic
188	C₂²×C₈₉	C₂×#102	1	1	yes	characteristic
189	C₂²×C₈₉	C₂×#103	1	1	yes	characteristic
190	C₂²×C₈₉	C₂×#103	1	1	yes	characteristic
191	C₂²×C₈₉	C₂×#106	1	1	yes	characteristic
192	C₂²×C₈₉	C₂×#107	1	1	yes	characteristic
193	C₄×C₈₉	—	2	1	no	—
194	C₄×C₈₉	—	2	1	no	—
195	C₄×C₈₉	—	2	1	no	—
196	C₄×C₈₉	—	2	1	no	—
197	C₄×C₈₉	—	2	1	no	—
198	C₄×C₈₉	—	2	1	no	—
199	C₄×C₈₉	—	8	4	no	—
200	C₄×C₈₉	H(3,ℤ/4)	1	2	yes	—
201	C₄×C₈₉	#340	1	2	yes	—
202	C₄×C₈₉	#340	1	2	yes	—
203	C₄×C₈₉	#340	1	2	yes	—
204	C₄×C₈₉	#340	1	2	yes	—
205	C₄×C₈₉	#410	1	2	yes	—
206	Dic₈₉	—	8	4	no	—
207	#7981	—	89	1	no	maximal, Sylow
208	C₂×C₈₉	—	2	1	no	—
209	C₂×C₈₉	—	2	1	no	—
210	C₂×C₈₉	—	2	1	no	—
211	C₂×C₈₉	—	2	1	no	—
212	C₂×C₈₉	—	2	1	no	—
213	C₂×C₈₉	—	2	1	no	—
214	C₂×C₈₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
215	C₂×C₈₉	C₂×#340	1	1	yes	characteristic
216	C₂×C₈₉	#1740	1	1	yes	characteristic
217	C₂×#431	—	89	1	no	—
218	#2285	—	89	1	no	—
219	#2285	D₈₉	1	1	yes	characteristic
220	#1289	—	89	4	no	—
221	C₈₉	#7981	1	1	yes	characteristic, complemented, Sylow
222	C₂×#117	—	2	1	no	—
223	C₂×#117	—	178	1	no	—
224	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
225	#431	—	178	1	no	—
226	#431	—	178	1	no	—
227	#431	—	178	1	no	—
228	#431	—	178	1	no	—
229	C₂×C₄⋊C₈	—	89	2	no	—
230	C₂×C₂²⋊C₈	—	89	2	no	—
231	C₂×C₄×C₈	—	89	2	no	—
232	#384	—	2	1	no	—
233	#384	—	178	1	no	—
234	#382	—	89	2	no	—
235	#382	Dic₈₉	1	2	yes	complemented
236	#380	—	2	1	no	—
237	#380	—	89	2	no	—
238	#380	—	178	1	no	—
239	#380	C₂×D₈₉	1	2	yes	—
240	C₄×C₄⋊C₄	—	2	1	no	—
241	C₄×C₄⋊C₄	—	89	2	no	—
242	C₄×C₄⋊C₄	—	178	1	no	—
243	C₄×C₄⋊C₄	Dic₈₉	1	2	yes	complemented
244	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
245	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
246	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
247	C₂²×C₈	—	89	4	no	—
248	#117	—	4	2	no	—
249	#117	—	4	2	no	—
250	#117	—	356	2	no	—
251	#117	—	356	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	178	2	no	—
256	C₂×C₄⋊C₄	—	178	2	no	—
257	C₂×C₄⋊C₄	—	178	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	178	2	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	178	2	no	—
262	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
263	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
264	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
265	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
266	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
267	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
268	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
269	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
270	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
271	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
272	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
273	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
274	C₄⋊C₈	—	178	2	no	—
275	C₄⋊C₈	—	178	2	no	—
276	C₂²⋊C₈	—	178	2	no	—
277	C₂²⋊C₈	—	178	2	no	—
278	C₄×C₈	—	178	2	no	—
279	C₄×C₈	—	178	2	no	—
280	#95	—	2	2	no	—
281	#95	—	89	4	no	—
282	#95	—	178	2	no	—
283	#95	C₂×Dic₈₉	1	4	yes	—
284	C₂⁴	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	178	4	no	—
289	C₂²×C₄	#13083551	1	1	yes	characteristic
290	C₂²×C₄	#13083551	1	1	yes	characteristic
291	C₂²×C₄	#13083551	1	1	yes	characteristic
292	C₂²×C₄	#13083551	1	1	yes	characteristic
293	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
294	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
295	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
296	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
297	C₂²×C₄	#13083553	1	1	yes	characteristic
298	C₂²×C₄	#13083553	1	1	yes	characteristic
299	C₂²×C₄	#13083553	1	1	yes	characteristic
300	C₂²×C₄	#13083553	1	1	yes	characteristic
301	C₂²×C₄	#13083559	1	2	yes	—
302	C₂²×C₄	#13083561	1	2	yes	—
303	C₂²×C₄	#13083562	1	2	yes	—
304	C₂²×C₄	#13083564	1	2	yes	—
305	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
307	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
310	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
311	C₂×C₈	—	356	4	no	—
312	C₂×C₈	—	178	4	no	—
313	C₄⋊C₄	—	4	4	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	4	4	no	—
316	C₄⋊C₄	—	356	4	no	—
317	C₄⋊C₄	—	356	4	no	—
318	C₄⋊C₄	—	356	4	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	356	2	no	—
322	C₂²⋊C₄	—	356	2	no	—
323	C₄²	—	4	4	no	—
324	C₄²	—	356	4	no	—
325	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
326	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
327	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
328	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
329	C₄²	#13083551	1	1	yes	characteristic
330	C₄²	#13083551	1	1	yes	characteristic
331	C₄²	#13083551	1	1	yes	characteristic
332	C₄²	#13083551	1	1	yes	characteristic
333	C₄²	#13083553	1	1	yes	characteristic
334	C₄²	#13083553	1	1	yes	characteristic
335	C₄²	#13083553	1	1	yes	characteristic
336	C₄²	#13083553	1	1	yes	characteristic
337	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
338	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
339	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
340	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	C₂×#13083551	1	1	yes	characteristic
344	C₂³	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
345	C₂³	C₂×#13083553	1	1	yes	characteristic
346	C₂³	C₂×#13083559	1	1	yes	characteristic
347	C₂³	C₂×#13083561	1	1	yes	characteristic
348	C₂³	C₂×#13083562	1	1	yes	characteristic
349	C₂³	C₂×#13083564	1	1	yes	characteristic
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	356	4	no	—
366	C₂×C₄	—	356	4	no	—
367	C₂×C₄	—	356	4	no	—
368	C₂×C₄	#15667919	1	1	yes	characteristic
369	C₂×C₄	#15667919	1	1	yes	characteristic
370	C₂×C₄	#15667919	1	1	yes	characteristic
371	C₂×C₄	#15667919	1	1	yes	characteristic
372	C₂×C₄	#15667919	1	1	yes	characteristic
373	C₂×C₄	#15667919	1	1	yes	characteristic
374	C₂×C₄	#15667919	1	1	yes	characteristic
375	C₂×C₄	#15667919	1	1	yes	characteristic
376	C₂×C₄	#15667932	1	2	yes	—
377	C₂×C₄	#15667932	1	2	yes	—
378	C₂×C₄	#15667933	1	2	yes	—
379	C₂×C₄	#15667933	1	2	yes	—
380	C₂×C₄	#15667935	1	2	yes	—
381	C₂×C₄	#15667935	1	2	yes	—
382	C₂×C₄	#15667936	1	2	yes	—
383	C₂×C₄	#15667936	1	2	yes	—
384	C₂×C₄	#15667943	1	2	yes	—
385	C₂×C₄	#15667943	1	2	yes	—
386	C₂×C₄	#15667945	1	2	yes	—
387	C₂×C₄	#15667945	1	2	yes	—
388	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
389	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
390	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
392	C₈	—	356	4	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	C₂×#15667919	1	1	yes	characteristic
404	C₂²	C₂×#15667932	1	1	yes	characteristic
405	C₂²	C₂×#15667933	1	1	yes	characteristic
406	C₂²	C₂×#15667935	1	1	yes	characteristic
407	C₂²	C₂×#15667936	1	1	yes	characteristic
408	C₂²	C₂×#15667943	1	1	yes	characteristic
409	C₂²	C₂×#15667945	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	8	4	no	—
417	C₄	—	712	4	no	—
418	C₄	#19151354	1	2	yes	—
419	C₄	#19151360	1	2	yes	—
420	C₄	#19151360	1	2	yes	—
421	C₄	#19151360	1	2	yes	—
422	C₄	#19151360	1	2	yes	—
423	C₄	#19151571	1	2	yes	—
424	C₂	—	2	1	no	—
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	2	1	no	—
430	C₂	C₂×#19151354	1	1	yes	characteristic
431	C₂	C₂×#19151360	1	1	yes	characteristic
432	C₂	#26019984	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15667919
commutator	C₂×C₄×C₈₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₈₉
Fitting	C₈₉×#2285	C₂
socle	C₂²×C₈₉	C₂×#95
prime radical	C₂⁴×C₈₉	C₂×D₄
cosocle	C₂³×C₄×C₈₉	C₂³
hypercenter	#2285	D₈₉
hypocenter	C₈₉	#7981
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2285

Complements

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

N	H ≅ G/N	type
10. C₂×C₄⋊#10623494	C₄	semidirect
12. C₂×C₄×#10623494	C₄	semidirect
14. #19151464	C₄	semidirect
18. C₄×C₄⋊Dic₈₉	C₄	semidirect
22. #382×C₈₉	C₄	semidirect
26. C₄×C₄⋊C₄×C₈₉	C₄	semidirect
221. C₈₉	#7981	semidirect
235. #382	Dic₈₉	semidirect
243. C₄×C₄⋊C₄	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
#26018119	2
C₈₉×#2285	2
#7981	89