Subgroups — #36444317

Order 22784.

650 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151655	C₂	1	1	yes	maximal, characteristic
2	#26022650	C₂	1	1	yes	maximal, characteristic
3	#26018119	C₂	1	4	yes	maximal
4	C₈₉×#2285	C₂	1	1	yes	maximal, characteristic
5	#19151655	—	2	1	no	—
6	#19151655	—	2	1	no	—
7	#19151655	—	2	1	no	—
8	#19151655	—	2	1	no	—
9	C₂×C₄⋊#10623494	C₄	1	2	yes	complemented
10	C₂×C₂²⋊#10623494	C₂²	1	2	yes	—
11	C₂×#15667923	C₄	1	2	yes	complemented
12	#19151466	C₄	1	2	yes	complemented
13	#19151464	—	2	1	no	—
14	#19151461	—	2	1	no	—
15	#19151458	C₂²	1	2	yes	—
16	C₄×C₄⋊Dic₈₉	—	2	1	no	—
17	C₄×C₂²⋊Dic₈₉	—	2	1	no	—
18	#19151444	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	C₂×C₄⋊Dic₈₉	—	2	2	no	—
29	C₂×C₂²⋊Dic₈₉	—	2	2	no	—
30	C₂×C₄×Dic₈₉	—	2	2	no	—
31	C₄⋊#10623494	—	2	2	no	—
32	C₄⋊#10623494	—	2	2	no	—
33	C₂²⋊#10623494	—	2	2	no	—
34	C₂²⋊#10623494	—	2	2	no	—
35	#15667923	—	2	2	no	—
36	#15667923	—	2	2	no	—
37	#15667919	—	2	2	no	—
38	#15667919	—	2	2	no	—
39	#15667919	—	2	2	no	—
40	#15667919	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
44	#117×C₈₉	—	4	4	no	—
45	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
49	C₂×C₄²×C₈₉	—	2	2	no	—
50	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
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	#95×C₈₉	—	2	2	no	—
63	#95×C₈₉	C₂×C₄	1	4	yes	—
64	C₂²×Dic₈₉	—	2	4	no	—
65	C₂×#10623494	—	2	4	no	—
66	C₂×#10623494	—	4	4	no	—
67	C₄⋊Dic₈₉	—	4	4	no	—
68	C₂²⋊Dic₈₉	—	4	2	no	—
69	C₂²⋊Dic₈₉	—	4	2	no	—
70	C₄×Dic₈₉	—	4	4	no	—
71	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₈₉	—	2	2	no	—
73	C₂²×C₄×C₈₉	—	2	2	no	—
74	C₂²×C₄×C₈₉	—	2	4	no	—
75	C₂²×C₄×C₈₉	—	4	2	no	—
76	C₂²×C₄×C₈₉	—	4	2	no	—
77	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
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	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
95	C₄⋊C₄×C₈₉	—	4	4	no	—
96	C₄⋊C₄×C₈₉	—	4	4	no	—
97	C₄⋊C₄×C₈₉	—	4	4	no	—
98	C₂²⋊C₄×C₈₉	—	4	4	no	—
99	C₄²×C₈₉	—	4	4	no	—
100	C₄²×C₈₉	C₄²	1	1	yes	characteristic
101	C₄²×C₈₉	C₄²	1	1	yes	characteristic
102	C₄²×C₈₉	C₄²	1	1	yes	characteristic
103	C₄²×C₈₉	C₄²	1	1	yes	characteristic
104	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₈₉	C₄⋊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	C₂³×C₈₉	—	4	1	no	—
117	C₂³×C₈₉	—	4	1	no	—
118	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
122	C₂³×C₈₉	#137	1	2	yes	—
123	C₂×C₄×C₈₉	—	2	2	no	—
124	C₂×C₄×C₈₉	—	2	2	no	—
125	C₂×C₄×C₈₉	—	2	1	no	—
126	C₂×C₄×C₈₉	—	2	1	no	—
127	C₂×C₄×C₈₉	—	2	1	no	—
128	C₂×C₄×C₈₉	—	2	1	no	—
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	—	2	2	no	—
136	C₂×C₄×C₈₉	—	2	2	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	—	4	1	no	—
142	C₂×C₄×C₈₉	—	4	1	no	—
143	C₂×C₄×C₈₉	—	4	4	no	—
144	C₂×C₄×C₈₉	—	4	4	no	—
145	C₂×C₄×C₈₉	—	4	4	no	—
146	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
147	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
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	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×Dic₈₉	—	4	4	no	—
159	C₂×Dic₈₉	—	4	4	no	—
160	C₂×Dic₈₉	—	4	4	no	—
161	#10623494	—	4	4	no	—
162	C₂²×C₈₉	—	2	1	no	—
163	C₂²×C₈₉	—	2	1	no	—
164	C₂²×C₈₉	—	2	1	no	—
165	C₂²×C₈₉	—	2	1	no	—
166	C₂²×C₈₉	—	2	1	no	—
167	C₂²×C₈₉	—	2	1	no	—
168	C₂²×C₈₉	—	4	2	no	—
169	C₂²×C₈₉	—	4	2	no	—
170	C₂²×C₈₉	C₂×#95	1	1	yes	characteristic
171	C₂²×C₈₉	#417	1	2	yes	—
172	C₂²×C₈₉	#418	1	1	yes	characteristic
173	C₂²×C₈₉	#419	1	1	yes	characteristic
174	C₂²×C₈₉	#428	1	2	yes	—
175	C₄×C₈₉	—	2	1	no	—
176	C₄×C₈₉	—	2	1	no	—
177	C₄×C₈₉	—	2	1	no	—
178	C₄×C₈₉	—	2	1	no	—
179	C₄×C₈₉	—	2	1	no	—
180	C₄×C₈₉	—	2	1	no	—
181	C₄×C₈₉	—	2	1	no	—
182	C₄×C₈₉	—	2	1	no	—
183	C₄×C₈₉	—	2	1	no	—
184	C₄×C₈₉	—	2	1	no	—
185	C₄×C₈₉	—	8	4	no	—
186	C₄×C₈₉	H(3,ℤ/4)	1	2	yes	—
187	C₄×C₈₉	#410	1	2	yes	—
188	Dic₈₉	—	8	4	no	—
189	#7984	—	89	1	no	maximal, Sylow
190	C₂×C₈₉	—	2	2	no	—
191	C₂×C₈₉	—	2	1	no	—
192	C₂×C₈₉	—	2	1	no	—
193	C₂×C₈₉	—	2	2	no	—
194	C₂×C₈₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
195	C₂×C₈₉	#1736	1	1	yes	characteristic
196	C₂×C₈₉	#1740	1	1	yes	characteristic
197	C₂×#432	—	89	1	no	—
198	#2285	D₈₉	1	1	yes	characteristic
199	#2283	—	89	1	no	—
200	#1289	—	89	4	no	—
201	C₈₉	#7984	1	1	yes	characteristic, complemented, Sylow
202	C₂×#117	—	2	1	no	—
203	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
204	#432	—	178	1	no	—
205	#432	—	178	1	no	—
206	#432	—	178	1	no	—
207	#432	—	178	1	no	—
208	C₂×C₄⋊C₈	—	89	2	no	—
209	C₂×C₂²⋊C₈	—	89	2	no	—
210	C₂×#97	—	89	2	no	—
211	#384	—	2	1	no	—
212	#383	—	89	2	no	—
213	#382	—	178	1	no	—
214	#382	Dic₈₉	1	2	yes	complemented
215	#381	—	178	1	no	—
216	#380	—	2	1	no	—
217	#380	—	89	2	no	—
218	#380	C₂×D₈₉	1	2	yes	—
219	C₄×C₄⋊C₄	—	2	1	no	—
220	C₄×C₄⋊C₄	—	178	1	no	—
221	C₄×C₄⋊C₄	Dic₈₉	1	2	yes	complemented
222	C₄×C₂²⋊C₄	—	178	1	no	—
223	#376	—	89	2	no	—
224	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
225	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
226	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
227	C₂²×C₈	—	89	4	no	—
228	#117	—	4	4	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	178	2	no	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₂²⋊C₄	—	178	2	no	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	—	178	2	no	—
237	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
238	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
239	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
240	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
241	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
242	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
243	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
244	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
245	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
246	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
247	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
248	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
249	C₄⋊C₈	—	178	2	no	—
250	C₄⋊C₈	—	178	2	no	—
251	C₂²⋊C₈	—	178	2	no	—
252	C₂²⋊C₈	—	178	2	no	—
253	#97	—	178	2	no	—
254	#97	—	178	2	no	—
255	#95	—	2	2	no	—
256	#95	—	89	4	no	—
257	#95	—	178	2	no	—
258	#95	—	178	2	no	—
259	#95	—	178	2	no	—
260	#95	C₂×Dic₈₉	1	4	yes	—
261	C₂⁴	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	178	4	no	—
268	C₂²×C₄	#13083551	1	1	yes	characteristic
269	C₂²×C₄	#13083551	1	1	yes	characteristic
270	C₂²×C₄	#13083551	1	1	yes	characteristic
271	C₂²×C₄	#13083551	1	1	yes	characteristic
272	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
276	C₂²×C₄	#13083553	1	1	yes	characteristic
277	C₂²×C₄	#13083553	1	1	yes	characteristic
278	C₂²×C₄	#13083553	1	1	yes	characteristic
279	C₂²×C₄	#13083553	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
282	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
285	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
286	C₂×C₈	—	356	4	no	—
287	C₂×C₈	—	178	4	no	—
288	C₄⋊C₄	—	4	4	no	—
289	C₄⋊C₄	—	4	4	no	—
290	C₄⋊C₄	—	4	4	no	—
291	C₄⋊C₄	—	356	4	no	—
292	C₂²⋊C₄	—	4	4	no	—
293	C₂²⋊C₄	—	356	2	no	—
294	C₂²⋊C₄	—	356	2	no	—
295	C₄²	—	4	4	no	—
296	C₄²	—	356	4	no	—
297	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
298	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
299	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
300	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
301	C₄²	#13083551	1	1	yes	characteristic
302	C₄²	#13083551	1	1	yes	characteristic
303	C₄²	#13083551	1	1	yes	characteristic
304	C₄²	#13083551	1	1	yes	characteristic
305	C₄²	#13083553	1	1	yes	characteristic
306	C₄²	#13083553	1	1	yes	characteristic
307	C₄²	#13083553	1	1	yes	characteristic
308	C₄²	#13083553	1	1	yes	characteristic
309	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
310	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
311	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
312	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	C₂×#13083551	1	1	yes	characteristic
316	C₂³	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
317	C₂³	C₂×#13083553	1	1	yes	characteristic
318	C₂³	#15668038	1	2	yes	—
319	C₂³	#15668043	1	2	yes	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	356	4	no	—
344	C₂×C₄	—	356	4	no	—
345	C₂×C₄	—	356	4	no	—
346	C₂×C₄	#15667919	1	1	yes	characteristic
347	C₂×C₄	#15667919	1	1	yes	characteristic
348	C₂×C₄	#15667919	1	1	yes	characteristic
349	C₂×C₄	#15667919	1	1	yes	characteristic
350	C₂×C₄	#15667919	1	1	yes	characteristic
351	C₂×C₄	#15667919	1	1	yes	characteristic
352	C₂×C₄	#15667919	1	1	yes	characteristic
353	C₂×C₄	#15667919	1	1	yes	characteristic
354	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
355	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
356	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
358	C₈	—	356	4	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	C₂×#15667919	1	1	yes	characteristic
368	C₂²	#19151597	1	2	yes	—
369	C₂²	#19151603	1	1	yes	characteristic
370	C₂²	#19151607	1	1	yes	characteristic
371	C₂²	#19151638	1	2	yes	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	8	4	no	—
383	C₄	—	712	4	no	—
384	C₄	#19151354	1	2	yes	—
385	C₄	#19151571	1	2	yes	—
386	C₂	—	2	1	no	—
387	C₂	—	2	2	no	—
388	C₂	—	2	2	no	—
389	C₂	—	2	1	no	—
390	C₂	C₂×#19151354	1	1	yes	characteristic
391	C₂	#26019971	1	1	yes	characteristic
392	C₂	#26019984	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#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	#7984
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ #2285

Complements

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

N	H ≅ G/N	type
9. C₂×C₄⋊#10623494	C₄	semidirect
11. C₂×#15667923	C₄	semidirect
12. #19151466	C₄	semidirect
18. #19151444	C₄	semidirect
22. #382×C₈₉	C₄	semidirect
26. C₄×C₄⋊C₄×C₈₉	C₄	semidirect
201. C₈₉	#7984	semidirect
214. #382	Dic₈₉	semidirect
221. 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×#19151655	2
#26022650	2
#26018119	2
C₈₉×#2285	2
#7984	89