Subgroups — #36460319

Order 22784.

782 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	C₂²×#15667948	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151636	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151358	C₂	1	2	yes	maximal
4	#26019948	C₂	1	2	yes	maximal
5	C₂²×#97×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×#13083558	C₂²	1	2	yes	—
7	C₂×#15667971	C₂²	1	2	yes	—
8	C₂×#15667948	—	2	2	no	—
9	C₂×#15667948	—	2	2	no	—
10	C₂×#15667948	C₄	1	4	yes	complemented
11	#19151636	—	2	2	no	—
12	#19151636	—	2	2	no	—
13	C₂×#15667946	C₄	1	2	yes	complemented
14	C₂×#15667944	C₄	1	2	yes	complemented
15	#19151358	—	2	4	no	—
16	#19151352	—	2	4	no	—
17	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#97×C₈₉	—	2	2	no	—
21	C₂×#97×C₈₉	—	2	2	no	—
22	C₂×#97×C₈₉	C₄	1	4	yes	complemented
23	C₂×#13083558	—	2	2	no	—
24	C₂×#13083558	—	2	2	no	—
25	C₂×#13083558	—	2	2	no	—
26	C₂×#13083558	—	2	2	no	—
27	C₂×#13083558	—	2	2	no	—
28	C₂×#13083558	C₂×C₄	1	4	yes	—
29	C₂²×#10623494	—	2	2	no	—
30	#15667971	—	2	2	no	—
31	#15667971	—	2	2	no	—
32	#15667971	—	2	2	no	—
33	#15667971	—	2	2	no	—
34	C₂×C₄⋊Dic₈₉	C₂×C₄	1	4	yes	—
35	C₂×C₂²⋊Dic₈₉	—	2	2	no	—
36	C₂×C₄×Dic₈₉	—	2	2	no	—
37	#15667948	—	2	8	no	—
38	#15667946	—	2	4	no	—
39	#15667944	—	2	4	no	—
40	C₂³×C₄×C₈₉	—	2	1	no	—
41	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₈₉	—	2	1	no	—
43	C₂²×C₈×C₈₉	—	2	1	no	—
44	C₂²×C₈×C₈₉	—	2	1	no	—
45	C₂²×C₈×C₈₉	—	2	1	no	—
46	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
50	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₈₉	D₄	1	2	yes	—
52	C₂²×C₈×C₈₉	D₄	1	2	yes	—
53	C₂²×C₈×C₈₉	D₄	1	2	yes	—
54	C₂²×C₈×C₈₉	D₄	1	2	yes	—
55	C₂²×C₈×C₈₉	Q₈	1	2	yes	—
56	C₂²×C₈×C₈₉	Q₈	1	2	yes	—
57	C₂×C₄²×C₈₉	—	2	1	no	—
58	C₂×C₄²×C₈₉	—	2	1	no	—
59	C₂×C₄²×C₈₉	—	2	1	no	—
60	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₈₉	D₄	1	2	yes	—
62	C₂×C₄²×C₈₉	Q₈	1	2	yes	—
63	#97×C₈₉	—	2	8	no	—
64	C₂²×Dic₈₉	—	2	4	no	—
65	#13083558	—	2	4	no	—
66	#13083558	—	2	4	no	—
67	#13083558	—	4	2	no	—
68	#13083558	—	4	2	no	—
69	C₂×#10623494	—	2	4	no	—
70	C₂×#10623494	—	4	2	no	—
71	C₂×#10623494	—	4	2	no	—
72	C₄⋊Dic₈₉	—	2	4	no	—
73	C₄⋊Dic₈₉	—	2	4	no	—
74	C₂²⋊Dic₈₉	—	4	2	no	—
75	C₂²⋊Dic₈₉	—	4	2	no	—
76	C₄×Dic₈₉	—	4	2	no	—
77	C₄×Dic₈₉	—	4	2	no	—
78	C₂⁴×C₈₉	#41	1	1	yes	characteristic
79	C₂²×C₄×C₈₉	—	2	2	no	—
80	C₂²×C₄×C₈₉	—	2	2	no	—
81	C₂²×C₄×C₈₉	—	2	2	no	—
82	C₂²×C₄×C₈₉	—	4	4	no	—
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	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
97	C₂×C₈×C₈₉	—	2	2	no	—
98	C₂×C₈×C₈₉	—	2	2	no	—
99	C₂×C₈×C₈₉	—	2	2	no	—
100	C₂×C₈×C₈₉	—	2	2	no	—
101	C₂×C₈×C₈₉	—	2	2	no	—
102	C₂×C₈×C₈₉	—	2	2	no	—
103	C₂×C₈×C₈₉	C₄²	1	2	yes	—
104	C₂×C₈×C₈₉	C₄²	1	2	yes	—
105	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
106	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
107	C₂×C₈×C₈₉	C₂²⋊C₄	1	4	yes	—
108	C₂×C₈×C₈₉	C₂²⋊C₄	1	4	yes	—
109	C₂×C₈×C₈₉	C₄⋊C₄	1	4	yes	—
110	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
111	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
112	C₂×C₈×C₈₉	C₄⋊C₄	1	4	yes	—
113	C₂×C₈×C₈₉	C₄⋊C₄	1	4	yes	—
114	C₄²×C₈₉	—	2	2	no	—
115	C₄²×C₈₉	—	2	2	no	—
116	C₄²×C₈₉	—	2	2	no	—
117	C₄²×C₈₉	C₄⋊C₄	1	4	yes	—
118	C₂³×C₈₉	—	2	4	no	—
119	C₂³×C₈₉	#117	1	1	yes	characteristic
120	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
121	C₂³×C₈₉	C₄×Q₈	1	1	yes	characteristic
122	C₂³×C₈₉	#121	1	1	yes	characteristic
123	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
124	C₂³×C₈₉	#124	1	1	yes	characteristic
125	C₂³×C₈₉	#125	1	1	yes	characteristic
126	C₂×C₄×C₈₉	—	2	4	no	—
127	C₂×C₄×C₈₉	—	4	4	no	—
128	C₂×C₄×C₈₉	—	4	4	no	—
129	C₂×C₄×C₈₉	—	4	4	no	—
130	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
131	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
140	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
147	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
148	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
153	C₂×C₄×C₈₉	#125	1	1	yes	characteristic
154	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₄⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₄⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₄⋊Q₈	1	1	yes	characteristic
158	C₂×Dic₈₉	—	4	4	no	—
159	C₂×Dic₈₉	—	4	8	no	—
160	C₈×C₈₉	—	2	4	no	—
161	C₈×C₈₉	#95	1	4	yes	—
162	C₈×C₈₉	#95	1	4	yes	—
163	#10623494	—	4	4	no	—
164	C₂²×C₈₉	—	2	2	no	—
165	C₂²×C₈₉	—	2	2	no	—
166	C₂²×C₈₉	—	2	2	no	—
167	C₂²×C₈₉	—	2	2	no	—
168	C₂²×C₈₉	—	2	2	no	—
169	C₂²×C₈₉	—	2	2	no	—
170	C₂²×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
171	C₂²×C₈₉	#380	1	1	yes	characteristic
172	C₂²×C₈₉	#382	1	1	yes	characteristic
173	C₂²×C₈₉	#389	1	1	yes	characteristic
174	C₂²×C₈₉	#389	1	1	yes	characteristic
175	C₂²×C₈₉	#390	1	1	yes	characteristic
176	C₂²×C₈₉	#391	1	1	yes	characteristic
177	C₂²×C₈₉	#444	1	4	yes	—
178	C₄×C₈₉	—	4	4	no	—
179	C₄×C₈₉	C₂×#95	1	1	yes	characteristic
180	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
181	C₄×C₈₉	#380	1	1	yes	characteristic
182	C₄×C₈₉	#384	1	1	yes	characteristic
183	C₄×C₈₉	#389	1	1	yes	characteristic
184	C₄×C₈₉	#389	1	1	yes	characteristic
185	C₄×C₈₉	#390	1	1	yes	characteristic
186	C₄×C₈₉	#391	1	1	yes	characteristic
187	Dic₈₉	—	8	4	no	—
188	#10860	—	89	1	no	maximal, Sylow
189	C₂×C₈₉	—	2	1	no	—
190	C₂×C₈₉	—	2	1	no	—
191	C₂×C₈₉	—	2	1	no	—
192	C₂×C₈₉	—	2	1	no	—
193	C₂×C₈₉	C₄⋊#95	1	1	yes	characteristic
194	C₂×C₈₉	#1773	1	2	yes	—
195	C₂×C₈₉	#1946	1	2	yes	—
196	C₂×C₈₉	#1975	1	2	yes	—
197	C₂²×#108	—	89	1	no	—
198	C₂×#427	—	89	1	no	—
199	C₂²×#97	D₈₉	1	1	yes	characteristic
200	C₂×#339	—	89	2	no	—
201	#1729	—	89	2	no	—
202	C₈₉	#10860	1	1	yes	characteristic, complemented, Sylow
203	C₂²×M₁₆	—	89	2	no	—
204	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
205	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
206	C₂×#117	—	89	2	no	—
207	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
208	C₂×#108	—	89	4	no	—
209	C₂×#108	—	178	2	no	—
210	C₂×#108	—	178	2	no	—
211	#427	—	178	2	no	—
212	#427	—	178	2	no	—
213	C₂×#107	—	89	2	no	—
214	C₂×#106	—	89	2	no	—
215	C₂×#97	—	2	2	no	—
216	C₂×#97	—	2	2	no	—
217	C₂×#97	Dic₈₉	1	4	yes	complemented
218	#339	—	178	4	no	—
219	#336	—	178	4	no	—
220	C₂³×C₄	—	2	1	no	—
221	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
222	C₂×M₁₆	—	89	4	no	—
223	C₂×M₁₆	—	178	2	no	—
224	C₂×M₁₆	—	178	2	no	—
225	C₂×M₁₆	—	178	2	no	—
226	C₂×M₁₆	—	178	2	no	—
227	C₂×M₁₆	—	178	2	no	—
228	C₂²×C₈	—	2	1	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	178	2	no	—
233	C₂²×C₈	Dic₁₇₈	1	2	yes	—
234	C₂²×C₈	Dic₁₇₈	1	2	yes	—
235	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
236	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
237	C₂²×C₈	C₄×D₈₉	1	2	yes	—
238	C₂²×C₈	D₃₅₆	1	2	yes	—
239	C₂²×C₈	D₃₅₆	1	2	yes	—
240	C₂²×C₈	C₂×Dic₈₉	1	2	yes	—
241	C₂²×C₈	C₂×Dic₈₉	1	2	yes	—
242	C₂²×C₈	C₂²⋊D₈₉	1	2	yes	—
243	C₂²×C₈	C₂²⋊D₈₉	1	2	yes	—
244	#117	—	178	2	no	—
245	#117	—	178	2	no	—
246	#117	—	178	2	no	—
247	#117	—	178	2	no	—
248	C₂×C₄⋊C₄	—	89	4	no	—
249	C₂×C₂²⋊C₄	—	178	2	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	—	2	1	no	—
252	C₂×C₄²	—	2	1	no	—
253	C₂×C₄²	—	178	2	no	—
254	C₂×C₄²	Dic₁₇₈	1	2	yes	—
255	C₂×C₄²	D₃₅₆	1	2	yes	—
256	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
257	#108	—	178	8	no	—
258	#107	—	178	4	no	—
259	#106	—	178	4	no	—
260	#97	—	2	8	no	—
261	C₂⁴	#13083574	1	1	yes	characteristic
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	4	4	no	—
266	C₂²×C₄	—	178	4	no	—
267	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
269	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
275	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
276	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
277	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
278	C₂²×C₄	#13083574	1	1	yes	characteristic
279	C₂²×C₄	#13083574	1	1	yes	characteristic
280	C₂²×C₄	#13083574	1	1	yes	characteristic
281	M₁₆	—	356	2	no	—
282	M₁₆	—	356	2	no	—
283	M₁₆	—	178	4	no	—
284	M₁₆	—	178	4	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	356	2	no	—
292	C₂×C₈	—	356	2	no	—
293	C₂×C₈	—	178	4	no	—
294	C₂×C₈	C₄×Dic₈₉	1	2	yes	—
295	C₂×C₈	C₄×Dic₈₉	1	2	yes	—
296	C₂×C₈	#13083551	1	2	yes	—
297	C₂×C₈	#13083551	1	2	yes	—
298	C₂×C₈	#13083551	1	4	yes	—
299	C₂×C₈	C₂²⋊Dic₈₉	1	4	yes	—
300	C₂×C₈	#13083553	1	2	yes	—
301	C₂×C₈	#13083553	1	2	yes	—
302	C₂×C₈	#13083553	1	4	yes	—
303	C₂×C₈	C₄⋊Dic₈₉	1	4	yes	—
304	C₂×C₈	C₄⋊Dic₈₉	1	4	yes	—
305	C₄⋊C₄	—	178	4	no	—
306	C₄⋊C₄	—	178	4	no	—
307	C₂²⋊C₄	—	356	2	no	—
308	C₂²⋊C₄	—	356	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	356	2	no	—
313	C₄²	—	356	2	no	—
314	C₄²	C₄⋊Dic₈₉	1	4	yes	—
315	C₂³	—	2	4	no	—
316	C₂³	#15667971	1	1	yes	characteristic
317	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
318	C₂³	C₄×Dic₁₇₈	1	1	yes	characteristic
319	C₂³	#15667986	1	1	yes	characteristic
320	C₂³	#15667991	1	1	yes	characteristic
321	C₂³	#15668000	1	1	yes	characteristic
322	C₂³	#15668004	1	1	yes	characteristic
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	356	8	no	—
328	C₂×C₄	—	356	4	no	—
329	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
330	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
331	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
332	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
333	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
334	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
335	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
336	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
337	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
338	C₂×C₄	#15667971	1	1	yes	characteristic
339	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
340	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
341	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
342	C₂×C₄	C₄×Dic₁₇₈	1	1	yes	characteristic
343	C₂×C₄	C₄×Dic₁₇₈	1	1	yes	characteristic
344	C₂×C₄	C₄×Dic₁₇₈	1	1	yes	characteristic
345	C₂×C₄	#15667986	1	1	yes	characteristic
346	C₂×C₄	#15667986	1	1	yes	characteristic
347	C₂×C₄	#15667986	1	1	yes	characteristic
348	C₂×C₄	#15667991	1	1	yes	characteristic
349	C₂×C₄	#15667991	1	1	yes	characteristic
350	C₂×C₄	#15667991	1	1	yes	characteristic
351	C₂×C₄	#15668000	1	1	yes	characteristic
352	C₂×C₄	#15668004	1	1	yes	characteristic
353	C₂×C₄	#15668009	1	1	yes	characteristic
354	C₂×C₄	#15668012	1	1	yes	characteristic
355	C₂×C₄	#15668012	1	1	yes	characteristic
356	C₂×C₄	#15668012	1	1	yes	characteristic
357	C₈	—	2	4	no	—
358	C₈	—	356	4	no	—
359	C₈	#15667919	1	4	yes	—
360	C₈	#15667919	1	4	yes	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	C₄×C₄⋊Dic₈₉	1	1	yes	characteristic
368	C₂²	#19151458	1	1	yes	characteristic
369	C₂²	#19151464	1	1	yes	characteristic
370	C₂²	#19151496	1	1	yes	characteristic
371	C₂²	#19151496	1	1	yes	characteristic
372	C₂²	#19151500	1	1	yes	characteristic
373	C₂²	#19151504	1	1	yes	characteristic
374	C₂²	#19151721	1	4	yes	—
375	C₄	—	4	4	no	—
376	C₄	—	712	4	no	—
377	C₄	C₂×#15667919	1	1	yes	characteristic
378	C₄	C₄×C₄⋊Dic₈₉	1	1	yes	characteristic
379	C₄	#19151458	1	1	yes	characteristic
380	C₄	#19151468	1	1	yes	characteristic
381	C₄	#19151496	1	1	yes	characteristic
382	C₄	#19151496	1	1	yes	characteristic
383	C₄	#19151500	1	1	yes	characteristic
384	C₄	#19151504	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	#26018482	1	1	yes	characteristic
390	C₂	#26020136	1	2	yes	—
391	C₂	#26021005	1	2	yes	—
392	C₂	#26021145	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₈₉
Fitting	C₂²×#97×C₈₉	C₂
socle	C₂³×C₈₉	C₄×D₄
prime radical	C₂⁴×C₈₉	#41
cosocle	C₂³×C₄×C₈₉	C₂³
hypercenter	C₂²×#97	D₈₉
hypocenter	C₈₉	#10860
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
10. C₂×#15667948	C₄	semidirect
13. C₂×#15667946	C₄	semidirect
14. C₂×#15667944	C₄	semidirect
22. C₂×#97×C₈₉	C₄	semidirect
202. C₈₉	#10860	semidirect
217. C₂×#97	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#15667948	2
C₂×#19151636	2
C₂×#19151358	2
#26019948	2
C₂²×#97×C₈₉	2
#10860	89