Subgroups — #36523576

Order 22784.

730 conjugacy classes of subgroups.

The subgroup lattice has 380 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	C₂×#19151622	C₂	1	1	yes	maximal, characteristic
3	#26019028	C₂	1	4	yes	maximal, complemented
4	#26019026	C₂	1	4	yes	maximal, complemented
5	#26019010	C₂	1	4	yes	maximal, complemented
6	C₂×#423×C₈₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×#13083558	—	2	1	no	—
8	#19151651	C₄	1	2	yes	—
9	#19151651	C₄	1	2	yes	—
10	#19151651	C₂²	1	2	yes	—
11	#19151651	C₂²	1	2	yes	—
12	#19151622	—	2	1	no	—
13	#19151622	—	2	1	no	—
14	#19151622	C₂²	1	2	yes	—
15	#19151622	C₂²	1	2	yes	—
16	C₂×C₄⋊#10623494	—	2	1	no	—
17	C₂×C₄⋊#10623494	C₄	1	2	yes	—
18	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
19	C₂×C₂²⋊#10623494	C₄	1	2	yes	—
20	C₂×C₄×#10623494	C₂²	1	2	yes	—
21	#19151350	C₂²	1	16	yes	complemented
22	C₂²×M₁₆×C₈₉	—	2	1	no	—
23	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
24	#423×C₈₉	—	2	1	no	—
25	#423×C₈₉	—	2	1	no	—
26	#423×C₈₉	C₂²	1	2	yes	—
27	#423×C₈₉	C₂²	1	2	yes	—
28	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
29	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
30	C₂×#13083558	—	2	2	no	—
31	C₂×#13083558	—	2	2	no	—
32	C₂×#13083558	—	4	4	no	—
33	C₂²×#10623494	—	2	2	no	—
34	C₂²×#10623494	C₂×C₄	1	4	yes	—
35	C₄⋊#10623494	—	2	2	no	—
36	C₄⋊#10623494	—	2	2	no	—
37	C₄⋊#10623494	—	2	2	no	—
38	C₄⋊#10623494	C₂×C₄	1	4	yes	—
39	C₄⋊#10623494	C₂×C₄	1	4	yes	—
40	C₄⋊#10623494	C₂³	1	4	yes	—
41	C₂²⋊#10623494	C₂×C₄	1	4	yes	—
42	C₂²⋊#10623494	C₂×C₄	1	4	yes	—
43	C₄×#10623494	C₂×C₄	1	4	yes	—
44	C₄×#10623494	C₂³	1	4	yes	—
45	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₈₉	Q₈	1	1	yes	characteristic
48	C₂×M₁₆×C₈₉	—	2	2	no	—
49	C₂×M₁₆×C₈₉	—	2	2	no	—
50	C₂×M₁₆×C₈₉	—	4	4	no	—
51	C₂²×C₈×C₈₉	—	2	2	no	—
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	D₄	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	Q₈	1	1	yes	characteristic
59	C₂×C₄²×C₈₉	Q₈	1	1	yes	characteristic
60	C₂×C₄²×C₈₉	Q₈	1	1	yes	characteristic
61	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₈₉	—	2	2	no	—
65	C₄⋊C₈×C₈₉	—	2	2	no	—
66	C₄⋊C₈×C₈₉	—	2	2	no	—
67	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
68	#13083558	—	4	4	no	—
69	#13083558	—	4	4	no	—
70	C₂×#10623494	—	2	4	no	—
71	C₂×#10623494	—	4	4	no	—
72	C₂×#10623494	—	4	4	no	—
73	C₂×#10623494	C₂²×C₄	1	8	yes	—
74	C₂⁴×C₈₉	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₈₉	—	4	2	no	—
76	C₂²×C₄×C₈₉	—	4	2	no	—
77	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₈₉	D₈	1	4	yes	—
87	C₂²×C₄×C₈₉	Q₁₆	1	4	yes	—
88	C₂²×C₄×C₈₉	C₂²×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	C₂×D₄	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	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
97	M₁₆×C₈₉	—	4	4	no	—
98	M₁₆×C₈₉	—	4	4	no	—
99	C₂×C₈×C₈₉	—	2	4	no	—
100	C₂×C₈×C₈₉	—	4	4	no	—
101	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₈₉	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
114	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
115	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
116	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
117	C₂³×C₈₉	—	4	1	no	—
118	C₂³×C₈₉	—	4	1	no	—
119	C₂³×C₈₉	#107	1	4	yes	—
120	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₈₉	—	2	2	no	—
124	C₂×C₄×C₈₉	—	2	2	no	—
125	C₂×C₄×C₈₉	—	2	2	no	—
126	C₂×C₄×C₈₉	—	2	2	no	—
127	C₂×C₄×C₈₉	—	2	2	no	—
128	C₂×C₄×C₈₉	—	2	2	no	—
129	C₂×C₄×C₈₉	—	4	1	no	—
130	C₂×C₄×C₈₉	—	4	1	no	—
131	C₂×C₄×C₈₉	—	4	1	no	—
132	C₂×C₄×C₈₉	—	4	1	no	—
133	C₂×C₄×C₈₉	—	4	1	no	—
134	C₂×C₄×C₈₉	—	4	1	no	—
135	C₂×C₄×C₈₉	#107	1	4	yes	—
136	C₂×C₄×C₈₉	#107	1	4	yes	—
137	C₂×C₄×C₈₉	#107	1	4	yes	—
138	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
148	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
149	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
150	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
151	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
152	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
153	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
156	C₈×C₈₉	—	4	4	no	—
157	#10623494	—	2	8	no	—
158	#10623494	—	4	4	no	—
159	C₂²×C₈₉	—	2	1	no	—
160	C₂²×C₈₉	—	2	1	no	—
161	C₂²×C₈₉	—	2	1	no	—
162	C₂²×C₈₉	—	2	1	no	—
163	C₂²×C₈₉	—	2	1	no	—
164	C₂²×C₈₉	—	2	1	no	—
165	C₂²×C₈₉	—	4	4	no	—
166	C₂²×C₈₉	C₂×#107	1	2	yes	—
167	C₂²×C₈₉	C₂×#107	1	2	yes	—
168	C₂²×C₈₉	C₂×#107	1	2	yes	—
169	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
170	C₄×C₈₉	—	2	1	no	—
171	C₄×C₈₉	—	2	1	no	—
172	C₄×C₈₉	—	2	1	no	—
173	C₄×C₈₉	—	2	1	no	—
174	C₄×C₈₉	—	2	1	no	—
175	C₄×C₈₉	—	2	1	no	—
176	C₄×C₈₉	C₂×#107	1	2	yes	—
177	C₄×C₈₉	C₂×#107	1	2	yes	—
178	C₄×C₈₉	C₂×#107	1	2	yes	—
179	C₄×C₈₉	#430	1	2	yes	—
180	C₄×C₈₉	#568	1	2	yes	—
181	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
182	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
183	#17814	—	89	1	no	maximal, Sylow
184	C₂×C₈₉	—	2	2	no	—
185	C₂×C₈₉	—	2	2	no	—
186	C₂×C₈₉	—	2	2	no	—
187	C₂×C₈₉	#2905	1	1	yes	characteristic
188	C₂×C₈₉	C₂²×#107	1	1	yes	characteristic
189	C₂×C₈₉	C₂×#430	1	1	yes	characteristic
190	C₂×#431	—	89	1	no	—
191	C₂×#423	—	89	1	no	—
192	C₂×#423	D₈₉	1	1	yes	characteristic
193	#1571	—	89	4	no	—
194	#1571	—	89	4	no	—
195	#1567	—	89	4	no	—
196	C₈₉	#17814	1	1	yes	characteristic, complemented, Sylow
197	C₂²×M₁₆	—	2	1	no	—
198	C₂²×M₁₆	—	178	1	no	—
199	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
200	#431	—	89	2	no	—
201	#431	—	89	2	no	—
202	#431	—	89	2	no	—
203	#431	—	89	2	no	—
204	#423	—	2	1	no	—
205	#423	—	2	1	no	—
206	#423	—	89	2	no	—
207	#423	—	89	2	no	—
208	#423	—	178	1	no	—
209	#423	—	178	1	no	—
210	#423	C₂×D₈₉	1	2	yes	—
211	#423	C₂×D₈₉	1	2	yes	—
212	C₂×C₄⋊C₈	—	2	1	no	—
213	C₂×C₄⋊C₈	—	89	2	no	—
214	C₂×C₄⋊C₈	—	89	2	no	—
215	C₂×C₄⋊C₈	—	178	1	no	—
216	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
217	C₂×C₂²⋊C₈	—	89	2	no	—
218	C₂×C₄×C₈	—	89	2	no	—
219	#335	—	89	16	no	—
220	C₂³×C₄	Dic₁₇₈	1	1	yes	characteristic
221	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
222	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	4	4	no	—
226	C₂×M₁₆	—	356	4	no	—
227	C₂×M₁₆	—	178	2	no	—
228	C₂×M₁₆	—	178	2	no	—
229	C₂²×C₈	—	2	2	no	—
230	C₂²×C₈	—	89	4	no	—
231	C₂²×C₈	—	178	2	no	—
232	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
233	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
234	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
235	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
236	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
237	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
238	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
240	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
241	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
242	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	—	2	2	no	—
247	C₄⋊C₈	—	89	4	no	—
248	C₄⋊C₈	—	89	4	no	—
249	C₄⋊C₈	—	89	4	no	—
250	C₄⋊C₈	—	178	2	no	—
251	C₄⋊C₈	—	178	2	no	—
252	C₄⋊C₈	—	178	2	no	—
253	C₄⋊C₈	C₂²×D₈₉	1	4	yes	—
254	C₂²⋊C₈	—	89	4	no	—
255	C₂²⋊C₈	—	89	4	no	—
256	C₄×C₈	—	89	4	no	—
257	C₄×C₈	—	89	4	no	—
258	C₂⁴	#13083553	1	1	yes	characteristic
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	#13083553	1	1	yes	characteristic
262	C₂²×C₄	#13083553	1	1	yes	characteristic
263	C₂²×C₄	#13083553	1	1	yes	characteristic
264	C₂²×C₄	#13083553	1	1	yes	characteristic
265	C₂²×C₄	#13083553	1	1	yes	characteristic
266	C₂²×C₄	#13083553	1	1	yes	characteristic
267	C₂²×C₄	#13083553	1	1	yes	characteristic
268	C₂²×C₄	#13083553	1	1	yes	characteristic
269	C₂²×C₄	#13083553	1	1	yes	characteristic
270	C₂²×C₄	#13083559	1	4	yes	—
271	C₂²×C₄	#13083564	1	4	yes	—
272	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
279	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
280	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
281	M₁₆	—	4	4	no	—
282	M₁₆	—	4	4	no	—
283	M₁₆	—	356	4	no	—
284	M₁₆	—	356	4	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	4	4	no	—
287	C₂×C₈	—	89	8	no	—
288	C₂×C₈	—	356	4	no	—
289	C₂×C₈	—	356	4	no	—
290	C₂×C₈	—	178	4	no	—
291	C₄²	#13083553	1	1	yes	characteristic
292	C₄²	#13083553	1	1	yes	characteristic
293	C₄²	#13083553	1	1	yes	characteristic
294	C₄²	#13083553	1	1	yes	characteristic
295	C₄²	#13083553	1	1	yes	characteristic
296	C₄²	#13083553	1	1	yes	characteristic
297	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
298	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
299	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
300	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
301	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
302	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
303	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
304	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
305	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
306	C₄²	C₂³×D₈₉	1	1	yes	characteristic
307	C₂³	—	4	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	#15667945	1	4	yes	—
310	C₂³	C₂×#13083553	1	1	yes	characteristic
311	C₂³	C₂×#13083553	1	1	yes	characteristic
312	C₂³	C₂×#13083553	1	1	yes	characteristic
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	#15667945	1	4	yes	—
326	C₂×C₄	#15667945	1	4	yes	—
327	C₂×C₄	#15667945	1	4	yes	—
328	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
329	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
330	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
331	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
332	C₂×C₄	C₂×#13083553	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×#13083553	1	1	yes	characteristic
336	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
337	C₂×C₄	C₂×#13083559	1	2	yes	—
338	C₂×C₄	C₂×#13083559	1	2	yes	—
339	C₂×C₄	C₂×#13083559	1	2	yes	—
340	C₂×C₄	C₂×#13083564	1	2	yes	—
341	C₂×C₄	C₂×#13083564	1	2	yes	—
342	C₂×C₄	C₂×#13083564	1	2	yes	—
343	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
345	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
346	C₈	—	4	4	no	—
347	C₈	—	356	4	no	—
348	C₈	—	178	8	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	4	4	no	—
356	C₂²	C₂×#15667945	1	2	yes	—
357	C₂²	C₂×#15667945	1	2	yes	—
358	C₂²	C₂×#15667945	1	2	yes	—
359	C₂²	C₂²×#13083553	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	C₂×#15667945	1	2	yes	—
367	C₄	C₂×#15667945	1	2	yes	—
368	C₄	C₂×#15667945	1	2	yes	—
369	C₄	#19151646	1	2	yes	—
370	C₄	#19152364	1	2	yes	—
371	C₄	C₂²×#13083559	1	1	yes	characteristic
372	C₄	C₂²×#13083564	1	1	yes	characteristic
373	C₂	—	2	2	no	—
374	C₂	—	2	2	no	—
375	C₂	—	2	2	no	—
376	C₂	#26028815	1	1	yes	characteristic
377	C₂	C₂²×#15667945	1	1	yes	characteristic
378	C₂	C₂×#19151646	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×#423×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₈₉	C₄⋊C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×#423	D₈₉
hypocenter	C₈₉	#17814
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×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. #26019028	C₂	semidirect
4. #26019026	C₂	semidirect
5. #26019010	C₂	semidirect
21. #19151350	C₂²	semidirect
196. C₈₉	#17814	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
C₂×#19151622	2
#26019028	2
#26019026	2
#26019010	2
C₂×#423×C₈₉	2
#17814	89