Subgroups — #36523463

Order 22784.

712 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	#26028885	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151655	C₂	1	1	yes	maximal, characteristic
3	#26019019	C₂	1	4	yes	maximal, complemented
4	#26019015	C₂	1	4	yes	maximal, complemented
5	#26019004	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
7	#19151655	—	2	1	no	—
8	#19151655	—	2	1	no	—
9	#19151655	—	2	1	no	—
10	#19151655	C₂²	1	2	yes	—
11	#19151655	C₂²	1	2	yes	—
12	#19151655	C₂²	1	2	yes	—
13	#19151651	—	2	1	no	—
14	#19151651	C₂²	1	2	yes	—
15	#19151622	C₂²	1	2	yes	—
16	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
17	#19151562	—	2	1	no	—
18	C₂×C₂²⋊#10623494	—	2	1	no	—
19	C₄×#13083558	—	2	1	no	—
20	C₂×#15667923	—	2	1	no	—
21	#19151351	C₂²	1	8	yes	complemented
22	#19151349	C₂²	1	8	yes	complemented
23	C₂²×M₁₆×C₈₉	C₄	1	2	yes	—
24	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
25	C₄×M₁₆×C₈₉	C₄	1	1	yes	characteristic
26	C₄×M₁₆×C₈₉	C₄	1	2	yes	—
27	C₄×M₁₆×C₈₉	C₄	1	1	yes	characteristic
28	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
29	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
30	C₂×#97×C₈₉	C₄	1	2	yes	—
31	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
32	C₂×#13083558	—	2	2	no	—
33	C₂²×#10623494	—	2	2	no	—
34	C₄⋊#10623494	—	2	2	no	—
35	C₄⋊#10623494	—	2	2	no	—
36	C₄⋊#10623494	C₂³	1	4	yes	—
37	C₄⋊#10623494	C₂³	1	4	yes	—
38	C₂²⋊#10623494	—	2	2	no	—
39	C₂²⋊#10623494	—	2	2	no	—
40	C₂²⋊#10623494	—	2	2	no	—
41	C₂²⋊#10623494	—	2	2	no	—
42	#15667923	—	2	2	no	—
43	#15667923	—	2	2	no	—
44	#15667923	—	2	2	no	—
45	C₄×#10623494	—	2	2	no	—
46	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₈₉	Q₈	1	1	yes	characteristic
49	C₂×M₁₆×C₈₉	—	2	8	no	—
50	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
51	C₂×M₁₆×C₈₉	C₂×C₄	1	4	yes	—
52	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
53	C₂²×C₈×C₈₉	C₂×C₄	1	4	yes	—
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	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	Q₈	1	1	yes	characteristic
63	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
66	#97×C₈₉	C₂×C₄	1	2	yes	—
67	#97×C₈₉	C₂×C₄	1	4	yes	—
68	#97×C₈₉	C₂×C₄	1	2	yes	—
69	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
70	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₈₉	C₂³	1	4	yes	—
72	#13083558	—	4	4	no	—
73	C₂×#10623494	—	2	4	no	—
74	C₂×#10623494	—	2	4	no	—
75	C₂×#10623494	—	4	4	no	—
76	C₂⁴×C₈₉	C₄⋊C₄	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	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	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×D₄	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	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
98	M₁₆×C₈₉	—	2	4	no	—
99	M₁₆×C₈₉	—	2	8	no	—
100	M₁₆×C₈₉	M₁₆	1	8	yes	complemented
101	C₂×C₈×C₈₉	—	2	8	no	—
102	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
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	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
117	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
118	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
119	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
120	C₂³×C₈₉	—	2	2	no	—
121	C₂³×C₈₉	—	2	2	no	—
122	C₂³×C₈₉	—	4	1	no	—
123	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
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	—	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	—	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	—	4	1	no	—
142	C₂×C₄×C₈₉	—	4	1	no	—
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×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂×M₁₆	1	4	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	—	2	4	no	—
157	C₈×C₈₉	C₂×M₁₆	1	8	yes	—
158	#10623494	—	4	4	no	—
159	#10623494	—	4	4	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	—	2	1	no	—
166	C₂²×C₈₉	—	2	1	no	—
167	C₂²×C₈₉	—	4	4	no	—
168	C₂²×C₈₉	#423	1	2	yes	—
169	C₂²×C₈₉	#430	1	2	yes	—
170	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
177	C₄×C₈₉	—	2	1	no	—
178	C₄×C₈₉	—	2	1	no	—
179	C₄×C₈₉	—	2	1	no	—
180	C₄×C₈₉	#423	1	2	yes	—
181	C₄×C₈₉	C₂²×M₁₆	1	2	yes	—
182	C₄×C₈₉	#575	1	2	yes	—
183	#17797	—	89	1	no	maximal, Sylow
184	C₂×C₈₉	—	2	2	no	—
185	C₂×C₈₉	—	2	2	no	—
186	C₂×C₈₉	—	4	1	no	—
187	C₂×C₈₉	C₂×#423	1	1	yes	characteristic
188	C₂×C₈₉	#2911	1	1	yes	characteristic
189	C₂×C₈₉	C₂×#430	1	1	yes	characteristic
190	#2920	—	89	1	no	—
191	C₂×#432	—	89	1	no	—
192	C₂×C₄×M₁₆	D₈₉	1	1	yes	characteristic
193	#1569	—	89	4	no	—
194	#1568	—	89	4	no	—
195	#1565	—	89	4	no	—
196	C₈₉	#17797	1	1	yes	characteristic, complemented, Sylow
197	C₂²×M₁₆	Dic₈₉	1	2	yes	—
198	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
199	#432	—	89	2	no	—
200	#432	—	89	2	no	—
201	#432	—	89	2	no	—
202	#432	—	178	1	no	—
203	#432	—	178	1	no	—
204	#432	—	178	1	no	—
205	#431	—	89	2	no	—
206	#431	—	178	1	no	—
207	#423	—	89	2	no	—
208	C₂×C₄⋊C₈	—	89	2	no	—
209	#407	—	178	1	no	—
210	C₂×C₂²⋊C₈	—	178	1	no	—
211	C₄×M₁₆	—	178	1	no	—
212	C₄×M₁₆	Dic₈₉	1	1	yes	characteristic
213	C₄×M₁₆	Dic₈₉	1	2	yes	—
214	C₄×M₁₆	Dic₈₉	1	1	yes	characteristic
215	C₄×M₁₆	C₂×D₈₉	1	2	yes	—
216	C₄×M₁₆	C₂×D₈₉	1	2	yes	—
217	C₂×#97	—	178	1	no	—
218	C₂×#97	Dic₈₉	1	2	yes	—
219	C₂×C₄×C₈	C₂×D₈₉	1	2	yes	—
220	#335	—	89	8	no	—
221	#334	—	89	8	no	—
222	C₂³×C₄	Dic₁₇₈	1	1	yes	characteristic
223	C₂³×C₄	D₃₅₆	1	1	yes	characteristic
224	C₂³×C₄	C₂×Dic₈₉	1	1	yes	characteristic
225	C₂×M₁₆	—	2	8	no	—
226	C₂×M₁₆	—	178	2	no	—
227	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
228	C₂×M₁₆	C₂×Dic₈₉	1	4	yes	—
229	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
230	C₂²×C₈	—	178	2	no	—
231	C₂²×C₈	C₂×Dic₈₉	1	4	yes	—
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	D₃₅₆	1	1	yes	characteristic
236	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
237	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
238	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
239	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
240	C₂×C₄²	C₂×Dic₈₉	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	—	89	4	no	—
245	C₄⋊C₈	—	89	4	no	—
246	C₄⋊C₈	—	178	2	no	—
247	C₄⋊C₈	—	178	2	no	—
248	C₂²⋊C₈	—	178	2	no	—
249	C₂²⋊C₈	—	178	2	no	—
250	C₂²⋊C₈	—	178	2	no	—
251	C₂²⋊C₈	—	178	2	no	—
252	#97	—	178	2	no	—
253	#97	—	178	2	no	—
254	#97	—	178	2	no	—
255	#97	C₂×Dic₈₉	1	2	yes	—
256	#97	C₂×Dic₈₉	1	4	yes	—
257	#97	C₂×Dic₈₉	1	2	yes	—
258	C₄×C₈	—	178	2	no	—
259	C₄×C₈	C₂×Dic₈₉	1	2	yes	—
260	C₄×C₈	C₂×Dic₈₉	1	2	yes	—
261	C₄×C₈	C₂²×D₈₉	1	4	yes	—
262	C₂⁴	C₄⋊Dic₈₉	1	1	yes	characteristic
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
272	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
273	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
274	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
276	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
277	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
281	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
282	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
283	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
284	M₁₆	—	2	4	no	—
285	M₁₆	—	2	8	no	—
286	M₁₆	—	356	4	no	—
287	M₁₆	#13083558	1	8	yes	complemented
288	C₂×C₈	—	2	8	no	—
289	C₂×C₈	—	356	4	no	—
290	C₂×C₈	—	178	4	no	—
291	C₂×C₈	—	178	4	no	—
292	C₂×C₈	C₂²×Dic₈₉	1	4	yes	—
293	C₂×C₈	C₂²×Dic₈₉	1	4	yes	—
294	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
295	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
296	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
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	C₂²×Dic₈₉	1	1	yes	characteristic
301	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
302	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
303	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
304	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
305	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
306	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
307	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
308	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
309	C₄²	C₂³×D₈₉	1	1	yes	characteristic
310	C₂³	—	2	2	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	4	1	no	—
313	C₂³	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
314	C₂³	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
315	C₂³	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
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	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄⋊Dic₈₉	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	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
339	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
342	C₂×C₄	C₂×#13083558	1	4	yes	—
343	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
345	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
346	C₈	—	2	4	no	—
347	C₈	—	356	4	no	—
348	C₈	—	356	4	no	—
349	C₈	C₂×#13083558	1	8	yes	—
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	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	4	4	no	—
358	C₂²	#19151622	1	2	yes	—
359	C₂²	#19151647	1	2	yes	—
360	C₂²	C₂²×C₄⋊Dic₈₉	1	1	yes	characteristic
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	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	#19151622	1	2	yes	—
371	C₄	C₂²×#13083558	1	2	yes	—
372	C₄	#19152398	1	2	yes	—
373	C₂	—	2	2	no	—
374	C₂	—	2	2	no	—
375	C₂	—	4	1	no	—
376	C₂	C₂×#19151622	1	1	yes	characteristic
377	C₂	#26028842	1	1	yes	characteristic
378	C₂	C₂×#19151647	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×C₄×M₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₈₉	C₄⋊C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₈₉
hypocenter	C₈₉	#17797
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #26019019	C₂	semidirect
4. #26019015	C₂	semidirect
5. #26019004	C₂	semidirect
21. #19151351	C₂²	semidirect
22. #19151349	C₂²	semidirect
100. M₁₆×C₈₉	M₁₆	semidirect
196. C₈₉	#17797	semidirect
287. M₁₆	#13083558	semidirect

Maximal subgroups

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

subgroup	index
#26028885	2
C₂×#19151655	2
#26019019	2
#26019015	2
#26019004	2
C₂×C₄×M₁₆×C₈₉	2
#17797	89