Subgroups — C₂×#26018149 #36444653

Order 22784.

666 conjugacy classes of subgroups.

The subgroup lattice has 406 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	#26018149	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×#13083558	—	2	1	no	—
6	#19151651	—	2	1	no	—
7	#19151651	—	2	1	no	—
8	#19151651	C₄	1	2	yes	—
9	#19151651	C₂²	1	2	yes	—
10	#19151622	—	2	1	no	—
11	#19151622	—	2	1	no	—
12	#19151622	C₄	1	2	yes	—
13	#19151622	C₂²	1	2	yes	—
14	C₂×C₄⋊#10623494	—	2	1	no	—
15	C₂×C₄⋊#10623494	—	2	1	no	—
16	C₂×C₄⋊#10623494	C₄	1	2	yes	—
17	C₂×C₂²⋊#10623494	C₄	1	2	yes	—
18	C₂×C₄×#10623494	—	2	1	no	—
19	C₂³×C₈×C₈₉	—	2	1	no	—
20	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
22	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
23	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
24	C₂×C₄⋊C₈×C₈₉	C₄	1	2	yes	—
25	C₂×C₄⋊C₈×C₈₉	C₄	1	2	yes	—
26	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
27	C₂×#13083558	—	2	2	no	—
28	C₂×#13083558	—	2	2	no	—
29	C₂×#13083558	—	4	2	no	—
30	C₂×#13083558	—	4	2	no	—
31	C₂²×#10623494	—	2	2	no	—
32	C₂²×#10623494	—	2	2	no	—
33	C₄⋊#10623494	—	2	2	no	—
34	C₄⋊#10623494	—	2	2	no	—
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	C₂²⋊#10623494	—	2	2	no	—
40	C₂²⋊#10623494	C₂×C₄	1	4	yes	—
41	C₄×#10623494	—	2	2	no	—
42	C₄×#10623494	—	2	2	no	—
43	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₈₉	Q₈	1	1	yes	characteristic
46	C₂²×C₈×C₈₉	—	2	2	no	—
47	C₂²×C₈×C₈₉	—	2	2	no	—
48	C₂²×C₈×C₈₉	—	2	2	no	—
49	C₂²×C₈×C₈₉	—	4	2	no	—
50	C₂²×C₈×C₈₉	—	4	2	no	—
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	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₈₉	Q₈	1	1	yes	characteristic
62	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₈₉	—	2	2	no	—
64	C₄⋊C₈×C₈₉	—	2	2	no	—
65	C₄⋊C₈×C₈₉	—	2	2	no	—
66	C₄⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
67	#13083558	—	4	4	no	—
68	#13083558	—	4	2	no	—
69	#13083558	—	4	2	no	—
70	C₂×#10623494	—	2	4	no	—
71	C₂×#10623494	—	2	4	no	—
72	C₂×#10623494	—	4	4	no	—
73	C₂×#10623494	—	4	4	no	—
74	C₂⁴×C₈₉	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₈₉	—	2	4	no	—
76	C₂²×C₄×C₈₉	—	4	2	no	—
77	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
78	C₂²×C₄×C₈₉	C₄²	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	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	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
99	C₂×C₈×C₈₉	—	2	4	no	—
100	C₂×C₈×C₈₉	—	4	4	no	—
101	C₂×C₈×C₈₉	—	4	4	no	—
102	C₂×C₈×C₈₉	—	4	2	no	—
103	C₂×C₈×C₈₉	—	4	2	no	—
104	C₄²×C₈₉	C₄²	1	1	yes	characteristic
105	C₄²×C₈₉	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₈₉	C₂²⋊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	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	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
120	C₂³×C₈₉	—	2	2	no	—
121	C₂³×C₈₉	—	2	2	no	—
122	C₂³×C₈₉	#95	1	1	yes	characteristic
123	C₂³×C₈₉	#95	1	1	yes	characteristic
124	C₂³×C₈₉	#106	1	2	yes	—
125	C₂³×C₈₉	#107	1	2	yes	—
126	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
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	—	4	1	no	—
135	C₂×C₄×C₈₉	—	4	1	no	—
136	C₂×C₄×C₈₉	—	4	1	no	—
137	C₂×C₄×C₈₉	—	4	1	no	—
138	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
139	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
140	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
141	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
142	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
143	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
144	C₂×C₄×C₈₉	#102	1	2	yes	—
145	C₂×C₄×C₈₉	#102	1	2	yes	—
146	C₂×C₄×C₈₉	#102	1	2	yes	—
147	C₂×C₄×C₈₉	#102	1	2	yes	—
148	C₂×C₄×C₈₉	#103	1	2	yes	—
149	C₂×C₄×C₈₉	#103	1	2	yes	—
150	C₂×C₄×C₈₉	#103	1	2	yes	—
151	C₂×C₄×C₈₉	#103	1	2	yes	—
152	C₂×C₄×C₈₉	#106	1	2	yes	—
153	C₂×C₄×C₈₉	#107	1	2	yes	—
154	C₂×C₄×C₈₉	#108	1	4	yes	—
155	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
165	C₈×C₈₉	—	4	4	no	—
166	#10623494	—	4	4	no	—
167	#10623494	—	4	4	no	—
168	C₂²×C₈₉	—	2	4	no	—
169	C₂²×C₈₉	—	2	4	no	—
170	C₂²×C₈₉	—	2	1	no	—
171	C₂²×C₈₉	—	2	1	no	—
172	C₂²×C₈₉	—	2	1	no	—
173	C₂²×C₈₉	—	2	1	no	—
174	C₂²×C₈₉	#340	1	2	yes	—
175	C₂²×C₈₉	#340	1	2	yes	—
176	C₂²×C₈₉	#341	1	2	yes	—
177	C₂²×C₈₉	#344	1	2	yes	—
178	C₂²×C₈₉	C₂×#95	1	1	yes	characteristic
179	C₂²×C₈₉	C₂×#106	1	1	yes	characteristic
180	C₂²×C₈₉	C₂×#107	1	1	yes	characteristic
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	—	2	1	no	—
186	C₄×C₈₉	—	2	1	no	—
187	C₄×C₈₉	#340	1	2	yes	—
188	C₄×C₈₉	#340	1	2	yes	—
189	C₄×C₈₉	#341	1	2	yes	—
190	C₄×C₈₉	C₂×#102	1	1	yes	characteristic
191	C₄×C₈₉	C₂×#102	1	1	yes	characteristic
192	C₄×C₈₉	C₂×#103	1	1	yes	characteristic
193	C₄×C₈₉	C₂×#103	1	1	yes	characteristic
194	C₄×C₈₉	C₂×#108	1	2	yes	—
195	C₂×#1301	—	89	1	no	maximal, Sylow
196	C₂×C₈₉	—	2	2	no	—
197	C₂×C₈₉	—	2	1	no	—
198	C₂×C₈₉	—	2	1	no	—
199	C₂×C₈₉	#1301	1	4	yes	complemented
200	C₂×C₈₉	C₂×#340	1	1	yes	characteristic
201	C₂×C₈₉	C₂×#341	1	1	yes	characteristic
202	C₂×C₈₉	C₂×#344	1	1	yes	characteristic
203	C₂×#431	—	89	1	no	—
204	C₂×#423	—	89	1	no	—
205	C₂²×C₄⋊C₈	D₈₉	1	1	yes	characteristic
206	#1301	—	89	4	no	—
207	C₈₉	C₂×#1301	1	1	yes	characteristic, complemented, Sylow
208	C₂²×M₁₆	—	178	1	no	—
209	C₂³×C₈	—	2	1	no	—
210	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
211	#431	—	89	2	no	—
212	#431	—	89	2	no	—
213	#431	—	178	1	no	—
214	#431	—	178	1	no	—
215	#423	—	89	2	no	—
216	#423	—	89	2	no	—
217	#423	—	178	1	no	—
218	#423	—	178	1	no	—
219	C₂×C₄⋊C₈	—	2	1	no	—
220	C₂×C₄⋊C₈	—	2	1	no	—
221	C₂×C₄⋊C₈	—	2	1	no	—
222	C₂×C₄⋊C₈	—	89	2	no	—
223	C₂×C₄⋊C₈	—	178	1	no	—
224	C₂×C₄⋊C₈	—	178	1	no	—
225	C₂×C₄⋊C₈	Dic₈₉	1	2	yes	—
226	C₂×C₄⋊C₈	Dic₈₉	1	2	yes	—
227	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
228	C₂×C₂²⋊C₈	—	89	2	no	—
229	C₂×C₄×C₈	—	178	1	no	—
230	C₂³×C₄	Dic₁₇₈	1	1	yes	characteristic
231	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
232	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
233	C₂×M₁₆	—	356	2	no	—
234	C₂×M₁₆	—	356	2	no	—
235	C₂×M₁₆	—	178	2	no	—
236	C₂×M₁₆	—	178	2	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	4	2	no	—
241	C₂²×C₈	—	4	2	no	—
242	C₂²×C₈	—	178	2	no	—
243	C₂²×C₈	—	178	2	no	—
244	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
245	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
246	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
247	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
248	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
249	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
250	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
251	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
253	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
254	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
255	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	2	2	no	—
259	C₄⋊C₈	—	89	4	no	—
260	C₄⋊C₈	—	178	2	no	—
261	C₄⋊C₈	—	178	2	no	—
262	C₄⋊C₈	—	178	2	no	—
263	C₄⋊C₈	—	178	2	no	—
264	C₄⋊C₈	—	178	2	no	—
265	C₄⋊C₈	C₂×Dic₈₉	1	4	yes	—
266	C₂²⋊C₈	—	89	4	no	—
267	C₂²⋊C₈	—	178	2	no	—
268	C₄×C₈	—	178	2	no	—
269	C₄×C₈	—	178	2	no	—
270	C₂⁴	#13083553	1	1	yes	characteristic
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
274	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
275	C₂²×C₄	#13083551	1	1	yes	characteristic
276	C₂²×C₄	#13083551	1	1	yes	characteristic
277	C₂²×C₄	#13083551	1	1	yes	characteristic
278	C₂²×C₄	#13083551	1	1	yes	characteristic
279	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
281	C₂²×C₄	#13083553	1	1	yes	characteristic
282	C₂²×C₄	#13083553	1	1	yes	characteristic
283	C₂²×C₄	#13083553	1	1	yes	characteristic
284	C₂²×C₄	#13083553	1	1	yes	characteristic
285	C₂²×C₄	#13083553	1	1	yes	characteristic
286	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
287	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
288	C₂²×C₄	#13083559	1	2	yes	—
289	C₂²×C₄	#13083561	1	2	yes	—
290	C₂²×C₄	#13083562	1	2	yes	—
291	C₂²×C₄	#13083564	1	2	yes	—
292	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
294	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
295	M₁₆	—	356	2	no	—
296	M₁₆	—	356	2	no	—
297	M₁₆	—	356	4	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	4	2	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	4	4	no	—
302	C₂×C₈	—	4	4	no	—
303	C₂×C₈	—	356	4	no	—
304	C₂×C₈	—	356	4	no	—
305	C₂×C₈	—	178	4	no	—
306	C₂×C₈	—	178	4	no	—
307	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
308	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
309	C₄²	#13083551	1	1	yes	characteristic
310	C₄²	#13083551	1	1	yes	characteristic
311	C₄²	#13083551	1	1	yes	characteristic
312	C₄²	#13083551	1	1	yes	characteristic
313	C₄²	C₂²⋊Dic₈₉	1	1	yes	characteristic
314	C₄²	C₂²⋊Dic₈₉	1	1	yes	characteristic
315	C₄²	#13083553	1	1	yes	characteristic
316	C₄²	#13083553	1	1	yes	characteristic
317	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
318	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
319	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
320	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
321	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
322	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	#15667919	1	1	yes	characteristic
326	C₂³	#15667919	1	1	yes	characteristic
327	C₂³	#15667943	1	2	yes	—
328	C₂³	#15667945	1	2	yes	—
329	C₂³	C₂×#13083553	1	1	yes	characteristic
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	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	#15667919	1	1	yes	characteristic
342	C₂×C₄	#15667919	1	1	yes	characteristic
343	C₂×C₄	#15667919	1	1	yes	characteristic
344	C₂×C₄	#15667919	1	1	yes	characteristic
345	C₂×C₄	#15667919	1	1	yes	characteristic
346	C₂×C₄	#15667919	1	1	yes	characteristic
347	C₂×C₄	#15667932	1	2	yes	—
348	C₂×C₄	#15667932	1	2	yes	—
349	C₂×C₄	#15667933	1	2	yes	—
350	C₂×C₄	#15667933	1	2	yes	—
351	C₂×C₄	#15667935	1	2	yes	—
352	C₂×C₄	#15667935	1	2	yes	—
353	C₂×C₄	#15667936	1	2	yes	—
354	C₂×C₄	#15667936	1	2	yes	—
355	C₂×C₄	#15667943	1	2	yes	—
356	C₂×C₄	#15667945	1	2	yes	—
357	C₂×C₄	#15667948	1	4	yes	—
358	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
359	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
360	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
362	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
364	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
365	C₂×C₄	C₂×#13083561	1	1	yes	characteristic
366	C₂×C₄	C₂×#13083562	1	1	yes	characteristic
367	C₂×C₄	C₂×#13083564	1	1	yes	characteristic
368	C₈	—	4	4	no	—
369	C₈	—	356	4	no	—
370	C₈	—	356	4	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	#19151360	1	2	yes	—
378	C₂²	#19151360	1	2	yes	—
379	C₂²	#19151363	1	2	yes	—
380	C₂²	#19151370	1	2	yes	—
381	C₂²	C₂×#15667919	1	1	yes	characteristic
382	C₂²	C₂×#15667943	1	1	yes	characteristic
383	C₂²	C₂×#15667945	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	#19151360	1	2	yes	—
391	C₄	#19151360	1	2	yes	—
392	C₄	#19151363	1	2	yes	—
393	C₄	C₂×#15667932	1	1	yes	characteristic
394	C₄	C₂×#15667933	1	1	yes	characteristic
395	C₄	C₂×#15667935	1	1	yes	characteristic
396	C₄	C₂×#15667936	1	1	yes	characteristic
397	C₄	C₂×#15667948	1	2	yes	—
398	C₂	—	2	2	no	—
399	C₂	—	2	1	no	—
400	C₂	—	2	1	no	—
401	C₂	#26018149	1	4	yes	direct product factor
402	C₂	C₂×#19151360	1	1	yes	characteristic
403	C₂	C₂×#19151363	1	1	yes	characteristic
404	C₂	C₂×#19151370	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#13083551
commutator	C₂×C₄×C₈₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₂²×C₄⋊C₈×C₈₉	C₂
socle	C₂³×C₈₉	#95
prime radical	C₂⁴×C₈₉	C₄⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₂²×C₄⋊C₈	D₈₉
hypocenter	C₈₉	C₂×#1301
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #26018149	C₂	direct (N × H)
199. C₂×C₈₉	#1301	semidirect
207. C₈₉	C₂×#1301	semidirect
401. C₂	#26018149	direct (N × H)

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
#26018149	2
C₂²×C₄⋊C₈×C₈₉	2
C₂×#1301	89

Subgroups — C2×#26018149 #36444653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26018149 #36444653