Subgroups — C₂×#26018102 #36444108

Order 22784.

722 conjugacy classes of subgroups.

The subgroup lattice has 392 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×C₄×#13083558	C₂	1	1	yes	maximal, characteristic
3	#26018102	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×#13083558	C₄	1	2	yes	—
6	#19151651	—	2	1	no	—
7	#19151651	—	2	1	no	—
8	#19151651	C₄	1	2	yes	—
9	#19151651	C₂²	1	2	yes	—
10	C₂×C₄⋊#10623494	—	2	1	no	—
11	C₂×C₂²⋊#10623494	C₄	1	2	yes	—
12	C₄×#13083558	—	2	1	no	—
13	C₄×#13083558	—	2	1	no	—
14	C₄×#13083558	C₄	1	2	yes	—
15	C₄×#13083558	C₂²	1	2	yes	—
16	C₂×#15667923	—	2	1	no	—
17	C₂×C₄×#10623494	—	2	1	no	—
18	C₂×C₄×#10623494	—	2	1	no	—
19	C₂³×C₈×C₈₉	C₄	1	2	yes	—
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	—	2	1	no	—
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	4	no	—
29	C₂×#13083558	C₈	1	8	yes	complemented
30	C₂×#13083558	C₂×C₄	1	4	yes	—
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	C₂²⋊#10623494	—	2	2	no	—
36	C₂²⋊#10623494	C₂×C₄	1	4	yes	—
37	#15667923	—	2	2	no	—
38	#15667923	—	2	2	no	—
39	C₄×#10623494	—	2	2	no	—
40	C₄×#10623494	—	2	2	no	—
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	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₈×C₈₉	—	2	2	no	—
47	C₂²×C₈×C₈₉	—	2	2	no	—
48	C₂²×C₈×C₈₉	—	4	4	no	—
49	C₂²×C₈×C₈₉	C₂×C₄	1	4	yes	—
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	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₈₉	D₄	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	D₄	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	C₄⋊C₈×C₈₉	—	2	2	no	—
63	C₄⋊C₈×C₈₉	—	2	2	no	—
64	C₄⋊C₈×C₈₉	—	2	2	no	—
65	C₄⋊C₈×C₈₉	—	2	2	no	—
66	#13083558	—	2	8	no	—
67	#13083558	—	2	4	no	—
68	#13083558	C₂×C₈	1	8	yes	complemented
69	C₂×#10623494	—	2	8	no	—
70	C₂×#10623494	—	2	4	no	—
71	C₂×#10623494	—	2	4	no	—
72	C₂×#10623494	—	4	4	no	—
73	C₂⁴×C₈₉	C₄²	1	1	yes	characteristic
74	C₂²×C₄×C₈₉	—	2	2	no	—
75	C₂²×C₄×C₈₉	—	2	2	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	C₄²	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	C₂²⋊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	C₂×C₈	1	4	yes	—
93	C₂²×C₄×C₈₉	M₁₆	1	4	yes	—
94	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₈₉	—	2	4	no	—
98	C₂×C₈×C₈₉	—	4	4	no	—
99	C₂×C₈×C₈₉	—	4	4	no	—
100	C₂×C₈×C₈₉	—	4	4	no	—
101	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₈₉	C₂²⋊C₄	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	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	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	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	C₂³×C₈₉	—	2	2	no	—
118	C₂³×C₈₉	—	2	2	no	—
119	C₂³×C₈₉	#95	1	1	yes	characteristic
120	C₂³×C₈₉	#95	1	1	yes	characteristic
121	C₂³×C₈₉	C₄×C₈	1	2	yes	—
122	C₂³×C₈₉	#97	1	2	yes	—
123	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
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	—	2	1	no	—
130	C₂×C₄×C₈₉	—	2	1	no	—
131	C₂×C₄×C₈₉	—	2	1	no	—
132	C₂×C₄×C₈₉	—	2	1	no	—
133	C₂×C₄×C₈₉	—	4	1	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	#95	1	1	yes	characteristic
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	C₄×C₈	1	2	yes	—
144	C₂×C₄×C₈₉	#97	1	2	yes	—
145	C₂×C₄×C₈₉	C₂²⋊C₈	1	4	yes	—
146	C₂×C₄×C₈₉	C₂²⋊C₈	1	4	yes	—
147	C₂×C₄×C₈₉	#100	1	2	yes	—
148	C₂×C₄×C₈₉	#101	1	2	yes	—
149	C₂×C₄×C₈₉	C₄⋊C₈	1	4	yes	—
150	C₂×C₄×C₈₉	C₄⋊C₈	1	4	yes	—
151	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
158	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
159	C₈×C₈₉	—	4	4	no	—
160	#10623494	—	2	8	no	—
161	#10623494	—	4	4	no	—
162	C₂²×C₈₉	—	2	4	no	—
163	C₂²×C₈₉	—	2	4	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	#336	1	2	yes	—
169	C₂²×C₈₉	#336	1	2	yes	—
170	C₂²×C₈₉	#343	1	2	yes	—
171	C₂²×C₈₉	#344	1	2	yes	—
172	C₂²×C₈₉	C₂×#95	1	1	yes	characteristic
173	C₂²×C₈₉	C₂×C₄×C₈	1	1	yes	characteristic
174	C₂²×C₈₉	C₂×#97	1	1	yes	characteristic
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	#336	1	2	yes	—
182	C₄×C₈₉	#336	1	2	yes	—
183	C₄×C₈₉	#343	1	2	yes	—
184	C₄×C₈₉	C₂×C₂²⋊C₈	1	2	yes	—
185	C₄×C₈₉	C₂×#100	1	1	yes	characteristic
186	C₄×C₈₉	C₂×#101	1	1	yes	characteristic
187	C₄×C₈₉	C₂×C₄⋊C₈	1	2	yes	—
188	C₂×#1283	—	89	1	no	maximal, Sylow
189	C₂×C₈₉	—	2	2	no	—
190	C₂×C₈₉	—	2	1	no	—
191	C₂×C₈₉	—	2	1	no	—
192	C₂×C₈₉	#1283	1	4	yes	complemented
193	C₂×C₈₉	C₂×#336	1	1	yes	characteristic
194	C₂×C₈₉	C₂×#343	1	1	yes	characteristic
195	C₂×C₈₉	C₂×#344	1	1	yes	characteristic
196	C₂×#431	—	89	1	no	—
197	C₂²×C₄⋊C₈	D₈₉	1	1	yes	characteristic
198	C₂×C₄×M₁₆	—	89	1	no	—
199	#1283	—	89	4	no	—
200	C₈₉	C₂×#1283	1	1	yes	characteristic, complemented, Sylow
201	C₂²×M₁₆	—	89	2	no	—
202	C₂³×C₈	Dic₈₉	1	2	yes	—
203	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
204	#431	—	89	2	no	—
205	#431	—	89	2	no	—
206	#431	—	178	1	no	—
207	#431	—	178	1	no	—
208	C₂×C₄⋊C₈	—	2	1	no	—
209	C₂×C₄⋊C₈	—	2	1	no	—
210	C₂×C₄⋊C₈	—	2	1	no	—
211	C₂×C₄⋊C₈	—	2	1	no	—
212	C₂×C₄⋊C₈	—	178	1	no	—
213	C₂×C₄⋊C₈	Dic₈₉	1	2	yes	—
214	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
215	C₂×C₂²⋊C₈	—	89	2	no	—
216	C₄×M₁₆	—	89	2	no	—
217	C₄×M₁₆	—	89	2	no	—
218	C₄×M₁₆	—	178	1	no	—
219	C₄×M₁₆	—	178	1	no	—
220	C₂×#97	—	178	1	no	—
221	C₂×C₄×C₈	—	178	1	no	—
222	C₂×C₄×C₈	—	178	1	no	—
223	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
224	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
225	C₂³×C₄	C₂×Dic₈₉	1	1	yes	characteristic
226	C₂×M₁₆	—	89	8	no	—
227	C₂×M₁₆	—	89	4	no	—
228	C₂×M₁₆	—	178	2	no	—
229	C₂×M₁₆	—	178	4	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	4	4	no	—
233	C₂²×C₈	—	178	2	no	—
234	C₂²×C₈	—	178	2	no	—
235	C₂²×C₈	C₂×Dic₈₉	1	4	yes	—
236	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
237	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
238	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
239	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
240	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
241	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
242	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
243	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
244	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
245	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
246	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
247	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	—	2	2	no	—
252	C₄⋊C₈	—	178	2	no	—
253	C₄⋊C₈	—	178	2	no	—
254	C₂²⋊C₈	—	89	4	no	—
255	C₂²⋊C₈	—	178	2	no	—
256	#97	—	178	2	no	—
257	#97	—	178	2	no	—
258	C₄×C₈	—	178	2	no	—
259	C₄×C₈	—	178	2	no	—
260	C₄×C₈	—	178	2	no	—
261	C₄×C₈	—	178	2	no	—
262	C₂⁴	C₄×Dic₈₉	1	1	yes	characteristic
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	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	#13083551	1	1	yes	characteristic
270	C₂²×C₄	#13083551	1	1	yes	characteristic
271	C₂²×C₄	#13083551	1	1	yes	characteristic
272	C₂²×C₄	#13083551	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	#13083553	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	C₄⋊Dic₈₉	1	1	yes	characteristic
280	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
281	C₂²×C₄	C₈×D₈₉	1	4	yes	—
282	C₂²×C₄	#13083557	1	4	yes	—
283	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
285	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
286	M₁₆	—	89	8	no	—
287	M₁₆	—	178	4	no	—
288	M₁₆	—	178	8	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	4	4	no	—
291	C₂×C₈	—	4	4	no	—
292	C₂×C₈	—	4	4	no	—
293	C₂×C₈	—	356	4	no	—
294	C₂×C₈	—	178	4	no	—
295	C₂×C₈	—	178	8	no	—
296	C₂×C₈	—	178	4	no	—
297	C₄²	#13083551	1	1	yes	characteristic
298	C₄²	#13083551	1	1	yes	characteristic
299	C₄²	#13083551	1	1	yes	characteristic
300	C₄²	#13083551	1	1	yes	characteristic
301	C₄²	C₂²⋊Dic₈₉	1	1	yes	characteristic
302	C₄²	C₂²⋊Dic₈₉	1	1	yes	characteristic
303	C₄²	#13083553	1	1	yes	characteristic
304	C₄²	#13083553	1	1	yes	characteristic
305	C₄²	#13083553	1	1	yes	characteristic
306	C₄²	#13083553	1	1	yes	characteristic
307	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
308	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
309	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
310	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
311	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
312	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	#15667919	1	1	yes	characteristic
316	C₂³	#15667919	1	1	yes	characteristic
317	C₂³	C₈×Dic₈₉	1	2	yes	—
318	C₂³	#15667922	1	2	yes	—
319	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
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	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	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	#15667919	1	1	yes	characteristic
334	C₂×C₄	#15667919	1	1	yes	characteristic
335	C₂×C₄	#15667919	1	1	yes	characteristic
336	C₂×C₄	#15667919	1	1	yes	characteristic
337	C₂×C₄	#15667919	1	1	yes	characteristic
338	C₂×C₄	#15667919	1	1	yes	characteristic
339	C₂×C₄	C₈×Dic₈₉	1	2	yes	—
340	C₂×C₄	#15667922	1	2	yes	—
341	C₂×C₄	#15667924	1	4	yes	—
342	C₂×C₄	#15667924	1	4	yes	—
343	C₂×C₄	#15667929	1	2	yes	—
344	C₂×C₄	#15667931	1	2	yes	—
345	C₂×C₄	#15667941	1	4	yes	—
346	C₂×C₄	#15667941	1	4	yes	—
347	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
348	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
349	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
350	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
351	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
353	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
354	C₂×C₄	C₂×#13083557	1	2	yes	—
355	C₈	—	4	4	no	—
356	C₈	—	356	4	no	—
357	C₈	—	178	8	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	#19151352	1	2	yes	—
365	C₂²	#19151352	1	2	yes	—
366	C₂²	#19151367	1	2	yes	—
367	C₂²	#19151369	1	2	yes	—
368	C₂²	C₂×#15667919	1	1	yes	characteristic
369	C₂²	C₂×C₈×Dic₈₉	1	1	yes	characteristic
370	C₂²	C₂×#15667922	1	1	yes	characteristic
371	C₄	—	2	1	no	—
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	#19151352	1	2	yes	—
378	C₄	#19151352	1	2	yes	—
379	C₄	#19151367	1	2	yes	—
380	C₄	C₂×#15667924	1	2	yes	—
381	C₄	C₂×#15667929	1	1	yes	characteristic
382	C₄	C₂×#15667931	1	1	yes	characteristic
383	C₄	C₂×#15667941	1	2	yes	—
384	C₂	—	2	1	no	—
385	C₂	—	2	1	no	—
386	C₂	—	2	2	no	—
387	C₂	#26018102	1	4	yes	direct product factor
388	C₂	C₂×#19151352	1	1	yes	characteristic
389	C₂	C₂×#19151367	1	1	yes	characteristic
390	C₂	C₂×#19151369	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₈₉
commutator	C₂²×C₈₉	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₂²×C₄⋊C₈×C₈₉	C₂
socle	C₂³×C₈₉	#95
prime radical	C₂⁴×C₈₉	C₄²
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₂²×C₄⋊C₈	D₈₉
hypocenter	C₈₉	C₂×#1283
LCS	G ▷ C₂²×C₈₉ ▷ C₂×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. #26018102	C₂	direct (N × H)
29. C₂×#13083558	C₈	semidirect
68. #13083558	C₂×C₈	semidirect
192. C₂×C₈₉	#1283	semidirect
200. C₈₉	C₂×#1283	semidirect
387. C₂	#26018102	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×C₄×#13083558	2
#26018102	2
C₂²×C₄⋊C₈×C₈₉	2
C₂×#1283	89

Subgroups — C2×#26018102 #36444108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26018102 #36444108