Subgroups — #36460366

Order 22784.

746 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151636	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151553	C₂	1	1	yes	maximal, characteristic
3	#26019985	C₂	1	2	yes	maximal
4	#26019961	C₂	1	2	yes	maximal
5	C₂×#427×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×#13083558	C₂²	1	1	yes	characteristic
7	C₂×#15667971	C₂²	1	2	yes	—
8	C₂×#15667971	C₂²	1	1	yes	characteristic
9	#19151636	—	2	2	no	—
10	#19151636	C₄	1	4	yes	complemented
11	C₂×#15667946	—	2	1	no	—
12	C₂×#15667944	—	2	1	no	—
13	#19151553	—	2	2	no	—
14	#19151553	C₄	1	4	yes	complemented
15	C₂×#15667922	—	2	1	no	—
16	C₂×C₈×Dic₈₉	—	2	1	no	—
17	#19151365	—	2	4	no	—
18	#19151357	—	2	4	no	—
19	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#117×C₈₉	C₂²	1	2	yes	—
21	#427×C₈₉	—	2	1	no	—
22	#427×C₈₉	—	2	1	no	—
23	#427×C₈₉	—	2	1	no	—
24	#427×C₈₉	—	2	1	no	—
25	C₂×#107×C₈₉	C₄	1	2	yes	complemented
26	C₂×#106×C₈₉	C₄	1	2	yes	complemented
27	C₂×#13083558	—	2	1	no	—
28	C₂×#13083558	—	2	1	no	—
29	C₂×#13083558	—	2	1	no	—
30	C₂×#13083558	C₂×C₄	1	2	yes	—
31	C₂×#13083558	D₄	1	2	yes	—
32	C₂×#13083558	Q₈	1	2	yes	—
33	C₂²×#10623494	—	2	1	no	—
34	#15667971	—	2	1	no	—
35	#15667971	—	2	2	no	—
36	#15667971	—	2	1	no	—
37	#15667971	—	2	2	no	—
38	#15667971	—	2	2	no	—
39	#15667971	C₂×C₄	1	4	yes	—
40	#15667971	C₂×C₄	1	2	yes	—
41	#15667971	Q₈	1	2	yes	—
42	C₂×C₄⋊Dic₈₉	—	2	2	no	—
43	C₂×C₄⋊Dic₈₉	—	2	1	no	—
44	C₂×C₂²⋊Dic₈₉	—	2	2	no	—
45	C₂×C₂²⋊Dic₈₉	D₄	1	2	yes	—
46	C₂×C₄×Dic₈₉	—	2	1	no	—
47	C₂×C₄×Dic₈₉	—	2	2	no	—
48	#15667946	—	2	4	no	—
49	#15667944	—	2	4	no	—
50	#15667922	—	2	4	no	—
51	C₈×Dic₈₉	—	2	4	no	—
52	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
55	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₈₉	D₄	1	2	yes	—
58	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₈₉	Q₈	1	2	yes	—
63	#117×C₈₉	—	2	2	no	—
64	#117×C₈₉	—	2	2	no	—
65	#117×C₈₉	—	2	2	no	—
66	#117×C₈₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	4	yes	—
68	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
69	C₂×C₄²×C₈₉	—	2	2	no	—
70	#107×C₈₉	—	2	2	no	—
71	#107×C₈₉	—	2	2	no	—
72	#106×C₈₉	—	2	2	no	—
73	#106×C₈₉	—	2	2	no	—
74	C₂²×Dic₈₉	—	2	2	no	—
75	C₂²×Dic₈₉	—	4	2	no	—
76	#13083558	—	2	2	no	—
77	#13083558	—	2	2	no	—
78	#13083558	—	2	2	no	—
79	#13083558	C₄⋊C₄	1	4	yes	—
80	C₂×#10623494	—	2	2	no	—
81	C₂×#10623494	—	2	2	no	—
82	C₂×#10623494	—	2	2	no	—
83	C₄⋊Dic₈₉	—	2	2	no	—
84	C₄⋊Dic₈₉	—	2	2	no	—
85	C₄⋊Dic₈₉	—	2	4	no	—
86	C₄⋊Dic₈₉	—	4	2	no	—
87	C₂²⋊Dic₈₉	—	2	2	no	—
88	C₂²⋊Dic₈₉	—	2	4	no	—
89	C₂²⋊Dic₈₉	—	4	2	no	—
90	C₂²⋊Dic₈₉	C₄⋊C₄	1	4	yes	—
91	C₄×Dic₈₉	—	2	2	no	—
92	C₄×Dic₈₉	—	2	2	no	—
93	C₄×Dic₈₉	—	2	4	no	—
94	C₄×Dic₈₉	—	4	2	no	—
95	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₈₉	—	2	4	no	—
97	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
108	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
109	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
111	C₂×C₈×C₈₉	C₄²	1	2	yes	—
112	C₂×C₈×C₈₉	C₄²	1	2	yes	—
113	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
114	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
115	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
116	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
117	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
122	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
123	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
124	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
125	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
126	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
127	C₄⋊C₄×C₈₉	—	2	4	no	—
128	C₄⋊C₄×C₈₉	—	2	4	no	—
129	C₂²⋊C₄×C₈₉	—	4	2	no	—
130	C₂²⋊C₄×C₈₉	—	4	2	no	—
131	C₄²×C₈₉	—	4	2	no	—
132	C₄²×C₈₉	—	4	2	no	—
133	C₂³×C₈₉	—	4	2	no	—
134	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
136	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
137	C₂³×C₈₉	#121	1	1	yes	characteristic
138	C₂³×C₈₉	#121	1	1	yes	characteristic
139	C₂³×C₈₉	#127	1	1	yes	characteristic
140	C₂³×C₈₉	C₄⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₈₉	—	4	4	no	—
142	C₂×C₄×C₈₉	—	8	4	no	—
143	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₂×C₂²⋊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	#117	1	1	yes	characteristic
152	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₄×D₄	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×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
160	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
166	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
167	C₂×C₄×C₈₉	#125	1	1	yes	characteristic
168	C₂×C₄×C₈₉	#125	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₄⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₄⋊Q₈	1	1	yes	characteristic
171	C₂×Dic₈₉	—	2	4	no	—
172	C₂×Dic₈₉	—	4	4	no	—
173	C₂×Dic₈₉	—	4	4	no	—
174	C₂×Dic₈₉	—	8	4	no	—
175	C₈×C₈₉	#95	1	2	yes	—
176	C₈×C₈₉	#95	1	2	yes	—
177	C₈×C₈₉	#95	1	2	yes	—
178	C₈×C₈₉	#95	1	2	yes	—
179	#10623494	—	2	4	no	—
180	C₂²×C₈₉	—	2	2	no	—
181	C₂²×C₈₉	—	2	2	no	—
182	C₂²×C₈₉	—	2	2	no	—
183	C₂²×C₈₉	—	4	1	no	—
184	C₂²×C₈₉	—	4	1	no	—
185	C₂²×C₈₉	—	4	1	no	—
186	C₂²×C₈₉	—	4	1	no	—
187	C₂²×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×C₈₉	#380	1	1	yes	characteristic
189	C₂²×C₈₉	#384	1	1	yes	characteristic
190	C₂²×C₈₉	#389	1	1	yes	characteristic
191	C₂²×C₈₉	#389	1	1	yes	characteristic
192	C₂²×C₈₉	#390	1	1	yes	characteristic
193	C₂²×C₈₉	#390	1	1	yes	characteristic
194	C₄×C₈₉	—	8	4	no	—
195	C₄×C₈₉	C₂×#95	1	1	yes	characteristic
196	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
197	C₄×C₈₉	#380	1	1	yes	characteristic
198	C₄×C₈₉	#382	1	1	yes	characteristic
199	C₄×C₈₉	#389	1	1	yes	characteristic
200	C₄×C₈₉	#389	1	1	yes	characteristic
201	C₄×C₈₉	#391	1	1	yes	characteristic
202	C₄×C₈₉	#391	1	1	yes	characteristic
203	Dic₈₉	—	4	4	no	—
204	Dic₈₉	—	8	4	no	—
205	#10871	—	89	1	no	maximal, Sylow
206	C₂×C₈₉	—	2	1	no	—
207	C₂×C₈₉	—	2	1	no	—
208	C₂×C₈₉	—	2	1	no	—
209	C₂×C₈₉	—	2	1	no	—
210	C₂×C₈₉	—	2	1	no	—
211	C₂×C₈₉	—	2	1	no	—
212	C₂×C₈₉	C₄⋊#95	1	1	yes	characteristic
213	C₂×C₈₉	#1976	1	2	yes	—
214	C₂×#427	—	89	1	no	—
215	C₂×#427	D₈₉	1	1	yes	characteristic
216	C₂×#405	—	89	1	no	—
217	#1740	—	89	2	no	—
218	#1733	—	89	2	no	—
219	C₈₉	#10871	1	1	yes	characteristic, complemented, Sylow
220	C₂²×M₁₆	—	89	1	no	—
221	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
222	C₂×#117	—	89	1	no	—
223	C₂×#117	—	89	2	no	—
224	C₂×#117	C₂×D₈₉	1	2	yes	—
225	#427	—	2	1	no	—
226	#427	—	2	1	no	—
227	#427	—	2	1	no	—
228	#427	—	2	1	no	—
229	#427	—	89	4	no	—
230	#427	—	178	2	no	—
231	C₂×#107	—	178	1	no	—
232	C₂×#107	Dic₈₉	1	2	yes	complemented
233	C₂×#106	—	178	1	no	—
234	C₂×#106	Dic₈₉	1	2	yes	complemented
235	#405	—	89	4	no	—
236	#405	—	178	2	no	—
237	C₂×#97	—	178	1	no	—
238	C₂×C₄×C₈	—	178	1	no	—
239	#342	—	178	4	no	—
240	#339	—	178	4	no	—
241	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
242	C₂×M₁₆	—	89	2	no	—
243	C₂×M₁₆	—	89	2	no	—
244	C₂×M₁₆	—	89	2	no	—
245	C₂×M₁₆	—	178	1	no	—
246	C₂×M₁₆	—	178	1	no	—
247	C₂×M₁₆	—	178	1	no	—
248	C₂²×C₈	—	178	1	no	—
249	C₂²×C₈	Dic₁₇₈	1	2	yes	—
250	C₂²×C₈	C₄×D₈₉	1	2	yes	—
251	C₂²×C₈	C₄×D₈₉	1	2	yes	—
252	C₂²×C₈	D₃₅₆	1	2	yes	—
253	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
254	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
255	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
256	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
257	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
258	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
259	#117	—	2	2	no	—
260	#117	—	2	2	no	—
261	#117	—	2	2	no	—
262	#117	—	2	2	no	—
263	#117	—	89	2	no	—
264	#117	—	89	2	no	—
265	#117	—	89	4	no	—
266	#117	—	178	2	no	—
267	#117	—	178	2	no	—
268	#117	—	178	2	no	—
269	#117	—	178	1	no	—
270	#117	—	178	1	no	—
271	C₂×C₄⋊C₄	—	178	2	no	—
272	C₂×C₄⋊C₄	—	178	1	no	—
273	C₂×C₄⋊C₄	C₂×Dic₈₉	1	4	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	89	2	no	—
276	C₂×C₂²⋊C₄	—	178	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	178	2	no	—
279	C₂×C₄²	—	178	1	no	—
280	#107	—	2	2	no	—
281	#107	—	2	2	no	—
282	#107	—	178	4	no	—
283	#106	—	2	2	no	—
284	#106	—	2	2	no	—
285	#106	—	178	4	no	—
286	#97	—	178	4	no	—
287	C₄×C₈	—	178	4	no	—
288	C₂⁴	D₄×D₈₉	1	1	yes	characteristic
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	356	2	no	—
291	C₂²×C₄	—	178	2	no	—
292	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
295	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
299	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
300	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
302	C₂²×C₄	#13083573	1	1	yes	characteristic
303	C₂²×C₄	#13083573	1	1	yes	characteristic
304	C₂²×C₄	#13083575	1	1	yes	characteristic
305	C₂²×C₄	#13083575	1	1	yes	characteristic
306	M₁₆	—	89	4	no	—
307	M₁₆	—	178	2	no	—
308	M₁₆	—	178	2	no	—
309	M₁₆	—	178	2	no	—
310	C₂×C₈	—	178	2	no	—
311	C₂×C₈	—	178	2	no	—
312	C₂×C₈	—	178	2	no	—
313	C₂×C₈	C₄×Dic₈₉	1	2	yes	—
314	C₂×C₈	C₄×Dic₈₉	1	2	yes	—
315	C₂×C₈	#13083551	1	2	yes	—
316	C₂×C₈	#13083551	1	2	yes	—
317	C₂×C₈	#13083551	1	2	yes	—
318	C₂×C₈	#13083551	1	2	yes	—
319	C₂×C₈	C₂²⋊Dic₈₉	1	1	yes	characteristic
320	C₂×C₈	C₂²⋊Dic₈₉	1	1	yes	characteristic
321	C₂×C₈	C₂²⋊Dic₈₉	1	1	yes	characteristic
322	C₂×C₈	C₂²⋊Dic₈₉	1	1	yes	characteristic
323	C₂×C₈	#13083553	1	2	yes	—
324	C₂×C₈	#13083553	1	2	yes	—
325	C₂×C₈	#13083553	1	2	yes	—
326	C₂×C₈	#13083553	1	2	yes	—
327	C₂×C₈	C₄⋊Dic₈₉	1	2	yes	—
328	C₂×C₈	C₄⋊Dic₈₉	1	2	yes	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	356	2	no	—
332	C₄⋊C₄	—	178	4	no	—
333	C₄⋊C₄	—	178	2	no	—
334	C₄⋊C₄	—	178	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	89	4	no	—
338	C₂²⋊C₄	—	356	2	no	—
339	C₂²⋊C₄	—	178	4	no	—
340	C₂²⋊C₄	—	178	2	no	—
341	C₄²	—	4	2	no	—
342	C₄²	—	4	2	no	—
343	C₄²	—	356	2	no	—
344	C₄²	—	178	4	no	—
345	C₄²	—	178	2	no	—
346	C₄²	—	178	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
349	C₂³	#15667974	1	1	yes	characteristic
350	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
351	C₂³	#15667983	1	1	yes	characteristic
352	C₂³	#15667987	1	1	yes	characteristic
353	C₂³	#15668008	1	1	yes	characteristic
354	C₂³	#15668011	1	1	yes	characteristic
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	8	4	no	—
357	C₂×C₄	—	356	4	no	—
358	C₂×C₄	—	356	4	no	—
359	C₂×C₄	—	178	4	no	—
360	C₂×C₄	—	712	4	no	—
361	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
362	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
363	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
364	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
365	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
366	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
367	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
369	C₂×C₄	#15667970	1	1	yes	characteristic
370	C₂×C₄	#15667970	1	1	yes	characteristic
371	C₂×C₄	#15667974	1	1	yes	characteristic
372	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
373	C₂×C₄	#15667977	1	1	yes	characteristic
374	C₂×C₄	#15667977	1	1	yes	characteristic
375	C₂×C₄	Q₈×Dic₈₉	1	1	yes	characteristic
376	C₂×C₄	Q₈×Dic₈₉	1	1	yes	characteristic
377	C₂×C₄	#15667983	1	1	yes	characteristic
378	C₂×C₄	#15667987	1	1	yes	characteristic
379	C₂×C₄	#15667988	1	1	yes	characteristic
380	C₂×C₄	#15667988	1	1	yes	characteristic
381	C₂×C₄	#15667992	1	1	yes	characteristic
382	C₂×C₄	#15667992	1	1	yes	characteristic
383	C₂×C₄	#15667999	1	1	yes	characteristic
384	C₂×C₄	#15668001	1	1	yes	characteristic
385	C₂×C₄	#15668003	1	1	yes	characteristic
386	C₂×C₄	#15668003	1	1	yes	characteristic
387	C₂×C₄	#15668010	1	1	yes	characteristic
388	C₂×C₄	#15668011	1	1	yes	characteristic
389	C₈	—	178	4	no	—
390	C₈	#15667919	1	2	yes	—
391	C₈	#15667919	1	2	yes	—
392	C₈	#15667919	1	2	yes	—
393	C₈	#15667919	1	2	yes	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	C₄⋊C₄×Dic₈₉	1	1	yes	characteristic
402	C₂²	#19151455	1	1	yes	characteristic
403	C₂²	#19151467	1	1	yes	characteristic
404	C₂²	#19151494	1	1	yes	characteristic
405	C₂²	#19151497	1	1	yes	characteristic
406	C₂²	#19151499	1	1	yes	characteristic
407	C₂²	#19151501	1	1	yes	characteristic
408	C₄	—	8	4	no	—
409	C₄	—	356	4	no	—
410	C₄	—	712	4	no	—
411	C₄	C₂×#15667919	1	1	yes	characteristic
412	C₄	C₄⋊C₄×Dic₈₉	1	1	yes	characteristic
413	C₄	#19151455	1	1	yes	characteristic
414	C₄	#19151463	1	1	yes	characteristic
415	C₄	#19151494	1	1	yes	characteristic
416	C₄	#19151497	1	1	yes	characteristic
417	C₄	#19151503	1	1	yes	characteristic
418	C₄	#19151505	1	1	yes	characteristic
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	#26018481	1	1	yes	characteristic
426	C₂	#26021151	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#15667983
commutator	C₂×C₄×C₈₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₈₉
Fitting	C₂×#427×C₈₉	C₂
socle	C₂²×C₈₉	#390
prime radical	C₂⁴×C₈₉	C₂×D₄
cosocle	C₂³×C₄×C₈₉	C₂³
hypercenter	C₂×#427	D₈₉
hypocenter	C₈₉	#10871
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
10. #19151636	C₄	semidirect
14. #19151553	C₄	semidirect
25. C₂×#107×C₈₉	C₄	semidirect
26. C₂×#106×C₈₉	C₄	semidirect
219. C₈₉	#10871	semidirect
232. C₂×#107	Dic₈₉	semidirect
234. C₂×#106	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151636	2
C₂×#19151553	2
#26019985	2
#26019961	2
C₂×#427×C₈₉	2
#10871	89