Subgroups — #36563105

Order 22784.

802 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151729	C₂	1	2	yes	maximal
2	#26021193	C₂	1	2	yes	maximal
3	#26020976	C₂	1	2	yes	maximal
4	#26020971	C₂	1	1	yes	maximal, characteristic
5	#26020971	C₂	1	1	yes	maximal, characteristic
6	#26020404	C₂	1	1	yes	maximal, characteristic
7	#26020127	C₂	1	2	yes	maximal
8	#26020121	C₂	1	1	yes	maximal, characteristic
9	C₄⋊C₄×#10623494	C₂	1	1	yes	maximal, characteristic
10	C₄×#15667923	C₂	1	1	yes	maximal, characteristic
11	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
12	#19151729	—	2	8	no	—
13	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
16	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
17	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
18	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
19	C₂×#15667923	C₂²	1	2	yes	—
20	C₂×#15667923	C₂²	1	1	yes	characteristic
21	C₂×#15667923	C₂²	1	1	yes	characteristic
22	C₂×#15667923	C₂²	1	1	yes	characteristic
23	C₂×#15667923	C₂²	1	1	yes	characteristic
24	C₂×C₄×#10623494	C₂²	1	2	yes	—
25	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
26	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
27	#19151353	C₂²	1	2	yes	—
28	#19151353	C₂²	1	2	yes	—
29	#19151353	C₂²	1	2	yes	—
30	#19151353	C₂²	1	2	yes	—
31	C₂×C₄⋊Q₈×C₈₉	C₄	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
33	#391×C₈₉	C₄	1	2	yes	—
34	#389×C₈₉	C₄	1	1	yes	characteristic
35	#389×C₈₉	C₄	1	1	yes	characteristic
36	#389×C₈₉	C₄	1	2	yes	—
37	#384×C₈₉	C₄	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
41	C₄³×C₈₉	C₂²	1	1	yes	characteristic
42	C₂²×#10623494	C₂³	1	2	yes	—
43	C₂²×#10623494	C₂³	1	2	yes	—
44	C₂²×#10623494	C₂³	1	1	yes	characteristic
45	C₂²×#10623494	C₂³	1	1	yes	characteristic
46	C₂²×#10623494	C₂³	1	1	yes	characteristic
47	C₂²×#10623494	C₂³	1	1	yes	characteristic
48	C₄⋊#10623494	—	2	4	no	—
49	C₄⋊#10623494	—	2	4	no	—
50	C₄⋊#10623494	—	2	4	no	—
51	C₄⋊#10623494	—	2	2	no	—
52	C₄⋊#10623494	—	2	2	no	—
53	C₄⋊#10623494	—	2	4	no	—
54	#15667923	—	2	4	no	—
55	#15667923	—	2	2	no	—
56	#15667923	—	2	2	no	—
57	#15667923	D₄	1	4	yes	—
58	#15667923	Q₈	1	4	yes	complemented
59	C₄×#10623494	—	2	4	no	—
60	C₄×#10623494	—	2	2	no	—
61	C₄×#10623494	Q₈	1	4	yes	complemented
62	C₂²×Q₈×C₈₉	C₂×C₄	1	2	yes	—
63	C₄⋊Q₈×C₈₉	—	2	4	no	—
64	C₄×Q₈×C₈₉	—	2	4	no	—
65	C₄×Q₈×C₈₉	—	2	4	no	—
66	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
70	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
80	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
81	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
84	#95×C₈₉	C₂×C₄	1	2	yes	—
85	#95×C₈₉	C₂×C₄	1	2	yes	—
86	#95×C₈₉	C₂×C₄	1	2	yes	—
87	#95×C₈₉	C₂×C₄	1	2	yes	—
88	C₂×#10623494	—	2	1	no	—
89	C₂×#10623494	—	2	1	no	—
90	C₂×#10623494	—	2	1	no	—
91	C₂×#10623494	—	2	1	no	—
92	C₂×#10623494	—	2	1	no	—
93	C₂×#10623494	—	2	1	no	—
94	C₂×#10623494	—	2	2	no	—
95	C₂×#10623494	—	2	2	no	—
96	C₂×#10623494	—	2	2	no	—
97	C₂×#10623494	—	2	2	no	—
98	C₂×#10623494	—	2	2	no	—
99	C₂×#10623494	—	2	2	no	—
100	C₂×#10623494	C₂×D₄	1	2	yes	—
101	C₂×#10623494	C₂×D₄	1	2	yes	—
102	C₂×#10623494	C₂×Q₈	1	2	yes	—
103	C₂×#10623494	C₂×Q₈	1	2	yes	—
104	C₂×#10623494	C₂×Q₈	1	2	yes	—
105	C₂×#10623494	C₂×Q₈	1	2	yes	—
106	C₂×Q₈×C₈₉	—	2	4	no	—
107	C₂×Q₈×C₈₉	—	2	4	no	—
108	C₂×Q₈×C₈₉	—	4	2	no	—
109	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
120	C₄⋊C₄×C₈₉	—	2	4	no	—
121	C₄⋊C₄×C₈₉	—	2	4	no	—
122	C₄⋊C₄×C₈₉	—	2	4	no	—
123	C₄⋊C₄×C₈₉	—	2	4	no	—
124	C₄⋊C₄×C₈₉	—	2	2	no	—
125	C₄⋊C₄×C₈₉	—	2	2	no	—
126	C₄⋊C₄×C₈₉	—	2	2	no	—
127	C₄⋊C₄×C₈₉	—	4	2	no	—
128	C₄⋊C₄×C₈₉	M₁₆	1	4	yes	—
129	C₄²×C₈₉	—	2	2	no	—
130	C₄²×C₈₉	—	2	2	no	—
131	C₄²×C₈₉	—	2	2	no	—
132	C₄²×C₈₉	—	2	2	no	—
133	C₄²×C₈₉	—	2	2	no	—
134	C₄²×C₈₉	—	2	2	no	—
135	C₄²×C₈₉	—	4	1	no	—
136	C₄²×C₈₉	—	4	1	no	—
137	C₄²×C₈₉	C₂×D₄	1	2	yes	—
138	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
139	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
140	C₄²×C₈₉	#41	1	2	yes	—
141	C₄²×C₈₉	#41	1	2	yes	—
142	C₄²×C₈₉	#41	1	2	yes	—
143	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
144	Q₈×C₈₉	—	4	8	no	—
145	C₂×C₄×C₈₉	—	2	2	no	—
146	C₂×C₄×C₈₉	—	2	1	no	—
147	C₂×C₄×C₈₉	—	2	1	no	—
148	C₂×C₄×C₈₉	—	2	1	no	—
149	C₂×C₄×C₈₉	—	2	1	no	—
150	C₂×C₄×C₈₉	—	2	1	no	—
151	C₂×C₄×C₈₉	—	2	1	no	—
152	C₂×C₄×C₈₉	—	2	1	no	—
153	C₂×C₄×C₈₉	—	2	1	no	—
154	C₂×C₄×C₈₉	—	2	1	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	—	2	2	no	—
158	C₂×C₄×C₈₉	—	2	2	no	—
159	C₂×C₄×C₈₉	—	2	2	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	2	2	no	—
165	C₂×C₄×C₈₉	—	2	2	no	—
166	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
169	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
170	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
171	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
172	C₂×C₄×C₈₉	C₂×M₁₆	1	4	yes	—
173	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
174	C₂×C₄×C₈₉	#131	1	2	yes	—
175	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
181	#10623494	—	2	2	no	—
182	#10623494	—	2	2	no	—
183	#10623494	—	2	2	no	—
184	#10623494	—	4	2	no	—
185	#10623494	—	4	2	no	—
186	#10623494	C₄⋊Q₈	1	4	yes	complemented
187	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
189	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
190	C₂²×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
191	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
192	C₂²×C₈₉	#568	1	1	yes	characteristic
193	C₂²×C₈₉	#568	1	1	yes	characteristic
194	C₄×C₈₉	—	2	2	no	—
195	C₄×C₈₉	—	2	4	no	—
196	C₄×C₈₉	—	2	2	no	—
197	C₄×C₈₉	—	2	2	no	—
198	C₄×C₈₉	—	2	2	no	—
199	C₄×C₈₉	—	2	2	no	—
200	C₄×C₈₉	—	4	2	no	—
201	C₄×C₈₉	—	4	2	no	—
202	C₄×C₈₉	—	4	2	no	—
203	C₄×C₈₉	#446	1	4	yes	complemented
204	C₄×C₈₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
205	C₄×C₈₉	#532	1	1	yes	characteristic
206	C₄×C₈₉	#533	1	1	yes	characteristic
207	C₄×C₈₉	#533	1	1	yes	characteristic
208	#21713	—	89	1	no	maximal, Sylow
209	C₂×C₈₉	C₄×C₄⋊Q₈	1	1	yes	characteristic
210	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
211	C₂×C₈₉	#2935	1	1	yes	characteristic
212	C₂×C₈₉	C₂×#446	1	1	yes	characteristic
213	C₂×C₈₉	#2961	1	1	yes	characteristic
214	C₂×C₈₉	#2962	1	1	yes	characteristic
215	C₂×C₈₉	Q₈×M₁₆	1	1	yes	characteristic
216	C₂×#446	—	89	2	no	—
217	C₄×C₄⋊Q₈	D₈₉	1	1	yes	characteristic
218	#1985	—	89	2	no	—
219	#1940	—	89	2	no	—
220	#1939	—	89	1	no	—
221	#1939	—	89	1	no	—
222	#1842	—	89	1	no	—
223	#1771	—	89	2	no	—
224	#1770	—	89	1	no	—
225	C₈×C₄⋊C₄	—	89	1	no	—
226	C₄×#97	—	89	1	no	—
227	C₈₉	#21713	1	1	yes	characteristic, complemented, Sylow
228	C₂×C₄⋊Q₈	Dic₈₉	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂×D₈₉	1	2	yes	—
230	#446	—	178	8	no	—
231	C₂×C₄⋊C₈	—	89	2	no	—
232	C₂×C₄⋊C₈	—	89	1	no	—
233	C₂×C₄⋊C₈	—	89	1	no	—
234	C₂×C₄⋊C₈	—	89	2	no	—
235	C₂×C₄⋊C₈	—	89	2	no	—
236	C₂×C₄⋊C₈	—	89	2	no	—
237	C₂×#97	—	89	1	no	—
238	C₂×#97	—	89	1	no	—
239	C₂×#97	—	89	2	no	—
240	C₂×#97	—	89	1	no	—
241	C₂×#97	—	89	1	no	—
242	C₂×C₄×C₈	—	89	1	no	—
243	C₂×C₄×C₈	—	89	2	no	—
244	C₂×C₄×C₈	—	89	1	no	—
245	#391	Dic₈₉	1	2	yes	—
246	#389	Dic₈₉	1	1	yes	characteristic
247	#389	Dic₈₉	1	1	yes	characteristic
248	#389	Dic₈₉	1	2	yes	—
249	#384	Dic₈₉	1	1	yes	characteristic
250	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
251	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
252	C₄×C₄⋊C₄	C₂×D₈₉	1	2	yes	—
253	C₄³	C₂×D₈₉	1	1	yes	characteristic
254	#336	—	89	2	no	—
255	#336	—	89	2	no	—
256	#336	—	89	2	no	—
257	#336	—	89	2	no	—
258	C₂²×Q₈	C₂×Dic₈₉	1	2	yes	—
259	C₂²×C₈	—	89	1	no	—
260	C₂²×C₈	—	89	1	no	—
261	C₂²×C₈	—	89	1	no	—
262	C₂²×C₈	—	89	1	no	—
263	C₂²×C₈	—	89	2	no	—
264	C₂²×C₈	—	89	2	no	—
265	C₄⋊Q₈	—	2	4	no	—
266	C₄×Q₈	—	2	4	no	—
267	C₄×Q₈	—	2	4	no	—
268	C₂×C₄⋊C₄	C₂×Dic₈₉	1	2	yes	—
269	C₂×C₄⋊C₄	C₂×Dic₈₉	1	2	yes	—
270	C₂×C₄⋊C₄	C₂×Dic₈₉	1	2	yes	—
271	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂×Dic₈₉	1	2	yes	—
273	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂×Dic₈₉	1	2	yes	—
276	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
277	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
278	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
279	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
280	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
281	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
282	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
283	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
284	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
285	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
286	C₄⋊C₈	—	178	4	no	—
287	C₄⋊C₈	—	178	4	no	—
288	C₄⋊C₈	—	178	4	no	—
289	C₄⋊C₈	—	178	2	no	—
290	C₄⋊C₈	—	178	2	no	—
291	C₄⋊C₈	—	178	4	no	—
292	#97	—	89	4	no	—
293	#97	—	89	4	no	—
294	#97	—	178	4	no	—
295	#97	—	178	2	no	—
296	#97	—	178	2	no	—
297	C₄×C₈	—	89	4	no	—
298	C₄×C₈	—	178	4	no	—
299	C₄×C₈	—	178	2	no	—
300	#95	C₂×Dic₈₉	1	2	yes	—
301	#95	C₂×Dic₈₉	1	2	yes	—
302	#95	C₂×Dic₈₉	1	2	yes	—
303	#95	C₂×Dic₈₉	1	2	yes	—
304	C₂×Q₈	—	2	4	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	4	2	no	—
307	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
308	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
309	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
310	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
311	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
312	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
313	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
314	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
315	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
316	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
317	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
318	C₂×C₈	—	89	2	no	—
319	C₂×C₈	—	89	2	no	—
320	C₂×C₈	—	89	2	no	—
321	C₂×C₈	—	89	2	no	—
322	C₂×C₈	—	89	2	no	—
323	C₂×C₈	—	89	2	no	—
324	C₂×C₈	—	178	2	no	—
325	C₂×C₈	—	178	2	no	—
326	C₂×C₈	—	178	2	no	—
327	C₂×C₈	—	178	2	no	—
328	C₂×C₈	—	178	2	no	—
329	C₂×C₈	—	178	2	no	—
330	C₂×C₈	—	178	1	no	—
331	C₂×C₈	—	178	1	no	—
332	C₂×C₈	—	178	1	no	—
333	C₂×C₈	—	178	1	no	—
334	C₂×C₈	—	178	1	no	—
335	C₂×C₈	—	178	1	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	#13083558	1	4	yes	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	4	1	no	—
352	C₄²	—	4	1	no	—
353	C₄²	D₄×D₈₉	1	2	yes	—
354	C₄²	Q₈×D₈₉	1	2	yes	—
355	C₄²	Q₈×D₈₉	1	2	yes	—
356	C₄²	#13083573	1	2	yes	—
357	C₄²	#13083575	1	2	yes	—
358	C₄²	#13083575	1	2	yes	—
359	C₂³	C₂³×Dic₈₉	1	1	yes	characteristic
360	Q₈	—	4	8	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
383	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
384	C₂×C₄	Q₈×Dic₈₉	1	2	yes	—
385	C₂×C₄	Q₈×Dic₈₉	1	2	yes	—
386	C₂×C₄	Q₈×Dic₈₉	1	2	yes	—
387	C₂×C₄	Q₈×Dic₈₉	1	2	yes	—
388	C₂×C₄	C₂×#13083558	1	4	yes	—
389	C₂×C₄	C₂×#13083558	1	2	yes	—
390	C₂×C₄	#15668019	1	2	yes	—
391	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
392	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
393	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
394	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
395	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
396	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
397	C₈	—	89	4	no	—
398	C₈	—	356	2	no	—
399	C₈	—	356	2	no	—
400	C₈	—	178	2	no	—
401	C₈	—	178	2	no	—
402	C₈	—	178	2	no	—
403	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
404	C₂²	C₂×Q₈×Dic₈₉	1	1	yes	characteristic
405	C₂²	C₂×Q₈×Dic₈₉	1	1	yes	characteristic
406	C₂²	C₂²×#13083558	1	1	yes	characteristic
407	C₂²	C₂×#15668019	1	1	yes	characteristic
408	C₂²	#19152365	1	1	yes	characteristic
409	C₂²	#19152365	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	4	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	#19151729	1	4	yes	complemented
420	C₄	C₄⋊Q₈×D₈₉	1	1	yes	characteristic
421	C₄	#19152149	1	1	yes	characteristic
422	C₄	#19152153	1	1	yes	characteristic
423	C₄	#19152153	1	1	yes	characteristic
424	C₂	C₄⋊Q₈×Dic₈₉	1	1	yes	characteristic
425	C₂	D₄×#13083558	1	1	yes	characteristic
426	C₂	#26028996	1	1	yes	characteristic
427	C₂	C₂×#19151729	1	1	yes	characteristic
428	C₂	#26029193	1	1	yes	characteristic
429	C₂	#26029201	1	1	yes	characteristic
430	C₂	Q₈×#13083558	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator, socle, prime radical	C₂³×C₈₉	C₂³×C₄
Fitting	C₄×C₄⋊Q₈×C₈₉	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄×C₄⋊Q₈	D₈₉
hypocenter	C₈₉	#21713
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
58. #15667923	Q₈	semidirect
61. C₄×#10623494	Q₈	semidirect
186. #10623494	C₄⋊Q₈	semidirect
203. C₄×C₈₉	#446	semidirect
227. C₈₉	#21713	semidirect
419. C₄	#19151729	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151729	2
#26021193	2
#26020976	2
#26020971	2
#26020404	2
#26020127	2
#26020121	2
C₄⋊C₄×#10623494	2
C₄×#15667923	2
C₄×C₄⋊Q₈×C₈₉	2
#21713	89