Subgroups — #36448950

Order 22784.

684 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊#10623494	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊#10623494	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊#10623494	C₂	1	2	yes	maximal, complemented
4	#26018093	C₂	1	2	yes	maximal, complemented
5	C₄×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂³×#10623494	—	2	1	no	—
7	C₂×C₄⋊#10623494	—	2	4	no	—
8	C₂×C₄⋊#10623494	—	2	1	no	—
9	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
10	C₂×C₂²⋊#10623494	—	2	1	no	—
11	C₂×C₄×#10623494	C₂²	1	2	yes	—
12	#19151353	—	2	1	no	—
13	Q₈⋊#10623494	—	2	4	no	—
14	C₂×C₂²⋊Q₈×C₈₉	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
17	#391×C₈₉	C₄	1	1	yes	characteristic
18	#389×C₈₉	C₄	1	1	yes	characteristic
19	#387×C₈₉	—	2	1	no	—
20	#385×C₈₉	—	2	1	no	—
21	#380×C₈₉	C₄	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
23	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
25	C₂²×#10623494	—	2	4	no	—
26	C₂²×#10623494	—	2	2	no	—
27	C₂²×#10623494	—	2	2	no	—
28	C₂²×#10623494	—	4	2	no	—
29	C₂²×#10623494	—	4	2	no	—
30	C₄⋊#10623494	—	2	4	no	—
31	C₄⋊#10623494	—	2	2	no	—
32	C₄⋊#10623494	D₄	1	4	yes	—
33	C₂²⋊#10623494	—	2	4	no	—
34	C₄×#10623494	—	2	2	no	—
35	C₄×#10623494	—	2	2	no	—
36	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
40	C₂²⋊Q₈×C₈₉	—	2	2	no	—
41	C₂²⋊Q₈×C₈₉	C₈	1	4	yes	complemented
42	C₄×Q₈×C₈₉	—	2	2	no	—
43	C₄×Q₈×C₈₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
52	C₂×C₄²×C₈₉	—	2	2	no	—
53	C₂×C₄²×C₈₉	—	2	2	no	—
54	C₂×C₄²×C₈₉	—	2	1	no	—
55	C₂×C₄²×C₈₉	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
60	#95×C₈₉	—	2	1	no	—
61	#95×C₈₉	—	2	1	no	—
62	#95×C₈₉	—	2	1	no	—
63	#95×C₈₉	—	2	1	no	—
64	#95×C₈₉	—	2	1	no	—
65	C₂×#10623494	—	2	4	no	—
66	C₂×#10623494	—	2	4	no	—
67	C₂×#10623494	—	4	2	no	—
68	C₂×#10623494	—	4	8	no	—
69	C₂×#10623494	—	4	2	no	—
70	C₂×#10623494	—	4	2	no	—
71	C₂×#10623494	—	4	2	no	—
72	C₂⁴×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×Q₈×C₈₉	—	2	1	no	—
74	C₂×Q₈×C₈₉	—	2	2	no	—
75	C₂×Q₈×C₈₉	—	2	2	no	—
76	C₂×Q₈×C₈₉	C₂×C₈	1	2	yes	complemented
77	C₂²×C₄×C₈₉	—	2	2	no	—
78	C₂²×C₄×C₈₉	—	2	1	no	—
79	C₂²×C₄×C₈₉	—	2	1	no	—
80	C₂²×C₄×C₈₉	—	2	2	no	—
81	C₂²×C₄×C₈₉	—	2	1	no	—
82	C₂²×C₄×C₈₉	—	2	1	no	—
83	C₂²×C₄×C₈₉	—	2	2	no	—
84	C₂²×C₄×C₈₉	—	2	1	no	—
85	C₂²×C₄×C₈₉	—	2	1	no	—
86	C₂²×C₄×C₈₉	—	2	2	no	—
87	C₂²×C₄×C₈₉	—	2	1	no	—
88	C₂²×C₄×C₈₉	—	2	1	no	—
89	C₂²×C₄×C₈₉	—	4	1	no	—
90	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	C₂×C₈	1	2	yes	—
94	C₂²×C₄×C₈₉	M₁₆	1	2	yes	—
95	C₂²×C₄×C₈₉	SD₁₆	1	2	yes	—
96	C₂²×C₄×C₈₉	Q₁₆	1	2	yes	—
97	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
100	C₄⋊C₄×C₈₉	—	2	4	no	—
101	C₄⋊C₄×C₈₉	—	2	1	no	—
102	C₄⋊C₄×C₈₉	—	2	2	no	—
103	C₄⋊C₄×C₈₉	—	2	2	no	—
104	C₄⋊C₄×C₈₉	—	4	2	no	—
105	C₄⋊C₄×C₈₉	—	4	2	no	—
106	C₄⋊C₄×C₈₉	C₂×C₈	1	2	yes	complemented
107	C₂²⋊C₄×C₈₉	—	2	4	no	—
108	C₂²⋊C₄×C₈₉	—	4	2	no	—
109	C₄²×C₈₉	—	2	2	no	—
110	C₄²×C₈₉	—	2	1	no	—
111	C₄²×C₈₉	—	2	2	no	—
112	C₄²×C₈₉	—	2	1	no	—
113	C₄²×C₈₉	—	4	1	no	—
114	C₄²×C₈₉	—	4	1	no	—
115	C₄²×C₈₉	—	4	1	no	—
116	C₄²×C₈₉	—	4	1	no	—
117	C₄²×C₈₉	C₂×D₄	1	2	yes	—
118	C₄²×C₈₉	#41	1	2	yes	—
119	C₂³×C₈₉	—	2	1	no	—
120	C₂³×C₈₉	—	2	1	no	—
121	C₂³×C₈₉	—	2	1	no	—
122	C₂³×C₈₉	—	2	1	no	—
123	C₂³×C₈₉	C₂²⋊C₈	1	2	yes	—
124	C₂³×C₈₉	#103	1	2	yes	—
125	C₂³×C₈₉	#104	1	2	yes	—
126	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	Q₈×C₈₉	—	2	4	no	—
128	Q₈×C₈₉	—	4	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	—	2	1	no	—
134	C₂×C₄×C₈₉	—	2	1	no	—
135	C₂×C₄×C₈₉	—	2	4	no	—
136	C₂×C₄×C₈₉	—	2	4	no	—
137	C₂×C₄×C₈₉	—	2	2	no	—
138	C₂×C₄×C₈₉	—	2	2	no	—
139	C₂×C₄×C₈₉	—	2	2	no	—
140	C₂×C₄×C₈₉	—	2	2	no	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	2	2	no	—
143	C₂×C₄×C₈₉	—	2	2	no	—
144	C₂×C₄×C₈₉	—	2	1	no	—
145	C₂×C₄×C₈₉	—	2	1	no	—
146	C₂×C₄×C₈₉	—	4	4	no	—
147	C₂×C₄×C₈₉	—	4	1	no	—
148	C₂×C₄×C₈₉	—	4	1	no	—
149	C₂×C₄×C₈₉	—	4	1	no	—
150	C₂×C₄×C₈₉	—	4	1	no	—
151	C₂×C₄×C₈₉	—	4	1	no	—
152	C₂×C₄×C₈₉	—	4	1	no	—
153	C₂×C₄×C₈₉	—	4	1	no	—
154	C₂×C₄×C₈₉	—	4	1	no	—
155	C₂×C₄×C₈₉	—	4	1	no	—
156	C₂×C₄×C₈₉	—	4	1	no	—
157	C₂×C₄×C₈₉	C₂²⋊C₈	1	2	yes	—
158	C₂×C₄×C₈₉	#103	1	2	yes	—
159	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
161	C₂×C₄×C₈₉	#121	1	2	yes	—
162	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
165	C₂×C₄×C₈₉	#131	1	2	yes	—
166	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
168	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
170	#10623494	—	4	4	no	—
171	#10623494	—	4	4	no	—
172	C₂²×C₈₉	—	2	2	no	—
173	C₂²×C₈₉	—	2	2	no	—
174	C₂²×C₈₉	—	2	2	no	—
175	C₂²×C₈₉	—	2	2	no	—
176	C₂²×C₈₉	—	2	2	no	—
177	C₂²×C₈₉	—	2	2	no	—
178	C₂²×C₈₉	Q₈⋊C₈	1	4	yes	complemented
179	C₂²×C₈₉	#386	1	1	yes	characteristic
180	C₂²×C₈₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
181	C₂²×C₈₉	#408	1	1	yes	characteristic
182	C₂²×C₈₉	C₂×#103	1	1	yes	characteristic
183	C₂²×C₈₉	#417	1	1	yes	characteristic
184	C₂²×C₈₉	C₂×#104	1	1	yes	characteristic
185	C₂²×C₈₉	#421	1	1	yes	characteristic
186	C₄×C₈₉	—	2	2	no	—
187	C₄×C₈₉	—	2	2	no	—
188	C₄×C₈₉	—	2	2	no	—
189	C₄×C₈₉	—	4	2	no	—
190	C₄×C₈₉	—	4	1	no	—
191	C₄×C₈₉	—	4	2	no	—
192	C₄×C₈₉	—	8	1	no	—
193	C₄×C₈₉	—	8	1	no	—
194	C₄×C₈₉	C₈×D₄	1	2	yes	—
195	C₄×C₈₉	#435	1	2	yes	—
196	C₄×C₈₉	#450	1	1	yes	characteristic
197	C₄×C₈₉	#451	1	1	yes	characteristic
198	C₄×C₈₉	#483	1	1	yes	characteristic
199	C₄×C₈₉	#484	1	1	yes	characteristic
200	#8937	—	89	1	no	maximal, Sylow
201	C₂×C₈₉	—	2	4	no	—
202	C₂×C₈₉	C₂×Q₈⋊C₈	1	1	yes	characteristic
203	C₂×C₈₉	#1477	1	1	yes	characteristic
204	C₂×C₈₉	#1481	1	1	yes	characteristic
205	C₂×C₈₉	#1483	1	1	yes	characteristic
206	C₂×C₈₉	#1869	1	1	yes	characteristic
207	C₂×C₈₉	#1871	1	1	yes	characteristic
208	C₂×C₈₉	#1872	1	1	yes	characteristic
209	C₂²×C₄⋊C₈	—	89	1	no	—
210	C₄×C₂²⋊Q₈	D₈₉	1	1	yes	characteristic
211	C₄×C₂²⋊C₈	—	89	1	no	—
212	C₂×Q₈⋊C₈	—	89	2	no	—
213	#1279	—	89	2	no	—
214	C₈₉	#8937	1	1	yes	characteristic, complemented, Sylow
215	C₂³×C₈	—	178	1	no	—
216	C₂×C₂²⋊Q₈	Dic₈₉	1	1	yes	characteristic
217	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
218	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
219	C₂×C₄⋊C₈	—	89	2	no	—
220	C₂×C₄⋊C₈	—	178	4	no	—
221	C₂×C₄⋊C₈	—	178	1	no	—
222	C₂×C₂²⋊C₈	—	178	1	no	—
223	C₂×C₄×C₈	—	89	2	no	—
224	#391	Dic₈₉	1	1	yes	characteristic
225	#389	Dic₈₉	1	1	yes	characteristic
226	#387	—	2	1	no	—
227	#385	—	2	1	no	—
228	#380	Dic₈₉	1	1	yes	characteristic
229	C₄×C₄⋊C₄	—	2	1	no	—
230	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
231	C₄×C₂²⋊C₄	—	2	1	no	—
232	#336	—	178	1	no	—
233	Q₈⋊C₈	—	178	4	no	—
234	C₂²×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
235	C₂³×C₄	C₂×Dic₈₉	1	1	yes	characteristic
236	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
237	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
238	C₂²×C₈	—	356	2	no	—
239	C₂²×C₈	—	356	2	no	—
240	C₂²×C₈	—	178	4	no	—
241	C₂²×C₈	—	178	2	no	—
242	C₂²×C₈	—	178	2	no	—
243	C₂²⋊Q₈	—	2	2	no	—
244	C₂²⋊Q₈	#10623494	1	4	yes	complemented
245	C₄×Q₈	—	2	2	no	—
246	C₄×Q₈	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
260	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
261	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
263	C₄⋊C₈	—	89	4	no	—
264	C₄⋊C₈	—	178	4	no	—
265	C₄⋊C₈	—	178	2	no	—
266	C₂²⋊C₈	—	178	4	no	—
267	C₄×C₈	—	178	2	no	—
268	C₄×C₈	—	178	2	no	—
269	#95	—	2	1	no	—
270	#95	—	2	1	no	—
271	#95	—	2	1	no	—
272	#95	—	2	1	no	—
273	#95	—	2	1	no	—
274	C₂⁴	C₂²⋊Dic₈₉	1	1	yes	characteristic
275	C₂×Q₈	—	2	1	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	C₂×#10623494	1	2	yes	complemented
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
293	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
294	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
295	C₂²×C₄	C₂×#10623494	1	2	yes	—
296	C₂²×C₄	#13083558	1	2	yes	—
297	C₂²×C₄	#13083561	1	2	yes	—
298	C₂²×C₄	#13083564	1	2	yes	—
299	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
302	C₂×C₈	—	356	8	no	—
303	C₂×C₈	—	356	2	no	—
304	C₂×C₈	—	356	2	no	—
305	C₂×C₈	—	356	2	no	—
306	C₂×C₈	—	356	2	no	—
307	C₂×C₈	—	178	4	no	—
308	C₂×C₈	—	178	4	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	C₂×#10623494	1	2	yes	complemented
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	4	1	no	—
323	C₄²	—	4	1	no	—
324	C₄²	—	4	1	no	—
325	C₄²	—	4	1	no	—
326	C₄²	D₄×D₈₉	1	2	yes	—
327	C₄²	#13083573	1	2	yes	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	C₂²⋊#10623494	1	2	yes	—
333	C₂³	#15667936	1	2	yes	—
334	C₂³	#15667939	1	2	yes	—
335	C₂³	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
336	Q₈	—	2	4	no	—
337	Q₈	—	4	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	C₂²⋊#10623494	1	2	yes	—
367	C₂×C₄	#15667936	1	2	yes	—
368	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
369	C₂×C₄	#15667980	1	1	yes	characteristic
370	C₂×C₄	#15667984	1	2	yes	—
371	C₂×C₄	#15667993	1	1	yes	characteristic
372	C₂×C₄	C₂²×#10623494	1	1	yes	characteristic
373	C₂×C₄	C₂×#13083558	1	1	yes	characteristic
374	C₂×C₄	#15668019	1	2	yes	—
375	C₂×C₄	C₂×#13083561	1	1	yes	characteristic
376	C₂×C₄	C₂×#13083564	1	1	yes	characteristic
377	C₂×C₄	#15668037	1	1	yes	characteristic
378	C₂×C₄	#15668042	1	1	yes	characteristic
379	C₈	—	356	4	no	—
380	C₈	—	356	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	Q₈⋊#10623494	1	4	yes	complemented
388	C₂²	#19151478	1	1	yes	characteristic
389	C₂²	C₂×C₂²⋊#10623494	1	1	yes	characteristic
390	C₂²	#19151565	1	1	yes	characteristic
391	C₂²	C₂×#15667936	1	1	yes	characteristic
392	C₂²	#19151599	1	1	yes	characteristic
393	C₂²	C₂×#15667939	1	1	yes	characteristic
394	C₂²	#19151615	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	1	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	D₄×#10623494	1	2	yes	—
404	C₄	#19151670	1	2	yes	—
405	C₄	#19151748	1	1	yes	characteristic
406	C₄	#19151753	1	1	yes	characteristic
407	C₄	#19151926	1	1	yes	characteristic
408	C₄	#19151931	1	1	yes	characteristic
409	C₂	—	2	4	no	—
410	C₂	C₂×Q₈⋊#10623494	1	1	yes	characteristic
411	C₂	#26018639	1	1	yes	characteristic
412	C₂	#26018655	1	1	yes	characteristic
413	C₂	#26018665	1	1	yes	characteristic
414	C₂	#26020545	1	1	yes	characteristic
415	C₂	#26020555	1	1	yes	characteristic
416	C₂	#26020560	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₄×C₂²⋊Q₈×C₈₉	C₂
socle	C₂³×C₈₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₈₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₄×C₂²⋊Q₈	D₈₉
hypocenter	C₈₉	#8937
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈⋊#10623494	C₂	semidirect
4. #26018093	C₂	semidirect
41. C₂²⋊Q₈×C₈₉	C₈	semidirect
76. C₂×Q₈×C₈₉	C₂×C₈	semidirect
106. C₄⋊C₄×C₈₉	C₂×C₈	semidirect
178. C₂²×C₈₉	Q₈⋊C₈	semidirect
214. C₈₉	#8937	semidirect
244. C₂²⋊Q₈	#10623494	semidirect
278. C₂×Q₈	C₂×#10623494	semidirect
315. C₄⋊C₄	C₂×#10623494	semidirect
387. C₂²	Q₈⋊#10623494	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊#10623494	2
C₄×C₂²⋊#10623494	2
C₂×Q₈⋊#10623494	2
#26018093	2
C₄×C₂²⋊Q₈×C₈₉	2
#8937	89