Subgroups — #36525977

Order 22784.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029266	C₂	1	1	yes	maximal, characteristic
2	Q₈×#13083558	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019161	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019149	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019124	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019110	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019103	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019089	C₂	1	1	yes	maximal, characteristic, complemented
9	SD₁₆⋊#10623494	C₂	1	1	yes	maximal, characteristic, complemented
10	SD₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019019	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018699	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018691	C₂	1	1	yes	maximal, characteristic
14	#26018555	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#137×C₈₉	C₂	1	1	yes	maximal, characteristic
16	#19151729	—	2	1	no	—
17	#19151729	—	2	1	no	—
18	#19151729	C₂²	1	1	yes	characteristic
19	#19151729	C₂²	1	1	yes	characteristic
20	#19151729	C₂²	1	1	yes	characteristic
21	#19151729	C₂²	1	1	yes	characteristic
22	Q₈×#10623494	C₂²	1	1	yes	characteristic
23	Q₈×#10623494	C₂²	1	1	yes	characteristic
24	#19151670	—	2	1	no	—
25	#19151670	—	2	1	no	—
26	D₄×#10623494	C₂²	1	1	yes	characteristic
27	D₄×#10623494	C₂²	1	1	yes	characteristic
28	#19151655	—	2	1	no	—
29	#19151655	C₂²	1	1	yes	characteristic
30	#19151622	—	2	1	no	—
31	#19151622	C₂²	1	1	yes	characteristic
32	C₄×#13083558	—	2	1	no	—
33	C₄×#13083558	C₂²	1	1	yes	characteristic
34	C₄×#13083558	C₂²	1	1	yes	characteristic
35	C₂×#15667923	—	2	1	no	—
36	#19151351	C₂²	1	1	yes	characteristic
37	#19151351	C₂²	1	1	yes	characteristic
38	#19151349	C₂²	1	1	yes	characteristic
39	#19151349	C₂²	1	1	yes	characteristic
40	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
41	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
42	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
43	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
44	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
45	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
46	D₄⋊#10623494	C₂²	1	1	yes	characteristic
47	D₄⋊#10623494	C₂²	1	1	yes	characteristic
48	#19151320	C₂²	1	1	yes	characteristic
49	#19151320	C₂²	1	1	yes	characteristic
50	#19151319	C₂²	1	1	yes	characteristic
51	C₈×#10623494	C₂²	1	1	yes	characteristic
52	C₂×#137×C₈₉	C₄	1	1	yes	characteristic
53	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
55	#441×C₈₉	C₄	1	1	yes	characteristic
56	#441×C₈₉	C₄	1	1	yes	characteristic
57	#440×C₈₉	C₄	1	1	yes	characteristic
58	#440×C₈₉	C₄	1	1	yes	characteristic
59	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
60	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
62	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
63	#428×C₈₉	C₄	1	1	yes	characteristic
64	#419×C₈₉	C₄	1	1	yes	characteristic
65	#417×C₈₉	C₄	1	1	yes	characteristic
66	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#13083558	—	2	1	no	—
68	C₂×#13083558	—	2	1	no	—
69	C₂×#13083558	D₄	1	1	yes	characteristic
70	C₂×#13083558	D₄	1	1	yes	characteristic
71	C₂²×#10623494	—	2	1	no	—
72	C₂²×#10623494	—	2	1	no	—
73	C₄⋊#10623494	—	2	1	no	—
74	C₄⋊#10623494	—	2	1	no	—
75	C₄⋊#10623494	—	2	1	no	—
76	C₄⋊#10623494	—	2	1	no	—
77	C₄⋊#10623494	—	2	1	no	—
78	C₄⋊#10623494	—	2	1	no	—
79	C₄⋊#10623494	—	2	1	no	—
80	C₄⋊#10623494	C₂³	1	1	yes	characteristic
81	C₄⋊#10623494	C₂³	1	1	yes	characteristic
82	C₄⋊#10623494	C₂³	1	1	yes	characteristic
83	C₄⋊#10623494	C₂³	1	1	yes	characteristic
84	C₂²⋊#10623494	—	2	1	no	—
85	C₂²⋊#10623494	—	2	1	no	—
86	C₂²⋊#10623494	—	2	1	no	—
87	#15667923	—	2	1	no	—
88	#15667923	—	2	1	no	—
89	#15667923	—	2	1	no	—
90	#15667923	—	2	1	no	—
91	#15667923	—	2	1	no	—
92	#15667923	—	2	1	no	—
93	#15667923	D₄	1	1	yes	characteristic
94	#15667923	D₄	1	1	yes	characteristic
95	C₄×#10623494	—	2	1	no	—
96	C₄×#10623494	—	2	1	no	—
97	C₄×#10623494	C₂³	1	1	yes	characteristic
98	C₄×#10623494	C₂³	1	1	yes	characteristic
99	C₄×#10623494	C₂³	1	1	yes	characteristic
100	C₄×#10623494	C₂³	1	1	yes	characteristic
101	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
102	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
103	#137×C₈₉	—	2	4	no	—
104	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
105	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
106	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
107	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
108	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
109	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
110	C₄×Q₈×C₈₉	—	2	1	no	—
111	C₄×Q₈×C₈₉	—	2	1	no	—
112	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
113	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
114	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
115	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
117	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
118	C₄×D₄×C₈₉	—	2	1	no	—
119	C₄×D₄×C₈₉	—	2	1	no	—
120	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
121	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
122	#117×C₈₉	—	2	1	no	—
123	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
125	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄²×C₈₉	—	2	1	no	—
127	C₂×C₄²×C₈₉	—	2	1	no	—
128	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
129	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
130	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
131	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
132	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
133	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
134	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
135	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
136	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
137	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
138	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
139	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
140	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
141	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
142	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
145	#13083558	—	2	2	no	—
146	#13083558	—	4	1	no	—
147	#13083558	—	4	2	no	—
148	#13083558	—	4	2	no	—
149	C₂×#10623494	—	2	1	no	—
150	C₂×#10623494	—	2	1	no	—
151	C₂×#10623494	—	2	1	no	—
152	C₂×#10623494	—	2	1	no	—
153	C₂×#10623494	—	2	1	no	—
154	C₂×#10623494	—	2	1	no	—
155	C₂×#10623494	—	4	2	no	—
156	C₂×#10623494	—	4	2	no	—
157	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
158	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
159	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
160	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
161	#41×C₈₉	—	2	2	no	—
162	#41×C₈₉	—	4	1	no	—
163	C₂×Q₈×C₈₉	—	2	1	no	—
164	C₂×Q₈×C₈₉	—	2	2	no	—
165	C₂×Q₈×C₈₉	—	4	1	no	—
166	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
169	C₂×D₄×C₈₉	—	2	1	no	—
170	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₈₉	—	2	1	no	—
172	C₂²×C₄×C₈₉	—	2	1	no	—
173	C₂²×C₄×C₈₉	—	2	1	no	—
174	C₂²×C₄×C₈₉	—	2	1	no	—
175	C₂²×C₄×C₈₉	—	2	1	no	—
176	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
179	Q₁₆×C₈₉	—	2	2	no	—
180	Q₁₆×C₈₉	—	2	2	no	—
181	SD₁₆×C₈₉	—	2	2	no	—
182	SD₁₆×C₈₉	M₁₆	1	4	yes	complemented
183	M₁₆×C₈₉	—	2	2	no	—
184	M₁₆×C₈₉	—	4	1	no	—
185	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
189	C₄⋊C₄×C₈₉	—	2	1	no	—
190	C₄⋊C₄×C₈₉	—	2	1	no	—
191	C₄⋊C₄×C₈₉	—	2	1	no	—
192	C₄⋊C₄×C₈₉	—	2	1	no	—
193	C₄⋊C₄×C₈₉	—	2	1	no	—
194	C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₄⋊C₄×C₈₉	—	2	1	no	—
196	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
199	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
200	C₂²⋊C₄×C₈₉	—	2	1	no	—
201	C₂²⋊C₄×C₈₉	—	2	1	no	—
202	C₂²⋊C₄×C₈₉	—	2	1	no	—
203	C₄²×C₈₉	—	2	1	no	—
204	C₄²×C₈₉	—	2	1	no	—
205	C₄²×C₈₉	—	2	1	no	—
206	C₄²×C₈₉	—	2	1	no	—
207	C₄²×C₈₉	—	2	1	no	—
208	C₄²×C₈₉	—	2	1	no	—
209	C₄²×C₈₉	—	2	1	no	—
210	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
211	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₈₉	#41	1	1	yes	characteristic
213	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
214	C₂³×C₈₉	—	2	1	no	—
215	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
216	Q₈×C₈₉	—	2	1	no	—
217	Q₈×C₈₉	—	2	1	no	—
218	Q₈×C₈₉	—	2	1	no	—
219	Q₈×C₈₉	—	2	1	no	—
220	Q₈×C₈₉	—	2	1	no	—
221	Q₈×C₈₉	—	4	2	no	—
222	Q₈×C₈₉	C₂×M₁₆	1	2	yes	—
223	D₄×C₈₉	—	2	1	no	—
224	D₄×C₈₉	—	4	2	no	—
225	D₄×C₈₉	C₂×M₁₆	1	2	yes	—
226	C₂×C₄×C₈₉	—	2	1	no	—
227	C₂×C₄×C₈₉	—	2	1	no	—
228	C₂×C₄×C₈₉	—	2	1	no	—
229	C₂×C₄×C₈₉	—	2	1	no	—
230	C₂×C₄×C₈₉	—	2	1	no	—
231	C₂×C₄×C₈₉	—	2	1	no	—
232	C₂×C₄×C₈₉	—	2	1	no	—
233	C₂×C₄×C₈₉	—	2	1	no	—
234	C₂×C₄×C₈₉	—	2	1	no	—
235	C₂×C₄×C₈₉	—	2	1	no	—
236	C₂×C₄×C₈₉	—	2	1	no	—
237	C₂×C₄×C₈₉	—	4	1	no	—
238	C₂×C₄×C₈₉	—	4	2	no	—
239	C₂×C₄×C₈₉	—	4	2	no	—
240	C₂×C₄×C₈₉	—	4	1	no	—
241	C₂×C₄×C₈₉	—	4	1	no	—
242	C₂×C₄×C₈₉	—	8	1	no	—
243	C₂×C₄×C₈₉	—	8	1	no	—
244	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
250	C₈×C₈₉	—	2	1	no	—
251	C₈×C₈₉	—	2	1	no	—
252	C₈×C₈₉	—	2	1	no	—
253	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
254	#10623494	—	2	2	no	—
255	#10623494	—	2	1	no	—
256	#10623494	—	2	1	no	—
257	#10623494	—	2	1	no	—
258	#10623494	—	4	1	no	—
259	#10623494	—	4	1	no	—
260	#10623494	—	4	1	no	—
261	#10623494	—	4	1	no	—
262	#10623494	—	4	1	no	—
263	#10623494	#137	1	2	yes	complemented
264	C₂²×C₈₉	—	2	1	no	—
265	C₂²×C₈₉	—	2	2	no	—
266	C₂²×C₈₉	—	2	1	no	—
267	C₂²×C₈₉	—	2	1	no	—
268	C₂²×C₈₉	—	4	1	no	—
269	C₂²×C₈₉	—	4	1	no	—
270	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
271	C₄×C₈₉	—	2	1	no	—
272	C₄×C₈₉	—	2	2	no	—
273	C₄×C₈₉	—	2	1	no	—
274	C₄×C₈₉	—	2	1	no	—
275	C₄×C₈₉	—	2	1	no	—
276	C₄×C₈₉	—	4	1	no	—
277	C₄×C₈₉	—	4	1	no	—
278	C₄×C₈₉	—	4	1	no	—
279	C₄×C₈₉	—	4	1	no	—
280	C₄×C₈₉	—	4	1	no	—
281	C₄×C₈₉	—	4	1	no	—
282	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
283	C₄×C₈₉	#568	1	1	yes	characteristic
284	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
285	C₄×C₈₉	#575	1	1	yes	characteristic
286	#18047	—	89	1	no	maximal, Sylow
287	C₂×C₈₉	—	4	1	no	—
288	C₂×C₈₉	—	4	2	no	—
289	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
290	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
291	C₂×C₈₉	#2956	1	1	yes	characteristic
292	#2970	—	89	1	no	—
293	Q₈×M₁₆	—	89	1	no	—
294	C₄×#137	D₈₉	1	1	yes	characteristic
295	#1593	—	89	1	no	—
296	#1591	—	89	1	no	—
297	#1587	—	89	1	no	—
298	#1585	—	89	1	no	—
299	#1584	—	89	1	no	—
300	#1582	—	89	1	no	—
301	SD₁₆⋊C₈	—	89	1	no	—
302	C₈×SD₁₆	—	89	1	no	—
303	#1569	—	89	1	no	—
304	#1491	—	89	1	no	—
305	#1489	—	89	1	no	—
306	#1455	—	89	1	no	—
307	C₈₉	#18047	1	1	yes	characteristic, complemented, Sylow
308	C₂×#137	Dic₈₉	1	1	yes	characteristic
309	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
310	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
311	#446	—	89	1	no	—
312	#446	—	89	1	no	—
313	#446	—	89	1	no	—
314	#446	—	89	1	no	—
315	#446	—	178	1	no	—
316	#446	—	178	1	no	—
317	C₈×Q₈	—	89	1	no	—
318	C₈×Q₈	—	89	1	no	—
319	#441	Dic₈₉	1	1	yes	characteristic
320	#441	Dic₈₉	1	1	yes	characteristic
321	#440	Dic₈₉	1	1	yes	characteristic
322	#440	Dic₈₉	1	1	yes	characteristic
323	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
324	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
325	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
326	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
327	#435	—	178	1	no	—
328	#435	—	178	1	no	—
329	C₈×D₄	—	89	1	no	—
330	C₈×D₄	—	89	1	no	—
331	#432	—	89	1	no	—
332	#432	—	178	1	no	—
333	#428	Dic₈₉	1	1	yes	characteristic
334	#423	—	89	1	no	—
335	#423	—	178	1	no	—
336	#419	Dic₈₉	1	1	yes	characteristic
337	#417	Dic₈₉	1	1	yes	characteristic
338	C₄×M₁₆	—	89	1	no	—
339	C₄×M₁₆	—	89	1	no	—
340	C₄×M₁₆	—	178	1	no	—
341	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
342	C₂×#97	—	178	1	no	—
343	#335	—	89	1	no	—
344	#335	—	89	1	no	—
345	#334	—	89	1	no	—
346	#334	—	89	1	no	—
347	Q₈⋊C₈	—	89	1	no	—
348	Q₈⋊C₈	—	89	1	no	—
349	Q₈⋊C₈	—	89	1	no	—
350	Q₈⋊C₈	—	89	1	no	—
351	Q₈⋊C₈	—	89	1	no	—
352	Q₈⋊C₈	—	89	1	no	—
353	D₄⋊C₈	—	89	1	no	—
354	D₄⋊C₈	—	89	1	no	—
355	#322	—	89	1	no	—
356	#322	—	89	1	no	—
357	#322	—	89	1	no	—
358	C₈²	—	89	1	no	—
359	C₂×#41	C₂×Dic₈₉	1	1	yes	characteristic
360	C₂²×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
361	#137	—	2	4	no	—
362	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic
363	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic
364	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
365	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
366	C₂×M₁₆	—	89	1	no	—
367	C₂×M₁₆	—	89	1	no	—
368	C₂×M₁₆	—	178	1	no	—
369	C₂×M₁₆	—	178	1	no	—
370	C₂×M₁₆	C₂×Dic₈₉	1	1	yes	characteristic
371	C₂×M₁₆	C₂×Dic₈₉	1	1	yes	characteristic
372	C₂²×C₈	—	178	1	no	—
373	C₂²×C₈	—	178	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	—	2	1	no	—
376	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
377	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
378	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
379	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
380	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
381	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
385	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
386	#117	—	2	1	no	—
387	#117	C₂×Dic₈₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
393	#107	C₂×Dic₈₉	1	1	yes	characteristic
394	#107	C₂×Dic₈₉	1	1	yes	characteristic
395	#106	C₂×Dic₈₉	1	1	yes	characteristic
396	#106	C₂×Dic₈₉	1	1	yes	characteristic
397	C₄⋊C₈	—	89	1	no	—
398	C₄⋊C₈	—	89	1	no	—
399	C₄⋊C₈	—	89	1	no	—
400	C₄⋊C₈	—	89	1	no	—
401	C₄⋊C₈	—	178	1	no	—
402	C₄⋊C₈	—	178	1	no	—
403	C₄⋊C₈	—	178	1	no	—
404	C₄⋊C₈	—	178	1	no	—
405	C₄⋊C₈	—	178	1	no	—
406	C₄⋊C₈	—	178	1	no	—
407	C₄⋊C₈	—	178	1	no	—
408	#103	C₂×Dic₈₉	1	1	yes	characteristic
409	#103	C₂×Dic₈₉	1	1	yes	characteristic
410	#103	C₂×Dic₈₉	1	1	yes	characteristic
411	#103	C₂×Dic₈₉	1	1	yes	characteristic
412	#103	C₂×Dic₈₉	1	1	yes	characteristic
413	#103	C₂×Dic₈₉	1	1	yes	characteristic
414	#102	C₂×Dic₈₉	1	1	yes	characteristic
415	#102	C₂×Dic₈₉	1	1	yes	characteristic
416	C₂²⋊C₈	—	178	1	no	—
417	C₂²⋊C₈	—	178	1	no	—
418	C₂²⋊C₈	—	178	1	no	—
419	#97	—	89	1	no	—
420	#97	—	89	1	no	—
421	#97	—	178	1	no	—
422	#97	—	178	1	no	—
423	#97	—	178	1	no	—
424	#97	—	178	1	no	—
425	#97	—	178	1	no	—
426	#97	—	178	1	no	—
427	#97	C₂×Dic₈₉	1	1	yes	characteristic
428	#97	C₂×Dic₈₉	1	1	yes	characteristic
429	C₄×C₈	—	89	1	no	—
430	C₄×C₈	—	89	1	no	—
431	C₄×C₈	—	89	1	no	—
432	C₄×C₈	—	89	1	no	—
433	C₄×C₈	—	178	1	no	—
434	C₄×C₈	—	178	1	no	—
435	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
436	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
437	#41	—	2	2	no	—
438	#41	—	4	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	4	1	no	—
442	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
443	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
444	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
453	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
454	C₂²×C₄	#13083573	1	1	yes	characteristic
455	Q₁₆	—	2	2	no	—
456	Q₁₆	—	2	2	no	—
457	SD₁₆	—	2	2	no	—
458	SD₁₆	#13083558	1	4	yes	complemented
459	M₁₆	—	2	2	no	—
460	M₁₆	—	4	1	no	—
461	M₁₆	—	356	2	no	—
462	M₁₆	—	356	2	no	—
463	M₁₆	—	356	1	no	—
464	M₁₆	—	178	2	no	—
465	C₂×C₈	—	89	1	no	—
466	C₂×C₈	—	89	1	no	—
467	C₂×C₈	—	89	1	no	—
468	C₂×C₈	—	89	1	no	—
469	C₂×C₈	—	356	2	no	—
470	C₂×C₈	—	356	2	no	—
471	C₂×C₈	—	178	1	no	—
472	C₂×C₈	—	178	1	no	—
473	C₂×C₈	—	178	1	no	—
474	C₂×C₈	—	178	1	no	—
475	C₂×C₈	—	178	1	no	—
476	C₂×C₈	—	178	1	no	—
477	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
478	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
479	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
480	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
503	C₄²	D₄×D₈₉	1	1	yes	characteristic
504	C₄²	#13083573	1	1	yes	characteristic
505	C₄²	C₂³×D₈₉	1	1	yes	characteristic
506	C₂³	—	2	1	no	—
507	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
508	Q₈	—	2	1	no	—
509	Q₈	—	2	1	no	—
510	Q₈	—	2	1	no	—
511	Q₈	—	2	1	no	—
512	Q₈	—	2	1	no	—
513	Q₈	—	4	2	no	—
514	Q₈	C₂×#13083558	1	2	yes	—
515	D₄	—	2	1	no	—
516	D₄	—	4	2	no	—
517	D₄	C₂×#13083558	1	2	yes	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	8	1	no	—
535	C₂×C₄	—	8	1	no	—
536	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
537	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
538	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
539	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
540	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
541	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
542	C₈	—	2	1	no	—
543	C₈	—	2	1	no	—
544	C₈	—	2	1	no	—
545	C₈	—	89	2	no	—
546	C₈	—	356	1	no	—
547	C₈	—	356	1	no	—
548	C₈	—	356	1	no	—
549	C₈	—	356	1	no	—
550	C₈	—	356	1	no	—
551	C₈	—	178	2	no	—
552	C₈	—	178	1	no	—
553	C₈	—	178	1	no	—
554	C₈	—	178	1	no	—
555	C₈	C₂×#13083558	1	2	yes	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	2	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	C₂²×#13083558	1	1	yes	characteristic
575	C₄	#19152365	1	1	yes	characteristic
576	C₄	#137×D₈₉	1	1	yes	characteristic
577	C₄	#19152397	1	1	yes	characteristic
578	C₂	—	4	1	no	—
579	C₂	—	4	2	no	—
580	C₂	D₄×#13083558	1	1	yes	characteristic
581	C₂	#137×Dic₈₉	1	1	yes	characteristic
582	C₂	#26029162	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₄×#137×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#41×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₄×#137	D₈₉
hypocenter	C₈₉	#18047
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#137

Complements

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

N	H ≅ G/N	type
2. Q₈×#13083558	C₂	semidirect
3. #26019161	C₂	semidirect
4. #26019149	C₂	semidirect
5. #26019124	C₂	semidirect
6. #26019110	C₂	semidirect
7. #26019103	C₂	semidirect
8. #26019089	C₂	semidirect
9. SD₁₆⋊#10623494	C₂	semidirect
10. SD₁₆×#10623494	C₂	semidirect
11. #26019019	C₂	semidirect
12. #26018699	C₂	semidirect
14. #26018555	C₂	semidirect
182. SD₁₆×C₈₉	M₁₆	semidirect
263. #10623494	#137	semidirect
307. C₈₉	#18047	semidirect
458. SD₁₆	#13083558	semidirect

Maximal subgroups

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

subgroup	index
#26029266	2
Q₈×#13083558	2
#26019161	2
#26019149	2
#26019124	2
#26019110	2
#26019103	2
#26019089	2
SD₁₆⋊#10623494	2
SD₁₆×#10623494	2
#26019019	2
#26018699	2
#26018691	2
#26018555	2
C₄×#137×C₈₉	2
#18047	89