Subgroups — #36526037

Order 22784.

626 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029377	C₂	1	1	yes	maximal, characteristic
2	#26029341	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	#26018686	C₂	1	1	yes	maximal, characteristic
13	#26018681	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018549	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	—	2	1	no	—
30	#19151655	C₂²	1	1	yes	characteristic
31	#19151651	—	2	1	no	—
32	#19151651	C₂²	1	1	yes	characteristic
33	#19151651	C₂²	1	1	yes	characteristic
34	#19151622	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊#10623494	—	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	C₂²×#10623494	—	2	1	no	—
69	C₂²×#10623494	—	2	1	no	—
70	C₄⋊#10623494	—	2	1	no	—
71	C₄⋊#10623494	—	2	1	no	—
72	C₄⋊#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	D₄	1	1	yes	characteristic
79	C₄⋊#10623494	D₄	1	1	yes	characteristic
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	C₂²⋊#10623494	—	2	1	no	—
88	C₂²⋊#10623494	D₄	1	1	yes	characteristic
89	C₂²⋊#10623494	D₄	1	1	yes	characteristic
90	#15667923	—	2	1	no	—
91	#15667923	—	2	1	no	—
92	#15667923	—	2	1	no	—
93	#15667923	—	2	1	no	—
94	#15667923	—	2	1	no	—
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	—	8	1	no	—
146	C₂×#10623494	—	2	1	no	—
147	C₂×#10623494	—	2	1	no	—
148	C₂×#10623494	—	2	1	no	—
149	C₂×#10623494	—	2	1	no	—
150	C₂×#10623494	—	2	1	no	—
151	C₂×#10623494	—	2	1	no	—
152	C₂×#10623494	—	8	1	no	—
153	C₂×#10623494	—	8	1	no	—
154	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
155	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
156	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
157	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
158	#41×C₈₉	—	2	2	no	—
159	#41×C₈₉	—	4	1	no	—
160	C₂×Q₈×C₈₉	—	2	1	no	—
161	C₂×Q₈×C₈₉	—	2	2	no	—
162	C₂×Q₈×C₈₉	—	4	1	no	—
163	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
166	C₂×D₄×C₈₉	—	2	1	no	—
167	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₉	—	2	1	no	—
169	C₂²×C₄×C₈₉	—	2	1	no	—
170	C₂²×C₄×C₈₉	—	2	1	no	—
171	C₂²×C₄×C₈₉	—	2	1	no	—
172	C₂²×C₄×C₈₉	—	2	1	no	—
173	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
176	Q₁₆×C₈₉	—	2	2	no	—
177	Q₁₆×C₈₉	—	2	2	no	—
178	SD₁₆×C₈₉	—	2	2	no	—
179	SD₁₆×C₈₉	M₁₆	1	4	yes	complemented
180	M₁₆×C₈₉	—	2	2	no	—
181	M₁₆×C₈₉	—	4	1	no	—
182	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
186	C₄⋊C₄×C₈₉	—	2	1	no	—
187	C₄⋊C₄×C₈₉	—	2	1	no	—
188	C₄⋊C₄×C₈₉	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
194	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
195	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
197	C₂²⋊C₄×C₈₉	—	2	1	no	—
198	C₂²⋊C₄×C₈₉	—	2	1	no	—
199	C₂²⋊C₄×C₈₉	—	2	1	no	—
200	C₄²×C₈₉	—	2	1	no	—
201	C₄²×C₈₉	—	2	1	no	—
202	C₄²×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	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₈₉	#41	1	1	yes	characteristic
210	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
211	C₂³×C₈₉	—	2	1	no	—
212	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
213	Q₈×C₈₉	—	2	1	no	—
214	Q₈×C₈₉	—	2	1	no	—
215	Q₈×C₈₉	—	2	1	no	—
216	Q₈×C₈₉	—	2	1	no	—
217	Q₈×C₈₉	—	2	1	no	—
218	Q₈×C₈₉	—	4	2	no	—
219	Q₈×C₈₉	C₂×M₁₆	1	2	yes	—
220	D₄×C₈₉	—	2	1	no	—
221	D₄×C₈₉	—	4	2	no	—
222	D₄×C₈₉	C₂×M₁₆	1	2	yes	—
223	C₂×C₄×C₈₉	—	2	1	no	—
224	C₂×C₄×C₈₉	—	2	1	no	—
225	C₂×C₄×C₈₉	—	2	1	no	—
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	—	4	1	no	—
235	C₂×C₄×C₈₉	—	4	2	no	—
236	C₂×C₄×C₈₉	—	4	2	no	—
237	C₂×C₄×C₈₉	—	4	2	no	—
238	C₂×C₄×C₈₉	—	4	2	no	—
239	C₂×C₄×C₈₉	—	4	1	no	—
240	C₂×C₄×C₈₉	—	4	1	no	—
241	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
247	C₈×C₈₉	—	2	1	no	—
248	C₈×C₈₉	—	2	1	no	—
249	C₈×C₈₉	—	2	1	no	—
250	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
251	#10623494	—	2	1	no	—
252	#10623494	—	2	1	no	—
253	#10623494	—	2	1	no	—
254	#10623494	—	2	1	no	—
255	#10623494	—	4	1	no	—
256	#10623494	—	4	1	no	—
257	#10623494	—	4	1	no	—
258	#10623494	—	4	1	no	—
259	#10623494	—	4	1	no	—
260	#10623494	—	4	1	no	—
261	C₂²×C₈₉	—	2	1	no	—
262	C₂²×C₈₉	—	2	2	no	—
263	C₂²×C₈₉	—	2	1	no	—
264	C₂²×C₈₉	—	2	1	no	—
265	C₂²×C₈₉	—	4	1	no	—
266	C₂²×C₈₉	—	4	1	no	—
267	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
268	C₄×C₈₉	—	2	1	no	—
269	C₄×C₈₉	—	2	2	no	—
270	C₄×C₈₉	—	2	1	no	—
271	C₄×C₈₉	—	2	1	no	—
272	C₄×C₈₉	—	2	1	no	—
273	C₄×C₈₉	—	4	1	no	—
274	C₄×C₈₉	—	4	1	no	—
275	C₄×C₈₉	—	4	1	no	—
276	C₄×C₈₉	—	4	1	no	—
277	C₄×C₈₉	—	4	1	no	—
278	C₄×C₈₉	—	4	1	no	—
279	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
280	C₄×C₈₉	#568	1	1	yes	characteristic
281	C₄×C₈₉	#577	1	1	yes	characteristic
282	C₄×C₈₉	#578	1	1	yes	characteristic
283	#18051	—	89	1	no	maximal, Sylow
284	C₂×C₈₉	—	4	1	no	—
285	C₂×C₈₉	—	4	2	no	—
286	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
287	C₂×C₈₉	#2947	1	1	yes	characteristic
288	C₂×C₈₉	#2955	1	1	yes	characteristic
289	#2990	—	89	1	no	—
290	#2984	—	89	1	no	—
291	C₄×#137	D₈₉	1	1	yes	characteristic
292	#1593	—	89	1	no	—
293	#1591	—	89	1	no	—
294	#1587	—	89	1	no	—
295	#1585	—	89	1	no	—
296	#1584	—	89	1	no	—
297	#1582	—	89	1	no	—
298	SD₁₆⋊C₈	—	89	1	no	—
299	C₈×SD₁₆	—	89	1	no	—
300	#1569	—	89	1	no	—
301	#1488	—	89	1	no	—
302	#1487	—	89	1	no	—
303	#1453	—	89	1	no	—
304	C₈₉	#18051	1	1	yes	characteristic, complemented, Sylow
305	C₂×#137	Dic₈₉	1	1	yes	characteristic
306	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
307	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
308	#446	—	89	1	no	—
309	#446	—	89	1	no	—
310	#446	—	89	1	no	—
311	#446	—	89	1	no	—
312	#446	—	178	1	no	—
313	#446	—	178	1	no	—
314	C₈×Q₈	—	89	1	no	—
315	C₈×Q₈	—	89	1	no	—
316	#441	Dic₈₉	1	1	yes	characteristic
317	#441	Dic₈₉	1	1	yes	characteristic
318	#440	Dic₈₉	1	1	yes	characteristic
319	#440	Dic₈₉	1	1	yes	characteristic
320	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
321	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
322	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
323	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
324	#435	—	178	1	no	—
325	#435	—	178	1	no	—
326	C₈×D₄	—	89	1	no	—
327	C₈×D₄	—	89	1	no	—
328	#432	—	89	1	no	—
329	#432	—	178	1	no	—
330	#432	—	178	1	no	—
331	#431	—	89	1	no	—
332	#431	—	89	1	no	—
333	#431	—	178	1	no	—
334	#428	Dic₈₉	1	1	yes	characteristic
335	#423	—	89	1	no	—
336	C₂×C₄⋊C₈	—	178	1	no	—
337	#419	Dic₈₉	1	1	yes	characteristic
338	#417	Dic₈₉	1	1	yes	characteristic
339	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
340	#335	—	89	1	no	—
341	#335	—	89	1	no	—
342	#334	—	89	1	no	—
343	#334	—	89	1	no	—
344	Q₈⋊C₈	—	89	1	no	—
345	Q₈⋊C₈	—	89	1	no	—
346	Q₈⋊C₈	—	89	1	no	—
347	Q₈⋊C₈	—	89	1	no	—
348	Q₈⋊C₈	—	89	1	no	—
349	Q₈⋊C₈	—	89	1	no	—
350	D₄⋊C₈	—	89	1	no	—
351	D₄⋊C₈	—	89	1	no	—
352	#322	—	89	1	no	—
353	#322	—	89	1	no	—
354	#322	—	89	1	no	—
355	C₈²	—	89	1	no	—
356	C₂×#41	C₂×Dic₈₉	1	1	yes	characteristic
357	C₂²×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
358	#137	—	2	4	no	—
359	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic
360	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic
361	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
362	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
363	C₂×M₁₆	—	178	1	no	—
364	C₂×M₁₆	C₂×Dic₈₉	1	1	yes	characteristic
365	C₂×M₁₆	C₂×Dic₈₉	1	1	yes	characteristic
366	C₂²×C₈	—	178	1	no	—
367	C₂²×C₈	—	178	1	no	—
368	C₄×Q₈	—	2	1	no	—
369	C₄×Q₈	—	2	1	no	—
370	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
371	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
372	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
373	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
374	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
375	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
379	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
380	#117	—	2	1	no	—
381	#117	C₂×Dic₈₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
387	#107	C₂×Dic₈₉	1	1	yes	characteristic
388	#107	C₂×Dic₈₉	1	1	yes	characteristic
389	#106	C₂×Dic₈₉	1	1	yes	characteristic
390	#106	C₂×Dic₈₉	1	1	yes	characteristic
391	C₄⋊C₈	—	89	1	no	—
392	C₄⋊C₈	—	89	1	no	—
393	C₄⋊C₈	—	89	1	no	—
394	C₄⋊C₈	—	89	1	no	—
395	C₄⋊C₈	—	89	1	no	—
396	C₄⋊C₈	—	89	1	no	—
397	C₄⋊C₈	—	178	1	no	—
398	C₄⋊C₈	—	178	1	no	—
399	C₄⋊C₈	—	178	1	no	—
400	C₄⋊C₈	—	178	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	#103	C₂×Dic₈₉	1	1	yes	characteristic
406	#103	C₂×Dic₈₉	1	1	yes	characteristic
407	#103	C₂×Dic₈₉	1	1	yes	characteristic
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	#102	C₂×Dic₈₉	1	1	yes	characteristic
412	#102	C₂×Dic₈₉	1	1	yes	characteristic
413	C₂²⋊C₈	—	89	1	no	—
414	C₂²⋊C₈	—	89	1	no	—
415	C₂²⋊C₈	—	178	1	no	—
416	C₂²⋊C₈	—	178	1	no	—
417	C₂²⋊C₈	—	178	1	no	—
418	C₂²⋊C₈	—	178	1	no	—
419	#97	—	178	1	no	—
420	#97	—	178	1	no	—
421	#97	—	178	1	no	—
422	#97	—	178	1	no	—
423	#97	—	178	1	no	—
424	#97	C₂×Dic₈₉	1	1	yes	characteristic
425	#97	C₂×Dic₈₉	1	1	yes	characteristic
426	C₄×C₈	—	89	1	no	—
427	C₄×C₈	—	89	1	no	—
428	C₄×C₈	—	89	1	no	—
429	C₄×C₈	—	89	1	no	—
430	C₄×C₈	—	178	1	no	—
431	C₄×C₈	—	178	1	no	—
432	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
434	#41	—	2	2	no	—
435	#41	—	4	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	4	1	no	—
439	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
440	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
441	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
450	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
451	C₂²×C₄	#13083573	1	1	yes	characteristic
452	Q₁₆	—	2	2	no	—
453	Q₁₆	—	2	2	no	—
454	SD₁₆	—	2	2	no	—
455	SD₁₆	#13083558	1	4	yes	complemented
456	M₁₆	—	2	2	no	—
457	M₁₆	—	4	1	no	—
458	M₁₆	—	712	1	no	—
459	C₂×C₈	—	89	1	no	—
460	C₂×C₈	—	89	1	no	—
461	C₂×C₈	—	89	1	no	—
462	C₂×C₈	—	89	1	no	—
463	C₂×C₈	—	178	1	no	—
464	C₂×C₈	—	178	1	no	—
465	C₂×C₈	—	178	1	no	—
466	C₂×C₈	—	178	1	no	—
467	C₂×C₈	—	178	1	no	—
468	C₂×C₈	—	178	1	no	—
469	C₂×C₈	—	712	1	no	—
470	C₂×C₈	—	712	1	no	—
471	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
472	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
473	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
474	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
497	C₄²	D₄×D₈₉	1	1	yes	characteristic
498	C₄²	#13083573	1	1	yes	characteristic
499	C₄²	C₂³×D₈₉	1	1	yes	characteristic
500	C₂³	—	2	1	no	—
501	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	4	2	no	—
508	Q₈	C₂×#13083558	1	2	yes	—
509	D₄	—	2	1	no	—
510	D₄	—	4	2	no	—
511	D₄	C₂×#13083558	1	2	yes	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
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	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
531	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
532	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
533	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
534	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
535	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	356	1	no	—
540	C₈	—	356	1	no	—
541	C₈	—	356	1	no	—
542	C₈	—	356	1	no	—
543	C₈	—	356	1	no	—
544	C₈	—	356	1	no	—
545	C₈	—	178	1	no	—
546	C₈	—	178	1	no	—
547	C₈	—	178	1	no	—
548	C₈	—	178	1	no	—
549	C₈	C₂×#13083558	1	2	yes	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	2	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	C₂²×#13083558	1	1	yes	characteristic
569	C₄	#19152365	1	1	yes	characteristic
570	C₄	#19152407	1	1	yes	characteristic
571	C₄	#19152414	1	1	yes	characteristic
572	C₂	—	4	1	no	—
573	C₂	—	4	2	no	—
574	C₂	D₄×#13083558	1	1	yes	characteristic
575	C₂	#26029096	1	1	yes	characteristic
576	C₂	#26029155	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	#18051
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. #26029341	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
13. #26018681	C₂	semidirect
14. #26018549	C₂	semidirect
179. SD₁₆×C₈₉	M₁₆	semidirect
304. C₈₉	#18051	semidirect
455. SD₁₆	#13083558	semidirect

Maximal subgroups

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

subgroup	index
#26029377	2
#26029341	2
#26019161	2
#26019149	2
#26019124	2
#26019110	2
#26019103	2
#26019089	2
SD₁₆⋊#10623494	2
SD₁₆×#10623494	2
#26019019	2
#26018686	2
#26018681	2
#26018549	2
C₄×#137×C₈₉	2
#18051	89