Subgroups — #36526031

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	#26029339	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#15668042	C₂	1	1	yes	maximal, characteristic
3	#26019159	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019147	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019121	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019109	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019100	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019088	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019064	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#13083562	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019017	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018686	C₂	1	1	yes	maximal, characteristic
13	#26018680	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018547	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2990	C₂	1	1	yes	maximal, characteristic
16	C₂×#15668042	C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
18	#19151728	C₂²	1	1	yes	characteristic
19	#19151728	C₂²	1	1	yes	characteristic
20	#19151727	—	2	1	no	—
21	#19151727	—	2	1	no	—
22	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
23	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
24	#19151703	C₄	1	1	yes	characteristic
25	#19151703	C₄	1	1	yes	characteristic
26	#19151698	C₄	1	1	yes	characteristic
27	#19151698	C₄	1	1	yes	characteristic
28	C₄×#13083564	C₂²	1	1	yes	characteristic
29	C₄×#13083564	C₂²	1	1	yes	characteristic
30	C₄×#13083562	C₂²	1	1	yes	characteristic
31	C₄×#13083562	C₂²	1	1	yes	characteristic
32	#19151655	C₂²	1	1	yes	characteristic
33	#19151652	—	2	1	no	—
34	#19151651	C₂²	1	1	yes	characteristic
35	#19151648	—	2	1	no	—
36	#19151641	C₄	1	1	yes	characteristic
37	#19151606	C₄	1	1	yes	characteristic
38	#19151599	C₄	1	1	yes	characteristic
39	C₄×#13083558	C₂²	1	1	yes	characteristic
40	#19151350	C₂²	1	1	yes	characteristic
41	#19151350	C₂²	1	1	yes	characteristic
42	#19151348	C₂²	1	1	yes	characteristic
43	#19151348	C₂²	1	1	yes	characteristic
44	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
45	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
46	#19151328	C₂²	1	1	yes	characteristic
47	#19151328	C₂²	1	1	yes	characteristic
48	#19151328	C₂²	1	1	yes	characteristic
49	#19151328	C₂²	1	1	yes	characteristic
50	D₄⋊#10623494	C₂²	1	1	yes	characteristic
51	D₄⋊#10623494	C₂²	1	1	yes	characteristic
52	#19151320	C₂²	1	1	yes	characteristic
53	#19151320	C₂²	1	1	yes	characteristic
54	#19151319	C₂²	1	1	yes	characteristic
55	C₈×#10623494	C₂²	1	1	yes	characteristic
56	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
57	#446×C₈₉	C₂²	1	1	yes	characteristic
58	#446×C₈₉	C₂²	1	1	yes	characteristic
59	#435×C₈₉	—	2	1	no	—
60	#435×C₈₉	—	2	1	no	—
61	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
63	#432×C₈₉	—	2	1	no	—
64	#431×C₈₉	C₂²	1	1	yes	characteristic
65	#423×C₈₉	C₂²	1	1	yes	characteristic
66	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
67	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
68	#15668042	—	2	4	no	—
69	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
72	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
73	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
74	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₁₇₈	—	2	1	no	—
76	C₄×Dic₁₇₈	—	2	1	no	—
77	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
78	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
80	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
82	C₂×#13083553	—	2	1	no	—
83	C₂×C₄×Dic₈₉	—	2	1	no	—
84	#15667945	C₂×C₄	1	1	yes	characteristic
85	#15667945	C₂×C₄	1	1	yes	characteristic
86	#15667943	C₂×C₄	1	1	yes	characteristic
87	#15667943	C₂×C₄	1	1	yes	characteristic
88	C₄⋊#10623494	—	2	1	no	—
89	C₄⋊#10623494	C₂³	1	1	yes	characteristic
90	C₄⋊#10623494	C₂³	1	1	yes	characteristic
91	#15667941	—	2	1	no	—
92	#15667941	—	2	1	no	—
93	#15667941	—	2	1	no	—
94	#15667941	—	2	1	no	—
95	#15667936	C₂×C₄	1	1	yes	characteristic
96	#15667936	C₂×C₄	1	1	yes	characteristic
97	#15667935	C₂×C₄	1	1	yes	characteristic
98	#15667935	C₂×C₄	1	1	yes	characteristic
99	#15667935	C₂×C₄	1	1	yes	characteristic
100	#15667935	C₂×C₄	1	1	yes	characteristic
101	#15667933	C₂×C₄	1	1	yes	characteristic
102	#15667933	C₂×C₄	1	1	yes	characteristic
103	C₂²⋊#10623494	—	2	1	no	—
104	C₂²⋊#10623494	—	2	1	no	—
105	#15667923	—	2	1	no	—
106	#15667923	C₂×C₄	1	1	yes	characteristic
107	#15667923	C₂×C₄	1	1	yes	characteristic
108	#15667922	—	2	1	no	—
109	#15667922	—	2	1	no	—
110	C₄×#10623494	C₂³	1	1	yes	characteristic
111	C₄×#10623494	C₂³	1	1	yes	characteristic
112	C₄×#10623494	C₂³	1	1	yes	characteristic
113	C₄×#10623494	C₂³	1	1	yes	characteristic
114	C₈×Dic₈₉	—	2	1	no	—
115	C₈×Dic₈₉	—	2	1	no	—
116	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
117	C₂×M₁₆×C₈₉	—	2	1	no	—
118	C₂²×C₈×C₈₉	—	2	1	no	—
119	C₂²×C₈×C₈₉	—	2	1	no	—
120	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
121	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₄×D₄×C₈₉	—	2	1	no	—
123	C₄×D₄×C₈₉	—	2	1	no	—
124	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
125	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
126	#117×C₈₉	—	2	1	no	—
127	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
128	C₂×C₄²×C₈₉	—	2	1	no	—
129	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
130	C₄⋊C₈×C₈₉	—	2	1	no	—
131	C₄⋊C₈×C₈₉	—	2	1	no	—
132	C₄⋊C₈×C₈₉	—	2	1	no	—
133	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
134	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
135	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
137	C₂²⋊C₈×C₈₉	—	2	1	no	—
138	C₂²⋊C₈×C₈₉	—	2	1	no	—
139	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
141	#97×C₈₉	—	2	1	no	—
142	#97×C₈₉	—	2	1	no	—
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×Dic₁₇₈	—	2	2	no	—
146	C₂×Dic₁₇₈	—	2	1	no	—
147	C₂×Dic₁₇₈	—	4	1	no	—
148	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
150	C₂²×Dic₈₉	—	2	1	no	—
151	C₂²×Dic₈₉	—	2	1	no	—
152	#13083564	—	2	2	no	—
153	#13083564	—	2	2	no	—
154	#13083562	—	2	2	no	—
155	#13083562	M₁₆	1	4	yes	complemented
156	#13083558	—	2	2	no	—
157	#13083558	—	4	1	no	—
158	C₂×#10623494	—	2	1	no	—
159	C₂×#10623494	—	2	1	no	—
160	C₂×#10623494	—	2	1	no	—
161	C₂×#10623494	—	2	1	no	—
162	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
163	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
164	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
165	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
166	C₄⋊Dic₈₉	—	2	1	no	—
167	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
169	#13083553	—	2	1	no	—
170	#13083553	—	2	1	no	—
171	#13083553	—	2	1	no	—
172	#13083553	—	2	1	no	—
173	C₄×Dic₈₉	—	2	1	no	—
174	C₄×Dic₈₉	—	2	1	no	—
175	C₄×Dic₈₉	—	2	1	no	—
176	C₄×Dic₈₉	—	2	1	no	—
177	#41×C₈₉	—	2	2	no	—
178	#41×C₈₉	—	4	1	no	—
179	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
180	C₂×D₄×C₈₉	—	2	1	no	—
181	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₈₉	—	2	1	no	—
183	C₂²×C₄×C₈₉	—	2	1	no	—
184	C₂²×C₄×C₈₉	—	2	1	no	—
185	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
188	M₁₆×C₈₉	—	8	1	no	—
189	C₂×C₈×C₈₉	—	2	1	no	—
190	C₂×C₈×C₈₉	—	2	1	no	—
191	C₂×C₈×C₈₉	—	8	1	no	—
192	C₂×C₈×C₈₉	—	8	1	no	—
193	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
197	C₄⋊C₄×C₈₉	—	2	1	no	—
198	C₄⋊C₄×C₈₉	—	2	1	no	—
199	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
200	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
201	C₂²⋊C₄×C₈₉	—	2	1	no	—
202	C₂²⋊C₄×C₈₉	—	2	1	no	—
203	C₂²⋊C₄×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	D₄×C₈₉	—	2	1	no	—
216	D₄×C₈₉	—	4	2	no	—
217	D₄×C₈₉	C₂×M₁₆	1	2	yes	—
218	C₂×C₄×C₈₉	—	2	1	no	—
219	C₂×C₄×C₈₉	—	2	1	no	—
220	C₂×C₄×C₈₉	—	2	1	no	—
221	C₂×C₄×C₈₉	—	2	1	no	—
222	C₂×C₄×C₈₉	—	2	1	no	—
223	C₂×C₄×C₈₉	—	2	1	no	—
224	C₂×C₄×C₈₉	—	2	1	no	—
225	C₂×C₄×C₈₉	—	4	1	no	—
226	C₂×C₄×C₈₉	—	4	2	no	—
227	C₂×C₄×C₈₉	—	4	2	no	—
228	C₂×C₄×C₈₉	—	4	1	no	—
229	C₂×C₄×C₈₉	—	4	1	no	—
230	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
236	C₂×Dic₈₉	—	2	1	no	—
237	C₂×Dic₈₉	—	2	1	no	—
238	C₂×Dic₈₉	—	2	1	no	—
239	C₂×Dic₈₉	—	2	1	no	—
240	C₂×Dic₈₉	—	4	2	no	—
241	C₂×Dic₈₉	—	4	2	no	—
242	Dic₁₇₈	—	2	1	no	—
243	Dic₁₇₈	—	2	1	no	—
244	Dic₁₇₈	—	2	1	no	—
245	Dic₁₇₈	—	4	2	no	—
246	Dic₁₇₈	C₂×M₁₆	1	2	yes	—
247	C₈×C₈₉	—	2	1	no	—
248	C₈×C₈₉	—	2	1	no	—
249	C₈×C₈₉	—	2	1	no	—
250	C₈×C₈₉	—	2	1	no	—
251	C₈×C₈₉	—	4	1	no	—
252	C₈×C₈₉	—	4	1	no	—
253	#10623494	—	2	1	no	—
254	#10623494	—	2	1	no	—
255	#10623494	—	2	1	no	—
256	#10623494	—	4	1	no	—
257	#10623494	—	4	1	no	—
258	#10623494	—	4	1	no	—
259	#10623494	—	4	1	no	—
260	#10623494	C₂×M₁₆	1	2	yes	—
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	1	no	—
270	C₄×C₈₉	—	2	1	no	—
271	C₄×C₈₉	—	2	1	no	—
272	C₄×C₈₉	—	4	1	no	—
273	C₄×C₈₉	—	4	1	no	—
274	C₄×C₈₉	—	4	1	no	—
275	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
276	C₄×C₈₉	#568	1	1	yes	characteristic
277	C₄×C₈₉	#577	1	1	yes	characteristic
278	C₄×C₈₉	#578	1	1	yes	characteristic
279	Dic₈₉	—	2	2	no	—
280	Dic₈₉	—	4	1	no	—
281	Dic₈₉	—	4	1	no	—
282	Dic₈₉	—	4	1	no	—
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	D₈₉	1	1	yes	characteristic
290	#2984	—	89	1	no	—
291	C₄×#137	—	89	1	no	—
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	—	89	1	no	—
306	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
307	C₂×C₄×Q₈	—	89	1	no	—
308	#446	—	89	1	no	—
309	#446	—	89	1	no	—
310	#446	—	178	1	no	—
311	#446	—	178	1	no	—
312	#446	C₂×D₈₉	1	1	yes	characteristic
313	#446	C₂×D₈₉	1	1	yes	characteristic
314	C₈×Q₈	—	89	1	no	—
315	C₈×Q₈	—	89	1	no	—
316	#441	—	89	1	no	—
317	#441	—	89	1	no	—
318	#440	—	89	1	no	—
319	#440	—	89	1	no	—
320	C₄×Q₁₆	—	89	1	no	—
321	C₄×Q₁₆	—	89	1	no	—
322	C₄×SD₁₆	—	89	1	no	—
323	C₄×SD₁₆	—	89	1	no	—
324	#435	—	2	1	no	—
325	#435	—	2	1	no	—
326	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
327	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
328	#432	—	2	1	no	—
329	#432	—	89	1	no	—
330	#432	—	178	1	no	—
331	#431	—	89	1	no	—
332	#431	—	178	1	no	—
333	#431	C₂×D₈₉	1	1	yes	characteristic
334	#428	—	89	1	no	—
335	#423	C₂×D₈₉	1	1	yes	characteristic
336	C₂×C₄⋊C₈	—	2	1	no	—
337	#419	—	89	1	no	—
338	#417	—	89	1	no	—
339	C₄×M₁₆	—	89	1	no	—
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	C₄×D₈₉	1	1	yes	characteristic
357	C₂²×Q₈	—	89	1	no	—
358	#137	—	178	4	no	—
359	C₂×Q₁₆	—	89	1	no	—
360	C₂×Q₁₆	—	89	1	no	—
361	C₂×SD₁₆	—	89	1	no	—
362	C₂×SD₁₆	—	89	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	89	1	no	—
365	C₂×M₁₆	—	89	1	no	—
366	C₂²×C₈	—	2	1	no	—
367	C₂²×C₈	—	2	1	no	—
368	C₄×Q₈	—	89	1	no	—
369	C₄×Q₈	—	89	1	no	—
370	C₄×Q₈	—	89	1	no	—
371	C₄×Q₈	—	89	1	no	—
372	C₄×Q₈	—	178	1	no	—
373	C₄×Q₈	—	178	1	no	—
374	C₄×Q₈	C₄×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	C₄×D₈₉	1	1	yes	characteristic
379	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
380	#117	—	2	1	no	—
381	#117	C₄×D₈₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	—	89	1	no	—
383	C₂×C₄⋊C₄	—	178	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	178	1	no	—
386	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
387	#107	—	89	1	no	—
388	#107	—	89	1	no	—
389	#106	—	89	1	no	—
390	#106	—	89	1	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	89	1	no	—
395	C₄⋊C₈	—	89	1	no	—
396	C₄⋊C₈	—	178	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	C₂²⋊D₈₉	1	1	yes	characteristic
402	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
403	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
404	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
405	#103	—	89	1	no	—
406	#103	—	89	1	no	—
407	#103	—	89	1	no	—
408	#103	—	89	1	no	—
409	#103	—	89	1	no	—
410	#103	—	89	1	no	—
411	#102	—	89	1	no	—
412	#102	—	89	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	—	2	1	no	—
415	C₂²⋊C₈	—	178	1	no	—
416	C₂²⋊C₈	—	178	1	no	—
417	C₂²⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
418	C₂²⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
419	#97	—	2	1	no	—
420	#97	—	2	1	no	—
421	#97	—	89	1	no	—
422	#97	—	89	1	no	—
423	#97	—	178	1	no	—
424	#97	—	178	1	no	—
425	#97	—	178	1	no	—
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	—	89	1	no	—
437	C₂×Q₈	—	89	1	no	—
438	C₂×Q₈	—	356	1	no	—
439	C₂×Q₈	—	178	2	no	—
440	C₂×Q₈	—	178	1	no	—
441	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	C₂×C₄×D₈₉	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	—	178	1	no	—
448	C₂²×C₄	—	178	1	no	—
449	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
451	C₂²×C₄	#13083574	1	1	yes	characteristic
452	Q₁₆	—	178	2	no	—
453	Q₁₆	—	178	2	no	—
454	SD₁₆	—	89	4	no	—
455	SD₁₆	—	178	2	no	—
456	M₁₆	—	8	1	no	—
457	M₁₆	—	356	1	no	—
458	M₁₆	—	178	2	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	8	1	no	—
462	C₂×C₈	—	8	1	no	—
463	C₂×C₈	—	89	1	no	—
464	C₂×C₈	—	89	1	no	—
465	C₂×C₈	—	89	1	no	—
466	C₂×C₈	—	89	1	no	—
467	C₂×C₈	—	178	1	no	—
468	C₂×C₈	—	178	1	no	—
469	C₂×C₈	—	178	1	no	—
470	C₂×C₈	—	178	1	no	—
471	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
472	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
473	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
474	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	89	1	no	—
478	C₄⋊C₄	—	89	1	no	—
479	C₄⋊C₄	—	178	1	no	—
480	C₄⋊C₄	—	178	1	no	—
481	C₄⋊C₄	—	178	1	no	—
482	C₄⋊C₄	—	178	1	no	—
483	C₄⋊C₄	—	178	1	no	—
484	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
485	C₄⋊C₄	C₂×C₄×D₈₉	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	—	178	1	no	—
493	C₄²	—	178	1	no	—
494	C₄²	—	178	1	no	—
495	C₄²	—	178	1	no	—
496	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
497	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
498	C₄²	#13083574	1	1	yes	characteristic
499	C₄²	C₂³×D₈₉	1	1	yes	characteristic
500	C₂³	—	2	1	no	—
501	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	89	2	no	—
505	Q₈	—	356	2	no	—
506	Q₈	—	178	1	no	—
507	Q₈	—	178	1	no	—
508	Q₈	—	178	1	no	—
509	D₄	—	2	1	no	—
510	D₄	—	4	2	no	—
511	D₄	M₁₆×D₈₉	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	—	4	1	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	356	2	no	—
525	C₂×C₄	—	356	2	no	—
526	C₂×C₄	—	178	1	no	—
527	C₂×C₄	—	178	1	no	—
528	C₂×C₄	—	178	1	no	—
529	C₂×C₄	—	178	1	no	—
530	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
531	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
532	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
533	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
534	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
535	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	89	2	no	—
543	C₈	—	356	1	no	—
544	C₈	—	356	1	no	—
545	C₈	—	356	1	no	—
546	C₈	—	356	1	no	—
547	C₈	—	178	1	no	—
548	C₈	—	178	1	no	—
549	C₈	—	178	1	no	—
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×C₄×C₂²⋊D₈₉	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	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	356	1	no	—
565	C₄	—	356	1	no	—
566	C₄	—	356	1	no	—
567	C₄	—	178	2	no	—
568	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
569	C₄	#19152364	1	1	yes	characteristic
570	C₄	#19152409	1	1	yes	characteristic
571	C₄	#19152413	1	1	yes	characteristic
572	C₂	—	4	1	no	—
573	C₂	—	4	2	no	—
574	C₂	M₁₆×C₂²⋊D₈₉	1	1	yes	characteristic
575	C₂	#26029091	1	1	yes	characteristic
576	C₂	#26029153	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2990	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#41×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2990	D₈₉
hypocenter	C₈₉	#18051
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2990

Complements

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

N	H ≅ G/N	type
1. #26029339	C₂	semidirect
3. #26019159	C₂	semidirect
4. #26019147	C₂	semidirect
5. #26019121	C₂	semidirect
6. #26019109	C₂	semidirect
7. #26019100	C₂	semidirect
8. #26019088	C₂	semidirect
9. #26019064	C₂	semidirect
10. C₈×#13083562	C₂	semidirect
11. #26019017	C₂	semidirect
13. #26018680	C₂	semidirect
14. #26018547	C₂	semidirect
155. #13083562	M₁₆	semidirect
304. C₈₉	#18051	semidirect

Maximal subgroups

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

subgroup	index
#26029339	2
C₄×#15668042	2
#26019159	2
#26019147	2
#26019121	2
#26019109	2
#26019100	2
#26019088	2
#26019064	2
C₈×#13083562	2
#26019017	2
#26018686	2
#26018680	2
#26018547	2
C₈₉×#2990	2
#18051	89