Subgroups — #36523475

Order 22784.

666 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029371	C₂	1	2	yes	maximal
2	C₄×#15668018	C₂	1	1	yes	maximal, characteristic
3	#26019020	C₂	1	2	yes	maximal, complemented
4	#26019016	C₂	1	2	yes	maximal, complemented
5	#26019014	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019011	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019009	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019001	C₂	1	2	yes	maximal, complemented
9	#26018999	C₂	1	1	yes	maximal, characteristic, complemented
10	#335×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	C₄	1	1	yes	characteristic
13	C₂×#15668018	C₄	1	1	yes	characteristic
14	C₄×#13083574	C₂²	1	1	yes	characteristic
15	#19151726	—	2	2	no	—
16	#19151673	—	2	2	no	—
17	#19151672	—	2	2	no	—
18	#19151671	—	2	2	no	—
19	#19151654	C₂²	1	2	yes	—
20	#19151650	C₂²	1	2	yes	—
21	#19151622	C₂²	1	2	yes	—
22	#19151620	C₂²	1	2	yes	—
23	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
24	#19151553	C₄	1	1	yes	characteristic
25	#19151553	C₄	1	1	yes	characteristic
26	#19151552	C₄	1	1	yes	characteristic
27	#19151552	C₄	1	1	yes	characteristic
28	#19151552	C₄	1	1	yes	characteristic
29	#19151552	C₄	1	1	yes	characteristic
30	C₄×#13083558	C₂²	1	1	yes	characteristic
31	C₄×#13083557	C₂²	1	1	yes	characteristic
32	C₄×#13083557	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
35	#19151351	C₂²	1	1	yes	characteristic
36	#19151351	C₂²	1	1	yes	characteristic
37	#19151351	C₂²	1	2	yes	—
38	#19151350	C₂²	1	2	yes	—
39	#19151350	C₂²	1	2	yes	—
40	#19151348	C₂²	1	2	yes	—
41	#19151348	C₂²	1	2	yes	—
42	#432×C₈₉	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
44	#335×C₈₉	C₂²	1	1	yes	characteristic
45	#335×C₈₉	C₂²	1	1	yes	characteristic
46	#334×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
48	#15668018	—	2	4	no	—
49	#15668018	—	2	4	no	—
50	C₂×#13083558	—	2	2	no	—
51	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
52	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
53	C₂×#13083557	—	2	2	no	—
54	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
55	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
56	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
57	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₈₉	—	2	2	no	—
59	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₁₇₈	D₄	1	1	yes	characteristic
64	C₄×Dic₁₇₈	Q₈	1	1	yes	characteristic
65	C₄×D₃₅₆	D₄	1	1	yes	characteristic
66	C₄×D₃₅₆	Q₈	1	1	yes	characteristic
67	C₄×C₂²⋊D₈₉	D₄	1	1	yes	characteristic
68	C₄×C₂²⋊D₈₉	D₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₈₉	Q₈	1	1	yes	characteristic
70	C₄×C₂²⋊D₈₉	Q₈	1	1	yes	characteristic
71	#15667971	C₂×C₄	1	1	yes	characteristic
72	#15667969	C₂×C₄	1	1	yes	characteristic
73	#15667969	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₈₉	C₂³	1	1	yes	characteristic
75	C₄²×D₈₉	C₂³	1	1	yes	characteristic
76	C₄⋊#10623494	—	2	2	no	—
77	C₄⋊#10623494	C₂³	1	2	yes	—
78	C₄⋊#10623494	C₂³	1	2	yes	—
79	#15667941	—	2	2	no	—
80	#15667941	—	2	2	no	—
81	#15667924	—	2	2	no	—
82	#15667924	—	2	2	no	—
83	#15667923	C₂×C₄	1	1	yes	characteristic
84	#15667923	C₂×C₄	1	1	yes	characteristic
85	#15667922	—	2	2	no	—
86	#15667922	C₂×C₄	1	1	yes	characteristic
87	#15667922	C₂×C₄	1	1	yes	characteristic
88	#15667922	C₂×C₄	1	1	yes	characteristic
89	#15667922	C₂×C₄	1	1	yes	characteristic
90	C₄×#10623494	C₂³	1	1	yes	characteristic
91	C₄×#10623494	C₂³	1	1	yes	characteristic
92	C₈×Dic₈₉	—	2	2	no	—
93	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
97	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
101	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
102	C₂²⋊C₈×C₈₉	—	2	2	no	—
103	#97×C₈₉	—	2	2	no	—
104	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
105	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
106	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	#13083574	—	2	2	no	—
109	#13083574	—	2	2	no	—
110	C₂×Dic₁₇₈	C₄⋊C₄	1	1	yes	characteristic
111	C₂×D₃₅₆	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₂²⋊D₈₉	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₂²⋊D₈₉	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
119	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
120	#13083558	—	2	2	no	—
121	#13083558	—	2	2	no	—
122	#13083558	—	8	2	no	—
123	#13083557	—	2	2	no	—
124	#13083557	—	2	2	no	—
125	#13083557	—	2	2	no	—
126	#13083557	—	8	2	no	—
127	#13083557	M₁₆	1	4	yes	complemented
128	C₂×#10623494	—	2	2	no	—
129	C₂×#10623494	—	2	2	no	—
130	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
131	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
132	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
133	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
134	C₈×D₈₉	—	2	2	no	—
135	C₈×D₈₉	—	2	2	no	—
136	C₈×D₈₉	—	2	2	no	—
137	C₈×D₈₉	—	8	2	no	—
138	C₈×D₈₉	M₁₆	1	4	yes	complemented
139	C₄⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
140	C₄⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
141	#13083553	C₄⋊C₄	1	1	yes	characteristic
142	#13083553	C₄⋊C₄	1	1	yes	characteristic
143	#13083553	C₄⋊C₄	1	1	yes	characteristic
144	#13083553	C₄⋊C₄	1	1	yes	characteristic
145	C₂²⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
146	C₂²⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
147	#13083551	C₄⋊C₄	1	1	yes	characteristic
148	#13083551	C₄⋊C₄	1	1	yes	characteristic
149	#13083551	C₄⋊C₄	1	1	yes	characteristic
150	#13083551	C₄⋊C₄	1	1	yes	characteristic
151	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
154	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
155	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
156	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
157	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
160	C₂×C₈×C₈₉	—	2	2	no	—
161	C₂×C₈×C₈₉	—	2	2	no	—
162	C₂×C₈×C₈₉	—	2	2	no	—
163	C₂×C₈×C₈₉	—	2	2	no	—
164	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
171	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
172	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	—	2	1	no	—
176	C₂×C₄×C₈₉	—	2	1	no	—
177	C₂×C₄×C₈₉	—	2	1	no	—
178	C₂×C₄×C₈₉	—	2	1	no	—
179	C₂×C₄×C₈₉	—	4	1	no	—
180	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
186	C₂²⋊D₈₉	—	2	2	no	—
187	C₂²⋊D₈₉	—	2	2	no	—
188	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
194	D₃₅₆	—	2	2	no	—
195	C₄×D₈₉	—	2	1	no	—
196	C₄×D₈₉	—	2	1	no	—
197	C₄×D₈₉	—	2	1	no	—
198	C₄×D₈₉	—	2	1	no	—
199	C₄×D₈₉	—	2	1	no	—
200	C₄×D₈₉	—	2	1	no	—
201	C₄×D₈₉	—	4	1	no	—
202	C₄×D₈₉	—	4	1	no	—
203	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
204	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
205	Dic₁₇₈	—	2	2	no	—
206	C₈×C₈₉	—	2	1	no	—
207	C₈×C₈₉	—	2	1	no	—
208	C₈×C₈₉	—	4	2	no	—
209	C₈×C₈₉	—	4	2	no	—
210	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
211	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
212	#10623494	—	2	1	no	—
213	#10623494	—	2	1	no	—
214	#10623494	—	4	2	no	—
215	#10623494	—	4	2	no	—
216	#10623494	C₂×M₁₆	1	2	yes	—
217	#10623494	C₂×M₁₆	1	2	yes	—
218	C₂²×C₈₉	—	2	1	no	—
219	C₂²×C₈₉	—	2	1	no	—
220	C₂²×C₈₉	—	2	1	no	—
221	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
222	C₂×D₈₉	—	2	1	no	—
223	C₂×D₈₉	—	2	1	no	—
224	C₂×D₈₉	—	2	1	no	—
225	C₂×D₈₉	—	2	1	no	—
226	C₂×D₈₉	—	2	1	no	—
227	C₂×D₈₉	#423	1	2	yes	—
228	C₄×C₈₉	—	2	1	no	—
229	C₄×C₈₉	—	2	1	no	—
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	—	2	1	no	—
232	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
233	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
234	C₄×C₈₉	#576	1	1	yes	characteristic
235	C₄×C₈₉	#578	1	1	yes	characteristic
236	Dic₈₉	—	2	1	no	—
237	Dic₈₉	—	2	1	no	—
238	Dic₈₉	—	2	1	no	—
239	Dic₈₉	—	2	1	no	—
240	Dic₈₉	—	2	1	no	—
241	Dic₈₉	#423	1	2	yes	—
242	#17799	—	89	1	no	maximal, Sylow
243	C₂×C₈₉	—	4	1	no	—
244	C₂×C₈₉	C₂×#423	1	1	yes	characteristic
245	C₂×C₈₉	#2913	1	1	yes	characteristic
246	C₂×C₈₉	#2916	1	1	yes	characteristic
247	D₈₉	—	2	2	no	—
248	D₈₉	—	4	1	no	—
249	#2989	—	89	2	no	—
250	C₄×#131	—	89	1	no	—
251	#1569	—	89	2	no	—
252	#1569	—	89	2	no	—
253	#1568	—	89	1	no	—
254	#1568	D₈₉	1	1	yes	characteristic, complemented
255	#1567	—	89	1	no	—
256	#1567	—	89	1	no	—
257	#1565	—	89	2	no	—
258	#1564	—	89	1	no	—
259	C₂×#335	—	89	1	no	—
260	C₈₉	#17799	1	1	yes	characteristic, complemented, Sylow
261	C₂×#131	—	89	1	no	—
262	C₂×#131	—	89	1	no	—
263	C₄×#41	—	89	1	no	—
264	#446	—	178	2	no	—
265	#436	—	178	2	no	—
266	#435	—	178	2	no	—
267	#435	—	178	2	no	—
268	#432	—	89	2	no	—
269	#432	C₂×D₈₉	1	2	yes	—
270	#431	—	89	2	no	—
271	#423	—	89	2	no	—
272	#423	—	89	2	no	—
273	C₂×C₄⋊C₈	—	89	2	no	—
274	#405	—	89	1	no	—
275	#405	—	89	1	no	—
276	#405	—	89	1	no	—
277	#405	—	89	1	no	—
278	#405	—	89	1	no	—
279	#405	—	89	1	no	—
280	C₄×M₁₆	—	89	1	no	—
281	C₄×M₁₆	—	89	1	no	—
282	C₄×M₁₆	—	89	1	no	—
283	C₂×C₄×C₈	—	89	1	no	—
284	C₂×C₄×C₈	—	89	1	no	—
285	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
286	#335	—	89	2	no	—
287	#335	—	89	2	no	—
288	#335	—	89	1	no	—
289	#335	—	89	1	no	—
290	#335	—	89	2	no	—
291	#335	C₂×D₈₉	1	1	yes	characteristic
292	#335	C₂×D₈₉	1	1	yes	characteristic
293	#334	—	89	2	no	—
294	#334	—	89	2	no	—
295	#334	C₂×D₈₉	1	2	yes	—
296	C₂×#41	—	89	1	no	—
297	#131	—	178	4	no	—
298	#131	—	178	4	no	—
299	C₂×M₁₆	—	89	1	no	—
300	C₂×M₁₆	—	89	1	no	—
301	C₂×M₁₆	—	89	1	no	—
302	C₂×M₁₆	—	89	1	no	—
303	C₂×M₁₆	—	89	1	no	—
304	C₂×M₁₆	—	89	1	no	—
305	C₂×M₁₆	—	178	2	no	—
306	C₂×M₁₆	—	178	2	no	—
307	C₂²×C₈	—	89	1	no	—
308	C₂²×C₈	—	89	1	no	—
309	C₂²×C₈	—	89	1	no	—
310	C₂²×C₈	—	89	1	no	—
311	C₂²×C₈	—	178	2	no	—
312	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
313	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
314	C₄×Q₈	—	89	1	no	—
315	C₄×Q₈	—	89	1	no	—
316	C₄×D₄	—	89	1	no	—
317	C₄×D₄	—	89	1	no	—
318	C₄×D₄	—	89	1	no	—
319	C₄×D₄	—	89	1	no	—
320	C₄×D₄	—	89	1	no	—
321	C₄×D₄	—	89	1	no	—
322	#117	—	89	1	no	—
323	#117	—	89	1	no	—
324	#117	—	89	1	no	—
325	C₂×C₄²	—	89	1	no	—
326	C₂×C₄²	—	89	1	no	—
327	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
328	C₄⋊C₈	—	89	2	no	—
329	C₄⋊C₈	—	89	2	no	—
330	C₄⋊C₈	—	178	2	no	—
331	C₄⋊C₈	—	178	2	no	—
332	C₄⋊C₈	—	178	2	no	—
333	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
334	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
335	C₂²⋊C₈	—	2	2	no	—
336	C₂²⋊C₈	—	178	2	no	—
337	C₂²⋊C₈	—	178	2	no	—
338	#97	—	2	2	no	—
339	#97	—	89	1	no	—
340	#97	—	89	1	no	—
341	#97	—	89	1	no	—
342	#97	—	89	1	no	—
343	#97	—	89	1	no	—
344	#97	—	89	1	no	—
345	#97	—	178	2	no	—
346	C₄×C₈	—	89	1	no	—
347	C₄×C₈	—	89	1	no	—
348	C₄×C₈	—	89	1	no	—
349	C₄×C₈	—	89	1	no	—
350	C₄×C₈	—	89	1	no	—
351	C₄×C₈	—	89	1	no	—
352	C₄×C₈	—	178	2	no	—
353	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
354	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
355	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
356	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
357	#41	—	178	2	no	—
358	#41	—	178	2	no	—
359	C₂×Q₈	—	89	1	no	—
360	C₂×D₄	—	89	1	no	—
361	C₂×D₄	—	89	1	no	—
362	C₂×D₄	—	89	1	no	—
363	C₂²×C₄	—	89	1	no	—
364	C₂²×C₄	—	89	1	no	—
365	C₂²×C₄	—	89	1	no	—
366	C₂²×C₄	—	89	1	no	—
367	C₂²×C₄	—	89	1	no	—
368	C₂²×C₄	—	89	1	no	—
369	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
370	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
371	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
372	M₁₆	—	89	4	no	—
373	M₁₆	—	178	2	no	—
374	M₁₆	—	178	2	no	—
375	M₁₆	—	178	2	no	—
376	M₁₆	—	178	2	no	—
377	M₁₆	—	178	2	no	—
378	M₁₆	—	712	2	no	—
379	M₁₆	—	712	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	89	1	no	—
385	C₂×C₈	—	89	1	no	—
386	C₂×C₈	—	89	4	no	—
387	C₂×C₈	—	89	1	no	—
388	C₂×C₈	—	89	1	no	—
389	C₂×C₈	—	178	2	no	—
390	C₂×C₈	—	178	2	no	—
391	C₂×C₈	—	178	2	no	—
392	C₂×C₈	—	178	2	no	—
393	C₂×C₈	—	178	2	no	—
394	C₂×C₈	—	712	2	no	—
395	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
396	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
397	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
398	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
399	C₄⋊C₄	—	89	1	no	—
400	C₄⋊C₄	—	89	1	no	—
401	C₄⋊C₄	—	89	1	no	—
402	C₄⋊C₄	—	89	1	no	—
403	C₄⋊C₄	—	89	1	no	—
404	C₄⋊C₄	—	89	1	no	—
405	C₂²⋊C₄	—	89	1	no	—
406	C₂²⋊C₄	—	89	1	no	—
407	C₂²⋊C₄	—	89	1	no	—
408	C₂²⋊C₄	—	89	1	no	—
409	C₂²⋊C₄	—	89	1	no	—
410	C₂²⋊C₄	—	89	1	no	—
411	C₄²	—	89	1	no	—
412	C₄²	—	89	1	no	—
413	C₄²	—	89	1	no	—
414	C₄²	—	89	1	no	—
415	C₄²	—	89	1	no	—
416	C₄²	—	89	1	no	—
417	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
418	C₄²	D₄×D₈₉	1	1	yes	characteristic
419	C₄²	Q₈×D₈₉	1	1	yes	characteristic
420	C₄²	C₂³×D₈₉	1	1	yes	characteristic
421	C₂³	—	89	1	no	—
422	C₂³	—	89	1	no	—
423	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
424	Q₈	—	178	2	no	—
425	D₄	—	178	2	no	—
426	D₄	—	178	2	no	—
427	D₄	—	178	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	89	1	no	—
434	C₂×C₄	—	89	2	no	—
435	C₂×C₄	—	89	2	no	—
436	C₂×C₄	—	89	1	no	—
437	C₂×C₄	—	89	1	no	—
438	C₂×C₄	—	89	1	no	—
439	C₂×C₄	—	89	1	no	—
440	C₂×C₄	—	89	1	no	—
441	C₂×C₄	—	356	1	no	—
442	C₂×C₄	—	356	1	no	—
443	C₂×C₄	—	178	1	no	—
444	C₂×C₄	—	178	1	no	—
445	C₂×C₄	—	178	1	no	—
446	C₂×C₄	—	178	1	no	—
447	C₂×C₄	—	178	1	no	—
448	C₂×C₄	—	178	1	no	—
449	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
450	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
451	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
453	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
454	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	4	2	no	—
458	C₈	—	4	2	no	—
459	C₈	—	89	2	no	—
460	C₈	—	89	2	no	—
461	C₈	—	356	2	no	—
462	C₈	—	356	2	no	—
463	C₈	—	178	1	no	—
464	C₈	—	178	1	no	—
465	C₈	M₁₆×D₈₉	1	2	yes	—
466	C₈	M₁₆×D₈₉	1	2	yes	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	89	2	no	—
471	C₂²	—	178	1	no	—
472	C₂²	—	178	1	no	—
473	C₂²	—	178	1	no	—
474	C₂²	—	178	1	no	—
475	C₂²	—	178	1	no	—
476	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	89	2	no	—
482	C₄	—	178	1	no	—
483	C₄	—	178	1	no	—
484	C₄	—	178	1	no	—
485	C₄	—	178	1	no	—
486	C₄	—	178	1	no	—
487	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
488	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
489	C₄	#19152400	1	1	yes	characteristic
490	C₄	#19152412	1	1	yes	characteristic
491	C₂	—	4	1	no	—
492	C₂	—	356	1	no	—
493	C₂	—	178	2	no	—
494	C₂	#423×D₈₉	1	1	yes	characteristic
495	C₂	#26028849	1	1	yes	characteristic
496	C₂	#26028860	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1568	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂×#13083574	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1568	D₈₉
hypocenter	C₈₉	#17799
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
3. #26019020	C₂	semidirect
4. #26019016	C₂	semidirect
5. #26019014	C₂	semidirect
6. #26019011	C₂	semidirect
7. #26019009	C₂	semidirect
8. #26019001	C₂	semidirect
9. #26018999	C₂	semidirect
10. #335×D₈₉	C₂	semidirect
11. C₈₉×#1568	C₂	semidirect
127. #13083557	M₁₆	semidirect
138. C₈×D₈₉	M₁₆	semidirect
254. #1568	D₈₉	semidirect
260. C₈₉	#17799	semidirect

Maximal subgroups

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

subgroup	index
#26029371	2
C₄×#15668018	2
#26019020	2
#26019016	2
#26019014	2
#26019011	2
#26019009	2
#26019001	2
#26018999	2
#335×D₈₉	2
C₈₉×#1568	2
#17799	89