Subgroups — #36523686

Order 22784.

588 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029214	C₂	1	1	yes	maximal, characteristic
2	#26028917	C₂	1	1	yes	maximal, characteristic
3	#26028913	C₂	1	1	yes	maximal, characteristic
4	#26019042	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019040	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019035	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019034	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019031	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019029	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019019	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019018	C₂	1	1	yes	maximal, characteristic, complemented
12	#26019014	C₂	1	1	yes	maximal, characteristic, complemented
13	#26019001	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018997	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1565	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#13083574	C₂²	1	1	yes	characteristic
17	#19151726	C₄	1	1	yes	characteristic
18	#19151726	C₄	1	1	yes	characteristic
19	#19151674	C₄	1	1	yes	characteristic
20	#19151674	C₄	1	1	yes	characteristic
21	#19151671	C₄	1	1	yes	characteristic
22	#19151671	C₄	1	1	yes	characteristic
23	#19151667	C₄	1	1	yes	characteristic
24	#19151667	C₄	1	1	yes	characteristic
25	#19151658	—	2	1	no	—
26	#19151658	—	2	1	no	—
27	#19151657	—	2	1	no	—
28	#19151656	—	2	1	no	—
29	#19151655	C₂²	1	1	yes	characteristic
30	#19151654	C₂²	1	1	yes	characteristic
31	#19151654	C₂²	1	1	yes	characteristic
32	#19151654	C₂²	1	1	yes	characteristic
33	#19151651	C₂²	1	1	yes	characteristic
34	#19151650	C₂²	1	1	yes	characteristic
35	#19151650	C₂²	1	1	yes	characteristic
36	#19151650	C₂²	1	1	yes	characteristic
37	#19151649	C₂²	1	1	yes	characteristic
38	#19151649	C₂²	1	1	yes	characteristic
39	#19151622	C₂²	1	1	yes	characteristic
40	#19151620	C₂²	1	1	yes	characteristic
41	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
42	#19151564	—	2	1	no	—
43	#19151563	—	2	1	no	—
44	#19151553	—	2	1	no	—
45	#19151552	—	2	1	no	—
46	C₄×#13083557	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
48	#19151351	C₂²	1	1	yes	characteristic
49	#19151351	C₂²	1	1	yes	characteristic
50	#19151350	C₂²	1	1	yes	characteristic
51	#19151350	C₂²	1	1	yes	characteristic
52	#19151350	C₂²	1	1	yes	characteristic
53	#19151350	C₂²	1	1	yes	characteristic
54	#19151349	C₂²	1	1	yes	characteristic
55	#19151349	C₂²	1	1	yes	characteristic
56	#19151348	C₂²	1	1	yes	characteristic
57	#19151348	C₂²	1	1	yes	characteristic
58	#19151348	C₂²	1	1	yes	characteristic
59	#19151348	C₂²	1	1	yes	characteristic
60	#431×C₈₉	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
62	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
63	#335×C₈₉	C₂²	1	1	yes	characteristic
64	#335×C₈₉	C₂²	1	1	yes	characteristic
65	#334×C₈₉	C₂²	1	1	yes	characteristic
66	#334×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#13083574	D₄	1	1	yes	characteristic
68	C₂×#13083558	—	2	1	no	—
69	C₂×#13083557	—	2	1	no	—
70	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₈₉	—	2	1	no	—
73	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
76	C₄×Dic₁₇₈	Q₈	1	1	yes	characteristic
77	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
78	C₄×D₃₅₆	Q₈	1	1	yes	characteristic
79	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
80	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
81	C₄×C₂²⋊D₈₉	Q₈	1	1	yes	characteristic
82	C₄×C₂²⋊D₈₉	Q₈	1	1	yes	characteristic
83	#15667971	D₄	1	1	yes	characteristic
84	#15667969	D₄	1	1	yes	characteristic
85	#15667969	D₄	1	1	yes	characteristic
86	C₄²×D₈₉	C₂³	1	1	yes	characteristic
87	C₄²×D₈₉	C₂³	1	1	yes	characteristic
88	C₄⋊#10623494	—	2	1	no	—
89	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
90	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
91	C₄⋊#10623494	C₂³	1	1	yes	characteristic
92	C₄⋊#10623494	C₂³	1	1	yes	characteristic
93	C₄⋊#10623494	C₂³	1	1	yes	characteristic
94	C₄⋊#10623494	C₂³	1	1	yes	characteristic
95	#15667941	—	2	1	no	—
96	#15667941	—	2	1	no	—
97	#15667941	C₂×C₄	1	1	yes	characteristic
98	#15667941	C₂×C₄	1	1	yes	characteristic
99	#15667941	C₂×C₄	1	1	yes	characteristic
100	#15667941	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊#10623494	—	2	1	no	—
102	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
103	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
104	#15667924	—	2	1	no	—
105	#15667924	—	2	1	no	—
106	#15667924	—	2	1	no	—
107	#15667924	—	2	1	no	—
108	#15667924	—	2	1	no	—
109	#15667924	—	2	1	no	—
110	#15667924	C₂×C₄	1	1	yes	characteristic
111	#15667924	C₂×C₄	1	1	yes	characteristic
112	#15667924	C₂×C₄	1	1	yes	characteristic
113	#15667924	C₂×C₄	1	1	yes	characteristic
114	#15667923	—	2	1	no	—
115	#15667922	—	2	1	no	—
116	#15667922	—	2	1	no	—
117	#15667922	—	2	1	no	—
118	#15667922	C₂×C₄	1	1	yes	characteristic
119	#15667922	C₂×C₄	1	1	yes	characteristic
120	C₄×#10623494	C₂³	1	1	yes	characteristic
121	C₄×#10623494	C₂³	1	1	yes	characteristic
122	C₈×Dic₈₉	—	2	1	no	—
123	C₈×Dic₈₉	—	2	1	no	—
124	C₈×Dic₈₉	—	2	1	no	—
125	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
126	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
127	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
128	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
129	C₂²×C₈×C₈₉	—	2	1	no	—
130	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
131	C₄⋊C₈×C₈₉	—	2	1	no	—
132	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
134	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
136	C₂²⋊C₈×C₈₉	—	2	1	no	—
137	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
138	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
139	C₄×C₈×C₈₉	—	2	1	no	—
140	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
142	#13083574	—	4	1	no	—
143	#13083574	—	4	1	no	—
144	C₂×Dic₁₇₈	C₄⋊C₄	1	1	yes	characteristic
145	C₂×D₃₅₆	C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₂²⋊D₈₉	C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₂²⋊D₈₉	C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
153	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
154	#13083558	—	4	2	no	—
155	#13083557	—	2	2	no	—
156	#13083557	—	4	1	no	—
157	#13083557	—	4	2	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	C₈×D₈₉	—	2	2	no	—
167	C₈×D₈₉	—	4	1	no	—
168	C₈×D₈₉	—	4	2	no	—
169	C₄⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
170	C₄⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
171	#13083553	C₄⋊C₄	1	1	yes	characteristic
172	#13083553	C₄⋊C₄	1	1	yes	characteristic
173	#13083553	C₄⋊C₄	1	1	yes	characteristic
174	#13083553	C₄⋊C₄	1	1	yes	characteristic
175	C₂²⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
176	C₂²⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
177	#13083551	C₄⋊C₄	1	1	yes	characteristic
178	#13083551	C₄⋊C₄	1	1	yes	characteristic
179	#13083551	C₄⋊C₄	1	1	yes	characteristic
180	#13083551	C₄⋊C₄	1	1	yes	characteristic
181	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
182	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
183	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
184	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
185	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
186	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
187	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
190	M₁₆×C₈₉	—	2	2	no	—
191	M₁₆×C₈₉	—	4	1	no	—
192	C₂×C₈×C₈₉	—	2	1	no	—
193	C₂×C₈×C₈₉	—	2	1	no	—
194	C₂×C₈×C₈₉	—	2	1	no	—
195	C₂×C₈×C₈₉	—	2	1	no	—
196	C₂×C₈×C₈₉	—	4	2	no	—
197	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
201	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
202	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
204	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
205	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₈₉	—	2	1	no	—
209	C₂×C₄×C₈₉	—	2	1	no	—
210	C₂×C₄×C₈₉	—	2	1	no	—
211	C₂×C₄×C₈₉	—	2	1	no	—
212	C₂×C₄×C₈₉	—	4	1	no	—
213	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
219	C₂²⋊D₈₉	—	4	1	no	—
220	C₂²⋊D₈₉	—	4	1	no	—
221	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
227	D₃₅₆	—	4	1	no	—
228	C₄×D₈₉	—	2	1	no	—
229	C₄×D₈₉	—	2	1	no	—
230	C₄×D₈₉	—	2	1	no	—
231	C₄×D₈₉	—	2	1	no	—
232	C₄×D₈₉	—	2	1	no	—
233	C₄×D₈₉	—	2	1	no	—
234	C₄×D₈₉	—	2	1	no	—
235	C₄×D₈₉	—	2	1	no	—
236	C₄×D₈₉	—	4	1	no	—
237	C₄×D₈₉	—	4	1	no	—
238	Dic₁₇₈	—	4	1	no	—
239	C₈×C₈₉	—	2	1	no	—
240	C₈×C₈₉	—	2	1	no	—
241	C₈×C₈₉	—	2	1	no	—
242	C₈×C₈₉	—	4	1	no	—
243	C₈×C₈₉	—	4	1	no	—
244	C₈×C₈₉	—	4	1	no	—
245	C₈×C₈₉	—	4	1	no	—
246	C₈×C₈₉	#131	1	2	yes	—
247	#10623494	—	2	1	no	—
248	#10623494	—	2	1	no	—
249	#10623494	—	2	1	no	—
250	#10623494	—	2	1	no	—
251	#10623494	—	4	1	no	—
252	#10623494	—	4	1	no	—
253	#10623494	—	4	1	no	—
254	#10623494	—	4	1	no	—
255	C₂²×C₈₉	—	2	1	no	—
256	C₂²×C₈₉	—	2	1	no	—
257	C₂²×C₈₉	—	2	1	no	—
258	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
259	C₂×D₈₉	—	2	1	no	—
260	C₂×D₈₉	—	2	1	no	—
261	C₂×D₈₉	—	2	1	no	—
262	C₂×D₈₉	—	2	1	no	—
263	C₂×D₈₉	—	2	1	no	—
264	C₂×D₈₉	—	2	1	no	—
265	C₄×C₈₉	—	2	1	no	—
266	C₄×C₈₉	—	2	1	no	—
267	C₄×C₈₉	—	2	1	no	—
268	C₄×C₈₉	—	2	1	no	—
269	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
270	C₄×C₈₉	#568	1	1	yes	characteristic
271	C₄×C₈₉	#575	1	1	yes	characteristic
272	C₄×C₈₉	#575	1	1	yes	characteristic
273	Dic₈₉	—	2	1	no	—
274	Dic₈₉	—	2	1	no	—
275	Dic₈₉	—	2	1	no	—
276	Dic₈₉	—	2	1	no	—
277	Dic₈₉	—	2	1	no	—
278	Dic₈₉	—	2	1	no	—
279	#17831	—	89	1	no	maximal, Sylow
280	C₂×C₈₉	—	4	1	no	—
281	C₂×C₈₉	#2906	1	1	yes	characteristic
282	C₂×C₈₉	#2911	1	1	yes	characteristic
283	C₂×C₈₉	#2916	1	1	yes	characteristic
284	D₈₉	—	4	1	no	—
285	D₈₉	—	4	1	no	—
286	#2965	—	89	1	no	—
287	#2925	—	89	1	no	—
288	#2925	—	89	1	no	—
289	#1574	—	89	1	no	—
290	#1574	—	89	1	no	—
291	#1573	—	89	1	no	—
292	#1573	—	89	1	no	—
293	#1572	—	89	1	no	—
294	#1572	—	89	1	no	—
295	#1569	—	89	1	no	—
296	#1569	—	89	1	no	—
297	#1568	—	89	1	no	—
298	#1565	—	89	1	no	—
299	#1565	D₈₉	1	1	yes	characteristic, complemented
300	#1564	—	89	1	no	—
301	C₈₉	#17831	1	1	yes	characteristic, complemented, Sylow
302	C₄×#41	—	89	1	no	—
303	#446	—	89	1	no	—
304	#446	—	89	1	no	—
305	#436	—	89	1	no	—
306	#436	—	89	1	no	—
307	#435	—	89	1	no	—
308	#435	—	89	1	no	—
309	#435	—	89	1	no	—
310	#435	—	89	1	no	—
311	#433	—	178	1	no	—
312	#433	—	178	1	no	—
313	#433	—	178	1	no	—
314	#433	—	178	1	no	—
315	#432	—	89	1	no	—
316	#432	—	89	1	no	—
317	#432	—	89	1	no	—
318	#432	—	89	1	no	—
319	#431	—	89	1	no	—
320	#431	—	89	1	no	—
321	#431	—	89	1	no	—
322	#431	—	89	1	no	—
323	#431	—	89	1	no	—
324	#431	—	89	1	no	—
325	#431	C₂×D₈₉	1	1	yes	characteristic
326	#423	—	89	1	no	—
327	#423	—	89	1	no	—
328	C₂×C₄⋊C₈	—	89	1	no	—
329	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
330	#408	—	178	1	no	—
331	#408	—	178	1	no	—
332	#405	—	178	1	no	—
333	#405	—	178	1	no	—
334	C₄×M₁₆	—	89	1	no	—
335	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
336	C₂×C₄×C₈	—	89	1	no	—
337	#335	—	89	1	no	—
338	#335	—	89	1	no	—
339	#335	—	89	1	no	—
340	#335	—	89	1	no	—
341	#335	—	89	1	no	—
342	#335	—	89	1	no	—
343	#335	C₂×D₈₉	1	1	yes	characteristic
344	#335	C₂×D₈₉	1	1	yes	characteristic
345	#334	—	89	1	no	—
346	#334	—	89	1	no	—
347	#334	—	89	1	no	—
348	#334	—	89	1	no	—
349	#334	—	89	1	no	—
350	#334	—	89	1	no	—
351	#334	C₂×D₈₉	1	1	yes	characteristic
352	#334	C₂×D₈₉	1	1	yes	characteristic
353	C₂×#41	—	89	1	no	—
354	C₂×M₁₆	—	89	1	no	—
355	C₂×M₁₆	—	89	1	no	—
356	C₂×M₁₆	—	178	1	no	—
357	C₂×M₁₆	—	178	1	no	—
358	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
359	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
360	C₂²×C₈	—	2	1	no	—
361	C₂²×C₈	—	89	1	no	—
362	C₂²×C₈	—	89	1	no	—
363	C₂²×C₈	—	178	1	no	—
364	C₄×Q₈	—	89	1	no	—
365	C₄×Q₈	—	89	1	no	—
366	C₄×D₄	—	89	1	no	—
367	C₄×D₄	—	89	1	no	—
368	C₄×D₄	—	89	1	no	—
369	C₄×D₄	—	89	1	no	—
370	C₄×D₄	—	89	1	no	—
371	C₄×D₄	—	89	1	no	—
372	#117	—	89	1	no	—
373	#117	—	89	1	no	—
374	#117	—	89	1	no	—
375	C₂×C₄²	—	89	1	no	—
376	C₂×C₄²	—	89	1	no	—
377	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	89	1	no	—
380	C₄⋊C₈	—	89	1	no	—
381	C₄⋊C₈	—	89	1	no	—
382	C₄⋊C₈	—	89	1	no	—
383	C₄⋊C₈	—	89	1	no	—
384	C₄⋊C₈	—	89	1	no	—
385	C₄⋊C₈	—	89	1	no	—
386	C₄⋊C₈	—	89	1	no	—
387	C₄⋊C₈	—	89	1	no	—
388	C₄⋊C₈	—	89	1	no	—
389	C₄⋊C₈	—	178	1	no	—
390	C₄⋊C₈	—	178	1	no	—
391	C₄⋊C₈	—	178	1	no	—
392	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
393	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
394	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
395	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
396	C₂²⋊C₈	—	2	1	no	—
397	C₂²⋊C₈	—	89	1	no	—
398	C₂²⋊C₈	—	89	1	no	—
399	C₂²⋊C₈	—	89	1	no	—
400	C₂²⋊C₈	—	89	1	no	—
401	C₂²⋊C₈	—	89	1	no	—
402	C₂²⋊C₈	—	89	1	no	—
403	C₂²⋊C₈	—	178	1	no	—
404	C₂²⋊C₈	—	178	1	no	—
405	C₂²⋊C₈	—	178	1	no	—
406	C₂²⋊C₈	—	178	1	no	—
407	C₂²⋊C₈	—	178	1	no	—
408	C₂²⋊C₈	—	178	1	no	—
409	C₂²⋊C₈	—	178	1	no	—
410	#97	—	89	1	no	—
411	#97	—	89	1	no	—
412	#97	—	178	1	no	—
413	#97	—	178	1	no	—
414	#97	—	178	1	no	—
415	#97	—	178	1	no	—
416	#97	C₄×D₈₉	1	1	yes	characteristic
417	#97	C₄×D₈₉	1	1	yes	characteristic
418	C₄×C₈	—	2	1	no	—
419	C₄×C₈	—	89	1	no	—
420	C₄×C₈	—	89	1	no	—
421	C₄×C₈	—	89	1	no	—
422	C₄×C₈	—	89	1	no	—
423	C₄×C₈	—	178	1	no	—
424	C₄×C₈	—	178	1	no	—
425	C₄×C₈	—	178	1	no	—
426	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
427	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
428	#41	—	356	1	no	—
429	#41	—	356	1	no	—
430	C₂×Q₈	—	89	1	no	—
431	C₂×D₄	—	89	1	no	—
432	C₂×D₄	—	89	1	no	—
433	C₂×D₄	—	89	1	no	—
434	C₂²×C₄	—	89	1	no	—
435	C₂²×C₄	—	89	1	no	—
436	C₂²×C₄	—	89	1	no	—
437	C₂²×C₄	—	89	1	no	—
438	C₂²×C₄	—	89	1	no	—
439	C₂²×C₄	—	89	1	no	—
440	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
441	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
442	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
443	M₁₆	—	2	2	no	—
444	M₁₆	—	4	1	no	—
445	M₁₆	—	356	1	no	—
446	M₁₆	—	356	2	no	—
447	M₁₆	—	356	2	no	—
448	M₁₆	—	178	2	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	4	2	no	—
454	C₂×C₈	—	89	1	no	—
455	C₂×C₈	—	89	1	no	—
456	C₂×C₈	—	89	1	no	—
457	C₂×C₈	—	89	1	no	—
458	C₂×C₈	—	356	1	no	—
459	C₂×C₈	—	356	2	no	—
460	C₂×C₈	—	178	1	no	—
461	C₂×C₈	—	178	1	no	—
462	C₂×C₈	—	178	1	no	—
463	C₂×C₈	—	178	1	no	—
464	C₂×C₈	—	178	2	no	—
465	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
466	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
467	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
468	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
469	C₄⋊C₄	—	89	1	no	—
470	C₄⋊C₄	—	89	1	no	—
471	C₄⋊C₄	—	89	1	no	—
472	C₄⋊C₄	—	89	1	no	—
473	C₄⋊C₄	—	89	1	no	—
474	C₄⋊C₄	—	89	1	no	—
475	C₂²⋊C₄	—	89	1	no	—
476	C₂²⋊C₄	—	89	1	no	—
477	C₂²⋊C₄	—	89	1	no	—
478	C₂²⋊C₄	—	89	1	no	—
479	C₂²⋊C₄	—	89	1	no	—
480	C₂²⋊C₄	—	89	1	no	—
481	C₄²	—	89	1	no	—
482	C₄²	—	89	1	no	—
483	C₄²	—	89	1	no	—
484	C₄²	—	89	1	no	—
485	C₄²	—	89	1	no	—
486	C₄²	—	89	1	no	—
487	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
488	C₄²	D₄×D₈₉	1	1	yes	characteristic
489	C₄²	Q₈×D₈₉	1	1	yes	characteristic
490	C₄²	C₂³×D₈₉	1	1	yes	characteristic
491	C₂³	—	89	1	no	—
492	C₂³	—	89	1	no	—
493	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
494	Q₈	—	356	1	no	—
495	D₄	—	356	1	no	—
496	D₄	—	356	1	no	—
497	D₄	—	356	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	89	1	no	—
504	C₂×C₄	—	89	1	no	—
505	C₂×C₄	—	89	1	no	—
506	C₂×C₄	—	89	1	no	—
507	C₂×C₄	—	89	1	no	—
508	C₂×C₄	—	89	1	no	—
509	C₂×C₄	—	356	1	no	—
510	C₂×C₄	—	356	1	no	—
511	C₂×C₄	—	178	1	no	—
512	C₂×C₄	—	178	1	no	—
513	C₂×C₄	—	178	1	no	—
514	C₂×C₄	—	178	1	no	—
515	C₂×C₄	—	178	1	no	—
516	C₂×C₄	—	178	1	no	—
517	C₂×C₄	—	178	1	no	—
518	C₂×C₄	—	178	1	no	—
519	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
520	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
521	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
522	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
523	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
524	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	356	1	no	—
533	C₈	—	356	1	no	—
534	C₈	—	356	1	no	—
535	C₈	—	356	1	no	—
536	C₈	—	178	1	no	—
537	C₈	—	178	1	no	—
538	C₈	—	178	1	no	—
539	C₈	—	178	1	no	—
540	C₈	#15668018	1	2	yes	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	178	1	no	—
545	C₂²	—	178	1	no	—
546	C₂²	—	178	1	no	—
547	C₂²	—	178	1	no	—
548	C₂²	—	178	1	no	—
549	C₂²	—	178	1	no	—
550	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	178	1	no	—
556	C₄	—	178	1	no	—
557	C₄	—	178	1	no	—
558	C₄	—	178	1	no	—
559	C₄	—	178	1	no	—
560	C₄	—	178	1	no	—
561	C₄	C₂×#15668018	1	1	yes	characteristic
562	C₄	#19152364	1	1	yes	characteristic
563	C₄	#19152394	1	1	yes	characteristic
564	C₄	#19152397	1	1	yes	characteristic
565	C₂	—	4	1	no	—
566	C₂	—	356	1	no	—
567	C₂	—	356	1	no	—
568	C₂	#26028817	1	1	yes	characteristic
569	C₂	#26028839	1	1	yes	characteristic
570	C₂	#26028862	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×#1565	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂×#13083574	D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1565	D₈₉
hypocenter	C₈₉	#17831
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
4. #26019042	C₂	semidirect
5. #26019040	C₂	semidirect
6. #26019035	C₂	semidirect
7. #26019034	C₂	semidirect
8. #26019031	C₂	semidirect
9. #26019029	C₂	semidirect
10. #26019019	C₂	semidirect
11. #26019018	C₂	semidirect
12. #26019014	C₂	semidirect
13. #26019001	C₂	semidirect
14. #26018997	C₂	semidirect
15. C₈₉×#1565	C₂	semidirect
299. #1565	D₈₉	semidirect
301. C₈₉	#17831	semidirect

Maximal subgroups

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

subgroup	index
#26029214	2
#26028917	2
#26028913	2
#26019042	2
#26019040	2
#26019035	2
#26019034	2
#26019031	2
#26019029	2
#26019019	2
#26019018	2
#26019014	2
#26019001	2
#26018997	2
C₈₉×#1565	2
#17831	89