Subgroups — #36523667

Order 22784.

610 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#13083574	C₂	1	1	yes	maximal, characteristic
2	#26028913	C₂	1	2	yes	maximal
3	#26019030	C₂	1	2	yes	maximal, complemented
4	#26019029	C₂	1	2	yes	maximal, complemented
5	#26019021	C₂	1	2	yes	maximal, complemented
6	#26019015	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019014	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019009	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018999	C₂	1	1	yes	maximal, characteristic, complemented
10	#335×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#13083574	C₂²	1	1	yes	characteristic
13	C₈×Dic₁₇₈	C₄	1	1	yes	characteristic
14	C₈×Dic₁₇₈	C₄	1	1	yes	characteristic
15	C₈×D₃₅₆	C₄	1	1	yes	characteristic
16	C₈×D₃₅₆	C₄	1	1	yes	characteristic
17	C₈×C₂²⋊D₈₉	C₄	1	1	yes	characteristic
18	C₈×C₂²⋊D₈₉	C₄	1	1	yes	characteristic
19	C₈×C₂²⋊D₈₉	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₈₉	C₄	1	1	yes	characteristic
21	#19151657	—	2	2	no	—
22	#19151656	—	2	2	no	—
23	#19151655	C₂²	1	2	yes	—
24	#19151654	C₂²	1	2	yes	—
25	#19151651	C₂²	1	1	yes	characteristic
26	#19151650	C₂²	1	2	yes	—
27	#19151649	C₂²	1	1	yes	characteristic
28	#19151649	C₂²	1	1	yes	characteristic
29	#19151620	C₂²	1	2	yes	—
30	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
31	#19151563	—	2	2	no	—
32	#19151552	—	2	2	no	—
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	#19151350	C₂²	1	2	yes	—
38	#19151350	C₂²	1	2	yes	—
39	#19151349	C₂²	1	2	yes	—
40	#19151348	C₂²	1	2	yes	—
41	#19151348	C₂²	1	2	yes	—
42	#431×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	D₄	1	1	yes	characteristic
48	C₂×#13083557	—	2	2	no	—
49	C₂×C₈×D₈₉	—	2	2	no	—
50	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
54	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
55	C₄×Dic₁₇₈	Q₈	1	1	yes	characteristic
56	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
57	C₄×D₃₅₆	Q₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
59	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
60	C₄×C₂²⋊D₈₉	Q₈	1	1	yes	characteristic
61	C₄×C₂²⋊D₈₉	Q₈	1	1	yes	characteristic
62	#15667971	D₄	1	1	yes	characteristic
63	#15667969	D₄	1	1	yes	characteristic
64	#15667969	D₄	1	1	yes	characteristic
65	C₄²×D₈₉	C₂³	1	1	yes	characteristic
66	C₄²×D₈₉	C₂³	1	1	yes	characteristic
67	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
68	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
69	C₄⋊#10623494	C₂³	1	2	yes	—
70	C₄⋊#10623494	C₂³	1	2	yes	—
71	#15667941	—	2	2	no	—
72	#15667941	—	2	2	no	—
73	#15667941	C₂×C₄	1	1	yes	characteristic
74	#15667941	C₂×C₄	1	1	yes	characteristic
75	#15667941	C₂×C₄	1	1	yes	characteristic
76	#15667941	C₂×C₄	1	1	yes	characteristic
77	C₂²⋊#10623494	—	2	2	no	—
78	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
79	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
80	#15667924	—	2	2	no	—
81	#15667924	—	2	2	no	—
82	#15667924	C₂×C₄	1	1	yes	characteristic
83	#15667924	C₂×C₄	1	1	yes	characteristic
84	#15667924	C₂×C₄	1	1	yes	characteristic
85	#15667924	C₂×C₄	1	1	yes	characteristic
86	#15667923	—	2	2	no	—
87	#15667922	—	2	2	no	—
88	C₄×#10623494	C₂³	1	1	yes	characteristic
89	C₄×#10623494	C₂³	1	1	yes	characteristic
90	C₈×Dic₈₉	—	2	2	no	—
91	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
95	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
96	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
99	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
100	C₂²⋊C₈×C₈₉	—	2	2	no	—
101	C₄×C₈×C₈₉	—	2	2	no	—
102	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
103	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
104	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
105	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
106	#13083574	—	2	2	no	—
107	#13083574	—	2	2	no	—
108	C₂×Dic₁₇₈	C₄⋊C₄	1	1	yes	characteristic
109	C₂×D₃₅₆	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₈₉	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₂²⋊D₈₉	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
117	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
118	#13083557	—	4	4	no	—
119	C₂×#10623494	—	2	2	no	—
120	C₂×#10623494	—	2	2	no	—
121	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
122	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
123	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
124	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
125	C₈×D₈₉	—	2	2	no	—
126	C₈×D₈₉	—	2	2	no	—
127	C₈×D₈₉	—	4	1	no	—
128	C₈×D₈₉	—	4	1	no	—
129	C₈×D₈₉	—	4	4	no	—
130	C₄⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
131	C₄⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
132	#13083553	C₄⋊C₄	1	1	yes	characteristic
133	#13083553	C₄⋊C₄	1	1	yes	characteristic
134	#13083553	C₄⋊C₄	1	1	yes	characteristic
135	#13083553	C₄⋊C₄	1	1	yes	characteristic
136	C₂²⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
137	C₂²⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
138	#13083551	C₄⋊C₄	1	1	yes	characteristic
139	#13083551	C₄⋊C₄	1	1	yes	characteristic
140	#13083551	C₄⋊C₄	1	1	yes	characteristic
141	#13083551	C₄⋊C₄	1	1	yes	characteristic
142	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
143	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
144	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
145	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
146	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
147	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
151	C₂×C₈×C₈₉	—	2	2	no	—
152	C₂×C₈×C₈₉	—	2	2	no	—
153	C₂×C₈×C₈₉	—	2	2	no	—
154	C₂×C₈×C₈₉	—	4	1	no	—
155	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
162	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
163	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	4	1	no	—
171	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
177	C₂²⋊D₈₉	—	2	2	no	—
178	C₂²⋊D₈₉	—	2	2	no	—
179	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
185	D₃₅₆	—	2	2	no	—
186	C₄×D₈₉	—	2	1	no	—
187	C₄×D₈₉	—	2	1	no	—
188	C₄×D₈₉	—	2	1	no	—
189	C₄×D₈₉	—	2	1	no	—
190	C₄×D₈₉	—	2	1	no	—
191	C₄×D₈₉	—	2	1	no	—
192	C₄×D₈₉	—	4	1	no	—
193	C₄×D₈₉	—	4	1	no	—
194	C₄×D₈₉	#135	1	2	yes	—
195	C₄×D₈₉	#135	1	2	yes	—
196	Dic₁₇₈	—	2	2	no	—
197	C₈×C₈₉	—	2	1	no	—
198	C₈×C₈₉	—	2	1	no	—
199	C₈×C₈₉	—	2	1	no	—
200	C₈×C₈₉	—	4	2	no	—
201	C₈×C₈₉	—	4	2	no	—
202	C₈×C₈₉	#131	1	2	yes	—
203	#10623494	—	2	1	no	—
204	#10623494	—	2	1	no	—
205	#10623494	—	2	1	no	—
206	#10623494	—	2	1	no	—
207	#10623494	—	4	2	no	—
208	#10623494	—	4	2	no	—
209	C₂²×C₈₉	—	2	1	no	—
210	C₂²×C₈₉	—	2	1	no	—
211	C₂²×C₈₉	—	2	1	no	—
212	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
213	C₂×D₈₉	—	2	1	no	—
214	C₂×D₈₉	—	2	1	no	—
215	C₂×D₈₉	—	2	1	no	—
216	C₂×D₈₉	—	2	1	no	—
217	C₂×D₈₉	—	2	1	no	—
218	C₂×D₈₉	#427	1	2	yes	—
219	C₄×C₈₉	—	2	1	no	—
220	C₄×C₈₉	—	2	1	no	—
221	C₄×C₈₉	—	2	1	no	—
222	C₄×C₈₉	—	2	1	no	—
223	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
224	C₄×C₈₉	#568	1	1	yes	characteristic
225	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
226	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
227	Dic₈₉	—	2	1	no	—
228	Dic₈₉	—	2	1	no	—
229	Dic₈₉	—	2	1	no	—
230	Dic₈₉	—	2	1	no	—
231	Dic₈₉	—	2	1	no	—
232	Dic₈₉	#427	1	2	yes	—
233	#17829	—	89	1	no	maximal, Sylow
234	C₂×C₈₉	—	4	1	no	—
235	C₂×C₈₉	#2906	1	1	yes	characteristic
236	C₂×C₈₉	C₂×#427	1	1	yes	characteristic
237	C₂×C₈₉	#2916	1	1	yes	characteristic
238	D₈₉	—	2	2	no	—
239	D₈₉	—	4	1	no	—
240	C₈×#41	—	89	1	no	—
241	#2925	—	89	2	no	—
242	#1572	—	89	2	no	—
243	#1572	—	89	2	no	—
244	#1570	—	89	2	no	—
245	#1568	—	89	1	no	—
246	#1568	—	89	1	no	—
247	#1567	—	89	1	no	—
248	#1564	—	89	1	no	—
249	#1564	D₈₉	1	1	yes	characteristic, complemented
250	C₂×#335	—	89	1	no	—
251	C₈₉	#17829	1	1	yes	characteristic, complemented, Sylow
252	C₄×#41	—	89	1	no	—
253	C₈×Q₈	—	89	1	no	—
254	C₈×Q₈	—	89	1	no	—
255	C₈×D₄	—	89	1	no	—
256	C₈×D₄	—	89	1	no	—
257	C₈×D₄	—	89	1	no	—
258	C₈×D₄	—	89	1	no	—
259	C₈×D₄	—	89	1	no	—
260	C₈×D₄	—	89	1	no	—
261	#433	—	178	2	no	—
262	#433	—	178	2	no	—
263	#432	—	89	2	no	—
264	#432	—	89	2	no	—
265	#431	—	89	1	no	—
266	#431	—	89	1	no	—
267	#431	—	89	1	no	—
268	#431	—	89	2	no	—
269	#431	C₂×D₈₉	1	2	yes	—
270	#423	—	89	2	no	—
271	C₂×C₄⋊C₈	—	89	2	no	—
272	#408	—	178	2	no	—
273	#405	—	178	2	no	—
274	C₂×C₄×C₈	—	89	1	no	—
275	C₂×C₄×C₈	—	89	1	no	—
276	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
277	#335	—	89	2	no	—
278	#335	—	89	2	no	—
279	#335	—	89	1	no	—
280	#335	—	89	1	no	—
281	#335	C₂×D₈₉	1	1	yes	characteristic
282	#335	C₂×D₈₉	1	1	yes	characteristic
283	#334	—	89	2	no	—
284	#334	—	89	2	no	—
285	#334	—	89	2	no	—
286	#334	C₂×D₈₉	1	2	yes	—
287	C₂×#41	—	89	1	no	—
288	C₂×M₁₆	—	178	2	no	—
289	C₂²×C₈	—	89	1	no	—
290	C₂²×C₈	—	89	1	no	—
291	C₂²×C₈	—	89	1	no	—
292	C₂²×C₈	—	89	1	no	—
293	C₂²×C₈	—	178	2	no	—
294	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
295	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
296	C₄×Q₈	—	89	1	no	—
297	C₄×Q₈	—	89	1	no	—
298	C₄×D₄	—	89	1	no	—
299	C₄×D₄	—	89	1	no	—
300	C₄×D₄	—	89	1	no	—
301	C₄×D₄	—	89	1	no	—
302	C₄×D₄	—	89	1	no	—
303	C₄×D₄	—	89	1	no	—
304	#117	—	89	1	no	—
305	#117	—	89	1	no	—
306	#117	—	89	1	no	—
307	C₂×C₄²	—	89	1	no	—
308	C₂×C₄²	—	89	1	no	—
309	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
310	C₄⋊C₈	—	89	1	no	—
311	C₄⋊C₈	—	89	1	no	—
312	C₄⋊C₈	—	89	1	no	—
313	C₄⋊C₈	—	89	1	no	—
314	C₄⋊C₈	—	89	1	no	—
315	C₄⋊C₈	—	89	1	no	—
316	C₄⋊C₈	—	89	2	no	—
317	C₄⋊C₈	—	89	2	no	—
318	C₄⋊C₈	—	178	2	no	—
319	C₄⋊C₈	—	178	2	no	—
320	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
321	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	—	89	1	no	—
324	C₂²⋊C₈	—	89	1	no	—
325	C₂²⋊C₈	—	89	1	no	—
326	C₂²⋊C₈	—	89	1	no	—
327	C₂²⋊C₈	—	89	1	no	—
328	C₂²⋊C₈	—	89	1	no	—
329	C₂²⋊C₈	—	178	2	no	—
330	C₂²⋊C₈	—	178	2	no	—
331	C₂²⋊C₈	—	178	2	no	—
332	#97	—	178	2	no	—
333	#97	—	178	2	no	—
334	C₄×C₈	—	2	2	no	—
335	C₄×C₈	—	89	1	no	—
336	C₄×C₈	—	89	1	no	—
337	C₄×C₈	—	89	1	no	—
338	C₄×C₈	—	89	1	no	—
339	C₄×C₈	—	89	1	no	—
340	C₄×C₈	—	89	1	no	—
341	C₄×C₈	—	178	2	no	—
342	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
343	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
344	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
345	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
346	#41	—	178	2	no	—
347	#41	—	178	2	no	—
348	C₂×Q₈	—	89	1	no	—
349	C₂×D₄	—	89	1	no	—
350	C₂×D₄	—	89	1	no	—
351	C₂×D₄	—	89	1	no	—
352	C₂²×C₄	—	89	1	no	—
353	C₂²×C₄	—	89	1	no	—
354	C₂²×C₄	—	89	1	no	—
355	C₂²×C₄	—	89	1	no	—
356	C₂²×C₄	—	89	1	no	—
357	C₂²×C₄	—	89	1	no	—
358	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
359	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
360	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
361	M₁₆	—	356	4	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	89	1	no	—
367	C₂×C₈	—	89	1	no	—
368	C₂×C₈	—	89	1	no	—
369	C₂×C₈	—	89	1	no	—
370	C₂×C₈	—	356	1	no	—
371	C₂×C₈	—	356	1	no	—
372	C₂×C₈	—	356	4	no	—
373	C₂×C₈	—	178	2	no	—
374	C₂×C₈	—	178	2	no	—
375	C₂×C₈	—	178	2	no	—
376	C₂×C₈	—	178	2	no	—
377	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
378	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
379	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
380	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
381	C₄⋊C₄	—	89	1	no	—
382	C₄⋊C₄	—	89	1	no	—
383	C₄⋊C₄	—	89	1	no	—
384	C₄⋊C₄	—	89	1	no	—
385	C₄⋊C₄	—	89	1	no	—
386	C₄⋊C₄	—	89	1	no	—
387	C₂²⋊C₄	—	89	1	no	—
388	C₂²⋊C₄	—	89	1	no	—
389	C₂²⋊C₄	—	89	1	no	—
390	C₂²⋊C₄	—	89	1	no	—
391	C₂²⋊C₄	—	89	1	no	—
392	C₂²⋊C₄	—	89	1	no	—
393	C₄²	—	89	1	no	—
394	C₄²	—	89	1	no	—
395	C₄²	—	89	1	no	—
396	C₄²	—	89	1	no	—
397	C₄²	—	89	1	no	—
398	C₄²	—	89	1	no	—
399	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
400	C₄²	D₄×D₈₉	1	1	yes	characteristic
401	C₄²	Q₈×D₈₉	1	1	yes	characteristic
402	C₄²	C₂³×D₈₉	1	1	yes	characteristic
403	C₂³	—	89	1	no	—
404	C₂³	—	89	1	no	—
405	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
406	Q₈	—	178	2	no	—
407	D₄	—	178	2	no	—
408	D₄	—	178	2	no	—
409	D₄	—	178	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	89	1	no	—
416	C₂×C₄	—	89	2	no	—
417	C₂×C₄	—	89	2	no	—
418	C₂×C₄	—	89	1	no	—
419	C₂×C₄	—	89	1	no	—
420	C₂×C₄	—	89	1	no	—
421	C₂×C₄	—	89	1	no	—
422	C₂×C₄	—	89	1	no	—
423	C₂×C₄	—	356	1	no	—
424	C₂×C₄	—	356	1	no	—
425	C₂×C₄	—	178	1	no	—
426	C₂×C₄	—	178	1	no	—
427	C₂×C₄	—	178	1	no	—
428	C₂×C₄	—	178	1	no	—
429	C₂×C₄	—	178	1	no	—
430	C₂×C₄	—	178	1	no	—
431	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
432	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
433	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
435	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
436	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	2	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	2	no	—
442	C₈	—	356	2	no	—
443	C₈	—	356	2	no	—
444	C₈	—	178	1	no	—
445	C₈	—	178	1	no	—
446	C₈	—	178	1	no	—
447	C₈	—	178	1	no	—
448	C₈	#15668018	1	2	yes	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	89	2	no	—
453	C₂²	—	178	1	no	—
454	C₂²	—	178	1	no	—
455	C₂²	—	178	1	no	—
456	C₂²	—	178	1	no	—
457	C₂²	—	178	1	no	—
458	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	89	2	no	—
464	C₄	—	178	1	no	—
465	C₄	—	178	1	no	—
466	C₄	—	178	1	no	—
467	C₄	—	178	1	no	—
468	C₄	—	178	1	no	—
469	C₄	C₂×#15668018	1	1	yes	characteristic
470	C₄	#19152364	1	1	yes	characteristic
471	C₄	#135×D₈₉	1	1	yes	characteristic
472	C₄	#135×D₈₉	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	356	1	no	—
475	C₂	—	178	2	no	—
476	C₂	#26028817	1	1	yes	characteristic
477	C₂	#427×D₈₉	1	1	yes	characteristic
478	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×#1564	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂×#13083574	D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1564	D₈₉
hypocenter	C₈₉	#17829
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
3. #26019030	C₂	semidirect
4. #26019029	C₂	semidirect
5. #26019021	C₂	semidirect
6. #26019015	C₂	semidirect
7. #26019014	C₂	semidirect
8. #26019009	C₂	semidirect
9. #26018999	C₂	semidirect
10. #335×D₈₉	C₂	semidirect
11. C₈₉×#1564	C₂	semidirect
249. #1564	D₈₉	semidirect
251. C₈₉	#17829	semidirect

Maximal subgroups

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

subgroup	index
C₈×#13083574	2
#26028913	2
#26019030	2
#26019029	2
#26019021	2
#26019015	2
#26019014	2
#26019009	2
#26018999	2
#335×D₈₉	2
C₈₉×#1564	2
#17829	89