Subgroups — #36524446

Order 22784.

712 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030301	C₂	1	1	yes	maximal, characteristic
2	#26029227	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019090	C₂	1	2	yes	maximal, complemented
5	#26019083	C₂	1	2	yes	maximal, complemented
6	#26019077	C₂	1	2	yes	maximal, complemented
7	#26019066	C₂	1	2	yes	maximal, complemented
8	#26019037	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018696	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018666	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₈₉	—	2	1	no	—
13	#19152132	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
15	#19151934	C₄	1	1	yes	characteristic
16	#19151917	C₄	1	1	yes	characteristic
17	#19151899	C₄	1	2	yes	—
18	#19151814	C₄	1	2	yes	—
19	#19151751	C₄	1	1	yes	characteristic
20	#19151734	C₄	1	1	yes	characteristic
21	#19151728	C₂²	1	1	yes	characteristic, complemented
22	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
23	C₄×#13083563	C₂²	1	2	yes	—
24	C₄×D₇₁₂	C₂²	1	2	yes	—
25	#19151677	C₂²	1	1	yes	characteristic, complemented
26	#19151669	—	2	1	no	—
27	C₈×D₃₅₆	—	2	1	no	—
28	C₈×D₃₅₆	—	2	1	no	—
29	C₈×D₃₅₆	C₂²	1	2	yes	—
30	C₈×D₃₅₆	C₂²	1	2	yes	—
31	C₈×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
32	C₈×C₂²⋊D₈₉	—	2	1	no	—
33	#19151657	—	2	1	no	—
34	#19151655	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
36	C₂×#15667924	—	2	1	no	—
37	#19151552	—	2	1	no	—
38	#19151351	C₂²	1	2	yes	complemented
39	#19151349	C₂²	1	2	yes	complemented
40	#19151330	C₂²	1	2	yes	complemented
41	#19151327	C₂²	1	2	yes	—
42	#19151327	C₂²	1	2	yes	—
43	#19151327	C₂²	1	2	yes	complemented
44	#431×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
47	#322×C₈₉	C₂²	1	2	yes	complemented
48	#322×C₈₉	C₂²	1	2	yes	complemented
49	C₂²×D₃₅₆	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₈₉	—	2	1	no	—
51	C₂×#13083563	C₂×C₄	1	2	yes	—
52	C₂×D₇₁₂	C₂×C₄	1	2	yes	—
53	C₂×#13083557	—	2	1	no	—
54	C₂²×#10623494	—	2	1	no	—
55	C₂×C₈×D₈₉	—	2	1	no	—
56	C₂×C₈×D₈₉	—	2	2	no	—
57	C₂×C₈×D₈₉	—	2	2	no	—
58	C₂×C₈×D₈₉	—	4	4	no	—
59	#15668006	—	2	1	no	—
60	#15668004	C₂×C₄	1	1	yes	characteristic
61	#15668000	C₂×C₄	1	1	yes	characteristic
62	#15667995	—	2	1	no	—
63	#15667991	C₂×C₄	1	1	yes	characteristic
64	#15667986	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
66	C₄×D₃₅₆	—	2	1	no	—
67	C₄×D₃₅₆	—	2	1	no	—
68	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
69	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
70	C₄×D₃₅₆	C₂³	1	2	yes	—
71	C₄×C₂²⋊D₈₉	—	2	1	no	—
72	#15667969	—	2	1	no	—
73	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
74	C₂×#13083551	—	2	1	no	—
75	#15667946	C₂×C₄	1	2	yes	—
76	#15667944	C₂×C₄	1	2	yes	—
77	C₄⋊#10623494	—	2	1	no	—
78	C₄⋊#10623494	C₂³	1	2	yes	—
79	C₄⋊#10623494	C₂³	1	1	yes	characteristic
80	C₄⋊#10623494	C₂³	1	1	yes	characteristic
81	#15667941	—	2	1	no	—
82	#15667941	—	2	1	no	—
83	#15667937	C₂×C₄	1	2	yes	—
84	#15667934	C₂×C₄	1	2	yes	—
85	#15667934	C₂×C₄	1	2	yes	—
86	#15667934	C₂×C₄	1	2	yes	—
87	C₂²⋊#10623494	—	2	1	no	—
88	#15667924	—	2	1	no	—
89	#15667924	—	2	1	no	—
90	#15667924	—	2	2	no	—
91	#15667924	—	2	2	no	—
92	#15667923	—	2	1	no	—
93	#15667922	—	2	1	no	—
94	C₈×Dic₈₉	—	2	1	no	—
95	C₂×M₁₆×C₈₉	—	2	1	no	—
96	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
100	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
102	#97×C₈₉	—	2	1	no	—
103	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
104	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
105	C₄×C₈×C₈₉	C₂³	1	2	yes	—
106	C₄×C₈×C₈₉	C₂³	1	2	yes	—
107	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂³×D₈₉	—	2	1	no	—
110	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
111	C₂×D₃₅₆	—	2	1	no	—
112	C₂×D₃₅₆	—	2	4	no	—
113	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
115	C₂×C₂²⋊D₈₉	—	2	1	no	—
116	C₂²×Dic₈₉	—	2	1	no	—
117	C₂×C₄×D₈₉	—	2	2	no	—
118	C₂×C₄×D₈₉	—	2	1	no	—
119	C₂×C₄×D₈₉	—	2	2	no	—
120	C₂×C₄×D₈₉	—	4	2	no	—
121	C₂×C₄×D₈₉	—	4	2	no	—
122	#13083563	—	2	4	no	—
123	D₇₁₂	—	2	4	no	—
124	#13083557	—	4	2	no	—
125	C₂×#10623494	—	2	2	no	—
126	C₂×#10623494	—	2	1	no	—
127	C₂×#10623494	—	2	1	no	—
128	C₂×#10623494	—	4	2	no	—
129	C₈×D₈₉	—	4	2	no	—
130	C₈×D₈₉	—	4	4	no	—
131	C₈×D₈₉	—	4	4	no	—
132	C₄⋊Dic₈₉	—	2	1	no	—
133	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
134	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
135	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
136	#13083553	—	2	1	no	—
137	#13083553	—	2	1	no	—
138	#13083553	—	2	1	no	—
139	#13083553	—	2	1	no	—
140	C₂²⋊Dic₈₉	—	2	1	no	—
141	#13083551	—	2	1	no	—
142	#13083551	—	2	1	no	—
143	#13083551	—	2	1	no	—
144	#13083551	—	2	2	no	—
145	#13083551	—	2	2	no	—
146	#13083551	—	2	1	no	—
147	C₄×Dic₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
151	M₁₆×C₈₉	—	4	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	2	yes	—
156	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
157	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₈₉	#41	1	1	yes	characteristic
164	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
165	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
166	C₂²×D₈₉	—	2	4	no	—
167	C₂²×D₈₉	—	2	2	no	—
168	C₂²×D₈₉	—	2	1	no	—
169	C₂²×D₈₉	—	4	2	no	—
170	C₂²×D₈₉	—	4	2	no	—
171	C₂×C₄×C₈₉	—	2	2	no	—
172	C₂×C₄×C₈₉	—	2	2	no	—
173	C₂×C₄×C₈₉	—	2	1	no	—
174	C₂×C₄×C₈₉	—	2	1	no	—
175	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
181	C₂²⋊D₈₉	—	4	2	no	—
182	C₂×Dic₈₉	—	2	1	no	—
183	C₂×Dic₈₉	—	2	1	no	—
184	C₂×Dic₈₉	—	2	2	no	—
185	C₂×Dic₈₉	—	2	1	no	—
186	C₂×Dic₈₉	—	4	2	no	—
187	D₃₅₆	—	2	4	no	—
188	D₃₅₆	—	2	2	no	—
189	D₃₅₆	—	2	2	no	—
190	D₃₅₆	#131	1	4	yes	—
191	C₄×D₈₉	—	4	4	no	—
192	C₄×D₈₉	—	4	2	no	—
193	C₄×D₈₉	—	4	1	no	—
194	C₄×D₈₉	—	4	1	no	—
195	C₄×D₈₉	—	4	2	no	—
196	Dic₁₇₈	—	2	2	no	—
197	C₈×C₈₉	—	2	2	no	—
198	C₈×C₈₉	—	2	2	no	—
199	C₈×C₈₉	—	2	1	no	—
200	C₈×C₈₉	—	2	1	no	—
201	C₈×C₈₉	—	2	1	no	—
202	C₈×C₈₉	—	4	2	no	—
203	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
204	#10623494	—	4	2	no	—
205	#10623494	—	4	1	no	—
206	#10623494	—	4	1	no	—
207	C₂²×C₈₉	—	2	1	no	—
208	C₂²×C₈₉	—	2	1	no	—
209	C₂²×C₈₉	#444	1	2	yes	—
210	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂×D₈₉	—	2	4	no	—
212	C₂×D₈₉	—	4	8	no	—
213	C₂×D₈₉	—	4	2	no	—
214	C₂×D₈₉	—	4	2	no	—
215	C₂×D₈₉	—	4	1	no	—
216	C₂×D₈₉	—	4	1	no	—
217	C₂×D₈₉	—	4	1	no	—
218	C₄×C₈₉	—	2	1	no	—
219	C₄×C₈₉	—	2	1	no	—
220	C₄×C₈₉	—	2	1	no	—
221	C₄×C₈₉	—	2	1	no	—
222	C₄×C₈₉	C₂×#131	1	2	yes	—
223	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₄×C₈₉	#575	1	1	yes	characteristic
225	Dic₈₉	—	4	1	no	—
226	Dic₈₉	—	4	2	no	—
227	Dic₈₉	—	4	1	no	—
228	Dic₈₉	—	4	1	no	—
229	#17914	—	89	1	no	maximal, Sylow
230	C₂×C₈₉	—	2	2	no	—
231	C₂×C₈₉	#2929	1	1	yes	characteristic
232	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
234	D₈₉	—	4	4	no	—
235	D₈₉	—	8	1	no	—
236	#3105	—	89	1	no	—
237	#2966	—	89	1	no	—
238	C₂×C₈×D₄	—	89	1	no	—
239	#1582	—	89	2	no	—
240	#1581	—	89	2	no	—
241	#1580	—	89	2	no	—
242	SD₁₆⋊C₈	—	89	2	no	—
243	#1573	—	89	1	no	—
244	#1490	—	89	1	no	—
245	#1483	—	89	1	no	—
246	#1451	D₈₉	1	1	yes	characteristic, complemented
247	C₈₉	#17914	1	1	yes	characteristic, complemented, Sylow
248	C₂³×C₈	—	178	1	no	—
249	#529	—	89	1	no	—
250	C₂×C₄×D₄	—	89	1	no	—
251	#484	—	89	1	no	—
252	#481	—	89	1	no	—
253	#478	—	89	2	no	—
254	#463	—	89	2	no	—
255	#450	—	89	1	no	—
256	#447	—	89	1	no	—
257	#446	—	89	1	no	—
258	C₈×Q₈	—	89	1	no	—
259	C₄×SD₁₆	—	89	2	no	—
260	C₄×D₈	—	89	2	no	—
261	#436	—	89	1	no	—
262	#435	—	178	1	no	—
263	C₈×D₄	—	89	2	no	—
264	C₈×D₄	—	89	1	no	—
265	C₈×D₄	—	89	2	no	—
266	C₈×D₄	—	178	1	no	—
267	C₈×D₄	—	178	1	no	—
268	C₈×D₄	—	178	1	no	—
269	#433	—	178	1	no	—
270	#432	—	89	1	no	—
271	#431	C₂×D₈₉	1	1	yes	characteristic
272	C₂×C₄⋊C₈	—	89	1	no	—
273	C₂×C₂²⋊C₈	—	178	1	no	—
274	#405	—	178	1	no	—
275	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
277	#335	—	89	2	no	—
278	#334	—	89	2	no	—
279	Q₈⋊C₈	—	89	2	no	—
280	D₄⋊C₈	—	89	2	no	—
281	D₄⋊C₈	—	89	2	no	—
282	D₄⋊C₈	—	89	2	no	—
283	#322	C₂×D₈₉	1	2	yes	complemented
284	#322	C₂×D₈₉	1	2	yes	complemented
285	C₂²×D₄	—	89	1	no	—
286	C₂³×C₄	—	178	1	no	—
287	C₂×SD₁₆	—	89	2	no	—
288	C₂×D₈	—	89	2	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	—	178	1	no	—
291	C₂²×C₈	—	356	4	no	—
292	C₂²×C₈	—	178	1	no	—
293	C₂²×C₈	—	178	2	no	—
294	C₂²×C₈	—	178	2	no	—
295	C₂²×C₈	—	178	1	no	—
296	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
297	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
298	#126	—	178	1	no	—
299	#125	—	89	1	no	—
300	#124	—	89	1	no	—
301	#123	—	178	1	no	—
302	C₂²⋊Q₈	—	89	1	no	—
303	#121	—	89	1	no	—
304	C₄×Q₈	—	89	1	no	—
305	C₄×D₄	—	89	2	no	—
306	C₄×D₄	—	89	2	no	—
307	C₄×D₄	—	89	1	no	—
308	C₄×D₄	—	178	1	no	—
309	C₄×D₄	—	178	1	no	—
310	C₄×D₄	—	178	1	no	—
311	#117	—	178	1	no	—
312	C₂×C₄⋊C₄	—	89	1	no	—
313	C₂×C₂²⋊C₄	—	178	1	no	—
314	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
315	#107	—	89	2	no	—
316	#106	—	89	2	no	—
317	C₄⋊C₈	—	89	1	no	—
318	C₄⋊C₈	—	89	1	no	—
319	C₄⋊C₈	—	89	2	no	—
320	C₄⋊C₈	—	178	1	no	—
321	C₄⋊C₈	—	178	1	no	—
322	C₄⋊C₈	—	178	1	no	—
323	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
324	#103	—	89	2	no	—
325	#102	—	89	2	no	—
326	#102	—	89	2	no	—
327	#102	—	89	2	no	—
328	C₂²⋊C₈	—	178	1	no	—
329	C₂²⋊C₈	—	178	2	no	—
330	C₂²⋊C₈	—	178	2	no	—
331	C₂²⋊C₈	—	178	1	no	—
332	C₂²⋊C₈	—	178	1	no	—
333	C₂²⋊C₈	C₄×D₈₉	1	1	yes	characteristic
334	C₂²⋊C₈	C₄×D₈₉	1	1	yes	characteristic
335	#97	—	2	1	no	—
336	#97	—	178	1	no	—
337	#97	—	178	1	no	—
338	C₄×C₈	—	178	1	no	—
339	C₄×C₈	D₃₅₆	1	1	yes	characteristic
340	C₄×C₈	D₃₅₆	1	1	yes	characteristic
341	C₄×C₈	C₂²×D₈₉	1	2	yes	—
342	C₄×C₈	C₂²×D₈₉	1	2	yes	—
343	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
344	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
345	C₂⁴	—	178	1	no	—
346	C₂×Q₈	—	89	1	no	—
347	C₂×D₄	—	89	2	no	—
348	C₂×D₄	—	89	1	no	—
349	C₂×D₄	—	178	4	no	—
350	C₂×D₄	—	178	1	no	—
351	C₂×D₄	—	178	1	no	—
352	C₂²×C₄	—	356	2	no	—
353	C₂²×C₄	—	356	2	no	—
354	C₂²×C₄	—	178	1	no	—
355	C₂²×C₄	—	178	2	no	—
356	C₂²×C₄	—	178	1	no	—
357	C₂²×C₄	—	178	2	no	—
358	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
360	C₂²×C₄	#13083574	1	1	yes	characteristic
361	SD₁₆	—	178	4	no	—
362	D₈	—	178	4	no	—
363	M₁₆	—	4	2	no	—
364	M₁₆	—	356	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	356	4	no	—
369	C₂×C₈	—	356	2	no	—
370	C₂×C₈	—	356	2	no	—
371	C₂×C₈	—	356	4	no	—
372	C₂×C₈	—	178	1	no	—
373	C₂×C₈	—	178	1	no	—
374	C₂×C₈	—	178	2	no	—
375	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
376	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
377	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
378	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
379	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
380	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
381	C₄⋊C₄	—	89	1	no	—
382	C₄⋊C₄	—	89	1	no	—
383	C₄⋊C₄	—	89	2	no	—
384	C₄⋊C₄	—	178	1	no	—
385	C₄⋊C₄	—	178	1	no	—
386	C₄⋊C₄	—	178	1	no	—
387	C₄⋊C₄	—	178	1	no	—
388	C₄⋊C₄	—	178	1	no	—
389	C₂²⋊C₄	—	178	1	no	—
390	C₂²⋊C₄	—	178	2	no	—
391	C₂²⋊C₄	—	178	1	no	—
392	C₂²⋊C₄	—	178	1	no	—
393	C₂²⋊C₄	—	178	1	no	—
394	C₂²⋊C₄	—	178	2	no	—
395	C₂²⋊C₄	—	178	1	no	—
396	C₄²	—	178	1	no	—
397	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
398	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
399	C₄²	#13083574	1	1	yes	characteristic
400	C₄²	C₂³×D₈₉	1	1	yes	characteristic
401	C₂³	—	356	2	no	—
402	C₂³	—	356	2	no	—
403	C₂³	—	178	4	no	—
404	C₂³	—	178	1	no	—
405	C₂³	—	178	2	no	—
406	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
407	Q₈	—	178	2	no	—
408	D₄	—	89	4	no	—
409	D₄	—	356	2	no	—
410	D₄	—	178	4	no	—
411	D₄	—	178	2	no	—
412	D₄	—	178	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	356	4	no	—
418	C₂×C₄	—	356	2	no	—
419	C₂×C₄	—	356	2	no	—
420	C₂×C₄	—	356	1	no	—
421	C₂×C₄	—	356	1	no	—
422	C₂×C₄	—	356	2	no	—
423	C₂×C₄	—	178	1	no	—
424	C₂×C₄	—	178	1	no	—
425	C₂×C₄	—	178	1	no	—
426	C₂×C₄	—	178	2	no	—
427	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
428	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
429	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
432	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
433	C₈	—	2	1	no	—
434	C₈	—	2	1	no	—
435	C₈	—	2	1	no	—
436	C₈	—	2	2	no	—
437	C₈	—	2	2	no	—
438	C₈	—	4	2	no	—
439	C₈	—	356	2	no	—
440	C₈	—	356	1	no	—
441	C₈	—	356	1	no	—
442	C₈	#15668040	1	2	yes	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	356	8	no	—
446	C₂²	—	356	2	no	—
447	C₂²	—	356	2	no	—
448	C₂²	—	356	1	no	—
449	C₂²	—	356	1	no	—
450	C₂²	—	356	1	no	—
451	C₂²	—	178	4	no	—
452	C₂²	#19151721	1	2	yes	—
453	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	356	2	no	—
459	C₄	—	356	1	no	—
460	C₄	—	356	1	no	—
461	C₄	—	356	1	no	—
462	C₄	#131×D₈₉	1	2	yes	—
463	C₄	C₂×#15668040	1	1	yes	characteristic
464	C₄	#19152398	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	356	4	no	—
467	C₂	—	712	1	no	—
468	C₂	#26028948	1	1	yes	characteristic
469	C₂	C₄×#15668040	1	1	yes	characteristic
470	C₂	C₂×#19151721	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1451	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#19151734	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1451	D₈₉
hypocenter	C₈₉	#17914
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1451

Complements

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

N	H ≅ G/N	type
2. #26029227	C₂	semidirect
3. C₂×C₈×D₃₅₆	C₂	semidirect
4. #26019090	C₂	semidirect
5. #26019083	C₂	semidirect
6. #26019077	C₂	semidirect
7. #26019066	C₂	semidirect
8. #26019037	C₂	semidirect
9. #26018696	C₂	semidirect
10. #26018666	C₂	semidirect
11. C₈₉×#1451	C₂	semidirect
21. #19151728	C₂²	semidirect
22. C₈×Dic₁₇₈	C₂²	semidirect
25. #19151677	C₂²	semidirect
31. C₈×D₃₅₆	C₂²	semidirect
38. #19151351	C₂²	semidirect
39. #19151349	C₂²	semidirect
40. #19151330	C₂²	semidirect
43. #19151327	C₂²	semidirect
47. #322×C₈₉	C₂²	semidirect
48. #322×C₈₉	C₂²	semidirect
246. #1451	D₈₉	semidirect
247. C₈₉	#17914	semidirect
283. #322	C₂×D₈₉	semidirect
284. #322	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26030301	2
#26029227	2
C₂×C₈×D₃₅₆	2
#26019090	2
#26019083	2
#26019077	2
#26019066	2
#26019037	2
#26018696	2
#26018666	2
C₈₉×#1451	2
#17914	89