Subgroups — #36572894

Order 22784.

870 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151716	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151714	C₂	1	1	yes	maximal, characteristic
3	#26029023	C₂	1	1	yes	maximal, characteristic
4	#26028819	C₂	1	2	yes	maximal, complemented
5	#26021001	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020528	C₂	1	2	yes	maximal, complemented
7	#26020526	C₂	1	2	yes	maximal, complemented
8	#26020422	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020271	C₂	1	2	yes	maximal, complemented
10	C₈×#13083553	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1945	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668034	C₂²	1	1	yes	characteristic
13	C₂×#15668020	C₂²	1	2	yes	—
14	C₂×#15668018	C₂²	1	2	yes	—
15	#19152066	C₂²	1	2	yes	—
16	#19151716	—	2	4	no	—
17	#19151714	—	2	4	no	—
18	#19151692	C₄	1	1	yes	characteristic, complemented
19	#19151692	C₄	1	1	yes	characteristic, complemented
20	#19151685	C₄	1	2	yes	complemented
21	#19151685	C₄	1	2	yes	complemented
22	#19151680	C₄	1	1	yes	characteristic, complemented
23	#19151680	C₄	1	1	yes	characteristic, complemented
24	C₂×#15667948	C₂²	1	1	yes	characteristic
25	C₂×#15667947	C₂²	1	2	yes	—
26	#19151625	C₂²	1	2	yes	—
27	#19151623	—	2	2	no	—
28	#19151623	—	2	2	no	—
29	#19151621	C₂²	1	2	yes	—
30	#19151620	—	2	2	no	—
31	C₂×#15667941	C₂²	1	1	yes	characteristic
32	C₄⋊C₈×D₈₉	—	2	2	no	—
33	C₂×#15667940	C₂²	1	2	yes	—
34	C₂×#15667938	C₂²	1	2	yes	—
35	#19151592	C₂²	1	2	yes	—
36	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
38	C₄×#13083553	C₂²	1	1	yes	characteristic
39	#19151357	C₂²	1	2	yes	—
40	#19151353	C₂²	1	1	yes	characteristic
41	#19151352	C₂²	1	1	yes	characteristic
42	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
43	#427×C₈₉	C₂²	1	1	yes	characteristic
44	#424×C₈₉	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
46	#339×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083574	C₂³	1	2	yes	—
48	#15668034	D₄	1	4	yes	—
49	#15668034	Q₈	1	4	yes	—
50	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
51	C₂×#13083563	C₂×C₄	1	2	yes	—
52	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
53	#15668020	—	2	4	no	—
54	#15668020	—	4	2	no	—
55	#15668018	—	2	4	no	—
56	#15668018	—	4	2	no	—
57	C₂×#13083558	C₂³	1	2	yes	—
58	C₂×#13083557	—	2	2	no	—
59	C₂×#13083557	—	2	2	no	—
60	C₂²×#10623494	C₂³	1	1	yes	characteristic
61	C₂²×#10623494	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₈₉	—	2	2	no	—
63	C₂×C₈×D₈₉	—	2	2	no	—
64	#15667977	C₂×C₄	1	2	yes	—
65	#15667977	C₂×C₄	1	2	yes	—
66	#15667974	C₂×C₄	1	2	yes	—
67	#15667974	C₂×C₄	1	2	yes	—
68	#15667972	—	2	2	no	—
69	#15667972	—	2	2	no	—
70	#15667969	—	2	2	no	—
71	C₂×#13083553	—	2	1	no	—
72	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
73	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
74	C₄²×D₈₉	—	2	2	no	—
75	#15667948	—	2	2	no	—
76	#15667947	—	4	2	no	—
77	C₄⋊#10623494	—	2	2	no	—
78	C₄⋊#10623494	—	2	2	no	—
79	#15667941	—	2	2	no	—
80	#15667941	—	2	2	no	—
81	#15667941	D₄	1	1	yes	characteristic
82	#15667941	D₄	1	1	yes	characteristic
83	#15667941	D₄	1	1	yes	characteristic
84	#15667941	D₄	1	1	yes	characteristic
85	#15667940	—	2	4	no	—
86	#15667938	—	2	4	no	—
87	#15667935	C₂×C₄	1	2	yes	—
88	#15667935	C₂×C₄	1	2	yes	—
89	#15667932	C₂×C₄	1	2	yes	—
90	#15667932	C₂×C₄	1	2	yes	—
91	C₈×Dic₈₉	—	2	2	no	—
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	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
96	#15667919	—	2	1	no	—
97	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
98	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
100	#117×C₈₉	C₂³	1	2	yes	—
101	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
102	#108×C₈₉	—	2	2	no	—
103	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
104	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
105	#106×C₈₉	C₂×C₄	1	2	yes	—
106	C₄⋊C₈×C₈₉	—	2	2	no	—
107	C₄⋊C₈×C₈₉	—	2	2	no	—
108	C₄×C₈×C₈₉	—	2	2	no	—
109	#13083574	—	2	2	no	—
110	#13083574	—	2	2	no	—
111	#13083574	C₂×D₄	1	4	yes	—
112	#13083574	C₂×Q₈	1	4	yes	—
113	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
114	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
115	C₂×C₂²⋊D₈₉	—	2	2	no	—
116	C₂²×Dic₈₉	—	2	1	no	—
117	C₂²×Dic₈₉	#41	1	1	yes	characteristic
118	C₂²×Dic₈₉	#41	1	1	yes	characteristic
119	C₂×C₄×D₈₉	—	2	2	no	—
120	C₂×C₄×D₈₉	—	2	2	no	—
121	C₂×C₄×D₈₉	—	2	2	no	—
122	Dic₃₅₆	C₄⋊C₄	1	4	yes	complemented
123	#13083563	C₄⋊C₄	1	8	yes	complemented
124	D₇₁₂	C₄⋊C₄	1	4	yes	complemented
125	#13083558	—	2	2	no	—
126	#13083558	—	2	2	no	—
127	#13083557	—	4	4	no	—
128	#13083557	—	4	4	no	—
129	C₂×#10623494	—	2	1	no	—
130	C₂×#10623494	—	2	1	no	—
131	C₂×#10623494	—	2	1	no	—
132	C₂×#10623494	—	2	1	no	—
133	C₂×#10623494	—	2	2	no	—
134	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
135	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
136	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
137	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
138	C₈×D₈₉	—	4	4	no	—
139	C₈×D₈₉	—	4	4	no	—
140	#13083553	—	2	4	no	—
141	#13083553	—	2	2	no	—
142	#13083553	—	2	2	no	—
143	#13083551	—	2	2	no	—
144	#13083551	—	2	2	no	—
145	C₄×Dic₈₉	—	2	2	no	—
146	C₄×Dic₈₉	—	2	2	no	—
147	C₄×Dic₈₉	—	2	1	no	—
148	C₄×Dic₈₉	—	2	1	no	—
149	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
152	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₈₉	—	2	1	no	—
154	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
155	M₁₆×C₈₉	—	2	2	no	—
156	M₁₆×C₈₉	—	2	2	no	—
157	C₂×C₈×C₈₉	—	2	1	no	—
158	C₂×C₈×C₈₉	—	2	1	no	—
159	C₂×C₈×C₈₉	—	2	2	no	—
160	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
166	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
167	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
168	C₂²⋊C₄×C₈₉	—	2	2	no	—
169	C₄²×C₈₉	—	2	2	no	—
170	C₄²×C₈₉	—	2	1	no	—
171	C₄²×C₈₉	—	2	1	no	—
172	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
173	C₂²×D₈₉	—	2	2	no	—
174	C₂×C₄×C₈₉	—	2	2	no	—
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	2	2	no	—
177	C₂×C₄×C₈₉	—	4	1	no	—
178	C₂×C₄×C₈₉	—	4	1	no	—
179	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
185	C₂²⋊D₈₉	—	2	4	no	—
186	C₂²⋊D₈₉	—	2	4	no	—
187	C₂×Dic₈₉	—	2	2	no	—
188	C₂×Dic₈₉	—	2	2	no	—
189	C₂×Dic₈₉	—	2	2	no	—
190	C₂×Dic₈₉	—	4	1	no	—
191	C₂×Dic₈₉	—	4	1	no	—
192	C₂×Dic₈₉	—	4	1	no	—
193	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
194	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
195	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
196	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
197	D₃₅₆	—	2	2	no	—
198	D₃₅₆	C₂×C₄⋊C₄	1	4	yes	—
199	C₄×D₈₉	—	2	4	no	—
200	C₄×D₈₉	—	2	4	no	—
201	C₄×D₈₉	—	4	4	no	—
202	C₄×D₈₉	—	8	2	no	—
203	Dic₁₇₈	—	2	2	no	—
204	Dic₁₇₈	C₂×C₄⋊C₄	1	4	yes	—
205	C₈×C₈₉	—	2	1	no	—
206	C₈×C₈₉	—	2	1	no	—
207	C₈×C₈₉	—	4	2	no	—
208	C₈×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
209	C₈×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
210	#10623494	—	2	1	no	—
211	#10623494	—	2	1	no	—
212	#10623494	—	2	1	no	—
213	#10623494	—	2	1	no	—
214	#10623494	—	4	2	no	—
215	C₂²×C₈₉	—	2	1	no	—
216	C₂²×C₈₉	—	2	1	no	—
217	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂²×C₈₉	#547	1	1	yes	characteristic
219	C₂²×C₈₉	#554	1	1	yes	characteristic
220	C₂×D₈₉	—	2	4	no	—
221	C₂×D₈₉	—	4	2	no	—
222	C₂×D₈₉	—	4	2	no	—
223	C₄×C₈₉	—	4	2	no	—
224	C₄×C₈₉	—	4	2	no	—
225	C₄×C₈₉	—	4	2	no	—
226	C₄×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
227	C₄×C₈₉	#520	1	1	yes	characteristic
228	C₄×C₈₉	D₄²	1	1	yes	characteristic
229	C₄×C₈₉	D₄×Q₈	1	1	yes	characteristic
230	Dic₈₉	—	2	4	no	—
231	Dic₈₉	—	2	1	no	—
232	Dic₈₉	—	2	1	no	—
233	Dic₈₉	—	2	1	no	—
234	Dic₈₉	—	4	2	no	—
235	Dic₈₉	#443	1	2	yes	complemented
236	#22688	—	89	1	no	maximal, Sylow
237	C₂×C₈₉	—	2	1	no	—
238	C₂×C₈₉	—	2	1	no	—
239	C₂×C₈₉	D₄×C₄⋊C₄	1	1	yes	characteristic
240	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
241	C₂×C₈₉	#2957	1	1	yes	characteristic
242	D₈₉	—	4	4	no	—
243	C₂×#443	—	89	1	no	—
244	C₂×#443	—	89	1	no	—
245	C₄×#135	—	89	1	no	—
246	#2906	—	89	2	no	—
247	#1945	—	89	1	no	—
248	#1945	D₈₉	1	1	yes	characteristic, complemented
249	#1866	—	89	2	no	—
250	#1866	—	89	2	no	—
251	#1848	—	89	1	no	—
252	#1806	—	89	2	no	—
253	C₈×C₄⋊C₄	—	89	1	no	—
254	C₈₉	#22688	1	1	yes	characteristic, complemented, Sylow
255	C₂×#135	—	89	1	no	—
256	C₂×#131	—	89	2	no	—
257	C₂×#131	—	89	2	no	—
258	C₄×#41	—	89	2	no	—
259	#443	—	178	4	no	—
260	#443	—	178	4	no	—
261	C₄×Q₁₆	—	89	1	no	—
262	C₄×Q₁₆	—	89	1	no	—
263	C₄×SD₁₆	—	89	2	no	—
264	C₄×SD₁₆	—	89	2	no	—
265	C₄×D₈	—	89	1	no	—
266	C₄×D₈	—	89	1	no	—
267	C₂×#108	—	89	2	no	—
268	C₂×#108	—	89	1	no	—
269	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
270	#427	C₂×D₈₉	1	1	yes	characteristic
271	#424	—	89	2	no	—
272	#424	—	178	2	no	—
273	#424	—	178	2	no	—
274	#424	C₂×D₈₉	1	2	yes	—
275	#423	—	89	2	no	—
276	#423	—	178	2	no	—
277	C₂×C₄⋊C₈	—	89	1	no	—
278	C₂×C₄⋊C₈	—	178	2	no	—
279	C₂×#104	—	89	2	no	—
280	C₂×#104	—	89	2	no	—
281	#416	—	89	2	no	—
282	C₂×C₄×C₈	—	89	1	no	—
283	C₂×C₄×C₈	—	89	1	no	—
284	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
285	C₄×C₄⋊C₄	—	89	1	no	—
286	#339	—	89	2	no	—
287	#339	C₂×D₈₉	1	2	yes	—
288	#336	—	89	1	no	—
289	#336	—	89	1	no	—
290	C₂×#41	—	89	2	no	—
291	#135	—	89	4	no	—
292	#135	—	89	4	no	—
293	C₂×Q₁₆	—	89	1	no	—
294	C₂×SD₁₆	—	89	2	no	—
295	C₂×D₈	—	89	1	no	—
296	#131	—	356	2	no	—
297	#131	—	356	2	no	—
298	#131	—	178	4	no	—
299	#131	—	178	4	no	—
300	C₂×M₁₆	—	89	2	no	—
301	C₂×M₁₆	—	178	2	no	—
302	C₂×M₁₆	—	178	2	no	—
303	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
304	C₂²×C₈	—	89	1	no	—
305	C₂²×C₈	—	89	1	no	—
306	C₂²×C₈	—	178	2	no	—
307	C₂²×C₈	—	178	2	no	—
308	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
309	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
310	C₄×Q₈	—	89	2	no	—
311	C₄×Q₈	—	89	2	no	—
312	C₄×D₄	—	89	2	no	—
313	C₄×D₄	—	89	2	no	—
314	C₄×D₄	—	178	2	no	—
315	C₄×D₄	—	178	2	no	—
316	#117	—	178	2	no	—
317	#117	C₂²×D₈₉	1	2	yes	—
318	C₂×C₄⋊C₄	—	178	1	no	—
319	C₂×C₄²	—	89	1	no	—
320	C₂×C₄²	—	89	1	no	—
321	C₂×C₄²	—	178	2	no	—
322	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
323	#108	—	2	2	no	—
324	#108	—	356	2	no	—
325	#108	—	178	2	no	—
326	#107	C₄×D₈₉	1	1	yes	characteristic
327	#107	C₄×D₈₉	1	1	yes	characteristic
328	#106	C₄×D₈₉	1	2	yes	—
329	C₄⋊C₈	—	2	2	no	—
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	89	1	no	—
332	C₄⋊C₈	—	89	1	no	—
333	C₄⋊C₈	—	89	1	no	—
334	C₄⋊C₈	—	89	1	no	—
335	C₄⋊C₈	—	178	2	no	—
336	C₄⋊C₈	—	178	2	no	—
337	C₄⋊C₈	—	178	2	no	—
338	C₄⋊C₈	—	178	2	no	—
339	#104	—	178	4	no	—
340	#104	—	178	4	no	—
341	#103	—	89	2	no	—
342	#103	—	89	2	no	—
343	#102	—	89	2	no	—
344	#102	—	89	2	no	—
345	C₄×C₈	—	2	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	—	178	2	no	—
351	#95	—	178	1	no	—
352	#41	—	89	4	no	—
353	#41	—	89	4	no	—
354	#41	—	178	2	no	—
355	#41	—	178	2	no	—
356	C₂×Q₈	—	89	2	no	—
357	C₂×D₄	—	89	2	no	—
358	C₂×D₄	—	178	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	89	1	no	—
361	C₂²×C₄	—	89	1	no	—
362	C₂²×C₄	—	178	2	no	—
363	C₂²×C₄	—	178	2	no	—
364	C₂²×C₄	—	178	1	no	—
365	C₂²×C₄	—	178	2	no	—
366	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
367	Q₁₆	—	89	4	no	—
368	SD₁₆	—	89	8	no	—
369	D₈	—	89	4	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	356	4	no	—
373	M₁₆	—	356	4	no	—
374	M₁₆	—	178	2	no	—
375	M₁₆	—	178	2	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	89	1	no	—
380	C₂×C₈	—	89	1	no	—
381	C₂×C₈	—	89	1	no	—
382	C₂×C₈	—	89	1	no	—
383	C₂×C₈	—	356	4	no	—
384	C₂×C₈	—	356	4	no	—
385	C₂×C₈	—	178	2	no	—
386	C₂×C₈	—	178	1	no	—
387	C₂×C₈	—	178	1	no	—
388	C₂×C₈	—	178	1	no	—
389	C₂×C₈	—	178	1	no	—
390	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
391	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
392	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
393	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
394	C₂×C₈	D₄×D₈₉	1	2	yes	—
395	C₂×C₈	Q₈×D₈₉	1	2	yes	—
396	C₄⋊C₄	—	178	2	no	—
397	C₄⋊C₄	—	178	2	no	—
398	C₄⋊C₄	—	178	4	no	—
399	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
400	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	178	2	no	—
403	C₂²⋊C₄	—	178	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	89	1	no	—
408	C₄²	—	89	1	no	—
409	C₄²	—	89	1	no	—
410	C₄²	—	89	1	no	—
411	C₄²	—	178	2	no	—
412	C₄²	—	178	2	no	—
413	C₄²	—	178	1	no	—
414	C₄²	—	178	1	no	—
415	C₂³	—	178	2	no	—
416	C₂³	#41×D₈₉	1	1	yes	characteristic
417	Q₈	—	89	4	no	—
418	Q₈	—	178	2	no	—
419	D₄	—	89	4	no	—
420	D₄	—	178	4	no	—
421	D₄	—	178	4	no	—
422	D₄	—	178	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	89	1	no	—
429	C₂×C₄	—	89	1	no	—
430	C₂×C₄	—	89	1	no	—
431	C₂×C₄	—	89	1	no	—
432	C₂×C₄	—	356	4	no	—
433	C₂×C₄	—	356	1	no	—
434	C₂×C₄	—	356	1	no	—
435	C₂×C₄	—	356	1	no	—
436	C₂×C₄	—	178	2	no	—
437	C₂×C₄	—	178	2	no	—
438	C₂×C₄	—	178	2	no	—
439	C₂×C₄	—	178	4	no	—
440	C₂×C₄	—	178	4	no	—
441	C₂×C₄	—	712	2	no	—
442	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
443	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
444	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
445	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
446	C₂×C₄	#15668058	1	1	yes	characteristic
447	C₂×C₄	#15668060	1	1	yes	characteristic
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	4	2	no	—
451	C₈	—	356	2	no	—
452	C₈	—	178	1	no	—
453	C₈	—	178	1	no	—
454	C₈	—	178	1	no	—
455	C₈	—	178	1	no	—
456	C₈	C₄⋊C₄×D₈₉	1	2	yes	—
457	C₈	C₄⋊C₄×D₈₉	1	2	yes	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	356	2	no	—
461	C₂²	—	356	2	no	—
462	C₂²	—	178	4	no	—
463	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
464	C₂²	#19152250	1	1	yes	characteristic
465	C₂²	#19152304	1	1	yes	characteristic
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	89	2	no	—
470	C₄	—	356	2	no	—
471	C₄	—	178	1	no	—
472	C₄	—	178	1	no	—
473	C₄	—	178	1	no	—
474	C₄	—	178	4	no	—
475	C₄	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
476	C₄	#19152080	1	1	yes	characteristic
477	C₄	#19152232	1	1	yes	characteristic
478	C₄	#19152263	1	1	yes	characteristic
479	C₂	—	2	1	no	—
480	C₂	—	2	1	no	—
481	C₂	—	356	4	no	—
482	C₂	#26023153	1	1	yes	characteristic
483	C₂	#443×D₈₉	1	1	yes	characteristic
484	C₂	#26029164	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1945	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668034	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1945	D₈₉
hypocenter	C₈₉	#22688
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1945

Complements

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

N	H ≅ G/N	type
4. #26028819	C₂	semidirect
5. #26021001	C₂	semidirect
6. #26020528	C₂	semidirect
7. #26020526	C₂	semidirect
8. #26020422	C₂	semidirect
9. #26020271	C₂	semidirect
10. C₈×#13083553	C₂	semidirect
11. C₈₉×#1945	C₂	semidirect
18. #19151692	C₄	semidirect
19. #19151692	C₄	semidirect
20. #19151685	C₄	semidirect
21. #19151685	C₄	semidirect
22. #19151680	C₄	semidirect
23. #19151680	C₄	semidirect
122. Dic₃₅₆	C₄⋊C₄	semidirect
123. #13083563	C₄⋊C₄	semidirect
124. D₇₁₂	C₄⋊C₄	semidirect
235. Dic₈₉	#443	semidirect
248. #1945	D₈₉	semidirect
254. C₈₉	#22688	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151716	2
C₂×#19151714	2
#26029023	2
#26028819	2
#26021001	2
#26020528	2
#26020526	2
#26020422	2
#26020271	2
C₈×#13083553	2
C₈₉×#1945	2
#22688	89