Subgroups — #36523875

Order 22784.

702 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029361	C₂	1	1	yes	maximal, characteristic
2	#26029332	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#15668045	C₂	1	1	yes	maximal, characteristic
4	#26019070	C₂	1	2	yes	maximal, complemented
5	#26019063	C₂	1	2	yes	maximal, complemented
6	#26019058	C₂	1	2	yes	maximal, complemented
7	#26019051	C₂	1	2	yes	maximal, complemented
8	#26018632	C₂	1	1	yes	maximal, characteristic
9	C₂×#19151328	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668045	C₄	1	1	yes	characteristic
13	C₄×#13083574	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
15	C₈×Dic₁₇₈	—	2	1	no	—
16	C₈×Dic₁₇₈	—	2	1	no	—
17	#19151722	C₂²	1	2	yes	—
18	#19151722	C₂²	1	2	yes	—
19	#19151722	C₂²	1	2	yes	—
20	#19151706	C₄	1	2	yes	—
21	#19151700	C₄	1	2	yes	—
22	C₄×Dic₃₅₆	C₂²	1	2	yes	—
23	C₄×#13083563	C₂²	1	2	yes	—
24	#19151663	C₂²	1	2	yes	—
25	C₈×C₂²⋊D₈₉	—	2	2	no	—
26	#19151651	C₂²	1	1	yes	characteristic
27	#19151650	—	2	1	no	—
28	#19151648	—	2	2	no	—
29	#19151640	C₄	1	1	yes	characteristic
30	C₄⋊C₈×D₈₉	—	2	1	no	—
31	#19151608	C₄	1	1	yes	characteristic
32	#19151600	C₄	1	1	yes	characteristic
33	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
34	#19151328	C₂²	1	2	yes	—
35	#19151328	C₂²	1	2	yes	—
36	#19151328	C₂²	1	1	yes	characteristic
37	#19151328	C₂²	1	1	yes	characteristic
38	#19151325	C₂²	1	1	yes	characteristic
39	#19151325	C₂²	1	1	yes	characteristic
40	#19151319	C₂²	1	2	yes	—
41	C₈×#10623494	C₂²	1	2	yes	—
42	#431×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
45	#335×C₈₉	C₂²	1	2	yes	—
46	#334×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
48	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
49	#15668045	C₈	1	8	yes	complemented
50	C₂×Dic₃₅₆	C₂×C₄	1	2	yes	—
51	C₂×#13083563	C₂×C₄	1	2	yes	—
52	C₂²×#10623494	—	2	1	no	—
53	C₂×C₈×D₈₉	—	2	2	no	—
54	C₄×Dic₁₇₈	—	2	1	no	—
55	C₄×Dic₁₇₈	—	2	1	no	—
56	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
57	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
58	C₄×Dic₁₇₈	C₂³	1	2	yes	—
59	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
60	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
61	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
62	C₄×C₂²⋊D₈₉	—	2	1	no	—
63	C₄×C₂²⋊D₈₉	—	2	1	no	—
64	#15667971	C₂×C₄	1	1	yes	characteristic
65	#15667969	—	2	1	no	—
66	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
67	C₂×#13083553	—	2	1	no	—
68	C₂×C₄×Dic₈₉	—	2	1	no	—
69	C₄²×D₈₉	—	2	1	no	—
70	#15667946	C₂×C₄	1	2	yes	—
71	#15667944	C₂×C₄	1	2	yes	—
72	C₄⋊#10623494	D₄	1	1	yes	characteristic
73	C₄⋊#10623494	D₄	1	1	yes	characteristic
74	#15667941	—	2	2	no	—
75	#15667941	—	2	2	no	—
76	#15667941	—	2	2	no	—
77	#15667937	C₂×C₄	1	2	yes	—
78	#15667937	C₂×C₄	1	2	yes	—
79	#15667937	C₂×C₄	1	2	yes	—
80	#15667934	C₂×C₄	1	2	yes	—
81	C₂²⋊#10623494	D₄	1	2	yes	—
82	#15667924	—	2	2	no	—
83	C₄×#10623494	—	2	1	no	—
84	C₄×#10623494	C₂³	1	1	yes	characteristic
85	C₄×#10623494	C₂³	1	1	yes	characteristic
86	C₄×#10623494	C₂³	1	2	yes	—
87	C₈×Dic₈₉	—	2	2	no	—
88	C₈×Dic₈₉	—	2	2	no	—
89	C₈×Dic₈₉	—	2	2	no	—
90	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
91	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
92	C₂²×C₈×C₈₉	—	2	1	no	—
93	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₈₉	—	2	1	no	—
95	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
96	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²⋊C₈×C₈₉	—	2	1	no	—
99	#97×C₈₉	C₂×C₄	1	2	yes	—
100	C₄×C₈×C₈₉	—	2	1	no	—
101	C₄×C₈×C₈₉	C₂³	1	2	yes	—
102	#13083574	—	2	2	no	—
103	#13083574	C₂×C₈	1	4	yes	—
104	C₂×Dic₁₇₈	—	2	1	no	—
105	C₂×Dic₁₇₈	—	2	2	no	—
106	C₂×Dic₁₇₈	C₂×C₈	1	4	yes	complemented
107	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
108	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
109	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₈₉	—	2	1	no	—
111	C₂²×Dic₈₉	—	2	1	no	—
112	C₂²×Dic₈₉	—	2	1	no	—
113	C₂×C₄×D₈₉	—	2	1	no	—
114	C₂×C₄×D₈₉	—	2	1	no	—
115	C₂×C₄×D₈₉	—	2	1	no	—
116	Dic₃₅₆	C₂×C₈	1	8	yes	complemented
117	#13083563	C₂×C₈	1	8	yes	complemented
118	C₂×#10623494	—	2	1	no	—
119	C₂×#10623494	—	2	1	no	—
120	C₂×#10623494	—	4	2	no	—
121	C₂×#10623494	C₂×D₄	1	2	yes	—
122	C₂×#10623494	C₂×D₄	1	2	yes	—
123	C₈×D₈₉	—	8	2	no	—
124	C₄⋊Dic₈₉	—	2	1	no	—
125	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
128	#13083553	—	2	1	no	—
129	#13083553	—	2	2	no	—
130	#13083553	—	2	1	no	—
131	#13083553	—	2	2	no	—
132	C₂²⋊Dic₈₉	—	2	1	no	—
133	#13083551	—	2	1	no	—
134	#13083551	—	2	1	no	—
135	C₄×Dic₈₉	—	2	1	no	—
136	C₄×Dic₈₉	—	2	1	no	—
137	C₄×Dic₈₉	—	2	2	no	—
138	C₄×Dic₈₉	—	2	1	no	—
139	C₄×Dic₈₉	—	2	2	no	—
140	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
143	M₁₆×C₈₉	—	2	2	no	—
144	M₁₆×C₈₉	C₂×C₈	1	4	yes	complemented
145	C₂×C₈×C₈₉	—	2	2	no	—
146	C₂×C₈×C₈₉	—	2	1	no	—
147	C₂×C₈×C₈₉	—	2	1	no	—
148	C₂×C₈×C₈₉	—	8	1	no	—
149	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
151	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₈₉	#41	1	1	yes	characteristic
154	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
155	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
156	C₂²×D₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	2	1	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	4	1	no	—
160	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
164	C₂×C₄×C₈₉	#131	1	2	yes	—
165	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
168	C₂²⋊D₈₉	—	2	4	no	—
169	C₂×Dic₈₉	—	2	1	no	—
170	C₂×Dic₈₉	—	2	2	no	—
171	C₂×Dic₈₉	—	2	4	no	—
172	C₂×Dic₈₉	—	2	1	no	—
173	C₂×Dic₈₉	—	2	1	no	—
174	C₂×Dic₈₉	—	2	2	no	—
175	C₂×Dic₈₉	—	8	1	no	—
176	D₃₅₆	—	2	1	no	—
177	D₃₅₆	C₂²×C₈	1	2	yes	—
178	C₄×D₈₉	—	2	4	no	—
179	C₄×D₈₉	—	4	1	no	—
180	C₄×D₈₉	—	4	1	no	—
181	C₄×D₈₉	—	8	1	no	—
182	Dic₁₇₈	—	2	2	no	—
183	Dic₁₇₈	—	2	1	no	—
184	Dic₁₇₈	—	2	4	no	—
185	Dic₁₇₈	C₂²×C₈	1	4	yes	—
186	Dic₁₇₈	C₂²×C₈	1	2	yes	—
187	C₈×C₈₉	—	2	2	no	—
188	C₈×C₈₉	—	4	1	no	—
189	C₈×C₈₉	—	4	2	no	—
190	C₈×C₈₉	—	4	1	no	—
191	C₈×C₈₉	C₂²×C₈	1	4	yes	—
192	#10623494	—	2	2	no	—
193	#10623494	—	2	2	no	—
194	#10623494	—	2	2	no	—
195	#10623494	—	4	1	no	—
196	C₂²×C₈₉	—	2	1	no	—
197	C₂²×C₈₉	—	2	1	no	—
198	C₂²×C₈₉	C₈×D₄	1	2	yes	—
199	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
200	C₂×D₈₉	—	2	2	no	—
201	C₂×D₈₉	—	4	1	no	—
202	C₂×D₈₉	—	4	1	no	—
203	C₄×C₈₉	—	2	1	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	C₈×D₄	1	2	yes	—
207	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
208	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
209	C₄×C₈₉	#577	1	1	yes	characteristic
210	C₄×C₈₉	#578	1	1	yes	characteristic
211	Dic₈₉	—	2	4	no	—
212	Dic₈₉	—	2	2	no	—
213	Dic₈₉	—	4	1	no	—
214	Dic₈₉	—	4	1	no	—
215	Dic₈₉	—	4	2	no	—
216	#17853	—	89	1	no	maximal, Sylow
217	C₂×C₈₉	—	2	2	no	—
218	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
219	C₂×C₈₉	#2947	1	1	yes	characteristic
220	C₂×C₈₉	#2956	1	1	yes	characteristic
221	D₈₉	—	4	2	no	—
222	#2988	—	89	1	no	—
223	#2982	—	89	1	no	—
224	C₄×#137	—	89	1	no	—
225	#1579	—	89	2	no	—
226	SD₁₆⋊C₈	—	89	2	no	—
227	C₈×Q₁₆	—	89	2	no	—
228	C₈×SD₁₆	—	89	2	no	—
229	#1565	D₈₉	1	1	yes	characteristic, complemented
230	#1476	—	89	1	no	—
231	C₂×Q₈⋊C₈	—	89	1	no	—
232	C₈×M₁₆	—	89	1	no	—
233	C₈₉	#17853	1	1	yes	characteristic, complemented, Sylow
234	C₂×#137	—	89	1	no	—
235	C₄×#41	—	89	1	no	—
236	C₂×C₄×Q₈	—	89	1	no	—
237	C₈×Q₈	—	89	2	no	—
238	C₈×Q₈	—	89	2	no	—
239	C₈×Q₈	—	89	2	no	—
240	C₈×Q₈	—	178	1	no	—
241	C₈×Q₈	—	178	1	no	—
242	#441	—	89	2	no	—
243	#440	—	89	2	no	—
244	C₄×Q₁₆	—	89	2	no	—
245	C₄×SD₁₆	—	89	2	no	—
246	C₈×D₄	—	89	2	no	—
247	C₈×D₄	—	178	2	no	—
248	#431	—	89	1	no	—
249	#431	—	178	2	no	—
250	#431	—	178	1	no	—
251	#431	C₂×D₈₉	1	1	yes	characteristic
252	#428	—	89	1	no	—
253	C₂×C₄⋊C₈	—	178	1	no	—
254	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
255	#419	—	89	1	no	—
256	#417	—	89	1	no	—
257	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
258	C₂×C₄×C₈	—	89	1	no	—
259	#335	C₂×D₈₉	1	2	yes	—
260	#334	C₂×D₈₉	1	2	yes	—
261	Q₈⋊C₈	—	89	2	no	—
262	Q₈⋊C₈	—	89	1	no	—
263	Q₈⋊C₈	—	89	2	no	—
264	Q₈⋊C₈	—	89	1	no	—
265	D₄⋊C₈	—	89	1	no	—
266	D₄⋊C₈	—	89	1	no	—
267	#322	—	89	2	no	—
268	C₈²	—	89	2	no	—
269	C₂×#41	—	89	1	no	—
270	C₂²×Q₈	—	89	1	no	—
271	#137	—	89	8	no	—
272	C₂×Q₁₆	—	89	2	no	—
273	C₂×SD₁₆	—	89	2	no	—
274	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
275	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	178	2	no	—
278	C₂²×C₈	—	178	1	no	—
279	C₄×Q₈	—	89	2	no	—
280	C₄×Q₈	—	89	1	no	—
281	C₄×Q₈	—	89	2	no	—
282	C₄×Q₈	—	89	1	no	—
283	C₄×Q₈	—	178	1	no	—
284	C₄×Q₈	—	178	1	no	—
285	C₄×D₄	—	89	1	no	—
286	C₄×D₄	—	89	1	no	—
287	C₄×D₄	—	178	1	no	—
288	C₄×D₄	—	178	1	no	—
289	#117	—	89	1	no	—
290	#117	—	178	1	no	—
291	C₂×C₄⋊C₄	—	89	1	no	—
292	C₂×C₄⋊C₄	—	178	1	no	—
293	C₂×C₄²	—	178	1	no	—
294	C₂×C₄²	—	178	1	no	—
295	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
296	#107	—	89	2	no	—
297	#106	—	89	2	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	89	1	no	—
300	C₄⋊C₈	—	89	1	no	—
301	C₄⋊C₈	—	178	2	no	—
302	C₄⋊C₈	—	178	2	no	—
303	C₄⋊C₈	—	178	2	no	—
304	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
305	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
306	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
307	#103	—	89	2	no	—
308	#103	—	89	2	no	—
309	#103	—	89	2	no	—
310	#102	—	89	2	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	89	2	no	—
313	C₂²⋊C₈	—	178	2	no	—
314	#97	C₄×D₈₉	1	2	yes	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	—	89	2	no	—
317	C₄×C₈	—	89	1	no	—
318	C₄×C₈	—	89	1	no	—
319	C₄×C₈	—	178	2	no	—
320	C₄×C₈	—	178	2	no	—
321	C₄×C₈	—	178	2	no	—
322	C₄×C₈	—	178	1	no	—
323	C₄×C₈	C₂²×D₈₉	1	2	yes	—
324	#41	—	89	4	no	—
325	#41	—	178	2	no	—
326	C₂×Q₈	—	89	4	no	—
327	C₂×Q₈	—	89	2	no	—
328	C₂×Q₈	—	89	1	no	—
329	C₂×Q₈	—	178	1	no	—
330	C₂×Q₈	—	178	2	no	—
331	C₂×D₄	—	89	1	no	—
332	C₂×D₄	—	178	1	no	—
333	C₂²×C₄	—	178	1	no	—
334	C₂²×C₄	—	178	1	no	—
335	C₂²×C₄	—	178	1	no	—
336	C₂²×C₄	—	178	1	no	—
337	C₂²×C₄	—	178	1	no	—
338	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
339	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
340	C₂²×C₄	#13083575	1	1	yes	characteristic
341	Q₁₆	—	89	8	no	—
342	SD₁₆	—	89	8	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	C₈×D₈₉	1	4	yes	complemented
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	8	1	no	—
349	C₂×C₈	—	89	2	no	—
350	C₂×C₈	—	89	2	no	—
351	C₂×C₈	—	356	2	no	—
352	C₂×C₈	—	178	1	no	—
353	C₂×C₈	—	178	1	no	—
354	C₂×C₈	—	712	2	no	—
355	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
356	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
357	C₄⋊C₄	—	89	2	no	—
358	C₄⋊C₄	—	89	1	no	—
359	C₄⋊C₄	—	89	1	no	—
360	C₄⋊C₄	—	178	1	no	—
361	C₄⋊C₄	—	178	2	no	—
362	C₄⋊C₄	—	178	1	no	—
363	C₄⋊C₄	—	178	2	no	—
364	C₄⋊C₄	—	178	1	no	—
365	C₂²⋊C₄	—	178	1	no	—
366	C₂²⋊C₄	—	178	1	no	—
367	C₂²⋊C₄	—	178	1	no	—
368	C₄²	—	178	1	no	—
369	C₄²	—	178	1	no	—
370	C₄²	—	178	2	no	—
371	C₄²	—	178	1	no	—
372	C₄²	—	178	2	no	—
373	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
374	C₄²	D₄×D₈₉	1	1	yes	characteristic
375	C₄²	#13083575	1	1	yes	characteristic
376	C₄²	C₂³×D₈₉	1	1	yes	characteristic
377	C₂³	—	178	1	no	—
378	C₂³	#15667974	1	1	yes	characteristic
379	Q₈	—	89	4	no	—
380	Q₈	—	89	2	no	—
381	Q₈	—	178	4	no	—
382	Q₈	—	178	2	no	—
383	Q₈	—	178	1	no	—
384	D₄	—	89	2	no	—
385	D₄	—	178	4	no	—
386	D₄	—	178	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	356	1	no	—
391	C₂×C₄	—	356	1	no	—
392	C₂×C₄	—	178	1	no	—
393	C₂×C₄	—	178	1	no	—
394	C₂×C₄	—	178	2	no	—
395	C₂×C₄	—	178	4	no	—
396	C₂×C₄	—	178	1	no	—
397	C₂×C₄	—	178	2	no	—
398	C₂×C₄	—	178	4	no	—
399	C₂×C₄	—	712	1	no	—
400	C₂×C₄	—	712	1	no	—
401	C₂×C₄	#15667974	1	1	yes	characteristic
402	C₂×C₄	#15667974	1	1	yes	characteristic
403	C₂×C₄	#15667974	1	1	yes	characteristic
404	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
405	C₂×C₄	#15668020	1	2	yes	—
406	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
407	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
408	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	2	no	—
412	C₈	—	4	1	no	—
413	C₈	—	356	1	no	—
414	C₈	—	178	2	no	—
415	C₈	—	178	2	no	—
416	C₈	—	178	2	no	—
417	C₈	C₂×C₈×D₈₉	1	4	yes	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	356	1	no	—
421	C₂²	—	356	1	no	—
422	C₂²	—	178	2	no	—
423	C₂²	#19151663	1	2	yes	—
424	C₂²	C₂×#15667974	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	356	1	no	—
429	C₄	—	356	1	no	—
430	C₄	—	356	2	no	—
431	C₄	—	178	2	no	—
432	C₄	—	178	4	no	—
433	C₄	#19151663	1	2	yes	—
434	C₄	C₂²×C₈×D₈₉	1	1	yes	characteristic
435	C₄	C₂×#15668020	1	1	yes	characteristic
436	C₄	#19152408	1	1	yes	characteristic
437	C₄	#19152414	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	356	2	no	—
440	C₂	C₂×#19151663	1	1	yes	characteristic
441	C₂	#26029093	1	1	yes	characteristic
442	C₂	#26029161	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1565	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#13083574	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1565	D₈₉
hypocenter	C₈₉	#17853
LCS	G ▷ 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
2. #26029332	C₂	semidirect
4. #26019070	C₂	semidirect
5. #26019063	C₂	semidirect
6. #26019058	C₂	semidirect
7. #26019051	C₂	semidirect
9. C₂×#19151328	C₂	semidirect
10. M₁₆×#10623494	C₂	semidirect
11. C₈₉×#1565	C₂	semidirect
49. #15668045	C₈	semidirect
106. C₂×Dic₁₇₈	C₂×C₈	semidirect
116. Dic₃₅₆	C₂×C₈	semidirect
117. #13083563	C₂×C₈	semidirect
144. M₁₆×C₈₉	C₂×C₈	semidirect
229. #1565	D₈₉	semidirect
233. C₈₉	#17853	semidirect
344. M₁₆	C₈×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029361	2
#26029332	2
C₄×#15668045	2
#26019070	2
#26019063	2
#26019058	2
#26019051	2
#26018632	2
C₂×#19151328	2
M₁₆×#10623494	2
C₈₉×#1565	2
#17853	89