Subgroups — #36574124

Order 22784.

722 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#135×Dic₈₉	C₂	1	1	yes	maximal, characteristic
2	#26028914	C₂	1	2	yes	maximal, complemented
3	#26021141	C₂	1	1	yes	maximal, characteristic
4	#26020903	C₂	1	2	yes	maximal, complemented
5	#26020897	C₂	1	2	yes	maximal, complemented
6	#26020422	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020270	C₂	1	2	yes	maximal, complemented
8	#26020134	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#13083553	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1974	C₂	1	1	yes	maximal, characteristic
12	#41×Dic₈₉	C₂²	1	2	yes	—
13	Q₁₆×Dic₈₉	C₄	1	1	yes	characteristic, complemented
14	Q₁₆×Dic₈₉	C₄	1	1	yes	characteristic, complemented
15	SD₁₆×Dic₈₉	C₄	1	2	yes	complemented
16	SD₁₆×Dic₈₉	C₄	1	2	yes	complemented
17	D₈×Dic₈₉	C₄	1	1	yes	characteristic, complemented
18	D₈×Dic₈₉	C₄	1	1	yes	characteristic, complemented
19	#19151656	—	2	2	no	—
20	#19151656	—	2	2	no	—
21	#19151652	—	2	2	no	—
22	#19151648	—	2	2	no	—
23	C₂×#15667948	C₂²	1	1	yes	characteristic
24	C₂×#15667947	C₂²	1	2	yes	—
25	#19151636	C₂²	1	1	yes	characteristic
26	#19151621	C₂²	1	2	yes	—
27	C₂×#15667941	C₂²	1	1	yes	characteristic
28	C₂×#15667939	C₂²	1	2	yes	—
29	#19151594	C₂²	1	2	yes	—
30	#19151565	C₂²	1	2	yes	—
31	#19151556	C₂²	1	2	yes	—
32	#19151553	C₂²	1	2	yes	—
33	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
35	C₄×#13083553	C₂²	1	1	yes	characteristic
36	#19151359	C₂²	1	2	yes	—
37	#19151358	C₂²	1	2	yes	—
38	#19151353	C₂²	1	1	yes	characteristic
39	#19151352	C₂²	1	1	yes	characteristic
40	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#104×C₈₉	C₂²	1	2	yes	—
43	#408×C₈₉	C₂²	1	2	yes	—
44	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#13083558	C₂³	1	2	yes	—
46	C₂²×#10623494	C₂³	1	1	yes	characteristic
47	C₂²×#10623494	C₂³	1	1	yes	characteristic
48	Q₈×Dic₈₉	C₂×C₄	1	2	yes	—
49	Q₈×Dic₈₉	C₂×C₄	1	2	yes	—
50	D₄×Dic₈₉	—	2	2	no	—
51	D₄×Dic₈₉	—	2	2	no	—
52	D₄×Dic₈₉	C₂×C₄	1	2	yes	—
53	D₄×Dic₈₉	C₂×C₄	1	2	yes	—
54	#15667971	—	2	2	no	—
55	#15667971	C₂³	1	2	yes	—
56	C₂×#13083553	—	2	1	no	—
57	C₂×C₄×Dic₈₉	—	2	2	no	—
58	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
60	#15667948	—	2	2	no	—
61	#15667947	—	4	2	no	—
62	#15667946	C₂×C₄	1	1	yes	characteristic
63	#15667946	C₂×C₄	1	1	yes	characteristic
64	#15667944	C₂×C₄	1	2	yes	—
65	#15667941	—	2	2	no	—
66	#15667941	—	2	2	no	—
67	#15667941	D₄	1	1	yes	characteristic
68	#15667941	D₄	1	1	yes	characteristic
69	#15667941	D₄	1	1	yes	characteristic
70	#15667941	D₄	1	1	yes	characteristic
71	#15667939	—	4	2	no	—
72	#15667936	C₂×C₄	1	2	yes	—
73	#15667936	C₂×C₄	1	2	yes	—
74	#15667933	C₂×C₄	1	2	yes	—
75	#15667933	C₂×C₄	1	2	yes	—
76	C₂²⋊#10623494	—	2	2	no	—
77	C₂²⋊#10623494	—	2	2	no	—
78	#15667922	—	2	2	no	—
79	#15667922	—	2	2	no	—
80	C₈×Dic₈₉	—	2	2	no	—
81	C₈×Dic₈₉	—	2	2	no	—
82	C₈×Dic₈₉	—	2	2	no	—
83	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
87	#15667919	—	2	1	no	—
88	C₂×#41×C₈₉	C₂³	1	2	yes	—
89	#135×C₈₉	—	2	2	no	—
90	#135×C₈₉	—	2	2	no	—
91	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
92	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
93	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
94	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
95	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
98	#108×C₈₉	—	2	2	no	—
99	#104×C₈₉	—	4	2	no	—
100	C₂²⋊C₈×C₈₉	—	2	2	no	—
101	C₂²⋊C₈×C₈₉	—	2	2	no	—
102	C₄×C₈×C₈₉	—	2	2	no	—
103	C₂²×Dic₈₉	—	2	1	no	—
104	C₂²×Dic₈₉	—	2	2	no	—
105	C₂²×Dic₈₉	—	2	2	no	—
106	C₂²×Dic₈₉	#41	1	1	yes	characteristic
107	C₂²×Dic₈₉	#41	1	1	yes	characteristic
108	#13083558	—	2	2	no	—
109	#13083558	—	2	2	no	—
110	C₂×#10623494	—	2	1	no	—
111	C₂×#10623494	—	2	1	no	—
112	C₂×#10623494	—	2	1	no	—
113	C₂×#10623494	—	2	1	no	—
114	C₂×#10623494	—	2	2	no	—
115	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
116	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
117	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
118	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
119	C₄⋊Dic₈₉	—	2	2	no	—
120	C₄⋊Dic₈₉	—	2	2	no	—
121	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
122	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
123	#13083553	—	2	4	no	—
124	C₂²⋊Dic₈₉	—	2	2	no	—
125	C₂²⋊Dic₈₉	—	2	2	no	—
126	C₂²⋊Dic₈₉	—	2	2	no	—
127	C₄×Dic₈₉	—	2	2	no	—
128	C₄×Dic₈₉	—	2	2	no	—
129	C₄×Dic₈₉	—	2	2	no	—
130	C₄×Dic₈₉	—	2	1	no	—
131	C₄×Dic₈₉	—	2	1	no	—
132	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
135	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
136	#41×C₈₉	—	2	2	no	—
137	#41×C₈₉	—	2	2	no	—
138	#41×C₈₉	—	2	2	no	—
139	#41×C₈₉	—	2	2	no	—
140	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
141	C₂×D₄×C₈₉	—	2	2	no	—
142	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₈₉	—	2	1	no	—
144	C₂²×C₄×C₈₉	—	2	2	no	—
145	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
146	Q₁₆×C₈₉	—	2	2	no	—
147	SD₁₆×C₈₉	—	2	4	no	—
148	D₈×C₈₉	—	2	2	no	—
149	M₁₆×C₈₉	—	2	2	no	—
150	M₁₆×C₈₉	—	2	2	no	—
151	C₂×C₈×C₈₉	—	2	1	no	—
152	C₂×C₈×C₈₉	—	2	1	no	—
153	C₂×C₈×C₈₉	—	2	2	no	—
154	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₈₉	#41	1	2	yes	—
159	C₂×C₈×C₈₉	#41	1	2	yes	—
160	C₄²×C₈₉	—	2	1	no	—
161	C₄²×C₈₉	—	2	1	no	—
162	C₂³×C₈₉	—	2	2	no	—
163	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
164	Q₈×C₈₉	—	2	2	no	—
165	Q₈×C₈₉	—	2	2	no	—
166	D₄×C₈₉	—	2	2	no	—
167	D₄×C₈₉	—	2	2	no	—
168	D₄×C₈₉	—	4	2	no	—
169	D₄×C₈₉	—	4	2	no	—
170	C₂×C₄×C₈₉	—	2	2	no	—
171	C₂×C₄×C₈₉	—	2	2	no	—
172	C₂×C₄×C₈₉	—	4	1	no	—
173	C₂×C₄×C₈₉	—	4	1	no	—
174	C₂×C₄×C₈₉	—	4	2	no	—
175	C₂×C₄×C₈₉	—	4	2	no	—
176	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
182	C₂×Dic₈₉	—	2	2	no	—
183	C₂×Dic₈₉	—	2	2	no	—
184	C₂×Dic₈₉	—	2	2	no	—
185	C₂×Dic₈₉	—	2	2	no	—
186	C₂×Dic₈₉	—	4	1	no	—
187	C₂×Dic₈₉	—	4	1	no	—
188	C₂×Dic₈₉	—	4	1	no	—
189	C₂×Dic₈₉	—	4	4	no	—
190	C₂×Dic₈₉	—	8	2	no	—
191	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
192	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
193	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
194	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
195	C₈×C₈₉	—	2	1	no	—
196	C₈×C₈₉	—	2	1	no	—
197	C₈×C₈₉	—	4	2	no	—
198	C₈×C₈₉	#117	1	2	yes	—
199	C₈×C₈₉	#117	1	2	yes	—
200	#10623494	—	2	1	no	—
201	#10623494	—	2	1	no	—
202	#10623494	—	2	1	no	—
203	#10623494	—	2	1	no	—
204	#10623494	—	4	2	no	—
205	C₂²×C₈₉	—	2	1	no	—
206	C₂²×C₈₉	—	2	1	no	—
207	C₂²×C₈₉	—	4	2	no	—
208	C₂²×C₈₉	—	4	2	no	—
209	C₂²×C₈₉	—	4	2	no	—
210	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂²×C₈₉	#555	1	1	yes	characteristic
212	C₂²×C₈₉	#556	1	1	yes	characteristic
213	C₄×C₈₉	—	4	2	no	—
214	C₄×C₈₉	—	4	2	no	—
215	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
216	C₄×C₈₉	#520	1	1	yes	characteristic
217	C₄×C₈₉	#547	1	1	yes	characteristic
218	C₄×C₈₉	#550	1	1	yes	characteristic
219	Dic₈₉	—	2	1	no	—
220	Dic₈₉	—	2	1	no	—
221	Dic₈₉	—	2	1	no	—
222	Dic₈₉	—	4	2	no	—
223	Dic₈₉	—	4	2	no	—
224	Dic₈₉	—	4	2	no	—
225	Dic₈₉	#443	1	2	yes	—
226	#22802	—	89	1	no	maximal, Sylow
227	C₂×C₈₉	—	2	1	no	—
228	C₂×C₈₉	—	2	1	no	—
229	C₂×C₈₉	—	8	2	no	—
230	C₂×C₈₉	#2354	1	1	yes	characteristic
231	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
232	C₂×C₈₉	#2957	1	1	yes	characteristic
233	C₄×#135	—	89	1	no	—
234	#2925	—	89	2	no	—
235	#1974	—	89	1	no	—
236	#1974	D₈₉	1	1	yes	characteristic
237	#1929	—	89	2	no	—
238	#1929	—	89	2	no	—
239	#1848	—	89	1	no	—
240	#1806	—	89	2	no	—
241	#1772	—	89	1	no	—
242	#1772	—	89	1	no	—
243	C₈×C₄⋊C₄	—	89	1	no	—
244	C₈₉	#22802	1	1	yes	characteristic, complemented, Sylow
245	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
246	C₄×#41	—	89	2	no	—
247	C₄×Q₁₆	—	89	1	no	—
248	C₄×Q₁₆	—	89	1	no	—
249	C₄×SD₁₆	—	89	2	no	—
250	C₄×SD₁₆	—	89	2	no	—
251	C₄×D₈	—	89	1	no	—
252	C₄×D₈	—	89	1	no	—
253	#433	—	178	2	no	—
254	#433	—	178	2	no	—
255	#432	—	178	2	no	—
256	#431	—	178	2	no	—
257	C₂×#108	—	89	2	no	—
258	C₂×#108	—	89	1	no	—
259	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
260	#427	—	89	1	no	—
261	#423	—	89	2	no	—
262	C₂×C₄⋊C₈	—	89	1	no	—
263	C₂×#104	—	89	2	no	—
264	C₂×#104	C₂×D₈₉	1	2	yes	—
265	#416	—	89	2	no	—
266	#408	—	89	2	no	—
267	#408	C₂×D₈₉	1	2	yes	—
268	#405	—	89	2	no	—
269	#405	—	89	2	no	—
270	C₂×C₄×C₈	—	89	1	no	—
271	C₂×C₄×C₈	—	89	1	no	—
272	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
273	C₄×C₄⋊C₄	—	89	1	no	—
274	#339	—	89	2	no	—
275	#339	—	89	2	no	—
276	#336	—	89	1	no	—
277	#336	—	89	1	no	—
278	C₂×#41	C₂²×D₈₉	1	2	yes	—
279	#135	—	2	2	no	—
280	#135	—	2	2	no	—
281	C₂×Q₁₆	C₄×D₈₉	1	1	yes	characteristic
282	C₂×SD₁₆	C₄×D₈₉	1	2	yes	—
283	C₂×D₈	C₄×D₈₉	1	1	yes	characteristic
284	C₂×M₁₆	—	89	2	no	—
285	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
286	C₂²×C₈	—	89	1	no	—
287	C₂²×C₈	—	89	1	no	—
288	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
289	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
290	C₄×Q₈	—	89	2	no	—
291	C₄×Q₈	—	89	2	no	—
292	C₄×D₄	—	89	2	no	—
293	C₄×D₄	—	89	2	no	—
294	C₄×D₄	—	178	2	no	—
295	C₄×D₄	—	178	2	no	—
296	#117	—	89	2	no	—
297	#117	—	178	2	no	—
298	C₂×C₄⋊C₄	—	178	1	no	—
299	C₂×C₄²	—	89	1	no	—
300	C₂×C₄²	—	89	1	no	—
301	C₂×C₄²	—	178	2	no	—
302	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
303	#108	—	2	2	no	—
304	#108	—	356	2	no	—
305	#108	—	178	2	no	—
306	#107	—	89	1	no	—
307	#107	—	89	1	no	—
308	#106	—	89	2	no	—
309	C₄⋊C₈	—	89	1	no	—
310	C₄⋊C₈	—	89	1	no	—
311	C₄⋊C₈	—	89	1	no	—
312	C₄⋊C₈	—	89	1	no	—
313	C₄⋊C₈	—	178	2	no	—
314	C₄⋊C₈	—	178	2	no	—
315	#104	—	4	2	no	—
316	#104	—	356	2	no	—
317	#103	—	89	2	no	—
318	#103	—	89	2	no	—
319	#102	—	89	2	no	—
320	#102	—	89	2	no	—
321	C₂²⋊C₈	—	2	2	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	—	178	2	no	—
324	C₂²⋊C₈	—	178	2	no	—
325	#97	—	178	2	no	—
326	#97	—	178	2	no	—
327	C₄×C₈	—	2	2	no	—
328	C₄×C₈	—	89	1	no	—
329	C₄×C₈	—	89	1	no	—
330	C₄×C₈	—	89	1	no	—
331	C₄×C₈	—	89	1	no	—
332	C₄×C₈	—	178	2	no	—
333	C₄×C₈	—	178	2	no	—
334	C₄×C₈	—	178	2	no	—
335	#95	—	178	1	no	—
336	#41	—	2	2	no	—
337	#41	—	2	2	no	—
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	C₂×Q₈	C₂×C₄×D₈₉	1	2	yes	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	C₂×C₄×D₈₉	1	2	yes	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	89	1	no	—
346	C₂²×C₄	—	89	1	no	—
347	C₂²×C₄	—	178	2	no	—
348	C₂²×C₄	—	178	2	no	—
349	C₂²×C₄	—	178	1	no	—
350	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
351	Q₁₆	—	2	2	no	—
352	SD₁₆	—	2	4	no	—
353	D₈	—	2	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	178	2	no	—
357	M₁₆	—	178	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	89	1	no	—
362	C₂×C₈	—	89	1	no	—
363	C₂×C₈	—	89	1	no	—
364	C₂×C₈	—	89	1	no	—
365	C₂×C₈	—	178	2	no	—
366	C₂×C₈	—	178	1	no	—
367	C₂×C₈	—	178	1	no	—
368	C₂×C₈	—	178	1	no	—
369	C₂×C₈	—	178	1	no	—
370	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
371	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
372	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
373	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
374	C₂×C₈	#13083573	1	2	yes	—
375	C₂×C₈	#13083573	1	2	yes	—
376	C₄⋊C₄	—	89	2	no	—
377	C₄⋊C₄	—	89	2	no	—
378	C₄⋊C₄	—	178	2	no	—
379	C₄⋊C₄	—	178	2	no	—
380	C₄⋊C₄	—	178	4	no	—
381	C₂²⋊C₄	—	178	2	no	—
382	C₂²⋊C₄	—	178	2	no	—
383	C₂²⋊C₄	—	178	2	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	89	1	no	—
387	C₄²	—	89	1	no	—
388	C₄²	—	89	1	no	—
389	C₄²	—	89	1	no	—
390	C₄²	—	178	2	no	—
391	C₄²	—	178	2	no	—
392	C₄²	—	178	1	no	—
393	C₄²	—	178	1	no	—
394	C₄²	—	178	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	#41×D₈₉	1	1	yes	characteristic
397	Q₈	—	2	2	no	—
398	Q₈	—	2	2	no	—
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	89	1	no	—
410	C₂×C₄	—	89	1	no	—
411	C₂×C₄	—	89	1	no	—
412	C₂×C₄	—	89	1	no	—
413	C₂×C₄	—	356	4	no	—
414	C₂×C₄	—	356	1	no	—
415	C₂×C₄	—	356	1	no	—
416	C₂×C₄	—	356	1	no	—
417	C₂×C₄	—	178	2	no	—
418	C₂×C₄	—	178	2	no	—
419	C₂×C₄	—	178	2	no	—
420	C₂×C₄	—	178	2	no	—
421	C₂×C₄	—	712	2	no	—
422	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
423	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
424	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
425	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
426	C₂×C₄	#15668057	1	1	yes	characteristic
427	C₂×C₄	#15668059	1	1	yes	characteristic
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	4	2	no	—
431	C₈	—	356	2	no	—
432	C₈	—	178	1	no	—
433	C₈	—	178	1	no	—
434	C₈	—	178	1	no	—
435	C₈	—	178	1	no	—
436	C₈	#15667968	1	2	yes	—
437	C₈	#15667968	1	2	yes	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
444	C₂²	#19152312	1	1	yes	characteristic
445	C₂²	#19152317	1	1	yes	characteristic
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	89	2	no	—
449	C₄	—	356	2	no	—
450	C₄	—	356	2	no	—
451	C₄	—	356	2	no	—
452	C₄	—	178	1	no	—
453	C₄	—	178	1	no	—
454	C₄	—	178	1	no	—
455	C₄	C₂×#15667968	1	1	yes	characteristic
456	C₄	#19152077	1	1	yes	characteristic
457	C₄	#19152248	1	1	yes	characteristic
458	C₄	#19152268	1	1	yes	characteristic
459	C₂	—	2	1	no	—
460	C₂	—	2	1	no	—
461	C₂	—	8	2	no	—
462	C₂	#26023200	1	1	yes	characteristic
463	C₂	#443×D₈₉	1	1	yes	characteristic
464	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×#1974	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#135×C₈₉	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1974	D₈₉
hypocenter	C₈₉	#22802
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1974

Complements

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

N	H ≅ G/N	type
2. #26028914	C₂	semidirect
4. #26020903	C₂	semidirect
5. #26020897	C₂	semidirect
6. #26020422	C₂	semidirect
7. #26020270	C₂	semidirect
8. #26020134	C₂	semidirect
9. #26020131	C₂	semidirect
10. C₈×#13083553	C₂	semidirect
13. Q₁₆×Dic₈₉	C₄	semidirect
14. Q₁₆×Dic₈₉	C₄	semidirect
15. SD₁₆×Dic₈₉	C₄	semidirect
16. SD₁₆×Dic₈₉	C₄	semidirect
17. D₈×Dic₈₉	C₄	semidirect
18. D₈×Dic₈₉	C₄	semidirect
244. C₈₉	#22802	semidirect

Maximal subgroups

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

subgroup	index
#135×Dic₈₉	2
#26028914	2
#26021141	2
#26020903	2
#26020897	2
#26020422	2
#26020270	2
#26020134	2
#26020131	2
C₈×#13083553	2
C₈₉×#1974	2
#22802	89