Subgroups — #36574121

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	#26029023	C₂	1	1	yes	maximal, characteristic
2	#26028916	C₂	1	2	yes	maximal, complemented
3	#26021140	C₂	1	1	yes	maximal, characteristic
4	#26021138	C₂	1	1	yes	maximal, characteristic
5	#26020900	C₂	1	2	yes	maximal, complemented
6	#26020898	C₂	1	2	yes	maximal, complemented
7	#26020422	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020271	C₂	1	2	yes	maximal, complemented
9	#26020133	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#13083553	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668034	C₂²	1	1	yes	characteristic
13	#19152066	C₂²	1	2	yes	—
14	#19151692	C₄	1	1	yes	characteristic, complemented
15	#19151692	C₄	1	1	yes	characteristic, complemented
16	#19151685	C₄	1	2	yes	complemented
17	#19151685	C₄	1	2	yes	complemented
18	#19151680	C₄	1	1	yes	characteristic, complemented
19	#19151680	C₄	1	1	yes	characteristic, complemented
20	#19151660	—	2	2	no	—
21	#19151657	—	2	2	no	—
22	#19151653	—	2	2	no	—
23	#19151649	—	2	2	no	—
24	C₂×#15667948	C₂²	1	1	yes	characteristic
25	C₂×#15667947	C₂²	1	2	yes	—
26	#19151621	C₂²	1	2	yes	—
27	C₂×#15667941	C₂²	1	1	yes	characteristic
28	C₂×#15667940	C₂²	1	2	yes	—
29	C₂×#15667938	C₂²	1	2	yes	—
30	#19151592	C₂²	1	2	yes	—
31	#19151566	C₂²	1	2	yes	—
32	#19151564	C₂²	1	2	yes	—
33	#19151554	C₂²	1	2	yes	—
34	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
36	C₄×#13083553	C₂²	1	1	yes	characteristic
37	#19151357	C₂²	1	2	yes	—
38	#19151353	C₂²	1	1	yes	characteristic
39	#19151352	C₂²	1	1	yes	characteristic
40	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
41	#427×C₈₉	C₂²	1	1	yes	characteristic
42	#405×C₈₉	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
44	#339×C₈₉	C₂²	1	2	yes	—
45	C₂×#13083574	C₂³	1	2	yes	—
46	#15668034	—	2	2	no	—
47	#15668034	—	2	2	no	—
48	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
49	C₂×#13083563	C₂×C₄	1	2	yes	—
50	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
51	C₂×#13083558	C₂³	1	2	yes	—
52	C₂²×#10623494	C₂³	1	1	yes	characteristic
53	C₂²×#10623494	C₂³	1	1	yes	characteristic
54	#15667977	C₂×C₄	1	2	yes	—
55	#15667977	C₂×C₄	1	2	yes	—
56	#15667974	C₂×C₄	1	2	yes	—
57	#15667974	C₂×C₄	1	2	yes	—
58	#15667972	—	2	2	no	—
59	#15667972	—	2	2	no	—
60	#15667969	—	2	2	no	—
61	C₂×#13083553	—	2	1	no	—
62	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
63	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
64	C₄²×D₈₉	—	2	2	no	—
65	#15667948	—	2	2	no	—
66	#15667947	—	4	2	no	—
67	#15667941	—	2	2	no	—
68	#15667941	—	2	2	no	—
69	#15667941	D₄	1	1	yes	characteristic
70	#15667941	D₄	1	1	yes	characteristic
71	#15667941	D₄	1	1	yes	characteristic
72	#15667941	D₄	1	1	yes	characteristic
73	#15667940	—	4	2	no	—
74	#15667938	—	4	2	no	—
75	#15667935	C₂×C₄	1	2	yes	—
76	#15667935	C₂×C₄	1	2	yes	—
77	#15667932	C₂×C₄	1	2	yes	—
78	#15667932	C₂×C₄	1	2	yes	—
79	#15667924	—	2	2	no	—
80	#15667924	—	2	2	no	—
81	#15667924	—	2	2	no	—
82	#15667924	—	2	2	no	—
83	#15667923	—	2	2	no	—
84	C₄×#10623494	—	2	2	no	—
85	C₈×Dic₈₉	—	2	2	no	—
86	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
90	#15667919	—	2	1	no	—
91	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
92	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	#117×C₈₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
96	#108×C₈₉	—	2	2	no	—
97	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
98	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
99	#106×C₈₉	C₂×C₄	1	2	yes	—
100	#97×C₈₉	—	2	2	no	—
101	C₄×C₈×C₈₉	—	2	2	no	—
102	C₄×C₈×C₈₉	—	2	2	no	—
103	#13083574	—	2	2	no	—
104	#13083574	—	2	2	no	—
105	#13083574	—	2	2	no	—
106	#13083574	—	2	2	no	—
107	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
108	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
109	C₂×C₂²⋊D₈₉	—	2	2	no	—
110	C₂²×Dic₈₉	—	2	1	no	—
111	C₂²×Dic₈₉	#41	1	1	yes	characteristic
112	C₂²×Dic₈₉	#41	1	1	yes	characteristic
113	C₂×C₄×D₈₉	—	2	2	no	—
114	C₂×C₄×D₈₉	—	2	2	no	—
115	C₂×C₄×D₈₉	—	2	2	no	—
116	Dic₃₅₆	—	2	2	no	—
117	#13083563	—	2	4	no	—
118	D₇₁₂	—	2	2	no	—
119	#13083558	—	2	2	no	—
120	#13083558	—	2	2	no	—
121	C₂×#10623494	—	2	1	no	—
122	C₂×#10623494	—	2	1	no	—
123	C₂×#10623494	—	2	1	no	—
124	C₂×#10623494	—	2	1	no	—
125	C₂×#10623494	—	2	2	no	—
126	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
127	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
128	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
129	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
130	#13083553	—	2	4	no	—
131	#13083553	—	2	2	no	—
132	#13083553	—	2	2	no	—
133	#13083551	—	2	2	no	—
134	#13083551	—	2	2	no	—
135	C₄×Dic₈₉	—	2	2	no	—
136	C₄×Dic₈₉	—	2	2	no	—
137	C₄×Dic₈₉	—	2	1	no	—
138	C₄×Dic₈₉	—	2	1	no	—
139	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
142	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₈₉	—	2	1	no	—
144	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
145	M₁₆×C₈₉	—	2	2	no	—
146	M₁₆×C₈₉	—	2	2	no	—
147	C₂×C₈×C₈₉	—	2	1	no	—
148	C₂×C₈×C₈₉	—	2	1	no	—
149	C₂×C₈×C₈₉	—	2	2	no	—
150	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₈₉	#41	1	2	yes	—
155	C₂×C₈×C₈₉	#41	1	2	yes	—
156	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
157	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
158	C₂²⋊C₄×C₈₉	—	2	2	no	—
159	C₄²×C₈₉	—	2	2	no	—
160	C₄²×C₈₉	—	2	1	no	—
161	C₄²×C₈₉	—	2	1	no	—
162	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
163	C₂²×D₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	2	2	no	—
165	C₂×C₄×C₈₉	—	2	2	no	—
166	C₂×C₄×C₈₉	—	2	2	no	—
167	C₂×C₄×C₈₉	—	4	1	no	—
168	C₂×C₄×C₈₉	—	4	1	no	—
169	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
175	C₂²⋊D₈₉	—	4	2	no	—
176	C₂²⋊D₈₉	—	4	2	no	—
177	C₂×Dic₈₉	—	2	2	no	—
178	C₂×Dic₈₉	—	2	2	no	—
179	C₂×Dic₈₉	—	2	2	no	—
180	C₂×Dic₈₉	—	4	1	no	—
181	C₂×Dic₈₉	—	4	1	no	—
182	C₂×Dic₈₉	—	4	1	no	—
183	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
184	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
185	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
186	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
187	D₃₅₆	—	2	2	no	—
188	D₃₅₆	—	2	2	no	—
189	C₄×D₈₉	—	4	2	no	—
190	C₄×D₈₉	—	4	2	no	—
191	C₄×D₈₉	—	4	4	no	—
192	C₄×D₈₉	—	8	2	no	—
193	Dic₁₇₈	—	2	2	no	—
194	Dic₁₇₈	—	2	2	no	—
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	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₈₉	#555	1	1	yes	characteristic
209	C₂²×C₈₉	#556	1	1	yes	characteristic
210	C₂×D₈₉	—	4	2	no	—
211	C₂×D₈₉	—	4	2	no	—
212	C₂×D₈₉	—	4	2	no	—
213	C₄×C₈₉	—	4	2	no	—
214	C₄×C₈₉	—	4	2	no	—
215	C₄×C₈₉	—	4	2	no	—
216	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
217	C₄×C₈₉	#520	1	1	yes	characteristic
218	C₄×C₈₉	#547	1	1	yes	characteristic
219	C₄×C₈₉	#550	1	1	yes	characteristic
220	Dic₈₉	—	2	1	no	—
221	Dic₈₉	—	2	1	no	—
222	Dic₈₉	—	2	1	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	#2354	1	1	yes	characteristic
230	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
231	C₂×C₈₉	#2957	1	1	yes	characteristic
232	D₈₉	—	8	2	no	—
233	C₄×#135	—	89	1	no	—
234	#2925	—	89	2	no	—
235	#1974	—	89	1	no	—
236	#1974	—	89	1	no	—
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	D₈₉	1	1	yes	characteristic, complemented
243	C₈×C₄⋊C₄	—	89	1	no	—
244	C₈₉	#22802	1	1	yes	characteristic, complemented, Sylow
245	C₂×#135	—	89	1	no	—
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	C₂×D₈₉	1	1	yes	characteristic
261	#423	—	89	2	no	—
262	C₂×C₄⋊C₈	—	89	1	no	—
263	C₂×#104	—	89	2	no	—
264	C₂×#104	—	89	2	no	—
265	#416	—	89	2	no	—
266	#408	—	89	2	no	—
267	#408	—	89	2	no	—
268	#405	—	89	2	no	—
269	#405	C₂×D₈₉	1	2	yes	—
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	C₂×D₈₉	1	2	yes	—
276	#336	—	89	1	no	—
277	#336	—	89	1	no	—
278	C₂×#41	—	89	2	no	—
279	#135	—	178	2	no	—
280	#135	—	178	2	no	—
281	C₂×Q₁₆	—	89	1	no	—
282	C₂×SD₁₆	—	89	2	no	—
283	C₂×D₈	—	89	1	no	—
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	—	178	2	no	—
297	#117	C₂²×D₈₉	1	2	yes	—
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	C₄×D₈₉	1	1	yes	characteristic
307	#107	C₄×D₈₉	1	1	yes	characteristic
308	#106	C₄×D₈₉	1	2	yes	—
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	—	356	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	—	178	2	no	—
322	C₂²⋊C₈	—	178	2	no	—
323	C₂²⋊C₈	—	178	2	no	—
324	C₂²⋊C₈	—	178	2	no	—
325	#97	—	2	2	no	—
326	#97	—	178	2	no	—
327	C₄×C₈	—	2	2	no	—
328	C₄×C₈	—	2	2	no	—
329	C₄×C₈	—	89	1	no	—
330	C₄×C₈	—	89	1	no	—
331	C₄×C₈	—	89	1	no	—
332	C₄×C₈	—	89	1	no	—
333	C₄×C₈	—	178	2	no	—
334	C₄×C₈	—	178	2	no	—
335	#95	—	178	1	no	—
336	#41	—	178	2	no	—
337	#41	—	178	2	no	—
338	#41	—	178	2	no	—
339	#41	—	178	2	no	—
340	C₂×Q₈	—	89	2	no	—
341	C₂×D₄	—	89	2	no	—
342	C₂×D₄	—	178	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	89	1	no	—
345	C₂²×C₄	—	89	1	no	—
346	C₂²×C₄	—	178	2	no	—
347	C₂²×C₄	—	178	2	no	—
348	C₂²×C₄	—	178	1	no	—
349	C₂²×C₄	—	178	2	no	—
350	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
351	Q₁₆	—	178	2	no	—
352	SD₁₆	—	178	4	no	—
353	D₈	—	178	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	#13083574	1	2	yes	—
375	C₂×C₈	#13083574	1	2	yes	—
376	C₄⋊C₄	—	178	2	no	—
377	C₄⋊C₄	—	178	2	no	—
378	C₄⋊C₄	—	178	4	no	—
379	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
380	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	178	2	no	—
383	C₂²⋊C₄	—	178	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	89	1	no	—
388	C₄²	—	89	1	no	—
389	C₄²	—	89	1	no	—
390	C₄²	—	89	1	no	—
391	C₄²	—	178	2	no	—
392	C₄²	—	178	2	no	—
393	C₄²	—	178	1	no	—
394	C₄²	—	178	1	no	—
395	C₂³	—	178	2	no	—
396	C₂³	#41×D₈₉	1	1	yes	characteristic
397	Q₈	—	178	2	no	—
398	Q₈	—	178	2	no	—
399	D₄	—	356	2	no	—
400	D₄	—	356	2	no	—
401	D₄	—	178	2	no	—
402	D₄	—	178	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	89	1	no	—
409	C₂×C₄	—	89	1	no	—
410	C₂×C₄	—	89	1	no	—
411	C₂×C₄	—	89	1	no	—
412	C₂×C₄	—	356	4	no	—
413	C₂×C₄	—	356	1	no	—
414	C₂×C₄	—	356	1	no	—
415	C₂×C₄	—	356	2	no	—
416	C₂×C₄	—	356	2	no	—
417	C₂×C₄	—	356	1	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×#13083574	1	1	yes	characteristic
425	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
426	C₂×C₄	#15668058	1	1	yes	characteristic
427	C₂×C₄	#15668060	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	#15667969	1	2	yes	—
437	C₈	#15667969	1	2	yes	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	356	2	no	—
441	C₂²	—	356	2	no	—
442	C₂²	—	356	2	no	—
443	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
444	C₂²	#19152311	1	1	yes	characteristic
445	C₂²	#19152320	1	1	yes	characteristic
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	89	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×#15667969	1	1	yes	characteristic
456	C₄	#19152080	1	1	yes	characteristic
457	C₄	#19152249	1	1	yes	characteristic
458	C₄	#19152269	1	1	yes	characteristic
459	C₂	—	2	1	no	—
460	C₂	—	2	1	no	—
461	C₂	—	712	2	no	—
462	C₂	#26023197	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×#1772	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668034	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1772	D₈₉
hypocenter	C₈₉	#22802
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
2. #26028916	C₂	semidirect
5. #26020900	C₂	semidirect
6. #26020898	C₂	semidirect
7. #26020422	C₂	semidirect
8. #26020271	C₂	semidirect
9. #26020133	C₂	semidirect
10. C₈×#13083553	C₂	semidirect
11. C₈₉×#1772	C₂	semidirect
14. #19151692	C₄	semidirect
15. #19151692	C₄	semidirect
16. #19151685	C₄	semidirect
17. #19151685	C₄	semidirect
18. #19151680	C₄	semidirect
19. #19151680	C₄	semidirect
242. #1772	D₈₉	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
#26029023	2
#26028916	2
#26021140	2
#26021138	2
#26020900	2
#26020898	2
#26020422	2
#26020271	2
#26020133	2
C₈×#13083553	2
C₈₉×#1772	2
#22802	89