Subgroups — #30843742

Order 17152.

784 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22571154	C₂	1	1	yes	maximal, characteristic, complemented
2	#22571124	C₂	1	1	yes	maximal, characteristic
3	#22570602	C₂	1	1	yes	maximal, characteristic, complemented
4	#22570585	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16863743	C₂	1	1	yes	maximal, characteristic, complemented
6	#22559867	C₂	1	2	yes	maximal, complemented
7	#22559846	C₂	1	2	yes	maximal, complemented
8	#22559822	C₂	1	2	yes	maximal, complemented
9	#22559813	C₂	1	2	yes	maximal, complemented
10	C₈×#11761612	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3167	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524043	C₂²	1	1	yes	characteristic
13	C₂×#14524040	C₂²	1	1	yes	characteristic
14	#16863775	C₂²	1	2	yes	complemented
15	#16863772	C₂²	1	2	yes	—
16	#16863762	—	2	2	no	—
17	#16863755	—	2	2	no	—
18	#16863748	C₂²	1	2	yes	complemented
19	#16863746	C₂²	1	2	yes	complemented
20	#16863744	C₂²	1	2	yes	—
21	#16863744	C₂²	1	2	yes	—
22	#16863744	C₂²	1	2	yes	—
23	#16863743	—	2	2	no	—
24	#16863743	C₂²	1	2	yes	—
25	#16863743	C₂²	1	2	yes	—
26	#16863742	C₂²	1	2	yes	complemented
27	#16863606	—	2	2	no	—
28	#16863591	—	2	2	no	—
29	#16863551	—	2	2	no	—
30	#16863529	—	2	2	no	—
31	#16863449	C₂²	1	1	yes	characteristic
32	#16863400	—	2	2	no	—
33	#16863397	—	2	2	no	—
34	C₂×#14523965	—	2	2	no	—
35	C₄×#11761612	C₂²	1	1	yes	characteristic
36	#16863118	C₂²	1	2	yes	complemented
37	C₈×C₆₇⋊C₈	C₂²	1	2	yes	complemented
38	#533×C₆₇	C₂²	1	1	yes	characteristic
39	#532×C₆₇	C₂²	1	1	yes	characteristic
40	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	#465×C₆₇	—	2	2	no	—
45	C₄×SD₁₆×C₆₇	—	2	2	no	—
46	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
47	C₂²×Dic₁₃₄	—	2	1	no	—
48	C₂²×D₂₆₈	—	2	1	no	—
49	C₂²×D₂₆₈	—	2	1	no	—
50	C₂²×D₂₆₈	—	2	1	no	—
51	C₂×#11761618	—	2	4	no	—
52	C₂×#11761613	—	2	4	no	—
53	C₂×#11761612	D₄	1	2	yes	—
54	#14524043	—	2	1	no	—
55	#14524043	—	2	1	no	—
56	#14524043	—	2	1	no	—
57	#14524043	C₂³	1	2	yes	—
58	#14524040	—	2	1	no	—
59	#14524040	—	2	1	no	—
60	#14524040	—	2	1	no	—
61	#14524040	C₂³	1	2	yes	—
62	C₂×C₄⋊Dic₆₇	—	2	1	no	—
63	C₂×C₄⋊Dic₆₇	—	2	1	no	—
64	C₄⋊(C₆₇⋊C₈)	D₄	1	2	yes	—
65	#14523967	—	2	4	no	—
66	#14523966	—	2	4	no	—
67	#14523965	—	2	4	no	—
68	#14523965	—	2	4	no	—
69	#14523964	—	2	4	no	—
70	#14523963	—	2	4	no	—
71	#14523963	—	2	4	no	—
72	#14523963	—	2	4	no	—
73	C₂²⋊(C₆₇⋊C₈)	D₄	1	2	yes	—
74	#14523954	D₄	1	2	yes	—
75	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
76	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
77	C₂×#41×C₆₇	—	2	1	no	—
78	C₂×SD₁₆×C₆₇	—	2	2	no	—
79	C₂²×C₈×C₆₇	D₄	1	2	yes	—
80	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
83	#127×C₆₇	C₂³	1	1	yes	characteristic
84	#125×C₆₇	—	2	1	no	—
85	#124×C₆₇	—	2	1	no	—
86	C₂²⋊Q₈×C₆₇	—	2	1	no	—
87	C₂²⋊Q₈×C₆₇	—	2	1	no	—
88	#121×C₆₇	—	2	1	no	—
89	#121×C₆₇	—	2	1	no	—
90	C₄×Q₈×C₆₇	—	2	1	no	—
91	C₄×Q₈×C₆₇	—	2	1	no	—
92	C₄×D₄×C₆₇	—	2	1	no	—
93	C₄×D₄×C₆₇	—	2	1	no	—
94	#117×C₆₇	—	2	1	no	—
95	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
96	#106×C₆₇	—	2	2	no	—
97	#103×C₆₇	—	2	2	no	—
98	#102×C₆₇	—	2	2	no	—
99	C₄×C₈×C₆₇	D₄	1	2	yes	—
100	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
102	C₂³×D₆₇	—	4	1	no	—
103	C₂×Dic₁₃₄	—	2	2	no	—
104	C₂×Dic₁₃₄	—	4	1	no	—
105	C₂×Dic₁₃₄	—	8	2	no	—
106	C₂×D₂₆₈	—	2	2	no	—
107	C₂×D₂₆₈	—	2	2	no	—
108	C₂×D₂₆₈	—	2	2	no	—
109	C₂×D₂₆₈	—	4	4	no	—
110	C₂×D₂₆₈	—	4	4	no	—
111	C₂×D₂₆₈	—	4	1	no	—
112	C₂×D₂₆₈	—	4	1	no	—
113	C₂×D₂₆₈	—	4	1	no	—
114	C₂×D₂₆₈	—	8	2	no	—
115	C₂²×Dic₆₇	—	4	1	no	—
116	#11761618	—	8	4	no	—
117	#11761613	—	8	4	no	—
118	#11761612	—	2	4	no	—
119	C₂×C₆₇⋊C₈	C₂×D₄	1	4	yes	—
120	C₂×C₆₇⋊C₈	C₂×D₄	1	4	yes	—
121	C₄⋊Dic₆₇	—	2	2	no	—
122	C₄⋊Dic₆₇	—	2	2	no	—
123	C₄⋊Dic₆₇	—	4	1	no	—
124	C₄⋊Dic₆₇	—	4	1	no	—
125	#41×C₆₇	—	4	4	no	—
126	C₂×Q₈×C₆₇	—	2	1	no	—
127	C₂×Q₈×C₆₇	—	2	1	no	—
128	C₂×Q₈×C₆₇	—	2	1	no	—
129	C₂×D₄×C₆₇	—	2	1	no	—
130	C₂×D₄×C₆₇	—	2	1	no	—
131	C₂×D₄×C₆₇	—	2	1	no	—
132	C₂×D₄×C₆₇	—	4	1	no	—
133	C₂²×C₄×C₆₇	—	4	1	no	—
134	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
137	SD₁₆×C₆₇	—	4	4	no	—
138	C₂×C₈×C₆₇	—	4	2	no	—
139	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₆₇	—	2	1	no	—
142	C₄⋊C₄×C₆₇	—	2	1	no	—
143	C₄⋊C₄×C₆₇	—	2	1	no	—
144	C₄⋊C₄×C₆₇	—	2	1	no	—
145	C₄⋊C₄×C₆₇	—	2	1	no	—
146	C₄⋊C₄×C₆₇	—	2	1	no	—
147	C₄⋊C₄×C₆₇	—	4	1	no	—
148	C₄⋊C₄×C₆₇	—	4	1	no	—
149	C₂²⋊C₄×C₆₇	—	4	1	no	—
150	C₂²⋊C₄×C₆₇	—	4	1	no	—
151	C₂²⋊C₄×C₆₇	—	4	1	no	—
152	C₄²×C₆₇	—	4	1	no	—
153	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
157	C₂³×C₆₇	—	4	1	no	—
158	C₂³×C₆₇	#127	1	1	yes	characteristic
159	C₂²×D₆₇	—	4	2	no	—
160	C₂²×D₆₇	—	8	2	no	—
161	C₂²×D₆₇	—	8	2	no	—
162	C₂²×D₆₇	—	8	2	no	—
163	Q₈×C₆₇	—	4	2	no	—
164	Q₈×C₆₇	—	4	2	no	—
165	Q₈×C₆₇	—	4	2	no	—
166	D₄×C₆₇	—	4	2	no	—
167	D₄×C₆₇	—	4	2	no	—
168	D₄×C₆₇	—	4	2	no	—
169	D₄×C₆₇	—	8	2	no	—
170	C₂×C₄×C₆₇	—	2	2	no	—
171	C₂×C₄×C₆₇	—	2	2	no	—
172	C₂×C₄×C₆₇	—	4	1	no	—
173	C₂×C₄×C₆₇	—	4	1	no	—
174	C₂×C₄×C₆₇	—	4	1	no	—
175	C₂×C₄×C₆₇	—	8	2	no	—
176	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
177	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
178	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
179	C₂×C₄×C₆₇	#135	1	4	yes	—
180	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×Dic₆₇	—	4	2	no	—
184	C₂×Dic₆₇	—	8	2	no	—
185	D₂₆₈	—	4	4	no	—
186	D₂₆₈	—	4	4	no	—
187	D₂₆₈	—	4	4	no	—
188	D₂₆₈	—	8	2	no	—
189	D₂₆₈	—	8	2	no	—
190	D₂₆₈	—	8	2	no	—
191	Dic₁₃₄	—	4	4	no	—
192	Dic₁₃₄	—	8	2	no	—
193	C₈×C₆₇	—	2	2	no	—
194	C₈×C₆₇	—	2	2	no	—
195	C₆₇⋊C₈	—	2	4	no	—
196	C₆₇⋊C₈	—	2	4	no	—
197	C₂²×C₆₇	—	2	1	no	—
198	C₂²×C₆₇	—	2	1	no	—
199	C₂²×C₆₇	—	8	1	no	—
200	C₂²×C₆₇	—	8	1	no	—
201	C₂²×C₆₇	—	8	1	no	—
202	C₂²×C₆₇	#495	1	2	yes	—
203	C₂²×C₆₇	C₂×#127	1	1	yes	characteristic
204	C₂×D₆₇	—	8	2	no	—
205	C₂×D₆₇	—	8	2	no	—
206	C₂×D₆₇	—	8	2	no	—
207	C₂×D₆₇	—	16	4	no	—
208	C₄×C₆₇	—	2	1	no	—
209	C₄×C₆₇	—	2	1	no	—
210	C₄×C₆₇	—	8	1	no	—
211	C₄×C₆₇	—	8	1	no	—
212	C₄×C₆₇	—	8	1	no	—
213	C₄×C₆₇	#495	1	2	yes	—
214	C₄×C₆₇	C₂×#135	1	2	yes	—
215	C₄×C₆₇	#575	1	2	yes	—
216	C₄×C₆₇	#576	1	2	yes	—
217	Dic₆₇	—	8	2	no	—
218	#19627	—	67	1	no	maximal, Sylow
219	C₂×C₆₇	—	2	2	no	—
220	C₂×C₆₇	—	16	1	no	—
221	C₂×C₆₇	C₂×#495	1	1	yes	characteristic
222	C₂×C₆₇	#3153	1	1	yes	characteristic
223	C₂×C₆₇	#3155	1	1	yes	characteristic
224	D₆₇	—	16	2	no	—
225	#3209	—	67	1	no	—
226	#3205	—	67	1	no	—
227	#3167	D₆₇	1	1	yes	characteristic, complemented
228	#3141	—	67	1	no	—
229	#3138	—	67	1	no	—
230	C₂×#486	—	67	1	no	—
231	#1720	—	67	2	no	—
232	#1717	—	67	2	no	—
233	#1711	—	67	2	no	—
234	#1709	—	67	2	no	—
235	C₈×M₁₆	—	67	1	no	—
236	C₆₇	#19627	1	1	yes	characteristic, complemented, Sylow
237	#533	C₂×D₆₇	1	1	yes	characteristic
238	#532	C₂×D₆₇	1	1	yes	characteristic
239	C₂×C₄⋊Q₈	—	67	1	no	—
240	C₂×#127	—	67	1	no	—
241	#498	C₂×D₆₇	1	1	yes	characteristic, complemented
242	#494	—	67	2	no	—
243	#493	—	67	2	no	—
244	#492	C₂×D₆₇	1	1	yes	characteristic, complemented
245	#490	—	134	2	no	—
246	#489	—	134	2	no	—
247	#487	—	67	2	no	—
248	#487	—	67	2	no	—
249	#487	C₂×D₆₇	1	1	yes	characteristic, complemented
250	#486	—	67	2	no	—
251	#486	—	67	2	no	—
252	#486	—	67	2	no	—
253	#486	—	67	2	no	—
254	#486	—	67	2	no	—
255	#486	—	67	2	no	—
256	#486	—	134	2	no	—
257	#486	C₂×D₆₇	1	1	yes	characteristic, complemented
258	#465	—	2	2	no	—
259	#462	—	134	2	no	—
260	#459	—	134	2	no	—
261	#451	—	134	2	no	—
262	#447	—	134	2	no	—
263	C₄×SD₁₆	—	2	2	no	—
264	#431	—	67	1	no	—
265	#418	—	134	2	no	—
266	#417	—	134	2	no	—
267	C₂×#102	—	134	2	no	—
268	C₄×M₁₆	—	67	1	no	—
269	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
270	#322	—	67	2	no	—
271	C₈²	—	67	2	no	—
272	C₂×#41	—	2	1	no	—
273	C₂²×Q₈	—	134	1	no	—
274	C₂²×D₄	—	134	1	no	—
275	C₂²×D₄	—	134	1	no	—
276	C₂²×D₄	—	134	1	no	—
277	C₂×Q₁₆	—	134	4	no	—
278	C₂×SD₁₆	—	2	2	no	—
279	C₂×D₈	—	134	4	no	—
280	C₂×M₁₆	—	67	2	no	—
281	C₂²×C₈	C₂²⋊D₆₇	1	2	yes	—
282	C₄⋊Q₈	—	67	2	no	—
283	C₄⋊Q₈	—	134	1	no	—
284	C₄⋊Q₈	—	134	1	no	—
285	C₄⋊Q₈	—	134	1	no	—
286	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
287	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
288	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
289	#127	—	67	2	no	—
290	#127	—	134	1	no	—
291	#127	—	134	1	no	—
292	#127	—	134	1	no	—
293	#127	C₂²×D₆₇	1	1	yes	characteristic
294	#125	—	2	1	no	—
295	#124	—	2	1	no	—
296	C₂²⋊Q₈	—	2	1	no	—
297	C₂²⋊Q₈	—	2	1	no	—
298	#121	—	2	1	no	—
299	#121	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	—	2	1	no	—
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	—	2	1	no	—
304	#117	—	2	1	no	—
305	C₂×C₄⋊C₄	—	134	1	no	—
306	C₂×C₄⋊C₄	—	134	1	no	—
307	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
308	#106	—	2	2	no	—
309	C₄⋊C₈	—	67	2	no	—
310	#103	—	2	2	no	—
311	#103	—	134	4	no	—
312	#103	—	134	4	no	—
313	#102	—	2	2	no	—
314	#102	—	134	4	no	—
315	#102	—	134	4	no	—
316	#102	—	134	4	no	—
317	#102	—	134	4	no	—
318	#102	—	134	4	no	—
319	#102	—	134	4	no	—
320	C₂²⋊C₈	—	67	2	no	—
321	#97	—	67	2	no	—
322	C₄×C₈	—	67	2	no	—
323	C₄×C₈	—	67	2	no	—
324	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
325	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
327	C₂⁴	—	268	1	no	—
328	#41	—	4	4	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	268	1	no	—
333	C₂×Q₈	—	536	2	no	—
334	C₂×Q₈	—	134	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	268	4	no	—
340	C₂×D₄	—	268	1	no	—
341	C₂×D₄	—	268	1	no	—
342	C₂×D₄	—	268	1	no	—
343	C₂×D₄	—	268	4	no	—
344	C₂×D₄	—	536	2	no	—
345	C₂×D₄	—	134	2	no	—
346	C₂×D₄	—	134	2	no	—
347	C₂×D₄	—	134	2	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	—	268	1	no	—
350	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
351	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
353	Q₁₆	—	536	4	no	—
354	SD₁₆	—	4	4	no	—
355	D₈	—	536	4	no	—
356	M₁₆	—	134	4	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	67	4	no	—
359	C₂×C₈	—	67	4	no	—
360	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
361	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	268	1	no	—
371	C₄⋊C₄	—	268	1	no	—
372	C₄⋊C₄	—	134	2	no	—
373	C₄⋊C₄	—	134	2	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₄²	—	4	1	no	—
378	C₄²	D₄×D₆₇	1	1	yes	characteristic
379	C₄²	D₄×D₆₇	1	1	yes	characteristic
380	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
381	C₄²	C₂³×D₆₇	1	1	yes	characteristic
382	C₂³	—	4	1	no	—
383	C₂³	—	268	2	no	—
384	C₂³	—	536	2	no	—
385	C₂³	—	536	2	no	—
386	C₂³	—	536	2	no	—
387	C₂³	#14524039	1	1	yes	characteristic
388	Q₈	—	4	2	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	268	4	no	—
392	Q₈	—	536	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	8	2	no	—
397	D₄	—	268	4	no	—
398	D₄	—	268	4	no	—
399	D₄	—	268	4	no	—
400	D₄	—	536	2	no	—
401	D₄	—	536	2	no	—
402	D₄	—	536	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	1	no	—
408	C₂×C₄	—	8	2	no	—
409	C₂×C₄	—	268	2	no	—
410	C₂×C₄	—	536	2	no	—
411	C₂×C₄	#14524039	1	1	yes	characteristic
412	C₂×C₄	#14524039	1	1	yes	characteristic
413	C₂×C₄	#14524039	1	1	yes	characteristic
414	C₂×C₄	#14524064	1	4	yes	—
415	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	134	4	no	—
421	C₈	—	134	4	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	536	2	no	—
428	C₂²	—	536	2	no	—
429	C₂²	—	536	2	no	—
430	C₂²	—	1072	4	no	—
431	C₂²	#16863777	1	2	yes	—
432	C₂²	C₂×#14524039	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	1	no	—
437	C₄	—	8	1	no	—
438	C₄	—	536	2	no	—
439	C₄	#16863777	1	2	yes	—
440	C₄	C₂×#14524064	1	2	yes	—
441	C₄	#16864194	1	2	yes	—
442	C₄	#16864198	1	2	yes	—
443	C₂	—	2	2	no	—
444	C₂	—	16	1	no	—
445	C₂	—	1072	2	no	—
446	C₂	C₂×#16863777	1	1	yes	characteristic
447	C₂	#22570677	1	1	yes	characteristic
448	C₂	#22570696	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14524039
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#3167	C₂
socle	C₂²×C₆₇	C₂×#127
prime radical	#22571124	C₂
hypercenter	#3167	D₆₇
hypocenter	C₆₇	#19627
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3167

Complements

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

N	H ≅ G/N	type
1. #22571154	C₂	semidirect
3. #22570602	C₂	semidirect
4. #22570585	C₂	semidirect
5. C₂×#16863743	C₂	semidirect
6. #22559867	C₂	semidirect
7. #22559846	C₂	semidirect
8. #22559822	C₂	semidirect
9. #22559813	C₂	semidirect
10. C₈×#11761612	C₂	semidirect
11. C₆₇×#3167	C₂	semidirect
14. #16863775	C₂²	semidirect
18. #16863748	C₂²	semidirect
19. #16863746	C₂²	semidirect
26. #16863742	C₂²	semidirect
36. #16863118	C₂²	semidirect
37. C₈×C₆₇⋊C₈	C₂²	semidirect
40. #498×C₆₇	C₂²	semidirect
41. #492×C₆₇	C₂²	semidirect
42. #487×C₆₇	C₂²	semidirect
43. #486×C₆₇	C₂²	semidirect
227. #3167	D₆₇	semidirect
236. C₆₇	#19627	semidirect
241. #498	C₂×D₆₇	semidirect
244. #492	C₂×D₆₇	semidirect
249. #487	C₂×D₆₇	semidirect
257. #486	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22571154	2
#22571124	2
#22570602	2
#22570585	2
C₂×#16863743	2
#22559867	2
#22559846	2
#22559822	2
#22559813	2
C₈×#11761612	2
C₆₇×#3167	2
#19627	67