Subgroups — #30838540

Order 17152.

704 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570788	C₂	1	1	yes	maximal, characteristic, complemented
2	#22569664	C₂	1	2	yes	maximal, complemented
3	#22559777	C₂	1	2	yes	maximal, complemented
4	#22559770	C₂	1	2	yes	maximal, complemented
5	#22559727	C₂	1	1	yes	maximal, characteristic, complemented
6	#22559722	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559693	C₂	1	1	yes	maximal, characteristic, complemented
8	#22559688	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16863147	C₂	1	1	yes	maximal, characteristic, complemented
10	#22558856	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2965	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524063	—	2	2	no	—
13	#16863946	C₂²	1	2	yes	—
14	#16863801	C₂²	1	1	yes	characteristic
15	#16863773	C₂²	1	1	yes	characteristic
16	#16863743	C₂²	1	2	yes	—
17	#16863632	—	2	1	no	—
18	#16863632	—	2	1	no	—
19	#16863618	—	2	2	no	—
20	#16863611	—	2	2	no	—
21	#16863606	C₂²	1	2	yes	—
22	#16863601	C₂²	1	2	yes	—
23	#16863596	C₂²	1	2	yes	—
24	#16863591	C₂²	1	2	yes	—
25	C₄×D₅₃₆	—	2	1	no	—
26	C₄×D₅₃₆	—	2	1	no	—
27	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
28	#16863390	—	2	2	no	—
29	#16863147	C₂²	1	2	yes	—
30	#16863147	C₂²	1	1	yes	characteristic
31	#16863147	C₂²	1	1	yes	characteristic
32	#16863141	C₂²	1	2	yes	—
33	#16863141	C₂²	1	2	yes	—
34	#16863139	C₂²	1	2	yes	—
35	#16863139	C₂²	1	2	yes	—
36	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
37	#446×C₆₇	C₂²	1	1	yes	characteristic
38	#446×C₆₇	C₂²	1	1	yes	characteristic
39	#436×C₆₇	C₂²	1	1	yes	characteristic
40	#436×C₆₇	C₂²	1	1	yes	characteristic
41	#435×C₆₇	—	2	1	no	—
42	#435×C₆₇	—	2	1	no	—
43	#431×C₆₇	—	2	1	no	—
44	#431×C₆₇	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₆₇	—	2	1	no	—
46	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#11761628	—	2	2	no	—
48	#14524063	—	4	8	no	—
49	C₂×#11761618	—	2	2	no	—
50	C₂×#11761616	—	2	2	no	—
51	C₂×#11761615	—	2	2	no	—
52	C₂×D₅₃₆	—	2	1	no	—
53	C₂×D₅₃₆	—	2	1	no	—
54	C₂×#11761613	—	2	2	no	—
55	C₂²×C₆₇⋊C₈	—	2	2	no	—
56	#14524043	C₂³	1	2	yes	—
57	#14524040	C₂³	1	2	yes	—
58	#14524031	—	2	2	no	—
59	#14524017	—	2	2	no	—
60	#14524017	—	2	2	no	—
61	C₄×D₂₆₈	—	2	2	no	—
62	C₄×D₂₆₈	—	2	2	no	—
63	#14523977	—	2	1	no	—
64	#14523977	—	2	1	no	—
65	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
66	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
67	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
68	#14523966	—	2	2	no	—
69	#14523966	—	2	2	no	—
70	#14523965	—	2	2	no	—
71	#14523965	—	2	2	no	—
72	#14523963	—	2	2	no	—
73	#14523963	—	2	2	no	—
74	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
75	C₂×M₁₆×C₆₇	—	2	1	no	—
76	C₂×M₁₆×C₆₇	—	2	1	no	—
77	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
80	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₄×D₄×C₆₇	—	2	1	no	—
82	C₄×D₄×C₆₇	—	2	1	no	—
83	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
84	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
85	#117×C₆₇	—	2	1	no	—
86	#117×C₆₇	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₆₇	—	2	1	no	—
88	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₆₇	—	2	1	no	—
90	C₄⋊C₈×C₆₇	—	2	1	no	—
91	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₂²⋊C₈×C₆₇	—	2	1	no	—
94	C₂²⋊C₈×C₆₇	—	2	1	no	—
95	C₂²⋊C₈×C₆₇	—	2	1	no	—
96	#97×C₆₇	—	2	1	no	—
97	#97×C₆₇	—	2	1	no	—
98	C₄×C₈×C₆₇	—	2	1	no	—
99	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
101	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
103	#11761628	—	4	4	no	—
104	#11761628	—	4	4	no	—
105	C₂×Dic₁₃₄	—	2	2	no	—
106	C₂×D₂₆₈	—	2	2	no	—
107	C₂×D₂₆₈	—	2	2	no	—
108	C₂×D₂₆₈	—	2	2	no	—
109	C₂×C₂²⋊D₆₇	—	4	2	no	—
110	C₂×C₄×D₆₇	—	4	2	no	—
111	#11761618	—	4	4	no	—
112	#11761616	—	4	4	no	—
113	#11761615	—	4	4	no	—
114	D₅₃₆	—	4	2	no	—
115	D₅₃₆	—	4	2	no	—
116	#11761613	—	4	4	no	—
117	C₂×C₆₇⋊C₈	—	2	2	no	—
118	C₂×C₆₇⋊C₈	—	2	2	no	—
119	C₂×C₆₇⋊C₈	—	4	4	no	—
120	C₄⋊Dic₆₇	—	2	2	no	—
121	C₄⋊Dic₆₇	—	2	2	no	—
122	(C₂×D₆₇)⋊C₄	—	4	2	no	—
123	(C₂×D₆₇)⋊C₄	—	4	2	no	—
124	#41×C₆₇	—	2	4	no	—
125	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
126	C₂×D₄×C₆₇	—	2	1	no	—
127	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₇	—	2	1	no	—
129	C₂²×C₄×C₆₇	—	2	1	no	—
130	C₂²×C₄×C₆₇	—	2	1	no	—
131	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
134	M₁₆×C₆₇	—	4	2	no	—
135	M₁₆×C₆₇	—	4	2	no	—
136	C₂×C₈×C₆₇	—	2	2	no	—
137	C₂×C₈×C₆₇	—	2	1	no	—
138	C₂×C₈×C₆₇	—	2	1	no	—
139	C₂×C₈×C₆₇	—	4	1	no	—
140	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
144	C₄⋊C₄×C₆₇	—	2	1	no	—
145	C₄⋊C₄×C₆₇	—	2	1	no	—
146	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
147	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₂²⋊C₄×C₆₇	—	2	1	no	—
149	C₂²⋊C₄×C₆₇	—	2	1	no	—
150	C₂²⋊C₄×C₆₇	—	2	1	no	—
151	C₄²×C₆₇	—	2	1	no	—
152	C₄²×C₆₇	—	2	1	no	—
153	C₄²×C₆₇	—	2	1	no	—
154	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₆₇	#41	1	1	yes	characteristic
157	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
158	C₂³×C₆₇	—	2	1	no	—
159	C₂³×C₆₇	#121	1	1	yes	characteristic
160	C₂²×D₆₇	—	4	2	no	—
161	Q₈×C₆₇	—	2	2	no	—
162	D₄×C₆₇	—	2	2	no	—
163	D₄×C₆₇	—	4	2	no	—
164	C₂×C₄×C₆₇	—	2	1	no	—
165	C₂×C₄×C₆₇	—	2	1	no	—
166	C₂×C₄×C₆₇	—	2	1	no	—
167	C₂×C₄×C₆₇	—	2	1	no	—
168	C₂×C₄×C₆₇	—	2	1	no	—
169	C₂×C₄×C₆₇	—	4	1	no	—
170	C₂×C₄×C₆₇	—	4	2	no	—
171	C₂×C₄×C₆₇	—	4	1	no	—
172	C₂×C₄×C₆₇	—	4	1	no	—
173	C₂×C₄×C₆₇	—	4	2	no	—
174	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
175	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
176	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
177	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
178	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
181	C₂²⋊D₆₇	—	8	4	no	—
182	C₂×Dic₆₇	—	4	2	no	—
183	D₂₆₈	—	4	2	no	—
184	D₂₆₈	—	4	2	no	—
185	D₂₆₈	—	4	2	no	—
186	D₂₆₈	—	4	2	no	—
187	D₂₆₈	—	8	2	no	—
188	C₄×D₆₇	—	8	4	no	—
189	Dic₁₃₄	—	4	2	no	—
190	Dic₁₃₄	—	4	2	no	—
191	C₈×C₆₇	—	2	1	no	—
192	C₈×C₆₇	—	2	1	no	—
193	C₈×C₆₇	—	2	1	no	—
194	C₈×C₆₇	—	4	1	no	—
195	C₈×C₆₇	—	4	1	no	—
196	C₈×C₆₇	#135	1	2	yes	complemented
197	C₆₇⋊C₈	—	4	2	no	—
198	C₆₇⋊C₈	—	4	2	no	—
199	C₂²×C₆₇	—	2	1	no	—
200	C₂²×C₆₇	—	2	1	no	—
201	C₂²×C₆₇	—	4	1	no	—
202	C₂²×C₆₇	—	4	1	no	—
203	C₂²×C₆₇	—	4	1	no	—
204	C₂²×C₆₇	#469	1	2	yes	—
205	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
206	C₂×D₆₇	—	8	2	no	—
207	C₂×D₆₇	—	8	2	no	—
208	C₂×D₆₇	—	8	2	no	—
209	C₄×C₆₇	—	2	1	no	—
210	C₄×C₆₇	—	2	1	no	—
211	C₄×C₆₇	—	2	1	no	—
212	C₄×C₆₇	—	4	1	no	—
213	C₄×C₆₇	—	4	1	no	—
214	C₄×C₆₇	—	4	1	no	—
215	C₄×C₆₇	#469	1	2	yes	—
216	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
217	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
218	C₄×C₆₇	#575	1	1	yes	characteristic
219	Dic₆₇	—	8	2	no	—
220	#19157	—	67	1	no	maximal, Sylow
221	C₂×C₆₇	—	2	2	no	—
222	C₂×C₆₇	—	8	1	no	—
223	C₂×C₆₇	#3035	1	1	yes	characteristic
224	C₂×C₆₇	C₂×#469	1	1	yes	characteristic
225	C₂×C₆₇	#3067	1	1	yes	characteristic
226	D₆₇	—	16	2	no	—
227	#3169	—	67	1	no	—
228	#3035	—	67	2	no	—
229	#2965	D₆₇	1	1	yes	characteristic, complemented
230	#1702	—	67	2	no	—
231	#1701	—	67	2	no	—
232	#1694	—	67	1	no	—
233	#1693	—	67	1	no	—
234	#1688	—	67	1	no	—
235	#1687	—	67	1	no	—
236	C₂×#334	—	67	1	no	—
237	#1540	—	67	2	no	—
238	C₆₇	#19157	1	1	yes	characteristic, complemented, Sylow
239	C₂×#135	—	134	2	no	—
240	#532	—	67	2	no	—
241	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
242	#500	—	67	1	no	—
243	#493	—	67	1	no	—
244	#486	—	67	2	no	—
245	#466	—	134	1	no	—
246	#466	—	134	1	no	—
247	#464	—	134	2	no	—
248	#463	—	134	2	no	—
249	#462	—	67	2	no	—
250	#461	—	67	2	no	—
251	#460	—	67	2	no	—
252	#459	—	67	2	no	—
253	#446	C₂×D₆₇	1	1	yes	characteristic
254	#446	C₂×D₆₇	1	1	yes	characteristic
255	C₄×D₈	—	134	1	no	—
256	C₄×D₈	—	134	1	no	—
257	#436	C₂×D₆₇	1	1	yes	characteristic
258	#436	C₂×D₆₇	1	1	yes	characteristic
259	#435	—	2	1	no	—
260	#435	—	2	1	no	—
261	#431	—	2	1	no	—
262	#431	C₂×D₆₇	1	1	yes	characteristic
263	C₂×C₄⋊C₈	—	67	2	no	—
264	#416	—	134	2	no	—
265	C₄×M₁₆	—	2	1	no	—
266	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
267	#334	—	67	1	no	—
268	#334	—	67	1	no	—
269	#334	—	67	2	no	—
270	#332	—	67	2	no	—
271	#332	—	67	2	no	—
272	#331	—	67	2	no	—
273	#331	—	67	2	no	—
274	C₂×#41	—	134	2	no	—
275	C₂×#41	D₂₆₈	1	1	yes	characteristic
276	#135	—	268	8	no	—
277	C₂×Q₁₆	—	134	2	no	—
278	C₂×SD₁₆	—	134	2	no	—
279	C₂×SD₁₆	—	134	2	no	—
280	C₂×D₈	—	134	2	no	—
281	C₂×D₈	—	134	1	no	—
282	C₂×D₈	—	134	1	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	1	no	—
285	C₂²×C₈	—	134	2	no	—
286	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
287	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
288	C₄⋊Q₈	—	67	2	no	—
289	#127	—	67	2	no	—
290	#124	—	134	2	no	—
291	#121	—	134	2	no	—
292	#121	—	134	2	no	—
293	C₄×Q₈	D₂₆₈	1	1	yes	characteristic
294	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	134	2	no	—
298	C₄×D₄	—	134	2	no	—
299	C₄×D₄	D₂₆₈	1	1	yes	characteristic
300	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
301	#117	—	2	1	no	—
302	#117	D₂₆₈	1	1	yes	characteristic
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
305	#107	—	134	1	no	—
306	#107	—	134	1	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	2	1	no	—
309	C₄⋊C₈	—	67	2	no	—
310	C₄⋊C₈	—	67	2	no	—
311	C₄⋊C₈	—	134	2	no	—
312	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
313	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
314	#103	—	134	2	no	—
315	#103	—	134	2	no	—
316	#102	—	134	2	no	—
317	#102	—	134	2	no	—
318	#102	—	134	2	no	—
319	#102	—	134	2	no	—
320	C₂²⋊C₈	—	2	1	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	2	1	no	—
323	#97	—	2	1	no	—
324	#97	—	2	1	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
327	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
328	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
330	#41	—	2	4	no	—
331	#41	—	268	4	no	—
332	#41	—	268	4	no	—
333	C₂×Q₈	—	134	2	no	—
334	C₂×Q₈	C₂×D₂₆₈	1	1	yes	characteristic
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	268	2	no	—
337	C₂×D₄	—	134	2	no	—
338	C₂×D₄	—	134	2	no	—
339	C₂×D₄	—	134	2	no	—
340	C₂×D₄	C₂×D₂₆₈	1	1	yes	characteristic
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	268	2	no	—
345	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
347	C₂²×C₄	#11761628	1	1	yes	characteristic
348	Q₁₆	—	268	4	no	—
349	SD₁₆	—	268	4	no	—
350	SD₁₆	—	268	4	no	—
351	D₈	—	268	2	no	—
352	D₈	—	268	4	no	—
353	D₈	—	268	2	no	—
354	M₁₆	—	4	2	no	—
355	M₁₆	—	4	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	268	4	no	—
361	C₂×C₈	—	134	2	no	—
362	C₂×C₈	—	134	2	no	—
363	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
364	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
365	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
366	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	134	2	no	—
370	C₄⋊C₄	—	134	2	no	—
371	C₄⋊C₄	C₂×D₂₆₈	1	1	yes	characteristic
372	C₄⋊C₄	C₂×D₂₆₈	1	1	yes	characteristic
373	C₂²⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	2	1	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	268	2	no	—
377	C₂²⋊C₄	—	268	2	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
382	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
383	C₄²	#11761628	1	1	yes	characteristic
384	C₄²	C₂³×D₆₇	1	1	yes	characteristic
385	C₂³	—	2	1	no	—
386	C₂³	—	268	2	no	—
387	C₂³	#14524017	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	268	2	no	—
390	Q₈	—	268	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	268	2	no	—
394	D₄	—	268	2	no	—
395	D₄	—	268	2	no	—
396	D₄	—	268	2	no	—
397	D₄	—	536	2	no	—
398	D₄	—	536	4	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	268	2	no	—
410	C₂×C₄	—	536	4	no	—
411	C₂×C₄	#14524017	1	1	yes	characteristic
412	C₂×C₄	#14524017	1	1	yes	characteristic
413	C₂×C₄	#14524017	1	1	yes	characteristic
414	C₂×C₄	#14524071	1	4	yes	—
415	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
417	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	4	1	no	—
422	C₈	—	4	1	no	—
423	C₈	—	268	2	no	—
424	C₈	—	268	2	no	—
425	C₈	#14524063	1	2	yes	complemented
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	536	2	no	—
432	C₂²	—	536	2	no	—
433	C₂²	—	536	2	no	—
434	C₂²	#16863649	1	2	yes	—
435	C₂²	C₂×#14524017	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	536	2	no	—
443	C₄	#16863649	1	2	yes	—
444	C₄	C₂×#14524063	1	1	yes	characteristic
445	C₄	C₂×#14524071	1	2	yes	—
446	C₄	#16864194	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	8	1	no	—
449	C₂	—	1072	2	no	—
450	C₂	#22569664	1	1	yes	characteristic
451	C₂	C₂×#16863649	1	1	yes	characteristic
452	C₂	#22569929	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14524017
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#2965	C₂
socle	C₂²×C₆₇	C₂×#121
hypercenter	#2965	D₆₇
hypocenter	C₆₇	#19157
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2965

Complements

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

N	H ≅ G/N	type
1. #22570788	C₂	semidirect
2. #22569664	C₂	semidirect
3. #22559777	C₂	semidirect
4. #22559770	C₂	semidirect
5. #22559727	C₂	semidirect
6. #22559722	C₂	semidirect
7. #22559693	C₂	semidirect
8. #22559688	C₂	semidirect
9. C₂×#16863147	C₂	semidirect
10. #22558856	C₂	semidirect
11. C₆₇×#2965	C₂	semidirect
196. C₈×C₆₇	#135	semidirect
229. #2965	D₆₇	semidirect
238. C₆₇	#19157	semidirect
425. C₈	#14524063	semidirect

Maximal subgroups

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

subgroup	index
#22570788	2
#22569664	2
#22559777	2
#22559770	2
#22559727	2
#22559722	2
#22559693	2
#22559688	2
C₂×#16863147	2
#22558856	2
C₆₇×#2965	2
#19157	67