Subgroups — #30838305

Order 17152.

664 conjugacy classes of subgroups.

The subgroup lattice has 452 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	#22570269	C₂	1	2	yes	maximal, complemented
3	#22559625	C₂	1	2	yes	maximal, complemented
4	#22559618	C₂	1	2	yes	maximal, complemented
5	#22559613	C₂	1	1	yes	maximal, characteristic, complemented
6	#22559608	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559569	C₂	1	1	yes	maximal, characteristic, complemented
8	#22559564	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558957	C₂	1	1	yes	maximal, characteristic, complemented
10	#22558869	C₂	1	2	yes	maximal, complemented
11	C₈×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863946	C₂²	1	2	yes	—
13	#16863801	C₂²	1	1	yes	characteristic
14	#16863773	C₂²	1	1	yes	characteristic
15	#16863743	C₂²	1	2	yes	—
16	#16863720	—	2	2	no	—
17	#16863691	C₂²	1	2	yes	—
18	#16863686	C₂²	1	2	yes	—
19	#16863632	—	2	1	no	—
20	#16863632	—	2	1	no	—
21	#16863596	C₂²	1	2	yes	—
22	#16863591	C₂²	1	2	yes	—
23	#16863541	—	2	2	no	—
24	C₄×#11761615	—	2	2	no	—
25	C₄×D₅₃₆	—	2	1	no	—
26	C₄×D₅₃₆	—	2	1	no	—
27	C₄×#11761613	—	2	2	no	—
28	#16863449	C₂²	1	2	yes	—
29	#16863149	C₂²	1	1	yes	characteristic
30	#16863149	C₂²	1	1	yes	characteristic
31	#16863147	C₂²	1	2	yes	—
32	#16863144	C₂²	1	2	yes	—
33	#16863144	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	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₆₇	—	2	1	no	—
40	C₈×D₄×C₆₇	—	2	1	no	—
41	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	#431×C₆₇	—	2	1	no	—
44	#431×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₆₇	—	2	1	no	—
46	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#11761628	—	2	2	no	—
48	C₂×#11761615	—	2	2	no	—
49	C₂×D₅₃₆	—	2	1	no	—
50	C₂×D₅₃₆	—	2	1	no	—
51	C₂×#11761613	—	2	2	no	—
52	#14524043	C₂³	1	2	yes	—
53	#14524040	C₂³	1	2	yes	—
54	#14524031	—	2	2	no	—
55	#14524017	—	2	2	no	—
56	#14524017	—	2	2	no	—
57	C₄×D₂₆₈	—	2	2	no	—
58	C₄×D₂₆₈	—	2	2	no	—
59	#14523977	—	2	1	no	—
60	#14523977	—	2	1	no	—
61	#14523976	—	2	2	no	—
62	#14523974	—	2	2	no	—
63	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
64	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
65	#14523967	—	2	2	no	—
66	#14523965	—	2	2	no	—
67	#14523965	—	2	2	no	—
68	#14523964	—	2	2	no	—
69	#14523963	—	2	2	no	—
70	#14523963	—	2	2	no	—
71	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
72	C₄×C₆₇⋊C₈	—	2	2	no	—
73	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₆₇	—	2	1	no	—
75	C₂²×C₈×C₆₇	—	2	1	no	—
76	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₆₇	—	2	1	no	—
81	C₄×D₄×C₆₇	—	2	1	no	—
82	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
83	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
84	#117×C₆₇	—	2	1	no	—
85	#117×C₆₇	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₆₇	—	2	1	no	—
87	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₆₇	—	2	1	no	—
89	C₄⋊C₈×C₆₇	—	2	1	no	—
90	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₆₇	—	2	1	no	—
93	C₂²⋊C₈×C₆₇	—	2	1	no	—
94	C₂²⋊C₈×C₆₇	—	2	1	no	—
95	C₄×C₈×C₆₇	—	2	1	no	—
96	C₄×C₈×C₆₇	—	2	1	no	—
97	C₄×C₈×C₆₇	—	2	1	no	—
98	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
99	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
102	#11761628	—	8	4	no	—
103	C₂×Dic₁₃₄	—	2	2	no	—
104	C₂×D₂₆₈	—	2	2	no	—
105	C₂×D₂₆₈	—	2	2	no	—
106	C₂×D₂₆₈	—	2	2	no	—
107	C₂×C₂²⋊D₆₇	—	4	2	no	—
108	C₂×C₄×D₆₇	—	4	2	no	—
109	#11761615	—	4	4	no	—
110	D₅₃₆	—	4	2	no	—
111	D₅₃₆	—	4	2	no	—
112	#11761613	—	4	4	no	—
113	C₂×C₆₇⋊C₈	—	2	2	no	—
114	C₂×C₆₇⋊C₈	—	2	2	no	—
115	C₄⋊Dic₆₇	—	2	2	no	—
116	C₄⋊Dic₆₇	—	2	2	no	—
117	(C₂×D₆₇)⋊C₄	—	4	2	no	—
118	(C₂×D₆₇)⋊C₄	—	4	2	no	—
119	#41×C₆₇	—	2	2	no	—
120	#41×C₆₇	—	2	2	no	—
121	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
122	C₂×D₄×C₆₇	—	2	1	no	—
123	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₇	—	2	1	no	—
125	C₂²×C₄×C₆₇	—	2	1	no	—
126	C₂²×C₄×C₆₇	—	2	1	no	—
127	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
130	C₂×C₈×C₆₇	—	2	2	no	—
131	C₂×C₈×C₆₇	—	2	1	no	—
132	C₂×C₈×C₆₇	—	2	1	no	—
133	C₂×C₈×C₆₇	—	4	1	no	—
134	C₂×C₈×C₆₇	—	4	2	no	—
135	C₂×C₈×C₆₇	—	4	2	no	—
136	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₆₇	—	2	1	no	—
141	C₄⋊C₄×C₆₇	—	2	1	no	—
142	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
143	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
144	C₂²⋊C₄×C₆₇	—	2	1	no	—
145	C₂²⋊C₄×C₆₇	—	2	1	no	—
146	C₂²⋊C₄×C₆₇	—	2	1	no	—
147	C₄²×C₆₇	—	2	1	no	—
148	C₄²×C₆₇	—	2	1	no	—
149	C₄²×C₆₇	—	2	1	no	—
150	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₆₇	#41	1	1	yes	characteristic
153	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
154	C₂³×C₆₇	—	2	1	no	—
155	C₂³×C₆₇	#121	1	1	yes	characteristic
156	C₂²×D₆₇	—	4	2	no	—
157	Q₈×C₆₇	—	2	1	no	—
158	Q₈×C₆₇	#135	1	2	yes	—
159	D₄×C₆₇	—	2	4	no	—
160	D₄×C₆₇	—	2	1	no	—
161	D₄×C₆₇	#135	1	2	yes	—
162	C₂×C₄×C₆₇	—	2	4	no	—
163	C₂×C₄×C₆₇	—	2	1	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	2	no	—
169	C₂×C₄×C₆₇	—	2	1	no	—
170	C₂×C₄×C₆₇	—	2	1	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	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₆₇	—	8	4	no	—
181	C₂×Dic₆₇	—	4	2	no	—
182	D₂₆₈	—	4	2	no	—
183	D₂₆₈	—	4	2	no	—
184	D₂₆₈	—	4	2	no	—
185	D₂₆₈	—	4	2	no	—
186	D₂₆₈	—	8	2	no	—
187	C₄×D₆₇	—	8	4	no	—
188	Dic₁₃₄	—	8	2	no	—
189	C₈×C₆₇	—	2	1	no	—
190	C₈×C₆₇	—	2	1	no	—
191	C₈×C₆₇	—	2	1	no	—
192	C₈×C₆₇	—	4	1	no	—
193	C₈×C₆₇	—	4	1	no	—
194	C₈×C₆₇	#135	1	2	yes	—
195	C₆₇⋊C₈	—	4	2	no	—
196	C₆₇⋊C₈	—	4	2	no	—
197	C₂²×C₆₇	—	2	1	no	—
198	C₂²×C₆₇	—	2	1	no	—
199	C₂²×C₆₇	—	2	2	no	—
200	C₂²×C₆₇	—	2	1	no	—
201	C₂²×C₆₇	—	4	1	no	—
202	C₂²×C₆₇	—	4	1	no	—
203	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
204	C₂×D₆₇	—	8	2	no	—
205	C₂×D₆₇	—	8	2	no	—
206	C₂×D₆₇	—	8	2	no	—
207	C₄×C₆₇	—	2	1	no	—
208	C₄×C₆₇	—	2	1	no	—
209	C₄×C₆₇	—	2	2	no	—
210	C₄×C₆₇	—	2	1	no	—
211	C₄×C₆₇	—	4	1	no	—
212	C₄×C₆₇	—	4	1	no	—
213	C₄×C₆₇	#472	1	2	yes	—
214	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
215	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
216	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
217	C₄×C₆₇	#575	1	1	yes	characteristic
218	Dic₆₇	—	8	2	no	—
219	#19128	—	67	1	no	maximal, Sylow
220	C₂×C₆₇	—	4	1	no	—
221	C₂×C₆₇	—	4	2	no	—
222	C₂×C₆₇	#3035	1	1	yes	characteristic
223	C₂×C₆₇	#3050	1	1	yes	characteristic
224	C₂×C₆₇	C₂×#472	1	1	yes	characteristic
225	D₆₇	—	16	2	no	—
226	#3169	—	67	1	no	—
227	#3106	—	67	2	no	—
228	C₈×#41	D₆₇	1	1	yes	characteristic, complemented
229	#1678	—	67	2	no	—
230	#1677	—	67	2	no	—
231	#1676	—	67	1	no	—
232	#1675	—	67	1	no	—
233	#1668	—	67	1	no	—
234	#1667	—	67	1	no	—
235	#1564	—	67	1	no	—
236	#1543	—	67	2	no	—
237	C₆₇	#19128	1	1	yes	characteristic, complemented, Sylow
238	#532	—	67	2	no	—
239	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
240	#500	—	67	1	no	—
241	#493	—	67	1	no	—
242	#486	—	67	2	no	—
243	#482	—	134	2	no	—
244	#477	—	67	2	no	—
245	#476	—	67	2	no	—
246	#466	—	134	1	no	—
247	#466	—	134	1	no	—
248	#460	—	67	2	no	—
249	#459	—	67	2	no	—
250	#449	—	134	2	no	—
251	C₈×Q₈	C₂×D₆₇	1	1	yes	characteristic
252	C₈×Q₈	C₂×D₆₇	1	1	yes	characteristic
253	C₄×SD₁₆	—	134	2	no	—
254	C₄×D₈	—	134	2	no	—
255	C₄×D₈	—	134	1	no	—
256	C₄×D₈	—	134	1	no	—
257	C₈×D₄	—	2	1	no	—
258	C₈×D₄	—	2	1	no	—
259	C₈×D₄	C₂×D₆₇	1	1	yes	characteristic
260	C₈×D₄	C₂×D₆₇	1	1	yes	characteristic
261	#431	—	2	1	no	—
262	#431	—	67	2	no	—
263	#431	C₂×D₆₇	1	1	yes	characteristic
264	C₂×C₄×C₈	—	2	1	no	—
265	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
266	#335	—	67	1	no	—
267	#335	—	67	1	no	—
268	#334	—	67	2	no	—
269	#333	—	67	2	no	—
270	#333	—	67	2	no	—
271	#331	—	67	2	no	—
272	#331	—	67	2	no	—
273	C₂×#41	—	134	2	no	—
274	C₂×#41	D₂₆₈	1	1	yes	characteristic
275	C₂×SD₁₆	—	134	2	no	—
276	C₂×D₈	—	134	2	no	—
277	C₂×D₈	—	134	1	no	—
278	C₂×D₈	—	134	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
282	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
283	C₄⋊Q₈	—	67	2	no	—
284	#127	—	67	2	no	—
285	#124	—	134	2	no	—
286	#121	—	134	2	no	—
287	#121	—	134	2	no	—
288	C₄×Q₈	D₂₆₈	1	1	yes	characteristic
289	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	134	2	no	—
293	C₄×D₄	—	134	2	no	—
294	C₄×D₄	D₂₆₈	1	1	yes	characteristic
295	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
296	#117	—	2	1	no	—
297	#117	D₂₆₈	1	1	yes	characteristic
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
300	#107	—	134	1	no	—
301	#107	—	134	1	no	—
302	#107	—	134	2	no	—
303	#106	—	134	2	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	67	2	no	—
307	C₄⋊C₈	—	67	2	no	—
308	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
309	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
310	#103	—	134	2	no	—
311	#102	—	134	2	no	—
312	#102	—	134	2	no	—
313	#102	—	134	2	no	—
314	#102	—	134	2	no	—
315	#102	—	134	2	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	C₂²⋊C₈	—	134	2	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	134	2	no	—
324	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
325	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
327	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	—	536	4	no	—
331	C₂×Q₈	—	134	2	no	—
332	C₂×Q₈	C₂×D₂₆₈	1	1	yes	characteristic
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	268	2	no	—
335	C₂×D₄	—	134	2	no	—
336	C₂×D₄	—	134	2	no	—
337	C₂×D₄	—	134	2	no	—
338	C₂×D₄	C₂×D₂₆₈	1	1	yes	characteristic
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	268	2	no	—
343	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
345	C₂²×C₄	#11761628	1	1	yes	characteristic
346	SD₁₆	—	268	4	no	—
347	D₈	—	268	2	no	—
348	D₈	—	268	4	no	—
349	D₈	—	268	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	4	2	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	134	2	no	—
357	C₂×C₈	—	134	2	no	—
358	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
359	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
360	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
361	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	134	2	no	—
365	C₄⋊C₄	—	134	2	no	—
366	C₄⋊C₄	C₂×D₂₆₈	1	1	yes	characteristic
367	C₄⋊C₄	C₂×D₂₆₈	1	1	yes	characteristic
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	268	2	no	—
372	C₂²⋊C₄	—	268	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
377	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
378	C₄²	#11761628	1	1	yes	characteristic
379	C₄²	C₂³×D₆₇	1	1	yes	characteristic
380	C₂³	—	2	1	no	—
381	C₂³	—	268	2	no	—
382	C₂³	#14524017	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	—	536	2	no	—
385	Q₈	#14524065	1	2	yes	—
386	D₄	—	2	4	no	—
387	D₄	—	2	1	no	—
388	D₄	—	268	2	no	—
389	D₄	—	268	2	no	—
390	D₄	—	268	2	no	—
391	D₄	—	268	2	no	—
392	D₄	—	536	2	no	—
393	D₄	—	536	4	no	—
394	D₄	#14524065	1	2	yes	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	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	1	no	—
407	C₂×C₄	—	268	2	no	—
408	C₂×C₄	—	536	4	no	—
409	C₂×C₄	#14524017	1	1	yes	characteristic
410	C₂×C₄	#14524017	1	1	yes	characteristic
411	C₂×C₄	#14524017	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
414	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	—	2	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	268	2	no	—
421	C₈	—	268	2	no	—
422	C₈	#14524063	1	2	yes	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	536	2	no	—
430	C₂²	—	536	2	no	—
431	C₂²	—	536	2	no	—
432	C₂²	C₂×#14524017	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	536	2	no	—
440	C₄	#16863666	1	2	yes	—
441	C₄	C₂×#14524063	1	1	yes	characteristic
442	C₄	C₂×#14524065	1	1	yes	characteristic
443	C₄	C₂×#14524065	1	1	yes	characteristic
444	C₄	#16864194	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	4	2	no	—
447	C₂	—	1072	2	no	—
448	C₂	#22569664	1	1	yes	characteristic
449	C₂	#22569790	1	1	yes	characteristic
450	C₂	C₂×#16863666	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14524017
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₈×#41×C₆₇	C₂
socle	C₂²×C₆₇	C₂×#121
hypercenter	C₈×#41	D₆₇
hypocenter	C₆₇	#19128
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #22570788	C₂	semidirect
2. #22570269	C₂	semidirect
3. #22559625	C₂	semidirect
4. #22559618	C₂	semidirect
5. #22559613	C₂	semidirect
6. #22559608	C₂	semidirect
7. #22559569	C₂	semidirect
8. #22559564	C₂	semidirect
9. #22558957	C₂	semidirect
10. #22558869	C₂	semidirect
11. C₈×#41×C₆₇	C₂	semidirect
228. C₈×#41	D₆₇	semidirect
237. C₆₇	#19128	semidirect

Maximal subgroups

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

subgroup	index
#22570788	2
#22570269	2
#22559625	2
#22559618	2
#22559613	2
#22559608	2
#22559569	2
#22559564	2
#22558957	2
#22558869	2
C₈×#41×C₆₇	2
#19128	67