Subgroups — #30826435

Order 17152.

662 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570805	C₂	1	1	yes	maximal, characteristic
2	#22568922	C₂	1	1	yes	maximal, characteristic, complemented
3	#22559099	C₂	1	2	yes	maximal, complemented
4	#22559092	C₂	1	2	yes	maximal, complemented
5	#22559031	C₂	1	2	yes	maximal, complemented
6	#22559019	C₂	1	2	yes	maximal, complemented
7	#22558977	C₂	1	1	yes	maximal, characteristic, complemented
8	#22558677	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558674	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11761612	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524049	—	2	1	no	—
13	#16863946	C₂²	1	1	yes	characteristic
14	#16863806	C₄	1	1	yes	characteristic
15	#16863786	C₄	1	1	yes	characteristic
16	#16863762	C₄	1	1	yes	characteristic
17	#16863755	C₄	1	1	yes	characteristic
18	#16863647	C₄	1	2	yes	—
19	#16863644	C₄	1	2	yes	—
20	C₄×#11761615	C₂²	1	2	yes	—
21	C₄×#11761613	C₂²	1	2	yes	—
22	#16863475	—	2	1	no	—
23	#16863475	C₂²	1	2	yes	—
24	C₈×D₂₆₈	—	2	1	no	—
25	C₈×D₂₆₈	C₂²	1	2	yes	—
26	#16863449	C₂²	1	1	yes	characteristic
27	#16863420	C₂²	1	1	yes	characteristic
28	#16863362	—	2	1	no	—
29	C₄×#11761612	C₂²	1	1	yes	characteristic
30	#16863148	C₂²	1	2	yes	—
31	#16863146	C₂²	1	2	yes	—
32	Q₈⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
33	D₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
34	#16863123	C₂²	1	2	yes	—
35	#16863123	C₂²	1	2	yes	—
36	#16863118	C₂²	1	2	yes	—
37	C₈×C₆₇⋊C₈	C₂²	1	2	yes	—
38	#529×C₆₇	C₂²	1	1	yes	characteristic
39	#446×C₆₇	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	#436×C₆₇	C₂²	1	1	yes	characteristic
42	#435×C₆₇	—	2	1	no	—
43	C₈×D₄×C₆₇	—	2	1	no	—
44	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	#433×C₆₇	—	2	1	no	—
46	#432×C₆₇	C₂²	1	1	yes	characteristic
47	#405×C₆₇	—	2	1	no	—
48	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×#11761628	—	2	1	no	—
50	C₂×#11761615	C₂×C₄	1	2	yes	—
51	C₂×#11761613	C₂×C₄	1	2	yes	—
52	#14524049	—	4	4	no	—
53	C₂×#11761612	—	2	1	no	—
54	C₂×#11761612	C₂×C₄	1	2	yes	—
55	C₂×#11761611	—	2	2	no	—
56	C₂×C₈×D₆₇	—	2	2	no	—
57	#14524043	C₂×C₄	1	1	yes	characteristic
58	#14524040	C₂×C₄	1	1	yes	characteristic
59	#14524031	—	2	1	no	—
60	#14524017	—	2	1	no	—
61	#14524017	C₂×C₄	1	2	yes	—
62	C₄×D₂₆₈	—	2	1	no	—
63	C₄×D₂₆₈	C₂³	1	2	yes	—
64	#14523976	C₂×C₄	1	2	yes	—
65	#14523974	C₂×C₄	1	2	yes	—
66	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
67	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
68	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
69	#14523967	C₂×C₄	1	2	yes	—
70	#14523964	C₂×C₄	1	2	yes	—
71	#14523963	C₂×C₄	1	2	yes	—
72	#14523963	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
74	(C₂×D₆₇)⋊C₈	—	2	2	no	—
75	(C₂×D₆₇)⋊C₈	—	2	2	no	—
76	#14523954	C₂×C₄	1	1	yes	characteristic
77	#14523954	C₂×C₄	1	1	yes	characteristic
78	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
79	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
80	C₂×M₁₆×C₆₇	—	2	1	no	—
81	C₂²×C₈×C₆₇	—	2	1	no	—
82	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
83	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
84	#126×C₆₇	—	2	1	no	—
85	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
86	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
87	#123×C₆₇	—	2	1	no	—
88	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
89	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
90	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₄×D₄×C₆₇	—	2	1	no	—
92	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
93	#117×C₆₇	—	2	1	no	—
94	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₆₇	—	2	1	no	—
96	C₄⋊C₈×C₆₇	—	2	1	no	—
97	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₂²⋊C₈×C₆₇	—	2	1	no	—
100	C₂²⋊C₈×C₆₇	—	2	1	no	—
101	C₂²⋊C₈×C₆₇	—	2	1	no	—
102	#97×C₆₇	—	2	1	no	—
103	#97×C₆₇	—	2	1	no	—
104	C₄×C₈×C₆₇	—	2	1	no	—
105	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
106	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
107	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
109	#11761628	—	4	2	no	—
110	#11761628	—	4	2	no	—
111	C₂×Dic₁₃₄	—	2	1	no	—
112	C₂×D₂₆₈	—	2	1	no	—
113	C₂×D₂₆₈	—	2	1	no	—
114	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
115	C₂×C₂²⋊D₆₇	—	2	2	no	—
116	C₂×C₄×D₆₇	—	2	2	no	—
117	#11761615	—	2	4	no	—
118	#11761613	—	2	4	no	—
119	#11761612	—	2	4	no	—
120	#11761612	—	4	2	no	—
121	#11761611	—	4	4	no	—
122	C₂×C₆₇⋊C₈	—	2	2	no	—
123	C₂×C₆₇⋊C₈	—	2	2	no	—
124	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
125	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
126	C₈×D₆₇	—	4	4	no	—
127	C₄⋊Dic₆₇	—	2	1	no	—
128	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
129	(C₂×D₆₇)⋊C₄	—	2	2	no	—
130	(C₂×D₆₇)⋊C₄	—	2	2	no	—
131	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
132	C₂×D₄×C₆₇	—	2	1	no	—
133	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₇	—	2	1	no	—
135	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
138	M₁₆×C₆₇	—	4	2	no	—
139	C₂×C₈×C₆₇	—	2	2	no	—
140	C₂×C₈×C₆₇	—	2	1	no	—
141	C₂×C₈×C₆₇	—	2	1	no	—
142	C₂×C₈×C₆₇	—	4	1	no	—
143	C₂×C₈×C₆₇	—	4	2	no	—
144	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₄⋊C₄×C₆₇	—	2	1	no	—
149	C₄⋊C₄×C₆₇	—	2	1	no	—
150	C₄⋊C₄×C₆₇	—	2	1	no	—
151	C₄⋊C₄×C₆₇	—	2	1	no	—
152	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
153	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
154	C₂²⋊C₄×C₆₇	—	2	1	no	—
155	C₂²⋊C₄×C₆₇	—	2	1	no	—
156	C₂²⋊C₄×C₆₇	—	2	1	no	—
157	C₂²⋊C₄×C₆₇	—	2	1	no	—
158	C₂²⋊C₄×C₆₇	—	2	1	no	—
159	C₄²×C₆₇	—	2	1	no	—
160	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₆₇	#41	1	1	yes	characteristic
163	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
164	C₂³×C₆₇	—	2	1	no	—
165	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
166	C₂²×D₆₇	—	2	2	no	—
167	Q₈×C₆₇	—	2	2	no	—
168	D₄×C₆₇	—	2	2	no	—
169	D₄×C₆₇	—	4	2	no	—
170	C₂×C₄×C₆₇	—	2	2	no	—
171	C₂×C₄×C₆₇	—	2	1	no	—
172	C₂×C₄×C₆₇	—	2	1	no	—
173	C₂×C₄×C₆₇	—	2	1	no	—
174	C₂×C₄×C₆₇	—	2	1	no	—
175	C₂×C₄×C₆₇	—	2	1	no	—
176	C₂×C₄×C₆₇	—	4	1	no	—
177	C₂×C₄×C₆₇	—	4	1	no	—
178	C₂×C₄×C₆₇	—	4	1	no	—
179	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
185	C₂²⋊D₆₇	—	4	4	no	—
186	C₂×Dic₆₇	—	2	2	no	—
187	D₂₆₈	—	2	2	no	—
188	D₂₆₈	—	2	2	no	—
189	D₂₆₈	—	4	2	no	—
190	D₂₆₈	—	4	2	no	—
191	C₄×D₆₇	—	4	2	no	—
192	C₄×D₆₇	—	4	2	no	—
193	Dic₁₃₄	—	4	2	no	—
194	C₈×C₆₇	—	2	1	no	—
195	C₈×C₆₇	—	2	1	no	—
196	C₈×C₆₇	—	2	1	no	—
197	C₈×C₆₇	—	4	1	no	—
198	C₈×C₆₇	—	4	1	no	—
199	C₈×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
200	C₆₇⋊C₈	—	2	2	no	—
201	C₆₇⋊C₈	—	4	2	no	—
202	C₆₇⋊C₈	—	4	2	no	—
203	C₆₇⋊C₈	#131	1	4	yes	complemented
204	C₂²×C₆₇	—	2	1	no	—
205	C₂²×C₆₇	—	2	1	no	—
206	C₂²×C₆₇	—	2	1	no	—
207	C₂²×C₆₇	—	4	1	no	—
208	C₂²×C₆₇	—	4	1	no	—
209	C₂²×C₆₇	—	4	1	no	—
210	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂×D₆₇	—	4	2	no	—
212	C₂×D₆₇	—	4	2	no	—
213	C₂×D₆₇	—	4	2	no	—
214	C₄×C₆₇	—	2	1	no	—
215	C₄×C₆₇	—	2	1	no	—
216	C₄×C₆₇	—	2	1	no	—
217	C₄×C₆₇	—	2	1	no	—
218	C₄×C₆₇	—	4	1	no	—
219	C₄×C₆₇	—	4	1	no	—
220	C₄×C₆₇	—	4	1	no	—
221	C₄×C₆₇	C₂×#131	1	2	yes	—
222	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₄×C₆₇	#575	1	1	yes	characteristic
224	Dic₆₇	—	4	2	no	—
225	#17966	—	67	1	no	maximal, Sylow
226	C₂×C₆₇	—	4	1	no	—
227	C₂×C₆₇	—	8	1	no	—
228	C₂×C₆₇	#2931	1	1	yes	characteristic
229	C₂×C₆₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₂×C₆₇	#2955	1	1	yes	characteristic
231	D₆₇	—	8	2	no	—
232	#3171	—	67	1	no	—
233	#2966	D₆₇	1	1	yes	characteristic, complemented
234	#2931	—	67	1	no	—
235	#1590	—	67	2	no	—
236	#1589	—	67	2	no	—
237	#1580	—	67	2	no	—
238	SD₁₆⋊C₈	—	67	2	no	—
239	#1569	—	67	1	no	—
240	#1496	—	67	1	no	—
241	#1495	—	67	1	no	—
242	C₈×M₁₆	—	67	1	no	—
243	C₆₇	#17966	1	1	yes	characteristic, complemented, Sylow
244	C₂×#131	—	134	1	no	—
245	#532	—	67	1	no	—
246	#529	C₂×D₆₇	1	1	yes	characteristic
247	#501	—	67	1	no	—
248	#496	—	67	1	no	—
249	#490	—	67	1	no	—
250	#489	—	67	1	no	—
251	#469	—	67	2	no	—
252	#468	—	67	2	no	—
253	#446	C₂×D₆₇	1	1	yes	characteristic
254	C₈×Q₈	C₂×D₆₇	1	1	yes	characteristic
255	C₄×SD₁₆	—	67	2	no	—
256	C₄×D₈	—	67	2	no	—
257	#436	—	67	2	no	—
258	#436	—	134	1	no	—
259	#436	C₂×D₆₇	1	1	yes	characteristic
260	#435	—	2	1	no	—
261	C₈×D₄	—	2	1	no	—
262	C₈×D₄	—	67	2	no	—
263	C₈×D₄	—	134	1	no	—
264	C₈×D₄	C₂×D₆₇	1	1	yes	characteristic
265	#433	—	2	1	no	—
266	#432	C₂×D₆₇	1	1	yes	characteristic
267	#431	—	67	1	no	—
268	#423	—	67	1	no	—
269	#408	—	134	1	no	—
270	#405	—	2	1	no	—
271	C₄×M₁₆	—	67	1	no	—
272	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
273	#335	—	67	2	no	—
274	#334	—	67	2	no	—
275	Q₈⋊C₈	—	67	2	no	—
276	D₄⋊C₈	—	67	2	no	—
277	D₄⋊C₈	—	67	2	no	—
278	D₄⋊C₈	—	67	2	no	—
279	#322	—	67	2	no	—
280	C₈²	—	67	2	no	—
281	C₂×#41	—	134	1	no	—
282	C₂×SD₁₆	—	67	2	no	—
283	C₂×D₈	—	67	2	no	—
284	#131	—	268	4	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	67	2	no	—
287	C₂×M₁₆	—	134	1	no	—
288	C₂×M₁₆	—	134	2	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	134	2	no	—
291	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
292	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
293	C₄⋊Q₈	—	67	1	no	—
294	#127	—	67	1	no	—
295	#126	—	2	1	no	—
296	#125	C₄×D₆₇	1	1	yes	characteristic
297	#124	—	134	1	no	—
298	#124	C₄×D₆₇	1	1	yes	characteristic
299	#123	—	2	1	no	—
300	C₂²⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
301	#121	—	67	2	no	—
302	#121	—	134	1	no	—
303	#121	C₄×D₆₇	1	1	yes	characteristic
304	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	67	2	no	—
307	C₄×D₄	—	134	1	no	—
308	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
309	#117	—	2	1	no	—
310	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
311	#107	—	67	2	no	—
312	#106	—	67	2	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	67	2	no	—
316	C₄⋊C₈	—	134	1	no	—
317	C₄⋊C₈	—	134	1	no	—
318	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
319	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
320	#103	—	67	2	no	—
321	#102	—	67	2	no	—
322	#102	—	67	2	no	—
323	#102	—	67	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	134	1	no	—
328	C₂²⋊C₈	—	134	2	no	—
329	C₂²⋊C₈	—	134	2	no	—
330	#97	—	2	1	no	—
331	#97	—	2	1	no	—
332	#97	—	67	1	no	—
333	#97	—	67	1	no	—
334	C₄×C₈	—	2	1	no	—
335	C₄×C₈	—	67	2	no	—
336	C₄×C₈	—	67	2	no	—
337	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
338	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
339	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
340	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
341	#41	—	268	2	no	—
342	#41	—	268	2	no	—
343	C₂×Q₈	—	134	1	no	—
344	C₂×Q₈	C₂×C₄×D₆₇	1	1	yes	characteristic
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	67	2	no	—
347	C₂×D₄	—	134	2	no	—
348	C₂×D₄	—	134	1	no	—
349	C₂×D₄	—	134	1	no	—
350	C₂×D₄	C₂×C₄×D₆₇	1	1	yes	characteristic
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	134	2	no	—
353	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
355	C₂²×C₄	#11761628	1	1	yes	characteristic
356	SD₁₆	—	134	4	no	—
357	D₈	—	134	4	no	—
358	M₁₆	—	4	2	no	—
359	M₁₆	—	268	2	no	—
360	M₁₆	—	268	4	no	—
361	M₁₆	—	134	4	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	4	2	no	—
367	C₂×C₈	—	268	4	no	—
368	C₂×C₈	—	67	2	no	—
369	C₂×C₈	—	67	2	no	—
370	C₂×C₈	—	134	2	no	—
371	C₂×C₈	—	134	2	no	—
372	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
373	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
374	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
375	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	67	2	no	—
381	C₄⋊C₄	—	134	1	no	—
382	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
383	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₂²⋊C₄	—	2	1	no	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	134	2	no	—
390	C₂²⋊C₄	—	134	2	no	—
391	C₄²	—	2	1	no	—
392	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
393	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
394	C₄²	#11761628	1	1	yes	characteristic
395	C₄²	C₂³×D₆₇	1	1	yes	characteristic
396	C₂³	—	2	1	no	—
397	C₂³	—	134	2	no	—
398	C₂³	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
399	Q₈	—	2	2	no	—
400	Q₈	—	268	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	4	2	no	—
403	D₄	—	268	2	no	—
404	D₄	—	268	2	no	—
405	D₄	—	268	4	no	—
406	D₄	—	134	2	no	—
407	D₄	—	134	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	268	2	no	—
418	C₂×C₄	—	268	2	no	—
419	C₂×C₄	—	134	2	no	—
420	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
421	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
422	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
424	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
425	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
426	C₈	—	2	1	no	—
427	C₈	—	2	1	no	—
428	C₈	—	2	1	no	—
429	C₈	—	4	1	no	—
430	C₈	—	4	1	no	—
431	C₈	—	268	2	no	—
432	C₈	—	268	2	no	—
433	C₈	—	67	4	no	—
434	C₈	—	134	2	no	—
435	C₈	#14524068	1	2	yes	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	268	2	no	—
443	C₂²	—	268	2	no	—
444	C₂²	—	268	2	no	—
445	C₂²	C₂×C₄×C₂²⋊D₆₇	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	1	no	—
453	C₄	—	268	2	no	—
454	C₄	#131×D₆₇	1	2	yes	—
455	C₄	C₂×#14524068	1	1	yes	characteristic
456	C₄	#16864194	1	1	yes	characteristic
457	C₂	—	4	1	no	—
458	C₂	—	8	1	no	—
459	C₂	—	536	2	no	—
460	C₂	#22568919	1	1	yes	characteristic
461	C₂	C₄×#14524068	1	1	yes	characteristic
462	C₂	#22569110	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#2966	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#22570805	C₂
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#2966	D₆₇
hypocenter	C₆₇	#17966
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2966

Complements

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

N	H ≅ G/N	type
2. #22568922	C₂	semidirect
3. #22559099	C₂	semidirect
4. #22559092	C₂	semidirect
5. #22559031	C₂	semidirect
6. #22559019	C₂	semidirect
7. #22558977	C₂	semidirect
8. #22558677	C₂	semidirect
9. #22558674	C₂	semidirect
10. C₈×#11761612	C₂	semidirect
11. C₆₇×#2966	C₂	semidirect
203. C₆₇⋊C₈	#131	semidirect
233. #2966	D₆₇	semidirect
243. C₆₇	#17966	semidirect

Maximal subgroups

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

subgroup	index
#22570805	2
#22568922	2
#22559099	2
#22559092	2
#22559031	2
#22559019	2
#22558977	2
#22558677	2
#22558674	2
C₈×#11761612	2
C₆₇×#2966	2
#17966	67