Subgroups — #30826437

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	#22570798	C₂	1	1	yes	maximal, characteristic
2	#22569184	C₂	1	1	yes	maximal, characteristic, complemented
3	#22559097	C₂	1	2	yes	maximal, complemented
4	#22559092	C₂	1	2	yes	maximal, complemented
5	#22559031	C₂	1	2	yes	maximal, complemented
6	#22559021	C₂	1	2	yes	maximal, complemented
7	#22558974	C₂	1	1	yes	maximal, characteristic, complemented
8	#22558678	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558672	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11761612	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863930	C₂²	1	1	yes	characteristic
13	#16863802	C₄	1	1	yes	characteristic
14	#16863783	C₄	1	1	yes	characteristic
15	#16863760	C₄	1	1	yes	characteristic
16	#16863758	C₄	1	1	yes	characteristic
17	#16863647	C₄	1	2	yes	—
18	#16863640	C₄	1	2	yes	—
19	#16863526	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
21	C₄×#11761616	C₂²	1	2	yes	—
22	C₄×#11761613	C₂²	1	2	yes	—
23	#16863475	C₂²	1	1	yes	characteristic
24	#16863467	—	2	1	no	—
25	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
26	C₈×C₂²⋊D₆₇	—	2	1	no	—
27	#16863455	—	2	1	no	—
28	#16863453	C₂²	1	1	yes	characteristic
29	#16863449	C₂²	1	1	yes	characteristic
30	#16863350	—	2	1	no	—
31	C₄×#11761612	C₂²	1	1	yes	characteristic
32	#16863148	C₂²	1	2	yes	—
33	#16863146	C₂²	1	2	yes	—
34	#16863126	C₂²	1	2	yes	—
35	D₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
36	D₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
37	#16863123	C₂²	1	2	yes	—
38	#16863118	C₂²	1	2	yes	—
39	C₈×C₆₇⋊C₈	C₂²	1	2	yes	—
40	C₂×#131×C₆₇	—	2	1	no	—
41	#532×C₆₇	C₂²	1	1	yes	characteristic
42	#436×C₆₇	—	2	1	no	—
43	#436×C₆₇	C₂²	1	2	yes	—
44	C₈×D₄×C₆₇	—	2	1	no	—
45	C₈×D₄×C₆₇	C₂²	1	2	yes	—
46	#423×C₆₇	C₂²	1	1	yes	characteristic
47	#408×C₆₇	—	2	1	no	—
48	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×#11761616	C₂×C₄	1	2	yes	—
50	C₂×#11761613	C₂×C₄	1	2	yes	—
51	C₂×#11761612	C₂×C₄	1	2	yes	—
52	C₂×#11761611	—	2	1	no	—
53	C₂×C₈×D₆₇	—	2	1	no	—
54	#14524037	—	2	1	no	—
55	#14524035	C₂×C₄	1	1	yes	characteristic
56	#14524031	C₂×C₄	1	1	yes	characteristic
57	#14524026	—	2	1	no	—
58	#14524022	C₂×C₄	1	1	yes	characteristic
59	#14524017	C₂×C₄	1	1	yes	characteristic
60	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
61	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
62	C₄×C₂²⋊D₆₇	—	2	1	no	—
63	#14524000	—	2	1	no	—
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)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
69	Dic₆₇⋊C₈	—	2	1	no	—
70	Dic₆₇⋊C₈	—	2	1	no	—
71	#14523966	C₂×C₄	1	2	yes	—
72	#14523964	C₂×C₄	1	2	yes	—
73	#14523964	C₂×C₄	1	2	yes	—
74	#14523963	C₂×C₄	1	2	yes	—
75	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
76	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
77	(C₂×D₆₇)⋊C₈	—	2	1	no	—
78	(C₂×D₆₇)⋊C₈	—	2	1	no	—
79	#14523954	—	2	1	no	—
80	#14523954	C₂×C₄	1	1	yes	characteristic
81	#14523954	C₂×C₄	1	1	yes	characteristic
82	#14523953	—	2	1	no	—
83	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
84	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
85	C₈×Dic₆₇	—	2	1	no	—
86	C₂×#41×C₆₇	—	2	1	no	—
87	#131×C₆₇	—	4	4	no	—
88	C₂×M₁₆×C₆₇	—	2	1	no	—
89	C₂×M₁₆×C₆₇	—	2	2	no	—
90	C₂²×C₈×C₆₇	—	2	2	no	—
91	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
93	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
94	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
95	#124×C₆₇	—	2	1	no	—
96	#121×C₆₇	—	2	1	no	—
97	#121×C₆₇	C₂×C₄	1	2	yes	—
98	C₄×D₄×C₆₇	—	2	1	no	—
99	C₄×D₄×C₆₇	C₂³	1	2	yes	—
100	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₆₇	—	2	1	no	—
102	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
103	C₂²⋊C₈×C₆₇	—	2	2	no	—
104	C₂²⋊C₈×C₆₇	—	2	2	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	C₂×Dic₁₃₄	C₂²×C₄	1	1	yes	characteristic
110	C₂×D₂₆₈	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₂²⋊D₆₇	—	2	1	no	—
112	C₂×C₄×D₆₇	—	2	1	no	—
113	#11761616	—	2	4	no	—
114	#11761613	—	2	4	no	—
115	#11761612	—	2	4	no	—
116	#11761611	—	4	2	no	—
117	C₂×C₆₇⋊C₈	—	2	1	no	—
118	C₂×C₆₇⋊C₈	—	2	1	no	—
119	C₂×C₆₇⋊C₈	—	2	2	no	—
120	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
121	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
122	C₈×D₆₇	—	4	2	no	—
123	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
124	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
125	Dic₆₇⋊C₄	—	2	1	no	—
126	Dic₆₇⋊C₄	—	2	1	no	—
127	Dic₆₇⋊C₄	—	2	1	no	—
128	Dic₆₇⋊C₄	—	2	1	no	—
129	C₂²⋊Dic₆₇	—	2	1	no	—
130	(C₂×D₆₇)⋊C₄	—	2	1	no	—
131	(C₂×D₆₇)⋊C₄	—	2	1	no	—
132	(C₂×D₆₇)⋊C₄	—	2	1	no	—
133	(C₂×D₆₇)⋊C₄	—	2	1	no	—
134	C₄×Dic₆₇	—	2	1	no	—
135	#41×C₆₇	—	4	2	no	—
136	#41×C₆₇	—	4	2	no	—
137	C₂×Q₈×C₆₇	—	2	1	no	—
138	C₂×D₄×C₆₇	—	2	2	no	—
139	C₂×D₄×C₆₇	—	2	1	no	—
140	C₂×D₄×C₆₇	—	2	1	no	—
141	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₆₇	—	2	2	no	—
143	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
146	M₁₆×C₆₇	—	4	2	no	—
147	M₁₆×C₆₇	—	4	4	no	—
148	C₂×C₈×C₆₇	—	2	2	no	—
149	C₂×C₈×C₆₇	—	2	2	no	—
150	C₂×C₈×C₆₇	—	4	1	no	—
151	C₂×C₈×C₆₇	—	4	4	no	—
152	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
156	C₄⋊C₄×C₆₇	—	2	1	no	—
157	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
158	C₂²⋊C₄×C₆₇	—	2	2	no	—
159	C₂²⋊C₄×C₆₇	—	2	2	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	2	no	—
165	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
166	C₂²×D₆₇	—	2	1	no	—
167	Q₈×C₆₇	—	4	2	no	—
168	D₄×C₆₇	—	2	2	no	—
169	D₄×C₆₇	—	2	2	no	—
170	D₄×C₆₇	—	4	2	no	—
171	D₄×C₆₇	—	4	2	no	—
172	D₄×C₆₇	—	4	4	no	—
173	C₂×C₄×C₆₇	—	2	2	no	—
174	C₂×C₄×C₆₇	—	2	1	no	—
175	C₂×C₄×C₆₇	—	2	1	no	—
176	C₂×C₄×C₆₇	—	2	2	no	—
177	C₂×C₄×C₆₇	—	4	1	no	—
178	C₂×C₄×C₆₇	—	4	2	no	—
179	C₂×C₄×C₆₇	—	4	2	no	—
180	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
186	C₂²⋊D₆₇	—	4	2	no	—
187	C₂×Dic₆₇	—	2	1	no	—
188	C₂×Dic₆₇	—	2	1	no	—
189	C₂×Dic₆₇	—	2	1	no	—
190	D₂₆₈	—	2	2	no	—
191	C₄×D₆₇	—	4	1	no	—
192	C₄×D₆₇	—	4	1	no	—
193	Dic₁₃₄	—	2	2	no	—
194	C₈×C₆₇	—	2	1	no	—
195	C₈×C₆₇	—	2	1	no	—
196	C₈×C₆₇	—	2	1	no	—
197	C₈×C₆₇	—	4	2	no	—
198	C₈×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
199	C₆₇⋊C₈	—	2	2	no	—
200	C₆₇⋊C₈	—	4	2	no	—
201	C₆₇⋊C₈	—	4	1	no	—
202	C₆₇⋊C₈	—	4	1	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	2	no	—
208	C₂²×C₆₇	—	4	2	no	—
209	C₂²×C₆₇	—	4	2	no	—
210	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂×D₆₇	—	4	1	no	—
212	C₂×D₆₇	—	4	1	no	—
213	C₂×D₆₇	—	4	1	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	2	no	—
219	C₄×C₆₇	C₂×#131	1	2	yes	—
220	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₄×C₆₇	#575	1	1	yes	characteristic
222	Dic₆₇	—	4	1	no	—
223	Dic₆₇	—	4	1	no	—
224	Dic₆₇	—	4	1	no	—
225	#17966	—	67	1	no	maximal, Sylow
226	C₂×C₆₇	—	4	1	no	—
227	C₂×C₆₇	—	8	2	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	1	no	—
232	#3171	—	67	1	no	—
233	#2966	—	67	1	no	—
234	#2931	D₆₇	1	1	yes	characteristic, complemented
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	—	2	1	no	—
245	#532	C₂×D₆₇	1	1	yes	characteristic
246	#529	—	67	1	no	—
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	—	67	1	no	—
254	C₈×Q₈	—	67	1	no	—
255	C₄×SD₁₆	—	67	2	no	—
256	C₄×D₈	—	67	2	no	—
257	#436	—	2	1	no	—
258	#436	—	67	1	no	—
259	#436	C₂×D₆₇	1	2	yes	—
260	#435	—	134	1	no	—
261	C₈×D₄	—	2	1	no	—
262	C₈×D₄	—	67	1	no	—
263	C₈×D₄	—	134	1	no	—
264	C₈×D₄	C₂×D₆₇	1	2	yes	—
265	#433	—	134	1	no	—
266	#432	—	67	1	no	—
267	#431	—	67	1	no	—
268	#423	C₂×D₆₇	1	1	yes	characteristic
269	#408	—	2	1	no	—
270	#405	—	134	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	—	2	1	no	—
282	C₂×SD₁₆	—	67	2	no	—
283	C₂×D₈	—	67	2	no	—
284	#131	—	4	4	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	67	2	no	—
288	C₂×M₁₆	—	134	1	no	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	134	1	no	—
291	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
292	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
293	C₄⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
294	#127	C₄×D₆₇	1	1	yes	characteristic
295	#126	—	134	1	no	—
296	#125	—	67	1	no	—
297	#124	—	2	1	no	—
298	#124	—	67	1	no	—
299	#123	—	134	1	no	—
300	C₂²⋊Q₈	—	67	1	no	—
301	#121	—	2	1	no	—
302	#121	—	67	1	no	—
303	#121	C₄×D₆₇	1	2	yes	—
304	C₄×Q₈	—	67	1	no	—
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	67	1	no	—
307	C₄×D₄	—	134	1	no	—
308	C₄×D₄	C₂²×D₆₇	1	2	yes	—
309	#117	—	134	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	—	67	1	no	—
315	C₄⋊C₈	—	67	1	no	—
316	C₄⋊C₈	—	134	1	no	—
317	C₄⋊C₈	—	134	1	no	—
318	C₄⋊C₈	—	134	1	no	—
319	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
320	#103	—	67	2	no	—
321	#102	—	67	2	no	—
322	#102	—	67	2	no	—
323	#102	—	67	2	no	—
324	C₂²⋊C₈	—	2	2	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	134	1	no	—
327	C₂²⋊C₈	—	134	1	no	—
328	C₂²⋊C₈	—	134	1	no	—
329	C₂²⋊C₈	—	134	1	no	—
330	#97	—	67	1	no	—
331	#97	—	67	1	no	—
332	#97	—	134	1	no	—
333	#97	—	134	1	no	—
334	C₄×C₈	—	67	2	no	—
335	C₄×C₈	—	67	2	no	—
336	C₄×C₈	—	134	1	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	—	4	2	no	—
342	#41	—	4	2	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	67	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	67	1	no	—
349	C₂×D₄	—	134	1	no	—
350	C₂×D₄	C₂×C₄×D₆₇	1	2	yes	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	134	1	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	—	4	4	no	—
360	M₁₆	—	268	2	no	—
361	M₁₆	—	134	4	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	4	no	—
366	C₂×C₈	—	268	2	no	—
367	C₂×C₈	—	67	2	no	—
368	C₂×C₈	—	67	2	no	—
369	C₂×C₈	—	134	1	no	—
370	C₂×C₈	—	134	1	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	—	67	1	no	—
378	C₄⋊C₄	—	67	1	no	—
379	C₄⋊C₄	—	134	1	no	—
380	C₄⋊C₄	—	134	1	no	—
381	C₄⋊C₄	—	134	1	no	—
382	C₄⋊C₄	—	134	1	no	—
383	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	134	1	no	—
387	C₂²⋊C₄	—	134	1	no	—
388	C₂²⋊C₄	—	134	1	no	—
389	C₂²⋊C₄	—	134	1	no	—
390	C₂²⋊C₄	—	134	1	no	—
391	C₄²	—	134	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	2	no	—
397	C₂³	—	134	1	no	—
398	C₂³	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
399	Q₈	—	4	2	no	—
400	Q₈	—	134	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	4	no	—
406	D₄	—	268	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	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	268	1	no	—
416	C₂×C₄	—	268	1	no	—
417	C₂×C₄	—	134	1	no	—
418	C₂×C₄	—	134	1	no	—
419	C₂×C₄	—	134	1	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	2	no	—
430	C₈	—	268	2	no	—
431	C₈	—	268	1	no	—
432	C₈	—	268	1	no	—
433	C₈	—	67	4	no	—
434	C₈	—	134	2	no	—
435	C₈	#14524069	1	2	yes	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	268	1	no	—
443	C₂²	—	268	1	no	—
444	C₂²	—	268	1	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	2	no	—
451	C₄	—	268	1	no	—
452	C₄	—	268	1	no	—
453	C₄	—	268	1	no	—
454	C₄	#131×D₆₇	1	2	yes	—
455	C₄	C₂×#14524069	1	1	yes	characteristic
456	C₄	#16864194	1	1	yes	characteristic
457	C₂	—	4	1	no	—
458	C₂	—	8	2	no	—
459	C₂	—	536	1	no	—
460	C₂	#22568919	1	1	yes	characteristic
461	C₂	C₄×#14524069	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×#2931	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#22570798	C₂
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#2931	D₆₇
hypocenter	C₆₇	#17966
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2931

Complements

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

N	H ≅ G/N	type
2. #22569184	C₂	semidirect
3. #22559097	C₂	semidirect
4. #22559092	C₂	semidirect
5. #22559031	C₂	semidirect
6. #22559021	C₂	semidirect
7. #22558974	C₂	semidirect
8. #22558678	C₂	semidirect
9. #22558672	C₂	semidirect
10. C₈×#11761612	C₂	semidirect
11. C₆₇×#2931	C₂	semidirect
203. C₆₇⋊C₈	#131	semidirect
234. #2931	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
#22570798	2
#22569184	2
#22559097	2
#22559092	2
#22559031	2
#22559021	2
#22558974	2
#22558678	2
#22558672	2
C₈×#11761612	2
C₆₇×#2931	2
#17966	67