Subgroups — #30825832

Order 17152.

632 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	#22570274	C₂	1	1	yes	maximal, characteristic
2	C₈×#11761628	C₂	1	1	yes	maximal, characteristic
3	#22559078	C₂	1	2	yes	maximal, complemented
4	#22559064	C₂	1	2	yes	maximal, complemented
5	C₈×#11761618	C₂	1	2	yes	maximal, complemented
6	C₈×#11761615	C₂	1	2	yes	maximal, complemented
7	#22559000	C₂	1	1	yes	maximal, characteristic, complemented
8	#22558646	C₂	1	1	yes	maximal, characteristic
9	#22558630	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11761612	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11761628	C₂²	1	1	yes	characteristic
13	#16863734	C₄	1	2	yes	—
14	#16863678	C₄	1	1	yes	characteristic
15	#16863673	C₄	1	1	yes	characteristic
16	#16863603	C₄	1	1	yes	characteristic
17	#16863598	C₄	1	1	yes	characteristic
18	#16863556	C₄	1	2	yes	—
19	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
21	C₄×#11761618	C₂²	1	2	yes	—
22	C₄×#11761615	C₂²	1	2	yes	—
23	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
24	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₆₇	—	2	1	no	—
26	C₈×C₂²⋊D₆₇	—	2	1	no	—
27	#16863449	C₂²	1	1	yes	characteristic
28	#16863449	C₂²	1	1	yes	characteristic
29	#16863447	—	2	1	no	—
30	C₄×#11761612	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₆₇	—	2	1	no	—
32	#16863148	C₂²	1	2	yes	—
33	#16863146	C₂²	1	2	yes	—
34	Q₈⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
35	Q₈⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
36	#16863126	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	#533×C₆₇	C₂²	1	1	yes	characteristic
41	#446×C₆₇	—	2	1	no	—
42	#446×C₆₇	C₂²	1	2	yes	—
43	C₈×Q₈×C₆₇	—	2	1	no	—
44	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
45	#424×C₆₇	—	2	1	no	—
46	#423×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	C₂×C₄	1	1	yes	characteristic
50	C₂×#11761618	C₂×C₄	1	2	yes	—
51	C₂×#11761615	C₂×C₄	1	2	yes	—
52	C₂×#11761612	—	2	1	no	—
53	C₂×C₈×D₆₇	—	2	1	no	—
54	C₂×C₈×D₆₇	—	2	1	no	—
55	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
56	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
57	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
58	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
59	C₄×C₂²⋊D₆₇	—	2	1	no	—
60	C₄×C₂²⋊D₆₇	—	2	1	no	—
61	#14524002	C₂×C₄	1	1	yes	characteristic
62	#14524000	—	2	1	no	—
63	C₄²×D₆₇	—	2	1	no	—
64	#14523976	C₂×C₄	1	2	yes	—
65	#14523974	C₂×C₄	1	2	yes	—
66	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
67	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
68	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
69	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
70	Dic₆₇⋊C₈	—	2	1	no	—
71	Dic₆₇⋊C₈	—	2	1	no	—
72	#14523967	C₂×C₄	1	2	yes	—
73	#14523967	C₂×C₄	1	2	yes	—
74	#14523966	C₂×C₄	1	2	yes	—
75	#14523963	C₂×C₄	1	2	yes	—
76	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
77	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
78	(C₂×D₆₇)⋊C₈	—	2	1	no	—
79	(C₂×D₆₇)⋊C₈	—	2	1	no	—
80	#14523954	—	2	1	no	—
81	C₄×C₆₇⋊C₈	—	2	1	no	—
82	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
83	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
84	C₈×Dic₆₇	—	2	1	no	—
85	C₈×Dic₆₇	—	2	1	no	—
86	C₂×M₁₆×C₆₇	—	2	1	no	—
87	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
88	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
89	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
90	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
91	#125×C₆₇	—	2	1	no	—
92	C₂²⋊Q₈×C₆₇	—	2	1	no	—
93	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
94	C₄×Q₈×C₆₇	—	2	1	no	—
95	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
96	#117×C₆₇	—	2	1	no	—
97	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₆₇	—	2	2	no	—
99	C₄⋊C₈×C₆₇	—	2	2	no	—
100	C₄⋊C₈×C₆₇	—	2	1	no	—
101	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
102	#97×C₆₇	—	2	2	no	—
103	C₄×C₈×C₆₇	—	2	2	no	—
104	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
105	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
106	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
108	#11761628	—	2	2	no	—
109	#11761628	—	2	2	no	—
110	C₂×Dic₁₃₄	C₂²×C₄	1	1	yes	characteristic
111	C₂×D₂₆₈	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊D₆₇	—	2	1	no	—
113	C₂×C₄×D₆₇	—	2	1	no	—
114	C₂×C₄×D₆₇	—	2	1	no	—
115	C₂×C₄×D₆₇	—	2	1	no	—
116	#11761618	—	2	4	no	—
117	#11761615	—	2	4	no	—
118	#11761612	—	2	4	no	—
119	C₂×C₆₇⋊C₈	—	2	2	no	—
120	C₂×C₆₇⋊C₈	—	2	1	no	—
121	C₂×C₆₇⋊C₈	—	2	1	no	—
122	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
123	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
124	C₈×D₆₇	—	4	2	no	—
125	C₈×D₆₇	—	4	2	no	—
126	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
127	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
128	Dic₆₇⋊C₄	—	2	1	no	—
129	Dic₆₇⋊C₄	—	2	1	no	—
130	C₂²⋊Dic₆₇	—	2	1	no	—
131	(C₂×D₆₇)⋊C₄	—	2	1	no	—
132	(C₂×D₆₇)⋊C₄	—	2	1	no	—
133	C₄×Dic₆₇	—	2	1	no	—
134	C₄×Dic₆₇	—	2	1	no	—
135	C₄×Dic₆₇	—	2	1	no	—
136	C₂×Q₈×C₆₇	—	2	1	no	—
137	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
141	M₁₆×C₆₇	—	4	2	no	—
142	C₂×C₈×C₆₇	—	2	2	no	—
143	C₂×C₈×C₆₇	—	2	2	no	—
144	C₂×C₈×C₆₇	—	4	1	no	—
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	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
153	C₄⋊C₄×C₆₇	—	2	2	no	—
154	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
155	C₂²⋊C₄×C₆₇	—	2	2	no	—
156	C₄²×C₆₇	—	2	2	no	—
157	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₆₇	#41	1	1	yes	characteristic
160	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
161	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
162	C₂²×D₆₇	—	2	1	no	—
163	Q₈×C₆₇	—	2	2	no	—
164	Q₈×C₆₇	—	2	2	no	—
165	Q₈×C₆₇	—	4	2	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	—	2	1	no	—
170	C₂×C₄×C₆₇	—	2	2	no	—
171	C₂×C₄×C₆₇	—	2	2	no	—
172	C₂×C₄×C₆₇	—	2	2	no	—
173	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
179	C₂²⋊D₆₇	—	2	4	no	—
180	C₂×Dic₆₇	—	2	1	no	—
181	C₂×Dic₆₇	—	2	1	no	—
182	C₂×Dic₆₇	—	2	1	no	—
183	D₂₆₈	—	2	1	no	—
184	D₂₆₈	#131	1	2	yes	—
185	C₄×D₆₇	—	2	4	no	—
186	C₄×D₆₇	—	4	1	no	—
187	C₄×D₆₇	—	4	1	no	—
188	C₄×D₆₇	—	4	2	no	—
189	Dic₁₃₄	—	2	1	no	—
190	Dic₁₃₄	#131	1	2	yes	—
191	C₈×C₆₇	—	2	1	no	—
192	C₈×C₆₇	—	2	1	no	—
193	C₈×C₆₇	—	2	1	no	—
194	C₈×C₆₇	—	4	2	no	—
195	C₈×C₆₇	#137	1	2	yes	—
196	C₆₇⋊C₈	—	2	4	no	—
197	C₆₇⋊C₈	—	2	2	no	—
198	C₆₇⋊C₈	—	2	2	no	—
199	C₆₇⋊C₈	—	4	1	no	—
200	C₆₇⋊C₈	—	4	1	no	—
201	C₂²×C₆₇	—	2	1	no	—
202	C₂²×C₆₇	—	2	1	no	—
203	C₂²×C₆₇	—	2	1	no	—
204	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂×D₆₇	—	2	2	no	—
206	C₂×D₆₇	—	4	1	no	—
207	C₂×D₆₇	—	4	1	no	—
208	C₄×C₆₇	—	2	1	no	—
209	C₄×C₆₇	—	2	1	no	—
210	C₄×C₆₇	—	2	1	no	—
211	C₄×C₆₇	—	4	2	no	—
212	C₄×C₆₇	—	4	2	no	—
213	C₄×C₆₇	#443	1	2	yes	—
214	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
215	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
216	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
217	C₄×C₆₇	#575	1	1	yes	characteristic
218	Dic₆₇	—	2	2	no	—
219	Dic₆₇	—	4	1	no	—
220	Dic₆₇	—	4	1	no	—
221	#17913	—	67	1	no	maximal, Sylow
222	C₂×C₆₇	—	4	1	no	—
223	C₂×C₆₇	#2929	1	1	yes	characteristic
224	C₂×C₆₇	C₄×#137	1	1	yes	characteristic
225	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
226	D₆₇	—	4	2	no	—
227	#3107	—	67	1	no	—
228	C₈×#41	—	67	1	no	—
229	#2960	D₆₇	1	1	yes	characteristic, complemented
230	#1587	—	67	2	no	—
231	#1585	—	67	2	no	—
232	C₈×Q₁₆	—	67	2	no	—
233	C₈×SD₁₆	—	67	2	no	—
234	#1574	—	67	1	no	—
235	#1489	—	67	1	no	—
236	#1485	—	67	1	no	—
237	C₈×M₁₆	—	67	1	no	—
238	C₆₇	#17913	1	1	yes	characteristic, complemented, Sylow
239	#533	C₂×D₆₇	1	1	yes	characteristic
240	C₄×#41	—	67	1	no	—
241	#485	—	67	2	no	—
242	#475	—	67	1	no	—
243	#474	—	67	1	no	—
244	#462	—	67	1	no	—
245	#461	—	67	1	no	—
246	#452	—	67	2	no	—
247	#446	—	2	1	no	—
248	#446	C₂×D₆₇	1	2	yes	—
249	C₈×Q₈	—	2	1	no	—
250	C₈×Q₈	—	67	1	no	—
251	C₈×Q₈	—	67	1	no	—
252	C₈×Q₈	C₂×D₆₇	1	2	yes	—
253	C₄×Q₁₆	—	67	2	no	—
254	C₄×SD₁₆	—	67	2	no	—
255	C₈×D₄	—	67	1	no	—
256	C₈×D₄	—	67	1	no	—
257	C₈×D₄	—	134	1	no	—
258	C₈×D₄	—	134	1	no	—
259	#431	—	67	1	no	—
260	#431	—	67	1	no	—
261	#431	—	134	1	no	—
262	#424	—	2	1	no	—
263	#423	C₂×D₆₇	1	1	yes	characteristic
264	#405	—	2	1	no	—
265	C₄×M₁₆	—	67	1	no	—
266	C₂×C₄×C₈	—	134	1	no	—
267	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
268	#335	—	67	2	no	—
269	#334	—	67	2	no	—
270	Q₈⋊C₈	—	67	2	no	—
271	Q₈⋊C₈	—	67	2	no	—
272	Q₈⋊C₈	—	67	2	no	—
273	D₄⋊C₈	—	67	2	no	—
274	#322	—	67	2	no	—
275	C₈²	—	67	2	no	—
276	C₂×#41	—	67	1	no	—
277	C₂×Q₁₆	—	67	2	no	—
278	C₂×SD₁₆	—	67	2	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	134	1	no	—
281	C₂²×C₈	—	134	1	no	—
282	C₂²×C₈	—	134	1	no	—
283	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
284	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
285	C₄⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
286	C₄⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
287	#125	—	2	1	no	—
288	C₂²⋊Q₈	—	2	1	no	—
289	C₂²⋊Q₈	C₄×D₆₇	1	2	yes	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	—	67	1	no	—
292	C₄×Q₈	—	67	1	no	—
293	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
294	C₄×D₄	—	67	1	no	—
295	C₄×D₄	—	67	1	no	—
296	C₄×D₄	—	134	1	no	—
297	C₄×D₄	—	134	1	no	—
298	#117	—	2	1	no	—
299	#117	—	67	1	no	—
300	#117	—	134	1	no	—
301	C₂×C₄²	—	134	1	no	—
302	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
303	#107	—	67	2	no	—
304	#106	—	67	2	no	—
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	67	1	no	—
309	C₄⋊C₈	—	67	1	no	—
310	C₄⋊C₈	—	67	1	no	—
311	C₄⋊C₈	—	67	1	no	—
312	C₄⋊C₈	—	134	1	no	—
313	C₄⋊C₈	—	134	1	no	—
314	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
315	#103	—	67	2	no	—
316	#103	—	67	2	no	—
317	#103	—	67	2	no	—
318	#102	—	67	2	no	—
319	C₂²⋊C₈	—	67	2	no	—
320	C₂²⋊C₈	—	134	1	no	—
321	C₂²⋊C₈	—	134	1	no	—
322	C₂²⋊C₈	—	134	1	no	—
323	#97	—	2	2	no	—
324	#97	—	134	1	no	—
325	C₄×C₈	—	2	2	no	—
326	C₄×C₈	—	67	2	no	—
327	C₄×C₈	—	67	2	no	—
328	C₄×C₈	—	134	1	no	—
329	C₄×C₈	—	134	1	no	—
330	C₄×C₈	—	134	1	no	—
331	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
332	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
334	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
335	#41	—	134	2	no	—
336	#41	—	134	2	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	67	1	no	—
339	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
340	C₂×D₄	—	67	1	no	—
341	C₂×D₄	—	134	1	no	—
342	C₂²×C₄	—	134	1	no	—
343	C₂²×C₄	—	134	1	no	—
344	C₂²×C₄	—	134	1	no	—
345	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
347	C₂²×C₄	#11761628	1	1	yes	characteristic
348	Q₁₆	—	134	4	no	—
349	SD₁₆	—	134	4	no	—
350	M₁₆	—	4	2	no	—
351	M₁₆	—	134	4	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	268	2	no	—
356	C₂×C₈	—	268	2	no	—
357	C₂×C₈	—	67	2	no	—
358	C₂×C₈	—	67	2	no	—
359	C₂×C₈	—	134	1	no	—
360	C₂×C₈	—	134	1	no	—
361	C₂×C₈	—	134	2	no	—
362	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
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	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	67	1	no	—
372	C₄⋊C₄	—	67	1	no	—
373	C₄⋊C₄	—	134	1	no	—
374	C₄⋊C₄	—	134	1	no	—
375	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	134	1	no	—
378	C₂²⋊C₄	—	134	1	no	—
379	C₂²⋊C₄	—	134	1	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	134	1	no	—
382	C₄²	—	134	1	no	—
383	C₄²	—	134	1	no	—
384	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
385	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
386	C₄²	#11761628	1	1	yes	characteristic
387	C₄²	C₂³×D₆₇	1	1	yes	characteristic
388	C₂³	—	134	1	no	—
389	C₂³	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	67	2	no	—
394	Q₈	—	134	1	no	—
395	D₄	—	67	2	no	—
396	D₄	—	134	4	no	—
397	D₄	—	134	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	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	268	2	no	—
406	C₂×C₄	—	268	1	no	—
407	C₂×C₄	—	268	1	no	—
408	C₂×C₄	—	134	4	no	—
409	C₂×C₄	—	134	1	no	—
410	C₂×C₄	—	134	1	no	—
411	C₂×C₄	—	134	1	no	—
412	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
413	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
414	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₂²⋊D₆₇	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	2	no	—
422	C₈	—	268	1	no	—
423	C₈	—	268	1	no	—
424	C₈	—	134	4	no	—
425	C₈	—	134	2	no	—
426	C₈	—	134	2	no	—
427	C₈	#14524074	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	268	1	no	—
432	C₂²	—	268	1	no	—
433	C₂²	—	134	2	no	—
434	C₂²	C₂×C₄×C₂²⋊D₆₇	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	268	1	no	—
441	C₄	—	268	1	no	—
442	C₄	—	134	2	no	—
443	C₄	#16863511	1	2	yes	—
444	C₄	#131×D₆₇	1	1	yes	characteristic
445	C₄	#131×D₆₇	1	1	yes	characteristic
446	C₄	C₂×#14524074	1	1	yes	characteristic
447	C₄	#16864194	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	268	2	no	—
450	C₂	#22568901	1	1	yes	characteristic
451	C₂	C₄×#14524074	1	1	yes	characteristic
452	C₂	C₂×#16863511	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#2960	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#11761628	C₂×C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#2960	D₆₇
hypocenter	C₆₇	#17913
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
3. #22559078	C₂	semidirect
4. #22559064	C₂	semidirect
5. C₈×#11761618	C₂	semidirect
6. C₈×#11761615	C₂	semidirect
7. #22559000	C₂	semidirect
9. #22558630	C₂	semidirect
10. C₈×#11761612	C₂	semidirect
11. C₆₇×#2960	C₂	semidirect
229. #2960	D₆₇	semidirect
238. C₆₇	#17913	semidirect

Maximal subgroups

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

subgroup	index
#22570274	2
C₈×#11761628	2
#22559078	2
#22559064	2
C₈×#11761618	2
C₈×#11761615	2
#22559000	2
#22558646	2
#22558630	2
C₈×#11761612	2
C₆₇×#2960	2
#17913	67