Subgroups — #30764447

Order 17152.

886 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14523976	C₂	1	1	yes	maximal, characteristic
2	C₂²×#14523974	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863158	C₂	1	1	yes	maximal, characteristic
4	C₂×#16863158	C₂	1	1	yes	maximal, characteristic
5	C₂×#16863151	C₂	1	1	yes	maximal, characteristic
6	#22558439	C₂	1	1	yes	maximal, characteristic
7	C₂×#382×C₆₇	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
9	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
12	C₂×#14523976	—	2	2	no	—
13	C₂×#14523976	—	2	2	no	—
14	C₂×#14523976	—	2	2	no	—
15	C₂×#14523974	—	2	2	no	—
16	C₂×#14523974	—	2	2	no	—
17	C₂×#14523974	—	2	2	no	—
18	C₂×C₆₇⋊#95	—	2	2	no	—
19	#16863158	—	2	2	no	—
20	#16863158	—	2	2	no	—
21	#16863151	C₄	1	4	yes	complemented
22	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
25	#382×C₆₇	—	2	2	no	—
26	#382×C₆₇	—	2	2	no	—
27	C₂×#95×C₆₇	—	2	2	no	—
28	C₂³×Dic₆₇	—	2	1	no	—
29	C₂³×Dic₆₇	—	2	1	no	—
30	C₂²×C₆₇⋊C₈	—	2	1	no	—
31	C₂²×C₆₇⋊C₈	—	2	1	no	—
32	C₂²×C₆₇⋊C₈	—	2	1	no	—
33	C₂²×C₆₇⋊C₈	—	2	1	no	—
34	C₂²×C₆₇⋊C₈	—	2	1	no	—
35	C₂²×C₆₇⋊C₈	—	2	1	no	—
36	C₂²×C₆₇⋊C₈	—	2	1	no	—
37	C₂²×C₆₇⋊C₈	—	2	1	no	—
38	C₂²×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
39	C₂²×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
40	C₂²×C₆₇⋊C₈	D₄	1	2	yes	—
41	C₂²×C₆₇⋊C₈	D₄	1	2	yes	—
42	C₂²×C₆₇⋊C₈	Q₈	1	2	yes	—
43	C₂²×C₆₇⋊C₈	Q₈	1	2	yes	—
44	C₂×C₄⋊Dic₆₇	—	2	1	no	—
45	C₂×C₄⋊Dic₆₇	—	2	1	no	—
46	C₂×C₄⋊Dic₆₇	—	2	1	no	—
47	C₂×C₄⋊Dic₆₇	—	2	1	no	—
48	C₂×C₄⋊Dic₆₇	—	2	1	no	—
49	C₂×C₄⋊Dic₆₇	—	2	1	no	—
50	C₂×C₄⋊Dic₆₇	—	2	1	no	—
51	C₂×C₄⋊Dic₆₇	—	2	1	no	—
52	C₂×C₄⋊Dic₆₇	—	2	1	no	—
53	C₂×C₄⋊Dic₆₇	—	2	1	no	—
54	C₂×C₄⋊Dic₆₇	D₄	1	2	yes	—
55	C₂×C₄⋊Dic₆₇	Q₈	1	2	yes	—
56	#14523976	—	2	8	no	—
57	#14523974	—	2	8	no	—
58	C₆₇⋊#95	—	4	4	no	—
59	C₂³×C₄×C₆₇	—	2	1	no	—
60	C₂³×C₄×C₆₇	—	2	1	no	—
61	C₂³×C₄×C₆₇	D₄	1	2	yes	—
62	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
75	C₂×C₄²×C₆₇	—	2	1	no	—
76	C₂×C₄²×C₆₇	—	2	1	no	—
77	C₂×C₄²×C₆₇	—	2	1	no	—
78	C₂×C₄²×C₆₇	—	2	1	no	—
79	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
80	C₂×C₄²×C₆₇	Q₈	1	2	yes	—
81	#95×C₆₇	—	2	8	no	—
82	C₂²×Dic₆₇	—	2	2	no	—
83	C₂²×Dic₆₇	—	2	2	no	—
84	C₂²×Dic₆₇	—	4	1	no	—
85	C₂²×Dic₆₇	—	4	1	no	—
86	C₂²×Dic₆₇	—	4	1	no	—
87	C₂²×Dic₆₇	—	4	1	no	—
88	C₂²×Dic₆₇	—	4	2	no	—
89	C₂²×Dic₆₇	—	4	2	no	—
90	C₂²×Dic₆₇	—	4	2	no	—
91	C₂²×Dic₆₇	—	4	2	no	—
92	C₂×C₆₇⋊C₈	—	2	2	no	—
93	C₂×C₆₇⋊C₈	—	2	2	no	—
94	C₂×C₆₇⋊C₈	—	2	2	no	—
95	C₂×C₆₇⋊C₈	—	2	2	no	—
96	C₂×C₆₇⋊C₈	—	2	2	no	—
97	C₂×C₆₇⋊C₈	—	2	2	no	—
98	C₂×C₆₇⋊C₈	—	2	2	no	—
99	C₂×C₆₇⋊C₈	—	2	2	no	—
100	C₂×C₆₇⋊C₈	—	2	2	no	—
101	C₂×C₆₇⋊C₈	—	2	2	no	—
102	C₂×C₆₇⋊C₈	—	2	2	no	—
103	C₂×C₆₇⋊C₈	—	2	2	no	—
104	C₂×C₆₇⋊C₈	C₄⋊C₄	1	4	yes	—
105	C₂×C₆₇⋊C₈	C₄⋊C₄	1	4	yes	—
106	C₄⋊Dic₆₇	—	2	2	no	—
107	C₄⋊Dic₆₇	—	2	2	no	—
108	C₄⋊Dic₆₇	—	2	2	no	—
109	C₄⋊Dic₆₇	—	2	2	no	—
110	C₄⋊Dic₆₇	—	4	1	no	—
111	C₄⋊Dic₆₇	—	4	1	no	—
112	C₄⋊Dic₆₇	—	4	1	no	—
113	C₄⋊Dic₆₇	—	4	1	no	—
114	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₇	—	2	2	no	—
116	C₂²×C₄×C₆₇	—	2	2	no	—
117	C₂²×C₄×C₆₇	—	2	2	no	—
118	C₂²×C₄×C₆₇	—	2	2	no	—
119	C₂²×C₄×C₆₇	—	2	2	no	—
120	C₂²×C₄×C₆₇	—	2	2	no	—
121	C₂²×C₄×C₆₇	—	2	2	no	—
122	C₂²×C₄×C₆₇	—	2	2	no	—
123	C₂²×C₄×C₆₇	—	4	1	no	—
124	C₂²×C₄×C₆₇	—	4	1	no	—
125	C₂²×C₄×C₆₇	—	4	1	no	—
126	C₂²×C₄×C₆₇	—	4	1	no	—
127	C₂²×C₄×C₆₇	—	4	2	no	—
128	C₂²×C₄×C₆₇	—	4	2	no	—
129	C₂²×C₄×C₆₇	—	4	2	no	—
130	C₂²×C₄×C₆₇	—	4	2	no	—
131	C₂²×C₄×C₆₇	C₄⋊C₄	1	4	yes	—
132	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
141	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
142	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
143	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
144	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
145	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
146	C₄⋊C₄×C₆₇	—	2	2	no	—
147	C₄⋊C₄×C₆₇	—	2	2	no	—
148	C₄⋊C₄×C₆₇	—	2	2	no	—
149	C₄⋊C₄×C₆₇	—	2	2	no	—
150	C₄⋊C₄×C₆₇	—	4	1	no	—
151	C₄⋊C₄×C₆₇	—	4	1	no	—
152	C₄⋊C₄×C₆₇	—	4	1	no	—
153	C₄⋊C₄×C₆₇	—	4	1	no	—
154	C₄²×C₆₇	—	2	2	no	—
155	C₄²×C₆₇	—	2	2	no	—
156	C₄²×C₆₇	—	2	2	no	—
157	C₄²×C₆₇	—	2	2	no	—
158	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂³×C₆₇	#120	1	1	yes	characteristic
160	C₂³×C₆₇	#121	1	1	yes	characteristic
161	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
162	C₂³×C₆₇	#123	1	1	yes	characteristic
163	C₂³×C₆₇	#127	1	1	yes	characteristic
164	C₂³×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
165	C₂³×C₆₇	#135	1	2	yes	—
166	C₂³×C₆₇	#135	1	2	yes	—
167	C₂³×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
168	C₂³×C₆₇	#137	1	2	yes	—
169	C₂×C₄×C₆₇	—	2	4	no	—
170	C₂×C₄×C₆₇	—	2	4	no	—
171	C₂×C₄×C₆₇	—	2	4	no	—
172	C₂×C₄×C₆₇	—	4	2	no	—
173	C₂×C₄×C₆₇	—	4	2	no	—
174	C₂×C₄×C₆₇	—	4	2	no	—
175	C₂×C₄×C₆₇	—	4	2	no	—
176	C₂×C₄×C₆₇	—	4	2	no	—
177	C₂×C₄×C₆₇	—	4	2	no	—
178	C₂×C₄×C₆₇	—	4	4	no	—
179	C₂×C₄×C₆₇	—	4	4	no	—
180	C₂×C₄×C₆₇	—	8	2	no	—
181	C₂×C₄×C₆₇	—	8	2	no	—
182	C₂×C₄×C₆₇	—	8	1	no	—
183	C₂×C₄×C₆₇	—	8	1	no	—
184	C₂×C₄×C₆₇	—	8	1	no	—
185	C₂×C₄×C₆₇	—	8	1	no	—
186	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₆₇	C₄×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
193	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
194	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
195	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
196	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
197	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
198	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
199	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
200	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
201	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
202	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
203	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
204	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
205	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
206	C₂×C₄×C₆₇	#125	1	1	yes	characteristic
207	C₂×C₄×C₆₇	#125	1	1	yes	characteristic
208	C₂×C₄×C₆₇	#125	1	1	yes	characteristic
209	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
210	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
211	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
212	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
213	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
214	C₂×Dic₆₇	—	4	2	no	—
215	C₂×Dic₆₇	—	4	2	no	—
216	C₂×Dic₆₇	—	4	4	no	—
217	C₂×Dic₆₇	—	4	4	no	—
218	C₂×Dic₆₇	—	8	2	no	—
219	C₂×Dic₆₇	—	8	2	no	—
220	C₂×Dic₆₇	—	8	1	no	—
221	C₂×Dic₆₇	—	8	1	no	—
222	C₂×Dic₆₇	—	8	1	no	—
223	C₂×Dic₆₇	—	8	1	no	—
224	C₆₇⋊C₈	—	2	4	no	—
225	C₆₇⋊C₈	—	2	4	no	—
226	C₂²×C₆₇	#384	1	1	yes	characteristic
227	C₂²×C₆₇	#385	1	1	yes	characteristic
228	C₂²×C₆₇	#389	1	1	yes	characteristic
229	C₂²×C₆₇	#392	1	1	yes	characteristic
230	C₂²×C₆₇	#395	1	1	yes	characteristic
231	C₂²×C₆₇	#398	1	1	yes	characteristic
232	C₂²×C₆₇	#399	1	1	yes	characteristic
233	C₂²×C₆₇	#427	1	2	yes	—
234	C₂²×C₆₇	#428	1	2	yes	—
235	C₂²×C₆₇	#449	1	2	yes	—
236	C₂²×C₆₇	#452	1	2	yes	—
237	C₂²×C₆₇	#463	1	2	yes	—
238	C₂²×C₆₇	#464	1	2	yes	—
239	C₂²×C₆₇	#478	1	2	yes	—
240	C₂²×C₆₇	#479	1	2	yes	—
241	C₂²×C₆₇	#482	1	2	yes	—
242	C₂²×C₆₇	#485	1	2	yes	—
243	C₂²×C₆₇	#495	1	1	yes	characteristic
244	C₂²×C₆₇	#495	1	1	yes	characteristic
245	C₂²×C₆₇	#496	1	1	yes	characteristic
246	C₂²×C₆₇	#497	1	1	yes	characteristic
247	C₂²×C₆₇	#499	1	2	yes	—
248	C₂²×C₆₇	#501	1	2	yes	—
249	C₄×C₆₇	—	4	4	no	—
250	C₄×C₆₇	—	8	2	no	—
251	C₄×C₆₇	—	8	2	no	—
252	C₄×C₆₇	#385	1	1	yes	characteristic
253	C₄×C₆₇	#385	1	1	yes	characteristic
254	C₄×C₆₇	#389	1	1	yes	characteristic
255	C₄×C₆₇	#389	1	1	yes	characteristic
256	C₄×C₆₇	#395	1	1	yes	characteristic
257	C₄×C₆₇	#395	1	1	yes	characteristic
258	C₄×C₆₇	#398	1	1	yes	characteristic
259	C₄×C₆₇	#398	1	1	yes	characteristic
260	Dic₆₇	—	8	2	no	—
261	Dic₆₇	—	8	2	no	—
262	#11325	—	67	1	no	maximal, Sylow
263	C₂×C₆₇	#1444	1	1	yes	characteristic
264	C₂×C₆₇	#1846	1	1	yes	characteristic
265	C₂×C₆₇	#1847	1	1	yes	characteristic
266	C₂×C₆₇	#1854	1	2	yes	—
267	C₂×C₆₇	#1949	1	2	yes	—
268	C₂×C₆₇	#2012	1	1	yes	characteristic
269	C₂×C₆₇	#2015	1	1	yes	characteristic
270	C₂×C₆₇	#2059	1	2	yes	—
271	C₂×C₆₇	#2085	1	2	yes	—
272	C₂×C₆₇	#2092	1	1	yes	characteristic
273	C₂×C₆₇	#2097	1	1	yes	characteristic
274	C₂²×#107	—	67	1	no	—
275	C₂²×#106	—	67	1	no	—
276	C₂×#382	D₆₇	1	1	yes	characteristic
277	C₂×#340	—	67	1	no	—
278	C₂×#340	—	67	1	no	—
279	C₂×#336	—	67	1	no	—
280	C₄⋊#95	—	67	1	no	—
281	C₆₇	#11325	1	1	yes	characteristic, complemented, Sylow
282	C₂³×C₈	—	67	1	no	—
283	C₂³×C₈	—	67	1	no	—
284	C₂²×C₄⋊C₄	—	67	1	no	—
285	C₂²×C₄⋊C₄	—	67	1	no	—
286	C₂²×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
287	C₂²×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
288	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
289	C₂×#107	—	134	2	no	—
290	C₂×#107	—	134	2	no	—
291	C₂×#107	—	134	2	no	—
292	C₂×#106	—	134	2	no	—
293	C₂×#106	—	134	2	no	—
294	C₂×#106	—	134	2	no	—
295	#382	—	2	2	no	—
296	#382	—	2	2	no	—
297	C₂×#95	—	2	2	no	—
298	C₂×#95	—	134	2	no	—
299	#340	—	134	2	no	—
300	#340	—	134	2	no	—
301	#336	—	67	4	no	—
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	—	134	1	no	—
305	C₂³×C₄	—	134	1	no	—
306	C₂³×C₄	C₂²⋊D₆₇	1	2	yes	—
307	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
308	C₂²×C₈	—	67	2	no	—
309	C₂²×C₈	—	67	2	no	—
310	C₂²×C₈	—	67	2	no	—
311	C₂²×C₈	—	67	2	no	—
312	C₂²×C₈	—	67	2	no	—
313	C₂²×C₈	—	67	2	no	—
314	C₂²×C₈	—	134	1	no	—
315	C₂²×C₈	—	134	1	no	—
316	C₂²×C₈	—	134	1	no	—
317	C₂²×C₈	—	134	1	no	—
318	C₂²×C₈	—	134	1	no	—
319	C₂²×C₈	—	134	1	no	—
320	C₂²×C₈	—	134	1	no	—
321	C₂²×C₈	—	134	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	67	2	no	—
333	C₂×C₄⋊C₄	—	67	2	no	—
334	C₂×C₄⋊C₄	—	134	1	no	—
335	C₂×C₄⋊C₄	—	134	1	no	—
336	C₂×C₄⋊C₄	—	134	1	no	—
337	C₂×C₄⋊C₄	—	134	1	no	—
338	C₂×C₄⋊C₄	—	134	1	no	—
339	C₂×C₄⋊C₄	—	134	1	no	—
340	C₂×C₄⋊C₄	—	134	1	no	—
341	C₂×C₄⋊C₄	—	134	1	no	—
342	C₂×C₄⋊C₄	—	134	1	no	—
343	C₂×C₄⋊C₄	—	134	1	no	—
344	C₂×C₄⋊C₄	C₂²⋊D₆₇	1	2	yes	—
345	C₂×C₄⋊C₄	C₂²⋊D₆₇	1	2	yes	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	Dic₁₃₄	1	2	yes	—
351	C₂×C₄²	C₄×D₆₇	1	2	yes	—
352	#107	—	134	8	no	—
353	#106	—	134	8	no	—
354	#95	—	2	8	no	—
355	#95	—	268	4	no	—
356	C₂⁴	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	—	4	1	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	268	1	no	—
374	C₂²×C₄	—	268	1	no	—
375	C₂²×C₄	—	268	1	no	—
376	C₂²×C₄	—	268	1	no	—
377	C₂²×C₄	—	268	2	no	—
378	C₂²×C₄	—	268	2	no	—
379	C₂²×C₄	—	268	2	no	—
380	C₂²×C₄	—	268	2	no	—
381	C₂²×C₄	—	134	2	no	—
382	C₂²×C₄	—	134	2	no	—
383	C₂²×C₄	Dic₆₇⋊C₄	1	4	yes	—
384	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
385	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
386	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
387	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
390	C₂²×C₄	Q₈×D₆₇	1	1	yes	characteristic
391	C₂²×C₄	Q₈×D₆₇	1	1	yes	characteristic
392	C₂²×C₄	Q₈×D₆₇	1	1	yes	characteristic
393	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
394	C₂²×C₄	#11761627	1	1	yes	characteristic
395	C₂²×C₄	#11761628	1	1	yes	characteristic
396	C₂²×C₄	#11761628	1	1	yes	characteristic
397	C₂²×C₄	#11761629	1	1	yes	characteristic
398	C₂×C₈	—	67	4	no	—
399	C₂×C₈	—	67	4	no	—
400	C₂×C₈	—	134	2	no	—
401	C₂×C₈	—	134	2	no	—
402	C₂×C₈	—	134	2	no	—
403	C₂×C₈	—	134	2	no	—
404	C₂×C₈	—	134	2	no	—
405	C₂×C₈	—	134	2	no	—
406	C₂×C₈	—	134	2	no	—
407	C₂×C₈	—	134	2	no	—
408	C₂×C₈	—	134	2	no	—
409	C₂×C₈	—	134	2	no	—
410	C₂×C₈	—	134	2	no	—
411	C₂×C₈	—	134	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	4	1	no	—
417	C₄⋊C₄	—	4	1	no	—
418	C₄⋊C₄	—	4	1	no	—
419	C₄⋊C₄	—	4	1	no	—
420	C₄⋊C₄	—	268	1	no	—
421	C₄⋊C₄	—	268	1	no	—
422	C₄⋊C₄	—	268	1	no	—
423	C₄⋊C₄	—	268	1	no	—
424	C₄⋊C₄	—	134	2	no	—
425	C₄⋊C₄	—	134	2	no	—
426	C₄⋊C₄	—	134	2	no	—
427	C₄⋊C₄	—	134	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
433	C₂³	#14524012	1	1	yes	characteristic
434	C₂³	#14524014	1	1	yes	characteristic
435	C₂³	#14524019	1	1	yes	characteristic
436	C₂³	#14524026	1	1	yes	characteristic
437	C₂³	#14524039	1	1	yes	characteristic
438	C₂³	#14524041	1	1	yes	characteristic
439	C₂³	#14524063	1	2	yes	—
440	C₂³	#14524063	1	2	yes	—
441	C₂³	#14524068	1	2	yes	—
442	C₂³	#14524073	1	2	yes	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	8	1	no	—
455	C₂×C₄	—	8	1	no	—
456	C₂×C₄	—	8	1	no	—
457	C₂×C₄	—	8	1	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	—	268	2	no	—
461	C₂×C₄	—	268	2	no	—
462	C₂×C₄	—	268	4	no	—
463	C₂×C₄	—	268	4	no	—
464	C₂×C₄	—	536	1	no	—
465	C₂×C₄	—	536	1	no	—
466	C₂×C₄	—	536	1	no	—
467	C₂×C₄	—	536	1	no	—
468	C₂×C₄	—	536	2	no	—
469	C₂×C₄	—	536	2	no	—
470	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
471	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
472	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
473	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
474	C₂×C₄	#14524005	1	1	yes	characteristic
475	C₂×C₄	#14524008	1	1	yes	characteristic
476	C₂×C₄	#14524011	1	1	yes	characteristic
477	C₂×C₄	#14524011	1	1	yes	characteristic
478	C₂×C₄	#14524015	1	1	yes	characteristic
479	C₂×C₄	#14524015	1	1	yes	characteristic
480	C₂×C₄	#14524019	1	1	yes	characteristic
481	C₂×C₄	#14524019	1	1	yes	characteristic
482	C₂×C₄	#14524021	1	1	yes	characteristic
483	C₂×C₄	#14524021	1	1	yes	characteristic
484	C₂×C₄	#14524021	1	1	yes	characteristic
485	C₂×C₄	#14524021	1	1	yes	characteristic
486	C₂×C₄	#14524022	1	1	yes	characteristic
487	C₂×C₄	#14524022	1	1	yes	characteristic
488	C₂×C₄	#14524028	1	1	yes	characteristic
489	C₂×C₄	#14524028	1	1	yes	characteristic
490	C₂×C₄	#14524033	1	1	yes	characteristic
491	C₂×C₄	#14524033	1	1	yes	characteristic
492	C₂×C₄	#14524034	1	1	yes	characteristic
493	C₂×C₄	#14524041	1	1	yes	characteristic
494	C₂×C₄	#14524041	1	1	yes	characteristic
495	C₂×C₄	#14524042	1	1	yes	characteristic
496	C₂×C₄	#14524042	1	1	yes	characteristic
497	C₂×C₄	#14524042	1	1	yes	characteristic
498	C₈	—	134	4	no	—
499	C₈	—	134	4	no	—
500	C₂²	#16863265	1	1	yes	characteristic
501	C₂²	#16863269	1	1	yes	characteristic
502	C₂²	#16863292	1	1	yes	characteristic
503	C₂²	#16863304	1	1	yes	characteristic
504	C₂²	#16863315	1	1	yes	characteristic
505	C₂²	#16863327	1	1	yes	characteristic
506	C₂²	#16863331	1	1	yes	characteristic
507	C₂²	#16863432	1	2	yes	—
508	C₂²	#16863439	1	2	yes	—
509	C₂²	#16863541	1	2	yes	—
510	C₂²	#16863558	1	2	yes	—
511	C₂²	#16863608	1	2	yes	—
512	C₂²	#16863615	1	2	yes	—
513	C₂²	#16863693	1	2	yes	—
514	C₂²	#16863700	1	2	yes	—
515	C₂²	#16863720	1	2	yes	—
516	C₂²	#16863737	1	2	yes	—
517	C₂²	#16863778	1	1	yes	characteristic
518	C₂²	#16863778	1	1	yes	characteristic
519	C₂²	#16863786	1	1	yes	characteristic
520	C₂²	#16863791	1	1	yes	characteristic
521	C₂²	#16863795	1	2	yes	—
522	C₂²	#16863806	1	2	yes	—
523	C₄	—	4	4	no	—
524	C₄	—	8	2	no	—
525	C₄	—	8	2	no	—
526	C₄	—	536	2	no	—
527	C₄	—	536	2	no	—
528	C₄	#16863267	1	1	yes	characteristic
529	C₄	#16863267	1	1	yes	characteristic
530	C₄	#16863291	1	1	yes	characteristic
531	C₄	#16863291	1	1	yes	characteristic
532	C₄	#16863316	1	1	yes	characteristic
533	C₄	#16863316	1	1	yes	characteristic
534	C₄	#16863329	1	1	yes	characteristic
535	C₄	#16863329	1	1	yes	characteristic
536	C₂	#22558472	1	1	yes	characteristic
537	C₂	#22560371	1	1	yes	characteristic
538	C₂	#22560378	1	1	yes	characteristic
539	C₂	#22560408	1	2	yes	—
540	C₂	#22560975	1	2	yes	—
541	C₂	#22561286	1	1	yes	characteristic
542	C₂	#22561303	1	1	yes	characteristic
543	C₂	#22561544	1	2	yes	—
544	C₂	#22561691	1	2	yes	—
545	C₂	#22561733	1	1	yes	characteristic
546	C₂	#22561760	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₆₇
commutator	C₂²×C₄×C₆₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₆₇
Fitting	C₂×#382×C₆₇	C₂
socle, prime radical	C₂⁴×C₆₇	C₂×D₄
cosocle	C₂³×C₄×C₆₇	C₂³
hypercenter	C₂×#382	D₆₇
hypocenter	C₆₇	#11325
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#382

Complements

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

N	H ≅ G/N	type
21. #16863151	C₄	semidirect
281. C₆₇	#11325	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14523976	2
C₂²×#14523974	2
C₂×#16863158	2
C₂×#16863151	2
#22558439	2
C₂×#382×C₆₇	2
#11325	67