Subgroups — C₆₇×#11096 #30690347

Order 17152.

1230 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#107×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#380×C₆₇	C₂	1	2	yes	maximal
4	C₂×#340×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#340×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
11	C₂²×C₂²⋊C₄×C₆₇	—	2	2	no	—
12	C₂×#107×C₆₇	—	2	2	no	—
13	C₂×#107×C₆₇	—	2	4	no	—
14	C₂×C₂²⋊C₈×C₆₇	—	2	2	no	—
15	C₂×C₂²⋊C₈×C₆₇	—	2	2	no	—
16	C₂×C₂²⋊C₈×C₆₇	C₄	1	4	yes	complemented
17	#380×C₆₇	—	2	4	no	—
18	#380×C₆₇	—	2	4	no	—
19	C₂×#95×C₆₇	—	2	2	no	—
20	#340×C₆₇	—	2	2	no	—
21	#340×C₆₇	—	2	4	no	—
22	C₂⁵×C₆₇	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₆₇	—	2	2	no	—
24	C₂³×C₄×C₆₇	—	2	2	no	—
25	C₂³×C₄×C₆₇	—	2	1	no	—
26	C₂³×C₄×C₆₇	—	2	1	no	—
27	C₂³×C₄×C₆₇	—	2	1	no	—
28	C₂³×C₄×C₆₇	—	2	1	no	—
29	C₂³×C₄×C₆₇	—	2	2	no	—
30	C₂³×C₄×C₆₇	—	2	2	no	—
31	C₂³×C₄×C₆₇	—	2	2	no	—
32	C₂³×C₄×C₆₇	—	2	2	no	—
33	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₆₇	Q₈	1	2	yes	—
36	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₆₇	—	2	2	no	—
38	C₂²×C₈×C₆₇	—	2	2	no	—
39	C₂²×C₈×C₆₇	—	2	2	no	—
40	C₂²×C₈×C₆₇	—	2	1	no	—
41	C₂²×C₈×C₆₇	—	2	1	no	—
42	C₂²×C₈×C₆₇	—	2	2	no	—
43	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₆₇	D₄	1	2	yes	—
46	C₂²×C₈×C₆₇	D₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₆₇	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₆₇	D₄	1	4	yes	—
59	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
60	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
61	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
62	#107×C₆₇	—	2	8	no	—
63	C₂²⋊C₈×C₆₇	—	2	8	no	—
64	#95×C₆₇	—	2	8	no	—
65	C₂⁴×C₆₇	—	2	2	no	—
66	C₂⁴×C₆₇	—	2	1	no	—
67	C₂⁴×C₆₇	—	2	1	no	—
68	C₂⁴×C₆₇	—	2	2	no	—
69	C₂⁴×C₆₇	—	2	1	no	—
70	C₂⁴×C₆₇	—	2	1	no	—
71	C₂⁴×C₆₇	—	2	2	no	—
72	C₂⁴×C₆₇	—	2	2	no	—
73	C₂⁴×C₆₇	C₄⋊C₄	1	2	yes	—
74	C₂⁴×C₆₇	D₈	1	2	yes	—
75	C₂⁴×C₆₇	Q₁₆	1	2	yes	—
76	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₇	—	2	2	no	—
78	C₂²×C₄×C₆₇	—	2	1	no	—
79	C₂²×C₄×C₆₇	—	2	1	no	—
80	C₂²×C₄×C₆₇	—	2	2	no	—
81	C₂²×C₄×C₆₇	—	2	2	no	—
82	C₂²×C₄×C₆₇	—	2	2	no	—
83	C₂²×C₄×C₆₇	—	2	4	no	—
84	C₂²×C₄×C₆₇	—	2	4	no	—
85	C₂²×C₄×C₆₇	—	2	2	no	—
86	C₂²×C₄×C₆₇	—	2	2	no	—
87	C₂²×C₄×C₆₇	—	2	4	no	—
88	C₂²×C₄×C₆₇	—	2	4	no	—
89	C₂²×C₄×C₆₇	—	2	4	no	—
90	C₂²×C₄×C₆₇	—	2	4	no	—
91	C₂²×C₄×C₆₇	—	4	1	no	—
92	C₂²×C₄×C₆₇	—	4	2	no	—
93	C₂²×C₄×C₆₇	—	4	2	no	—
94	C₂²×C₄×C₆₇	—	4	2	no	—
95	C₂²×C₄×C₆₇	—	4	2	no	—
96	C₂²×C₄×C₆₇	—	4	1	no	—
97	C₂²×C₄×C₆₇	—	4	2	no	—
98	C₂²×C₄×C₆₇	—	4	1	no	—
99	C₂²×C₄×C₆₇	—	4	2	no	—
100	C₂²×C₄×C₆₇	—	4	1	no	—
101	C₂²×C₄×C₆₇	—	4	2	no	—
102	C₂²×C₄×C₆₇	—	4	2	no	—
103	C₂²×C₄×C₆₇	—	4	2	no	—
104	C₂²×C₄×C₆₇	—	4	2	no	—
105	C₂²×C₄×C₆₇	—	4	2	no	—
106	C₂²×C₄×C₆₇	—	4	2	no	—
107	C₂²×C₄×C₆₇	—	4	2	no	—
108	C₂²×C₄×C₆₇	—	4	2	no	—
109	C₂²×C₄×C₆₇	—	4	2	no	—
110	C₂²×C₄×C₆₇	—	4	2	no	—
111	C₂²×C₄×C₆₇	—	4	2	no	—
112	C₂²×C₄×C₆₇	—	4	2	no	—
113	C₂²×C₄×C₆₇	C₄⋊C₄	1	2	yes	—
114	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
120	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
121	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
122	C₂²×C₄×C₆₇	#41	1	2	yes	—
123	C₂²×C₄×C₆₇	#41	1	2	yes	—
124	C₂×C₈×C₆₇	—	2	4	no	—
125	C₂×C₈×C₆₇	—	2	2	no	—
126	C₂×C₈×C₆₇	—	2	4	no	—
127	C₂×C₈×C₆₇	—	2	2	no	—
128	C₂×C₈×C₆₇	—	2	2	no	—
129	C₂×C₈×C₆₇	—	2	4	no	—
130	C₂×C₈×C₆₇	—	4	2	no	—
131	C₂×C₈×C₆₇	—	4	1	no	—
132	C₂×C₈×C₆₇	—	4	1	no	—
133	C₂×C₈×C₆₇	C₂²⋊C₄	1	4	yes	complemented
134	C₄⋊C₄×C₆₇	—	2	4	no	—
135	C₄⋊C₄×C₆₇	—	2	4	no	—
136	C₄⋊C₄×C₆₇	—	2	4	no	—
137	C₄⋊C₄×C₆₇	—	2	4	no	—
138	C₄⋊C₄×C₆₇	—	4	2	no	—
139	C₄⋊C₄×C₆₇	—	4	2	no	—
140	C₄⋊C₄×C₆₇	—	4	2	no	—
141	C₄⋊C₄×C₆₇	—	4	2	no	—
142	C₂²⋊C₄×C₆₇	—	4	16	no	—
143	C₂³×C₆₇	—	2	2	no	—
144	C₂³×C₆₇	—	2	4	no	—
145	C₂³×C₆₇	—	2	2	no	—
146	C₂³×C₆₇	—	2	4	no	—
147	C₂³×C₆₇	—	2	4	no	—
148	C₂³×C₆₇	—	2	4	no	—
149	C₂³×C₆₇	—	2	2	no	—
150	C₂³×C₆₇	—	2	2	no	—
151	C₂³×C₆₇	—	2	2	no	—
152	C₂³×C₆₇	—	2	2	no	—
153	C₂³×C₆₇	—	2	4	no	—
154	C₂³×C₆₇	—	2	4	no	—
155	C₂³×C₆₇	—	4	1	no	—
156	C₂³×C₆₇	—	4	2	no	—
157	C₂³×C₆₇	—	4	1	no	—
158	C₂³×C₆₇	—	4	2	no	—
159	C₂³×C₆₇	—	4	2	no	—
160	C₂³×C₆₇	—	4	2	no	—
161	C₂³×C₆₇	—	4	1	no	—
162	C₂³×C₆₇	—	4	1	no	—
163	C₂³×C₆₇	—	4	2	no	—
164	C₂³×C₆₇	—	4	2	no	—
165	C₂³×C₆₇	#107	1	4	yes	complemented
166	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂³×C₆₇	#120	1	2	yes	—
168	C₂³×C₆₇	#121	1	1	yes	characteristic
169	C₂³×C₆₇	#121	1	1	yes	characteristic
170	C₂³×C₆₇	#123	1	2	yes	—
171	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
172	C₂³×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
173	C₂³×C₆₇	#135	1	1	yes	characteristic
174	C₂³×C₆₇	#135	1	1	yes	characteristic
175	C₂³×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
176	C₂³×C₆₇	#137	1	2	yes	—
177	C₂×C₄×C₆₇	—	2	2	no	—
178	C₂×C₄×C₆₇	—	2	4	no	—
179	C₂×C₄×C₆₇	—	4	1	no	—
180	C₂×C₄×C₆₇	—	4	2	no	—
181	C₂×C₄×C₆₇	—	4	1	no	—
182	C₂×C₄×C₆₇	—	4	2	no	—
183	C₂×C₄×C₆₇	—	4	4	no	—
184	C₂×C₄×C₆₇	—	4	2	no	—
185	C₂×C₄×C₆₇	—	4	2	no	—
186	C₂×C₄×C₆₇	—	4	4	no	—
187	C₂×C₄×C₆₇	—	4	2	no	—
188	C₂×C₄×C₆₇	—	4	4	no	—
189	C₂×C₄×C₆₇	—	4	4	no	—
190	C₂×C₄×C₆₇	—	4	4	no	—
191	C₂×C₄×C₆₇	—	4	4	no	—
192	C₂×C₄×C₆₇	—	4	4	no	—
193	C₂×C₄×C₆₇	—	4	4	no	—
194	C₂×C₄×C₆₇	—	8	2	no	—
195	C₂×C₄×C₆₇	—	8	2	no	—
196	C₂×C₄×C₆₇	—	8	2	no	—
197	C₂×C₄×C₆₇	—	8	2	no	—
198	C₂×C₄×C₆₇	—	8	2	no	—
199	C₂×C₄×C₆₇	—	8	2	no	—
200	C₂×C₄×C₆₇	—	8	2	no	—
201	C₂×C₄×C₆₇	—	8	2	no	—
202	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
204	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
207	C₂×C₄×C₆₇	#121	1	2	yes	—
208	C₂×C₄×C₆₇	#121	1	2	yes	—
209	C₂×C₄×C₆₇	#121	1	2	yes	—
210	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
211	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
212	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
213	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
214	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
215	C₂×C₄×C₆₇	#123	1	2	yes	—
216	C₂×C₄×C₆₇	#124	1	2	yes	—
217	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
218	C₂×C₄×C₆₇	#126	1	2	yes	—
219	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
220	C₈×C₆₇	—	2	4	no	—
221	C₈×C₆₇	—	4	2	no	—
222	C₂²×C₆₇	—	2	4	no	—
223	C₂²×C₆₇	—	2	8	no	—
224	C₂²×C₆₇	—	4	2	no	—
225	C₂²×C₆₇	—	4	2	no	—
226	C₂²×C₆₇	—	4	2	no	—
227	C₂²×C₆₇	—	4	4	no	—
228	C₂²×C₆₇	—	4	2	no	—
229	C₂²×C₆₇	—	4	2	no	—
230	C₂²×C₆₇	—	4	2	no	—
231	C₂²×C₆₇	—	4	4	no	—
232	C₂²×C₆₇	—	4	4	no	—
233	C₂²×C₆₇	#380	1	1	yes	characteristic
234	C₂²×C₆₇	#385	1	2	yes	—
235	C₂²×C₆₇	#392	1	1	yes	characteristic
236	C₂²×C₆₇	#394	1	2	yes	—
237	C₂²×C₆₇	#397	1	1	yes	characteristic
238	C₂²×C₆₇	C₂×#107	1	1	yes	characteristic
239	C₂²×C₆₇	#427	1	1	yes	characteristic
240	C₂²×C₆₇	#428	1	2	yes	—
241	C₂²×C₆₇	#447	1	2	yes	—
242	C₂²×C₆₇	#449	1	2	yes	—
243	C₂²×C₆₇	#451	1	2	yes	—
244	C₂²×C₆₇	#452	1	2	yes	—
245	C₂²×C₆₇	#466	1	1	yes	characteristic
246	C₂²×C₆₇	#466	1	1	yes	characteristic
247	C₂²×C₆₇	#467	1	1	yes	characteristic
248	C₂²×C₆₇	#467	1	1	yes	characteristic
249	C₂²×C₆₇	#468	1	2	yes	—
250	C₂²×C₆₇	#469	1	1	yes	characteristic
251	C₂²×C₆₇	#470	1	1	yes	characteristic
252	C₂²×C₆₇	#480	1	2	yes	—
253	C₂²×C₆₇	#482	1	2	yes	—
254	C₂²×C₆₇	#484	1	2	yes	—
255	C₂²×C₆₇	#485	1	2	yes	—
256	C₄×C₆₇	—	4	2	no	—
257	C₄×C₆₇	—	8	4	no	—
258	C₄×C₆₇	—	8	4	no	—
259	C₄×C₆₇	#386	1	1	yes	characteristic
260	C₄×C₆₇	#388	1	2	yes	—
261	C₄×C₆₇	#390	1	1	yes	characteristic
262	C₄×C₆₇	#393	1	1	yes	characteristic
263	C₄×C₆₇	#396	1	2	yes	—
264	C₄×C₆₇	#399	1	1	yes	characteristic
265	#11096	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂×C₆₇	—	4	4	no	—
267	C₂×C₆₇	#1439	1	1	yes	characteristic
268	C₂×C₆₇	#1808	1	1	yes	characteristic
269	C₂×C₆₇	#1809	1	1	yes	characteristic
270	C₂×C₆₇	#1852	1	2	yes	—
271	C₂×C₆₇	#1854	1	2	yes	—
272	C₂×C₆₇	#1999	1	1	yes	characteristic
273	C₂×C₆₇	#2001	1	1	yes	characteristic
274	C₂×C₆₇	#2033	1	2	yes	—
275	C₂×C₆₇	#2036	1	2	yes	—
276	C₂×C₆₇	#2075	1	1	yes	characteristic
277	C₂×C₆₇	#2076	1	1	yes	characteristic
278	C₂²×#107	C₂×C₆₇	1	1	yes	characteristic, complemented
279	C₂²×C₂²⋊C₈	C₂×C₆₇	1	1	yes	characteristic
280	C₂×#380	C₂×C₆₇	1	2	yes	—
281	C₂×#340	C₂×C₆₇	1	2	yes	complemented
282	C₂×#340	C₂×C₆₇	1	1	yes	characteristic, complemented
283	C₆₇	#11096	1	1	yes	characteristic, direct product factor, Sylow
284	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
285	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
286	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
287	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
288	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
289	C₂²×C₂²⋊C₄	—	2	2	no	—
290	C₂×#107	—	2	2	no	—
291	C₂×#107	—	2	4	no	—
292	C₂×C₂²⋊C₈	—	2	2	no	—
293	C₂×C₂²⋊C₈	—	2	2	no	—
294	C₂×C₂²⋊C₈	C₄×C₆₇	1	4	yes	complemented
295	#380	—	2	4	no	—
296	#380	—	2	4	no	—
297	C₂×#95	—	2	2	no	—
298	#340	—	2	2	no	—
299	#340	—	2	4	no	—
300	C₂⁵	D₄×C₆₇	1	1	yes	characteristic
301	C₂³×C₄	—	2	2	no	—
302	C₂³×C₄	—	2	2	no	—
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	—	2	1	no	—
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	—	2	2	no	—
308	C₂³×C₄	—	2	2	no	—
309	C₂³×C₄	—	2	2	no	—
310	C₂³×C₄	—	2	2	no	—
311	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
312	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
313	C₂³×C₄	Q₈×C₆₇	1	2	yes	—
314	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	—	2	2	no	—
317	C₂²×C₈	—	2	2	no	—
318	C₂²×C₈	—	2	1	no	—
319	C₂²×C₈	—	2	1	no	—
320	C₂²×C₈	—	2	2	no	—
321	C₂²×C₈	C₂×C₄×C₆₇	1	2	yes	—
322	C₂²×C₈	C₂×C₄×C₆₇	1	2	yes	—
323	C₂²×C₈	D₄×C₆₇	1	2	yes	—
324	C₂²×C₈	D₄×C₆₇	1	2	yes	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	D₄×C₆₇	1	4	yes	—
336	C₂×C₄⋊C₄	D₄×C₆₇	1	4	yes	—
337	C₂×C₂²⋊C₄	—	2	8	no	—
338	C₂×C₂²⋊C₄	—	4	4	no	—
339	C₂×C₂²⋊C₄	—	4	4	no	—
340	#107	—	2	8	no	—
341	C₂²⋊C₈	—	2	8	no	—
342	#95	—	2	8	no	—
343	C₂⁴	—	2	2	no	—
344	C₂⁴	—	2	1	no	—
345	C₂⁴	—	2	1	no	—
346	C₂⁴	—	2	2	no	—
347	C₂⁴	—	2	1	no	—
348	C₂⁴	—	2	1	no	—
349	C₂⁴	—	2	2	no	—
350	C₂⁴	—	2	2	no	—
351	C₂⁴	C₄⋊C₄×C₆₇	1	2	yes	—
352	C₂⁴	D₈×C₆₇	1	2	yes	—
353	C₂⁴	Q₁₆×C₆₇	1	2	yes	—
354	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	C₄⋊C₄×C₆₇	1	2	yes	—
392	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
397	C₂²×C₄	C₂×Q₈×C₆₇	1	1	yes	characteristic
398	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
399	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
400	C₂²×C₄	#41×C₆₇	1	2	yes	—
401	C₂²×C₄	#41×C₆₇	1	2	yes	—
402	C₂×C₈	—	2	4	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	4	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	4	no	—
408	C₂×C₈	—	4	2	no	—
409	C₂×C₈	—	4	1	no	—
410	C₂×C₈	—	4	1	no	—
411	C₂×C₈	C₂²⋊C₄×C₆₇	1	4	yes	complemented
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	4	16	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	1	no	—
443	C₂³	#107×C₆₇	1	4	yes	complemented
444	C₂³	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
445	C₂³	#120×C₆₇	1	2	yes	—
446	C₂³	#121×C₆₇	1	1	yes	characteristic
447	C₂³	#121×C₆₇	1	1	yes	characteristic
448	C₂³	#123×C₆₇	1	2	yes	—
449	C₂³	C₂×D₈×C₆₇	1	1	yes	characteristic
450	C₂³	C₂×Q₁₆×C₆₇	1	1	yes	characteristic
451	C₂³	#135×C₆₇	1	1	yes	characteristic
452	C₂³	#135×C₆₇	1	1	yes	characteristic
453	C₂³	AGL(1,ℤ/8)×C₆₇	1	2	yes	—
454	C₂³	#137×C₆₇	1	2	yes	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	8	2	no	—
473	C₂×C₄	—	8	2	no	—
474	C₂×C₄	—	8	2	no	—
475	C₂×C₄	—	8	2	no	—
476	C₂×C₄	—	8	2	no	—
477	C₂×C₄	—	8	2	no	—
478	C₂×C₄	—	8	2	no	—
479	C₂×C₄	—	8	2	no	—
480	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
481	C₂×C₄	#117×C₆₇	1	1	yes	characteristic
482	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
483	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
484	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
485	C₂×C₄	#121×C₆₇	1	2	yes	—
486	C₂×C₄	#121×C₆₇	1	2	yes	—
487	C₂×C₄	#121×C₆₇	1	2	yes	—
488	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
489	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
490	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
491	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
492	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
493	C₂×C₄	#123×C₆₇	1	2	yes	—
494	C₂×C₄	#124×C₆₇	1	2	yes	—
495	C₂×C₄	#124×C₆₇	1	1	yes	characteristic
496	C₂×C₄	#126×C₆₇	1	2	yes	—
497	C₂×C₄	#127×C₆₇	1	1	yes	characteristic
498	C₈	—	2	4	no	—
499	C₈	—	4	2	no	—
500	C₂²	—	2	4	no	—
501	C₂²	—	2	8	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	2	no	—
511	C₂²	#380×C₆₇	1	1	yes	characteristic
512	C₂²	#385×C₆₇	1	2	yes	—
513	C₂²	#392×C₆₇	1	1	yes	characteristic
514	C₂²	#394×C₆₇	1	2	yes	—
515	C₂²	#397×C₆₇	1	1	yes	characteristic
516	C₂²	C₂×#107×C₆₇	1	1	yes	characteristic
517	C₂²	#427×C₆₇	1	1	yes	characteristic
518	C₂²	#428×C₆₇	1	2	yes	—
519	C₂²	#447×C₆₇	1	2	yes	—
520	C₂²	#449×C₆₇	1	2	yes	—
521	C₂²	#451×C₆₇	1	2	yes	—
522	C₂²	#452×C₆₇	1	2	yes	—
523	C₂²	#466×C₆₇	1	1	yes	characteristic
524	C₂²	#466×C₆₇	1	1	yes	characteristic
525	C₂²	#467×C₆₇	1	1	yes	characteristic
526	C₂²	#467×C₆₇	1	1	yes	characteristic
527	C₂²	#468×C₆₇	1	2	yes	—
528	C₂²	#469×C₆₇	1	1	yes	characteristic
529	C₂²	#470×C₆₇	1	1	yes	characteristic
530	C₂²	#480×C₆₇	1	2	yes	—
531	C₂²	#482×C₆₇	1	2	yes	—
532	C₂²	#484×C₆₇	1	2	yes	—
533	C₂²	#485×C₆₇	1	2	yes	—
534	C₄	—	4	2	no	—
535	C₄	—	8	4	no	—
536	C₄	—	8	4	no	—
537	C₄	#386×C₆₇	1	1	yes	characteristic
538	C₄	#388×C₆₇	1	2	yes	—
539	C₄	#390×C₆₇	1	1	yes	characteristic
540	C₄	#393×C₆₇	1	1	yes	characteristic
541	C₄	#396×C₆₇	1	2	yes	—
542	C₄	#399×C₆₇	1	1	yes	characteristic
543	C₂	—	4	4	no	—
544	C₂	C₆₇×#1439	1	1	yes	characteristic
545	C₂	C₆₇×#1808	1	1	yes	characteristic
546	C₂	C₆₇×#1809	1	1	yes	characteristic
547	C₂	C₆₇×#1852	1	2	yes	—
548	C₂	C₆₇×#1854	1	2	yes	—
549	C₂	C₆₇×#1999	1	1	yes	characteristic
550	C₂	C₆₇×#2001	1	1	yes	characteristic
551	C₂	C₆₇×#2033	1	2	yes	—
552	C₂	C₆₇×#2036	1	2	yes	—
553	C₂	C₆₇×#2075	1	1	yes	characteristic
554	C₂	C₆₇×#2076	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₆₇	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₆₇
Frattini, cosocle	C₂³×C₄	C₂³×C₆₇
prime radical	C₂⁵×C₆₇	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₇ ◁ C₂⁴×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#107×C₆₇	C₂	semidirect
4. C₂×#340×C₆₇	C₂	semidirect
5. C₂×#340×C₆₇	C₂	semidirect
16. C₂×C₂²⋊C₈×C₆₇	C₄	semidirect
133. C₂×C₈×C₆₇	C₂²⋊C₄	semidirect
165. C₂³×C₆₇	#107	semidirect
265. #11096	C₆₇	direct (N × H)
278. C₂²×#107	C₂×C₆₇	semidirect
281. C₂×#340	C₂×C₆₇	semidirect
282. C₂×#340	C₂×C₆₇	semidirect
283. C₆₇	#11096	direct (N × H)
294. C₂×C₂²⋊C₈	C₄×C₆₇	semidirect
411. C₂×C₈	C₂²⋊C₄×C₆₇	semidirect
443. C₂³	#107×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#107×C₆₇	2
C₂²×C₂²⋊C₈×C₆₇	2
C₂×#380×C₆₇	2
C₂×#340×C₆₇	2
#11096	67

Subgroups — C67×#11096 #30690347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#11096 #30690347