Subgroups — C₆₇×#17916 #30697167

Order 17152.

624 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	C₆₇×#3107	C₂	1	1	yes	maximal, characteristic
2	C₈×#41×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1584	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1582	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1579	C₂	1	2	yes	maximal, complemented
7	C₆₇×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1574	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1489	C₂	1	1	yes	maximal, characteristic
10	C₆₇×#1485	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	#533×C₆₇	C₂²	1	1	yes	characteristic
13	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
14	#485×C₆₇	C₄	1	2	yes	—
15	#475×C₆₇	C₄	1	1	yes	characteristic
16	#474×C₆₇	C₄	1	1	yes	characteristic
17	#462×C₆₇	C₄	1	1	yes	characteristic
18	#461×C₆₇	C₄	1	1	yes	characteristic
19	#452×C₆₇	C₄	1	2	yes	—
20	#446×C₆₇	—	2	1	no	—
21	#446×C₆₇	C₂²	1	2	yes	—
22	C₈×Q₈×C₆₇	—	2	1	no	—
23	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
24	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
27	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
28	C₈×D₄×C₆₇	—	2	1	no	—
29	C₈×D₄×C₆₇	—	2	1	no	—
30	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
32	#431×C₆₇	—	2	1	no	—
33	#431×C₆₇	C₂²	1	1	yes	characteristic
34	#431×C₆₇	C₂²	1	1	yes	characteristic
35	#424×C₆₇	—	2	1	no	—
36	#423×C₆₇	C₂²	1	1	yes	characteristic
37	#405×C₆₇	—	2	1	no	—
38	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₆₇	—	2	1	no	—
40	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
41	#335×C₆₇	C₂²	1	2	yes	—
42	#334×C₆₇	C₂²	1	2	yes	—
43	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
44	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
45	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
46	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
47	#322×C₆₇	C₂²	1	2	yes	—
48	#322×C₆₇	C₂²	1	2	yes	—
49	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
50	C₂×Q₁₆×C₆₇	C₂×C₄	1	2	yes	—
51	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
52	C₂×M₁₆×C₆₇	—	2	1	no	—
53	C₂×M₁₆×C₆₇	—	2	1	no	—
54	C₂²×C₈×C₆₇	—	2	1	no	—
55	C₂²×C₈×C₆₇	—	2	1	no	—
56	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
58	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
59	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
60	#125×C₆₇	—	2	1	no	—
61	C₂²⋊Q₈×C₆₇	—	2	1	no	—
62	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
63	C₄×Q₈×C₆₇	—	2	1	no	—
64	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
65	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
66	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
67	C₄×D₄×C₆₇	—	2	1	no	—
68	C₄×D₄×C₆₇	—	2	1	no	—
69	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
71	#117×C₆₇	—	2	1	no	—
72	#117×C₆₇	—	2	1	no	—
73	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₆₇	—	2	1	no	—
75	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
76	#107×C₆₇	C₂×C₄	1	2	yes	—
77	#106×C₆₇	C₂×C₄	1	2	yes	—
78	C₄⋊C₈×C₆₇	—	2	2	no	—
79	C₄⋊C₈×C₆₇	—	2	2	no	—
80	C₄⋊C₈×C₆₇	—	2	1	no	—
81	C₄⋊C₈×C₆₇	—	2	1	no	—
82	C₄⋊C₈×C₆₇	—	2	1	no	—
83	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
84	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
85	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
86	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
88	#103×C₆₇	C₂×C₄	1	2	yes	—
89	#103×C₆₇	C₂×C₄	1	2	yes	—
90	#103×C₆₇	C₂×C₄	1	2	yes	—
91	#102×C₆₇	C₂×C₄	1	2	yes	—
92	C₂²⋊C₈×C₆₇	—	2	1	no	—
93	C₂²⋊C₈×C₆₇	—	2	1	no	—
94	C₂²⋊C₈×C₆₇	—	2	1	no	—
95	C₂²⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
96	#97×C₆₇	—	2	2	no	—
97	#97×C₆₇	—	2	1	no	—
98	C₄×C₈×C₆₇	—	2	1	no	—
99	C₄×C₈×C₆₇	—	2	1	no	—
100	C₄×C₈×C₆₇	—	2	2	no	—
101	C₄×C₈×C₆₇	—	2	1	no	—
102	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
103	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
104	C₄×C₈×C₆₇	C₂³	1	2	yes	—
105	C₄×C₈×C₆₇	C₂³	1	2	yes	—
106	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
108	#41×C₆₇	—	2	2	no	—
109	#41×C₆₇	—	2	2	no	—
110	C₂×Q₈×C₆₇	—	2	1	no	—
111	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
112	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₄×C₆₇	—	2	1	no	—
114	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₇	—	2	1	no	—
116	C₂²×C₄×C₆₇	—	2	1	no	—
117	C₂²×C₄×C₆₇	—	2	1	no	—
118	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
121	Q₁₆×C₆₇	—	2	4	no	—
122	SD₁₆×C₆₇	—	2	4	no	—
123	M₁₆×C₆₇	—	4	2	no	—
124	M₁₆×C₆₇	—	4	2	no	—
125	C₂×C₈×C₆₇	—	2	2	no	—
126	C₂×C₈×C₆₇	—	2	2	no	—
127	C₂×C₈×C₆₇	—	2	1	no	—
128	C₂×C₈×C₆₇	—	2	1	no	—
129	C₂×C₈×C₆₇	—	2	2	no	—
130	C₂×C₈×C₆₇	—	4	1	no	—
131	C₂×C₈×C₆₇	—	4	2	no	—
132	C₂×C₈×C₆₇	—	4	2	no	—
133	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
139	C₄⋊C₄×C₆₇	—	2	1	no	—
140	C₄⋊C₄×C₆₇	—	2	1	no	—
141	C₄⋊C₄×C₆₇	—	2	1	no	—
142	C₄⋊C₄×C₆₇	—	2	1	no	—
143	C₄⋊C₄×C₆₇	—	2	2	no	—
144	C₄⋊C₄×C₆₇	—	2	1	no	—
145	C₄⋊C₄×C₆₇	—	2	2	no	—
146	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
147	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²⋊C₄×C₆₇	—	2	2	no	—
150	C₂²⋊C₄×C₆₇	—	2	1	no	—
151	C₂²⋊C₄×C₆₇	—	2	1	no	—
152	C₂²⋊C₄×C₆₇	—	2	1	no	—
153	C₄²×C₆₇	—	2	1	no	—
154	C₄²×C₆₇	—	2	1	no	—
155	C₄²×C₆₇	—	2	1	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	—	2	1	no	—
162	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
163	Q₈×C₆₇	—	2	1	no	—
164	Q₈×C₆₇	—	2	2	no	—
165	Q₈×C₆₇	—	2	2	no	—
166	Q₈×C₆₇	—	4	2	no	—
167	Q₈×C₆₇	#131	1	2	yes	—
168	D₄×C₆₇	—	2	4	no	—
169	D₄×C₆₇	—	2	1	no	—
170	D₄×C₆₇	#131	1	2	yes	—
171	C₂×C₄×C₆₇	—	2	4	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	—	2	1	no	—
177	C₂×C₄×C₆₇	—	2	2	no	—
178	C₂×C₄×C₆₇	—	2	1	no	—
179	C₂×C₄×C₆₇	—	2	1	no	—
180	C₂×C₄×C₆₇	—	2	2	no	—
181	C₂×C₄×C₆₇	—	2	2	no	—
182	C₂×C₄×C₆₇	—	4	1	no	—
183	C₂×C₄×C₆₇	—	4	1	no	—
184	C₂×C₄×C₆₇	—	4	2	no	—
185	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
191	C₈×C₆₇	—	2	2	no	—
192	C₈×C₆₇	—	2	2	no	—
193	C₈×C₆₇	—	2	1	no	—
194	C₈×C₆₇	—	2	1	no	—
195	C₈×C₆₇	—	2	1	no	—
196	C₈×C₆₇	—	4	2	no	—
197	C₈×C₆₇	—	4	1	no	—
198	C₈×C₆₇	—	4	1	no	—
199	C₈×C₆₇	—	4	2	no	—
200	C₈×C₆₇	#137	1	2	yes	—
201	C₂²×C₆₇	—	2	1	no	—
202	C₂²×C₆₇	—	2	2	no	—
203	C₂²×C₆₇	—	2	1	no	—
204	C₂²×C₆₇	—	2	1	no	—
205	C₂²×C₆₇	—	4	1	no	—
206	C₂²×C₆₇	—	4	1	no	—
207	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
208	C₄×C₆₇	—	2	1	no	—
209	C₄×C₆₇	—	2	2	no	—
210	C₄×C₆₇	—	2	1	no	—
211	C₄×C₆₇	—	2	1	no	—
212	C₄×C₆₇	—	4	2	no	—
213	C₄×C₆₇	—	4	1	no	—
214	C₄×C₆₇	—	4	1	no	—
215	C₄×C₆₇	—	4	2	no	—
216	C₄×C₆₇	#444	1	2	yes	—
217	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
218	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
219	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
220	C₄×C₆₇	#575	1	1	yes	characteristic
221	#17916	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂×C₆₇	—	4	1	no	—
223	C₂×C₆₇	—	4	2	no	—
224	C₂×C₆₇	#2929	1	1	yes	characteristic
225	C₂×C₆₇	C₄×#137	1	1	yes	characteristic
226	C₂×C₆₇	C₂×#444	1	1	yes	characteristic
227	#3107	C₂×C₆₇	1	1	yes	characteristic
228	C₈×#41	C₂×C₆₇	1	1	yes	characteristic
229	#2960	C₂×C₆₇	1	1	yes	characteristic, complemented
230	#1584	C₂×C₆₇	1	2	yes	complemented
231	#1582	C₂×C₆₇	1	2	yes	complemented
232	#1579	C₂×C₆₇	1	2	yes	complemented
233	SD₁₆⋊C₈	C₂×C₆₇	1	2	yes	complemented
234	#1574	C₂×C₆₇	1	1	yes	characteristic, complemented
235	#1489	C₂×C₆₇	1	1	yes	characteristic
236	#1485	C₂×C₆₇	1	1	yes	characteristic, complemented
237	#1451	C₂×C₆₇	1	1	yes	characteristic, complemented
238	C₆₇	#17916	1	1	yes	characteristic, direct product factor, Sylow
239	#533	C₂²×C₆₇	1	1	yes	characteristic
240	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
241	#485	C₄×C₆₇	1	2	yes	—
242	#475	C₄×C₆₇	1	1	yes	characteristic
243	#474	C₄×C₆₇	1	1	yes	characteristic
244	#462	C₄×C₆₇	1	1	yes	characteristic
245	#461	C₄×C₆₇	1	1	yes	characteristic
246	#452	C₄×C₆₇	1	2	yes	—
247	#446	—	2	1	no	—
248	#446	C₂²×C₆₇	1	2	yes	—
249	C₈×Q₈	—	2	1	no	—
250	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
251	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
252	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
253	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
254	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
255	C₈×D₄	—	2	1	no	—
256	C₈×D₄	—	2	1	no	—
257	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
258	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
259	#431	—	2	1	no	—
260	#431	C₂²×C₆₇	1	1	yes	characteristic
261	#431	C₂²×C₆₇	1	1	yes	characteristic
262	#424	—	2	1	no	—
263	#423	C₂²×C₆₇	1	1	yes	characteristic
264	#405	—	2	1	no	—
265	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
266	C₂×C₄×C₈	—	2	1	no	—
267	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
268	#335	C₂²×C₆₇	1	2	yes	—
269	#334	C₂²×C₆₇	1	2	yes	—
270	Q₈⋊C₈	C₂²×C₆₇	1	2	yes	—
271	Q₈⋊C₈	C₂²×C₆₇	1	2	yes	—
272	Q₈⋊C₈	C₂²×C₆₇	1	2	yes	—
273	D₄⋊C₈	C₂²×C₆₇	1	2	yes	—
274	#322	C₂²×C₆₇	1	2	yes	—
275	#322	C₂²×C₆₇	1	2	yes	—
276	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
277	C₂×Q₁₆	C₂×C₄×C₆₇	1	2	yes	—
278	C₂×SD₁₆	C₂×C₄×C₆₇	1	2	yes	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
284	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
285	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
286	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
287	#125	—	2	1	no	—
288	C₂²⋊Q₈	—	2	1	no	—
289	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
292	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
293	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
297	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
298	#117	—	2	1	no	—
299	#117	—	2	1	no	—
300	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
303	#107	C₂×C₄×C₆₇	1	2	yes	—
304	#106	C₂×C₄×C₆₇	1	2	yes	—
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	2	1	no	—
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
311	C₄⋊C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
312	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
313	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
314	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
315	#103	C₂×C₄×C₆₇	1	2	yes	—
316	#103	C₂×C₄×C₆₇	1	2	yes	—
317	#103	C₂×C₄×C₆₇	1	2	yes	—
318	#102	C₂×C₄×C₆₇	1	2	yes	—
319	C₂²⋊C₈	—	2	1	no	—
320	C₂²⋊C₈	—	2	1	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	C₂×C₄×C₆₇	1	2	yes	—
323	#97	—	2	2	no	—
324	#97	—	2	1	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	—	2	1	no	—
327	C₄×C₈	—	2	2	no	—
328	C₄×C₈	—	2	1	no	—
329	C₄×C₈	D₄×C₆₇	1	1	yes	characteristic
330	C₄×C₈	D₄×C₆₇	1	1	yes	characteristic
331	C₄×C₈	C₂³×C₆₇	1	2	yes	—
332	C₄×C₈	C₂³×C₆₇	1	2	yes	—
333	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
334	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
335	#41	—	2	2	no	—
336	#41	—	2	2	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
339	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
347	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
348	Q₁₆	—	2	4	no	—
349	SD₁₆	—	2	4	no	—
350	M₁₆	—	4	2	no	—
351	M₁₆	—	4	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	4	2	no	—
359	C₂×C₈	—	4	2	no	—
360	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
361	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
363	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
364	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
365	C₂×C₈	C₂×D₄×C₆₇	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	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
374	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
375	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	2	no	—
384	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
385	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
386	C₄²	#41×C₆₇	1	1	yes	characteristic
387	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
388	C₂³	—	2	1	no	—
389	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
390	Q₈	—	2	1	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	#131×C₆₇	1	2	yes	—
395	D₄	—	2	4	no	—
396	D₄	—	2	1	no	—
397	D₄	#131×C₆₇	1	2	yes	—
398	C₂×C₄	—	2	4	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	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
413	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
414	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
415	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	2	no	—
427	C₈	#137×C₆₇	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	2	no	—
443	C₄	#444×C₆₇	1	2	yes	—
444	C₄	C₂×#131×C₆₇	1	1	yes	characteristic
445	C₄	C₂×#131×C₆₇	1	1	yes	characteristic
446	C₄	C₂×#137×C₆₇	1	1	yes	characteristic
447	C₄	#575×C₆₇	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	4	2	no	—
450	C₂	C₆₇×#2929	1	1	yes	characteristic
451	C₂	C₄×#137×C₆₇	1	1	yes	characteristic
452	C₂	C₂×#444×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₄²	C₂⁴×C₆₇
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#41×C₆₇	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂×C₄×C₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₆₇×#2960	C₂	semidirect
4. C₆₇×#1584	C₂	semidirect
5. C₆₇×#1582	C₂	semidirect
6. C₆₇×#1579	C₂	semidirect
7. C₆₇×SD₁₆⋊C₈	C₂	semidirect
8. C₆₇×#1574	C₂	semidirect
10. C₆₇×#1485	C₂	semidirect
11. C₆₇×#1451	C₂	semidirect
221. #17916	C₆₇	direct (N × H)
229. #2960	C₂×C₆₇	semidirect
230. #1584	C₂×C₆₇	semidirect
231. #1582	C₂×C₆₇	semidirect
232. #1579	C₂×C₆₇	semidirect
233. SD₁₆⋊C₈	C₂×C₆₇	semidirect
234. #1574	C₂×C₆₇	semidirect
236. #1485	C₂×C₆₇	semidirect
237. #1451	C₂×C₆₇	semidirect
238. C₆₇	#17916	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3107	2
C₈×#41×C₆₇	2
C₆₇×#2960	2
C₆₇×#1584	2
C₆₇×#1582	2
C₆₇×#1579	2
C₆₇×SD₁₆⋊C₈	2
C₆₇×#1574	2
C₆₇×#1489	2
C₆₇×#1485	2
C₆₇×#1451	2
#17916	67

Subgroups — C67×#17916 #30697167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#17916 #30697167