Subgroups — C₆₇×#17923 #30697174

Order 17152.

626 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3103	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2982	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2981	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#1588	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1583	C₂	1	2	yes	maximal, complemented
6	C₆₇×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₈×SD₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1572	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1491	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1484	C₂	1	1	yes	maximal, characteristic
11	C₆₇×#1453	C₂	1	1	yes	maximal, characteristic, complemented
12	#532×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
14	#481×C₆₇	C₄	1	2	yes	—
15	#475×C₆₇	C₄	1	2	yes	—
16	#460×C₆₇	C₄	1	2	yes	—
17	#448×C₆₇	C₄	1	2	yes	—
18	C₈×Q₈×C₆₇	—	2	2	no	—
19	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
20	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
21	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
22	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
23	#436×C₆₇	C₂²	1	2	yes	—
24	#435×C₆₇	—	2	2	no	—
25	C₈×D₄×C₆₇	C₂²	1	2	yes	—
26	#432×C₆₇	C₂²	1	1	yes	characteristic
27	#431×C₆₇	—	2	2	no	—
28	#431×C₆₇	C₂²	1	1	yes	characteristic
29	#431×C₆₇	C₂²	1	1	yes	characteristic
30	#431×C₆₇	C₂²	1	1	yes	characteristic
31	#408×C₆₇	—	2	2	no	—
32	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
33	#335×C₆₇	C₂²	1	2	yes	—
34	#334×C₆₇	C₂²	1	2	yes	—
35	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
36	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
37	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
38	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
39	#322×C₆₇	C₂²	1	1	yes	characteristic
40	#322×C₆₇	C₂²	1	1	yes	characteristic
41	#322×C₆₇	C₂²	1	1	yes	characteristic
42	C₈²×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#41×C₆₇	—	2	1	no	—
44	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
45	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
46	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
47	C₂×M₁₆×C₆₇	—	2	1	no	—
48	C₂×M₁₆×C₆₇	—	2	2	no	—
49	C₂²×C₈×C₆₇	—	2	2	no	—
50	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
51	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
52	#124×C₆₇	—	2	1	no	—
53	#121×C₆₇	—	2	1	no	—
54	#121×C₆₇	C₂×C₄	1	2	yes	—
55	C₄×Q₈×C₆₇	—	2	1	no	—
56	C₄×Q₈×C₆₇	—	2	1	no	—
57	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
58	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
59	C₄×D₄×C₆₇	—	2	1	no	—
60	C₄×D₄×C₆₇	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₆₇	—	2	1	no	—
64	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
65	#106×C₆₇	C₂×C₄	1	2	yes	—
66	#106×C₆₇	C₂×C₄	1	2	yes	—
67	C₄⋊C₈×C₆₇	—	2	2	no	—
68	C₄⋊C₈×C₆₇	—	2	2	no	—
69	C₄⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
70	C₄⋊C₈×C₆₇	D₄	1	2	yes	—
71	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
72	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
73	#103×C₆₇	C₂×C₄	1	2	yes	—
74	#103×C₆₇	C₂×C₄	1	2	yes	—
75	#102×C₆₇	C₂×C₄	1	2	yes	—
76	#102×C₆₇	C₂×C₄	1	2	yes	—
77	C₂²⋊C₈×C₆₇	—	2	1	no	—
78	C₂²⋊C₈×C₆₇	—	2	1	no	—
79	C₂²⋊C₈×C₆₇	—	2	2	no	—
80	C₂²⋊C₈×C₆₇	—	2	2	no	—
81	C₂²⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
82	C₂²⋊C₈×C₆₇	D₄	1	2	yes	—
83	#97×C₆₇	—	2	1	no	—
84	#97×C₆₇	—	2	1	no	—
85	C₄×C₈×C₆₇	—	2	2	no	—
86	C₄×C₈×C₆₇	—	2	2	no	—
87	C₄×C₈×C₆₇	—	2	1	no	—
88	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	#41×C₆₇	—	8	2	no	—
95	C₂×Q₈×C₆₇	—	2	4	no	—
96	C₂×Q₈×C₆₇	—	2	1	no	—
97	C₂×Q₈×C₆₇	—	2	1	no	—
98	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
99	C₂×D₄×C₆₇	—	2	2	no	—
100	C₂×D₄×C₆₇	—	2	1	no	—
101	C₂×D₄×C₆₇	—	2	1	no	—
102	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₆₇	—	2	1	no	—
104	C₂²×C₄×C₆₇	—	2	1	no	—
105	C₂²×C₄×C₆₇	—	2	2	no	—
106	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
109	SD₁₆×C₆₇	—	2	4	no	—
110	SD₁₆×C₆₇	—	2	4	no	—
111	M₁₆×C₆₇	—	4	2	no	—
112	M₁₆×C₆₇	—	8	2	no	—
113	C₂×C₈×C₆₇	—	2	1	no	—
114	C₂×C₈×C₆₇	—	2	2	no	—
115	C₂×C₈×C₆₇	—	2	2	no	—
116	C₂×C₈×C₆₇	—	2	1	no	—
117	C₂×C₈×C₆₇	—	8	2	no	—
118	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
122	C₄⋊C₄×C₆₇	—	2	2	no	—
123	C₄⋊C₄×C₆₇	—	2	1	no	—
124	C₄⋊C₄×C₆₇	—	2	1	no	—
125	C₄⋊C₄×C₆₇	—	2	2	no	—
126	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
127	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
128	C₂²⋊C₄×C₆₇	—	2	2	no	—
129	C₂²⋊C₄×C₆₇	—	2	2	no	—
130	C₄²×C₆₇	—	2	2	no	—
131	C₄²×C₆₇	—	2	2	no	—
132	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₆₇	#41	1	1	yes	characteristic
135	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
136	C₂³×C₆₇	—	2	2	no	—
137	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
138	Q₈×C₆₇	—	2	4	no	—
139	Q₈×C₆₇	—	2	2	no	—
140	Q₈×C₆₇	—	8	1	no	—
141	Q₈×C₆₇	#131	1	4	yes	—
142	D₄×C₆₇	—	2	2	no	—
143	D₄×C₆₇	—	2	2	no	—
144	D₄×C₆₇	—	8	1	no	—
145	D₄×C₆₇	—	8	1	no	—
146	D₄×C₆₇	—	8	2	no	—
147	C₂×C₄×C₆₇	—	2	4	no	—
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	2	2	no	—
151	C₂×C₄×C₆₇	—	2	2	no	—
152	C₂×C₄×C₆₇	—	2	2	no	—
153	C₂×C₄×C₆₇	—	4	1	no	—
154	C₂×C₄×C₆₇	—	4	2	no	—
155	C₂×C₄×C₆₇	—	4	2	no	—
156	C₂×C₄×C₆₇	—	8	1	no	—
157	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
163	C₈×C₆₇	—	2	2	no	—
164	C₈×C₆₇	—	2	2	no	—
165	C₈×C₆₇	—	2	2	no	—
166	C₈×C₆₇	—	2	2	no	—
167	C₈×C₆₇	—	2	2	no	—
168	C₈×C₆₇	—	4	1	no	—
169	C₈×C₆₇	—	4	2	no	—
170	C₈×C₆₇	—	4	2	no	—
171	C₂²×C₆₇	—	2	1	no	—
172	C₂²×C₆₇	—	2	1	no	—
173	C₂²×C₆₇	—	2	1	no	—
174	C₂²×C₆₇	—	4	2	no	—
175	C₂²×C₆₇	—	4	2	no	—
176	C₂²×C₆₇	—	4	2	no	—
177	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
178	C₄×C₆₇	—	2	4	no	—
179	C₄×C₆₇	—	2	1	no	—
180	C₄×C₆₇	—	2	1	no	—
181	C₄×C₆₇	—	2	1	no	—
182	C₄×C₆₇	—	2	1	no	—
183	C₄×C₆₇	—	4	2	no	—
184	C₄×C₆₇	—	4	2	no	—
185	C₄×C₆₇	C₂×#131	1	2	yes	—
186	C₄×C₆₇	#577	1	2	yes	—
187	#17923	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂×C₆₇	—	4	1	no	—
189	C₂×C₆₇	—	8	2	no	—
190	C₂×C₆₇	#2929	1	1	yes	characteristic
191	C₂×C₆₇	#2949	1	1	yes	characteristic
192	C₂×C₆₇	#2956	1	1	yes	characteristic
193	#3103	C₂×C₆₇	1	1	yes	characteristic
194	#2982	C₂×C₆₇	1	1	yes	characteristic, complemented
195	#2981	C₂×C₆₇	1	1	yes	characteristic
196	#1588	C₂×C₆₇	1	2	yes	complemented
197	#1583	C₂×C₆₇	1	2	yes	complemented
198	SD₁₆⋊C₈	C₂×C₆₇	1	2	yes	complemented
199	C₈×SD₁₆	C₂×C₆₇	1	2	yes	complemented
200	#1572	C₂×C₆₇	1	1	yes	characteristic, complemented
201	#1491	C₂×C₆₇	1	1	yes	characteristic, complemented
202	#1484	C₂×C₆₇	1	1	yes	characteristic
203	#1453	C₂×C₆₇	1	1	yes	characteristic, complemented
204	C₆₇	#17923	1	1	yes	characteristic, direct product factor, Sylow
205	#532	C₂²×C₆₇	1	1	yes	characteristic
206	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
207	#481	C₄×C₆₇	1	2	yes	—
208	#475	C₄×C₆₇	1	2	yes	—
209	#460	C₄×C₆₇	1	2	yes	—
210	#448	C₄×C₆₇	1	2	yes	—
211	C₈×Q₈	—	2	2	no	—
212	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
213	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
214	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
215	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
216	#436	C₂²×C₆₇	1	2	yes	—
217	#435	—	2	2	no	—
218	C₈×D₄	C₂²×C₆₇	1	2	yes	—
219	#432	C₂²×C₆₇	1	1	yes	characteristic
220	#431	—	2	2	no	—
221	#431	C₂²×C₆₇	1	1	yes	characteristic
222	#431	C₂²×C₆₇	1	1	yes	characteristic
223	#431	C₂²×C₆₇	1	1	yes	characteristic
224	#408	—	2	2	no	—
225	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
226	#335	C₂²×C₆₇	1	2	yes	—
227	#334	C₂²×C₆₇	1	2	yes	—
228	Q₈⋊C₈	C₂²×C₆₇	1	2	yes	—
229	Q₈⋊C₈	C₂²×C₆₇	1	2	yes	—
230	D₄⋊C₈	C₂²×C₆₇	1	2	yes	—
231	D₄⋊C₈	C₂²×C₆₇	1	2	yes	—
232	#322	C₂²×C₆₇	1	1	yes	characteristic
233	#322	C₂²×C₆₇	1	1	yes	characteristic
234	#322	C₂²×C₆₇	1	1	yes	characteristic
235	C₈²	C₂²×C₆₇	1	1	yes	characteristic
236	C₂×#41	—	2	1	no	—
237	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
238	C₂×SD₁₆	C₂×C₄×C₆₇	1	2	yes	—
239	C₂×SD₁₆	C₂×C₄×C₆₇	1	2	yes	—
240	C₂×M₁₆	—	2	1	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
244	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
245	#124	—	2	1	no	—
246	#121	—	2	1	no	—
247	#121	C₂×C₄×C₆₇	1	2	yes	—
248	C₄×Q₈	—	2	1	no	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
251	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	C₂³×C₆₇	1	2	yes	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
258	#106	C₂×C₄×C₆₇	1	2	yes	—
259	#106	C₂×C₄×C₆₇	1	2	yes	—
260	C₄⋊C₈	—	2	2	no	—
261	C₄⋊C₈	—	2	2	no	—
262	C₄⋊C₈	C₂×C₄×C₆₇	1	2	yes	—
263	C₄⋊C₈	D₄×C₆₇	1	2	yes	—
264	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
265	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
266	#103	C₂×C₄×C₆₇	1	2	yes	—
267	#103	C₂×C₄×C₆₇	1	2	yes	—
268	#102	C₂×C₄×C₆₇	1	2	yes	—
269	#102	C₂×C₄×C₆₇	1	2	yes	—
270	C₂²⋊C₈	—	2	1	no	—
271	C₂²⋊C₈	—	2	1	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	—	2	2	no	—
274	C₂²⋊C₈	C₂×C₄×C₆₇	1	2	yes	—
275	C₂²⋊C₈	D₄×C₆₇	1	2	yes	—
276	#97	—	2	1	no	—
277	#97	—	2	1	no	—
278	C₄×C₈	—	2	2	no	—
279	C₄×C₈	—	2	2	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
282	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
287	#41	—	8	2	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
301	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
302	SD₁₆	—	2	4	no	—
303	SD₁₆	—	2	4	no	—
304	M₁₆	—	4	2	no	—
305	M₁₆	—	8	2	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	8	2	no	—
311	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
312	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
313	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
314	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
320	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
327	C₄²	#41×C₆₇	1	1	yes	characteristic
328	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
329	C₂³	—	2	2	no	—
330	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
331	Q₈	—	2	4	no	—
332	Q₈	—	2	2	no	—
333	Q₈	—	8	1	no	—
334	Q₈	#131×C₆₇	1	4	yes	—
335	D₄	—	2	2	no	—
336	D₄	—	2	2	no	—
337	D₄	—	8	1	no	—
338	D₄	—	8	1	no	—
339	D₄	—	8	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	1	no	—
350	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
351	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
352	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
353	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
355	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
356	C₈	—	2	2	no	—
357	C₈	—	2	2	no	—
358	C₈	—	2	2	no	—
359	C₈	—	2	2	no	—
360	C₈	—	2	2	no	—
361	C₈	—	4	1	no	—
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
371	C₄	—	2	4	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	C₂×#131×C₆₇	1	2	yes	—
379	C₄	#577×C₆₇	1	2	yes	—
380	C₂	—	4	1	no	—
381	C₂	—	8	2	no	—
382	C₂	C₆₇×#2929	1	1	yes	characteristic
383	C₂	C₆₇×#2949	1	1	yes	characteristic
384	C₂	C₆₇×#2956	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	#532×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ #431×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2982	C₂	semidirect
4. C₆₇×#1588	C₂	semidirect
5. C₆₇×#1583	C₂	semidirect
6. C₆₇×SD₁₆⋊C₈	C₂	semidirect
7. C₈×SD₁₆×C₆₇	C₂	semidirect
8. C₆₇×#1572	C₂	semidirect
9. C₆₇×#1491	C₂	semidirect
11. C₆₇×#1453	C₂	semidirect
187. #17923	C₆₇	direct (N × H)
194. #2982	C₂×C₆₇	semidirect
196. #1588	C₂×C₆₇	semidirect
197. #1583	C₂×C₆₇	semidirect
198. SD₁₆⋊C₈	C₂×C₆₇	semidirect
199. C₈×SD₁₆	C₂×C₆₇	semidirect
200. #1572	C₂×C₆₇	semidirect
201. #1491	C₂×C₆₇	semidirect
203. #1453	C₂×C₆₇	semidirect
204. C₆₇	#17923	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×#3103	2
C₆₇×#2982	2
C₆₇×#2981	2
C₆₇×#1588	2
C₆₇×#1583	2
C₆₇×SD₁₆⋊C₈	2
C₈×SD₁₆×C₆₇	2
C₆₇×#1572	2
C₆₇×#1491	2
C₆₇×#1484	2
C₆₇×#1453	2
#17923	67

Subgroups — C67×#17923 #30697174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#17923 #30697174