Subgroups — C₆₇×#17974 #30697225

Order 17152.

592 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3168	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2993	C₂	1	2	yes	maximal, complemented
3	C₆₇×#1594	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1590	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1580	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1579	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×SD₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1566	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1495	C₂	1	2	yes	maximal, complemented
11	C₆₇×#1450	C₂	1	1	yes	maximal, characteristic, complemented
12	#529×C₆₇	C₂²	1	2	yes	—
13	#499×C₆₇	C₄	1	1	yes	characteristic
14	#495×C₆₇	C₄	1	1	yes	characteristic
15	#488×C₆₇	C₄	1	2	yes	—
16	#467×C₆₇	C₄	1	1	yes	characteristic
17	#466×C₆₇	C₄	1	1	yes	characteristic
18	#465×C₆₇	C₄	1	2	yes	—
19	#446×C₆₇	C₂²	1	2	yes	—
20	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
21	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
22	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
23	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
24	#436×C₆₇	—	2	2	no	—
25	#436×C₆₇	C₂²	1	2	yes	—
26	#435×C₆₇	—	2	2	no	—
27	C₈×D₄×C₆₇	C₂²	1	2	yes	—
28	#433×C₆₇	—	2	2	no	—
29	#431×C₆₇	C₂²	1	1	yes	characteristic
30	#431×C₆₇	C₂²	1	1	yes	characteristic
31	#424×C₆₇	—	2	2	no	—
32	#423×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
34	#334×C₆₇	C₂²	1	2	yes	—
35	#334×C₆₇	C₂²	1	1	yes	characteristic
36	#334×C₆₇	C₂²	1	1	yes	characteristic
37	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
38	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
39	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
40	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
41	#322×C₆₇	C₂²	1	1	yes	characteristic
42	#322×C₆₇	C₂²	1	1	yes	characteristic
43	C₈²×C₆₇	C₂²	1	1	yes	characteristic
44	C₈²×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
46	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
47	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
48	C₂×M₁₆×C₆₇	—	2	2	no	—
49	C₂×M₁₆×C₆₇	—	2	2	no	—
50	C₂²×C₈×C₆₇	—	2	2	no	—
51	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
53	#126×C₆₇	—	2	2	no	—
54	#125×C₆₇	C₂×C₄	1	2	yes	—
55	#124×C₆₇	C₂×C₄	1	2	yes	—
56	#123×C₆₇	—	2	2	no	—
57	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
58	#121×C₆₇	C₂×C₄	1	2	yes	—
59	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
60	C₄×D₄×C₆₇	—	2	2	no	—
61	C₄×D₄×C₆₇	C₂³	1	2	yes	—
62	#117×C₆₇	—	2	2	no	—
63	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
64	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
65	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
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	—	2	2	no	—
70	C₄⋊C₈×C₆₇	—	2	1	no	—
71	C₄⋊C₈×C₆₇	D₄	1	2	yes	—
72	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
73	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
74	#103×C₆₇	C₂×C₄	1	2	yes	—
75	#103×C₆₇	C₂×C₄	1	2	yes	—
76	#102×C₆₇	C₂×C₄	1	2	yes	—
77	#102×C₆₇	C₂×C₄	1	2	yes	—
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	D₄	1	2	yes	—
82	#97×C₆₇	—	2	2	no	—
83	C₄×C₈×C₆₇	—	2	2	no	—
84	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
85	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
86	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
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	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
93	C₂×D₄×C₆₇	—	2	2	no	—
94	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₆₇	—	2	2	no	—
96	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
99	Q₁₆×C₆₇	—	2	2	no	—
100	SD₁₆×C₆₇	—	2	4	no	—
101	D₈×C₆₇	—	2	2	no	—
102	M₁₆×C₆₇	—	8	2	no	—
103	M₁₆×C₆₇	—	8	2	no	—
104	C₂×C₈×C₆₇	—	2	2	no	—
105	C₂×C₈×C₆₇	—	2	2	no	—
106	C₂×C₈×C₆₇	—	2	2	no	—
107	C₂×C₈×C₆₇	—	2	2	no	—
108	C₂×C₈×C₆₇	—	2	1	no	—
109	C₂×C₈×C₆₇	—	2	1	no	—
110	C₂×C₈×C₆₇	—	8	2	no	—
111	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
117	C₄⋊C₄×C₆₇	—	2	2	no	—
118	C₄⋊C₄×C₆₇	—	2	2	no	—
119	C₄⋊C₄×C₆₇	—	2	2	no	—
120	C₄⋊C₄×C₆₇	—	2	2	no	—
121	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
122	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
123	C₂²⋊C₄×C₆₇	—	2	2	no	—
124	C₂²⋊C₄×C₆₇	—	2	2	no	—
125	C₂²⋊C₄×C₆₇	—	2	2	no	—
126	C₂²⋊C₄×C₆₇	—	2	2	no	—
127	C₂²⋊C₄×C₆₇	—	2	2	no	—
128	C₄²×C₆₇	—	2	2	no	—
129	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₆₇	#41	1	1	yes	characteristic
132	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
133	C₂³×C₆₇	—	2	2	no	—
134	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
135	Q₈×C₆₇	—	2	2	no	—
136	Q₈×C₆₇	—	2	2	no	—
137	D₄×C₆₇	—	2	2	no	—
138	D₄×C₆₇	—	2	2	no	—
139	D₄×C₆₇	—	8	2	no	—
140	C₂×C₄×C₆₇	—	2	1	no	—
141	C₂×C₄×C₆₇	—	2	1	no	—
142	C₂×C₄×C₆₇	—	2	2	no	—
143	C₂×C₄×C₆₇	—	2	2	no	—
144	C₂×C₄×C₆₇	—	2	2	no	—
145	C₂×C₄×C₆₇	—	2	2	no	—
146	C₂×C₄×C₆₇	—	4	1	no	—
147	C₂×C₄×C₆₇	—	4	2	no	—
148	C₂×C₄×C₆₇	—	4	2	no	—
149	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
155	C₈×C₆₇	—	2	1	no	—
156	C₈×C₆₇	—	2	1	no	—
157	C₈×C₆₇	—	2	2	no	—
158	C₈×C₆₇	—	2	2	no	—
159	C₈×C₆₇	—	4	1	no	—
160	C₈×C₆₇	—	4	1	no	—
161	C₈×C₆₇	—	4	2	no	—
162	C₈×C₆₇	—	4	2	no	—
163	C₈×C₆₇	#131	1	2	yes	—
164	C₈×C₆₇	#131	1	2	yes	—
165	C₂²×C₆₇	—	2	1	no	—
166	C₂²×C₆₇	—	2	1	no	—
167	C₂²×C₆₇	—	2	1	no	—
168	C₂²×C₆₇	—	4	2	no	—
169	C₂²×C₆₇	—	4	2	no	—
170	C₂²×C₆₇	—	4	2	no	—
171	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
172	C₄×C₆₇	—	2	1	no	—
173	C₄×C₆₇	—	2	1	no	—
174	C₄×C₆₇	—	2	1	no	—
175	C₄×C₆₇	—	2	1	no	—
176	C₄×C₆₇	—	4	2	no	—
177	C₄×C₆₇	—	4	2	no	—
178	C₄×C₆₇	—	4	2	no	—
179	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
180	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
181	C₄×C₆₇	#577	1	2	yes	—
182	#17974	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂×C₆₇	—	4	1	no	—
184	C₂×C₆₇	—	8	2	no	—
185	C₂×C₆₇	#2931	1	1	yes	characteristic
186	C₂×C₆₇	#2952	1	1	yes	characteristic
187	C₂×C₆₇	#2957	1	1	yes	characteristic
188	#3168	C₂×C₆₇	1	1	yes	characteristic
189	#2993	C₂×C₆₇	1	2	yes	complemented
190	#1594	C₂×C₆₇	1	1	yes	characteristic, complemented
191	#1593	C₂×C₆₇	1	1	yes	characteristic, complemented
192	#1590	C₂×C₆₇	1	2	yes	complemented
193	#1580	C₂×C₆₇	1	1	yes	characteristic, complemented
194	#1579	C₂×C₆₇	1	1	yes	characteristic, complemented
195	C₈×SD₁₆	C₂×C₆₇	1	2	yes	complemented
196	#1566	C₂×C₆₇	1	1	yes	characteristic, complemented
197	#1495	C₂×C₆₇	1	2	yes	complemented
198	#1450	C₂×C₆₇	1	1	yes	characteristic, complemented
199	C₆₇	#17974	1	1	yes	characteristic, direct product factor, Sylow
200	#529	C₂²×C₆₇	1	2	yes	—
201	#499	C₄×C₆₇	1	1	yes	characteristic
202	#495	C₄×C₆₇	1	1	yes	characteristic
203	#488	C₄×C₆₇	1	2	yes	—
204	#467	C₄×C₆₇	1	1	yes	characteristic
205	#466	C₄×C₆₇	1	1	yes	characteristic
206	#465	C₄×C₆₇	1	2	yes	—
207	#446	C₂²×C₆₇	1	2	yes	—
208	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
209	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
210	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
211	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
212	#436	—	2	2	no	—
213	#436	C₂²×C₆₇	1	2	yes	—
214	#435	—	2	2	no	—
215	C₈×D₄	C₂²×C₆₇	1	2	yes	—
216	#433	—	2	2	no	—
217	#431	C₂²×C₆₇	1	1	yes	characteristic
218	#431	C₂²×C₆₇	1	1	yes	characteristic
219	#424	—	2	2	no	—
220	#423	C₂²×C₆₇	1	2	yes	—
221	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
222	#334	C₂²×C₆₇	1	2	yes	—
223	#334	C₂²×C₆₇	1	1	yes	characteristic
224	#334	C₂²×C₆₇	1	1	yes	characteristic
225	Q₈⋊C₈	C₂²×C₆₇	1	2	yes	—
226	Q₈⋊C₈	C₂²×C₆₇	1	2	yes	—
227	D₄⋊C₈	C₂²×C₆₇	1	2	yes	—
228	D₄⋊C₈	C₂²×C₆₇	1	2	yes	—
229	#322	C₂²×C₆₇	1	1	yes	characteristic
230	#322	C₂²×C₆₇	1	1	yes	characteristic
231	C₈²	C₂²×C₆₇	1	1	yes	characteristic
232	C₈²	C₂²×C₆₇	1	1	yes	characteristic
233	C₂×Q₁₆	C₂×C₄×C₆₇	1	1	yes	characteristic
234	C₂×SD₁₆	C₂×C₄×C₆₇	1	2	yes	—
235	C₂×D₈	C₂×C₄×C₆₇	1	1	yes	characteristic
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
240	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
241	#126	—	2	2	no	—
242	#125	C₂×C₄×C₆₇	1	2	yes	—
243	#124	C₂×C₄×C₆₇	1	2	yes	—
244	#123	—	2	2	no	—
245	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
246	#121	C₂×C₄×C₆₇	1	2	yes	—
247	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
248	C₄×D₄	—	2	2	no	—
249	C₄×D₄	C₂³×C₆₇	1	2	yes	—
250	#117	—	2	2	no	—
251	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
252	#107	C₂×C₄×C₆₇	1	1	yes	characteristic
253	#107	C₂×C₄×C₆₇	1	1	yes	characteristic
254	#106	C₂×C₄×C₆₇	1	2	yes	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	D₄×C₆₇	1	2	yes	—
260	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
261	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
262	#103	C₂×C₄×C₆₇	1	2	yes	—
263	#103	C₂×C₄×C₆₇	1	2	yes	—
264	#102	C₂×C₄×C₆₇	1	2	yes	—
265	#102	C₂×C₄×C₆₇	1	2	yes	—
266	C₂²⋊C₈	—	2	1	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	—	2	2	no	—
269	C₂²⋊C₈	D₄×C₆₇	1	2	yes	—
270	#97	—	2	2	no	—
271	C₄×C₈	—	2	2	no	—
272	C₄×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
273	C₄×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
275	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
276	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
280	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
286	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
287	Q₁₆	—	2	2	no	—
288	SD₁₆	—	2	4	no	—
289	D₈	—	2	2	no	—
290	M₁₆	—	8	2	no	—
291	M₁₆	—	8	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	8	2	no	—
299	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
300	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
302	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
304	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
310	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
318	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
319	C₄²	#41×C₆₇	1	1	yes	characteristic
320	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
321	C₂³	—	2	2	no	—
322	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	Q₈	—	2	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	8	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
338	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
339	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
340	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
342	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
343	C₈	—	2	1	no	—
344	C₈	—	2	1	no	—
345	C₈	—	2	2	no	—
346	C₈	—	2	2	no	—
347	C₈	—	4	1	no	—
348	C₈	—	4	1	no	—
349	C₈	—	4	2	no	—
350	C₈	—	4	2	no	—
351	C₈	#131×C₆₇	1	2	yes	—
352	C₈	#131×C₆₇	1	2	yes	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	C₂×#131×C₆₇	1	1	yes	characteristic
368	C₄	C₂×#131×C₆₇	1	1	yes	characteristic
369	C₄	#577×C₆₇	1	2	yes	—
370	C₂	—	4	1	no	—
371	C₂	—	8	2	no	—
372	C₂	C₆₇×#2931	1	1	yes	characteristic
373	C₂	C₆₇×#2952	1	1	yes	characteristic
374	C₂	C₆₇×#2957	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	#466×C₆₇	C₄
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×#2993	C₂	semidirect
3. C₆₇×#1594	C₂	semidirect
4. C₆₇×#1593	C₂	semidirect
5. C₆₇×#1590	C₂	semidirect
6. C₆₇×#1580	C₂	semidirect
7. C₆₇×#1579	C₂	semidirect
8. C₈×SD₁₆×C₆₇	C₂	semidirect
9. C₆₇×#1566	C₂	semidirect
10. C₆₇×#1495	C₂	semidirect
11. C₆₇×#1450	C₂	semidirect
182. #17974	C₆₇	direct (N × H)
189. #2993	C₂×C₆₇	semidirect
190. #1594	C₂×C₆₇	semidirect
191. #1593	C₂×C₆₇	semidirect
192. #1590	C₂×C₆₇	semidirect
193. #1580	C₂×C₆₇	semidirect
194. #1579	C₂×C₆₇	semidirect
195. C₈×SD₁₆	C₂×C₆₇	semidirect
196. #1566	C₂×C₆₇	semidirect
197. #1495	C₂×C₆₇	semidirect
198. #1450	C₂×C₆₇	semidirect
199. C₆₇	#17974	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×#3168	2
C₆₇×#2993	2
C₆₇×#1594	2
C₆₇×#1593	2
C₆₇×#1590	2
C₆₇×#1580	2
C₆₇×#1579	2
C₈×SD₁₆×C₆₇	2
C₆₇×#1566	2
C₆₇×#1495	2
C₆₇×#1450	2
#17974	67

Subgroups — C67×#17974 #30697225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#17974 #30697225