Subgroups — C₆₇×#60688 #30739939

Order 17152.

2010 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3444	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3181	C₂	1	8	yes	maximal, complemented
3	C₆₇×#3180	C₂	1	8	yes	maximal, complemented
4	C₆₇×#3162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3135	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3050	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2943	C₂	1	4	yes	maximal, complemented
9	C₂²×#97×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#135×C₆₇	C₂²	1	4	yes	—
11	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
12	#533×C₆₇	C₂²	1	4	yes	—
13	#533×C₆₇	C₂²	1	2	yes	—
14	#532×C₆₇	C₂²	1	2	yes	—
15	#532×C₆₇	C₂²	1	4	yes	—
16	#529×C₆₇	—	2	4	no	—
17	#529×C₆₇	—	2	4	no	—
18	#529×C₆₇	C₂²	1	8	yes	—
19	#525×C₆₇	—	2	4	no	—
20	#525×C₆₇	C₂²	1	4	yes	—
21	C₄×#41×C₆₇	—	2	4	no	—
22	C₄×#41×C₆₇	C₂²	1	4	yes	—
23	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
24	#501×C₆₇	C₂²	1	8	yes	complemented
25	#497×C₆₇	C₂²	1	4	yes	complemented
26	#496×C₆₇	C₂²	1	4	yes	complemented
27	#491×C₆₇	C₂²	1	4	yes	complemented
28	#490×C₆₇	C₂²	1	4	yes	complemented
29	#489×C₆₇	C₂²	1	8	yes	complemented
30	#467×C₆₇	C₂²	1	8	yes	—
31	#466×C₆₇	C₂²	1	8	yes	—
32	#465×C₆₇	C₂²	1	16	yes	—
33	#442×C₆₇	C₂²	1	8	yes	complemented
34	#441×C₆₇	C₂²	1	8	yes	complemented
35	#440×C₆₇	C₂²	1	16	yes	complemented
36	#427×C₆₇	C₂²	1	4	yes	—
37	#416×C₆₇	C₂²	1	8	yes	—
38	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#97×C₆₇	C₂²	1	8	yes	—
41	C₂×#97×C₆₇	C₂²	1	2	yes	—
42	C₂×#41×C₆₇	—	2	4	no	—
43	C₂×#41×C₆₇	C₂³	1	4	yes	—
44	C₂³×C₄×C₆₇	D₄	1	2	yes	—
45	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
46	#135×C₆₇	—	2	16	no	—
47	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
48	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
49	C₂×D₈×C₆₇	C₂³	1	4	yes	—
50	C₂²×C₈×C₆₇	—	2	8	no	—
51	C₂²×C₈×C₆₇	C₂³	1	8	yes	—
52	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
53	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
56	#127×C₆₇	C₂³	1	2	yes	—
57	#126×C₆₇	—	2	8	no	—
58	#125×C₆₇	—	2	4	no	—
59	#125×C₆₇	C₂³	1	4	yes	—
60	#124×C₆₇	—	2	4	no	—
61	#124×C₆₇	C₂³	1	4	yes	—
62	#123×C₆₇	—	2	8	no	—
63	#123×C₆₇	—	2	4	no	—
64	C₂²⋊Q₈×C₆₇	—	2	4	no	—
65	C₂²⋊Q₈×C₆₇	—	2	4	no	—
66	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
67	#121×C₆₇	—	2	4	no	—
68	#121×C₆₇	—	2	4	no	—
69	#121×C₆₇	C₂³	1	8	yes	—
70	#120×C₆₇	—	2	4	no	—
71	C₄×Q₈×C₆₇	—	2	4	no	—
72	C₄×Q₈×C₆₇	—	2	4	no	—
73	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
74	C₄×D₄×C₆₇	—	2	8	no	—
75	C₄×D₄×C₆₇	—	2	8	no	—
76	C₄×D₄×C₆₇	—	2	8	no	—
77	C₄×D₄×C₆₇	—	2	4	no	—
78	C₄×D₄×C₆₇	—	2	4	no	—
79	C₄×D₄×C₆₇	C₂³	1	8	yes	—
80	#117×C₆₇	—	2	4	no	—
81	#117×C₆₇	—	2	8	no	—
82	#117×C₆₇	—	2	4	no	—
83	#117×C₆₇	C₂³	1	4	yes	—
84	C₂×C₄²×C₆₇	—	2	4	no	—
85	C₂×C₄²×C₆₇	D₄	1	4	yes	—
86	C₂×C₄²×C₆₇	D₄	1	2	yes	—
87	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
89	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
90	#107×C₆₇	C₂³	1	8	yes	—
91	#106×C₆₇	C₂³	1	8	yes	—
92	#103×C₆₇	C₂³	1	16	yes	—
93	#102×C₆₇	C₂³	1	16	yes	—
94	#97×C₆₇	C₂³	1	4	yes	—
95	#97×C₆₇	C₂³	1	4	yes	—
96	#97×C₆₇	C₂³	1	8	yes	—
97	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
98	#41×C₆₇	—	2	16	no	—
99	#41×C₆₇	—	4	16	no	—
100	C₂×Q₈×C₆₇	—	2	4	no	—
101	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
102	C₂×D₄×C₆₇	—	2	4	no	—
103	C₂×D₄×C₆₇	—	2	8	no	—
104	C₂×D₄×C₆₇	—	2	4	no	—
105	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₆₇	—	2	4	no	—
107	C₂²×C₄×C₆₇	—	2	8	no	—
108	C₂²×C₄×C₆₇	—	2	4	no	—
109	C₂²×C₄×C₆₇	—	4	4	no	—
110	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₆₇	—	2	8	no	—
119	SD₁₆×C₆₇	—	2	16	no	—
120	D₈×C₆₇	—	2	8	no	—
121	C₂×C₈×C₆₇	—	2	4	no	—
122	C₂×C₈×C₆₇	—	2	16	no	—
123	C₂×C₈×C₆₇	#41	1	8	yes	complemented
124	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
125	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
126	C₄⋊C₄×C₆₇	—	2	4	no	—
127	C₄⋊C₄×C₆₇	—	2	4	no	—
128	C₄⋊C₄×C₆₇	—	2	8	no	—
129	C₄⋊C₄×C₆₇	—	2	8	no	—
130	C₄⋊C₄×C₆₇	—	2	8	no	—
131	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
132	C₂²⋊C₄×C₆₇	—	2	8	no	—
133	C₂²⋊C₄×C₆₇	—	2	4	no	—
134	C₂²⋊C₄×C₆₇	—	2	8	no	—
135	C₂²⋊C₄×C₆₇	—	2	8	no	—
136	C₂²⋊C₄×C₆₇	—	2	8	no	—
137	C₄²×C₆₇	—	2	8	no	—
138	C₄²×C₆₇	—	2	4	no	—
139	C₄²×C₆₇	C₂×D₄	1	4	yes	—
140	C₄²×C₆₇	C₂×D₄	1	4	yes	—
141	C₄²×C₆₇	C₂×D₄	1	2	yes	—
142	C₄²×C₆₇	C₂×D₄	1	2	yes	—
143	C₄²×C₆₇	C₂⁴	1	2	yes	—
144	C₄²×C₆₇	C₂⁴	1	2	yes	—
145	C₂³×C₆₇	—	2	2	no	—
146	C₂³×C₆₇	—	2	4	no	—
147	C₂³×C₆₇	—	2	4	no	—
148	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
149	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
150	Q₈×C₆₇	—	2	8	no	—
151	Q₈×C₆₇	—	4	8	no	—
152	D₄×C₆₇	—	2	8	no	—
153	D₄×C₆₇	—	4	8	no	—
154	D₄×C₆₇	—	4	8	no	—
155	D₄×C₆₇	—	4	16	no	—
156	C₂×C₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	—	2	8	no	—
158	C₂×C₄×C₆₇	—	2	4	no	—
159	C₂×C₄×C₆₇	—	2	4	no	—
160	C₂×C₄×C₆₇	—	2	4	no	—
161	C₂×C₄×C₆₇	—	2	8	no	—
162	C₂×C₄×C₆₇	—	4	2	no	—
163	C₂×C₄×C₆₇	—	4	4	no	—
164	C₂×C₄×C₆₇	—	4	2	no	—
165	C₂×C₄×C₆₇	—	4	16	no	—
166	C₂×C₄×C₆₇	—	4	8	no	—
167	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
168	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
170	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
172	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
173	C₈×C₆₇	—	2	4	no	—
174	C₈×C₆₇	C₂×#41	1	8	yes	—
175	C₂²×C₆₇	—	2	8	no	—
176	C₂²×C₆₇	—	2	2	no	—
177	C₂²×C₆₇	—	2	2	no	—
178	C₂²×C₆₇	—	2	2	no	—
179	C₂²×C₆₇	—	4	4	no	—
180	C₂²×C₆₇	—	4	8	no	—
181	C₂²×C₆₇	#532	1	2	yes	—
182	C₂²×C₆₇	#575	1	4	yes	—
183	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
184	C₄×C₆₇	—	2	2	no	—
185	C₄×C₆₇	—	2	4	no	—
186	C₄×C₆₇	—	2	4	no	—
187	C₄×C₆₇	—	4	4	no	—
188	C₄×C₆₇	—	4	8	no	—
189	C₄×C₆₇	#532	1	2	yes	—
190	C₄×C₆₇	C₂²×#41	1	2	yes	—
191	#60688	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₆₇	—	2	2	no	—
193	C₂×C₆₇	—	2	4	no	—
194	C₂×C₆₇	—	8	4	no	—
195	C₂×C₆₇	C₂×#532	1	1	yes	characteristic
196	C₂×C₆₇	C₂×#575	1	2	yes	—
197	#3444	C₂×C₆₇	1	2	yes	complemented
198	#3181	C₂×C₆₇	1	8	yes	complemented
199	#3180	C₂×C₆₇	1	8	yes	complemented
200	#3162	C₂×C₆₇	1	1	yes	characteristic, complemented
201	#3150	C₂×C₆₇	1	1	yes	characteristic, complemented
202	#3135	C₂×C₆₇	1	2	yes	complemented
203	#3050	C₂×C₆₇	1	4	yes	complemented
204	#2943	C₂×C₆₇	1	4	yes	complemented
205	C₂²×#97	C₂×C₆₇	1	1	yes	characteristic, complemented
206	C₆₇	#60688	1	1	yes	characteristic, direct product factor, Sylow
207	C₂×#135	C₂²×C₆₇	1	4	yes	—
208	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
209	#533	C₂²×C₆₇	1	4	yes	—
210	#533	C₂²×C₆₇	1	2	yes	—
211	#532	C₂²×C₆₇	1	2	yes	—
212	#532	C₂²×C₆₇	1	4	yes	—
213	#529	—	2	4	no	—
214	#529	—	2	4	no	—
215	#529	C₂²×C₆₇	1	8	yes	—
216	#525	—	2	4	no	—
217	#525	C₂²×C₆₇	1	4	yes	—
218	C₄×#41	—	2	4	no	—
219	C₄×#41	C₂²×C₆₇	1	4	yes	—
220	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
221	#501	C₂²×C₆₇	1	8	yes	complemented
222	#497	C₂²×C₆₇	1	4	yes	complemented
223	#496	C₂²×C₆₇	1	4	yes	complemented
224	#491	C₂²×C₆₇	1	4	yes	complemented
225	#490	C₂²×C₆₇	1	4	yes	complemented
226	#489	C₂²×C₆₇	1	8	yes	complemented
227	#467	C₂²×C₆₇	1	8	yes	—
228	#466	C₂²×C₆₇	1	8	yes	—
229	#465	C₂²×C₆₇	1	16	yes	—
230	#442	C₂²×C₆₇	1	8	yes	complemented
231	#441	C₂²×C₆₇	1	8	yes	complemented
232	#440	C₂²×C₆₇	1	16	yes	complemented
233	#427	C₂²×C₆₇	1	4	yes	—
234	#416	C₂²×C₆₇	1	8	yes	—
235	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
236	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
237	C₂×#97	C₂²×C₆₇	1	8	yes	—
238	C₂×#97	C₂²×C₆₇	1	2	yes	—
239	C₂×#41	—	2	4	no	—
240	C₂×#41	C₂³×C₆₇	1	4	yes	—
241	C₂³×C₄	D₄×C₆₇	1	2	yes	—
242	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
243	#135	—	2	16	no	—
244	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
245	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	—
246	C₂×D₈	C₂³×C₆₇	1	4	yes	—
247	C₂²×C₈	—	2	8	no	—
248	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
249	C₂²×C₈	C₂³×C₆₇	1	8	yes	—
250	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
251	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
252	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
253	#127	C₂³×C₆₇	1	2	yes	—
254	#126	—	2	8	no	—
255	#125	—	2	4	no	—
256	#125	C₂³×C₆₇	1	4	yes	—
257	#124	—	2	4	no	—
258	#124	C₂³×C₆₇	1	4	yes	—
259	#123	—	2	8	no	—
260	#123	—	2	4	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
264	#121	—	2	4	no	—
265	#121	—	2	4	no	—
266	#121	C₂³×C₆₇	1	8	yes	—
267	#120	—	2	4	no	—
268	C₄×Q₈	—	2	4	no	—
269	C₄×Q₈	—	2	4	no	—
270	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
271	C₄×D₄	—	2	8	no	—
272	C₄×D₄	—	2	8	no	—
273	C₄×D₄	—	2	8	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	—	2	4	no	—
276	C₄×D₄	C₂³×C₆₇	1	8	yes	—
277	#117	—	2	4	no	—
278	#117	—	2	8	no	—
279	#117	—	2	4	no	—
280	#117	C₂³×C₆₇	1	4	yes	—
281	C₂×C₄²	—	2	4	no	—
282	C₂×C₄²	D₄×C₆₇	1	4	yes	—
283	C₂×C₄²	D₄×C₆₇	1	2	yes	—
284	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
286	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
287	#107	C₂³×C₆₇	1	8	yes	—
288	#106	C₂³×C₆₇	1	8	yes	—
289	#103	C₂³×C₆₇	1	16	yes	—
290	#102	C₂³×C₆₇	1	16	yes	—
291	#97	C₂³×C₆₇	1	8	yes	—
292	#97	C₂³×C₆₇	1	4	yes	—
293	#97	C₂³×C₆₇	1	4	yes	—
294	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
295	#41	—	2	16	no	—
296	#41	—	4	16	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
310	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
312	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
315	Q₁₆	—	2	8	no	—
316	SD₁₆	—	2	16	no	—
317	D₈	—	2	8	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	16	no	—
320	C₂×C₈	#41×C₆₇	1	8	yes	complemented
321	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
322	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₂²⋊C₄	—	2	8	no	—
333	C₂²⋊C₄	—	2	8	no	—
334	C₄²	—	2	8	no	—
335	C₄²	—	2	4	no	—
336	C₄²	C₂×D₄×C₆₇	1	2	yes	—
337	C₄²	C₂×D₄×C₆₇	1	4	yes	—
338	C₄²	C₂×D₄×C₆₇	1	2	yes	—
339	C₄²	C₂×D₄×C₆₇	1	4	yes	—
340	C₄²	C₂⁴×C₆₇	1	2	yes	—
341	C₄²	C₂⁴×C₆₇	1	2	yes	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	4	no	—
345	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
346	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
347	Q₈	—	2	8	no	—
348	Q₈	—	4	8	no	—
349	D₄	—	2	8	no	—
350	D₄	—	4	8	no	—
351	D₄	—	4	8	no	—
352	D₄	—	4	16	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	16	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
365	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
366	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
367	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
368	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
369	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
370	C₈	—	2	4	no	—
371	C₈	C₂×#41×C₆₇	1	8	yes	—
372	C₂²	—	2	8	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	4	8	no	—
377	C₂²	—	4	4	no	—
378	C₂²	#532×C₆₇	1	2	yes	—
379	C₂²	#575×C₆₇	1	4	yes	—
380	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
381	C₄	—	2	4	no	—
382	C₄	—	2	4	no	—
383	C₄	—	2	2	no	—
384	C₄	—	4	8	no	—
385	C₄	—	4	4	no	—
386	C₄	#532×C₆₇	1	2	yes	—
387	C₄	C₂²×#41×C₆₇	1	2	yes	—
388	C₂	—	2	2	no	—
389	C₂	—	2	4	no	—
390	C₂	—	8	4	no	—
391	C₂	C₂×#532×C₆₇	1	1	yes	characteristic
392	C₂	C₂×#575×C₆₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3444	C₂	semidirect
2. C₆₇×#3181	C₂	semidirect
3. C₆₇×#3180	C₂	semidirect
4. C₆₇×#3162	C₂	semidirect
5. C₆₇×#3150	C₂	semidirect
6. C₆₇×#3135	C₂	semidirect
7. C₆₇×#3050	C₂	semidirect
8. C₆₇×#2943	C₂	semidirect
9. C₂²×#97×C₆₇	C₂	semidirect
24. #501×C₆₇	C₂²	semidirect
25. #497×C₆₇	C₂²	semidirect
26. #496×C₆₇	C₂²	semidirect
27. #491×C₆₇	C₂²	semidirect
28. #490×C₆₇	C₂²	semidirect
29. #489×C₆₇	C₂²	semidirect
33. #442×C₆₇	C₂²	semidirect
34. #441×C₆₇	C₂²	semidirect
35. #440×C₆₇	C₂²	semidirect
123. C₂×C₈×C₆₇	#41	semidirect
191. #60688	C₆₇	direct (N × H)
197. #3444	C₂×C₆₇	semidirect
198. #3181	C₂×C₆₇	semidirect
199. #3180	C₂×C₆₇	semidirect
200. #3162	C₂×C₆₇	semidirect
201. #3150	C₂×C₆₇	semidirect
202. #3135	C₂×C₆₇	semidirect
203. #3050	C₂×C₆₇	semidirect
204. #2943	C₂×C₆₇	semidirect
205. C₂²×#97	C₂×C₆₇	semidirect
206. C₆₇	#60688	direct (N × H)
221. #501	C₂²×C₆₇	semidirect
222. #497	C₂²×C₆₇	semidirect
223. #496	C₂²×C₆₇	semidirect
224. #491	C₂²×C₆₇	semidirect
225. #490	C₂²×C₆₇	semidirect
226. #489	C₂²×C₆₇	semidirect
230. #442	C₂²×C₆₇	semidirect
231. #441	C₂²×C₆₇	semidirect
232. #440	C₂²×C₆₇	semidirect
320. C₂×C₈	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3444	2
C₆₇×#3181	2
C₆₇×#3180	2
C₆₇×#3162	2
C₆₇×#3150	2
C₆₇×#3135	2
C₆₇×#3050	2
C₆₇×#2943	2
C₂²×#97×C₆₇	2
#60688	67

Subgroups — C67×#60688 #30739939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60688 #30739939