Subgroups — C₆₇×#61485 #30740736

Order 17152.

1862 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3522	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3375	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3338	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3334	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3333	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3308	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3287	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3285	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3175	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3124	C₂	1	4	yes	maximal, complemented
14	C₆₇×#3112	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2951	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₆₇	C₂²	1	2	yes	—
19	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
20	#559×C₆₇	—	2	2	no	—
21	#559×C₆₇	C₂²	1	2	yes	—
22	Q₈²×C₆₇	C₂²	1	2	yes	—
23	#554×C₆₇	—	2	2	no	—
24	#554×C₆₇	C₂²	1	2	yes	—
25	#550×C₆₇	C₂²	1	2	yes	—
26	#548×C₆₇	C₂²	1	4	yes	—
27	#547×C₆₇	—	2	4	no	—
28	#547×C₆₇	C₂²	1	4	yes	—
29	#542×C₆₇	—	2	4	no	—
30	#542×C₆₇	C₂²	1	4	yes	—
31	#532×C₆₇	—	2	2	no	—
32	#532×C₆₇	C₂²	1	2	yes	—
33	#529×C₆₇	—	2	2	no	—
34	#529×C₆₇	C₂²	1	1	yes	characteristic
35	#520×C₆₇	C₂²	1	4	yes	—
36	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
37	#500×C₆₇	C₂²	1	2	yes	—
38	#500×C₆₇	C₂²	1	1	yes	characteristic
39	#495×C₆₇	C₂²	1	2	yes	—
40	#493×C₆₇	C₂²	1	1	yes	characteristic
41	#489×C₆₇	C₂²	1	4	yes	—
42	#486×C₆₇	C₂²	1	2	yes	—
43	#484×C₆₇	C₂²	1	4	yes	—
44	#480×C₆₇	C₂²	1	4	yes	—
45	#480×C₆₇	C₂²	1	4	yes	—
46	#477×C₆₇	C₂²	1	4	yes	—
47	#477×C₆₇	C₂²	1	2	yes	—
48	#477×C₆₇	C₂²	1	2	yes	—
49	#474×C₆₇	C₂²	1	4	yes	—
50	#468×C₆₇	C₂²	1	4	yes	—
51	#467×C₆₇	C₂²	1	2	yes	—
52	#466×C₆₇	C₂²	1	2	yes	—
53	#466×C₆₇	C₂²	1	2	yes	—
54	#466×C₆₇	C₂²	1	2	yes	—
55	#464×C₆₇	C₂²	1	4	yes	—
56	#463×C₆₇	C₂²	1	4	yes	—
57	#460×C₆₇	C₂²	1	2	yes	—
58	#460×C₆₇	C₂²	1	2	yes	—
59	#452×C₆₇	C₂²	1	4	yes	—
60	#449×C₆₇	C₂²	1	4	yes	—
61	#448×C₆₇	C₂²	1	4	yes	—
62	#446×C₆₇	C₂²	1	1	yes	characteristic
63	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
64	#440×C₆₇	C₂²	1	4	yes	—
65	#440×C₆₇	C₂²	1	4	yes	—
66	#440×C₆₇	C₂²	1	4	yes	—
67	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
68	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
69	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
70	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
71	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
72	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
73	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
74	C₄×D₈×C₆₇	C₂²	1	2	yes	—
75	C₄×D₈×C₆₇	C₂²	1	2	yes	—
76	C₄×D₈×C₆₇	C₂²	1	2	yes	—
77	#436×C₆₇	C₂²	1	1	yes	characteristic
78	#435×C₆₇	C₂²	1	2	yes	—
79	C₈×D₄×C₆₇	C₂²	1	2	yes	—
80	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
81	#433×C₆₇	C₂²	1	2	yes	—
82	#432×C₆₇	C₂²	1	1	yes	characteristic
83	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
84	C₂×#107×C₆₇	C₂²	1	2	yes	—
85	#417×C₆₇	C₂²	1	4	yes	—
86	C₂×#103×C₆₇	C₂²	1	2	yes	—
87	#405×C₆₇	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
89	C₂×#41×C₆₇	—	2	4	no	—
90	C₂×#41×C₆₇	—	2	2	no	—
91	C₂×#41×C₆₇	C₂³	1	4	yes	—
92	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
93	#135×C₆₇	—	2	8	no	—
94	C₂×Q₁₆×C₆₇	—	2	4	no	—
95	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
96	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
97	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
98	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×D₈×C₆₇	C₂³	1	2	yes	—
101	C₂×D₈×C₆₇	C₂³	1	2	yes	—
102	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
103	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
105	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
106	C₄⋊Q₈×C₆₇	—	2	2	no	—
107	C₄⋊Q₈×C₆₇	—	2	4	no	—
108	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
109	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
110	#127×C₆₇	—	2	2	no	—
111	#127×C₆₇	C₂³	1	2	yes	—
112	#126×C₆₇	—	2	4	no	—
113	#126×C₆₇	D₄	1	2	yes	—
114	#125×C₆₇	—	2	2	no	—
115	#125×C₆₇	D₄	1	1	yes	characteristic
116	#124×C₆₇	—	2	2	no	—
117	#124×C₆₇	—	2	4	no	—
118	#124×C₆₇	—	2	4	no	—
119	#124×C₆₇	—	2	2	no	—
120	#124×C₆₇	D₄	1	1	yes	characteristic
121	#124×C₆₇	C₂³	1	4	yes	—
122	#123×C₆₇	—	2	4	no	—
123	#123×C₆₇	—	2	4	no	—
124	#123×C₆₇	—	2	4	no	—
125	#123×C₆₇	—	2	4	no	—
126	#123×C₆₇	D₄	1	2	yes	—
127	C₂²⋊Q₈×C₆₇	—	2	4	no	—
128	C₂²⋊Q₈×C₆₇	—	2	4	no	—
129	C₂²⋊Q₈×C₆₇	—	2	4	no	—
130	C₂²⋊Q₈×C₆₇	—	2	4	no	—
131	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
132	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
133	#121×C₆₇	—	2	4	no	—
134	#121×C₆₇	—	2	2	no	—
135	#121×C₆₇	—	2	4	no	—
136	#121×C₆₇	D₄	1	1	yes	characteristic
137	#121×C₆₇	C₂³	1	4	yes	—
138	#121×C₆₇	C₂³	1	4	yes	—
139	C₄×Q₈×C₆₇	—	2	2	no	—
140	C₄×Q₈×C₆₇	—	2	2	no	—
141	C₄×Q₈×C₆₇	—	2	2	no	—
142	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
143	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
144	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
145	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
146	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
147	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
148	C₄×D₄×C₆₇	—	2	2	no	—
149	C₄×D₄×C₆₇	—	2	2	no	—
150	C₄×D₄×C₆₇	—	2	2	no	—
151	C₄×D₄×C₆₇	—	2	4	no	—
152	C₄×D₄×C₆₇	—	2	4	no	—
153	C₄×D₄×C₆₇	—	2	4	no	—
154	C₄×D₄×C₆₇	—	2	2	no	—
155	C₄×D₄×C₆₇	C₂³	1	4	yes	—
156	C₄×D₄×C₆₇	C₂³	1	4	yes	—
157	C₄×D₄×C₆₇	C₂³	1	2	yes	—
158	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
159	#117×C₆₇	—	2	4	no	—
160	#117×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
162	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
165	C₂×C₄²×C₆₇	—	2	2	no	—
166	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
167	#107×C₆₇	C₂³	1	1	yes	characteristic
168	#107×C₆₇	C₂³	1	2	yes	—
169	#107×C₆₇	C₂³	1	2	yes	—
170	#107×C₆₇	C₂³	1	4	yes	—
171	#107×C₆₇	C₂³	1	2	yes	—
172	#107×C₆₇	C₂³	1	4	yes	—
173	#107×C₆₇	C₂³	1	1	yes	characteristic
174	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
175	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
176	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
177	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
178	#103×C₆₇	C₂³	1	4	yes	—
179	#103×C₆₇	C₂³	1	4	yes	—
180	#103×C₆₇	C₂³	1	2	yes	—
181	#103×C₆₇	C₂³	1	2	yes	—
182	#103×C₆₇	C₂³	1	2	yes	—
183	#103×C₆₇	C₂³	1	2	yes	—
184	#102×C₆₇	C₂³	1	4	yes	—
185	#102×C₆₇	C₂³	1	4	yes	—
186	#102×C₆₇	C₂³	1	4	yes	—
187	#102×C₆₇	C₂³	1	4	yes	—
188	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
191	#97×C₆₇	C₂³	1	2	yes	—
192	#97×C₆₇	C₂³	1	2	yes	—
193	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₆₇	C₂³	1	2	yes	—
196	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
198	#41×C₆₇	—	2	8	no	—
199	#41×C₆₇	—	4	4	no	—
200	#41×C₆₇	—	8	4	no	—
201	#41×C₆₇	—	8	8	no	—
202	C₂×Q₈×C₆₇	—	2	2	no	—
203	C₂×Q₈×C₆₇	—	2	4	no	—
204	C₂×Q₈×C₆₇	—	2	2	no	—
205	C₂×Q₈×C₆₇	—	2	4	no	—
206	C₂×Q₈×C₆₇	—	4	2	no	—
207	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
208	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
210	C₂×D₄×C₆₇	—	2	4	no	—
211	C₂×D₄×C₆₇	—	2	4	no	—
212	C₂×D₄×C₆₇	—	2	4	no	—
213	C₂×D₄×C₆₇	—	2	2	no	—
214	C₂×D₄×C₆₇	—	2	2	no	—
215	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
217	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₆₇	—	2	2	no	—
219	C₂²×C₄×C₆₇	—	2	2	no	—
220	C₂²×C₄×C₆₇	—	2	4	no	—
221	C₂²×C₄×C₆₇	—	2	4	no	—
222	C₂²×C₄×C₆₇	—	2	4	no	—
223	C₂²×C₄×C₆₇	—	2	4	no	—
224	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
228	Q₁₆×C₆₇	—	2	4	no	—
229	Q₁₆×C₆₇	—	2	2	no	—
230	Q₁₆×C₆₇	#41	1	4	yes	complemented
231	SD₁₆×C₆₇	—	2	8	no	—
232	SD₁₆×C₆₇	—	4	4	no	—
233	D₈×C₆₇	—	2	4	no	—
234	D₈×C₆₇	—	4	2	no	—
235	M₁₆×C₆₇	—	4	2	no	—
236	C₂×C₈×C₆₇	—	2	2	no	—
237	C₂×C₈×C₆₇	—	2	4	no	—
238	C₂×C₈×C₆₇	—	4	1	no	—
239	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
242	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
243	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
245	C₄⋊C₄×C₆₇	—	2	2	no	—
246	C₄⋊C₄×C₆₇	—	2	4	no	—
247	C₄⋊C₄×C₆₇	—	2	4	no	—
248	C₄⋊C₄×C₆₇	—	2	2	no	—
249	C₄⋊C₄×C₆₇	—	2	2	no	—
250	C₄⋊C₄×C₆₇	—	2	2	no	—
251	C₄⋊C₄×C₆₇	—	2	2	no	—
252	C₄⋊C₄×C₆₇	—	2	2	no	—
253	C₄⋊C₄×C₆₇	—	2	4	no	—
254	C₄⋊C₄×C₆₇	—	2	4	no	—
255	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
258	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
259	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
263	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²⋊C₄×C₆₇	—	2	4	no	—
265	C₂²⋊C₄×C₆₇	—	2	4	no	—
266	C₂²⋊C₄×C₆₇	—	2	4	no	—
267	C₂²⋊C₄×C₆₇	—	2	4	no	—
268	C₂²⋊C₄×C₆₇	—	2	4	no	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	4	no	—
271	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
272	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
273	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
274	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
275	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
276	C₄²×C₆₇	—	2	2	no	—
277	C₄²×C₆₇	—	2	2	no	—
278	C₄²×C₆₇	—	2	2	no	—
279	C₄²×C₆₇	—	2	2	no	—
280	C₄²×C₆₇	—	2	4	no	—
281	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₄²×C₆₇	C₂⁴	1	2	yes	—
285	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂³×C₆₇	—	2	4	no	—
287	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
288	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
289	Q₈×C₆₇	—	2	2	no	—
290	Q₈×C₆₇	—	2	2	no	—
291	Q₈×C₆₇	—	2	2	no	—
292	Q₈×C₆₇	—	2	2	no	—
293	Q₈×C₆₇	—	4	4	no	—
294	Q₈×C₆₇	—	8	2	no	—
295	Q₈×C₆₇	—	8	4	no	—
296	Q₈×C₆₇	C₂×#41	1	4	yes	—
297	D₄×C₆₇	—	2	4	no	—
298	D₄×C₆₇	—	2	2	no	—
299	D₄×C₆₇	—	2	4	no	—
300	D₄×C₆₇	—	2	4	no	—
301	D₄×C₆₇	—	4	8	no	—
302	D₄×C₆₇	—	4	8	no	—
303	D₄×C₆₇	—	4	4	no	—
304	D₄×C₆₇	—	8	2	no	—
305	D₄×C₆₇	—	8	4	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	1	no	—
310	C₂×C₄×C₆₇	—	2	2	no	—
311	C₂×C₄×C₆₇	—	2	1	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	4	no	—
317	C₂×C₄×C₆₇	—	4	8	no	—
318	C₂×C₄×C₆₇	—	4	4	no	—
319	C₂×C₄×C₆₇	—	4	4	no	—
320	C₂×C₄×C₆₇	—	8	4	no	—
321	C₂×C₄×C₆₇	—	8	4	no	—
322	C₂×C₄×C₆₇	—	8	4	no	—
323	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
332	C₈×C₆₇	—	2	2	no	—
333	C₈×C₆₇	—	2	1	no	—
334	C₈×C₆₇	—	2	1	no	—
335	C₈×C₆₇	—	2	1	no	—
336	C₈×C₆₇	—	2	2	no	—
337	C₈×C₆₇	C₂×#41	1	2	yes	—
338	C₂²×C₆₇	—	2	1	no	—
339	C₂²×C₆₇	—	2	1	no	—
340	C₂²×C₆₇	—	2	2	no	—
341	C₂²×C₆₇	—	2	2	no	—
342	C₂²×C₆₇	—	2	2	no	—
343	C₂²×C₆₇	—	4	4	no	—
344	C₂²×C₆₇	—	4	4	no	—
345	C₂²×C₆₇	—	4	4	no	—
346	C₂²×C₆₇	#576	1	2	yes	—
347	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
348	C₄×C₆₇	—	2	2	no	—
349	C₄×C₆₇	—	2	1	no	—
350	C₄×C₆₇	—	2	4	no	—
351	C₄×C₆₇	—	2	1	no	—
352	C₄×C₆₇	—	2	1	no	—
353	C₄×C₆₇	—	2	2	no	—
354	C₄×C₆₇	—	2	1	no	—
355	C₄×C₆₇	—	2	2	no	—
356	C₄×C₆₇	—	4	2	no	—
357	C₄×C₆₇	—	4	2	no	—
358	C₄×C₆₇	—	4	2	no	—
359	C₄×C₆₇	—	4	4	no	—
360	C₄×C₆₇	#578	1	2	yes	—
361	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
362	C₄×C₆₇	#585	1	1	yes	characteristic
363	#61485	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
364	C₂×C₆₇	—	2	2	no	—
365	C₂×C₆₇	—	4	2	no	—
366	C₂×C₆₇	—	8	4	no	—
367	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
368	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
369	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
370	#3522	C₂×C₆₇	1	2	yes	complemented
371	#3396	C₂×C₆₇	1	1	yes	characteristic, complemented
372	Q₈×Q₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
373	#3375	C₂×C₆₇	1	2	yes	complemented
374	#3338	C₂×C₆₇	1	1	yes	characteristic, complemented
375	#3334	C₂×C₆₇	1	2	yes	complemented
376	#3333	C₂×C₆₇	1	2	yes	complemented
377	#3308	C₂×C₆₇	1	4	yes	complemented
378	#3287	C₂×C₆₇	1	1	yes	characteristic, complemented
379	#3285	C₂×C₆₇	1	2	yes	complemented
380	#3175	C₂×C₆₇	1	2	yes	complemented
381	#3169	C₂×C₆₇	1	1	yes	characteristic, complemented
382	#3124	C₂×C₆₇	1	4	yes	complemented
383	#3112	C₂×C₆₇	1	2	yes	complemented
384	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
385	#2951	C₂×C₆₇	1	2	yes	complemented
386	C₂×C₄×Q₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
387	C₆₇	#61485	1	1	yes	characteristic, direct product factor, Sylow
388	C₂×#135	C₂²×C₆₇	1	2	yes	—
389	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
390	#559	—	2	2	no	—
391	#559	C₂²×C₆₇	1	2	yes	—
392	Q₈²	C₂²×C₆₇	1	2	yes	—
393	#554	—	2	2	no	—
394	#554	C₂²×C₆₇	1	2	yes	—
395	#550	C₂²×C₆₇	1	2	yes	—
396	#548	C₂²×C₆₇	1	4	yes	—
397	#547	—	2	4	no	—
398	#547	C₂²×C₆₇	1	4	yes	—
399	#542	—	2	4	no	—
400	#542	C₂²×C₆₇	1	4	yes	—
401	#532	—	2	2	no	—
402	#532	C₂²×C₆₇	1	2	yes	—
403	#529	—	2	2	no	—
404	#529	C₂²×C₆₇	1	1	yes	characteristic
405	#520	C₂²×C₆₇	1	4	yes	—
406	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
407	#500	C₂²×C₆₇	1	2	yes	—
408	#500	C₂²×C₆₇	1	1	yes	characteristic
409	#495	C₂²×C₆₇	1	2	yes	—
410	#493	C₂²×C₆₇	1	1	yes	characteristic
411	#489	C₂²×C₆₇	1	4	yes	—
412	#486	C₂²×C₆₇	1	2	yes	—
413	#484	C₂²×C₆₇	1	4	yes	—
414	#480	C₂²×C₆₇	1	4	yes	—
415	#480	C₂²×C₆₇	1	4	yes	—
416	#477	C₂²×C₆₇	1	2	yes	—
417	#477	C₂²×C₆₇	1	2	yes	—
418	#477	C₂²×C₆₇	1	4	yes	—
419	#474	C₂²×C₆₇	1	4	yes	—
420	#468	C₂²×C₆₇	1	4	yes	—
421	#467	C₂²×C₆₇	1	2	yes	—
422	#466	C₂²×C₆₇	1	2	yes	—
423	#466	C₂²×C₆₇	1	2	yes	—
424	#466	C₂²×C₆₇	1	2	yes	—
425	#464	C₂²×C₆₇	1	4	yes	—
426	#463	C₂²×C₆₇	1	4	yes	—
427	#460	C₂²×C₆₇	1	2	yes	—
428	#460	C₂²×C₆₇	1	2	yes	—
429	#452	C₂²×C₆₇	1	4	yes	—
430	#449	C₂²×C₆₇	1	4	yes	—
431	#448	C₂²×C₆₇	1	4	yes	—
432	#446	C₂²×C₆₇	1	1	yes	characteristic
433	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
434	#440	C₂²×C₆₇	1	4	yes	—
435	#440	C₂²×C₆₇	1	4	yes	—
436	#440	C₂²×C₆₇	1	4	yes	—
437	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
438	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
439	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
440	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
441	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
442	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
443	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
444	C₄×D₈	C₂²×C₆₇	1	2	yes	—
445	C₄×D₈	C₂²×C₆₇	1	2	yes	—
446	C₄×D₈	C₂²×C₆₇	1	2	yes	—
447	#436	C₂²×C₆₇	1	1	yes	characteristic
448	#435	C₂²×C₆₇	1	2	yes	—
449	C₈×D₄	C₂²×C₆₇	1	2	yes	—
450	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
451	#433	C₂²×C₆₇	1	2	yes	—
452	#432	C₂²×C₆₇	1	1	yes	characteristic
453	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
454	C₂×#107	C₂²×C₆₇	1	2	yes	—
455	#417	C₂²×C₆₇	1	4	yes	—
456	C₂×#103	C₂²×C₆₇	1	2	yes	—
457	#405	C₂²×C₆₇	1	2	yes	—
458	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
459	C₂×#41	—	2	4	no	—
460	C₂×#41	—	2	2	no	—
461	C₂×#41	C₂³×C₆₇	1	4	yes	—
462	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
463	#135	—	2	8	no	—
464	C₂×Q₁₆	—	2	4	no	—
465	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
466	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
467	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
468	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
469	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
470	C₂×D₈	C₂³×C₆₇	1	2	yes	—
471	C₂×D₈	C₂³×C₆₇	1	2	yes	—
472	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
473	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
475	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
476	C₄⋊Q₈	—	2	2	no	—
477	C₄⋊Q₈	—	2	4	no	—
478	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
479	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
480	#127	—	2	2	no	—
481	#127	C₂³×C₆₇	1	2	yes	—
482	#126	—	2	4	no	—
483	#126	D₄×C₆₇	1	2	yes	—
484	#125	—	2	2	no	—
485	#125	D₄×C₆₇	1	1	yes	characteristic
486	#124	—	2	2	no	—
487	#124	—	2	4	no	—
488	#124	—	2	4	no	—
489	#124	—	2	2	no	—
490	#124	D₄×C₆₇	1	1	yes	characteristic
491	#124	C₂³×C₆₇	1	4	yes	—
492	#123	—	2	4	no	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	#123	—	2	4	no	—
496	#123	D₄×C₆₇	1	2	yes	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
502	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
503	#121	—	2	4	no	—
504	#121	—	2	2	no	—
505	#121	—	2	4	no	—
506	#121	D₄×C₆₇	1	1	yes	characteristic
507	#121	C₂³×C₆₇	1	4	yes	—
508	#121	C₂³×C₆₇	1	4	yes	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	—	2	2	no	—
511	C₄×Q₈	—	2	2	no	—
512	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
513	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
514	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
515	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
516	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
517	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	—	2	4	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	C₂³×C₆₇	1	4	yes	—
526	C₄×D₄	C₂³×C₆₇	1	4	yes	—
527	C₄×D₄	C₂³×C₆₇	1	2	yes	—
528	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
529	#117	—	2	4	no	—
530	#117	C₂³×C₆₇	1	2	yes	—
531	C₂×C₄⋊C₄	—	2	2	no	—
532	C₂×C₄⋊C₄	—	2	4	no	—
533	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
535	C₂×C₄²	—	2	2	no	—
536	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
537	#107	C₂³×C₆₇	1	1	yes	characteristic
538	#107	C₂³×C₆₇	1	2	yes	—
539	#107	C₂³×C₆₇	1	1	yes	characteristic
540	#107	C₂³×C₆₇	1	2	yes	—
541	#107	C₂³×C₆₇	1	4	yes	—
542	#107	C₂³×C₆₇	1	2	yes	—
543	#107	C₂³×C₆₇	1	4	yes	—
544	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
545	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
546	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
547	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
548	#103	C₂³×C₆₇	1	2	yes	—
549	#103	C₂³×C₆₇	1	2	yes	—
550	#103	C₂³×C₆₇	1	2	yes	—
551	#103	C₂³×C₆₇	1	2	yes	—
552	#103	C₂³×C₆₇	1	4	yes	—
553	#103	C₂³×C₆₇	1	4	yes	—
554	#102	C₂³×C₆₇	1	4	yes	—
555	#102	C₂³×C₆₇	1	4	yes	—
556	#102	C₂³×C₆₇	1	4	yes	—
557	#102	C₂³×C₆₇	1	4	yes	—
558	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
559	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
560	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
561	#97	C₂³×C₆₇	1	2	yes	—
562	#97	C₂³×C₆₇	1	2	yes	—
563	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
564	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
565	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
566	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
567	C₄×C₈	C₂³×C₆₇	1	2	yes	—
568	#41	—	2	8	no	—
569	#41	—	4	4	no	—
570	#41	—	8	4	no	—
571	#41	—	8	8	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	2	4	no	—
576	C₂×Q₈	—	4	2	no	—
577	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
578	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
579	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
586	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
587	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
598	Q₁₆	—	2	4	no	—
599	Q₁₆	—	2	2	no	—
600	Q₁₆	#41×C₆₇	1	4	yes	complemented
601	SD₁₆	—	2	8	no	—
602	SD₁₆	—	4	4	no	—
603	D₈	—	2	4	no	—
604	D₈	—	4	2	no	—
605	M₁₆	—	4	2	no	—
606	C₂×C₈	—	2	2	no	—
607	C₂×C₈	—	2	4	no	—
608	C₂×C₈	—	4	1	no	—
609	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
610	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
611	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
612	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
613	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
614	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
626	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
627	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
628	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
629	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
630	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
631	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
632	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
633	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
642	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
643	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
644	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
645	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
646	C₄²	—	2	2	no	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	2	no	—
650	C₄²	—	2	4	no	—
651	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
652	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
653	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
654	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
655	C₄²	C₂⁴×C₆₇	1	2	yes	—
656	C₂³	—	2	4	no	—
657	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
658	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
659	Q₈	—	2	2	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	2	2	no	—
663	Q₈	—	4	4	no	—
664	Q₈	—	8	2	no	—
665	Q₈	—	8	4	no	—
666	Q₈	C₂×#41×C₆₇	1	4	yes	—
667	D₄	—	2	4	no	—
668	D₄	—	2	2	no	—
669	D₄	—	2	4	no	—
670	D₄	—	2	4	no	—
671	D₄	—	4	8	no	—
672	D₄	—	4	8	no	—
673	D₄	—	4	4	no	—
674	D₄	—	8	2	no	—
675	D₄	—	8	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	4	8	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	—	8	4	no	—
691	C₂×C₄	—	8	4	no	—
692	C₂×C₄	—	8	4	no	—
693	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
695	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
696	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
697	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
698	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
699	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
700	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
701	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
702	C₈	—	2	2	no	—
703	C₈	—	2	1	no	—
704	C₈	—	2	1	no	—
705	C₈	—	2	1	no	—
706	C₈	—	2	2	no	—
707	C₈	C₂×#41×C₆₇	1	2	yes	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	4	4	no	—
714	C₂²	—	4	4	no	—
715	C₂²	—	4	4	no	—
716	C₂²	#576×C₆₇	1	2	yes	—
717	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	1	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	1	no	—
725	C₄	—	2	4	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	4	no	—
729	C₄	—	4	2	no	—
730	C₄	#578×C₆₇	1	2	yes	—
731	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
732	C₄	#585×C₆₇	1	1	yes	characteristic
733	C₂	—	2	2	no	—
734	C₂	—	4	2	no	—
735	C₂	—	8	4	no	—
736	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
737	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
738	C₂	C₂×#578×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #529×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3522	C₂	semidirect
2. C₆₇×#3396	C₂	semidirect
3. Q₈×Q₁₆×C₆₇	C₂	semidirect
4. C₆₇×#3375	C₂	semidirect
5. C₆₇×#3338	C₂	semidirect
6. C₆₇×#3334	C₂	semidirect
7. C₆₇×#3333	C₂	semidirect
8. C₆₇×#3308	C₂	semidirect
9. C₆₇×#3287	C₂	semidirect
10. C₆₇×#3285	C₂	semidirect
11. C₆₇×#3175	C₂	semidirect
12. C₆₇×#3169	C₂	semidirect
13. C₆₇×#3124	C₂	semidirect
14. C₆₇×#3112	C₂	semidirect
15. C₆₇×#2966	C₂	semidirect
16. C₆₇×#2951	C₂	semidirect
17. C₂×C₄×Q₁₆×C₆₇	C₂	semidirect
230. Q₁₆×C₆₇	#41	semidirect
363. #61485	C₆₇	direct (N × H)
370. #3522	C₂×C₆₇	semidirect
371. #3396	C₂×C₆₇	semidirect
372. Q₈×Q₁₆	C₂×C₆₇	semidirect
373. #3375	C₂×C₆₇	semidirect
374. #3338	C₂×C₆₇	semidirect
375. #3334	C₂×C₆₇	semidirect
376. #3333	C₂×C₆₇	semidirect
377. #3308	C₂×C₆₇	semidirect
378. #3287	C₂×C₆₇	semidirect
379. #3285	C₂×C₆₇	semidirect
380. #3175	C₂×C₆₇	semidirect
381. #3169	C₂×C₆₇	semidirect
382. #3124	C₂×C₆₇	semidirect
383. #3112	C₂×C₆₇	semidirect
384. #2966	C₂×C₆₇	semidirect
385. #2951	C₂×C₆₇	semidirect
386. C₂×C₄×Q₁₆	C₂×C₆₇	semidirect
387. C₆₇	#61485	direct (N × H)
600. Q₁₆	#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×#3522	2
C₆₇×#3396	2
Q₈×Q₁₆×C₆₇	2
C₆₇×#3375	2
C₆₇×#3338	2
C₆₇×#3334	2
C₆₇×#3333	2
C₆₇×#3308	2
C₆₇×#3287	2
C₆₇×#3285	2
C₆₇×#3175	2
C₆₇×#3169	2
C₆₇×#3124	2
C₆₇×#3112	2
C₆₇×#2966	2
C₆₇×#2951	2
C₂×C₄×Q₁₆×C₆₇	2
#61485	67

Subgroups — C67×#61485 #30740736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61485 #30740736