Subgroups — C₆₇×#61221 #30740472

Order 17152.

2018 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3497	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3317	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3316	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3313	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3312	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3135	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3099	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3063	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3011	C₂	1	2	yes	maximal, complemented
13	C₂×#441×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2898	C₂	1	2	yes	maximal, complemented
16	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	—
17	C₂×#137×C₆₇	C₂²	1	2	yes	—
18	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#131×C₆₇	C₂²	1	2	yes	—
20	#559×C₆₇	—	2	1	no	—
21	#557×C₆₇	—	2	1	no	—
22	#556×C₆₇	—	2	2	no	—
23	#556×C₆₇	C₂²	1	2	yes	—
24	#554×C₆₇	C₂²	1	2	yes	—
25	#552×C₆₇	C₂²	1	4	yes	—
26	#550×C₆₇	—	2	1	no	—
27	#550×C₆₇	C₂²	1	2	yes	—
28	D₄×Q₈×C₆₇	—	2	1	no	—
29	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
30	#548×C₆₇	—	2	2	no	—
31	#548×C₆₇	C₂²	1	4	yes	—
32	#539×C₆₇	—	2	2	no	—
33	#537×C₆₇	—	2	2	no	—
34	#537×C₆₇	C₂²	1	2	yes	—
35	#536×C₆₇	C₂²	1	2	yes	—
36	#533×C₆₇	C₂²	1	1	yes	characteristic
37	#532×C₆₇	—	2	2	no	—
38	#532×C₆₇	C₂²	1	1	yes	characteristic
39	#532×C₆₇	C₂²	1	1	yes	characteristic
40	#529×C₆₇	—	2	2	no	—
41	#520×C₆₇	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
44	#491×C₆₇	C₂²	1	2	yes	—
45	#490×C₆₇	C₂²	1	2	yes	—
46	#489×C₆₇	C₂²	1	2	yes	—
47	#489×C₆₇	C₂²	1	2	yes	—
48	#485×C₆₇	C₂²	1	4	yes	—
49	#483×C₆₇	C₂²	1	4	yes	—
50	#482×C₆₇	C₂²	1	4	yes	—
51	#481×C₆₇	C₂²	1	4	yes	—
52	#479×C₆₇	C₂²	1	4	yes	—
53	#477×C₆₇	C₂²	1	2	yes	—
54	#475×C₆₇	C₂²	1	2	yes	—
55	#470×C₆₇	C₂²	1	4	yes	—
56	#468×C₆₇	C₂²	1	4	yes	—
57	#467×C₆₇	C₂²	1	4	yes	—
58	#465×C₆₇	C₂²	1	4	yes	—
59	#464×C₆₇	C₂²	1	4	yes	—
60	#462×C₆₇	C₂²	1	2	yes	—
61	#460×C₆₇	C₂²	1	2	yes	—
62	#452×C₆₇	C₂²	1	4	yes	—
63	#452×C₆₇	C₂²	1	4	yes	—
64	#451×C₆₇	C₂²	1	4	yes	—
65	#451×C₆₇	C₂²	1	4	yes	—
66	#441×C₆₇	C₂²	1	4	yes	—
67	#441×C₆₇	C₂²	1	4	yes	—
68	#435×C₆₇	C₂²	1	4	yes	—
69	#435×C₆₇	C₂²	1	4	yes	—
70	#428×C₆₇	C₂²	1	2	yes	—
71	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
72	#423×C₆₇	C₂²	1	1	yes	characteristic
73	#419×C₆₇	C₂²	1	2	yes	—
74	#419×C₆₇	C₂²	1	4	yes	—
75	#417×C₆₇	C₂²	1	2	yes	—
76	#417×C₆₇	C₂²	1	4	yes	—
77	#416×C₆₇	C₂²	1	2	yes	—
78	#416×C₆₇	C₂²	1	4	yes	—
79	#416×C₆₇	C₂²	1	2	yes	—
80	C₂×#103×C₆₇	C₂²	1	4	yes	—
81	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
82	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
83	#408×C₆₇	C₂²	1	2	yes	—
84	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
85	2₋¹⁺⁴×C₆₇	—	2	8	no	—
86	2₋¹⁺⁴×C₆₇	—	4	4	no	—
87	C₂×#41×C₆₇	—	2	4	no	—
88	C₂×#41×C₆₇	—	2	2	no	—
89	C₂×#41×C₆₇	C₂³	1	2	yes	—
90	C₂×#41×C₆₇	C₂³	1	4	yes	—
91	C₂×#41×C₆₇	C₂³	1	2	yes	—
92	C₂²×Q₈×C₆₇	—	2	2	no	—
93	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
95	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
96	#137×C₆₇	—	4	4	no	—
97	C₂×Q₁₆×C₆₇	—	2	4	no	—
98	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
99	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
101	#131×C₆₇	—	4	4	no	—
102	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
103	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
104	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
107	C₄⋊Q₈×C₆₇	—	2	2	no	—
108	C₄⋊Q₈×C₆₇	—	2	2	no	—
109	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
110	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
113	#127×C₆₇	—	2	2	no	—
114	#127×C₆₇	D₄	1	1	yes	characteristic
115	#127×C₆₇	C₂³	1	1	yes	characteristic
116	#126×C₆₇	—	2	4	no	—
117	#126×C₆₇	—	2	4	no	—
118	#125×C₆₇	—	2	2	no	—
119	#125×C₆₇	—	2	4	no	—
120	#125×C₆₇	C₂³	1	2	yes	—
121	#124×C₆₇	—	2	2	no	—
122	#124×C₆₇	—	2	2	no	—
123	#124×C₆₇	—	2	4	no	—
124	#124×C₆₇	D₄	1	2	yes	—
125	#124×C₆₇	C₂³	1	2	yes	—
126	#123×C₆₇	—	2	4	no	—
127	#123×C₆₇	—	2	4	no	—
128	C₂²⋊Q₈×C₆₇	—	2	2	no	—
129	C₂²⋊Q₈×C₆₇	—	2	1	no	—
130	C₂²⋊Q₈×C₆₇	—	2	1	no	—
131	C₂²⋊Q₈×C₆₇	—	2	4	no	—
132	C₂²⋊Q₈×C₆₇	—	2	4	no	—
133	C₂²⋊Q₈×C₆₇	—	2	4	no	—
134	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
135	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
136	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
137	#121×C₆₇	—	2	4	no	—
138	#121×C₆₇	—	2	4	no	—
139	#121×C₆₇	—	2	2	no	—
140	#121×C₆₇	—	2	1	no	—
141	#121×C₆₇	—	2	1	no	—
142	#121×C₆₇	—	2	4	no	—
143	#121×C₆₇	D₄	1	2	yes	—
144	#121×C₆₇	D₄	1	2	yes	—
145	#121×C₆₇	C₂³	1	4	yes	—
146	C₄×Q₈×C₆₇	—	2	2	no	—
147	C₄×Q₈×C₆₇	—	2	2	no	—
148	C₄×Q₈×C₆₇	—	2	1	no	—
149	C₄×Q₈×C₆₇	—	2	1	no	—
150	C₄×Q₈×C₆₇	—	2	1	no	—
151	C₄×Q₈×C₆₇	—	2	1	no	—
152	C₄×Q₈×C₆₇	—	2	1	no	—
153	C₄×Q₈×C₆₇	—	2	1	no	—
154	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
155	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
156	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
157	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
158	C₄×D₄×C₆₇	—	2	4	no	—
159	C₄×D₄×C₆₇	—	2	2	no	—
160	C₄×D₄×C₆₇	—	2	2	no	—
161	C₄×D₄×C₆₇	—	2	2	no	—
162	C₄×D₄×C₆₇	—	2	2	no	—
163	C₄×D₄×C₆₇	—	2	4	no	—
164	C₄×D₄×C₆₇	—	2	1	no	—
165	C₄×D₄×C₆₇	—	2	1	no	—
166	C₄×D₄×C₆₇	C₂³	1	2	yes	—
167	C₄×D₄×C₆₇	C₂³	1	2	yes	—
168	#117×C₆₇	—	2	4	no	—
169	#117×C₆₇	C₂³	1	4	yes	—
170	#117×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
172	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₆₇	—	2	1	no	—
177	C₂×C₄²×C₆₇	—	2	1	no	—
178	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
179	#107×C₆₇	C₂³	1	4	yes	—
180	#106×C₆₇	C₂³	1	4	yes	—
181	#106×C₆₇	C₂³	1	4	yes	—
182	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
183	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
184	#103×C₆₇	C₂³	1	2	yes	—
185	#103×C₆₇	C₂³	1	2	yes	—
186	#103×C₆₇	C₂³	1	4	yes	—
187	#103×C₆₇	C₂³	1	4	yes	—
188	#103×C₆₇	C₂³	1	4	yes	—
189	#103×C₆₇	C₂³	1	4	yes	—
190	#103×C₆₇	C₂³	1	2	yes	—
191	#103×C₆₇	C₂³	1	2	yes	—
192	#103×C₆₇	C₂³	1	4	yes	—
193	#102×C₆₇	C₂³	1	2	yes	—
194	#102×C₆₇	C₂³	1	2	yes	—
195	#102×C₆₇	C₂³	1	4	yes	—
196	#102×C₆₇	C₂³	1	2	yes	—
197	#102×C₆₇	C₂³	1	2	yes	—
198	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
199	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
200	#97×C₆₇	C₂³	1	2	yes	—
201	#97×C₆₇	C₂³	1	2	yes	—
202	#41×C₆₇	—	2	4	no	—
203	#41×C₆₇	—	2	4	no	—
204	#41×C₆₇	—	2	8	no	—
205	#41×C₆₇	—	2	4	no	—
206	#41×C₆₇	—	2	4	no	—
207	#41×C₆₇	—	4	4	no	—
208	#41×C₆₇	—	4	16	no	—
209	#41×C₆₇	—	4	8	no	—
210	C₂×Q₈×C₆₇	—	2	1	no	—
211	C₂×Q₈×C₆₇	—	2	1	no	—
212	C₂×Q₈×C₆₇	—	2	1	no	—
213	C₂×Q₈×C₆₇	—	2	4	no	—
214	C₂×Q₈×C₆₇	—	2	1	no	—
215	C₂×Q₈×C₆₇	—	2	2	no	—
216	C₂×Q₈×C₆₇	—	2	8	no	—
217	C₂×Q₈×C₆₇	—	2	2	no	—
218	C₂×Q₈×C₆₇	—	2	2	no	—
219	C₂×Q₈×C₆₇	—	4	4	no	—
220	C₂×Q₈×C₆₇	—	4	8	no	—
221	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
222	C₂×Q₈×C₆₇	#41	1	4	yes	—
223	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
224	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
225	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
226	C₂×D₄×C₆₇	—	2	2	no	—
227	C₂×D₄×C₆₇	—	2	4	no	—
228	C₂×D₄×C₆₇	—	2	4	no	—
229	C₂×D₄×C₆₇	—	2	1	no	—
230	C₂×D₄×C₆₇	—	2	1	no	—
231	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
232	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₆₇	—	2	1	no	—
237	C₂²×C₄×C₆₇	—	2	1	no	—
238	C₂²×C₄×C₆₇	—	2	4	no	—
239	C₂²×C₄×C₆₇	—	2	1	no	—
240	C₂²×C₄×C₆₇	—	2	1	no	—
241	C₂²×C₄×C₆₇	—	2	4	no	—
242	C₂²×C₄×C₆₇	—	2	4	no	—
243	C₂²×C₄×C₆₇	—	2	2	no	—
244	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	Q₁₆×C₆₇	—	2	8	no	—
249	Q₁₆×C₆₇	—	4	4	no	—
250	SD₁₆×C₆₇	—	4	4	no	—
251	M₁₆×C₆₇	—	2	4	no	—
252	M₁₆×C₆₇	—	4	4	no	—
253	C₂×C₈×C₆₇	—	2	2	no	—
254	C₂×C₈×C₆₇	—	2	2	no	—
255	C₂×C₈×C₆₇	—	4	4	no	—
256	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
257	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
258	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
259	C₄⋊C₄×C₆₇	—	2	2	no	—
260	C₄⋊C₄×C₆₇	—	2	2	no	—
261	C₄⋊C₄×C₆₇	—	2	2	no	—
262	C₄⋊C₄×C₆₇	—	2	2	no	—
263	C₄⋊C₄×C₆₇	—	2	1	no	—
264	C₄⋊C₄×C₆₇	—	2	4	no	—
265	C₄⋊C₄×C₆₇	—	2	1	no	—
266	C₄⋊C₄×C₆₇	—	2	2	no	—
267	C₄⋊C₄×C₆₇	—	2	4	no	—
268	C₄⋊C₄×C₆₇	—	2	1	no	—
269	C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	2	no	—
273	C₄⋊C₄×C₆₇	—	2	1	no	—
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₂²⋊C₄×C₆₇	—	2	4	no	—
282	C₂²⋊C₄×C₆₇	—	2	2	no	—
283	C₂²⋊C₄×C₆₇	—	2	4	no	—
284	C₂²⋊C₄×C₆₇	—	2	4	no	—
285	C₂²⋊C₄×C₆₇	—	2	4	no	—
286	C₂²⋊C₄×C₆₇	—	2	2	no	—
287	C₂²⋊C₄×C₆₇	—	2	2	no	—
288	C₂²⋊C₄×C₆₇	—	2	4	no	—
289	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
290	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
291	C₄²×C₆₇	—	2	2	no	—
292	C₄²×C₆₇	—	2	2	no	—
293	C₄²×C₆₇	—	2	2	no	—
294	C₄²×C₆₇	—	2	2	no	—
295	C₄²×C₆₇	—	2	4	no	—
296	C₄²×C₆₇	—	2	2	no	—
297	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
300	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₂³×C₆₇	—	2	2	no	—
302	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
303	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
304	Q₈×C₆₇	—	2	4	no	—
305	Q₈×C₆₇	—	2	4	no	—
306	Q₈×C₆₇	—	2	2	no	—
307	Q₈×C₆₇	—	2	2	no	—
308	Q₈×C₆₇	—	2	2	no	—
309	Q₈×C₆₇	—	2	2	no	—
310	Q₈×C₆₇	—	2	2	no	—
311	Q₈×C₆₇	—	4	8	no	—
312	Q₈×C₆₇	—	4	2	no	—
313	Q₈×C₆₇	—	4	2	no	—
314	Q₈×C₆₇	—	8	1	no	—
315	Q₈×C₆₇	C₂×#41	1	4	yes	—
316	D₄×C₆₇	—	2	8	no	—
317	D₄×C₆₇	—	2	4	no	—
318	D₄×C₆₇	—	2	2	no	—
319	D₄×C₆₇	—	2	2	no	—
320	D₄×C₆₇	—	4	2	no	—
321	D₄×C₆₇	—	4	2	no	—
322	D₄×C₆₇	—	4	8	no	—
323	D₄×C₆₇	—	4	2	no	—
324	D₄×C₆₇	—	4	4	no	—
325	D₄×C₆₇	—	8	1	no	—
326	D₄×C₆₇	—	8	4	no	—
327	C₂×C₄×C₆₇	—	2	4	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	4	no	—
330	C₂×C₄×C₆₇	—	2	4	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	2	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	4	1	no	—
338	C₂×C₄×C₆₇	—	4	1	no	—
339	C₂×C₄×C₆₇	—	4	8	no	—
340	C₂×C₄×C₆₇	—	4	8	no	—
341	C₂×C₄×C₆₇	—	4	2	no	—
342	C₂×C₄×C₆₇	—	4	4	no	—
343	C₂×C₄×C₆₇	—	8	1	no	—
344	C₂×C₄×C₆₇	—	8	4	no	—
345	C₂×C₄×C₆₇	—	8	1	no	—
346	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
351	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
353	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
354	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
355	C₈×C₆₇	—	2	2	no	—
356	C₈×C₆₇	—	2	2	no	—
357	C₈×C₆₇	—	2	4	no	—
358	C₂²×C₆₇	—	2	1	no	—
359	C₂²×C₆₇	—	2	1	no	—
360	C₂²×C₆₇	—	2	4	no	—
361	C₂²×C₆₇	—	2	4	no	—
362	C₂²×C₆₇	—	2	4	no	—
363	C₂²×C₆₇	—	4	2	no	—
364	C₂²×C₆₇	—	4	2	no	—
365	C₂²×C₆₇	—	4	2	no	—
366	C₂²×C₆₇	#546	1	2	yes	—
367	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
368	C₄×C₆₇	—	2	1	no	—
369	C₄×C₆₇	—	2	1	no	—
370	C₄×C₆₇	—	2	1	no	—
371	C₄×C₆₇	—	2	1	no	—
372	C₄×C₆₇	—	2	4	no	—
373	C₄×C₆₇	—	2	4	no	—
374	C₄×C₆₇	—	4	2	no	—
375	C₄×C₆₇	—	4	2	no	—
376	C₄×C₆₇	—	4	2	no	—
377	C₄×C₆₇	—	4	2	no	—
378	C₄×C₆₇	—	4	2	no	—
379	C₄×C₆₇	—	4	2	no	—
380	C₄×C₆₇	#546	1	2	yes	—
381	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
382	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
383	#61221	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
384	C₂×C₆₇	—	2	2	no	—
385	C₂×C₆₇	—	4	4	no	—
386	C₂×C₆₇	—	8	2	no	—
387	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
388	C₂×C₆₇	#3586	1	1	yes	characteristic
389	C₂×C₆₇	#3586	1	1	yes	characteristic
390	#3507	C₂×C₆₇	1	1	yes	characteristic, complemented
391	#3497	C₂×C₆₇	1	1	yes	characteristic
392	#3317	C₂×C₆₇	1	4	yes	complemented
393	#3316	C₂×C₆₇	1	4	yes	complemented
394	#3313	C₂×C₆₇	1	4	yes	complemented
395	#3312	C₂×C₆₇	1	4	yes	complemented
396	#3135	C₂×C₆₇	1	1	yes	characteristic, complemented
397	#3099	C₂×C₆₇	1	2	yes	complemented
398	#3078	C₂×C₆₇	1	1	yes	characteristic, complemented
399	#3063	C₂×C₆₇	1	2	yes	complemented
400	#3037	C₂×C₆₇	1	1	yes	characteristic, complemented
401	#3011	C₂×C₆₇	1	2	yes	complemented
402	C₂×#441	C₂×C₆₇	1	1	yes	characteristic, complemented
403	#2932	C₂×C₆₇	1	1	yes	characteristic, complemented
404	#2898	C₂×C₆₇	1	2	yes	complemented
405	C₆₇	#61221	1	1	yes	characteristic, direct product factor, Sylow
406	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	—
407	C₂×#137	C₂²×C₆₇	1	2	yes	—
408	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
409	C₂×#131	C₂²×C₆₇	1	2	yes	—
410	#559	—	2	1	no	—
411	#557	—	2	1	no	—
412	#556	—	2	2	no	—
413	#556	C₂²×C₆₇	1	2	yes	—
414	#554	C₂²×C₆₇	1	2	yes	—
415	#552	C₂²×C₆₇	1	4	yes	—
416	#550	—	2	1	no	—
417	#550	C₂²×C₆₇	1	2	yes	—
418	D₄×Q₈	—	2	1	no	—
419	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
420	#548	—	2	2	no	—
421	#548	C₂²×C₆₇	1	4	yes	—
422	#539	—	2	2	no	—
423	#537	—	2	2	no	—
424	#537	C₂²×C₆₇	1	2	yes	—
425	#536	C₂²×C₆₇	1	2	yes	—
426	#533	C₂²×C₆₇	1	1	yes	characteristic
427	#532	—	2	2	no	—
428	#532	C₂²×C₆₇	1	1	yes	characteristic
429	#532	C₂²×C₆₇	1	1	yes	characteristic
430	#529	—	2	2	no	—
431	#520	C₂²×C₆₇	1	2	yes	—
432	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
433	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
434	#491	C₂²×C₆₇	1	2	yes	—
435	#490	C₂²×C₆₇	1	2	yes	—
436	#489	C₂²×C₆₇	1	2	yes	—
437	#489	C₂²×C₆₇	1	2	yes	—
438	#485	C₂²×C₆₇	1	4	yes	—
439	#483	C₂²×C₆₇	1	4	yes	—
440	#482	C₂²×C₆₇	1	4	yes	—
441	#481	C₂²×C₆₇	1	4	yes	—
442	#479	C₂²×C₆₇	1	4	yes	—
443	#477	C₂²×C₆₇	1	2	yes	—
444	#475	C₂²×C₆₇	1	2	yes	—
445	#470	C₂²×C₆₇	1	4	yes	—
446	#468	C₂²×C₆₇	1	4	yes	—
447	#467	C₂²×C₆₇	1	4	yes	—
448	#465	C₂²×C₆₇	1	4	yes	—
449	#464	C₂²×C₆₇	1	4	yes	—
450	#462	C₂²×C₆₇	1	2	yes	—
451	#460	C₂²×C₆₇	1	2	yes	—
452	#452	C₂²×C₆₇	1	4	yes	—
453	#452	C₂²×C₆₇	1	4	yes	—
454	#451	C₂²×C₆₇	1	4	yes	—
455	#451	C₂²×C₆₇	1	4	yes	—
456	#441	C₂²×C₆₇	1	4	yes	—
457	#441	C₂²×C₆₇	1	4	yes	—
458	#435	C₂²×C₆₇	1	4	yes	—
459	#435	C₂²×C₆₇	1	4	yes	—
460	#428	C₂²×C₆₇	1	2	yes	—
461	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
462	#423	C₂²×C₆₇	1	1	yes	characteristic
463	#419	C₂²×C₆₇	1	2	yes	—
464	#419	C₂²×C₆₇	1	4	yes	—
465	#417	C₂²×C₆₇	1	2	yes	—
466	#417	C₂²×C₆₇	1	4	yes	—
467	#416	C₂²×C₆₇	1	2	yes	—
468	#416	C₂²×C₆₇	1	2	yes	—
469	#416	C₂²×C₆₇	1	4	yes	—
470	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
471	C₂×#103	C₂²×C₆₇	1	4	yes	—
472	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
473	#408	C₂²×C₆₇	1	2	yes	—
474	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
475	2₋¹⁺⁴	—	2	8	no	—
476	2₋¹⁺⁴	—	4	4	no	—
477	C₂×#41	—	2	4	no	—
478	C₂×#41	—	2	2	no	—
479	C₂×#41	C₂³×C₆₇	1	2	yes	—
480	C₂×#41	C₂³×C₆₇	1	4	yes	—
481	C₂×#41	C₂³×C₆₇	1	2	yes	—
482	C₂²×Q₈	—	2	2	no	—
483	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
484	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
485	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
486	#137	—	4	4	no	—
487	C₂×Q₁₆	—	2	4	no	—
488	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
489	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
490	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
491	#131	—	4	4	no	—
492	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
493	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
494	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
497	C₄⋊Q₈	—	2	2	no	—
498	C₄⋊Q₈	—	2	2	no	—
499	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
500	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
501	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
502	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
503	#127	—	2	2	no	—
504	#127	D₄×C₆₇	1	1	yes	characteristic
505	#127	C₂³×C₆₇	1	1	yes	characteristic
506	#126	—	2	4	no	—
507	#126	—	2	4	no	—
508	#125	—	2	2	no	—
509	#125	—	2	4	no	—
510	#125	C₂³×C₆₇	1	2	yes	—
511	#124	—	2	2	no	—
512	#124	—	2	2	no	—
513	#124	—	2	4	no	—
514	#124	D₄×C₆₇	1	2	yes	—
515	#124	C₂³×C₆₇	1	2	yes	—
516	#123	—	2	4	no	—
517	#123	—	2	4	no	—
518	C₂²⋊Q₈	—	2	2	no	—
519	C₂²⋊Q₈	—	2	1	no	—
520	C₂²⋊Q₈	—	2	1	no	—
521	C₂²⋊Q₈	—	2	4	no	—
522	C₂²⋊Q₈	—	2	4	no	—
523	C₂²⋊Q₈	—	2	4	no	—
524	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
525	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
526	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
527	#121	—	2	4	no	—
528	#121	—	2	4	no	—
529	#121	—	2	2	no	—
530	#121	—	2	1	no	—
531	#121	—	2	1	no	—
532	#121	—	2	4	no	—
533	#121	D₄×C₆₇	1	2	yes	—
534	#121	D₄×C₆₇	1	2	yes	—
535	#121	C₂³×C₆₇	1	4	yes	—
536	C₄×Q₈	—	2	2	no	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	1	no	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	—	2	1	no	—
544	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
545	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
546	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
547	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
548	C₄×D₄	—	2	4	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	4	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	—	2	1	no	—
556	C₄×D₄	C₂³×C₆₇	1	2	yes	—
557	C₄×D₄	C₂³×C₆₇	1	2	yes	—
558	#117	—	2	4	no	—
559	#117	C₂³×C₆₇	1	2	yes	—
560	#117	C₂³×C₆₇	1	4	yes	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
566	C₂×C₄²	—	2	1	no	—
567	C₂×C₄²	—	2	1	no	—
568	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
569	#107	C₂³×C₆₇	1	4	yes	—
570	#106	C₂³×C₆₇	1	4	yes	—
571	#106	C₂³×C₆₇	1	4	yes	—
572	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
573	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
574	#103	C₂³×C₆₇	1	4	yes	—
575	#103	C₂³×C₆₇	1	2	yes	—
576	#103	C₂³×C₆₇	1	4	yes	—
577	#103	C₂³×C₆₇	1	4	yes	—
578	#103	C₂³×C₆₇	1	4	yes	—
579	#103	C₂³×C₆₇	1	4	yes	—
580	#103	C₂³×C₆₇	1	2	yes	—
581	#103	C₂³×C₆₇	1	2	yes	—
582	#103	C₂³×C₆₇	1	2	yes	—
583	#102	C₂³×C₆₇	1	2	yes	—
584	#102	C₂³×C₆₇	1	4	yes	—
585	#102	C₂³×C₆₇	1	2	yes	—
586	#102	C₂³×C₆₇	1	2	yes	—
587	#102	C₂³×C₆₇	1	2	yes	—
588	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
589	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
590	#97	C₂³×C₆₇	1	2	yes	—
591	#97	C₂³×C₆₇	1	2	yes	—
592	#41	—	2	4	no	—
593	#41	—	2	4	no	—
594	#41	—	2	8	no	—
595	#41	—	2	4	no	—
596	#41	—	2	4	no	—
597	#41	—	4	4	no	—
598	#41	—	4	16	no	—
599	#41	—	4	8	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	4	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	2	8	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	4	4	no	—
610	C₂×Q₈	—	4	8	no	—
611	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
612	C₂×Q₈	#41×C₆₇	1	4	yes	—
613	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
614	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
615	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
622	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
623	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
624	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
625	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
637	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
638	Q₁₆	—	2	8	no	—
639	Q₁₆	—	4	4	no	—
640	SD₁₆	—	4	4	no	—
641	M₁₆	—	2	4	no	—
642	M₁₆	—	4	4	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	2	no	—
645	C₂×C₈	—	4	4	no	—
646	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
647	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
648	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
666	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
680	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
681	C₄²	—	2	2	no	—
682	C₄²	—	2	2	no	—
683	C₄²	—	2	2	no	—
684	C₄²	—	2	2	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	2	no	—
687	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
688	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
689	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
690	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
691	C₂³	—	2	2	no	—
692	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
693	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
694	Q₈	—	2	4	no	—
695	Q₈	—	2	4	no	—
696	Q₈	—	2	2	no	—
697	Q₈	—	2	2	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	2	2	no	—
701	Q₈	—	4	8	no	—
702	Q₈	—	4	2	no	—
703	Q₈	—	4	2	no	—
704	Q₈	—	8	1	no	—
705	Q₈	C₂×#41×C₆₇	1	4	yes	—
706	D₄	—	2	8	no	—
707	D₄	—	2	4	no	—
708	D₄	—	2	2	no	—
709	D₄	—	2	2	no	—
710	D₄	—	4	2	no	—
711	D₄	—	4	2	no	—
712	D₄	—	4	8	no	—
713	D₄	—	4	2	no	—
714	D₄	—	4	4	no	—
715	D₄	—	8	1	no	—
716	D₄	—	8	4	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	8	no	—
730	C₂×C₄	—	4	8	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	4	4	no	—
733	C₂×C₄	—	8	1	no	—
734	C₂×C₄	—	8	4	no	—
735	C₂×C₄	—	8	1	no	—
736	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
738	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
739	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
740	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
741	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
742	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
743	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
744	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
745	C₈	—	2	2	no	—
746	C₈	—	2	2	no	—
747	C₈	—	2	4	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	1	no	—
750	C₂²	—	2	4	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	4	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	#546×C₆₇	1	2	yes	—
757	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
758	C₄	—	2	1	no	—
759	C₄	—	2	1	no	—
760	C₄	—	2	1	no	—
761	C₄	—	2	1	no	—
762	C₄	—	2	4	no	—
763	C₄	—	2	4	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	#546×C₆₇	1	2	yes	—
771	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
772	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
773	C₂	—	2	2	no	—
774	C₂	—	4	4	no	—
775	C₂	—	8	2	no	—
776	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
777	C₂	C₆₇×#3586	1	1	yes	characteristic
778	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3497	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3507	C₂	semidirect
3. C₆₇×#3317	C₂	semidirect
4. C₆₇×#3316	C₂	semidirect
5. C₆₇×#3313	C₂	semidirect
6. C₆₇×#3312	C₂	semidirect
7. C₆₇×#3135	C₂	semidirect
8. C₆₇×#3099	C₂	semidirect
9. C₆₇×#3078	C₂	semidirect
10. C₆₇×#3063	C₂	semidirect
11. C₆₇×#3037	C₂	semidirect
12. C₆₇×#3011	C₂	semidirect
13. C₂×#441×C₆₇	C₂	semidirect
14. C₆₇×#2932	C₂	semidirect
15. C₆₇×#2898	C₂	semidirect
383. #61221	C₆₇	direct (N × H)
390. #3507	C₂×C₆₇	semidirect
392. #3317	C₂×C₆₇	semidirect
393. #3316	C₂×C₆₇	semidirect
394. #3313	C₂×C₆₇	semidirect
395. #3312	C₂×C₆₇	semidirect
396. #3135	C₂×C₆₇	semidirect
397. #3099	C₂×C₆₇	semidirect
398. #3078	C₂×C₆₇	semidirect
399. #3063	C₂×C₆₇	semidirect
400. #3037	C₂×C₆₇	semidirect
401. #3011	C₂×C₆₇	semidirect
402. C₂×#441	C₂×C₆₇	semidirect
403. #2932	C₂×C₆₇	semidirect
404. #2898	C₂×C₆₇	semidirect
405. C₆₇	#61221	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×#3507	2
C₆₇×#3497	2
C₆₇×#3317	2
C₆₇×#3316	2
C₆₇×#3313	2
C₆₇×#3312	2
C₆₇×#3135	2
C₆₇×#3099	2
C₆₇×#3078	2
C₆₇×#3063	2
C₆₇×#3037	2
C₆₇×#3011	2
C₂×#441×C₆₇	2
C₆₇×#2932	2
C₆₇×#2898	2
#61221	67

Subgroups — C67×#61221 #30740472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61221 #30740472