Subgroups — C₆₇×#61291 #30740542

Order 17152.

1810 conjugacy classes of subgroups.

The subgroup lattice has 750 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×#3506	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3350	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3348	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3346	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3343	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3162	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3097	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3096	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3057	C₂	1	2	yes	maximal, complemented
13	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2913	C₂	1	2	yes	maximal, complemented
16	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×#131×C₆₇	C₂²	1	2	yes	—
18	#559×C₆₇	—	2	1	no	—
19	#559×C₆₇	—	2	2	no	—
20	#557×C₆₇	—	2	1	no	—
21	#556×C₆₇	—	2	1	no	—
22	#556×C₆₇	—	2	2	no	—
23	#556×C₆₇	C₂²	1	2	yes	complemented
24	#555×C₆₇	C₂²	1	2	yes	—
25	#554×C₆₇	C₂²	1	2	yes	complemented
26	#553×C₆₇	C₂²	1	4	yes	—
27	#552×C₆₇	C₂²	1	4	yes	complemented
28	#550×C₆₇	—	2	1	no	—
29	#547×C₆₇	C₂²	1	2	yes	—
30	#539×C₆₇	—	2	2	no	—
31	#538×C₆₇	—	2	2	no	—
32	#536×C₆₇	C₂²	1	2	yes	—
33	#535×C₆₇	C₂²	1	2	yes	—
34	#533×C₆₇	C₂²	1	1	yes	characteristic
35	#533×C₆₇	C₂²	1	1	yes	characteristic
36	#532×C₆₇	C₂²	1	1	yes	characteristic
37	#529×C₆₇	—	2	2	no	—
38	#525×C₆₇	—	2	2	no	—
39	#520×C₆₇	C₂²	1	2	yes	—
40	#520×C₆₇	C₂²	1	2	yes	—
41	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	#501×C₆₇	C₂²	1	2	yes	complemented
44	#501×C₆₇	C₂²	1	2	yes	complemented
45	#501×C₆₇	C₂²	1	2	yes	complemented
46	#501×C₆₇	C₂²	1	2	yes	complemented
47	#485×C₆₇	C₂²	1	4	yes	complemented
48	#485×C₆₇	C₂²	1	4	yes	complemented
49	#484×C₆₇	C₂²	1	4	yes	complemented
50	#483×C₆₇	C₂²	1	4	yes	complemented
51	#482×C₆₇	C₂²	1	4	yes	—
52	#482×C₆₇	C₂²	1	4	yes	—
53	#481×C₆₇	C₂²	1	4	yes	—
54	#480×C₆₇	C₂²	1	4	yes	—
55	#479×C₆₇	C₂²	1	4	yes	complemented
56	#478×C₆₇	C₂²	1	4	yes	—
57	#477×C₆₇	C₂²	1	2	yes	complemented
58	#476×C₆₇	C₂²	1	2	yes	—
59	#475×C₆₇	C₂²	1	2	yes	complemented
60	#474×C₆₇	C₂²	1	2	yes	—
61	#468×C₆₇	C₂²	1	4	yes	—
62	#468×C₆₇	C₂²	1	4	yes	—
63	#465×C₆₇	C₂²	1	4	yes	—
64	#465×C₆₇	C₂²	1	4	yes	—
65	#440×C₆₇	C₂²	1	4	yes	—
66	#440×C₆₇	C₂²	1	4	yes	—
67	#435×C₆₇	C₂²	1	4	yes	complemented
68	#435×C₆₇	C₂²	1	4	yes	complemented
69	#428×C₆₇	C₂²	1	2	yes	—
70	#428×C₆₇	C₂²	1	2	yes	—
71	#428×C₆₇	C₂²	1	4	yes	complemented
72	#428×C₆₇	C₂²	1	4	yes	complemented
73	#427×C₆₇	C₂²	1	2	yes	—
74	#427×C₆₇	C₂²	1	2	yes	—
75	#427×C₆₇	C₂²	1	4	yes	complemented
76	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
77	C₂×#107×C₆₇	C₂²	1	4	yes	complemented
78	#423×C₆₇	C₂²	1	1	yes	characteristic
79	#419×C₆₇	C₂²	1	2	yes	—
80	#418×C₆₇	C₂²	1	2	yes	—
81	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
82	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
83	#408×C₆₇	C₂²	1	2	yes	—
84	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
85	C₂×#41×C₆₇	—	2	2	no	—
86	C₂×#41×C₆₇	C₂³	1	2	yes	—
87	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₆₇	—	2	1	no	—
90	C₂×SD₁₆×C₆₇	—	2	4	no	—
91	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
92	#131×C₆₇	—	2	8	no	—
93	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
94	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
95	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
96	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₆₇	—	2	2	no	—
99	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
100	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
102	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
104	#127×C₆₇	—	2	2	no	—
105	#127×C₆₇	D₄	1	1	yes	characteristic
106	#126×C₆₇	—	2	4	no	—
107	#126×C₆₇	—	2	4	no	—
108	#126×C₆₇	—	2	4	no	—
109	#125×C₆₇	—	2	2	no	—
110	#125×C₆₇	—	2	4	no	—
111	#125×C₆₇	C₂³	1	2	yes	—
112	#125×C₆₇	C₂³	1	2	yes	—
113	#124×C₆₇	—	2	2	no	—
114	#124×C₆₇	—	2	2	no	—
115	#124×C₆₇	—	2	2	no	—
116	#124×C₆₇	—	2	4	no	—
117	#124×C₆₇	D₄	1	2	yes	—
118	#123×C₆₇	—	2	4	no	—
119	#123×C₆₇	—	2	4	no	—
120	#123×C₆₇	—	2	4	no	—
121	#123×C₆₇	—	2	4	no	—
122	C₂²⋊Q₈×C₆₇	—	2	1	no	—
123	C₂²⋊Q₈×C₆₇	—	2	1	no	—
124	C₂²⋊Q₈×C₆₇	—	2	1	no	—
125	C₂²⋊Q₈×C₆₇	—	2	1	no	—
126	C₂²⋊Q₈×C₆₇	—	2	2	no	—
127	C₂²⋊Q₈×C₆₇	—	2	4	no	—
128	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
129	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
130	#121×C₆₇	—	2	2	no	—
131	#121×C₆₇	—	2	4	no	—
132	#121×C₆₇	D₄	1	2	yes	—
133	#121×C₆₇	D₄	1	2	yes	—
134	#121×C₆₇	C₂³	1	4	yes	—
135	#121×C₆₇	C₂³	1	4	yes	—
136	#120×C₆₇	—	2	4	no	—
137	C₄×Q₈×C₆₇	—	2	2	no	—
138	C₄×Q₈×C₆₇	—	2	2	no	—
139	C₄×Q₈×C₆₇	—	2	2	no	—
140	C₄×Q₈×C₆₇	—	2	1	no	—
141	C₄×Q₈×C₆₇	—	2	1	no	—
142	C₄×Q₈×C₆₇	—	2	1	no	—
143	C₄×Q₈×C₆₇	—	2	1	no	—
144	C₄×Q₈×C₆₇	—	2	1	no	—
145	C₄×Q₈×C₆₇	—	2	1	no	—
146	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
147	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
148	C₄×D₄×C₆₇	—	2	4	no	—
149	C₄×D₄×C₆₇	—	2	4	no	—
150	C₄×D₄×C₆₇	—	2	2	no	—
151	C₄×D₄×C₆₇	—	2	2	no	—
152	C₄×D₄×C₆₇	—	2	2	no	—
153	C₄×D₄×C₆₇	—	2	4	no	—
154	C₄×D₄×C₆₇	—	2	1	no	—
155	C₄×D₄×C₆₇	—	2	1	no	—
156	C₄×D₄×C₆₇	C₂³	1	2	yes	—
157	C₄×D₄×C₆₇	C₂³	1	2	yes	—
158	C₄×D₄×C₆₇	C₂³	1	2	yes	—
159	C₄×D₄×C₆₇	C₂³	1	2	yes	—
160	#117×C₆₇	—	2	2	no	—
161	#117×C₆₇	—	2	4	no	—
162	#117×C₆₇	C₂³	1	4	yes	—
163	#117×C₆₇	C₂³	1	4	yes	—
164	#117×C₆₇	C₂³	1	2	yes	—
165	#117×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
172	C₂×C₄²×C₆₇	—	2	1	no	—
173	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
174	#107×C₆₇	C₂³	1	2	yes	—
175	#107×C₆₇	C₂³	1	2	yes	—
176	#107×C₆₇	C₂³	1	4	yes	—
177	#107×C₆₇	C₂³	1	4	yes	—
178	#107×C₆₇	C₂³	1	2	yes	—
179	#107×C₆₇	C₂³	1	2	yes	—
180	#107×C₆₇	C₂³	1	4	yes	—
181	#106×C₆₇	C₂³	1	2	yes	—
182	#106×C₆₇	C₂³	1	2	yes	—
183	#106×C₆₇	C₂³	1	4	yes	—
184	#106×C₆₇	C₂³	1	4	yes	—
185	#106×C₆₇	C₂³	1	2	yes	—
186	#106×C₆₇	C₂³	1	2	yes	—
187	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
188	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
189	#103×C₆₇	C₂³	1	4	yes	—
190	#103×C₆₇	C₂³	1	4	yes	—
191	#103×C₆₇	C₂³	1	4	yes	—
192	#102×C₆₇	C₂³	1	4	yes	—
193	#102×C₆₇	C₂³	1	4	yes	—
194	#102×C₆₇	C₂³	1	4	yes	—
195	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
196	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
197	#97×C₆₇	C₂³	1	2	yes	—
198	#97×C₆₇	C₂³	1	2	yes	—
199	C₂⁴×C₆₇	—	2	1	no	—
200	#41×C₆₇	—	2	4	no	—
201	#41×C₆₇	—	2	4	no	—
202	#41×C₆₇	—	8	4	no	—
203	C₂×Q₈×C₆₇	—	2	1	no	—
204	C₂×Q₈×C₆₇	—	2	1	no	—
205	C₂×Q₈×C₆₇	—	2	1	no	—
206	C₂×Q₈×C₆₇	—	2	1	no	—
207	C₂×Q₈×C₆₇	—	2	1	no	—
208	C₂×Q₈×C₆₇	—	2	2	no	—
209	C₂×Q₈×C₆₇	—	2	2	no	—
210	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
211	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
212	C₂×D₄×C₆₇	—	2	4	no	—
213	C₂×D₄×C₆₇	—	2	4	no	—
214	C₂×D₄×C₆₇	—	2	1	no	—
215	C₂×D₄×C₆₇	—	2	2	no	—
216	C₂×D₄×C₆₇	—	2	2	no	—
217	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
218	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
219	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₆₇	—	2	1	no	—
223	C₂²×C₄×C₆₇	—	2	1	no	—
224	C₂²×C₄×C₆₇	—	2	1	no	—
225	C₂²×C₄×C₆₇	—	2	4	no	—
226	C₂²×C₄×C₆₇	—	2	4	no	—
227	C₂²×C₄×C₆₇	—	2	2	no	—
228	C₂²×C₄×C₆₇	—	2	2	no	—
229	C₂²×C₄×C₆₇	—	8	2	no	—
230	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
233	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
234	SD₁₆×C₆₇	—	2	8	no	—
235	M₁₆×C₆₇	—	2	4	no	—
236	M₁₆×C₆₇	—	2	8	no	—
237	C₂×C₈×C₆₇	—	2	2	no	—
238	C₂×C₈×C₆₇	—	2	8	no	—
239	C₂×C₈×C₆₇	#41	1	4	yes	complemented
240	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
241	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
242	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
243	C₄⋊C₄×C₆₇	—	2	2	no	—
244	C₄⋊C₄×C₆₇	—	2	2	no	—
245	C₄⋊C₄×C₆₇	—	2	1	no	—
246	C₄⋊C₄×C₆₇	—	2	1	no	—
247	C₄⋊C₄×C₆₇	—	2	4	no	—
248	C₄⋊C₄×C₆₇	—	2	4	no	—
249	C₄⋊C₄×C₆₇	—	2	1	no	—
250	C₄⋊C₄×C₆₇	—	2	2	no	—
251	C₄⋊C₄×C₆₇	—	2	4	no	—
252	C₄⋊C₄×C₆₇	—	2	2	no	—
253	C₄⋊C₄×C₆₇	—	2	1	no	—
254	C₄⋊C₄×C₆₇	—	2	2	no	—
255	C₄⋊C₄×C₆₇	—	2	1	no	—
256	C₄⋊C₄×C₆₇	—	2	2	no	—
257	C₄⋊C₄×C₆₇	—	2	1	no	—
258	C₄⋊C₄×C₆₇	—	2	4	no	—
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	2	yes	—
263	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²⋊C₄×C₆₇	—	2	4	no	—
268	C₂²⋊C₄×C₆₇	—	2	2	no	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	2	no	—
271	C₂²⋊C₄×C₆₇	—	2	4	no	—
272	C₂²⋊C₄×C₆₇	—	2	4	no	—
273	C₂²⋊C₄×C₆₇	—	2	2	no	—
274	C₂²⋊C₄×C₆₇	—	2	2	no	—
275	C₂²⋊C₄×C₆₇	—	2	4	no	—
276	C₂²⋊C₄×C₆₇	—	2	4	no	—
277	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
278	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
279	C₄²×C₆₇	—	2	2	no	—
280	C₄²×C₆₇	—	2	2	no	—
281	C₄²×C₆₇	—	2	4	no	—
282	C₄²×C₆₇	—	2	4	no	—
283	C₄²×C₆₇	—	2	2	no	—
284	C₄²×C₆₇	—	2	2	no	—
285	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
287	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
288	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂³×C₆₇	—	2	2	no	—
290	C₂³×C₆₇	—	4	2	no	—
291	C₂³×C₆₇	—	8	1	no	—
292	C₂³×C₆₇	—	8	1	no	—
293	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
294	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₆₇	—	2	4	no	—
296	Q₈×C₆₇	—	2	2	no	—
297	Q₈×C₆₇	—	2	2	no	—
298	Q₈×C₆₇	—	4	2	no	—
299	Q₈×C₆₇	—	4	2	no	—
300	Q₈×C₆₇	—	4	2	no	—
301	Q₈×C₆₇	—	8	1	no	—
302	Q₈×C₆₇	—	8	1	no	—
303	D₄×C₆₇	—	2	8	no	—
304	D₄×C₆₇	—	2	4	no	—
305	D₄×C₆₇	—	2	2	no	—
306	D₄×C₆₇	—	2	2	no	—
307	D₄×C₆₇	—	4	2	no	—
308	D₄×C₆₇	—	4	2	no	—
309	D₄×C₆₇	—	4	2	no	—
310	D₄×C₆₇	—	8	4	no	—
311	D₄×C₆₇	—	8	4	no	—
312	C₂×C₄×C₆₇	—	2	4	no	—
313	C₂×C₄×C₆₇	—	2	4	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	4	1	no	—
322	C₂×C₄×C₆₇	—	4	1	no	—
323	C₂×C₄×C₆₇	—	4	4	no	—
324	C₂×C₄×C₆₇	—	4	2	no	—
325	C₂×C₄×C₆₇	—	8	2	no	—
326	C₂×C₄×C₆₇	—	8	1	no	—
327	C₂×C₄×C₆₇	—	8	4	no	—
328	C₂×C₄×C₆₇	—	8	1	no	—
329	C₂×C₄×C₆₇	—	8	4	no	—
330	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
337	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
338	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
339	C₈×C₆₇	—	2	4	no	—
340	C₈×C₆₇	—	2	2	no	—
341	C₈×C₆₇	C₂×#41	1	4	yes	—
342	C₂²×C₆₇	—	2	1	no	—
343	C₂²×C₆₇	—	2	1	no	—
344	C₂²×C₆₇	—	2	4	no	—
345	C₂²×C₆₇	—	2	4	no	—
346	C₂²×C₆₇	—	2	4	no	—
347	C₂²×C₆₇	—	4	2	no	—
348	C₂²×C₆₇	—	4	2	no	—
349	C₂²×C₆₇	—	4	2	no	—
350	C₂²×C₆₇	—	8	4	no	—
351	C₂²×C₆₇	#547	1	2	yes	—
352	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
353	C₄×C₆₇	—	2	1	no	—
354	C₄×C₆₇	—	2	1	no	—
355	C₄×C₆₇	—	2	1	no	—
356	C₄×C₆₇	—	2	1	no	—
357	C₄×C₆₇	—	2	4	no	—
358	C₄×C₆₇	—	4	2	no	—
359	C₄×C₆₇	—	4	2	no	—
360	C₄×C₆₇	—	4	2	no	—
361	C₄×C₆₇	—	4	2	no	—
362	C₄×C₆₇	—	4	2	no	—
363	C₄×C₆₇	—	4	2	no	—
364	C₄×C₆₇	—	4	2	no	—
365	C₄×C₆₇	#547	1	2	yes	—
366	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
367	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
368	#61291	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
369	C₂×C₆₇	—	2	2	no	—
370	C₂×C₆₇	—	4	4	no	—
371	C₂×C₆₇	—	8	2	no	—
372	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
373	C₂×C₆₇	#3585	1	1	yes	characteristic
374	C₂×C₆₇	#3586	1	1	yes	characteristic
375	#3507	C₂×C₆₇	1	1	yes	characteristic, complemented
376	#3506	C₂×C₆₇	1	1	yes	characteristic
377	#3350	C₂×C₆₇	1	4	yes	complemented
378	#3348	C₂×C₆₇	1	4	yes	complemented
379	#3346	C₂×C₆₇	1	4	yes	complemented
380	#3343	C₂×C₆₇	1	4	yes	complemented
381	#3162	C₂×C₆₇	1	1	yes	characteristic, complemented
382	#3097	C₂×C₆₇	1	2	yes	complemented
383	#3096	C₂×C₆₇	1	2	yes	complemented
384	#3078	C₂×C₆₇	1	1	yes	characteristic, complemented
385	#3077	C₂×C₆₇	1	1	yes	characteristic, complemented
386	#3057	C₂×C₆₇	1	2	yes	complemented
387	C₂×#440	C₂×C₆₇	1	1	yes	characteristic, complemented
388	#2932	C₂×C₆₇	1	1	yes	characteristic, complemented
389	#2913	C₂×C₆₇	1	2	yes	complemented
390	C₆₇	#61291	1	1	yes	characteristic, direct product factor, Sylow
391	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
392	C₂×#131	C₂²×C₆₇	1	2	yes	—
393	#559	—	2	1	no	—
394	#559	—	2	2	no	—
395	#557	—	2	1	no	—
396	#556	—	2	1	no	—
397	#556	—	2	2	no	—
398	#556	C₂²×C₆₇	1	2	yes	complemented
399	#555	C₂²×C₆₇	1	2	yes	—
400	#554	C₂²×C₆₇	1	2	yes	complemented
401	#553	C₂²×C₆₇	1	4	yes	—
402	#552	C₂²×C₆₇	1	4	yes	complemented
403	#550	—	2	1	no	—
404	#547	C₂²×C₆₇	1	2	yes	—
405	#539	—	2	2	no	—
406	#538	—	2	2	no	—
407	#536	C₂²×C₆₇	1	2	yes	—
408	#535	C₂²×C₆₇	1	2	yes	—
409	#533	C₂²×C₆₇	1	1	yes	characteristic
410	#533	C₂²×C₆₇	1	1	yes	characteristic
411	#532	C₂²×C₆₇	1	1	yes	characteristic
412	#529	—	2	2	no	—
413	#525	—	2	2	no	—
414	#520	C₂²×C₆₇	1	2	yes	—
415	#520	C₂²×C₆₇	1	2	yes	—
416	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
418	#501	C₂²×C₆₇	1	2	yes	complemented
419	#501	C₂²×C₆₇	1	2	yes	complemented
420	#501	C₂²×C₆₇	1	2	yes	complemented
421	#501	C₂²×C₆₇	1	2	yes	complemented
422	#485	C₂²×C₆₇	1	4	yes	complemented
423	#485	C₂²×C₆₇	1	4	yes	complemented
424	#484	C₂²×C₆₇	1	4	yes	complemented
425	#483	C₂²×C₆₇	1	4	yes	complemented
426	#482	C₂²×C₆₇	1	4	yes	—
427	#482	C₂²×C₆₇	1	4	yes	—
428	#481	C₂²×C₆₇	1	4	yes	—
429	#480	C₂²×C₆₇	1	4	yes	—
430	#479	C₂²×C₆₇	1	4	yes	complemented
431	#478	C₂²×C₆₇	1	4	yes	—
432	#477	C₂²×C₆₇	1	2	yes	complemented
433	#476	C₂²×C₆₇	1	2	yes	—
434	#475	C₂²×C₆₇	1	2	yes	complemented
435	#474	C₂²×C₆₇	1	2	yes	—
436	#468	C₂²×C₆₇	1	4	yes	—
437	#468	C₂²×C₆₇	1	4	yes	—
438	#465	C₂²×C₆₇	1	4	yes	—
439	#465	C₂²×C₆₇	1	4	yes	—
440	#440	C₂²×C₆₇	1	4	yes	—
441	#440	C₂²×C₆₇	1	4	yes	—
442	#435	C₂²×C₆₇	1	4	yes	complemented
443	#435	C₂²×C₆₇	1	4	yes	complemented
444	#428	C₂²×C₆₇	1	2	yes	—
445	#428	C₂²×C₆₇	1	2	yes	—
446	#428	C₂²×C₆₇	1	4	yes	complemented
447	#428	C₂²×C₆₇	1	4	yes	complemented
448	#427	C₂²×C₆₇	1	2	yes	—
449	#427	C₂²×C₆₇	1	2	yes	—
450	#427	C₂²×C₆₇	1	4	yes	complemented
451	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
452	C₂×#107	C₂²×C₆₇	1	4	yes	complemented
453	#423	C₂²×C₆₇	1	1	yes	characteristic
454	#419	C₂²×C₆₇	1	2	yes	—
455	#418	C₂²×C₆₇	1	2	yes	—
456	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
457	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
458	#408	C₂²×C₆₇	1	2	yes	—
459	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
460	C₂×#41	—	2	2	no	—
461	C₂×#41	C₂³×C₆₇	1	2	yes	—
462	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
463	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
464	C₂³×C₄	—	2	1	no	—
465	C₂×SD₁₆	—	2	4	no	—
466	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
467	#131	—	2	8	no	—
468	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
469	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
470	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
471	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
473	C₄⋊Q₈	—	2	2	no	—
474	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
475	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
476	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
478	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
479	#127	—	2	2	no	—
480	#127	D₄×C₆₇	1	1	yes	characteristic
481	#126	—	2	4	no	—
482	#126	—	2	4	no	—
483	#126	—	2	4	no	—
484	#125	—	2	2	no	—
485	#125	—	2	4	no	—
486	#125	C₂³×C₆₇	1	2	yes	—
487	#125	C₂³×C₆₇	1	2	yes	—
488	#124	—	2	2	no	—
489	#124	—	2	2	no	—
490	#124	—	2	2	no	—
491	#124	—	2	4	no	—
492	#124	D₄×C₆₇	1	2	yes	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	#123	—	2	4	no	—
496	#123	—	2	4	no	—
497	C₂²⋊Q₈	—	2	1	no	—
498	C₂²⋊Q₈	—	2	1	no	—
499	C₂²⋊Q₈	—	2	1	no	—
500	C₂²⋊Q₈	—	2	1	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
504	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
505	#121	—	2	2	no	—
506	#121	—	2	4	no	—
507	#121	D₄×C₆₇	1	2	yes	—
508	#121	D₄×C₆₇	1	2	yes	—
509	#121	C₂³×C₆₇	1	4	yes	—
510	#121	C₂³×C₆₇	1	4	yes	—
511	#120	—	2	4	no	—
512	C₄×Q₈	—	2	2	no	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	1	no	—
516	C₄×Q₈	—	2	1	no	—
517	C₄×Q₈	—	2	1	no	—
518	C₄×Q₈	—	2	1	no	—
519	C₄×Q₈	—	2	1	no	—
520	C₄×Q₈	—	2	1	no	—
521	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
522	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
523	C₄×D₄	—	2	4	no	—
524	C₄×D₄	—	2	4	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	4	no	—
529	C₄×D₄	—	2	1	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	C₂³×C₆₇	1	2	yes	—
532	C₄×D₄	C₂³×C₆₇	1	2	yes	—
533	C₄×D₄	C₂³×C₆₇	1	2	yes	—
534	C₄×D₄	C₂³×C₆₇	1	2	yes	—
535	#117	—	2	2	no	—
536	#117	—	2	4	no	—
537	#117	C₂³×C₆₇	1	2	yes	—
538	#117	C₂³×C₆₇	1	2	yes	—
539	#117	C₂³×C₆₇	1	4	yes	—
540	#117	C₂³×C₆₇	1	4	yes	—
541	C₂×C₄⋊C₄	—	2	1	no	—
542	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
545	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₄²	—	2	1	no	—
548	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
549	#107	C₂³×C₆₇	1	4	yes	—
550	#107	C₂³×C₆₇	1	2	yes	—
551	#107	C₂³×C₆₇	1	4	yes	—
552	#107	C₂³×C₆₇	1	4	yes	—
553	#107	C₂³×C₆₇	1	2	yes	—
554	#107	C₂³×C₆₇	1	2	yes	—
555	#107	C₂³×C₆₇	1	2	yes	—
556	#106	C₂³×C₆₇	1	2	yes	—
557	#106	C₂³×C₆₇	1	2	yes	—
558	#106	C₂³×C₆₇	1	2	yes	—
559	#106	C₂³×C₆₇	1	2	yes	—
560	#106	C₂³×C₆₇	1	4	yes	—
561	#106	C₂³×C₆₇	1	4	yes	—
562	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
563	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
564	#103	C₂³×C₆₇	1	4	yes	—
565	#103	C₂³×C₆₇	1	4	yes	—
566	#103	C₂³×C₆₇	1	4	yes	—
567	#102	C₂³×C₆₇	1	4	yes	—
568	#102	C₂³×C₆₇	1	4	yes	—
569	#102	C₂³×C₆₇	1	4	yes	—
570	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
571	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
572	#97	C₂³×C₆₇	1	2	yes	—
573	#97	C₂³×C₆₇	1	2	yes	—
574	C₂⁴	—	2	1	no	—
575	#41	—	2	4	no	—
576	#41	—	2	4	no	—
577	#41	—	8	4	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
586	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
593	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
594	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
595	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
596	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	8	2	no	—
605	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
608	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
609	SD₁₆	—	2	8	no	—
610	M₁₆	—	2	4	no	—
611	M₁₆	—	2	8	no	—
612	C₂×C₈	—	2	2	no	—
613	C₂×C₈	—	2	8	no	—
614	C₂×C₈	#41×C₆₇	1	4	yes	complemented
615	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
616	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
617	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
635	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
636	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
653	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	2	no	—
660	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
661	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
662	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
663	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
664	C₂³	—	2	2	no	—
665	C₂³	—	4	2	no	—
666	C₂³	—	8	1	no	—
667	C₂³	—	8	1	no	—
668	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
669	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
670	Q₈	—	2	4	no	—
671	Q₈	—	2	2	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	4	2	no	—
674	Q₈	—	4	2	no	—
675	Q₈	—	4	2	no	—
676	Q₈	—	8	1	no	—
677	Q₈	—	8	1	no	—
678	D₄	—	2	8	no	—
679	D₄	—	2	4	no	—
680	D₄	—	2	2	no	—
681	D₄	—	2	2	no	—
682	D₄	—	4	2	no	—
683	D₄	—	4	2	no	—
684	D₄	—	4	2	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	4	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	2	no	—
700	C₂×C₄	—	8	2	no	—
701	C₂×C₄	—	8	1	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	—	8	1	no	—
704	C₂×C₄	—	8	4	no	—
705	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
708	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
711	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
712	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
713	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
714	C₈	—	2	4	no	—
715	C₈	—	2	2	no	—
716	C₈	C₂×#41×C₆₇	1	4	yes	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	4	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	8	4	no	—
726	C₂²	#547×C₆₇	1	2	yes	—
727	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	4	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	#547×C₆₇	1	2	yes	—
741	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
742	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
743	C₂	—	2	2	no	—
744	C₂	—	4	4	no	—
745	C₂	—	8	2	no	—
746	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
747	C₂	C₆₇×#3585	1	1	yes	characteristic
748	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×#3506	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×#3350	C₂	semidirect
4. C₆₇×#3348	C₂	semidirect
5. C₆₇×#3346	C₂	semidirect
6. C₆₇×#3343	C₂	semidirect
7. C₆₇×#3162	C₂	semidirect
8. C₆₇×#3097	C₂	semidirect
9. C₆₇×#3096	C₂	semidirect
10. C₆₇×#3078	C₂	semidirect
11. C₆₇×#3077	C₂	semidirect
12. C₆₇×#3057	C₂	semidirect
13. C₂×#440×C₆₇	C₂	semidirect
14. C₆₇×#2932	C₂	semidirect
15. C₆₇×#2913	C₂	semidirect
23. #556×C₆₇	C₂²	semidirect
25. #554×C₆₇	C₂²	semidirect
27. #552×C₆₇	C₂²	semidirect
43. #501×C₆₇	C₂²	semidirect
44. #501×C₆₇	C₂²	semidirect
45. #501×C₆₇	C₂²	semidirect
46. #501×C₆₇	C₂²	semidirect
47. #485×C₆₇	C₂²	semidirect
48. #485×C₆₇	C₂²	semidirect
49. #484×C₆₇	C₂²	semidirect
50. #483×C₆₇	C₂²	semidirect
55. #479×C₆₇	C₂²	semidirect
57. #477×C₆₇	C₂²	semidirect
59. #475×C₆₇	C₂²	semidirect
67. #435×C₆₇	C₂²	semidirect
68. #435×C₆₇	C₂²	semidirect
71. #428×C₆₇	C₂²	semidirect
72. #428×C₆₇	C₂²	semidirect
75. #427×C₆₇	C₂²	semidirect
77. C₂×#107×C₆₇	C₂²	semidirect
239. C₂×C₈×C₆₇	#41	semidirect
368. #61291	C₆₇	direct (N × H)
375. #3507	C₂×C₆₇	semidirect
377. #3350	C₂×C₆₇	semidirect
378. #3348	C₂×C₆₇	semidirect
379. #3346	C₂×C₆₇	semidirect
380. #3343	C₂×C₆₇	semidirect
381. #3162	C₂×C₆₇	semidirect
382. #3097	C₂×C₆₇	semidirect
383. #3096	C₂×C₆₇	semidirect
384. #3078	C₂×C₆₇	semidirect
385. #3077	C₂×C₆₇	semidirect
386. #3057	C₂×C₆₇	semidirect
387. C₂×#440	C₂×C₆₇	semidirect
388. #2932	C₂×C₆₇	semidirect
389. #2913	C₂×C₆₇	semidirect
390. C₆₇	#61291	direct (N × H)
398. #556	C₂²×C₆₇	semidirect
400. #554	C₂²×C₆₇	semidirect
402. #552	C₂²×C₆₇	semidirect
418. #501	C₂²×C₆₇	semidirect
419. #501	C₂²×C₆₇	semidirect
420. #501	C₂²×C₆₇	semidirect
421. #501	C₂²×C₆₇	semidirect
422. #485	C₂²×C₆₇	semidirect
423. #485	C₂²×C₆₇	semidirect
424. #484	C₂²×C₆₇	semidirect
425. #483	C₂²×C₆₇	semidirect
430. #479	C₂²×C₆₇	semidirect
432. #477	C₂²×C₆₇	semidirect
434. #475	C₂²×C₆₇	semidirect
442. #435	C₂²×C₆₇	semidirect
443. #435	C₂²×C₆₇	semidirect
446. #428	C₂²×C₆₇	semidirect
447. #428	C₂²×C₆₇	semidirect
450. #427	C₂²×C₆₇	semidirect
452. C₂×#107	C₂²×C₆₇	semidirect
614. 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×#3507	2
C₆₇×#3506	2
C₆₇×#3350	2
C₆₇×#3348	2
C₆₇×#3346	2
C₆₇×#3343	2
C₆₇×#3162	2
C₆₇×#3097	2
C₆₇×#3096	2
C₆₇×#3078	2
C₆₇×#3077	2
C₆₇×#3057	2
C₂×#440×C₆₇	2
C₆₇×#2932	2
C₆₇×#2913	2
#61291	67

Subgroups — C67×#61291 #30740542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61291 #30740542