Subgroups — C₆₇×#61019 #30740270

Order 17152.

1788 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3260	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3259	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3240	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3234	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3217	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3214	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3198	C₂	1	4	yes	maximal, complemented
10	C₆₇×#3180	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3171	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3123	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3122	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3119	C₂	1	4	yes	maximal, complemented
15	C₆₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	#559×C₆₇	—	2	2	no	—
17	#553×C₆₇	—	2	2	no	—
18	#553×C₆₇	—	2	2	no	—
19	#553×C₆₇	—	2	2	no	—
20	#552×C₆₇	—	2	2	no	—
21	#550×C₆₇	—	2	2	no	—
22	#546×C₆₇	—	2	2	no	—
23	#546×C₆₇	—	2	2	no	—
24	#541×C₆₇	C₂²	1	1	yes	characteristic
25	#541×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	#540×C₆₇	C₂²	1	2	yes	—
27	#540×C₆₇	C₂²	1	1	yes	characteristic
28	#540×C₆₇	C₂²	1	2	yes	—
29	#540×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	#537×C₆₇	C₂²	1	2	yes	—
31	#535×C₆₇	C₂²	1	2	yes	—
32	#533×C₆₇	C₂²	1	1	yes	characteristic
33	#532×C₆₇	C₂²	1	2	yes	—
34	#532×C₆₇	C₂²	1	2	yes	—
35	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
37	#529×C₆₇	C₂²	1	2	yes	—
38	#529×C₆₇	C₂²	1	2	yes	complemented
39	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#520×C₆₇	C₂²	1	2	yes	complemented
41	#518×C₆₇	C₂²	1	2	yes	—
42	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
43	#501×C₆₇	C₂²	1	2	yes	complemented
44	#501×C₆₇	C₂²	1	2	yes	complemented
45	#496×C₆₇	C₂²	1	2	yes	—
46	#496×C₆₇	C₂²	1	2	yes	—
47	#490×C₆₇	C₂²	1	2	yes	—
48	#490×C₆₇	C₂²	1	2	yes	—
49	#489×C₆₇	C₂²	1	2	yes	complemented
50	#489×C₆₇	C₂²	1	2	yes	complemented
51	#485×C₆₇	C₂²	1	4	yes	—
52	#482×C₆₇	C₂²	1	4	yes	—
53	#481×C₆₇	C₂²	1	4	yes	complemented
54	#480×C₆₇	C₂²	1	4	yes	complemented
55	#479×C₆₇	C₂²	1	4	yes	complemented
56	#478×C₆₇	C₂²	1	4	yes	complemented
57	#478×C₆₇	C₂²	1	4	yes	complemented
58	#478×C₆₇	C₂²	1	4	yes	complemented
59	#469×C₆₇	C₂²	1	4	yes	complemented
60	#468×C₆₇	C₂²	1	4	yes	complemented
61	#466×C₆₇	C₂²	1	4	yes	complemented
62	#465×C₆₇	C₂²	1	4	yes	complemented
63	#461×C₆₇	C₂²	1	4	yes	complemented
64	#460×C₆₇	C₂²	1	4	yes	—
65	#459×C₆₇	C₂²	1	4	yes	—
66	#459×C₆₇	C₂²	1	4	yes	complemented
67	#450×C₆₇	C₂²	1	4	yes	—
68	#449×C₆₇	C₂²	1	4	yes	complemented
69	#449×C₆₇	C₂²	1	4	yes	complemented
70	#447×C₆₇	C₂²	1	4	yes	—
71	#442×C₆₇	C₂²	1	4	yes	complemented
72	#440×C₆₇	C₂²	1	4	yes	complemented
73	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
74	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
75	#433×C₆₇	C₂²	1	2	yes	—
76	#433×C₆₇	C₂²	1	2	yes	complemented
77	#432×C₆₇	C₂²	1	2	yes	—
78	#432×C₆₇	C₂²	1	2	yes	complemented
79	#424×C₆₇	C₂²	1	2	yes	complemented
80	#408×C₆₇	C₂²	1	2	yes	—
81	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	C₂×#41×C₆₇	—	2	2	no	—
84	C₂×#41×C₆₇	—	2	2	no	—
85	C₂×#41×C₆₇	C₂³	1	2	yes	—
86	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₆₇	—	2	2	no	—
88	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
89	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
90	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
91	C₂×D₈×C₆₇	C₂³	1	4	yes	—
92	C₂×D₈×C₆₇	C₂³	1	4	yes	—
93	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
94	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
95	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
97	#127×C₆₇	—	2	2	no	—
98	#127×C₆₇	—	2	2	no	—
99	#127×C₆₇	C₂³	1	2	yes	—
100	#127×C₆₇	C₂³	1	1	yes	characteristic
101	#127×C₆₇	C₂³	1	2	yes	—
102	#126×C₆₇	—	2	2	no	—
103	#126×C₆₇	—	2	2	no	—
104	#126×C₆₇	—	2	2	no	—
105	#126×C₆₇	—	2	2	no	—
106	#125×C₆₇	—	2	2	no	—
107	#125×C₆₇	—	2	2	no	—
108	#125×C₆₇	—	2	2	no	—
109	#125×C₆₇	C₂³	1	1	yes	characteristic
110	#125×C₆₇	C₂³	1	1	yes	characteristic
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	C₂³	1	2	yes	—
117	#123×C₆₇	—	2	2	no	—
118	#123×C₆₇	—	2	2	no	—
119	#123×C₆₇	—	2	4	no	—
120	#123×C₆₇	—	2	4	no	—
121	#123×C₆₇	—	2	2	no	—
122	#123×C₆₇	—	2	2	no	—
123	C₂²⋊Q₈×C₆₇	—	2	2	no	—
124	C₂²⋊Q₈×C₆₇	—	2	2	no	—
125	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
126	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
127	#121×C₆₇	—	2	2	no	—
128	#121×C₆₇	—	2	2	no	—
129	#121×C₆₇	—	2	2	no	—
130	#121×C₆₇	—	2	2	no	—
131	#121×C₆₇	—	2	2	no	—
132	#121×C₆₇	—	2	2	no	—
133	#121×C₆₇	—	2	4	no	—
134	#121×C₆₇	—	2	4	no	—
135	#121×C₆₇	—	2	2	no	—
136	#121×C₆₇	—	2	2	no	—
137	#121×C₆₇	C₂³	1	4	yes	—
138	#121×C₆₇	C₂³	1	4	yes	—
139	#121×C₆₇	C₂³	1	2	yes	—
140	#121×C₆₇	C₂³	1	2	yes	—
141	#120×C₆₇	—	2	2	no	—
142	#120×C₆₇	—	2	2	no	—
143	C₄×Q₈×C₆₇	—	2	2	no	—
144	C₄×Q₈×C₆₇	D₄	1	2	yes	—
145	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
146	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
147	C₄×D₄×C₆₇	—	2	2	no	—
148	C₄×D₄×C₆₇	—	2	2	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	2	no	—
154	C₄×D₄×C₆₇	—	2	2	no	—
155	C₄×D₄×C₆₇	D₄	1	2	yes	—
156	C₄×D₄×C₆₇	D₄	1	2	yes	—
157	C₄×D₄×C₆₇	D₄	1	2	yes	—
158	C₄×D₄×C₆₇	C₂³	1	2	yes	—
159	C₄×D₄×C₆₇	C₂³	1	4	yes	—
160	C₄×D₄×C₆₇	C₂³	1	4	yes	—
161	C₄×D₄×C₆₇	C₂³	1	2	yes	—
162	#117×C₆₇	—	2	2	no	—
163	#117×C₆₇	—	2	2	no	—
164	#117×C₆₇	—	2	2	no	—
165	#117×C₆₇	C₂³	1	2	yes	—
166	#117×C₆₇	C₂³	1	1	yes	characteristic
167	#117×C₆₇	C₂³	1	1	yes	characteristic
168	#117×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
170	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
173	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
176	#107×C₆₇	C₂³	1	4	yes	—
177	#107×C₆₇	C₂³	1	4	yes	—
178	#106×C₆₇	C₂³	1	4	yes	—
179	#106×C₆₇	C₂³	1	4	yes	—
180	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
181	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
182	#103×C₆₇	C₂³	1	4	yes	—
183	#103×C₆₇	C₂³	1	4	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	#102×C₆₇	C₂³	1	4	yes	—
189	#102×C₆₇	C₂³	1	4	yes	—
190	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
191	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
192	#97×C₆₇	C₂³	1	2	yes	—
193	#97×C₆₇	C₂³	1	2	yes	—
194	#97×C₆₇	C₂³	1	2	yes	—
195	C₄×C₈×C₆₇	C₂³	1	2	yes	—
196	C₂⁴×C₆₇	—	2	2	no	—
197	#41×C₆₇	—	4	2	no	—
198	#41×C₆₇	—	4	4	no	—
199	#41×C₆₇	—	8	4	no	—
200	#41×C₆₇	—	8	4	no	—
201	C₂×Q₈×C₆₇	—	2	2	no	—
202	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
203	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
204	C₂×D₄×C₆₇	—	2	2	no	—
205	C₂×D₄×C₆₇	—	2	2	no	—
206	C₂×D₄×C₆₇	—	2	2	no	—
207	C₂×D₄×C₆₇	—	2	4	no	—
208	C₂×D₄×C₆₇	—	2	4	no	—
209	C₂×D₄×C₆₇	—	2	2	no	—
210	C₂×D₄×C₆₇	—	2	2	no	—
211	C₂×D₄×C₆₇	—	2	2	no	—
212	C₂×D₄×C₆₇	—	2	2	no	—
213	C₂×D₄×C₆₇	—	2	4	no	—
214	C₂×D₄×C₆₇	—	4	4	no	—
215	C₂×D₄×C₆₇	—	8	4	no	—
216	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
219	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
220	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₆₇	—	2	2	no	—
222	C₂²×C₄×C₆₇	—	2	2	no	—
223	C₂²×C₄×C₆₇	—	2	4	no	—
224	C₂²×C₄×C₆₇	—	2	4	no	—
225	C₂²×C₄×C₆₇	—	2	2	no	—
226	C₂²×C₄×C₆₇	—	2	2	no	—
227	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
230	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
233	SD₁₆×C₆₇	—	4	4	no	—
234	SD₁₆×C₆₇	—	4	4	no	—
235	D₈×C₆₇	—	4	4	no	—
236	D₈×C₆₇	—	4	4	no	—
237	M₁₆×C₆₇	—	4	2	no	—
238	C₂×C₈×C₆₇	—	4	2	no	—
239	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
240	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
241	C₄⋊C₄×C₆₇	—	2	2	no	—
242	C₄⋊C₄×C₆₇	—	2	2	no	—
243	C₄⋊C₄×C₆₇	—	2	2	no	—
244	C₄⋊C₄×C₆₇	—	2	2	no	—
245	C₄⋊C₄×C₆₇	—	2	2	no	—
246	C₄⋊C₄×C₆₇	—	2	2	no	—
247	C₄⋊C₄×C₆₇	—	2	2	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	4	no	—
253	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
259	C₂²⋊C₄×C₆₇	—	2	2	no	—
260	C₂²⋊C₄×C₆₇	—	2	2	no	—
261	C₂²⋊C₄×C₆₇	—	2	2	no	—
262	C₂²⋊C₄×C₆₇	—	2	4	no	—
263	C₂²⋊C₄×C₆₇	—	2	4	no	—
264	C₂²⋊C₄×C₆₇	—	2	2	no	—
265	C₂²⋊C₄×C₆₇	—	2	2	no	—
266	C₂²⋊C₄×C₆₇	—	2	2	no	—
267	C₂²⋊C₄×C₆₇	—	2	2	no	—
268	C₂²⋊C₄×C₆₇	—	2	2	no	—
269	C₂²⋊C₄×C₆₇	—	2	2	no	—
270	C₂²⋊C₄×C₆₇	—	2	4	no	—
271	C₂²⋊C₄×C₆₇	—	2	4	no	—
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	C₄²×C₆₇	—	2	2	no	—
276	C₄²×C₆₇	—	2	2	no	—
277	C₄²×C₆₇	—	2	2	no	—
278	C₄²×C₆₇	C₂×D₄	1	2	yes	—
279	C₄²×C₆₇	C₂×D₄	1	2	yes	—
280	C₄²×C₆₇	C₂×D₄	1	2	yes	—
281	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
282	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
283	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₂³×C₆₇	—	2	2	no	—
286	C₂³×C₆₇	—	2	4	no	—
287	C₂³×C₆₇	—	4	4	no	—
288	C₂³×C₆₇	—	8	4	no	—
289	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
290	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
291	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
292	Q₈×C₆₇	—	2	4	no	—
293	Q₈×C₆₇	—	4	1	no	—
294	Q₈×C₆₇	—	4	4	no	—
295	D₄×C₆₇	—	2	4	no	—
296	D₄×C₆₇	—	2	4	no	—
297	D₄×C₆₇	—	2	4	no	—
298	D₄×C₆₇	—	4	1	no	—
299	D₄×C₆₇	—	4	1	no	—
300	D₄×C₆₇	—	4	1	no	—
301	D₄×C₆₇	—	4	4	no	—
302	D₄×C₆₇	—	4	4	no	—
303	D₄×C₆₇	—	4	4	no	—
304	D₄×C₆₇	—	4	4	no	—
305	D₄×C₆₇	—	8	2	no	—
306	D₄×C₆₇	—	8	4	no	—
307	D₄×C₆₇	—	8	2	no	—
308	D₄×C₆₇	—	8	2	no	—
309	D₄×C₆₇	—	8	4	no	—
310	D₄×C₆₇	—	8	4	no	—
311	C₂×C₄×C₆₇	—	2	2	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	4	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	4	2	no	—
319	C₂×C₄×C₆₇	—	4	2	no	—
320	C₂×C₄×C₆₇	—	4	2	no	—
321	C₂×C₄×C₆₇	—	4	4	no	—
322	C₂×C₄×C₆₇	—	8	2	no	—
323	C₂×C₄×C₆₇	—	8	2	no	—
324	C₂×C₄×C₆₇	—	8	4	no	—
325	C₂×C₄×C₆₇	—	8	4	no	—
326	C₂×C₄×C₆₇	—	8	2	no	—
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	2	yes	—
331	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
335	C₈×C₆₇	—	2	4	no	—
336	C₈×C₆₇	—	2	4	no	—
337	C₂²×C₆₇	—	2	2	no	—
338	C₂²×C₆₇	—	2	2	no	—
339	C₂²×C₆₇	—	2	2	no	—
340	C₂²×C₆₇	—	2	1	no	—
341	C₂²×C₆₇	—	2	1	no	—
342	C₂²×C₆₇	—	2	1	no	—
343	C₂²×C₆₇	—	4	2	no	—
344	C₂²×C₆₇	—	4	4	no	—
345	C₂²×C₆₇	—	4	4	no	—
346	C₂²×C₆₇	—	4	2	no	—
347	C₂²×C₆₇	—	4	2	no	—
348	C₂²×C₆₇	—	4	4	no	—
349	C₂²×C₆₇	—	16	4	no	—
350	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
351	C₄×C₆₇	—	2	2	no	—
352	C₄×C₆₇	—	2	2	no	—
353	C₄×C₆₇	—	2	2	no	—
354	C₄×C₆₇	—	2	2	no	—
355	C₄×C₆₇	—	2	1	no	—
356	C₄×C₆₇	—	2	1	no	—
357	C₄×C₆₇	—	2	1	no	—
358	C₄×C₆₇	—	4	2	no	—
359	C₄×C₆₇	—	4	2	no	—
360	C₄×C₆₇	—	4	4	no	—
361	C₄×C₆₇	—	4	2	no	—
362	C₄×C₆₇	#585	1	2	yes	—
363	#61019	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
364	C₂×C₆₇	—	4	1	no	—
365	C₂×C₆₇	—	4	1	no	—
366	C₂×C₆₇	—	4	1	no	—
367	C₂×C₆₇	—	8	2	no	—
368	C₂×C₆₇	—	8	4	no	—
369	C₂×C₆₇	#3449	1	1	yes	characteristic
370	C₂×C₆₇	#3585	1	2	yes	—
371	#3512	C₂×C₆₇	1	1	yes	characteristic, complemented
372	#3508	C₂×C₆₇	1	1	yes	characteristic, complemented
373	#3260	C₂×C₆₇	1	2	yes	complemented
374	#3259	C₂×C₆₇	1	2	yes	complemented
375	#3240	C₂×C₆₇	1	2	yes	complemented
376	#3234	C₂×C₆₇	1	2	yes	complemented
377	#3217	C₂×C₆₇	1	2	yes	complemented
378	#3214	C₂×C₆₇	1	2	yes	complemented
379	#3198	C₂×C₆₇	1	4	yes	complemented
380	#3180	C₂×C₆₇	1	2	yes	complemented
381	#3171	C₂×C₆₇	1	2	yes	complemented
382	#3123	C₂×C₆₇	1	2	yes	complemented
383	#3122	C₂×C₆₇	1	2	yes	complemented
384	#3119	C₂×C₆₇	1	4	yes	complemented
385	#2923	C₂×C₆₇	1	1	yes	characteristic, complemented
386	C₆₇	#61019	1	1	yes	characteristic, direct product factor, Sylow
387	#559	—	2	2	no	—
388	#553	—	2	2	no	—
389	#553	—	2	2	no	—
390	#553	—	2	2	no	—
391	#552	—	2	2	no	—
392	#550	—	2	2	no	—
393	#546	—	2	2	no	—
394	#546	—	2	2	no	—
395	#541	C₂²×C₆₇	1	1	yes	characteristic
396	#541	C₂²×C₆₇	1	1	yes	characteristic, complemented
397	#540	C₂²×C₆₇	1	2	yes	—
398	#540	C₂²×C₆₇	1	1	yes	characteristic
399	#540	C₂²×C₆₇	1	2	yes	—
400	#540	C₂²×C₆₇	1	1	yes	characteristic, complemented
401	#537	C₂²×C₆₇	1	2	yes	—
402	#535	C₂²×C₆₇	1	2	yes	—
403	#533	C₂²×C₆₇	1	1	yes	characteristic
404	#532	C₂²×C₆₇	1	2	yes	—
405	#532	C₂²×C₆₇	1	2	yes	—
406	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
407	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
408	#529	C₂²×C₆₇	1	2	yes	—
409	#529	C₂²×C₆₇	1	2	yes	complemented
410	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
411	#520	C₂²×C₆₇	1	2	yes	complemented
412	#518	C₂²×C₆₇	1	2	yes	—
413	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
414	#501	C₂²×C₆₇	1	2	yes	complemented
415	#501	C₂²×C₆₇	1	2	yes	complemented
416	#496	C₂²×C₆₇	1	2	yes	—
417	#496	C₂²×C₆₇	1	2	yes	—
418	#490	C₂²×C₆₇	1	2	yes	—
419	#490	C₂²×C₆₇	1	2	yes	—
420	#489	C₂²×C₆₇	1	2	yes	complemented
421	#489	C₂²×C₆₇	1	2	yes	complemented
422	#485	C₂²×C₆₇	1	4	yes	—
423	#482	C₂²×C₆₇	1	4	yes	—
424	#481	C₂²×C₆₇	1	4	yes	complemented
425	#480	C₂²×C₆₇	1	4	yes	complemented
426	#479	C₂²×C₆₇	1	4	yes	complemented
427	#478	C₂²×C₆₇	1	4	yes	complemented
428	#478	C₂²×C₆₇	1	4	yes	complemented
429	#478	C₂²×C₆₇	1	4	yes	complemented
430	#469	C₂²×C₆₇	1	4	yes	complemented
431	#468	C₂²×C₆₇	1	4	yes	complemented
432	#466	C₂²×C₆₇	1	4	yes	complemented
433	#465	C₂²×C₆₇	1	4	yes	complemented
434	#461	C₂²×C₆₇	1	4	yes	complemented
435	#460	C₂²×C₆₇	1	4	yes	—
436	#459	C₂²×C₆₇	1	4	yes	—
437	#459	C₂²×C₆₇	1	4	yes	complemented
438	#450	C₂²×C₆₇	1	4	yes	—
439	#449	C₂²×C₆₇	1	4	yes	complemented
440	#449	C₂²×C₆₇	1	4	yes	complemented
441	#447	C₂²×C₆₇	1	4	yes	—
442	#442	C₂²×C₆₇	1	4	yes	complemented
443	#440	C₂²×C₆₇	1	4	yes	complemented
444	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
445	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
446	#433	C₂²×C₆₇	1	2	yes	—
447	#433	C₂²×C₆₇	1	2	yes	complemented
448	#432	C₂²×C₆₇	1	2	yes	—
449	#432	C₂²×C₆₇	1	2	yes	complemented
450	#424	C₂²×C₆₇	1	2	yes	complemented
451	#408	C₂²×C₆₇	1	2	yes	—
452	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
453	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
454	C₂×#41	—	2	2	no	—
455	C₂×#41	—	2	2	no	—
456	C₂×#41	C₂³×C₆₇	1	2	yes	—
457	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
458	C₂²×D₄	—	2	2	no	—
459	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
460	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
461	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
462	C₂×D₈	C₂³×C₆₇	1	4	yes	—
463	C₂×D₈	C₂³×C₆₇	1	4	yes	—
464	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
465	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
466	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
468	#127	—	2	2	no	—
469	#127	—	2	2	no	—
470	#127	C₂³×C₆₇	1	2	yes	—
471	#127	C₂³×C₆₇	1	2	yes	—
472	#127	C₂³×C₆₇	1	1	yes	characteristic
473	#126	—	2	2	no	—
474	#126	—	2	2	no	—
475	#126	—	2	2	no	—
476	#126	—	2	2	no	—
477	#125	—	2	2	no	—
478	#125	—	2	2	no	—
479	#125	—	2	2	no	—
480	#125	C₂³×C₆₇	1	2	yes	—
481	#125	C₂³×C₆₇	1	1	yes	characteristic
482	#125	C₂³×C₆₇	1	1	yes	characteristic
483	#125	C₂³×C₆₇	1	2	yes	—
484	#124	—	2	2	no	—
485	#124	—	2	2	no	—
486	#124	—	2	2	no	—
487	#124	C₂³×C₆₇	1	2	yes	—
488	#123	—	2	2	no	—
489	#123	—	2	2	no	—
490	#123	—	2	4	no	—
491	#123	—	2	4	no	—
492	#123	—	2	2	no	—
493	#123	—	2	2	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
497	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
498	#121	—	2	2	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	2	2	no	—
502	#121	—	2	2	no	—
503	#121	—	2	2	no	—
504	#121	—	2	4	no	—
505	#121	—	2	4	no	—
506	#121	—	2	2	no	—
507	#121	—	2	2	no	—
508	#121	C₂³×C₆₇	1	2	yes	—
509	#121	C₂³×C₆₇	1	2	yes	—
510	#121	C₂³×C₆₇	1	4	yes	—
511	#121	C₂³×C₆₇	1	4	yes	—
512	#120	—	2	2	no	—
513	#120	—	2	2	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	D₄×C₆₇	1	2	yes	—
516	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
517	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	4	no	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	D₄×C₆₇	1	2	yes	—
527	C₄×D₄	D₄×C₆₇	1	2	yes	—
528	C₄×D₄	D₄×C₆₇	1	2	yes	—
529	C₄×D₄	C₂³×C₆₇	1	4	yes	—
530	C₄×D₄	C₂³×C₆₇	1	4	yes	—
531	C₄×D₄	C₂³×C₆₇	1	2	yes	—
532	C₄×D₄	C₂³×C₆₇	1	2	yes	—
533	#117	—	2	2	no	—
534	#117	—	2	2	no	—
535	#117	—	2	2	no	—
536	#117	C₂³×C₆₇	1	2	yes	—
537	#117	C₂³×C₆₇	1	1	yes	characteristic
538	#117	C₂³×C₆₇	1	1	yes	characteristic
539	#117	C₂³×C₆₇	1	1	yes	characteristic
540	C₂×C₄⋊C₄	—	2	2	no	—
541	C₂×C₄⋊C₄	—	2	2	no	—
542	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
543	C₂×C₂²⋊C₄	—	2	4	no	—
544	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
547	#107	C₂³×C₆₇	1	4	yes	—
548	#107	C₂³×C₆₇	1	4	yes	—
549	#106	C₂³×C₆₇	1	4	yes	—
550	#106	C₂³×C₆₇	1	4	yes	—
551	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
552	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
553	#103	C₂³×C₆₇	1	4	yes	—
554	#103	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	#102	C₂³×C₆₇	1	4	yes	—
559	#102	C₂³×C₆₇	1	4	yes	—
560	#102	C₂³×C₆₇	1	4	yes	—
561	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
562	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
563	#97	C₂³×C₆₇	1	2	yes	—
564	#97	C₂³×C₆₇	1	2	yes	—
565	#97	C₂³×C₆₇	1	2	yes	—
566	C₄×C₈	C₂³×C₆₇	1	2	yes	—
567	C₂⁴	—	2	2	no	—
568	#41	—	4	2	no	—
569	#41	—	4	4	no	—
570	#41	—	8	4	no	—
571	#41	—	8	4	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
574	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	4	4	no	—
586	C₂×D₄	—	8	4	no	—
587	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
588	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
589	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
590	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
591	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
599	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
600	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
604	SD₁₆	—	4	4	no	—
605	SD₁₆	—	4	4	no	—
606	D₈	—	4	4	no	—
607	D₈	—	4	4	no	—
608	M₁₆	—	4	2	no	—
609	C₂×C₈	—	4	2	no	—
610	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
611	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	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	C₂×D₄×C₆₇	1	2	yes	—
625	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
626	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
629	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
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	C₂×D₄×C₆₇	1	2	yes	—
650	C₄²	C₂×D₄×C₆₇	1	2	yes	—
651	C₄²	C₂×D₄×C₆₇	1	2	yes	—
652	C₄²	C₂⁴×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	1	yes	characteristic
656	C₂³	—	2	2	no	—
657	C₂³	—	2	4	no	—
658	C₂³	—	4	4	no	—
659	C₂³	—	8	4	no	—
660	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
661	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
662	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
663	Q₈	—	2	4	no	—
664	Q₈	—	4	1	no	—
665	Q₈	—	4	4	no	—
666	D₄	—	2	4	no	—
667	D₄	—	2	4	no	—
668	D₄	—	2	4	no	—
669	D₄	—	4	1	no	—
670	D₄	—	4	1	no	—
671	D₄	—	4	1	no	—
672	D₄	—	4	4	no	—
673	D₄	—	4	4	no	—
674	D₄	—	4	4	no	—
675	D₄	—	4	4	no	—
676	D₄	—	8	4	no	—
677	D₄	—	8	2	no	—
678	D₄	—	8	4	no	—
679	D₄	—	8	4	no	—
680	D₄	—	8	2	no	—
681	D₄	—	8	2	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	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	—	8	4	no	—
694	C₂×C₄	—	8	4	no	—
695	C₂×C₄	—	8	2	no	—
696	C₂×C₄	—	8	2	no	—
697	C₂×C₄	—	8	2	no	—
698	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
700	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
703	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
705	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
706	C₈	—	2	4	no	—
707	C₈	—	2	4	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	4	no	—
716	C₂²	—	4	4	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	4	no	—
720	C₂²	—	16	4	no	—
721	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	2	1	no	—
727	C₄	—	2	1	no	—
728	C₄	—	2	1	no	—
729	C₄	—	4	4	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	#585×C₆₇	1	2	yes	—
734	C₂	—	4	1	no	—
735	C₂	—	4	1	no	—
736	C₂	—	4	1	no	—
737	C₂	—	8	4	no	—
738	C₂	—	8	2	no	—
739	C₂	C₆₇×#3449	1	1	yes	characteristic
740	C₂	C₆₇×#3585	1	2	yes	—

	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 ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3512	C₂	semidirect
2. C₆₇×#3508	C₂	semidirect
3. C₆₇×#3260	C₂	semidirect
4. C₆₇×#3259	C₂	semidirect
5. C₆₇×#3240	C₂	semidirect
6. C₆₇×#3234	C₂	semidirect
7. C₆₇×#3217	C₂	semidirect
8. C₆₇×#3214	C₂	semidirect
9. C₆₇×#3198	C₂	semidirect
10. C₆₇×#3180	C₂	semidirect
11. C₆₇×#3171	C₂	semidirect
12. C₆₇×#3123	C₂	semidirect
13. C₆₇×#3122	C₂	semidirect
14. C₆₇×#3119	C₂	semidirect
15. C₆₇×#2923	C₂	semidirect
25. #541×C₆₇	C₂²	semidirect
29. #540×C₆₇	C₂²	semidirect
35. #532×C₆₇	C₂²	semidirect
38. #529×C₆₇	C₂²	semidirect
39. C₂×#125×C₆₇	C₂²	semidirect
40. #520×C₆₇	C₂²	semidirect
43. #501×C₆₇	C₂²	semidirect
44. #501×C₆₇	C₂²	semidirect
49. #489×C₆₇	C₂²	semidirect
50. #489×C₆₇	C₂²	semidirect
53. #481×C₆₇	C₂²	semidirect
54. #480×C₆₇	C₂²	semidirect
55. #479×C₆₇	C₂²	semidirect
56. #478×C₆₇	C₂²	semidirect
57. #478×C₆₇	C₂²	semidirect
58. #478×C₆₇	C₂²	semidirect
59. #469×C₆₇	C₂²	semidirect
60. #468×C₆₇	C₂²	semidirect
61. #466×C₆₇	C₂²	semidirect
62. #465×C₆₇	C₂²	semidirect
63. #461×C₆₇	C₂²	semidirect
66. #459×C₆₇	C₂²	semidirect
68. #449×C₆₇	C₂²	semidirect
69. #449×C₆₇	C₂²	semidirect
71. #442×C₆₇	C₂²	semidirect
72. #440×C₆₇	C₂²	semidirect
73. C₄×SD₁₆×C₆₇	C₂²	semidirect
74. C₄×D₈×C₆₇	C₂²	semidirect
76. #433×C₆₇	C₂²	semidirect
78. #432×C₆₇	C₂²	semidirect
79. #424×C₆₇	C₂²	semidirect
81. C₄×M₁₆×C₆₇	C₂²	semidirect
82. C₂×#97×C₆₇	C₂²	semidirect
363. #61019	C₆₇	direct (N × H)
371. #3512	C₂×C₆₇	semidirect
372. #3508	C₂×C₆₇	semidirect
373. #3260	C₂×C₆₇	semidirect
374. #3259	C₂×C₆₇	semidirect
375. #3240	C₂×C₆₇	semidirect
376. #3234	C₂×C₆₇	semidirect
377. #3217	C₂×C₆₇	semidirect
378. #3214	C₂×C₆₇	semidirect
379. #3198	C₂×C₆₇	semidirect
380. #3180	C₂×C₆₇	semidirect
381. #3171	C₂×C₆₇	semidirect
382. #3123	C₂×C₆₇	semidirect
383. #3122	C₂×C₆₇	semidirect
384. #3119	C₂×C₆₇	semidirect
385. #2923	C₂×C₆₇	semidirect
386. C₆₇	#61019	direct (N × H)
396. #541	C₂²×C₆₇	semidirect
400. #540	C₂²×C₆₇	semidirect
406. #532	C₂²×C₆₇	semidirect
409. #529	C₂²×C₆₇	semidirect
410. C₂×#125	C₂²×C₆₇	semidirect
411. #520	C₂²×C₆₇	semidirect
414. #501	C₂²×C₆₇	semidirect
415. #501	C₂²×C₆₇	semidirect
420. #489	C₂²×C₆₇	semidirect
421. #489	C₂²×C₆₇	semidirect
424. #481	C₂²×C₆₇	semidirect
425. #480	C₂²×C₆₇	semidirect
426. #479	C₂²×C₆₇	semidirect
427. #478	C₂²×C₆₇	semidirect
428. #478	C₂²×C₆₇	semidirect
429. #478	C₂²×C₆₇	semidirect
430. #469	C₂²×C₆₇	semidirect
431. #468	C₂²×C₆₇	semidirect
432. #466	C₂²×C₆₇	semidirect
433. #465	C₂²×C₆₇	semidirect
434. #461	C₂²×C₆₇	semidirect
437. #459	C₂²×C₆₇	semidirect
439. #449	C₂²×C₆₇	semidirect
440. #449	C₂²×C₆₇	semidirect
442. #442	C₂²×C₆₇	semidirect
443. #440	C₂²×C₆₇	semidirect
444. C₄×SD₁₆	C₂²×C₆₇	semidirect
445. C₄×D₈	C₂²×C₆₇	semidirect
447. #433	C₂²×C₆₇	semidirect
449. #432	C₂²×C₆₇	semidirect
450. #424	C₂²×C₆₇	semidirect
452. C₄×M₁₆	C₂²×C₆₇	semidirect
453. C₂×#97	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3512	2
C₆₇×#3508	2
C₆₇×#3260	2
C₆₇×#3259	2
C₆₇×#3240	2
C₆₇×#3234	2
C₆₇×#3217	2
C₆₇×#3214	2
C₆₇×#3198	2
C₆₇×#3180	2
C₆₇×#3171	2
C₆₇×#3123	2
C₆₇×#3122	2
C₆₇×#3119	2
C₆₇×#2923	2
#61019	67

Subgroups — C67×#61019 #30740270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61019 #30740270