Subgroups — C₆₇×#60267 #30739518

Order 17152.

1790 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3455	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2995	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2994	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2993	C₂	1	4	yes	maximal, complemented
5	C₆₇×#2992	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2962	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2935	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2930	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2929	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2925	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2921	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2906	C₂	1	2	yes	maximal, complemented
13	C₂×#424×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#131×C₆₇	C₂²	1	2	yes	—
15	C₂×#131×C₆₇	C₂²	1	2	yes	—
16	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
18	#542×C₆₇	C₄	1	2	yes	—
19	#542×C₆₇	C₄	1	2	yes	—
20	#541×C₆₇	C₄	1	1	yes	characteristic
21	#541×C₆₇	C₄	1	1	yes	characteristic
22	#540×C₆₇	C₄	1	1	yes	characteristic
23	#540×C₆₇	C₄	1	1	yes	characteristic
24	#539×C₆₇	C₄	1	4	yes	—
25	#538×C₆₇	C₄	1	4	yes	—
26	#533×C₆₇	C₂²	1	1	yes	characteristic
27	#532×C₆₇	C₂²	1	1	yes	characteristic
28	#529×C₆₇	C₂²	1	4	yes	—
29	#529×C₆₇	C₂²	1	4	yes	—
30	#525×C₆₇	C₂²	1	2	yes	—
31	C₄×#41×C₆₇	C₂²	1	2	yes	—
32	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
33	#446×C₆₇	C₂²	1	4	yes	complemented
34	#446×C₆₇	C₂²	1	4	yes	complemented
35	#446×C₆₇	C₂²	1	4	yes	complemented
36	C₈×Q₈×C₆₇	C₂²	1	4	yes	complemented
37	#436×C₆₇	C₂²	1	4	yes	—
38	#436×C₆₇	C₂²	1	4	yes	—
39	#436×C₆₇	C₂²	1	4	yes	complemented
40	#435×C₆₇	C₂²	1	4	yes	—
41	#435×C₆₇	C₂²	1	4	yes	—
42	#435×C₆₇	C₂²	1	4	yes	—
43	#435×C₆₇	C₂²	1	4	yes	—
44	#435×C₆₇	C₂²	1	4	yes	complemented
45	#435×C₆₇	C₂²	1	4	yes	complemented
46	C₈×D₄×C₆₇	C₂²	1	4	yes	—
47	C₈×D₄×C₆₇	C₂²	1	4	yes	—
48	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
49	#433×C₆₇	C₂²	1	4	yes	—
50	#433×C₆₇	C₂²	1	4	yes	—
51	#433×C₆₇	C₂²	1	4	yes	complemented
52	#433×C₆₇	C₂²	1	4	yes	complemented
53	#432×C₆₇	C₂²	1	4	yes	complemented
54	#431×C₆₇	C₂²	1	4	yes	complemented
55	#424×C₆₇	C₂²	1	2	yes	—
56	#424×C₆₇	C₂²	1	2	yes	—
57	#424×C₆₇	C₂²	1	2	yes	—
58	#424×C₆₇	C₂²	1	2	yes	—
59	#424×C₆₇	C₂²	1	2	yes	—
60	#424×C₆₇	C₂²	1	2	yes	—
61	#424×C₆₇	C₂²	1	4	yes	complemented
62	#424×C₆₇	C₂²	1	4	yes	complemented
63	#423×C₆₇	C₂²	1	1	yes	characteristic
64	#423×C₆₇	C₂²	1	1	yes	characteristic
65	#423×C₆₇	C₂²	1	4	yes	complemented
66	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
67	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
68	C₂×C₄⋊C₈×C₆₇	C₂²	1	4	yes	complemented
69	#408×C₆₇	C₂²	1	2	yes	—
70	#408×C₆₇	C₂²	1	2	yes	—
71	#407×C₆₇	C₂²	1	2	yes	—
72	#405×C₆₇	C₂²	1	2	yes	—
73	#405×C₆₇	C₂²	1	2	yes	—
74	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
75	C₂×#41×C₆₇	C₂³	1	2	yes	—
76	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
77	#131×C₆₇	—	4	4	no	—
78	#131×C₆₇	—	4	4	no	—
79	C₂×M₁₆×C₆₇	—	4	2	no	—
80	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
81	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
82	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
84	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
86	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
87	C₂²×C₈×C₆₇	—	4	2	no	—
88	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
89	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
90	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
92	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
94	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
95	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
96	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
97	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
98	#126×C₆₇	C₂×C₄	1	4	yes	—
99	#126×C₆₇	C₂×C₄	1	4	yes	—
100	#126×C₆₇	C₂×C₄	1	4	yes	—
101	#126×C₆₇	C₂×C₄	1	4	yes	—
102	#125×C₆₇	C₂×C₄	1	4	yes	—
103	#125×C₆₇	C₂×C₄	1	4	yes	—
104	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
105	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
106	#124×C₆₇	C₂×C₄	1	4	yes	—
107	#124×C₆₇	C₂×C₄	1	4	yes	—
108	#124×C₆₇	C₂×C₄	1	2	yes	—
109	#123×C₆₇	C₂×C₄	1	4	yes	—
110	#123×C₆₇	C₂×C₄	1	4	yes	—
111	#123×C₆₇	C₂×C₄	1	4	yes	—
112	#123×C₆₇	C₂×C₄	1	4	yes	—
113	#123×C₆₇	C₂×C₄	1	4	yes	—
114	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
115	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
116	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
117	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
118	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
119	#121×C₆₇	C₂×C₄	1	2	yes	—
120	#121×C₆₇	C₂×C₄	1	2	yes	—
121	#121×C₆₇	C₂×C₄	1	4	yes	—
122	#121×C₆₇	C₂×C₄	1	4	yes	—
123	#121×C₆₇	C₂×C₄	1	4	yes	—
124	#120×C₆₇	C₂×C₄	1	4	yes	—
125	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
126	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
127	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
128	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
129	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
130	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
131	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
132	C₄×D₄×C₆₇	C₂³	1	4	yes	—
133	C₄×D₄×C₆₇	C₂³	1	4	yes	—
134	C₄×D₄×C₆₇	C₂³	1	4	yes	—
135	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
136	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
137	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
138	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
139	#117×C₆₇	C₂³	1	2	yes	—
140	#117×C₆₇	C₂³	1	2	yes	—
141	#117×C₆₇	C₂³	1	2	yes	—
142	#117×C₆₇	C₂³	1	4	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
144	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
145	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
148	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
149	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
150	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
151	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
152	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
153	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
154	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
155	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
156	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
157	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
158	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
159	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
160	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
161	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
162	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
163	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
164	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
165	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
166	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
167	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
168	#97×C₆₇	C₂³	1	4	yes	—
169	#97×C₆₇	C₂³	1	4	yes	—
170	#97×C₆₇	C₂³	1	4	yes	—
171	C₄×C₈×C₆₇	C₂³	1	4	yes	—
172	C₄×C₈×C₆₇	C₂³	1	4	yes	—
173	C₄×C₈×C₆₇	C₂³	1	4	yes	—
174	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
175	#41×C₆₇	—	2	4	no	—
176	#41×C₆₇	—	2	4	no	—
177	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
178	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
179	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
180	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
181	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
182	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
183	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
184	C₂²×C₄×C₆₇	—	2	2	no	—
185	C₂²×C₄×C₆₇	—	2	2	no	—
186	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
190	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
191	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
197	M₁₆×C₆₇	—	2	4	no	—
198	M₁₆×C₆₇	—	2	4	no	—
199	M₁₆×C₆₇	—	4	1	no	—
200	M₁₆×C₆₇	—	4	2	no	—
201	M₁₆×C₆₇	—	4	1	no	—
202	M₁₆×C₆₇	—	4	4	no	—
203	M₁₆×C₆₇	—	4	4	no	—
204	C₂×C₈×C₆₇	—	2	4	no	—
205	C₂×C₈×C₆₇	—	2	4	no	—
206	C₂×C₈×C₆₇	—	4	1	no	—
207	C₂×C₈×C₆₇	—	4	2	no	—
208	C₂×C₈×C₆₇	—	4	1	no	—
209	C₂×C₈×C₆₇	—	4	4	no	—
210	C₂×C₈×C₆₇	—	4	4	no	—
211	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
212	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
213	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
214	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
215	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
216	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
217	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
218	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
219	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
220	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
221	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
222	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
223	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
224	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
225	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
226	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
227	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
228	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
229	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
230	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
231	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
232	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
233	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
234	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
235	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
236	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
237	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
238	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
239	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
240	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
241	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
242	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
243	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
244	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
245	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
246	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
247	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
248	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
249	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
250	C₄²×C₆₇	C₂⁴	1	2	yes	—
251	C₄²×C₆₇	C₂⁴	1	2	yes	—
252	C₄²×C₆₇	C₂⁴	1	4	yes	—
253	C₂³×C₆₇	—	2	2	no	—
254	C₂³×C₆₇	—	4	2	no	—
255	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
256	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
257	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
258	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
259	Q₈×C₆₇	—	2	4	no	—
260	Q₈×C₆₇	—	4	4	no	—
261	D₄×C₆₇	—	2	8	no	—
262	D₄×C₆₇	—	2	4	no	—
263	D₄×C₆₇	—	4	4	no	—
264	D₄×C₆₇	—	4	4	no	—
265	D₄×C₆₇	—	4	4	no	—
266	C₂×C₄×C₆₇	—	2	2	no	—
267	C₂×C₄×C₆₇	—	2	2	no	—
268	C₂×C₄×C₆₇	—	2	2	no	—
269	C₂×C₄×C₆₇	—	2	1	no	—
270	C₂×C₄×C₆₇	—	2	1	no	—
271	C₂×C₄×C₆₇	—	2	4	no	—
272	C₂×C₄×C₆₇	—	2	1	no	—
273	C₂×C₄×C₆₇	—	2	1	no	—
274	C₂×C₄×C₆₇	—	2	4	no	—
275	C₂×C₄×C₆₇	—	4	2	no	—
276	C₂×C₄×C₆₇	—	4	4	no	—
277	C₂×C₄×C₆₇	—	4	4	no	—
278	C₂×C₄×C₆₇	—	4	2	no	—
279	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
280	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
281	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
282	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
283	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
284	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
285	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
286	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
287	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
288	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
289	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
290	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
291	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
292	C₈×C₆₇	—	2	2	no	—
293	C₈×C₆₇	—	2	2	no	—
294	C₈×C₆₇	—	2	2	no	—
295	C₈×C₆₇	—	2	2	no	—
296	C₈×C₆₇	—	2	4	no	—
297	C₈×C₆₇	—	2	4	no	—
298	C₂²×C₆₇	—	2	2	no	—
299	C₂²×C₆₇	—	2	1	no	—
300	C₂²×C₆₇	—	2	1	no	—
301	C₂²×C₆₇	—	2	4	no	—
302	C₂²×C₆₇	—	2	4	no	—
303	C₂²×C₆₇	—	2	4	no	—
304	C₂²×C₆₇	—	2	2	no	—
305	C₂²×C₆₇	—	2	2	no	—
306	C₂²×C₆₇	—	4	4	no	—
307	C₂²×C₆₇	#520	1	2	yes	—
308	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
309	C₄×C₆₇	—	2	1	no	—
310	C₄×C₆₇	—	2	1	no	—
311	C₄×C₆₇	—	2	4	no	—
312	C₄×C₆₇	—	2	2	no	—
313	C₄×C₆₇	—	2	2	no	—
314	C₄×C₆₇	—	2	2	no	—
315	C₄×C₆₇	—	2	4	no	—
316	C₄×C₆₇	—	2	4	no	—
317	C₄×C₆₇	—	2	2	no	—
318	C₄×C₆₇	#520	1	2	yes	—
319	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
320	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
321	#60267	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂×C₆₇	—	2	2	no	—
323	C₂×C₆₇	—	4	4	no	—
324	C₂×C₆₇	—	4	1	no	—
325	C₂×C₆₇	—	4	1	no	—
326	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
327	C₂×C₆₇	#3573	1	2	yes	—
328	#3455	C₂×C₆₇	1	1	yes	characteristic
329	#2995	C₂×C₆₇	1	4	yes	complemented
330	#2994	C₂×C₆₇	1	4	yes	complemented
331	#2993	C₂×C₆₇	1	4	yes	complemented
332	#2992	C₂×C₆₇	1	4	yes	complemented
333	#2962	C₂×C₆₇	1	2	yes	complemented
334	#2935	C₂×C₆₇	1	2	yes	complemented
335	#2930	C₂×C₆₇	1	2	yes	complemented
336	#2929	C₂×C₆₇	1	2	yes	complemented
337	#2925	C₂×C₆₇	1	2	yes	complemented
338	#2921	C₂×C₆₇	1	1	yes	characteristic, complemented
339	#2906	C₂×C₆₇	1	2	yes	complemented
340	C₂×#424	C₂×C₆₇	1	1	yes	characteristic, complemented
341	C₆₇	#60267	1	1	yes	characteristic, direct product factor, Sylow
342	C₂×#131	C₂²×C₆₇	1	2	yes	—
343	C₂×#131	C₂²×C₆₇	1	2	yes	—
344	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
345	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
346	#542	C₄×C₆₇	1	2	yes	—
347	#542	C₄×C₆₇	1	2	yes	—
348	#541	C₄×C₆₇	1	1	yes	characteristic
349	#541	C₄×C₆₇	1	1	yes	characteristic
350	#540	C₄×C₆₇	1	1	yes	characteristic
351	#540	C₄×C₆₇	1	1	yes	characteristic
352	#539	C₄×C₆₇	1	4	yes	—
353	#538	C₄×C₆₇	1	4	yes	—
354	#533	C₂²×C₆₇	1	1	yes	characteristic
355	#532	C₂²×C₆₇	1	1	yes	characteristic
356	#529	C₂²×C₆₇	1	4	yes	—
357	#529	C₂²×C₆₇	1	4	yes	—
358	#525	C₂²×C₆₇	1	2	yes	—
359	C₄×#41	C₂²×C₆₇	1	2	yes	—
360	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
361	#446	C₂²×C₆₇	1	4	yes	complemented
362	#446	C₂²×C₆₇	1	4	yes	complemented
363	#446	C₂²×C₆₇	1	4	yes	complemented
364	C₈×Q₈	C₂²×C₆₇	1	4	yes	complemented
365	#436	C₂²×C₆₇	1	4	yes	—
366	#436	C₂²×C₆₇	1	4	yes	—
367	#436	C₂²×C₆₇	1	4	yes	complemented
368	#435	C₂²×C₆₇	1	4	yes	—
369	#435	C₂²×C₆₇	1	4	yes	—
370	#435	C₂²×C₆₇	1	4	yes	—
371	#435	C₂²×C₆₇	1	4	yes	—
372	#435	C₂²×C₆₇	1	4	yes	complemented
373	#435	C₂²×C₆₇	1	4	yes	complemented
374	C₈×D₄	C₂²×C₆₇	1	4	yes	—
375	C₈×D₄	C₂²×C₆₇	1	4	yes	—
376	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
377	#433	C₂²×C₆₇	1	4	yes	—
378	#433	C₂²×C₆₇	1	4	yes	—
379	#433	C₂²×C₆₇	1	4	yes	complemented
380	#433	C₂²×C₆₇	1	4	yes	complemented
381	#432	C₂²×C₆₇	1	4	yes	complemented
382	#431	C₂²×C₆₇	1	4	yes	complemented
383	#424	C₂²×C₆₇	1	2	yes	—
384	#424	C₂²×C₆₇	1	2	yes	—
385	#424	C₂²×C₆₇	1	2	yes	—
386	#424	C₂²×C₆₇	1	2	yes	—
387	#424	C₂²×C₆₇	1	2	yes	—
388	#424	C₂²×C₆₇	1	2	yes	—
389	#424	C₂²×C₆₇	1	4	yes	complemented
390	#424	C₂²×C₆₇	1	4	yes	complemented
391	#423	C₂²×C₆₇	1	1	yes	characteristic
392	#423	C₂²×C₆₇	1	1	yes	characteristic
393	#423	C₂²×C₆₇	1	4	yes	complemented
394	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
395	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
396	C₂×C₄⋊C₈	C₂²×C₆₇	1	4	yes	complemented
397	#408	C₂²×C₆₇	1	2	yes	—
398	#408	C₂²×C₆₇	1	2	yes	—
399	#407	C₂²×C₆₇	1	2	yes	—
400	#405	C₂²×C₆₇	1	2	yes	—
401	#405	C₂²×C₆₇	1	2	yes	—
402	C₄×M₁₆	C₂²×C₆₇	1	2	yes	—
403	C₂×#41	C₂³×C₆₇	1	2	yes	—
404	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
405	#131	—	4	4	no	—
406	#131	—	4	4	no	—
407	C₂×M₁₆	—	4	2	no	—
408	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
409	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
410	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
411	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
412	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
413	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
414	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
415	C₂²×C₈	—	4	2	no	—
416	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
417	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
418	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
420	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
422	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
423	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
424	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
425	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
426	#126	C₂×C₄×C₆₇	1	4	yes	—
427	#126	C₂×C₄×C₆₇	1	4	yes	—
428	#126	C₂×C₄×C₆₇	1	4	yes	—
429	#126	C₂×C₄×C₆₇	1	4	yes	—
430	#125	C₂×C₄×C₆₇	1	4	yes	—
431	#125	C₂×C₄×C₆₇	1	4	yes	—
432	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
433	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
434	#124	C₂×C₄×C₆₇	1	4	yes	—
435	#124	C₂×C₄×C₆₇	1	4	yes	—
436	#124	C₂×C₄×C₆₇	1	2	yes	—
437	#123	C₂×C₄×C₆₇	1	4	yes	—
438	#123	C₂×C₄×C₆₇	1	4	yes	—
439	#123	C₂×C₄×C₆₇	1	4	yes	—
440	#123	C₂×C₄×C₆₇	1	4	yes	—
441	#123	C₂×C₄×C₆₇	1	4	yes	—
442	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
443	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
444	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
445	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
446	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
447	#121	C₂×C₄×C₆₇	1	2	yes	—
448	#121	C₂×C₄×C₆₇	1	2	yes	—
449	#121	C₂×C₄×C₆₇	1	4	yes	—
450	#121	C₂×C₄×C₆₇	1	4	yes	—
451	#121	C₂×C₄×C₆₇	1	4	yes	—
452	#120	C₂×C₄×C₆₇	1	4	yes	—
453	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
454	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
455	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
456	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
457	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
458	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
459	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
460	C₄×D₄	C₂³×C₆₇	1	4	yes	—
461	C₄×D₄	C₂³×C₆₇	1	4	yes	—
462	C₄×D₄	C₂³×C₆₇	1	4	yes	—
463	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
464	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
465	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
466	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
467	#117	C₂³×C₆₇	1	2	yes	—
468	#117	C₂³×C₆₇	1	2	yes	—
469	#117	C₂³×C₆₇	1	2	yes	—
470	#117	C₂³×C₆₇	1	4	yes	—
471	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
473	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
476	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
477	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
478	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
479	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
480	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
481	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
482	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
483	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
484	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
485	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
486	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
487	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
488	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
489	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
490	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
491	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
492	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
493	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
494	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
495	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
496	#97	C₂³×C₆₇	1	4	yes	—
497	#97	C₂³×C₆₇	1	4	yes	—
498	#97	C₂³×C₆₇	1	4	yes	—
499	C₄×C₈	C₂³×C₆₇	1	4	yes	—
500	C₄×C₈	C₂³×C₆₇	1	4	yes	—
501	C₄×C₈	C₂³×C₆₇	1	4	yes	—
502	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
503	#41	—	2	4	no	—
504	#41	—	2	4	no	—
505	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
506	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
507	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
508	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
509	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
510	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
511	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
515	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
516	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
517	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
518	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
519	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
520	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
521	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
522	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
525	M₁₆	—	2	4	no	—
526	M₁₆	—	2	4	no	—
527	M₁₆	—	4	1	no	—
528	M₁₆	—	4	2	no	—
529	M₁₆	—	4	1	no	—
530	M₁₆	—	4	4	no	—
531	M₁₆	—	4	4	no	—
532	C₂×C₈	—	2	4	no	—
533	C₂×C₈	—	2	4	no	—
534	C₂×C₈	—	4	1	no	—
535	C₂×C₈	—	4	2	no	—
536	C₂×C₈	—	4	1	no	—
537	C₂×C₈	—	4	4	no	—
538	C₂×C₈	—	4	4	no	—
539	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
540	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
541	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
542	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
543	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
544	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
545	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
546	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
547	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
548	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
549	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
550	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
551	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
552	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
553	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
554	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
555	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
556	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
557	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
558	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
559	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
560	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
561	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
562	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
563	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
564	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
565	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
567	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
568	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
569	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
570	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
571	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
572	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
573	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
574	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
575	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
576	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
577	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
578	C₄²	C₂⁴×C₆₇	1	2	yes	—
579	C₄²	C₂⁴×C₆₇	1	4	yes	—
580	C₄²	C₂⁴×C₆₇	1	2	yes	—
581	C₂³	—	2	2	no	—
582	C₂³	—	4	2	no	—
583	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
584	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
585	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
586	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
587	Q₈	—	2	4	no	—
588	Q₈	—	4	4	no	—
589	D₄	—	2	8	no	—
590	D₄	—	2	4	no	—
591	D₄	—	4	4	no	—
592	D₄	—	4	4	no	—
593	D₄	—	4	4	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	4	no	—
605	C₂×C₄	—	4	4	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
608	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
609	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
610	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
611	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
612	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
613	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
614	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
615	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
616	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
617	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
618	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
619	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
620	C₈	—	2	2	no	—
621	C₈	—	2	2	no	—
622	C₈	—	2	2	no	—
623	C₈	—	2	2	no	—
624	C₈	—	2	4	no	—
625	C₈	—	2	4	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	4	no	—
628	C₂²	—	2	4	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	4	4	no	—
635	C₂²	#520×C₆₇	1	2	yes	—
636	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	4	no	—
641	C₄	—	2	4	no	—
642	C₄	—	2	2	no	—
643	C₄	—	2	1	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	4	no	—
646	C₄	#520×C₆₇	1	2	yes	—
647	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
648	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
649	C₂	—	2	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	4	1	no	—
652	C₂	—	4	4	no	—
653	C₂	C₂×#520×C₆₇	1	1	yes	characteristic
654	C₂	C₆₇×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	C₆₇×#3455	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2995	C₂	semidirect
3. C₆₇×#2994	C₂	semidirect
4. C₆₇×#2993	C₂	semidirect
5. C₆₇×#2992	C₂	semidirect
6. C₆₇×#2962	C₂	semidirect
7. C₆₇×#2935	C₂	semidirect
8. C₆₇×#2930	C₂	semidirect
9. C₆₇×#2929	C₂	semidirect
10. C₆₇×#2925	C₂	semidirect
11. C₆₇×#2921	C₂	semidirect
12. C₆₇×#2906	C₂	semidirect
13. C₂×#424×C₆₇	C₂	semidirect
33. #446×C₆₇	C₂²	semidirect
34. #446×C₆₇	C₂²	semidirect
35. #446×C₆₇	C₂²	semidirect
36. C₈×Q₈×C₆₇	C₂²	semidirect
39. #436×C₆₇	C₂²	semidirect
44. #435×C₆₇	C₂²	semidirect
45. #435×C₆₇	C₂²	semidirect
48. C₈×D₄×C₆₇	C₂²	semidirect
51. #433×C₆₇	C₂²	semidirect
52. #433×C₆₇	C₂²	semidirect
53. #432×C₆₇	C₂²	semidirect
54. #431×C₆₇	C₂²	semidirect
61. #424×C₆₇	C₂²	semidirect
62. #424×C₆₇	C₂²	semidirect
65. #423×C₆₇	C₂²	semidirect
68. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
321. #60267	C₆₇	direct (N × H)
329. #2995	C₂×C₆₇	semidirect
330. #2994	C₂×C₆₇	semidirect
331. #2993	C₂×C₆₇	semidirect
332. #2992	C₂×C₆₇	semidirect
333. #2962	C₂×C₆₇	semidirect
334. #2935	C₂×C₆₇	semidirect
335. #2930	C₂×C₆₇	semidirect
336. #2929	C₂×C₆₇	semidirect
337. #2925	C₂×C₆₇	semidirect
338. #2921	C₂×C₆₇	semidirect
339. #2906	C₂×C₆₇	semidirect
340. C₂×#424	C₂×C₆₇	semidirect
341. C₆₇	#60267	direct (N × H)
361. #446	C₂²×C₆₇	semidirect
362. #446	C₂²×C₆₇	semidirect
363. #446	C₂²×C₆₇	semidirect
364. C₈×Q₈	C₂²×C₆₇	semidirect
367. #436	C₂²×C₆₇	semidirect
372. #435	C₂²×C₆₇	semidirect
373. #435	C₂²×C₆₇	semidirect
376. C₈×D₄	C₂²×C₆₇	semidirect
379. #433	C₂²×C₆₇	semidirect
380. #433	C₂²×C₆₇	semidirect
381. #432	C₂²×C₆₇	semidirect
382. #431	C₂²×C₆₇	semidirect
389. #424	C₂²×C₆₇	semidirect
390. #424	C₂²×C₆₇	semidirect
393. #423	C₂²×C₆₇	semidirect
396. C₂×C₄⋊C₈	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×#3455	2
C₆₇×#2995	2
C₆₇×#2994	2
C₆₇×#2993	2
C₆₇×#2992	2
C₆₇×#2962	2
C₆₇×#2935	2
C₆₇×#2930	2
C₆₇×#2929	2
C₆₇×#2925	2
C₆₇×#2921	2
C₆₇×#2906	2
C₂×#424×C₆₇	2
#60267	67

Subgroups — C67×#60267 #30739518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60267 #30739518