Subgroups — C₆₇×#60318 #30739569

Order 17152.

1812 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3529	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2995	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2993	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2980	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2979	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2977	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2976	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2968	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2966	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2933	C₂	1	4	yes	maximal, complemented
11	C₆₇×#2932	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2930	C₂	1	2	yes	maximal, complemented
14	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×#131×C₆₇	C₂²	1	2	yes	—
16	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
17	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
18	#563×C₆₇	C₄	1	2	yes	—
19	#563×C₆₇	C₄	1	1	yes	characteristic
20	#562×C₆₇	C₄	1	4	yes	—
21	#562×C₆₇	C₄	1	2	yes	—
22	H(3,𝔽₄)×C₆₇	C₄	1	1	yes	characteristic
23	#560×C₆₇	C₄	1	4	yes	—
24	#560×C₆₇	C₄	1	2	yes	—
25	#532×C₆₇	C₂²	1	1	yes	characteristic
26	#532×C₆₇	C₂²	1	2	yes	—
27	#529×C₆₇	C₂²	1	2	yes	—
28	#529×C₆₇	C₂²	1	4	yes	—
29	#525×C₆₇	C₂²	1	2	yes	—
30	#525×C₆₇	C₂²	1	4	yes	—
31	#446×C₆₇	C₂²	1	2	yes	complemented
32	#446×C₆₇	C₂²	1	4	yes	complemented
33	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
34	#436×C₆₇	C₂²	1	4	yes	—
35	#436×C₆₇	C₂²	1	2	yes	—
36	#436×C₆₇	C₂²	1	4	yes	complemented
37	#436×C₆₇	C₂²	1	4	yes	complemented
38	#436×C₆₇	C₂²	1	4	yes	complemented
39	#435×C₆₇	C₂²	1	4	yes	—
40	#435×C₆₇	C₂²	1	4	yes	—
41	#435×C₆₇	C₂²	1	4	yes	—
42	#435×C₆₇	C₂²	1	4	yes	complemented
43	#435×C₆₇	C₂²	1	4	yes	complemented
44	#435×C₆₇	C₂²	1	4	yes	complemented
45	#435×C₆₇	C₂²	1	4	yes	complemented
46	#435×C₆₇	C₂²	1	4	yes	complemented
47	#435×C₆₇	C₂²	1	4	yes	complemented
48	C₈×D₄×C₆₇	C₂²	1	4	yes	—
49	C₈×D₄×C₆₇	C₂²	1	2	yes	—
50	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
51	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
52	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
53	#433×C₆₇	C₂²	1	4	yes	complemented
54	#433×C₆₇	C₂²	1	4	yes	complemented
55	#433×C₆₇	C₂²	1	4	yes	complemented
56	#432×C₆₇	C₂²	1	2	yes	complemented
57	#431×C₆₇	C₂²	1	4	yes	complemented
58	#424×C₆₇	C₂²	1	2	yes	complemented
59	#424×C₆₇	C₂²	1	4	yes	complemented
60	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#423×C₆₇	C₂²	1	2	yes	complemented
62	#408×C₆₇	C₂²	1	2	yes	—
63	#408×C₆₇	C₂²	1	1	yes	characteristic
64	#408×C₆₇	C₂²	1	2	yes	—
65	#408×C₆₇	C₂²	1	4	yes	—
66	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#408×C₆₇	C₂²	1	2	yes	complemented
68	#407×C₆₇	C₂²	1	2	yes	complemented
69	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	complemented
70	#405×C₆₇	C₂²	1	2	yes	complemented
71	#405×C₆₇	C₂²	1	4	yes	complemented
72	C₂×#97×C₆₇	C₂²	1	2	yes	complemented
73	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
75	C₂×#41×C₆₇	C₂³	1	2	yes	—
76	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
78	#131×C₆₇	—	4	2	no	—
79	#131×C₆₇	—	4	2	no	—
80	#131×C₆₇	—	4	4	no	—
81	C₂×M₁₆×C₆₇	—	4	4	no	—
82	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
83	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
84	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
85	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
86	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
89	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
90	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
91	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
93	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
94	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
95	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
97	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
98	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
99	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
100	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
101	#127×C₆₇	C₂×C₄	1	2	yes	—
102	#126×C₆₇	C₂×C₄	1	4	yes	—
103	#126×C₆₇	C₂×C₄	1	4	yes	—
104	#126×C₆₇	C₂×C₄	1	4	yes	—
105	#125×C₆₇	C₂×C₄	1	2	yes	—
106	#125×C₆₇	C₂×C₄	1	4	yes	—
107	#124×C₆₇	C₂×C₄	1	2	yes	—
108	#124×C₆₇	C₂×C₄	1	4	yes	—
109	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
110	#124×C₆₇	C₂×C₄	1	2	yes	—
111	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
112	#124×C₆₇	C₂×C₄	1	2	yes	—
113	#123×C₆₇	C₂×C₄	1	2	yes	—
114	#123×C₆₇	C₂×C₄	1	4	yes	—
115	#123×C₆₇	C₂×C₄	1	2	yes	—
116	#123×C₆₇	C₂×C₄	1	4	yes	—
117	#123×C₆₇	C₂×C₄	1	4	yes	—
118	#123×C₆₇	C₂×C₄	1	4	yes	—
119	#123×C₆₇	C₂×C₄	1	4	yes	—
120	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
121	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
122	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
123	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
124	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
125	#121×C₆₇	C₂×C₄	1	4	yes	—
126	#121×C₆₇	C₂×C₄	1	4	yes	—
127	#121×C₆₇	C₂×C₄	1	4	yes	—
128	#121×C₆₇	C₂×C₄	1	2	yes	—
129	#121×C₆₇	C₂×C₄	1	4	yes	—
130	#121×C₆₇	C₂×C₄	1	4	yes	—
131	#121×C₆₇	C₂×C₄	1	4	yes	—
132	#121×C₆₇	C₂×C₄	1	4	yes	—
133	#120×C₆₇	C₂×C₄	1	2	yes	—
134	#120×C₆₇	C₂×C₄	1	4	yes	—
135	#120×C₆₇	C₂×C₄	1	2	yes	—
136	#120×C₆₇	C₂×C₄	1	4	yes	—
137	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
138	C₄×D₄×C₆₇	C₂³	1	4	yes	—
139	C₄×D₄×C₆₇	C₂³	1	2	yes	—
140	C₄×D₄×C₆₇	C₂³	1	4	yes	—
141	C₄×D₄×C₆₇	C₂³	1	4	yes	—
142	C₄×D₄×C₆₇	C₂³	1	4	yes	—
143	#117×C₆₇	C₂³	1	2	yes	—
144	#117×C₆₇	C₂³	1	4	yes	—
145	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
147	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
148	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
149	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
150	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
151	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
152	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
153	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
154	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
155	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
156	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
157	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
158	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
159	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
160	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
161	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
162	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
163	#97×C₆₇	C₂³	1	4	yes	—
164	#97×C₆₇	C₂³	1	4	yes	—
165	#97×C₆₇	C₂³	1	4	yes	—
166	C₄×C₈×C₆₇	C₂³	1	2	yes	—
167	C₄×C₈×C₆₇	C₂³	1	2	yes	—
168	C₄×C₈×C₆₇	C₂³	1	4	yes	—
169	C₄×C₈×C₆₇	C₂³	1	4	yes	—
170	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
171	#41×C₆₇	—	4	1	no	—
172	#41×C₆₇	—	4	1	no	—
173	#41×C₆₇	—	4	2	no	—
174	#41×C₆₇	—	4	2	no	—
175	#41×C₆₇	—	4	1	no	—
176	#41×C₆₇	—	4	1	no	—
177	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
178	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
179	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
180	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
181	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
182	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
183	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
184	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
185	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
186	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
187	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
188	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
189	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
190	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
191	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	—	4	2	no	—
193	C₂²×C₄×C₆₇	—	4	2	no	—
194	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
195	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
197	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
198	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
202	M₁₆×C₆₇	—	2	8	no	—
203	M₁₆×C₆₇	—	4	4	no	—
204	M₁₆×C₆₇	—	4	2	no	—
205	M₁₆×C₆₇	—	4	1	no	—
206	M₁₆×C₆₇	—	4	2	no	—
207	M₁₆×C₆₇	—	4	2	no	—
208	M₁₆×C₆₇	—	4	1	no	—
209	M₁₆×C₆₇	—	4	2	no	—
210	C₂×C₈×C₆₇	—	2	4	no	—
211	C₂×C₈×C₆₇	—	2	4	no	—
212	C₂×C₈×C₆₇	—	2	2	no	—
213	C₂×C₈×C₆₇	—	4	1	no	—
214	C₂×C₈×C₆₇	—	4	4	no	—
215	C₂×C₈×C₆₇	—	4	2	no	—
216	C₂×C₈×C₆₇	—	4	2	no	—
217	C₂×C₈×C₆₇	—	4	4	no	—
218	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
219	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
220	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
221	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
222	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
223	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
224	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
232	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
233	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
234	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
235	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
236	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
237	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	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	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
245	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
246	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
247	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
248	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
249	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
250	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
251	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
252	C₄²×C₆₇	C₂⁴	1	4	yes	—
253	C₄²×C₆₇	C₂⁴	1	2	yes	—
254	C₂³×C₆₇	—	4	2	no	—
255	C₂³×C₆₇	—	4	4	no	—
256	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
257	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
258	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
259	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
260	Q₈×C₆₇	—	4	2	no	—
261	Q₈×C₆₇	—	4	1	no	—
262	Q₈×C₆₇	—	4	2	no	—
263	Q₈×C₆₇	—	4	1	no	—
264	D₄×C₆₇	—	4	4	no	—
265	D₄×C₆₇	—	4	4	no	—
266	D₄×C₆₇	—	4	4	no	—
267	D₄×C₆₇	—	4	4	no	—
268	D₄×C₆₇	—	4	2	no	—
269	D₄×C₆₇	—	4	2	no	—
270	D₄×C₆₇	—	4	4	no	—
271	D₄×C₆₇	—	4	1	no	—
272	D₄×C₆₇	—	4	2	no	—
273	D₄×C₆₇	—	4	2	no	—
274	D₄×C₆₇	—	4	1	no	—
275	C₂×C₄×C₆₇	—	2	2	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	1	no	—
278	C₂×C₄×C₆₇	—	2	4	no	—
279	C₂×C₄×C₆₇	—	2	4	no	—
280	C₂×C₄×C₆₇	—	2	1	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	2	no	—
283	C₂×C₄×C₆₇	—	4	4	no	—
284	C₂×C₄×C₆₇	—	4	2	no	—
285	C₂×C₄×C₆₇	—	4	2	no	—
286	C₂×C₄×C₆₇	—	4	4	no	—
287	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
288	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
289	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
290	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
291	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
293	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
294	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
295	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
296	C₈×C₆₇	—	2	2	no	—
297	C₈×C₆₇	—	2	2	no	—
298	C₈×C₆₇	—	2	1	no	—
299	C₈×C₆₇	—	2	4	no	—
300	C₈×C₆₇	—	2	2	no	—
301	C₈×C₆₇	—	2	4	no	—
302	C₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
303	C₂²×C₆₇	—	2	2	no	—
304	C₂²×C₆₇	—	2	4	no	—
305	C₂²×C₆₇	—	2	2	no	—
306	C₂²×C₆₇	—	2	1	no	—
307	C₂²×C₆₇	—	2	2	no	—
308	C₂²×C₆₇	—	2	4	no	—
309	C₂²×C₆₇	—	2	4	no	—
310	C₂²×C₆₇	—	2	4	no	—
311	C₂²×C₆₇	—	2	4	no	—
312	C₂²×C₆₇	—	8	4	no	—
313	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
314	C₄×C₆₇	—	2	2	no	—
315	C₄×C₆₇	—	2	4	no	—
316	C₄×C₆₇	—	2	2	no	—
317	C₄×C₆₇	—	2	1	no	—
318	C₄×C₆₇	—	2	2	no	—
319	C₄×C₆₇	—	2	4	no	—
320	C₄×C₆₇	—	2	2	no	—
321	C₄×C₆₇	—	2	4	no	—
322	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
323	C₄×C₆₇	#585	1	1	yes	characteristic
324	#60318	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
325	C₂×C₆₇	—	4	2	no	—
326	C₂×C₆₇	—	4	1	no	—
327	C₂×C₆₇	—	4	2	no	—
328	C₂×C₆₇	—	4	4	no	—
329	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₆₇	#3573	1	2	yes	—
331	#3529	C₂×C₆₇	1	1	yes	characteristic
332	#2995	C₂×C₆₇	1	2	yes	complemented
333	#2993	C₂×C₆₇	1	4	yes	complemented
334	#2980	C₂×C₆₇	1	1	yes	characteristic, complemented
335	#2979	C₂×C₆₇	1	2	yes	complemented
336	#2977	C₂×C₆₇	1	2	yes	complemented
337	#2976	C₂×C₆₇	1	4	yes	complemented
338	#2968	C₂×C₆₇	1	4	yes	complemented
339	#2966	C₂×C₆₇	1	2	yes	complemented
340	#2933	C₂×C₆₇	1	4	yes	complemented
341	#2932	C₂×C₆₇	1	2	yes	complemented
342	#2931	C₂×C₆₇	1	1	yes	characteristic, complemented
343	#2930	C₂×C₆₇	1	2	yes	complemented
344	C₆₇	#60318	1	1	yes	characteristic, direct product factor, Sylow
345	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
346	C₂×#131	C₂²×C₆₇	1	2	yes	—
347	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
348	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
349	#563	C₄×C₆₇	1	2	yes	—
350	#563	C₄×C₆₇	1	1	yes	characteristic
351	#562	C₄×C₆₇	1	4	yes	—
352	#562	C₄×C₆₇	1	2	yes	—
353	H(3,𝔽₄)	C₄×C₆₇	1	1	yes	characteristic
354	#560	C₄×C₆₇	1	4	yes	—
355	#560	C₄×C₆₇	1	2	yes	—
356	#532	C₂²×C₆₇	1	1	yes	characteristic
357	#532	C₂²×C₆₇	1	2	yes	—
358	#529	C₂²×C₆₇	1	2	yes	—
359	#529	C₂²×C₆₇	1	4	yes	—
360	#525	C₂²×C₆₇	1	2	yes	—
361	#525	C₂²×C₆₇	1	4	yes	—
362	#446	C₂²×C₆₇	1	2	yes	complemented
363	#446	C₂²×C₆₇	1	4	yes	complemented
364	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
365	#436	C₂²×C₆₇	1	4	yes	—
366	#436	C₂²×C₆₇	1	2	yes	—
367	#436	C₂²×C₆₇	1	4	yes	complemented
368	#436	C₂²×C₆₇	1	4	yes	complemented
369	#436	C₂²×C₆₇	1	4	yes	complemented
370	#435	C₂²×C₆₇	1	4	yes	—
371	#435	C₂²×C₆₇	1	4	yes	—
372	#435	C₂²×C₆₇	1	4	yes	—
373	#435	C₂²×C₆₇	1	4	yes	complemented
374	#435	C₂²×C₆₇	1	4	yes	complemented
375	#435	C₂²×C₆₇	1	4	yes	complemented
376	#435	C₂²×C₆₇	1	4	yes	complemented
377	#435	C₂²×C₆₇	1	4	yes	complemented
378	#435	C₂²×C₆₇	1	4	yes	complemented
379	C₈×D₄	C₂²×C₆₇	1	4	yes	—
380	C₈×D₄	C₂²×C₆₇	1	2	yes	—
381	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
382	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
383	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
384	#433	C₂²×C₆₇	1	4	yes	complemented
385	#433	C₂²×C₆₇	1	4	yes	complemented
386	#433	C₂²×C₆₇	1	4	yes	complemented
387	#432	C₂²×C₆₇	1	2	yes	complemented
388	#431	C₂²×C₆₇	1	4	yes	complemented
389	#424	C₂²×C₆₇	1	2	yes	complemented
390	#424	C₂²×C₆₇	1	4	yes	complemented
391	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
392	#423	C₂²×C₆₇	1	2	yes	complemented
393	#408	C₂²×C₆₇	1	2	yes	—
394	#408	C₂²×C₆₇	1	1	yes	characteristic
395	#408	C₂²×C₆₇	1	2	yes	—
396	#408	C₂²×C₆₇	1	4	yes	—
397	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
398	#408	C₂²×C₆₇	1	2	yes	complemented
399	#407	C₂²×C₆₇	1	2	yes	complemented
400	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	complemented
401	#405	C₂²×C₆₇	1	2	yes	complemented
402	#405	C₂²×C₆₇	1	4	yes	complemented
403	C₂×#97	C₂²×C₆₇	1	2	yes	complemented
404	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
405	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
406	C₂×#41	C₂³×C₆₇	1	2	yes	—
407	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
408	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
409	#131	—	4	2	no	—
410	#131	—	4	2	no	—
411	#131	—	4	4	no	—
412	C₂×M₁₆	—	4	4	no	—
413	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
414	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
415	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
416	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
417	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
418	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
419	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
420	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
421	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
422	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
424	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
425	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
426	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
427	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
428	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
429	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
430	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
431	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
432	#127	C₂×C₄×C₆₇	1	2	yes	—
433	#126	C₂×C₄×C₆₇	1	4	yes	—
434	#126	C₂×C₄×C₆₇	1	4	yes	—
435	#126	C₂×C₄×C₆₇	1	4	yes	—
436	#125	C₂×C₄×C₆₇	1	2	yes	—
437	#125	C₂×C₄×C₆₇	1	4	yes	—
438	#124	C₂×C₄×C₆₇	1	2	yes	—
439	#124	C₂×C₄×C₆₇	1	4	yes	—
440	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
441	#124	C₂×C₄×C₆₇	1	2	yes	—
442	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
443	#124	C₂×C₄×C₆₇	1	2	yes	—
444	#123	C₂×C₄×C₆₇	1	2	yes	—
445	#123	C₂×C₄×C₆₇	1	4	yes	—
446	#123	C₂×C₄×C₆₇	1	2	yes	—
447	#123	C₂×C₄×C₆₇	1	4	yes	—
448	#123	C₂×C₄×C₆₇	1	4	yes	—
449	#123	C₂×C₄×C₆₇	1	4	yes	—
450	#123	C₂×C₄×C₆₇	1	4	yes	—
451	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
452	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
453	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
454	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
455	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
456	#121	C₂×C₄×C₆₇	1	4	yes	—
457	#121	C₂×C₄×C₆₇	1	4	yes	—
458	#121	C₂×C₄×C₆₇	1	4	yes	—
459	#121	C₂×C₄×C₆₇	1	2	yes	—
460	#121	C₂×C₄×C₆₇	1	4	yes	—
461	#121	C₂×C₄×C₆₇	1	4	yes	—
462	#121	C₂×C₄×C₆₇	1	4	yes	—
463	#121	C₂×C₄×C₆₇	1	4	yes	—
464	#120	C₂×C₄×C₆₇	1	2	yes	—
465	#120	C₂×C₄×C₆₇	1	4	yes	—
466	#120	C₂×C₄×C₆₇	1	2	yes	—
467	#120	C₂×C₄×C₆₇	1	4	yes	—
468	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
469	C₄×D₄	C₂³×C₆₇	1	4	yes	—
470	C₄×D₄	C₂³×C₆₇	1	2	yes	—
471	C₄×D₄	C₂³×C₆₇	1	4	yes	—
472	C₄×D₄	C₂³×C₆₇	1	4	yes	—
473	C₄×D₄	C₂³×C₆₇	1	4	yes	—
474	#117	C₂³×C₆₇	1	2	yes	—
475	#117	C₂³×C₆₇	1	4	yes	—
476	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
478	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
479	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
480	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
481	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
482	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
483	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
484	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
485	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
486	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
487	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
488	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
489	C₂²⋊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	#97	C₂³×C₆₇	1	4	yes	—
495	#97	C₂³×C₆₇	1	4	yes	—
496	#97	C₂³×C₆₇	1	4	yes	—
497	C₄×C₈	C₂³×C₆₇	1	2	yes	—
498	C₄×C₈	C₂³×C₆₇	1	2	yes	—
499	C₄×C₈	C₂³×C₆₇	1	4	yes	—
500	C₄×C₈	C₂³×C₆₇	1	4	yes	—
501	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
502	#41	—	4	1	no	—
503	#41	—	4	1	no	—
504	#41	—	4	2	no	—
505	#41	—	4	2	no	—
506	#41	—	4	1	no	—
507	#41	—	4	1	no	—
508	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
509	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
510	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
511	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
512	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
513	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
514	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
515	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
516	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
517	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
518	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
519	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
520	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
521	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
522	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
526	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
527	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
528	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
533	M₁₆	—	2	8	no	—
534	M₁₆	—	4	4	no	—
535	M₁₆	—	4	1	no	—
536	M₁₆	—	4	2	no	—
537	M₁₆	—	4	2	no	—
538	M₁₆	—	4	1	no	—
539	M₁₆	—	4	2	no	—
540	M₁₆	—	4	2	no	—
541	C₂×C₈	—	2	4	no	—
542	C₂×C₈	—	2	4	no	—
543	C₂×C₈	—	2	2	no	—
544	C₂×C₈	—	4	2	no	—
545	C₂×C₈	—	4	4	no	—
546	C₂×C₈	—	4	1	no	—
547	C₂×C₈	—	4	4	no	—
548	C₂×C₈	—	4	2	no	—
549	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
550	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
551	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
552	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
553	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
554	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
555	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
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	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
560	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
561	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
562	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
563	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
564	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
565	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
567	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
568	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	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	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
573	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
574	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
575	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
576	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
577	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
578	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
579	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
580	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
581	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
582	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
583	C₄²	C₂⁴×C₆₇	1	2	yes	—
584	C₄²	C₂⁴×C₆₇	1	4	yes	—
585	C₂³	—	4	2	no	—
586	C₂³	—	4	4	no	—
587	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
588	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
589	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
590	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
591	Q₈	—	4	1	no	—
592	Q₈	—	4	2	no	—
593	Q₈	—	4	1	no	—
594	Q₈	—	4	2	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	4	no	—
597	D₄	—	4	1	no	—
598	D₄	—	4	2	no	—
599	D₄	—	4	2	no	—
600	D₄	—	4	1	no	—
601	D₄	—	4	4	no	—
602	D₄	—	4	4	no	—
603	D₄	—	4	4	no	—
604	D₄	—	4	4	no	—
605	D₄	—	4	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	4	4	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	4	no	—
618	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
619	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
620	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
621	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
622	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
623	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
624	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
625	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
626	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
627	C₈	—	2	2	no	—
628	C₈	—	2	2	no	—
629	C₈	—	2	1	no	—
630	C₈	—	2	4	no	—
631	C₈	—	2	2	no	—
632	C₈	—	2	4	no	—
633	C₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	4	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	8	4	no	—
644	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
645	C₄	—	2	2	no	—
646	C₄	—	2	4	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	4	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	4	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
654	C₄	#585×C₆₇	1	1	yes	characteristic
655	C₂	—	4	2	no	—
656	C₂	—	4	4	no	—
657	C₂	—	4	1	no	—
658	C₂	—	4	2	no	—
659	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
660	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×#3529	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×#2993	C₂	semidirect
4. C₆₇×#2980	C₂	semidirect
5. C₆₇×#2979	C₂	semidirect
6. C₆₇×#2977	C₂	semidirect
7. C₆₇×#2976	C₂	semidirect
8. C₆₇×#2968	C₂	semidirect
9. C₆₇×#2966	C₂	semidirect
10. C₆₇×#2933	C₂	semidirect
11. C₆₇×#2932	C₂	semidirect
12. C₆₇×#2931	C₂	semidirect
13. C₆₇×#2930	C₂	semidirect
16. C₂×#131×C₆₇	C₂²	semidirect
17. C₂²×M₁₆×C₆₇	C₂²	semidirect
31. #446×C₆₇	C₂²	semidirect
32. #446×C₆₇	C₂²	semidirect
33. C₈×Q₈×C₆₇	C₂²	semidirect
36. #436×C₆₇	C₂²	semidirect
37. #436×C₆₇	C₂²	semidirect
38. #436×C₆₇	C₂²	semidirect
42. #435×C₆₇	C₂²	semidirect
43. #435×C₆₇	C₂²	semidirect
44. #435×C₆₇	C₂²	semidirect
45. #435×C₆₇	C₂²	semidirect
46. #435×C₆₇	C₂²	semidirect
47. #435×C₆₇	C₂²	semidirect
50. C₈×D₄×C₆₇	C₂²	semidirect
51. C₈×D₄×C₆₇	C₂²	semidirect
52. C₈×D₄×C₆₇	C₂²	semidirect
53. #433×C₆₇	C₂²	semidirect
54. #433×C₆₇	C₂²	semidirect
55. #433×C₆₇	C₂²	semidirect
56. #432×C₆₇	C₂²	semidirect
57. #431×C₆₇	C₂²	semidirect
58. #424×C₆₇	C₂²	semidirect
59. #424×C₆₇	C₂²	semidirect
60. #423×C₆₇	C₂²	semidirect
61. #423×C₆₇	C₂²	semidirect
66. #408×C₆₇	C₂²	semidirect
67. #408×C₆₇	C₂²	semidirect
68. #407×C₆₇	C₂²	semidirect
69. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
70. #405×C₆₇	C₂²	semidirect
71. #405×C₆₇	C₂²	semidirect
72. C₂×#97×C₆₇	C₂²	semidirect
73. C₂×C₄×C₈×C₆₇	C₂²	semidirect
324. #60318	C₆₇	direct (N × H)
332. #2995	C₂×C₆₇	semidirect
333. #2993	C₂×C₆₇	semidirect
334. #2980	C₂×C₆₇	semidirect
335. #2979	C₂×C₆₇	semidirect
336. #2977	C₂×C₆₇	semidirect
337. #2976	C₂×C₆₇	semidirect
338. #2968	C₂×C₆₇	semidirect
339. #2966	C₂×C₆₇	semidirect
340. #2933	C₂×C₆₇	semidirect
341. #2932	C₂×C₆₇	semidirect
342. #2931	C₂×C₆₇	semidirect
343. #2930	C₂×C₆₇	semidirect
344. C₆₇	#60318	direct (N × H)
347. C₂×#131	C₂²×C₆₇	semidirect
348. C₂²×M₁₆	C₂²×C₆₇	semidirect
362. #446	C₂²×C₆₇	semidirect
363. #446	C₂²×C₆₇	semidirect
364. C₈×Q₈	C₂²×C₆₇	semidirect
367. #436	C₂²×C₆₇	semidirect
368. #436	C₂²×C₆₇	semidirect
369. #436	C₂²×C₆₇	semidirect
373. #435	C₂²×C₆₇	semidirect
374. #435	C₂²×C₆₇	semidirect
375. #435	C₂²×C₆₇	semidirect
376. #435	C₂²×C₆₇	semidirect
377. #435	C₂²×C₆₇	semidirect
378. #435	C₂²×C₆₇	semidirect
381. C₈×D₄	C₂²×C₆₇	semidirect
382. C₈×D₄	C₂²×C₆₇	semidirect
383. C₈×D₄	C₂²×C₆₇	semidirect
384. #433	C₂²×C₆₇	semidirect
385. #433	C₂²×C₆₇	semidirect
386. #433	C₂²×C₆₇	semidirect
387. #432	C₂²×C₆₇	semidirect
388. #431	C₂²×C₆₇	semidirect
389. #424	C₂²×C₆₇	semidirect
390. #424	C₂²×C₆₇	semidirect
391. #423	C₂²×C₆₇	semidirect
392. #423	C₂²×C₆₇	semidirect
397. #408	C₂²×C₆₇	semidirect
398. #408	C₂²×C₆₇	semidirect
399. #407	C₂²×C₆₇	semidirect
400. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
401. #405	C₂²×C₆₇	semidirect
402. #405	C₂²×C₆₇	semidirect
403. C₂×#97	C₂²×C₆₇	semidirect
404. 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×#3529	2
C₆₇×#2995	2
C₆₇×#2993	2
C₆₇×#2980	2
C₆₇×#2979	2
C₆₇×#2977	2
C₆₇×#2976	2
C₆₇×#2968	2
C₆₇×#2966	2
C₆₇×#2933	2
C₆₇×#2932	2
C₆₇×#2931	2
C₆₇×#2930	2
#60318	67

Subgroups — C67×#60318 #30739569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60318 #30739569