Subgroups — C₆₇×#34275 #30713526

Order 17152.

3410 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#520×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#518×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2363	C₂	1	4	yes	maximal, complemented
5	C₆₇×#2361	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2358	C₂	1	8	yes	maximal, complemented
7	C₆₇×#2328	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2326	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2317	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#127×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₄×#124×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2297	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#390×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
17	#535×C₆₇	C₄	1	16	yes	complemented
18	C₂×#127×C₆₇	C₂²	1	2	yes	—
19	C₂×#124×C₆₇	C₂²	1	2	yes	—
20	C₂×#121×C₆₇	C₂²	1	4	yes	—
21	C₂×#120×C₆₇	C₂²	1	4	yes	—
22	#520×C₆₇	—	2	8	no	—
23	#518×C₆₇	—	2	8	no	—
24	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
25	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
31	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
32	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
36	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
38	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
39	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
40	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
41	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#390×C₆₇	C₂²	1	2	yes	—
44	#390×C₆₇	C₂²	1	2	yes	—
45	#390×C₆₇	C₂²	1	4	yes	—
46	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#390×C₆₇	C₂²	1	8	yes	complemented
49	#389×C₆₇	C₂²	1	4	yes	complemented
50	#388×C₆₇	C₂²	1	8	yes	complemented
51	#388×C₆₇	C₂²	1	8	yes	complemented
52	#386×C₆₇	C₂²	1	4	yes	—
53	#386×C₆₇	C₂²	1	8	yes	complemented
54	#386×C₆₇	C₂²	1	8	yes	complemented
55	#385×C₆₇	C₂²	1	4	yes	—
56	#385×C₆₇	C₂²	1	8	yes	complemented
57	#384×C₆₇	C₂²	1	2	yes	complemented
58	#382×C₆₇	C₂²	1	2	yes	complemented
59	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
60	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
62	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
63	C₄×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	complemented
64	#376×C₆₇	C₂²	1	2	yes	complemented
65	C₄³×C₆₇	C₂²	1	2	yes	complemented
66	C₂⁵×C₆₇	C₂³	1	2	yes	—
67	C₂×#41×C₆₇	—	2	4	no	—
68	C₂×#41×C₆₇	—	2	4	no	—
69	C₂×#41×C₆₇	C₂×C₄	1	8	yes	complemented
70	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₆₇	—	2	4	no	—
72	C₂²×D₄×C₆₇	—	2	4	no	—
73	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
74	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
75	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
76	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
77	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
79	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
80	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
81	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
82	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
83	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
84	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
85	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
86	#127×C₆₇	C₂×C₄	1	16	yes	complemented
87	#124×C₆₇	C₂×C₄	1	16	yes	complemented
88	#121×C₆₇	C₂×C₄	1	32	yes	complemented
89	#120×C₆₇	C₂×C₄	1	32	yes	complemented
90	C₄×Q₈×C₆₇	—	2	8	no	—
91	C₄×D₄×C₆₇	—	2	8	no	—
92	C₄×D₄×C₆₇	—	2	8	no	—
93	C₄×D₄×C₆₇	—	2	16	no	—
94	C₄×D₄×C₆₇	—	2	8	no	—
95	C₄×D₄×C₆₇	—	2	8	no	—
96	C₄×D₄×C₆₇	—	2	8	no	—
97	C₄×D₄×C₆₇	—	4	16	no	—
98	#117×C₆₇	—	2	4	no	—
99	#117×C₆₇	—	2	8	no	—
100	#117×C₆₇	C₂×C₄	1	8	yes	complemented
101	#117×C₆₇	D₄	1	8	yes	complemented
102	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
103	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
104	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
114	C₂×C₂²⋊C₄×C₆₇	—	4	8	no	—
115	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
119	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
122	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
125	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₄²×C₆₇	—	2	4	no	—
127	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
130	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
131	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
132	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
133	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
134	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
136	#95×C₆₇	C₂³	1	4	yes	—
137	#95×C₆₇	C₂³	1	4	yes	—
138	#95×C₆₇	C₂³	1	4	yes	—
139	#95×C₆₇	C₂³	1	8	yes	—
140	#95×C₆₇	C₂³	1	4	yes	—
141	C₂⁴×C₆₇	—	2	4	no	—
142	C₂⁴×C₆₇	—	2	4	no	—
143	C₂⁴×C₆₇	—	4	4	no	—
144	C₂⁴×C₆₇	—	4	4	no	—
145	C₂⁴×C₆₇	C₂²×C₄	1	8	yes	—
146	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
147	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
148	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
149	#41×C₆₇	—	2	32	no	—
150	C₂×Q₈×C₆₇	—	2	2	no	—
151	C₂×Q₈×C₆₇	—	2	2	no	—
152	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
153	C₂×D₄×C₆₇	—	2	4	no	—
154	C₂×D₄×C₆₇	—	2	4	no	—
155	C₂×D₄×C₆₇	—	2	32	no	—
156	C₂×D₄×C₆₇	—	2	4	no	—
157	C₂×D₄×C₆₇	—	2	4	no	—
158	C₂×D₄×C₆₇	—	2	2	no	—
159	C₂×D₄×C₆₇	—	2	4	no	—
160	C₂×D₄×C₆₇	—	2	4	no	—
161	C₂×D₄×C₆₇	—	2	2	no	—
162	C₂×D₄×C₆₇	—	4	8	no	—
163	C₂×D₄×C₆₇	—	4	8	no	—
164	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
165	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
166	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
167	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
168	C₂×D₄×C₆₇	C₂²×C₄	1	32	yes	—
169	C₂²×C₄×C₆₇	—	2	4	no	—
170	C₂²×C₄×C₆₇	—	2	4	no	—
171	C₂²×C₄×C₆₇	—	2	4	no	—
172	C₂²×C₄×C₆₇	—	2	4	no	—
173	C₂²×C₄×C₆₇	—	2	4	no	—
174	C₂²×C₄×C₆₇	—	2	8	no	—
175	C₂²×C₄×C₆₇	—	2	8	no	—
176	C₂²×C₄×C₆₇	—	2	8	no	—
177	C₂²×C₄×C₆₇	—	4	2	no	—
178	C₂²×C₄×C₆₇	—	4	4	no	—
179	C₂²×C₄×C₆₇	—	4	8	no	—
180	C₂²×C₄×C₆₇	—	4	8	no	—
181	C₂²×C₄×C₆₇	—	4	8	no	—
182	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
183	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
184	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
185	C₂²×C₄×C₆₇	#41	1	4	yes	—
186	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
197	C₄⋊C₄×C₆₇	—	2	4	no	—
198	C₄⋊C₄×C₆₇	—	2	8	no	—
199	C₄⋊C₄×C₆₇	—	2	4	no	—
200	C₄⋊C₄×C₆₇	—	2	2	no	—
201	C₄⋊C₄×C₆₇	—	2	2	no	—
202	C₄⋊C₄×C₆₇	—	4	8	no	—
203	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
204	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
205	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
206	C₂²⋊C₄×C₆₇	—	2	4	no	—
207	C₂²⋊C₄×C₆₇	—	2	8	no	—
208	C₂²⋊C₄×C₆₇	—	2	8	no	—
209	C₂²⋊C₄×C₆₇	—	2	8	no	—
210	C₂²⋊C₄×C₆₇	—	2	16	no	—
211	C₂²⋊C₄×C₆₇	—	2	8	no	—
212	C₂²⋊C₄×C₆₇	—	4	8	no	—
213	C₂²⋊C₄×C₆₇	—	4	4	no	—
214	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
215	C₂²⋊C₄×C₆₇	C₂²×C₄	1	32	yes	—
216	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
217	C₄²×C₆₇	—	2	4	no	—
218	C₄²×C₆₇	—	2	8	no	—
219	C₄²×C₆₇	—	2	2	no	—
220	C₄²×C₆₇	—	2	4	no	—
221	C₄²×C₆₇	—	2	2	no	—
222	C₄²×C₆₇	—	2	8	no	—
223	C₄²×C₆₇	—	4	4	no	—
224	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
225	C₄²×C₆₇	C₂×D₄	1	8	yes	—
226	C₂³×C₆₇	—	2	2	no	—
227	C₂³×C₆₇	—	2	2	no	—
228	C₂³×C₆₇	—	2	2	no	—
229	C₂³×C₆₇	—	2	4	no	—
230	C₂³×C₆₇	—	2	2	no	—
231	C₂³×C₆₇	—	2	4	no	—
232	C₂³×C₆₇	—	2	8	no	—
233	C₂³×C₆₇	—	2	4	no	—
234	C₂³×C₆₇	—	2	4	no	—
235	C₂³×C₆₇	—	2	8	no	—
236	C₂³×C₆₇	—	2	16	no	—
237	C₂³×C₆₇	—	4	16	no	—
238	C₂³×C₆₇	—	8	8	no	—
239	C₂³×C₆₇	—	8	4	no	—
240	C₂³×C₆₇	—	8	4	no	—
241	C₂³×C₆₇	C₂³×C₄	1	8	yes	—
242	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
243	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
244	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
245	C₂³×C₆₇	C₂×#41	1	2	yes	—
246	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
247	Q₈×C₆₇	—	2	8	no	—
248	D₄×C₆₇	—	2	16	no	—
249	D₄×C₆₇	—	2	16	no	—
250	D₄×C₆₇	—	2	16	no	—
251	D₄×C₆₇	—	2	8	no	—
252	D₄×C₆₇	—	4	32	no	—
253	C₂×C₄×C₆₇	—	2	2	no	—
254	C₂×C₄×C₆₇	—	2	2	no	—
255	C₂×C₄×C₆₇	—	2	2	no	—
256	C₂×C₄×C₆₇	—	2	4	no	—
257	C₂×C₄×C₆₇	—	2	4	no	—
258	C₂×C₄×C₆₇	—	2	2	no	—
259	C₂×C₄×C₆₇	—	2	4	no	—
260	C₂×C₄×C₆₇	—	2	4	no	—
261	C₂×C₄×C₆₇	—	2	16	no	—
262	C₂×C₄×C₆₇	—	2	2	no	—
263	C₂×C₄×C₆₇	—	2	2	no	—
264	C₂×C₄×C₆₇	—	2	4	no	—
265	C₂×C₄×C₆₇	—	2	2	no	—
266	C₂×C₄×C₆₇	—	2	8	no	—
267	C₂×C₄×C₆₇	—	2	4	no	—
268	C₂×C₄×C₆₇	—	2	2	no	—
269	C₂×C₄×C₆₇	—	2	2	no	—
270	C₂×C₄×C₆₇	—	2	4	no	—
271	C₂×C₄×C₆₇	—	4	8	no	—
272	C₂×C₄×C₆₇	—	8	8	no	—
273	C₂×C₄×C₆₇	—	8	8	no	—
274	C₂×C₄×C₆₇	—	8	8	no	—
275	C₂×C₄×C₆₇	—	8	4	no	—
276	C₂×C₄×C₆₇	C₄×D₄	1	16	yes	complemented
277	C₂×C₄×C₆₇	C₂³×C₄	1	8	yes	—
278	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
279	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
280	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
281	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
282	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
283	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
284	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
286	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
287	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
288	C₂²×C₆₇	—	2	4	no	—
289	C₂²×C₆₇	—	2	4	no	—
290	C₂²×C₆₇	—	2	2	no	—
291	C₂²×C₆₇	—	2	2	no	—
292	C₂²×C₆₇	—	2	4	no	—
293	C₂²×C₆₇	—	2	8	no	—
294	C₂²×C₆₇	—	2	8	no	—
295	C₂²×C₆₇	—	2	16	no	—
296	C₂²×C₆₇	—	4	4	no	—
297	C₂²×C₆₇	—	4	8	no	—
298	C₂²×C₆₇	—	4	2	no	—
299	C₂²×C₆₇	—	4	4	no	—
300	C₂²×C₆₇	—	4	4	no	—
301	C₂²×C₆₇	—	4	2	no	—
302	C₂²×C₆₇	—	8	16	no	—
303	C₂²×C₆₇	C₂×C₄×D₄	1	4	yes	—
304	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
305	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
306	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
307	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
308	C₂²×C₆₇	#585	1	2	yes	—
309	C₄×C₆₇	—	2	4	no	—
310	C₄×C₆₇	—	2	8	no	—
311	C₄×C₆₇	—	2	4	no	—
312	C₄×C₆₇	—	2	4	no	—
313	C₄×C₆₇	—	2	4	no	—
314	C₄×C₆₇	—	4	2	no	—
315	C₄×C₆₇	—	4	2	no	—
316	C₄×C₆₇	—	4	4	no	—
317	C₄×C₆₇	—	4	2	no	—
318	C₄×C₆₇	C₂×C₄×D₄	1	4	yes	—
319	C₄×C₆₇	C₂×C₄×D₄	1	4	yes	—
320	#34275	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
321	C₂×C₆₇	—	2	4	no	—
322	C₂×C₆₇	—	4	4	no	—
323	C₂×C₆₇	—	4	8	no	—
324	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
325	C₂×C₆₇	C₄×H(5,𝔽₂)	1	2	yes	—
326	C₂×C₆₇	#3494	1	2	yes	—
327	C₂×C₆₇	#3498	1	1	yes	characteristic
328	C₂×C₆₇	#3500	1	1	yes	characteristic
329	C₂×#535	C₂×C₆₇	1	1	yes	characteristic
330	C₂×#520	C₂×C₆₇	1	1	yes	characteristic, complemented
331	C₂×#518	C₂×C₆₇	1	1	yes	characteristic, complemented
332	#2363	C₂×C₆₇	1	4	yes	complemented
333	#2361	C₂×C₆₇	1	4	yes	complemented
334	#2358	C₂×C₆₇	1	8	yes	complemented
335	#2328	C₂×C₆₇	1	2	yes	complemented
336	#2326	C₂×C₆₇	1	2	yes	complemented
337	#2317	C₂×C₆₇	1	1	yes	characteristic, complemented
338	C₄×#127	C₂×C₆₇	1	2	yes	complemented
339	C₄×#124	C₂×C₆₇	1	2	yes	complemented
340	#2297	C₂×C₆₇	1	1	yes	characteristic, complemented
341	C₂×#390	C₂×C₆₇	1	1	yes	characteristic, complemented
342	C₄×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
343	C₆₇	#34275	1	1	yes	characteristic, direct product factor, Sylow
344	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
345	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
346	#535	C₄×C₆₇	1	16	yes	complemented
347	C₂×#127	C₂²×C₆₇	1	2	yes	—
348	C₂×#124	C₂²×C₆₇	1	2	yes	—
349	C₂×#121	C₂²×C₆₇	1	4	yes	—
350	C₂×#120	C₂²×C₆₇	1	4	yes	—
351	#520	—	2	8	no	—
352	#518	—	2	8	no	—
353	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
354	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
355	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
356	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
357	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
358	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
359	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
360	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
361	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
362	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
363	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
364	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
365	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
366	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
367	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
368	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
369	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
370	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
371	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
372	#390	C₂²×C₆₇	1	2	yes	—
373	#390	C₂²×C₆₇	1	2	yes	—
374	#390	C₂²×C₆₇	1	4	yes	—
375	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
376	#390	C₂²×C₆₇	1	8	yes	complemented
377	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
378	#389	C₂²×C₆₇	1	4	yes	complemented
379	#388	C₂²×C₆₇	1	8	yes	complemented
380	#388	C₂²×C₆₇	1	8	yes	complemented
381	#386	C₂²×C₆₇	1	4	yes	—
382	#386	C₂²×C₆₇	1	8	yes	complemented
383	#386	C₂²×C₆₇	1	8	yes	complemented
384	#385	C₂²×C₆₇	1	4	yes	—
385	#385	C₂²×C₆₇	1	8	yes	complemented
386	#384	C₂²×C₆₇	1	2	yes	complemented
387	#382	C₂²×C₆₇	1	2	yes	complemented
388	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
389	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
390	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
391	C₄×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	complemented
392	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
393	#376	C₂²×C₆₇	1	2	yes	complemented
394	C₄³	C₂²×C₆₇	1	2	yes	complemented
395	C₂⁵	C₂³×C₆₇	1	2	yes	—
396	C₂×#41	—	2	4	no	—
397	C₂×#41	—	2	4	no	—
398	C₂×#41	C₂×C₄×C₆₇	1	8	yes	complemented
399	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
400	C₂²×D₄	—	2	4	no	—
401	C₂²×D₄	—	2	4	no	—
402	C₂²×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
403	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
404	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
405	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
406	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
407	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
408	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
409	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
410	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
411	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
412	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
413	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
414	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
415	#127	C₂×C₄×C₆₇	1	16	yes	complemented
416	#124	C₂×C₄×C₆₇	1	16	yes	complemented
417	#121	C₂×C₄×C₆₇	1	32	yes	complemented
418	#120	C₂×C₄×C₆₇	1	32	yes	complemented
419	C₄×Q₈	—	2	8	no	—
420	C₄×D₄	—	2	8	no	—
421	C₄×D₄	—	2	8	no	—
422	C₄×D₄	—	2	16	no	—
423	C₄×D₄	—	2	8	no	—
424	C₄×D₄	—	2	8	no	—
425	C₄×D₄	—	2	8	no	—
426	C₄×D₄	—	4	16	no	—
427	#117	—	2	4	no	—
428	#117	—	2	8	no	—
429	#117	C₂×C₄×C₆₇	1	8	yes	complemented
430	#117	D₄×C₆₇	1	8	yes	complemented
431	C₂×C₄⋊C₄	—	2	4	no	—
432	C₂×C₄⋊C₄	—	2	8	no	—
433	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
436	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
439	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	—	2	16	no	—
443	C₂×C₂²⋊C₄	—	4	8	no	—
444	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
455	C₂×C₄²	—	2	4	no	—
456	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
457	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
458	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
459	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
461	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
462	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
463	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
464	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
465	#95	C₂³×C₆₇	1	4	yes	—
466	#95	C₂³×C₆₇	1	4	yes	—
467	#95	C₂³×C₆₇	1	4	yes	—
468	#95	C₂³×C₆₇	1	8	yes	—
469	#95	C₂³×C₆₇	1	4	yes	—
470	C₂⁴	—	2	4	no	—
471	C₂⁴	—	2	4	no	—
472	C₂⁴	—	4	4	no	—
473	C₂⁴	—	4	4	no	—
474	C₂⁴	C₂²×C₄×C₆₇	1	8	yes	—
475	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
476	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
477	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
478	#41	—	2	32	no	—
479	C₂×Q₈	—	2	2	no	—
480	C₂×Q₈	—	2	2	no	—
481	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	2	4	no	—
484	C₂×D₄	—	2	32	no	—
485	C₂×D₄	—	2	4	no	—
486	C₂×D₄	—	2	4	no	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	4	8	no	—
492	C₂×D₄	—	4	8	no	—
493	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
494	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
495	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
496	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
497	C₂×D₄	C₂²×C₄×C₆₇	1	32	yes	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	4	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	2	4	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	8	no	—
504	C₂²×C₄	—	2	8	no	—
505	C₂²×C₄	—	2	8	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	—	4	4	no	—
508	C₂²×C₄	—	4	8	no	—
509	C₂²×C₄	—	4	8	no	—
510	C₂²×C₄	—	4	8	no	—
511	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
512	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
513	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
514	C₂²×C₄	#41×C₆₇	1	4	yes	—
515	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
516	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
517	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
518	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
519	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
520	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	8	no	—
528	C₄⋊C₄	—	2	4	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	4	8	no	—
532	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
533	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
534	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	2	8	no	—
537	C₂²⋊C₄	—	2	8	no	—
538	C₂²⋊C₄	—	2	8	no	—
539	C₂²⋊C₄	—	2	16	no	—
540	C₂²⋊C₄	—	2	8	no	—
541	C₂²⋊C₄	—	4	8	no	—
542	C₂²⋊C₄	—	4	4	no	—
543	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
544	C₂²⋊C₄	C₂²×C₄×C₆₇	1	32	yes	—
545	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
546	C₄²	—	2	4	no	—
547	C₄²	—	2	8	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	2	4	no	—
550	C₄²	—	2	2	no	—
551	C₄²	—	2	8	no	—
552	C₄²	—	4	4	no	—
553	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
554	C₄²	C₂×D₄×C₆₇	1	8	yes	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	2	2	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	2	8	no	—
562	C₂³	—	2	4	no	—
563	C₂³	—	2	4	no	—
564	C₂³	—	2	8	no	—
565	C₂³	—	2	16	no	—
566	C₂³	—	4	16	no	—
567	C₂³	—	8	8	no	—
568	C₂³	—	8	4	no	—
569	C₂³	—	8	4	no	—
570	C₂³	C₂³×C₄×C₆₇	1	8	yes	—
571	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
572	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
573	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
574	C₂³	C₂×#41×C₆₇	1	2	yes	—
575	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
576	Q₈	—	2	8	no	—
577	D₄	—	2	16	no	—
578	D₄	—	2	16	no	—
579	D₄	—	2	16	no	—
580	D₄	—	2	8	no	—
581	D₄	—	4	32	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	16	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	8	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	4	8	no	—
601	C₂×C₄	—	8	8	no	—
602	C₂×C₄	—	8	8	no	—
603	C₂×C₄	—	8	8	no	—
604	C₂×C₄	—	8	4	no	—
605	C₂×C₄	C₄×D₄×C₆₇	1	16	yes	complemented
606	C₂×C₄	C₂³×C₄×C₆₇	1	8	yes	—
607	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
608	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
609	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
610	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
611	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
612	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
613	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
614	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
615	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
616	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
617	C₂²	—	2	4	no	—
618	C₂²	—	2	4	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	4	no	—
622	C₂²	—	2	8	no	—
623	C₂²	—	2	8	no	—
624	C₂²	—	2	16	no	—
625	C₂²	—	4	8	no	—
626	C₂²	—	4	4	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	4	no	—
629	C₂²	—	4	4	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	8	16	no	—
632	C₂²	C₂×C₄×D₄×C₆₇	1	4	yes	—
633	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
634	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
635	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
636	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
637	C₂²	#585×C₆₇	1	2	yes	—
638	C₄	—	2	4	no	—
639	C₄	—	2	8	no	—
640	C₄	—	2	4	no	—
641	C₄	—	2	4	no	—
642	C₄	—	2	4	no	—
643	C₄	—	4	2	no	—
644	C₄	—	4	2	no	—
645	C₄	—	4	4	no	—
646	C₄	—	4	2	no	—
647	C₄	C₂×C₄×D₄×C₆₇	1	4	yes	—
648	C₄	C₂×C₄×D₄×C₆₇	1	4	yes	—
649	C₂	—	2	4	no	—
650	C₂	—	4	8	no	—
651	C₂	—	4	4	no	—
652	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
653	C₂	C₄×H(5,𝔽₂)×C₆₇	1	2	yes	—
654	C₂	C₆₇×#3494	1	2	yes	—
655	C₂	C₆₇×#3498	1	1	yes	characteristic
656	C₂	C₆₇×#3500	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#535×C₆₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#520×C₆₇	C₂	semidirect
3. C₂×#518×C₆₇	C₂	semidirect
4. C₆₇×#2363	C₂	semidirect
5. C₆₇×#2361	C₂	semidirect
6. C₆₇×#2358	C₂	semidirect
7. C₆₇×#2328	C₂	semidirect
8. C₆₇×#2326	C₂	semidirect
9. C₆₇×#2317	C₂	semidirect
10. C₄×#127×C₆₇	C₂	semidirect
11. C₄×#124×C₆₇	C₂	semidirect
12. C₆₇×#2297	C₂	semidirect
13. C₂×#390×C₆₇	C₂	semidirect
14. C₄×#117×C₆₇	C₂	semidirect
17. #535×C₆₇	C₄	semidirect
24. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
30. C₂×C₄×D₄×C₆₇	C₂²	semidirect
31. C₂×C₄×D₄×C₆₇	C₂²	semidirect
35. C₂×#117×C₆₇	C₂²	semidirect
37. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
41. #391×C₆₇	C₂²	semidirect
42. #391×C₆₇	C₂²	semidirect
46. #390×C₆₇	C₂²	semidirect
47. #390×C₆₇	C₂²	semidirect
48. #390×C₆₇	C₂²	semidirect
49. #389×C₆₇	C₂²	semidirect
50. #388×C₆₇	C₂²	semidirect
51. #388×C₆₇	C₂²	semidirect
53. #386×C₆₇	C₂²	semidirect
54. #386×C₆₇	C₂²	semidirect
56. #385×C₆₇	C₂²	semidirect
57. #384×C₆₇	C₂²	semidirect
58. #382×C₆₇	C₂²	semidirect
59. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
60. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
62. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
63. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
64. #376×C₆₇	C₂²	semidirect
65. C₄³×C₆₇	C₂²	semidirect
69. C₂×#41×C₆₇	C₂×C₄	semidirect
73. C₂²×D₄×C₆₇	C₂×C₄	semidirect
86. #127×C₆₇	C₂×C₄	semidirect
87. #124×C₆₇	C₂×C₄	semidirect
88. #121×C₆₇	C₂×C₄	semidirect
89. #120×C₆₇	C₂×C₄	semidirect
100. #117×C₆₇	C₂×C₄	semidirect
101. #117×C₆₇	D₄	semidirect
276. C₂×C₄×C₆₇	C₄×D₄	semidirect
320. #34275	C₆₇	direct (N × H)
330. C₂×#520	C₂×C₆₇	semidirect
331. C₂×#518	C₂×C₆₇	semidirect
332. #2363	C₂×C₆₇	semidirect
333. #2361	C₂×C₆₇	semidirect
334. #2358	C₂×C₆₇	semidirect
335. #2328	C₂×C₆₇	semidirect
336. #2326	C₂×C₆₇	semidirect
337. #2317	C₂×C₆₇	semidirect
338. C₄×#127	C₂×C₆₇	semidirect
339. C₄×#124	C₂×C₆₇	semidirect
340. #2297	C₂×C₆₇	semidirect
341. C₂×#390	C₂×C₆₇	semidirect
342. C₄×#117	C₂×C₆₇	semidirect
343. C₆₇	#34275	direct (N × H)
346. #535	C₄×C₆₇	semidirect
353. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
359. C₂×C₄×D₄	C₂²×C₆₇	semidirect
360. C₂×C₄×D₄	C₂²×C₆₇	semidirect
364. C₂×#117	C₂²×C₆₇	semidirect
366. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
370. #391	C₂²×C₆₇	semidirect
371. #391	C₂²×C₆₇	semidirect
375. #390	C₂²×C₆₇	semidirect
376. #390	C₂²×C₆₇	semidirect
377. #390	C₂²×C₆₇	semidirect
378. #389	C₂²×C₆₇	semidirect
379. #388	C₂²×C₆₇	semidirect
380. #388	C₂²×C₆₇	semidirect
382. #386	C₂²×C₆₇	semidirect
383. #386	C₂²×C₆₇	semidirect
385. #385	C₂²×C₆₇	semidirect
386. #384	C₂²×C₆₇	semidirect
387. #382	C₂²×C₆₇	semidirect
388. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
389. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
391. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
392. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
393. #376	C₂²×C₆₇	semidirect
394. C₄³	C₂²×C₆₇	semidirect
398. C₂×#41	C₂×C₄×C₆₇	semidirect
402. C₂²×D₄	C₂×C₄×C₆₇	semidirect
415. #127	C₂×C₄×C₆₇	semidirect
416. #124	C₂×C₄×C₆₇	semidirect
417. #121	C₂×C₄×C₆₇	semidirect
418. #120	C₂×C₄×C₆₇	semidirect
429. #117	C₂×C₄×C₆₇	semidirect
430. #117	D₄×C₆₇	semidirect
605. C₂×C₄	C₄×D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#535×C₆₇	2
C₂×#520×C₆₇	2
C₂×#518×C₆₇	2
C₆₇×#2363	2
C₆₇×#2361	2
C₆₇×#2358	2
C₆₇×#2328	2
C₆₇×#2326	2
C₆₇×#2317	2
C₄×#127×C₆₇	2
C₄×#124×C₆₇	2
C₆₇×#2297	2
C₂×#390×C₆₇	2
C₄×#117×C₆₇	2
#34275	67

Subgroups — C67×#34275 #30713526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34275 #30713526