Subgroups — C₆₇×#34980 #30714231

Order 17152.

7786 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#534×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂²×#120×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2849	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2846	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2613	C₂	1	4	yes	maximal, complemented
7	C₆₇×#2410	C₂	1	8	yes	maximal, complemented
8	C₆₇×#2405	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2403	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2308	C₂	1	2	yes	maximal, complemented
11	C₂×#379×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁶×C₆₇	C₂²	1	1	yes	characteristic
13	C₂⁶×C₆₇	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₄×C₆₇	—	2	8	no	—
15	C₂³×D₄×C₆₇	—	2	16	no	—
16	C₂³×D₄×C₆₇	C₂²	1	4	yes	—
17	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
18	C₂³×D₄×C₆₇	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₆₇	C₂²	1	4	yes	complemented
20	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄×C₆₇	C₂²	1	2	yes	complemented
22	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	#534×C₆₇	—	2	16	no	—
24	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
25	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
26	C₂×#121×C₆₇	C₂²	1	8	yes	complemented
27	C₂×#120×C₆₇	—	2	8	no	—
28	C₂×#120×C₆₇	C₂²	1	2	yes	—
29	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
30	C₂×#120×C₆₇	C₂²	1	2	yes	complemented
31	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
32	C₂×#120×C₆₇	C₂²	1	8	yes	complemented
33	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
34	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
35	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
37	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
38	#394×C₆₇	C₂²	1	16	yes	complemented
39	#392×C₆₇	C₂²	1	16	yes	complemented
40	#386×C₆₇	C₂²	1	8	yes	complemented
41	#386×C₆₇	C₂²	1	8	yes	complemented
42	#386×C₆₇	C₂²	1	8	yes	complemented
43	#385×C₆₇	C₂²	1	8	yes	complemented
44	#381×C₆₇	C₂²	1	4	yes	complemented
45	#379×C₆₇	C₂²	1	2	yes	complemented
46	#379×C₆₇	C₂²	1	2	yes	complemented
47	#379×C₆₇	C₂²	1	4	yes	complemented
48	#379×C₆₇	C₂²	1	4	yes	complemented
49	#379×C₆₇	C₂²	1	8	yes	complemented
50	C₂⁵×C₆₇	—	2	8	no	—
51	C₂⁵×C₆₇	—	2	4	no	—
52	C₂⁵×C₆₇	—	2	8	no	—
53	C₂⁵×C₆₇	—	4	8	no	—
54	C₂⁵×C₆₇	—	4	8	no	—
55	C₂⁵×C₆₇	D₄	1	8	yes	complemented
56	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
57	C₂⁵×C₆₇	C₂³	1	4	yes	—
58	C₂⁵×C₆₇	C₂³	1	2	yes	—
59	C₂⁵×C₆₇	C₂³	1	2	yes	—
60	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
61	C₂⁵×C₆₇	C₂³	1	2	yes	—
62	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
63	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic, complemented
64	C₂²×D₄×C₆₇	—	2	128	no	—
65	C₂²×D₄×C₆₇	—	2	16	no	—
66	C₂²×D₄×C₆₇	—	2	8	no	—
67	C₂²×D₄×C₆₇	—	2	8	no	—
68	C₂²×D₄×C₆₇	—	2	16	no	—
69	C₂²×D₄×C₆₇	—	2	8	no	—
70	C₂²×D₄×C₆₇	—	2	8	no	—
71	C₂²×D₄×C₆₇	—	2	32	no	—
72	C₂²×D₄×C₆₇	—	2	32	no	—
73	C₂²×D₄×C₆₇	—	2	8	no	—
74	C₂²×D₄×C₆₇	—	2	4	no	—
75	C₂²×D₄×C₆₇	—	2	8	no	—
76	C₂²×D₄×C₆₇	—	2	8	no	—
77	C₂²×D₄×C₆₇	—	4	8	no	—
78	C₂²×D₄×C₆₇	D₄	1	16	yes	complemented
79	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
80	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
81	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
82	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
83	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
84	C₂²×D₄×C₆₇	C₂³	1	2	yes	complemented
85	C₂²×D₄×C₆₇	C₂³	1	8	yes	complemented
86	C₂²×D₄×C₆₇	C₂³	1	4	yes	complemented
87	C₂³×C₄×C₆₇	—	2	4	no	—
88	C₂³×C₄×C₆₇	—	2	8	no	—
89	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
90	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
91	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
92	C₂³×C₄×C₆₇	C₂³	1	4	yes	complemented
93	C₂³×C₄×C₆₇	C₂³	1	2	yes	complemented
94	#123×C₆₇	—	2	16	no	—
95	#123×C₆₇	—	2	16	no	—
96	#121×C₆₇	—	2	32	no	—
97	#120×C₆₇	—	2	8	no	—
98	#120×C₆₇	—	2	16	no	—
99	#120×C₆₇	—	2	8	no	—
100	#120×C₆₇	—	2	16	no	—
101	#120×C₆₇	—	2	16	no	—
102	#120×C₆₇	—	4	16	no	—
103	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
104	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
105	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
106	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
107	C₂×C₂²⋊C₄×C₆₇	—	4	8	no	—
108	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
112	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	complemented
113	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	complemented
114	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	complemented
115	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	complemented
116	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	complemented
117	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	complemented
118	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
119	#95×C₆₇	C₂³	1	16	yes	complemented
120	C₂⁴×C₆₇	—	2	4	no	—
121	C₂⁴×C₆₇	—	2	8	no	—
122	C₂⁴×C₆₇	—	2	32	no	—
123	C₂⁴×C₆₇	—	2	32	no	—
124	C₂⁴×C₆₇	—	2	16	no	—
125	C₂⁴×C₆₇	—	2	8	no	—
126	C₂⁴×C₆₇	—	2	8	no	—
127	C₂⁴×C₆₇	—	2	8	no	—
128	C₂⁴×C₆₇	—	2	4	no	—
129	C₂⁴×C₆₇	—	2	4	no	—
130	C₂⁴×C₆₇	—	2	4	no	—
131	C₂⁴×C₆₇	—	2	8	no	—
132	C₂⁴×C₆₇	—	2	8	no	—
133	C₂⁴×C₆₇	—	2	2	no	—
134	C₂⁴×C₆₇	—	2	16	no	—
135	C₂⁴×C₆₇	—	2	4	no	—
136	C₂⁴×C₆₇	—	4	32	no	—
137	C₂⁴×C₆₇	—	4	4	no	—
138	C₂⁴×C₆₇	—	4	4	no	—
139	C₂⁴×C₆₇	—	4	4	no	—
140	C₂⁴×C₆₇	—	4	4	no	—
141	C₂⁴×C₆₇	—	4	8	no	—
142	C₂⁴×C₆₇	—	4	8	no	—
143	C₂⁴×C₆₇	—	4	4	no	—
144	C₂⁴×C₆₇	—	4	64	no	—
145	C₂⁴×C₆₇	—	4	64	no	—
146	C₂⁴×C₆₇	—	4	32	no	—
147	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
148	C₂⁴×C₆₇	C₂×D₄	1	8	yes	—
149	C₂⁴×C₆₇	C₂×D₄	1	8	yes	—
150	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
151	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
152	C₂⁴×C₆₇	C₂×D₄	1	8	yes	—
153	C₂⁴×C₆₇	C₂×D₄	1	8	yes	complemented
154	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
155	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
156	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
157	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
158	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
159	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
160	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
161	C₂×D₄×C₆₇	—	2	128	no	—
162	C₂×D₄×C₆₇	—	2	128	no	—
163	C₂×D₄×C₆₇	—	2	64	no	—
164	C₂×D₄×C₆₇	—	2	64	no	—
165	C₂×D₄×C₆₇	—	2	16	no	—
166	C₂×D₄×C₆₇	—	2	16	no	—
167	C₂×D₄×C₆₇	—	2	8	no	—
168	C₂×D₄×C₆₇	—	2	8	no	—
169	C₂×D₄×C₆₇	—	2	8	no	—
170	C₂×D₄×C₆₇	—	2	8	no	—
171	C₂×D₄×C₆₇	—	2	4	no	—
172	C₂×D₄×C₆₇	—	2	8	no	—
173	C₂×D₄×C₆₇	—	2	8	no	—
174	C₂×D₄×C₆₇	—	2	4	no	—
175	C₂×D₄×C₆₇	—	2	8	no	—
176	C₂×D₄×C₆₇	—	2	8	no	—
177	C₂×D₄×C₆₇	—	2	16	no	—
178	C₂×D₄×C₆₇	—	2	16	no	—
179	C₂×D₄×C₆₇	—	2	16	no	—
180	C₂×D₄×C₆₇	—	4	8	no	—
181	C₂×D₄×C₆₇	—	4	16	no	—
182	C₂×D₄×C₆₇	—	4	32	no	—
183	C₂×D₄×C₆₇	—	4	16	no	—
184	C₂×D₄×C₆₇	C₂×D₄	1	16	yes	—
185	C₂×D₄×C₆₇	C₂×D₄	1	16	yes	complemented
186	C₂²×C₄×C₆₇	—	2	32	no	—
187	C₂²×C₄×C₆₇	—	2	8	no	—
188	C₂²×C₄×C₆₇	—	2	4	no	—
189	C₂²×C₄×C₆₇	—	2	4	no	—
190	C₂²×C₄×C₆₇	—	2	16	no	—
191	C₂²×C₄×C₆₇	—	2	4	no	—
192	C₂²×C₄×C₆₇	—	2	2	no	—
193	C₂²×C₄×C₆₇	—	2	4	no	—
194	C₂²×C₄×C₆₇	—	2	8	no	—
195	C₂²×C₄×C₆₇	—	4	4	no	—
196	C₂²×C₄×C₆₇	—	4	8	no	—
197	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	complemented
198	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
199	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
202	C₄⋊C₄×C₆₇	—	2	16	no	—
203	C₂²⋊C₄×C₆₇	—	2	4	no	—
204	C₂²⋊C₄×C₆₇	—	2	8	no	—
205	C₂²⋊C₄×C₆₇	—	2	8	no	—
206	C₂²⋊C₄×C₆₇	—	2	8	no	—
207	C₂²⋊C₄×C₆₇	—	2	4	no	—
208	C₂²⋊C₄×C₆₇	—	2	8	no	—
209	C₂²⋊C₄×C₆₇	—	2	16	no	—
210	C₂²⋊C₄×C₆₇	—	2	16	no	—
211	C₂²⋊C₄×C₆₇	—	2	16	no	—
212	C₂²⋊C₄×C₆₇	—	4	8	no	—
213	C₂²⋊C₄×C₆₇	—	4	16	no	—
214	C₂³×C₆₇	—	2	32	no	—
215	C₂³×C₆₇	—	2	8	no	—
216	C₂³×C₆₇	—	2	16	no	—
217	C₂³×C₆₇	—	2	4	no	—
218	C₂³×C₆₇	—	2	4	no	—
219	C₂³×C₆₇	—	2	4	no	—
220	C₂³×C₆₇	—	2	4	no	—
221	C₂³×C₆₇	—	2	4	no	—
222	C₂³×C₆₇	—	2	32	no	—
223	C₂³×C₆₇	—	2	16	no	—
224	C₂³×C₆₇	—	2	16	no	—
225	C₂³×C₆₇	—	2	8	no	—
226	C₂³×C₆₇	—	2	16	no	—
227	C₂³×C₆₇	—	2	16	no	—
228	C₂³×C₆₇	—	2	16	no	—
229	C₂³×C₆₇	—	2	4	no	—
230	C₂³×C₆₇	—	2	4	no	—
231	C₂³×C₆₇	—	2	4	no	—
232	C₂³×C₆₇	—	2	4	no	—
233	C₂³×C₆₇	—	2	16	no	—
234	C₂³×C₆₇	—	2	4	no	—
235	C₂³×C₆₇	—	2	4	no	—
236	C₂³×C₆₇	—	2	2	no	—
237	C₂³×C₆₇	—	2	8	no	—
238	C₂³×C₆₇	—	4	8	no	—
239	C₂³×C₆₇	—	4	8	no	—
240	C₂³×C₆₇	—	4	8	no	—
241	C₂³×C₆₇	—	4	8	no	—
242	C₂³×C₆₇	—	4	16	no	—
243	C₂³×C₆₇	—	4	16	no	—
244	C₂³×C₆₇	—	4	32	no	—
245	C₂³×C₆₇	—	4	32	no	—
246	C₂³×C₆₇	—	4	64	no	—
247	C₂³×C₆₇	—	4	128	no	—
248	C₂³×C₆₇	—	4	128	no	—
249	C₂³×C₆₇	—	4	16	no	—
250	C₂³×C₆₇	—	4	16	no	—
251	C₂³×C₆₇	—	4	16	no	—
252	C₂³×C₆₇	—	4	16	no	—
253	C₂³×C₆₇	—	4	8	no	—
254	C₂³×C₆₇	—	4	16	no	—
255	C₂³×C₆₇	—	4	4	no	—
256	C₂³×C₆₇	—	8	8	no	—
257	C₂³×C₆₇	#120	1	16	yes	complemented
258	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
259	C₂³×C₆₇	C₂²×D₄	1	8	yes	—
260	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
261	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
262	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
263	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
264	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
265	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
266	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
267	C₂³×C₆₇	H(5,𝔽₂)	1	8	yes	—
268	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
269	D₄×C₆₇	—	2	64	no	—
270	D₄×C₆₇	—	2	32	no	—
271	D₄×C₆₇	—	2	32	no	—
272	D₄×C₆₇	—	4	16	no	—
273	D₄×C₆₇	—	4	8	no	—
274	D₄×C₆₇	—	4	8	no	—
275	D₄×C₆₇	—	4	16	no	—
276	D₄×C₆₇	—	8	16	no	—
277	C₂×C₄×C₆₇	—	2	32	no	—
278	C₂×C₄×C₆₇	—	2	16	no	—
279	C₂×C₄×C₆₇	—	2	4	no	—
280	C₂×C₄×C₆₇	—	2	4	no	—
281	C₂×C₄×C₆₇	—	2	8	no	—
282	C₂×C₄×C₆₇	—	2	2	no	—
283	C₂×C₄×C₆₇	—	2	4	no	—
284	C₂×C₄×C₆₇	—	2	4	no	—
285	C₂×C₄×C₆₇	—	2	16	no	—
286	C₂×C₄×C₆₇	—	2	8	no	—
287	C₂×C₄×C₆₇	—	4	8	no	—
288	C₂×C₄×C₆₇	—	4	4	no	—
289	C₂×C₄×C₆₇	—	8	8	no	—
290	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
291	C₂²×C₆₇	—	2	32	no	—
292	C₂²×C₆₇	—	2	4	no	—
293	C₂²×C₆₇	—	2	4	no	—
294	C₂²×C₆₇	—	2	4	no	—
295	C₂²×C₆₇	—	2	4	no	—
296	C₂²×C₆₇	—	2	4	no	—
297	C₂²×C₆₇	—	2	8	no	—
298	C₂²×C₆₇	—	2	8	no	—
299	C₂²×C₆₇	—	2	16	no	—
300	C₂²×C₆₇	—	2	8	no	—
301	C₂²×C₆₇	—	2	4	no	—
302	C₂²×C₆₇	—	2	8	no	—
303	C₂²×C₆₇	—	2	4	no	—
304	C₂²×C₆₇	—	2	4	no	—
305	C₂²×C₆₇	—	2	16	no	—
306	C₂²×C₆₇	—	4	16	no	—
307	C₂²×C₆₇	—	4	32	no	—
308	C₂²×C₆₇	—	4	32	no	—
309	C₂²×C₆₇	—	4	16	no	—
310	C₂²×C₆₇	—	4	32	no	—
311	C₂²×C₆₇	—	4	64	no	—
312	C₂²×C₆₇	—	4	8	no	—
313	C₂²×C₆₇	—	4	8	no	—
314	C₂²×C₆₇	—	4	8	no	—
315	C₂²×C₆₇	—	4	2	no	—
316	C₂²×C₆₇	—	4	4	no	—
317	C₂²×C₆₇	—	4	8	no	—
318	C₂²×C₆₇	—	8	8	no	—
319	C₂²×C₆₇	C₂×#120	1	4	yes	—
320	C₂²×C₆₇	C₂×#120	1	4	yes	—
321	C₂²×C₆₇	C₂×#120	1	4	yes	—
322	C₂²×C₆₇	#534	1	8	yes	complemented
323	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
324	C₂²×C₆₇	C₂³×D₄	1	2	yes	—
325	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
326	C₄×C₆₇	—	2	8	no	—
327	C₄×C₆₇	—	4	2	no	—
328	C₄×C₆₇	—	4	4	no	—
329	C₄×C₆₇	—	4	8	no	—
330	#34980	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
331	C₂×C₆₇	—	2	4	no	—
332	C₂×C₆₇	—	2	8	no	—
333	C₂×C₆₇	—	2	4	no	—
334	C₂×C₆₇	—	2	4	no	—
335	C₂×C₆₇	—	4	4	no	—
336	C₂×C₆₇	—	4	8	no	—
337	C₂×C₆₇	—	8	2	no	—
338	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
339	C₂×C₆₇	C₂×#534	1	2	yes	—
340	C₂×C₆₇	#3484	1	4	yes	—
341	C₂⁴×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
342	C₂×#534	C₂×C₆₇	1	2	yes	complemented
343	C₂²×#120	C₂×C₆₇	1	1	yes	characteristic, complemented
344	#2849	C₂×C₆₇	1	2	yes	complemented
345	#2846	C₂×C₆₇	1	2	yes	complemented
346	#2613	C₂×C₆₇	1	4	yes	complemented
347	#2410	C₂×C₆₇	1	8	yes	complemented
348	#2405	C₂×C₆₇	1	4	yes	complemented
349	#2403	C₂×C₆₇	1	4	yes	complemented
350	#2308	C₂×C₆₇	1	2	yes	complemented
351	C₂×#379	C₂×C₆₇	1	1	yes	characteristic, complemented
352	C₆₇	#34980	1	1	yes	characteristic, direct product factor, Sylow
353	C₂⁶	C₂²×C₆₇	1	1	yes	characteristic
354	C₂⁶	C₂²×C₆₇	1	1	yes	characteristic, complemented
355	C₂³×D₄	—	2	8	no	—
356	C₂³×D₄	—	2	16	no	—
357	C₂³×D₄	C₂²×C₆₇	1	4	yes	—
358	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
359	C₂³×D₄	C₂²×C₆₇	1	2	yes	complemented
360	C₂³×D₄	C₂²×C₆₇	1	4	yes	complemented
361	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
362	C₂³×D₄	C₂²×C₆₇	1	2	yes	complemented
363	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
364	#534	—	2	16	no	—
365	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
366	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
367	C₂×#121	C₂²×C₆₇	1	8	yes	complemented
368	C₂×#120	—	2	8	no	—
369	C₂×#120	C₂²×C₆₇	1	2	yes	—
370	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
371	C₂×#120	C₂²×C₆₇	1	2	yes	complemented
372	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
373	C₂×#120	C₂²×C₆₇	1	8	yes	complemented
374	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
375	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
376	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
377	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
378	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
379	#394	C₂²×C₆₇	1	16	yes	complemented
380	#392	C₂²×C₆₇	1	16	yes	complemented
381	#386	C₂²×C₆₇	1	8	yes	complemented
382	#386	C₂²×C₆₇	1	8	yes	complemented
383	#386	C₂²×C₆₇	1	8	yes	complemented
384	#385	C₂²×C₆₇	1	8	yes	complemented
385	#381	C₂²×C₆₇	1	4	yes	complemented
386	#379	C₂²×C₆₇	1	2	yes	complemented
387	#379	C₂²×C₆₇	1	4	yes	complemented
388	#379	C₂²×C₆₇	1	8	yes	complemented
389	#379	C₂²×C₆₇	1	2	yes	complemented
390	#379	C₂²×C₆₇	1	4	yes	complemented
391	C₂⁵	—	2	8	no	—
392	C₂⁵	—	2	4	no	—
393	C₂⁵	—	2	8	no	—
394	C₂⁵	—	4	8	no	—
395	C₂⁵	—	4	8	no	—
396	C₂⁵	D₄×C₆₇	1	8	yes	complemented
397	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
398	C₂⁵	C₂³×C₆₇	1	4	yes	—
399	C₂⁵	C₂³×C₆₇	1	2	yes	—
400	C₂⁵	C₂³×C₆₇	1	2	yes	—
401	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
402	C₂⁵	C₂³×C₆₇	1	2	yes	—
403	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
404	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic, complemented
405	C₂²×D₄	—	2	128	no	—
406	C₂²×D₄	—	2	16	no	—
407	C₂²×D₄	—	2	8	no	—
408	C₂²×D₄	—	2	8	no	—
409	C₂²×D₄	—	2	16	no	—
410	C₂²×D₄	—	2	8	no	—
411	C₂²×D₄	—	2	8	no	—
412	C₂²×D₄	—	2	32	no	—
413	C₂²×D₄	—	2	32	no	—
414	C₂²×D₄	—	2	8	no	—
415	C₂²×D₄	—	2	4	no	—
416	C₂²×D₄	—	2	8	no	—
417	C₂²×D₄	—	2	8	no	—
418	C₂²×D₄	—	4	8	no	—
419	C₂²×D₄	D₄×C₆₇	1	16	yes	complemented
420	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
421	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
422	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
423	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
424	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
425	C₂²×D₄	C₂³×C₆₇	1	2	yes	complemented
426	C₂²×D₄	C₂³×C₆₇	1	8	yes	complemented
427	C₂²×D₄	C₂³×C₆₇	1	4	yes	complemented
428	C₂³×C₄	—	2	4	no	—
429	C₂³×C₄	—	2	8	no	—
430	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
431	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
432	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
433	C₂³×C₄	C₂³×C₆₇	1	4	yes	complemented
434	C₂³×C₄	C₂³×C₆₇	1	2	yes	complemented
435	#123	—	2	16	no	—
436	#123	—	2	16	no	—
437	#121	—	2	32	no	—
438	#120	—	2	8	no	—
439	#120	—	2	16	no	—
440	#120	—	2	8	no	—
441	#120	—	2	16	no	—
442	#120	—	2	16	no	—
443	#120	—	4	16	no	—
444	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	complemented
445	C₂×C₂²⋊C₄	—	2	8	no	—
446	C₂×C₂²⋊C₄	—	2	4	no	—
447	C₂×C₂²⋊C₄	—	2	8	no	—
448	C₂×C₂²⋊C₄	—	4	8	no	—
449	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	complemented
454	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	complemented
455	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	complemented
456	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	complemented
457	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	complemented
458	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	complemented
459	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	complemented
460	#95	C₂³×C₆₇	1	16	yes	complemented
461	C₂⁴	—	2	4	no	—
462	C₂⁴	—	2	8	no	—
463	C₂⁴	—	2	32	no	—
464	C₂⁴	—	2	32	no	—
465	C₂⁴	—	2	16	no	—
466	C₂⁴	—	2	8	no	—
467	C₂⁴	—	2	8	no	—
468	C₂⁴	—	2	8	no	—
469	C₂⁴	—	2	4	no	—
470	C₂⁴	—	2	4	no	—
471	C₂⁴	—	2	4	no	—
472	C₂⁴	—	2	8	no	—
473	C₂⁴	—	2	8	no	—
474	C₂⁴	—	2	2	no	—
475	C₂⁴	—	2	16	no	—
476	C₂⁴	—	2	4	no	—
477	C₂⁴	—	4	32	no	—
478	C₂⁴	—	4	4	no	—
479	C₂⁴	—	4	4	no	—
480	C₂⁴	—	4	4	no	—
481	C₂⁴	—	4	4	no	—
482	C₂⁴	—	4	8	no	—
483	C₂⁴	—	4	8	no	—
484	C₂⁴	—	4	4	no	—
485	C₂⁴	—	4	64	no	—
486	C₂⁴	—	4	64	no	—
487	C₂⁴	—	4	32	no	—
488	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
489	C₂⁴	C₂×D₄×C₆₇	1	8	yes	—
490	C₂⁴	C₂×D₄×C₆₇	1	8	yes	—
491	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
492	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
493	C₂⁴	C₂×D₄×C₆₇	1	8	yes	—
494	C₂⁴	C₂×D₄×C₆₇	1	8	yes	complemented
495	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
496	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
497	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
498	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
499	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
500	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
501	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
502	C₂×D₄	—	2	128	no	—
503	C₂×D₄	—	2	128	no	—
504	C₂×D₄	—	2	64	no	—
505	C₂×D₄	—	2	64	no	—
506	C₂×D₄	—	2	16	no	—
507	C₂×D₄	—	2	16	no	—
508	C₂×D₄	—	2	8	no	—
509	C₂×D₄	—	2	8	no	—
510	C₂×D₄	—	2	8	no	—
511	C₂×D₄	—	2	8	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	8	no	—
514	C₂×D₄	—	2	8	no	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	8	no	—
517	C₂×D₄	—	2	8	no	—
518	C₂×D₄	—	2	16	no	—
519	C₂×D₄	—	2	16	no	—
520	C₂×D₄	—	2	16	no	—
521	C₂×D₄	—	4	8	no	—
522	C₂×D₄	—	4	16	no	—
523	C₂×D₄	—	4	32	no	—
524	C₂×D₄	—	4	16	no	—
525	C₂×D₄	C₂×D₄×C₆₇	1	16	yes	—
526	C₂×D₄	C₂×D₄×C₆₇	1	16	yes	complemented
527	C₂²×C₄	—	2	32	no	—
528	C₂²×C₄	—	2	8	no	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	16	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	8	no	—
536	C₂²×C₄	—	4	4	no	—
537	C₂²×C₄	—	4	8	no	—
538	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	complemented
539	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
540	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
541	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
543	C₄⋊C₄	—	2	16	no	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	2	8	no	—
546	C₂²⋊C₄	—	2	8	no	—
547	C₂²⋊C₄	—	2	8	no	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	8	no	—
550	C₂²⋊C₄	—	2	16	no	—
551	C₂²⋊C₄	—	2	16	no	—
552	C₂²⋊C₄	—	2	16	no	—
553	C₂²⋊C₄	—	4	8	no	—
554	C₂²⋊C₄	—	4	16	no	—
555	C₂³	—	2	32	no	—
556	C₂³	—	2	8	no	—
557	C₂³	—	2	16	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	4	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	2	4	no	—
562	C₂³	—	2	4	no	—
563	C₂³	—	2	32	no	—
564	C₂³	—	2	16	no	—
565	C₂³	—	2	16	no	—
566	C₂³	—	2	8	no	—
567	C₂³	—	2	16	no	—
568	C₂³	—	2	16	no	—
569	C₂³	—	2	16	no	—
570	C₂³	—	2	4	no	—
571	C₂³	—	2	4	no	—
572	C₂³	—	2	4	no	—
573	C₂³	—	2	4	no	—
574	C₂³	—	2	16	no	—
575	C₂³	—	2	4	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	8	no	—
579	C₂³	—	4	8	no	—
580	C₂³	—	4	8	no	—
581	C₂³	—	4	8	no	—
582	C₂³	—	4	8	no	—
583	C₂³	—	4	16	no	—
584	C₂³	—	4	16	no	—
585	C₂³	—	4	32	no	—
586	C₂³	—	4	32	no	—
587	C₂³	—	4	64	no	—
588	C₂³	—	4	128	no	—
589	C₂³	—	4	128	no	—
590	C₂³	—	4	16	no	—
591	C₂³	—	4	16	no	—
592	C₂³	—	4	16	no	—
593	C₂³	—	4	16	no	—
594	C₂³	—	4	8	no	—
595	C₂³	—	4	16	no	—
596	C₂³	—	4	4	no	—
597	C₂³	—	8	8	no	—
598	C₂³	#120×C₆₇	1	16	yes	complemented
599	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
600	C₂³	C₂²×D₄×C₆₇	1	8	yes	—
601	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
602	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
603	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
604	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
605	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
606	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
607	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
608	C₂³	H(5,𝔽₂)×C₆₇	1	8	yes	—
609	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
610	D₄	—	2	64	no	—
611	D₄	—	2	32	no	—
612	D₄	—	2	32	no	—
613	D₄	—	4	16	no	—
614	D₄	—	4	8	no	—
615	D₄	—	4	8	no	—
616	D₄	—	4	16	no	—
617	D₄	—	8	16	no	—
618	C₂×C₄	—	2	32	no	—
619	C₂×C₄	—	2	16	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	16	no	—
627	C₂×C₄	—	2	8	no	—
628	C₂×C₄	—	4	8	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	8	8	no	—
631	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
632	C₂²	—	2	32	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	2	4	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	2	8	no	—
639	C₂²	—	2	8	no	—
640	C₂²	—	2	16	no	—
641	C₂²	—	2	8	no	—
642	C₂²	—	2	4	no	—
643	C₂²	—	2	8	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	2	16	no	—
647	C₂²	—	4	16	no	—
648	C₂²	—	4	32	no	—
649	C₂²	—	4	32	no	—
650	C₂²	—	4	16	no	—
651	C₂²	—	4	32	no	—
652	C₂²	—	4	64	no	—
653	C₂²	—	4	8	no	—
654	C₂²	—	4	8	no	—
655	C₂²	—	4	8	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	4	no	—
658	C₂²	—	4	8	no	—
659	C₂²	—	8	8	no	—
660	C₂²	C₂×#120×C₆₇	1	4	yes	—
661	C₂²	C₂×#120×C₆₇	1	4	yes	—
662	C₂²	C₂×#120×C₆₇	1	4	yes	—
663	C₂²	#534×C₆₇	1	8	yes	complemented
664	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
665	C₂²	C₂³×D₄×C₆₇	1	2	yes	—
666	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
667	C₄	—	2	8	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	4	no	—
670	C₄	—	4	8	no	—
671	C₂	—	2	4	no	—
672	C₂	—	2	8	no	—
673	C₂	—	2	4	no	—
674	C₂	—	2	4	no	—
675	C₂	—	4	4	no	—
676	C₂	—	4	8	no	—
677	C₂	—	8	2	no	—
678	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
679	C₂	C₂×#534×C₆₇	1	2	yes	—
680	C₂	C₆₇×#3484	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₄×C₆₇	C₂	semidirect
2. C₂×#534×C₆₇	C₂	semidirect
3. C₂²×#120×C₆₇	C₂	semidirect
4. C₆₇×#2849	C₂	semidirect
5. C₆₇×#2846	C₂	semidirect
6. C₆₇×#2613	C₂	semidirect
7. C₆₇×#2410	C₂	semidirect
8. C₆₇×#2405	C₂	semidirect
9. C₆₇×#2403	C₂	semidirect
10. C₆₇×#2308	C₂	semidirect
11. C₂×#379×C₆₇	C₂	semidirect
13. C₂⁶×C₆₇	C₂²	semidirect
18. C₂³×D₄×C₆₇	C₂²	semidirect
19. C₂³×D₄×C₆₇	C₂²	semidirect
20. C₂³×D₄×C₆₇	C₂²	semidirect
21. C₂³×D₄×C₆₇	C₂²	semidirect
22. C₂⁴×C₄×C₆₇	C₂²	semidirect
24. C₂×#123×C₆₇	C₂²	semidirect
25. C₂×#123×C₆₇	C₂²	semidirect
26. C₂×#121×C₆₇	C₂²	semidirect
29. C₂×#120×C₆₇	C₂²	semidirect
30. C₂×#120×C₆₇	C₂²	semidirect
31. C₂×#120×C₆₇	C₂²	semidirect
32. C₂×#120×C₆₇	C₂²	semidirect
33. C₂×#120×C₆₇	C₂²	semidirect
34. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
35. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
36. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
37. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
38. #394×C₆₇	C₂²	semidirect
39. #392×C₆₇	C₂²	semidirect
40. #386×C₆₇	C₂²	semidirect
41. #386×C₆₇	C₂²	semidirect
42. #386×C₆₇	C₂²	semidirect
43. #385×C₆₇	C₂²	semidirect
44. #381×C₆₇	C₂²	semidirect
45. #379×C₆₇	C₂²	semidirect
46. #379×C₆₇	C₂²	semidirect
47. #379×C₆₇	C₂²	semidirect
48. #379×C₆₇	C₂²	semidirect
49. #379×C₆₇	C₂²	semidirect
55. C₂⁵×C₆₇	D₄	semidirect
63. C₂⁵×C₆₇	C₂³	semidirect
78. C₂²×D₄×C₆₇	D₄	semidirect
84. C₂²×D₄×C₆₇	C₂³	semidirect
85. C₂²×D₄×C₆₇	C₂³	semidirect
86. C₂²×D₄×C₆₇	C₂³	semidirect
91. C₂³×C₄×C₆₇	C₂³	semidirect
92. C₂³×C₄×C₆₇	C₂³	semidirect
93. C₂³×C₄×C₆₇	C₂³	semidirect
103. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
112. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
113. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
114. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
115. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
116. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
117. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
118. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
119. #95×C₆₇	C₂³	semidirect
153. C₂⁴×C₆₇	C₂×D₄	semidirect
185. C₂×D₄×C₆₇	C₂×D₄	semidirect
197. C₂²×C₄×C₆₇	C₂×D₄	semidirect
257. C₂³×C₆₇	#120	semidirect
322. C₂²×C₆₇	#534	semidirect
330. #34980	C₆₇	direct (N × H)
341. C₂⁴×D₄	C₂×C₆₇	semidirect
342. C₂×#534	C₂×C₆₇	semidirect
343. C₂²×#120	C₂×C₆₇	semidirect
344. #2849	C₂×C₆₇	semidirect
345. #2846	C₂×C₆₇	semidirect
346. #2613	C₂×C₆₇	semidirect
347. #2410	C₂×C₆₇	semidirect
348. #2405	C₂×C₆₇	semidirect
349. #2403	C₂×C₆₇	semidirect
350. #2308	C₂×C₆₇	semidirect
351. C₂×#379	C₂×C₆₇	semidirect
352. C₆₇	#34980	direct (N × H)
354. C₂⁶	C₂²×C₆₇	semidirect
359. C₂³×D₄	C₂²×C₆₇	semidirect
360. C₂³×D₄	C₂²×C₆₇	semidirect
361. C₂³×D₄	C₂²×C₆₇	semidirect
362. C₂³×D₄	C₂²×C₆₇	semidirect
363. C₂⁴×C₄	C₂²×C₆₇	semidirect
365. C₂×#123	C₂²×C₆₇	semidirect
366. C₂×#123	C₂²×C₆₇	semidirect
367. C₂×#121	C₂²×C₆₇	semidirect
370. C₂×#120	C₂²×C₆₇	semidirect
371. C₂×#120	C₂²×C₆₇	semidirect
372. C₂×#120	C₂²×C₆₇	semidirect
373. C₂×#120	C₂²×C₆₇	semidirect
374. C₂×#120	C₂²×C₆₇	semidirect
375. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
376. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
377. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
378. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
379. #394	C₂²×C₆₇	semidirect
380. #392	C₂²×C₆₇	semidirect
381. #386	C₂²×C₆₇	semidirect
382. #386	C₂²×C₆₇	semidirect
383. #386	C₂²×C₆₇	semidirect
384. #385	C₂²×C₆₇	semidirect
385. #381	C₂²×C₆₇	semidirect
386. #379	C₂²×C₆₇	semidirect
387. #379	C₂²×C₆₇	semidirect
388. #379	C₂²×C₆₇	semidirect
389. #379	C₂²×C₆₇	semidirect
390. #379	C₂²×C₆₇	semidirect
396. C₂⁵	D₄×C₆₇	semidirect
404. C₂⁵	C₂³×C₆₇	semidirect
419. C₂²×D₄	D₄×C₆₇	semidirect
425. C₂²×D₄	C₂³×C₆₇	semidirect
426. C₂²×D₄	C₂³×C₆₇	semidirect
427. C₂²×D₄	C₂³×C₆₇	semidirect
432. C₂³×C₄	C₂³×C₆₇	semidirect
433. C₂³×C₄	C₂³×C₆₇	semidirect
434. C₂³×C₄	C₂³×C₆₇	semidirect
444. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
453. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
454. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
455. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
456. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
457. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
458. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
459. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
460. #95	C₂³×C₆₇	semidirect
494. C₂⁴	C₂×D₄×C₆₇	semidirect
526. C₂×D₄	C₂×D₄×C₆₇	semidirect
538. C₂²×C₄	C₂×D₄×C₆₇	semidirect
598. C₂³	#120×C₆₇	semidirect
663. C₂²	#534×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₆₇	2
C₂×#534×C₆₇	2
C₂²×#120×C₆₇	2
C₆₇×#2849	2
C₆₇×#2846	2
C₆₇×#2613	2
C₆₇×#2410	2
C₆₇×#2405	2
C₆₇×#2403	2
C₆₇×#2308	2
C₂×#379×C₆₇	2
#34980	67

Subgroups — C67×#34980 #30714231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34980 #30714231