Subgroups — C₂×C₆₇×#3490 #30742017

Order 17152.

9502 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3490	C₂	1	32	yes	maximal, direct product factor
2	C₂×#551×C₆₇	C₂	1	8	yes	maximal, complemented
3	C₂×#546×C₆₇	C₂	1	8	yes	maximal, complemented
4	C₂×#543×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#538×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂×#534×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#525×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂²×#120×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#518×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂³×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁶×C₆₇	C₂²	1	1	yes	characteristic
12	C₂²×#41×C₆₇	C₂²	1	4	yes	complemented
13	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
14	C₂³×D₄×C₆₇	C₂²	1	4	yes	complemented
15	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	complemented
16	#551×C₆₇	C₂²	1	128	yes	complemented
17	#546×C₆₇	C₂²	1	128	yes	complemented
18	#543×C₆₇	C₂²	1	16	yes	complemented
19	#538×C₆₇	C₂²	1	64	yes	complemented
20	#534×C₆₇	C₂²	1	16	yes	complemented
21	C₂×#126×C₆₇	C₂²	1	8	yes	complemented
22	C₂×#124×C₆₇	C₂²	1	8	yes	complemented
23	#525×C₆₇	C₂²	1	64	yes	complemented
24	C₂×#123×C₆₇	C₂²	1	8	yes	complemented
25	C₂×#123×C₆₇	C₂²	1	8	yes	complemented
26	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
28	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	8	yes	complemented
30	C₂×#121×C₆₇	C₂²	1	8	yes	complemented
31	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
32	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
33	C₂×#120×C₆₇	C₂²	1	8	yes	—
34	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
35	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
36	C₂×#120×C₆₇	C₂²	1	32	yes	complemented
37	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
38	#518×C₆₇	C₂²	1	32	yes	complemented
39	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
40	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
41	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
42	C₂×#117×C₆₇	C₂²	1	4	yes	complemented
43	C₂×#117×C₆₇	C₂²	1	4	yes	complemented
44	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
47	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
48	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	complemented
49	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
50	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	16	yes	complemented
51	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
52	C₂⁵×C₆₇	—	2	8	no	—
53	C₂⁵×C₆₇	—	4	8	no	—
54	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
55	C₂⁵×C₆₇	C₂³	1	4	yes	—
56	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
57	C₂⁵×C₆₇	C₂³	1	8	yes	—
58	C₂⁵×C₆₇	C₂³	1	2	yes	—
59	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
60	C₂×#41×C₆₇	—	4	16	no	—
61	C₂×#41×C₆₇	C₂³	1	32	yes	complemented
62	C₂²×Q₈×C₆₇	C₂³	1	4	yes	complemented
63	C₂²×D₄×C₆₇	—	2	16	no	—
64	C₂²×D₄×C₆₇	—	4	16	no	—
65	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
66	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
67	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
68	C₂²×D₄×C₆₇	C₂³	1	16	yes	—
69	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
70	C₂²×D₄×C₆₇	C₂³	1	32	yes	complemented
71	C₂²×D₄×C₆₇	C₂³	1	4	yes	complemented
72	C₂³×C₄×C₆₇	—	4	8	no	—
73	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
74	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
75	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
76	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
77	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
78	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
79	C₂³×C₄×C₆₇	C₂³	1	16	yes	complemented
80	C₂³×C₄×C₆₇	C₂³	1	8	yes	complemented
81	#126×C₆₇	C₂³	1	64	yes	complemented
82	#124×C₆₇	C₂³	1	64	yes	complemented
83	#123×C₆₇	C₂³	1	64	yes	complemented
84	#123×C₆₇	C₂³	1	64	yes	complemented
85	#123×C₆₇	C₂³	1	32	yes	complemented
86	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
87	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
88	C₂²⋊Q₈×C₆₇	C₂³	1	64	yes	complemented
89	#121×C₆₇	C₂³	1	64	yes	complemented
90	#121×C₆₇	C₂³	1	32	yes	complemented
91	#121×C₆₇	C₂³	1	32	yes	complemented
92	#120×C₆₇	C₂³	1	64	yes	—
93	#120×C₆₇	C₂³	1	32	yes	complemented
94	#120×C₆₇	C₂³	1	32	yes	complemented
95	#120×C₆₇	C₂³	1	32	yes	complemented
96	C₄×D₄×C₆₇	C₂³	1	64	yes	complemented
97	C₄×D₄×C₆₇	C₂³	1	64	yes	complemented
98	C₄×D₄×C₆₇	C₂³	1	64	yes	complemented
99	#117×C₆₇	C₂³	1	32	yes	complemented
100	#117×C₆₇	C₂³	1	32	yes	complemented
101	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
102	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	complemented
103	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	complemented
104	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
105	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
107	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	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	16	yes	—
112	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
113	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
114	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
115	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
116	C₂×C₂²⋊C₄×C₆₇	C₂³	1	64	yes	complemented
117	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
118	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
119	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	complemented
120	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	complemented
121	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
122	C₂⁴×C₆₇	—	2	4	no	—
123	C₂⁴×C₆₇	—	2	8	no	—
124	C₂⁴×C₆₇	—	2	16	no	—
125	C₂⁴×C₆₇	—	2	4	no	—
126	C₂⁴×C₆₇	—	2	32	no	—
127	C₂⁴×C₆₇	—	2	16	no	—
128	C₂⁴×C₆₇	—	2	8	no	—
129	C₂⁴×C₆₇	—	4	4	no	—
130	C₂⁴×C₆₇	—	4	8	no	—
131	C₂⁴×C₆₇	—	4	32	no	—
132	C₂⁴×C₆₇	—	4	4	no	—
133	C₂⁴×C₆₇	—	4	8	no	—
134	C₂⁴×C₆₇	—	4	64	no	—
135	C₂⁴×C₆₇	#41	1	8	yes	complemented
136	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
137	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
138	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
139	C₂⁴×C₆₇	C₂⁴	1	16	yes	—
140	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
141	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
142	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
143	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
144	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
145	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
146	#41×C₆₇	—	4	64	no	—
147	C₂×Q₈×C₆₇	—	4	8	no	—
148	C₂×Q₈×C₆₇	C₂⁴	1	16	yes	complemented
149	C₂×D₄×C₆₇	—	2	16	no	—
150	C₂×D₄×C₆₇	—	2	16	no	—
151	C₂×D₄×C₆₇	—	2	64	no	—
152	C₂×D₄×C₆₇	—	2	32	no	—
153	C₂×D₄×C₆₇	—	4	16	no	—
154	C₂×D₄×C₆₇	—	4	8	no	—
155	C₂×D₄×C₆₇	—	4	64	no	—
156	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
157	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
158	C₂×D₄×C₆₇	C₂⁴	1	32	yes	—
159	C₂×D₄×C₆₇	C₂⁴	1	32	yes	—
160	C₂×D₄×C₆₇	C₂⁴	1	16	yes	complemented
161	C₂²×C₄×C₆₇	—	2	8	no	—
162	C₂²×C₄×C₆₇	—	2	16	no	—
163	C₂²×C₄×C₆₇	—	4	4	no	—
164	C₂²×C₄×C₆₇	—	4	8	no	—
165	C₂²×C₄×C₆₇	—	4	4	no	—
166	C₂²×C₄×C₆₇	—	4	32	no	—
167	C₂²×C₄×C₆₇	—	4	8	no	—
168	C₂²×C₄×C₆₇	—	4	16	no	—
169	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
170	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
171	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
174	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
176	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
177	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
178	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
179	C₂²×C₄×C₆₇	C₂⁴	1	32	yes	complemented
180	C₄⋊C₄×C₆₇	C₂⁴	1	32	yes	complemented
181	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	complemented
182	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	complemented
183	C₄⋊C₄×C₆₇	C₂⁴	1	32	yes	complemented
184	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
185	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
186	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
187	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
188	C₂²⋊C₄×C₆₇	C₂⁴	1	32	yes	—
189	C₂²⋊C₄×C₆₇	C₂⁴	1	32	yes	—
190	C₂²⋊C₄×C₆₇	C₂⁴	1	32	yes	—
191	C₂²⋊C₄×C₆₇	C₂⁴	1	32	yes	complemented
192	C₂²⋊C₄×C₆₇	C₂⁴	1	32	yes	complemented
193	C₄²×C₆₇	C₂⁴	1	32	yes	complemented
194	C₂³×C₆₇	—	2	32	no	—
195	C₂³×C₆₇	—	2	8	no	—
196	C₂³×C₆₇	—	2	4	no	—
197	C₂³×C₆₇	—	2	16	no	—
198	C₂³×C₆₇	—	2	4	no	—
199	C₂³×C₆₇	—	2	4	no	—
200	C₂³×C₆₇	—	2	8	no	—
201	C₂³×C₆₇	—	2	8	no	—
202	C₂³×C₆₇	—	2	32	no	—
203	C₂³×C₆₇	—	2	8	no	—
204	C₂³×C₆₇	—	2	4	no	—
205	C₂³×C₆₇	—	2	16	no	—
206	C₂³×C₆₇	—	2	32	no	—
207	C₂³×C₆₇	—	2	8	no	—
208	C₂³×C₆₇	—	2	16	no	—
209	C₂³×C₆₇	—	4	16	no	—
210	C₂³×C₆₇	—	4	8	no	—
211	C₂³×C₆₇	—	4	16	no	—
212	C₂³×C₆₇	—	4	8	no	—
213	C₂³×C₆₇	—	4	16	no	—
214	C₂³×C₆₇	—	4	64	no	—
215	C₂³×C₆₇	—	4	128	no	—
216	C₂³×C₆₇	—	4	16	no	—
217	C₂³×C₆₇	—	8	16	no	—
218	C₂³×C₆₇	C₂×#41	1	8	yes	—
219	C₂³×C₆₇	C₂×#41	1	4	yes	—
220	C₂³×C₆₇	C₂×#41	1	16	yes	complemented
221	C₂³×C₆₇	H(5,𝔽₂)	1	8	yes	—
222	C₂³×C₆₇	C₂⁵	1	4	yes	—
223	C₂³×C₆₇	C₂⁵	1	8	yes	—
224	C₂³×C₆₇	C₂⁵	1	4	yes	—
225	C₂³×C₆₇	C₂⁵	1	2	yes	—
226	C₂³×C₆₇	C₂⁵	1	4	yes	—
227	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
228	Q₈×C₆₇	—	4	16	no	—
229	D₄×C₆₇	—	2	32	no	—
230	D₄×C₆₇	—	2	32	no	—
231	D₄×C₆₇	—	2	64	no	—
232	D₄×C₆₇	—	4	32	no	—
233	D₄×C₆₇	—	4	16	no	—
234	C₂×C₄×C₆₇	—	2	16	no	—
235	C₂×C₄×C₆₇	—	2	8	no	—
236	C₂×C₄×C₆₇	—	2	8	no	—
237	C₂×C₄×C₆₇	—	2	8	no	—
238	C₂×C₄×C₆₇	—	2	32	no	—
239	C₂×C₄×C₆₇	—	2	16	no	—
240	C₂×C₄×C₆₇	—	4	8	no	—
241	C₂×C₄×C₆₇	—	4	16	no	—
242	C₂×C₄×C₆₇	—	4	8	no	—
243	C₂×C₄×C₆₇	—	4	16	no	—
244	C₂×C₄×C₆₇	—	4	32	no	—
245	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
246	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
247	C₂×C₄×C₆₇	C₂⁵	1	16	yes	—
248	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
249	C₂²×C₆₇	—	2	32	no	—
250	C₂²×C₆₇	—	2	4	no	—
251	C₂²×C₆₇	—	2	4	no	—
252	C₂²×C₆₇	—	2	4	no	—
253	C₂²×C₆₇	—	2	8	no	—
254	C₂²×C₆₇	—	2	8	no	—
255	C₂²×C₆₇	—	2	16	no	—
256	C₂²×C₆₇	—	2	16	no	—
257	C₂²×C₆₇	—	2	8	no	—
258	C₂²×C₆₇	—	2	4	no	—
259	C₂²×C₆₇	—	2	16	no	—
260	C₂²×C₆₇	—	2	8	no	—
261	C₂²×C₆₇	—	4	16	no	—
262	C₂²×C₆₇	—	4	64	no	—
263	C₂²×C₆₇	—	4	16	no	—
264	C₂²×C₆₇	—	4	8	no	—
265	C₂²×C₆₇	—	4	16	no	—
266	C₂²×C₆₇	—	8	16	no	—
267	C₂²×C₆₇	C₂²×#41	1	8	yes	—
268	C₂²×C₆₇	C₂²×#41	1	4	yes	—
269	C₂²×C₆₇	C₂²×#41	1	2	yes	—
270	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	8	yes	—
271	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
272	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
273	C₄×C₆₇	—	2	8	no	—
274	C₄×C₆₇	—	2	8	no	—
275	C₄×C₆₇	—	2	8	no	—
276	C₄×C₆₇	—	2	16	no	—
277	C₂×#3490	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂×C₆₇	—	2	4	no	—
279	C₂×C₆₇	—	2	8	no	—
280	C₂×C₆₇	—	2	8	no	—
281	C₂×C₆₇	—	4	4	no	—
282	C₂×C₆₇	—	4	8	no	—
283	C₂×C₆₇	#3490	1	4	yes	direct product factor
284	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
285	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	2	yes	—
286	#3490	C₂×C₆₇	1	32	yes	direct product factor
287	C₂×#551	C₂×C₆₇	1	8	yes	complemented
288	C₂×#546	C₂×C₆₇	1	8	yes	complemented
289	C₂×#543	C₂×C₆₇	1	1	yes	characteristic, complemented
290	C₂×#538	C₂×C₆₇	1	4	yes	complemented
291	C₂×#534	C₂×C₆₇	1	1	yes	characteristic, complemented
292	C₂×#525	C₂×C₆₇	1	4	yes	complemented
293	C₂²×#120	C₂×C₆₇	1	2	yes	complemented
294	C₂×#518	C₂×C₆₇	1	2	yes	complemented
295	C₂³×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
296	C₆₇	C₂×#3490	1	1	yes	characteristic, direct product factor, Sylow
297	C₂⁶	C₂²×C₆₇	1	1	yes	characteristic
298	C₂²×#41	C₂²×C₆₇	1	4	yes	complemented
299	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
300	C₂³×D₄	C₂²×C₆₇	1	4	yes	complemented
301	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	complemented
302	#551	C₂²×C₆₇	1	128	yes	complemented
303	#546	C₂²×C₆₇	1	128	yes	complemented
304	#543	C₂²×C₆₇	1	16	yes	complemented
305	#538	C₂²×C₆₇	1	64	yes	complemented
306	#534	C₂²×C₆₇	1	16	yes	complemented
307	C₂×#126	C₂²×C₆₇	1	8	yes	complemented
308	C₂×#124	C₂²×C₆₇	1	8	yes	complemented
309	#525	C₂²×C₆₇	1	64	yes	complemented
310	C₂×#123	C₂²×C₆₇	1	8	yes	complemented
311	C₂×#123	C₂²×C₆₇	1	8	yes	complemented
312	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
313	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
314	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
315	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	8	yes	complemented
316	C₂×#121	C₂²×C₆₇	1	8	yes	complemented
317	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
318	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
319	C₂×#120	C₂²×C₆₇	1	8	yes	—
320	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
321	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
322	C₂×#120	C₂²×C₆₇	1	32	yes	complemented
323	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
324	#518	C₂²×C₆₇	1	32	yes	complemented
325	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
326	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
327	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
328	C₂×#117	C₂²×C₆₇	1	4	yes	complemented
329	C₂×#117	C₂²×C₆₇	1	4	yes	complemented
330	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
331	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
332	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
333	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
334	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	complemented
335	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
336	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	16	yes	complemented
337	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
338	C₂⁵	—	2	8	no	—
339	C₂⁵	—	4	8	no	—
340	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
341	C₂⁵	C₂³×C₆₇	1	4	yes	—
342	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
343	C₂⁵	C₂³×C₆₇	1	8	yes	—
344	C₂⁵	C₂³×C₆₇	1	2	yes	—
345	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
346	C₂×#41	—	4	16	no	—
347	C₂×#41	C₂³×C₆₇	1	32	yes	complemented
348	C₂²×Q₈	C₂³×C₆₇	1	4	yes	complemented
349	C₂²×D₄	—	2	16	no	—
350	C₂²×D₄	—	4	16	no	—
351	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
352	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
353	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
354	C₂²×D₄	C₂³×C₆₇	1	16	yes	—
355	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
356	C₂²×D₄	C₂³×C₆₇	1	32	yes	complemented
357	C₂²×D₄	C₂³×C₆₇	1	4	yes	complemented
358	C₂³×C₄	—	4	8	no	—
359	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
360	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
361	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
362	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
363	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
364	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
365	C₂³×C₄	C₂³×C₆₇	1	16	yes	complemented
366	C₂³×C₄	C₂³×C₆₇	1	8	yes	complemented
367	#126	C₂³×C₆₇	1	64	yes	complemented
368	#124	C₂³×C₆₇	1	64	yes	complemented
369	#123	C₂³×C₆₇	1	64	yes	complemented
370	#123	C₂³×C₆₇	1	64	yes	complemented
371	#123	C₂³×C₆₇	1	32	yes	complemented
372	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
373	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
374	C₂²⋊Q₈	C₂³×C₆₇	1	64	yes	complemented
375	#121	C₂³×C₆₇	1	64	yes	complemented
376	#121	C₂³×C₆₇	1	32	yes	complemented
377	#121	C₂³×C₆₇	1	32	yes	complemented
378	#120	C₂³×C₆₇	1	64	yes	—
379	#120	C₂³×C₆₇	1	32	yes	complemented
380	#120	C₂³×C₆₇	1	32	yes	complemented
381	#120	C₂³×C₆₇	1	32	yes	complemented
382	C₄×D₄	C₂³×C₆₇	1	64	yes	complemented
383	C₄×D₄	C₂³×C₆₇	1	64	yes	complemented
384	C₄×D₄	C₂³×C₆₇	1	64	yes	complemented
385	#117	C₂³×C₆₇	1	32	yes	complemented
386	#117	C₂³×C₆₇	1	32	yes	complemented
387	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	complemented
388	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	complemented
389	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	complemented
390	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	complemented
391	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	complemented
402	C₂×C₂²⋊C₄	C₂³×C₆₇	1	64	yes	complemented
403	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	complemented
404	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	complemented
405	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	complemented
406	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	complemented
407	C₂×C₄²	C₂³×C₆₇	1	8	yes	complemented
408	C₂⁴	—	2	4	no	—
409	C₂⁴	—	2	8	no	—
410	C₂⁴	—	2	16	no	—
411	C₂⁴	—	2	4	no	—
412	C₂⁴	—	2	32	no	—
413	C₂⁴	—	2	16	no	—
414	C₂⁴	—	2	8	no	—
415	C₂⁴	—	4	4	no	—
416	C₂⁴	—	4	8	no	—
417	C₂⁴	—	4	32	no	—
418	C₂⁴	—	4	4	no	—
419	C₂⁴	—	4	8	no	—
420	C₂⁴	—	4	64	no	—
421	C₂⁴	#41×C₆₇	1	8	yes	complemented
422	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
423	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
424	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
425	C₂⁴	C₂⁴×C₆₇	1	16	yes	—
426	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
427	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
428	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
429	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
430	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
431	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
432	#41	—	4	64	no	—
433	C₂×Q₈	—	4	8	no	—
434	C₂×Q₈	C₂⁴×C₆₇	1	16	yes	complemented
435	C₂×D₄	—	2	16	no	—
436	C₂×D₄	—	2	16	no	—
437	C₂×D₄	—	2	64	no	—
438	C₂×D₄	—	2	32	no	—
439	C₂×D₄	—	4	16	no	—
440	C₂×D₄	—	4	8	no	—
441	C₂×D₄	—	4	64	no	—
442	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
443	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
444	C₂×D₄	C₂⁴×C₆₇	1	32	yes	—
445	C₂×D₄	C₂⁴×C₆₇	1	32	yes	—
446	C₂×D₄	C₂⁴×C₆₇	1	16	yes	complemented
447	C₂²×C₄	—	2	8	no	—
448	C₂²×C₄	—	2	16	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	—	4	8	no	—
451	C₂²×C₄	—	4	4	no	—
452	C₂²×C₄	—	4	32	no	—
453	C₂²×C₄	—	4	8	no	—
454	C₂²×C₄	—	4	16	no	—
455	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
457	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
458	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
459	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
460	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
461	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
462	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
463	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
464	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
465	C₂²×C₄	C₂⁴×C₆₇	1	32	yes	complemented
466	C₄⋊C₄	C₂⁴×C₆₇	1	32	yes	complemented
467	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	complemented
468	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	complemented
469	C₄⋊C₄	C₂⁴×C₆₇	1	32	yes	complemented
470	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
471	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
472	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
473	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
474	C₂²⋊C₄	C₂⁴×C₆₇	1	32	yes	—
475	C₂²⋊C₄	C₂⁴×C₆₇	1	32	yes	—
476	C₂²⋊C₄	C₂⁴×C₆₇	1	32	yes	—
477	C₂²⋊C₄	C₂⁴×C₆₇	1	32	yes	complemented
478	C₂²⋊C₄	C₂⁴×C₆₇	1	32	yes	complemented
479	C₄²	C₂⁴×C₆₇	1	32	yes	complemented
480	C₂³	—	2	32	no	—
481	C₂³	—	2	8	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	16	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	2	8	no	—
487	C₂³	—	2	8	no	—
488	C₂³	—	2	32	no	—
489	C₂³	—	2	8	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	16	no	—
492	C₂³	—	2	32	no	—
493	C₂³	—	2	8	no	—
494	C₂³	—	2	16	no	—
495	C₂³	—	4	16	no	—
496	C₂³	—	4	8	no	—
497	C₂³	—	4	16	no	—
498	C₂³	—	4	8	no	—
499	C₂³	—	4	16	no	—
500	C₂³	—	4	64	no	—
501	C₂³	—	4	128	no	—
502	C₂³	—	4	16	no	—
503	C₂³	—	8	16	no	—
504	C₂³	C₂×#41×C₆₇	1	8	yes	—
505	C₂³	C₂×#41×C₆₇	1	4	yes	—
506	C₂³	C₂×#41×C₆₇	1	16	yes	complemented
507	C₂³	H(5,𝔽₂)×C₆₇	1	8	yes	—
508	C₂³	C₂⁵×C₆₇	1	4	yes	—
509	C₂³	C₂⁵×C₆₇	1	8	yes	—
510	C₂³	C₂⁵×C₆₇	1	4	yes	—
511	C₂³	C₂⁵×C₆₇	1	2	yes	—
512	C₂³	C₂⁵×C₆₇	1	4	yes	—
513	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
514	Q₈	—	4	16	no	—
515	D₄	—	2	32	no	—
516	D₄	—	2	32	no	—
517	D₄	—	2	64	no	—
518	D₄	—	4	32	no	—
519	D₄	—	4	16	no	—
520	C₂×C₄	—	2	16	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	2	8	no	—
524	C₂×C₄	—	2	32	no	—
525	C₂×C₄	—	2	16	no	—
526	C₂×C₄	—	4	8	no	—
527	C₂×C₄	—	4	16	no	—
528	C₂×C₄	—	4	8	no	—
529	C₂×C₄	—	4	16	no	—
530	C₂×C₄	—	4	32	no	—
531	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
532	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
533	C₂×C₄	C₂⁵×C₆₇	1	16	yes	—
534	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
535	C₂²	—	2	32	no	—
536	C₂²	—	2	4	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	2	4	no	—
539	C₂²	—	2	8	no	—
540	C₂²	—	2	8	no	—
541	C₂²	—	2	16	no	—
542	C₂²	—	2	16	no	—
543	C₂²	—	2	8	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	16	no	—
546	C₂²	—	2	8	no	—
547	C₂²	—	4	16	no	—
548	C₂²	—	4	64	no	—
549	C₂²	—	4	16	no	—
550	C₂²	—	4	8	no	—
551	C₂²	—	4	16	no	—
552	C₂²	—	8	16	no	—
553	C₂²	C₂²×#41×C₆₇	1	8	yes	—
554	C₂²	C₂²×#41×C₆₇	1	4	yes	—
555	C₂²	C₂²×#41×C₆₇	1	2	yes	—
556	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	8	yes	—
557	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
558	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
559	C₄	—	2	8	no	—
560	C₄	—	2	8	no	—
561	C₄	—	2	8	no	—
562	C₄	—	2	16	no	—
563	C₂	—	2	4	no	—
564	C₂	—	2	8	no	—
565	C₂	—	2	8	no	—
566	C₂	—	4	4	no	—
567	C₂	—	4	8	no	—
568	C₂	C₆₇×#3490	1	4	yes	direct product factor
569	C₂	C₂³×#41×C₆₇	1	1	yes	characteristic
570	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
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
1. C₆₇×#3490	C₂	direct (N × H)
2. C₂×#551×C₆₇	C₂	semidirect
3. C₂×#546×C₆₇	C₂	semidirect
4. C₂×#543×C₆₇	C₂	semidirect
5. C₂×#538×C₆₇	C₂	semidirect
6. C₂×#534×C₆₇	C₂	semidirect
7. C₂×#525×C₆₇	C₂	semidirect
8. C₂²×#120×C₆₇	C₂	semidirect
9. C₂×#518×C₆₇	C₂	semidirect
10. C₂³×C₂²⋊C₄×C₆₇	C₂	semidirect
12. C₂²×#41×C₆₇	C₂²	semidirect
14. C₂³×D₄×C₆₇	C₂²	semidirect
15. C₂⁴×C₄×C₆₇	C₂²	semidirect
16. #551×C₆₇	C₂²	semidirect
17. #546×C₆₇	C₂²	semidirect
18. #543×C₆₇	C₂²	semidirect
19. #538×C₆₇	C₂²	semidirect
20. #534×C₆₇	C₂²	semidirect
21. C₂×#126×C₆₇	C₂²	semidirect
22. C₂×#124×C₆₇	C₂²	semidirect
23. #525×C₆₇	C₂²	semidirect
24. C₂×#123×C₆₇	C₂²	semidirect
25. C₂×#123×C₆₇	C₂²	semidirect
26. C₂×#123×C₆₇	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
30. C₂×#121×C₆₇	C₂²	semidirect
31. C₂×#121×C₆₇	C₂²	semidirect
32. C₂×#121×C₆₇	C₂²	semidirect
34. C₂×#120×C₆₇	C₂²	semidirect
35. C₂×#120×C₆₇	C₂²	semidirect
36. C₂×#120×C₆₇	C₂²	semidirect
37. C₂×#120×C₆₇	C₂²	semidirect
38. #518×C₆₇	C₂²	semidirect
39. C₂×C₄×D₄×C₆₇	C₂²	semidirect
40. C₂×C₄×D₄×C₆₇	C₂²	semidirect
41. C₂×C₄×D₄×C₆₇	C₂²	semidirect
42. C₂×#117×C₆₇	C₂²	semidirect
43. C₂×#117×C₆₇	C₂²	semidirect
47. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
48. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
49. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
50. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
51. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
61. C₂×#41×C₆₇	C₂³	semidirect
62. C₂²×Q₈×C₆₇	C₂³	semidirect
70. C₂²×D₄×C₆₇	C₂³	semidirect
71. C₂²×D₄×C₆₇	C₂³	semidirect
79. C₂³×C₄×C₆₇	C₂³	semidirect
80. C₂³×C₄×C₆₇	C₂³	semidirect
81. #126×C₆₇	C₂³	semidirect
82. #124×C₆₇	C₂³	semidirect
83. #123×C₆₇	C₂³	semidirect
84. #123×C₆₇	C₂³	semidirect
85. #123×C₆₇	C₂³	semidirect
86. C₂²⋊Q₈×C₆₇	C₂³	semidirect
87. C₂²⋊Q₈×C₆₇	C₂³	semidirect
88. C₂²⋊Q₈×C₆₇	C₂³	semidirect
89. #121×C₆₇	C₂³	semidirect
90. #121×C₆₇	C₂³	semidirect
91. #121×C₆₇	C₂³	semidirect
93. #120×C₆₇	C₂³	semidirect
94. #120×C₆₇	C₂³	semidirect
95. #120×C₆₇	C₂³	semidirect
96. C₄×D₄×C₆₇	C₂³	semidirect
97. C₄×D₄×C₆₇	C₂³	semidirect
98. C₄×D₄×C₆₇	C₂³	semidirect
99. #117×C₆₇	C₂³	semidirect
100. #117×C₆₇	C₂³	semidirect
101. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
102. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
103. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
104. C₂×C₄⋊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. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
120. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
121. C₂×C₄²×C₆₇	C₂³	semidirect
135. C₂⁴×C₆₇	#41	semidirect
148. C₂×Q₈×C₆₇	C₂⁴	semidirect
160. C₂×D₄×C₆₇	C₂⁴	semidirect
179. C₂²×C₄×C₆₇	C₂⁴	semidirect
180. C₄⋊C₄×C₆₇	C₂⁴	semidirect
181. C₄⋊C₄×C₆₇	C₂⁴	semidirect
182. C₄⋊C₄×C₆₇	C₂⁴	semidirect
183. C₄⋊C₄×C₆₇	C₂⁴	semidirect
191. C₂²⋊C₄×C₆₇	C₂⁴	semidirect
192. C₂²⋊C₄×C₆₇	C₂⁴	semidirect
193. C₄²×C₆₇	C₂⁴	semidirect
220. C₂³×C₆₇	C₂×#41	semidirect
277. C₂×#3490	C₆₇	direct (N × H)
283. C₂×C₆₇	#3490	direct (N × H)
286. #3490	C₂×C₆₇	direct (N × H)
287. C₂×#551	C₂×C₆₇	semidirect
288. C₂×#546	C₂×C₆₇	semidirect
289. C₂×#543	C₂×C₆₇	semidirect
290. C₂×#538	C₂×C₆₇	semidirect
291. C₂×#534	C₂×C₆₇	semidirect
292. C₂×#525	C₂×C₆₇	semidirect
293. C₂²×#120	C₂×C₆₇	semidirect
294. C₂×#518	C₂×C₆₇	semidirect
295. C₂³×C₂²⋊C₄	C₂×C₆₇	semidirect
296. C₆₇	C₂×#3490	direct (N × H)
298. C₂²×#41	C₂²×C₆₇	semidirect
300. C₂³×D₄	C₂²×C₆₇	semidirect
301. C₂⁴×C₄	C₂²×C₆₇	semidirect
302. #551	C₂²×C₆₇	semidirect
303. #546	C₂²×C₆₇	semidirect
304. #543	C₂²×C₆₇	semidirect
305. #538	C₂²×C₆₇	semidirect
306. #534	C₂²×C₆₇	semidirect
307. C₂×#126	C₂²×C₆₇	semidirect
308. C₂×#124	C₂²×C₆₇	semidirect
309. #525	C₂²×C₆₇	semidirect
310. C₂×#123	C₂²×C₆₇	semidirect
311. C₂×#123	C₂²×C₆₇	semidirect
312. C₂×#123	C₂²×C₆₇	semidirect
313. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
314. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
315. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
316. C₂×#121	C₂²×C₆₇	semidirect
317. C₂×#121	C₂²×C₆₇	semidirect
318. C₂×#121	C₂²×C₆₇	semidirect
320. C₂×#120	C₂²×C₆₇	semidirect
321. C₂×#120	C₂²×C₆₇	semidirect
322. C₂×#120	C₂²×C₆₇	semidirect
323. C₂×#120	C₂²×C₆₇	semidirect
324. #518	C₂²×C₆₇	semidirect
325. C₂×C₄×D₄	C₂²×C₆₇	semidirect
326. C₂×C₄×D₄	C₂²×C₆₇	semidirect
327. C₂×C₄×D₄	C₂²×C₆₇	semidirect
328. C₂×#117	C₂²×C₆₇	semidirect
329. C₂×#117	C₂²×C₆₇	semidirect
333. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
334. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
335. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
336. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
337. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
347. C₂×#41	C₂³×C₆₇	semidirect
348. C₂²×Q₈	C₂³×C₆₇	semidirect
356. C₂²×D₄	C₂³×C₆₇	semidirect
357. C₂²×D₄	C₂³×C₆₇	semidirect
365. C₂³×C₄	C₂³×C₆₇	semidirect
366. C₂³×C₄	C₂³×C₆₇	semidirect
367. #126	C₂³×C₆₇	semidirect
368. #124	C₂³×C₆₇	semidirect
369. #123	C₂³×C₆₇	semidirect
370. #123	C₂³×C₆₇	semidirect
371. #123	C₂³×C₆₇	semidirect
372. C₂²⋊Q₈	C₂³×C₆₇	semidirect
373. C₂²⋊Q₈	C₂³×C₆₇	semidirect
374. C₂²⋊Q₈	C₂³×C₆₇	semidirect
375. #121	C₂³×C₆₇	semidirect
376. #121	C₂³×C₆₇	semidirect
377. #121	C₂³×C₆₇	semidirect
379. #120	C₂³×C₆₇	semidirect
380. #120	C₂³×C₆₇	semidirect
381. #120	C₂³×C₆₇	semidirect
382. C₄×D₄	C₂³×C₆₇	semidirect
383. C₄×D₄	C₂³×C₆₇	semidirect
384. C₄×D₄	C₂³×C₆₇	semidirect
385. #117	C₂³×C₆₇	semidirect
386. #117	C₂³×C₆₇	semidirect
387. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
388. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
389. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
390. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
401. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
402. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
403. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
404. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
405. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
406. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
407. C₂×C₄²	C₂³×C₆₇	semidirect
421. C₂⁴	#41×C₆₇	semidirect
434. C₂×Q₈	C₂⁴×C₆₇	semidirect
446. C₂×D₄	C₂⁴×C₆₇	semidirect
465. C₂²×C₄	C₂⁴×C₆₇	semidirect
466. C₄⋊C₄	C₂⁴×C₆₇	semidirect
467. C₄⋊C₄	C₂⁴×C₆₇	semidirect
468. C₄⋊C₄	C₂⁴×C₆₇	semidirect
469. C₄⋊C₄	C₂⁴×C₆₇	semidirect
477. C₂²⋊C₄	C₂⁴×C₆₇	semidirect
478. C₂²⋊C₄	C₂⁴×C₆₇	semidirect
479. C₄²	C₂⁴×C₆₇	semidirect
506. C₂³	C₂×#41×C₆₇	semidirect
568. C₂	C₆₇×#3490	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3490	2
C₂×#551×C₆₇	2
C₂×#546×C₆₇	2
C₂×#543×C₆₇	2
C₂×#538×C₆₇	2
C₂×#534×C₆₇	2
C₂×#525×C₆₇	2
C₂²×#120×C₆₇	2
C₂×#518×C₆₇	2
C₂³×C₂²⋊C₄×C₆₇	2
C₂×#3490	67

Subgroups — C2×C67×#3490 #30742017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3490 #30742017