Subgroups — C₆₇×#61582 #30740833

Order 17152.

2570 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3325	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3324	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3274	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3272	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3194	C₂	1	4	yes	maximal, complemented
10	C₆₇×#3101	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3003	C₂	1	4	yes	maximal, complemented
13	C₆₇×#2975	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×D₄×C₆₇	—	2	1	no	—
15	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
16	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	8	yes	complemented
17	#559×C₆₇	—	2	2	no	—
18	#556×C₆₇	C₂²	1	2	yes	complemented
19	#555×C₆₇	C₂²	1	2	yes	complemented
20	#553×C₆₇	—	2	2	no	—
21	#550×C₆₇	C₂²	1	2	yes	complemented
22	#547×C₆₇	C₂²	1	2	yes	complemented
23	D₄²×C₆₇	—	2	2	no	—
24	D₄²×C₆₇	—	2	2	no	—
25	D₄²×C₆₇	C₂²	1	4	yes	—
26	D₄²×C₆₇	C₂²	1	4	yes	—
27	#538×C₆₇	—	2	2	no	—
28	#535×C₆₇	—	2	1	no	—
29	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
32	#525×C₆₇	C₂²	1	4	yes	complemented
33	C₂×#121×C₆₇	—	2	1	no	—
34	C₂×#121×C₆₇	C₂²	1	2	yes	—
35	C₂×#120×C₆₇	—	2	2	no	—
36	#520×C₆₇	—	2	1	no	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
39	#493×C₆₇	C₂²	1	2	yes	complemented
40	#492×C₆₇	C₂²	1	2	yes	complemented
41	#486×C₆₇	C₂²	1	2	yes	complemented
42	#486×C₆₇	C₂²	1	2	yes	complemented
43	#483×C₆₇	C₂²	1	2	yes	complemented
44	#482×C₆₇	C₂²	1	8	yes	complemented
45	#480×C₆₇	C₂²	1	2	yes	complemented
46	#476×C₆₇	C₂²	1	2	yes	complemented
47	#474×C₆₇	C₂²	1	2	yes	complemented
48	#469×C₆₇	C₂²	1	8	yes	complemented
49	#468×C₆₇	C₂²	1	8	yes	complemented
50	#461×C₆₇	C₂²	1	2	yes	complemented
51	#460×C₆₇	C₂²	1	4	yes	complemented
52	#459×C₆₇	C₂²	1	2	yes	complemented
53	#459×C₆₇	C₂²	1	4	yes	complemented
54	#450×C₆₇	C₂²	1	2	yes	—
55	#450×C₆₇	C₂²	1	8	yes	complemented
56	#450×C₆₇	C₂²	1	4	yes	complemented
57	#449×C₆₇	C₂²	1	8	yes	complemented
58	#447×C₆₇	C₂²	1	2	yes	—
59	#447×C₆₇	C₂²	1	8	yes	complemented
60	#447×C₆₇	C₂²	1	4	yes	complemented
61	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
62	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
63	#436×C₆₇	C₂²	1	4	yes	complemented
64	#436×C₆₇	C₂²	1	4	yes	complemented
65	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#418×C₆₇	C₂²	1	8	yes	complemented
68	#407×C₆₇	C₂²	1	4	yes	complemented
69	C₂⁵×C₆₇	—	2	2	no	—
70	C₂×#41×C₆₇	—	2	1	no	—
71	C₂×#41×C₆₇	C₂³	1	4	yes	complemented
72	C₂²×D₄×C₆₇	—	2	2	no	—
73	C₂²×D₄×C₆₇	—	2	4	no	—
74	C₂²×D₄×C₆₇	—	2	4	no	—
75	C₂²×D₄×C₆₇	—	2	2	no	—
76	C₂²×D₄×C₆₇	—	2	1	no	—
77	C₂²×D₄×C₆₇	—	2	4	no	—
78	C₂²×D₄×C₆₇	—	2	1	no	—
79	C₂²×D₄×C₆₇	—	4	8	no	—
80	C₂²×D₄×C₆₇	—	4	8	no	—
81	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
84	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
85	C₂³×C₄×C₆₇	—	2	1	no	—
86	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
87	AGL(1,ℤ/8)×C₆₇	—	4	16	no	—
88	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
89	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	complemented
90	C₂×D₈×C₆₇	C₂³	1	4	yes	—
91	C₂×D₈×C₆₇	C₂³	1	8	yes	complemented
92	C₂×M₁₆×C₆₇	C₂³	1	8	yes	complemented
93	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
94	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
95	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
96	#127×C₆₇	—	2	2	no	—
97	#127×C₆₇	—	2	1	no	—
98	#127×C₆₇	—	2	1	no	—
99	#127×C₆₇	C₂³	1	2	yes	—
100	#127×C₆₇	C₂³	1	2	yes	—
101	#127×C₆₇	C₂³	1	1	yes	characteristic, complemented
102	#126×C₆₇	—	2	4	no	—
103	#125×C₆₇	—	2	1	no	—
104	#124×C₆₇	—	2	2	no	—
105	#124×C₆₇	—	2	4	no	—
106	#124×C₆₇	—	2	1	no	—
107	#123×C₆₇	—	2	4	no	—
108	#123×C₆₇	—	2	4	no	—
109	C₂²⋊Q₈×C₆₇	—	2	1	no	—
110	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
111	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	complemented
112	#121×C₆₇	—	2	2	no	—
113	#121×C₆₇	—	2	2	no	—
114	#121×C₆₇	—	2	4	no	—
115	#121×C₆₇	—	2	1	no	—
116	#121×C₆₇	—	2	4	no	—
117	#121×C₆₇	—	2	4	no	—
118	#121×C₆₇	—	2	4	no	—
119	#121×C₆₇	C₂³	1	8	yes	—
120	#121×C₆₇	C₂³	1	2	yes	—
121	#121×C₆₇	C₂³	1	4	yes	complemented
122	#120×C₆₇	—	2	4	no	—
123	#120×C₆₇	—	2	8	no	—
124	#120×C₆₇	—	2	8	no	—
125	C₄×Q₈×C₆₇	—	2	2	no	—
126	C₄×Q₈×C₆₇	—	2	1	no	—
127	C₄×Q₈×C₆₇	C₂³	1	2	yes	complemented
128	C₄×D₄×C₆₇	—	2	4	no	—
129	C₄×D₄×C₆₇	—	2	4	no	—
130	C₄×D₄×C₆₇	—	2	2	no	—
131	C₄×D₄×C₆₇	—	2	1	no	—
132	C₄×D₄×C₆₇	—	2	1	no	—
133	C₄×D₄×C₆₇	—	2	1	no	—
134	C₄×D₄×C₆₇	D₄	1	2	yes	—
135	C₄×D₄×C₆₇	D₄	1	2	yes	—
136	C₄×D₄×C₆₇	C₂³	1	2	yes	—
137	C₄×D₄×C₆₇	C₂³	1	2	yes	—
138	C₄×D₄×C₆₇	C₂³	1	2	yes	—
139	C₄×D₄×C₆₇	C₂³	1	2	yes	—
140	C₄×D₄×C₆₇	C₂³	1	2	yes	complemented
141	#117×C₆₇	—	2	1	no	—
142	#117×C₆₇	—	2	2	no	—
143	#117×C₆₇	C₂³	1	4	yes	complemented
144	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
145	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
149	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
150	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
151	#107×C₆₇	C₂³	1	4	yes	complemented
152	#106×C₆₇	C₂³	1	4	yes	complemented
153	C₄⋊C₈×C₆₇	C₂³	1	2	yes	complemented
154	C₄⋊C₈×C₆₇	C₂³	1	2	yes	complemented
155	#103×C₆₇	C₂³	1	4	yes	complemented
156	#102×C₆₇	C₂³	1	4	yes	—
157	#102×C₆₇	C₂³	1	4	yes	—
158	#102×C₆₇	C₂³	1	4	yes	complemented
159	#102×C₆₇	C₂³	1	8	yes	complemented
160	#102×C₆₇	C₂³	1	8	yes	complemented
161	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
162	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
163	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	complemented
164	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
165	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
166	C₂⁴×C₆₇	—	2	1	no	—
167	C₂⁴×C₆₇	—	2	2	no	—
168	C₂⁴×C₆₇	—	2	8	no	—
169	C₂⁴×C₆₇	—	4	8	no	—
170	C₂⁴×C₆₇	—	4	8	no	—
171	C₂⁴×C₆₇	—	8	4	no	—
172	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
173	#41×C₆₇	—	4	8	no	—
174	#41×C₆₇	—	4	4	no	—
175	C₂×Q₈×C₆₇	—	2	1	no	—
176	C₂×Q₈×C₆₇	—	2	1	no	—
177	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
178	C₂×D₄×C₆₇	—	2	4	no	—
179	C₂×D₄×C₆₇	—	2	16	no	—
180	C₂×D₄×C₆₇	—	2	2	no	—
181	C₂×D₄×C₆₇	—	2	8	no	—
182	C₂×D₄×C₆₇	—	2	4	no	—
183	C₂×D₄×C₆₇	—	2	4	no	—
184	C₂×D₄×C₆₇	—	2	4	no	—
185	C₂×D₄×C₆₇	—	2	1	no	—
186	C₂×D₄×C₆₇	—	2	1	no	—
187	C₂×D₄×C₆₇	—	2	8	no	—
188	C₂×D₄×C₆₇	—	2	2	no	—
189	C₂×D₄×C₆₇	—	2	2	no	—
190	C₂×D₄×C₆₇	—	2	2	no	—
191	C₂×D₄×C₆₇	—	2	1	no	—
192	C₂×D₄×C₆₇	—	2	2	no	—
193	C₂×D₄×C₆₇	—	2	2	no	—
194	C₂×D₄×C₆₇	—	4	8	no	—
195	C₂×D₄×C₆₇	—	4	4	no	—
196	C₂×D₄×C₆₇	—	4	16	no	—
197	C₂×D₄×C₆₇	—	4	16	no	—
198	C₂×D₄×C₆₇	—	4	16	no	—
199	C₂×D₄×C₆₇	—	4	8	no	—
200	C₂×D₄×C₆₇	—	4	8	no	—
201	C₂×D₄×C₆₇	—	4	4	no	—
202	C₂×D₄×C₆₇	—	8	2	no	—
203	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
204	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
205	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
206	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
207	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₆₇	—	2	1	no	—
209	C₂²×C₄×C₆₇	—	2	2	no	—
210	C₂²×C₄×C₆₇	—	2	2	no	—
211	C₂²×C₄×C₆₇	—	2	2	no	—
212	C₂²×C₄×C₆₇	—	2	4	no	—
213	C₂²×C₄×C₆₇	—	4	4	no	—
214	C₂²×C₄×C₆₇	—	4	4	no	—
215	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
217	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
218	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
221	SD₁₆×C₆₇	—	2	8	no	—
222	SD₁₆×C₆₇	—	4	8	no	—
223	D₈×C₆₇	—	2	8	no	—
224	D₈×C₆₇	—	4	8	no	—
225	M₁₆×C₆₇	—	4	8	no	—
226	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
227	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
228	C₄⋊C₄×C₆₇	—	2	1	no	—
229	C₄⋊C₄×C₆₇	—	2	4	no	—
230	C₄⋊C₄×C₆₇	—	2	1	no	—
231	C₄⋊C₄×C₆₇	—	2	1	no	—
232	C₄⋊C₄×C₆₇	—	2	2	no	—
233	C₄⋊C₄×C₆₇	—	2	1	no	—
234	C₄⋊C₄×C₆₇	—	2	1	no	—
235	C₄⋊C₄×C₆₇	—	2	2	no	—
236	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
237	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
238	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
239	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
240	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
241	C₂²⋊C₄×C₆₇	—	2	2	no	—
242	C₂²⋊C₄×C₆₇	—	2	4	no	—
243	C₂²⋊C₄×C₆₇	—	2	4	no	—
244	C₂²⋊C₄×C₆₇	—	2	2	no	—
245	C₂²⋊C₄×C₆₇	—	2	2	no	—
246	C₂²⋊C₄×C₆₇	—	2	8	no	—
247	C₂²⋊C₄×C₆₇	—	2	4	no	—
248	C₂²⋊C₄×C₆₇	—	2	2	no	—
249	C₂²⋊C₄×C₆₇	—	2	2	no	—
250	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
251	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
252	C₄²×C₆₇	—	2	4	no	—
253	C₄²×C₆₇	—	2	2	no	—
254	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
255	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
256	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂³×C₆₇	—	2	4	no	—
259	C₂³×C₆₇	—	2	4	no	—
260	C₂³×C₆₇	—	2	2	no	—
261	C₂³×C₆₇	—	2	2	no	—
262	C₂³×C₆₇	—	2	4	no	—
263	C₂³×C₆₇	—	4	2	no	—
264	C₂³×C₆₇	—	4	2	no	—
265	C₂³×C₆₇	—	4	16	no	—
266	C₂³×C₆₇	—	4	2	no	—
267	C₂³×C₆₇	—	4	4	no	—
268	C₂³×C₆₇	—	4	16	no	—
269	C₂³×C₆₇	—	4	4	no	—
270	C₂³×C₆₇	—	4	2	no	—
271	C₂³×C₆₇	—	4	4	no	—
272	C₂³×C₆₇	—	8	8	no	—
273	C₂³×C₆₇	—	8	32	no	—
274	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
275	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
276	Q₈×C₆₇	—	2	4	no	—
277	Q₈×C₆₇	—	4	2	no	—
278	Q₈×C₆₇	—	8	1	no	—
279	D₄×C₆₇	—	2	4	no	—
280	D₄×C₆₇	—	2	4	no	—
281	D₄×C₆₇	—	2	4	no	—
282	D₄×C₆₇	—	2	2	no	—
283	D₄×C₆₇	—	2	4	no	—
284	D₄×C₆₇	—	2	8	no	—
285	D₄×C₆₇	—	4	16	no	—
286	D₄×C₆₇	—	4	4	no	—
287	D₄×C₆₇	—	4	16	no	—
288	D₄×C₆₇	—	4	4	no	—
289	D₄×C₆₇	—	4	4	no	—
290	D₄×C₆₇	—	4	4	no	—
291	D₄×C₆₇	—	4	2	no	—
292	D₄×C₆₇	—	8	1	no	—
293	D₄×C₆₇	—	8	2	no	—
294	D₄×C₆₇	—	8	2	no	—
295	D₄×C₆₇	—	8	4	no	—
296	D₄×C₆₇	—	8	4	no	—
297	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
298	C₂×C₄×C₆₇	—	2	8	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	2	no	—
303	C₂×C₄×C₆₇	—	2	2	no	—
304	C₂×C₄×C₆₇	—	4	4	no	—
305	C₂×C₄×C₆₇	—	4	2	no	—
306	C₂×C₄×C₆₇	—	4	1	no	—
307	C₂×C₄×C₆₇	—	4	2	no	—
308	C₂×C₄×C₆₇	—	4	4	no	—
309	C₂×C₄×C₆₇	—	4	4	no	—
310	C₂×C₄×C₆₇	—	4	4	no	—
311	C₂×C₄×C₆₇	—	8	4	no	—
312	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	4	yes	complemented
313	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
314	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
320	C₈×C₆₇	—	2	4	no	—
321	C₈×C₆₇	—	2	4	no	—
322	C₂²×C₆₇	—	2	1	no	—
323	C₂²×C₆₇	—	2	1	no	—
324	C₂²×C₆₇	—	2	4	no	—
325	C₂²×C₆₇	—	2	4	no	—
326	C₂²×C₆₇	—	2	4	no	—
327	C₂²×C₆₇	—	2	4	no	—
328	C₂²×C₆₇	—	4	8	no	—
329	C₂²×C₆₇	—	4	8	no	—
330	C₂²×C₆₇	—	4	2	no	—
331	C₂²×C₆₇	—	4	2	no	—
332	C₂²×C₆₇	—	4	2	no	—
333	C₂²×C₆₇	—	4	4	no	—
334	C₂²×C₆₇	—	4	2	no	—
335	C₂²×C₆₇	—	4	4	no	—
336	C₂²×C₆₇	—	4	2	no	—
337	C₂²×C₆₇	—	4	4	no	—
338	C₂²×C₆₇	—	8	8	no	—
339	C₂²×C₆₇	—	8	32	no	—
340	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
341	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
342	C₄×C₆₇	—	2	1	no	—
343	C₄×C₆₇	—	2	1	no	—
344	C₄×C₆₇	—	2	1	no	—
345	C₄×C₆₇	—	2	4	no	—
346	C₄×C₆₇	—	4	2	no	—
347	C₄×C₆₇	—	4	2	no	—
348	C₄×C₆₇	—	4	2	no	—
349	C₄×C₆₇	—	4	2	no	—
350	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
351	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
352	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
353	#61582	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
354	C₂×C₆₇	—	2	2	no	—
355	C₂×C₆₇	—	4	4	no	—
356	C₂×C₆₇	—	4	4	no	—
357	C₂×C₆₇	—	8	2	no	—
358	C₂×C₆₇	—	8	4	no	—
359	C₂×C₆₇	#3484	1	1	yes	characteristic
360	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
361	C₂×C₆₇	#3585	1	1	yes	characteristic
362	#3506	C₂×C₆₇	1	1	yes	characteristic, complemented
363	C₂×D₄²	C₂×C₆₇	1	1	yes	characteristic, complemented
364	#3325	C₂×C₆₇	1	4	yes	complemented
365	#3324	C₂×C₆₇	1	4	yes	complemented
366	#3274	C₂×C₆₇	1	4	yes	complemented
367	#3272	C₂×C₆₇	1	4	yes	complemented
368	#3208	C₂×C₆₇	1	1	yes	characteristic, complemented
369	#3205	C₂×C₆₇	1	1	yes	characteristic, complemented
370	#3194	C₂×C₆₇	1	4	yes	complemented
371	#3101	C₂×C₆₇	1	1	yes	characteristic, complemented
372	#3100	C₂×C₆₇	1	1	yes	characteristic, complemented
373	#3003	C₂×C₆₇	1	4	yes	complemented
374	#2975	C₂×C₆₇	1	1	yes	characteristic, complemented
375	C₆₇	#61582	1	1	yes	characteristic, direct product factor, Sylow
376	C₂³×D₄	—	2	1	no	—
377	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
378	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	8	yes	complemented
379	#559	—	2	2	no	—
380	#556	C₂²×C₆₇	1	2	yes	complemented
381	#555	C₂²×C₆₇	1	2	yes	complemented
382	#553	—	2	2	no	—
383	#550	C₂²×C₆₇	1	2	yes	complemented
384	#547	C₂²×C₆₇	1	2	yes	complemented
385	D₄²	—	2	2	no	—
386	D₄²	—	2	2	no	—
387	D₄²	C₂²×C₆₇	1	4	yes	—
388	D₄²	C₂²×C₆₇	1	4	yes	—
389	#538	—	2	2	no	—
390	#535	—	2	1	no	—
391	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
392	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
393	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
394	#525	C₂²×C₆₇	1	4	yes	complemented
395	C₂×#121	—	2	1	no	—
396	C₂×#121	C₂²×C₆₇	1	2	yes	—
397	C₂×#120	—	2	2	no	—
398	#520	—	2	1	no	—
399	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
401	#493	C₂²×C₆₇	1	2	yes	complemented
402	#492	C₂²×C₆₇	1	2	yes	complemented
403	#486	C₂²×C₆₇	1	2	yes	complemented
404	#486	C₂²×C₆₇	1	2	yes	complemented
405	#483	C₂²×C₆₇	1	2	yes	complemented
406	#482	C₂²×C₆₇	1	8	yes	complemented
407	#480	C₂²×C₆₇	1	2	yes	complemented
408	#476	C₂²×C₆₇	1	2	yes	complemented
409	#474	C₂²×C₆₇	1	2	yes	complemented
410	#469	C₂²×C₆₇	1	8	yes	complemented
411	#468	C₂²×C₆₇	1	8	yes	complemented
412	#461	C₂²×C₆₇	1	2	yes	complemented
413	#460	C₂²×C₆₇	1	4	yes	complemented
414	#459	C₂²×C₆₇	1	2	yes	complemented
415	#459	C₂²×C₆₇	1	4	yes	complemented
416	#450	C₂²×C₆₇	1	2	yes	—
417	#450	C₂²×C₆₇	1	4	yes	complemented
418	#450	C₂²×C₆₇	1	8	yes	complemented
419	#449	C₂²×C₆₇	1	8	yes	complemented
420	#447	C₂²×C₆₇	1	2	yes	—
421	#447	C₂²×C₆₇	1	4	yes	complemented
422	#447	C₂²×C₆₇	1	8	yes	complemented
423	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
424	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
425	#436	C₂²×C₆₇	1	4	yes	complemented
426	#436	C₂²×C₆₇	1	4	yes	complemented
427	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
428	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
429	#418	C₂²×C₆₇	1	8	yes	complemented
430	#407	C₂²×C₆₇	1	4	yes	complemented
431	C₂⁵	—	2	2	no	—
432	C₂×#41	—	2	1	no	—
433	C₂×#41	C₂³×C₆₇	1	4	yes	complemented
434	C₂²×D₄	—	2	2	no	—
435	C₂²×D₄	—	2	4	no	—
436	C₂²×D₄	—	2	4	no	—
437	C₂²×D₄	—	2	2	no	—
438	C₂²×D₄	—	2	1	no	—
439	C₂²×D₄	—	2	4	no	—
440	C₂²×D₄	—	2	1	no	—
441	C₂²×D₄	—	4	8	no	—
442	C₂²×D₄	—	4	8	no	—
443	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
444	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
445	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
446	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
447	C₂³×C₄	—	2	1	no	—
448	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
449	AGL(1,ℤ/8)	—	4	16	no	—
450	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
451	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	complemented
452	C₂×D₈	C₂³×C₆₇	1	4	yes	—
453	C₂×D₈	C₂³×C₆₇	1	8	yes	complemented
454	C₂×M₁₆	C₂³×C₆₇	1	8	yes	complemented
455	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
456	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
457	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
458	#127	—	2	2	no	—
459	#127	—	2	1	no	—
460	#127	—	2	1	no	—
461	#127	C₂³×C₆₇	1	2	yes	—
462	#127	C₂³×C₆₇	1	2	yes	—
463	#127	C₂³×C₆₇	1	1	yes	characteristic, complemented
464	#126	—	2	4	no	—
465	#125	—	2	1	no	—
466	#124	—	2	2	no	—
467	#124	—	2	4	no	—
468	#124	—	2	1	no	—
469	#123	—	2	4	no	—
470	#123	—	2	4	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
473	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	complemented
474	#121	—	2	2	no	—
475	#121	—	2	2	no	—
476	#121	—	2	4	no	—
477	#121	—	2	1	no	—
478	#121	—	2	4	no	—
479	#121	—	2	4	no	—
480	#121	—	2	4	no	—
481	#121	C₂³×C₆₇	1	8	yes	—
482	#121	C₂³×C₆₇	1	2	yes	—
483	#121	C₂³×C₆₇	1	4	yes	complemented
484	#120	—	2	4	no	—
485	#120	—	2	8	no	—
486	#120	—	2	8	no	—
487	C₄×Q₈	—	2	2	no	—
488	C₄×Q₈	—	2	1	no	—
489	C₄×Q₈	C₂³×C₆₇	1	2	yes	complemented
490	C₄×D₄	—	2	4	no	—
491	C₄×D₄	—	2	4	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	—	2	1	no	—
495	C₄×D₄	—	2	1	no	—
496	C₄×D₄	D₄×C₆₇	1	2	yes	—
497	C₄×D₄	D₄×C₆₇	1	2	yes	—
498	C₄×D₄	C₂³×C₆₇	1	2	yes	—
499	C₄×D₄	C₂³×C₆₇	1	2	yes	—
500	C₄×D₄	C₂³×C₆₇	1	2	yes	—
501	C₄×D₄	C₂³×C₆₇	1	2	yes	—
502	C₄×D₄	C₂³×C₆₇	1	2	yes	complemented
503	#117	—	2	1	no	—
504	#117	—	2	2	no	—
505	#117	C₂³×C₆₇	1	4	yes	complemented
506	C₂×C₄⋊C₄	—	2	2	no	—
507	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	2	no	—
511	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
512	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
513	#107	C₂³×C₆₇	1	4	yes	complemented
514	#106	C₂³×C₆₇	1	4	yes	complemented
515	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
516	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
517	#103	C₂³×C₆₇	1	4	yes	complemented
518	#102	C₂³×C₆₇	1	4	yes	—
519	#102	C₂³×C₆₇	1	4	yes	—
520	#102	C₂³×C₆₇	1	8	yes	complemented
521	#102	C₂³×C₆₇	1	8	yes	complemented
522	#102	C₂³×C₆₇	1	4	yes	complemented
523	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
524	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
525	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	complemented
526	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
527	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
528	C₂⁴	—	2	1	no	—
529	C₂⁴	—	2	2	no	—
530	C₂⁴	—	2	8	no	—
531	C₂⁴	—	4	8	no	—
532	C₂⁴	—	4	8	no	—
533	C₂⁴	—	8	4	no	—
534	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
535	#41	—	4	8	no	—
536	#41	—	4	4	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	16	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	8	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	8	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	4	8	no	—
557	C₂×D₄	—	4	4	no	—
558	C₂×D₄	—	4	16	no	—
559	C₂×D₄	—	4	16	no	—
560	C₂×D₄	—	4	16	no	—
561	C₂×D₄	—	4	8	no	—
562	C₂×D₄	—	4	8	no	—
563	C₂×D₄	—	4	4	no	—
564	C₂×D₄	—	8	2	no	—
565	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
566	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
567	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
568	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
569	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	4	4	no	—
576	C₂²×C₄	—	4	4	no	—
577	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
579	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
580	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
583	SD₁₆	—	2	8	no	—
584	SD₁₆	—	4	8	no	—
585	D₈	—	2	8	no	—
586	D₈	—	4	8	no	—
587	M₁₆	—	4	8	no	—
588	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
589	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
599	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
600	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
601	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
602	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	8	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
613	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
614	C₄²	—	2	4	no	—
615	C₄²	—	2	2	no	—
616	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
617	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
618	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
619	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
620	C₂³	—	2	4	no	—
621	C₂³	—	2	4	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	4	no	—
625	C₂³	—	4	2	no	—
626	C₂³	—	4	2	no	—
627	C₂³	—	4	16	no	—
628	C₂³	—	4	2	no	—
629	C₂³	—	4	4	no	—
630	C₂³	—	4	16	no	—
631	C₂³	—	4	4	no	—
632	C₂³	—	4	2	no	—
633	C₂³	—	4	4	no	—
634	C₂³	—	8	8	no	—
635	C₂³	—	8	32	no	—
636	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
637	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
638	Q₈	—	2	4	no	—
639	Q₈	—	4	2	no	—
640	Q₈	—	8	1	no	—
641	D₄	—	2	4	no	—
642	D₄	—	2	4	no	—
643	D₄	—	2	4	no	—
644	D₄	—	2	2	no	—
645	D₄	—	2	4	no	—
646	D₄	—	2	8	no	—
647	D₄	—	4	16	no	—
648	D₄	—	4	4	no	—
649	D₄	—	4	16	no	—
650	D₄	—	4	4	no	—
651	D₄	—	4	4	no	—
652	D₄	—	4	4	no	—
653	D₄	—	4	2	no	—
654	D₄	—	8	2	no	—
655	D₄	—	8	2	no	—
656	D₄	—	8	1	no	—
657	D₄	—	8	4	no	—
658	D₄	—	8	4	no	—
659	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
660	C₂×C₄	—	2	8	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	4	no	—
671	C₂×C₄	—	4	4	no	—
672	C₂×C₄	—	4	4	no	—
673	C₂×C₄	—	8	4	no	—
674	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	4	yes	complemented
675	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
676	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
677	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
678	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
679	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
680	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
681	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
682	C₈	—	2	4	no	—
683	C₈	—	2	4	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	4	8	no	—
691	C₂²	—	4	8	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	4	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	4	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	8	8	no	—
701	C₂²	—	8	32	no	—
702	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
703	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
704	C₄	—	2	1	no	—
705	C₄	—	2	1	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	4	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
713	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
714	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
715	C₂	—	2	2	no	—
716	C₂	—	4	4	no	—
717	C₂	—	4	4	no	—
718	C₂	—	8	4	no	—
719	C₂	—	8	2	no	—
720	C₂	C₆₇×#3484	1	1	yes	characteristic
721	C₂	C₂²×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
722	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3506	C₂	semidirect
2. C₂×D₄²×C₆₇	C₂	semidirect
3. C₆₇×#3325	C₂	semidirect
4. C₆₇×#3324	C₂	semidirect
5. C₆₇×#3274	C₂	semidirect
6. C₆₇×#3272	C₂	semidirect
7. C₆₇×#3208	C₂	semidirect
8. C₆₇×#3205	C₂	semidirect
9. C₆₇×#3194	C₂	semidirect
10. C₆₇×#3101	C₂	semidirect
11. C₆₇×#3100	C₂	semidirect
12. C₆₇×#3003	C₂	semidirect
13. C₆₇×#2975	C₂	semidirect
16. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
18. #556×C₆₇	C₂²	semidirect
19. #555×C₆₇	C₂²	semidirect
21. #550×C₆₇	C₂²	semidirect
22. #547×C₆₇	C₂²	semidirect
29. #533×C₆₇	C₂²	semidirect
30. #532×C₆₇	C₂²	semidirect
32. #525×C₆₇	C₂²	semidirect
39. #493×C₆₇	C₂²	semidirect
40. #492×C₆₇	C₂²	semidirect
41. #486×C₆₇	C₂²	semidirect
42. #486×C₆₇	C₂²	semidirect
43. #483×C₆₇	C₂²	semidirect
44. #482×C₆₇	C₂²	semidirect
45. #480×C₆₇	C₂²	semidirect
46. #476×C₆₇	C₂²	semidirect
47. #474×C₆₇	C₂²	semidirect
48. #469×C₆₇	C₂²	semidirect
49. #468×C₆₇	C₂²	semidirect
50. #461×C₆₇	C₂²	semidirect
51. #460×C₆₇	C₂²	semidirect
52. #459×C₆₇	C₂²	semidirect
53. #459×C₆₇	C₂²	semidirect
55. #450×C₆₇	C₂²	semidirect
56. #450×C₆₇	C₂²	semidirect
57. #449×C₆₇	C₂²	semidirect
59. #447×C₆₇	C₂²	semidirect
60. #447×C₆₇	C₂²	semidirect
61. C₄×SD₁₆×C₆₇	C₂²	semidirect
62. C₄×D₈×C₆₇	C₂²	semidirect
63. #436×C₆₇	C₂²	semidirect
64. #436×C₆₇	C₂²	semidirect
65. #431×C₆₇	C₂²	semidirect
66. #431×C₆₇	C₂²	semidirect
67. #418×C₆₇	C₂²	semidirect
68. #407×C₆₇	C₂²	semidirect
71. C₂×#41×C₆₇	C₂³	semidirect
89. C₂×SD₁₆×C₆₇	C₂³	semidirect
91. C₂×D₈×C₆₇	C₂³	semidirect
92. C₂×M₁₆×C₆₇	C₂³	semidirect
93. C₄⋊Q₈×C₆₇	C₂³	semidirect
94. C₄⋊Q₈×C₆₇	C₂³	semidirect
95. C₄⋊Q₈×C₆₇	C₂³	semidirect
101. #127×C₆₇	C₂³	semidirect
111. C₂²⋊Q₈×C₆₇	C₂³	semidirect
121. #121×C₆₇	C₂³	semidirect
127. C₄×Q₈×C₆₇	C₂³	semidirect
140. C₄×D₄×C₆₇	C₂³	semidirect
143. #117×C₆₇	C₂³	semidirect
151. #107×C₆₇	C₂³	semidirect
152. #106×C₆₇	C₂³	semidirect
153. C₄⋊C₈×C₆₇	C₂³	semidirect
154. C₄⋊C₈×C₆₇	C₂³	semidirect
155. #103×C₆₇	C₂³	semidirect
158. #102×C₆₇	C₂³	semidirect
159. #102×C₆₇	C₂³	semidirect
160. #102×C₆₇	C₂³	semidirect
163. C₂²⋊C₈×C₆₇	C₂³	semidirect
164. C₄×C₈×C₆₇	C₂³	semidirect
165. C₄×C₈×C₆₇	C₂³	semidirect
312. C₂×C₄×C₆₇	AGL(1,ℤ/8)	semidirect
353. #61582	C₆₇	direct (N × H)
362. #3506	C₂×C₆₇	semidirect
363. C₂×D₄²	C₂×C₆₇	semidirect
364. #3325	C₂×C₆₇	semidirect
365. #3324	C₂×C₆₇	semidirect
366. #3274	C₂×C₆₇	semidirect
367. #3272	C₂×C₆₇	semidirect
368. #3208	C₂×C₆₇	semidirect
369. #3205	C₂×C₆₇	semidirect
370. #3194	C₂×C₆₇	semidirect
371. #3101	C₂×C₆₇	semidirect
372. #3100	C₂×C₆₇	semidirect
373. #3003	C₂×C₆₇	semidirect
374. #2975	C₂×C₆₇	semidirect
375. C₆₇	#61582	direct (N × H)
378. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
380. #556	C₂²×C₆₇	semidirect
381. #555	C₂²×C₆₇	semidirect
383. #550	C₂²×C₆₇	semidirect
384. #547	C₂²×C₆₇	semidirect
391. #533	C₂²×C₆₇	semidirect
392. #532	C₂²×C₆₇	semidirect
394. #525	C₂²×C₆₇	semidirect
401. #493	C₂²×C₆₇	semidirect
402. #492	C₂²×C₆₇	semidirect
403. #486	C₂²×C₆₇	semidirect
404. #486	C₂²×C₆₇	semidirect
405. #483	C₂²×C₆₇	semidirect
406. #482	C₂²×C₆₇	semidirect
407. #480	C₂²×C₆₇	semidirect
408. #476	C₂²×C₆₇	semidirect
409. #474	C₂²×C₆₇	semidirect
410. #469	C₂²×C₆₇	semidirect
411. #468	C₂²×C₆₇	semidirect
412. #461	C₂²×C₆₇	semidirect
413. #460	C₂²×C₆₇	semidirect
414. #459	C₂²×C₆₇	semidirect
415. #459	C₂²×C₆₇	semidirect
417. #450	C₂²×C₆₇	semidirect
418. #450	C₂²×C₆₇	semidirect
419. #449	C₂²×C₆₇	semidirect
421. #447	C₂²×C₆₇	semidirect
422. #447	C₂²×C₆₇	semidirect
423. C₄×SD₁₆	C₂²×C₆₇	semidirect
424. C₄×D₈	C₂²×C₆₇	semidirect
425. #436	C₂²×C₆₇	semidirect
426. #436	C₂²×C₆₇	semidirect
427. #431	C₂²×C₆₇	semidirect
428. #431	C₂²×C₆₇	semidirect
429. #418	C₂²×C₆₇	semidirect
430. #407	C₂²×C₆₇	semidirect
433. C₂×#41	C₂³×C₆₇	semidirect
451. C₂×SD₁₆	C₂³×C₆₇	semidirect
453. C₂×D₈	C₂³×C₆₇	semidirect
454. C₂×M₁₆	C₂³×C₆₇	semidirect
455. C₄⋊Q₈	C₂³×C₆₇	semidirect
456. C₄⋊Q₈	C₂³×C₆₇	semidirect
457. C₄⋊Q₈	C₂³×C₆₇	semidirect
463. #127	C₂³×C₆₇	semidirect
473. C₂²⋊Q₈	C₂³×C₆₇	semidirect
483. #121	C₂³×C₆₇	semidirect
489. C₄×Q₈	C₂³×C₆₇	semidirect
502. C₄×D₄	C₂³×C₆₇	semidirect
505. #117	C₂³×C₆₇	semidirect
513. #107	C₂³×C₆₇	semidirect
514. #106	C₂³×C₆₇	semidirect
515. C₄⋊C₈	C₂³×C₆₇	semidirect
516. C₄⋊C₈	C₂³×C₆₇	semidirect
517. #103	C₂³×C₆₇	semidirect
520. #102	C₂³×C₆₇	semidirect
521. #102	C₂³×C₆₇	semidirect
522. #102	C₂³×C₆₇	semidirect
525. C₂²⋊C₈	C₂³×C₆₇	semidirect
526. C₄×C₈	C₂³×C₆₇	semidirect
527. C₄×C₈	C₂³×C₆₇	semidirect
674. C₂×C₄	AGL(1,ℤ/8)×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3506	2
C₂×D₄²×C₆₇	2
C₆₇×#3325	2
C₆₇×#3324	2
C₆₇×#3274	2
C₆₇×#3272	2
C₆₇×#3208	2
C₆₇×#3205	2
C₆₇×#3194	2
C₆₇×#3101	2
C₆₇×#3100	2
C₆₇×#3003	2
C₆₇×#2975	2
#61582	67

Subgroups — C67×#61582 #30740833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61582 #30740833