Subgroups — C₆₇×#61630 #30740881

Order 17152.

2350 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3318	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3297	C₂	1	4	yes	maximal, complemented
5	D₄×D₈×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3264	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3220	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3199	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3188	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3122	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3008	C₂	1	2	yes	maximal, complemented
12	C₂×#447×C₆₇	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2977	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
15	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
16	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
17	C₂²×D₈×C₆₇	C₂²	1	4	yes	complemented
18	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
19	#560×C₆₇	—	2	2	no	—
20	#553×C₆₇	C₂²	1	4	yes	complemented
21	#546×C₆₇	—	2	2	no	—
22	#546×C₆₇	C₂²	1	4	yes	complemented
23	D₄²×C₆₇	—	2	2	no	—
24	D₄²×C₆₇	—	2	2	no	—
25	D₄²×C₆₇	C₂²	1	4	yes	complemented
26	D₄²×C₆₇	C₂²	1	4	yes	complemented
27	#540×C₆₇	C₂²	1	2	yes	complemented
28	#538×C₆₇	—	2	2	no	—
29	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#535×C₆₇	C₂²	1	2	yes	complemented
32	#534×C₆₇	—	2	2	no	—
33	#534×C₆₇	—	2	2	no	—
34	#525×C₆₇	C₂²	1	1	yes	characteristic
35	#525×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
37	C₂×#120×C₆₇	—	2	2	no	—
38	#518×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#496×C₆₇	C₂²	1	2	yes	complemented
40	#493×C₆₇	C₂²	1	2	yes	complemented
41	#490×C₆₇	C₂²	1	2	yes	complemented
42	#488×C₆₇	C₂²	1	2	yes	complemented
43	#484×C₆₇	C₂²	1	2	yes	complemented
44	#482×C₆₇	C₂²	1	4	yes	complemented
45	#482×C₆₇	C₂²	1	4	yes	complemented
46	#481×C₆₇	C₂²	1	2	yes	complemented
47	#478×C₆₇	C₂²	1	4	yes	complemented
48	#469×C₆₇	C₂²	1	4	yes	complemented
49	#466×C₆₇	C₂²	1	4	yes	complemented
50	#466×C₆₇	C₂²	1	4	yes	complemented
51	#465×C₆₇	C₂²	1	4	yes	complemented
52	#463×C₆₇	C₂²	1	4	yes	complemented
53	#459×C₆₇	C₂²	1	4	yes	complemented
54	#459×C₆₇	C₂²	1	4	yes	complemented
55	#450×C₆₇	C₂²	1	2	yes	complemented
56	#449×C₆₇	C₂²	1	4	yes	complemented
57	#449×C₆₇	C₂²	1	4	yes	complemented
58	#447×C₆₇	C₂²	1	4	yes	complemented
59	#447×C₆₇	C₂²	1	4	yes	complemented
60	#447×C₆₇	C₂²	1	4	yes	complemented
61	#447×C₆₇	C₂²	1	4	yes	complemented
62	#447×C₆₇	C₂²	1	4	yes	complemented
63	#447×C₆₇	C₂²	1	4	yes	complemented
64	#447×C₆₇	C₂²	1	2	yes	complemented
65	#442×C₆₇	C₂²	1	4	yes	complemented
66	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
67	#435×C₆₇	C₂²	1	4	yes	complemented
68	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
69	#433×C₆₇	C₂²	1	2	yes	complemented
70	#418×C₆₇	C₂²	1	2	yes	complemented
71	#416×C₆₇	C₂²	1	2	yes	complemented
72	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
73	#408×C₆₇	C₂²	1	2	yes	complemented
74	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
75	C₂⁵×C₆₇	—	2	1	no	—
76	H(5,𝔽₂)×C₆₇	—	4	4	no	—
77	C₂×#41×C₆₇	—	2	1	no	—
78	C₂×#41×C₆₇	C₂³	1	2	yes	—
79	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
80	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₆₇	—	2	2	no	—
82	C₂²×D₄×C₆₇	—	2	2	no	—
83	C₂²×D₄×C₆₇	—	2	1	no	—
84	C₂²×D₄×C₆₇	—	2	4	no	—
85	C₂²×D₄×C₆₇	—	2	4	no	—
86	C₂²×D₄×C₆₇	—	2	1	no	—
87	C₂²×D₄×C₆₇	—	2	2	no	—
88	C₂²×D₄×C₆₇	—	4	4	no	—
89	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
91	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
92	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
93	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₆₇	C₂³	1	2	yes	complemented
95	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
96	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
97	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
98	C₂×D₈×C₆₇	—	4	8	no	—
99	C₂×D₈×C₆₇	—	4	4	no	—
100	C₂×D₈×C₆₇	C₂³	1	4	yes	—
101	C₂×D₈×C₆₇	C₂³	1	4	yes	—
102	C₂×D₈×C₆₇	C₂³	1	4	yes	—
103	C₂×D₈×C₆₇	C₂³	1	4	yes	—
104	C₂×D₈×C₆₇	C₂³	1	4	yes	complemented
105	C₂×M₁₆×C₆₇	C₂³	1	2	yes	complemented
106	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
107	C₂²×C₈×C₆₇	C₂³	1	2	yes	complemented
108	#127×C₆₇	—	2	1	no	—
109	#127×C₆₇	—	2	2	no	—
110	#127×C₆₇	C₂³	1	2	yes	—
111	#127×C₆₇	C₂³	1	2	yes	complemented
112	#126×C₆₇	—	2	4	no	—
113	#125×C₆₇	C₂³	1	2	yes	complemented
114	#124×C₆₇	—	2	2	no	—
115	#124×C₆₇	—	2	1	no	—
116	#124×C₆₇	C₂³	1	2	yes	—
117	#123×C₆₇	—	2	1	no	—
118	#123×C₆₇	—	2	4	no	—
119	#123×C₆₇	—	2	4	no	—
120	#123×C₆₇	—	2	4	no	—
121	#123×C₆₇	D₄	1	2	yes	—
122	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
123	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
124	#121×C₆₇	—	2	4	no	—
125	#121×C₆₇	—	2	2	no	—
126	#121×C₆₇	—	2	2	no	—
127	#121×C₆₇	—	2	4	no	—
128	#121×C₆₇	—	2	2	no	—
129	#121×C₆₇	—	2	4	no	—
130	#121×C₆₇	—	2	4	no	—
131	#121×C₆₇	—	2	4	no	—
132	#121×C₆₇	D₄	1	2	yes	—
133	#121×C₆₇	C₂³	1	4	yes	—
134	#121×C₆₇	C₂³	1	4	yes	—
135	#121×C₆₇	C₂³	1	2	yes	—
136	#121×C₆₇	C₂³	1	4	yes	—
137	#121×C₆₇	C₂³	1	4	yes	complemented
138	#120×C₆₇	—	2	1	no	—
139	#120×C₆₇	—	2	2	no	—
140	#120×C₆₇	—	2	4	no	—
141	#120×C₆₇	—	2	2	no	—
142	#120×C₆₇	—	2	2	no	—
143	#120×C₆₇	—	2	2	no	—
144	#120×C₆₇	—	2	4	no	—
145	#120×C₆₇	—	2	4	no	—
146	#120×C₆₇	—	2	4	no	—
147	#120×C₆₇	—	2	4	no	—
148	#120×C₆₇	D₄	1	2	yes	—
149	C₄×D₄×C₆₇	—	2	2	no	—
150	C₄×D₄×C₆₇	—	2	2	no	—
151	C₄×D₄×C₆₇	—	2	4	no	—
152	C₄×D₄×C₆₇	C₂³	1	4	yes	—
153	C₄×D₄×C₆₇	C₂³	1	4	yes	—
154	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
155	#117×C₆₇	C₂³	1	1	yes	characteristic
156	#117×C₆₇	C₂³	1	1	yes	characteristic
157	#117×C₆₇	C₂³	1	2	yes	complemented
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
160	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
161	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
162	#107×C₆₇	C₂³	1	4	yes	complemented
163	#106×C₆₇	C₂³	1	4	yes	complemented
164	C₄⋊C₈×C₆₇	C₂³	1	4	yes	complemented
165	#103×C₆₇	C₂³	1	4	yes	complemented
166	#102×C₆₇	C₂³	1	4	yes	—
167	#102×C₆₇	C₂³	1	4	yes	—
168	#102×C₆₇	C₂³	1	4	yes	—
169	#102×C₆₇	C₂³	1	4	yes	—
170	#102×C₆₇	C₂³	1	4	yes	complemented
171	#102×C₆₇	C₂³	1	4	yes	complemented
172	#102×C₆₇	C₂³	1	4	yes	complemented
173	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
174	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
175	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
176	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	complemented
177	#97×C₆₇	C₂³	1	2	yes	complemented
178	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
179	C₂⁴×C₆₇	—	2	1	no	—
180	C₂⁴×C₆₇	—	2	4	no	—
181	C₂⁴×C₆₇	—	2	2	no	—
182	C₂⁴×C₆₇	—	2	1	no	—
183	C₂⁴×C₆₇	—	2	2	no	—
184	C₂⁴×C₆₇	—	2	2	no	—
185	C₂⁴×C₆₇	—	4	4	no	—
186	C₂⁴×C₆₇	—	8	4	no	—
187	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
188	#41×C₆₇	—	2	4	no	—
189	#41×C₆₇	—	4	2	no	—
190	#41×C₆₇	—	4	2	no	—
191	#41×C₆₇	—	4	2	no	—
192	#41×C₆₇	—	4	4	no	—
193	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
194	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
195	C₂×D₄×C₆₇	—	2	4	no	—
196	C₂×D₄×C₆₇	—	2	8	no	—
197	C₂×D₄×C₆₇	—	2	4	no	—
198	C₂×D₄×C₆₇	—	2	2	no	—
199	C₂×D₄×C₆₇	—	2	4	no	—
200	C₂×D₄×C₆₇	—	2	1	no	—
201	C₂×D₄×C₆₇	—	2	2	no	—
202	C₂×D₄×C₆₇	—	2	4	no	—
203	C₂×D₄×C₆₇	—	2	4	no	—
204	C₂×D₄×C₆₇	—	2	4	no	—
205	C₂×D₄×C₆₇	—	2	1	no	—
206	C₂×D₄×C₆₇	—	2	2	no	—
207	C₂×D₄×C₆₇	—	2	4	no	—
208	C₂×D₄×C₆₇	—	2	1	no	—
209	C₂×D₄×C₆₇	—	2	4	no	—
210	C₂×D₄×C₆₇	—	2	2	no	—
211	C₂×D₄×C₆₇	—	2	4	no	—
212	C₂×D₄×C₆₇	—	2	2	no	—
213	C₂×D₄×C₆₇	—	4	4	no	—
214	C₂×D₄×C₆₇	—	4	2	no	—
215	C₂×D₄×C₆₇	—	4	2	no	—
216	C₂×D₄×C₆₇	—	4	4	no	—
217	C₂×D₄×C₆₇	—	4	2	no	—
218	C₂×D₄×C₆₇	—	4	2	no	—
219	C₂×D₄×C₆₇	—	4	8	no	—
220	C₂×D₄×C₆₇	—	4	4	no	—
221	C₂×D₄×C₆₇	—	4	4	no	—
222	C₂×D₄×C₆₇	—	4	8	no	—
223	C₂×D₄×C₆₇	—	8	8	no	—
224	C₂×D₄×C₆₇	—	8	8	no	—
225	C₂×D₄×C₆₇	—	8	4	no	—
226	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
227	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
228	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
229	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
230	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
232	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₆₇	—	2	2	no	—
234	C₂²×C₄×C₆₇	—	2	2	no	—
235	C₂²×C₄×C₆₇	—	2	1	no	—
236	C₂²×C₄×C₆₇	—	2	4	no	—
237	C₂²×C₄×C₆₇	—	2	4	no	—
238	C₂²×C₄×C₆₇	—	4	2	no	—
239	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
244	SD₁₆×C₆₇	—	4	4	no	—
245	D₈×C₆₇	—	2	8	no	—
246	D₈×C₆₇	—	2	8	no	—
247	D₈×C₆₇	—	4	4	no	—
248	D₈×C₆₇	—	4	4	no	—
249	D₈×C₆₇	—	4	4	no	—
250	M₁₆×C₆₇	—	4	2	no	—
251	C₂×C₈×C₆₇	—	4	4	no	—
252	C₂×C₈×C₆₇	—	4	2	no	—
253	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
254	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
255	C₄⋊C₄×C₆₇	—	2	2	no	—
256	C₄⋊C₄×C₆₇	—	2	2	no	—
257	C₄⋊C₄×C₆₇	—	2	4	no	—
258	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
260	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
261	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²⋊C₄×C₆₇	—	2	1	no	—
263	C₂²⋊C₄×C₆₇	—	2	2	no	—
264	C₂²⋊C₄×C₆₇	—	2	2	no	—
265	C₂²⋊C₄×C₆₇	—	2	4	no	—
266	C₂²⋊C₄×C₆₇	—	2	4	no	—
267	C₂²⋊C₄×C₆₇	—	2	4	no	—
268	C₂²⋊C₄×C₆₇	—	2	4	no	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	2	no	—
271	C₂²⋊C₄×C₆₇	—	2	4	no	—
272	C₂²⋊C₄×C₆₇	—	2	4	no	—
273	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
274	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
275	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
276	C₄²×C₆₇	—	2	1	no	—
277	C₄²×C₆₇	—	2	2	no	—
278	C₄²×C₆₇	C₂⁴	1	2	yes	—
279	C₂³×C₆₇	—	2	4	no	—
280	C₂³×C₆₇	—	2	4	no	—
281	C₂³×C₆₇	—	2	2	no	—
282	C₂³×C₆₇	—	2	4	no	—
283	C₂³×C₆₇	—	2	2	no	—
284	C₂³×C₆₇	—	2	1	no	—
285	C₂³×C₆₇	—	4	1	no	—
286	C₂³×C₆₇	—	4	8	no	—
287	C₂³×C₆₇	—	4	4	no	—
288	C₂³×C₆₇	—	4	2	no	—
289	C₂³×C₆₇	—	4	8	no	—
290	C₂³×C₆₇	—	4	4	no	—
291	C₂³×C₆₇	—	8	4	no	—
292	C₂³×C₆₇	—	8	2	no	—
293	C₂³×C₆₇	—	8	2	no	—
294	C₂³×C₆₇	—	8	2	no	—
295	C₂³×C₆₇	—	8	2	no	—
296	C₂³×C₆₇	—	8	2	no	—
297	C₂³×C₆₇	—	8	4	no	—
298	C₂³×C₆₇	—	8	4	no	—
299	C₂³×C₆₇	—	8	16	no	—
300	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
301	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
302	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
303	Q₈×C₆₇	—	2	2	no	—
304	Q₈×C₆₇	—	4	1	no	—
305	D₄×C₆₇	—	2	4	no	—
306	D₄×C₆₇	—	2	8	no	—
307	D₄×C₆₇	—	2	2	no	—
308	D₄×C₆₇	—	2	4	no	—
309	D₄×C₆₇	—	2	4	no	—
310	D₄×C₆₇	—	2	4	no	—
311	D₄×C₆₇	—	2	2	no	—
312	D₄×C₆₇	—	4	1	no	—
313	D₄×C₆₇	—	4	2	no	—
314	D₄×C₆₇	—	4	8	no	—
315	D₄×C₆₇	—	4	4	no	—
316	D₄×C₆₇	—	4	2	no	—
317	D₄×C₆₇	—	4	4	no	—
318	D₄×C₆₇	—	4	2	no	—
319	D₄×C₆₇	—	4	4	no	—
320	D₄×C₆₇	—	4	8	no	—
321	D₄×C₆₇	—	8	2	no	—
322	D₄×C₆₇	—	8	2	no	—
323	D₄×C₆₇	—	8	4	no	—
324	D₄×C₆₇	—	8	4	no	—
325	D₄×C₆₇	—	8	4	no	—
326	D₄×C₆₇	—	8	4	no	—
327	D₄×C₆₇	—	8	4	no	—
328	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
329	C₂×C₄×C₆₇	—	2	4	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	4	no	—
335	C₂×C₄×C₆₇	—	2	1	no	—
336	C₂×C₄×C₆₇	—	4	2	no	—
337	C₂×C₄×C₆₇	—	4	1	no	—
338	C₂×C₄×C₆₇	—	4	4	no	—
339	C₂×C₄×C₆₇	—	4	2	no	—
340	C₂×C₄×C₆₇	—	8	4	no	—
341	C₂×C₄×C₆₇	—	8	4	no	—
342	C₂×C₄×C₆₇	—	8	2	no	—
343	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
346	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
348	C₈×C₆₇	—	2	4	no	—
349	C₈×C₆₇	—	2	4	no	—
350	C₂²×C₆₇	—	2	2	no	—
351	C₂²×C₆₇	—	2	2	no	—
352	C₂²×C₆₇	—	2	1	no	—
353	C₂²×C₆₇	—	2	2	no	—
354	C₂²×C₆₇	—	2	4	no	—
355	C₂²×C₆₇	—	2	4	no	—
356	C₂²×C₆₇	—	2	2	no	—
357	C₂²×C₆₇	—	4	4	no	—
358	C₂²×C₆₇	—	4	4	no	—
359	C₂²×C₆₇	—	4	1	no	—
360	C₂²×C₆₇	—	4	2	no	—
361	C₂²×C₆₇	—	4	4	no	—
362	C₂²×C₆₇	—	4	4	no	—
363	C₂²×C₆₇	—	4	2	no	—
364	C₂²×C₆₇	—	4	4	no	—
365	C₂²×C₆₇	—	4	4	no	—
366	C₂²×C₆₇	—	8	16	no	—
367	C₂²×C₆₇	—	8	4	no	—
368	C₂²×C₆₇	—	8	4	no	—
369	C₂²×C₆₇	—	16	4	no	—
370	C₂²×C₆₇	—	16	4	no	—
371	C₂²×C₆₇	—	16	4	no	—
372	C₂²×C₆₇	#576	1	4	yes	—
373	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
374	C₄×C₆₇	—	2	1	no	—
375	C₄×C₆₇	—	2	2	no	—
376	C₄×C₆₇	—	2	2	no	—
377	C₄×C₆₇	—	2	4	no	—
378	C₄×C₆₇	—	4	1	no	—
379	C₄×C₆₇	—	4	2	no	—
380	C₄×C₆₇	—	4	4	no	—
381	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
382	#61630	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₂×C₆₇	—	2	4	no	—
384	C₂×C₆₇	—	4	1	no	—
385	C₂×C₆₇	—	4	2	no	—
386	C₂×C₆₇	—	4	4	no	—
387	C₂×C₆₇	—	8	2	no	—
388	C₂×C₆₇	—	8	1	no	—
389	C₂×C₆₇	—	8	4	no	—
390	C₂×C₆₇	#3484	1	1	yes	characteristic
391	C₂×C₆₇	C₂×#576	1	2	yes	—
392	#3537	C₂×C₆₇	1	1	yes	characteristic, complemented
393	#3484	C₂×C₆₇	1	1	yes	characteristic, complemented
394	#3318	C₂×C₆₇	1	4	yes	complemented
395	#3297	C₂×C₆₇	1	4	yes	complemented
396	D₄×D₈	C₂×C₆₇	1	4	yes	complemented
397	#3264	C₂×C₆₇	1	4	yes	complemented
398	#3220	C₂×C₆₇	1	2	yes	complemented
399	#3199	C₂×C₆₇	1	2	yes	complemented
400	#3188	C₂×C₆₇	1	2	yes	complemented
401	#3122	C₂×C₆₇	1	2	yes	complemented
402	#3008	C₂×C₆₇	1	2	yes	complemented
403	C₂×#447	C₂×C₆₇	1	2	yes	complemented
404	#2977	C₂×C₆₇	1	1	yes	characteristic, complemented
405	C₆₇	#61630	1	1	yes	characteristic, direct product factor, Sylow
406	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
407	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
408	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
409	C₂²×D₈	C₂²×C₆₇	1	4	yes	complemented
410	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
411	#560	—	2	2	no	—
412	#553	C₂²×C₆₇	1	4	yes	complemented
413	#546	—	2	2	no	—
414	#546	C₂²×C₆₇	1	4	yes	complemented
415	D₄²	—	2	2	no	—
416	D₄²	—	2	2	no	—
417	D₄²	C₂²×C₆₇	1	4	yes	complemented
418	D₄²	C₂²×C₆₇	1	4	yes	complemented
419	#540	C₂²×C₆₇	1	2	yes	complemented
420	#538	—	2	2	no	—
421	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
422	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
423	#535	C₂²×C₆₇	1	2	yes	complemented
424	#534	—	2	2	no	—
425	#534	—	2	2	no	—
426	#525	C₂²×C₆₇	1	1	yes	characteristic
427	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
428	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
429	C₂×#120	—	2	2	no	—
430	#518	C₂²×C₆₇	1	1	yes	characteristic, complemented
431	#496	C₂²×C₆₇	1	2	yes	complemented
432	#493	C₂²×C₆₇	1	2	yes	complemented
433	#490	C₂²×C₆₇	1	2	yes	complemented
434	#488	C₂²×C₆₇	1	2	yes	complemented
435	#484	C₂²×C₆₇	1	2	yes	complemented
436	#482	C₂²×C₆₇	1	4	yes	complemented
437	#482	C₂²×C₆₇	1	4	yes	complemented
438	#481	C₂²×C₆₇	1	2	yes	complemented
439	#478	C₂²×C₆₇	1	4	yes	complemented
440	#469	C₂²×C₆₇	1	4	yes	complemented
441	#466	C₂²×C₆₇	1	4	yes	complemented
442	#466	C₂²×C₆₇	1	4	yes	complemented
443	#465	C₂²×C₆₇	1	4	yes	complemented
444	#463	C₂²×C₆₇	1	4	yes	complemented
445	#459	C₂²×C₆₇	1	4	yes	complemented
446	#459	C₂²×C₆₇	1	4	yes	complemented
447	#450	C₂²×C₆₇	1	2	yes	complemented
448	#449	C₂²×C₆₇	1	4	yes	complemented
449	#449	C₂²×C₆₇	1	4	yes	complemented
450	#447	C₂²×C₆₇	1	4	yes	complemented
451	#447	C₂²×C₆₇	1	4	yes	complemented
452	#447	C₂²×C₆₇	1	4	yes	complemented
453	#447	C₂²×C₆₇	1	4	yes	complemented
454	#447	C₂²×C₆₇	1	2	yes	complemented
455	#447	C₂²×C₆₇	1	4	yes	complemented
456	#447	C₂²×C₆₇	1	4	yes	complemented
457	#442	C₂²×C₆₇	1	4	yes	complemented
458	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
459	#435	C₂²×C₆₇	1	4	yes	complemented
460	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
461	#433	C₂²×C₆₇	1	2	yes	complemented
462	#418	C₂²×C₆₇	1	2	yes	complemented
463	#416	C₂²×C₆₇	1	2	yes	complemented
464	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
465	#408	C₂²×C₆₇	1	2	yes	complemented
466	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
467	C₂⁵	—	2	1	no	—
468	H(5,𝔽₂)	—	4	4	no	—
469	C₂×#41	—	2	1	no	—
470	C₂×#41	C₂³×C₆₇	1	2	yes	—
471	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
472	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
473	C₂²×D₄	—	2	2	no	—
474	C₂²×D₄	—	2	2	no	—
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	—	2	4	no	—
477	C₂²×D₄	—	2	4	no	—
478	C₂²×D₄	—	2	1	no	—
479	C₂²×D₄	—	2	2	no	—
480	C₂²×D₄	—	4	4	no	—
481	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
482	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
483	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
484	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
485	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
486	C₂²×D₄	C₂³×C₆₇	1	2	yes	complemented
487	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
488	AGL(1,ℤ/8)	—	4	4	no	—
489	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
490	C₂×D₈	—	4	8	no	—
491	C₂×D₈	—	4	4	no	—
492	C₂×D₈	C₂³×C₆₇	1	4	yes	—
493	C₂×D₈	C₂³×C₆₇	1	4	yes	—
494	C₂×D₈	C₂³×C₆₇	1	4	yes	—
495	C₂×D₈	C₂³×C₆₇	1	4	yes	—
496	C₂×D₈	C₂³×C₆₇	1	4	yes	complemented
497	C₂×M₁₆	C₂³×C₆₇	1	2	yes	complemented
498	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
499	C₂²×C₈	C₂³×C₆₇	1	2	yes	complemented
500	#127	—	2	1	no	—
501	#127	—	2	2	no	—
502	#127	C₂³×C₆₇	1	2	yes	—
503	#127	C₂³×C₆₇	1	2	yes	complemented
504	#126	—	2	4	no	—
505	#125	C₂³×C₆₇	1	2	yes	complemented
506	#124	—	2	2	no	—
507	#124	—	2	1	no	—
508	#124	C₂³×C₆₇	1	2	yes	—
509	#123	—	2	1	no	—
510	#123	—	2	4	no	—
511	#123	—	2	4	no	—
512	#123	—	2	4	no	—
513	#123	D₄×C₆₇	1	2	yes	—
514	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
515	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
516	#121	—	2	4	no	—
517	#121	—	2	2	no	—
518	#121	—	2	2	no	—
519	#121	—	2	4	no	—
520	#121	—	2	2	no	—
521	#121	—	2	4	no	—
522	#121	—	2	4	no	—
523	#121	—	2	4	no	—
524	#121	D₄×C₆₇	1	2	yes	—
525	#121	C₂³×C₆₇	1	4	yes	—
526	#121	C₂³×C₆₇	1	4	yes	—
527	#121	C₂³×C₆₇	1	2	yes	—
528	#121	C₂³×C₆₇	1	4	yes	—
529	#121	C₂³×C₆₇	1	4	yes	complemented
530	#120	—	2	1	no	—
531	#120	—	2	2	no	—
532	#120	—	2	4	no	—
533	#120	—	2	2	no	—
534	#120	—	2	2	no	—
535	#120	—	2	2	no	—
536	#120	—	2	4	no	—
537	#120	—	2	4	no	—
538	#120	—	2	4	no	—
539	#120	—	2	4	no	—
540	#120	D₄×C₆₇	1	2	yes	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	2	4	no	—
544	C₄×D₄	C₂³×C₆₇	1	4	yes	—
545	C₄×D₄	C₂³×C₆₇	1	4	yes	—
546	C₄×D₄	C₂³×C₆₇	1	4	yes	complemented
547	#117	C₂³×C₆₇	1	1	yes	characteristic
548	#117	C₂³×C₆₇	1	1	yes	characteristic
549	#117	C₂³×C₆₇	1	2	yes	complemented
550	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
551	C₂×C₂²⋊C₄	—	2	2	no	—
552	C₂×C₂²⋊C₄	—	2	2	no	—
553	C₂×C₂²⋊C₄	—	2	4	no	—
554	#107	C₂³×C₆₇	1	4	yes	complemented
555	#106	C₂³×C₆₇	1	4	yes	complemented
556	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
557	#103	C₂³×C₆₇	1	4	yes	complemented
558	#102	C₂³×C₆₇	1	4	yes	—
559	#102	C₂³×C₆₇	1	4	yes	—
560	#102	C₂³×C₆₇	1	4	yes	—
561	#102	C₂³×C₆₇	1	4	yes	—
562	#102	C₂³×C₆₇	1	4	yes	complemented
563	#102	C₂³×C₆₇	1	4	yes	complemented
564	#102	C₂³×C₆₇	1	4	yes	complemented
565	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
566	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
567	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
568	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	complemented
569	#97	C₂³×C₆₇	1	2	yes	complemented
570	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
571	C₂⁴	—	2	1	no	—
572	C₂⁴	—	2	4	no	—
573	C₂⁴	—	2	2	no	—
574	C₂⁴	—	2	1	no	—
575	C₂⁴	—	2	2	no	—
576	C₂⁴	—	2	2	no	—
577	C₂⁴	—	4	4	no	—
578	C₂⁴	—	8	4	no	—
579	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
580	#41	—	2	4	no	—
581	#41	—	4	2	no	—
582	#41	—	4	2	no	—
583	#41	—	4	2	no	—
584	#41	—	4	4	no	—
585	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
586	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	8	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	2	no	—
608	C₂×D₄	—	4	4	no	—
609	C₂×D₄	—	4	2	no	—
610	C₂×D₄	—	4	2	no	—
611	C₂×D₄	—	4	8	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	8	no	—
615	C₂×D₄	—	8	8	no	—
616	C₂×D₄	—	8	8	no	—
617	C₂×D₄	—	8	4	no	—
618	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
619	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
620	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
621	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
622	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
623	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
624	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
632	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
636	SD₁₆	—	4	4	no	—
637	D₈	—	2	8	no	—
638	D₈	—	2	8	no	—
639	D₈	—	4	4	no	—
640	D₈	—	4	4	no	—
641	D₈	—	4	4	no	—
642	M₁₆	—	4	2	no	—
643	C₂×C₈	—	4	4	no	—
644	C₂×C₈	—	4	2	no	—
645	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
646	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
651	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
652	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
653	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
654	C₂²⋊C₄	—	2	1	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
666	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
667	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
668	C₄²	—	2	1	no	—
669	C₄²	—	2	2	no	—
670	C₄²	C₂⁴×C₆₇	1	2	yes	—
671	C₂³	—	2	4	no	—
672	C₂³	—	2	4	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	4	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	8	no	—
679	C₂³	—	4	4	no	—
680	C₂³	—	4	2	no	—
681	C₂³	—	4	8	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	8	4	no	—
684	C₂³	—	8	2	no	—
685	C₂³	—	8	2	no	—
686	C₂³	—	8	2	no	—
687	C₂³	—	8	2	no	—
688	C₂³	—	8	2	no	—
689	C₂³	—	8	4	no	—
690	C₂³	—	8	4	no	—
691	C₂³	—	8	16	no	—
692	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
693	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
694	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
695	Q₈	—	2	2	no	—
696	Q₈	—	4	1	no	—
697	D₄	—	2	4	no	—
698	D₄	—	2	8	no	—
699	D₄	—	2	2	no	—
700	D₄	—	2	4	no	—
701	D₄	—	2	4	no	—
702	D₄	—	2	4	no	—
703	D₄	—	2	2	no	—
704	D₄	—	4	1	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	8	no	—
707	D₄	—	4	4	no	—
708	D₄	—	4	2	no	—
709	D₄	—	4	4	no	—
710	D₄	—	4	2	no	—
711	D₄	—	4	4	no	—
712	D₄	—	4	8	no	—
713	D₄	—	8	2	no	—
714	D₄	—	8	2	no	—
715	D₄	—	8	4	no	—
716	D₄	—	8	4	no	—
717	D₄	—	8	4	no	—
718	D₄	—	8	4	no	—
719	D₄	—	8	4	no	—
720	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	4	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	8	4	no	—
733	C₂×C₄	—	8	4	no	—
734	C₂×C₄	—	8	2	no	—
735	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
736	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
738	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
739	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
740	C₈	—	2	4	no	—
741	C₈	—	2	4	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	4	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	2	4	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	4	no	—
758	C₂²	—	8	16	no	—
759	C₂²	—	8	4	no	—
760	C₂²	—	8	4	no	—
761	C₂²	—	16	4	no	—
762	C₂²	—	16	4	no	—
763	C₂²	—	16	4	no	—
764	C₂²	#576×C₆₇	1	4	yes	—
765	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
766	C₄	—	2	4	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	2	no	—
769	C₄	—	2	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	4	no	—
772	C₄	—	4	1	no	—
773	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
774	C₂	—	2	4	no	—
775	C₂	—	4	1	no	—
776	C₂	—	4	2	no	—
777	C₂	—	4	4	no	—
778	C₂	—	8	2	no	—
779	C₂	—	8	4	no	—
780	C₂	—	8	1	no	—
781	C₂	C₆₇×#3484	1	1	yes	characteristic
782	C₂	C₂×#576×C₆₇	1	2	yes	—

	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 ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3537	C₂	semidirect
2. C₆₇×#3484	C₂	semidirect
3. C₆₇×#3318	C₂	semidirect
4. C₆₇×#3297	C₂	semidirect
5. D₄×D₈×C₆₇	C₂	semidirect
6. C₆₇×#3264	C₂	semidirect
7. C₆₇×#3220	C₂	semidirect
8. C₆₇×#3199	C₂	semidirect
9. C₆₇×#3188	C₂	semidirect
10. C₆₇×#3122	C₂	semidirect
11. C₆₇×#3008	C₂	semidirect
12. C₂×#447×C₆₇	C₂	semidirect
13. C₆₇×#2977	C₂	semidirect
14. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
15. C₂³×D₄×C₆₇	C₂²	semidirect
16. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
17. C₂²×D₈×C₆₇	C₂²	semidirect
18. C₂²×D₈×C₆₇	C₂²	semidirect
20. #553×C₆₇	C₂²	semidirect
22. #546×C₆₇	C₂²	semidirect
25. D₄²×C₆₇	C₂²	semidirect
26. D₄²×C₆₇	C₂²	semidirect
27. #540×C₆₇	C₂²	semidirect
29. #535×C₆₇	C₂²	semidirect
30. #535×C₆₇	C₂²	semidirect
31. #535×C₆₇	C₂²	semidirect
35. #525×C₆₇	C₂²	semidirect
36. C₂×#121×C₆₇	C₂²	semidirect
38. #518×C₆₇	C₂²	semidirect
39. #496×C₆₇	C₂²	semidirect
40. #493×C₆₇	C₂²	semidirect
41. #490×C₆₇	C₂²	semidirect
42. #488×C₆₇	C₂²	semidirect
43. #484×C₆₇	C₂²	semidirect
44. #482×C₆₇	C₂²	semidirect
45. #482×C₆₇	C₂²	semidirect
46. #481×C₆₇	C₂²	semidirect
47. #478×C₆₇	C₂²	semidirect
48. #469×C₆₇	C₂²	semidirect
49. #466×C₆₇	C₂²	semidirect
50. #466×C₆₇	C₂²	semidirect
51. #465×C₆₇	C₂²	semidirect
52. #463×C₆₇	C₂²	semidirect
53. #459×C₆₇	C₂²	semidirect
54. #459×C₆₇	C₂²	semidirect
55. #450×C₆₇	C₂²	semidirect
56. #449×C₆₇	C₂²	semidirect
57. #449×C₆₇	C₂²	semidirect
58. #447×C₆₇	C₂²	semidirect
59. #447×C₆₇	C₂²	semidirect
60. #447×C₆₇	C₂²	semidirect
61. #447×C₆₇	C₂²	semidirect
62. #447×C₆₇	C₂²	semidirect
63. #447×C₆₇	C₂²	semidirect
64. #447×C₆₇	C₂²	semidirect
65. #442×C₆₇	C₂²	semidirect
66. C₄×D₈×C₆₇	C₂²	semidirect
67. #435×C₆₇	C₂²	semidirect
68. C₈×D₄×C₆₇	C₂²	semidirect
69. #433×C₆₇	C₂²	semidirect
70. #418×C₆₇	C₂²	semidirect
71. #416×C₆₇	C₂²	semidirect
72. C₂×#102×C₆₇	C₂²	semidirect
73. #408×C₆₇	C₂²	semidirect
74. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
94. C₂²×D₄×C₆₇	C₂³	semidirect
97. C₂×SD₁₆×C₆₇	C₂³	semidirect
104. C₂×D₈×C₆₇	C₂³	semidirect
105. C₂×M₁₆×C₆₇	C₂³	semidirect
107. C₂²×C₈×C₆₇	C₂³	semidirect
111. #127×C₆₇	C₂³	semidirect
113. #125×C₆₇	C₂³	semidirect
137. #121×C₆₇	C₂³	semidirect
154. C₄×D₄×C₆₇	C₂³	semidirect
157. #117×C₆₇	C₂³	semidirect
162. #107×C₆₇	C₂³	semidirect
163. #106×C₆₇	C₂³	semidirect
164. C₄⋊C₈×C₆₇	C₂³	semidirect
165. #103×C₆₇	C₂³	semidirect
170. #102×C₆₇	C₂³	semidirect
171. #102×C₆₇	C₂³	semidirect
172. #102×C₆₇	C₂³	semidirect
176. C₂²⋊C₈×C₆₇	C₂³	semidirect
177. #97×C₆₇	C₂³	semidirect
178. C₄×C₈×C₆₇	C₂³	semidirect
382. #61630	C₆₇	direct (N × H)
392. #3537	C₂×C₆₇	semidirect
393. #3484	C₂×C₆₇	semidirect
394. #3318	C₂×C₆₇	semidirect
395. #3297	C₂×C₆₇	semidirect
396. D₄×D₈	C₂×C₆₇	semidirect
397. #3264	C₂×C₆₇	semidirect
398. #3220	C₂×C₆₇	semidirect
399. #3199	C₂×C₆₇	semidirect
400. #3188	C₂×C₆₇	semidirect
401. #3122	C₂×C₆₇	semidirect
402. #3008	C₂×C₆₇	semidirect
403. C₂×#447	C₂×C₆₇	semidirect
404. #2977	C₂×C₆₇	semidirect
405. C₆₇	#61630	direct (N × H)
406. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
407. C₂³×D₄	C₂²×C₆₇	semidirect
408. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
409. C₂²×D₈	C₂²×C₆₇	semidirect
410. C₂²×D₈	C₂²×C₆₇	semidirect
412. #553	C₂²×C₆₇	semidirect
414. #546	C₂²×C₆₇	semidirect
417. D₄²	C₂²×C₆₇	semidirect
418. D₄²	C₂²×C₆₇	semidirect
419. #540	C₂²×C₆₇	semidirect
421. #535	C₂²×C₆₇	semidirect
422. #535	C₂²×C₆₇	semidirect
423. #535	C₂²×C₆₇	semidirect
427. #525	C₂²×C₆₇	semidirect
428. C₂×#121	C₂²×C₆₇	semidirect
430. #518	C₂²×C₆₇	semidirect
431. #496	C₂²×C₆₇	semidirect
432. #493	C₂²×C₆₇	semidirect
433. #490	C₂²×C₆₇	semidirect
434. #488	C₂²×C₆₇	semidirect
435. #484	C₂²×C₆₇	semidirect
436. #482	C₂²×C₆₇	semidirect
437. #482	C₂²×C₆₇	semidirect
438. #481	C₂²×C₆₇	semidirect
439. #478	C₂²×C₆₇	semidirect
440. #469	C₂²×C₆₇	semidirect
441. #466	C₂²×C₆₇	semidirect
442. #466	C₂²×C₆₇	semidirect
443. #465	C₂²×C₆₇	semidirect
444. #463	C₂²×C₆₇	semidirect
445. #459	C₂²×C₆₇	semidirect
446. #459	C₂²×C₆₇	semidirect
447. #450	C₂²×C₆₇	semidirect
448. #449	C₂²×C₆₇	semidirect
449. #449	C₂²×C₆₇	semidirect
450. #447	C₂²×C₆₇	semidirect
451. #447	C₂²×C₆₇	semidirect
452. #447	C₂²×C₆₇	semidirect
453. #447	C₂²×C₆₇	semidirect
454. #447	C₂²×C₆₇	semidirect
455. #447	C₂²×C₆₇	semidirect
456. #447	C₂²×C₆₇	semidirect
457. #442	C₂²×C₆₇	semidirect
458. C₄×D₈	C₂²×C₆₇	semidirect
459. #435	C₂²×C₆₇	semidirect
460. C₈×D₄	C₂²×C₆₇	semidirect
461. #433	C₂²×C₆₇	semidirect
462. #418	C₂²×C₆₇	semidirect
463. #416	C₂²×C₆₇	semidirect
464. C₂×#102	C₂²×C₆₇	semidirect
465. #408	C₂²×C₆₇	semidirect
466. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
486. C₂²×D₄	C₂³×C₆₇	semidirect
489. C₂×SD₁₆	C₂³×C₆₇	semidirect
496. C₂×D₈	C₂³×C₆₇	semidirect
497. C₂×M₁₆	C₂³×C₆₇	semidirect
499. C₂²×C₈	C₂³×C₆₇	semidirect
503. #127	C₂³×C₆₇	semidirect
505. #125	C₂³×C₆₇	semidirect
529. #121	C₂³×C₆₇	semidirect
546. C₄×D₄	C₂³×C₆₇	semidirect
549. #117	C₂³×C₆₇	semidirect
554. #107	C₂³×C₆₇	semidirect
555. #106	C₂³×C₆₇	semidirect
556. C₄⋊C₈	C₂³×C₆₇	semidirect
557. #103	C₂³×C₆₇	semidirect
562. #102	C₂³×C₆₇	semidirect
563. #102	C₂³×C₆₇	semidirect
564. #102	C₂³×C₆₇	semidirect
568. C₂²⋊C₈	C₂³×C₆₇	semidirect
569. #97	C₂³×C₆₇	semidirect
570. C₄×C₈	C₂³×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3537	2
C₆₇×#3484	2
C₆₇×#3318	2
C₆₇×#3297	2
D₄×D₈×C₆₇	2
C₆₇×#3264	2
C₆₇×#3220	2
C₆₇×#3199	2
C₆₇×#3188	2
C₆₇×#3122	2
C₆₇×#3008	2
C₂×#447×C₆₇	2
C₆₇×#2977	2
#61630	67

Subgroups — C67×#61630 #30740881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61630 #30740881