Subgroups — C₆₇×#61651 #30740902

Order 17152.

2158 conjugacy classes of subgroups.

The subgroup lattice has 758 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×#3487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3326	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3309	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3274	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3265	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×#3194	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3126	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3010	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3006	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2978	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
15	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
16	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
17	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
18	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
19	#560×C₆₇	—	2	2	no	—
20	#553×C₆₇	C₂²	1	4	yes	complemented
21	#550×C₆₇	—	2	2	no	—
22	#550×C₆₇	C₂²	1	4	yes	complemented
23	#548×C₆₇	—	2	2	no	—
24	#548×C₆₇	C₂²	1	4	yes	complemented
25	D₄²×C₆₇	—	2	2	no	—
26	D₄²×C₆₇	C₂²	1	4	yes	complemented
27	#540×C₆₇	C₂²	1	2	yes	—
28	#538×C₆₇	—	2	2	no	—
29	#535×C₆₇	—	2	2	no	—
30	#535×C₆₇	C₂²	1	2	yes	—
31	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#534×C₆₇	—	2	2	no	—
34	#525×C₆₇	—	2	2	no	—
35	#525×C₆₇	C₂²	1	1	yes	characteristic
36	#525×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×#121×C₆₇	C₂²	1	2	yes	—
38	#519×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	#483×C₆₇	C₂²	1	2	yes	complemented
44	#482×C₆₇	C₂²	1	4	yes	complemented
45	#482×C₆₇	C₂²	1	4	yes	complemented
46	#480×C₆₇	C₂²	1	2	yes	complemented
47	#479×C₆₇	C₂²	1	4	yes	complemented
48	#469×C₆₇	C₂²	1	4	yes	complemented
49	#469×C₆₇	C₂²	1	4	yes	complemented
50	#468×C₆₇	C₂²	1	4	yes	complemented
51	#466×C₆₇	C₂²	1	4	yes	complemented
52	#463×C₆₇	C₂²	1	4	yes	complemented
53	#460×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	#449×C₆₇	C₂²	1	4	yes	complemented
59	#449×C₆₇	C₂²	1	4	yes	complemented
60	#448×C₆₇	C₂²	1	4	yes	complemented
61	#448×C₆₇	C₂²	1	4	yes	complemented
62	#447×C₆₇	C₂²	1	4	yes	complemented
63	#447×C₆₇	C₂²	1	2	yes	complemented
64	#447×C₆₇	C₂²	1	4	yes	complemented
65	#440×C₆₇	C₂²	1	4	yes	complemented
66	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
67	#436×C₆₇	C₂²	1	4	yes	complemented
68	#435×C₆₇	C₂²	1	4	yes	complemented
69	#433×C₆₇	C₂²	1	2	yes	complemented
70	#419×C₆₇	C₂²	1	2	yes	complemented
71	#417×C₆₇	C₂²	1	4	yes	complemented
72	#416×C₆₇	C₂²	1	2	yes	complemented
73	#408×C₆₇	C₂²	1	2	yes	complemented
74	#407×C₆₇	C₂²	1	2	yes	complemented
75	2₋¹⁺⁴×C₆₇	—	4	4	no	—
76	C₂×#41×C₆₇	—	2	2	no	—
77	C₂×#41×C₆₇	—	2	1	no	—
78	C₂×#41×C₆₇	—	2	2	no	—
79	C₂×#41×C₆₇	—	4	4	no	—
80	C₂×#41×C₆₇	C₂³	1	4	yes	—
81	C₂×#41×C₆₇	C₂³	1	2	yes	—
82	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
83	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₆₇	—	2	1	no	—
85	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
87	C₂²×D₄×C₆₇	—	2	1	no	—
88	C₂²×D₄×C₆₇	—	2	2	no	—
89	C₂²×D₄×C₆₇	—	2	4	no	—
90	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
91	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
92	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₆₇	—	2	1	no	—
94	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
95	AGL(1,ℤ/8)×C₆₇	—	4	8	no	—
96	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
97	C₂×SD₁₆×C₆₇	—	4	4	no	—
98	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×SD₁₆×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×M₁₆×C₆₇	C₂³	1	4	yes	—
105	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
106	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
107	#127×C₆₇	—	2	4	no	—
108	#127×C₆₇	—	2	2	no	—
109	#127×C₆₇	—	2	1	no	—
110	#127×C₆₇	C₂³	1	2	yes	—
111	#127×C₆₇	C₂³	1	2	yes	—
112	#126×C₆₇	—	2	4	no	—
113	#125×C₆₇	C₂³	1	2	yes	—
114	#124×C₆₇	—	2	2	no	—
115	#124×C₆₇	—	2	1	no	—
116	#124×C₆₇	—	2	4	no	—
117	#124×C₆₇	C₂³	1	2	yes	—
118	#123×C₆₇	—	2	1	no	—
119	#123×C₆₇	—	2	4	no	—
120	#123×C₆₇	—	2	4	no	—
121	#123×C₆₇	D₄	1	2	yes	—
122	C₂²⋊Q₈×C₆₇	—	2	4	no	—
123	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
124	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
125	#121×C₆₇	—	2	4	no	—
126	#121×C₆₇	—	2	4	no	—
127	#121×C₆₇	—	2	2	no	—
128	#121×C₆₇	—	2	2	no	—
129	#121×C₆₇	—	2	2	no	—
130	#121×C₆₇	—	2	4	no	—
131	#121×C₆₇	—	2	4	no	—
132	#121×C₆₇	—	2	4	no	—
133	#121×C₆₇	—	2	4	no	—
134	#121×C₆₇	D₄	1	2	yes	—
135	#121×C₆₇	C₂³	1	4	yes	—
136	#121×C₆₇	C₂³	1	4	yes	—
137	#121×C₆₇	C₂³	1	4	yes	—
138	#121×C₆₇	C₂³	1	4	yes	—
139	#121×C₆₇	C₂³	1	2	yes	—
140	#120×C₆₇	—	2	1	no	—
141	#120×C₆₇	—	2	2	no	—
142	#120×C₆₇	—	2	2	no	—
143	#120×C₆₇	—	2	2	no	—
144	#120×C₆₇	—	2	2	no	—
145	#120×C₆₇	—	2	4	no	—
146	#120×C₆₇	—	2	4	no	—
147	#120×C₆₇	D₄	1	2	yes	—
148	C₄×Q₈×C₆₇	—	2	2	no	—
149	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
150	C₄×D₄×C₆₇	—	2	2	no	—
151	C₄×D₄×C₆₇	—	2	4	no	—
152	C₄×D₄×C₆₇	—	2	4	no	—
153	C₄×D₄×C₆₇	—	2	4	no	—
154	C₄×D₄×C₆₇	C₂³	1	4	yes	—
155	C₄×D₄×C₆₇	C₂³	1	4	yes	—
156	#117×C₆₇	—	2	2	no	—
157	#117×C₆₇	C₂³	1	1	yes	characteristic
158	#117×C₆₇	C₂³	1	2	yes	—
159	#117×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
162	#107×C₆₇	C₂³	1	4	yes	—
163	#106×C₆₇	C₂³	1	4	yes	—
164	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
165	#103×C₆₇	C₂³	1	4	yes	—
166	#103×C₆₇	C₂³	1	4	yes	—
167	#103×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	—
171	#102×C₆₇	C₂³	1	4	yes	—
172	#102×C₆₇	C₂³	1	4	yes	—
173	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
174	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
175	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
176	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
177	#97×C₆₇	C₂³	1	2	yes	—
178	C₄×C₈×C₆₇	C₂³	1	2	yes	—
179	C₂⁴×C₆₇	—	2	2	no	—
180	C₂⁴×C₆₇	—	2	1	no	—
181	C₂⁴×C₆₇	—	2	2	no	—
182	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
183	#41×C₆₇	—	2	8	no	—
184	#41×C₆₇	—	2	4	no	—
185	#41×C₆₇	—	4	2	no	—
186	#41×C₆₇	—	4	4	no	—
187	#41×C₆₇	—	4	2	no	—
188	#41×C₆₇	—	4	2	no	—
189	#41×C₆₇	—	4	8	no	—
190	#41×C₆₇	—	4	8	no	—
191	#41×C₆₇	—	4	4	no	—
192	C₂×Q₈×C₆₇	—	2	4	no	—
193	C₂×Q₈×C₆₇	—	2	1	no	—
194	C₂×Q₈×C₆₇	—	2	2	no	—
195	C₂×Q₈×C₆₇	—	2	4	no	—
196	C₂×Q₈×C₆₇	—	4	2	no	—
197	C₂×Q₈×C₆₇	—	4	4	no	—
198	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
199	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
200	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
201	C₂×D₄×C₆₇	—	2	4	no	—
202	C₂×D₄×C₆₇	—	2	1	no	—
203	C₂×D₄×C₆₇	—	2	4	no	—
204	C₂×D₄×C₆₇	—	2	2	no	—
205	C₂×D₄×C₆₇	—	2	4	no	—
206	C₂×D₄×C₆₇	—	2	2	no	—
207	C₂×D₄×C₆₇	—	2	4	no	—
208	C₂×D₄×C₆₇	—	2	4	no	—
209	C₂×D₄×C₆₇	—	2	1	no	—
210	C₂×D₄×C₆₇	—	2	4	no	—
211	C₂×D₄×C₆₇	—	2	2	no	—
212	C₂×D₄×C₆₇	—	2	4	no	—
213	C₂×D₄×C₆₇	—	2	2	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	4	no	—
219	C₂×D₄×C₆₇	—	8	8	no	—
220	C₂×D₄×C₆₇	—	8	4	no	—
221	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
222	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
223	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
224	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
225	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
226	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₆₇	—	2	1	no	—
228	C₂²×C₄×C₆₇	—	2	2	no	—
229	C₂²×C₄×C₆₇	—	2	2	no	—
230	C₂²×C₄×C₆₇	—	2	2	no	—
231	C₂²×C₄×C₆₇	—	2	1	no	—
232	C₂²×C₄×C₆₇	—	2	4	no	—
233	C₂²×C₄×C₆₇	—	2	4	no	—
234	C₂²×C₄×C₆₇	—	4	2	no	—
235	C₂²×C₄×C₆₇	—	4	4	no	—
236	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
237	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
241	SD₁₆×C₆₇	—	2	8	no	—
242	SD₁₆×C₆₇	—	2	8	no	—
243	SD₁₆×C₆₇	—	4	4	no	—
244	D₈×C₆₇	—	4	4	no	—
245	D₈×C₆₇	—	4	4	no	—
246	D₈×C₆₇	—	4	4	no	—
247	M₁₆×C₆₇	—	4	4	no	—
248	M₁₆×C₆₇	—	4	2	no	—
249	C₂×C₈×C₆₇	—	4	2	no	—
250	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
251	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
252	C₄⋊C₄×C₆₇	—	2	2	no	—
253	C₄⋊C₄×C₆₇	—	2	4	no	—
254	C₄⋊C₄×C₆₇	—	2	2	no	—
255	C₄⋊C₄×C₆₇	—	2	4	no	—
256	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
258	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
260	C₂²⋊C₄×C₆₇	—	2	1	no	—
261	C₂²⋊C₄×C₆₇	—	2	2	no	—
262	C₂²⋊C₄×C₆₇	—	2	2	no	—
263	C₂²⋊C₄×C₆₇	—	2	4	no	—
264	C₂²⋊C₄×C₆₇	—	2	4	no	—
265	C₂²⋊C₄×C₆₇	—	2	2	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	C₂×D₄	1	2	yes	—
271	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
272	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
273	C₄²×C₆₇	—	2	4	no	—
274	C₄²×C₆₇	—	2	1	no	—
275	C₄²×C₆₇	—	2	2	no	—
276	C₄²×C₆₇	C₂⁴	1	2	yes	—
277	C₂³×C₆₇	—	2	2	no	—
278	C₂³×C₆₇	—	2	4	no	—
279	C₂³×C₆₇	—	2	1	no	—
280	C₂³×C₆₇	—	4	1	no	—
281	C₂³×C₆₇	—	4	2	no	—
282	C₂³×C₆₇	—	4	2	no	—
283	C₂³×C₆₇	—	4	4	no	—
284	C₂³×C₆₇	—	8	2	no	—
285	C₂³×C₆₇	—	8	2	no	—
286	C₂³×C₆₇	—	8	2	no	—
287	C₂³×C₆₇	—	8	2	no	—
288	C₂³×C₆₇	—	8	4	no	—
289	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
290	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
291	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
292	Q₈×C₆₇	—	2	4	no	—
293	Q₈×C₆₇	—	2	2	no	—
294	Q₈×C₆₇	—	2	2	no	—
295	Q₈×C₆₇	—	4	1	no	—
296	Q₈×C₆₇	—	4	4	no	—
297	Q₈×C₆₇	H(5,𝔽₂)	1	4	yes	—
298	D₄×C₆₇	—	2	4	no	—
299	D₄×C₆₇	—	2	4	no	—
300	D₄×C₆₇	—	2	2	no	—
301	D₄×C₆₇	—	2	4	no	—
302	D₄×C₆₇	—	4	4	no	—
303	D₄×C₆₇	—	4	1	no	—
304	D₄×C₆₇	—	4	2	no	—
305	D₄×C₆₇	—	4	8	no	—
306	D₄×C₆₇	—	4	4	no	—
307	D₄×C₆₇	—	4	2	no	—
308	D₄×C₆₇	—	4	8	no	—
309	D₄×C₆₇	—	4	2	no	—
310	D₄×C₆₇	—	8	4	no	—
311	D₄×C₆₇	—	8	2	no	—
312	D₄×C₆₇	—	8	2	no	—
313	D₄×C₆₇	—	8	4	no	—
314	D₄×C₆₇	—	8	2	no	—
315	D₄×C₆₇	—	8	4	no	—
316	D₄×C₆₇	—	8	4	no	—
317	D₄×C₆₇	—	8	4	no	—
318	C₂×C₄×C₆₇	—	2	4	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	4	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	4	no	—
326	C₂×C₄×C₆₇	—	2	1	no	—
327	C₂×C₄×C₆₇	—	4	1	no	—
328	C₂×C₄×C₆₇	—	4	2	no	—
329	C₂×C₄×C₆₇	—	4	8	no	—
330	C₂×C₄×C₆₇	—	4	4	no	—
331	C₂×C₄×C₆₇	—	4	4	no	—
332	C₂×C₄×C₆₇	—	4	2	no	—
333	C₂×C₄×C₆₇	—	8	4	no	—
334	C₂×C₄×C₆₇	—	8	2	no	—
335	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
336	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
340	C₈×C₆₇	—	2	4	no	—
341	C₈×C₆₇	—	2	4	no	—
342	C₂²×C₆₇	—	2	2	no	—
343	C₂²×C₆₇	—	2	2	no	—
344	C₂²×C₆₇	—	2	4	no	—
345	C₂²×C₆₇	—	2	2	no	—
346	C₂²×C₆₇	—	2	1	no	—
347	C₂²×C₆₇	—	2	2	no	—
348	C₂²×C₆₇	—	2	2	no	—
349	C₂²×C₆₇	—	4	4	no	—
350	C₂²×C₆₇	—	4	4	no	—
351	C₂²×C₆₇	—	4	2	no	—
352	C₂²×C₆₇	—	4	4	no	—
353	C₂²×C₆₇	—	4	1	no	—
354	C₂²×C₆₇	—	4	2	no	—
355	C₂²×C₆₇	—	4	4	no	—
356	C₂²×C₆₇	—	8	2	no	—
357	C₂²×C₆₇	—	8	4	no	—
358	C₂²×C₆₇	—	16	4	no	—
359	C₂²×C₆₇	—	16	4	no	—
360	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
361	C₄×C₆₇	—	2	4	no	—
362	C₄×C₆₇	—	2	4	no	—
363	C₄×C₆₇	—	2	2	no	—
364	C₄×C₆₇	—	2	1	no	—
365	C₄×C₆₇	—	2	2	no	—
366	C₄×C₆₇	—	4	4	no	—
367	C₄×C₆₇	—	4	2	no	—
368	C₄×C₆₇	—	4	1	no	—
369	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
370	#61651	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
371	C₂×C₆₇	—	4	1	no	—
372	C₂×C₆₇	—	4	2	no	—
373	C₂×C₆₇	—	4	2	no	—
374	C₂×C₆₇	—	8	1	no	—
375	C₂×C₆₇	—	8	2	no	—
376	C₂×C₆₇	—	8	4	no	—
377	C₂×C₆₇	#3484	1	1	yes	characteristic
378	C₂×C₆₇	#3585	1	2	yes	—
379	#3537	C₂×C₆₇	1	1	yes	characteristic, complemented
380	#3487	C₂×C₆₇	1	1	yes	characteristic, complemented
381	#3326	C₂×C₆₇	1	4	yes	complemented
382	#3309	C₂×C₆₇	1	4	yes	complemented
383	#3274	C₂×C₆₇	1	4	yes	complemented
384	#3265	C₂×C₆₇	1	4	yes	complemented
385	#3220	C₂×C₆₇	1	2	yes	complemented
386	#3199	C₂×C₆₇	1	2	yes	complemented
387	#3194	C₂×C₆₇	1	2	yes	complemented
388	#3126	C₂×C₆₇	1	2	yes	complemented
389	#3010	C₂×C₆₇	1	2	yes	complemented
390	#3006	C₂×C₆₇	1	2	yes	complemented
391	#2978	C₂×C₆₇	1	1	yes	characteristic, complemented
392	C₆₇	#61651	1	1	yes	characteristic, direct product factor, Sylow
393	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
394	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
395	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
396	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
397	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
398	#560	—	2	2	no	—
399	#553	C₂²×C₆₇	1	4	yes	complemented
400	#550	—	2	2	no	—
401	#550	C₂²×C₆₇	1	4	yes	complemented
402	#548	—	2	2	no	—
403	#548	C₂²×C₆₇	1	4	yes	complemented
404	D₄²	—	2	2	no	—
405	D₄²	C₂²×C₆₇	1	4	yes	complemented
406	#540	C₂²×C₆₇	1	2	yes	—
407	#538	—	2	2	no	—
408	#535	—	2	2	no	—
409	#535	C₂²×C₆₇	1	2	yes	—
410	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
411	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
412	#534	—	2	2	no	—
413	#525	—	2	2	no	—
414	#525	C₂²×C₆₇	1	1	yes	characteristic
415	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
416	C₂×#121	C₂²×C₆₇	1	2	yes	—
417	#519	C₂²×C₆₇	1	1	yes	characteristic, complemented
418	#496	C₂²×C₆₇	1	2	yes	complemented
419	#493	C₂²×C₆₇	1	2	yes	complemented
420	#490	C₂²×C₆₇	1	2	yes	complemented
421	#488	C₂²×C₆₇	1	2	yes	complemented
422	#483	C₂²×C₆₇	1	2	yes	complemented
423	#482	C₂²×C₆₇	1	4	yes	complemented
424	#482	C₂²×C₆₇	1	4	yes	complemented
425	#480	C₂²×C₆₇	1	2	yes	complemented
426	#479	C₂²×C₆₇	1	4	yes	complemented
427	#469	C₂²×C₆₇	1	4	yes	complemented
428	#469	C₂²×C₆₇	1	4	yes	complemented
429	#468	C₂²×C₆₇	1	4	yes	complemented
430	#466	C₂²×C₆₇	1	4	yes	complemented
431	#463	C₂²×C₆₇	1	4	yes	complemented
432	#460	C₂²×C₆₇	1	4	yes	complemented
433	#459	C₂²×C₆₇	1	4	yes	complemented
434	#450	C₂²×C₆₇	1	2	yes	complemented
435	#449	C₂²×C₆₇	1	4	yes	complemented
436	#449	C₂²×C₆₇	1	4	yes	complemented
437	#449	C₂²×C₆₇	1	4	yes	complemented
438	#449	C₂²×C₆₇	1	4	yes	complemented
439	#448	C₂²×C₆₇	1	4	yes	complemented
440	#448	C₂²×C₆₇	1	4	yes	complemented
441	#447	C₂²×C₆₇	1	2	yes	complemented
442	#447	C₂²×C₆₇	1	4	yes	complemented
443	#447	C₂²×C₆₇	1	4	yes	complemented
444	#440	C₂²×C₆₇	1	4	yes	complemented
445	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
446	#436	C₂²×C₆₇	1	4	yes	complemented
447	#435	C₂²×C₆₇	1	4	yes	complemented
448	#433	C₂²×C₆₇	1	2	yes	complemented
449	#419	C₂²×C₆₇	1	2	yes	complemented
450	#417	C₂²×C₆₇	1	4	yes	complemented
451	#416	C₂²×C₆₇	1	2	yes	complemented
452	#408	C₂²×C₆₇	1	2	yes	complemented
453	#407	C₂²×C₆₇	1	2	yes	complemented
454	2₋¹⁺⁴	—	4	4	no	—
455	C₂×#41	—	2	2	no	—
456	C₂×#41	—	2	1	no	—
457	C₂×#41	—	2	2	no	—
458	C₂×#41	—	4	4	no	—
459	C₂×#41	C₂³×C₆₇	1	4	yes	—
460	C₂×#41	C₂³×C₆₇	1	2	yes	—
461	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
462	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
463	C₂²×Q₈	—	2	1	no	—
464	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
465	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	2	no	—
468	C₂²×D₄	—	2	4	no	—
469	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
470	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
471	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
474	AGL(1,ℤ/8)	—	4	8	no	—
475	AGL(1,ℤ/8)	—	4	4	no	—
476	C₂×SD₁₆	—	4	4	no	—
477	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
478	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
479	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
480	C₂×D₈	C₂³×C₆₇	1	4	yes	—
481	C₂×D₈	C₂³×C₆₇	1	4	yes	—
482	C₂×D₈	C₂³×C₆₇	1	4	yes	—
483	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
484	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
485	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
486	#127	—	2	4	no	—
487	#127	—	2	2	no	—
488	#127	—	2	1	no	—
489	#127	C₂³×C₆₇	1	2	yes	—
490	#127	C₂³×C₆₇	1	2	yes	—
491	#126	—	2	4	no	—
492	#125	C₂³×C₆₇	1	2	yes	—
493	#124	—	2	2	no	—
494	#124	—	2	1	no	—
495	#124	—	2	4	no	—
496	#124	C₂³×C₆₇	1	2	yes	—
497	#123	—	2	1	no	—
498	#123	—	2	4	no	—
499	#123	—	2	4	no	—
500	#123	D₄×C₆₇	1	2	yes	—
501	C₂²⋊Q₈	—	2	4	no	—
502	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
503	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
504	#121	—	2	4	no	—
505	#121	—	2	4	no	—
506	#121	—	2	2	no	—
507	#121	—	2	2	no	—
508	#121	—	2	2	no	—
509	#121	—	2	4	no	—
510	#121	—	2	4	no	—
511	#121	—	2	4	no	—
512	#121	—	2	4	no	—
513	#121	D₄×C₆₇	1	2	yes	—
514	#121	C₂³×C₆₇	1	4	yes	—
515	#121	C₂³×C₆₇	1	4	yes	—
516	#121	C₂³×C₆₇	1	2	yes	—
517	#121	C₂³×C₆₇	1	4	yes	—
518	#121	C₂³×C₆₇	1	4	yes	—
519	#120	—	2	1	no	—
520	#120	—	2	2	no	—
521	#120	—	2	2	no	—
522	#120	—	2	2	no	—
523	#120	—	2	2	no	—
524	#120	—	2	4	no	—
525	#120	—	2	4	no	—
526	#120	D₄×C₆₇	1	2	yes	—
527	C₄×Q₈	—	2	2	no	—
528	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	4	no	—
531	C₄×D₄	—	2	4	no	—
532	C₄×D₄	—	2	4	no	—
533	C₄×D₄	C₂³×C₆₇	1	4	yes	—
534	C₄×D₄	C₂³×C₆₇	1	4	yes	—
535	#117	—	2	2	no	—
536	#117	C₂³×C₆₇	1	1	yes	characteristic
537	#117	C₂³×C₆₇	1	2	yes	—
538	#117	C₂³×C₆₇	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
540	C₂×C₂²⋊C₄	—	2	2	no	—
541	#107	C₂³×C₆₇	1	4	yes	—
542	#106	C₂³×C₆₇	1	4	yes	—
543	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
544	#103	C₂³×C₆₇	1	4	yes	—
545	#103	C₂³×C₆₇	1	4	yes	—
546	#103	C₂³×C₆₇	1	4	yes	—
547	#102	C₂³×C₆₇	1	4	yes	—
548	#102	C₂³×C₆₇	1	4	yes	—
549	#102	C₂³×C₆₇	1	4	yes	—
550	#102	C₂³×C₆₇	1	4	yes	—
551	#102	C₂³×C₆₇	1	4	yes	—
552	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
553	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
554	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
555	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
556	#97	C₂³×C₆₇	1	2	yes	—
557	C₄×C₈	C₂³×C₆₇	1	2	yes	—
558	C₂⁴	—	2	2	no	—
559	C₂⁴	—	2	1	no	—
560	C₂⁴	—	2	2	no	—
561	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
562	#41	—	2	8	no	—
563	#41	—	2	4	no	—
564	#41	—	4	2	no	—
565	#41	—	4	4	no	—
566	#41	—	4	2	no	—
567	#41	—	4	2	no	—
568	#41	—	4	8	no	—
569	#41	—	4	8	no	—
570	#41	—	4	4	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	4	2	no	—
576	C₂×Q₈	—	4	4	no	—
577	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
578	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
579	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂×D₄	—	4	4	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	—	8	8	no	—
599	C₂×D₄	—	8	4	no	—
600	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
601	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
602	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
603	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
604	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
605	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	4	2	no	—
614	C₂²×C₄	—	4	4	no	—
615	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
616	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
620	SD₁₆	—	2	8	no	—
621	SD₁₆	—	2	8	no	—
622	SD₁₆	—	4	4	no	—
623	D₈	—	4	4	no	—
624	D₈	—	4	4	no	—
625	D₈	—	4	4	no	—
626	M₁₆	—	4	4	no	—
627	M₁₆	—	4	2	no	—
628	C₂×C₈	—	4	2	no	—
629	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
630	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
636	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
637	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
650	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
651	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
652	C₄²	—	2	4	no	—
653	C₄²	—	2	1	no	—
654	C₄²	—	2	2	no	—
655	C₄²	C₂⁴×C₆₇	1	2	yes	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	4	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	2	no	—
661	C₂³	—	4	2	no	—
662	C₂³	—	4	4	no	—
663	C₂³	—	8	2	no	—
664	C₂³	—	8	2	no	—
665	C₂³	—	8	2	no	—
666	C₂³	—	8	2	no	—
667	C₂³	—	8	4	no	—
668	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
669	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
670	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
671	Q₈	—	2	4	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	4	1	no	—
675	Q₈	—	4	4	no	—
676	Q₈	H(5,𝔽₂)×C₆₇	1	4	yes	—
677	D₄	—	2	4	no	—
678	D₄	—	2	4	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	4	no	—
681	D₄	—	4	4	no	—
682	D₄	—	4	1	no	—
683	D₄	—	4	2	no	—
684	D₄	—	4	8	no	—
685	D₄	—	4	4	no	—
686	D₄	—	4	2	no	—
687	D₄	—	4	8	no	—
688	D₄	—	4	2	no	—
689	D₄	—	8	2	no	—
690	D₄	—	8	2	no	—
691	D₄	—	8	4	no	—
692	D₄	—	8	4	no	—
693	D₄	—	8	4	no	—
694	D₄	—	8	4	no	—
695	D₄	—	8	2	no	—
696	D₄	—	8	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	2	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	2	no	—
714	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
715	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
718	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
719	C₈	—	2	4	no	—
720	C₈	—	2	4	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	4	4	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	8	2	no	—
736	C₂²	—	8	4	no	—
737	C₂²	—	16	4	no	—
738	C₂²	—	16	4	no	—
739	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
740	C₄	—	2	4	no	—
741	C₄	—	2	4	no	—
742	C₄	—	2	2	no	—
743	C₄	—	2	1	no	—
744	C₄	—	2	2	no	—
745	C₄	—	4	4	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	1	no	—
748	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
749	C₂	—	4	1	no	—
750	C₂	—	4	2	no	—
751	C₂	—	4	2	no	—
752	C₂	—	8	2	no	—
753	C₂	—	8	4	no	—
754	C₂	—	8	1	no	—
755	C₂	C₆₇×#3484	1	1	yes	characteristic
756	C₂	C₆₇×#3585	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×#3487	C₂	semidirect
3. C₆₇×#3326	C₂	semidirect
4. C₆₇×#3309	C₂	semidirect
5. C₆₇×#3274	C₂	semidirect
6. C₆₇×#3265	C₂	semidirect
7. C₆₇×#3220	C₂	semidirect
8. C₆₇×#3199	C₂	semidirect
9. C₆₇×#3194	C₂	semidirect
10. C₆₇×#3126	C₂	semidirect
11. C₆₇×#3010	C₂	semidirect
12. C₆₇×#3006	C₂	semidirect
13. C₆₇×#2978	C₂	semidirect
14. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
15. C₂²×#41×C₆₇	C₂²	semidirect
16. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
17. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
18. C₂²×SD₁₆×C₆₇	C₂²	semidirect
20. #553×C₆₇	C₂²	semidirect
22. #550×C₆₇	C₂²	semidirect
24. #548×C₆₇	C₂²	semidirect
26. D₄²×C₆₇	C₂²	semidirect
31. #535×C₆₇	C₂²	semidirect
32. #535×C₆₇	C₂²	semidirect
36. #525×C₆₇	C₂²	semidirect
38. #519×C₆₇	C₂²	semidirect
39. #496×C₆₇	C₂²	semidirect
40. #493×C₆₇	C₂²	semidirect
41. #490×C₆₇	C₂²	semidirect
42. #488×C₆₇	C₂²	semidirect
43. #483×C₆₇	C₂²	semidirect
44. #482×C₆₇	C₂²	semidirect
45. #482×C₆₇	C₂²	semidirect
46. #480×C₆₇	C₂²	semidirect
47. #479×C₆₇	C₂²	semidirect
48. #469×C₆₇	C₂²	semidirect
49. #469×C₆₇	C₂²	semidirect
50. #468×C₆₇	C₂²	semidirect
51. #466×C₆₇	C₂²	semidirect
52. #463×C₆₇	C₂²	semidirect
53. #460×C₆₇	C₂²	semidirect
54. #459×C₆₇	C₂²	semidirect
55. #450×C₆₇	C₂²	semidirect
56. #449×C₆₇	C₂²	semidirect
57. #449×C₆₇	C₂²	semidirect
58. #449×C₆₇	C₂²	semidirect
59. #449×C₆₇	C₂²	semidirect
60. #448×C₆₇	C₂²	semidirect
61. #448×C₆₇	C₂²	semidirect
62. #447×C₆₇	C₂²	semidirect
63. #447×C₆₇	C₂²	semidirect
64. #447×C₆₇	C₂²	semidirect
65. #440×C₆₇	C₂²	semidirect
66. C₄×SD₁₆×C₆₇	C₂²	semidirect
67. #436×C₆₇	C₂²	semidirect
68. #435×C₆₇	C₂²	semidirect
69. #433×C₆₇	C₂²	semidirect
70. #419×C₆₇	C₂²	semidirect
71. #417×C₆₇	C₂²	semidirect
72. #416×C₆₇	C₂²	semidirect
73. #408×C₆₇	C₂²	semidirect
74. #407×C₆₇	C₂²	semidirect
370. #61651	C₆₇	direct (N × H)
379. #3537	C₂×C₆₇	semidirect
380. #3487	C₂×C₆₇	semidirect
381. #3326	C₂×C₆₇	semidirect
382. #3309	C₂×C₆₇	semidirect
383. #3274	C₂×C₆₇	semidirect
384. #3265	C₂×C₆₇	semidirect
385. #3220	C₂×C₆₇	semidirect
386. #3199	C₂×C₆₇	semidirect
387. #3194	C₂×C₆₇	semidirect
388. #3126	C₂×C₆₇	semidirect
389. #3010	C₂×C₆₇	semidirect
390. #3006	C₂×C₆₇	semidirect
391. #2978	C₂×C₆₇	semidirect
392. C₆₇	#61651	direct (N × H)
393. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
394. C₂²×#41	C₂²×C₆₇	semidirect
395. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
396. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
397. C₂²×SD₁₆	C₂²×C₆₇	semidirect
399. #553	C₂²×C₆₇	semidirect
401. #550	C₂²×C₆₇	semidirect
403. #548	C₂²×C₆₇	semidirect
405. D₄²	C₂²×C₆₇	semidirect
410. #535	C₂²×C₆₇	semidirect
411. #535	C₂²×C₆₇	semidirect
415. #525	C₂²×C₆₇	semidirect
417. #519	C₂²×C₆₇	semidirect
418. #496	C₂²×C₆₇	semidirect
419. #493	C₂²×C₆₇	semidirect
420. #490	C₂²×C₆₇	semidirect
421. #488	C₂²×C₆₇	semidirect
422. #483	C₂²×C₆₇	semidirect
423. #482	C₂²×C₆₇	semidirect
424. #482	C₂²×C₆₇	semidirect
425. #480	C₂²×C₆₇	semidirect
426. #479	C₂²×C₆₇	semidirect
427. #469	C₂²×C₆₇	semidirect
428. #469	C₂²×C₆₇	semidirect
429. #468	C₂²×C₆₇	semidirect
430. #466	C₂²×C₆₇	semidirect
431. #463	C₂²×C₆₇	semidirect
432. #460	C₂²×C₆₇	semidirect
433. #459	C₂²×C₆₇	semidirect
434. #450	C₂²×C₆₇	semidirect
435. #449	C₂²×C₆₇	semidirect
436. #449	C₂²×C₆₇	semidirect
437. #449	C₂²×C₆₇	semidirect
438. #449	C₂²×C₆₇	semidirect
439. #448	C₂²×C₆₇	semidirect
440. #448	C₂²×C₆₇	semidirect
441. #447	C₂²×C₆₇	semidirect
442. #447	C₂²×C₆₇	semidirect
443. #447	C₂²×C₆₇	semidirect
444. #440	C₂²×C₆₇	semidirect
445. C₄×SD₁₆	C₂²×C₆₇	semidirect
446. #436	C₂²×C₆₇	semidirect
447. #435	C₂²×C₆₇	semidirect
448. #433	C₂²×C₆₇	semidirect
449. #419	C₂²×C₆₇	semidirect
450. #417	C₂²×C₆₇	semidirect
451. #416	C₂²×C₆₇	semidirect
452. #408	C₂²×C₆₇	semidirect
453. #407	C₂²×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×#3487	2
C₆₇×#3326	2
C₆₇×#3309	2
C₆₇×#3274	2
C₆₇×#3265	2
C₆₇×#3220	2
C₆₇×#3199	2
C₆₇×#3194	2
C₆₇×#3126	2
C₆₇×#3010	2
C₆₇×#3006	2
C₆₇×#2978	2
#61651	67

Subgroups — C67×#61651 #30740902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61651 #30740902