Subgroups — C₆₇×#61648 #30740899

Order 17152.

2170 conjugacy classes of subgroups.

The subgroup lattice has 760 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×#3485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3322	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3307	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3272	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3264	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3221	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3200	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3194	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	C₆₇×#3006	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2978	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×H(5,𝔽₂)×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	2	yes	complemented
17	C₂×AGL(1,ℤ/8)×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	#547×C₆₇	—	2	2	no	—
22	#547×C₆₇	C₂²	1	4	yes	complemented
23	#546×C₆₇	—	2	2	no	—
24	#546×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	complemented
28	#538×C₆₇	—	2	2	no	—
29	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#535×C₆₇	C₂²	1	2	yes	—
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×#123×C₆₇	—	2	2	no	—
37	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
38	#518×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#496×C₆₇	C₂²	1	2	yes	complemented
40	#492×C₆₇	C₂²	1	2	yes	complemented
41	#491×C₆₇	C₂²	1	2	yes	complemented
42	#488×C₆₇	C₂²	1	2	yes	complemented
43	#485×C₆₇	C₂²	1	4	yes	complemented
44	#483×C₆₇	C₂²	1	2	yes	complemented
45	#482×C₆₇	C₂²	1	4	yes	complemented
46	#480×C₆₇	C₂²	1	2	yes	complemented
47	#478×C₆₇	C₂²	1	4	yes	complemented
48	#469×C₆₇	C₂²	1	4	yes	complemented
49	#468×C₆₇	C₂²	1	4	yes	complemented
50	#468×C₆₇	C₂²	1	4	yes	complemented
51	#465×C₆₇	C₂²	1	4	yes	complemented
52	#463×C₆₇	C₂²	1	4	yes	complemented
53	#461×C₆₇	C₂²	1	4	yes	complemented
54	#459×C₆₇	C₂²	1	4	yes	complemented
55	#450×C₆₇	C₂²	1	2	yes	complemented
56	#450×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	#449×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	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	#436×C₆₇	C₂²	1	4	yes	complemented
68	#435×C₆₇	C₂²	1	4	yes	complemented
69	#433×C₆₇	C₂²	1	2	yes	complemented
70	#418×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	H(5,𝔽₂)×C₆₇	—	4	4	no	—
76	C₂×#41×C₆₇	—	2	1	no	—
77	C₂×#41×C₆₇	—	2	2	no	—
78	C₂×#41×C₆₇	—	4	4	no	—
79	C₂×#41×C₆₇	C₂³	1	4	yes	—
80	C₂×#41×C₆₇	C₂³	1	2	yes	—
81	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
82	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₆₇	—	2	1	no	—
85	C₂²×D₄×C₆₇	—	2	2	no	—
86	C₂²×D₄×C₆₇	—	2	2	no	—
87	C₂²×D₄×C₆₇	—	2	1	no	—
88	C₂²×D₄×C₆₇	—	2	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	2	yes	—
92	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
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	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×D₈×C₆₇	—	4	4	no	—
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	2	yes	—
105	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
106	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
107	C₄⋊Q₈×C₆₇	—	2	1	no	—
108	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
109	#127×C₆₇	—	2	2	no	—
110	#127×C₆₇	C₂³	1	2	yes	—
111	#126×C₆₇	—	2	4	no	—
112	#125×C₆₇	C₂³	1	2	yes	—
113	#124×C₆₇	—	2	2	no	—
114	#124×C₆₇	—	2	1	no	—
115	#124×C₆₇	C₂³	1	2	yes	—
116	#123×C₆₇	—	2	2	no	—
117	#123×C₆₇	—	2	1	no	—
118	#123×C₆₇	—	2	4	no	—
119	#123×C₆₇	—	2	4	no	—
120	#123×C₆₇	—	2	2	no	—
121	#123×C₆₇	—	2	4	no	—
122	#123×C₆₇	—	2	4	no	—
123	#123×C₆₇	—	2	4	no	—
124	#123×C₆₇	D₄	1	2	yes	—
125	C₂²⋊Q₈×C₆₇	—	2	2	no	—
126	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
127	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
128	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
129	#121×C₆₇	—	2	4	no	—
130	#121×C₆₇	—	2	4	no	—
131	#121×C₆₇	—	2	2	no	—
132	#121×C₆₇	—	2	2	no	—
133	#121×C₆₇	—	2	4	no	—
134	#121×C₆₇	—	2	4	no	—
135	#121×C₆₇	—	2	4	no	—
136	#121×C₆₇	D₄	1	2	yes	—
137	#121×C₆₇	C₂³	1	4	yes	—
138	#121×C₆₇	C₂³	1	4	yes	—
139	#121×C₆₇	C₂³	1	4	yes	—
140	#121×C₆₇	C₂³	1	2	yes	—
141	#120×C₆₇	—	2	1	no	—
142	#120×C₆₇	—	2	2	no	—
143	#120×C₆₇	—	2	4	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×D₄×C₆₇	—	2	2	no	—
149	C₄×D₄×C₆₇	—	2	2	no	—
150	C₄×D₄×C₆₇	—	2	4	no	—
151	C₄×D₄×C₆₇	C₂³	1	4	yes	—
152	C₄×D₄×C₆₇	C₂³	1	4	yes	—
153	C₄×D₄×C₆₇	C₂³	1	4	yes	—
154	#117×C₆₇	C₂³	1	1	yes	characteristic
155	#117×C₆₇	C₂³	1	2	yes	—
156	#117×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
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	—
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	2	yes	—
175	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
176	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
177	#97×C₆₇	C₂³	1	2	yes	—
178	C₄×C₈×C₆₇	C₂³	1	2	yes	—
179	C₂⁴×C₆₇	—	2	1	no	—
180	C₂⁴×C₆₇	—	2	2	no	—
181	C₂⁴×C₆₇	—	2	2	no	—
182	C₂⁴×C₆₇	—	2	2	no	—
183	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
184	#41×C₆₇	—	2	8	no	—
185	#41×C₆₇	—	2	4	no	—
186	#41×C₆₇	—	4	2	no	—
187	#41×C₆₇	—	4	4	no	—
188	#41×C₆₇	—	4	2	no	—
189	#41×C₆₇	—	4	2	no	—
190	#41×C₆₇	—	4	8	no	—
191	#41×C₆₇	—	4	4	no	—
192	C₂×Q₈×C₆₇	—	2	1	no	—
193	C₂×Q₈×C₆₇	—	4	2	no	—
194	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
195	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
196	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
197	C₂×D₄×C₆₇	—	2	4	no	—
198	C₂×D₄×C₆₇	—	2	4	no	—
199	C₂×D₄×C₆₇	—	2	4	no	—
200	C₂×D₄×C₆₇	—	2	4	no	—
201	C₂×D₄×C₆₇	—	2	1	no	—
202	C₂×D₄×C₆₇	—	2	2	no	—
203	C₂×D₄×C₆₇	—	2	2	no	—
204	C₂×D₄×C₆₇	—	2	4	no	—
205	C₂×D₄×C₆₇	—	2	4	no	—
206	C₂×D₄×C₆₇	—	2	1	no	—
207	C₂×D₄×C₆₇	—	2	2	no	—
208	C₂×D₄×C₆₇	—	2	2	no	—
209	C₂×D₄×C₆₇	—	2	4	no	—
210	C₂×D₄×C₆₇	—	2	2	no	—
211	C₂×D₄×C₆₇	—	4	2	no	—
212	C₂×D₄×C₆₇	—	4	2	no	—
213	C₂×D₄×C₆₇	—	4	4	no	—
214	C₂×D₄×C₆₇	—	4	2	no	—
215	C₂×D₄×C₆₇	—	4	4	no	—
216	C₂×D₄×C₆₇	—	4	4	no	—
217	C₂×D₄×C₆₇	—	4	8	no	—
218	C₂×D₄×C₆₇	—	8	8	no	—
219	C₂×D₄×C₆₇	—	8	4	no	—
220	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
221	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
223	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
225	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₆₇	—	2	1	no	—
227	C₂²×C₄×C₆₇	—	2	2	no	—
228	C₂²×C₄×C₆₇	—	2	4	no	—
229	C₂²×C₄×C₆₇	—	2	2	no	—
230	C₂²×C₄×C₆₇	—	2	1	no	—
231	C₂²×C₄×C₆₇	—	2	4	no	—
232	C₂²×C₄×C₆₇	—	2	4	no	—
233	C₂²×C₄×C₆₇	—	4	2	no	—
234	C₂²×C₄×C₆₇	—	4	4	no	—
235	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
240	SD₁₆×C₆₇	—	4	4	no	—
241	SD₁₆×C₆₇	—	4	4	no	—
242	SD₁₆×C₆₇	—	4	4	no	—
243	D₈×C₆₇	—	2	8	no	—
244	D₈×C₆₇	—	2	8	no	—
245	D₈×C₆₇	—	4	4	no	—
246	M₁₆×C₆₇	—	4	4	no	—
247	M₁₆×C₆₇	—	4	2	no	—
248	C₂×C₈×C₆₇	—	4	2	no	—
249	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
250	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
251	C₄⋊C₄×C₆₇	—	2	2	no	—
252	C₄⋊C₄×C₆₇	—	2	4	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	4	yes	—
257	C₄⋊C₄×C₆₇	C₂×D₄	1	2	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	4	no	—
262	C₂²⋊C₄×C₆₇	—	2	2	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	4	no	—
271	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
272	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
273	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
274	C₄²×C₆₇	—	2	1	no	—
275	C₄²×C₆₇	—	2	2	no	—
276	C₄²×C₆₇	C₂⁴	1	2	yes	—
277	C₂³×C₆₇	—	2	4	no	—
278	C₂³×C₆₇	—	2	2	no	—
279	C₂³×C₆₇	—	2	1	no	—
280	C₂³×C₆₇	—	2	4	no	—
281	C₂³×C₆₇	—	4	1	no	—
282	C₂³×C₆₇	—	4	2	no	—
283	C₂³×C₆₇	—	4	4	no	—
284	C₂³×C₆₇	—	4	4	no	—
285	C₂³×C₆₇	—	8	2	no	—
286	C₂³×C₆₇	—	8	2	no	—
287	C₂³×C₆₇	—	8	2	no	—
288	C₂³×C₆₇	—	8	2	no	—
289	C₂³×C₆₇	—	8	4	no	—
290	C₂³×C₆₇	—	8	4	no	—
291	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
292	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
293	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
294	Q₈×C₆₇	—	2	4	no	—
295	Q₈×C₆₇	—	2	2	no	—
296	Q₈×C₆₇	—	4	1	no	—
297	Q₈×C₆₇	—	4	2	no	—
298	D₄×C₆₇	—	2	4	no	—
299	D₄×C₆₇	—	2	2	no	—
300	D₄×C₆₇	—	2	4	no	—
301	D₄×C₆₇	—	2	4	no	—
302	D₄×C₆₇	—	2	2	no	—
303	D₄×C₆₇	—	4	1	no	—
304	D₄×C₆₇	—	4	2	no	—
305	D₄×C₆₇	—	4	4	no	—
306	D₄×C₆₇	—	4	4	no	—
307	D₄×C₆₇	—	4	4	no	—
308	D₄×C₆₇	—	4	8	no	—
309	D₄×C₆₇	—	4	2	no	—
310	D₄×C₆₇	—	4	8	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	H(5,𝔽₂)	1	4	yes	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	4	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	4	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	1	no	—
326	C₂×C₄×C₆₇	—	4	1	no	—
327	C₂×C₄×C₆₇	—	4	2	no	—
328	C₂×C₄×C₆₇	—	4	8	no	—
329	C₂×C₄×C₆₇	—	4	4	no	—
330	C₂×C₄×C₆₇	—	4	2	no	—
331	C₂×C₄×C₆₇	—	4	2	no	—
332	C₂×C₄×C₆₇	—	8	4	no	—
333	C₂×C₄×C₆₇	—	8	4	no	—
334	C₂×C₄×C₆₇	—	8	2	no	—
335	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
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	—	2	4	no	—
350	C₂²×C₆₇	—	4	4	no	—
351	C₂²×C₆₇	—	4	4	no	—
352	C₂²×C₆₇	—	4	4	no	—
353	C₂²×C₆₇	—	4	2	no	—
354	C₂²×C₆₇	—	4	1	no	—
355	C₂²×C₆₇	—	4	4	no	—
356	C₂²×C₆₇	—	8	4	no	—
357	C₂²×C₆₇	—	8	2	no	—
358	C₂²×C₆₇	—	16	4	no	—
359	C₂²×C₆₇	—	16	4	no	—
360	C₂²×C₆₇	—	16	4	no	—
361	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
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	—	4	2	no	—
370	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
371	#61648	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
372	C₂×C₆₇	—	4	1	no	—
373	C₂×C₆₇	—	4	2	no	—
374	C₂×C₆₇	—	4	2	no	—
375	C₂×C₆₇	—	4	4	no	—
376	C₂×C₆₇	—	8	4	no	—
377	C₂×C₆₇	—	8	1	no	—
378	C₂×C₆₇	#3484	1	1	yes	characteristic
379	C₂×C₆₇	#3585	1	2	yes	—
380	#3537	C₂×C₆₇	1	1	yes	characteristic, complemented
381	#3485	C₂×C₆₇	1	1	yes	characteristic, complemented
382	#3322	C₂×C₆₇	1	4	yes	complemented
383	#3307	C₂×C₆₇	1	4	yes	complemented
384	#3272	C₂×C₆₇	1	4	yes	complemented
385	#3264	C₂×C₆₇	1	4	yes	complemented
386	#3221	C₂×C₆₇	1	2	yes	complemented
387	#3200	C₂×C₆₇	1	2	yes	complemented
388	#3194	C₂×C₆₇	1	2	yes	complemented
389	#3122	C₂×C₆₇	1	2	yes	complemented
390	#3008	C₂×C₆₇	1	2	yes	complemented
391	#3006	C₂×C₆₇	1	2	yes	complemented
392	#2978	C₂×C₆₇	1	1	yes	characteristic, complemented
393	C₆₇	#61648	1	1	yes	characteristic, direct product factor, Sylow
394	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
395	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
396	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
397	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
398	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
399	#560	—	2	2	no	—
400	#553	C₂²×C₆₇	1	4	yes	complemented
401	#547	—	2	2	no	—
402	#547	C₂²×C₆₇	1	4	yes	complemented
403	#546	—	2	2	no	—
404	#546	C₂²×C₆₇	1	4	yes	complemented
405	D₄²	—	2	2	no	—
406	D₄²	C₂²×C₆₇	1	4	yes	complemented
407	#540	C₂²×C₆₇	1	2	yes	complemented
408	#538	—	2	2	no	—
409	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
410	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
411	#535	C₂²×C₆₇	1	2	yes	—
412	#534	—	2	2	no	—
413	#534	—	2	2	no	—
414	#525	C₂²×C₆₇	1	1	yes	characteristic
415	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
416	C₂×#123	—	2	2	no	—
417	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
418	#518	C₂²×C₆₇	1	1	yes	characteristic, complemented
419	#496	C₂²×C₆₇	1	2	yes	complemented
420	#492	C₂²×C₆₇	1	2	yes	complemented
421	#491	C₂²×C₆₇	1	2	yes	complemented
422	#488	C₂²×C₆₇	1	2	yes	complemented
423	#485	C₂²×C₆₇	1	4	yes	complemented
424	#483	C₂²×C₆₇	1	2	yes	complemented
425	#482	C₂²×C₆₇	1	4	yes	complemented
426	#480	C₂²×C₆₇	1	2	yes	complemented
427	#478	C₂²×C₆₇	1	4	yes	complemented
428	#469	C₂²×C₆₇	1	4	yes	complemented
429	#468	C₂²×C₆₇	1	4	yes	complemented
430	#468	C₂²×C₆₇	1	4	yes	complemented
431	#465	C₂²×C₆₇	1	4	yes	complemented
432	#463	C₂²×C₆₇	1	4	yes	complemented
433	#461	C₂²×C₆₇	1	4	yes	complemented
434	#459	C₂²×C₆₇	1	4	yes	complemented
435	#450	C₂²×C₆₇	1	2	yes	complemented
436	#450	C₂²×C₆₇	1	4	yes	complemented
437	#449	C₂²×C₆₇	1	4	yes	complemented
438	#449	C₂²×C₆₇	1	4	yes	complemented
439	#449	C₂²×C₆₇	1	4	yes	complemented
440	#449	C₂²×C₆₇	1	4	yes	complemented
441	#448	C₂²×C₆₇	1	4	yes	complemented
442	#447	C₂²×C₆₇	1	4	yes	complemented
443	#447	C₂²×C₆₇	1	2	yes	complemented
444	#447	C₂²×C₆₇	1	4	yes	complemented
445	#442	C₂²×C₆₇	1	4	yes	complemented
446	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
447	#436	C₂²×C₆₇	1	4	yes	complemented
448	#435	C₂²×C₆₇	1	4	yes	complemented
449	#433	C₂²×C₆₇	1	2	yes	complemented
450	#418	C₂²×C₆₇	1	2	yes	complemented
451	#417	C₂²×C₆₇	1	4	yes	complemented
452	#416	C₂²×C₆₇	1	2	yes	complemented
453	#408	C₂²×C₆₇	1	2	yes	complemented
454	#407	C₂²×C₆₇	1	2	yes	complemented
455	H(5,𝔽₂)	—	4	4	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	C₂³×C₆₇	1	1	yes	characteristic
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	2	no	—
466	C₂²×D₄	—	2	2	no	—
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	—	2	4	no	—
469	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
471	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
472	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
473	C₂³×C₄	—	2	1	no	—
474	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
475	AGL(1,ℤ/8)	—	4	8	no	—
476	AGL(1,ℤ/8)	—	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	—	4	4	no	—
481	C₂×D₈	C₂³×C₆₇	1	4	yes	—
482	C₂×D₈	C₂³×C₆₇	1	4	yes	—
483	C₂×D₈	C₂³×C₆₇	1	4	yes	—
484	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
485	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
486	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
487	C₄⋊Q₈	—	2	1	no	—
488	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
489	#127	—	2	2	no	—
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	C₂³×C₆₇	1	2	yes	—
496	#123	—	2	2	no	—
497	#123	—	2	1	no	—
498	#123	—	2	4	no	—
499	#123	—	2	4	no	—
500	#123	—	2	2	no	—
501	#123	—	2	4	no	—
502	#123	—	2	4	no	—
503	#123	—	2	4	no	—
504	#123	D₄×C₆₇	1	2	yes	—
505	C₂²⋊Q₈	—	2	2	no	—
506	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
507	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
508	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
509	#121	—	2	4	no	—
510	#121	—	2	4	no	—
511	#121	—	2	2	no	—
512	#121	—	2	2	no	—
513	#121	—	2	4	no	—
514	#121	—	2	4	no	—
515	#121	—	2	4	no	—
516	#121	D₄×C₆₇	1	2	yes	—
517	#121	C₂³×C₆₇	1	4	yes	—
518	#121	C₂³×C₆₇	1	4	yes	—
519	#121	C₂³×C₆₇	1	2	yes	—
520	#121	C₂³×C₆₇	1	4	yes	—
521	#120	—	2	1	no	—
522	#120	—	2	2	no	—
523	#120	—	2	4	no	—
524	#120	—	2	2	no	—
525	#120	—	2	4	no	—
526	#120	—	2	4	no	—
527	#120	D₄×C₆₇	1	2	yes	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	4	no	—
531	C₄×D₄	C₂³×C₆₇	1	4	yes	—
532	C₄×D₄	C₂³×C₆₇	1	4	yes	—
533	C₄×D₄	C₂³×C₆₇	1	4	yes	—
534	#117	C₂³×C₆₇	1	1	yes	characteristic
535	#117	C₂³×C₆₇	1	2	yes	—
536	#117	C₂³×C₆₇	1	1	yes	characteristic
537	C₂×C₄⋊C₄	—	2	4	no	—
538	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
539	C₂×C₂²⋊C₄	—	2	2	no	—
540	C₂×C₂²⋊C₄	—	2	2	no	—
541	C₂×C₂²⋊C₄	—	2	4	no	—
542	#107	C₂³×C₆₇	1	4	yes	—
543	#106	C₂³×C₆₇	1	4	yes	—
544	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
545	#103	C₂³×C₆₇	1	4	yes	—
546	#103	C₂³×C₆₇	1	4	yes	—
547	#103	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	#102	C₂³×C₆₇	1	4	yes	—
553	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
554	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
555	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
556	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
557	#97	C₂³×C₆₇	1	2	yes	—
558	C₄×C₈	C₂³×C₆₇	1	2	yes	—
559	C₂⁴	—	2	1	no	—
560	C₂⁴	—	2	2	no	—
561	C₂⁴	—	2	2	no	—
562	C₂⁴	—	2	2	no	—
563	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
564	#41	—	2	8	no	—
565	#41	—	2	4	no	—
566	#41	—	4	2	no	—
567	#41	—	4	4	no	—
568	#41	—	4	2	no	—
569	#41	—	4	2	no	—
570	#41	—	4	8	no	—
571	#41	—	4	4	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	4	2	no	—
574	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
575	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
576	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	4	2	no	—
592	C₂×D₄	—	4	2	no	—
593	C₂×D₄	—	4	4	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂×D₄	—	4	4	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	8	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	1	yes	characteristic
602	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
603	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
604	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
605	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	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	—	4	4	no	—
621	SD₁₆	—	4	4	no	—
622	SD₁₆	—	4	4	no	—
623	D₈	—	2	8	no	—
624	D₈	—	2	8	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	4	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
637	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	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	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
652	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
653	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
654	C₄²	—	2	1	no	—
655	C₄²	—	2	2	no	—
656	C₄²	C₂⁴×C₆₇	1	2	yes	—
657	C₂³	—	2	4	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	4	no	—
664	C₂³	—	4	4	no	—
665	C₂³	—	8	2	no	—
666	C₂³	—	8	2	no	—
667	C₂³	—	8	2	no	—
668	C₂³	—	8	2	no	—
669	C₂³	—	8	4	no	—
670	C₂³	—	8	4	no	—
671	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
672	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
673	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
674	Q₈	—	2	4	no	—
675	Q₈	—	2	2	no	—
676	Q₈	—	4	1	no	—
677	Q₈	—	4	2	no	—
678	D₄	—	2	4	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	4	no	—
681	D₄	—	2	4	no	—
682	D₄	—	2	2	no	—
683	D₄	—	4	1	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	4	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	4	no	—
688	D₄	—	4	8	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	8	no	—
691	D₄	—	8	2	no	—
692	D₄	—	8	2	no	—
693	D₄	—	8	4	no	—
694	D₄	—	8	4	no	—
695	D₄	—	8	4	no	—
696	D₄	—	8	2	no	—
697	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	2	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	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	4	no	—
714	C₂×C₄	—	8	2	no	—
715	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
716	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
718	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
719	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
720	C₈	—	2	4	no	—
721	C₈	—	2	4	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	4	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	4	no	—
736	C₂²	—	8	4	no	—
737	C₂²	—	8	2	no	—
738	C₂²	—	16	4	no	—
739	C₂²	—	16	4	no	—
740	C₂²	—	16	4	no	—
741	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
742	C₄	—	2	4	no	—
743	C₄	—	2	2	no	—
744	C₄	—	2	1	no	—
745	C₄	—	2	2	no	—
746	C₄	—	4	4	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	1	no	—
749	C₄	—	4	2	no	—
750	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
751	C₂	—	4	1	no	—
752	C₂	—	4	2	no	—
753	C₂	—	4	2	no	—
754	C₂	—	4	4	no	—
755	C₂	—	8	4	no	—
756	C₂	—	8	1	no	—
757	C₂	C₆₇×#3484	1	1	yes	characteristic
758	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×#3485	C₂	semidirect
3. C₆₇×#3322	C₂	semidirect
4. C₆₇×#3307	C₂	semidirect
5. C₆₇×#3272	C₂	semidirect
6. C₆₇×#3264	C₂	semidirect
7. C₆₇×#3221	C₂	semidirect
8. C₆₇×#3200	C₂	semidirect
9. C₆₇×#3194	C₂	semidirect
10. C₆₇×#3122	C₂	semidirect
11. C₆₇×#3008	C₂	semidirect
12. C₆₇×#3006	C₂	semidirect
13. C₆₇×#2978	C₂	semidirect
14. C₂×H(5,𝔽₂)×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×D₈×C₆₇	C₂²	semidirect
20. #553×C₆₇	C₂²	semidirect
22. #547×C₆₇	C₂²	semidirect
24. #546×C₆₇	C₂²	semidirect
26. D₄²×C₆₇	C₂²	semidirect
27. #540×C₆₇	C₂²	semidirect
29. #536×C₆₇	C₂²	semidirect
30. #536×C₆₇	C₂²	semidirect
35. #525×C₆₇	C₂²	semidirect
37. C₂×#121×C₆₇	C₂²	semidirect
38. #518×C₆₇	C₂²	semidirect
39. #496×C₆₇	C₂²	semidirect
40. #492×C₆₇	C₂²	semidirect
41. #491×C₆₇	C₂²	semidirect
42. #488×C₆₇	C₂²	semidirect
43. #485×C₆₇	C₂²	semidirect
44. #483×C₆₇	C₂²	semidirect
45. #482×C₆₇	C₂²	semidirect
46. #480×C₆₇	C₂²	semidirect
47. #478×C₆₇	C₂²	semidirect
48. #469×C₆₇	C₂²	semidirect
49. #468×C₆₇	C₂²	semidirect
50. #468×C₆₇	C₂²	semidirect
51. #465×C₆₇	C₂²	semidirect
52. #463×C₆₇	C₂²	semidirect
53. #461×C₆₇	C₂²	semidirect
54. #459×C₆₇	C₂²	semidirect
55. #450×C₆₇	C₂²	semidirect
56. #450×C₆₇	C₂²	semidirect
57. #449×C₆₇	C₂²	semidirect
58. #449×C₆₇	C₂²	semidirect
59. #449×C₆₇	C₂²	semidirect
60. #449×C₆₇	C₂²	semidirect
61. #448×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. #436×C₆₇	C₂²	semidirect
68. #435×C₆₇	C₂²	semidirect
69. #433×C₆₇	C₂²	semidirect
70. #418×C₆₇	C₂²	semidirect
71. #417×C₆₇	C₂²	semidirect
72. #416×C₆₇	C₂²	semidirect
73. #408×C₆₇	C₂²	semidirect
74. #407×C₆₇	C₂²	semidirect
371. #61648	C₆₇	direct (N × H)
380. #3537	C₂×C₆₇	semidirect
381. #3485	C₂×C₆₇	semidirect
382. #3322	C₂×C₆₇	semidirect
383. #3307	C₂×C₆₇	semidirect
384. #3272	C₂×C₆₇	semidirect
385. #3264	C₂×C₆₇	semidirect
386. #3221	C₂×C₆₇	semidirect
387. #3200	C₂×C₆₇	semidirect
388. #3194	C₂×C₆₇	semidirect
389. #3122	C₂×C₆₇	semidirect
390. #3008	C₂×C₆₇	semidirect
391. #3006	C₂×C₆₇	semidirect
392. #2978	C₂×C₆₇	semidirect
393. C₆₇	#61648	direct (N × H)
394. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
395. C₂²×#41	C₂²×C₆₇	semidirect
396. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
397. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
398. C₂²×D₈	C₂²×C₆₇	semidirect
400. #553	C₂²×C₆₇	semidirect
402. #547	C₂²×C₆₇	semidirect
404. #546	C₂²×C₆₇	semidirect
406. D₄²	C₂²×C₆₇	semidirect
407. #540	C₂²×C₆₇	semidirect
409. #536	C₂²×C₆₇	semidirect
410. #536	C₂²×C₆₇	semidirect
415. #525	C₂²×C₆₇	semidirect
417. C₂×#121	C₂²×C₆₇	semidirect
418. #518	C₂²×C₆₇	semidirect
419. #496	C₂²×C₆₇	semidirect
420. #492	C₂²×C₆₇	semidirect
421. #491	C₂²×C₆₇	semidirect
422. #488	C₂²×C₆₇	semidirect
423. #485	C₂²×C₆₇	semidirect
424. #483	C₂²×C₆₇	semidirect
425. #482	C₂²×C₆₇	semidirect
426. #480	C₂²×C₆₇	semidirect
427. #478	C₂²×C₆₇	semidirect
428. #469	C₂²×C₆₇	semidirect
429. #468	C₂²×C₆₇	semidirect
430. #468	C₂²×C₆₇	semidirect
431. #465	C₂²×C₆₇	semidirect
432. #463	C₂²×C₆₇	semidirect
433. #461	C₂²×C₆₇	semidirect
434. #459	C₂²×C₆₇	semidirect
435. #450	C₂²×C₆₇	semidirect
436. #450	C₂²×C₆₇	semidirect
437. #449	C₂²×C₆₇	semidirect
438. #449	C₂²×C₆₇	semidirect
439. #449	C₂²×C₆₇	semidirect
440. #449	C₂²×C₆₇	semidirect
441. #448	C₂²×C₆₇	semidirect
442. #447	C₂²×C₆₇	semidirect
443. #447	C₂²×C₆₇	semidirect
444. #447	C₂²×C₆₇	semidirect
445. #442	C₂²×C₆₇	semidirect
446. C₄×D₈	C₂²×C₆₇	semidirect
447. #436	C₂²×C₆₇	semidirect
448. #435	C₂²×C₆₇	semidirect
449. #433	C₂²×C₆₇	semidirect
450. #418	C₂²×C₆₇	semidirect
451. #417	C₂²×C₆₇	semidirect
452. #416	C₂²×C₆₇	semidirect
453. #408	C₂²×C₆₇	semidirect
454. #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×#3485	2
C₆₇×#3322	2
C₆₇×#3307	2
C₆₇×#3272	2
C₆₇×#3264	2
C₆₇×#3221	2
C₆₇×#3200	2
C₆₇×#3194	2
C₆₇×#3122	2
C₆₇×#3008	2
C₆₇×#3006	2
C₆₇×#2978	2
#61648	67

Subgroups — C67×#61648 #30740899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61648 #30740899