Subgroups — C₆₇×#61572 #30740823

Order 17152.

2374 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#548×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3308	C₂	1	8	yes	maximal, complemented
4	C₆₇×#3265	C₂	1	8	yes	maximal, complemented
5	C₆₇×#3213	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3193	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3186	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3112	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3006	C₂	1	2	yes	maximal, complemented
10	C₂×#448×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₆₇	—	2	1	no	—
13	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
14	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
15	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
16	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
17	#548×C₆₇	—	2	4	no	—
18	#548×C₆₇	C₂²	1	8	yes	complemented
19	#547×C₆₇	C₂²	1	4	yes	complemented
20	#546×C₆₇	—	2	4	no	—
21	D₄²×C₆₇	C₂²	1	4	yes	complemented
22	#537×C₆₇	—	2	1	no	—
23	#534×C₆₇	—	2	1	no	—
24	#534×C₆₇	—	2	1	no	—
25	#532×C₆₇	C₂²	1	2	yes	—
26	C₂×#124×C₆₇	—	2	1	no	—
27	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×#121×C₆₇	—	2	1	no	—
31	C₂×#121×C₆₇	C₂²	1	2	yes	—
32	C₂×#121×C₆₇	C₂²	1	2	yes	—
33	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₆₇	—	2	1	no	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
37	#496×C₆₇	C₂²	1	4	yes	complemented
38	#489×C₆₇	C₂²	1	4	yes	complemented
39	#484×C₆₇	C₂²	1	4	yes	complemented
40	#480×C₆₇	C₂²	1	4	yes	complemented
41	#480×C₆₇	C₂²	1	4	yes	complemented
42	#477×C₆₇	C₂²	1	4	yes	complemented
43	#468×C₆₇	C₂²	1	8	yes	complemented
44	#466×C₆₇	C₂²	1	8	yes	complemented
45	#463×C₆₇	C₂²	1	8	yes	complemented
46	#460×C₆₇	C₂²	1	4	yes	complemented
47	#450×C₆₇	C₂²	1	4	yes	complemented
48	#449×C₆₇	C₂²	1	8	yes	complemented
49	#448×C₆₇	C₂²	1	8	yes	complemented
50	#448×C₆₇	C₂²	1	4	yes	complemented
51	#448×C₆₇	C₂²	1	4	yes	complemented
52	#447×C₆₇	C₂²	1	4	yes	complemented
53	#447×C₆₇	C₂²	1	4	yes	complemented
54	#440×C₆₇	C₂²	1	8	yes	complemented
55	#435×C₆₇	C₂²	1	8	yes	complemented
56	#432×C₆₇	C₂²	1	2	yes	complemented
57	#417×C₆₇	C₂²	1	4	yes	complemented
58	C₂×#103×C₆₇	C₂²	1	4	yes	complemented
59	#407×C₆₇	C₂²	1	2	yes	complemented
60	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
61	H(5,𝔽₂)×C₆₇	—	4	8	no	—
62	C₂×#41×C₆₇	—	2	4	no	—
63	C₂×#41×C₆₇	—	2	2	no	—
64	C₂×#41×C₆₇	—	2	2	no	—
65	C₂×#41×C₆₇	—	4	4	no	—
66	C₂×#41×C₆₇	C₂³	1	4	yes	—
67	C₂²×Q₈×C₆₇	—	2	1	no	—
68	C₂²×Q₈×C₆₇	—	2	2	no	—
69	C₂²×Q₈×C₆₇	—	4	4	no	—
70	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
72	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₆₇	—	2	1	no	—
74	C₂²×D₄×C₆₇	—	2	1	no	—
75	C₂²×D₄×C₆₇	—	2	2	no	—
76	C₂²×D₄×C₆₇	—	2	2	no	—
77	C₂²×D₄×C₆₇	—	2	4	no	—
78	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
79	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
80	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
81	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₆₇	—	2	1	no	—
83	C₂³×C₄×C₆₇	—	2	1	no	—
84	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
86	AGL(1,ℤ/8)×C₆₇	—	4	8	no	—
87	C₂×SD₁₆×C₆₇	—	4	8	no	—
88	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
89	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
90	C₂×D₈×C₆₇	C₂³	1	8	yes	—
91	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
92	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
93	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
94	#127×C₆₇	C₂³	1	2	yes	—
95	#124×C₆₇	—	2	8	no	—
96	#124×C₆₇	—	2	2	no	—
97	#124×C₆₇	—	2	2	no	—
98	#124×C₆₇	C₂³	1	4	yes	—
99	#123×C₆₇	—	2	4	no	—
100	#123×C₆₇	—	2	4	no	—
101	C₂²⋊Q₈×C₆₇	—	2	2	no	—
102	C₂²⋊Q₈×C₆₇	—	2	8	no	—
103	C₂²⋊Q₈×C₆₇	—	2	4	no	—
104	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
105	#121×C₆₇	—	2	8	no	—
106	#121×C₆₇	—	2	2	no	—
107	#121×C₆₇	—	2	2	no	—
108	#121×C₆₇	—	2	2	no	—
109	#121×C₆₇	—	2	2	no	—
110	#121×C₆₇	—	2	2	no	—
111	#121×C₆₇	—	2	2	no	—
112	#121×C₆₇	—	2	4	no	—
113	#121×C₆₇	C₂³	1	4	yes	—
114	#121×C₆₇	C₂³	1	4	yes	—
115	#121×C₆₇	C₂³	1	4	yes	—
116	#121×C₆₇	C₂³	1	4	yes	—
117	#120×C₆₇	—	2	4	no	—
118	#120×C₆₇	—	2	4	no	—
119	C₄×Q₈×C₆₇	—	2	2	no	—
120	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
121	C₄×D₄×C₆₇	—	2	8	no	—
122	C₄×D₄×C₆₇	—	2	2	no	—
123	C₄×D₄×C₆₇	D₄	1	4	yes	—
124	C₄×D₄×C₆₇	C₂³	1	4	yes	—
125	C₄×D₄×C₆₇	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
127	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
128	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
136	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
137	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
138	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
140	C₂×C₄²×C₆₇	—	2	1	no	—
141	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
142	#107×C₆₇	C₂³	1	8	yes	—
143	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
144	#103×C₆₇	C₂³	1	8	yes	—
145	#103×C₆₇	C₂³	1	8	yes	—
146	#102×C₆₇	C₂³	1	8	yes	—
147	#102×C₆₇	C₂³	1	8	yes	—
148	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
149	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
150	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
151	#97×C₆₇	C₂³	1	4	yes	—
152	C₂⁴×C₆₇	—	2	1	no	—
153	C₂⁴×C₆₇	—	2	2	no	—
154	C₂⁴×C₆₇	—	2	2	no	—
155	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
156	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
157	#41×C₆₇	—	2	8	no	—
158	#41×C₆₇	—	4	4	no	—
159	#41×C₆₇	—	4	8	no	—
160	#41×C₆₇	—	4	16	no	—
161	#41×C₆₇	—	4	8	no	—
162	C₂×Q₈×C₆₇	—	2	4	no	—
163	C₂×Q₈×C₆₇	—	2	1	no	—
164	C₂×Q₈×C₆₇	—	2	4	no	—
165	C₂×Q₈×C₆₇	—	2	1	no	—
166	C₂×Q₈×C₆₇	—	2	2	no	—
167	C₂×Q₈×C₆₇	—	2	8	no	—
168	C₂×Q₈×C₆₇	—	4	4	no	—
169	C₂×Q₈×C₆₇	—	4	2	no	—
170	C₂×Q₈×C₆₇	—	4	4	no	—
171	C₂×Q₈×C₆₇	—	4	8	no	—
172	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
173	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
174	C₂×D₄×C₆₇	—	2	4	no	—
175	C₂×D₄×C₆₇	—	2	4	no	—
176	C₂×D₄×C₆₇	—	2	4	no	—
177	C₂×D₄×C₆₇	—	2	4	no	—
178	C₂×D₄×C₆₇	—	2	4	no	—
179	C₂×D₄×C₆₇	—	2	4	no	—
180	C₂×D₄×C₆₇	—	2	1	no	—
181	C₂×D₄×C₆₇	—	2	2	no	—
182	C₂×D₄×C₆₇	—	2	2	no	—
183	C₂×D₄×C₆₇	—	2	2	no	—
184	C₂×D₄×C₆₇	—	2	2	no	—
185	C₂×D₄×C₆₇	—	4	2	no	—
186	C₂×D₄×C₆₇	—	4	4	no	—
187	C₂×D₄×C₆₇	—	4	4	no	—
188	C₂×D₄×C₆₇	—	4	4	no	—
189	C₂×D₄×C₆₇	—	4	16	no	—
190	C₂×D₄×C₆₇	—	4	8	no	—
191	C₂×D₄×C₆₇	—	4	4	no	—
192	C₂×D₄×C₆₇	—	4	8	no	—
193	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
194	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
195	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₆₇	—	2	1	no	—
197	C₂²×C₄×C₆₇	—	2	1	no	—
198	C₂²×C₄×C₆₇	—	2	1	no	—
199	C₂²×C₄×C₆₇	—	2	2	no	—
200	C₂²×C₄×C₆₇	—	2	2	no	—
201	C₂²×C₄×C₆₇	—	2	4	no	—
202	C₂²×C₄×C₆₇	—	2	4	no	—
203	C₂²×C₄×C₆₇	—	2	4	no	—
204	C₂²×C₄×C₆₇	—	4	2	no	—
205	C₂²×C₄×C₆₇	—	4	2	no	—
206	C₂²×C₄×C₆₇	—	4	4	no	—
207	C₂²×C₄×C₆₇	—	4	4	no	—
208	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
217	SD₁₆×C₆₇	—	2	16	no	—
218	SD₁₆×C₆₇	—	4	8	no	—
219	D₈×C₆₇	—	4	8	no	—
220	M₁₆×C₆₇	—	4	4	no	—
221	C₂×C₈×C₆₇	—	4	4	no	—
222	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
223	C₄⋊C₄×C₆₇	—	2	4	no	—
224	C₄⋊C₄×C₆₇	—	2	4	no	—
225	C₄⋊C₄×C₆₇	—	2	1	no	—
226	C₄⋊C₄×C₆₇	—	2	2	no	—
227	C₄⋊C₄×C₆₇	—	2	2	no	—
228	C₄⋊C₄×C₆₇	—	2	2	no	—
229	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
230	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
231	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
232	C₂²⋊C₄×C₆₇	—	2	4	no	—
233	C₂²⋊C₄×C₆₇	—	2	4	no	—
234	C₂²⋊C₄×C₆₇	—	2	4	no	—
235	C₂²⋊C₄×C₆₇	—	2	4	no	—
236	C₂²⋊C₄×C₆₇	—	2	4	no	—
237	C₂²⋊C₄×C₆₇	—	2	4	no	—
238	C₂²⋊C₄×C₆₇	—	2	4	no	—
239	C₂²⋊C₄×C₆₇	—	2	4	no	—
240	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
241	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
242	C₄²×C₆₇	—	2	4	no	—
243	C₄²×C₆₇	C₂×D₄	1	2	yes	—
244	C₄²×C₆₇	C₂⁴	1	2	yes	—
245	C₂³×C₆₇	—	2	2	no	—
246	C₂³×C₆₇	—	2	2	no	—
247	C₂³×C₆₇	—	2	4	no	—
248	C₂³×C₆₇	—	4	1	no	—
249	C₂³×C₆₇	—	4	1	no	—
250	C₂³×C₆₇	—	4	1	no	—
251	C₂³×C₆₇	—	4	1	no	—
252	C₂³×C₆₇	—	4	2	no	—
253	C₂³×C₆₇	—	4	2	no	—
254	C₂³×C₆₇	—	4	4	no	—
255	C₂³×C₆₇	—	4	2	no	—
256	C₂³×C₆₇	—	4	4	no	—
257	C₂³×C₆₇	—	8	2	no	—
258	C₂³×C₆₇	—	8	2	no	—
259	C₂³×C₆₇	—	8	2	no	—
260	C₂³×C₆₇	—	8	2	no	—
261	C₂³×C₆₇	AGL(1,ℤ/8)	1	4	yes	complemented
262	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
263	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
264	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
265	Q₈×C₆₇	—	2	4	no	—
266	Q₈×C₆₇	—	2	2	no	—
267	Q₈×C₆₇	—	2	4	no	—
268	Q₈×C₆₇	—	4	8	no	—
269	Q₈×C₆₇	—	4	2	no	—
270	Q₈×C₆₇	—	4	4	no	—
271	Q₈×C₆₇	H(5,𝔽₂)	1	4	yes	complemented
272	D₄×C₆₇	—	2	8	no	—
273	D₄×C₆₇	—	2	4	no	—
274	D₄×C₆₇	—	2	8	no	—
275	D₄×C₆₇	—	4	8	no	—
276	D₄×C₆₇	—	4	4	no	—
277	D₄×C₆₇	—	4	2	no	—
278	D₄×C₆₇	—	4	8	no	—
279	D₄×C₆₇	—	4	8	no	—
280	D₄×C₆₇	—	4	8	no	—
281	D₄×C₆₇	—	4	8	no	—
282	D₄×C₆₇	—	8	2	no	—
283	D₄×C₆₇	—	8	2	no	—
284	D₄×C₆₇	—	8	2	no	—
285	C₂×C₄×C₆₇	—	2	4	no	—
286	C₂×C₄×C₆₇	—	2	2	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	4	no	—
289	C₂×C₄×C₆₇	—	2	4	no	—
290	C₂×C₄×C₆₇	—	2	2	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	4	no	—
294	C₂×C₄×C₆₇	—	4	1	no	—
295	C₂×C₄×C₆₇	—	4	2	no	—
296	C₂×C₄×C₆₇	—	4	1	no	—
297	C₂×C₄×C₆₇	—	4	2	no	—
298	C₂×C₄×C₆₇	—	4	1	no	—
299	C₂×C₄×C₆₇	—	4	8	no	—
300	C₂×C₄×C₆₇	—	4	8	no	—
301	C₂×C₄×C₆₇	—	4	8	no	—
302	C₂×C₄×C₆₇	—	4	2	no	—
303	C₂×C₄×C₆₇	—	4	4	no	—
304	C₂×C₄×C₆₇	—	4	2	no	—
305	C₂×C₄×C₆₇	—	4	4	no	—
306	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
312	C₈×C₆₇	—	2	8	no	—
313	C₂²×C₆₇	—	2	1	no	—
314	C₂²×C₆₇	—	2	2	no	—
315	C₂²×C₆₇	—	2	1	no	—
316	C₂²×C₆₇	—	2	2	no	—
317	C₂²×C₆₇	—	2	2	no	—
318	C₂²×C₆₇	—	2	2	no	—
319	C₂²×C₆₇	—	2	2	no	—
320	C₂²×C₆₇	—	4	4	no	—
321	C₂²×C₆₇	—	4	4	no	—
322	C₂²×C₆₇	—	4	2	no	—
323	C₂²×C₆₇	—	4	2	no	—
324	C₂²×C₆₇	—	4	4	no	—
325	C₂²×C₆₇	—	4	4	no	—
326	C₂²×C₆₇	—	4	2	no	—
327	C₂²×C₆₇	—	8	2	no	—
328	C₂²×C₆₇	—	8	4	no	—
329	C₂²×C₆₇	—	16	4	no	—
330	C₂²×C₆₇	—	16	4	no	—
331	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
332	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
333	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
334	C₄×C₆₇	—	2	2	no	—
335	C₄×C₆₇	—	2	4	no	—
336	C₄×C₆₇	—	2	2	no	—
337	C₄×C₆₇	—	2	1	no	—
338	C₄×C₆₇	—	2	2	no	—
339	C₄×C₆₇	—	2	2	no	—
340	C₄×C₆₇	—	4	2	no	—
341	C₄×C₆₇	—	4	4	no	—
342	C₄×C₆₇	—	4	2	no	—
343	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
344	#61572	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂×C₆₇	—	2	2	no	—
346	C₂×C₆₇	—	2	4	no	—
347	C₂×C₆₇	—	4	2	no	—
348	C₂×C₆₇	—	8	2	no	—
349	C₂×C₆₇	—	8	4	no	—
350	C₂×C₆₇	#3484	1	1	yes	characteristic
351	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
352	C₂×C₆₇	#3586	1	1	yes	characteristic
353	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
354	C₂×#548	C₂×C₆₇	1	1	yes	characteristic, complemented
355	#3308	C₂×C₆₇	1	8	yes	complemented
356	#3265	C₂×C₆₇	1	8	yes	complemented
357	#3213	C₂×C₆₇	1	2	yes	complemented
358	#3193	C₂×C₆₇	1	2	yes	complemented
359	#3186	C₂×C₆₇	1	2	yes	complemented
360	#3112	C₂×C₆₇	1	2	yes	complemented
361	#3006	C₂×C₆₇	1	2	yes	complemented
362	C₂×#448	C₂×C₆₇	1	2	yes	complemented
363	#2973	C₂×C₆₇	1	1	yes	characteristic, complemented
364	C₆₇	#61572	1	1	yes	characteristic, direct product factor, Sylow
365	C₂×H(5,𝔽₂)	—	2	1	no	—
366	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
367	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
368	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
369	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
370	#548	—	2	4	no	—
371	#548	C₂²×C₆₇	1	8	yes	complemented
372	#547	C₂²×C₆₇	1	4	yes	complemented
373	#546	—	2	4	no	—
374	D₄²	C₂²×C₆₇	1	4	yes	complemented
375	#537	—	2	1	no	—
376	#534	—	2	1	no	—
377	#534	—	2	1	no	—
378	#532	C₂²×C₆₇	1	2	yes	—
379	C₂×#124	—	2	1	no	—
380	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
381	C₂×C₂²⋊Q₈	—	2	1	no	—
382	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
383	C₂×#121	—	2	1	no	—
384	C₂×#121	C₂²×C₆₇	1	2	yes	—
385	C₂×#121	C₂²×C₆₇	1	2	yes	—
386	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
387	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
388	C₂×C₄×D₄	—	2	1	no	—
389	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
390	#496	C₂²×C₆₇	1	4	yes	complemented
391	#489	C₂²×C₆₇	1	4	yes	complemented
392	#484	C₂²×C₆₇	1	4	yes	complemented
393	#480	C₂²×C₆₇	1	4	yes	complemented
394	#480	C₂²×C₆₇	1	4	yes	complemented
395	#477	C₂²×C₆₇	1	4	yes	complemented
396	#468	C₂²×C₆₇	1	8	yes	complemented
397	#466	C₂²×C₆₇	1	8	yes	complemented
398	#463	C₂²×C₆₇	1	8	yes	complemented
399	#460	C₂²×C₆₇	1	4	yes	complemented
400	#450	C₂²×C₆₇	1	4	yes	complemented
401	#449	C₂²×C₆₇	1	8	yes	complemented
402	#448	C₂²×C₆₇	1	4	yes	complemented
403	#448	C₂²×C₆₇	1	4	yes	complemented
404	#448	C₂²×C₆₇	1	8	yes	complemented
405	#447	C₂²×C₆₇	1	4	yes	complemented
406	#447	C₂²×C₆₇	1	4	yes	complemented
407	#440	C₂²×C₆₇	1	8	yes	complemented
408	#435	C₂²×C₆₇	1	8	yes	complemented
409	#432	C₂²×C₆₇	1	2	yes	complemented
410	#417	C₂²×C₆₇	1	4	yes	complemented
411	C₂×#103	C₂²×C₆₇	1	4	yes	complemented
412	#407	C₂²×C₆₇	1	2	yes	complemented
413	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
414	H(5,𝔽₂)	—	4	8	no	—
415	C₂×#41	—	2	4	no	—
416	C₂×#41	—	2	2	no	—
417	C₂×#41	—	2	2	no	—
418	C₂×#41	—	4	4	no	—
419	C₂×#41	C₂³×C₆₇	1	4	yes	—
420	C₂²×Q₈	—	2	1	no	—
421	C₂²×Q₈	—	2	2	no	—
422	C₂²×Q₈	—	4	4	no	—
423	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
424	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
425	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
426	C₂²×D₄	—	2	1	no	—
427	C₂²×D₄	—	2	1	no	—
428	C₂²×D₄	—	2	2	no	—
429	C₂²×D₄	—	2	2	no	—
430	C₂²×D₄	—	2	4	no	—
431	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
433	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
434	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
435	C₂³×C₄	—	2	1	no	—
436	C₂³×C₄	—	2	1	no	—
437	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
438	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
439	AGL(1,ℤ/8)	—	4	8	no	—
440	C₂×SD₁₆	—	4	8	no	—
441	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	—
442	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	—
443	C₂×D₈	C₂³×C₆₇	1	8	yes	—
444	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
445	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
446	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
447	#127	C₂³×C₆₇	1	2	yes	—
448	#124	—	2	8	no	—
449	#124	—	2	2	no	—
450	#124	—	2	2	no	—
451	#124	C₂³×C₆₇	1	4	yes	—
452	#123	—	2	4	no	—
453	#123	—	2	4	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	—	2	8	no	—
456	C₂²⋊Q₈	—	2	4	no	—
457	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
458	#121	—	2	8	no	—
459	#121	—	2	2	no	—
460	#121	—	2	2	no	—
461	#121	—	2	2	no	—
462	#121	—	2	2	no	—
463	#121	—	2	2	no	—
464	#121	—	2	2	no	—
465	#121	—	2	4	no	—
466	#121	C₂³×C₆₇	1	4	yes	—
467	#121	C₂³×C₆₇	1	4	yes	—
468	#121	C₂³×C₆₇	1	4	yes	—
469	#121	C₂³×C₆₇	1	4	yes	—
470	#120	—	2	4	no	—
471	#120	—	2	4	no	—
472	C₄×Q₈	—	2	2	no	—
473	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
474	C₄×D₄	—	2	8	no	—
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	D₄×C₆₇	1	4	yes	—
477	C₄×D₄	C₂³×C₆₇	1	4	yes	—
478	C₄×D₄	C₂³×C₆₇	1	4	yes	—
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	—	2	1	no	—
481	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	—	2	2	no	—
489	C₂×C₂²⋊C₄	—	2	2	no	—
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
493	C₂×C₄²	—	2	1	no	—
494	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
495	#107	C₂³×C₆₇	1	8	yes	—
496	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
497	#103	C₂³×C₆₇	1	8	yes	—
498	#103	C₂³×C₆₇	1	8	yes	—
499	#102	C₂³×C₆₇	1	8	yes	—
500	#102	C₂³×C₆₇	1	8	yes	—
501	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
502	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
503	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
504	#97	C₂³×C₆₇	1	4	yes	—
505	C₂⁴	—	2	1	no	—
506	C₂⁴	—	2	2	no	—
507	C₂⁴	—	2	2	no	—
508	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
509	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
510	#41	—	2	8	no	—
511	#41	—	4	4	no	—
512	#41	—	4	8	no	—
513	#41	—	4	16	no	—
514	#41	—	4	8	no	—
515	C₂×Q₈	—	2	4	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	4	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	2	no	—
520	C₂×Q₈	—	2	8	no	—
521	C₂×Q₈	—	4	4	no	—
522	C₂×Q₈	—	4	2	no	—
523	C₂×Q₈	—	4	4	no	—
524	C₂×Q₈	—	4	8	no	—
525	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
526	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	4	2	no	—
539	C₂×D₄	—	4	4	no	—
540	C₂×D₄	—	4	4	no	—
541	C₂×D₄	—	4	4	no	—
542	C₂×D₄	—	4	16	no	—
543	C₂×D₄	—	4	8	no	—
544	C₂×D₄	—	4	8	no	—
545	C₂×D₄	—	4	4	no	—
546	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
547	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
548	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	4	2	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	—	4	4	no	—
560	C₂²×C₄	—	4	4	no	—
561	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
565	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
566	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
568	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
570	SD₁₆	—	2	16	no	—
571	SD₁₆	—	4	8	no	—
572	D₈	—	4	8	no	—
573	M₁₆	—	4	4	no	—
574	C₂×C₈	—	4	4	no	—
575	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
583	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
584	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
594	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
595	C₄²	—	2	4	no	—
596	C₄²	C₂×D₄×C₆₇	1	2	yes	—
597	C₄²	C₂⁴×C₆₇	1	2	yes	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	4	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	2	no	—
606	C₂³	—	4	2	no	—
607	C₂³	—	4	4	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	4	no	—
610	C₂³	—	8	2	no	—
611	C₂³	—	8	2	no	—
612	C₂³	—	8	2	no	—
613	C₂³	—	8	2	no	—
614	C₂³	AGL(1,ℤ/8)×C₆₇	1	4	yes	complemented
615	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
616	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
617	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
618	Q₈	—	2	4	no	—
619	Q₈	—	2	2	no	—
620	Q₈	—	2	4	no	—
621	Q₈	—	4	8	no	—
622	Q₈	—	4	2	no	—
623	Q₈	—	4	4	no	—
624	Q₈	H(5,𝔽₂)×C₆₇	1	4	yes	complemented
625	D₄	—	2	8	no	—
626	D₄	—	2	4	no	—
627	D₄	—	2	8	no	—
628	D₄	—	4	8	no	—
629	D₄	—	4	4	no	—
630	D₄	—	4	2	no	—
631	D₄	—	4	8	no	—
632	D₄	—	4	8	no	—
633	D₄	—	4	8	no	—
634	D₄	—	4	8	no	—
635	D₄	—	8	2	no	—
636	D₄	—	8	2	no	—
637	D₄	—	8	2	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	2	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	8	no	—
653	C₂×C₄	—	4	8	no	—
654	C₂×C₄	—	4	8	no	—
655	C₂×C₄	—	4	2	no	—
656	C₂×C₄	—	4	4	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
660	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
661	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
662	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
663	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
664	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
665	C₈	—	2	8	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	4	4	no	—
674	C₂²	—	4	4	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	4	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	4	no	—
680	C₂²	—	8	2	no	—
681	C₂²	—	8	4	no	—
682	C₂²	—	16	4	no	—
683	C₂²	—	16	4	no	—
684	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
685	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	4	yes	—
686	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	4	no	—
690	C₄	—	2	2	no	—
691	C₄	—	2	1	no	—
692	C₄	—	2	2	no	—
693	C₄	—	4	4	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	2	no	—
696	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
697	C₂	—	2	2	no	—
698	C₂	—	2	4	no	—
699	C₂	—	4	2	no	—
700	C₂	—	8	2	no	—
701	C₂	—	8	4	no	—
702	C₂	C₆₇×#3484	1	1	yes	characteristic
703	C₂	C₂²×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
704	C₂	C₆₇×#3586	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×#3496	C₂	semidirect
2. C₂×#548×C₆₇	C₂	semidirect
3. C₆₇×#3308	C₂	semidirect
4. C₆₇×#3265	C₂	semidirect
5. C₆₇×#3213	C₂	semidirect
6. C₆₇×#3193	C₂	semidirect
7. C₆₇×#3186	C₂	semidirect
8. C₆₇×#3112	C₂	semidirect
9. C₆₇×#3006	C₂	semidirect
10. C₂×#448×C₆₇	C₂	semidirect
11. C₆₇×#2973	C₂	semidirect
13. C₂²×#41×C₆₇	C₂²	semidirect
14. C₂³×Q₈×C₆₇	C₂²	semidirect
15. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
16. C₂²×SD₁₆×C₆₇	C₂²	semidirect
18. #548×C₆₇	C₂²	semidirect
19. #547×C₆₇	C₂²	semidirect
21. D₄²×C₆₇	C₂²	semidirect
27. C₂×#124×C₆₇	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
33. C₂×#121×C₆₇	C₂²	semidirect
34. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
37. #496×C₆₇	C₂²	semidirect
38. #489×C₆₇	C₂²	semidirect
39. #484×C₆₇	C₂²	semidirect
40. #480×C₆₇	C₂²	semidirect
41. #480×C₆₇	C₂²	semidirect
42. #477×C₆₇	C₂²	semidirect
43. #468×C₆₇	C₂²	semidirect
44. #466×C₆₇	C₂²	semidirect
45. #463×C₆₇	C₂²	semidirect
46. #460×C₆₇	C₂²	semidirect
47. #450×C₆₇	C₂²	semidirect
48. #449×C₆₇	C₂²	semidirect
49. #448×C₆₇	C₂²	semidirect
50. #448×C₆₇	C₂²	semidirect
51. #448×C₆₇	C₂²	semidirect
52. #447×C₆₇	C₂²	semidirect
53. #447×C₆₇	C₂²	semidirect
54. #440×C₆₇	C₂²	semidirect
55. #435×C₆₇	C₂²	semidirect
56. #432×C₆₇	C₂²	semidirect
57. #417×C₆₇	C₂²	semidirect
58. C₂×#103×C₆₇	C₂²	semidirect
59. #407×C₆₇	C₂²	semidirect
60. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
261. C₂³×C₆₇	AGL(1,ℤ/8)	semidirect
271. Q₈×C₆₇	H(5,𝔽₂)	semidirect
344. #61572	C₆₇	direct (N × H)
353. #3496	C₂×C₆₇	semidirect
354. C₂×#548	C₂×C₆₇	semidirect
355. #3308	C₂×C₆₇	semidirect
356. #3265	C₂×C₆₇	semidirect
357. #3213	C₂×C₆₇	semidirect
358. #3193	C₂×C₆₇	semidirect
359. #3186	C₂×C₆₇	semidirect
360. #3112	C₂×C₆₇	semidirect
361. #3006	C₂×C₆₇	semidirect
362. C₂×#448	C₂×C₆₇	semidirect
363. #2973	C₂×C₆₇	semidirect
364. C₆₇	#61572	direct (N × H)
366. C₂²×#41	C₂²×C₆₇	semidirect
367. C₂³×Q₈	C₂²×C₆₇	semidirect
368. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
369. C₂²×SD₁₆	C₂²×C₆₇	semidirect
371. #548	C₂²×C₆₇	semidirect
372. #547	C₂²×C₆₇	semidirect
374. D₄²	C₂²×C₆₇	semidirect
380. C₂×#124	C₂²×C₆₇	semidirect
382. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
386. C₂×#121	C₂²×C₆₇	semidirect
387. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
390. #496	C₂²×C₆₇	semidirect
391. #489	C₂²×C₆₇	semidirect
392. #484	C₂²×C₆₇	semidirect
393. #480	C₂²×C₆₇	semidirect
394. #480	C₂²×C₆₇	semidirect
395. #477	C₂²×C₆₇	semidirect
396. #468	C₂²×C₆₇	semidirect
397. #466	C₂²×C₆₇	semidirect
398. #463	C₂²×C₆₇	semidirect
399. #460	C₂²×C₆₇	semidirect
400. #450	C₂²×C₆₇	semidirect
401. #449	C₂²×C₆₇	semidirect
402. #448	C₂²×C₆₇	semidirect
403. #448	C₂²×C₆₇	semidirect
404. #448	C₂²×C₆₇	semidirect
405. #447	C₂²×C₆₇	semidirect
406. #447	C₂²×C₆₇	semidirect
407. #440	C₂²×C₆₇	semidirect
408. #435	C₂²×C₆₇	semidirect
409. #432	C₂²×C₆₇	semidirect
410. #417	C₂²×C₆₇	semidirect
411. C₂×#103	C₂²×C₆₇	semidirect
412. #407	C₂²×C₆₇	semidirect
413. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
614. C₂³	AGL(1,ℤ/8)×C₆₇	semidirect
624. Q₈	H(5,𝔽₂)×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3496	2
C₂×#548×C₆₇	2
C₆₇×#3308	2
C₆₇×#3265	2
C₆₇×#3213	2
C₆₇×#3193	2
C₆₇×#3186	2
C₆₇×#3112	2
C₆₇×#3006	2
C₂×#448×C₆₇	2
C₆₇×#2973	2
#61572	67

Subgroups — C67×#61572 #30740823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61572 #30740823