Subgroups — C₆₇×#61109 #30740360

Order 17152.

2626 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3586	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3585	C₂	1	2	yes	maximal, complemented
3	C₆₇×#3290	C₂	1	8	yes	maximal, complemented
4	C₆₇×#3289	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3288	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3153	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3069	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3068	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3018	C₂	1	2	yes	maximal, complemented
10	C₂×#454×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#455×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2956	C₂	1	2	yes	maximal, complemented
13	#585×C₆₇	C₂²	1	2	yes	complemented
14	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
15	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
16	#578×C₆₇	—	2	4	no	—
17	#578×C₆₇	C₂²	1	8	yes	complemented
18	#577×C₆₇	—	2	4	no	—
19	#577×C₆₇	—	2	4	no	—
20	#577×C₆₇	C₂²	1	8	yes	complemented
21	#577×C₆₇	C₂²	1	8	yes	complemented
22	#576×C₆₇	—	2	4	no	—
23	#576×C₆₇	C₂²	1	8	yes	complemented
24	#575×C₆₇	—	2	4	no	—
25	#575×C₆₇	—	2	4	no	—
26	#575×C₆₇	C₂²	1	2	yes	—
27	#575×C₆₇	C₂²	1	2	yes	—
28	#575×C₆₇	C₂²	1	2	yes	complemented
29	C₂×#137×C₆₇	—	2	4	no	—
30	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
31	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
32	C₂×AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
33	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
34	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
35	#568×C₆₇	C₂²	1	2	yes	complemented
36	#568×C₆₇	C₂²	1	2	yes	complemented
37	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#497×C₆₇	C₂²	1	2	yes	complemented
40	#496×C₆₇	C₂²	1	2	yes	complemented
41	#495×C₆₇	C₂²	1	4	yes	complemented
42	#473×C₆₇	C₂²	1	8	yes	complemented
43	#472×C₆₇	C₂²	1	8	yes	complemented
44	#471×C₆₇	C₂²	1	8	yes	complemented
45	#471×C₆₇	C₂²	1	8	yes	complemented
46	#456×C₆₇	C₂²	1	4	yes	complemented
47	#455×C₆₇	C₂²	1	4	yes	complemented
48	#455×C₆₇	C₂²	1	4	yes	complemented
49	#455×C₆₇	C₂²	1	4	yes	complemented
50	#454×C₆₇	C₂²	1	4	yes	complemented
51	#454×C₆₇	C₂²	1	4	yes	complemented
52	#454×C₆₇	C₂²	1	4	yes	complemented
53	#453×C₆₇	C₂²	1	4	yes	complemented
54	#444×C₆₇	C₂²	1	8	yes	complemented
55	#443×C₆₇	C₂²	1	8	yes	complemented
56	#430×C₆₇	C₂²	1	2	yes	complemented
57	C₂×#104×C₆₇	C₂²	1	2	yes	complemented
58	C₂×#104×C₆₇	C₂²	1	2	yes	complemented
59	#413×C₆₇	C₂²	1	2	yes	complemented
60	C₂×#101×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×#100×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	2₋¹⁺⁴×C₆₇	—	2	4	no	—
64	2₋¹⁺⁴×C₆₇	—	2	2	no	—
65	2₋¹⁺⁴×C₆₇	—	2	2	no	—
66	2₋¹⁺⁴×C₆₇	—	4	1	no	—
67	2₋¹⁺⁴×C₆₇	C₂³	1	4	yes	—
68	2₋¹⁺⁴×C₆₇	C₂³	1	4	yes	complemented
69	H(5,𝔽₂)×C₆₇	—	2	4	no	—
70	H(5,𝔽₂)×C₆₇	—	2	2	no	—
71	H(5,𝔽₂)×C₆₇	—	2	2	no	—
72	H(5,𝔽₂)×C₆₇	—	4	2	no	—
73	H(5,𝔽₂)×C₆₇	—	4	1	no	—
74	H(5,𝔽₂)×C₆₇	C₂³	1	4	yes	—
75	H(5,𝔽₂)×C₆₇	C₂³	1	4	yes	—
76	C₂×#41×C₆₇	—	2	4	no	—
77	C₂×#41×C₆₇	—	2	4	no	—
78	C₂×#41×C₆₇	—	2	2	no	—
79	C₂×#41×C₆₇	—	2	2	no	—
80	C₂×#41×C₆₇	—	4	1	no	—
81	C₂×#41×C₆₇	—	4	2	no	—
82	C₂×#41×C₆₇	C₂³	1	2	yes	—
83	C₂×#41×C₆₇	C₂³	1	2	yes	—
84	C₂×#41×C₆₇	C₂³	1	2	yes	—
85	C₂²×Q₈×C₆₇	—	2	2	no	—
86	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₆₇	—	2	2	no	—
88	C₂²×D₄×C₆₇	—	4	1	no	—
89	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
90	#137×C₆₇	—	2	4	no	—
91	#137×C₆₇	—	2	2	no	—
92	#137×C₆₇	—	2	2	no	—
93	#137×C₆₇	—	2	8	no	—
94	#137×C₆₇	—	2	8	no	—
95	#137×C₆₇	—	2	8	no	—
96	#137×C₆₇	—	2	8	no	—
97	#137×C₆₇	—	2	4	no	—
98	#137×C₆₇	—	2	4	no	—
99	#137×C₆₇	D₄	1	4	yes	complemented
100	#137×C₆₇	D₄	1	4	yes	complemented
101	#137×C₆₇	C₂³	1	8	yes	—
102	#137×C₆₇	C₂³	1	4	yes	—
103	#137×C₆₇	C₂³	1	4	yes	complemented
104	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
105	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
106	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
107	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
108	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
109	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
110	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
111	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
112	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
113	AGL(1,ℤ/8)×C₆₇	D₄	1	4	yes	complemented
114	AGL(1,ℤ/8)×C₆₇	D₄	1	4	yes	complemented
115	AGL(1,ℤ/8)×C₆₇	C₂³	1	4	yes	—
116	AGL(1,ℤ/8)×C₆₇	C₂³	1	8	yes	—
117	AGL(1,ℤ/8)×C₆₇	C₂³	1	4	yes	complemented
118	#135×C₆₇	—	2	4	no	—
119	#135×C₆₇	—	2	4	no	—
120	#135×C₆₇	—	2	8	no	—
121	#135×C₆₇	—	2	8	no	—
122	#135×C₆₇	—	2	8	no	—
123	#135×C₆₇	—	2	8	no	—
124	#135×C₆₇	C₂³	1	8	yes	—
125	C₂×Q₁₆×C₆₇	—	2	2	no	—
126	C₂×Q₁₆×C₆₇	—	2	8	no	—
127	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	complemented
128	C₂×SD₁₆×C₆₇	—	2	2	no	—
129	C₂×SD₁₆×C₆₇	—	2	2	no	—
130	C₂×SD₁₆×C₆₇	—	2	8	no	—
131	C₂×SD₁₆×C₆₇	—	2	8	no	—
132	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
133	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
134	C₂×D₈×C₆₇	—	2	2	no	—
135	C₂×D₈×C₆₇	—	2	8	no	—
136	C₂×D₈×C₆₇	C₂³	1	4	yes	—
137	#131×C₆₇	—	2	4	no	—
138	#131×C₆₇	—	2	4	no	—
139	#131×C₆₇	C₂³	1	8	yes	—
140	#131×C₆₇	C₂³	1	8	yes	complemented
141	C₂×M₁₆×C₆₇	—	2	4	no	—
142	C₂×M₁₆×C₆₇	—	2	4	no	—
143	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
144	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
145	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
146	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
147	#127×C₆₇	C₂³	1	1	yes	characteristic, complemented
148	#124×C₆₇	—	4	1	no	—
149	#124×C₆₇	C₂³	1	2	yes	—
150	#124×C₆₇	C₂³	1	2	yes	—
151	#124×C₆₇	C₂³	1	2	yes	complemented
152	#121×C₆₇	—	4	1	no	—
153	C₄×D₄×C₆₇	—	4	1	no	—
154	C₂×C₂²⋊C₄×C₆₇	—	4	1	no	—
155	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
156	#108×C₆₇	C₂³	1	8	yes	complemented
157	#104×C₆₇	C₂³	1	4	yes	—
158	#104×C₆₇	C₂³	1	4	yes	—
159	#104×C₆₇	C₂³	1	4	yes	complemented
160	#104×C₆₇	C₂³	1	4	yes	complemented
161	#101×C₆₇	C₂³	1	4	yes	complemented
162	#101×C₆₇	C₂³	1	4	yes	complemented
163	#100×C₆₇	C₂³	1	4	yes	—
164	#100×C₆₇	C₂³	1	4	yes	complemented
165	#97×C₆₇	C₂³	1	2	yes	complemented
166	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
167	C₂⁴×C₆₇	—	2	1	no	—
168	C₂⁴×C₆₇	—	4	1	no	—
169	#41×C₆₇	—	2	2	no	—
170	#41×C₆₇	—	2	2	no	—
171	#41×C₆₇	—	2	2	no	—
172	#41×C₆₇	—	2	2	no	—
173	#41×C₆₇	—	2	4	no	—
174	#41×C₆₇	—	2	8	no	—
175	#41×C₆₇	—	2	4	no	—
176	#41×C₆₇	—	2	4	no	—
177	#41×C₆₇	—	2	8	no	—
178	#41×C₆₇	—	2	4	no	—
179	#41×C₆₇	—	2	2	no	—
180	#41×C₆₇	—	2	2	no	—
181	#41×C₆₇	—	2	2	no	—
182	#41×C₆₇	—	2	2	no	—
183	#41×C₆₇	—	4	4	no	—
184	#41×C₆₇	—	4	4	no	—
185	#41×C₆₇	—	4	4	no	—
186	#41×C₆₇	—	4	4	no	—
187	#41×C₆₇	—	4	4	no	—
188	#41×C₆₇	—	4	4	no	—
189	#41×C₆₇	—	4	4	no	—
190	#41×C₆₇	—	4	4	no	—
191	#41×C₆₇	—	4	2	no	—
192	#41×C₆₇	—	4	2	no	—
193	#41×C₆₇	C₂×D₄	1	4	yes	—
194	#41×C₆₇	C₂×D₄	1	4	yes	—
195	#41×C₆₇	C₂⁴	1	4	yes	—
196	#41×C₆₇	C₂⁴	1	4	yes	—
197	C₂×Q₈×C₆₇	—	2	1	no	—
198	C₂×Q₈×C₆₇	—	2	4	no	—
199	C₂×Q₈×C₆₇	—	2	8	no	—
200	C₂×Q₈×C₆₇	—	2	4	no	—
201	C₂×Q₈×C₆₇	—	2	2	no	—
202	C₂×Q₈×C₆₇	—	2	2	no	—
203	C₂×Q₈×C₆₇	—	4	1	no	—
204	C₂×Q₈×C₆₇	—	4	4	no	—
205	C₂×Q₈×C₆₇	—	4	2	no	—
206	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
207	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
210	C₂×D₄×C₆₇	—	2	2	no	—
211	C₂×D₄×C₆₇	—	2	2	no	—
212	C₂×D₄×C₆₇	—	2	4	no	—
213	C₂×D₄×C₆₇	—	2	8	no	—
214	C₂×D₄×C₆₇	—	2	4	no	—
215	C₂×D₄×C₆₇	—	2	2	no	—
216	C₂×D₄×C₆₇	—	2	2	no	—
217	C₂×D₄×C₆₇	—	2	2	no	—
218	C₂×D₄×C₆₇	—	2	1	no	—
219	C₂×D₄×C₆₇	—	4	4	no	—
220	C₂×D₄×C₆₇	—	4	2	no	—
221	C₂×D₄×C₆₇	—	4	1	no	—
222	C₂×D₄×C₆₇	—	4	4	no	—
223	C₂×D₄×C₆₇	—	4	4	no	—
224	C₂×D₄×C₆₇	—	4	4	no	—
225	C₂×D₄×C₆₇	—	4	2	no	—
226	C₂×D₄×C₆₇	—	4	4	no	—
227	C₂×D₄×C₆₇	—	4	4	no	—
228	C₂×D₄×C₆₇	—	4	1	no	—
229	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
230	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
231	C₂×D₄×C₆₇	C₂⁴	1	2	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	1	no	—
237	C₂²×C₄×C₆₇	—	2	2	no	—
238	C₂²×C₄×C₆₇	—	4	1	no	—
239	C₂²×C₄×C₆₇	—	4	4	no	—
240	C₂²×C₄×C₆₇	—	4	2	no	—
241	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	Q₁₆×C₆₇	—	2	8	no	—
243	Q₁₆×C₆₇	—	2	4	no	—
244	Q₁₆×C₆₇	—	2	4	no	—
245	Q₁₆×C₆₇	—	2	8	no	—
246	Q₁₆×C₆₇	C₂×D₄	1	8	yes	—
247	SD₁₆×C₆₇	—	2	8	no	—
248	SD₁₆×C₆₇	—	2	4	no	—
249	SD₁₆×C₆₇	—	2	4	no	—
250	SD₁₆×C₆₇	—	2	4	no	—
251	SD₁₆×C₆₇	—	2	8	no	—
252	SD₁₆×C₆₇	—	2	4	no	—
253	SD₁₆×C₆₇	—	2	8	no	—
254	SD₁₆×C₆₇	—	2	8	no	—
255	SD₁₆×C₆₇	C₂×D₄	1	8	yes	—
256	SD₁₆×C₆₇	C₂×D₄	1	8	yes	—
257	D₈×C₆₇	—	2	4	no	—
258	D₈×C₆₇	—	2	8	no	—
259	D₈×C₆₇	—	2	4	no	—
260	D₈×C₆₇	—	2	8	no	—
261	D₈×C₆₇	C₂×D₄	1	8	yes	—
262	M₁₆×C₆₇	—	2	2	no	—
263	M₁₆×C₆₇	—	2	2	no	—
264	M₁₆×C₆₇	—	2	8	no	—
265	M₁₆×C₆₇	—	2	8	no	—
266	M₁₆×C₆₇	C₂×D₄	1	4	yes	—
267	M₁₆×C₆₇	C₂×D₄	1	4	yes	—
268	M₁₆×C₆₇	C₂⁴	1	4	yes	—
269	M₁₆×C₆₇	C₂⁴	1	4	yes	—
270	C₂×C₈×C₆₇	—	2	2	no	—
271	C₂×C₈×C₆₇	—	2	2	no	—
272	C₂×C₈×C₆₇	—	2	8	no	—
273	C₂×C₈×C₆₇	—	2	8	no	—
274	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
275	C₄⋊C₄×C₆₇	—	4	1	no	—
276	C₂²⋊C₄×C₆₇	—	4	2	no	—
277	C₂²⋊C₄×C₆₇	—	4	2	no	—
278	C₂²⋊C₄×C₆₇	—	4	2	no	—
279	C₄²×C₆₇	—	2	1	no	—
280	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
281	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
282	C₂³×C₆₇	—	2	2	no	—
283	C₂³×C₆₇	—	2	2	no	—
284	C₂³×C₆₇	—	2	2	no	—
285	C₂³×C₆₇	—	2	2	no	—
286	C₂³×C₆₇	—	4	4	no	—
287	C₂³×C₆₇	—	4	4	no	—
288	C₂³×C₆₇	—	4	1	no	—
289	C₂³×C₆₇	—	4	1	no	—
290	C₂³×C₆₇	—	8	2	no	—
291	C₂³×C₆₇	—	16	2	no	—
292	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
293	Q₈×C₆₇	—	2	2	no	—
294	Q₈×C₆₇	—	2	2	no	—
295	Q₈×C₆₇	—	2	2	no	—
296	Q₈×C₆₇	—	2	4	no	—
297	Q₈×C₆₇	—	2	2	no	—
298	Q₈×C₆₇	—	4	4	no	—
299	Q₈×C₆₇	—	4	4	no	—
300	Q₈×C₆₇	—	4	2	no	—
301	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
302	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
303	D₄×C₆₇	—	2	4	no	—
304	D₄×C₆₇	—	2	4	no	—
305	D₄×C₆₇	—	2	4	no	—
306	D₄×C₆₇	—	2	4	no	—
307	D₄×C₆₇	—	2	2	no	—
308	D₄×C₆₇	—	2	2	no	—
309	D₄×C₆₇	—	2	2	no	—
310	D₄×C₆₇	—	2	4	no	—
311	D₄×C₆₇	—	2	2	no	—
312	D₄×C₆₇	—	4	8	no	—
313	D₄×C₆₇	—	4	4	no	—
314	D₄×C₆₇	—	4	4	no	—
315	D₄×C₆₇	—	4	4	no	—
316	D₄×C₆₇	—	4	4	no	—
317	D₄×C₆₇	—	4	2	no	—
318	D₄×C₆₇	—	4	2	no	—
319	D₄×C₆₇	—	4	2	no	—
320	D₄×C₆₇	—	8	2	no	—
321	D₄×C₆₇	C₂²×D₄	1	4	yes	—
322	D₄×C₆₇	C₂²×D₄	1	4	yes	—
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	4	no	—
327	C₂×C₄×C₆₇	—	2	4	no	—
328	C₂×C₄×C₆₇	—	2	4	no	—
329	C₂×C₄×C₆₇	—	2	1	no	—
330	C₂×C₄×C₆₇	—	2	1	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	4	4	no	—
334	C₂×C₄×C₆₇	—	4	4	no	—
335	C₂×C₄×C₆₇	—	4	4	no	—
336	C₂×C₄×C₆₇	—	4	4	no	—
337	C₂×C₄×C₆₇	—	4	8	no	—
338	C₂×C₄×C₆₇	—	4	1	no	—
339	C₂×C₄×C₆₇	—	4	1	no	—
340	C₂×C₄×C₆₇	—	4	2	no	—
341	C₂×C₄×C₆₇	—	4	2	no	—
342	C₂×C₄×C₆₇	—	8	1	no	—
343	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
347	C₈×C₆₇	—	2	4	no	—
348	C₈×C₆₇	—	2	4	no	—
349	C₈×C₆₇	C₂²×D₄	1	8	yes	—
350	C₂²×C₆₇	—	2	4	no	—
351	C₂²×C₆₇	—	2	4	no	—
352	C₂²×C₆₇	—	4	1	no	—
353	C₂²×C₆₇	—	4	2	no	—
354	C₂²×C₆₇	—	4	2	no	—
355	C₂²×C₆₇	—	8	2	no	—
356	C₂²×C₆₇	—	8	2	no	—
357	C₂²×C₆₇	—	8	2	no	—
358	C₂²×C₆₇	—	8	2	no	—
359	C₂²×C₆₇	—	8	2	no	—
360	C₂²×C₆₇	—	16	1	no	—
361	C₂²×C₆₇	—	16	4	no	—
362	C₂²×C₆₇	—	16	4	no	—
363	C₂²×C₆₇	D₄²	1	1	yes	characteristic
364	C₂²×C₆₇	D₄²	1	1	yes	characteristic
365	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
366	C₄×C₆₇	—	2	4	no	—
367	C₄×C₆₇	—	2	4	no	—
368	C₄×C₆₇	—	4	1	no	—
369	C₄×C₆₇	—	4	1	no	—
370	C₄×C₆₇	—	4	2	no	—
371	C₄×C₆₇	—	4	2	no	—
372	C₄×C₆₇	D₄²	1	2	yes	—
373	C₄×C₆₇	C₂³×D₄	1	2	yes	—
374	#61109	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
375	C₂×C₆₇	—	2	1	no	—
376	C₂×C₆₇	—	2	1	no	—
377	C₂×C₆₇	—	2	1	no	—
378	C₂×C₆₇	—	4	4	no	—
379	C₂×C₆₇	—	4	4	no	—
380	C₂×C₆₇	—	8	2	no	—
381	C₂×C₆₇	—	8	2	no	—
382	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
383	#3586	C₂×C₆₇	1	2	yes	complemented
384	#3585	C₂×C₆₇	1	2	yes	complemented
385	#3290	C₂×C₆₇	1	8	yes	complemented
386	#3289	C₂×C₆₇	1	4	yes	complemented
387	#3288	C₂×C₆₇	1	4	yes	complemented
388	#3153	C₂×C₆₇	1	1	yes	characteristic, complemented
389	#3069	C₂×C₆₇	1	2	yes	complemented
390	#3068	C₂×C₆₇	1	2	yes	complemented
391	#3018	C₂×C₆₇	1	2	yes	complemented
392	C₂×#454	C₂×C₆₇	1	1	yes	characteristic, complemented
393	C₂×#455	C₂×C₆₇	1	1	yes	characteristic, complemented
394	#2956	C₂×C₆₇	1	2	yes	complemented
395	C₆₇	#61109	1	1	yes	characteristic, direct product factor, Sylow
396	#585	C₂²×C₆₇	1	2	yes	complemented
397	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
398	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
399	#578	—	2	4	no	—
400	#578	C₂²×C₆₇	1	8	yes	complemented
401	#577	—	2	4	no	—
402	#577	—	2	4	no	—
403	#577	C₂²×C₆₇	1	8	yes	complemented
404	#577	C₂²×C₆₇	1	8	yes	complemented
405	#576	—	2	4	no	—
406	#576	C₂²×C₆₇	1	8	yes	complemented
407	#575	—	2	4	no	—
408	#575	—	2	4	no	—
409	#575	C₂²×C₆₇	1	2	yes	—
410	#575	C₂²×C₆₇	1	2	yes	—
411	#575	C₂²×C₆₇	1	2	yes	complemented
412	C₂×#137	—	2	4	no	—
413	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
414	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
415	C₂×AGL(1,ℤ/8)	—	2	4	no	—
416	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
417	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
418	#568	C₂²×C₆₇	1	2	yes	complemented
419	#568	C₂²×C₆₇	1	2	yes	complemented
420	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
421	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
422	#497	C₂²×C₆₇	1	2	yes	complemented
423	#496	C₂²×C₆₇	1	2	yes	complemented
424	#495	C₂²×C₆₇	1	4	yes	complemented
425	#473	C₂²×C₆₇	1	8	yes	complemented
426	#472	C₂²×C₆₇	1	8	yes	complemented
427	#471	C₂²×C₆₇	1	8	yes	complemented
428	#471	C₂²×C₆₇	1	8	yes	complemented
429	#456	C₂²×C₆₇	1	4	yes	complemented
430	#455	C₂²×C₆₇	1	4	yes	complemented
431	#455	C₂²×C₆₇	1	4	yes	complemented
432	#455	C₂²×C₆₇	1	4	yes	complemented
433	#454	C₂²×C₆₇	1	4	yes	complemented
434	#454	C₂²×C₆₇	1	4	yes	complemented
435	#454	C₂²×C₆₇	1	4	yes	complemented
436	#453	C₂²×C₆₇	1	4	yes	complemented
437	#444	C₂²×C₆₇	1	8	yes	complemented
438	#443	C₂²×C₆₇	1	8	yes	complemented
439	#430	C₂²×C₆₇	1	2	yes	complemented
440	C₂×#104	C₂²×C₆₇	1	2	yes	complemented
441	C₂×#104	C₂²×C₆₇	1	2	yes	complemented
442	#413	C₂²×C₆₇	1	2	yes	complemented
443	C₂×#101	C₂²×C₆₇	1	1	yes	characteristic, complemented
444	C₂×#100	C₂²×C₆₇	1	1	yes	characteristic, complemented
445	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
446	2₋¹⁺⁴	—	2	4	no	—
447	2₋¹⁺⁴	—	2	2	no	—
448	2₋¹⁺⁴	—	2	2	no	—
449	2₋¹⁺⁴	—	4	1	no	—
450	2₋¹⁺⁴	C₂³×C₆₇	1	4	yes	—
451	2₋¹⁺⁴	C₂³×C₆₇	1	4	yes	complemented
452	H(5,𝔽₂)	—	2	4	no	—
453	H(5,𝔽₂)	—	2	2	no	—
454	H(5,𝔽₂)	—	2	2	no	—
455	H(5,𝔽₂)	—	4	2	no	—
456	H(5,𝔽₂)	—	4	1	no	—
457	H(5,𝔽₂)	C₂³×C₆₇	1	4	yes	—
458	H(5,𝔽₂)	C₂³×C₆₇	1	4	yes	—
459	C₂×#41	—	2	4	no	—
460	C₂×#41	—	2	4	no	—
461	C₂×#41	—	2	2	no	—
462	C₂×#41	—	2	2	no	—
463	C₂×#41	—	4	1	no	—
464	C₂×#41	—	4	2	no	—
465	C₂×#41	C₂³×C₆₇	1	2	yes	—
466	C₂×#41	C₂³×C₆₇	1	2	yes	—
467	C₂×#41	C₂³×C₆₇	1	2	yes	—
468	C₂²×Q₈	—	2	2	no	—
469	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
470	C₂²×D₄	—	2	2	no	—
471	C₂²×D₄	—	4	1	no	—
472	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
473	#137	—	2	4	no	—
474	#137	—	2	2	no	—
475	#137	—	2	2	no	—
476	#137	—	2	8	no	—
477	#137	—	2	8	no	—
478	#137	—	2	8	no	—
479	#137	—	2	8	no	—
480	#137	—	2	4	no	—
481	#137	—	2	4	no	—
482	#137	D₄×C₆₇	1	4	yes	complemented
483	#137	D₄×C₆₇	1	4	yes	complemented
484	#137	C₂³×C₆₇	1	8	yes	—
485	#137	C₂³×C₆₇	1	4	yes	—
486	#137	C₂³×C₆₇	1	4	yes	complemented
487	AGL(1,ℤ/8)	—	2	4	no	—
488	AGL(1,ℤ/8)	—	2	2	no	—
489	AGL(1,ℤ/8)	—	2	2	no	—
490	AGL(1,ℤ/8)	—	2	8	no	—
491	AGL(1,ℤ/8)	—	2	8	no	—
492	AGL(1,ℤ/8)	—	2	8	no	—
493	AGL(1,ℤ/8)	—	2	8	no	—
494	AGL(1,ℤ/8)	—	2	4	no	—
495	AGL(1,ℤ/8)	—	2	4	no	—
496	AGL(1,ℤ/8)	D₄×C₆₇	1	4	yes	complemented
497	AGL(1,ℤ/8)	D₄×C₆₇	1	4	yes	complemented
498	AGL(1,ℤ/8)	C₂³×C₆₇	1	8	yes	—
499	AGL(1,ℤ/8)	C₂³×C₆₇	1	4	yes	—
500	AGL(1,ℤ/8)	C₂³×C₆₇	1	4	yes	complemented
501	#135	—	2	4	no	—
502	#135	—	2	4	no	—
503	#135	—	2	8	no	—
504	#135	—	2	8	no	—
505	#135	—	2	8	no	—
506	#135	—	2	8	no	—
507	#135	C₂³×C₆₇	1	8	yes	—
508	C₂×Q₁₆	—	2	2	no	—
509	C₂×Q₁₆	—	2	8	no	—
510	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	complemented
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	2	2	no	—
513	C₂×SD₁₆	—	2	8	no	—
514	C₂×SD₁₆	—	2	8	no	—
515	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
516	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
517	C₂×D₈	—	2	2	no	—
518	C₂×D₈	—	2	8	no	—
519	C₂×D₈	C₂³×C₆₇	1	4	yes	—
520	#131	—	2	4	no	—
521	#131	—	2	4	no	—
522	#131	C₂³×C₆₇	1	8	yes	—
523	#131	C₂³×C₆₇	1	8	yes	complemented
524	C₂×M₁₆	—	2	4	no	—
525	C₂×M₁₆	—	2	4	no	—
526	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
527	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
528	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
529	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
530	#127	C₂³×C₆₇	1	1	yes	characteristic, complemented
531	#124	—	4	1	no	—
532	#124	C₂³×C₆₇	1	2	yes	—
533	#124	C₂³×C₆₇	1	2	yes	—
534	#124	C₂³×C₆₇	1	2	yes	complemented
535	#121	—	4	1	no	—
536	C₄×D₄	—	4	1	no	—
537	C₂×C₂²⋊C₄	—	4	1	no	—
538	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
539	#108	C₂³×C₆₇	1	8	yes	complemented
540	#104	C₂³×C₆₇	1	4	yes	—
541	#104	C₂³×C₆₇	1	4	yes	—
542	#104	C₂³×C₆₇	1	4	yes	complemented
543	#104	C₂³×C₆₇	1	4	yes	complemented
544	#101	C₂³×C₆₇	1	4	yes	complemented
545	#101	C₂³×C₆₇	1	4	yes	complemented
546	#100	C₂³×C₆₇	1	4	yes	—
547	#100	C₂³×C₆₇	1	4	yes	complemented
548	#97	C₂³×C₆₇	1	2	yes	complemented
549	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
550	C₂⁴	—	2	1	no	—
551	C₂⁴	—	4	1	no	—
552	#41	—	2	2	no	—
553	#41	—	2	2	no	—
554	#41	—	2	2	no	—
555	#41	—	2	2	no	—
556	#41	—	2	4	no	—
557	#41	—	2	8	no	—
558	#41	—	2	4	no	—
559	#41	—	2	4	no	—
560	#41	—	2	8	no	—
561	#41	—	2	4	no	—
562	#41	—	2	2	no	—
563	#41	—	2	2	no	—
564	#41	—	2	2	no	—
565	#41	—	2	2	no	—
566	#41	—	4	4	no	—
567	#41	—	4	4	no	—
568	#41	—	4	4	no	—
569	#41	—	4	4	no	—
570	#41	—	4	4	no	—
571	#41	—	4	4	no	—
572	#41	—	4	4	no	—
573	#41	—	4	4	no	—
574	#41	—	4	2	no	—
575	#41	—	4	2	no	—
576	#41	C₂×D₄×C₆₇	1	4	yes	—
577	#41	C₂×D₄×C₆₇	1	4	yes	—
578	#41	C₂⁴×C₆₇	1	4	yes	—
579	#41	C₂⁴×C₆₇	1	4	yes	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	4	no	—
582	C₂×Q₈	—	2	8	no	—
583	C₂×Q₈	—	2	4	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	4	1	no	—
587	C₂×Q₈	—	4	4	no	—
588	C₂×Q₈	—	4	2	no	—
589	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
590	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
591	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
592	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	4	4	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	1	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	4	2	no	—
609	C₂×D₄	—	4	4	no	—
610	C₂×D₄	—	4	4	no	—
611	C₂×D₄	—	4	1	no	—
612	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
613	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
614	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
615	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	4	1	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	2	no	—
624	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
625	Q₁₆	—	2	8	no	—
626	Q₁₆	—	2	4	no	—
627	Q₁₆	—	2	4	no	—
628	Q₁₆	—	2	8	no	—
629	Q₁₆	C₂×D₄×C₆₇	1	8	yes	—
630	SD₁₆	—	2	8	no	—
631	SD₁₆	—	2	4	no	—
632	SD₁₆	—	2	4	no	—
633	SD₁₆	—	2	4	no	—
634	SD₁₆	—	2	8	no	—
635	SD₁₆	—	2	4	no	—
636	SD₁₆	—	2	8	no	—
637	SD₁₆	—	2	8	no	—
638	SD₁₆	C₂×D₄×C₆₇	1	8	yes	—
639	SD₁₆	C₂×D₄×C₆₇	1	8	yes	—
640	D₈	—	2	4	no	—
641	D₈	—	2	8	no	—
642	D₈	—	2	4	no	—
643	D₈	—	2	8	no	—
644	D₈	C₂×D₄×C₆₇	1	8	yes	—
645	M₁₆	—	2	2	no	—
646	M₁₆	—	2	2	no	—
647	M₁₆	—	2	8	no	—
648	M₁₆	—	2	8	no	—
649	M₁₆	C₂×D₄×C₆₇	1	4	yes	—
650	M₁₆	C₂×D₄×C₆₇	1	4	yes	—
651	M₁₆	C₂⁴×C₆₇	1	4	yes	—
652	M₁₆	C₂⁴×C₆₇	1	4	yes	—
653	C₂×C₈	—	2	2	no	—
654	C₂×C₈	—	2	2	no	—
655	C₂×C₈	—	2	8	no	—
656	C₂×C₈	—	2	8	no	—
657	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
658	C₄⋊C₄	—	4	1	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	2	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₄²	—	2	1	no	—
663	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
664	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	4	4	no	—
670	C₂³	—	4	4	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	8	2	no	—
674	C₂³	—	16	2	no	—
675	C₂³	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
676	Q₈	—	2	2	no	—
677	Q₈	—	2	2	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	2	4	no	—
680	Q₈	—	2	2	no	—
681	Q₈	—	4	4	no	—
682	Q₈	—	4	4	no	—
683	Q₈	—	4	2	no	—
684	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
685	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
686	D₄	—	2	4	no	—
687	D₄	—	2	4	no	—
688	D₄	—	2	4	no	—
689	D₄	—	2	4	no	—
690	D₄	—	2	2	no	—
691	D₄	—	2	2	no	—
692	D₄	—	2	2	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	2	no	—
695	D₄	—	4	8	no	—
696	D₄	—	4	4	no	—
697	D₄	—	4	4	no	—
698	D₄	—	4	4	no	—
699	D₄	—	4	4	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	2	no	—
702	D₄	—	4	2	no	—
703	D₄	—	8	2	no	—
704	D₄	C₂²×D₄×C₆₇	1	4	yes	—
705	D₄	C₂²×D₄×C₆₇	1	4	yes	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	8	1	no	—
726	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
728	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
729	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
730	C₈	—	2	4	no	—
731	C₈	—	2	4	no	—
732	C₈	C₂²×D₄×C₆₇	1	8	yes	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	8	2	no	—
739	C₂²	—	8	2	no	—
740	C₂²	—	8	2	no	—
741	C₂²	—	8	2	no	—
742	C₂²	—	8	2	no	—
743	C₂²	—	16	1	no	—
744	C₂²	—	16	4	no	—
745	C₂²	—	16	4	no	—
746	C₂²	D₄²×C₆₇	1	1	yes	characteristic
747	C₂²	D₄²×C₆₇	1	1	yes	characteristic
748	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
749	C₄	—	2	4	no	—
750	C₄	—	2	4	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	D₄²×C₆₇	1	2	yes	—
756	C₄	C₂³×D₄×C₆₇	1	2	yes	—
757	C₂	—	2	1	no	—
758	C₂	—	2	1	no	—
759	C₂	—	2	1	no	—
760	C₂	—	4	4	no	—
761	C₂	—	4	4	no	—
762	C₂	—	8	2	no	—
763	C₂	—	8	2	no	—
764	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₆₇	C₂×D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₇ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3586	C₂	semidirect
2. C₆₇×#3585	C₂	semidirect
3. C₆₇×#3290	C₂	semidirect
4. C₆₇×#3289	C₂	semidirect
5. C₆₇×#3288	C₂	semidirect
6. C₆₇×#3153	C₂	semidirect
7. C₆₇×#3069	C₂	semidirect
8. C₆₇×#3068	C₂	semidirect
9. C₆₇×#3018	C₂	semidirect
10. C₂×#454×C₆₇	C₂	semidirect
11. C₂×#455×C₆₇	C₂	semidirect
12. C₆₇×#2956	C₂	semidirect
13. #585×C₆₇	C₂²	semidirect
14. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
17. #578×C₆₇	C₂²	semidirect
20. #577×C₆₇	C₂²	semidirect
21. #577×C₆₇	C₂²	semidirect
23. #576×C₆₇	C₂²	semidirect
28. #575×C₆₇	C₂²	semidirect
30. C₂×#137×C₆₇	C₂²	semidirect
31. C₂×#137×C₆₇	C₂²	semidirect
33. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
34. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
35. #568×C₆₇	C₂²	semidirect
36. #568×C₆₇	C₂²	semidirect
37. #532×C₆₇	C₂²	semidirect
38. C₂×#124×C₆₇	C₂²	semidirect
39. #497×C₆₇	C₂²	semidirect
40. #496×C₆₇	C₂²	semidirect
41. #495×C₆₇	C₂²	semidirect
42. #473×C₆₇	C₂²	semidirect
43. #472×C₆₇	C₂²	semidirect
44. #471×C₆₇	C₂²	semidirect
45. #471×C₆₇	C₂²	semidirect
46. #456×C₆₇	C₂²	semidirect
47. #455×C₆₇	C₂²	semidirect
48. #455×C₆₇	C₂²	semidirect
49. #455×C₆₇	C₂²	semidirect
50. #454×C₆₇	C₂²	semidirect
51. #454×C₆₇	C₂²	semidirect
52. #454×C₆₇	C₂²	semidirect
53. #453×C₆₇	C₂²	semidirect
54. #444×C₆₇	C₂²	semidirect
55. #443×C₆₇	C₂²	semidirect
56. #430×C₆₇	C₂²	semidirect
57. C₂×#104×C₆₇	C₂²	semidirect
58. C₂×#104×C₆₇	C₂²	semidirect
59. #413×C₆₇	C₂²	semidirect
60. C₂×#101×C₆₇	C₂²	semidirect
61. C₂×#100×C₆₇	C₂²	semidirect
62. C₄×M₁₆×C₆₇	C₂²	semidirect
68. 2₋¹⁺⁴×C₆₇	C₂³	semidirect
99. #137×C₆₇	D₄	semidirect
100. #137×C₆₇	D₄	semidirect
103. #137×C₆₇	C₂³	semidirect
113. AGL(1,ℤ/8)×C₆₇	D₄	semidirect
114. AGL(1,ℤ/8)×C₆₇	D₄	semidirect
117. AGL(1,ℤ/8)×C₆₇	C₂³	semidirect
127. C₂×Q₁₆×C₆₇	C₂³	semidirect
133. C₂×SD₁₆×C₆₇	C₂³	semidirect
140. #131×C₆₇	C₂³	semidirect
146. C₄⋊Q₈×C₆₇	C₂³	semidirect
147. #127×C₆₇	C₂³	semidirect
151. #124×C₆₇	C₂³	semidirect
156. #108×C₆₇	C₂³	semidirect
159. #104×C₆₇	C₂³	semidirect
160. #104×C₆₇	C₂³	semidirect
161. #101×C₆₇	C₂³	semidirect
162. #101×C₆₇	C₂³	semidirect
164. #100×C₆₇	C₂³	semidirect
165. #97×C₆₇	C₂³	semidirect
166. C₄×C₈×C₆₇	C₂³	semidirect
374. #61109	C₆₇	direct (N × H)
383. #3586	C₂×C₆₇	semidirect
384. #3585	C₂×C₆₇	semidirect
385. #3290	C₂×C₆₇	semidirect
386. #3289	C₂×C₆₇	semidirect
387. #3288	C₂×C₆₇	semidirect
388. #3153	C₂×C₆₇	semidirect
389. #3069	C₂×C₆₇	semidirect
390. #3068	C₂×C₆₇	semidirect
391. #3018	C₂×C₆₇	semidirect
392. C₂×#454	C₂×C₆₇	semidirect
393. C₂×#455	C₂×C₆₇	semidirect
394. #2956	C₂×C₆₇	semidirect
395. C₆₇	#61109	direct (N × H)
396. #585	C₂²×C₆₇	semidirect
397. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
400. #578	C₂²×C₆₇	semidirect
403. #577	C₂²×C₆₇	semidirect
404. #577	C₂²×C₆₇	semidirect
406. #576	C₂²×C₆₇	semidirect
411. #575	C₂²×C₆₇	semidirect
413. C₂×#137	C₂²×C₆₇	semidirect
414. C₂×#137	C₂²×C₆₇	semidirect
416. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
417. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
418. #568	C₂²×C₆₇	semidirect
419. #568	C₂²×C₆₇	semidirect
420. #532	C₂²×C₆₇	semidirect
421. C₂×#124	C₂²×C₆₇	semidirect
422. #497	C₂²×C₆₇	semidirect
423. #496	C₂²×C₆₇	semidirect
424. #495	C₂²×C₆₇	semidirect
425. #473	C₂²×C₆₇	semidirect
426. #472	C₂²×C₆₇	semidirect
427. #471	C₂²×C₆₇	semidirect
428. #471	C₂²×C₆₇	semidirect
429. #456	C₂²×C₆₇	semidirect
430. #455	C₂²×C₆₇	semidirect
431. #455	C₂²×C₆₇	semidirect
432. #455	C₂²×C₆₇	semidirect
433. #454	C₂²×C₆₇	semidirect
434. #454	C₂²×C₆₇	semidirect
435. #454	C₂²×C₆₇	semidirect
436. #453	C₂²×C₆₇	semidirect
437. #444	C₂²×C₆₇	semidirect
438. #443	C₂²×C₆₇	semidirect
439. #430	C₂²×C₆₇	semidirect
440. C₂×#104	C₂²×C₆₇	semidirect
441. C₂×#104	C₂²×C₆₇	semidirect
442. #413	C₂²×C₆₇	semidirect
443. C₂×#101	C₂²×C₆₇	semidirect
444. C₂×#100	C₂²×C₆₇	semidirect
445. C₄×M₁₆	C₂²×C₆₇	semidirect
451. 2₋¹⁺⁴	C₂³×C₆₇	semidirect
482. #137	D₄×C₆₇	semidirect
483. #137	D₄×C₆₇	semidirect
486. #137	C₂³×C₆₇	semidirect
496. AGL(1,ℤ/8)	D₄×C₆₇	semidirect
497. AGL(1,ℤ/8)	D₄×C₆₇	semidirect
500. AGL(1,ℤ/8)	C₂³×C₆₇	semidirect
510. C₂×Q₁₆	C₂³×C₆₇	semidirect
516. C₂×SD₁₆	C₂³×C₆₇	semidirect
523. #131	C₂³×C₆₇	semidirect
529. C₄⋊Q₈	C₂³×C₆₇	semidirect
530. #127	C₂³×C₆₇	semidirect
534. #124	C₂³×C₆₇	semidirect
539. #108	C₂³×C₆₇	semidirect
542. #104	C₂³×C₆₇	semidirect
543. #104	C₂³×C₆₇	semidirect
544. #101	C₂³×C₆₇	semidirect
545. #101	C₂³×C₆₇	semidirect
547. #100	C₂³×C₆₇	semidirect
548. #97	C₂³×C₆₇	semidirect
549. 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×#3586	2
C₆₇×#3585	2
C₆₇×#3290	2
C₆₇×#3289	2
C₆₇×#3288	2
C₆₇×#3153	2
C₆₇×#3069	2
C₆₇×#3068	2
C₆₇×#3018	2
C₂×#454×C₆₇	2
C₂×#455×C₆₇	2
C₆₇×#2956	2
#61109	67

Subgroups — C67×#61109 #30740360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61109 #30740360