Subgroups — C₆₇×#61090 #30740341

Order 17152.

2714 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#578×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#576×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3500	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3285	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3280	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3275	C₂	1	8	yes	maximal, complemented
7	C₂×#495×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3059	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3058	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3040	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3010	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3009	C₂	1	2	yes	maximal, complemented
13	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	complemented
16	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
17	#578×C₆₇	—	2	8	no	—
18	#576×C₆₇	—	2	8	no	—
19	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
20	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
21	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
22	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	—
23	C₂×#135×C₆₇	C₂²	1	2	yes	—
24	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
26	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
27	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
29	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
30	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#548×C₆₇	C₂²	1	8	yes	complemented
34	#546×C₆₇	—	2	8	no	—
35	#546×C₆₇	C₂²	1	8	yes	complemented
36	#536×C₆₇	—	2	2	no	—
37	#536×C₆₇	C₂²	1	2	yes	—
38	#535×C₆₇	—	2	2	no	—
39	#535×C₆₇	C₂²	1	2	yes	complemented
40	#532×C₆₇	—	2	2	no	—
41	#532×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#124×C₆₇	—	2	2	no	—
43	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
44	C₄×#41×C₆₇	C₂²	1	2	yes	complemented
45	#495×C₆₇	C₂²	1	4	yes	complemented
46	#495×C₆₇	C₂²	1	4	yes	complemented
47	#470×C₆₇	C₂²	1	4	yes	complemented
48	#469×C₆₇	C₂²	1	4	yes	complemented
49	#467×C₆₇	C₂²	1	4	yes	complemented
50	#466×C₆₇	C₂²	1	4	yes	complemented
51	#464×C₆₇	C₂²	1	8	yes	complemented
52	#463×C₆₇	C₂²	1	8	yes	complemented
53	#452×C₆₇	C₂²	1	8	yes	complemented
54	#450×C₆₇	C₂²	1	8	yes	complemented
55	#449×C₆₇	C₂²	1	8	yes	complemented
56	#448×C₆₇	C₂²	1	8	yes	complemented
57	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
58	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
59	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
60	#436×C₆₇	C₂²	1	4	yes	complemented
61	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
62	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#419×C₆₇	C₂²	1	2	yes	complemented
65	#418×C₆₇	C₂²	1	2	yes	complemented
66	#416×C₆₇	C₂²	1	2	yes	complemented
67	#408×C₆₇	C₂²	1	1	yes	characteristic
68	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	2₋¹⁺⁴×C₆₇	—	2	8	no	—
71	2₋¹⁺⁴×C₆₇	—	4	4	no	—
72	H(5,𝔽₂)×C₆₇	—	2	8	no	—
73	H(5,𝔽₂)×C₆₇	—	4	4	no	—
74	C₂×#41×C₆₇	—	2	2	no	—
75	C₂×#41×C₆₇	—	2	2	no	—
76	C₂×#41×C₆₇	—	2	4	no	—
77	C₂×#41×C₆₇	C₂³	1	4	yes	—
78	C₂×#41×C₆₇	C₂³	1	4	yes	—
79	C₂×#41×C₆₇	C₂³	1	2	yes	—
80	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
81	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₆₇	—	2	2	no	—
83	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
84	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
85	C₂²×D₄×C₆₇	—	2	2	no	—
86	C₂²×D₄×C₆₇	—	2	4	no	—
87	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
88	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
89	#137×C₆₇	—	2	8	no	—
90	#137×C₆₇	—	2	16	no	—
91	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
92	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
93	#135×C₆₇	—	2	8	no	—
94	#135×C₆₇	—	2	8	no	—
95	#135×C₆₇	D₄	1	8	yes	complemented
96	C₂×Q₁₆×C₆₇	—	2	8	no	—
97	C₂×Q₁₆×C₆₇	—	2	4	no	—
98	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
99	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
102	C₂×SD₁₆×C₆₇	—	4	4	no	—
103	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
106	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
107	C₂×D₈×C₆₇	—	2	8	no	—
108	C₂×D₈×C₆₇	—	2	4	no	—
109	C₂×D₈×C₆₇	C₂³	1	4	yes	—
110	C₂×D₈×C₆₇	C₂³	1	2	yes	—
111	C₂×D₈×C₆₇	C₂³	1	2	yes	—
112	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
113	#131×C₆₇	—	2	4	no	—
114	#131×C₆₇	—	2	4	no	—
115	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
116	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
117	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
120	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
121	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₆₇	—	2	2	no	—
124	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
125	#127×C₆₇	—	2	2	no	—
126	#127×C₆₇	D₄	1	1	yes	characteristic
127	#124×C₆₇	—	2	2	no	—
128	#124×C₆₇	—	2	2	no	—
129	#124×C₆₇	—	2	8	no	—
130	#124×C₆₇	—	2	2	no	—
131	#124×C₆₇	—	2	2	no	—
132	#124×C₆₇	D₄	1	1	yes	characteristic
133	#124×C₆₇	D₄	1	1	yes	characteristic
134	#124×C₆₇	C₂³	1	8	yes	—
135	#123×C₆₇	—	2	4	no	—
136	#123×C₆₇	—	2	8	no	—
137	C₂²⋊Q₈×C₆₇	—	2	8	no	—
138	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
139	#121×C₆₇	—	2	8	no	—
140	#121×C₆₇	—	2	8	no	—
141	#121×C₆₇	D₄	1	4	yes	—
142	#121×C₆₇	C₂³	1	8	yes	—
143	#120×C₆₇	—	2	8	no	—
144	#120×C₆₇	—	2	4	no	—
145	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
146	C₄×D₄×C₆₇	—	2	4	no	—
147	C₄×D₄×C₆₇	—	2	8	no	—
148	C₄×D₄×C₆₇	C₂³	1	4	yes	—
149	C₄×D₄×C₆₇	C₂³	1	4	yes	—
150	#117×C₆₇	—	2	2	no	—
151	#117×C₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
153	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
154	C₂×C₄²×C₆₇	—	2	2	no	—
155	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
156	#107×C₆₇	C₂³	1	2	yes	—
157	#106×C₆₇	C₂³	1	2	yes	—
158	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
159	#103×C₆₇	C₂³	1	4	yes	—
160	#103×C₆₇	C₂³	1	8	yes	—
161	#102×C₆₇	C₂³	1	4	yes	—
162	#102×C₆₇	C₂³	1	8	yes	—
163	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
164	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
165	C₄×C₈×C₆₇	C₂³	1	2	yes	—
166	C₄×C₈×C₆₇	C₂³	1	2	yes	—
167	C₂⁴×C₆₇	—	2	4	no	—
168	C₂⁴×C₆₇	—	2	2	no	—
169	#41×C₆₇	—	2	2	no	—
170	#41×C₆₇	—	2	2	no	—
171	#41×C₆₇	—	2	2	no	—
172	#41×C₆₇	—	2	4	no	—
173	#41×C₆₇	—	2	2	no	—
174	#41×C₆₇	—	2	8	no	—
175	#41×C₆₇	—	2	8	no	—
176	#41×C₆₇	—	4	4	no	—
177	#41×C₆₇	—	4	4	no	—
178	#41×C₆₇	—	4	8	no	—
179	#41×C₆₇	—	4	8	no	—
180	#41×C₆₇	—	4	16	no	—
181	#41×C₆₇	C₂×D₄	1	8	yes	—
182	C₂×Q₈×C₆₇	—	2	4	no	—
183	C₂×Q₈×C₆₇	—	2	2	no	—
184	C₂×Q₈×C₆₇	—	2	8	no	—
185	C₂×Q₈×C₆₇	—	2	4	no	—
186	C₂×Q₈×C₆₇	—	2	4	no	—
187	C₂×Q₈×C₆₇	—	4	4	no	—
188	C₂×Q₈×C₆₇	—	4	8	no	—
189	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
191	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
192	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
193	C₂×D₄×C₆₇	—	2	2	no	—
194	C₂×D₄×C₆₇	—	2	8	no	—
195	C₂×D₄×C₆₇	—	2	4	no	—
196	C₂×D₄×C₆₇	—	2	4	no	—
197	C₂×D₄×C₆₇	—	2	8	no	—
198	C₂×D₄×C₆₇	—	2	4	no	—
199	C₂×D₄×C₆₇	—	2	4	no	—
200	C₂×D₄×C₆₇	—	2	2	no	—
201	C₂×D₄×C₆₇	—	2	4	no	—
202	C₂×D₄×C₆₇	—	4	4	no	—
203	C₂×D₄×C₆₇	—	4	8	no	—
204	C₂×D₄×C₆₇	—	4	16	no	—
205	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
206	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
207	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
208	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
209	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
210	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
211	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₆₇	—	2	2	no	—
213	C₂²×C₄×C₆₇	—	2	2	no	—
214	C₂²×C₄×C₆₇	—	2	4	no	—
215	C₂²×C₄×C₆₇	—	2	4	no	—
216	C₂²×C₄×C₆₇	—	2	4	no	—
217	C₂²×C₄×C₆₇	—	2	4	no	—
218	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
222	Q₁₆×C₆₇	—	2	8	no	—
223	Q₁₆×C₆₇	—	2	4	no	—
224	Q₁₆×C₆₇	—	2	4	no	—
225	Q₁₆×C₆₇	C₂×D₄	1	4	yes	—
226	SD₁₆×C₆₇	—	2	8	no	—
227	SD₁₆×C₆₇	—	2	8	no	—
228	SD₁₆×C₆₇	—	4	8	no	—
229	SD₁₆×C₆₇	C₂×D₄	1	8	yes	—
230	D₈×C₆₇	—	2	8	no	—
231	D₈×C₆₇	—	2	4	no	—
232	D₈×C₆₇	—	2	4	no	—
233	D₈×C₆₇	C₂×D₄	1	4	yes	—
234	M₁₆×C₆₇	—	2	2	no	—
235	M₁₆×C₆₇	—	2	2	no	—
236	M₁₆×C₆₇	—	2	4	no	—
237	M₁₆×C₆₇	—	2	4	no	—
238	C₂×C₈×C₆₇	—	2	2	no	—
239	C₂×C₈×C₆₇	—	2	4	no	—
240	C₂×C₈×C₆₇	—	2	4	no	—
241	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
242	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
243	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
244	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
245	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₄⋊C₄×C₆₇	—	2	4	no	—
248	C₄⋊C₄×C₆₇	—	2	8	no	—
249	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
250	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
251	C₂²⋊C₄×C₆₇	—	2	8	no	—
252	C₂²⋊C₄×C₆₇	—	2	2	no	—
253	C₂²⋊C₄×C₆₇	—	2	8	no	—
254	C₂²⋊C₄×C₆₇	—	2	8	no	—
255	C₂²⋊C₄×C₆₇	—	2	8	no	—
256	C₂²⋊C₄×C₆₇	—	2	4	no	—
257	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
258	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
259	C₄²×C₆₇	—	2	2	no	—
260	C₄²×C₆₇	—	2	4	no	—
261	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₆₇	C₂⁴	1	2	yes	—
264	C₂³×C₆₇	—	2	2	no	—
265	C₂³×C₆₇	—	2	4	no	—
266	C₂³×C₆₇	—	4	8	no	—
267	C₂³×C₆₇	—	4	4	no	—
268	C₂³×C₆₇	—	8	4	no	—
269	C₂³×C₆₇	—	8	8	no	—
270	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
271	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
272	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
273	Q₈×C₆₇	—	2	2	no	—
274	Q₈×C₆₇	—	2	2	no	—
275	Q₈×C₆₇	—	2	2	no	—
276	Q₈×C₆₇	—	2	4	no	—
277	Q₈×C₆₇	—	2	4	no	—
278	Q₈×C₆₇	—	4	8	no	—
279	Q₈×C₆₇	—	4	4	no	—
280	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
281	D₄×C₆₇	—	2	8	no	—
282	D₄×C₆₇	—	2	4	no	—
283	D₄×C₆₇	—	2	4	no	—
284	D₄×C₆₇	—	2	2	no	—
285	D₄×C₆₇	—	2	2	no	—
286	D₄×C₆₇	—	2	4	no	—
287	D₄×C₆₇	—	2	2	no	—
288	D₄×C₆₇	—	2	4	no	—
289	D₄×C₆₇	—	4	4	no	—
290	D₄×C₆₇	—	4	8	no	—
291	D₄×C₆₇	—	4	8	no	—
292	D₄×C₆₇	—	4	8	no	—
293	D₄×C₆₇	—	4	4	no	—
294	D₄×C₆₇	—	8	8	no	—
295	D₄×C₆₇	C₂²×D₄	1	4	yes	—
296	C₂×C₄×C₆₇	—	2	2	no	—
297	C₂×C₄×C₆₇	—	2	8	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	4	no	—
303	C₂×C₄×C₆₇	—	2	4	no	—
304	C₂×C₄×C₆₇	—	4	2	no	—
305	C₂×C₄×C₆₇	—	4	8	no	—
306	C₂×C₄×C₆₇	—	4	8	no	—
307	C₂×C₄×C₆₇	—	4	8	no	—
308	C₂×C₄×C₆₇	—	4	4	no	—
309	C₂×C₄×C₆₇	—	8	4	no	—
310	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
314	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
317	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
318	C₈×C₆₇	—	2	2	no	—
319	C₈×C₆₇	—	2	2	no	—
320	C₈×C₆₇	—	2	2	no	—
321	C₈×C₆₇	C₂²×D₄	1	2	yes	—
322	C₈×C₆₇	C₂²×D₄	1	2	yes	—
323	C₂²×C₆₇	—	2	2	no	—
324	C₂²×C₆₇	—	2	4	no	—
325	C₂²×C₆₇	—	2	4	no	—
326	C₂²×C₆₇	—	2	2	no	—
327	C₂²×C₆₇	—	2	4	no	—
328	C₂²×C₆₇	—	2	2	no	—
329	C₂²×C₆₇	—	4	4	no	—
330	C₂²×C₆₇	—	4	8	no	—
331	C₂²×C₆₇	—	4	4	no	—
332	C₂²×C₆₇	—	16	4	no	—
333	C₂²×C₆₇	—	16	8	no	—
334	C₂²×C₆₇	D₄²	1	2	yes	—
335	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
336	C₄×C₆₇	—	2	2	no	—
337	C₄×C₆₇	—	2	2	no	—
338	C₄×C₆₇	—	2	4	no	—
339	C₄×C₆₇	—	2	2	no	—
340	C₄×C₆₇	—	2	2	no	—
341	C₄×C₆₇	—	4	4	no	—
342	C₄×C₆₇	—	4	4	no	—
343	C₄×C₆₇	D₄²	1	2	yes	—
344	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
345	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
346	#61090	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
347	C₂×C₆₇	—	2	2	no	—
348	C₂×C₆₇	—	4	2	no	—
349	C₂×C₆₇	—	4	2	no	—
350	C₂×C₆₇	—	4	4	no	—
351	C₂×C₆₇	—	8	4	no	—
352	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
353	C₂×C₆₇	#3584	1	2	yes	—
354	C₂×#578	C₂×C₆₇	1	1	yes	characteristic, complemented
355	C₂×#576	C₂×C₆₇	1	1	yes	characteristic, complemented
356	#3500	C₂×C₆₇	1	2	yes	complemented
357	#3285	C₂×C₆₇	1	4	yes	complemented
358	#3280	C₂×C₆₇	1	4	yes	complemented
359	#3275	C₂×C₆₇	1	8	yes	complemented
360	C₂×#495	C₂×C₆₇	1	1	yes	characteristic, complemented
361	#3059	C₂×C₆₇	1	1	yes	characteristic, complemented
362	#3058	C₂×C₆₇	1	1	yes	characteristic, complemented
363	#3040	C₂×C₆₇	1	2	yes	complemented
364	#3010	C₂×C₆₇	1	2	yes	complemented
365	#3009	C₂×C₆₇	1	2	yes	complemented
366	C₄×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
367	#2931	C₂×C₆₇	1	1	yes	characteristic, complemented
368	C₆₇	#61090	1	1	yes	characteristic, direct product factor, Sylow
369	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	complemented
370	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
371	#578	—	2	8	no	—
372	#576	—	2	8	no	—
373	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
374	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
375	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
376	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	—
377	C₂×#135	C₂²×C₆₇	1	2	yes	—
378	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
379	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
380	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
381	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
382	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
383	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
384	C₂²×D₈	C₂²×C₆₇	1	2	yes	—
385	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
386	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
387	#548	C₂²×C₆₇	1	8	yes	complemented
388	#546	—	2	8	no	—
389	#546	C₂²×C₆₇	1	8	yes	complemented
390	#536	—	2	2	no	—
391	#536	C₂²×C₆₇	1	2	yes	—
392	#535	—	2	2	no	—
393	#535	C₂²×C₆₇	1	2	yes	complemented
394	#532	—	2	2	no	—
395	#532	C₂²×C₆₇	1	1	yes	characteristic
396	C₂×#124	—	2	2	no	—
397	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
398	C₄×#41	C₂²×C₆₇	1	2	yes	complemented
399	#495	C₂²×C₆₇	1	4	yes	complemented
400	#495	C₂²×C₆₇	1	4	yes	complemented
401	#470	C₂²×C₆₇	1	4	yes	complemented
402	#469	C₂²×C₆₇	1	4	yes	complemented
403	#467	C₂²×C₆₇	1	4	yes	complemented
404	#466	C₂²×C₆₇	1	4	yes	complemented
405	#464	C₂²×C₆₇	1	8	yes	complemented
406	#463	C₂²×C₆₇	1	8	yes	complemented
407	#452	C₂²×C₆₇	1	8	yes	complemented
408	#450	C₂²×C₆₇	1	8	yes	complemented
409	#449	C₂²×C₆₇	1	8	yes	complemented
410	#448	C₂²×C₆₇	1	8	yes	complemented
411	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
412	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
413	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
414	#436	C₂²×C₆₇	1	4	yes	complemented
415	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
416	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
417	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
418	#419	C₂²×C₆₇	1	2	yes	complemented
419	#418	C₂²×C₆₇	1	2	yes	complemented
420	#416	C₂²×C₆₇	1	2	yes	complemented
421	#408	C₂²×C₆₇	1	1	yes	characteristic
422	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
423	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
424	2₋¹⁺⁴	—	2	8	no	—
425	2₋¹⁺⁴	—	4	4	no	—
426	H(5,𝔽₂)	—	2	8	no	—
427	H(5,𝔽₂)	—	4	4	no	—
428	C₂×#41	—	2	2	no	—
429	C₂×#41	—	2	2	no	—
430	C₂×#41	—	2	4	no	—
431	C₂×#41	C₂³×C₆₇	1	4	yes	—
432	C₂×#41	C₂³×C₆₇	1	4	yes	—
433	C₂×#41	C₂³×C₆₇	1	2	yes	—
434	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
435	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
436	C₂²×Q₈	—	2	2	no	—
437	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
438	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
439	C₂²×D₄	—	2	2	no	—
440	C₂²×D₄	—	2	4	no	—
441	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
442	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
443	#137	—	2	8	no	—
444	#137	—	2	16	no	—
445	AGL(1,ℤ/8)	—	2	8	no	—
446	AGL(1,ℤ/8)	—	2	16	no	—
447	#135	—	2	8	no	—
448	#135	—	2	8	no	—
449	#135	D₄×C₆₇	1	8	yes	complemented
450	C₂×Q₁₆	—	2	8	no	—
451	C₂×Q₁₆	—	2	4	no	—
452	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
453	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
454	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
455	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
456	C₂×SD₁₆	—	4	4	no	—
457	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
458	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
459	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	—
460	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
461	C₂×D₈	—	2	8	no	—
462	C₂×D₈	—	2	4	no	—
463	C₂×D₈	C₂³×C₆₇	1	2	yes	—
464	C₂×D₈	C₂³×C₆₇	1	4	yes	—
465	C₂×D₈	C₂³×C₆₇	1	2	yes	—
466	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
467	#131	—	2	4	no	—
468	#131	—	2	4	no	—
469	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
470	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
471	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
472	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
473	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
474	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
475	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
477	C₄⋊Q₈	—	2	2	no	—
478	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
479	#127	—	2	2	no	—
480	#127	D₄×C₆₇	1	1	yes	characteristic
481	#124	—	2	2	no	—
482	#124	—	2	2	no	—
483	#124	—	2	8	no	—
484	#124	—	2	2	no	—
485	#124	—	2	2	no	—
486	#124	D₄×C₆₇	1	1	yes	characteristic
487	#124	D₄×C₆₇	1	1	yes	characteristic
488	#124	C₂³×C₆₇	1	8	yes	—
489	#123	—	2	4	no	—
490	#123	—	2	8	no	—
491	C₂²⋊Q₈	—	2	8	no	—
492	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
493	#121	—	2	8	no	—
494	#121	—	2	8	no	—
495	#121	D₄×C₆₇	1	4	yes	—
496	#121	C₂³×C₆₇	1	8	yes	—
497	#120	—	2	8	no	—
498	#120	—	2	4	no	—
499	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
500	C₄×D₄	—	2	4	no	—
501	C₄×D₄	—	2	8	no	—
502	C₄×D₄	C₂³×C₆₇	1	4	yes	—
503	C₄×D₄	C₂³×C₆₇	1	4	yes	—
504	#117	—	2	2	no	—
505	#117	C₂³×C₆₇	1	2	yes	—
506	C₂×C₂²⋊C₄	—	2	4	no	—
507	C₂×C₂²⋊C₄	—	2	8	no	—
508	C₂×C₄²	—	2	2	no	—
509	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
510	#107	C₂³×C₆₇	1	2	yes	—
511	#106	C₂³×C₆₇	1	2	yes	—
512	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
513	#103	C₂³×C₆₇	1	4	yes	—
514	#103	C₂³×C₆₇	1	8	yes	—
515	#102	C₂³×C₆₇	1	4	yes	—
516	#102	C₂³×C₆₇	1	8	yes	—
517	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
518	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
519	C₄×C₈	C₂³×C₆₇	1	2	yes	—
520	C₄×C₈	C₂³×C₆₇	1	2	yes	—
521	C₂⁴	—	2	4	no	—
522	C₂⁴	—	2	2	no	—
523	#41	—	2	2	no	—
524	#41	—	2	2	no	—
525	#41	—	2	2	no	—
526	#41	—	2	4	no	—
527	#41	—	2	2	no	—
528	#41	—	2	8	no	—
529	#41	—	2	8	no	—
530	#41	—	4	4	no	—
531	#41	—	4	4	no	—
532	#41	—	4	8	no	—
533	#41	—	4	8	no	—
534	#41	—	4	16	no	—
535	#41	C₂×D₄×C₆₇	1	8	yes	—
536	C₂×Q₈	—	2	4	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	2	8	no	—
539	C₂×Q₈	—	2	4	no	—
540	C₂×Q₈	—	2	4	no	—
541	C₂×Q₈	—	4	4	no	—
542	C₂×Q₈	—	4	8	no	—
543	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
544	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
545	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
546	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	8	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	8	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	8	no	—
558	C₂×D₄	—	4	16	no	—
559	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
560	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
561	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
562	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
563	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
564	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
565	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
576	Q₁₆	—	2	8	no	—
577	Q₁₆	—	2	4	no	—
578	Q₁₆	—	2	4	no	—
579	Q₁₆	C₂×D₄×C₆₇	1	4	yes	—
580	SD₁₆	—	2	8	no	—
581	SD₁₆	—	2	8	no	—
582	SD₁₆	—	4	8	no	—
583	SD₁₆	C₂×D₄×C₆₇	1	8	yes	—
584	D₈	—	2	8	no	—
585	D₈	—	2	4	no	—
586	D₈	—	2	4	no	—
587	D₈	C₂×D₄×C₆₇	1	4	yes	—
588	M₁₆	—	2	2	no	—
589	M₁₆	—	2	2	no	—
590	M₁₆	—	2	4	no	—
591	M₁₆	—	2	4	no	—
592	C₂×C₈	—	2	2	no	—
593	C₂×C₈	—	2	4	no	—
594	C₂×C₈	—	2	4	no	—
595	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
596	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
597	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
598	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
599	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
600	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	8	no	—
603	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
604	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
605	C₂²⋊C₄	—	2	8	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	8	no	—
608	C₂²⋊C₄	—	2	8	no	—
609	C₂²⋊C₄	—	2	8	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
612	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
613	C₄²	—	2	2	no	—
614	C₄²	—	2	4	no	—
615	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
616	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
617	C₄²	C₂⁴×C₆₇	1	2	yes	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	4	8	no	—
621	C₂³	—	4	4	no	—
622	C₂³	—	8	4	no	—
623	C₂³	—	8	8	no	—
624	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
625	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
626	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
627	Q₈	—	2	2	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	4	no	—
631	Q₈	—	2	4	no	—
632	Q₈	—	4	8	no	—
633	Q₈	—	4	4	no	—
634	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
635	D₄	—	2	8	no	—
636	D₄	—	2	4	no	—
637	D₄	—	2	4	no	—
638	D₄	—	2	2	no	—
639	D₄	—	2	2	no	—
640	D₄	—	2	4	no	—
641	D₄	—	2	2	no	—
642	D₄	—	2	4	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	8	no	—
645	D₄	—	4	8	no	—
646	D₄	—	4	8	no	—
647	D₄	—	4	4	no	—
648	D₄	—	8	8	no	—
649	D₄	C₂²×D₄×C₆₇	1	4	yes	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	8	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	8	no	—
660	C₂×C₄	—	4	8	no	—
661	C₂×C₄	—	4	8	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	8	4	no	—
664	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
665	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
666	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
667	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
668	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
669	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
670	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
671	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
672	C₈	—	2	2	no	—
673	C₈	—	2	2	no	—
674	C₈	—	2	2	no	—
675	C₈	C₂²×D₄×C₆₇	1	2	yes	—
676	C₈	C₂²×D₄×C₆₇	1	2	yes	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	4	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	4	4	no	—
684	C₂²	—	4	8	no	—
685	C₂²	—	4	4	no	—
686	C₂²	—	16	4	no	—
687	C₂²	—	16	8	no	—
688	C₂²	D₄²×C₆₇	1	2	yes	—
689	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
690	C₄	—	2	2	no	—
691	C₄	—	2	2	no	—
692	C₄	—	2	4	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	4	4	no	—
696	C₄	—	4	4	no	—
697	C₄	D₄²×C₆₇	1	2	yes	—
698	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
699	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
700	C₂	—	2	2	no	—
701	C₂	—	4	2	no	—
702	C₂	—	4	2	no	—
703	C₂	—	4	4	no	—
704	C₂	—	8	4	no	—
705	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
706	C₂	C₆₇×#3584	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 ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#578×C₆₇	C₂	semidirect
2. C₂×#576×C₆₇	C₂	semidirect
3. C₆₇×#3500	C₂	semidirect
4. C₆₇×#3285	C₂	semidirect
5. C₆₇×#3280	C₂	semidirect
6. C₆₇×#3275	C₂	semidirect
7. C₂×#495×C₆₇	C₂	semidirect
8. C₆₇×#3059	C₂	semidirect
9. C₆₇×#3058	C₂	semidirect
10. C₆₇×#3040	C₂	semidirect
11. C₆₇×#3010	C₂	semidirect
12. C₆₇×#3009	C₂	semidirect
13. C₄×#135×C₆₇	C₂	semidirect
14. C₆₇×#2931	C₂	semidirect
15. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
19. C₂×#137×C₆₇	C₂²	semidirect
20. C₂×#137×C₆₇	C₂²	semidirect
25. C₂×#135×C₆₇	C₂²	semidirect
26. C₂²×Q₁₆×C₆₇	C₂²	semidirect
27. C₂²×Q₁₆×C₆₇	C₂²	semidirect
28. C₂²×SD₁₆×C₆₇	C₂²	semidirect
32. C₂×#131×C₆₇	C₂²	semidirect
33. #548×C₆₇	C₂²	semidirect
35. #546×C₆₇	C₂²	semidirect
39. #535×C₆₇	C₂²	semidirect
43. C₂×#124×C₆₇	C₂²	semidirect
44. C₄×#41×C₆₇	C₂²	semidirect
45. #495×C₆₇	C₂²	semidirect
46. #495×C₆₇	C₂²	semidirect
47. #470×C₆₇	C₂²	semidirect
48. #469×C₆₇	C₂²	semidirect
49. #467×C₆₇	C₂²	semidirect
50. #466×C₆₇	C₂²	semidirect
51. #464×C₆₇	C₂²	semidirect
52. #463×C₆₇	C₂²	semidirect
53. #452×C₆₇	C₂²	semidirect
54. #450×C₆₇	C₂²	semidirect
55. #449×C₆₇	C₂²	semidirect
56. #448×C₆₇	C₂²	semidirect
57. C₄×Q₁₆×C₆₇	C₂²	semidirect
58. C₄×SD₁₆×C₆₇	C₂²	semidirect
59. C₄×D₈×C₆₇	C₂²	semidirect
60. #436×C₆₇	C₂²	semidirect
61. C₈×D₄×C₆₇	C₂²	semidirect
62. #427×C₆₇	C₂²	semidirect
63. #423×C₆₇	C₂²	semidirect
64. #419×C₆₇	C₂²	semidirect
65. #418×C₆₇	C₂²	semidirect
66. #416×C₆₇	C₂²	semidirect
68. #408×C₆₇	C₂²	semidirect
69. C₂×C₄×C₈×C₆₇	C₂²	semidirect
95. #135×C₆₇	D₄	semidirect
346. #61090	C₆₇	direct (N × H)
354. C₂×#578	C₂×C₆₇	semidirect
355. C₂×#576	C₂×C₆₇	semidirect
356. #3500	C₂×C₆₇	semidirect
357. #3285	C₂×C₆₇	semidirect
358. #3280	C₂×C₆₇	semidirect
359. #3275	C₂×C₆₇	semidirect
360. C₂×#495	C₂×C₆₇	semidirect
361. #3059	C₂×C₆₇	semidirect
362. #3058	C₂×C₆₇	semidirect
363. #3040	C₂×C₆₇	semidirect
364. #3010	C₂×C₆₇	semidirect
365. #3009	C₂×C₆₇	semidirect
366. C₄×#135	C₂×C₆₇	semidirect
367. #2931	C₂×C₆₇	semidirect
368. C₆₇	#61090	direct (N × H)
369. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
373. C₂×#137	C₂²×C₆₇	semidirect
374. C₂×#137	C₂²×C₆₇	semidirect
379. C₂×#135	C₂²×C₆₇	semidirect
380. C₂²×Q₁₆	C₂²×C₆₇	semidirect
381. C₂²×Q₁₆	C₂²×C₆₇	semidirect
382. C₂²×SD₁₆	C₂²×C₆₇	semidirect
386. C₂×#131	C₂²×C₆₇	semidirect
387. #548	C₂²×C₆₇	semidirect
389. #546	C₂²×C₆₇	semidirect
393. #535	C₂²×C₆₇	semidirect
397. C₂×#124	C₂²×C₆₇	semidirect
398. C₄×#41	C₂²×C₆₇	semidirect
399. #495	C₂²×C₆₇	semidirect
400. #495	C₂²×C₆₇	semidirect
401. #470	C₂²×C₆₇	semidirect
402. #469	C₂²×C₆₇	semidirect
403. #467	C₂²×C₆₇	semidirect
404. #466	C₂²×C₆₇	semidirect
405. #464	C₂²×C₆₇	semidirect
406. #463	C₂²×C₆₇	semidirect
407. #452	C₂²×C₆₇	semidirect
408. #450	C₂²×C₆₇	semidirect
409. #449	C₂²×C₆₇	semidirect
410. #448	C₂²×C₆₇	semidirect
411. C₄×Q₁₆	C₂²×C₆₇	semidirect
412. C₄×SD₁₆	C₂²×C₆₇	semidirect
413. C₄×D₈	C₂²×C₆₇	semidirect
414. #436	C₂²×C₆₇	semidirect
415. C₈×D₄	C₂²×C₆₇	semidirect
416. #427	C₂²×C₆₇	semidirect
417. #423	C₂²×C₆₇	semidirect
418. #419	C₂²×C₆₇	semidirect
419. #418	C₂²×C₆₇	semidirect
420. #416	C₂²×C₆₇	semidirect
422. #408	C₂²×C₆₇	semidirect
423. C₂×C₄×C₈	C₂²×C₆₇	semidirect
449. #135	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#578×C₆₇	2
C₂×#576×C₆₇	2
C₆₇×#3500	2
C₆₇×#3285	2
C₆₇×#3280	2
C₆₇×#3275	2
C₂×#495×C₆₇	2
C₆₇×#3059	2
C₆₇×#3058	2
C₆₇×#3040	2
C₆₇×#3010	2
C₆₇×#3009	2
C₄×#135×C₆₇	2
C₆₇×#2931	2
#61090	67

Subgroups — C67×#61090 #30740341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61090 #30740341