Subgroups — C₂×C₆₇×#3344 #30740487

Order 17152.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#552×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3344	C₂	1	16	yes	maximal, direct product factor
4	C₂×#501×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#484×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#485×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#483×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#483×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#479×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#475×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#470×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#467×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#441×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#435×C₆₇	C₂	1	1	yes	maximal, characteristic
15	C₂×#428×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#106×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
20	#554×C₆₇	—	2	4	no	—
21	#554×C₆₇	C₂²	1	8	yes	—
22	#552×C₆₇	—	2	4	no	—
23	#552×C₆₇	C₂²	1	8	yes	—
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#126×C₆₇	—	2	1	no	—
26	C₂×#125×C₆₇	—	2	1	no	—
27	C₂×#125×C₆₇	—	2	1	no	—
28	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#123×C₆₇	—	2	1	no	—
30	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
31	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
32	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	—	2	1	no	—
39	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#117×C₆₇	—	2	1	no	—
41	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
45	#501×C₆₇	C₂²	1	8	yes	complemented
46	#485×C₆₇	C₂²	1	8	yes	complemented
47	#484×C₆₇	C₂²	1	8	yes	complemented
48	#483×C₆₇	C₂²	1	8	yes	complemented
49	#483×C₆₇	C₂²	1	8	yes	complemented
50	#479×C₆₇	C₂²	1	8	yes	complemented
51	#475×C₆₇	C₂²	1	8	yes	complemented
52	#470×C₆₇	C₂²	1	8	yes	complemented
53	#467×C₆₇	C₂²	1	8	yes	complemented
54	#441×C₆₇	C₂²	1	8	yes	complemented
55	#435×C₆₇	C₂²	1	8	yes	—
56	#428×C₆₇	C₂²	1	8	yes	complemented
57	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
65	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
66	C₂×#106×C₆₇	C₂²	1	8	yes	complemented
67	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
68	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
69	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
70	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
71	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
72	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
73	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
75	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
76	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₆₇	—	2	1	no	—
78	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₆₇	—	2	1	no	—
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	C₂×Q₁₆×C₆₇	—	2	4	no	—
87	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
88	C₂×M₁₆×C₆₇	—	2	4	no	—
89	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
90	C₂²×C₈×C₆₇	—	2	4	no	—
91	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
92	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₄⋊Q₈×C₆₇	—	2	2	no	—
97	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
98	#126×C₆₇	—	2	8	no	—
99	#125×C₆₇	—	2	8	no	—
100	#125×C₆₇	—	2	8	no	—
101	#125×C₆₇	—	2	2	no	—
102	#125×C₆₇	C₂³	1	4	yes	—
103	#123×C₆₇	—	2	8	no	—
104	C₂²⋊Q₈×C₆₇	—	2	2	no	—
105	C₂²⋊Q₈×C₆₇	—	2	2	no	—
106	C₂²⋊Q₈×C₆₇	—	2	2	no	—
107	C₂²⋊Q₈×C₆₇	—	2	2	no	—
108	C₂²⋊Q₈×C₆₇	—	2	8	no	—
109	C₂²⋊Q₈×C₆₇	—	2	8	no	—
110	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
111	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
112	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
113	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
114	C₄×Q₈×C₆₇	—	2	2	no	—
115	C₄×Q₈×C₆₇	—	2	2	no	—
116	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
117	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
118	C₄×D₄×C₆₇	—	2	8	no	—
119	C₄×D₄×C₆₇	D₄	1	4	yes	—
120	C₄×D₄×C₆₇	C₂³	1	4	yes	—
121	#117×C₆₇	—	2	2	no	—
122	#117×C₆₇	—	2	8	no	—
123	#117×C₆₇	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
125	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
126	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
127	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
128	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
129	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
130	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
131	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
132	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
133	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
134	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
135	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
136	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
137	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
138	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
139	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
156	C₂×C₄²×C₆₇	—	2	1	no	—
157	C₂×C₄²×C₆₇	—	2	1	no	—
158	C₂×C₄²×C₆₇	—	2	1	no	—
159	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
160	#107×C₆₇	C₂³	1	4	yes	—
161	#107×C₆₇	C₂³	1	4	yes	—
162	#107×C₆₇	C₂³	1	4	yes	—
163	#106×C₆₇	C₂³	1	4	yes	—
164	#106×C₆₇	C₂³	1	4	yes	—
165	#106×C₆₇	C₂³	1	4	yes	—
166	#106×C₆₇	C₂³	1	4	yes	—
167	#106×C₆₇	C₂³	1	4	yes	—
168	#106×C₆₇	C₂³	1	4	yes	—
169	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
170	#103×C₆₇	C₂³	1	4	yes	—
171	#103×C₆₇	C₂³	1	4	yes	—
172	#103×C₆₇	C₂³	1	4	yes	—
173	#103×C₆₇	C₂³	1	4	yes	—
174	#103×C₆₇	C₂³	1	4	yes	—
175	#103×C₆₇	C₂³	1	4	yes	—
176	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
177	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
178	#97×C₆₇	C₂³	1	4	yes	—
179	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
180	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
181	C₂×Q₈×C₆₇	—	2	1	no	—
182	C₂×Q₈×C₆₇	—	2	1	no	—
183	C₂×Q₈×C₆₇	—	2	4	no	—
184	C₂×Q₈×C₆₇	—	2	2	no	—
185	C₂×Q₈×C₆₇	—	2	2	no	—
186	C₂×Q₈×C₆₇	—	2	2	no	—
187	C₂×Q₈×C₆₇	—	2	2	no	—
188	C₂×Q₈×C₆₇	—	8	2	no	—
189	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
190	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
191	C₂×D₄×C₆₇	—	2	4	no	—
192	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
193	C₂²×C₄×C₆₇	—	2	2	no	—
194	C₂²×C₄×C₆₇	—	2	2	no	—
195	C₂²×C₄×C₆₇	—	2	2	no	—
196	C₂²×C₄×C₆₇	—	2	2	no	—
197	C₂²×C₄×C₆₇	—	2	4	no	—
198	C₂²×C₄×C₆₇	—	2	1	no	—
199	C₂²×C₄×C₆₇	—	2	1	no	—
200	C₂²×C₄×C₆₇	—	2	1	no	—
201	C₂²×C₄×C₆₇	—	2	1	no	—
202	C₂²×C₄×C₆₇	—	2	1	no	—
203	C₂²×C₄×C₆₇	—	2	1	no	—
204	C₂²×C₄×C₆₇	—	2	1	no	—
205	C₂²×C₄×C₆₇	—	2	1	no	—
206	C₂²×C₄×C₆₇	—	2	4	no	—
207	C₂²×C₄×C₆₇	—	2	4	no	—
208	C₂²×C₄×C₆₇	—	4	4	no	—
209	C₂²×C₄×C₆₇	—	8	2	no	—
210	C₂²×C₄×C₆₇	—	8	2	no	—
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	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
220	Q₁₆×C₆₇	—	2	8	no	—
221	M₁₆×C₆₇	—	2	8	no	—
222	C₂×C₈×C₆₇	—	2	2	no	—
223	C₂×C₈×C₆₇	—	2	2	no	—
224	C₂×C₈×C₆₇	—	2	2	no	—
225	C₂×C₈×C₆₇	—	2	8	no	—
226	C₂×C₈×C₆₇	#41	1	4	yes	—
227	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
228	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
229	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
230	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
231	C₄⋊C₄×C₆₇	—	2	1	no	—
232	C₄⋊C₄×C₆₇	—	2	1	no	—
233	C₄⋊C₄×C₆₇	—	2	4	no	—
234	C₄⋊C₄×C₆₇	—	2	4	no	—
235	C₄⋊C₄×C₆₇	—	2	1	no	—
236	C₄⋊C₄×C₆₇	—	2	1	no	—
237	C₄⋊C₄×C₆₇	—	2	1	no	—
238	C₄⋊C₄×C₆₇	—	2	4	no	—
239	C₄⋊C₄×C₆₇	—	2	4	no	—
240	C₄⋊C₄×C₆₇	—	2	4	no	—
241	C₄⋊C₄×C₆₇	—	2	4	no	—
242	C₄⋊C₄×C₆₇	—	2	4	no	—
243	C₄⋊C₄×C₆₇	—	2	4	no	—
244	C₄⋊C₄×C₆₇	—	2	4	no	—
245	C₄⋊C₄×C₆₇	—	2	4	no	—
246	C₄⋊C₄×C₆₇	—	2	4	no	—
247	C₄⋊C₄×C₆₇	—	2	4	no	—
248	C₄⋊C₄×C₆₇	—	2	1	no	—
249	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
250	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
252	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
254	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²⋊C₄×C₆₇	—	2	4	no	—
257	C₂²⋊C₄×C₆₇	—	2	4	no	—
258	C₂²⋊C₄×C₆₇	—	2	4	no	—
259	C₂²⋊C₄×C₆₇	—	2	4	no	—
260	C₂²⋊C₄×C₆₇	—	2	4	no	—
261	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
262	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
263	C₄²×C₆₇	—	2	4	no	—
264	C₄²×C₆₇	—	2	4	no	—
265	C₄²×C₆₇	—	2	4	no	—
266	C₄²×C₆₇	C₂×D₄	1	2	yes	—
267	C₄²×C₆₇	C₂⁴	1	2	yes	—
268	C₂³×C₆₇	—	2	2	no	—
269	C₂³×C₆₇	—	2	2	no	—
270	C₂³×C₆₇	—	2	2	no	—
271	C₂³×C₆₇	—	2	2	no	—
272	C₂³×C₆₇	—	2	2	no	—
273	C₂³×C₆₇	#137	1	4	yes	—
274	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
275	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
276	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
277	Q₈×C₆₇	—	2	2	no	—
278	Q₈×C₆₇	—	2	2	no	—
279	Q₈×C₆₇	—	2	2	no	—
280	Q₈×C₆₇	—	2	2	no	—
281	Q₈×C₆₇	—	4	2	no	—
282	Q₈×C₆₇	—	4	2	no	—
283	Q₈×C₆₇	—	8	4	no	—
284	D₄×C₆₇	—	2	8	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	2	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	2	no	—
289	C₂×C₄×C₆₇	—	2	4	no	—
290	C₂×C₄×C₆₇	—	2	4	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	2	no	—
294	C₂×C₄×C₆₇	—	2	2	no	—
295	C₂×C₄×C₆₇	—	2	2	no	—
296	C₂×C₄×C₆₇	—	2	2	no	—
297	C₂×C₄×C₆₇	—	2	2	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	2	no	—
303	C₂×C₄×C₆₇	—	4	2	no	—
304	C₂×C₄×C₆₇	—	4	2	no	—
305	C₂×C₄×C₆₇	—	4	8	no	—
306	C₂×C₄×C₆₇	—	4	2	no	—
307	C₂×C₄×C₆₇	—	4	2	no	—
308	C₂×C₄×C₆₇	—	4	2	no	—
309	C₂×C₄×C₆₇	—	4	2	no	—
310	C₂×C₄×C₆₇	—	4	2	no	—
311	C₂×C₄×C₆₇	—	4	2	no	—
312	C₂×C₄×C₆₇	—	8	4	no	—
313	C₂×C₄×C₆₇	—	8	4	no	—
314	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
320	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
321	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
322	C₈×C₆₇	—	2	2	no	—
323	C₈×C₆₇	—	2	2	no	—
324	C₈×C₆₇	—	2	2	no	—
325	C₈×C₆₇	C₂×#41	1	4	yes	—
326	C₂²×C₆₇	—	2	8	no	—
327	C₂²×C₆₇	—	2	2	no	—
328	C₂²×C₆₇	—	2	2	no	—
329	C₂²×C₆₇	—	2	2	no	—
330	C₂²×C₆₇	—	2	2	no	—
331	C₂²×C₆₇	—	2	2	no	—
332	C₂²×C₆₇	—	4	4	no	—
333	C₂²×C₆₇	#547	1	2	yes	—
334	C₂²×C₆₇	C₂×#137	1	4	yes	—
335	C₂²×C₆₇	C₂×#137	1	2	yes	—
336	C₂²×C₆₇	#577	1	2	yes	—
337	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
338	C₄×C₆₇	—	2	2	no	—
339	C₄×C₆₇	—	2	2	no	—
340	C₄×C₆₇	—	2	2	no	—
341	C₄×C₆₇	—	2	2	no	—
342	C₄×C₆₇	—	4	2	no	—
343	C₄×C₆₇	—	4	2	no	—
344	C₄×C₆₇	—	4	2	no	—
345	C₄×C₆₇	—	4	2	no	—
346	C₄×C₆₇	—	4	2	no	—
347	C₄×C₆₇	—	4	2	no	—
348	C₄×C₆₇	—	4	2	no	—
349	C₄×C₆₇	—	4	2	no	—
350	C₄×C₆₇	#547	1	2	yes	—
351	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
352	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
353	C₂×#3344	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
354	C₂×C₆₇	—	2	4	no	—
355	C₂×C₆₇	—	4	2	no	—
356	C₂×C₆₇	#3344	1	4	yes	direct product factor
357	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
358	C₂×C₆₇	C₂²×#137	1	1	yes	characteristic
359	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
360	C₂×#554	C₂×C₆₇	1	1	yes	characteristic
361	C₂×#552	C₂×C₆₇	1	1	yes	characteristic
362	#3344	C₂×C₆₇	1	16	yes	direct product factor
363	C₂×#501	C₂×C₆₇	1	1	yes	characteristic, complemented
364	C₂×#484	C₂×C₆₇	1	1	yes	characteristic, complemented
365	C₂×#485	C₂×C₆₇	1	1	yes	characteristic, complemented
366	C₂×#483	C₂×C₆₇	1	1	yes	characteristic, complemented
367	C₂×#483	C₂×C₆₇	1	1	yes	characteristic, complemented
368	C₂×#479	C₂×C₆₇	1	1	yes	characteristic, complemented
369	C₂×#475	C₂×C₆₇	1	1	yes	characteristic, complemented
370	C₂×#470	C₂×C₆₇	1	1	yes	characteristic, complemented
371	C₂×#467	C₂×C₆₇	1	1	yes	characteristic, complemented
372	C₂×#441	C₂×C₆₇	1	1	yes	characteristic, complemented
373	C₂×#435	C₂×C₆₇	1	1	yes	characteristic
374	C₂×#428	C₂×C₆₇	1	1	yes	characteristic, complemented
375	C₂²×#106	C₂×C₆₇	1	1	yes	characteristic, complemented
376	C₆₇	C₂×#3344	1	1	yes	characteristic, direct product factor, Sylow
377	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
378	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
379	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
380	#554	—	2	4	no	—
381	#554	C₂²×C₆₇	1	8	yes	—
382	#552	—	2	4	no	—
383	#552	C₂²×C₆₇	1	8	yes	—
384	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
385	C₂×#126	—	2	1	no	—
386	C₂×#125	—	2	1	no	—
387	C₂×#125	—	2	1	no	—
388	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
389	C₂×#123	—	2	1	no	—
390	C₂×C₂²⋊Q₈	—	2	1	no	—
391	C₂×C₂²⋊Q₈	—	2	1	no	—
392	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
393	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
394	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
395	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
396	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
397	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
398	C₂×C₄×D₄	—	2	1	no	—
399	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
400	C₂×#117	—	2	1	no	—
401	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
402	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
403	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
404	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
405	#501	C₂²×C₆₇	1	8	yes	complemented
406	#485	C₂²×C₆₇	1	8	yes	complemented
407	#484	C₂²×C₆₇	1	8	yes	complemented
408	#483	C₂²×C₆₇	1	8	yes	complemented
409	#483	C₂²×C₆₇	1	8	yes	complemented
410	#479	C₂²×C₆₇	1	8	yes	complemented
411	#475	C₂²×C₆₇	1	8	yes	complemented
412	#470	C₂²×C₆₇	1	8	yes	complemented
413	#467	C₂²×C₆₇	1	8	yes	complemented
414	#441	C₂²×C₆₇	1	8	yes	complemented
415	#435	C₂²×C₆₇	1	8	yes	—
416	#428	C₂²×C₆₇	1	8	yes	complemented
417	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
418	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
419	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
420	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
421	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
422	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
423	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
424	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
425	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
426	C₂×#106	C₂²×C₆₇	1	8	yes	complemented
427	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
428	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
429	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
430	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
431	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
432	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
433	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
434	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
435	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
436	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
437	C₂²×Q₈	—	2	1	no	—
438	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
439	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
440	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
441	C₂³×C₄	—	2	1	no	—
442	C₂³×C₄	—	2	1	no	—
443	C₂³×C₄	—	2	1	no	—
444	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
446	C₂×Q₁₆	—	2	4	no	—
447	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
448	C₂×M₁₆	—	2	4	no	—
449	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
450	C₂²×C₈	—	2	4	no	—
451	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
453	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
455	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
456	C₄⋊Q₈	—	2	2	no	—
457	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
458	#126	—	2	8	no	—
459	#125	—	2	8	no	—
460	#125	—	2	8	no	—
461	#125	—	2	2	no	—
462	#125	C₂³×C₆₇	1	4	yes	—
463	#123	—	2	8	no	—
464	C₂²⋊Q₈	—	2	2	no	—
465	C₂²⋊Q₈	—	2	2	no	—
466	C₂²⋊Q₈	—	2	2	no	—
467	C₂²⋊Q₈	—	2	2	no	—
468	C₂²⋊Q₈	—	2	8	no	—
469	C₂²⋊Q₈	—	2	8	no	—
470	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
471	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
472	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
473	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
474	C₄×Q₈	—	2	2	no	—
475	C₄×Q₈	—	2	2	no	—
476	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
477	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
478	C₄×D₄	—	2	8	no	—
479	C₄×D₄	D₄×C₆₇	1	4	yes	—
480	C₄×D₄	C₂³×C₆₇	1	4	yes	—
481	#117	—	2	2	no	—
482	#117	—	2	8	no	—
483	#117	C₂³×C₆₇	1	4	yes	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	—	2	2	no	—
488	C₂×C₄⋊C₄	—	2	2	no	—
489	C₂×C₄⋊C₄	—	2	2	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
506	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
508	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
516	C₂×C₄²	—	2	1	no	—
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
520	#107	C₂³×C₆₇	1	4	yes	—
521	#107	C₂³×C₆₇	1	4	yes	—
522	#107	C₂³×C₆₇	1	4	yes	—
523	#106	C₂³×C₆₇	1	4	yes	—
524	#106	C₂³×C₆₇	1	4	yes	—
525	#106	C₂³×C₆₇	1	4	yes	—
526	#106	C₂³×C₆₇	1	4	yes	—
527	#106	C₂³×C₆₇	1	4	yes	—
528	#106	C₂³×C₆₇	1	4	yes	—
529	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
530	#103	C₂³×C₆₇	1	4	yes	—
531	#103	C₂³×C₆₇	1	4	yes	—
532	#103	C₂³×C₆₇	1	4	yes	—
533	#103	C₂³×C₆₇	1	4	yes	—
534	#103	C₂³×C₆₇	1	4	yes	—
535	#103	C₂³×C₆₇	1	4	yes	—
536	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
537	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
538	#97	C₂³×C₆₇	1	4	yes	—
539	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
540	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	4	no	—
544	C₂×Q₈	—	2	2	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	8	2	no	—
549	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
550	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	4	4	no	—
569	C₂²×C₄	—	8	2	no	—
570	C₂²×C₄	—	8	2	no	—
571	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
574	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
575	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
576	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
580	Q₁₆	—	2	8	no	—
581	M₁₆	—	2	8	no	—
582	C₂×C₈	—	2	2	no	—
583	C₂×C₈	—	2	2	no	—
584	C₂×C₈	—	2	2	no	—
585	C₂×C₈	—	2	8	no	—
586	C₂×C₈	#41×C₆₇	1	4	yes	—
587	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
588	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
589	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
590	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
610	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
611	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
612	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
613	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
614	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
615	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
622	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	4	no	—
626	C₄²	C₂×D₄×C₆₇	1	2	yes	—
627	C₄²	C₂⁴×C₆₇	1	2	yes	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	#137×C₆₇	1	4	yes	—
634	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
635	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
636	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
637	Q₈	—	2	2	no	—
638	Q₈	—	2	2	no	—
639	Q₈	—	2	2	no	—
640	Q₈	—	2	2	no	—
641	Q₈	—	4	2	no	—
642	Q₈	—	4	2	no	—
643	Q₈	—	8	4	no	—
644	D₄	—	2	8	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	2	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	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	4	2	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	8	no	—
666	C₂×C₄	—	4	2	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	2	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	2	no	—
671	C₂×C₄	—	4	2	no	—
672	C₂×C₄	—	8	4	no	—
673	C₂×C₄	—	8	4	no	—
674	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
675	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
676	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
677	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
678	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
679	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
680	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
681	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
682	C₈	—	2	2	no	—
683	C₈	—	2	2	no	—
684	C₈	—	2	2	no	—
685	C₈	C₂×#41×C₆₇	1	4	yes	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	8	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	4	4	no	—
693	C₂²	#547×C₆₇	1	2	yes	—
694	C₂²	C₂×#137×C₆₇	1	4	yes	—
695	C₂²	C₂×#137×C₆₇	1	2	yes	—
696	C₂²	#577×C₆₇	1	2	yes	—
697	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	2	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₄	#547×C₆₇	1	2	yes	—
711	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
712	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
713	C₂	—	2	4	no	—
714	C₂	—	4	2	no	—
715	C₂	C₆₇×#3344	1	4	yes	direct product factor
716	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
717	C₂	C₂²×#137×C₆₇	1	1	yes	characteristic
718	C₂	C₂×#577×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂²×D₄×C₆₇	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₆₇×#3344	C₂	direct (N × H)
4. C₂×#501×C₆₇	C₂	semidirect
5. C₂×#484×C₆₇	C₂	semidirect
6. C₂×#485×C₆₇	C₂	semidirect
7. C₂×#483×C₆₇	C₂	semidirect
8. C₂×#483×C₆₇	C₂	semidirect
9. C₂×#479×C₆₇	C₂	semidirect
10. C₂×#475×C₆₇	C₂	semidirect
11. C₂×#470×C₆₇	C₂	semidirect
12. C₂×#467×C₆₇	C₂	semidirect
13. C₂×#441×C₆₇	C₂	semidirect
15. C₂×#428×C₆₇	C₂	semidirect
16. C₂²×#106×C₆₇	C₂	semidirect
45. #501×C₆₇	C₂²	semidirect
46. #485×C₆₇	C₂²	semidirect
47. #484×C₆₇	C₂²	semidirect
48. #483×C₆₇	C₂²	semidirect
49. #483×C₆₇	C₂²	semidirect
50. #479×C₆₇	C₂²	semidirect
51. #475×C₆₇	C₂²	semidirect
52. #470×C₆₇	C₂²	semidirect
53. #467×C₆₇	C₂²	semidirect
54. #441×C₆₇	C₂²	semidirect
56. #428×C₆₇	C₂²	semidirect
66. C₂×#106×C₆₇	C₂²	semidirect
353. C₂×#3344	C₆₇	direct (N × H)
356. C₂×C₆₇	#3344	direct (N × H)
362. #3344	C₂×C₆₇	direct (N × H)
363. C₂×#501	C₂×C₆₇	semidirect
364. C₂×#484	C₂×C₆₇	semidirect
365. C₂×#485	C₂×C₆₇	semidirect
366. C₂×#483	C₂×C₆₇	semidirect
367. C₂×#483	C₂×C₆₇	semidirect
368. C₂×#479	C₂×C₆₇	semidirect
369. C₂×#475	C₂×C₆₇	semidirect
370. C₂×#470	C₂×C₆₇	semidirect
371. C₂×#467	C₂×C₆₇	semidirect
372. C₂×#441	C₂×C₆₇	semidirect
374. C₂×#428	C₂×C₆₇	semidirect
375. C₂²×#106	C₂×C₆₇	semidirect
376. C₆₇	C₂×#3344	direct (N × H)
405. #501	C₂²×C₆₇	semidirect
406. #485	C₂²×C₆₇	semidirect
407. #484	C₂²×C₆₇	semidirect
408. #483	C₂²×C₆₇	semidirect
409. #483	C₂²×C₆₇	semidirect
410. #479	C₂²×C₆₇	semidirect
411. #475	C₂²×C₆₇	semidirect
412. #470	C₂²×C₆₇	semidirect
413. #467	C₂²×C₆₇	semidirect
414. #441	C₂²×C₆₇	semidirect
416. #428	C₂²×C₆₇	semidirect
426. C₂×#106	C₂²×C₆₇	semidirect
715. C₂	C₆₇×#3344	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#554×C₆₇	2
C₂×#552×C₆₇	2
C₆₇×#3344	2
C₂×#501×C₆₇	2
C₂×#484×C₆₇	2
C₂×#485×C₆₇	2
C₂×#483×C₆₇	2
C₂×#479×C₆₇	2
C₂×#475×C₆₇	2
C₂×#470×C₆₇	2
C₂×#467×C₆₇	2
C₂×#441×C₆₇	2
C₂×#435×C₆₇	2
C₂×#428×C₆₇	2
C₂²×#106×C₆₇	2
C₂×#3344	67

Subgroups — C2×C67×#3344 #30740487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3344 #30740487