Subgroups — C₂×C₆₇×#3520 #30742023

Order 17152.

7910 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3520	C₂	1	32	yes	maximal, direct product factor
2	C₂×#556×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#554×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂×#552×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₂×#551×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂×D₄×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#548×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#546×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₂×#542×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₂×#539×C₆₇	C₂	1	4	yes	maximal, complemented
13	C₂×#533×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#525×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₂²×C₂²⋊Q₈×C₆₇	C₂	1	2	yes	maximal, complemented
17	C₂×#520×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41×C₆₇	C₂²	1	2	yes	—
20	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
21	C₂³×Q₈×C₆₇	C₂²	1	2	yes	complemented
22	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	—
24	#556×C₆₇	C₂²	1	16	yes	complemented
25	#554×C₆₇	C₂²	1	32	yes	complemented
26	#552×C₆₇	C₂²	1	32	yes	complemented
27	#551×C₆₇	C₂²	1	64	yes	complemented
28	D₄×Q₈×C₆₇	C₂²	1	16	yes	complemented
29	#548×C₆₇	C₂²	1	32	yes	complemented
30	#547×C₆₇	C₂²	1	16	yes	complemented
31	#547×C₆₇	C₂²	1	16	yes	complemented
32	#546×C₆₇	C₂²	1	32	yes	complemented
33	#542×C₆₇	C₂²	1	32	yes	complemented
34	#539×C₆₇	C₂²	1	64	yes	complemented
35	#533×C₆₇	C₂²	1	16	yes	complemented
36	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
39	#529×C₆₇	C₂²	1	16	yes	complemented
40	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
41	C₂×#126×C₆₇	C₂²	1	4	yes	complemented
42	C₂×#126×C₆₇	C₂²	1	4	yes	complemented
43	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	C₂×#125×C₆₇	C₂²	1	2	yes	complemented
45	C₂×#125×C₆₇	C₂²	1	4	yes	complemented
46	C₂×#124×C₆₇	C₂²	1	2	yes	—
47	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
49	#525×C₆₇	C₂²	1	32	yes	complemented
50	C₂×#123×C₆₇	C₂²	1	2	yes	—
51	C₂×#123×C₆₇	C₂²	1	4	yes	—
52	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
53	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
54	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
55	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
57	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
58	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
59	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
60	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
61	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
62	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
63	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
64	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
65	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
66	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	32	yes	complemented
67	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
68	C₂×#121×C₆₇	C₂²	1	4	yes	—
69	C₂×#121×C₆₇	C₂²	1	2	yes	—
70	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
71	C₂×#120×C₆₇	C₂²	1	4	yes	—
72	#520×C₆₇	C₂²	1	32	yes	complemented
73	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
74	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
75	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
77	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
78	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
79	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
80	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
81	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
82	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
83	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
84	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
85	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
86	C₂×C₄×D₄×C₆₇	C₂²	1	16	yes	complemented
87	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
88	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
89	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	C₂×#117×C₆₇	C₂²	1	2	yes	—
91	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
92	C₂×#117×C₆₇	C₂²	1	4	yes	complemented
93	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
94	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
95	C₂²×C₄⋊C₄×C₆₇	C₂²	1	4	yes	complemented
96	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
97	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
98	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
100	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
101	C₂⁵×C₆₇	C₂³	1	2	yes	—
102	C₂×#41×C₆₇	—	2	16	no	—
103	C₂×#41×C₆₇	—	4	8	no	—
104	C₂×#41×C₆₇	C₂³	1	16	yes	—
105	C₂×#41×C₆₇	C₂³	1	16	yes	complemented
106	C₂²×Q₈×C₆₇	—	4	8	no	—
107	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
108	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
110	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
111	C₂²×Q₈×C₆₇	C₂³	1	16	yes	complemented
112	C₂²×D₄×C₆₇	—	2	8	no	—
113	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
114	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
115	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
118	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
120	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₆₇	—	4	8	no	—
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
126	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
128	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
129	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
131	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
133	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₆₇	C₂³	1	16	yes	—
135	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
136	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
137	C₄⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
138	#126×C₆₇	C₂³	1	16	yes	complemented
139	#126×C₆₇	C₂³	1	32	yes	complemented
140	#126×C₆₇	C₂³	1	32	yes	complemented
141	#125×C₆₇	C₂³	1	8	yes	complemented
142	#125×C₆₇	C₂³	1	16	yes	complemented
143	#125×C₆₇	C₂³	1	32	yes	complemented
144	#124×C₆₇	C₂³	1	16	yes	—
145	#124×C₆₇	C₂³	1	8	yes	complemented
146	#124×C₆₇	C₂³	1	32	yes	complemented
147	#123×C₆₇	C₂³	1	16	yes	—
148	#123×C₆₇	C₂³	1	32	yes	—
149	#123×C₆₇	C₂³	1	32	yes	complemented
150	#123×C₆₇	C₂³	1	32	yes	complemented
151	#123×C₆₇	C₂³	1	32	yes	complemented
152	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
153	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
154	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
155	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
156	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
157	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
158	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
159	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
160	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
161	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
162	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
163	#121×C₆₇	C₂³	1	8	yes	—
164	#121×C₆₇	C₂³	1	32	yes	—
165	#121×C₆₇	C₂³	1	16	yes	—
166	#121×C₆₇	C₂³	1	16	yes	complemented
167	#120×C₆₇	C₂³	1	32	yes	—
168	C₄×Q₈×C₆₇	C₂³	1	16	yes	complemented
169	C₄×Q₈×C₆₇	C₂³	1	16	yes	complemented
170	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
171	C₄×Q₈×C₆₇	C₂³	1	16	yes	complemented
172	C₄×D₄×C₆₇	C₂³	1	8	yes	—
173	C₄×D₄×C₆₇	C₂³	1	16	yes	—
174	C₄×D₄×C₆₇	C₂³	1	8	yes	—
175	C₄×D₄×C₆₇	C₂³	1	8	yes	—
176	C₄×D₄×C₆₇	C₂³	1	8	yes	—
177	C₄×D₄×C₆₇	C₂³	1	16	yes	—
178	C₄×D₄×C₆₇	C₂³	1	16	yes	—
179	C₄×D₄×C₆₇	C₂³	1	32	yes	—
180	C₄×D₄×C₆₇	C₂³	1	16	yes	—
181	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
182	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
183	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
184	#117×C₆₇	C₂³	1	16	yes	—
185	#117×C₆₇	C₂³	1	16	yes	complemented
186	#117×C₆₇	C₂³	1	32	yes	complemented
187	#117×C₆₇	C₂³	1	16	yes	complemented
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
198	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
205	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
207	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₆₇	C₂³	1	32	yes	complemented
209	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	complemented
210	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	complemented
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
220	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	—
221	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
222	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
225	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
227	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
228	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
233	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
234	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
235	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
236	C₂⁴×C₆₇	—	2	8	no	—
237	C₂⁴×C₆₇	—	2	8	no	—
238	C₂⁴×C₆₇	—	4	4	no	—
239	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
240	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
241	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
242	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
243	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
244	#41×C₆₇	—	2	64	no	—
245	#41×C₆₇	—	4	32	no	—
246	C₂×Q₈×C₆₇	—	2	8	no	—
247	C₂×Q₈×C₆₇	—	2	4	no	—
248	C₂×Q₈×C₆₇	—	2	8	no	—
249	C₂×Q₈×C₆₇	—	4	8	no	—
250	C₂×Q₈×C₆₇	—	4	32	no	—
251	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
252	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
253	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
254	C₂×Q₈×C₆₇	C₂⁴	1	16	yes	—
255	C₂×D₄×C₆₇	—	2	8	no	—
256	C₂×D₄×C₆₇	—	2	16	no	—
257	C₂×D₄×C₆₇	—	2	8	no	—
258	C₂×D₄×C₆₇	—	2	32	no	—
259	C₂×D₄×C₆₇	—	2	4	no	—
260	C₂×D₄×C₆₇	—	2	4	no	—
261	C₂×D₄×C₆₇	—	4	8	no	—
262	C₂×D₄×C₆₇	#41	1	8	yes	complemented
263	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
264	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
265	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
266	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
267	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
268	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
269	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₆₇	—	2	16	no	—
271	C₂²×C₄×C₆₇	—	2	4	no	—
272	C₂²×C₄×C₆₇	—	2	4	no	—
273	C₂²×C₄×C₆₇	—	2	8	no	—
274	C₂²×C₄×C₆₇	—	2	4	no	—
275	C₂²×C₄×C₆₇	—	2	8	no	—
276	C₂²×C₄×C₆₇	—	2	8	no	—
277	C₂²×C₄×C₆₇	—	4	32	no	—
278	C₂²×C₄×C₆₇	—	4	4	no	—
279	C₂²×C₄×C₆₇	—	4	4	no	—
280	C₂²×C₄×C₆₇	—	4	4	no	—
281	C₂²×C₄×C₆₇	—	4	8	no	—
282	C₂²×C₄×C₆₇	—	4	8	no	—
283	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
284	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
285	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
286	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
287	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
288	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
299	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
302	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
303	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
304	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
305	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
306	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
309	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
310	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
311	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
312	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
313	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
314	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
315	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
316	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
317	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
318	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
319	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
320	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
321	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
322	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
323	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
324	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
325	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
326	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
327	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
328	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
329	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
330	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
331	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
332	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
333	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
334	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
335	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
336	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
337	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
338	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
339	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
340	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
341	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
342	C₄²×C₆₇	C₂⁴	1	4	yes	—
343	C₄²×C₆₇	C₂⁴	1	4	yes	—
344	C₄²×C₆₇	C₂⁴	1	4	yes	—
345	C₄²×C₆₇	C₂⁴	1	4	yes	—
346	C₄²×C₆₇	C₂⁴	1	16	yes	—
347	C₄²×C₆₇	C₂⁴	1	16	yes	—
348	C₄²×C₆₇	C₂⁴	1	8	yes	—
349	C₂³×C₆₇	—	2	2	no	—
350	C₂³×C₆₇	—	2	4	no	—
351	C₂³×C₆₇	—	2	2	no	—
352	C₂³×C₆₇	—	2	4	no	—
353	C₂³×C₆₇	—	2	4	no	—
354	C₂³×C₆₇	—	2	16	no	—
355	C₂³×C₆₇	—	2	4	no	—
356	C₂³×C₆₇	—	2	4	no	—
357	C₂³×C₆₇	—	2	4	no	—
358	C₂³×C₆₇	—	2	4	no	—
359	C₂³×C₆₇	—	2	16	no	—
360	C₂³×C₆₇	—	2	4	no	—
361	C₂³×C₆₇	—	4	8	no	—
362	C₂³×C₆₇	—	4	32	no	—
363	C₂³×C₆₇	C₂×#41	1	8	yes	—
364	C₂³×C₆₇	2₋¹⁺⁴	1	4	yes	—
365	C₂³×C₆₇	C₂⁵	1	4	yes	—
366	C₂³×C₆₇	C₂⁵	1	4	yes	—
367	C₂³×C₆₇	C₂⁵	1	4	yes	—
368	C₂³×C₆₇	C₂⁵	1	2	yes	—
369	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
370	Q₈×C₆₇	—	2	16	no	—
371	Q₈×C₆₇	—	2	8	no	—
372	Q₈×C₆₇	—	2	16	no	—
373	Q₈×C₆₇	—	4	16	no	—
374	D₄×C₆₇	—	2	16	no	—
375	D₄×C₆₇	—	2	32	no	—
376	D₄×C₆₇	—	2	16	no	—
377	D₄×C₆₇	—	2	8	no	—
378	D₄×C₆₇	—	2	8	no	—
379	D₄×C₆₇	—	4	16	no	—
380	D₄×C₆₇	C₂×#41	1	16	yes	complemented
381	C₂×C₄×C₆₇	—	2	4	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	8	no	—
384	C₂×C₄×C₆₇	—	2	32	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	4	no	—
387	C₂×C₄×C₆₇	—	2	4	no	—
388	C₂×C₄×C₆₇	—	2	8	no	—
389	C₂×C₄×C₆₇	—	2	4	no	—
390	C₂×C₄×C₆₇	—	2	8	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	4	no	—
394	C₂×C₄×C₆₇	—	2	8	no	—
395	C₂×C₄×C₆₇	—	2	16	no	—
396	C₂×C₄×C₆₇	—	2	8	no	—
397	C₂×C₄×C₆₇	—	2	16	no	—
398	C₂×C₄×C₆₇	—	2	16	no	—
399	C₂×C₄×C₆₇	—	4	8	no	—
400	C₂×C₄×C₆₇	—	4	8	no	—
401	C₂×C₄×C₆₇	—	4	8	no	—
402	C₂×C₄×C₆₇	—	4	16	no	—
403	C₂×C₄×C₆₇	—	4	16	no	—
404	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
405	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
406	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
407	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
408	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
409	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
410	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
411	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
412	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
413	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
414	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
415	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
416	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
417	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
418	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
419	C₂²×C₆₇	—	2	2	no	—
420	C₂²×C₆₇	—	2	4	no	—
421	C₂²×C₆₇	—	2	2	no	—
422	C₂²×C₆₇	—	2	4	no	—
423	C₂²×C₆₇	—	2	8	no	—
424	C₂²×C₆₇	—	2	16	no	—
425	C₂²×C₆₇	—	2	4	no	—
426	C₂²×C₆₇	—	2	4	no	—
427	C₂²×C₆₇	—	2	4	no	—
428	C₂²×C₆₇	—	2	4	no	—
429	C₂²×C₆₇	—	2	4	no	—
430	C₂²×C₆₇	—	2	4	no	—
431	C₂²×C₆₇	—	4	32	no	—
432	C₂²×C₆₇	—	4	8	no	—
433	C₂²×C₆₇	—	4	8	no	—
434	C₂²×C₆₇	C₂²×#41	1	8	yes	—
435	C₂²×C₆₇	C₂²×#41	1	2	yes	—
436	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
437	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	4	yes	—
438	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
439	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
440	C₄×C₆₇	—	2	4	no	—
441	C₄×C₆₇	—	2	2	no	—
442	C₄×C₆₇	—	2	8	no	—
443	C₄×C₆₇	—	2	2	no	—
444	C₄×C₆₇	—	2	4	no	—
445	C₄×C₆₇	—	2	4	no	—
446	C₄×C₆₇	—	2	8	no	—
447	C₄×C₆₇	—	2	4	no	—
448	C₄×C₆₇	—	2	2	no	—
449	C₄×C₆₇	—	2	2	no	—
450	C₄×C₆₇	—	2	4	no	—
451	C₄×C₆₇	C₂²×#41	1	4	yes	—
452	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
453	C₂×#3520	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
454	C₂×C₆₇	—	2	4	no	—
455	C₂×C₆₇	—	2	8	no	—
456	C₂×C₆₇	—	4	4	no	—
457	C₂×C₆₇	—	4	4	no	—
458	C₂×C₆₇	#3520	1	4	yes	direct product factor
459	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
460	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂×C₆₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
462	#3520	C₂×C₆₇	1	32	yes	direct product factor
463	C₂×#556	C₂×C₆₇	1	1	yes	characteristic, complemented
464	C₂×#554	C₂×C₆₇	1	2	yes	complemented
465	C₂×#552	C₂×C₆₇	1	2	yes	complemented
466	C₂×#551	C₂×C₆₇	1	4	yes	complemented
467	C₂×D₄×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
468	C₂×#548	C₂×C₆₇	1	2	yes	complemented
469	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
470	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
471	C₂×#546	C₂×C₆₇	1	2	yes	complemented
472	C₂×#542	C₂×C₆₇	1	2	yes	complemented
473	C₂×#539	C₂×C₆₇	1	4	yes	complemented
474	C₂×#533	C₂×C₆₇	1	1	yes	characteristic, complemented
475	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
476	C₂×#525	C₂×C₆₇	1	2	yes	complemented
477	C₂²×C₂²⋊Q₈	C₂×C₆₇	1	2	yes	complemented
478	C₂×#520	C₂×C₆₇	1	2	yes	complemented
479	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
480	C₆₇	C₂×#3520	1	1	yes	characteristic, direct product factor, Sylow
481	C₂²×#41	C₂²×C₆₇	1	2	yes	—
482	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
483	C₂³×Q₈	C₂²×C₆₇	1	2	yes	complemented
484	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
485	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	—
486	#556	C₂²×C₆₇	1	16	yes	complemented
487	#554	C₂²×C₆₇	1	32	yes	complemented
488	#552	C₂²×C₆₇	1	32	yes	complemented
489	#551	C₂²×C₆₇	1	64	yes	complemented
490	D₄×Q₈	C₂²×C₆₇	1	16	yes	complemented
491	#548	C₂²×C₆₇	1	32	yes	complemented
492	#547	C₂²×C₆₇	1	16	yes	complemented
493	#547	C₂²×C₆₇	1	16	yes	complemented
494	#546	C₂²×C₆₇	1	32	yes	complemented
495	#542	C₂²×C₆₇	1	32	yes	complemented
496	#539	C₂²×C₆₇	1	64	yes	complemented
497	#533	C₂²×C₆₇	1	16	yes	complemented
498	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
499	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
500	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
501	#529	C₂²×C₆₇	1	16	yes	complemented
502	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
503	C₂×#126	C₂²×C₆₇	1	4	yes	complemented
504	C₂×#126	C₂²×C₆₇	1	4	yes	complemented
505	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
506	C₂×#125	C₂²×C₆₇	1	2	yes	complemented
507	C₂×#125	C₂²×C₆₇	1	4	yes	complemented
508	C₂×#124	C₂²×C₆₇	1	2	yes	—
509	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
510	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
511	#525	C₂²×C₆₇	1	32	yes	complemented
512	C₂×#123	C₂²×C₆₇	1	2	yes	—
513	C₂×#123	C₂²×C₆₇	1	4	yes	—
514	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
515	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
516	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
517	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
518	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
519	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
520	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
521	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
522	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
523	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
524	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
525	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
526	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
527	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
528	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	32	yes	complemented
529	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
530	C₂×#121	C₂²×C₆₇	1	4	yes	—
531	C₂×#121	C₂²×C₆₇	1	2	yes	—
532	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
533	C₂×#120	C₂²×C₆₇	1	4	yes	—
534	#520	C₂²×C₆₇	1	32	yes	complemented
535	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
536	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
537	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
538	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
539	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
540	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
541	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
542	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
543	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
544	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
545	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
546	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
547	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
548	C₂×C₄×D₄	C₂²×C₆₇	1	16	yes	complemented
549	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
550	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
551	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
552	C₂×#117	C₂²×C₆₇	1	2	yes	—
553	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
554	C₂×#117	C₂²×C₆₇	1	4	yes	complemented
555	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
556	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
557	C₂²×C₄⋊C₄	C₂²×C₆₇	1	4	yes	complemented
558	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
559	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
560	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
561	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
562	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
563	C₂⁵	C₂³×C₆₇	1	2	yes	—
564	C₂×#41	—	2	16	no	—
565	C₂×#41	—	4	8	no	—
566	C₂×#41	C₂³×C₆₇	1	16	yes	—
567	C₂×#41	C₂³×C₆₇	1	16	yes	complemented
568	C₂²×Q₈	—	4	8	no	—
569	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
570	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
571	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
572	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
573	C₂²×Q₈	C₂³×C₆₇	1	16	yes	complemented
574	C₂²×D₄	—	2	8	no	—
575	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
576	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
577	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
579	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
580	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
581	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
582	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
583	C₂³×C₄	—	4	8	no	—
584	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
586	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
588	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
589	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
590	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
591	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
592	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
593	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
594	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
595	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
596	C₂³×C₄	C₂³×C₆₇	1	16	yes	—
597	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
598	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
599	C₄⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
600	#126	C₂³×C₆₇	1	16	yes	complemented
601	#126	C₂³×C₆₇	1	32	yes	complemented
602	#126	C₂³×C₆₇	1	32	yes	complemented
603	#125	C₂³×C₆₇	1	8	yes	complemented
604	#125	C₂³×C₆₇	1	16	yes	complemented
605	#125	C₂³×C₆₇	1	32	yes	complemented
606	#124	C₂³×C₆₇	1	16	yes	—
607	#124	C₂³×C₆₇	1	8	yes	complemented
608	#124	C₂³×C₆₇	1	32	yes	complemented
609	#123	C₂³×C₆₇	1	16	yes	—
610	#123	C₂³×C₆₇	1	32	yes	—
611	#123	C₂³×C₆₇	1	32	yes	complemented
612	#123	C₂³×C₆₇	1	32	yes	complemented
613	#123	C₂³×C₆₇	1	32	yes	complemented
614	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
615	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
616	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
617	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
618	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
619	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
620	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
621	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
622	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
623	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
624	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
625	#121	C₂³×C₆₇	1	8	yes	—
626	#121	C₂³×C₆₇	1	32	yes	—
627	#121	C₂³×C₆₇	1	16	yes	—
628	#121	C₂³×C₆₇	1	16	yes	complemented
629	#120	C₂³×C₆₇	1	32	yes	—
630	C₄×Q₈	C₂³×C₆₇	1	16	yes	complemented
631	C₄×Q₈	C₂³×C₆₇	1	16	yes	complemented
632	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
633	C₄×Q₈	C₂³×C₆₇	1	16	yes	complemented
634	C₄×D₄	C₂³×C₆₇	1	8	yes	—
635	C₄×D₄	C₂³×C₆₇	1	16	yes	—
636	C₄×D₄	C₂³×C₆₇	1	8	yes	—
637	C₄×D₄	C₂³×C₆₇	1	8	yes	—
638	C₄×D₄	C₂³×C₆₇	1	8	yes	—
639	C₄×D₄	C₂³×C₆₇	1	16	yes	—
640	C₄×D₄	C₂³×C₆₇	1	16	yes	—
641	C₄×D₄	C₂³×C₆₇	1	32	yes	—
642	C₄×D₄	C₂³×C₆₇	1	16	yes	—
643	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
644	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
645	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
646	#117	C₂³×C₆₇	1	16	yes	—
647	#117	C₂³×C₆₇	1	16	yes	complemented
648	#117	C₂³×C₆₇	1	32	yes	complemented
649	#117	C₂³×C₆₇	1	16	yes	complemented
650	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
654	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
656	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
660	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
661	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
662	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
667	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
669	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₆₇	1	32	yes	complemented
671	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	complemented
672	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	complemented
673	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
690	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
691	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
693	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
694	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
698	C₂⁴	—	2	8	no	—
699	C₂⁴	—	2	8	no	—
700	C₂⁴	—	4	4	no	—
701	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
702	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
703	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
704	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
705	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
706	#41	—	2	64	no	—
707	#41	—	4	32	no	—
708	C₂×Q₈	—	2	8	no	—
709	C₂×Q₈	—	2	4	no	—
710	C₂×Q₈	—	2	8	no	—
711	C₂×Q₈	—	4	8	no	—
712	C₂×Q₈	—	4	32	no	—
713	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
714	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
715	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
716	C₂×Q₈	C₂⁴×C₆₇	1	16	yes	—
717	C₂×D₄	—	2	8	no	—
718	C₂×D₄	—	2	16	no	—
719	C₂×D₄	—	2	8	no	—
720	C₂×D₄	—	2	32	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	4	8	no	—
724	C₂×D₄	#41×C₆₇	1	8	yes	complemented
725	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
726	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
727	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
728	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
729	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
730	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
731	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
732	C₂²×C₄	—	2	16	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	2	4	no	—
735	C₂²×C₄	—	2	8	no	—
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	2	8	no	—
738	C₂²×C₄	—	2	8	no	—
739	C₂²×C₄	—	4	32	no	—
740	C₂²×C₄	—	4	4	no	—
741	C₂²×C₄	—	4	4	no	—
742	C₂²×C₄	—	4	4	no	—
743	C₂²×C₄	—	4	8	no	—
744	C₂²×C₄	—	4	8	no	—
745	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
749	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
750	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
754	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
755	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
757	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
760	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
761	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
762	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
763	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
764	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
765	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
766	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
767	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
768	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
770	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
771	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
772	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
773	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
774	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
775	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
776	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
777	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
778	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
779	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
780	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
781	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
782	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
783	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
784	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
785	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
786	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
787	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
788	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
789	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
790	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
791	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
792	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
793	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
794	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
795	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
796	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
797	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
798	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
799	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
800	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
801	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
802	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
803	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
804	C₄²	C₂⁴×C₆₇	1	4	yes	—
805	C₄²	C₂⁴×C₆₇	1	4	yes	—
806	C₄²	C₂⁴×C₆₇	1	4	yes	—
807	C₄²	C₂⁴×C₆₇	1	4	yes	—
808	C₄²	C₂⁴×C₆₇	1	16	yes	—
809	C₄²	C₂⁴×C₆₇	1	16	yes	—
810	C₄²	C₂⁴×C₆₇	1	8	yes	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	4	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	4	no	—
816	C₂³	—	2	16	no	—
817	C₂³	—	2	4	no	—
818	C₂³	—	2	4	no	—
819	C₂³	—	2	4	no	—
820	C₂³	—	2	4	no	—
821	C₂³	—	2	16	no	—
822	C₂³	—	2	4	no	—
823	C₂³	—	4	8	no	—
824	C₂³	—	4	32	no	—
825	C₂³	C₂×#41×C₆₇	1	8	yes	—
826	C₂³	2₋¹⁺⁴×C₆₇	1	4	yes	—
827	C₂³	C₂⁵×C₆₇	1	4	yes	—
828	C₂³	C₂⁵×C₆₇	1	4	yes	—
829	C₂³	C₂⁵×C₆₇	1	4	yes	—
830	C₂³	C₂⁵×C₆₇	1	2	yes	—
831	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
832	Q₈	—	2	16	no	—
833	Q₈	—	2	8	no	—
834	Q₈	—	2	16	no	—
835	Q₈	—	4	16	no	—
836	D₄	—	2	16	no	—
837	D₄	—	2	32	no	—
838	D₄	—	2	16	no	—
839	D₄	—	2	8	no	—
840	D₄	—	2	8	no	—
841	D₄	—	4	16	no	—
842	D₄	C₂×#41×C₆₇	1	16	yes	complemented
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	8	no	—
846	C₂×C₄	—	2	32	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	8	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	8	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	8	no	—
857	C₂×C₄	—	2	16	no	—
858	C₂×C₄	—	2	8	no	—
859	C₂×C₄	—	2	16	no	—
860	C₂×C₄	—	2	16	no	—
861	C₂×C₄	—	4	8	no	—
862	C₂×C₄	—	4	8	no	—
863	C₂×C₄	—	4	8	no	—
864	C₂×C₄	—	4	16	no	—
865	C₂×C₄	—	4	16	no	—
866	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
867	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
868	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
869	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
870	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
871	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
872	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
873	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
874	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
875	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
876	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
877	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
878	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
879	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
880	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	4	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	8	no	—
886	C₂²	—	2	16	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	2	4	no	—
890	C₂²	—	2	4	no	—
891	C₂²	—	2	4	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	4	32	no	—
894	C₂²	—	4	8	no	—
895	C₂²	—	4	8	no	—
896	C₂²	C₂²×#41×C₆₇	1	8	yes	—
897	C₂²	C₂²×#41×C₆₇	1	2	yes	—
898	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
899	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	4	yes	—
900	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	2	yes	—
901	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
902	C₄	—	2	4	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	8	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	4	no	—
907	C₄	—	2	4	no	—
908	C₄	—	2	8	no	—
909	C₄	—	2	4	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	4	no	—
913	C₄	C₂²×#41×C₆₇	1	4	yes	—
914	C₄	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
915	C₂	—	2	4	no	—
916	C₂	—	2	8	no	—
917	C₂	—	4	4	no	—
918	C₂	—	4	4	no	—
919	C₂	C₆₇×#3520	1	4	yes	direct product factor
920	C₂	C₂³×#41×C₆₇	1	1	yes	characteristic
921	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
922	C₂	C₂²×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3520	C₂	direct (N × H)
2. C₂×#556×C₆₇	C₂	semidirect
3. C₂×#554×C₆₇	C₂	semidirect
4. C₂×#552×C₆₇	C₂	semidirect
5. C₂×#551×C₆₇	C₂	semidirect
6. C₂×D₄×Q₈×C₆₇	C₂	semidirect
7. C₂×#548×C₆₇	C₂	semidirect
8. C₂×#547×C₆₇	C₂	semidirect
9. C₂×#547×C₆₇	C₂	semidirect
10. C₂×#546×C₆₇	C₂	semidirect
11. C₂×#542×C₆₇	C₂	semidirect
12. C₂×#539×C₆₇	C₂	semidirect
13. C₂×#533×C₆₇	C₂	semidirect
14. C₂×#529×C₆₇	C₂	semidirect
15. C₂×#525×C₆₇	C₂	semidirect
16. C₂²×C₂²⋊Q₈×C₆₇	C₂	semidirect
17. C₂×#520×C₆₇	C₂	semidirect
18. C₂²×C₄×D₄×C₆₇	C₂	semidirect
20. C₂²×#41×C₆₇	C₂²	semidirect
21. C₂³×Q₈×C₆₇	C₂²	semidirect
24. #556×C₆₇	C₂²	semidirect
25. #554×C₆₇	C₂²	semidirect
26. #552×C₆₇	C₂²	semidirect
27. #551×C₆₇	C₂²	semidirect
28. D₄×Q₈×C₆₇	C₂²	semidirect
29. #548×C₆₇	C₂²	semidirect
30. #547×C₆₇	C₂²	semidirect
31. #547×C₆₇	C₂²	semidirect
32. #546×C₆₇	C₂²	semidirect
33. #542×C₆₇	C₂²	semidirect
34. #539×C₆₇	C₂²	semidirect
35. #533×C₆₇	C₂²	semidirect
36. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
37. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
38. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
39. #529×C₆₇	C₂²	semidirect
40. C₂×#126×C₆₇	C₂²	semidirect
41. C₂×#126×C₆₇	C₂²	semidirect
42. C₂×#126×C₆₇	C₂²	semidirect
43. C₂×#125×C₆₇	C₂²	semidirect
44. C₂×#125×C₆₇	C₂²	semidirect
45. C₂×#125×C₆₇	C₂²	semidirect
47. C₂×#124×C₆₇	C₂²	semidirect
48. C₂×#124×C₆₇	C₂²	semidirect
49. #525×C₆₇	C₂²	semidirect
52. C₂×#123×C₆₇	C₂²	semidirect
53. C₂×#123×C₆₇	C₂²	semidirect
54. C₂×#123×C₆₇	C₂²	semidirect
59. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
60. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
61. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
62. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
63. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
64. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
65. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
66. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
70. C₂×#121×C₆₇	C₂²	semidirect
72. #520×C₆₇	C₂²	semidirect
73. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
74. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
75. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
76. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
86. C₂×C₄×D₄×C₆₇	C₂²	semidirect
87. C₂×C₄×D₄×C₆₇	C₂²	semidirect
88. C₂×C₄×D₄×C₆₇	C₂²	semidirect
89. C₂×C₄×D₄×C₆₇	C₂²	semidirect
91. C₂×#117×C₆₇	C₂²	semidirect
92. C₂×#117×C₆₇	C₂²	semidirect
93. C₂×#117×C₆₇	C₂²	semidirect
95. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
96. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
97. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
105. C₂×#41×C₆₇	C₂³	semidirect
111. C₂²×Q₈×C₆₇	C₂³	semidirect
135. C₄⋊Q₈×C₆₇	C₂³	semidirect
136. C₄⋊Q₈×C₆₇	C₂³	semidirect
137. C₄⋊Q₈×C₆₇	C₂³	semidirect
138. #126×C₆₇	C₂³	semidirect
139. #126×C₆₇	C₂³	semidirect
140. #126×C₆₇	C₂³	semidirect
141. #125×C₆₇	C₂³	semidirect
142. #125×C₆₇	C₂³	semidirect
143. #125×C₆₇	C₂³	semidirect
145. #124×C₆₇	C₂³	semidirect
146. #124×C₆₇	C₂³	semidirect
149. #123×C₆₇	C₂³	semidirect
150. #123×C₆₇	C₂³	semidirect
151. #123×C₆₇	C₂³	semidirect
156. C₂²⋊Q₈×C₆₇	C₂³	semidirect
157. C₂²⋊Q₈×C₆₇	C₂³	semidirect
158. C₂²⋊Q₈×C₆₇	C₂³	semidirect
159. C₂²⋊Q₈×C₆₇	C₂³	semidirect
160. C₂²⋊Q₈×C₆₇	C₂³	semidirect
161. C₂²⋊Q₈×C₆₇	C₂³	semidirect
162. C₂²⋊Q₈×C₆₇	C₂³	semidirect
166. #121×C₆₇	C₂³	semidirect
168. C₄×Q₈×C₆₇	C₂³	semidirect
169. C₄×Q₈×C₆₇	C₂³	semidirect
170. C₄×Q₈×C₆₇	C₂³	semidirect
171. C₄×Q₈×C₆₇	C₂³	semidirect
181. C₄×D₄×C₆₇	C₂³	semidirect
182. C₄×D₄×C₆₇	C₂³	semidirect
183. C₄×D₄×C₆₇	C₂³	semidirect
185. #117×C₆₇	C₂³	semidirect
186. #117×C₆₇	C₂³	semidirect
187. #117×C₆₇	C₂³	semidirect
208. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
209. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
210. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
262. C₂×D₄×C₆₇	#41	semidirect
380. D₄×C₆₇	C₂×#41	semidirect
453. C₂×#3520	C₆₇	direct (N × H)
458. C₂×C₆₇	#3520	direct (N × H)
462. #3520	C₂×C₆₇	direct (N × H)
463. C₂×#556	C₂×C₆₇	semidirect
464. C₂×#554	C₂×C₆₇	semidirect
465. C₂×#552	C₂×C₆₇	semidirect
466. C₂×#551	C₂×C₆₇	semidirect
467. C₂×D₄×Q₈	C₂×C₆₇	semidirect
468. C₂×#548	C₂×C₆₇	semidirect
469. C₂×#547	C₂×C₆₇	semidirect
470. C₂×#547	C₂×C₆₇	semidirect
471. C₂×#546	C₂×C₆₇	semidirect
472. C₂×#542	C₂×C₆₇	semidirect
473. C₂×#539	C₂×C₆₇	semidirect
474. C₂×#533	C₂×C₆₇	semidirect
475. C₂×#529	C₂×C₆₇	semidirect
476. C₂×#525	C₂×C₆₇	semidirect
477. C₂²×C₂²⋊Q₈	C₂×C₆₇	semidirect
478. C₂×#520	C₂×C₆₇	semidirect
479. C₂²×C₄×D₄	C₂×C₆₇	semidirect
480. C₆₇	C₂×#3520	direct (N × H)
482. C₂²×#41	C₂²×C₆₇	semidirect
483. C₂³×Q₈	C₂²×C₆₇	semidirect
486. #556	C₂²×C₆₇	semidirect
487. #554	C₂²×C₆₇	semidirect
488. #552	C₂²×C₆₇	semidirect
489. #551	C₂²×C₆₇	semidirect
490. D₄×Q₈	C₂²×C₆₇	semidirect
491. #548	C₂²×C₆₇	semidirect
492. #547	C₂²×C₆₇	semidirect
493. #547	C₂²×C₆₇	semidirect
494. #546	C₂²×C₆₇	semidirect
495. #542	C₂²×C₆₇	semidirect
496. #539	C₂²×C₆₇	semidirect
497. #533	C₂²×C₆₇	semidirect
498. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
499. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
500. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
501. #529	C₂²×C₆₇	semidirect
502. C₂×#126	C₂²×C₆₇	semidirect
503. C₂×#126	C₂²×C₆₇	semidirect
504. C₂×#126	C₂²×C₆₇	semidirect
505. C₂×#125	C₂²×C₆₇	semidirect
506. C₂×#125	C₂²×C₆₇	semidirect
507. C₂×#125	C₂²×C₆₇	semidirect
509. C₂×#124	C₂²×C₆₇	semidirect
510. C₂×#124	C₂²×C₆₇	semidirect
511. #525	C₂²×C₆₇	semidirect
514. C₂×#123	C₂²×C₆₇	semidirect
515. C₂×#123	C₂²×C₆₇	semidirect
516. C₂×#123	C₂²×C₆₇	semidirect
521. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
522. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
523. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
524. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
525. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
526. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
527. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
528. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
532. C₂×#121	C₂²×C₆₇	semidirect
534. #520	C₂²×C₆₇	semidirect
535. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
536. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
537. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
538. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
548. C₂×C₄×D₄	C₂²×C₆₇	semidirect
549. C₂×C₄×D₄	C₂²×C₆₇	semidirect
550. C₂×C₄×D₄	C₂²×C₆₇	semidirect
551. C₂×C₄×D₄	C₂²×C₆₇	semidirect
553. C₂×#117	C₂²×C₆₇	semidirect
554. C₂×#117	C₂²×C₆₇	semidirect
555. C₂×#117	C₂²×C₆₇	semidirect
557. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
558. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
559. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
567. C₂×#41	C₂³×C₆₇	semidirect
573. C₂²×Q₈	C₂³×C₆₇	semidirect
597. C₄⋊Q₈	C₂³×C₆₇	semidirect
598. C₄⋊Q₈	C₂³×C₆₇	semidirect
599. C₄⋊Q₈	C₂³×C₆₇	semidirect
600. #126	C₂³×C₆₇	semidirect
601. #126	C₂³×C₆₇	semidirect
602. #126	C₂³×C₆₇	semidirect
603. #125	C₂³×C₆₇	semidirect
604. #125	C₂³×C₆₇	semidirect
605. #125	C₂³×C₆₇	semidirect
607. #124	C₂³×C₆₇	semidirect
608. #124	C₂³×C₆₇	semidirect
611. #123	C₂³×C₆₇	semidirect
612. #123	C₂³×C₆₇	semidirect
613. #123	C₂³×C₆₇	semidirect
618. C₂²⋊Q₈	C₂³×C₆₇	semidirect
619. C₂²⋊Q₈	C₂³×C₆₇	semidirect
620. C₂²⋊Q₈	C₂³×C₆₇	semidirect
621. C₂²⋊Q₈	C₂³×C₆₇	semidirect
622. C₂²⋊Q₈	C₂³×C₆₇	semidirect
623. C₂²⋊Q₈	C₂³×C₆₇	semidirect
624. C₂²⋊Q₈	C₂³×C₆₇	semidirect
628. #121	C₂³×C₆₇	semidirect
630. C₄×Q₈	C₂³×C₆₇	semidirect
631. C₄×Q₈	C₂³×C₆₇	semidirect
632. C₄×Q₈	C₂³×C₆₇	semidirect
633. C₄×Q₈	C₂³×C₆₇	semidirect
643. C₄×D₄	C₂³×C₆₇	semidirect
644. C₄×D₄	C₂³×C₆₇	semidirect
645. C₄×D₄	C₂³×C₆₇	semidirect
647. #117	C₂³×C₆₇	semidirect
648. #117	C₂³×C₆₇	semidirect
649. #117	C₂³×C₆₇	semidirect
670. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
671. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
672. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
724. C₂×D₄	#41×C₆₇	semidirect
842. D₄	C₂×#41×C₆₇	semidirect
919. C₂	C₆₇×#3520	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3520	2
C₂×#556×C₆₇	2
C₂×#554×C₆₇	2
C₂×#552×C₆₇	2
C₂×#551×C₆₇	2
C₂×D₄×Q₈×C₆₇	2
C₂×#548×C₆₇	2
C₂×#547×C₆₇	2
C₂×#546×C₆₇	2
C₂×#542×C₆₇	2
C₂×#539×C₆₇	2
C₂×#533×C₆₇	2
C₂×#529×C₆₇	2
C₂×#525×C₆₇	2
C₂²×C₂²⋊Q₈×C₆₇	2
C₂×#520×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₂×#3520	67

Subgroups — C2×C67×#3520 #30742023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3520 #30742023