Subgroups — C₂×C₆₇×#3558 #30741981

Order 17152.

8122 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3558	C₂	1	32	yes	maximal, direct product factor
2	C₂×#562×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×H(3,𝔽₄)×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂×#559×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₂×#548×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#546×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#546×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂×D₄²×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#542×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×#538×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₂×#538×C₆₇	C₂	1	4	yes	maximal, complemented
12	C₂×#535×C₆₇	C₂	1	2	yes	maximal, complemented
13	C₂×#534×C₆₇	C₂	1	2	yes	maximal, complemented
14	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
18	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
19	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₆₇	C₂²	1	4	yes	complemented
22	C₂³×D₄×C₆₇	C₂²	1	2	yes	complemented
23	#562×C₆₇	C₂²	1	32	yes	complemented
24	H(3,𝔽₄)×C₆₇	C₂²	1	32	yes	complemented
25	#559×C₆₇	C₂²	1	32	yes	complemented
26	#548×C₆₇	C₂²	1	32	yes	complemented
27	#546×C₆₇	C₂²	1	32	yes	complemented
28	#546×C₆₇	C₂²	1	64	yes	complemented
29	D₄²×C₆₇	C₂²	1	32	yes	complemented
30	#542×C₆₇	C₂²	1	32	yes	complemented
31	#538×C₆₇	C₂²	1	32	yes	complemented
32	#538×C₆₇	C₂²	1	64	yes	complemented
33	#535×C₆₇	C₂²	1	32	yes	complemented
34	#534×C₆₇	C₂²	1	32	yes	complemented
35	#532×C₆₇	C₂²	1	16	yes	complemented
36	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×#127×C₆₇	C₂²	1	2	yes	—
38	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, 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×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
45	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
46	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
47	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
48	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
49	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
50	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
51	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
52	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
53	C₂×#124×C₆₇	C₂²	1	16	yes	complemented
54	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
55	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
56	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
57	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
58	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
59	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
60	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
61	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
63	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×#121×C₆₇	C₂²	1	2	yes	—
65	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
66	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
67	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
68	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
69	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
70	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
71	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
72	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
73	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
74	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
75	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
76	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
77	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
79	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
80	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
82	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
83	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
84	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
85	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
86	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
87	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
88	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
89	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
90	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	C₂⁵×C₆₇	C₂³	1	2	yes	—
92	C₂⁵×C₆₇	C₂³	1	4	yes	—
93	C₂×#41×C₆₇	—	4	8	no	—
94	C₂×#41×C₆₇	—	4	8	no	—
95	C₂×#41×C₆₇	C₂³	1	16	yes	complemented
96	C₂×#41×C₆₇	C₂³	1	16	yes	complemented
97	C₂²×Q₈×C₆₇	—	4	4	no	—
98	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
99	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
101	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
102	C₂²×Q₈×C₆₇	C₂³	1	8	yes	complemented
103	C₂²×D₄×C₆₇	—	4	4	no	—
104	C₂²×D₄×C₆₇	—	4	8	no	—
105	C₂²×D₄×C₆₇	—	4	16	no	—
106	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
107	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
108	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
110	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
113	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
114	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
115	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
116	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
118	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
119	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
120	C₂²×D₄×C₆₇	C₂³	1	32	yes	complemented
121	C₂²×D₄×C₆₇	C₂³	1	16	yes	complemented
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
125	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
128	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
129	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
130	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
131	#127×C₆₇	C₂³	1	16	yes	—
132	#127×C₆₇	C₂³	1	8	yes	complemented
133	#126×C₆₇	C₂³	1	16	yes	complemented
134	#126×C₆₇	C₂³	1	32	yes	complemented
135	#125×C₆₇	C₂³	1	8	yes	complemented
136	#124×C₆₇	C₂³	1	16	yes	complemented
137	#124×C₆₇	C₂³	1	16	yes	complemented
138	#124×C₆₇	C₂³	1	16	yes	complemented
139	#124×C₆₇	C₂³	1	16	yes	complemented
140	#124×C₆₇	C₂³	1	8	yes	complemented
141	#124×C₆₇	C₂³	1	16	yes	complemented
142	#124×C₆₇	C₂³	1	16	yes	complemented
143	#124×C₆₇	C₂³	1	32	yes	complemented
144	#124×C₆₇	C₂³	1	32	yes	complemented
145	#124×C₆₇	C₂³	1	32	yes	complemented
146	#123×C₆₇	C₂³	1	16	yes	complemented
147	#123×C₆₇	C₂³	1	32	yes	complemented
148	#123×C₆₇	C₂³	1	32	yes	complemented
149	#123×C₆₇	C₂³	1	32	yes	complemented
150	#123×C₆₇	C₂³	1	32	yes	complemented
151	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
152	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
153	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
154	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
155	#121×C₆₇	C₂³	1	8	yes	—
156	#121×C₆₇	C₂³	1	16	yes	—
157	#121×C₆₇	C₂³	1	16	yes	complemented
158	#121×C₆₇	C₂³	1	16	yes	complemented
159	#121×C₆₇	C₂³	1	32	yes	complemented
160	#121×C₆₇	C₂³	1	32	yes	complemented
161	#121×C₆₇	C₂³	1	32	yes	complemented
162	#121×C₆₇	C₂³	1	32	yes	complemented
163	#121×C₆₇	C₂³	1	32	yes	complemented
164	#120×C₆₇	C₂³	1	32	yes	complemented
165	#120×C₆₇	C₂³	1	32	yes	complemented
166	#120×C₆₇	C₂³	1	32	yes	complemented
167	#120×C₆₇	C₂³	1	32	yes	complemented
168	#120×C₆₇	C₂³	1	32	yes	complemented
169	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
170	C₄×Q₈×C₆₇	C₂³	1	16	yes	complemented
171	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
172	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
173	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
174	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
175	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
176	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
177	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
178	#117×C₆₇	C₂³	1	16	yes	complemented
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
208	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
213	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
214	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
215	C₂⁴×C₆₇	—	2	8	no	—
216	C₂⁴×C₆₇	—	4	4	no	—
217	C₂⁴×C₆₇	—	4	8	no	—
218	C₂⁴×C₆₇	—	4	8	no	—
219	C₂⁴×C₆₇	—	4	4	no	—
220	C₂⁴×C₆₇	—	4	8	no	—
221	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
222	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
223	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
224	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
225	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
226	C₂⁴×C₆₇	C₂⁴	1	16	yes	—
227	#41×C₆₇	—	4	32	no	—
228	#41×C₆₇	—	4	32	no	—
229	C₂×Q₈×C₆₇	—	2	8	no	—
230	C₂×Q₈×C₆₇	—	4	4	no	—
231	C₂×Q₈×C₆₇	—	4	2	no	—
232	C₂×Q₈×C₆₇	—	4	4	no	—
233	C₂×Q₈×C₆₇	—	4	16	no	—
234	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
235	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
236	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
237	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
238	C₂×D₄×C₆₇	—	2	8	no	—
239	C₂×D₄×C₆₇	—	2	16	no	—
240	C₂×D₄×C₆₇	—	2	8	no	—
241	C₂×D₄×C₆₇	—	2	8	no	—
242	C₂×D₄×C₆₇	—	4	16	no	—
243	C₂×D₄×C₆₇	—	4	32	no	—
244	C₂×D₄×C₆₇	—	4	8	no	—
245	C₂×D₄×C₆₇	—	4	4	no	—
246	C₂×D₄×C₆₇	—	4	8	no	—
247	C₂×D₄×C₆₇	—	4	8	no	—
248	C₂×D₄×C₆₇	—	4	4	no	—
249	C₂×D₄×C₆₇	—	4	2	no	—
250	C₂×D₄×C₆₇	—	4	8	no	—
251	C₂×D₄×C₆₇	—	4	4	no	—
252	C₂×D₄×C₆₇	—	4	8	no	—
253	C₂×D₄×C₆₇	—	4	64	no	—
254	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
255	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
256	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
257	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
258	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
259	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
260	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
261	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
262	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
263	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
264	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
265	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
266	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
267	C₂²×C₄×C₆₇	—	2	4	no	—
268	C₂²×C₄×C₆₇	—	2	4	no	—
269	C₂²×C₄×C₆₇	—	2	8	no	—
270	C₂²×C₄×C₆₇	—	4	2	no	—
271	C₂²×C₄×C₆₇	—	4	8	no	—
272	C₂²×C₄×C₆₇	—	4	4	no	—
273	C₂²×C₄×C₆₇	—	4	8	no	—
274	C₂²×C₄×C₆₇	—	4	8	no	—
275	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
276	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
277	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
278	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
285	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
286	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
291	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
293	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
294	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
295	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
296	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
297	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
298	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
299	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
300	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
301	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
302	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
303	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
304	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
305	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
306	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
307	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
308	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
309	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
310	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
311	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
312	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
313	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
314	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
315	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
316	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
317	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
318	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
319	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
320	C₄²×C₆₇	C₂⁴	1	4	yes	—
321	C₄²×C₆₇	C₂⁴	1	4	yes	—
322	C₄²×C₆₇	C₂⁴	1	4	yes	—
323	C₄²×C₆₇	C₂⁴	1	4	yes	—
324	C₄²×C₆₇	C₂⁴	1	8	yes	—
325	C₄²×C₆₇	C₂⁴	1	16	yes	—
326	C₂³×C₆₇	—	2	2	no	—
327	C₂³×C₆₇	—	2	2	no	—
328	C₂³×C₆₇	—	2	4	no	—
329	C₂³×C₆₇	—	2	8	no	—
330	C₂³×C₆₇	—	2	8	no	—
331	C₂³×C₆₇	—	2	8	no	—
332	C₂³×C₆₇	—	2	4	no	—
333	C₂³×C₆₇	—	2	8	no	—
334	C₂³×C₆₇	—	2	8	no	—
335	C₂³×C₆₇	—	2	4	no	—
336	C₂³×C₆₇	—	2	8	no	—
337	C₂³×C₆₇	—	2	16	no	—
338	C₂³×C₆₇	—	4	8	no	—
339	C₂³×C₆₇	—	4	16	no	—
340	C₂³×C₆₇	—	4	16	no	—
341	C₂³×C₆₇	—	4	8	no	—
342	C₂³×C₆₇	—	4	16	no	—
343	C₂³×C₆₇	—	8	16	no	—
344	C₂³×C₆₇	—	8	32	no	—
345	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
346	C₂³×C₆₇	C₂⁵	1	4	yes	—
347	C₂³×C₆₇	C₂⁵	1	8	yes	—
348	C₂³×C₆₇	C₂⁵	1	8	yes	—
349	C₂³×C₆₇	C₂⁵	1	2	yes	—
350	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
351	Q₈×C₆₇	—	2	16	no	—
352	Q₈×C₆₇	—	4	8	no	—
353	Q₈×C₆₇	—	4	4	no	—
354	Q₈×C₆₇	—	4	8	no	—
355	D₄×C₆₇	—	2	16	no	—
356	D₄×C₆₇	—	2	32	no	—
357	D₄×C₆₇	—	2	16	no	—
358	D₄×C₆₇	—	2	16	no	—
359	D₄×C₆₇	—	4	16	no	—
360	D₄×C₆₇	—	4	8	no	—
361	D₄×C₆₇	—	4	16	no	—
362	D₄×C₆₇	—	4	16	no	—
363	D₄×C₆₇	—	4	8	no	—
364	D₄×C₆₇	—	4	4	no	—
365	D₄×C₆₇	—	4	16	no	—
366	D₄×C₆₇	—	4	8	no	—
367	D₄×C₆₇	—	4	16	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	4	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	8	no	—
373	C₂×C₄×C₆₇	—	2	4	no	—
374	C₂×C₄×C₆₇	—	2	8	no	—
375	C₂×C₄×C₆₇	—	2	8	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	4	no	—
379	C₂×C₄×C₆₇	—	2	8	no	—
380	C₂×C₄×C₆₇	—	2	16	no	—
381	C₂×C₄×C₆₇	—	4	4	no	—
382	C₂×C₄×C₆₇	—	4	16	no	—
383	C₂×C₄×C₆₇	—	4	8	no	—
384	C₂×C₄×C₆₇	—	4	16	no	—
385	C₂×C₄×C₆₇	—	4	16	no	—
386	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
387	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
388	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
389	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
390	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
391	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
392	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
393	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
394	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
395	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
396	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
397	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
398	C₂²×C₆₇	—	2	2	no	—
399	C₂²×C₆₇	—	2	2	no	—
400	C₂²×C₆₇	—	2	8	no	—
401	C₂²×C₆₇	—	2	4	no	—
402	C₂²×C₆₇	—	2	8	no	—
403	C₂²×C₆₇	—	2	8	no	—
404	C₂²×C₆₇	—	2	8	no	—
405	C₂²×C₆₇	—	2	4	no	—
406	C₂²×C₆₇	—	2	8	no	—
407	C₂²×C₆₇	—	2	8	no	—
408	C₂²×C₆₇	—	2	4	no	—
409	C₂²×C₆₇	—	2	8	no	—
410	C₂²×C₆₇	—	4	16	no	—
411	C₂²×C₆₇	—	4	8	no	—
412	C₂²×C₆₇	—	4	16	no	—
413	C₂²×C₆₇	—	8	16	no	—
414	C₂²×C₆₇	—	8	32	no	—
415	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
416	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
417	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
418	C₂²×C₆₇	#585	1	2	yes	—
419	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
420	C₄×C₆₇	—	2	2	no	—
421	C₄×C₆₇	—	2	4	no	—
422	C₄×C₆₇	—	2	2	no	—
423	C₄×C₆₇	—	2	2	no	—
424	C₄×C₆₇	—	2	4	no	—
425	C₄×C₆₇	—	2	8	no	—
426	C₄×C₆₇	—	2	8	no	—
427	C₄×C₆₇	—	2	2	no	—
428	C₄×C₆₇	—	2	2	no	—
429	C₄×C₆₇	—	2	4	no	—
430	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
431	C₂×#3558	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
432	C₂×C₆₇	—	2	4	no	—
433	C₂×C₆₇	—	4	8	no	—
434	C₂×C₆₇	—	4	4	no	—
435	C₂×C₆₇	—	4	8	no	—
436	C₂×C₆₇	#3558	1	4	yes	direct product factor
437	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
440	#3558	C₂×C₆₇	1	32	yes	direct product factor
441	C₂×#562	C₂×C₆₇	1	2	yes	complemented
442	C₂×H(3,𝔽₄)	C₂×C₆₇	1	2	yes	complemented
443	C₂×#559	C₂×C₆₇	1	2	yes	complemented
444	C₂×#548	C₂×C₆₇	1	2	yes	complemented
445	C₂×#546	C₂×C₆₇	1	2	yes	complemented
446	C₂×#546	C₂×C₆₇	1	4	yes	complemented
447	C₂×D₄²	C₂×C₆₇	1	2	yes	complemented
448	C₂×#542	C₂×C₆₇	1	2	yes	complemented
449	C₂×#538	C₂×C₆₇	1	2	yes	complemented
450	C₂×#538	C₂×C₆₇	1	4	yes	complemented
451	C₂×#535	C₂×C₆₇	1	2	yes	complemented
452	C₂×#534	C₂×C₆₇	1	2	yes	complemented
453	C₂×#532	C₂×C₆₇	1	1	yes	characteristic, complemented
454	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
455	C₂²×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
456	C₆₇	C₂×#3558	1	1	yes	characteristic, direct product factor, Sylow
457	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
458	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
459	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
460	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
461	C₂³×D₄	C₂²×C₆₇	1	4	yes	complemented
462	C₂³×D₄	C₂²×C₆₇	1	2	yes	complemented
463	#562	C₂²×C₆₇	1	32	yes	complemented
464	H(3,𝔽₄)	C₂²×C₆₇	1	32	yes	complemented
465	#559	C₂²×C₆₇	1	32	yes	complemented
466	#548	C₂²×C₆₇	1	32	yes	complemented
467	#546	C₂²×C₆₇	1	32	yes	complemented
468	#546	C₂²×C₆₇	1	64	yes	complemented
469	D₄²	C₂²×C₆₇	1	32	yes	complemented
470	#542	C₂²×C₆₇	1	32	yes	complemented
471	#538	C₂²×C₆₇	1	32	yes	complemented
472	#538	C₂²×C₆₇	1	64	yes	complemented
473	#535	C₂²×C₆₇	1	32	yes	complemented
474	#534	C₂²×C₆₇	1	32	yes	complemented
475	#532	C₂²×C₆₇	1	16	yes	complemented
476	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
477	C₂×#127	C₂²×C₆₇	1	2	yes	—
478	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic, complemented
479	#529	C₂²×C₆₇	1	16	yes	complemented
480	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
481	C₂×#126	C₂²×C₆₇	1	4	yes	complemented
482	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
483	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
484	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
485	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
486	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
487	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
488	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
489	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
490	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
491	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
492	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
493	C₂×#124	C₂²×C₆₇	1	16	yes	complemented
494	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
495	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
496	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
497	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
498	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
499	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
500	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
501	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
502	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
503	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
504	C₂×#121	C₂²×C₆₇	1	2	yes	—
505	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
506	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
507	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
508	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
509	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
510	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
511	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
512	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
513	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
514	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
515	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
516	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
517	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
518	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
519	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
520	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
521	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
522	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
523	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
524	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
525	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
526	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
527	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
528	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
529	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
530	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
531	C₂⁵	C₂³×C₆₇	1	2	yes	—
532	C₂⁵	C₂³×C₆₇	1	4	yes	—
533	C₂×#41	—	4	8	no	—
534	C₂×#41	—	4	8	no	—
535	C₂×#41	C₂³×C₆₇	1	16	yes	complemented
536	C₂×#41	C₂³×C₆₇	1	16	yes	complemented
537	C₂²×Q₈	—	4	4	no	—
538	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
539	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
540	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
541	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
542	C₂²×Q₈	C₂³×C₆₇	1	8	yes	complemented
543	C₂²×D₄	—	4	4	no	—
544	C₂²×D₄	—	4	8	no	—
545	C₂²×D₄	—	4	16	no	—
546	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
547	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
548	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
549	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
550	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
551	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
552	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
553	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
554	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
555	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
556	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
557	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
558	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
559	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
560	C₂²×D₄	C₂³×C₆₇	1	32	yes	complemented
561	C₂²×D₄	C₂³×C₆₇	1	16	yes	complemented
562	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
564	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
566	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
568	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
569	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
570	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
571	#127	C₂³×C₆₇	1	16	yes	—
572	#127	C₂³×C₆₇	1	8	yes	complemented
573	#126	C₂³×C₆₇	1	16	yes	complemented
574	#126	C₂³×C₆₇	1	32	yes	complemented
575	#125	C₂³×C₆₇	1	8	yes	complemented
576	#124	C₂³×C₆₇	1	16	yes	complemented
577	#124	C₂³×C₆₇	1	16	yes	complemented
578	#124	C₂³×C₆₇	1	16	yes	complemented
579	#124	C₂³×C₆₇	1	16	yes	complemented
580	#124	C₂³×C₆₇	1	8	yes	complemented
581	#124	C₂³×C₆₇	1	16	yes	complemented
582	#124	C₂³×C₆₇	1	16	yes	complemented
583	#124	C₂³×C₆₇	1	32	yes	complemented
584	#124	C₂³×C₆₇	1	32	yes	complemented
585	#124	C₂³×C₆₇	1	32	yes	complemented
586	#123	C₂³×C₆₇	1	16	yes	complemented
587	#123	C₂³×C₆₇	1	32	yes	complemented
588	#123	C₂³×C₆₇	1	32	yes	complemented
589	#123	C₂³×C₆₇	1	32	yes	complemented
590	#123	C₂³×C₆₇	1	32	yes	complemented
591	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
592	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
593	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
594	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
595	#121	C₂³×C₆₇	1	8	yes	—
596	#121	C₂³×C₆₇	1	16	yes	—
597	#121	C₂³×C₆₇	1	16	yes	complemented
598	#121	C₂³×C₆₇	1	16	yes	complemented
599	#121	C₂³×C₆₇	1	32	yes	complemented
600	#121	C₂³×C₆₇	1	32	yes	complemented
601	#121	C₂³×C₆₇	1	32	yes	complemented
602	#121	C₂³×C₆₇	1	32	yes	complemented
603	#121	C₂³×C₆₇	1	32	yes	complemented
604	#120	C₂³×C₆₇	1	32	yes	complemented
605	#120	C₂³×C₆₇	1	32	yes	complemented
606	#120	C₂³×C₆₇	1	32	yes	complemented
607	#120	C₂³×C₆₇	1	32	yes	complemented
608	#120	C₂³×C₆₇	1	32	yes	complemented
609	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
610	C₄×Q₈	C₂³×C₆₇	1	16	yes	complemented
611	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
612	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
613	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
614	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
615	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
616	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
617	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
618	#117	C₂³×C₆₇	1	16	yes	complemented
619	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
625	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	complemented
646	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	complemented
647	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	complemented
648	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
650	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
652	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₆₇	1	8	yes	complemented
655	C₂⁴	—	2	8	no	—
656	C₂⁴	—	4	4	no	—
657	C₂⁴	—	4	8	no	—
658	C₂⁴	—	4	8	no	—
659	C₂⁴	—	4	4	no	—
660	C₂⁴	—	4	8	no	—
661	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
662	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
663	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
664	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
665	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
666	C₂⁴	C₂⁴×C₆₇	1	16	yes	—
667	#41	—	4	32	no	—
668	#41	—	4	32	no	—
669	C₂×Q₈	—	2	8	no	—
670	C₂×Q₈	—	4	4	no	—
671	C₂×Q₈	—	4	4	no	—
672	C₂×Q₈	—	4	2	no	—
673	C₂×Q₈	—	4	16	no	—
674	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
675	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
676	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
677	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
678	C₂×D₄	—	2	8	no	—
679	C₂×D₄	—	2	16	no	—
680	C₂×D₄	—	2	8	no	—
681	C₂×D₄	—	2	8	no	—
682	C₂×D₄	—	4	16	no	—
683	C₂×D₄	—	4	32	no	—
684	C₂×D₄	—	4	8	no	—
685	C₂×D₄	—	4	4	no	—
686	C₂×D₄	—	4	8	no	—
687	C₂×D₄	—	4	8	no	—
688	C₂×D₄	—	4	4	no	—
689	C₂×D₄	—	4	8	no	—
690	C₂×D₄	—	4	4	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	8	no	—
693	C₂×D₄	—	4	64	no	—
694	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
695	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
696	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
697	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
698	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
699	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
700	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
701	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
702	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
703	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
704	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
705	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
706	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	8	no	—
710	C₂²×C₄	—	4	8	no	—
711	C₂²×C₄	—	4	4	no	—
712	C₂²×C₄	—	4	8	no	—
713	C₂²×C₄	—	4	8	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
722	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
723	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
725	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
726	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
728	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
729	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
730	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
731	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
732	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
733	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
734	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
735	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
736	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
737	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
738	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
739	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
740	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
741	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
742	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
743	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
744	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
745	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
746	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
747	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
748	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
749	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
750	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
751	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
752	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
753	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
754	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
755	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
756	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
757	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
758	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
759	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
760	C₄²	C₂⁴×C₆₇	1	4	yes	—
761	C₄²	C₂⁴×C₆₇	1	4	yes	—
762	C₄²	C₂⁴×C₆₇	1	4	yes	—
763	C₄²	C₂⁴×C₆₇	1	4	yes	—
764	C₄²	C₂⁴×C₆₇	1	8	yes	—
765	C₄²	C₂⁴×C₆₇	1	16	yes	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	2	8	no	—
770	C₂³	—	2	8	no	—
771	C₂³	—	2	8	no	—
772	C₂³	—	2	4	no	—
773	C₂³	—	2	8	no	—
774	C₂³	—	2	8	no	—
775	C₂³	—	2	4	no	—
776	C₂³	—	2	8	no	—
777	C₂³	—	2	16	no	—
778	C₂³	—	4	8	no	—
779	C₂³	—	4	16	no	—
780	C₂³	—	4	16	no	—
781	C₂³	—	4	8	no	—
782	C₂³	—	4	16	no	—
783	C₂³	—	8	16	no	—
784	C₂³	—	8	32	no	—
785	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
786	C₂³	C₂⁵×C₆₇	1	4	yes	—
787	C₂³	C₂⁵×C₆₇	1	8	yes	—
788	C₂³	C₂⁵×C₆₇	1	8	yes	—
789	C₂³	C₂⁵×C₆₇	1	2	yes	—
790	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
791	Q₈	—	2	16	no	—
792	Q₈	—	4	8	no	—
793	Q₈	—	4	8	no	—
794	Q₈	—	4	4	no	—
795	D₄	—	2	16	no	—
796	D₄	—	2	32	no	—
797	D₄	—	2	16	no	—
798	D₄	—	2	16	no	—
799	D₄	—	4	16	no	—
800	D₄	—	4	8	no	—
801	D₄	—	4	16	no	—
802	D₄	—	4	16	no	—
803	D₄	—	4	8	no	—
804	D₄	—	4	16	no	—
805	D₄	—	4	8	no	—
806	D₄	—	4	4	no	—
807	D₄	—	4	16	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	8	no	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	2	8	no	—
815	C₂×C₄	—	2	8	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	8	no	—
820	C₂×C₄	—	2	16	no	—
821	C₂×C₄	—	4	16	no	—
822	C₂×C₄	—	4	8	no	—
823	C₂×C₄	—	4	16	no	—
824	C₂×C₄	—	4	16	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
827	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
828	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
829	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
830	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
831	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
832	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
833	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
834	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
835	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
836	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
837	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
838	C₂²	—	2	8	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	8	no	—
843	C₂²	—	2	8	no	—
844	C₂²	—	2	8	no	—
845	C₂²	—	2	4	no	—
846	C₂²	—	2	8	no	—
847	C₂²	—	2	8	no	—
848	C₂²	—	2	4	no	—
849	C₂²	—	2	8	no	—
850	C₂²	—	4	8	no	—
851	C₂²	—	4	16	no	—
852	C₂²	—	4	16	no	—
853	C₂²	—	8	16	no	—
854	C₂²	—	8	32	no	—
855	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
856	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
857	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
858	C₂²	#585×C₆₇	1	2	yes	—
859	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
860	C₄	—	2	2	no	—
861	C₄	—	2	4	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	4	no	—
865	C₄	—	2	8	no	—
866	C₄	—	2	8	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	4	no	—
870	C₄	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
871	C₂	—	2	4	no	—
872	C₂	—	4	4	no	—
873	C₂	—	4	8	no	—
874	C₂	—	4	8	no	—
875	C₂	C₆₇×#3558	1	4	yes	direct product factor
876	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
877	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
878	C₂	C₂×#585×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×#3558	C₂	direct (N × H)
2. C₂×#562×C₆₇	C₂	semidirect
3. C₂×H(3,𝔽₄)×C₆₇	C₂	semidirect
4. C₂×#559×C₆₇	C₂	semidirect
5. C₂×#548×C₆₇	C₂	semidirect
6. C₂×#546×C₆₇	C₂	semidirect
7. C₂×#546×C₆₇	C₂	semidirect
8. C₂×D₄²×C₆₇	C₂	semidirect
9. C₂×#542×C₆₇	C₂	semidirect
10. C₂×#538×C₆₇	C₂	semidirect
11. C₂×#538×C₆₇	C₂	semidirect
12. C₂×#535×C₆₇	C₂	semidirect
13. C₂×#534×C₆₇	C₂	semidirect
14. C₂×#532×C₆₇	C₂	semidirect
15. C₂×#529×C₆₇	C₂	semidirect
16. C₂²×#124×C₆₇	C₂	semidirect
17. C₂²×#41×C₆₇	C₂²	semidirect
18. C₂²×#41×C₆₇	C₂²	semidirect
19. C₂³×Q₈×C₆₇	C₂²	semidirect
21. C₂³×D₄×C₆₇	C₂²	semidirect
22. C₂³×D₄×C₆₇	C₂²	semidirect
23. #562×C₆₇	C₂²	semidirect
24. H(3,𝔽₄)×C₆₇	C₂²	semidirect
25. #559×C₆₇	C₂²	semidirect
26. #548×C₆₇	C₂²	semidirect
27. #546×C₆₇	C₂²	semidirect
28. #546×C₆₇	C₂²	semidirect
29. D₄²×C₆₇	C₂²	semidirect
30. #542×C₆₇	C₂²	semidirect
31. #538×C₆₇	C₂²	semidirect
32. #538×C₆₇	C₂²	semidirect
33. #535×C₆₇	C₂²	semidirect
34. #534×C₆₇	C₂²	semidirect
35. #532×C₆₇	C₂²	semidirect
36. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
38. C₂×#127×C₆₇	C₂²	semidirect
39. #529×C₆₇	C₂²	semidirect
40. C₂×#126×C₆₇	C₂²	semidirect
41. C₂×#126×C₆₇	C₂²	semidirect
42. C₂×#125×C₆₇	C₂²	semidirect
43. C₂×#124×C₆₇	C₂²	semidirect
44. C₂×#124×C₆₇	C₂²	semidirect
45. C₂×#124×C₆₇	C₂²	semidirect
46. C₂×#124×C₆₇	C₂²	semidirect
47. C₂×#124×C₆₇	C₂²	semidirect
48. C₂×#124×C₆₇	C₂²	semidirect
49. C₂×#124×C₆₇	C₂²	semidirect
50. C₂×#124×C₆₇	C₂²	semidirect
51. C₂×#124×C₆₇	C₂²	semidirect
52. C₂×#124×C₆₇	C₂²	semidirect
53. C₂×#124×C₆₇	C₂²	semidirect
54. C₂×#123×C₆₇	C₂²	semidirect
55. C₂×#123×C₆₇	C₂²	semidirect
56. C₂×#123×C₆₇	C₂²	semidirect
57. C₂×#123×C₆₇	C₂²	semidirect
58. 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
65. C₂×#121×C₆₇	C₂²	semidirect
66. C₂×#121×C₆₇	C₂²	semidirect
67. C₂×#121×C₆₇	C₂²	semidirect
68. C₂×#121×C₆₇	C₂²	semidirect
69. C₂×#121×C₆₇	C₂²	semidirect
70. C₂×#121×C₆₇	C₂²	semidirect
71. C₂×#121×C₆₇	C₂²	semidirect
72. C₂×#120×C₆₇	C₂²	semidirect
73. C₂×#120×C₆₇	C₂²	semidirect
74. C₂×#120×C₆₇	C₂²	semidirect
75. C₂×#120×C₆₇	C₂²	semidirect
76. C₂×#120×C₆₇	C₂²	semidirect
77. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
78. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
79. C₂×C₄×D₄×C₆₇	C₂²	semidirect
80. C₂×C₄×D₄×C₆₇	C₂²	semidirect
81. C₂×C₄×D₄×C₆₇	C₂²	semidirect
82. C₂×C₄×D₄×C₆₇	C₂²	semidirect
83. C₂×C₄×D₄×C₆₇	C₂²	semidirect
84. C₂×C₄×D₄×C₆₇	C₂²	semidirect
85. C₂×C₄×D₄×C₆₇	C₂²	semidirect
86. C₂×#117×C₆₇	C₂²	semidirect
87. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
88. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
89. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
90. C₂²×C₄²×C₆₇	C₂²	semidirect
95. C₂×#41×C₆₇	C₂³	semidirect
96. C₂×#41×C₆₇	C₂³	semidirect
102. C₂²×Q₈×C₆₇	C₂³	semidirect
120. C₂²×D₄×C₆₇	C₂³	semidirect
121. C₂²×D₄×C₆₇	C₂³	semidirect
130. C₄⋊Q₈×C₆₇	C₂³	semidirect
132. #127×C₆₇	C₂³	semidirect
133. #126×C₆₇	C₂³	semidirect
134. #126×C₆₇	C₂³	semidirect
135. #125×C₆₇	C₂³	semidirect
136. #124×C₆₇	C₂³	semidirect
137. #124×C₆₇	C₂³	semidirect
138. #124×C₆₇	C₂³	semidirect
139. #124×C₆₇	C₂³	semidirect
140. #124×C₆₇	C₂³	semidirect
141. #124×C₆₇	C₂³	semidirect
142. #124×C₆₇	C₂³	semidirect
143. #124×C₆₇	C₂³	semidirect
144. #124×C₆₇	C₂³	semidirect
145. #124×C₆₇	C₂³	semidirect
146. #123×C₆₇	C₂³	semidirect
147. #123×C₆₇	C₂³	semidirect
148. #123×C₆₇	C₂³	semidirect
149. #123×C₆₇	C₂³	semidirect
150. #123×C₆₇	C₂³	semidirect
151. C₂²⋊Q₈×C₆₇	C₂³	semidirect
152. C₂²⋊Q₈×C₆₇	C₂³	semidirect
153. C₂²⋊Q₈×C₆₇	C₂³	semidirect
154. C₂²⋊Q₈×C₆₇	C₂³	semidirect
157. #121×C₆₇	C₂³	semidirect
158. #121×C₆₇	C₂³	semidirect
159. #121×C₆₇	C₂³	semidirect
160. #121×C₆₇	C₂³	semidirect
161. #121×C₆₇	C₂³	semidirect
162. #121×C₆₇	C₂³	semidirect
163. #121×C₆₇	C₂³	semidirect
164. #120×C₆₇	C₂³	semidirect
165. #120×C₆₇	C₂³	semidirect
166. #120×C₆₇	C₂³	semidirect
167. #120×C₆₇	C₂³	semidirect
168. #120×C₆₇	C₂³	semidirect
169. C₄×Q₈×C₆₇	C₂³	semidirect
170. C₄×Q₈×C₆₇	C₂³	semidirect
171. C₄×D₄×C₆₇	C₂³	semidirect
172. C₄×D₄×C₆₇	C₂³	semidirect
173. C₄×D₄×C₆₇	C₂³	semidirect
174. C₄×D₄×C₆₇	C₂³	semidirect
175. C₄×D₄×C₆₇	C₂³	semidirect
176. C₄×D₄×C₆₇	C₂³	semidirect
177. C₄×D₄×C₆₇	C₂³	semidirect
178. #117×C₆₇	C₂³	semidirect
205. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
206. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
207. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
214. C₂×C₄²×C₆₇	C₂³	semidirect
431. C₂×#3558	C₆₇	direct (N × H)
436. C₂×C₆₇	#3558	direct (N × H)
440. #3558	C₂×C₆₇	direct (N × H)
441. C₂×#562	C₂×C₆₇	semidirect
442. C₂×H(3,𝔽₄)	C₂×C₆₇	semidirect
443. C₂×#559	C₂×C₆₇	semidirect
444. C₂×#548	C₂×C₆₇	semidirect
445. C₂×#546	C₂×C₆₇	semidirect
446. C₂×#546	C₂×C₆₇	semidirect
447. C₂×D₄²	C₂×C₆₇	semidirect
448. C₂×#542	C₂×C₆₇	semidirect
449. C₂×#538	C₂×C₆₇	semidirect
450. C₂×#538	C₂×C₆₇	semidirect
451. C₂×#535	C₂×C₆₇	semidirect
452. C₂×#534	C₂×C₆₇	semidirect
453. C₂×#532	C₂×C₆₇	semidirect
454. C₂×#529	C₂×C₆₇	semidirect
455. C₂²×#124	C₂×C₆₇	semidirect
456. C₆₇	C₂×#3558	direct (N × H)
457. C₂²×#41	C₂²×C₆₇	semidirect
458. C₂²×#41	C₂²×C₆₇	semidirect
459. C₂³×Q₈	C₂²×C₆₇	semidirect
461. C₂³×D₄	C₂²×C₆₇	semidirect
462. C₂³×D₄	C₂²×C₆₇	semidirect
463. #562	C₂²×C₆₇	semidirect
464. H(3,𝔽₄)	C₂²×C₆₇	semidirect
465. #559	C₂²×C₆₇	semidirect
466. #548	C₂²×C₆₇	semidirect
467. #546	C₂²×C₆₇	semidirect
468. #546	C₂²×C₆₇	semidirect
469. D₄²	C₂²×C₆₇	semidirect
470. #542	C₂²×C₆₇	semidirect
471. #538	C₂²×C₆₇	semidirect
472. #538	C₂²×C₆₇	semidirect
473. #535	C₂²×C₆₇	semidirect
474. #534	C₂²×C₆₇	semidirect
475. #532	C₂²×C₆₇	semidirect
476. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
478. C₂×#127	C₂²×C₆₇	semidirect
479. #529	C₂²×C₆₇	semidirect
480. C₂×#126	C₂²×C₆₇	semidirect
481. C₂×#126	C₂²×C₆₇	semidirect
482. C₂×#125	C₂²×C₆₇	semidirect
483. C₂×#124	C₂²×C₆₇	semidirect
484. C₂×#124	C₂²×C₆₇	semidirect
485. C₂×#124	C₂²×C₆₇	semidirect
486. C₂×#124	C₂²×C₆₇	semidirect
487. C₂×#124	C₂²×C₆₇	semidirect
488. C₂×#124	C₂²×C₆₇	semidirect
489. C₂×#124	C₂²×C₆₇	semidirect
490. C₂×#124	C₂²×C₆₇	semidirect
491. C₂×#124	C₂²×C₆₇	semidirect
492. C₂×#124	C₂²×C₆₇	semidirect
493. C₂×#124	C₂²×C₆₇	semidirect
494. C₂×#123	C₂²×C₆₇	semidirect
495. C₂×#123	C₂²×C₆₇	semidirect
496. C₂×#123	C₂²×C₆₇	semidirect
497. C₂×#123	C₂²×C₆₇	semidirect
498. C₂×#123	C₂²×C₆₇	semidirect
499. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
500. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
501. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
502. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
505. C₂×#121	C₂²×C₆₇	semidirect
506. C₂×#121	C₂²×C₆₇	semidirect
507. C₂×#121	C₂²×C₆₇	semidirect
508. C₂×#121	C₂²×C₆₇	semidirect
509. C₂×#121	C₂²×C₆₇	semidirect
510. C₂×#121	C₂²×C₆₇	semidirect
511. C₂×#121	C₂²×C₆₇	semidirect
512. C₂×#120	C₂²×C₆₇	semidirect
513. C₂×#120	C₂²×C₆₇	semidirect
514. C₂×#120	C₂²×C₆₇	semidirect
515. C₂×#120	C₂²×C₆₇	semidirect
516. C₂×#120	C₂²×C₆₇	semidirect
517. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
518. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
519. C₂×C₄×D₄	C₂²×C₆₇	semidirect
520. C₂×C₄×D₄	C₂²×C₆₇	semidirect
521. C₂×C₄×D₄	C₂²×C₆₇	semidirect
522. C₂×C₄×D₄	C₂²×C₆₇	semidirect
523. C₂×C₄×D₄	C₂²×C₆₇	semidirect
524. C₂×C₄×D₄	C₂²×C₆₇	semidirect
525. C₂×C₄×D₄	C₂²×C₆₇	semidirect
526. C₂×#117	C₂²×C₆₇	semidirect
527. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
528. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
529. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
530. C₂²×C₄²	C₂²×C₆₇	semidirect
535. C₂×#41	C₂³×C₆₇	semidirect
536. C₂×#41	C₂³×C₆₇	semidirect
542. C₂²×Q₈	C₂³×C₆₇	semidirect
560. C₂²×D₄	C₂³×C₆₇	semidirect
561. C₂²×D₄	C₂³×C₆₇	semidirect
570. C₄⋊Q₈	C₂³×C₆₇	semidirect
572. #127	C₂³×C₆₇	semidirect
573. #126	C₂³×C₆₇	semidirect
574. #126	C₂³×C₆₇	semidirect
575. #125	C₂³×C₆₇	semidirect
576. #124	C₂³×C₆₇	semidirect
577. #124	C₂³×C₆₇	semidirect
578. #124	C₂³×C₆₇	semidirect
579. #124	C₂³×C₆₇	semidirect
580. #124	C₂³×C₆₇	semidirect
581. #124	C₂³×C₆₇	semidirect
582. #124	C₂³×C₆₇	semidirect
583. #124	C₂³×C₆₇	semidirect
584. #124	C₂³×C₆₇	semidirect
585. #124	C₂³×C₆₇	semidirect
586. #123	C₂³×C₆₇	semidirect
587. #123	C₂³×C₆₇	semidirect
588. #123	C₂³×C₆₇	semidirect
589. #123	C₂³×C₆₇	semidirect
590. #123	C₂³×C₆₇	semidirect
591. C₂²⋊Q₈	C₂³×C₆₇	semidirect
592. C₂²⋊Q₈	C₂³×C₆₇	semidirect
593. C₂²⋊Q₈	C₂³×C₆₇	semidirect
594. C₂²⋊Q₈	C₂³×C₆₇	semidirect
597. #121	C₂³×C₆₇	semidirect
598. #121	C₂³×C₆₇	semidirect
599. #121	C₂³×C₆₇	semidirect
600. #121	C₂³×C₆₇	semidirect
601. #121	C₂³×C₆₇	semidirect
602. #121	C₂³×C₆₇	semidirect
603. #121	C₂³×C₆₇	semidirect
604. #120	C₂³×C₆₇	semidirect
605. #120	C₂³×C₆₇	semidirect
606. #120	C₂³×C₆₇	semidirect
607. #120	C₂³×C₆₇	semidirect
608. #120	C₂³×C₆₇	semidirect
609. C₄×Q₈	C₂³×C₆₇	semidirect
610. C₄×Q₈	C₂³×C₆₇	semidirect
611. C₄×D₄	C₂³×C₆₇	semidirect
612. C₄×D₄	C₂³×C₆₇	semidirect
613. C₄×D₄	C₂³×C₆₇	semidirect
614. C₄×D₄	C₂³×C₆₇	semidirect
615. C₄×D₄	C₂³×C₆₇	semidirect
616. C₄×D₄	C₂³×C₆₇	semidirect
617. C₄×D₄	C₂³×C₆₇	semidirect
618. #117	C₂³×C₆₇	semidirect
645. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
646. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
647. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
654. C₂×C₄²	C₂³×C₆₇	semidirect
875. C₂	C₆₇×#3558	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×#3558	2
C₂×#562×C₆₇	2
C₂×H(3,𝔽₄)×C₆₇	2
C₂×#559×C₆₇	2
C₂×#548×C₆₇	2
C₂×#546×C₆₇	2
C₂×D₄²×C₆₇	2
C₂×#542×C₆₇	2
C₂×#538×C₆₇	2
C₂×#535×C₆₇	2
C₂×#534×C₆₇	2
C₂×#532×C₆₇	2
C₂×#529×C₆₇	2
C₂²×#124×C₆₇	2
C₂×#3558	67

Subgroups — C2×C67×#3558 #30741981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3558 #30741981