Subgroups — #22573872

Order 8576.

1658 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14524088	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864067	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864064	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864056	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864054	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864038	C₂	1	2	yes	maximal, complemented
8	#16864036	C₂	1	2	yes	maximal, complemented
9	#16864034	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864030	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864028	C₂	1	2	yes	maximal, complemented
14	#16863976	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863973	C₂	1	2	yes	maximal, complemented
16	#16863964	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863961	C₂	1	2	yes	maximal, complemented
18	#16863905	C₂	1	1	yes	maximal, characteristic, complemented
19	#16863904	C₂	1	2	yes	maximal, complemented
20	C₂×#14524016	C₂	1	2	yes	maximal, complemented
21	#121×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	#16863875	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	#14524088	—	2	8	no	—
25	C₂×#11761629	C₂²	1	1	yes	characteristic, complemented
26	C₂×#11761628	C₂²	1	2	yes	complemented
27	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
28	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
29	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
30	C₂×#11761627	C₂²	1	1	yes	characteristic
31	C₂×#11761627	C₂²	1	1	yes	characteristic, complemented
32	C₂×#11761627	C₂²	1	2	yes	complemented
33	C₂×#11761627	C₂²	1	2	yes	complemented
34	#41×D₆₇	—	2	8	no	—
35	C₂×Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂²×D₂₆₈	C₂²	1	2	yes	complemented
37	C₂²×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
38	C₂²×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
39	C₂²×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
40	C₂×D₄×D₆₇	C₂²	1	2	yes	complemented
41	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₆₇	C₂²	1	2	yes	complemented
43	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
44	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₆₇	C₂²	1	2	yes	complemented
46	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₄×D₆₇	C₂²	1	2	yes	complemented
48	#14524040	C₂²	1	1	yes	characteristic, complemented
49	#14524039	C₂²	1	2	yes	complemented
50	#14524039	C₂²	1	1	yes	characteristic, complemented
51	#14524039	C₂²	1	2	yes	complemented
52	#14524032	C₂²	1	1	yes	characteristic, complemented
53	#14524029	C₂²	1	2	yes	complemented
54	#14524029	C₂²	1	2	yes	complemented
55	#14524028	C₂²	1	1	yes	characteristic, complemented
56	#14524026	C₂²	1	2	yes	complemented
57	#14524025	C₂²	1	1	yes	characteristic, complemented
58	#14524021	C₂²	1	2	yes	complemented
59	#14524021	C₂²	1	1	yes	characteristic, complemented
60	#14524021	C₂²	1	2	yes	complemented
61	#14524020	C₂²	1	2	yes	complemented
62	#14524020	C₂²	1	1	yes	characteristic, complemented
63	#14524019	C₂²	1	1	yes	characteristic, complemented
64	#14524018	C₂²	1	2	yes	complemented
65	#14524018	C₂²	1	1	yes	characteristic, complemented
66	#14524018	C₂²	1	1	yes	characteristic, complemented
67	#14524017	C₂²	1	1	yes	characteristic, complemented
68	#14524017	C₂²	1	2	yes	complemented
69	#14524017	C₂²	1	1	yes	characteristic, complemented
70	#14524016	C₂²	1	2	yes	complemented
71	#14524016	C₂²	1	2	yes	complemented
72	#14524016	C₂²	1	2	yes	complemented
73	#14524016	C₂²	1	2	yes	complemented
74	#14524016	C₂²	1	2	yes	complemented
75	#14524016	C₂²	1	2	yes	complemented
76	#14524016	C₂²	1	2	yes	complemented
77	#14524016	C₂²	1	1	yes	characteristic, complemented
78	#14524016	C₂²	1	2	yes	complemented
79	#14524016	C₂²	1	2	yes	complemented
80	#14524016	C₂²	1	2	yes	complemented
81	#14524015	C₂²	1	2	yes	complemented
82	#14524015	C₂²	1	2	yes	complemented
83	#14524015	C₂²	1	2	yes	complemented
84	#14524015	C₂²	1	2	yes	complemented
85	#14524015	C₂²	1	1	yes	characteristic, complemented
86	#14524014	C₂²	1	1	yes	characteristic, complemented
87	#14524013	C₂²	1	2	yes	complemented
88	#14524013	C₂²	1	2	yes	complemented
89	#14524013	C₂²	1	1	yes	characteristic, complemented
90	#14524013	C₂²	1	2	yes	complemented
91	#14524013	C₂²	1	2	yes	complemented
92	#14524012	C₂²	1	2	yes	complemented
93	#14524011	C₂²	1	1	yes	characteristic, complemented
94	#14524011	C₂²	1	2	yes	complemented
95	#14524011	C₂²	1	2	yes	complemented
96	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
97	#14524008	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
99	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
100	#14524005	C₂²	1	2	yes	complemented
101	#14524005	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
105	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
106	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
107	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
108	#14524000	C₂²	1	1	yes	characteristic, complemented
109	#14523999	C₂²	1	2	yes	complemented
110	C₂×Dic₆₇⋊C₄	C₂²	1	2	yes	complemented
111	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
112	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	complemented
113	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
114	C₂×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₂²×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#123×C₆₇	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	#121×C₆₇	C₂²	1	2	yes	complemented
120	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#120×C₆₇	C₂²	1	2	yes	complemented
122	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
125	C₂³×D₆₇	C₂³	1	1	yes	characteristic
126	C₂³×D₆₇	C₂³	1	2	yes	—
127	C₂³×D₆₇	C₂³	1	2	yes	—
128	C₂³×D₆₇	C₂³	1	2	yes	—
129	#11761629	—	2	4	no	—
130	#11761628	—	2	8	no	—
131	#11761628	—	2	4	no	—
132	#11761628	—	2	4	no	—
133	#11761628	—	2	4	no	—
134	#11761627	—	2	8	no	—
135	#11761627	—	2	8	no	—
136	#11761627	—	2	4	no	—
137	#11761627	D₄	1	8	yes	complemented
138	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
139	C₂×Dic₁₃₄	C₂³	1	2	yes	—
140	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
141	Q₈×D₆₇	—	2	4	no	—
142	C₂×D₂₆₈	—	4	4	no	—
143	C₂×D₂₆₈	C₂³	1	2	yes	—
144	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
145	C₂×D₂₆₈	C₂³	1	2	yes	—
146	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
147	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
148	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
149	C₂×D₂₆₈	C₂³	1	2	yes	—
150	C₂×D₂₆₈	C₂³	1	2	yes	—
151	C₂×D₂₆₈	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₆₇	—	2	8	no	—
153	C₂×C₂²⋊D₆₇	—	2	8	no	—
154	C₂×C₂²⋊D₆₇	—	4	4	no	—
155	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
171	D₄×D₆₇	—	2	4	no	—
172	D₄×D₆₇	—	2	4	no	—
173	D₄×D₆₇	—	2	8	no	—
174	D₄×D₆₇	—	2	8	no	—
175	D₄×D₆₇	—	2	4	no	—
176	D₄×D₆₇	—	4	4	no	—
177	C₂²×Dic₆₇	C₂³	1	2	yes	—
178	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
179	C₂²×Dic₆₇	C₂³	1	2	yes	—
180	C₂²×Dic₆₇	C₂³	1	2	yes	—
181	C₂×C₄×D₆₇	—	2	8	no	—
182	C₂×C₄×D₆₇	—	2	4	no	—
183	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₆₇	C₂³	1	2	yes	—
185	C₂×C₄×D₆₇	C₂³	1	2	yes	—
186	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄×D₆₇	C₂³	1	2	yes	—
189	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄×D₆₇	C₂³	1	2	yes	—
191	C₂×C₄×D₆₇	C₂³	1	2	yes	—
192	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
195	Dic₆₇⋊C₄	C₂³	1	2	yes	—
196	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
197	Dic₆₇⋊C₄	C₂³	1	2	yes	—
198	Dic₆₇⋊C₄	C₂³	1	2	yes	—
199	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
200	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
201	Dic₆₇⋊C₄	C₂³	1	2	yes	—
202	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
203	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
204	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
205	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
206	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
207	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
209	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
210	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
211	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
213	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
214	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
215	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
216	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
217	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
218	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
219	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
220	C₄×Dic₆₇	C₂³	1	2	yes	—
221	C₄×Dic₆₇	C₂³	1	2	yes	—
222	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
223	C₂⁴×C₆₇	C₂³	1	2	yes	—
224	#41×C₆₇	—	2	4	no	—
225	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×D₄×C₆₇	—	2	4	no	—
227	C₂×D₄×C₆₇	C₂³	1	2	yes	—
228	C₂×D₄×C₆₇	C₂³	1	2	yes	—
229	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×D₄×C₆₇	C₂³	1	2	yes	—
232	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
233	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
234	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
235	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
236	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
237	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
238	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
239	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
240	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
241	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
242	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
243	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
244	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
245	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
246	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
247	C₄²×C₆₇	C₂³	1	1	yes	characteristic
248	C₂³×C₆₇	—	2	4	no	—
249	C₂³×C₆₇	—	4	2	no	—
250	C₂³×C₆₇	—	4	2	no	—
251	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂³×C₆₇	C₂⁴	1	2	yes	—
253	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂³×C₆₇	C₂⁴	1	2	yes	—
255	C₂²×D₆₇	—	2	4	no	—
256	C₂²×D₆₇	—	2	4	no	—
257	C₂²×D₆₇	—	2	2	no	—
258	C₂²×D₆₇	—	2	2	no	—
259	C₂²×D₆₇	—	2	4	no	—
260	C₂²×D₆₇	—	2	4	no	—
261	C₂²×D₆₇	—	4	1	no	—
262	C₂²×D₆₇	—	4	2	no	—
263	C₂²×D₆₇	—	4	2	no	—
264	C₂²×D₆₇	—	4	2	no	—
265	C₂²×D₆₇	—	4	2	no	—
266	C₂²×D₆₇	—	4	2	no	—
267	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
268	C₂²×D₆₇	C₂⁴	1	2	yes	—
269	C₂²×D₆₇	C₂⁴	1	2	yes	—
270	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
271	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
272	Q₈×C₆₇	—	2	2	no	—
273	D₄×C₆₇	—	2	4	no	—
274	D₄×C₆₇	—	2	4	no	—
275	D₄×C₆₇	—	2	2	no	—
276	D₄×C₆₇	—	4	1	no	—
277	D₄×C₆₇	—	4	2	no	—
278	D₄×C₆₇	C₂×D₄	1	4	yes	complemented
279	C₂×C₄×C₆₇	—	2	4	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	4	2	no	—
283	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
286	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₂²⋊D₆₇	—	2	4	no	—
291	C₂²⋊D₆₇	—	2	4	no	—
292	C₂²⋊D₆₇	—	2	2	no	—
293	C₂²⋊D₆₇	—	2	4	no	—
294	C₂²⋊D₆₇	—	2	2	no	—
295	C₂²⋊D₆₇	—	2	4	no	—
296	C₂²⋊D₆₇	—	2	4	no	—
297	C₂²⋊D₆₇	—	2	4	no	—
298	C₂²⋊D₆₇	—	2	4	no	—
299	C₂²⋊D₆₇	—	2	2	no	—
300	C₂²⋊D₆₇	—	4	2	no	—
301	C₂²⋊D₆₇	—	4	2	no	—
302	C₂²⋊D₆₇	—	4	2	no	—
303	C₂²⋊D₆₇	—	4	2	no	—
304	C₂²⋊D₆₇	—	4	1	no	—
305	C₂²⋊D₆₇	C₂×D₄	1	8	yes	complemented
306	C₂×Dic₆₇	—	2	2	no	—
307	C₂×Dic₆₇	—	2	4	no	—
308	C₂×Dic₆₇	—	4	2	no	—
309	C₂×Dic₆₇	C₂×D₄	1	8	yes	complemented
310	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
311	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
312	C₂×Dic₆₇	C₂⁴	1	2	yes	—
313	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
314	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
315	C₂×Dic₆₇	C₂⁴	1	2	yes	—
316	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
317	D₂₆₈	—	2	2	no	—
318	D₂₆₈	—	2	4	no	—
319	D₂₆₈	—	2	4	no	—
320	D₂₆₈	—	2	2	no	—
321	D₂₆₈	—	2	2	no	—
322	D₂₆₈	—	2	2	no	—
323	D₂₆₈	—	4	2	no	—
324	D₂₆₈	—	4	2	no	—
325	D₂₆₈	—	4	2	no	—
326	C₄×D₆₇	—	2	2	no	—
327	C₄×D₆₇	—	2	2	no	—
328	C₄×D₆₇	—	2	2	no	—
329	C₄×D₆₇	—	2	2	no	—
330	C₄×D₆₇	—	2	4	no	—
331	C₄×D₆₇	—	2	4	no	—
332	C₄×D₆₇	—	2	4	no	—
333	C₄×D₆₇	—	2	4	no	—
334	C₄×D₆₇	—	4	2	no	—
335	C₄×D₆₇	C₂×D₄	1	4	yes	complemented
336	Dic₁₃₄	—	2	4	no	—
337	Dic₁₃₄	—	2	2	no	—
338	Dic₁₃₄	C₂×D₄	1	4	yes	complemented
339	C₂²×C₆₇	—	2	2	no	—
340	C₂²×C₆₇	—	2	2	no	—
341	C₂²×C₆₇	—	2	1	no	—
342	C₂²×C₆₇	—	2	2	no	—
343	C₂²×C₆₇	—	2	1	no	—
344	C₂²×C₆₇	—	2	1	no	—
345	C₂²×C₆₇	—	2	2	no	—
346	C₂²×C₆₇	—	2	1	no	—
347	C₂²×C₆₇	—	2	1	no	—
348	C₂²×C₆₇	—	2	2	no	—
349	C₂²×C₆₇	—	2	1	no	—
350	C₂²×C₆₇	—	8	4	no	—
351	C₂²×C₆₇	C₂²×D₄	1	4	yes	—
352	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
353	C₂×D₆₇	—	2	1	no	—
354	C₂×D₆₇	—	2	1	no	—
355	C₂×D₆₇	—	2	1	no	—
356	C₂×D₆₇	—	2	1	no	—
357	C₂×D₆₇	—	2	2	no	—
358	C₂×D₆₇	—	2	1	no	—
359	C₂×D₆₇	—	2	2	no	—
360	C₂×D₆₇	—	2	1	no	—
361	C₂×D₆₇	—	2	2	no	—
362	C₂×D₆₇	—	2	2	no	—
363	C₂×D₆₇	—	2	2	no	—
364	C₂×D₆₇	—	2	2	no	—
365	C₂×D₆₇	—	2	1	no	—
366	C₂×D₆₇	—	4	4	no	—
367	C₂×D₆₇	—	4	8	no	—
368	C₂×D₆₇	—	8	4	no	—
369	C₂×D₆₇	—	8	4	no	—
370	C₂×D₆₇	C₂²×D₄	1	2	yes	—
371	C₂×D₆₇	H(5,𝔽₂)	1	2	yes	complemented
372	C₄×C₆₇	—	2	1	no	—
373	C₄×C₆₇	—	2	2	no	—
374	C₄×C₆₇	—	2	1	no	—
375	C₄×C₆₇	—	2	2	no	—
376	C₄×C₆₇	—	2	1	no	—
377	C₄×C₆₇	—	2	1	no	—
378	C₄×C₆₇	C₂²×D₄	1	2	yes	—
379	Dic₆₇	—	2	1	no	—
380	Dic₆₇	—	2	1	no	—
381	Dic₆₇	—	2	2	no	—
382	Dic₆₇	—	2	1	no	—
383	Dic₆₇	—	2	1	no	—
384	Dic₆₇	C₂²×D₄	1	4	yes	—
385	Dic₆₇	C₂²×D₄	1	2	yes	—
386	C₂×C₆₇	—	2	4	no	—
387	C₂×C₆₇	—	4	1	no	—
388	C₂×C₆₇	—	4	2	no	—
389	C₂×C₆₇	—	4	1	no	—
390	C₂×C₆₇	C₂³×D₄	1	1	yes	characteristic
391	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
392	C₂×C₆₇	#585	1	1	yes	characteristic
393	D₆₇	—	2	2	no	—
394	D₆₇	—	2	2	no	—
395	D₆₇	—	4	2	no	—
396	D₆₇	—	4	1	no	—
397	D₆₇	—	4	2	no	—
398	#3488	—	67	1	no	maximal, Sylow
399	C₆₇	#3488	1	1	yes	characteristic, complemented, Sylow
400	C₂×H(5,𝔽₂)	—	67	1	no	—
401	C₂²×#41	—	67	1	no	—
402	#550	—	67	1	no	—
403	#550	—	67	1	no	—
404	#548	—	67	1	no	—
405	#548	—	67	1	no	—
406	#546	—	67	1	no	—
407	#546	—	67	2	no	—
408	#546	—	67	2	no	—
409	#546	D₆₇	1	1	yes	characteristic, complemented
410	D₄²	—	67	1	no	—
411	D₄²	—	67	2	no	—
412	D₄²	—	67	2	no	—
413	D₄²	—	67	1	no	—
414	#537	—	67	1	no	—
415	#537	—	67	2	no	—
416	#535	—	67	1	no	—
417	#535	—	67	2	no	—
418	#525	—	67	2	no	—
419	#525	—	67	1	no	—
420	C₂×#121	—	67	1	no	—
421	C₂×#121	—	67	2	no	—
422	#520	—	67	1	no	—
423	H(5,𝔽₂)	—	134	8	no	—
424	C₂×#41	—	67	1	no	—
425	C₂×#41	—	67	1	no	—
426	C₂×#41	—	67	2	no	—
427	C₂×#41	—	67	2	no	—
428	C₂×#41	—	67	1	no	—
429	C₂×#41	—	67	1	no	—
430	C₂×#41	—	67	2	no	—
431	C₂×#41	—	67	1	no	—
432	C₂×#41	—	67	1	no	—
433	C₂×#41	—	134	8	no	—
434	C₂×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
435	C₂²×Q₈	—	67	1	no	—
436	C₂²×D₄	—	67	2	no	—
437	C₂²×D₄	—	67	2	no	—
438	C₂²×D₄	—	67	2	no	—
439	C₂²×D₄	—	67	2	no	—
440	C₂²×D₄	—	67	1	no	—
441	C₂²×D₄	—	67	2	no	—
442	C₂²×D₄	—	67	1	no	—
443	C₂²×D₄	—	67	2	no	—
444	C₂²×D₄	—	67	1	no	—
445	C₂²×D₄	—	67	2	no	—
446	C₂²×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
447	C₂³×C₄	—	67	2	no	—
448	C₂³×C₄	—	67	1	no	—
449	#127	—	67	1	no	—
450	#127	—	67	2	no	—
451	#127	—	67	2	no	—
452	#127	—	67	1	no	—
453	#124	—	67	1	no	—
454	#124	—	67	2	no	—
455	#124	—	67	2	no	—
456	#124	C₂×D₆₇	1	1	yes	characteristic, complemented
457	#123	—	67	2	no	—
458	#123	—	67	1	no	—
459	#123	—	67	1	no	—
460	#123	C₂×D₆₇	1	2	yes	complemented
461	C₂²⋊Q₈	—	67	1	no	—
462	C₂²⋊Q₈	—	67	1	no	—
463	C₂²⋊Q₈	—	67	2	no	—
464	C₂²⋊Q₈	—	67	2	no	—
465	C₂²⋊Q₈	—	67	1	no	—
466	C₂²⋊Q₈	—	67	2	no	—
467	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
468	#121	—	67	2	no	—
469	#121	—	67	1	no	—
470	#121	—	67	1	no	—
471	#121	—	67	2	no	—
472	#121	—	67	2	no	—
473	#121	—	67	2	no	—
474	#121	—	67	1	no	—
475	#121	—	67	2	no	—
476	#121	—	67	1	no	—
477	#121	—	67	1	no	—
478	#121	—	67	2	no	—
479	#121	—	67	1	no	—
480	#121	—	67	2	no	—
481	#121	—	67	1	no	—
482	#121	—	67	2	no	—
483	#121	—	67	2	no	—
484	#121	—	67	2	no	—
485	#121	—	67	2	no	—
486	#121	—	67	2	no	—
487	#121	—	67	2	no	—
488	#121	—	67	2	no	—
489	#121	—	67	2	no	—
490	#121	—	67	2	no	—
491	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
492	#121	C₂×D₆₇	1	2	yes	complemented
493	#120	—	67	2	no	—
494	#120	—	67	2	no	—
495	#120	—	67	1	no	—
496	#120	—	67	2	no	—
497	#120	—	67	1	no	—
498	#120	—	67	2	no	—
499	#120	—	67	2	no	—
500	#120	—	67	2	no	—
501	#120	—	67	2	no	—
502	#120	C₂×D₆₇	1	2	yes	complemented
503	C₄×Q₈	—	67	1	no	—
504	C₄×Q₈	—	67	1	no	—
505	C₄×D₄	—	67	1	no	—
506	C₄×D₄	—	67	2	no	—
507	C₄×D₄	—	67	1	no	—
508	C₄×D₄	—	67	1	no	—
509	C₄×D₄	—	67	2	no	—
510	C₄×D₄	—	67	2	no	—
511	C₄×D₄	—	67	2	no	—
512	C₄×D₄	—	67	2	no	—
513	C₄×D₄	—	67	2	no	—
514	C₄×D₄	—	67	1	no	—
515	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
516	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
517	#117	—	67	2	no	—
518	#117	—	67	1	no	—
519	C₂×C₄⋊C₄	—	67	2	no	—
520	C₂×C₄⋊C₄	—	67	1	no	—
521	C₂×C₂²⋊C₄	—	67	2	no	—
522	C₂×C₂²⋊C₄	—	67	2	no	—
523	C₂×C₂²⋊C₄	C₂×D₆₇	1	2	yes	complemented
524	C₂⁴	—	67	2	no	—
525	C₂⁴	—	67	2	no	—
526	C₂⁴	—	67	1	no	—
527	C₂⁴	—	67	2	no	—
528	C₂⁴	C₂²×D₆₇	1	2	yes	—
529	#41	—	2	4	no	—
530	#41	—	67	8	no	—
531	#41	—	134	4	no	—
532	#41	—	134	8	no	—
533	#41	—	134	4	no	—
534	#41	—	134	4	no	—
535	#41	—	134	8	no	—
536	#41	—	134	8	no	—
537	#41	—	134	4	no	—
538	#41	—	134	4	no	—
539	C₂×Q₈	—	67	1	no	—
540	C₂×Q₈	—	67	1	no	—
541	C₂×Q₈	—	67	2	no	—
542	C₂×Q₈	—	134	4	no	—
543	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	268	4	no	—
546	C₂×D₄	—	268	4	no	—
547	C₂×D₄	—	268	4	no	—
548	C₂×D₄	—	67	1	no	—
549	C₂×D₄	—	67	2	no	—
550	C₂×D₄	—	67	2	no	—
551	C₂×D₄	—	67	2	no	—
552	C₂×D₄	—	67	2	no	—
553	C₂×D₄	—	67	2	no	—
554	C₂×D₄	—	67	2	no	—
555	C₂×D₄	—	67	1	no	—
556	C₂×D₄	—	67	2	no	—
557	C₂×D₄	—	67	1	no	—
558	C₂×D₄	—	67	2	no	—
559	C₂×D₄	—	67	2	no	—
560	C₂×D₄	—	67	1	no	—
561	C₂×D₄	—	67	2	no	—
562	C₂×D₄	—	67	2	no	—
563	C₂×D₄	—	67	2	no	—
564	C₂×D₄	—	67	2	no	—
565	C₂×D₄	—	67	2	no	—
566	C₂×D₄	—	67	2	no	—
567	C₂×D₄	—	67	2	no	—
568	C₂×D₄	—	67	1	no	—
569	C₂×D₄	—	67	2	no	—
570	C₂×D₄	—	67	1	no	—
571	C₂×D₄	—	67	1	no	—
572	C₂×D₄	—	67	1	no	—
573	C₂×D₄	—	134	4	no	—
574	C₂×D₄	—	134	8	no	—
575	C₂×D₄	—	134	8	no	—
576	C₂×D₄	—	134	8	no	—
577	C₂×D₄	—	134	8	no	—
578	C₂×D₄	—	134	4	no	—
579	C₂×D₄	—	134	4	no	—
580	C₂×D₄	C₂²×D₆₇	1	2	yes	—
581	C₂×D₄	C₂²×D₆₇	1	2	yes	—
582	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
583	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
584	C₂×D₄	C₂²×D₆₇	1	2	yes	—
585	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
586	C₂²×C₄	—	67	2	no	—
587	C₂²×C₄	—	67	2	no	—
588	C₂²×C₄	—	67	2	no	—
589	C₂²×C₄	—	67	1	no	—
590	C₂²×C₄	—	67	2	no	—
591	C₂²×C₄	—	67	1	no	—
592	C₂²×C₄	—	67	1	no	—
593	C₂²×C₄	—	67	2	no	—
594	C₂²×C₄	—	67	1	no	—
595	C₂²×C₄	—	67	2	no	—
596	C₂²×C₄	—	67	2	no	—
597	C₂²×C₄	—	67	1	no	—
598	C₂²×C₄	—	67	1	no	—
599	C₂²×C₄	—	67	2	no	—
600	C₂²×C₄	—	134	8	no	—
601	C₂²×C₄	—	134	4	no	—
602	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
603	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
604	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
605	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
606	C₄⋊C₄	—	67	2	no	—
607	C₄⋊C₄	—	67	1	no	—
608	C₄⋊C₄	—	67	2	no	—
609	C₄⋊C₄	—	67	2	no	—
610	C₄⋊C₄	—	67	1	no	—
611	C₄⋊C₄	—	67	1	no	—
612	C₄⋊C₄	—	67	1	no	—
613	C₄⋊C₄	—	67	1	no	—
614	C₄⋊C₄	—	67	2	no	—
615	C₄⋊C₄	—	67	1	no	—
616	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
617	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
618	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
619	C₂²⋊C₄	—	67	2	no	—
620	C₂²⋊C₄	—	67	2	no	—
621	C₂²⋊C₄	—	67	1	no	—
622	C₂²⋊C₄	—	67	1	no	—
623	C₂²⋊C₄	—	67	1	no	—
624	C₂²⋊C₄	—	67	2	no	—
625	C₂²⋊C₄	—	67	2	no	—
626	C₂²⋊C₄	—	67	2	no	—
627	C₂²⋊C₄	—	67	2	no	—
628	C₂²⋊C₄	—	67	1	no	—
629	C₂²⋊C₄	—	67	1	no	—
630	C₂²⋊C₄	—	67	1	no	—
631	C₂²⋊C₄	—	67	1	no	—
632	C₂²⋊C₄	—	67	2	no	—
633	C₂²⋊C₄	—	67	1	no	—
634	C₂²⋊C₄	—	67	2	no	—
635	C₂²⋊C₄	—	67	2	no	—
636	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
637	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
638	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
639	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
640	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
641	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
642	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
643	C₄²	—	67	2	no	—
644	C₄²	—	67	2	no	—
645	C₄²	—	67	1	no	—
646	C₄²	C₂²×D₆₇	1	1	yes	characteristic
647	C₂³	—	2	4	no	—
648	C₂³	—	4	2	no	—
649	C₂³	—	4	2	no	—
650	C₂³	—	268	2	no	—
651	C₂³	—	268	1	no	—
652	C₂³	—	268	2	no	—
653	C₂³	—	268	2	no	—
654	C₂³	—	268	2	no	—
655	C₂³	—	268	2	no	—
656	C₂³	—	67	1	no	—
657	C₂³	—	67	1	no	—
658	C₂³	—	67	1	no	—
659	C₂³	—	67	2	no	—
660	C₂³	—	67	2	no	—
661	C₂³	—	134	2	no	—
662	C₂³	—	134	4	no	—
663	C₂³	—	134	2	no	—
664	C₂³	—	134	4	no	—
665	C₂³	—	134	4	no	—
666	C₂³	—	134	4	no	—
667	C₂³	C₂³×D₆₇	1	2	yes	—
668	C₂³	C₂³×D₆₇	1	1	yes	characteristic
669	C₂³	C₂³×D₆₇	1	1	yes	characteristic
670	C₂³	C₂³×D₆₇	1	2	yes	—
671	Q₈	—	2	2	no	—
672	Q₈	—	67	4	no	—
673	Q₈	—	134	4	no	—
674	Q₈	—	134	2	no	—
675	D₄	—	2	4	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	4	2	no	—
679	D₄	—	4	1	no	—
680	D₄	—	268	2	no	—
681	D₄	—	268	2	no	—
682	D₄	—	268	2	no	—
683	D₄	—	268	2	no	—
684	D₄	—	268	2	no	—
685	D₄	—	268	2	no	—
686	D₄	—	268	1	no	—
687	D₄	—	268	2	no	—
688	D₄	—	67	8	no	—
689	D₄	—	134	2	no	—
690	D₄	—	134	4	no	—
691	D₄	—	134	2	no	—
692	D₄	—	134	4	no	—
693	D₄	—	134	2	no	—
694	D₄	—	134	4	no	—
695	D₄	—	134	4	no	—
696	D₄	—	134	4	no	—
697	D₄	—	134	4	no	—
698	D₄	—	134	4	no	—
699	D₄	—	134	2	no	—
700	D₄	—	134	2	no	—
701	D₄	—	134	4	no	—
702	D₄	—	134	4	no	—
703	D₄	—	134	2	no	—
704	D₄	—	134	2	no	—
705	D₄	D₄×D₆₇	1	4	yes	complemented
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	268	2	no	—
711	C₂×C₄	—	268	2	no	—
712	C₂×C₄	—	67	8	no	—
713	C₂×C₄	—	67	2	no	—
714	C₂×C₄	—	67	1	no	—
715	C₂×C₄	—	67	4	no	—
716	C₂×C₄	—	67	1	no	—
717	C₂×C₄	—	67	2	no	—
718	C₂×C₄	—	67	1	no	—
719	C₂×C₄	—	67	1	no	—
720	C₂×C₄	—	67	1	no	—
721	C₂×C₄	—	134	2	no	—
722	C₂×C₄	—	134	4	no	—
723	C₂×C₄	—	134	4	no	—
724	C₂×C₄	—	134	4	no	—
725	C₂×C₄	—	134	4	no	—
726	C₂×C₄	—	134	2	no	—
727	C₂×C₄	—	134	2	no	—
728	C₂×C₄	—	134	4	no	—
729	C₂×C₄	—	134	2	no	—
730	C₂×C₄	—	134	2	no	—
731	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
732	C₂×C₄	C₂³×D₆₇	1	2	yes	—
733	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
734	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
735	C₂×C₄	C₂³×D₆₇	1	2	yes	—
736	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
737	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	8	4	no	—
750	C₂²	—	268	8	no	—
751	C₂²	—	268	4	no	—
752	C₂²	—	536	4	no	—
753	C₂²	—	536	4	no	—
754	C₂²	—	67	2	no	—
755	C₂²	—	67	2	no	—
756	C₂²	—	134	2	no	—
757	C₂²	—	134	2	no	—
758	C₂²	—	134	1	no	—
759	C₂²	—	134	2	no	—
760	C₂²	—	134	1	no	—
761	C₂²	—	134	2	no	—
762	C₂²	—	134	2	no	—
763	C₂²	—	134	2	no	—
764	C₂²	—	134	1	no	—
765	C₂²	—	134	1	no	—
766	C₂²	—	134	1	no	—
767	C₂²	—	134	1	no	—
768	C₂²	—	134	1	no	—
769	C₂²	C₂×D₄×D₆₇	1	4	yes	—
770	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
771	C₄	—	2	1	no	—
772	C₄	—	2	1	no	—
773	C₄	—	2	2	no	—
774	C₄	—	2	1	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	1	no	—
777	C₄	—	67	2	no	—
778	C₄	—	67	4	no	—
779	C₄	—	134	1	no	—
780	C₄	—	134	1	no	—
781	C₄	—	134	2	no	—
782	C₄	—	134	1	no	—
783	C₄	—	134	1	no	—
784	C₄	C₂×D₄×D₆₇	1	2	yes	—
785	C₂	—	2	4	no	—
786	C₂	—	4	1	no	—
787	C₂	—	4	2	no	—
788	C₂	—	4	1	no	—
789	C₂	—	268	2	no	—
790	C₂	—	268	1	no	—
791	C₂	—	268	2	no	—
792	C₂	—	134	2	no	—
793	C₂	—	134	2	no	—
794	C₂	C₂²×D₄×D₆₇	1	1	yes	characteristic
795	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
796	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#546×C₆₇	C₂
hypercenter	#546	D₆₇
hypocenter	C₆₇	#3488
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₂×#14524088	C₂	semidirect
2. C₂×#41×D₆₇	C₂	semidirect
3. #16864067	C₂	semidirect
4. #16864064	C₂	semidirect
5. #16864056	C₂	semidirect
6. #16864054	C₂	semidirect
7. #16864038	C₂	semidirect
8. #16864036	C₂	semidirect
9. #16864034	C₂	semidirect
10. D₄×D₂₆₈	C₂	semidirect
11. #16864030	C₂	semidirect
12. D₄×C₂²⋊D₆₇	C₂	semidirect
13. #16864028	C₂	semidirect
14. #16863976	C₂	semidirect
15. #16863973	C₂	semidirect
16. #16863964	C₂	semidirect
17. #16863961	C₂	semidirect
18. #16863905	C₂	semidirect
19. #16863904	C₂	semidirect
20. C₂×#14524016	C₂	semidirect
21. #121×D₆₇	C₂	semidirect
22. #16863875	C₂	semidirect
23. #546×C₆₇	C₂	semidirect
25. C₂×#11761629	C₂²	semidirect
26. C₂×#11761628	C₂²	semidirect
27. C₂×#11761628	C₂²	semidirect
28. C₂×#11761628	C₂²	semidirect
29. C₂×#11761628	C₂²	semidirect
31. C₂×#11761627	C₂²	semidirect
32. C₂×#11761627	C₂²	semidirect
33. C₂×#11761627	C₂²	semidirect
35. C₂×Q₈×D₆₇	C₂²	semidirect
36. C₂²×D₂₆₈	C₂²	semidirect
37. C₂²×C₂²⋊D₆₇	C₂²	semidirect
38. C₂²×C₂²⋊D₆₇	C₂²	semidirect
39. C₂²×C₂²⋊D₆₇	C₂²	semidirect
40. C₂×D₄×D₆₇	C₂²	semidirect
41. C₂×D₄×D₆₇	C₂²	semidirect
42. C₂×D₄×D₆₇	C₂²	semidirect
43. C₂×D₄×D₆₇	C₂²	semidirect
44. C₂×D₄×D₆₇	C₂²	semidirect
45. C₂×D₄×D₆₇	C₂²	semidirect
46. C₂²×C₄×D₆₇	C₂²	semidirect
47. C₂²×C₄×D₆₇	C₂²	semidirect
48. #14524040	C₂²	semidirect
49. #14524039	C₂²	semidirect
50. #14524039	C₂²	semidirect
51. #14524039	C₂²	semidirect
52. #14524032	C₂²	semidirect
53. #14524029	C₂²	semidirect
54. #14524029	C₂²	semidirect
55. #14524028	C₂²	semidirect
56. #14524026	C₂²	semidirect
57. #14524025	C₂²	semidirect
58. #14524021	C₂²	semidirect
59. #14524021	C₂²	semidirect
60. #14524021	C₂²	semidirect
61. #14524020	C₂²	semidirect
62. #14524020	C₂²	semidirect
63. #14524019	C₂²	semidirect
64. #14524018	C₂²	semidirect
65. #14524018	C₂²	semidirect
66. #14524018	C₂²	semidirect
67. #14524017	C₂²	semidirect
68. #14524017	C₂²	semidirect
69. #14524017	C₂²	semidirect
70. #14524016	C₂²	semidirect
71. #14524016	C₂²	semidirect
72. #14524016	C₂²	semidirect
73. #14524016	C₂²	semidirect
74. #14524016	C₂²	semidirect
75. #14524016	C₂²	semidirect
76. #14524016	C₂²	semidirect
77. #14524016	C₂²	semidirect
78. #14524016	C₂²	semidirect
79. #14524016	C₂²	semidirect
80. #14524016	C₂²	semidirect
81. #14524015	C₂²	semidirect
82. #14524015	C₂²	semidirect
83. #14524015	C₂²	semidirect
84. #14524015	C₂²	semidirect
85. #14524015	C₂²	semidirect
86. #14524014	C₂²	semidirect
87. #14524013	C₂²	semidirect
88. #14524013	C₂²	semidirect
89. #14524013	C₂²	semidirect
90. #14524013	C₂²	semidirect
91. #14524013	C₂²	semidirect
92. #14524012	C₂²	semidirect
93. #14524011	C₂²	semidirect
94. #14524011	C₂²	semidirect
95. #14524011	C₂²	semidirect
96. C₄×Dic₁₃₄	C₂²	semidirect
97. #14524008	C₂²	semidirect
98. C₄×D₂₆₈	C₂²	semidirect
99. D₄×Dic₆₇	C₂²	semidirect
100. #14524005	C₂²	semidirect
101. #14524005	C₂²	semidirect
102. C₄×C₂²⋊D₆₇	C₂²	semidirect
103. C₄×C₂²⋊D₆₇	C₂²	semidirect
104. C₄×C₂²⋊D₆₇	C₂²	semidirect
105. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
106. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
107. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
108. #14524000	C₂²	semidirect
109. #14523999	C₂²	semidirect
110. C₂×Dic₆₇⋊C₄	C₂²	semidirect
111. C₄⋊C₄×D₆₇	C₂²	semidirect
112. C₂×(C₂×D₆₇)⋊C₄	C₂²	semidirect
113. C₂²⋊C₄×D₆₇	C₂²	semidirect
114. C₂×#41×C₆₇	C₂²	semidirect
115. C₂²×D₄×C₆₇	C₂²	semidirect
116. #124×C₆₇	C₂²	semidirect
117. #123×C₆₇	C₂²	semidirect
118. C₂²⋊Q₈×C₆₇	C₂²	semidirect
119. #121×C₆₇	C₂²	semidirect
120. #121×C₆₇	C₂²	semidirect
121. #120×C₆₇	C₂²	semidirect
122. C₄×D₄×C₆₇	C₂²	semidirect
123. C₄×D₄×C₆₇	C₂²	semidirect
124. C₂×C₂²⋊C₄×C₆₇	C₂²	semidirect
137. #11761627	D₄	semidirect
278. D₄×C₆₇	C₂×D₄	semidirect
305. C₂²⋊D₆₇	C₂×D₄	semidirect
309. C₂×Dic₆₇	C₂×D₄	semidirect
335. C₄×D₆₇	C₂×D₄	semidirect
338. Dic₁₃₄	C₂×D₄	semidirect
371. C₂×D₆₇	H(5,𝔽₂)	semidirect
399. C₆₇	#3488	semidirect
409. #546	D₆₇	semidirect
434. C₂×#41	C₂×D₆₇	semidirect
446. C₂²×D₄	C₂×D₆₇	semidirect
456. #124	C₂×D₆₇	semidirect
460. #123	C₂×D₆₇	semidirect
467. C₂²⋊Q₈	C₂×D₆₇	semidirect
491. #121	C₂×D₆₇	semidirect
492. #121	C₂×D₆₇	semidirect
502. #120	C₂×D₆₇	semidirect
515. C₄×D₄	C₂×D₆₇	semidirect
516. C₄×D₄	C₂×D₆₇	semidirect
523. C₂×C₂²⋊C₄	C₂×D₆₇	semidirect
705. D₄	D₄×D₆₇	semidirect