Subgroups — #22573909

Order 8576.

1124 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864106	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864104	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864102	C₂	1	2	yes	maximal, complemented
4	#16864099	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864097	C₂	1	2	yes	maximal, complemented
6	#16864090	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864088	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864079	C₂	1	2	yes	maximal, complemented
9	#16864050	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864047	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864044	C₂	1	2	yes	maximal, complemented
12	#16864026	C₂	1	1	yes	maximal, characteristic, complemented
13	#16863994	C₂	1	2	yes	maximal, complemented
14	#16863987	C₂	1	2	yes	maximal, complemented
15	#16863976	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863909	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863908	C₂	1	2	yes	maximal, complemented
18	#16863905	C₂	1	1	yes	maximal, characteristic, complemented
19	#16863904	C₂	1	2	yes	maximal, complemented
20	#16863878	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863876	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄⋊C₄×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761629	C₂²	1	1	yes	characteristic
25	C₂×#11761628	C₂²	1	1	yes	characteristic
26	C₂×#11761628	C₂²	1	2	yes	—
27	C₂×#11761627	C₂²	1	2	yes	—
28	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₆₇	C₂²	1	2	yes	—
30	#14524043	C₂²	1	1	yes	characteristic, complemented
31	#14524042	C₂²	1	2	yes	complemented
32	#14524042	C₂²	1	1	yes	characteristic, complemented
33	#14524038	C₂²	1	2	yes	complemented
34	#14524038	C₂²	1	2	yes	complemented
35	#14524037	C₂²	1	2	yes	complemented
36	#14524035	C₂²	1	2	yes	complemented
37	#14524034	C₂²	1	1	yes	characteristic, complemented
38	#14524034	C₂²	1	2	yes	complemented
39	#14524033	C₂²	1	2	yes	complemented
40	#14524033	C₂²	1	2	yes	complemented
41	#14524028	C₂²	1	1	yes	characteristic
42	#14524028	C₂²	1	2	yes	—
43	#14524028	C₂²	1	2	yes	complemented
44	#14524028	C₂²	1	2	yes	complemented
45	#14524027	C₂²	1	2	yes	—
46	#14524027	C₂²	1	2	yes	—
47	#14524027	C₂²	1	2	yes	complemented
48	#14524026	C₂²	1	2	yes	—
49	#14524025	C₂²	1	1	yes	characteristic
50	#14524025	C₂²	1	2	yes	complemented
51	#14524023	C₂²	1	2	yes	—
52	#14524023	C₂²	1	2	yes	—
53	#14524023	C₂²	1	2	yes	complemented
54	#14524021	C₂²	1	2	yes	—
55	#14524021	C₂²	1	1	yes	characteristic
56	#14524021	C₂²	1	2	yes	—
57	#14524021	C₂²	1	2	yes	complemented
58	#14524021	C₂²	1	2	yes	complemented
59	#14524021	C₂²	1	2	yes	complemented
60	#14524020	C₂²	1	1	yes	characteristic
61	#14524020	C₂²	1	2	yes	complemented
62	#14524019	C₂²	1	1	yes	characteristic
63	#14524019	C₂²	1	1	yes	characteristic, complemented
64	#14524018	C₂²	1	1	yes	characteristic
65	#14524018	C₂²	1	2	yes	—
66	#14524018	C₂²	1	2	yes	—
67	#14524018	C₂²	1	1	yes	characteristic, complemented
68	#14524017	C₂²	1	1	yes	characteristic
69	#14524017	C₂²	1	1	yes	characteristic, complemented
70	#14524016	C₂²	1	2	yes	—
71	#14524016	C₂²	1	1	yes	characteristic
72	#14524016	C₂²	1	2	yes	—
73	#14524016	C₂²	1	2	yes	complemented
74	#14524015	C₂²	1	1	yes	characteristic
75	#14524013	C₂²	1	2	yes	—
76	#14524013	C₂²	1	1	yes	characteristic
77	#14524011	C₂²	1	1	yes	characteristic
78	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
80	C₄×D₂₆₈	C₂²	1	2	yes	—
81	C₄×D₂₆₈	C₂²	1	2	yes	—
82	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
83	C₄×D₂₆₈	C₂²	1	2	yes	—
84	C₄×D₂₆₈	C₂²	1	2	yes	—
85	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
86	#14524005	C₂²	1	2	yes	—
87	#14524005	C₂²	1	2	yes	—
88	#14524005	C₂²	1	2	yes	—
89	#14524005	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
92	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
93	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
94	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
95	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
96	#14524001	C₂²	1	1	yes	characteristic
97	#14524001	C₂²	1	1	yes	characteristic, complemented
98	#14524000	C₂²	1	1	yes	characteristic
99	#14524000	C₂²	1	2	yes	complemented
100	#14523999	C₂²	1	2	yes	—
101	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
102	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
103	C₂×Dic₆₇⋊C₄	C₂²	1	2	yes	—
104	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
105	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
106	C₄⋊C₄×D₆₇	C₂²	1	2	yes	—
107	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₆₇	C₂²	1	2	yes	—
110	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
111	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
112	#126×C₆₇	C₂²	1	2	yes	complemented
113	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#125×C₆₇	C₂²	1	2	yes	complemented
115	#123×C₆₇	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
120	#117×C₆₇	C₂²	1	2	yes	—
121	#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
123	C₂³×D₆₇	C₂³	1	1	yes	characteristic
124	#11761629	—	2	4	no	—
125	#11761628	—	2	4	no	—
126	#11761628	—	4	4	no	—
127	#11761627	—	4	4	no	—
128	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₃₄	C₂³	1	2	yes	—
130	C₂×Dic₁₃₄	C₂³	1	2	yes	—
131	C₂×D₂₆₈	C₂³	1	2	yes	—
132	C₂×D₂₆₈	C₂³	1	2	yes	—
133	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
134	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
135	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
136	C₂×D₂₆₈	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
143	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
144	C₂²×Dic₆₇	C₂³	1	2	yes	—
145	C₂²×Dic₆₇	C₂³	1	2	yes	—
146	C₂×C₄×D₆₇	—	2	4	no	—
147	C₂×C₄×D₆₇	—	4	4	no	—
148	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₆₇	C₂³	1	2	yes	—
152	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₆₇	C₂³	1	2	yes	—
154	C₂×C₄×D₆₇	C₂³	1	2	yes	—
155	C₂×C₄×D₆₇	C₂³	1	2	yes	—
156	C₂×C₄×D₆₇	C₂³	1	2	yes	—
157	C₂×C₄×D₆₇	C₂³	1	2	yes	—
158	C₂×C₄×D₆₇	C₂³	1	2	yes	—
159	C₂×C₄×D₆₇	C₂³	1	2	yes	—
160	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₆₇	C₂³	1	2	yes	—
164	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₆₇	C₂³	1	2	yes	—
166	C₄⋊Dic₆₇	C₂³	1	2	yes	—
167	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
168	C₄⋊Dic₆₇	C₂³	1	2	yes	—
169	C₄⋊Dic₆₇	C₂³	1	2	yes	—
170	Dic₆₇⋊C₄	C₂³	1	2	yes	—
171	Dic₆₇⋊C₄	C₂³	1	2	yes	—
172	Dic₆₇⋊C₄	C₂³	1	2	yes	—
173	Dic₆₇⋊C₄	C₂³	1	2	yes	—
174	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
175	Dic₆₇⋊C₄	C₂³	1	2	yes	—
176	Dic₆₇⋊C₄	C₂³	1	2	yes	—
177	Dic₆₇⋊C₄	C₂³	1	2	yes	—
178	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
179	Dic₆₇⋊C₄	C₂³	1	2	yes	—
180	Dic₆₇⋊C₄	C₂³	1	2	yes	—
181	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
182	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
185	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
201	C₄×Dic₆₇	C₂³	1	2	yes	—
202	C₄×Dic₆₇	C₂³	1	2	yes	—
203	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
204	C₄×Dic₆₇	C₂³	1	2	yes	—
205	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
208	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₄²×C₆₇	C₂³	1	2	yes	—
226	C₄²×C₆₇	C₂³	1	2	yes	—
227	C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
230	C₂²×D₆₇	—	2	2	no	—
231	C₂²×D₆₇	—	2	2	no	—
232	C₂²×D₆₇	—	2	2	no	—
233	C₂²×D₆₇	C₂⁴	1	2	yes	—
234	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
235	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
236	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
237	Q₈×C₆₇	—	2	2	no	—
238	D₄×C₆₇	—	2	2	no	—
239	C₂×C₄×C₆₇	—	2	4	no	—
240	C₂×C₄×C₆₇	—	2	2	no	—
241	C₂×C₄×C₆₇	—	2	2	no	—
242	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
246	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
247	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
250	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₆₇	—	2	4	no	—
252	C₂²⋊D₆₇	—	2	2	no	—
253	C₂²⋊D₆₇	—	2	2	no	—
254	C₂²⋊D₆₇	—	2	2	no	—
255	C₂²⋊D₆₇	—	2	2	no	—
256	C₂²⋊D₆₇	—	4	2	no	—
257	C₂×Dic₆₇	—	2	4	no	—
258	C₂×Dic₆₇	—	2	2	no	—
259	C₂×Dic₆₇	—	4	2	no	—
260	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₆₇	C₂⁴	1	2	yes	—
263	C₂×Dic₆₇	C₂⁴	1	2	yes	—
264	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₆₇	C₂⁴	1	2	yes	—
267	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
268	D₂₆₈	—	2	2	no	—
269	D₂₆₈	—	2	4	no	—
270	D₂₆₈	—	2	4	no	—
271	D₂₆₈	—	2	2	no	—
272	D₂₆₈	—	2	2	no	—
273	D₂₆₈	—	4	2	no	—
274	C₄×D₆₇	—	2	2	no	—
275	C₄×D₆₇	—	2	2	no	—
276	C₄×D₆₇	—	2	2	no	—
277	C₄×D₆₇	—	2	2	no	—
278	C₄×D₆₇	—	2	4	no	—
279	C₄×D₆₇	—	4	2	no	—
280	C₄×D₆₇	—	4	2	no	—
281	C₄×D₆₇	—	4	2	no	—
282	C₄×D₆₇	—	4	2	no	—
283	C₄×D₆₇	—	4	2	no	—
284	C₄×D₆₇	—	4	2	no	—
285	C₄×D₆₇	—	4	2	no	—
286	C₄×D₆₇	#41	1	4	yes	complemented
287	Dic₁₃₄	—	2	2	no	—
288	Dic₁₃₄	—	4	2	no	—
289	Dic₁₃₄	—	4	2	no	—
290	C₂²×C₆₇	—	2	1	no	—
291	C₂²×C₆₇	—	2	1	no	—
292	C₂²×C₆₇	—	2	1	no	—
293	C₂²×C₆₇	—	2	1	no	—
294	C₂²×C₆₇	—	2	1	no	—
295	C₂²×C₆₇	H(5,𝔽₂)	1	2	yes	—
296	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
297	C₂×D₆₇	—	2	8	no	—
298	C₂×D₆₇	—	2	1	no	—
299	C₂×D₆₇	—	2	1	no	—
300	C₂×D₆₇	—	2	1	no	—
301	C₂×D₆₇	—	2	1	no	—
302	C₂×D₆₇	—	2	2	no	—
303	C₂×D₆₇	—	2	1	no	—
304	C₂×D₆₇	—	2	1	no	—
305	C₂×D₆₇	—	2	2	no	—
306	C₂×D₆₇	—	2	2	no	—
307	C₂×D₆₇	—	2	1	no	—
308	C₂×D₆₇	C₂×#41	1	2	yes	—
309	C₂×D₆₇	2₋¹⁺⁴	1	2	yes	—
310	C₄×C₆₇	—	2	1	no	—
311	C₄×C₆₇	—	2	1	no	—
312	C₄×C₆₇	—	2	2	no	—
313	C₄×C₆₇	—	2	1	no	—
314	C₄×C₆₇	—	2	2	no	—
315	C₄×C₆₇	—	2	2	no	—
316	C₄×C₆₇	—	2	1	no	—
317	C₄×C₆₇	—	2	2	no	—
318	C₄×C₆₇	C₂×#41	1	2	yes	—
319	Dic₆₇	—	2	1	no	—
320	Dic₆₇	—	2	1	no	—
321	Dic₆₇	—	2	1	no	—
322	Dic₆₇	—	2	2	no	—
323	Dic₆₇	—	2	2	no	—
324	Dic₆₇	—	2	2	no	—
325	Dic₆₇	—	2	1	no	—
326	Dic₆₇	C₂×#41	1	2	yes	—
327	C₂×C₆₇	—	2	2	no	—
328	C₂×C₆₇	—	4	1	no	—
329	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
330	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
331	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
332	D₆₇	—	2	2	no	—
333	D₆₇	—	2	2	no	—
334	D₆₇	—	4	2	no	—
335	D₆₇	—	4	1	no	—
336	#3492	—	67	1	no	maximal, Sylow
337	C₆₇	#3492	1	1	yes	characteristic, complemented, Sylow
338	#554	—	67	2	no	—
339	#554	—	67	1	no	—
340	#554	—	67	1	no	—
341	#553	—	67	2	no	—
342	#553	—	67	1	no	—
343	#553	—	67	1	no	—
344	#552	—	67	1	no	—
345	#552	—	67	2	no	—
346	#552	D₆₇	1	1	yes	characteristic, complemented
347	#547	—	67	2	no	—
348	#547	—	67	1	no	—
349	#547	—	67	1	no	—
350	#544	—	67	1	no	—
351	#539	—	67	2	no	—
352	#539	—	67	2	no	—
353	#537	—	67	1	no	—
354	#525	—	67	2	no	—
355	#525	—	67	1	no	—
356	#525	—	67	1	no	—
357	#525	—	67	2	no	—
358	#520	—	67	1	no	—
359	#520	—	67	1	no	—
360	C₂²×C₄⋊C₄	—	67	1	no	—
361	C₂×#41	—	67	1	no	—
362	C₂×#41	—	67	2	no	—
363	C₂×#41	—	67	2	no	—
364	C₂×#41	—	67	1	no	—
365	C₂³×C₄	—	67	2	no	—
366	C₂³×C₄	—	67	1	no	—
367	C₄⋊Q₈	—	67	2	no	—
368	C₄⋊Q₈	—	67	1	no	—
369	C₄⋊Q₈	—	67	1	no	—
370	#126	—	67	2	no	—
371	#126	—	67	2	no	—
372	#126	—	67	2	no	—
373	#126	C₂×D₆₇	1	2	yes	complemented
374	#125	—	67	2	no	—
375	#125	—	67	2	no	—
376	#125	—	67	2	no	—
377	#125	—	67	1	no	—
378	#125	—	67	2	no	—
379	#125	C₂×D₆₇	1	2	yes	complemented
380	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
381	#123	—	67	2	no	—
382	#123	—	67	2	no	—
383	#123	—	67	1	no	—
384	#123	—	67	2	no	—
385	#123	—	67	2	no	—
386	#123	—	67	1	no	—
387	#123	—	67	2	no	—
388	#123	—	67	2	no	—
389	#123	—	67	2	no	—
390	#123	—	67	2	no	—
391	#123	C₂×D₆₇	1	2	yes	—
392	C₂²⋊Q₈	—	67	1	no	—
393	C₂²⋊Q₈	—	67	1	no	—
394	C₂²⋊Q₈	—	67	2	no	—
395	C₂²⋊Q₈	—	67	2	no	—
396	C₂²⋊Q₈	—	67	1	no	—
397	C₂²⋊Q₈	—	67	2	no	—
398	C₂²⋊Q₈	—	67	2	no	—
399	C₂²⋊Q₈	—	67	2	no	—
400	C₂²⋊Q₈	—	67	2	no	—
401	C₂²⋊Q₈	—	67	2	no	—
402	C₂²⋊Q₈	—	67	2	no	—
403	C₂²⋊Q₈	—	67	1	no	—
404	C₂²⋊Q₈	—	67	2	no	—
405	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
406	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
407	#121	—	67	1	no	—
408	#121	—	67	1	no	—
409	#121	—	67	1	no	—
410	#121	—	67	2	no	—
411	#121	—	67	2	no	—
412	#121	—	67	1	no	—
413	#121	—	67	1	no	—
414	#121	—	67	2	no	—
415	#121	—	67	2	no	—
416	#121	—	67	1	no	—
417	#121	—	67	2	no	—
418	#120	—	67	1	no	—
419	#120	—	67	2	no	—
420	#120	—	67	1	no	—
421	C₄×Q₈	—	67	1	no	—
422	C₄×Q₈	—	67	2	no	—
423	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
424	C₄×D₄	—	67	1	no	—
425	C₄×D₄	—	67	1	no	—
426	C₄×D₄	—	67	2	no	—
427	C₄×D₄	—	67	1	no	—
428	C₄×D₄	—	67	2	no	—
429	C₄×D₄	—	67	2	no	—
430	C₄×D₄	—	67	2	no	—
431	C₄×D₄	—	67	2	no	—
432	C₄×D₄	—	67	2	no	—
433	C₄×D₄	—	67	2	no	—
434	C₄×D₄	—	67	2	no	—
435	C₄×D₄	—	67	2	no	—
436	C₄×D₄	—	67	1	no	—
437	C₄×D₄	—	67	2	no	—
438	C₄×D₄	—	67	1	no	—
439	C₄×D₄	—	67	2	no	—
440	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
441	#117	—	67	1	no	—
442	#117	—	67	1	no	—
443	#117	—	67	2	no	—
444	#117	—	67	1	no	—
445	#117	—	67	2	no	—
446	#117	C₂×D₆₇	1	2	yes	—
447	#117	C₂×D₆₇	1	1	yes	characteristic, complemented
448	C₂×C₄⋊C₄	—	67	2	no	—
449	C₂×C₄⋊C₄	—	67	1	no	—
450	C₂×C₄⋊C₄	—	67	1	no	—
451	C₂×C₄⋊C₄	—	67	1	no	—
452	C₂×C₄⋊C₄	—	67	1	no	—
453	C₂×C₄⋊C₄	—	67	2	no	—
454	C₂×C₄⋊C₄	—	67	2	no	—
455	C₂×C₄⋊C₄	—	67	1	no	—
456	C₂×C₄⋊C₄	—	67	1	no	—
457	C₂×C₄⋊C₄	—	67	2	no	—
458	C₂×C₄⋊C₄	—	67	1	no	—
459	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
460	C₂⁴	—	67	1	no	—
461	#41	—	268	4	no	—
462	#41	—	268	4	no	—
463	#41	—	134	4	no	—
464	#41	—	134	4	no	—
465	C₂×Q₈	—	67	2	no	—
466	C₂×Q₈	—	67	2	no	—
467	C₂×Q₈	—	67	1	no	—
468	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
469	C₂×D₄	—	67	2	no	—
470	C₂×D₄	—	67	1	no	—
471	C₂×D₄	—	67	1	no	—
472	C₂×D₄	—	67	1	no	—
473	C₂×D₄	—	67	1	no	—
474	C₂×D₄	—	67	2	no	—
475	C₂×D₄	—	67	2	no	—
476	C₂×D₄	—	67	2	no	—
477	C₂×D₄	—	67	1	no	—
478	C₂×D₄	—	67	2	no	—
479	C₂×D₄	—	67	1	no	—
480	C₂×D₄	—	67	1	no	—
481	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
482	C₂²×C₄	—	268	4	no	—
483	C₂²×C₄	—	67	2	no	—
484	C₂²×C₄	—	67	2	no	—
485	C₂²×C₄	—	67	2	no	—
486	C₂²×C₄	—	67	2	no	—
487	C₂²×C₄	—	67	2	no	—
488	C₂²×C₄	—	67	2	no	—
489	C₂²×C₄	—	67	2	no	—
490	C₂²×C₄	—	67	2	no	—
491	C₂²×C₄	—	67	1	no	—
492	C₂²×C₄	—	67	2	no	—
493	C₂²×C₄	—	67	1	no	—
494	C₂²×C₄	—	67	1	no	—
495	C₂²×C₄	—	67	1	no	—
496	C₂²×C₄	—	67	1	no	—
497	C₂²×C₄	—	67	2	no	—
498	C₂²×C₄	—	67	1	no	—
499	C₂²×C₄	—	134	4	no	—
500	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
501	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
503	C₄⋊C₄	—	67	2	no	—
504	C₄⋊C₄	—	67	1	no	—
505	C₄⋊C₄	—	67	2	no	—
506	C₄⋊C₄	—	67	1	no	—
507	C₄⋊C₄	—	67	2	no	—
508	C₄⋊C₄	—	67	2	no	—
509	C₄⋊C₄	—	67	2	no	—
510	C₄⋊C₄	—	67	1	no	—
511	C₄⋊C₄	—	67	1	no	—
512	C₄⋊C₄	—	67	2	no	—
513	C₄⋊C₄	—	67	2	no	—
514	C₄⋊C₄	—	67	2	no	—
515	C₄⋊C₄	—	67	1	no	—
516	C₄⋊C₄	—	67	2	no	—
517	C₄⋊C₄	—	67	2	no	—
518	C₄⋊C₄	—	67	1	no	—
519	C₄⋊C₄	—	67	2	no	—
520	C₄⋊C₄	—	67	2	no	—
521	C₄⋊C₄	—	67	2	no	—
522	C₄⋊C₄	—	67	2	no	—
523	C₄⋊C₄	—	67	1	no	—
524	C₄⋊C₄	—	67	1	no	—
525	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
528	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
529	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
531	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
532	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
533	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
534	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
535	C₂²⋊C₄	—	67	1	no	—
536	C₂²⋊C₄	—	67	1	no	—
537	C₂²⋊C₄	—	67	1	no	—
538	C₂²⋊C₄	—	67	2	no	—
539	C₂²⋊C₄	—	67	1	no	—
540	C₂²⋊C₄	—	67	2	no	—
541	C₂²⋊C₄	—	67	2	no	—
542	C₂²⋊C₄	—	67	2	no	—
543	C₂²⋊C₄	—	67	1	no	—
544	C₂²⋊C₄	—	67	2	no	—
545	C₂²⋊C₄	—	67	1	no	—
546	C₂²⋊C₄	—	67	2	no	—
547	C₂²⋊C₄	—	67	2	no	—
548	C₂²⋊C₄	—	67	2	no	—
549	C₂²⋊C₄	—	67	2	no	—
550	C₂²⋊C₄	—	67	1	no	—
551	C₂²⋊C₄	—	67	1	no	—
552	C₂²⋊C₄	—	67	2	no	—
553	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
555	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
558	C₄²	—	67	2	no	—
559	C₄²	—	67	2	no	—
560	C₄²	—	67	2	no	—
561	C₄²	—	67	1	no	—
562	C₄²	C₂²×D₆₇	1	2	yes	—
563	C₄²	C₂²×D₆₇	1	1	yes	characteristic
564	C₄²	C₂²×D₆₇	1	2	yes	—
565	C₂³	—	67	1	no	—
566	C₂³	—	67	1	no	—
567	C₂³	—	67	2	no	—
568	C₂³	—	67	1	no	—
569	C₂³	—	134	2	no	—
570	C₂³	—	134	2	no	—
571	C₂³	—	134	2	no	—
572	C₂³	C₂³×D₆₇	1	1	yes	characteristic
573	C₂³	C₂³×D₆₇	1	1	yes	characteristic
574	Q₈	—	2	2	no	—
575	Q₈	—	268	2	no	—
576	Q₈	—	268	2	no	—
577	Q₈	—	134	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	268	2	no	—
580	D₄	—	268	2	no	—
581	D₄	—	134	2	no	—
582	D₄	—	134	4	no	—
583	D₄	—	134	4	no	—
584	D₄	—	134	2	no	—
585	D₄	—	134	2	no	—
586	D₄	—	134	2	no	—
587	D₄	—	134	2	no	—
588	D₄	—	134	2	no	—
589	D₄	—	134	4	no	—
590	D₄	—	134	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	268	2	no	—
595	C₂×C₄	—	268	2	no	—
596	C₂×C₄	—	268	2	no	—
597	C₂×C₄	—	268	2	no	—
598	C₂×C₄	—	268	2	no	—
599	C₂×C₄	—	268	2	no	—
600	C₂×C₄	—	268	2	no	—
601	C₂×C₄	—	268	2	no	—
602	C₂×C₄	—	67	1	no	—
603	C₂×C₄	—	67	4	no	—
604	C₂×C₄	—	67	1	no	—
605	C₂×C₄	—	67	1	no	—
606	C₂×C₄	—	67	2	no	—
607	C₂×C₄	—	67	1	no	—
608	C₂×C₄	—	67	2	no	—
609	C₂×C₄	—	67	1	no	—
610	C₂×C₄	—	67	2	no	—
611	C₂×C₄	—	134	2	no	—
612	C₂×C₄	—	134	4	no	—
613	C₂×C₄	—	134	2	no	—
614	C₂×C₄	—	134	2	no	—
615	C₂×C₄	—	134	4	no	—
616	C₂×C₄	—	134	2	no	—
617	C₂×C₄	—	134	2	no	—
618	C₂×C₄	C₂³×D₆₇	1	2	yes	—
619	C₂×C₄	C₂³×D₆₇	1	2	yes	—
620	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₆₇	1	2	yes	—
623	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₆₇	1	2	yes	—
626	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	67	2	no	—
633	C₂²	—	67	2	no	—
634	C₂²	—	134	8	no	—
635	C₂²	—	134	2	no	—
636	C₂²	—	134	1	no	—
637	C₂²	—	134	1	no	—
638	C₂²	—	134	2	no	—
639	C₂²	—	134	2	no	—
640	C₂²	—	134	1	no	—
641	C₂²	—	134	1	no	—
642	C₂²	—	134	1	no	—
643	C₂²	—	134	1	no	—
644	C₂²	—	134	1	no	—
645	C₂²	#14524089	1	2	yes	—
646	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	1	no	—
655	C₄	—	67	2	no	—
656	C₄	—	134	1	no	—
657	C₄	—	134	1	no	—
658	C₄	—	134	2	no	—
659	C₄	—	134	2	no	—
660	C₄	—	134	1	no	—
661	C₄	—	134	2	no	—
662	C₄	—	134	1	no	—
663	C₄	#41×D₆₇	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	268	2	no	—
667	C₂	—	268	1	no	—
668	C₂	—	134	2	no	—
669	C₂	—	134	2	no	—
670	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
671	C₂	C₂×#14524089	1	1	yes	characteristic
672	C₂	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#552×C₆₇	C₂
hypercenter	#552	D₆₇
hypocenter	C₆₇	#3492
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #16864106	C₂	semidirect
2. #16864104	C₂	semidirect
3. #16864102	C₂	semidirect
4. #16864099	C₂	semidirect
5. #16864097	C₂	semidirect
6. #16864090	C₂	semidirect
7. #16864088	C₂	semidirect
8. #16864079	C₂	semidirect
9. #16864050	C₂	semidirect
10. #16864047	C₂	semidirect
11. #16864044	C₂	semidirect
12. #16864026	C₂	semidirect
13. #16863994	C₂	semidirect
14. #16863987	C₂	semidirect
15. #16863976	C₂	semidirect
16. #16863909	C₂	semidirect
17. #16863908	C₂	semidirect
18. #16863905	C₂	semidirect
19. #16863904	C₂	semidirect
20. #16863878	C₂	semidirect
21. #16863876	C₂	semidirect
22. C₂×C₄⋊C₄×D₆₇	C₂	semidirect
23. #552×C₆₇	C₂	semidirect
30. #14524043	C₂²	semidirect
31. #14524042	C₂²	semidirect
32. #14524042	C₂²	semidirect
33. #14524038	C₂²	semidirect
34. #14524038	C₂²	semidirect
35. #14524037	C₂²	semidirect
36. #14524035	C₂²	semidirect
37. #14524034	C₂²	semidirect
38. #14524034	C₂²	semidirect
39. #14524033	C₂²	semidirect
40. #14524033	C₂²	semidirect
43. #14524028	C₂²	semidirect
44. #14524028	C₂²	semidirect
47. #14524027	C₂²	semidirect
50. #14524025	C₂²	semidirect
53. #14524023	C₂²	semidirect
57. #14524021	C₂²	semidirect
58. #14524021	C₂²	semidirect
59. #14524021	C₂²	semidirect
61. #14524020	C₂²	semidirect
63. #14524019	C₂²	semidirect
67. #14524018	C₂²	semidirect
69. #14524017	C₂²	semidirect
73. #14524016	C₂²	semidirect
78. Q₈×Dic₆₇	C₂²	semidirect
79. C₄×Dic₁₃₄	C₂²	semidirect
85. C₄×D₂₆₈	C₂²	semidirect
89. #14524005	C₂²	semidirect
95. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
97. #14524001	C₂²	semidirect
99. #14524000	C₂²	semidirect
102. C₂×C₄⋊Dic₆₇	C₂²	semidirect
110. C₄⋊C₄×D₆₇	C₂²	semidirect
111. C₄⋊C₄×D₆₇	C₂²	semidirect
112. #126×C₆₇	C₂²	semidirect
113. #125×C₆₇	C₂²	semidirect
114. #125×C₆₇	C₂²	semidirect
117. C₂²⋊Q₈×C₆₇	C₂²	semidirect
118. C₄×Q₈×C₆₇	C₂²	semidirect
121. #117×C₆₇	C₂²	semidirect
286. C₄×D₆₇	#41	semidirect
337. C₆₇	#3492	semidirect
346. #552	D₆₇	semidirect
373. #126	C₂×D₆₇	semidirect
379. #125	C₂×D₆₇	semidirect
380. #125	C₂×D₆₇	semidirect
406. C₂²⋊Q₈	C₂×D₆₇	semidirect
423. C₄×Q₈	C₂×D₆₇	semidirect
447. #117	C₂×D₆₇	semidirect