Subgroups — #542×D₆₇ #22573579

Order 8576.

1132 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864020	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864019	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864018	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864017	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864016	C₂	1	2	yes	maximal, complemented
6	#16864015	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864014	C₂	1	2	yes	maximal, complemented
8	#16864013	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864012	C₂	1	2	yes	maximal, complemented
10	#16864011	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864010	C₂	1	2	yes	maximal, complemented
12	C₄⋊Q₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#126×D₆₇	C₂	1	2	yes	maximal, complemented
14	#124×D₆₇	C₂	1	2	yes	maximal, complemented
15	#124×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	#123×D₆₇	C₂	1	2	yes	maximal, complemented
17	C₂²⋊Q₈×D₆₇	C₂	1	2	yes	maximal, complemented
18	C₂²⋊Q₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	#121×D₆₇	C₂	1	1	yes	maximal, characteristic
20	C₄×Q₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#542×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₆₇	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₆₇	C₂²	1	2	yes	—
26	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₆₇	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	1	yes	characteristic, complemented
32	#14524042	C₂²	1	2	yes	complemented
33	#14524042	C₂²	1	1	yes	characteristic, complemented
34	#14524041	C₂²	1	2	yes	complemented
35	#14524038	C₂²	1	2	yes	complemented
36	#14524038	C₂²	1	2	yes	complemented
37	#14524038	C₂²	1	2	yes	complemented
38	#14524037	C₂²	1	2	yes	complemented
39	#14524036	C₂²	1	2	yes	complemented
40	#14524036	C₂²	1	2	yes	complemented
41	#14524036	C₂²	1	2	yes	complemented
42	#14524032	C₂²	1	2	yes	complemented
43	#14524032	C₂²	1	1	yes	characteristic, complemented
44	#14524031	C₂²	1	2	yes	complemented
45	#14524031	C₂²	1	1	yes	characteristic, complemented
46	#14524030	C₂²	1	1	yes	characteristic, complemented
47	#14524030	C₂²	1	2	yes	complemented
48	#14524029	C₂²	1	2	yes	complemented
49	#14524029	C₂²	1	2	yes	complemented
50	#14524029	C₂²	1	2	yes	complemented
51	#14524029	C₂²	1	2	yes	complemented
52	#14524029	C₂²	1	2	yes	complemented
53	#14524029	C₂²	1	2	yes	complemented
54	#14524028	C₂²	1	2	yes	complemented
55	#14524028	C₂²	1	2	yes	complemented
56	#14524027	C₂²	1	2	yes	complemented
57	#14524026	C₂²	1	2	yes	complemented
58	#14524025	C₂²	1	2	yes	complemented
59	#14524025	C₂²	1	2	yes	complemented
60	#14524024	C₂²	1	2	yes	complemented
61	#14524023	C₂²	1	1	yes	characteristic, complemented
62	#14524023	C₂²	1	2	yes	complemented
63	#14524022	C₂²	1	2	yes	complemented
64	#14524022	C₂²	1	1	yes	characteristic, complemented
65	#14524021	C₂²	1	2	yes	complemented
66	#14524021	C₂²	1	2	yes	complemented
67	#14524021	C₂²	1	2	yes	complemented
68	#14524020	C₂²	1	2	yes	complemented
69	#14524020	C₂²	1	2	yes	complemented
70	#14524020	C₂²	1	2	yes	complemented
71	#14524019	C₂²	1	2	yes	complemented
72	#14524019	C₂²	1	1	yes	characteristic, complemented
73	#14524018	C₂²	1	1	yes	characteristic
74	#14524017	C₂²	1	1	yes	characteristic
75	#14524016	C₂²	1	2	yes	—
76	#14524015	C₂²	1	2	yes	—
77	#14524014	C₂²	1	1	yes	characteristic
78	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
80	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
81	#14524008	C₂²	1	1	yes	characteristic, complemented
82	#14524008	C₂²	1	2	yes	complemented
83	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
84	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
85	#14524005	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
87	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
88	#14524002	C₂²	1	1	yes	characteristic, complemented
89	#14524001	C₂²	1	1	yes	characteristic, complemented
90	#14524001	C₂²	1	1	yes	characteristic, complemented
91	#14524000	C₂²	1	1	yes	characteristic, complemented
92	#14524000	C₂²	1	1	yes	characteristic, complemented
93	#14523999	C₂²	1	1	yes	characteristic, complemented
94	#14523999	C₂²	1	1	yes	characteristic, complemented
95	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
96	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
97	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
98	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
99	C₄⋊C₄×D₆₇	C₂²	1	2	yes	—
100	C₄⋊C₄×D₆₇	C₂²	1	2	yes	—
101	C₄⋊C₄×D₆₇	C₂²	1	2	yes	—
102	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
103	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
104	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
105	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
106	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
109	C₄²×D₆₇	C₂²	1	1	yes	characteristic
110	C₄²×D₆₇	C₂²	1	1	yes	characteristic
111	C₄²×D₆₇	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#126×C₆₇	C₂²	1	2	yes	complemented
114	#124×C₆₇	C₂²	1	2	yes	complemented
115	#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	#123×C₆₇	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	#121×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₇	C₂³	1	1	yes	characteristic
124	C₂³×D₆₇	C₂³	1	2	yes	—
125	C₂×Dic₁₃₄	C₂³	1	2	yes	—
126	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₃₄	C₂³	1	2	yes	—
128	C₂×Dic₁₃₄	C₂³	1	2	yes	—
129	C₂×Dic₁₃₄	C₂³	1	2	yes	—
130	Q₈×D₆₇	—	2	4	no	—
131	Q₈×D₆₇	—	4	4	no	—
132	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
133	C₂×D₂₆₈	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
137	D₄×D₆₇	—	2	4	no	—
138	D₄×D₆₇	—	4	4	no	—
139	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
140	C₂²×Dic₆₇	C₂³	1	2	yes	—
141	C₂×C₄×D₆₇	—	2	4	no	—
142	C₂×C₄×D₆₇	—	4	4	no	—
143	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₆₇	C₂³	1	2	yes	—
146	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₆₇	C₂³	1	2	yes	—
149	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₆₇	C₂³	1	2	yes	—
151	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
156	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₆₇	C₂³	1	2	yes	—
161	C₄⋊Dic₆₇	C₂³	1	2	yes	—
162	C₄⋊Dic₆₇	C₂³	1	2	yes	—
163	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
164	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
165	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₆₇⋊C₄	C₂³	1	2	yes	—
168	Dic₆₇⋊C₄	C₂³	1	2	yes	—
169	Dic₆₇⋊C₄	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	2	yes	—
175	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
182	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
194	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
196	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
197	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
198	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
199	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
200	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
201	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
202	C₄×Dic₆₇	C₂³	1	2	yes	—
203	C₄×Dic₆₇	C₂³	1	2	yes	—
204	C₄×Dic₆₇	C₂³	1	2	yes	—
205	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
207	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₆₇	C₂³	1	2	yes	—
209	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
211	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₄²×C₆₇	C₂³	1	2	yes	—
228	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂³×C₆₇	C₂⁴	1	2	yes	—
230	C₂²×D₆₇	—	2	2	no	—
231	C₂²×D₆₇	—	2	4	no	—
232	C₂²×D₆₇	—	2	4	no	—
233	C₂²×D₆₇	—	2	2	no	—
234	C₂²×D₆₇	—	2	2	no	—
235	C₂²×D₆₇	—	2	4	no	—
236	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
237	C₂²×D₆₇	C₂⁴	1	2	yes	—
238	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
239	Q₈×C₆₇	—	2	2	no	—
240	Q₈×C₆₇	—	4	2	no	—
241	D₄×C₆₇	—	2	2	no	—
242	D₄×C₆₇	—	4	2	no	—
243	C₂×C₄×C₆₇	—	2	2	no	—
244	C₂×C₄×C₆₇	—	4	2	no	—
245	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
248	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
251	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂²⋊D₆₇	—	2	4	no	—
255	C₂²⋊D₆₇	—	4	2	no	—
256	C₂²⋊D₆₇	—	4	2	no	—
257	C₂×Dic₆₇	—	2	2	no	—
258	C₂×Dic₆₇	—	4	2	no	—
259	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₆₇	C₂⁴	1	2	yes	—
262	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₆₇	C₂⁴	1	2	yes	—
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	—	4	2	no	—
270	C₄×D₆₇	—	2	2	no	—
271	C₄×D₆₇	—	2	4	no	—
272	C₄×D₆₇	—	2	2	no	—
273	C₄×D₆₇	—	2	4	no	—
274	C₄×D₆₇	—	2	4	no	—
275	C₄×D₆₇	—	2	2	no	—
276	C₄×D₆₇	—	2	2	no	—
277	C₄×D₆₇	—	2	2	no	—
278	C₄×D₆₇	—	2	2	no	—
279	C₄×D₆₇	—	2	2	no	—
280	C₄×D₆₇	—	4	2	no	—
281	C₄×D₆₇	—	4	2	no	—
282	C₄×D₆₇	#41	1	4	yes	—
283	Dic₁₃₄	—	2	2	no	—
284	Dic₁₃₄	—	2	4	no	—
285	Dic₁₃₄	—	4	2	no	—
286	Dic₁₃₄	—	4	2	no	—
287	Dic₁₃₄	—	4	2	no	—
288	C₂²×C₆₇	—	2	1	no	—
289	C₂²×C₆₇	—	2	2	no	—
290	C₂²×C₆₇	—	2	2	no	—
291	C₂²×C₆₇	—	2	1	no	—
292	C₂²×C₆₇	—	2	1	no	—
293	C₂²×C₆₇	—	2	2	no	—
294	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
295	C₂×D₆₇	—	2	1	no	—
296	C₂×D₆₇	—	2	2	no	—
297	C₂×D₆₇	—	2	2	no	—
298	C₂×D₆₇	—	2	1	no	—
299	C₂×D₆₇	—	2	1	no	—
300	C₂×D₆₇	—	2	2	no	—
301	C₂×D₆₇	—	4	4	no	—
302	C₂×D₆₇	—	4	8	no	—
303	C₂×D₆₇	C₂×#41	1	2	yes	—
304	C₂×D₆₇	H(5,𝔽₂)	1	2	yes	—
305	C₂×D₆₇	2₋¹⁺⁴	1	2	yes	—
306	C₄×C₆₇	—	2	2	no	—
307	C₄×C₆₇	—	2	1	no	—
308	C₄×C₆₇	—	2	1	no	—
309	C₄×C₆₇	—	2	2	no	—
310	C₄×C₆₇	—	2	2	no	—
311	C₄×C₆₇	—	2	1	no	—
312	C₄×C₆₇	—	2	1	no	—
313	C₄×C₆₇	—	2	1	no	—
314	C₄×C₆₇	C₂×#41	1	2	yes	—
315	Dic₆₇	—	2	2	no	—
316	Dic₆₇	—	2	1	no	—
317	Dic₆₇	—	2	1	no	—
318	Dic₆₇	—	2	2	no	—
319	Dic₆₇	—	2	2	no	—
320	Dic₆₇	—	2	1	no	—
321	Dic₆₇	—	2	1	no	—
322	Dic₆₇	—	2	1	no	—
323	Dic₆₇	C₂×#41	1	2	yes	—
324	C₂×C₆₇	—	4	1	no	—
325	C₂×C₆₇	—	4	2	no	—
326	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
327	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
328	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
329	D₆₇	—	4	1	no	—
330	D₆₇	—	4	2	no	—
331	D₆₇	#542	1	4	yes	direct product factor
332	C₂×#542	—	67	1	no	maximal, Sylow
333	C₆₇	C₂×#542	1	1	yes	characteristic, complemented, Sylow
334	#542	—	67	1	no	—
335	#542	—	67	2	no	—
336	#542	—	67	2	no	—
337	#542	—	67	1	no	—
338	#542	—	67	2	no	—
339	#542	—	67	2	no	—
340	#542	—	67	1	no	—
341	#542	—	67	1	no	—
342	#542	—	67	1	no	—
343	#542	—	67	1	no	—
344	#542	—	67	1	no	—
345	#542	D₆₇	1	1	yes	characteristic, direct product factor
346	C₂×C₄⋊Q₈	—	67	1	no	—
347	C₂×#126	—	67	2	no	—
348	C₂×#124	—	67	1	no	—
349	C₂×#124	—	67	2	no	—
350	C₂×#123	—	67	2	no	—
351	C₂×C₂²⋊Q₈	—	67	2	no	—
352	C₂×C₂²⋊Q₈	—	67	1	no	—
353	C₂×#121	—	67	1	no	—
354	C₂×C₄×Q₈	—	67	1	no	—
355	C₂×C₄×D₄	—	67	1	no	—
356	C₂×#117	—	67	1	no	—
357	C₂²×Q₈	—	67	2	no	—
358	C₂²×Q₈	—	67	1	no	—
359	C₂²×D₄	—	67	2	no	—
360	C₂²×D₄	—	67	1	no	—
361	C₂³×C₄	—	67	2	no	—
362	C₂³×C₄	—	67	1	no	—
363	C₄⋊Q₈	—	67	2	no	—
364	C₄⋊Q₈	—	67	2	no	—
365	C₄⋊Q₈	—	67	1	no	—
366	C₄⋊Q₈	—	67	1	no	—
367	C₄⋊Q₈	—	67	1	no	—
368	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
369	#126	—	67	2	no	—
370	#126	—	67	2	no	—
371	#126	—	67	2	no	—
372	#126	—	67	2	no	—
373	#126	—	67	2	no	—
374	#126	—	67	2	no	—
375	#126	—	67	2	no	—
376	#126	C₂×D₆₇	1	2	yes	complemented
377	#124	—	67	1	no	—
378	#124	—	67	2	no	—
379	#124	—	67	1	no	—
380	#124	—	67	2	no	—
381	#124	—	67	2	no	—
382	#124	—	67	2	no	—
383	#124	—	67	2	no	—
384	#124	—	67	2	no	—
385	#124	—	67	2	no	—
386	#124	—	67	2	no	—
387	#124	—	67	1	no	—
388	#124	—	67	2	no	—
389	#124	C₂×D₆₇	1	1	yes	characteristic, complemented
390	#124	C₂×D₆₇	1	2	yes	complemented
391	#123	—	67	2	no	—
392	#123	—	67	2	no	—
393	#123	—	67	2	no	—
394	#123	—	67	2	no	—
395	#123	—	67	2	no	—
396	#123	—	67	2	no	—
397	#123	—	67	2	no	—
398	#123	C₂×D₆₇	1	2	yes	complemented
399	C₂²⋊Q₈	—	67	2	no	—
400	C₂²⋊Q₈	—	67	1	no	—
401	C₂²⋊Q₈	—	67	2	no	—
402	C₂²⋊Q₈	—	67	1	no	—
403	C₂²⋊Q₈	—	67	2	no	—
404	C₂²⋊Q₈	—	67	2	no	—
405	C₂²⋊Q₈	—	67	2	no	—
406	C₂²⋊Q₈	—	67	2	no	—
407	C₂²⋊Q₈	—	67	1	no	—
408	C₂²⋊Q₈	—	67	2	no	—
409	C₂²⋊Q₈	—	67	2	no	—
410	C₂²⋊Q₈	—	67	2	no	—
411	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
412	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
413	#121	—	67	1	no	—
414	#121	—	67	2	no	—
415	#121	—	67	1	no	—
416	#121	—	67	1	no	—
417	#121	—	67	2	no	—
418	#121	C₂×D₆₇	1	1	yes	characteristic
419	C₄×Q₈	—	67	1	no	—
420	C₄×Q₈	—	67	2	no	—
421	C₄×Q₈	—	67	1	no	—
422	C₄×Q₈	—	67	2	no	—
423	C₄×Q₈	—	67	1	no	—
424	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
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	1	no	—
430	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
431	#117	—	67	1	no	—
432	#117	—	67	1	no	—
433	#117	—	67	1	no	—
434	#117	—	67	1	no	—
435	#117	—	67	1	no	—
436	#117	—	67	1	no	—
437	#117	—	67	1	no	—
438	#117	C₂×D₆₇	1	1	yes	characteristic, complemented
439	C₂×C₄⋊C₄	—	67	1	no	—
440	C₂×C₄⋊C₄	—	67	1	no	—
441	C₂×C₄⋊C₄	—	67	1	no	—
442	C₂×C₄⋊C₄	—	67	1	no	—
443	C₂×C₄⋊C₄	—	67	2	no	—
444	C₂×C₄⋊C₄	—	67	2	no	—
445	C₂×C₄⋊C₄	—	67	2	no	—
446	C₂×C₂²⋊C₄	—	67	1	no	—
447	C₂×C₂²⋊C₄	—	67	1	no	—
448	C₂×C₂²⋊C₄	—	67	2	no	—
449	C₂×C₂²⋊C₄	—	67	2	no	—
450	C₂×C₂²⋊C₄	—	67	2	no	—
451	C₂×C₂²⋊C₄	—	67	2	no	—
452	C₂×C₂²⋊C₄	—	67	2	no	—
453	C₂×C₄²	—	67	1	no	—
454	C₂×C₄²	—	67	1	no	—
455	C₂×C₄²	—	67	2	no	—
456	C₂⁴	—	67	2	no	—
457	C₂⁴	—	67	1	no	—
458	C₂×Q₈	—	268	4	no	—
459	C₂×Q₈	—	67	2	no	—
460	C₂×Q₈	—	67	2	no	—
461	C₂×Q₈	—	67	2	no	—
462	C₂×Q₈	—	67	2	no	—
463	C₂×Q₈	—	67	1	no	—
464	C₂×Q₈	—	134	4	no	—
465	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
466	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
467	C₂×D₄	—	268	4	no	—
468	C₂×D₄	—	67	2	no	—
469	C₂×D₄	—	67	2	no	—
470	C₂×D₄	—	67	2	no	—
471	C₂×D₄	—	67	2	no	—
472	C₂×D₄	—	67	1	no	—
473	C₂×D₄	—	134	4	no	—
474	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
475	C₂×D₄	C₂²×D₆₇	1	2	yes	—
476	C₂²×C₄	—	268	4	no	—
477	C₂²×C₄	—	67	2	no	—
478	C₂²×C₄	—	67	2	no	—
479	C₂²×C₄	—	67	2	no	—
480	C₂²×C₄	—	67	1	no	—
481	C₂²×C₄	—	67	1	no	—
482	C₂²×C₄	—	67	1	no	—
483	C₂²×C₄	—	67	1	no	—
484	C₂²×C₄	—	67	2	no	—
485	C₂²×C₄	—	67	1	no	—
486	C₂²×C₄	—	67	1	no	—
487	C₂²×C₄	—	67	2	no	—
488	C₂²×C₄	—	67	1	no	—
489	C₂²×C₄	—	67	2	no	—
490	C₂²×C₄	—	67	1	no	—
491	C₂²×C₄	—	67	1	no	—
492	C₂²×C₄	—	134	4	no	—
493	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
494	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
495	C₄⋊C₄	—	67	1	no	—
496	C₄⋊C₄	—	67	1	no	—
497	C₄⋊C₄	—	67	1	no	—
498	C₄⋊C₄	—	67	1	no	—
499	C₄⋊C₄	—	67	1	no	—
500	C₄⋊C₄	—	67	1	no	—
501	C₄⋊C₄	—	67	2	no	—
502	C₄⋊C₄	—	67	1	no	—
503	C₄⋊C₄	—	67	2	no	—
504	C₄⋊C₄	—	67	1	no	—
505	C₄⋊C₄	—	67	2	no	—
506	C₄⋊C₄	—	67	2	no	—
507	C₄⋊C₄	—	67	2	no	—
508	C₄⋊C₄	—	67	2	no	—
509	C₄⋊C₄	—	67	2	no	—
510	C₄⋊C₄	—	67	2	no	—
511	C₄⋊C₄	—	67	2	no	—
512	C₄⋊C₄	—	67	2	no	—
513	C₄⋊C₄	—	67	2	no	—
514	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
519	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
520	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
521	C₂²⋊C₄	—	67	1	no	—
522	C₂²⋊C₄	—	67	1	no	—
523	C₂²⋊C₄	—	67	2	no	—
524	C₂²⋊C₄	—	67	2	no	—
525	C₂²⋊C₄	—	67	2	no	—
526	C₂²⋊C₄	—	67	2	no	—
527	C₂²⋊C₄	—	67	2	no	—
528	C₂²⋊C₄	—	67	1	no	—
529	C₂²⋊C₄	—	67	1	no	—
530	C₂²⋊C₄	—	67	1	no	—
531	C₂²⋊C₄	—	67	1	no	—
532	C₂²⋊C₄	—	67	2	no	—
533	C₂²⋊C₄	—	67	2	no	—
534	C₂²⋊C₄	—	67	2	no	—
535	C₂²⋊C₄	—	67	2	no	—
536	C₂²⋊C₄	—	67	2	no	—
537	C₂²⋊C₄	—	67	2	no	—
538	C₂²⋊C₄	—	67	2	no	—
539	C₂²⋊C₄	—	67	2	no	—
540	C₂²⋊C₄	—	67	2	no	—
541	C₂²⋊C₄	—	67	2	no	—
542	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
543	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
544	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
548	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
549	C₄²	—	67	1	no	—
550	C₄²	—	67	1	no	—
551	C₄²	—	67	1	no	—
552	C₄²	—	67	1	no	—
553	C₄²	—	67	1	no	—
554	C₄²	—	67	1	no	—
555	C₄²	—	67	2	no	—
556	C₄²	—	67	2	no	—
557	C₄²	—	67	2	no	—
558	C₄²	C₂²×D₆₇	1	1	yes	characteristic
559	C₄²	C₂²×D₆₇	1	1	yes	characteristic
560	C₄²	C₂²×D₆₇	1	2	yes	—
561	C₂³	—	67	1	no	—
562	C₂³	—	67	1	no	—
563	C₂³	—	67	2	no	—
564	C₂³	—	134	4	no	—
565	C₂³	—	134	2	no	—
566	C₂³	—	134	2	no	—
567	C₂³	—	134	4	no	—
568	C₂³	—	134	4	no	—
569	C₂³	—	134	2	no	—
570	C₂³	C₂³×D₆₇	1	1	yes	characteristic
571	C₂³	C₂³×D₆₇	1	2	yes	—
572	Q₈	—	2	2	no	—
573	Q₈	—	4	2	no	—
574	Q₈	—	268	2	no	—
575	Q₈	—	268	2	no	—
576	Q₈	—	268	2	no	—
577	Q₈	—	134	4	no	—
578	Q₈	—	134	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	268	2	no	—
582	D₄	—	268	2	no	—
583	D₄	—	268	2	no	—
584	D₄	—	134	4	no	—
585	D₄	—	134	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	268	2	no	—
589	C₂×C₄	—	268	2	no	—
590	C₂×C₄	—	268	2	no	—
591	C₂×C₄	—	67	1	no	—
592	C₂×C₄	—	67	4	no	—
593	C₂×C₄	—	67	1	no	—
594	C₂×C₄	—	67	1	no	—
595	C₂×C₄	—	67	2	no	—
596	C₂×C₄	—	67	1	no	—
597	C₂×C₄	—	67	1	no	—
598	C₂×C₄	—	67	2	no	—
599	C₂×C₄	—	67	1	no	—
600	C₂×C₄	—	67	2	no	—
601	C₂×C₄	—	134	2	no	—
602	C₂×C₄	—	134	2	no	—
603	C₂×C₄	—	134	4	no	—
604	C₂×C₄	—	134	2	no	—
605	C₂×C₄	—	134	4	no	—
606	C₂×C₄	—	134	2	no	—
607	C₂×C₄	—	134	4	no	—
608	C₂×C₄	—	134	2	no	—
609	C₂×C₄	—	134	2	no	—
610	C₂×C₄	—	134	2	no	—
611	C₂×C₄	—	134	2	no	—
612	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₆₇	1	2	yes	—
615	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₆₇	1	2	yes	—
618	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₆₇	1	2	yes	—
620	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
621	C₂²	—	2	1	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	268	8	no	—
628	C₂²	—	268	4	no	—
629	C₂²	—	67	2	no	—
630	C₂²	—	67	2	no	—
631	C₂²	—	67	2	no	—
632	C₂²	—	134	1	no	—
633	C₂²	—	134	2	no	—
634	C₂²	—	134	2	no	—
635	C₂²	—	134	1	no	—
636	C₂²	—	134	1	no	—
637	C₂²	—	134	2	no	—
638	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
639	C₄	—	2	1	no	—
640	C₄	—	2	2	no	—
641	C₄	—	2	1	no	—
642	C₄	—	2	2	no	—
643	C₄	—	2	2	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	67	2	no	—
648	C₄	—	134	1	no	—
649	C₄	—	134	2	no	—
650	C₄	—	134	1	no	—
651	C₄	—	134	2	no	—
652	C₄	—	134	2	no	—
653	C₄	—	134	1	no	—
654	C₄	—	134	1	no	—
655	C₄	—	134	1	no	—
656	C₄	#41×D₆₇	1	2	yes	—
657	C₂	—	4	1	no	—
658	C₂	—	4	2	no	—
659	C₂	—	268	1	no	—
660	C₂	—	268	2	no	—
661	C₂	—	67	4	no	—
662	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
663	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
664	C₂	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#542×C₆₇	C₂
hypercenter	#542	D₆₇
hypocenter	C₆₇	C₂×#542
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #16864020	C₂	semidirect
2. #16864019	C₂	semidirect
3. #16864018	C₂	semidirect
4. #16864017	C₂	semidirect
5. #16864016	C₂	semidirect
6. #16864015	C₂	semidirect
7. #16864014	C₂	semidirect
8. #16864013	C₂	semidirect
9. #16864012	C₂	semidirect
10. #16864011	C₂	semidirect
11. #16864010	C₂	semidirect
12. C₄⋊Q₈×D₆₇	C₂	semidirect
13. #126×D₆₇	C₂	semidirect
14. #124×D₆₇	C₂	semidirect
15. #124×D₆₇	C₂	semidirect
16. #123×D₆₇	C₂	semidirect
17. C₂²⋊Q₈×D₆₇	C₂	semidirect
18. C₂²⋊Q₈×D₆₇	C₂	semidirect
20. C₄×Q₈×D₆₇	C₂	semidirect
21. C₄×D₄×D₆₇	C₂	semidirect
22. #117×D₆₇	C₂	semidirect
23. #542×C₆₇	C₂	semidirect
30. #14524043	C₂²	semidirect
31. #14524042	C₂²	semidirect
32. #14524042	C₂²	semidirect
33. #14524042	C₂²	semidirect
34. #14524041	C₂²	semidirect
35. #14524038	C₂²	semidirect
36. #14524038	C₂²	semidirect
37. #14524038	C₂²	semidirect
38. #14524037	C₂²	semidirect
39. #14524036	C₂²	semidirect
40. #14524036	C₂²	semidirect
41. #14524036	C₂²	semidirect
42. #14524032	C₂²	semidirect
43. #14524032	C₂²	semidirect
44. #14524031	C₂²	semidirect
45. #14524031	C₂²	semidirect
46. #14524030	C₂²	semidirect
47. #14524030	C₂²	semidirect
48. #14524029	C₂²	semidirect
49. #14524029	C₂²	semidirect
50. #14524029	C₂²	semidirect
51. #14524029	C₂²	semidirect
52. #14524029	C₂²	semidirect
53. #14524029	C₂²	semidirect
54. #14524028	C₂²	semidirect
55. #14524028	C₂²	semidirect
56. #14524027	C₂²	semidirect
57. #14524026	C₂²	semidirect
58. #14524025	C₂²	semidirect
59. #14524025	C₂²	semidirect
60. #14524024	C₂²	semidirect
61. #14524023	C₂²	semidirect
62. #14524023	C₂²	semidirect
63. #14524022	C₂²	semidirect
64. #14524022	C₂²	semidirect
65. #14524021	C₂²	semidirect
66. #14524021	C₂²	semidirect
67. #14524021	C₂²	semidirect
68. #14524020	C₂²	semidirect
69. #14524020	C₂²	semidirect
70. #14524020	C₂²	semidirect
71. #14524019	C₂²	semidirect
72. #14524019	C₂²	semidirect
78. Q₈×Dic₆₇	C₂²	semidirect
79. C₄×Dic₁₃₄	C₂²	semidirect
80. C₄×Dic₁₃₄	C₂²	semidirect
81. #14524008	C₂²	semidirect
82. #14524008	C₂²	semidirect
83. C₄×D₂₆₈	C₂²	semidirect
84. D₄×Dic₆₇	C₂²	semidirect
85. #14524005	C₂²	semidirect
86. C₄×C₂²⋊D₆₇	C₂²	semidirect
87. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
88. #14524002	C₂²	semidirect
89. #14524001	C₂²	semidirect
90. #14524001	C₂²	semidirect
91. #14524000	C₂²	semidirect
92. #14524000	C₂²	semidirect
93. #14523999	C₂²	semidirect
94. #14523999	C₂²	semidirect
112. C₄⋊Q₈×C₆₇	C₂²	semidirect
113. #126×C₆₇	C₂²	semidirect
114. #124×C₆₇	C₂²	semidirect
115. #124×C₆₇	C₂²	semidirect
116. #123×C₆₇	C₂²	semidirect
117. C₂²⋊Q₈×C₆₇	C₂²	semidirect
118. C₂²⋊Q₈×C₆₇	C₂²	semidirect
120. C₄×Q₈×C₆₇	C₂²	semidirect
121. C₄×D₄×C₆₇	C₂²	semidirect
122. #117×C₆₇	C₂²	semidirect
331. D₆₇	#542	direct (N × H)
333. C₆₇	C₂×#542	semidirect
345. #542	D₆₇	direct (N × H)
368. C₄⋊Q₈	C₂×D₆₇	semidirect
376. #126	C₂×D₆₇	semidirect
389. #124	C₂×D₆₇	semidirect
390. #124	C₂×D₆₇	semidirect
398. #123	C₂×D₆₇	semidirect
411. C₂²⋊Q₈	C₂×D₆₇	semidirect
412. C₂²⋊Q₈	C₂×D₆₇	semidirect
424. C₄×Q₈	C₂×D₆₇	semidirect
430. C₄×D₄	C₂×D₆₇	semidirect
438. #117	C₂×D₆₇	semidirect

Subgroups — #542×D67 #22573579

Conjugacy classes of subgroups

Complements

Subgroups — #542×D₆₇ #22573579