Subgroups — #31764371

Order 17152.

11534 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16864232	C₂	1	1	yes	maximal, characteristic, complemented
2	#22573889	C₂	1	8	yes	maximal, complemented
3	#22573878	C₂	1	8	yes	maximal, complemented
4	#22573867	C₂	1	2	yes	maximal, complemented
5	#22573860	C₂	1	2	yes	maximal, complemented
6	#22573853	C₂	1	6	yes	maximal, complemented
7	#22573844	C₂	1	6	yes	maximal, complemented
8	#41×C₂²⋊D₆₇	C₂	1	16	yes	maximal, complemented
9	#22573538	C₂	1	6	yes	maximal, complemented
10	C₂×#16863907	C₂	1	6	yes	maximal, complemented
11	#22573412	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864232	—	2	16	no	—
14	C₂×#14524091	C₂²	1	2	yes	complemented
15	C₂×#14524090	C₂²	1	4	yes	complemented
16	C₂×#14524089	C₂²	1	4	yes	complemented
17	C₂×#14524088	C₂²	1	6	yes	complemented
18	C₂²×#11761628	C₂²	1	6	yes	complemented
19	C₂×#41×D₆₇	C₂²	1	8	yes	complemented
20	#16864065	C₂²	1	16	yes	complemented
21	Q₈×C₂²⋊D₆₇	C₂²	1	16	yes	complemented
22	#16864057	C₂²	1	16	yes	complemented
23	#16864053	C₂²	1	16	yes	complemented
24	#16864045	C₂²	1	48	yes	complemented
25	#16864040	C₂²	1	48	yes	complemented
26	#16864034	C₂²	1	48	yes	complemented
27	D₄×C₂²⋊D₆₇	C₂²	1	48	yes	complemented
28	#16863974	C₂²	1	24	yes	complemented
29	#16863970	C₂²	1	12	yes	complemented
30	#16863967	C₂²	1	12	yes	complemented
31	#16863963	C₂²	1	12	yes	complemented
32	#16863960	C₂²	1	12	yes	complemented
33	#16863955	C₂²	1	24	yes	complemented
34	#16863942	C₂²	1	24	yes	complemented
35	#16863907	C₂²	1	12	yes	complemented
36	#16863907	C₂²	1	4	yes	complemented
37	#16863907	C₂²	1	12	yes	complemented
38	#16863907	C₂²	1	12	yes	complemented
39	#16863907	C₂²	1	24	yes	complemented
40	#16863907	C₂²	1	24	yes	complemented
41	#16863903	C₂²	1	24	yes	complemented
42	C₂×#14524026	C₂²	1	12	yes	complemented
43	C₂×#14524022	C₂²	1	12	yes	complemented
44	C₂×#14524017	C₂²	1	12	yes	complemented
45	C₂×#14524012	C₂²	1	12	yes	complemented
46	#16863879	C₂²	1	8	yes	complemented
47	#16863874	C₂²	1	2	yes	complemented
48	#16863871	C₂²	1	6	yes	complemented
49	#41×Dic₆₇	C₂²	1	8	yes	complemented
50	C₂×C₄×C₂²⋊D₆₇	C₂²	1	24	yes	complemented
51	C₂×#14524002	C₂²	1	6	yes	complemented
52	C₂²×#41×C₆₇	—	2	16	no	—
53	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
54	C₂²×#41×C₆₇	C₂²	1	3	yes	complemented
55	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₂²×#41×C₆₇	C₂²	1	8	yes	complemented
57	C₂²×#41×C₆₇	C₂²	1	8	yes	complemented
58	C₂²×#41×C₆₇	C₂²	1	3	yes	complemented
59	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₄×C₆₇	C₂²	1	3	yes	complemented
61	C₂⁴×C₄×C₆₇	C₂²	1	3	yes	complemented
62	#14524091	—	2	16	no	—
63	#14524090	—	2	32	no	—
64	#14524089	—	2	32	no	—
65	#14524088	—	2	48	no	—
66	C₂×#11761629	C₂³	1	8	yes	complemented
67	C₂×#11761628	—	2	48	no	—
68	C₂×#11761628	C₂³	1	4	yes	—
69	C₂×#11761628	C₂³	1	12	yes	—
70	C₂×#11761628	C₂³	1	12	yes	complemented
71	C₂×#11761628	C₂³	1	12	yes	complemented
72	C₂×#11761627	C₂³	1	24	yes	complemented
73	#41×D₆₇	—	2	64	no	—
74	C₂²×Dic₁₃₄	C₂³	1	6	yes	complemented
75	C₂×Q₈×D₆₇	C₂³	1	8	yes	complemented
76	C₂²×D₂₆₈	C₂³	1	6	yes	complemented
77	C₂²×C₂²⋊D₆₇	C₂³	1	12	yes	—
78	C₂²×C₂²⋊D₆₇	C₂³	1	24	yes	—
79	C₂×D₄×D₆₇	C₂³	1	24	yes	complemented
80	C₂²×C₄×D₆₇	C₂³	1	12	yes	complemented
81	#14524041	C₂³	1	24	yes	complemented
82	#14524039	C₂³	1	24	yes	complemented
83	#14524032	C₂³	1	24	yes	complemented
84	#14524030	C₂³	1	24	yes	complemented
85	#14524026	C₂³	1	8	yes	—
86	#14524026	C₂³	1	24	yes	—
87	#14524026	C₂³	1	48	yes	complemented
88	#14524024	C₂³	1	48	yes	complemented
89	#14524022	C₂³	1	24	yes	—
90	#14524022	C₂³	1	8	yes	—
91	#14524022	C₂³	1	24	yes	complemented
92	#14524022	C₂³	1	24	yes	complemented
93	#14524019	C₂³	1	48	yes	complemented
94	#14524017	C₂³	1	24	yes	—
95	#14524017	C₂³	1	8	yes	—
96	#14524017	C₂³	1	24	yes	complemented
97	#14524017	C₂³	1	24	yes	complemented
98	#14524015	C₂³	1	96	yes	complemented
99	#14524014	C₂³	1	48	yes	complemented
100	#14524012	C₂³	1	48	yes	—
101	#14524012	C₂³	1	8	yes	—
102	#14524012	C₂³	1	24	yes	—
103	#14524011	C₂³	1	48	yes	complemented
104	Q₈×Dic₆₇	C₂³	1	16	yes	complemented
105	D₄×Dic₆₇	C₂³	1	48	yes	complemented
106	C₄×C₂²⋊D₆₇	C₂³	1	48	yes	—
107	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	—
108	C₄×C₂²⋊D₆₇	C₂³	1	48	yes	complemented
109	C₄×C₂²⋊D₆₇	C₂³	1	48	yes	complemented
110	#14524002	C₂³	1	4	yes	—
111	#14524002	C₂³	1	12	yes	—
112	#14524002	C₂³	1	12	yes	complemented
113	#14524002	C₂³	1	12	yes	complemented
114	C₂×C₄⋊Dic₆₇	C₂³	1	12	yes	complemented
115	C₂×Dic₆₇⋊C₄	C₂³	1	24	yes	complemented
116	C₂×C₂²⋊Dic₆₇	C₂³	1	24	yes	—
117	C₂×C₂²⋊Dic₆₇	C₂³	1	12	yes	—
118	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	24	yes	complemented
119	C₂×C₄×Dic₆₇	C₂³	1	12	yes	complemented
120	C₂⁵×C₆₇	C₂³	1	3	yes	—
121	C₂×#41×C₆₇	—	2	64	no	—
122	C₂×#41×C₆₇	—	2	64	no	—
123	C₂×#41×C₆₇	—	2	8	no	—
124	C₂×#41×C₆₇	—	2	24	no	—
125	C₂×#41×C₆₇	—	2	24	no	—
126	C₂×#41×C₆₇	D₄	1	16	yes	complemented
127	C₂×#41×C₆₇	C₂³	1	24	yes	—
128	C₂×#41×C₆₇	C₂³	1	8	yes	—
129	C₂×#41×C₆₇	C₂³	1	12	yes	—
130	C₂×#41×C₆₇	C₂³	1	12	yes	—
131	C₂×#41×C₆₇	C₂³	1	4	yes	—
132	C₂×#41×C₆₇	C₂³	1	4	yes	—
133	C₂²×Q₈×C₆₇	—	2	8	no	—
134	C₂²×Q₈×C₆₇	C₂³	1	8	yes	—
135	C₂²×Q₈×C₆₇	C₂³	1	3	yes	—
136	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₆₇	—	2	24	no	—
138	C₂²×D₄×C₆₇	C₂³	1	24	yes	—
139	C₂²×D₄×C₆₇	C₂³	1	6	yes	—
140	C₂²×D₄×C₆₇	C₂³	1	3	yes	—
141	C₂²×D₄×C₆₇	C₂³	1	3	yes	—
142	C₂³×C₄×C₆₇	—	2	24	no	—
143	C₂³×C₄×C₆₇	C₂³	1	12	yes	—
144	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
146	C₂³×C₄×C₆₇	C₂³	1	12	yes	—
147	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
148	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
149	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
150	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
151	C₂³×D₆₇	C₂⁴	1	12	yes	—
152	#11761629	—	2	32	no	—
153	#11761628	—	2	48	no	—
154	#11761628	—	2	16	no	—
155	#11761628	—	2	48	no	—
156	#11761628	—	2	48	no	—
157	#11761627	—	2	96	no	—
158	C₂×Dic₁₃₄	—	2	24	no	—
159	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
160	C₂×Dic₁₃₄	C₂⁴	1	12	yes	—
161	Q₈×D₆₇	—	2	32	no	—
162	C₂×D₂₆₈	—	2	24	no	—
163	C₂×D₂₆₈	C₂⁴	1	4	yes	—
164	C₂×D₂₆₈	C₂⁴	1	12	yes	—
165	C₂×C₂²⋊D₆₇	—	2	48	no	—
166	C₂×C₂²⋊D₆₇	—	4	48	no	—
167	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
168	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
169	C₂×C₂²⋊D₆₇	C₂⁴	1	24	yes	—
170	C₂×C₂²⋊D₆₇	C₂⁴	1	48	yes	—
171	D₄×D₆₇	—	2	96	no	—
172	C₂²×Dic₆₇	C₂⁴	1	12	yes	—
173	C₂²×Dic₆₇	C₂⁴	1	24	yes	—
174	C₂×C₄×D₆₇	—	2	48	no	—
175	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
176	C₂×C₄×D₆₇	C₂⁴	1	24	yes	—
177	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
178	C₄⋊Dic₆₇	C₂⁴	1	24	yes	—
179	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
180	Dic₆₇⋊C₄	C₂⁴	1	48	yes	—
181	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
182	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
183	C₂²⋊Dic₆₇	C₂⁴	1	24	yes	—
184	C₂²⋊Dic₆₇	C₂⁴	1	48	yes	—
185	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
186	(C₂×D₆₇)⋊C₄	C₂⁴	1	48	yes	—
187	C₄×Dic₆₇	C₂⁴	1	8	yes	—
188	C₄×Dic₆₇	C₂⁴	1	24	yes	—
189	C₂⁴×C₆₇	—	2	12	no	—
190	C₂⁴×C₆₇	—	4	12	no	—
191	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
192	C₂⁴×C₆₇	C₂⁴	1	12	yes	—
193	C₂⁴×C₆₇	C₂⁴	1	3	yes	—
194	C₂⁴×C₆₇	C₂⁴	1	3	yes	—
195	#41×C₆₇	—	2	32	no	—
196	#41×C₆₇	—	2	96	no	—
197	#41×C₆₇	—	2	48	no	—
198	#41×C₆₇	—	2	48	no	—
199	#41×C₆₇	C₂×D₄	1	32	yes	complemented
200	#41×C₆₇	C₂×D₄	1	32	yes	complemented
201	C₂×Q₈×C₆₇	—	2	32	no	—
202	C₂×Q₈×C₆₇	—	2	12	no	—
203	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	complemented
204	C₂×Q₈×C₆₇	C₂⁴	1	12	yes	—
205	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
206	C₂×D₄×C₆₇	—	2	24	no	—
207	C₂×D₄×C₆₇	—	2	96	no	—
208	C₂×D₄×C₆₇	—	2	12	no	—
209	C₂×D₄×C₆₇	C₂×D₄	1	24	yes	complemented
210	C₂×D₄×C₆₇	C₂⁴	1	24	yes	—
211	C₂×D₄×C₆₇	C₂⁴	1	12	yes	—
212	C₂×D₄×C₆₇	C₂⁴	1	12	yes	—
213	C₂²×C₄×C₆₇	—	2	12	no	—
214	C₂²×C₄×C₆₇	—	2	4	no	—
215	C₂²×C₄×C₆₇	—	2	12	no	—
216	C₂²×C₄×C₆₇	—	2	12	no	—
217	C₂²×C₄×C₆₇	—	2	12	no	—
218	C₂²×C₄×C₆₇	—	2	48	no	—
219	C₂²×C₄×C₆₇	—	2	48	no	—
220	C₂²×C₄×C₆₇	C₂×D₄	1	24	yes	complemented
221	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₆₇	C₂⁴	1	12	yes	—
225	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
226	C₂²×C₄×C₆₇	C₂⁴	1	12	yes	—
227	C₂²×C₄×C₆₇	C₂⁴	1	6	yes	—
228	C₂²×C₄×C₆₇	C₂⁴	1	12	yes	—
229	C₂²×C₄×C₆₇	C₂⁴	1	6	yes	—
230	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
232	C₂²×C₄×C₆₇	C₂⁴	1	6	yes	—
233	C₂²×C₄×C₆₇	C₂⁴	1	6	yes	—
234	C₂³×C₆₇	—	2	2	no	—
235	C₂³×C₆₇	—	2	4	no	—
236	C₂³×C₆₇	—	2	24	no	—
237	C₂³×C₆₇	—	2	6	no	—
238	C₂³×C₆₇	—	2	24	no	—
239	C₂³×C₆₇	—	4	6	no	—
240	C₂³×C₆₇	—	4	12	no	—
241	C₂³×C₆₇	—	4	6	no	—
242	C₂³×C₆₇	—	4	48	no	—
243	C₂³×C₆₇	C₂²×D₄	1	12	yes	—
244	C₂³×C₆₇	C₂⁵	1	6	yes	—
245	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
246	C₂³×C₆₇	C₂⁵	1	6	yes	—
247	C₂³×C₆₇	C₂⁵	1	2	yes	—
248	C₂²×D₆₇	—	2	24	no	—
249	C₂²×D₆₇	—	4	24	no	—
250	C₂²×D₆₇	C₂⁵	1	8	yes	—
251	Q₈×C₆₇	—	2	24	no	—
252	Q₈×C₆₇	C₂²×D₄	1	16	yes	—
253	D₄×C₆₇	—	2	48	no	—
254	D₄×C₆₇	—	2	24	no	—
255	D₄×C₆₇	C₂²×D₄	1	48	yes	—
256	C₂×C₄×C₆₇	—	2	2	no	—
257	C₂×C₄×C₆₇	—	2	6	no	—
258	C₂×C₄×C₆₇	—	2	24	no	—
259	C₂×C₄×C₆₇	—	2	4	no	—
260	C₂×C₄×C₆₇	—	2	4	no	—
261	C₂×C₄×C₆₇	—	2	24	no	—
262	C₂×C₄×C₆₇	—	2	24	no	—
263	C₂×C₄×C₆₇	—	2	12	no	—
264	C₂×C₄×C₆₇	—	2	12	no	—
265	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
266	C₂×C₄×C₆₇	C₂²×D₄	1	12	yes	—
267	C₂×C₄×C₆₇	C₂²×D₄	1	24	yes	—
268	C₂×C₄×C₆₇	C₂²×D₄	1	24	yes	—
269	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
270	C₂×C₄×C₆₇	C₂⁵	1	6	yes	—
271	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
272	C₂×C₄×C₆₇	C₂⁵	1	6	yes	—
273	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
274	C₂²⋊D₆₇	—	2	48	no	—
275	C₂²⋊D₆₇	—	2	16	no	—
276	C₂²⋊D₆₇	—	2	32	no	—
277	C₂²⋊D₆₇	—	4	48	no	—
278	C₂×Dic₆₇	—	2	24	no	—
279	C₂×Dic₆₇	—	4	24	no	—
280	C₂×Dic₆₇	C₂⁵	1	16	yes	—
281	C₂×Dic₆₇	C₂⁵	1	8	yes	—
282	D₂₆₈	—	2	24	no	—
283	D₂₆₈	—	2	8	no	—
284	C₄×D₆₇	—	2	16	no	—
285	C₄×D₆₇	—	2	48	no	—
286	Dic₁₃₄	—	2	24	no	—
287	Dic₁₃₄	—	2	8	no	—
288	C₂²×C₆₇	—	2	8	no	—
289	C₂²×C₆₇	—	2	2	no	—
290	C₂²×C₆₇	—	2	12	no	—
291	C₂²×C₆₇	—	2	2	no	—
292	C₂²×C₆₇	—	2	2	no	—
293	C₂²×C₆₇	—	2	6	no	—
294	C₂²×C₆₇	—	2	12	no	—
295	C₂²×C₆₇	—	4	12	no	—
296	C₂²×C₆₇	—	4	48	no	—
297	C₂²×C₆₇	—	4	12	no	—
298	C₂²×C₆₇	C₂³×D₄	1	12	yes	—
299	C₂²×C₆₇	C₂³×D₄	1	2	yes	—
300	C₂²×C₆₇	#585	1	4	yes	complemented
301	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
302	C₂×D₆₇	—	2	8	no	—
303	C₂×D₆₇	—	2	16	no	—
304	C₂×D₆₇	—	8	24	no	—
305	C₄×C₆₇	—	2	2	no	—
306	C₄×C₆₇	—	2	6	no	—
307	C₄×C₆₇	C₂³×D₄	1	2	yes	—
308	C₄×C₆₇	C₂³×D₄	1	12	yes	—
309	C₄×C₆₇	C₂³×D₄	1	2	yes	—
310	Dic₆₇	—	2	8	no	—
311	Dic₆₇	—	2	16	no	—
312	#62811	—	67	1	no	maximal, Sylow
313	C₂×C₆₇	—	2	12	no	—
314	C₂×C₆₇	—	2	2	no	—
315	C₂×C₆₇	—	2	4	no	—
316	C₂×C₆₇	—	4	6	no	—
317	C₂×C₆₇	C₂⁴×D₄	1	1	yes	characteristic
318	C₂×C₆₇	C₂×#585	1	2	yes	—
319	D₆₇	—	4	8	no	—
320	C₂×#585	—	67	1	no	—
321	C₂³×#41	D₆₇	1	1	yes	characteristic, complemented
322	#3489	—	67	8	no	—
323	#3488	—	67	8	no	—
324	#3487	—	67	2	no	—
325	#3486	—	67	2	no	—
326	#3485	—	67	6	no	—
327	#3484	—	67	6	no	—
328	D₄×#41	—	67	16	no	—
329	#3449	—	67	6	no	—
330	C₂×#525	—	67	6	no	—
331	#3428	—	67	1	no	—
332	C₆₇	#62811	1	1	yes	characteristic, complemented, Sylow
333	#585	—	134	16	no	—
334	C₂×2₋¹⁺⁴	—	67	4	no	—
335	C₂×2₋¹⁺⁴	—	67	2	no	—
336	C₂×H(5,𝔽₂)	—	67	4	no	—
337	C₂×H(5,𝔽₂)	—	67	6	no	—
338	C₂²×#41	—	2	16	no	—
339	C₂²×#41	—	67	8	no	—
340	C₂²×#41	—	67	6	no	—
341	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
342	C₂²×#41	C₂×D₆₇	1	3	yes	complemented
343	C₂²×#41	C₂×D₆₇	1	8	yes	complemented
344	C₂²×#41	C₂×D₆₇	1	3	yes	complemented
345	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
346	C₂²×#41	C₂×D₆₇	1	8	yes	complemented
347	C₂³×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
348	C₂³×D₄	C₂×D₆₇	1	3	yes	complemented
349	C₂⁴×C₄	C₂×D₆₇	1	3	yes	complemented
350	#550	—	67	16	no	—
351	D₄×Q₈	—	67	16	no	—
352	#548	—	67	16	no	—
353	#548	—	67	16	no	—
354	#547	—	67	48	no	—
355	#546	—	67	48	no	—
356	#546	—	67	48	no	—
357	D₄²	—	67	48	no	—
358	#537	—	67	24	no	—
359	#536	—	67	12	no	—
360	#536	—	67	12	no	—
361	#535	—	67	12	no	—
362	#535	—	67	12	no	—
363	#534	—	67	24	no	—
364	#532	—	67	24	no	—
365	#525	—	67	24	no	—
366	#525	—	67	4	no	—
367	#525	—	67	12	no	—
368	#525	—	67	24	no	—
369	#525	—	67	12	no	—
370	#525	—	67	12	no	—
371	#525	—	67	24	no	—
372	C₂×#123	—	67	12	no	—
373	C₂×C₂²⋊Q₈	—	67	12	no	—
374	C₂×#121	—	67	12	no	—
375	C₂×#120	—	67	12	no	—
376	#520	—	67	8	no	—
377	#519	—	67	2	no	—
378	#518	—	67	6	no	—
379	C₄×#41	—	67	8	no	—
380	C₂×C₄×D₄	—	67	24	no	—
381	C₂×#117	—	67	6	no	—
382	C₂⁵	C₂²×D₆₇	1	3	yes	—
383	2₋¹⁺⁴	—	134	32	no	—
384	2₋¹⁺⁴	—	134	16	no	—
385	H(5,𝔽₂)	—	134	32	no	—
386	H(5,𝔽₂)	—	134	48	no	—
387	C₂×#41	—	2	64	no	—
388	C₂×#41	—	2	64	no	—
389	C₂×#41	—	2	8	no	—
390	C₂×#41	—	2	24	no	—
391	C₂×#41	—	2	24	no	—
392	C₂×#41	—	67	8	no	—
393	C₂×#41	—	67	24	no	—
394	C₂×#41	—	67	4	no	—
395	C₂×#41	—	67	12	no	—
396	C₂×#41	—	67	12	no	—
397	C₂×#41	—	67	12	no	—
398	C₂×#41	—	134	64	no	—
399	C₂×#41	—	134	48	no	—
400	C₂×#41	C₂²⋊D₆₇	1	16	yes	complemented
401	C₂×#41	C₂²×D₆₇	1	12	yes	—
402	C₂×#41	C₂²×D₆₇	1	12	yes	—
403	C₂×#41	C₂²×D₆₇	1	24	yes	—
404	C₂×#41	C₂²×D₆₇	1	8	yes	—
405	C₂×#41	C₂²×D₆₇	1	4	yes	—
406	C₂×#41	C₂²×D₆₇	1	4	yes	—
407	C₂²×Q₈	—	2	8	no	—
408	C₂²×Q₈	—	67	8	no	—
409	C₂²×Q₈	—	67	6	no	—
410	C₂²×Q₈	C₂²×D₆₇	1	3	yes	—
411	C₂²×Q₈	C₂²×D₆₇	1	8	yes	—
412	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
413	C₂²×D₄	—	2	24	no	—
414	C₂²×D₄	—	67	24	no	—
415	C₂²×D₄	—	67	12	no	—
416	C₂²×D₄	—	67	24	no	—
417	C₂²×D₄	—	67	6	no	—
418	C₂²×D₄	C₂²×D₆₇	1	6	yes	—
419	C₂²×D₄	C₂²×D₆₇	1	3	yes	—
420	C₂²×D₄	C₂²×D₆₇	1	24	yes	—
421	C₂²×D₄	C₂²×D₆₇	1	3	yes	—
422	C₂³×C₄	—	2	24	no	—
423	C₂³×C₄	—	67	12	no	—
424	C₂³×C₄	C₂²×D₆₇	1	12	yes	—
425	C₂³×C₄	C₂²×D₆₇	1	12	yes	—
426	C₂³×C₄	C₂²×D₆₇	1	3	yes	—
427	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
428	C₂³×C₄	C₂²×D₆₇	1	3	yes	—
429	C₂³×C₄	C₂²×D₆₇	1	3	yes	—
430	C₂³×C₄	C₂²×D₆₇	1	3	yes	—
431	C₂³×C₄	C₂²×D₆₇	1	3	yes	—
432	C₄⋊Q₈	—	67	24	no	—
433	#127	—	67	24	no	—
434	#124	—	67	24	no	—
435	#124	—	67	24	no	—
436	#123	—	67	48	no	—
437	#123	—	67	8	no	—
438	#123	—	67	24	no	—
439	#123	—	67	48	no	—
440	C₂²⋊Q₈	—	67	48	no	—
441	C₂²⋊Q₈	—	67	8	no	—
442	C₂²⋊Q₈	—	67	24	no	—
443	C₂²⋊Q₈	—	67	24	no	—
444	C₂²⋊Q₈	—	67	24	no	—
445	#121	—	67	48	no	—
446	#121	—	67	96	no	—
447	#121	—	67	8	no	—
448	#121	—	67	24	no	—
449	#121	—	67	24	no	—
450	#121	—	67	24	no	—
451	#120	—	67	8	no	—
452	#120	—	67	24	no	—
453	#120	—	67	48	no	—
454	#120	—	67	48	no	—
455	C₄×Q₈	—	67	16	no	—
456	C₄×D₄	—	67	48	no	—
457	C₄×D₄	—	67	16	no	—
458	C₄×D₄	—	67	48	no	—
459	C₄×D₄	—	67	48	no	—
460	C₄×D₄	—	67	48	no	—
461	#117	—	67	4	no	—
462	#117	—	67	12	no	—
463	#117	—	67	12	no	—
464	#117	—	67	12	no	—
465	C₂×C₄⋊C₄	—	67	12	no	—
466	C₂×C₄⋊C₄	—	67	24	no	—
467	C₂×C₂²⋊C₄	—	67	12	no	—
468	C₂×C₂²⋊C₄	—	67	24	no	—
469	C₂×C₂²⋊C₄	—	67	24	no	—
470	C₂×C₄²	—	67	12	no	—
471	C₂⁴	—	2	12	no	—
472	C₂⁴	—	4	12	no	—
473	C₂⁴	—	67	12	no	—
474	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
475	C₂⁴	C₂³×D₆₇	1	12	yes	—
476	C₂⁴	C₂³×D₆₇	1	3	yes	—
477	C₂⁴	C₂³×D₆₇	1	3	yes	—
478	#41	—	2	32	no	—
479	#41	—	2	96	no	—
480	#41	—	2	48	no	—
481	#41	—	2	48	no	—
482	#41	—	134	32	no	—
483	#41	—	134	96	no	—
484	#41	—	134	16	no	—
485	#41	—	134	48	no	—
486	#41	—	134	48	no	—
487	#41	—	134	48	no	—
488	#41	C₂×C₂²⋊D₆₇	1	32	yes	complemented
489	#41	C₂×C₂²⋊D₆₇	1	32	yes	complemented
490	C₂×Q₈	—	2	32	no	—
491	C₂×Q₈	—	2	12	no	—
492	C₂×Q₈	—	67	4	no	—
493	C₂×Q₈	—	67	12	no	—
494	C₂×Q₈	—	134	32	no	—
495	C₂×Q₈	—	134	24	no	—
496	C₂×Q₈	C₂×C₂²⋊D₆₇	1	8	yes	complemented
497	C₂×Q₈	C₂³×D₆₇	1	12	yes	—
498	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
499	C₂×D₄	—	2	24	no	—
500	C₂×D₄	—	2	96	no	—
501	C₂×D₄	—	2	12	no	—
502	C₂×D₄	—	268	48	no	—
503	C₂×D₄	—	67	48	no	—
504	C₂×D₄	—	67	16	no	—
505	C₂×D₄	—	67	8	no	—
506	C₂×D₄	—	67	24	no	—
507	C₂×D₄	—	67	4	no	—
508	C₂×D₄	—	67	12	no	—
509	C₂×D₄	—	134	48	no	—
510	C₂×D₄	—	134	96	no	—
511	C₂×D₄	—	134	24	no	—
512	C₂×D₄	C₂×C₂²⋊D₆₇	1	24	yes	complemented
513	C₂×D₄	C₂³×D₆₇	1	24	yes	—
514	C₂×D₄	C₂³×D₆₇	1	12	yes	—
515	C₂×D₄	C₂³×D₆₇	1	12	yes	—
516	C₂²×C₄	—	2	12	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	12	no	—
519	C₂²×C₄	—	2	12	no	—
520	C₂²×C₄	—	2	12	no	—
521	C₂²×C₄	—	2	48	no	—
522	C₂²×C₄	—	2	48	no	—
523	C₂²×C₄	—	67	24	no	—
524	C₂²×C₄	—	67	12	no	—
525	C₂²×C₄	—	67	24	no	—
526	C₂²×C₄	—	67	8	no	—
527	C₂²×C₄	—	134	48	no	—
528	C₂²×C₄	C₂×C₂²⋊D₆₇	1	24	yes	complemented
529	C₂²×C₄	C₂³×D₆₇	1	12	yes	—
530	C₂²×C₄	C₂³×D₆₇	1	12	yes	—
531	C₂²×C₄	C₂³×D₆₇	1	12	yes	—
532	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
533	C₂²×C₄	C₂³×D₆₇	1	6	yes	—
534	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
535	C₂²×C₄	C₂³×D₆₇	1	3	yes	—
536	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
537	C₂²×C₄	C₂³×D₆₇	1	6	yes	—
538	C₂²×C₄	C₂³×D₆₇	1	6	yes	—
539	C₂²×C₄	C₂³×D₆₇	1	3	yes	—
540	C₂²×C₄	C₂³×D₆₇	1	6	yes	—
541	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
542	C₄⋊C₄	—	67	8	no	—
543	C₄⋊C₄	—	67	16	no	—
544	C₄⋊C₄	—	67	24	no	—
545	C₄⋊C₄	—	67	48	no	—
546	C₂²⋊C₄	—	67	8	no	—
547	C₂²⋊C₄	—	67	16	no	—
548	C₂²⋊C₄	—	67	24	no	—
549	C₂²⋊C₄	—	67	48	no	—
550	C₂²⋊C₄	—	67	16	no	—
551	C₂²⋊C₄	—	67	48	no	—
552	C₄²	—	67	24	no	—
553	C₄²	—	67	8	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	4	no	—
556	C₂³	—	2	24	no	—
557	C₂³	—	2	6	no	—
558	C₂³	—	2	24	no	—
559	C₂³	—	4	6	no	—
560	C₂³	—	4	12	no	—
561	C₂³	—	4	6	no	—
562	C₂³	—	4	48	no	—
563	C₂³	—	268	24	no	—
564	C₂³	—	67	8	no	—
565	C₂³	—	134	24	no	—
566	C₂³	C₂²×C₂²⋊D₆₇	1	12	yes	—
567	C₂³	C₂⁴×D₆₇	1	6	yes	—
568	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
569	C₂³	C₂⁴×D₆₇	1	6	yes	—
570	C₂³	C₂⁴×D₆₇	1	2	yes	—
571	Q₈	—	2	24	no	—
572	Q₈	—	134	8	no	—
573	Q₈	—	134	24	no	—
574	Q₈	C₂²×C₂²⋊D₆₇	1	16	yes	—
575	D₄	—	2	48	no	—
576	D₄	—	2	24	no	—
577	D₄	—	268	48	no	—
578	D₄	—	134	16	no	—
579	D₄	—	134	48	no	—
580	D₄	—	134	32	no	—
581	D₄	—	134	8	no	—
582	D₄	—	134	24	no	—
583	D₄	C₂²×C₂²⋊D₆₇	1	48	yes	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	6	no	—
586	C₂×C₄	—	2	24	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	24	no	—
590	C₂×C₄	—	2	24	no	—
591	C₂×C₄	—	2	12	no	—
592	C₂×C₄	—	2	12	no	—
593	C₂×C₄	—	268	24	no	—
594	C₂×C₄	—	67	16	no	—
595	C₂×C₄	—	67	8	no	—
596	C₂×C₄	—	134	24	no	—
597	C₂×C₄	—	134	16	no	—
598	C₂×C₄	—	134	48	no	—
599	C₂×C₄	C₂²×C₂²⋊D₆₇	1	4	yes	—
600	C₂×C₄	C₂²×C₂²⋊D₆₇	1	24	yes	—
601	C₂×C₄	C₂²×C₂²⋊D₆₇	1	12	yes	—
602	C₂×C₄	C₂²×C₂²⋊D₆₇	1	24	yes	—
603	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
604	C₂×C₄	C₂⁴×D₆₇	1	6	yes	—
605	C₂×C₄	C₂⁴×D₆₇	1	6	yes	—
606	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
607	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
608	C₂²	—	2	8	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	12	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	6	no	—
614	C₂²	—	2	12	no	—
615	C₂²	—	4	12	no	—
616	C₂²	—	4	48	no	—
617	C₂²	—	4	12	no	—
618	C₂²	—	536	24	no	—
619	C₂²	—	134	8	no	—
620	C₂²	—	134	16	no	—
621	C₂²	C₂³×C₂²⋊D₆₇	1	2	yes	—
622	C₂²	C₂³×C₂²⋊D₆₇	1	12	yes	—
623	C₂²	#16864232	1	4	yes	complemented
624	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
625	C₄	—	2	2	no	—
626	C₄	—	2	6	no	—
627	C₄	—	134	8	no	—
628	C₄	—	134	16	no	—
629	C₄	C₂³×C₂²⋊D₆₇	1	2	yes	—
630	C₄	C₂³×C₂²⋊D₆₇	1	2	yes	—
631	C₄	C₂³×C₂²⋊D₆₇	1	12	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	2	4	no	—
634	C₂	—	2	12	no	—
635	C₂	—	4	6	no	—
636	C₂	—	268	8	no	—
637	C₂	C₂⁴×C₂²⋊D₆₇	1	1	yes	characteristic
638	C₂	C₂×#16864232	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₆₇
commutator, socle, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂³×#41×C₆₇	C₂
hypercenter	C₂³×#41	D₆₇
hypocenter	C₆₇	#62811
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#16864232	C₂	semidirect
2. #22573889	C₂	semidirect
3. #22573878	C₂	semidirect
4. #22573867	C₂	semidirect
5. #22573860	C₂	semidirect
6. #22573853	C₂	semidirect
7. #22573844	C₂	semidirect
8. #41×C₂²⋊D₆₇	C₂	semidirect
9. #22573538	C₂	semidirect
10. C₂×#16863907	C₂	semidirect
11. #22573412	C₂	semidirect
12. C₂³×#41×C₆₇	C₂	semidirect
14. C₂×#14524091	C₂²	semidirect
15. C₂×#14524090	C₂²	semidirect
16. C₂×#14524089	C₂²	semidirect
17. C₂×#14524088	C₂²	semidirect
18. C₂²×#11761628	C₂²	semidirect
19. C₂×#41×D₆₇	C₂²	semidirect
20. #16864065	C₂²	semidirect
21. Q₈×C₂²⋊D₆₇	C₂²	semidirect
22. #16864057	C₂²	semidirect
23. #16864053	C₂²	semidirect
24. #16864045	C₂²	semidirect
25. #16864040	C₂²	semidirect
26. #16864034	C₂²	semidirect
27. D₄×C₂²⋊D₆₇	C₂²	semidirect
28. #16863974	C₂²	semidirect
29. #16863970	C₂²	semidirect
30. #16863967	C₂²	semidirect
31. #16863963	C₂²	semidirect
32. #16863960	C₂²	semidirect
33. #16863955	C₂²	semidirect
34. #16863942	C₂²	semidirect
35. #16863907	C₂²	semidirect
36. #16863907	C₂²	semidirect
37. #16863907	C₂²	semidirect
38. #16863907	C₂²	semidirect
39. #16863907	C₂²	semidirect
40. #16863907	C₂²	semidirect
41. #16863903	C₂²	semidirect
42. C₂×#14524026	C₂²	semidirect
43. C₂×#14524022	C₂²	semidirect
44. C₂×#14524017	C₂²	semidirect
45. C₂×#14524012	C₂²	semidirect
46. #16863879	C₂²	semidirect
47. #16863874	C₂²	semidirect
48. #16863871	C₂²	semidirect
49. #41×Dic₆₇	C₂²	semidirect
50. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
51. C₂×#14524002	C₂²	semidirect
54. C₂²×#41×C₆₇	C₂²	semidirect
55. C₂²×#41×C₆₇	C₂²	semidirect
56. C₂²×#41×C₆₇	C₂²	semidirect
57. C₂²×#41×C₆₇	C₂²	semidirect
58. C₂²×#41×C₆₇	C₂²	semidirect
59. C₂³×Q₈×C₆₇	C₂²	semidirect
60. C₂³×D₄×C₆₇	C₂²	semidirect
61. C₂⁴×C₄×C₆₇	C₂²	semidirect
66. C₂×#11761629	C₂³	semidirect
70. C₂×#11761628	C₂³	semidirect
71. C₂×#11761628	C₂³	semidirect
72. C₂×#11761627	C₂³	semidirect
74. C₂²×Dic₁₃₄	C₂³	semidirect
75. C₂×Q₈×D₆₇	C₂³	semidirect
76. C₂²×D₂₆₈	C₂³	semidirect
79. C₂×D₄×D₆₇	C₂³	semidirect
80. C₂²×C₄×D₆₇	C₂³	semidirect
81. #14524041	C₂³	semidirect
82. #14524039	C₂³	semidirect
83. #14524032	C₂³	semidirect
84. #14524030	C₂³	semidirect
87. #14524026	C₂³	semidirect
88. #14524024	C₂³	semidirect
91. #14524022	C₂³	semidirect
92. #14524022	C₂³	semidirect
93. #14524019	C₂³	semidirect
96. #14524017	C₂³	semidirect
97. #14524017	C₂³	semidirect
98. #14524015	C₂³	semidirect
99. #14524014	C₂³	semidirect
103. #14524011	C₂³	semidirect
104. Q₈×Dic₆₇	C₂³	semidirect
105. D₄×Dic₆₇	C₂³	semidirect
108. C₄×C₂²⋊D₆₇	C₂³	semidirect
109. C₄×C₂²⋊D₆₇	C₂³	semidirect
112. #14524002	C₂³	semidirect
113. #14524002	C₂³	semidirect
114. C₂×C₄⋊Dic₆₇	C₂³	semidirect
115. C₂×Dic₆₇⋊C₄	C₂³	semidirect
118. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
119. C₂×C₄×Dic₆₇	C₂³	semidirect
126. C₂×#41×C₆₇	D₄	semidirect
199. #41×C₆₇	C₂×D₄	semidirect
200. #41×C₆₇	C₂×D₄	semidirect
203. C₂×Q₈×C₆₇	C₂×D₄	semidirect
209. C₂×D₄×C₆₇	C₂×D₄	semidirect
220. C₂²×C₄×C₆₇	C₂×D₄	semidirect
300. C₂²×C₆₇	#585	semidirect
321. C₂³×#41	D₆₇	semidirect
332. C₆₇	#62811	semidirect
342. C₂²×#41	C₂×D₆₇	semidirect
343. C₂²×#41	C₂×D₆₇	semidirect
344. C₂²×#41	C₂×D₆₇	semidirect
345. C₂²×#41	C₂×D₆₇	semidirect
346. C₂²×#41	C₂×D₆₇	semidirect
347. C₂³×Q₈	C₂×D₆₇	semidirect
348. C₂³×D₄	C₂×D₆₇	semidirect
349. C₂⁴×C₄	C₂×D₆₇	semidirect
400. C₂×#41	C₂²⋊D₆₇	semidirect
488. #41	C₂×C₂²⋊D₆₇	semidirect
489. #41	C₂×C₂²⋊D₆₇	semidirect
496. C₂×Q₈	C₂×C₂²⋊D₆₇	semidirect
512. C₂×D₄	C₂×C₂²⋊D₆₇	semidirect
528. C₂²×C₄	C₂×C₂²⋊D₆₇	semidirect
623. C₂²	#16864232	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16864232	2
#22573889	2
#22573878	2
#22573867	2
#22573860	2
#22573853	2
#22573844	2
#41×C₂²⋊D₆₇	2
#22573538	2
C₂×#16863907	2
#22573412	2
C₂³×#41×C₆₇	2
#62811	67