Subgroups — #30854392

Order 17152.

1006 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863516	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863511	C₂	1	1	yes	maximal, characteristic
3	#22569007	C₂	1	1	yes	maximal, characteristic
4	C₄×#14524049	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560116	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560094	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560089	C₂	1	1	yes	maximal, characteristic, complemented
8	#22560055	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560051	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560048	C₂	1	1	yes	maximal, characteristic, complemented
11	#22560044	C₂	1	1	yes	maximal, characteristic, complemented
12	#22560022	C₂	1	1	yes	maximal, characteristic, complemented
13	#22560019	C₂	1	1	yes	maximal, characteristic, complemented
14	#22559895	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#131×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14524063	C₂²	1	1	yes	characteristic
17	C₂×#14524049	C₂²	1	1	yes	characteristic
18	C₂×#14524049	C₂²	1	1	yes	characteristic
19	C₄×#11761628	C₂²	1	1	yes	characteristic
20	#16863516	C₄	1	8	yes	complemented
21	#16863511	C₄	1	8	yes	complemented
22	#16863506	C₄	1	2	yes	complemented
23	#16863501	C₄	1	2	yes	complemented
24	#16863496	C₄	1	2	yes	complemented
25	#16863494	C₄	1	2	yes	complemented
26	C₂×#14523978	C₂²	1	1	yes	characteristic
27	C₂×#14523978	C₂²	1	1	yes	characteristic
28	#16863432	C₂²	1	1	yes	characteristic
29	C₂×#14523970	C₂²	1	1	yes	characteristic
30	C₂×#14523970	C₂²	1	1	yes	characteristic
31	C₂×#14523969	C₂²	1	1	yes	characteristic
32	C₂×#14523969	C₂²	1	1	yes	characteristic
33	#16863392	C₂²	1	1	yes	characteristic
34	#16863390	C₂²	1	1	yes	characteristic
35	#16863351	C₂²	1	1	yes	characteristic
36	#16863351	C₂²	1	1	yes	characteristic
37	#16863350	—	2	1	no	—
38	#16863350	—	2	1	no	—
39	C₄×#11761612	C₂²	1	1	yes	characteristic
40	C₄×#11761611	—	2	1	no	—
41	C₂×#14523954	C₂²	1	1	yes	characteristic
42	C₂×#14523953	C₂²	1	1	yes	characteristic
43	C₂×#14523953	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₆₇	—	2	1	no	—
47	#16863242	C₂²	1	1	yes	characteristic
48	#16863160	C₂²	1	1	yes	characteristic
49	#16863160	C₂²	1	1	yes	characteristic
50	#16863157	C₂²	1	1	yes	characteristic
51	#16863157	C₂²	1	1	yes	characteristic
52	#16863155	C₂²	1	1	yes	characteristic
53	#16863155	C₂²	1	1	yes	characteristic
54	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
56	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
57	#405×C₆₇	—	2	1	no	—
58	#405×C₆₇	—	2	1	no	—
59	#405×C₆₇	C₂²	1	1	yes	characteristic
60	#405×C₆₇	C₂²	1	1	yes	characteristic
61	C₄×M₁₆×C₆₇	—	2	1	no	—
62	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×C₄×C₈×C₆₇	—	2	1	no	—
64	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
65	C₂×#11761628	C₂³	1	1	yes	characteristic
66	#14524063	C₂×C₄	1	4	yes	—
67	#14524063	C₂×C₄	1	4	yes	—
68	C₂×#11761618	C₂×C₄	1	1	yes	characteristic
69	C₂×#11761616	C₂×C₄	1	1	yes	characteristic
70	C₂×#11761615	C₂×C₄	1	1	yes	characteristic
71	C₂×#11761613	C₂×C₄	1	1	yes	characteristic
72	#14524049	—	2	2	no	—
73	#14524049	—	2	2	no	—
74	#14524049	C₂×C₄	1	4	yes	complemented
75	#14524049	C₂×C₄	1	4	yes	complemented
76	C₂×#11761612	C₂³	1	1	yes	characteristic
77	C₂×#11761612	C₂³	1	1	yes	characteristic
78	C₂×#11761611	—	2	1	no	—
79	C₂×#11761611	—	2	1	no	—
80	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
82	C₂×C₈×D₆₇	—	2	1	no	—
83	C₂×C₈×D₆₇	—	2	1	no	—
84	C₄×Dic₁₃₄	C₂×C₄	1	2	yes	—
85	C₄×D₂₆₈	C₂×C₄	1	2	yes	—
86	C₄×C₂²⋊D₆₇	—	2	2	no	—
87	#14524002	C₂³	1	1	yes	characteristic
88	#14524000	—	2	1	no	—
89	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
90	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
91	C₄²×D₆₇	—	2	1	no	—
92	#14523978	C₂×C₄	1	4	yes	complemented
93	#14523978	C₂×C₄	1	4	yes	complemented
94	#14523976	C₂×C₄	1	2	yes	—
95	#14523974	C₂×C₄	1	2	yes	—
96	#14523970	C₂×C₄	1	4	yes	complemented
97	#14523970	C₂×C₄	1	4	yes	complemented
98	#14523969	C₂×C₄	1	4	yes	complemented
99	#14523969	C₂×C₄	1	4	yes	complemented
100	#14523967	C₂×C₄	1	2	yes	—
101	#14523966	C₂×C₄	1	2	yes	—
102	#14523964	C₂×C₄	1	2	yes	—
103	#14523963	C₂×C₄	1	2	yes	—
104	#14523954	—	2	1	no	—
105	#14523954	C₂×C₄	1	2	yes	—
106	#14523954	C₂×C₄	1	2	yes	—
107	#14523953	—	2	1	no	—
108	#14523953	—	2	1	no	—
109	#14523953	—	2	2	no	—
110	#14523953	C₂×C₄	1	4	yes	complemented
111	C₄×C₆₇⋊C₈	—	2	1	no	—
112	C₈×Dic₆₇	—	2	1	no	—
113	C₈×Dic₆₇	—	2	1	no	—
114	C₈×Dic₆₇	—	2	2	no	—
115	C₈×Dic₆₇	C₂×C₄	1	4	yes	complemented
116	C₆₇⋊#95	—	2	2	no	—
117	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
118	#131×C₆₇	—	2	2	no	—
119	#131×C₆₇	—	2	2	no	—
120	#131×C₆₇	C₂×C₄	1	4	yes	complemented
121	#131×C₆₇	C₂×C₄	1	4	yes	complemented
122	C₂×M₁₆×C₆₇	—	2	1	no	—
123	C₂×M₁₆×C₆₇	—	2	1	no	—
124	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
125	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₆₇	—	2	1	no	—
127	C₂²×C₈×C₆₇	—	2	1	no	—
128	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
130	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
131	C₄×D₄×C₆₇	—	2	2	no	—
132	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
133	#117×C₆₇	—	2	1	no	—
134	#117×C₆₇	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₆₇	—	2	1	no	—
136	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
137	#97×C₆₇	—	2	1	no	—
138	#97×C₆₇	—	2	1	no	—
139	#97×C₆₇	—	2	1	no	—
140	C₄×C₈×C₆₇	—	2	1	no	—
141	C₄×C₈×C₆₇	—	2	1	no	—
142	C₄×C₈×C₆₇	—	2	1	no	—
143	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
144	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
145	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
146	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
147	#11761628	—	2	1	no	—
148	#11761628	—	2	1	no	—
149	#11761628	C₂²×C₄	1	2	yes	—
150	#11761628	C₂²×C₄	1	2	yes	—
151	C₂×Dic₁₃₄	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₂₆₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₂²⋊D₆₇	—	2	1	no	—
154	C₂²×Dic₆₇	—	2	1	no	—
155	C₂²×Dic₆₇	—	2	1	no	—
156	C₂×C₄×D₆₇	—	2	1	no	—
157	C₂×C₄×D₆₇	—	2	2	no	—
158	#11761618	C₄²	1	4	yes	—
159	#11761616	C₄²	1	4	yes	—
160	#11761615	C₄²	1	4	yes	—
161	#11761613	C₄²	1	4	yes	—
162	#11761612	—	2	1	no	—
163	#11761612	—	2	1	no	—
164	#11761612	C₂²×C₄	1	2	yes	—
165	#11761612	C₂²×C₄	1	2	yes	—
166	#11761611	—	2	4	no	—
167	#11761611	—	2	4	no	—
168	C₂×C₆₇⋊C₈	—	2	1	no	—
169	C₂×C₆₇⋊C₈	—	2	1	no	—
170	C₂×C₆₇⋊C₈	—	2	1	no	—
171	C₂×C₆₇⋊C₈	—	2	1	no	—
172	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
173	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
174	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
175	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
177	C₈×D₆₇	—	2	4	no	—
178	C₈×D₆₇	—	2	4	no	—
179	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
180	Dic₆₇⋊C₄	—	2	2	no	—
181	C₂²⋊Dic₆₇	—	2	1	no	—
182	(C₂×D₆₇)⋊C₄	—	2	2	no	—
183	C₄×Dic₆₇	—	2	2	no	—
184	C₄×Dic₆₇	—	2	1	no	—
185	C₄×Dic₆₇	—	2	1	no	—
186	C₄×Dic₆₇	—	2	1	no	—
187	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
188	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
189	#41×C₆₇	—	2	1	no	—
190	#41×C₆₇	—	2	1	no	—
191	#41×C₆₇	C₂²×C₄	1	2	yes	—
192	#41×C₆₇	C₂²×C₄	1	2	yes	—
193	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
194	C₂×D₄×C₆₇	—	2	1	no	—
195	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	—	2	1	no	—
197	C₂²×C₄×C₆₇	—	2	2	no	—
198	C₂²×C₄×C₆₇	#41	1	2	yes	—
199	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
200	M₁₆×C₆₇	—	2	1	no	—
201	M₁₆×C₆₇	—	2	1	no	—
202	M₁₆×C₆₇	—	2	4	no	—
203	M₁₆×C₆₇	—	2	4	no	—
204	M₁₆×C₆₇	C₂²×C₄	1	2	yes	—
205	M₁₆×C₆₇	C₂²×C₄	1	2	yes	—
206	C₂×C₈×C₆₇	—	2	1	no	—
207	C₂×C₈×C₆₇	—	2	1	no	—
208	C₂×C₈×C₆₇	—	2	4	no	—
209	C₂×C₈×C₆₇	—	2	4	no	—
210	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
211	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
212	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
213	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
214	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
215	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
216	C₂×C₈×C₆₇	#41	1	2	yes	—
217	C₂×C₈×C₆₇	#41	1	2	yes	—
218	C₄⋊C₄×C₆₇	—	2	2	no	—
219	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
220	C₂²⋊C₄×C₆₇	—	2	1	no	—
221	C₂²⋊C₄×C₆₇	—	2	2	no	—
222	C₄²×C₆₇	—	2	2	no	—
223	C₄²×C₆₇	—	2	1	no	—
224	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
225	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₆₇	—	2	1	no	—
228	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
229	C₂²×D₆₇	—	2	1	no	—
230	Q₈×C₆₇	—	2	1	no	—
231	Q₈×C₆₇	C₂×C₄²	1	2	yes	—
232	D₄×C₆₇	—	2	2	no	—
233	D₄×C₆₇	—	2	2	no	—
234	D₄×C₆₇	—	2	1	no	—
235	D₄×C₆₇	C₂×C₄²	1	2	yes	—
236	C₂×C₄×C₆₇	—	2	1	no	—
237	C₂×C₄×C₆₇	—	2	2	no	—
238	C₂×C₄×C₆₇	—	2	2	no	—
239	C₂×C₄×C₆₇	—	2	2	no	—
240	C₂×C₄×C₆₇	—	4	2	no	—
241	C₂×C₄×C₆₇	—	4	4	no	—
242	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
243	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
244	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
250	C₂²⋊D₆₇	—	2	2	no	—
251	C₂²⋊D₆₇	—	2	2	no	—
252	C₂×Dic₆₇	—	2	1	no	—
253	C₂×Dic₆₇	—	2	2	no	—
254	C₂×Dic₆₇	—	2	2	no	—
255	C₂×Dic₆₇	—	2	2	no	—
256	C₂×Dic₆₇	—	4	2	no	—
257	C₂×Dic₆₇	—	4	2	no	—
258	D₂₆₈	—	2	1	no	—
259	D₂₆₈	C₂×C₄²	1	2	yes	—
260	C₄×D₆₇	—	2	2	no	—
261	C₄×D₆₇	—	2	2	no	—
262	C₄×D₆₇	—	4	4	no	—
263	Dic₁₃₄	—	2	1	no	—
264	Dic₁₃₄	C₂×C₄²	1	2	yes	—
265	C₈×C₆₇	—	2	2	no	—
266	C₈×C₆₇	—	2	2	no	—
267	C₈×C₆₇	C₄×D₄	1	2	yes	—
268	C₈×C₆₇	C₄×D₄	1	2	yes	—
269	C₈×C₆₇	C₄×D₄	1	2	yes	—
270	C₈×C₆₇	C₄×D₄	1	2	yes	—
271	C₆₇⋊C₈	—	2	2	no	—
272	C₆₇⋊C₈	—	2	2	no	—
273	C₆₇⋊C₈	—	2	2	no	—
274	C₆₇⋊C₈	C₂×C₄²	1	2	yes	—
275	C₆₇⋊C₈	C₂×C₄²	1	2	yes	—
276	C₂²×C₆₇	—	2	2	no	—
277	C₂²×C₆₇	—	2	2	no	—
278	C₂²×C₆₇	—	4	2	no	—
279	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
280	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
281	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
282	C₂×D₆₇	—	2	2	no	—
283	C₂×D₆₇	—	4	2	no	—
284	C₄×C₆₇	—	2	2	no	—
285	C₄×C₆₇	—	2	2	no	—
286	C₄×C₆₇	—	2	2	no	—
287	C₄×C₆₇	—	4	2	no	—
288	C₄×C₆₇	C₂²×C₄²	1	1	yes	characteristic
289	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
290	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
291	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
292	Dic₆₇	—	2	2	no	—
293	Dic₆₇	—	4	2	no	—
294	Dic₆₇	—	4	2	no	—
295	Dic₆₇	—	4	2	no	—
296	#20510	—	67	1	no	maximal, Sylow
297	C₂×C₆₇	—	2	1	no	—
298	C₂×C₆₇	—	2	1	no	—
299	C₂×C₆₇	—	4	2	no	—
300	C₂×C₆₇	C₄²×D₄	1	1	yes	characteristic
301	C₂×C₆₇	#2955	1	2	yes	—
302	D₆₇	—	4	2	no	—
303	C₂×#444	—	67	1	no	—
304	C₂×#443	—	67	1	no	—
305	#2943	—	67	1	no	—
306	C₄×#131	—	67	1	no	—
307	C₄×#131	D₆₇	1	1	yes	characteristic, complemented
308	#1778	—	67	1	no	—
309	#1773	—	67	1	no	—
310	#1772	—	67	1	no	—
311	#1765	—	67	1	no	—
312	#1765	—	67	1	no	—
313	#1764	—	67	1	no	—
314	#1764	—	67	1	no	—
315	#1759	—	67	1	no	—
316	#1759	—	67	1	no	—
317	#1726	—	67	1	no	—
318	C₆₇	#20510	1	1	yes	characteristic, complemented, Sylow
319	C₂×#135	—	67	1	no	—
320	C₂×#131	—	67	1	no	—
321	C₂×#131	—	67	1	no	—
322	C₂×#131	C₂×D₆₇	1	1	yes	characteristic
323	C₂×#131	C₂×D₆₇	1	1	yes	characteristic
324	C₄×#41	—	67	1	no	—
325	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
326	#444	—	67	8	no	—
327	#443	—	67	8	no	—
328	#442	—	67	2	no	—
329	#441	—	67	2	no	—
330	#440	—	67	2	no	—
331	#440	—	67	2	no	—
332	C₂×#108	—	67	1	no	—
333	C₂×#108	—	67	1	no	—
334	#427	—	67	1	no	—
335	C₂×#104	—	67	1	no	—
336	C₂×#104	—	67	1	no	—
337	C₂×#104	—	67	1	no	—
338	C₂×#104	—	67	1	no	—
339	#416	—	67	1	no	—
340	#416	—	67	1	no	—
341	#405	—	2	1	no	—
342	#405	—	2	1	no	—
343	#405	—	67	1	no	—
344	#405	—	67	1	no	—
345	#405	—	134	1	no	—
346	#405	—	134	1	no	—
347	#405	C₂×D₆₇	1	1	yes	characteristic
348	#405	C₂×D₆₇	1	1	yes	characteristic
349	C₄×M₁₆	—	2	1	no	—
350	C₄×M₁₆	—	67	1	no	—
351	C₄×M₁₆	—	134	1	no	—
352	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic
353	C₂×#97	—	67	1	no	—
354	C₂×#97	—	67	1	no	—
355	C₂×#97	—	67	1	no	—
356	C₂×C₄×C₈	—	2	1	no	—
357	C₂×C₄×C₈	—	67	1	no	—
358	C₂×C₄×C₈	—	67	1	no	—
359	C₂×C₄×C₈	—	134	1	no	—
360	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
361	#376	—	67	1	no	—
362	#341	—	67	1	no	—
363	#341	—	67	1	no	—
364	#339	—	67	1	no	—
365	#339	—	67	1	no	—
366	#339	—	67	1	no	—
367	#339	—	67	1	no	—
368	C₂×#41	—	67	1	no	—
369	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
370	#135	—	67	4	no	—
371	#135	—	67	4	no	—
372	C₂×Q₁₆	—	67	1	no	—
373	C₂×SD₁₆	—	67	1	no	—
374	C₂×SD₁₆	—	67	1	no	—
375	C₂×D₈	—	67	1	no	—
376	#131	—	2	2	no	—
377	#131	—	2	2	no	—
378	#131	—	67	4	no	—
379	#131	—	67	4	no	—
380	#131	—	134	2	no	—
381	#131	—	134	2	no	—
382	#131	C₄×D₆₇	1	4	yes	complemented
383	#131	C₄×D₆₇	1	4	yes	complemented
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	67	1	no	—
387	C₂×M₁₆	—	67	1	no	—
388	C₂×M₁₆	—	134	1	no	—
389	C₂×M₁₆	—	134	1	no	—
390	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
391	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	—	67	1	no	—
395	C₂²×C₈	—	67	1	no	—
396	C₂²×C₈	—	134	1	no	—
397	C₂²×C₈	—	134	1	no	—
398	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
399	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
400	C₄×Q₈	—	67	2	no	—
401	C₄×Q₈	C₄×D₆₇	1	2	yes	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	67	2	no	—
404	C₄×D₄	—	134	2	no	—
405	C₄×D₄	C₄×D₆₇	1	2	yes	—
406	#117	—	2	1	no	—
407	#117	—	67	1	no	—
408	#117	—	134	1	no	—
409	#117	C₂²×D₆₇	1	1	yes	characteristic
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	—	67	1	no	—
412	C₂×C₄²	—	67	1	no	—
413	C₂×C₄²	—	134	1	no	—
414	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
415	#108	—	67	4	no	—
416	#108	—	67	4	no	—
417	#107	—	67	2	no	—
418	#106	—	67	2	no	—
419	#104	—	67	4	no	—
420	#104	—	67	4	no	—
421	#104	—	67	4	no	—
422	#104	—	67	4	no	—
423	#103	—	67	2	no	—
424	#103	—	67	2	no	—
425	#102	—	67	2	no	—
426	#102	—	67	2	no	—
427	#97	—	2	1	no	—
428	#97	—	2	1	no	—
429	#97	—	2	1	no	—
430	#97	—	67	4	no	—
431	#97	—	67	2	no	—
432	#97	—	67	2	no	—
433	#97	—	134	1	no	—
434	#97	—	134	1	no	—
435	#97	—	134	2	no	—
436	#97	—	134	1	no	—
437	C₄×C₈	—	2	1	no	—
438	C₄×C₈	—	2	1	no	—
439	C₄×C₈	—	2	1	no	—
440	C₄×C₈	—	67	4	no	—
441	C₄×C₈	—	134	1	no	—
442	C₄×C₈	—	134	1	no	—
443	C₄×C₈	—	134	2	no	—
444	C₄×C₈	—	134	1	no	—
445	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
446	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
447	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
448	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
449	#95	—	134	2	no	—
450	#41	—	2	1	no	—
451	#41	—	2	1	no	—
452	#41	—	67	2	no	—
453	#41	—	67	2	no	—
454	#41	—	134	1	no	—
455	#41	—	134	1	no	—
456	#41	C₂×C₄×D₆₇	1	2	yes	—
457	#41	C₂×C₄×D₆₇	1	2	yes	—
458	C₂×Q₈	—	67	1	no	—
459	C₂×Q₈	C₂×C₄×D₆₇	1	1	yes	characteristic
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	67	1	no	—
462	C₂×D₄	—	134	1	no	—
463	C₂×D₄	C₂×C₄×D₆₇	1	1	yes	characteristic
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	134	1	no	—
467	C₂²×C₄	—	134	1	no	—
468	C₂²×C₄	—	134	2	no	—
469	C₂²×C₄	—	134	1	no	—
470	C₂²×C₄	#11761628	1	2	yes	—
471	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
472	Q₁₆	—	67	4	no	—
473	SD₁₆	—	67	4	no	—
474	SD₁₆	—	67	4	no	—
475	D₈	—	67	4	no	—
476	M₁₆	—	2	1	no	—
477	M₁₆	—	2	1	no	—
478	M₁₆	—	2	4	no	—
479	M₁₆	—	2	4	no	—
480	M₁₆	—	67	2	no	—
481	M₁₆	—	67	2	no	—
482	M₁₆	—	134	1	no	—
483	M₁₆	—	134	1	no	—
484	M₁₆	—	134	4	no	—
485	M₁₆	—	134	4	no	—
486	M₁₆	C₂×C₄×D₆₇	1	2	yes	—
487	M₁₆	C₂×C₄×D₆₇	1	2	yes	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	4	no	—
491	C₂×C₈	—	2	4	no	—
492	C₂×C₈	—	67	2	no	—
493	C₂×C₈	—	67	1	no	—
494	C₂×C₈	—	67	1	no	—
495	C₂×C₈	—	67	2	no	—
496	C₂×C₈	—	67	2	no	—
497	C₂×C₈	—	134	1	no	—
498	C₂×C₈	—	134	1	no	—
499	C₂×C₈	—	134	1	no	—
500	C₂×C₈	—	134	1	no	—
501	C₂×C₈	—	134	4	no	—
502	C₂×C₈	—	134	4	no	—
503	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
504	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
505	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
506	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
507	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
508	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
509	C₂×C₈	#11761628	1	2	yes	—
510	C₂×C₈	#11761628	1	2	yes	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	67	2	no	—
513	C₄⋊C₄	—	134	2	no	—
514	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	134	1	no	—
518	C₂²⋊C₄	—	134	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	67	2	no	—
522	C₄²	—	67	2	no	—
523	C₄²	—	134	2	no	—
524	C₄²	—	134	1	no	—
525	C₄²	—	134	1	no	—
526	C₄²	—	134	1	no	—
527	C₄²	C₂×C₄×D₆₇	1	2	yes	—
528	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
529	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
530	C₂³	—	2	1	no	—
531	C₂³	—	134	1	no	—
532	C₂³	C₂×#11761628	1	1	yes	characteristic
533	Q₈	—	2	1	no	—
534	Q₈	—	67	2	no	—
535	Q₈	—	134	1	no	—
536	Q₈	C₄²×D₆₇	1	2	yes	—
537	D₄	—	2	2	no	—
538	D₄	—	2	2	no	—
539	D₄	—	2	1	no	—
540	D₄	—	67	2	no	—
541	D₄	—	134	2	no	—
542	D₄	—	134	2	no	—
543	D₄	—	134	1	no	—
544	D₄	C₄²×D₆₇	1	2	yes	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	268	4	no	—
552	C₂×C₄	—	268	2	no	—
553	C₂×C₄	—	268	2	no	—
554	C₂×C₄	—	134	2	no	—
555	C₂×C₄	—	134	2	no	—
556	C₂×C₄	—	134	2	no	—
557	C₂×C₄	—	134	1	no	—
558	C₂×C₄	—	134	2	no	—
559	C₂×C₄	—	134	2	no	—
560	C₂×C₄	C₄×C₂²⋊D₆₇	1	2	yes	—
561	C₂×C₄	C₄×C₂²⋊D₆₇	1	2	yes	—
562	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
563	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
564	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
565	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
566	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
567	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
568	C₈	—	2	2	no	—
569	C₈	—	2	2	no	—
570	C₈	—	67	2	no	—
571	C₈	—	67	2	no	—
572	C₈	—	134	2	no	—
573	C₈	—	134	2	no	—
574	C₈	—	134	2	no	—
575	C₈	C₄×C₂²⋊D₆₇	1	2	yes	—
576	C₈	C₄×C₂²⋊D₆₇	1	2	yes	—
577	C₈	C₄×C₂²⋊D₆₇	1	2	yes	—
578	C₈	C₄×C₂²⋊D₆₇	1	2	yes	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	268	2	no	—
583	C₂²	—	134	2	no	—
584	C₂²	C₂×C₄×C₂²⋊D₆₇	1	1	yes	characteristic
585	C₂²	C₄×#11761628	1	1	yes	characteristic
586	C₂²	C₄×#11761628	1	1	yes	characteristic
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	4	2	no	—
591	C₄	—	268	2	no	—
592	C₄	—	268	2	no	—
593	C₄	—	268	2	no	—
594	C₄	—	134	2	no	—
595	C₄	C₂×C₄²×D₆₇	1	1	yes	characteristic
596	C₄	C₂×C₄×C₂²⋊D₆₇	1	1	yes	characteristic
597	C₄	C₂×C₄×C₂²⋊D₆₇	1	1	yes	characteristic
598	C₄	C₄×#11761628	1	1	yes	characteristic
599	C₂	—	2	1	no	—
600	C₂	—	2	1	no	—
601	C₂	—	4	2	no	—
602	C₂	—	268	2	no	—
603	C₂	C₄²×C₂²⋊D₆₇	1	1	yes	characteristic
604	C₂	#22569110	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₆₇
commutator	C₄×C₆₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₄×#131×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#14524063	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₄×#131	D₆₇
hypocenter	C₆₇	#20510
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
4. C₄×#14524049	C₂	semidirect
5. #22560116	C₂	semidirect
6. #22560094	C₂	semidirect
7. #22560089	C₂	semidirect
8. #22560055	C₂	semidirect
9. #22560051	C₂	semidirect
10. #22560048	C₂	semidirect
11. #22560044	C₂	semidirect
12. #22560022	C₂	semidirect
13. #22560019	C₂	semidirect
14. #22559895	C₂	semidirect
15. C₄×#131×C₆₇	C₂	semidirect
20. #16863516	C₄	semidirect
21. #16863511	C₄	semidirect
22. #16863506	C₄	semidirect
23. #16863501	C₄	semidirect
24. #16863496	C₄	semidirect
25. #16863494	C₄	semidirect
74. #14524049	C₂×C₄	semidirect
75. #14524049	C₂×C₄	semidirect
92. #14523978	C₂×C₄	semidirect
93. #14523978	C₂×C₄	semidirect
96. #14523970	C₂×C₄	semidirect
97. #14523970	C₂×C₄	semidirect
98. #14523969	C₂×C₄	semidirect
99. #14523969	C₂×C₄	semidirect
110. #14523953	C₂×C₄	semidirect
115. C₈×Dic₆₇	C₂×C₄	semidirect
120. #131×C₆₇	C₂×C₄	semidirect
121. #131×C₆₇	C₂×C₄	semidirect
307. C₄×#131	D₆₇	semidirect
318. C₆₇	#20510	semidirect
382. #131	C₄×D₆₇	semidirect
383. #131	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863516	2
C₂×#16863511	2
#22569007	2
C₄×#14524049	2
#22560116	2
#22560094	2
#22560089	2
#22560055	2
#22560051	2
#22560048	2
#22560044	2
#22560022	2
#22560019	2
#22559895	2
C₄×#131×C₆₇	2
#20510	67