Subgroups — #30858095

Order 17152.

790 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	#427×D₆₇	C₂	1	1	yes	maximal, characteristic
2	#22568770	C₂	1	1	yes	maximal, characteristic
3	#22568625	C₂	1	1	yes	maximal, characteristic
4	#22560811	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560810	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560809	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560808	C₂	1	1	yes	maximal, characteristic, complemented
8	#22560807	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560806	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560805	C₂	1	1	yes	maximal, characteristic, complemented
11	#341×D₆₇	C₂	1	1	yes	maximal, characteristic
12	#22559917	C₂	1	1	yes	maximal, characteristic
13	#22559917	C₂	1	1	yes	maximal, characteristic
14	#22559904	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#1922	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#11761611	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×D₆₇	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×D₆₇	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
20	C₂×#14524000	C₂²	1	1	yes	characteristic
21	#117×D₆₇	C₂²	1	1	yes	characteristic
22	#117×D₆₇	C₂²	1	1	yes	characteristic
23	#16863434	C₂²	1	1	yes	characteristic
24	#16863433	C₄	1	1	yes	characteristic, complemented
25	#16863433	C₄	1	1	yes	characteristic, complemented
26	#16863432	C₂²	1	1	yes	characteristic
27	#16863432	C₂²	1	1	yes	characteristic
28	#16863431	C₄	1	1	yes	characteristic, complemented
29	#16863431	C₄	1	1	yes	characteristic, complemented
30	#107×D₆₇	C₄	1	1	yes	characteristic, complemented
31	#107×D₆₇	C₄	1	1	yes	characteristic, complemented
32	#106×D₆₇	C₄	1	1	yes	characteristic, complemented
33	#106×D₆₇	C₄	1	1	yes	characteristic, complemented
34	#16863424	C₂²	1	1	yes	characteristic
35	#16863423	C₂²	1	1	yes	characteristic
36	#16863422	C₂²	1	1	yes	characteristic
37	#16863421	—	2	1	no	—
38	#16863421	—	2	1	no	—
39	#16863418	—	2	1	no	—
40	#16863418	—	2	1	no	—
41	#16863354	C₂²	1	1	yes	characteristic
42	#16863353	—	2	1	no	—
43	#16863352	C₂²	1	1	yes	characteristic
44	#16863351	C₂²	1	1	yes	characteristic
45	#16863350	—	2	1	no	—
46	#16863348	—	2	1	no	—
47	C₄×#11761611	—	2	1	no	—
48	#16863161	C₂²	1	1	yes	characteristic
49	#16863160	C₂²	1	1	yes	characteristic
50	#16863160	C₂²	1	1	yes	characteristic
51	#16863157	C₂²	1	1	yes	characteristic
52	#16863157	C₂²	1	1	yes	characteristic
53	#16863156	C₂²	1	1	yes	characteristic
54	#16863156	C₂²	1	1	yes	characteristic
55	#16863155	C₂²	1	1	yes	characteristic
56	#16863155	C₂²	1	1	yes	characteristic
57	#16863151	C₂²	1	1	yes	characteristic
58	#16863150	C₂²	1	1	yes	characteristic
59	#16863150	C₂²	1	1	yes	characteristic
60	#427×C₆₇	C₂²	1	1	yes	characteristic
61	#424×C₆₇	C₂²	1	1	yes	characteristic
62	#405×C₆₇	C₂²	1	1	yes	characteristic
63	#341×C₆₇	C₂²	1	1	yes	characteristic
64	#339×C₆₇	C₂²	1	1	yes	characteristic
65	#339×C₆₇	C₂²	1	1	yes	characteristic
66	#336×C₆₇	C₂²	1	1	yes	characteristic
67	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
68	C₂×#11761612	C₂³	1	1	yes	characteristic
69	C₂×#11761612	C₂³	1	1	yes	characteristic
70	C₂×#11761611	—	2	1	no	—
71	C₂×#11761611	—	2	2	no	—
72	C₂×#11761611	—	2	2	no	—
73	C₂×#11761611	—	2	1	no	—
74	C₂×#11761611	D₄	1	1	yes	characteristic
75	C₂×#11761611	D₄	1	1	yes	characteristic
76	C₂×#11761611	D₄	1	1	yes	characteristic
77	C₂×#11761611	D₄	1	1	yes	characteristic
78	M₁₆×D₆₇	—	2	2	no	—
79	M₁₆×D₆₇	—	2	2	no	—
80	M₁₆×D₆₇	—	2	2	no	—
81	M₁₆×D₆₇	Q₈	1	4	yes	—
82	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
84	C₂×C₈×D₆₇	—	2	1	no	—
85	C₂×C₈×D₆₇	—	2	2	no	—
86	C₂×C₈×D₆₇	—	2	2	no	—
87	C₂×C₈×D₆₇	—	2	1	no	—
88	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
92	#14524002	C₂³	1	1	yes	characteristic
93	#14524002	C₂³	1	1	yes	characteristic
94	#14524001	C₂×C₄	1	1	yes	characteristic
95	#14524001	C₂×C₄	1	1	yes	characteristic
96	#14524001	C₂×C₄	1	1	yes	characteristic
97	#14524001	C₂×C₄	1	1	yes	characteristic
98	#14524000	—	2	1	no	—
99	#14524000	—	2	1	no	—
100	#14524000	—	2	2	no	—
101	#14524000	—	2	2	no	—
102	#14523999	—	2	1	no	—
103	#14523999	—	2	1	no	—
104	C₂×Dic₆₇⋊C₄	—	2	1	no	—
105	C₄⋊C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
106	C₄⋊C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
107	C₄⋊C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
108	C₄⋊C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
109	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
110	C₂²⋊C₄×D₆₇	—	2	1	no	—
111	C₂²⋊C₄×D₆₇	—	2	1	no	—
112	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
113	C₄²×D₆₇	—	2	1	no	—
114	C₄²×D₆₇	—	2	1	no	—
115	#14523977	C₂×C₄	1	1	yes	characteristic
116	#14523977	C₂×C₄	1	1	yes	characteristic
117	#14523976	C₂×C₄	1	1	yes	characteristic
118	#14523976	C₂×C₄	1	1	yes	characteristic
119	#14523976	C₂×C₄	1	1	yes	characteristic
120	#14523976	C₂×C₄	1	1	yes	characteristic
121	#14523975	C₂×C₄	1	1	yes	characteristic
122	#14523975	C₂×C₄	1	1	yes	characteristic
123	#14523974	C₂×C₄	1	1	yes	characteristic
124	#14523974	C₂×C₄	1	1	yes	characteristic
125	#14523974	C₂×C₄	1	1	yes	characteristic
126	#14523974	C₂×C₄	1	1	yes	characteristic
127	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
128	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
129	Dic₆₇⋊C₈	—	2	1	no	—
130	Dic₆₇⋊C₈	—	2	1	no	—
131	Dic₆₇⋊C₈	—	2	1	no	—
132	Dic₆₇⋊C₈	—	2	1	no	—
133	#14523954	—	2	1	no	—
134	#14523953	—	2	1	no	—
135	#14523953	—	2	1	no	—
136	C₄×C₆₇⋊C₈	—	2	1	no	—
137	C₈×Dic₆₇	—	2	1	no	—
138	C₈×Dic₆₇	—	2	1	no	—
139	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
143	#117×C₆₇	C₂³	1	1	yes	characteristic
144	#117×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
146	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
147	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
148	#106×C₆₇	C₂×C₄	1	1	yes	characteristic
149	#106×C₆₇	C₂×C₄	1	1	yes	characteristic
150	C₄⋊C₈×C₆₇	—	2	1	no	—
151	C₄⋊C₈×C₆₇	—	2	1	no	—
152	#97×C₆₇	—	2	1	no	—
153	C₄×C₈×C₆₇	—	2	1	no	—
154	C₂³×D₆₇	#41	1	1	yes	characteristic
155	C₂²×Dic₆₇	—	2	1	no	—
156	C₂²×Dic₆₇	#41	1	1	yes	characteristic
157	C₂×C₄×D₆₇	—	2	1	no	—
158	C₂×C₄×D₆₇	—	2	1	no	—
159	C₂×C₄×D₆₇	—	2	1	no	—
160	C₂×C₄×D₆₇	—	2	1	no	—
161	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄×D₆₇	C₂×Q₈	1	2	yes	—
166	C₂×C₄×D₆₇	#41	1	2	yes	—
167	C₂×C₄×D₆₇	#41	1	2	yes	—
168	C₂×C₄×D₆₇	#41	1	2	yes	—
169	#11761612	—	2	1	no	—
170	#11761612	—	2	1	no	—
171	#11761612	—	2	1	no	—
172	#11761612	C₂×Q₈	1	2	yes	—
173	#11761611	—	2	4	no	—
174	#11761611	—	2	2	no	—
175	#11761611	—	2	2	no	—
176	#11761611	—	2	2	no	—
177	#11761611	—	2	2	no	—
178	#11761611	—	4	2	no	—
179	C₂×C₆₇⋊C₈	—	2	1	no	—
180	C₂×C₆₇⋊C₈	—	2	1	no	—
181	C₂×C₆₇⋊C₈	—	2	1	no	—
182	C₂×C₆₇⋊C₈	—	2	1	no	—
183	C₂×C₆₇⋊C₈	—	2	1	no	—
184	C₂×C₆₇⋊C₈	—	2	1	no	—
185	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
188	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
189	C₈×D₆₇	—	2	2	no	—
190	C₈×D₆₇	—	2	2	no	—
191	C₈×D₆₇	—	2	2	no	—
192	C₈×D₆₇	—	2	2	no	—
193	C₈×D₆₇	—	2	4	no	—
194	C₈×D₆₇	—	4	2	no	—
195	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
198	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
199	Dic₆₇⋊C₄	—	2	1	no	—
200	Dic₆₇⋊C₄	—	2	1	no	—
201	Dic₆₇⋊C₄	—	2	1	no	—
202	Dic₆₇⋊C₄	—	2	1	no	—
203	Dic₆₇⋊C₄	—	4	2	no	—
204	C₂²⋊Dic₆₇	—	2	1	no	—
205	C₂²⋊Dic₆₇	—	2	1	no	—
206	(C₂×D₆₇)⋊C₄	—	2	1	no	—
207	(C₂×D₆₇)⋊C₄	—	2	1	no	—
208	(C₂×D₆₇)⋊C₄	—	2	1	no	—
209	(C₂×D₆₇)⋊C₄	—	2	1	no	—
210	(C₂×D₆₇)⋊C₄	—	4	2	no	—
211	C₄×Dic₆₇	—	2	1	no	—
212	C₄×Dic₆₇	—	2	1	no	—
213	C₄×Dic₆₇	—	2	1	no	—
214	C₄×Dic₆₇	—	2	1	no	—
215	C₄×Dic₆₇	—	2	1	no	—
216	C₄×Dic₆₇	—	2	1	no	—
217	C₄×Dic₆₇	—	2	1	no	—
218	C₄×Dic₆₇	—	2	1	no	—
219	C₂²×C₄×C₆₇	—	2	1	no	—
220	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
221	M₁₆×C₆₇	—	2	1	no	—
222	M₁₆×C₆₇	—	2	1	no	—
223	M₁₆×C₆₇	—	2	1	no	—
224	M₁₆×C₆₇	C₂×Q₈	1	2	yes	—
225	C₂×C₈×C₆₇	—	2	1	no	—
226	C₂×C₈×C₆₇	—	2	1	no	—
227	C₂×C₈×C₆₇	—	2	1	no	—
228	C₂×C₈×C₆₇	—	2	1	no	—
229	C₂×C₈×C₆₇	—	2	1	no	—
230	C₂×C₈×C₆₇	—	2	1	no	—
231	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
232	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
233	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
234	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
235	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
236	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
237	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
238	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
239	C₂²⋊C₄×C₆₇	—	2	1	no	—
240	C₂²⋊C₄×C₆₇	—	2	1	no	—
241	C₄²×C₆₇	—	2	1	no	—
242	C₄²×C₆₇	—	2	1	no	—
243	C₄²×C₆₇	—	2	1	no	—
244	C₄²×C₆₇	—	2	1	no	—
245	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
246	C₂²×D₆₇	—	4	1	no	—
247	C₂²×D₆₇	—	4	1	no	—
248	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
249	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
250	C₂²×D₆₇	#125	1	2	yes	—
251	C₂²×D₆₇	#126	1	2	yes	—
252	C₂×C₄×C₆₇	—	2	1	no	—
253	C₂×C₄×C₆₇	—	2	1	no	—
254	C₂×C₄×C₆₇	—	2	1	no	—
255	C₂×C₄×C₆₇	—	2	1	no	—
256	C₂×C₄×C₆₇	—	4	1	no	—
257	C₂×C₄×C₆₇	—	4	1	no	—
258	C₂×C₄×C₆₇	—	4	1	no	—
259	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
260	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
262	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
265	C₂×Dic₆₇	—	2	1	no	—
266	C₂×Dic₆₇	—	2	1	no	—
267	C₂×Dic₆₇	—	2	1	no	—
268	C₂×Dic₆₇	—	2	1	no	—
269	C₂×Dic₆₇	—	4	1	no	—
270	C₂×Dic₆₇	—	4	1	no	—
271	C₂×Dic₆₇	—	4	1	no	—
272	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
273	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
274	C₂×Dic₆₇	#125	1	2	yes	—
275	C₂×Dic₆₇	#126	1	2	yes	—
276	C₄×D₆₇	—	8	1	no	—
277	C₄×D₆₇	—	8	1	no	—
278	C₄×D₆₇	—	8	1	no	—
279	C₄×D₆₇	—	8	1	no	—
280	C₄×D₆₇	#117	1	2	yes	—
281	C₄×D₆₇	#117	1	2	yes	—
282	C₄×D₆₇	C₄×Q₈	1	2	yes	—
283	C₄×D₆₇	C₄×Q₈	1	2	yes	—
284	C₄×D₆₇	C₂²⋊Q₈	1	2	yes	—
285	C₄×D₆₇	C₂²⋊Q₈	1	2	yes	—
286	C₄×D₆₇	#123	1	2	yes	—
287	C₄×D₆₇	#123	1	2	yes	—
288	C₈×C₆₇	—	2	1	no	—
289	C₈×C₆₇	—	2	1	no	—
290	C₈×C₆₇	—	2	2	no	—
291	C₈×C₆₇	—	2	1	no	—
292	C₈×C₆₇	—	2	1	no	—
293	C₈×C₆₇	—	4	1	no	—
294	C₆₇⋊C₈	—	2	1	no	—
295	C₆₇⋊C₈	—	2	1	no	—
296	C₆₇⋊C₈	—	2	2	no	—
297	C₆₇⋊C₈	—	2	1	no	—
298	C₆₇⋊C₈	—	2	1	no	—
299	C₆₇⋊C₈	—	4	1	no	—
300	C₂²×C₆₇	—	2	1	no	—
301	C₂²×C₆₇	—	2	1	no	—
302	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
303	C₂²×C₆₇	C₂×#125	1	1	yes	characteristic
304	C₂²×C₆₇	C₂×#126	1	1	yes	characteristic
305	C₂×D₆₇	—	2	1	no	—
306	C₂×D₆₇	—	2	1	no	—
307	C₂×D₆₇	—	2	1	no	—
308	C₂×D₆₇	—	2	1	no	—
309	C₂×D₆₇	—	4	2	no	—
310	C₂×D₆₇	—	4	2	no	—
311	C₂×D₆₇	#387	1	2	yes	—
312	C₂×D₆₇	#387	1	2	yes	—
313	C₄×C₆₇	—	4	1	no	—
314	C₄×C₆₇	—	4	1	no	—
315	C₄×C₆₇	—	4	1	no	—
316	C₄×C₆₇	—	4	1	no	—
317	C₄×C₆₇	—	8	1	no	—
318	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
319	C₄×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
320	C₄×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
321	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
322	Dic₆₇	—	4	1	no	—
323	Dic₆₇	—	4	1	no	—
324	Dic₆₇	—	4	1	no	—
325	Dic₆₇	—	4	1	no	—
326	Dic₆₇	—	8	1	no	—
327	Dic₆₇	#387	1	2	yes	—
328	Dic₆₇	#387	1	2	yes	—
329	#21043	—	67	1	no	maximal, Sylow
330	C₂×C₆₇	—	2	1	no	—
331	C₂×C₆₇	—	2	1	no	—
332	C₂×C₆₇	C₂×#387	1	1	yes	characteristic
333	C₂×C₆₇	#2957	1	1	yes	characteristic
334	C₂×C₆₇	#2957	1	1	yes	characteristic
335	D₆₇	—	2	2	no	—
336	D₆₇	—	2	2	no	—
337	C₂×#427	—	67	1	no	—
338	#2905	—	67	1	no	—
339	#2873	—	67	1	no	—
340	#1922	—	67	1	no	—
341	#1922	—	67	1	no	—
342	#1922	—	67	1	no	—
343	#1922	—	67	1	no	—
344	#1922	—	67	1	no	—
345	#1922	—	67	1	no	—
346	#1922	—	67	1	no	—
347	#1922	D₆₇	1	1	yes	characteristic, complemented
348	C₂×#341	—	67	1	no	—
349	#1733	—	67	1	no	—
350	#1733	—	67	1	no	—
351	#1729	—	67	1	no	—
352	C₆₇	#21043	1	1	yes	characteristic, complemented, Sylow
353	C₂²×M₁₆	—	67	1	no	—
354	C₂²×M₁₆	—	67	1	no	—
355	C₂²×M₁₆	—	67	1	no	—
356	C₂³×C₈	—	67	1	no	—
357	C₂×#117	—	67	1	no	—
358	C₂×#117	—	67	1	no	—
359	C₂×#117	—	67	1	no	—
360	#427	—	67	1	no	—
361	#427	—	67	1	no	—
362	#427	—	67	1	no	—
363	#427	—	67	1	no	—
364	#427	—	67	1	no	—
365	#427	—	67	1	no	—
366	#427	—	67	1	no	—
367	#427	C₂×D₆₇	1	1	yes	characteristic
368	C₂×#107	—	67	1	no	—
369	C₂×#107	—	67	1	no	—
370	C₂×#106	—	67	1	no	—
371	C₂×#106	—	67	1	no	—
372	#424	—	67	1	no	—
373	#424	—	67	1	no	—
374	#424	—	67	1	no	—
375	#424	—	134	1	no	—
376	#424	—	134	1	no	—
377	#424	C₂×D₆₇	1	1	yes	characteristic
378	#423	—	134	1	no	—
379	#423	—	134	1	no	—
380	#405	—	67	1	no	—
381	#405	—	67	1	no	—
382	#405	—	67	1	no	—
383	#405	—	134	1	no	—
384	#405	—	134	1	no	—
385	#405	C₂×D₆₇	1	1	yes	characteristic
386	C₄×M₁₆	—	134	1	no	—
387	C₄×M₁₆	—	134	1	no	—
388	#341	—	67	1	no	—
389	#341	—	67	1	no	—
390	#341	—	67	1	no	—
391	#341	C₂×D₆₇	1	1	yes	characteristic
392	#339	—	67	1	no	—
393	#339	—	67	1	no	—
394	#339	—	67	1	no	—
395	#339	—	67	1	no	—
396	#339	—	67	1	no	—
397	#339	—	67	1	no	—
398	#339	C₂×D₆₇	1	1	yes	characteristic
399	#339	C₂×D₆₇	1	1	yes	characteristic
400	#336	—	67	1	no	—
401	#336	—	67	1	no	—
402	#336	—	67	1	no	—
403	#336	C₂×D₆₇	1	1	yes	characteristic
404	C₂³×C₄	—	67	1	no	—
405	C₂×M₁₆	—	67	1	no	—
406	C₂×M₁₆	—	67	1	no	—
407	C₂×M₁₆	—	67	1	no	—
408	C₂×M₁₆	—	67	1	no	—
409	C₂×M₁₆	—	67	1	no	—
410	C₂×M₁₆	—	67	4	no	—
411	C₂×M₁₆	—	67	1	no	—
412	C₂×M₁₆	—	134	1	no	—
413	C₂×M₁₆	—	134	2	no	—
414	C₂×M₁₆	—	134	2	no	—
415	C₂×M₁₆	—	134	1	no	—
416	C₂×M₁₆	—	134	2	no	—
417	C₂×M₁₆	—	134	2	no	—
418	C₂×M₁₆	—	134	2	no	—
419	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
420	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
421	C₂²×C₈	—	67	1	no	—
422	C₂²×C₈	—	67	1	no	—
423	C₂²×C₈	—	67	1	no	—
424	C₂²×C₈	—	67	1	no	—
425	C₂²×C₈	—	67	1	no	—
426	C₂²×C₈	—	67	1	no	—
427	C₂²×C₈	—	134	1	no	—
428	C₂²×C₈	—	134	2	no	—
429	C₂²×C₈	—	134	2	no	—
430	C₂²×C₈	—	134	1	no	—
431	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
432	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
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	—	67	1	no	—
439	#117	—	134	2	no	—
440	#117	—	134	2	no	—
441	#117	—	134	1	no	—
442	#117	—	134	1	no	—
443	#117	—	134	1	no	—
444	#117	—	134	1	no	—
445	#117	C₂²×D₆₇	1	1	yes	characteristic
446	#117	C₂²×D₆₇	1	1	yes	characteristic
447	C₂×C₄⋊C₄	—	67	1	no	—
448	C₂×C₄⋊C₄	—	67	1	no	—
449	C₂×C₄⋊C₄	—	67	1	no	—
450	C₂×C₄⋊C₄	—	67	1	no	—
451	C₂×C₄⋊C₄	—	134	1	no	—
452	C₂×C₂²⋊C₄	—	134	1	no	—
453	C₂×C₂²⋊C₄	—	134	1	no	—
454	C₂×C₂²⋊C₄	—	134	1	no	—
455	C₂×C₄²	—	67	1	no	—
456	C₂×C₄²	—	134	1	no	—
457	C₂×C₄²	—	134	1	no	—
458	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
459	#107	—	67	1	no	—
460	#107	—	67	1	no	—
461	#107	—	67	1	no	—
462	#107	—	67	1	no	—
463	#107	—	67	1	no	—
464	#107	—	67	1	no	—
465	#107	C₄×D₆₇	1	1	yes	characteristic
466	#107	C₄×D₆₇	1	1	yes	characteristic
467	#106	—	67	1	no	—
468	#106	—	67	1	no	—
469	#106	—	67	1	no	—
470	#106	—	67	1	no	—
471	#106	—	67	1	no	—
472	#106	—	67	1	no	—
473	#106	C₄×D₆₇	1	1	yes	characteristic
474	#106	C₄×D₆₇	1	1	yes	characteristic
475	C₄⋊C₈	—	2	1	no	—
476	C₄⋊C₈	—	2	1	no	—
477	C₄⋊C₈	—	134	1	no	—
478	C₄⋊C₈	—	134	1	no	—
479	C₄⋊C₈	—	134	1	no	—
480	C₄⋊C₈	—	134	1	no	—
481	C₄⋊C₈	—	134	1	no	—
482	C₄⋊C₈	—	134	1	no	—
483	#97	—	2	1	no	—
484	#97	—	134	1	no	—
485	#97	—	134	1	no	—
486	#97	—	134	1	no	—
487	C₄×C₈	—	2	1	no	—
488	C₄×C₈	—	134	1	no	—
489	C₄×C₈	—	134	1	no	—
490	C₄×C₈	—	134	1	no	—
491	C₂⁴	—	67	1	no	—
492	C₂²×C₄	—	2	1	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	1	no	—
498	C₂²×C₄	—	67	2	no	—
499	C₂²×C₄	—	67	2	no	—
500	C₂²×C₄	—	67	2	no	—
501	C₂²×C₄	—	67	2	no	—
502	C₂²×C₄	—	134	1	no	—
503	C₂²×C₄	—	134	1	no	—
504	C₂²×C₄	—	134	1	no	—
505	C₂²×C₄	—	134	1	no	—
506	C₂²×C₄	—	134	1	no	—
507	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
508	M₁₆	—	2	1	no	—
509	M₁₆	—	2	1	no	—
510	M₁₆	—	2	1	no	—
511	M₁₆	—	268	2	no	—
512	M₁₆	—	67	2	no	—
513	M₁₆	—	134	4	no	—
514	M₁₆	—	134	2	no	—
515	M₁₆	—	134	2	no	—
516	M₁₆	—	134	2	no	—
517	M₁₆	—	134	2	no	—
518	M₁₆	—	134	1	no	—
519	M₁₆	—	134	1	no	—
520	M₁₆	—	134	1	no	—
521	M₁₆	Q₈×D₆₇	1	2	yes	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	268	2	no	—
529	C₂×C₈	—	67	1	no	—
530	C₂×C₈	—	67	1	no	—
531	C₂×C₈	—	67	1	no	—
532	C₂×C₈	—	67	1	no	—
533	C₂×C₈	—	134	2	no	—
534	C₂×C₈	—	134	2	no	—
535	C₂×C₈	—	134	2	no	—
536	C₂×C₈	—	134	2	no	—
537	C₂×C₈	—	134	4	no	—
538	C₂×C₈	—	134	1	no	—
539	C₂×C₈	—	134	1	no	—
540	C₂×C₈	—	134	1	no	—
541	C₂×C₈	—	134	1	no	—
542	C₂×C₈	—	134	1	no	—
543	C₂×C₈	—	134	1	no	—
544	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
545	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
546	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
547	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
548	C₄⋊C₄	—	268	2	no	—
549	C₄⋊C₄	—	67	1	no	—
550	C₄⋊C₄	—	67	1	no	—
551	C₄⋊C₄	—	67	1	no	—
552	C₄⋊C₄	—	67	1	no	—
553	C₄⋊C₄	—	134	1	no	—
554	C₄⋊C₄	—	134	1	no	—
555	C₄⋊C₄	—	134	1	no	—
556	C₄⋊C₄	—	134	1	no	—
557	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
558	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
559	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
560	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
561	C₂²⋊C₄	—	2	1	no	—
562	C₂²⋊C₄	—	2	1	no	—
563	C₂²⋊C₄	—	268	2	no	—
564	C₂²⋊C₄	—	134	1	no	—
565	C₂²⋊C₄	—	134	1	no	—
566	C₂²⋊C₄	—	134	1	no	—
567	C₂²⋊C₄	—	134	1	no	—
568	C₂²⋊C₄	—	134	1	no	—
569	C₂²⋊C₄	—	134	1	no	—
570	C₄²	—	2	1	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	134	1	no	—
575	C₄²	—	134	1	no	—
576	C₄²	—	134	1	no	—
577	C₄²	—	134	1	no	—
578	C₄²	—	134	1	no	—
579	C₄²	—	134	1	no	—
580	C₄²	—	134	1	no	—
581	C₄²	—	134	1	no	—
582	C₂³	—	268	1	no	—
583	C₂³	—	268	1	no	—
584	C₂³	—	67	2	no	—
585	C₂³	—	67	2	no	—
586	C₂³	—	67	1	no	—
587	C₂³	—	67	1	no	—
588	C₂³	#41×D₆₇	1	1	yes	characteristic
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	268	1	no	—
597	C₂×C₄	—	268	1	no	—
598	C₂×C₄	—	268	1	no	—
599	C₂×C₄	—	536	1	no	—
600	C₂×C₄	—	536	1	no	—
601	C₂×C₄	—	536	1	no	—
602	C₂×C₄	—	536	1	no	—
603	C₂×C₄	—	67	1	no	—
604	C₂×C₄	—	67	1	no	—
605	C₂×C₄	—	67	2	no	—
606	C₂×C₄	—	67	2	no	—
607	C₂×C₄	—	67	2	no	—
608	C₂×C₄	—	67	2	no	—
609	C₂×C₄	—	67	2	no	—
610	C₂×C₄	—	67	2	no	—
611	C₂×C₄	—	67	2	no	—
612	C₂×C₄	—	67	2	no	—
613	C₂×C₄	—	67	2	no	—
614	C₂×C₄	—	67	2	no	—
615	C₂×C₄	—	134	1	no	—
616	C₂×C₄	—	134	1	no	—
617	C₂×C₄	—	134	1	no	—
618	C₂×C₄	—	134	1	no	—
619	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
620	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
621	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
622	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
623	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
624	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
625	C₈	—	2	1	no	—
626	C₈	—	2	1	no	—
627	C₈	—	2	2	no	—
628	C₈	—	2	1	no	—
629	C₈	—	2	1	no	—
630	C₈	—	4	1	no	—
631	C₈	—	268	1	no	—
632	C₈	—	134	1	no	—
633	C₈	—	134	1	no	—
634	C₈	—	134	2	no	—
635	C₈	—	134	1	no	—
636	C₈	—	134	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	268	2	no	—
640	C₂²	—	268	2	no	—
641	C₂²	—	67	2	no	—
642	C₂²	—	67	2	no	—
643	C₂²	—	134	1	no	—
644	C₂²	—	134	1	no	—
645	C₂²	—	134	1	no	—
646	C₂²	—	134	1	no	—
647	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
648	C₂²	#125×D₆₇	1	1	yes	characteristic
649	C₂²	#126×D₆₇	1	1	yes	characteristic
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	8	1	no	—
655	C₄	—	268	1	no	—
656	C₄	—	268	1	no	—
657	C₄	—	268	1	no	—
658	C₄	—	268	1	no	—
659	C₄	—	536	1	no	—
660	C₄	—	67	2	no	—
661	C₄	—	67	2	no	—
662	C₄	#117×D₆₇	1	1	yes	characteristic
663	C₄	C₄×Q₈×D₆₇	1	1	yes	characteristic
664	C₄	C₂²⋊Q₈×D₆₇	1	1	yes	characteristic
665	C₄	#123×D₆₇	1	1	yes	characteristic
666	C₂	—	2	1	no	—
667	C₂	—	2	1	no	—
668	C₂	—	134	2	no	—
669	C₂	—	134	2	no	—
670	C₂	#387×D₆₇	1	1	yes	characteristic
671	C₂	#22569121	1	1	yes	characteristic
672	C₂	#22569123	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1922	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂³×D₆₇	#41
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1922	D₆₇
hypocenter	C₆₇	#21043
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1922

Complements

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

N	H ≅ G/N	type
4. #22560811	C₂	semidirect
5. #22560810	C₂	semidirect
6. #22560809	C₂	semidirect
7. #22560808	C₂	semidirect
8. #22560807	C₂	semidirect
9. #22560806	C₂	semidirect
10. #22560805	C₂	semidirect
15. C₆₇×#1922	C₂	semidirect
24. #16863433	C₄	semidirect
25. #16863433	C₄	semidirect
28. #16863431	C₄	semidirect
29. #16863431	C₄	semidirect
30. #107×D₆₇	C₄	semidirect
31. #107×D₆₇	C₄	semidirect
32. #106×D₆₇	C₄	semidirect
33. #106×D₆₇	C₄	semidirect
347. #1922	D₆₇	semidirect
352. C₆₇	#21043	semidirect

Maximal subgroups

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

subgroup	index
#427×D₆₇	2
#22568770	2
#22568625	2
#22560811	2
#22560810	2
#22560809	2
#22560808	2
#22560807	2
#22560806	2
#22560805	2
#341×D₆₇	2
#22559917	2
#22559904	2
C₆₇×#1922	2
#21043	67