Subgroups — #30863211

Order 17152.

794 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570120	C₂	1	1	yes	maximal, characteristic
2	#22568906	C₂	1	1	yes	maximal, characteristic
3	#405×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#22560854	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560809	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560808	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560508	C₂	1	1	yes	maximal, characteristic
8	#22560412	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560307	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560091	C₂	1	1	yes	maximal, characteristic, complemented
11	#22560087	C₂	1	1	yes	maximal, characteristic, complemented
12	#22560049	C₂	1	1	yes	maximal, characteristic, complemented
13	#22560047	C₂	1	1	yes	maximal, characteristic, complemented
14	#22559979	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#1929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14524050	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×D₆₇	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
19	#16863903	C₂²	1	1	yes	characteristic
20	#117×D₆₇	C₂²	1	1	yes	characteristic
21	#16863736	C₄	1	1	yes	characteristic, complemented
22	#16863735	C₄	1	1	yes	characteristic, complemented
23	#16863730	C₄	1	1	yes	characteristic, complemented
24	#16863725	C₄	1	1	yes	characteristic, complemented
25	#16863719	C₄	1	1	yes	characteristic, complemented
26	#16863718	C₄	1	1	yes	characteristic, complemented
27	#16863713	C₄	1	1	yes	characteristic, complemented
28	#16863708	C₄	1	1	yes	characteristic, complemented
29	#16863470	—	2	1	no	—
30	#16863470	—	2	1	no	—
31	(C₂²⋊D₆₇)⋊C₈	—	2	1	no	—
32	(C₂²⋊D₆₇)⋊C₈	—	2	1	no	—
33	C₂×#14523978	C₂²	1	1	yes	characteristic
34	#16863434	C₂²	1	1	yes	characteristic
35	#16863432	C₂²	1	1	yes	characteristic
36	#16863422	C₂²	1	1	yes	characteristic
37	C₂×#14523970	C₂²	1	1	yes	characteristic
38	#16863392	C₂²	1	1	yes	characteristic
39	#16863359	C₂²	1	1	yes	characteristic
40	C₂×(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
41	#16863354	C₂²	1	1	yes	characteristic
42	#16863354	C₂²	1	1	yes	characteristic
43	#16863353	—	2	1	no	—
44	#16863352	C₂²	1	1	yes	characteristic
45	#16863351	C₂²	1	1	yes	characteristic
46	#16863350	—	2	1	no	—
47	#97×D₆₇	—	2	1	no	—
48	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
50	C₄×C₈×D₆₇	—	2	1	no	—
51	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
52	#16863161	C₂²	1	1	yes	characteristic
53	#16863160	C₂²	1	1	yes	characteristic
54	#16863157	C₂²	1	1	yes	characteristic
55	#16863157	C₂²	1	1	yes	characteristic
56	#16863156	C₂²	1	1	yes	characteristic
57	#16863156	C₂²	1	1	yes	characteristic
58	#16863155	C₂²	1	1	yes	characteristic
59	#16863150	C₂²	1	1	yes	characteristic
60	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×#104×C₆₇	C₂²	1	1	yes	characteristic
62	#416×C₆₇	C₂²	1	1	yes	characteristic
63	#408×C₆₇	C₂²	1	1	yes	characteristic
64	#405×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	#14524050	—	2	2	no	—
69	#14524050	—	2	2	no	—
70	C₂×#11761612	—	2	1	no	—
71	C₂×#11761612	C₂³	1	1	yes	characteristic
72	C₂×#11761612	C₂³	1	1	yes	characteristic
73	C₂×#11761611	—	2	1	no	—
74	M₁₆×D₆₇	—	2	2	no	—
75	M₁₆×D₆₇	—	2	2	no	—
76	C₂²×C₆₇⋊C₈	—	2	1	no	—
77	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₂×C₈×D₆₇	—	2	1	no	—
80	C₂×C₈×D₆₇	—	2	2	no	—
81	C₂×C₈×D₆₇	—	2	2	no	—
82	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
83	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
84	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
85	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
86	#14524024	—	2	1	no	—
87	#14524019	C₂×C₄	1	1	yes	characteristic
88	#14524019	C₂×C₄	1	1	yes	characteristic
89	#14524014	C₂×C₄	1	1	yes	characteristic
90	#14524014	C₂×C₄	1	1	yes	characteristic
91	#14524011	—	2	1	no	—
92	C₄×C₂²⋊D₆₇	—	2	1	no	—
93	C₄×C₂²⋊D₆₇	—	2	1	no	—
94	#14524002	C₂³	1	1	yes	characteristic
95	#14524002	C₂³	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	#14523999	—	2	1	no	—
100	C₄⋊C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
101	C₄⋊C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
102	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
103	C₂²⋊C₄×D₆₇	—	2	1	no	—
104	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
105	C₄²×D₆₇	—	2	1	no	—
106	#14523978	—	2	2	no	—
107	#14523977	C₂×C₄	1	1	yes	characteristic
108	#14523977	C₂×C₄	1	1	yes	characteristic
109	#14523976	C₂×C₄	1	1	yes	characteristic
110	#14523976	C₂×C₄	1	1	yes	characteristic
111	#14523975	C₂×C₄	1	1	yes	characteristic
112	#14523975	C₂×C₄	1	1	yes	characteristic
113	#14523974	C₂×C₄	1	1	yes	characteristic
114	#14523974	C₂×C₄	1	1	yes	characteristic
115	Dic₆₇⋊C₈	—	2	1	no	—
116	Dic₆₇⋊C₈	—	2	1	no	—
117	#14523970	—	2	2	no	—
118	#14523967	C₂×C₄	1	1	yes	characteristic
119	#14523967	C₂×C₄	1	1	yes	characteristic
120	#14523964	C₂×C₄	1	1	yes	characteristic
121	#14523964	C₂×C₄	1	1	yes	characteristic
122	(C₂×D₆₇)⋊C₈	—	2	1	no	—
123	(C₂×D₆₇)⋊C₈	—	2	1	no	—
124	(C₂×D₆₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
125	(C₂×D₆₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
126	(C₂×D₆₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
127	(C₂×D₆₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
128	#14523954	—	2	1	no	—
129	#14523953	—	2	1	no	—
130	#14523953	—	2	1	no	—
131	#14523953	—	2	1	no	—
132	C₄×C₆₇⋊C₈	—	2	1	no	—
133	C₄×C₆₇⋊C₈	—	2	2	no	—
134	C₈×Dic₆₇	—	2	1	no	—
135	C₈×Dic₆₇	—	2	1	no	—
136	C₈×Dic₆₇	—	2	2	no	—
137	C₈×Dic₆₇	—	2	1	no	—
138	C₆₇⋊#95	—	2	1	no	—
139	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
144	#117×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
146	#108×C₆₇	—	2	2	no	—
147	#104×C₆₇	—	2	2	no	—
148	#103×C₆₇	C₂×C₄	1	1	yes	characteristic
149	#103×C₆₇	C₂×C₄	1	1	yes	characteristic
150	#102×C₆₇	C₂×C₄	1	1	yes	characteristic
151	#102×C₆₇	C₂×C₄	1	1	yes	characteristic
152	C₂²⋊C₈×C₆₇	—	2	1	no	—
153	C₂²⋊C₈×C₆₇	—	2	1	no	—
154	#97×C₆₇	—	2	1	no	—
155	C₄×C₈×C₆₇	—	2	1	no	—
156	C₂³×D₆₇	#41	1	1	yes	characteristic
157	C₂×C₂²⋊D₆₇	—	2	1	no	—
158	C₂×C₂²⋊D₆₇	—	2	1	no	—
159	C₂²×Dic₆₇	—	2	1	no	—
160	C₂²×Dic₆₇	#41	1	1	yes	characteristic
161	C₂×C₄×D₆₇	—	2	1	no	—
162	C₂×C₄×D₆₇	—	2	1	no	—
163	C₂×C₄×D₆₇	—	2	1	no	—
164	C₂×C₄×D₆₇	—	2	1	no	—
165	C₂×C₄×D₆₇	—	2	1	no	—
166	C₂×C₄×D₆₇	—	2	1	no	—
167	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
170	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
171	#11761612	—	2	1	no	—
172	#11761612	—	2	1	no	—
173	#11761612	—	2	1	no	—
174	#11761612	—	4	2	no	—
175	#11761612	#41	1	2	yes	—
176	#11761611	—	2	4	no	—
177	C₂×C₆₇⋊C₈	—	2	1	no	—
178	C₂×C₆₇⋊C₈	—	2	1	no	—
179	C₂×C₆₇⋊C₈	—	2	1	no	—
180	C₂×C₆₇⋊C₈	—	2	1	no	—
181	C₂×C₆₇⋊C₈	—	4	2	no	—
182	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
185	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
186	C₂×C₆₇⋊C₈	#41	1	2	yes	—
187	C₂×C₆₇⋊C₈	#41	1	2	yes	—
188	C₈×D₆₇	—	2	4	no	—
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	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
194	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
195	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
197	Dic₆₇⋊C₄	—	2	1	no	—
198	Dic₆₇⋊C₄	—	2	1	no	—
199	Dic₆₇⋊C₄	—	2	1	no	—
200	Dic₆₇⋊C₄	—	2	1	no	—
201	C₂²⋊Dic₆₇	—	2	1	no	—
202	C₂²⋊Dic₆₇	—	2	1	no	—
203	C₂²⋊Dic₆₇	—	2	1	no	—
204	C₂²⋊Dic₆₇	—	2	1	no	—
205	(C₂×D₆₇)⋊C₄	—	2	4	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	C₄×Dic₆₇	—	2	1	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	#41×C₆₇	—	2	1	no	—
217	#41×C₆₇	—	2	1	no	—
218	#41×C₆₇	—	2	1	no	—
219	#41×C₆₇	—	2	1	no	—
220	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
221	C₂×D₄×C₆₇	—	2	1	no	—
222	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
223	C₂²×C₄×C₆₇	—	2	1	no	—
224	C₂²×C₄×C₆₇	—	2	1	no	—
225	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
226	M₁₆×C₆₇	—	2	1	no	—
227	M₁₆×C₆₇	—	2	1	no	—
228	M₁₆×C₆₇	—	2	1	no	—
229	M₁₆×C₆₇	#41	1	2	yes	—
230	C₂×C₈×C₆₇	—	2	1	no	—
231	C₂×C₈×C₆₇	—	2	1	no	—
232	C₂×C₈×C₆₇	—	2	1	no	—
233	C₂×C₈×C₆₇	—	2	1	no	—
234	C₂×C₈×C₆₇	—	2	1	no	—
235	C₂×C₈×C₆₇	—	2	1	no	—
236	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
237	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
238	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
239	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
240	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
241	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
242	C₂²⋊C₄×C₆₇	—	2	1	no	—
243	C₄²×C₆₇	—	2	1	no	—
244	C₄²×C₆₇	—	2	1	no	—
245	C₄²×C₆₇	—	2	1	no	—
246	C₂³×C₆₇	—	2	1	no	—
247	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
248	C₂²×D₆₇	—	2	1	no	—
249	C₂²×D₆₇	—	2	1	no	—
250	C₂²×D₆₇	—	2	2	no	—
251	C₂²×D₆₇	—	4	1	no	—
252	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
253	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
254	Q₈×C₆₇	—	2	1	no	—
255	Q₈×C₆₇	—	2	1	no	—
256	D₄×C₆₇	—	2	1	no	—
257	D₄×C₆₇	—	2	1	no	—
258	D₄×C₆₇	—	4	1	no	—
259	D₄×C₆₇	—	4	1	no	—
260	C₂×C₄×C₆₇	—	2	2	no	—
261	C₂×C₄×C₆₇	—	2	1	no	—
262	C₂×C₄×C₆₇	—	2	1	no	—
263	C₂×C₄×C₆₇	—	2	1	no	—
264	C₂×C₄×C₆₇	—	4	1	no	—
265	C₂×C₄×C₆₇	—	4	1	no	—
266	C₂×C₄×C₆₇	—	4	1	no	—
267	C₂×C₄×C₆₇	—	4	1	no	—
268	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
269	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
273	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
274	C₂²⋊D₆₇	—	4	2	no	—
275	C₂²⋊D₆₇	—	4	2	no	—
276	C₂×Dic₆₇	—	2	1	no	—
277	C₂×Dic₆₇	—	2	1	no	—
278	C₂×Dic₆₇	—	2	2	no	—
279	C₂×Dic₆₇	—	2	1	no	—
280	C₂×Dic₆₇	—	2	1	no	—
281	C₂×Dic₆₇	—	2	1	no	—
282	C₂×Dic₆₇	—	2	1	no	—
283	C₂×Dic₆₇	—	4	1	no	—
284	C₂×Dic₆₇	—	4	1	no	—
285	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
286	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
287	C₄×D₆₇	—	2	1	no	—
288	C₄×D₆₇	—	2	1	no	—
289	C₄×D₆₇	—	2	1	no	—
290	C₄×D₆₇	—	2	1	no	—
291	C₄×D₆₇	—	2	1	no	—
292	C₄×D₆₇	—	2	1	no	—
293	C₄×D₆₇	—	2	1	no	—
294	C₄×D₆₇	—	2	1	no	—
295	C₄×D₆₇	—	4	2	no	—
296	C₄×D₆₇	—	4	2	no	—
297	C₈×C₆₇	—	2	1	no	—
298	C₈×C₆₇	—	2	1	no	—
299	C₈×C₆₇	—	2	1	no	—
300	C₈×C₆₇	—	2	1	no	—
301	C₈×C₆₇	—	2	2	no	—
302	C₈×C₆₇	—	4	1	no	—
303	C₆₇⋊C₈	—	2	1	no	—
304	C₆₇⋊C₈	—	2	1	no	—
305	C₆₇⋊C₈	—	2	2	no	—
306	C₆₇⋊C₈	—	4	1	no	—
307	C₆₇⋊C₈	#123	1	2	yes	—
308	C₆₇⋊C₈	#123	1	2	yes	—
309	C₂²×C₆₇	—	2	1	no	—
310	C₂²×C₆₇	—	2	1	no	—
311	C₂²×C₆₇	—	4	1	no	—
312	C₂²×C₆₇	—	4	1	no	—
313	C₂²×C₆₇	—	4	1	no	—
314	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
315	C₂²×C₆₇	#529	1	1	yes	characteristic
316	C₂²×C₆₇	#529	1	1	yes	characteristic
317	C₂×D₆₇	—	2	1	no	—
318	C₂×D₆₇	—	2	1	no	—
319	C₂×D₆₇	—	2	1	no	—
320	C₂×D₆₇	—	2	1	no	—
321	C₂×D₆₇	—	2	1	no	—
322	C₂×D₆₇	—	4	2	no	—
323	C₂×D₆₇	—	4	2	no	—
324	C₂×D₆₇	#443	1	2	yes	—
325	C₄×C₆₇	—	4	2	no	—
326	C₄×C₆₇	—	4	1	no	—
327	C₄×C₆₇	—	4	1	no	—
328	C₄×C₆₇	—	4	1	no	—
329	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
330	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
331	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
332	C₄×C₆₇	#525	1	1	yes	characteristic
333	Dic₆₇	—	2	1	no	—
334	Dic₆₇	—	2	1	no	—
335	Dic₆₇	—	4	2	no	—
336	Dic₆₇	—	4	1	no	—
337	Dic₆₇	—	4	1	no	—
338	Dic₆₇	—	4	1	no	—
339	Dic₆₇	—	4	1	no	—
340	#21592	—	67	1	no	maximal, Sylow
341	C₂×C₆₇	—	2	1	no	—
342	C₂×C₆₇	—	2	1	no	—
343	C₂×C₆₇	—	8	1	no	—
344	C₂×C₆₇	C₄×#123	1	1	yes	characteristic
345	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
346	C₂×C₆₇	#2955	1	1	yes	characteristic
347	D₆₇	—	2	2	no	—
348	D₆₇	—	4	1	no	—
349	#3091	—	67	1	no	—
350	#2929	—	67	1	no	—
351	C₂×#405	—	67	1	no	—
352	#1929	—	67	1	no	—
353	#1929	D₆₇	1	1	yes	characteristic, complemented
354	#1922	—	67	1	no	—
355	#1922	—	67	1	no	—
356	#1871	—	67	1	no	—
357	#1855	—	67	1	no	—
358	#1826	—	67	1	no	—
359	#1772	—	67	1	no	—
360	#1772	—	67	1	no	—
361	#1764	—	67	1	no	—
362	#1764	—	67	1	no	—
363	C₈×C₂²⋊C₄	—	67	1	no	—
364	C₆₇	#21592	1	1	yes	characteristic, complemented, Sylow
365	C₂×#131	—	67	1	no	—
366	C₂²×M₁₆	—	67	1	no	—
367	C₂³×C₈	—	67	1	no	—
368	#525	—	67	1	no	—
369	C₂×#117	—	67	1	no	—
370	#485	—	67	1	no	—
371	#485	—	67	1	no	—
372	#484	—	67	1	no	—
373	#483	—	67	1	no	—
374	#482	—	67	1	no	—
375	#482	—	67	1	no	—
376	#481	—	67	1	no	—
377	#480	—	67	1	no	—
378	#435	—	134	1	no	—
379	#435	—	134	1	no	—
380	C₈×D₄	—	134	1	no	—
381	C₈×D₄	—	134	1	no	—
382	C₂×#108	—	67	1	no	—
383	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
384	#427	—	67	1	no	—
385	#427	—	67	1	no	—
386	#424	—	67	1	no	—
387	C₂×#104	—	67	1	no	—
388	C₂×#104	C₂×D₆₇	1	1	yes	characteristic
389	#416	—	67	1	no	—
390	#416	C₂×D₆₇	1	1	yes	characteristic
391	#408	C₂×D₆₇	1	1	yes	characteristic
392	#407	—	67	1	no	—
393	C₂×C₂²⋊C₈	—	67	1	no	—
394	#405	—	67	1	no	—
395	#405	—	67	1	no	—
396	#405	—	67	1	no	—
397	#405	—	67	1	no	—
398	#405	—	134	1	no	—
399	#405	—	134	1	no	—
400	#405	C₂×D₆₇	1	1	yes	characteristic
401	C₂×#97	—	134	1	no	—
402	C₂×C₄×C₈	—	67	1	no	—
403	C₂×C₄×C₈	—	67	1	no	—
404	C₂×C₄×C₈	—	134	1	no	—
405	C₄×C₂²⋊C₄	—	67	1	no	—
406	#341	—	67	1	no	—
407	#341	—	67	1	no	—
408	#339	—	67	1	no	—
409	#339	—	67	1	no	—
410	#339	—	67	1	no	—
411	#339	—	67	1	no	—
412	#339	—	67	1	no	—
413	#339	C₂×D₆₇	1	1	yes	characteristic
414	#336	—	67	1	no	—
415	#336	C₂×D₆₇	1	1	yes	characteristic
416	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
417	C₂³×C₄	—	67	1	no	—
418	#131	—	134	2	no	—
419	#131	—	134	2	no	—
420	C₂×M₁₆	—	67	1	no	—
421	C₂×M₁₆	—	67	1	no	—
422	C₂×M₁₆	—	134	1	no	—
423	C₂×M₁₆	—	134	1	no	—
424	C₂×M₁₆	—	134	2	no	—
425	C₂×M₁₆	—	134	2	no	—
426	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
427	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
428	C₂²×C₈	—	67	1	no	—
429	C₂²×C₈	—	67	1	no	—
430	C₂²×C₈	—	67	1	no	—
431	C₂²×C₈	—	67	1	no	—
432	C₂²×C₈	—	67	1	no	—
433	C₂²×C₈	—	67	1	no	—
434	C₂²×C₈	—	134	2	no	—
435	C₂²×C₈	—	134	2	no	—
436	C₂²×C₈	—	134	1	no	—
437	C₂²×C₈	—	134	1	no	—
438	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
439	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
440	#123	—	134	1	no	—
441	C₂²⋊Q₈	—	67	1	no	—
442	C₂²⋊Q₈	—	67	1	no	—
443	#121	—	67	1	no	—
444	#121	—	67	1	no	—
445	#120	—	134	1	no	—
446	C₄×D₄	—	134	1	no	—
447	C₄×D₄	—	134	1	no	—
448	#117	—	67	1	no	—
449	#117	—	67	1	no	—
450	#117	—	67	1	no	—
451	#117	—	67	1	no	—
452	#117	—	134	1	no	—
453	#117	—	134	1	no	—
454	#117	C₂²×D₆₇	1	1	yes	characteristic
455	C₂×C₄⋊C₄	—	67	1	no	—
456	C₂×C₄⋊C₄	—	67	1	no	—
457	C₂×C₂²⋊C₄	—	134	1	no	—
458	C₂×C₂²⋊C₄	—	134	1	no	—
459	C₂×C₄²	—	67	1	no	—
460	C₂×C₄²	—	134	1	no	—
461	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
462	#108	—	2	2	no	—
463	#108	—	134	2	no	—
464	#107	—	67	1	no	—
465	#107	—	67	1	no	—
466	#107	—	67	1	no	—
467	#107	—	67	1	no	—
468	#106	—	67	1	no	—
469	#106	—	67	1	no	—
470	#106	—	67	1	no	—
471	#106	—	67	1	no	—
472	C₄⋊C₈	—	134	1	no	—
473	C₄⋊C₈	—	134	1	no	—
474	#104	—	2	2	no	—
475	#104	—	134	2	no	—
476	#103	—	67	1	no	—
477	#103	—	67	1	no	—
478	#103	C₄×D₆₇	1	1	yes	characteristic
479	#103	C₄×D₆₇	1	1	yes	characteristic
480	#102	—	67	1	no	—
481	#102	—	67	1	no	—
482	#102	C₄×D₆₇	1	1	yes	characteristic
483	#102	C₄×D₆₇	1	1	yes	characteristic
484	C₂²⋊C₈	—	2	1	no	—
485	C₂²⋊C₈	—	2	1	no	—
486	C₂²⋊C₈	—	67	1	no	—
487	C₂²⋊C₈	—	67	1	no	—
488	C₂²⋊C₈	—	67	1	no	—
489	C₂²⋊C₈	—	67	1	no	—
490	C₂²⋊C₈	—	134	1	no	—
491	C₂²⋊C₈	—	134	1	no	—
492	#97	—	2	1	no	—
493	#97	—	134	1	no	—
494	#97	—	134	1	no	—
495	#97	—	134	1	no	—
496	#97	—	134	1	no	—
497	C₄×C₈	—	2	1	no	—
498	C₄×C₈	—	134	2	no	—
499	C₄×C₈	—	134	1	no	—
500	C₄×C₈	—	134	2	no	—
501	C₄×C₈	—	134	1	no	—
502	C₄×C₈	—	134	1	no	—
503	C₄×C₈	—	134	1	no	—
504	#95	—	134	1	no	—
505	C₂⁴	—	67	1	no	—
506	#41	—	2	1	no	—
507	#41	—	2	1	no	—
508	#41	—	2	1	no	—
509	#41	—	2	1	no	—
510	C₂×Q₈	C₂×C₄×D₆₇	1	1	yes	characteristic
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	134	1	no	—
513	C₂×D₄	—	134	1	no	—
514	C₂×D₄	C₂×C₄×D₆₇	1	1	yes	characteristic
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	67	1	no	—
518	C₂²×C₄	—	67	1	no	—
519	C₂²×C₄	—	67	1	no	—
520	C₂²×C₄	—	67	1	no	—
521	C₂²×C₄	—	67	1	no	—
522	C₂²×C₄	—	134	1	no	—
523	C₂²×C₄	—	134	1	no	—
524	C₂²×C₄	—	134	1	no	—
525	C₂²×C₄	—	134	1	no	—
526	C₂²×C₄	—	134	1	no	—
527	C₂²×C₄	—	134	1	no	—
528	C₂²×C₄	—	134	1	no	—
529	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
530	M₁₆	—	2	1	no	—
531	M₁₆	—	2	1	no	—
532	M₁₆	—	2	1	no	—
533	M₁₆	—	268	2	no	—
534	M₁₆	—	67	2	no	—
535	M₁₆	—	134	4	no	—
536	M₁₆	—	134	1	no	—
537	M₁₆	—	134	1	no	—
538	M₁₆	—	134	1	no	—
539	M₁₆	#11761627	1	2	yes	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	268	2	no	—
547	C₂×C₈	—	67	1	no	—
548	C₂×C₈	—	67	1	no	—
549	C₂×C₈	—	67	2	no	—
550	C₂×C₈	—	67	2	no	—
551	C₂×C₈	—	67	1	no	—
552	C₂×C₈	—	67	1	no	—
553	C₂×C₈	—	134	2	no	—
554	C₂×C₈	—	134	2	no	—
555	C₂×C₈	—	134	2	no	—
556	C₂×C₈	—	134	2	no	—
557	C₂×C₈	—	134	4	no	—
558	C₂×C₈	—	134	1	no	—
559	C₂×C₈	—	134	1	no	—
560	C₂×C₈	—	134	1	no	—
561	C₂×C₈	—	134	1	no	—
562	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
563	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
564	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
565	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
566	C₄⋊C₄	—	67	1	no	—
567	C₄⋊C₄	—	67	1	no	—
568	C₄⋊C₄	—	67	1	no	—
569	C₄⋊C₄	—	67	1	no	—
570	C₄⋊C₄	—	134	1	no	—
571	C₄⋊C₄	—	134	1	no	—
572	C₄⋊C₄	—	134	1	no	—
573	C₄⋊C₄	—	134	1	no	—
574	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
575	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
576	C₂²⋊C₄	—	2	1	no	—
577	C₂²⋊C₄	—	134	1	no	—
578	C₂²⋊C₄	—	134	1	no	—
579	C₂²⋊C₄	—	134	1	no	—
580	C₂²⋊C₄	—	134	1	no	—
581	C₂²⋊C₄	—	134	4	no	—
582	C₂²⋊C₄	—	134	1	no	—
583	C₂²⋊C₄	—	134	1	no	—
584	C₂²⋊C₄	—	134	1	no	—
585	C₂²⋊C₄	—	134	1	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	134	1	no	—
590	C₄²	—	134	1	no	—
591	C₄²	—	134	1	no	—
592	C₄²	—	134	1	no	—
593	C₄²	—	134	1	no	—
594	C₄²	—	134	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	268	1	no	—
597	C₂³	—	67	1	no	—
598	C₂³	—	67	1	no	—
599	C₂³	—	134	2	no	—
600	C₂³	—	134	1	no	—
601	C₂³	—	134	1	no	—
602	C₂³	#41×D₆₇	1	1	yes	characteristic
603	Q₈	—	2	1	no	—
604	Q₈	—	2	1	no	—
605	D₄	—	2	1	no	—
606	D₄	—	2	1	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	1	no	—
609	D₄	—	268	2	no	—
610	D₄	—	268	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	268	2	no	—
620	C₂×C₄	—	268	2	no	—
621	C₂×C₄	—	268	1	no	—
622	C₂×C₄	—	268	1	no	—
623	C₂×C₄	—	67	1	no	—
624	C₂×C₄	—	67	1	no	—
625	C₂×C₄	—	134	2	no	—
626	C₂×C₄	—	134	1	no	—
627	C₂×C₄	—	134	1	no	—
628	C₂×C₄	—	134	1	no	—
629	C₂×C₄	—	134	1	no	—
630	C₂×C₄	—	134	1	no	—
631	C₂×C₄	—	134	1	no	—
632	C₂×C₄	—	134	1	no	—
633	C₂×C₄	—	134	1	no	—
634	C₂×C₄	—	134	1	no	—
635	C₂×C₄	—	134	1	no	—
636	C₂×C₄	—	134	1	no	—
637	C₂×C₄	—	134	1	no	—
638	C₂×C₄	—	134	1	no	—
639	C₂×C₄	—	134	1	no	—
640	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
641	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
642	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
643	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
644	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
645	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
646	C₈	—	2	1	no	—
647	C₈	—	2	1	no	—
648	C₈	—	2	1	no	—
649	C₈	—	2	1	no	—
650	C₈	—	2	2	no	—
651	C₈	—	4	1	no	—
652	C₈	—	268	1	no	—
653	C₈	—	67	2	no	—
654	C₈	—	67	2	no	—
655	C₈	—	134	1	no	—
656	C₈	—	134	1	no	—
657	C₈	—	134	2	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	268	2	no	—
664	C₂²	—	268	2	no	—
665	C₂²	—	67	2	no	—
666	C₂²	—	134	1	no	—
667	C₂²	—	134	1	no	—
668	C₂²	—	134	1	no	—
669	C₂²	—	134	1	no	—
670	C₂²	—	134	1	no	—
671	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
672	C₂²	#16863925	1	1	yes	characteristic
673	C₂²	#16863929	1	1	yes	characteristic
674	C₄	—	4	2	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	268	2	no	—
679	C₄	—	268	1	no	—
680	C₄	—	268	1	no	—
681	C₄	—	268	1	no	—
682	C₄	—	268	1	no	—
683	C₄	—	134	1	no	—
684	C₄	—	134	1	no	—
685	C₄	C₄×#11761627	1	1	yes	characteristic
686	C₄	#16863864	1	1	yes	characteristic
687	C₄	#123×D₆₇	1	1	yes	characteristic
688	C₄	#16863906	1	1	yes	characteristic
689	C₂	—	2	1	no	—
690	C₂	—	2	1	no	—
691	C₂	—	8	1	no	—
692	C₂	—	268	1	no	—
693	C₂	—	134	2	no	—
694	C₂	#22562736	1	1	yes	characteristic
695	C₂	#443×D₆₇	1	1	yes	characteristic
696	C₂	#22569109	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×#1929	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#16863903	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1929	D₆₇
hypocenter	C₆₇	#21592
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1929

Complements

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

N	H ≅ G/N	type
3. #405×D₆₇	C₂	semidirect
4. #22560854	C₂	semidirect
5. #22560809	C₂	semidirect
6. #22560808	C₂	semidirect
8. #22560412	C₂	semidirect
9. #22560307	C₂	semidirect
10. #22560091	C₂	semidirect
11. #22560087	C₂	semidirect
12. #22560049	C₂	semidirect
13. #22560047	C₂	semidirect
14. #22559979	C₂	semidirect
15. C₆₇×#1929	C₂	semidirect
21. #16863736	C₄	semidirect
22. #16863735	C₄	semidirect
23. #16863730	C₄	semidirect
24. #16863725	C₄	semidirect
25. #16863719	C₄	semidirect
26. #16863718	C₄	semidirect
27. #16863713	C₄	semidirect
28. #16863708	C₄	semidirect
353. #1929	D₆₇	semidirect
364. C₆₇	#21592	semidirect

Maximal subgroups

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

subgroup	index
#22570120	2
#22568906	2
#405×D₆₇	2
#22560854	2
#22560809	2
#22560808	2
#22560508	2
#22560412	2
#22560307	2
#22560091	2
#22560087	2
#22560049	2
#22560047	2
#22559979	2
C₆₇×#1929	2
#21592	67