Subgroups — #1953×D₆₇ #30859395

Order 17152.

858 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#430×D₆₇	C₂	1	2	yes	maximal
2	C₂×#108×D₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#108×D₆₇	C₂	1	1	yes	maximal, characteristic
4	#405×D₆₇	C₂	1	1	yes	maximal, characteristic
5	#22561000	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560999	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560998	C₂	1	2	yes	maximal, complemented
8	#22560997	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560996	C₂	1	2	yes	maximal, complemented
10	#344×D₆₇	C₂	1	2	yes	maximal
11	C₆₇×#1953	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₆₇	C₂²	1	2	yes	—
13	C₂×M₁₆×D₆₇	C₂²	1	2	yes	—
14	C₂×M₁₆×D₆₇	C₂²	1	1	yes	characteristic
15	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
16	#117×D₆₇	C₂²	1	1	yes	characteristic
17	#16863445	C₂²	1	2	yes	—
18	#16863444	C₂²	1	2	yes	—
19	#16863444	C₂²	1	2	yes	—
20	#16863443	—	2	4	no	—
21	C₂×#14523979	C₂²	1	1	yes	characteristic
22	C₂×#14523979	C₂²	1	1	yes	characteristic
23	C₂×#14523978	C₂²	1	2	yes	—
24	C₂×#14523978	C₂²	1	2	yes	—
25	#108×D₆₇	—	2	4	no	—
26	#108×D₆₇	—	2	1	no	—
27	#108×D₆₇	—	2	1	no	—
28	#108×D₆₇	—	2	1	no	—
29	#108×D₆₇	—	2	1	no	—
30	#108×D₆₇	C₄	1	4	yes	complemented
31	#108×D₆₇	C₄	1	4	yes	complemented
32	#16863354	C₂²	1	1	yes	characteristic
33	#16863353	—	2	1	no	—
34	#16863352	C₂²	1	1	yes	characteristic
35	#16863351	C₂²	1	1	yes	characteristic
36	#16863350	—	2	1	no	—
37	#97×D₆₇	—	2	1	no	—
38	C₄×C₈×D₆₇	—	2	1	no	—
39	#16863168	C₂²	1	2	yes	—
40	#16863167	C₂²	1	2	yes	—
41	#16863166	C₂²	1	2	yes	—
42	#430×C₆₇	C₂²	1	2	yes	—
43	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
45	#405×C₆₇	C₂²	1	1	yes	characteristic
46	#344×C₆₇	C₂²	1	2	yes	—
47	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
48	C₂×#11761612	C₂³	1	2	yes	—
49	C₂×#11761612	C₂³	1	2	yes	—
50	C₂×#11761612	C₂³	1	1	yes	characteristic
51	C₂×#11761611	—	2	1	no	—
52	C₂×#11761611	—	2	2	no	—
53	C₂×#11761611	—	2	2	no	—
54	M₁₆×D₆₇	—	2	2	no	—
55	M₁₆×D₆₇	—	2	2	no	—
56	M₁₆×D₆₇	—	2	1	no	—
57	M₁₆×D₆₇	—	2	1	no	—
58	M₁₆×D₆₇	—	2	2	no	—
59	M₁₆×D₆₇	—	2	2	no	—
60	M₁₆×D₆₇	—	2	2	no	—
61	M₁₆×D₆₇	—	2	2	no	—
62	M₁₆×D₆₇	C₂×C₄	1	4	yes	—
63	M₁₆×D₆₇	C₂×C₄	1	4	yes	—
64	M₁₆×D₆₇	D₄	1	2	yes	—
65	M₁₆×D₆₇	D₄	1	2	yes	—
66	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₆₇	—	2	1	no	—
68	C₂×C₈×D₆₇	—	2	2	no	—
69	C₂×C₈×D₆₇	—	2	2	no	—
70	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
71	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
72	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
73	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
74	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
75	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
76	C₂×C₈×D₆₇	Q₈	1	2	yes	—
77	C₂×C₈×D₆₇	Q₈	1	2	yes	—
78	#14524002	C₂³	1	1	yes	characteristic
79	#14524001	—	2	1	no	—
80	#14524000	—	2	1	no	—
81	#14523999	Q₈	1	2	yes	—
82	C₄⋊C₄×D₆₇	—	2	1	no	—
83	C₂²⋊C₄×D₆₇	Q₈	1	2	yes	—
84	C₄²×D₆₇	—	2	1	no	—
85	#14523979	—	2	4	no	—
86	#14523979	—	2	1	no	—
87	#14523979	—	2	1	no	—
88	#14523979	C₂×C₄	1	4	yes	complemented
89	#14523978	—	2	4	no	—
90	#14523978	—	2	2	no	—
91	#14523978	—	2	2	no	—
92	#14523978	—	2	4	no	—
93	#14523978	C₂×C₄	1	8	yes	complemented
94	#14523954	—	2	1	no	—
95	#14523953	—	2	1	no	—
96	#14523953	—	2	1	no	—
97	C₄×C₆₇⋊C₈	—	2	1	no	—
98	C₈×Dic₆₇	—	2	1	no	—
99	C₈×Dic₆₇	—	2	1	no	—
100	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
101	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
102	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
104	#117×C₆₇	C₂³	1	1	yes	characteristic
105	#108×C₆₇	—	2	4	no	—
106	#108×C₆₇	—	2	1	no	—
107	#108×C₆₇	—	2	1	no	—
108	#108×C₆₇	C₂×C₄	1	4	yes	complemented
109	#97×C₆₇	—	2	1	no	—
110	C₄×C₈×C₆₇	—	2	1	no	—
111	C₂³×D₆₇	C₂×Q₈	1	1	yes	characteristic
112	C₂²×Dic₆₇	C₂×Q₈	1	1	yes	characteristic
113	C₂×C₄×D₆₇	—	2	2	no	—
114	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₆₇	C₂×Q₈	1	1	yes	characteristic
121	C₂×C₄×D₆₇	C₂×Q₈	1	1	yes	characteristic
122	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
123	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
124	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
125	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
126	#11761612	—	2	2	no	—
127	#11761612	—	2	1	no	—
128	#11761612	—	2	2	no	—
129	#11761612	—	2	2	no	—
130	#11761612	C₂²×C₄	1	4	yes	—
131	#11761612	C₂×D₄	1	2	yes	—
132	#11761611	—	2	4	no	—
133	#11761611	—	2	4	no	—
134	#11761611	—	2	2	no	—
135	#11761611	—	2	2	no	—
136	#11761611	—	4	2	no	—
137	#11761611	—	4	2	no	—
138	C₂×C₆₇⋊C₈	—	2	1	no	—
139	C₂×C₆₇⋊C₈	—	2	2	no	—
140	C₂×C₆₇⋊C₈	—	2	2	no	—
141	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
142	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
143	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₆₇⋊C₈	C₂×Q₈	1	2	yes	—
145	C₈×D₆₇	—	2	4	no	—
146	C₈×D₆₇	—	2	4	no	—
147	C₈×D₆₇	—	2	2	no	—
148	C₈×D₆₇	—	2	2	no	—
149	C₈×D₆₇	—	4	2	no	—
150	C₈×D₆₇	—	4	2	no	—
151	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
152	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
153	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
154	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
155	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
156	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
157	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
158	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
159	C₄⋊Dic₆₇	—	2	1	no	—
160	Dic₆₇⋊C₄	—	2	2	no	—
161	C₂²⋊Dic₆₇	C₂×Q₈	1	2	yes	—
162	(C₂×D₆₇)⋊C₄	—	2	2	no	—
163	C₄×Dic₆₇	—	2	1	no	—
164	C₄×Dic₆₇	—	2	2	no	—
165	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
166	M₁₆×C₆₇	—	2	2	no	—
167	M₁₆×C₆₇	—	2	1	no	—
168	M₁₆×C₆₇	—	2	2	no	—
169	M₁₆×C₆₇	—	2	2	no	—
170	M₁₆×C₆₇	C₂²×C₄	1	4	yes	—
171	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
172	C₂×C₈×C₆₇	—	2	2	no	—
173	C₂×C₈×C₆₇	—	2	1	no	—
174	C₂×C₈×C₆₇	—	2	2	no	—
175	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
176	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₆₇	C₂×Q₈	1	2	yes	—
179	C₄⋊C₄×C₆₇	—	2	1	no	—
180	C₂²⋊C₄×C₆₇	C₂×Q₈	1	2	yes	—
181	C₄²×C₆₇	—	2	1	no	—
182	C₂³×C₆₇	C₂²×Q₈	1	1	yes	characteristic
183	C₂²×D₆₇	—	4	2	no	—
184	C₂²×D₆₇	C₄×Q₈	1	1	yes	characteristic
185	C₂²×D₆₇	C₄×Q₈	1	1	yes	characteristic
186	C₂²×D₆₇	C₂²⋊Q₈	1	1	yes	characteristic
187	C₂²×D₆₇	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂²×D₆₇	C₄⋊Q₈	1	1	yes	characteristic
189	C₂²×D₆₇	C₄⋊Q₈	1	1	yes	characteristic
190	C₂×C₄×C₆₇	—	2	2	no	—
191	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
197	C₂×Dic₆₇	—	2	2	no	—
198	C₂×Dic₆₇	C₄×Q₈	1	1	yes	characteristic
199	C₂×Dic₆₇	C₄×Q₈	1	1	yes	characteristic
200	C₂×Dic₆₇	C₂²⋊Q₈	1	1	yes	characteristic
201	C₂×Dic₆₇	C₂²⋊Q₈	1	1	yes	characteristic
202	C₂×Dic₆₇	C₄⋊Q₈	1	1	yes	characteristic
203	C₂×Dic₆₇	C₄⋊Q₈	1	1	yes	characteristic
204	C₄×D₆₇	—	4	4	no	—
205	C₄×D₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₄×D₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₄×D₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₄×D₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
210	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
211	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
212	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
213	C₄×D₆₇	#121	1	1	yes	characteristic
214	C₄×D₆₇	#121	1	1	yes	characteristic
215	C₄×D₆₇	#121	1	1	yes	characteristic
216	C₄×D₆₇	#121	1	1	yes	characteristic
217	C₄×D₆₇	#125	1	1	yes	characteristic
218	C₄×D₆₇	#125	1	1	yes	characteristic
219	C₄×D₆₇	#125	1	1	yes	characteristic
220	C₄×D₆₇	#125	1	1	yes	characteristic
221	C₈×C₆₇	—	2	4	no	—
222	C₈×C₆₇	—	2	2	no	—
223	C₈×C₆₇	—	4	2	no	—
224	C₈×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
225	C₈×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
226	C₆₇⋊C₈	—	2	4	no	—
227	C₆₇⋊C₈	—	2	2	no	—
228	C₆₇⋊C₈	—	4	2	no	—
229	C₆₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
230	C₆₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
231	C₂²×C₆₇	—	4	1	no	—
232	C₂²×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
233	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
234	C₂²×C₆₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
235	C₂×D₆₇	—	2	2	no	—
236	C₂×D₆₇	—	2	2	no	—
237	C₂×D₆₇	—	2	2	no	—
238	C₂×D₆₇	—	4	1	no	—
239	C₂×D₆₇	—	4	1	no	—
240	C₂×D₆₇	—	4	1	no	—
241	C₂×D₆₇	#389	1	1	yes	characteristic
242	C₂×D₆₇	#389	1	1	yes	characteristic
243	C₂×D₆₇	#389	1	1	yes	characteristic
244	C₂×D₆₇	#389	1	1	yes	characteristic
245	C₄×C₆₇	—	4	2	no	—
246	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
247	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
248	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
249	C₄×C₆₇	C₂×#125	1	1	yes	characteristic
250	Dic₆₇	—	4	2	no	—
251	Dic₆₇	#389	1	1	yes	characteristic
252	Dic₆₇	#389	1	1	yes	characteristic
253	Dic₆₇	#389	1	1	yes	characteristic
254	Dic₆₇	#389	1	1	yes	characteristic
255	C₂×#1953	—	67	1	no	maximal, Sylow
256	C₂×C₆₇	—	2	1	no	—
257	C₂×C₆₇	—	2	1	no	—
258	C₂×C₆₇	—	2	1	no	—
259	C₂×C₆₇	C₂×#389	1	1	yes	characteristic
260	D₆₇	—	2	1	no	—
261	D₆₇	—	2	1	no	—
262	D₆₇	—	2	1	no	—
263	D₆₇	#1953	1	2	yes	direct product factor
264	C₂×#430	—	67	2	no	—
265	C₂²×#108	—	67	1	no	—
266	C₂²×#108	—	67	1	no	—
267	C₂×#405	—	67	1	no	—
268	#1953	—	67	2	no	—
269	#1953	—	67	1	no	—
270	#1953	—	67	1	no	—
271	#1953	—	67	1	no	—
272	#1953	—	67	2	no	—
273	#1953	D₆₇	1	1	yes	characteristic, direct product factor
274	C₂×#344	—	67	2	no	—
275	C₆₇	C₂×#1953	1	1	yes	characteristic, complemented, Sylow
276	C₂²×M₁₆	—	67	1	no	—
277	C₂²×M₁₆	—	67	2	no	—
278	C₂²×M₁₆	—	67	2	no	—
279	C₂³×C₈	—	67	1	no	—
280	C₂×#117	—	67	1	no	—
281	#430	—	67	2	no	—
282	#430	—	67	2	no	—
283	#430	—	67	2	no	—
284	#430	—	134	4	no	—
285	#430	C₂×D₆₇	1	2	yes	—
286	C₂×#108	—	67	2	no	—
287	C₂×#108	—	67	1	no	—
288	C₂×#108	—	67	4	no	—
289	C₂×#108	—	67	4	no	—
290	C₂×#108	—	67	2	no	—
291	C₂×#108	—	67	1	no	—
292	C₂×#108	—	134	1	no	—
293	C₂×#108	—	134	1	no	—
294	C₂×#108	—	134	1	no	—
295	C₂×#108	—	134	1	no	—
296	C₂×#108	—	134	4	no	—
297	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
298	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
299	#405	—	67	1	no	—
300	#405	—	67	1	no	—
301	#405	—	67	1	no	—
302	#405	—	134	1	no	—
303	#405	—	134	1	no	—
304	#405	C₂×D₆₇	1	1	yes	characteristic
305	C₂×#97	—	134	1	no	—
306	C₂×C₄×C₈	—	134	1	no	—
307	#344	—	67	2	no	—
308	#344	—	67	2	no	—
309	#344	—	67	2	no	—
310	#344	C₂×D₆₇	1	2	yes	—
311	C₂³×C₄	—	67	1	no	—
312	C₂×M₁₆	—	67	2	no	—
313	C₂×M₁₆	—	67	1	no	—
314	C₂×M₁₆	—	67	4	no	—
315	C₂×M₁₆	—	67	4	no	—
316	C₂×M₁₆	—	67	2	no	—
317	C₂×M₁₆	—	67	2	no	—
318	C₂×M₁₆	—	67	2	no	—
319	C₂×M₁₆	—	134	2	no	—
320	C₂×M₁₆	—	134	1	no	—
321	C₂×M₁₆	—	134	2	no	—
322	C₂×M₁₆	—	134	2	no	—
323	C₂×M₁₆	—	134	2	no	—
324	C₂×M₁₆	—	134	2	no	—
325	C₂×M₁₆	—	134	2	no	—
326	C₂×M₁₆	—	134	2	no	—
327	C₂×M₁₆	—	134	2	no	—
328	C₂×M₁₆	—	134	1	no	—
329	C₂×M₁₆	—	134	1	no	—
330	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
331	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
332	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
333	C₂²×C₈	—	67	1	no	—
334	C₂²×C₈	—	67	2	no	—
335	C₂²×C₈	—	67	2	no	—
336	C₂²×C₈	—	67	1	no	—
337	C₂²×C₈	—	67	1	no	—
338	C₂²×C₈	—	67	1	no	—
339	C₂²×C₈	—	67	1	no	—
340	C₂²×C₈	—	67	2	no	—
341	C₂²×C₈	—	67	2	no	—
342	C₂²×C₈	—	134	2	no	—
343	C₂²×C₈	—	134	1	no	—
344	C₂²×C₈	—	134	2	no	—
345	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
346	#117	—	67	1	no	—
347	#117	—	67	2	no	—
348	#117	—	134	1	no	—
349	#117	—	134	1	no	—
350	#117	C₂²×D₆₇	1	1	yes	characteristic
351	C₂×C₄⋊C₄	—	134	1	no	—
352	C₂×C₂²⋊C₄	—	67	2	no	—
353	C₂×C₄²	—	134	1	no	—
354	#108	—	2	4	no	—
355	#108	—	2	1	no	—
356	#108	—	2	1	no	—
357	#108	—	67	8	no	—
358	#108	—	67	4	no	—
359	#108	—	134	4	no	—
360	#108	—	134	2	no	—
361	#108	—	134	2	no	—
362	#108	—	134	4	no	—
363	#108	—	134	4	no	—
364	#108	—	134	1	no	—
365	#108	—	134	1	no	—
366	#108	C₄×D₆₇	1	4	yes	complemented
367	#97	—	2	1	no	—
368	#97	—	134	1	no	—
369	#97	—	134	1	no	—
370	#97	—	134	1	no	—
371	C₄×C₈	—	2	1	no	—
372	C₄×C₈	—	134	1	no	—
373	C₄×C₈	—	134	1	no	—
374	C₄×C₈	—	134	1	no	—
375	C₂⁴	—	67	1	no	—
376	C₂²×C₄	—	67	1	no	—
377	C₂²×C₄	—	67	1	no	—
378	C₂²×C₄	—	67	1	no	—
379	C₂²×C₄	—	67	1	no	—
380	C₂²×C₄	—	67	1	no	—
381	C₂²×C₄	—	67	1	no	—
382	C₂²×C₄	—	67	1	no	—
383	C₂²×C₄	—	67	1	no	—
384	C₂²×C₄	—	67	1	no	—
385	C₂²×C₄	—	67	1	no	—
386	C₂²×C₄	—	67	1	no	—
387	C₂²×C₄	—	67	1	no	—
388	C₂²×C₄	—	67	1	no	—
389	C₂²×C₄	—	134	2	no	—
390	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
391	M₁₆	—	2	2	no	—
392	M₁₆	—	2	1	no	—
393	M₁₆	—	2	2	no	—
394	M₁₆	—	2	2	no	—
395	M₁₆	—	268	2	no	—
396	M₁₆	—	268	2	no	—
397	M₁₆	—	67	4	no	—
398	M₁₆	—	67	2	no	—
399	M₁₆	—	134	4	no	—
400	M₁₆	—	134	4	no	—
401	M₁₆	—	134	2	no	—
402	M₁₆	—	134	2	no	—
403	M₁₆	—	134	2	no	—
404	M₁₆	—	134	2	no	—
405	M₁₆	—	134	2	no	—
406	M₁₆	—	134	1	no	—
407	M₁₆	C₂×C₄×D₆₇	1	4	yes	—
408	M₁₆	D₄×D₆₇	1	2	yes	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	268	2	no	—
413	C₂×C₈	—	268	2	no	—
414	C₂×C₈	—	67	2	no	—
415	C₂×C₈	—	67	1	no	—
416	C₂×C₈	—	67	1	no	—
417	C₂×C₈	—	67	2	no	—
418	C₂×C₈	—	67	2	no	—
419	C₂×C₈	—	67	2	no	—
420	C₂×C₈	—	67	2	no	—
421	C₂×C₈	—	67	2	no	—
422	C₂×C₈	—	67	2	no	—
423	C₂×C₈	—	67	2	no	—
424	C₂×C₈	—	67	2	no	—
425	C₂×C₈	—	67	2	no	—
426	C₂×C₈	—	134	4	no	—
427	C₂×C₈	—	134	4	no	—
428	C₂×C₈	—	134	2	no	—
429	C₂×C₈	—	134	2	no	—
430	C₂×C₈	—	134	2	no	—
431	C₂×C₈	—	134	1	no	—
432	C₂×C₈	—	134	2	no	—
433	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
434	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
435	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
436	C₂×C₈	Q₈×D₆₇	1	2	yes	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	134	2	no	—
439	C₄⋊C₄	—	134	1	no	—
440	C₂²⋊C₄	—	67	2	no	—
441	C₂²⋊C₄	—	134	2	no	—
442	C₂²⋊C₄	Q₈×D₆₇	1	2	yes	—
443	C₄²	—	2	1	no	—
444	C₄²	—	134	2	no	—
445	C₄²	—	134	1	no	—
446	C₂³	—	268	2	no	—
447	C₂³	—	67	1	no	—
448	C₂³	—	67	1	no	—
449	C₂³	—	67	1	no	—
450	C₂³	—	67	1	no	—
451	C₂³	—	67	1	no	—
452	C₂³	—	67	1	no	—
453	C₂³	C₂×Q₈×D₆₇	1	1	yes	characteristic
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	268	4	no	—
456	C₂×C₄	—	67	1	no	—
457	C₂×C₄	—	67	1	no	—
458	C₂×C₄	—	67	1	no	—
459	C₂×C₄	—	67	1	no	—
460	C₂×C₄	—	67	1	no	—
461	C₂×C₄	—	67	1	no	—
462	C₂×C₄	—	67	1	no	—
463	C₂×C₄	—	67	1	no	—
464	C₂×C₄	—	67	1	no	—
465	C₂×C₄	—	67	1	no	—
466	C₂×C₄	—	67	1	no	—
467	C₂×C₄	—	67	1	no	—
468	C₂×C₄	—	67	1	no	—
469	C₂×C₄	—	67	1	no	—
470	C₂×C₄	—	67	1	no	—
471	C₂×C₄	—	67	1	no	—
472	C₂×C₄	—	67	1	no	—
473	C₂×C₄	—	67	1	no	—
474	C₂×C₄	—	67	1	no	—
475	C₂×C₄	—	67	1	no	—
476	C₂×C₄	—	67	1	no	—
477	C₂×C₄	—	67	1	no	—
478	C₂×C₄	—	134	2	no	—
479	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
480	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
481	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
482	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
483	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
484	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
485	C₈	—	2	4	no	—
486	C₈	—	2	2	no	—
487	C₈	—	4	2	no	—
488	C₈	—	268	2	no	—
489	C₈	—	67	2	no	—
490	C₈	—	67	2	no	—
491	C₈	—	134	4	no	—
492	C₈	—	134	2	no	—
493	C₈	C₄⋊C₄×D₆₇	1	2	yes	—
494	C₈	C₄⋊C₄×D₆₇	1	2	yes	—
495	C₂²	—	4	1	no	—
496	C₂²	—	268	1	no	—
497	C₂²	—	268	1	no	—
498	C₂²	—	268	1	no	—
499	C₂²	—	67	1	no	—
500	C₂²	—	67	1	no	—
501	C₂²	—	67	1	no	—
502	C₂²	—	67	1	no	—
503	C₂²	—	134	2	no	—
504	C₂²	—	134	2	no	—
505	C₂²	—	134	2	no	—
506	C₂²	C₄×Q₈×D₆₇	1	1	yes	characteristic
507	C₂²	C₂²⋊Q₈×D₆₇	1	1	yes	characteristic
508	C₂²	C₄⋊Q₈×D₆₇	1	1	yes	characteristic
509	C₄	—	4	2	no	—
510	C₄	—	268	2	no	—
511	C₄	—	67	1	no	—
512	C₄	—	67	1	no	—
513	C₄	—	67	1	no	—
514	C₄	—	67	1	no	—
515	C₄	C₂×C₄⋊C₄×D₆₇	1	1	yes	characteristic
516	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
517	C₄	#121×D₆₇	1	1	yes	characteristic
518	C₄	#125×D₆₇	1	1	yes	characteristic
519	C₂	—	2	1	no	—
520	C₂	—	2	1	no	—
521	C₂	—	2	1	no	—
522	C₂	—	67	2	no	—
523	C₂	—	134	1	no	—
524	C₂	—	134	1	no	—
525	C₂	—	134	1	no	—
526	C₂	#389×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#121×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1953	C₂
socle	C₂×C₆₇	C₂×#389
prime radical	C₂³×D₆₇	C₂×Q₈
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1953	D₆₇
hypocenter	C₆₇	C₂×#1953
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1953

Complements

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

N	H ≅ G/N	type
5. #22561000	C₂	semidirect
6. #22560999	C₂	semidirect
7. #22560998	C₂	semidirect
8. #22560997	C₂	semidirect
9. #22560996	C₂	semidirect
11. C₆₇×#1953	C₂	semidirect
30. #108×D₆₇	C₄	semidirect
31. #108×D₆₇	C₄	semidirect
88. #14523979	C₂×C₄	semidirect
93. #14523978	C₂×C₄	semidirect
108. #108×C₆₇	C₂×C₄	semidirect
263. D₆₇	#1953	direct (N × H)
273. #1953	D₆₇	direct (N × H)
275. C₆₇	C₂×#1953	semidirect
366. #108	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#430×D₆₇	2
C₂×#108×D₆₇	2
#405×D₆₇	2
#22561000	2
#22560999	2
#22560998	2
#22560997	2
#22560996	2
#344×D₆₇	2
C₆₇×#1953	2
C₂×#1953	67

Subgroups — #1953×D67 #30859395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1953×D₆₇ #30859395