Subgroups — #1378×D₆₇ #30770694

Order 17152.

586 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×M₃₂×D₆₇	C₂	1	1	yes	maximal, characteristic
3	#405×D₆₇	C₂	1	1	yes	maximal, characteristic
4	#22558296	C₂	1	1	yes	maximal, characteristic, complemented
5	#22558295	C₂	1	1	yes	maximal, characteristic, complemented
6	#22558294	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1378	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₆₇	C₄	1	1	yes	characteristic
9	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
10	#117×D₆₇	C₄	1	1	yes	characteristic
11	C₂×#14523983	C₂²	1	1	yes	characteristic
12	C₂×#14523983	C₂²	1	1	yes	characteristic
13	C₂×#14523982	—	2	1	no	—
14	C₂×#14523982	C₄	1	2	yes	complemented
15	M₃₂×D₆₇	—	2	1	no	—
16	M₃₂×D₆₇	—	2	1	no	—
17	M₃₂×D₆₇	—	2	1	no	—
18	M₃₂×D₆₇	—	2	1	no	—
19	M₃₂×D₆₇	—	2	1	no	—
20	M₃₂×D₆₇	—	2	1	no	—
21	M₃₂×D₆₇	C₄	1	2	yes	complemented
22	M₃₂×D₆₇	C₄	1	2	yes	complemented
23	C₂×C₁₆×D₆₇	—	2	1	no	—
24	C₂×C₁₆×D₆₇	C₄	1	2	yes	complemented
25	#16863354	C₄	1	1	yes	characteristic
26	#16863353	—	2	1	no	—
27	#16863352	C₄	1	1	yes	characteristic
28	#16863351	C₂²	1	1	yes	characteristic
29	#16863350	—	2	1	no	—
30	#97×D₆₇	—	2	1	no	—
31	C₄×C₈×D₆₇	—	2	1	no	—
32	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
34	#405×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
36	C₂×#11761612	C₂×C₄	1	1	yes	characteristic
37	C₂×#11761611	—	2	1	no	—
38	M₁₆×D₆₇	—	2	1	no	—
39	M₁₆×D₆₇	—	2	1	no	—
40	M₁₆×D₆₇	C₈	1	2	yes	—
41	M₁₆×D₆₇	C₈	1	2	yes	—
42	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₆₇	—	2	1	no	—
44	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
49	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
50	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
51	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
52	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
53	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
54	C₂×C₈×D₆₇	Q₈	1	1	yes	characteristic
55	C₂×C₈×D₆₇	Q₈	1	1	yes	characteristic
56	#14524002	C₂×C₄	1	1	yes	characteristic
57	#14524001	—	2	1	no	—
58	#14524000	—	2	1	no	—
59	#14523999	C₈	1	2	yes	—
60	C₄⋊C₄×D₆₇	—	2	1	no	—
61	C₂²⋊C₄×D₆₇	C₈	1	2	yes	—
62	C₄²×D₆₇	—	2	1	no	—
63	#14523983	—	2	1	no	—
64	#14523983	—	2	1	no	—
65	#14523983	—	2	1	no	—
66	#14523983	C₂×C₄	1	2	yes	complemented
67	#14523982	—	2	2	no	—
68	#14523982	—	2	2	no	—
69	#14523982	—	2	2	no	—
70	#14523982	—	2	2	no	—
71	C₂×C₆₇⋊C₁₆	—	2	1	no	—
72	C₂×C₆₇⋊C₁₆	C₂×C₄	1	2	yes	complemented
73	C₁₆×D₆₇	—	2	2	no	—
74	C₁₆×D₆₇	—	2	2	no	—
75	C₁₆×D₆₇	—	2	2	no	—
76	C₁₆×D₆₇	—	2	2	no	—
77	#14523954	—	2	1	no	—
78	#14523953	—	2	1	no	—
79	#14523953	—	2	1	no	—
80	C₄×C₆₇⋊C₈	—	2	1	no	—
81	C₈×Dic₆₇	—	2	1	no	—
82	C₈×Dic₆₇	—	2	1	no	—
83	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
85	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
86	M₃₂×C₆₇	—	2	1	no	—
87	M₃₂×C₆₇	—	2	1	no	—
88	M₃₂×C₆₇	—	2	1	no	—
89	M₃₂×C₆₇	C₂×C₄	1	2	yes	complemented
90	C₂×C₁₆×C₆₇	—	2	1	no	—
91	C₂×C₁₆×C₆₇	C₂×C₄	1	2	yes	complemented
92	#97×C₆₇	—	2	1	no	—
93	C₄×C₈×C₆₇	—	2	1	no	—
94	C₂³×D₆₇	C₂×C₈	1	1	yes	characteristic
95	C₂²×Dic₆₇	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₆₇	—	2	2	no	—
97	C₂×C₄×D₆₇	C₄²	1	1	yes	characteristic
98	C₂×C₄×D₆₇	C₄²	1	1	yes	characteristic
99	C₂×C₄×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₆₇	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₆₇	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₆₇	M₁₆	1	1	yes	characteristic
106	C₂×C₄×D₆₇	M₁₆	1	1	yes	characteristic
107	C₂×C₄×D₆₇	M₁₆	1	1	yes	characteristic
108	C₂×C₄×D₆₇	M₁₆	1	1	yes	characteristic
109	#11761612	—	2	1	no	—
110	#11761612	C₂×C₈	1	2	yes	—
111	#11761611	—	2	2	no	—
112	#11761611	—	2	2	no	—
113	C₂×C₆₇⋊C₈	—	2	1	no	—
114	C₂×C₆₇⋊C₈	C₄²	1	1	yes	characteristic
115	C₂×C₆₇⋊C₈	C₄²	1	1	yes	characteristic
116	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₆₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₆₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
120	C₈×D₆₇	—	2	2	no	—
121	C₈×D₆₇	—	2	2	no	—
122	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
123	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
124	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
125	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
126	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
127	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
128	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
129	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
130	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
131	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
132	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
133	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
134	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
135	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
136	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
137	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
138	C₄⋊Dic₆₇	—	2	1	no	—
139	Dic₆₇⋊C₄	—	2	2	no	—
140	C₂²⋊Dic₆₇	C₂×C₈	1	2	yes	—
141	(C₂×D₆₇)⋊C₄	—	2	2	no	—
142	C₄×Dic₆₇	—	2	1	no	—
143	C₄×Dic₆₇	—	2	2	no	—
144	C₆₇⋊C₁₆	—	2	2	no	—
145	C₆₇⋊C₁₆	—	2	2	no	—
146	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
147	M₁₆×C₆₇	—	2	1	no	—
148	M₁₆×C₆₇	C₂×C₈	1	2	yes	—
149	C₂×C₈×C₆₇	—	2	1	no	—
150	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₆₇	C₂×Q₈	1	1	yes	characteristic
156	C₄⋊C₄×C₆₇	—	2	1	no	—
157	C₂²⋊C₄×C₆₇	C₂×C₈	1	2	yes	—
158	C₄²×C₆₇	—	2	1	no	—
159	C₁₆×C₆₇	—	2	2	no	—
160	C₁₆×C₆₇	—	2	2	no	—
161	C₂³×C₆₇	C₂²×C₈	1	1	yes	characteristic
162	C₂²×D₆₇	—	4	2	no	—
163	C₂²×D₆₇	C₄×C₈	1	1	yes	characteristic
164	C₂²×D₆₇	C₄×C₈	1	1	yes	characteristic
165	C₂²×D₆₇	C₂²⋊C₈	1	1	yes	characteristic
166	C₂²×D₆₇	C₂²⋊C₈	1	1	yes	characteristic
167	C₂²×D₆₇	C₄⋊C₈	1	1	yes	characteristic
168	C₂²×D₆₇	C₄⋊C₈	1	1	yes	characteristic
169	C₂×C₄×C₆₇	—	2	2	no	—
170	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
171	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₂×M₁₆	1	1	yes	characteristic
175	C₂×C₄×C₆₇	C₂×M₁₆	1	1	yes	characteristic
176	C₂×Dic₆₇	—	2	2	no	—
177	C₂×Dic₆₇	C₄×C₈	1	1	yes	characteristic
178	C₂×Dic₆₇	C₄×C₈	1	1	yes	characteristic
179	C₂×Dic₆₇	C₂²⋊C₈	1	1	yes	characteristic
180	C₂×Dic₆₇	C₂²⋊C₈	1	1	yes	characteristic
181	C₂×Dic₆₇	C₄⋊C₈	1	1	yes	characteristic
182	C₂×Dic₆₇	C₄⋊C₈	1	1	yes	characteristic
183	C₄×D₆₇	—	4	4	no	—
184	C₄×D₆₇	#95	1	1	yes	characteristic
185	C₄×D₆₇	#95	1	1	yes	characteristic
186	C₄×D₆₇	#95	1	1	yes	characteristic
187	C₄×D₆₇	#95	1	1	yes	characteristic
188	C₄×D₆₇	#97	1	1	yes	characteristic
189	C₄×D₆₇	#97	1	1	yes	characteristic
190	C₄×D₆₇	#97	1	1	yes	characteristic
191	C₄×D₆₇	#97	1	1	yes	characteristic
192	C₄×D₆₇	C₂²⋊C₈	1	1	yes	characteristic
193	C₄×D₆₇	C₂²⋊C₈	1	1	yes	characteristic
194	C₄×D₆₇	C₂²⋊C₈	1	1	yes	characteristic
195	C₄×D₆₇	C₂²⋊C₈	1	1	yes	characteristic
196	C₄×D₆₇	C₄⋊C₈	1	1	yes	characteristic
197	C₄×D₆₇	C₄⋊C₈	1	1	yes	characteristic
198	C₄×D₆₇	C₄⋊C₈	1	1	yes	characteristic
199	C₄×D₆₇	C₄⋊C₈	1	1	yes	characteristic
200	C₈×C₆₇	—	2	2	no	—
201	C₈×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₈×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₆₇⋊C₈	—	2	2	no	—
206	C₆₇⋊C₈	#95	1	1	yes	characteristic
207	C₆₇⋊C₈	#95	1	1	yes	characteristic
208	C₆₇⋊C₈	#95	1	1	yes	characteristic
209	C₆₇⋊C₈	#95	1	1	yes	characteristic
210	C₂²×C₆₇	—	4	1	no	—
211	C₂²×C₆₇	C₂×C₄×C₈	1	1	yes	characteristic
212	C₂²×C₆₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
213	C₂²×C₆₇	C₂×C₄⋊C₈	1	1	yes	characteristic
214	C₂×D₆₇	—	2	2	no	—
215	C₂×D₆₇	—	2	2	no	—
216	C₂×D₆₇	—	2	2	no	—
217	C₂×D₆₇	—	4	1	no	—
218	C₂×D₆₇	—	4	1	no	—
219	C₂×D₆₇	—	4	1	no	—
220	C₂×D₆₇	#336	1	1	yes	characteristic
221	C₂×D₆₇	#336	1	1	yes	characteristic
222	C₂×D₆₇	#336	1	1	yes	characteristic
223	C₂×D₆₇	#336	1	1	yes	characteristic
224	C₄×C₆₇	—	4	2	no	—
225	C₄×C₆₇	C₂×#95	1	1	yes	characteristic
226	C₄×C₆₇	C₂×#97	1	1	yes	characteristic
227	C₄×C₆₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
228	C₄×C₆₇	C₂×C₄⋊C₈	1	1	yes	characteristic
229	Dic₆₇	—	4	2	no	—
230	Dic₆₇	#336	1	1	yes	characteristic
231	Dic₆₇	#336	1	1	yes	characteristic
232	Dic₆₇	#336	1	1	yes	characteristic
233	Dic₆₇	#336	1	1	yes	characteristic
234	C₂×#1378	—	67	1	no	maximal, Sylow
235	C₂×C₆₇	—	2	1	no	—
236	C₂×C₆₇	—	2	1	no	—
237	C₂×C₆₇	—	2	1	no	—
238	C₂×C₆₇	C₂×#336	1	1	yes	characteristic
239	D₆₇	—	2	1	no	—
240	D₆₇	—	2	1	no	—
241	D₆₇	—	2	1	no	—
242	D₆₇	#1378	1	2	yes	direct product factor
243	C₂²×M₃₂	—	67	1	no	—
244	C₂²×M₃₂	—	67	1	no	—
245	C₂×#405	—	67	1	no	—
246	#1378	—	67	1	no	—
247	#1378	—	67	1	no	—
248	#1378	—	67	1	no	—
249	#1378	D₆₇	1	1	yes	characteristic, direct product factor
250	C₆₇	C₂×#1378	1	1	yes	characteristic, complemented, Sylow
251	C₂²×M₁₆	—	67	1	no	—
252	C₂³×C₈	—	67	1	no	—
253	C₂×#117	—	67	1	no	—
254	C₂×M₃₂	—	67	1	no	—
255	C₂×M₃₂	—	67	2	no	—
256	C₂×M₃₂	—	67	1	no	—
257	C₂×M₃₂	—	67	2	no	—
258	C₂×M₃₂	—	67	2	no	—
259	C₂×M₃₂	—	134	1	no	—
260	C₂×M₃₂	—	134	1	no	—
261	C₂×M₃₂	—	134	1	no	—
262	C₂×M₃₂	—	134	1	no	—
263	C₂×M₃₂	—	134	1	no	—
264	C₂×M₃₂	—	134	1	no	—
265	C₂×M₃₂	—	134	1	no	—
266	C₂×M₃₂	C₂×D₆₇	1	1	yes	characteristic
267	C₂×M₃₂	C₂×D₆₇	1	1	yes	characteristic
268	C₂²×C₁₆	—	67	2	no	—
269	C₂²×C₁₆	—	134	1	no	—
270	#405	—	67	1	no	—
271	#405	—	67	1	no	—
272	#405	—	67	1	no	—
273	#405	—	134	1	no	—
274	#405	—	134	1	no	—
275	#405	C₂×D₆₇	1	1	yes	characteristic
276	C₂×#97	—	134	1	no	—
277	C₂×C₄×C₈	—	134	1	no	—
278	C₂³×C₄	—	67	1	no	—
279	C₂×M₁₆	—	67	1	no	—
280	C₂×M₁₆	—	67	2	no	—
281	C₂×M₁₆	—	67	2	no	—
282	C₂×M₁₆	—	134	1	no	—
283	C₂×M₁₆	—	134	1	no	—
284	C₂×M₁₆	—	134	1	no	—
285	C₂×M₁₆	C₄×D₆₇	1	1	yes	characteristic
286	C₂²×C₈	—	67	1	no	—
287	C₂²×C₈	—	67	1	no	—
288	C₂²×C₈	—	67	1	no	—
289	C₂²×C₈	—	67	1	no	—
290	C₂²×C₈	—	67	1	no	—
291	C₂²×C₈	—	67	1	no	—
292	C₂²×C₈	—	67	1	no	—
293	C₂²×C₈	—	67	1	no	—
294	C₂²×C₈	—	67	1	no	—
295	C₂²×C₈	—	67	1	no	—
296	C₂²×C₈	—	67	1	no	—
297	C₂²×C₈	—	67	1	no	—
298	C₂²×C₈	—	67	1	no	—
299	C₂²×C₈	—	134	1	no	—
300	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
301	#117	—	67	1	no	—
302	#117	—	67	2	no	—
303	#117	—	134	1	no	—
304	#117	—	134	1	no	—
305	#117	C₄×D₆₇	1	1	yes	characteristic
306	C₂×C₄⋊C₄	—	134	1	no	—
307	C₂×C₂²⋊C₄	—	67	2	no	—
308	C₂×C₄²	—	134	1	no	—
309	M₃₂	—	2	1	no	—
310	M₃₂	—	2	1	no	—
311	M₃₂	—	2	1	no	—
312	M₃₂	—	67	2	no	—
313	M₃₂	—	134	2	no	—
314	M₃₂	—	134	2	no	—
315	M₃₂	—	134	2	no	—
316	M₃₂	—	134	2	no	—
317	M₃₂	—	134	1	no	—
318	M₃₂	—	134	1	no	—
319	M₃₂	—	134	1	no	—
320	M₃₂	C₄×D₆₇	1	2	yes	complemented
321	C₂×C₁₆	—	2	1	no	—
322	C₂×C₁₆	—	67	2	no	—
323	C₂×C₁₆	—	134	2	no	—
324	C₂×C₁₆	—	134	2	no	—
325	C₂×C₁₆	—	134	2	no	—
326	C₂×C₁₆	—	134	2	no	—
327	C₂×C₁₆	—	134	1	no	—
328	C₂×C₁₆	C₄×D₆₇	1	2	yes	complemented
329	#97	—	2	1	no	—
330	#97	—	134	1	no	—
331	#97	—	134	1	no	—
332	#97	—	134	1	no	—
333	C₄×C₈	—	2	1	no	—
334	C₄×C₈	—	134	1	no	—
335	C₄×C₈	—	134	1	no	—
336	C₄×C₈	—	134	1	no	—
337	C₂⁴	—	67	1	no	—
338	C₂²×C₄	—	67	1	no	—
339	C₂²×C₄	—	67	1	no	—
340	C₂²×C₄	—	67	1	no	—
341	C₂²×C₄	—	67	1	no	—
342	C₂²×C₄	—	67	1	no	—
343	C₂²×C₄	—	67	1	no	—
344	C₂²×C₄	—	67	1	no	—
345	C₂²×C₄	—	67	1	no	—
346	C₂²×C₄	—	67	1	no	—
347	C₂²×C₄	—	67	1	no	—
348	C₂²×C₄	—	67	1	no	—
349	C₂²×C₄	—	67	1	no	—
350	C₂²×C₄	—	67	1	no	—
351	C₂²×C₄	—	134	2	no	—
352	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
353	M₁₆	—	2	1	no	—
354	M₁₆	—	67	2	no	—
355	M₁₆	—	134	2	no	—
356	M₁₆	—	134	2	no	—
357	M₁₆	—	134	1	no	—
358	M₁₆	C₈×D₆₇	1	2	yes	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	67	1	no	—
361	C₂×C₈	—	67	1	no	—
362	C₂×C₈	—	67	1	no	—
363	C₂×C₈	—	67	1	no	—
364	C₂×C₈	—	67	1	no	—
365	C₂×C₈	—	67	1	no	—
366	C₂×C₈	—	67	1	no	—
367	C₂×C₈	—	67	1	no	—
368	C₂×C₈	—	67	1	no	—
369	C₂×C₈	—	67	1	no	—
370	C₂×C₈	—	67	1	no	—
371	C₂×C₈	—	67	1	no	—
372	C₂×C₈	—	67	1	no	—
373	C₂×C₈	—	67	1	no	—
374	C₂×C₈	—	67	1	no	—
375	C₂×C₈	—	67	1	no	—
376	C₂×C₈	—	67	1	no	—
377	C₂×C₈	—	67	1	no	—
378	C₂×C₈	—	67	1	no	—
379	C₂×C₈	—	67	1	no	—
380	C₂×C₈	—	67	1	no	—
381	C₂×C₈	—	67	1	no	—
382	C₂×C₈	—	134	2	no	—
383	C₂×C₈	—	134	2	no	—
384	C₂×C₈	—	134	1	no	—
385	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
386	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
387	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
388	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
389	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
390	C₂×C₈	Q₈×D₆₇	1	1	yes	characteristic
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	134	2	no	—
393	C₄⋊C₄	—	134	1	no	—
394	C₂²⋊C₄	—	67	2	no	—
395	C₂²⋊C₄	—	134	2	no	—
396	C₂²⋊C₄	C₈×D₆₇	1	2	yes	—
397	C₄²	—	2	1	no	—
398	C₄²	—	134	2	no	—
399	C₄²	—	134	1	no	—
400	C₁₆	—	2	2	no	—
401	C₁₆	—	2	2	no	—
402	C₁₆	—	134	2	no	—
403	C₁₆	—	134	2	no	—
404	C₂³	—	268	2	no	—
405	C₂³	—	67	1	no	—
406	C₂³	—	67	1	no	—
407	C₂³	—	67	1	no	—
408	C₂³	—	67	1	no	—
409	C₂³	—	67	1	no	—
410	C₂³	—	67	1	no	—
411	C₂³	C₂×C₈×D₆₇	1	1	yes	characteristic
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	268	4	no	—
414	C₂×C₄	—	67	1	no	—
415	C₂×C₄	—	67	1	no	—
416	C₂×C₄	—	67	1	no	—
417	C₂×C₄	—	67	1	no	—
418	C₂×C₄	—	67	1	no	—
419	C₂×C₄	—	67	1	no	—
420	C₂×C₄	—	67	1	no	—
421	C₂×C₄	—	67	1	no	—
422	C₂×C₄	—	67	1	no	—
423	C₂×C₄	—	67	1	no	—
424	C₂×C₄	—	67	1	no	—
425	C₂×C₄	—	67	1	no	—
426	C₂×C₄	—	67	1	no	—
427	C₂×C₄	—	67	1	no	—
428	C₂×C₄	—	67	1	no	—
429	C₂×C₄	—	67	1	no	—
430	C₂×C₄	—	67	1	no	—
431	C₂×C₄	—	67	1	no	—
432	C₂×C₄	—	67	1	no	—
433	C₂×C₄	—	67	1	no	—
434	C₂×C₄	—	67	1	no	—
435	C₂×C₄	—	67	1	no	—
436	C₂×C₄	—	134	2	no	—
437	C₂×C₄	C₄²×D₆₇	1	1	yes	characteristic
438	C₂×C₄	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
439	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
440	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
441	C₂×C₄	M₁₆×D₆₇	1	1	yes	characteristic
442	C₂×C₄	M₁₆×D₆₇	1	1	yes	characteristic
443	C₈	—	2	2	no	—
444	C₈	—	67	1	no	—
445	C₈	—	67	1	no	—
446	C₈	—	67	1	no	—
447	C₈	—	67	1	no	—
448	C₈	—	134	2	no	—
449	C₈	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
450	C₈	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
451	C₈	C₄⋊C₄×D₆₇	1	1	yes	characteristic
452	C₈	C₄⋊C₄×D₆₇	1	1	yes	characteristic
453	C₂²	—	4	1	no	—
454	C₂²	—	268	1	no	—
455	C₂²	—	268	1	no	—
456	C₂²	—	268	1	no	—
457	C₂²	—	67	1	no	—
458	C₂²	—	67	1	no	—
459	C₂²	—	67	1	no	—
460	C₂²	—	67	1	no	—
461	C₂²	—	134	2	no	—
462	C₂²	—	134	2	no	—
463	C₂²	—	134	2	no	—
464	C₂²	C₄×C₈×D₆₇	1	1	yes	characteristic
465	C₂²	C₂²⋊C₈×D₆₇	1	1	yes	characteristic
466	C₂²	C₄⋊C₈×D₆₇	1	1	yes	characteristic
467	C₄	—	4	2	no	—
468	C₄	—	268	2	no	—
469	C₄	—	67	1	no	—
470	C₄	—	67	1	no	—
471	C₄	—	67	1	no	—
472	C₄	—	67	1	no	—
473	C₄	#95×D₆₇	1	1	yes	characteristic
474	C₄	#97×D₆₇	1	1	yes	characteristic
475	C₄	C₂²⋊C₈×D₆₇	1	1	yes	characteristic
476	C₄	C₄⋊C₈×D₆₇	1	1	yes	characteristic
477	C₂	—	2	1	no	—
478	C₂	—	2	1	no	—
479	C₂	—	2	1	no	—
480	C₂	—	67	2	no	—
481	C₂	—	134	1	no	—
482	C₂	—	134	1	no	—
483	C₂	—	134	1	no	—
484	C₂	#336×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊C₄×D₆₇
commutator	C₂²×C₆₇	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₆₇×#1378	C₂
socle	C₂×C₆₇	C₂×#336
prime radical	C₂³×D₆₇	C₂×C₈
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	#1378	D₆₇
hypocenter	C₆₇	C₂×#1378
LCS	G ▷ C₂²×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #1378

Complements

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

N	H ≅ G/N	type
4. #22558296	C₂	semidirect
5. #22558295	C₂	semidirect
6. #22558294	C₂	semidirect
7. C₆₇×#1378	C₂	semidirect
14. C₂×#14523982	C₄	semidirect
21. M₃₂×D₆₇	C₄	semidirect
22. M₃₂×D₆₇	C₄	semidirect
24. C₂×C₁₆×D₆₇	C₄	semidirect
66. #14523983	C₂×C₄	semidirect
72. C₂×C₆₇⋊C₁₆	C₂×C₄	semidirect
89. M₃₂×C₆₇	C₂×C₄	semidirect
91. C₂×C₁₆×C₆₇	C₂×C₄	semidirect
242. D₆₇	#1378	direct (N × H)
249. #1378	D₆₇	direct (N × H)
250. C₆₇	C₂×#1378	semidirect
320. M₃₂	C₄×D₆₇	semidirect
328. C₂×C₁₆	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×M₃₂×D₆₇	2
#405×D₆₇	2
#22558296	2
#22558295	2
#22558294	2
C₆₇×#1378	2
C₂×#1378	67

Subgroups — #1378×D67 #30770694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1378×D₆₇ #30770694