Subgroups — #30874743

Order 17152.

740 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863527	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#22560933	C₂	1	2	yes	maximal
4	#22560928	C₂	1	1	yes	maximal, characteristic
5	#22560928	C₂	1	1	yes	maximal, characteristic
6	#22560928	C₂	1	2	yes	maximal
7	#22560329	C₂	1	2	yes	maximal
8	#22560326	C₂	1	1	yes	maximal, characteristic
9	#22560066	C₂	1	2	yes	maximal
10	C₄×C₄⋊(C₆₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
11	C₆₇×#2295	C₂	1	1	yes	maximal, characteristic
12	#16863527	—	2	4	no	—
13	Q₈×C₆₇⋊C₈	—	2	4	no	—
14	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
22	C₂×#14523954	C₂²	1	2	yes	—
23	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₆₇⋊C₈	C₂²	1	2	yes	—
26	#16863151	C₂²	1	1	yes	characteristic
27	#16863151	C₂²	1	1	yes	characteristic
28	#16863151	C₂²	1	2	yes	—
29	#16863151	C₂²	1	2	yes	—
30	#16863151	C₂²	1	2	yes	—
31	#16863151	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	#391×C₆₇	C₄	1	1	yes	characteristic
34	#391×C₆₇	C₄	1	1	yes	characteristic
35	#389×C₆₇	C₄	1	1	yes	characteristic
36	#389×C₆₇	C₄	1	1	yes	characteristic
37	#387×C₆₇	C₄	1	2	yes	—
38	#387×C₆₇	C₄	1	2	yes	—
39	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
41	#376×C₆₇	C₂²	1	2	yes	—
42	C₄³×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
50	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
51	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
52	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
53	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
54	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
55	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
56	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
57	#14523954	—	2	4	no	—
58	C₄×C₆₇⋊C₈	—	2	2	no	—
59	C₄×C₆₇⋊C₈	—	2	4	no	—
60	C₄×C₆₇⋊C₈	—	2	2	no	—
61	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
62	C₄×Q₈×C₆₇	D₄	1	4	yes	—
63	C₄×Q₈×C₆₇	Q₈	1	4	yes	—
64	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
79	#95×C₆₇	C₂×C₄	1	2	yes	—
80	#95×C₆₇	C₂×C₄	1	2	yes	—
81	#95×C₆₇	C₂×C₄	1	2	yes	—
82	#95×C₆₇	C₂×C₄	1	2	yes	—
83	#95×C₆₇	C₂×C₄	1	2	yes	—
84	#95×C₆₇	C₂×C₄	1	2	yes	—
85	#95×C₆₇	C₂×C₄	1	2	yes	—
86	C₂×C₆₇⋊C₈	—	2	1	no	—
87	C₂×C₆₇⋊C₈	—	2	1	no	—
88	C₂×C₆₇⋊C₈	—	2	1	no	—
89	C₂×C₆₇⋊C₈	—	2	1	no	—
90	C₂×C₆₇⋊C₈	—	2	1	no	—
91	C₂×C₆₇⋊C₈	—	2	2	no	—
92	C₂×C₆₇⋊C₈	—	2	1	no	—
93	C₂×C₆₇⋊C₈	—	2	2	no	—
94	C₂×C₆₇⋊C₈	—	2	1	no	—
95	C₂×C₆₇⋊C₈	—	2	1	no	—
96	C₂×C₆₇⋊C₈	—	2	2	no	—
97	C₂×C₆₇⋊C₈	—	2	2	no	—
98	C₂×C₆₇⋊C₈	—	2	1	no	—
99	C₂×C₆₇⋊C₈	—	2	1	no	—
100	C₂×C₆₇⋊C₈	—	2	2	no	—
101	C₂×C₆₇⋊C₈	—	2	2	no	—
102	C₂×C₆₇⋊C₈	#41	1	2	yes	—
103	C₂×C₆₇⋊C₈	#41	1	2	yes	—
104	C₂×Q₈×C₆₇	—	2	2	no	—
105	C₂×Q₈×C₆₇	—	2	2	no	—
106	C₂×Q₈×C₆₇	C₄⋊C₄	1	4	yes	—
107	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
118	C₄⋊C₄×C₆₇	—	2	4	no	—
119	C₄⋊C₄×C₆₇	—	2	2	no	—
120	C₄⋊C₄×C₆₇	—	2	2	no	—
121	C₄⋊C₄×C₆₇	—	4	2	no	—
122	C₄⋊C₄×C₆₇	C₄⋊C₄	1	8	yes	—
123	C₄⋊C₄×C₆₇	C₄⋊C₄	1	4	yes	—
124	C₄²×C₆₇	—	2	2	no	—
125	C₄²×C₆₇	—	2	2	no	—
126	C₄²×C₆₇	—	2	2	no	—
127	C₄²×C₆₇	—	2	1	no	—
128	C₄²×C₆₇	—	2	1	no	—
129	C₄²×C₆₇	—	2	2	no	—
130	C₄²×C₆₇	—	2	2	no	—
131	C₄²×C₆₇	—	2	1	no	—
132	C₄²×C₆₇	—	2	1	no	—
133	C₄²×C₆₇	—	4	1	no	—
134	C₄²×C₆₇	C₂×D₄	1	2	yes	—
135	C₄²×C₆₇	C₂×D₄	1	4	yes	—
136	C₄²×C₆₇	C₂×Q₈	1	4	yes	—
137	C₄²×C₆₇	C₂×Q₈	1	2	yes	—
138	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
139	Q₈×C₆₇	—	2	8	no	—
140	C₂×C₄×C₆₇	—	2	1	no	—
141	C₂×C₄×C₆₇	—	2	1	no	—
142	C₂×C₄×C₆₇	—	2	1	no	—
143	C₂×C₄×C₆₇	—	2	2	no	—
144	C₂×C₄×C₆₇	—	2	2	no	—
145	C₂×C₄×C₆₇	—	2	2	no	—
146	C₂×C₄×C₆₇	—	2	1	no	—
147	C₂×C₄×C₆₇	—	2	2	no	—
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	—	2	1	no	—
150	C₂×C₄×C₆₇	—	2	2	no	—
151	C₂×C₄×C₆₇	—	2	1	no	—
152	C₂×C₄×C₆₇	—	2	1	no	—
153	C₂×C₄×C₆₇	—	2	1	no	—
154	C₂×C₄×C₆₇	—	2	1	no	—
155	C₂×C₄×C₆₇	—	2	1	no	—
156	C₂×C₄×C₆₇	—	2	1	no	—
157	C₂×C₄×C₆₇	—	2	2	no	—
158	C₂×C₄×C₆₇	—	2	2	no	—
159	C₂×C₄×C₆₇	—	2	2	no	—
160	C₂×C₄×C₆₇	—	2	1	no	—
161	C₂×C₄×C₆₇	—	2	1	no	—
162	C₂×C₄×C₆₇	—	2	2	no	—
163	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
165	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
166	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
167	C₂×C₄×C₆₇	#131	1	2	yes	—
168	C₂×C₄×C₆₇	#131	1	2	yes	—
169	C₂×C₄×C₆₇	#131	1	2	yes	—
170	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
175	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
176	C₆₇⋊C₈	—	2	2	no	—
177	C₆₇⋊C₈	—	2	2	no	—
178	C₆₇⋊C₈	—	4	1	no	—
179	C₆₇⋊C₈	—	4	2	no	—
180	C₆₇⋊C₈	—	4	1	no	—
181	C₆₇⋊C₈	—	4	2	no	—
182	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
184	C₂²×C₆₇	#519	1	1	yes	characteristic
185	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
186	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
187	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
188	C₂²×C₆₇	#568	1	1	yes	characteristic
189	C₄×C₆₇	—	2	4	no	—
190	C₄×C₆₇	—	2	2	no	—
191	C₄×C₆₇	—	2	4	no	—
192	C₄×C₆₇	—	2	2	no	—
193	C₄×C₆₇	—	4	2	no	—
194	C₄×C₆₇	—	4	1	no	—
195	C₄×C₆₇	—	4	2	no	—
196	C₄×C₆₇	—	4	1	no	—
197	C₄×C₆₇	—	4	1	no	—
198	C₄×C₆₇	#424	1	4	yes	—
199	C₄×C₆₇	#548	1	1	yes	characteristic
200	C₄×C₆₇	#548	1	1	yes	characteristic
201	C₄×C₆₇	#557	1	1	yes	characteristic
202	C₄×C₆₇	#557	1	1	yes	characteristic
203	#22735	—	67	1	no	maximal, Sylow
204	C₂×C₆₇	#2351	1	1	yes	characteristic
205	C₂×C₆₇	C₂×#424	1	1	yes	characteristic
206	C₂×C₆₇	#2906	1	1	yes	characteristic
207	C₂×C₆₇	#2966	1	1	yes	characteristic
208	C₂×C₆₇	#2969	1	1	yes	characteristic
209	C₂×C₆₇	#2985	1	1	yes	characteristic
210	C₂×C₆₇	#2986	1	1	yes	characteristic
211	C₂×#446	—	67	1	no	—
212	C₂×C₈×Q₈	—	67	1	no	—
213	#2295	D₆₇	1	1	yes	characteristic
214	#1940	—	67	2	no	—
215	#1939	—	67	2	no	—
216	#1939	—	67	1	no	—
217	#1939	—	67	1	no	—
218	#1832	—	67	2	no	—
219	#1831	—	67	1	no	—
220	#1768	—	67	2	no	—
221	C₄×C₄⋊C₈	—	67	1	no	—
222	C₆₇	#22735	1	1	yes	characteristic, complemented, Sylow
223	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
224	#446	—	134	4	no	—
225	C₈×Q₈	—	134	4	no	—
226	C₂×C₄⋊C₈	—	67	1	no	—
227	C₂×C₄⋊C₈	—	67	1	no	—
228	C₂×C₄⋊C₈	—	67	2	no	—
229	C₂×C₄⋊C₈	—	67	2	no	—
230	C₂×C₄⋊C₈	—	67	1	no	—
231	C₂×C₄⋊C₈	—	67	2	no	—
232	C₂×C₄⋊C₈	—	67	2	no	—
233	C₂×C₄⋊C₈	—	67	1	no	—
234	C₂×#97	—	67	2	no	—
235	C₂×C₄×C₈	—	67	1	no	—
236	C₂×C₄×C₈	—	67	2	no	—
237	C₂×C₄×C₈	—	67	1	no	—
238	#391	Dic₆₇	1	1	yes	characteristic
239	#391	Dic₆₇	1	1	yes	characteristic
240	#389	Dic₆₇	1	1	yes	characteristic
241	#389	Dic₆₇	1	1	yes	characteristic
242	#387	Dic₆₇	1	2	yes	—
243	#387	Dic₆₇	1	2	yes	—
244	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
245	C₄×C₄⋊C₄	C₂×D₆₇	1	2	yes	—
246	#376	C₂×D₆₇	1	2	yes	—
247	C₄³	C₂×D₆₇	1	1	yes	characteristic
248	#336	—	67	2	no	—
249	#336	—	67	2	no	—
250	#336	—	67	1	no	—
251	#336	—	67	2	no	—
252	#336	—	67	2	no	—
253	#336	—	67	1	no	—
254	C₂²×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
255	C₂²×C₈	—	67	1	no	—
256	C₂²×C₈	—	67	1	no	—
257	C₂²×C₈	—	67	2	no	—
258	C₂²×C₈	—	67	1	no	—
259	C₂²×C₈	—	67	1	no	—
260	C₂²×C₈	—	67	2	no	—
261	C₄×Q₈	Dic₁₃₄	1	4	yes	—
262	C₄×Q₈	D₂₆₈	1	4	yes	—
263	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
264	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
267	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
268	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
269	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
270	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
271	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
272	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
273	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
275	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
276	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
277	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
278	C₄⋊C₈	—	134	2	no	—
279	C₄⋊C₈	—	134	4	no	—
280	C₄⋊C₈	—	134	4	no	—
281	C₄⋊C₈	—	134	2	no	—
282	C₄⋊C₈	—	134	2	no	—
283	C₄⋊C₈	—	134	4	no	—
284	C₄⋊C₈	—	134	2	no	—
285	C₄⋊C₈	—	134	4	no	—
286	#97	—	134	4	no	—
287	C₄×C₈	—	134	2	no	—
288	C₄×C₈	—	134	4	no	—
289	C₄×C₈	—	134	2	no	—
290	#95	C₂×Dic₆₇	1	2	yes	—
291	#95	C₂×Dic₆₇	1	2	yes	—
292	#95	C₂×Dic₆₇	1	2	yes	—
293	#95	C₂×Dic₆₇	1	2	yes	—
294	#95	C₂×Dic₆₇	1	2	yes	—
295	#95	C₂×Dic₆₇	1	2	yes	—
296	#95	C₂×Dic₆₇	1	2	yes	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	C₄⋊Dic₆₇	1	4	yes	—
300	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
301	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
302	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
303	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
304	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
305	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
306	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
307	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
308	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
309	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
310	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
311	C₂×C₈	—	67	2	no	—
312	C₂×C₈	—	67	2	no	—
313	C₂×C₈	—	134	1	no	—
314	C₂×C₈	—	134	2	no	—
315	C₂×C₈	—	134	1	no	—
316	C₂×C₈	—	134	2	no	—
317	C₂×C₈	—	134	1	no	—
318	C₂×C₈	—	134	2	no	—
319	C₂×C₈	—	134	1	no	—
320	C₂×C₈	—	134	2	no	—
321	C₂×C₈	—	134	2	no	—
322	C₂×C₈	—	134	1	no	—
323	C₂×C₈	—	134	1	no	—
324	C₂×C₈	—	134	2	no	—
325	C₂×C₈	—	134	1	no	—
326	C₂×C₈	—	134	1	no	—
327	C₂×C₈	—	134	1	no	—
328	C₂×C₈	—	134	1	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	C₄⋊Dic₆₇	1	8	yes	—
334	C₄⋊C₄	C₄⋊Dic₆₇	1	4	yes	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	4	1	no	—
345	C₄²	C₂×D₂₆₈	1	2	yes	—
346	C₄²	C₂×D₂₆₈	1	4	yes	—
347	C₄²	C₂×Dic₁₃₄	1	4	yes	—
348	C₄²	C₂×Dic₁₃₄	1	2	yes	—
349	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
350	Q₈	—	2	8	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
375	C₂×C₄	C₂×C₄⋊Dic₆₇	1	4	yes	—
376	C₂×C₄	C₂×C₄⋊Dic₆₇	1	4	yes	—
377	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
378	C₂×C₄	#14524050	1	2	yes	—
379	C₂×C₄	#14524050	1	2	yes	—
380	C₂×C₄	#14524050	1	2	yes	—
381	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
382	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
383	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
384	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
385	C₂×C₄	#14524091	1	1	yes	characteristic
386	C₂×C₄	#14524091	1	1	yes	characteristic
387	C₈	—	268	1	no	—
388	C₈	—	268	2	no	—
389	C₈	—	268	1	no	—
390	C₈	—	268	2	no	—
391	C₈	—	134	2	no	—
392	C₈	—	134	2	no	—
393	C₂²	C₂²×C₄⋊Dic₆₇	1	1	yes	characteristic
394	C₂²	#41×Dic₆₇	1	1	yes	characteristic
395	C₂²	#16863874	1	1	yes	characteristic
396	C₂²	C₂×#14524050	1	1	yes	characteristic
397	C₂²	C₂×#14524050	1	1	yes	characteristic
398	C₂²	C₂×#14524050	1	1	yes	characteristic
399	C₂²	#16864163	1	1	yes	characteristic
400	C₄	—	2	4	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	4	no	—
403	C₄	—	2	2	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	2	no	—
409	C₄	#16863423	1	4	yes	—
410	C₄	#16864058	1	1	yes	characteristic
411	C₄	#16864058	1	1	yes	characteristic
412	C₄	#16864122	1	1	yes	characteristic
413	C₄	#16864122	1	1	yes	characteristic
414	C₂	#22563130	1	1	yes	characteristic
415	C₂	C₂×#16863423	1	1	yes	characteristic
416	C₂	#22568777	1	1	yes	characteristic
417	C₂	#22569185	1	1	yes	characteristic
418	C₂	#22569214	1	1	yes	characteristic
419	C₂	#22569304	1	1	yes	characteristic
420	C₂	#22569311	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₇
commutator, socle, prime radical	C₂³×C₆₇	C₂³×C₄
Fitting	C₆₇×#2295	C₂
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#2295	D₆₇
hypocenter	C₆₇	#22735
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2295

Complements

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

N	H ≅ G/N	type
222. C₆₇	#22735	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863527	2
C₂×Q₈×C₆₇⋊C₈	2
#22560933	2
#22560928	2
#22560329	2
#22560326	2
#22560066	2
C₄×C₄⋊(C₆₇⋊C₈)	2
C₆₇×#2295	2
#22735	67