Subgroups — #31009353

Order 17152.

558 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#11761628	C₂	1	1	yes	maximal, characteristic
2	#22562115	C₂	1	2	yes	maximal, complemented
3	#22562039	C₂	1	2	yes	maximal, complemented
4	#22562036	C₂	1	2	yes	maximal, complemented
5	#22562032	C₂	1	2	yes	maximal, complemented
6	#22562008	C₂	1	1	yes	maximal, characteristic, complemented
7	#22562006	C₂	1	1	yes	maximal, characteristic, complemented
8	#22562006	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#14523982	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₆×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×M₃₂×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11761628	C₄	1	1	yes	characteristic
13	C₂×#14523982	C₂²	1	2	yes	—
14	C₂×C₁₆×D₆₇	C₂²	1	2	yes	—
15	C₈×Dic₁₃₄	C₄	1	1	yes	characteristic
16	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
17	C₈×D₂₆₈	C₄	1	1	yes	characteristic
18	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
19	C₈×C₂²⋊D₆₇	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₆₇	C₄	1	1	yes	characteristic
21	C₈×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
22	C₈×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
23	#16863449	C₄	1	1	yes	characteristic
24	#16863447	C₄	1	1	yes	characteristic
25	#16863447	C₄	1	1	yes	characteristic
26	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
28	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	2	yes	—
29	Dic₆₇⋊C₁₆	C₂²	1	2	yes	—
30	Dic₆₇⋊C₁₆	C₂²	1	2	yes	—
31	C₂²⋊(C₆₇⋊C₁₆)	C₂²	1	2	yes	—
32	(C₂×D₆₇)⋊C₁₆	C₂²	1	2	yes	—
33	(C₂×D₆₇)⋊C₁₆	C₂²	1	2	yes	—
34	#16863171	C₂²	1	2	yes	—
35	C₄×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₄×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₁₆×Dic₆₇	C₂²	1	2	yes	—
38	C₂×M₃₂×C₆₇	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
40	#346×C₆₇	C₂²	1	2	yes	—
41	C₄×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#11761628	C₈	1	1	yes	characteristic
44	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
47	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
48	C₄×Dic₁₃₄	C₈	1	1	yes	characteristic
49	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
50	C₄×D₂₆₈	C₈	1	1	yes	characteristic
51	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
52	C₄×C₂²⋊D₆₇	C₈	1	1	yes	characteristic
53	C₄×C₂²⋊D₆₇	C₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
55	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
56	#14524002	C₈	1	1	yes	characteristic
57	#14524000	C₈	1	1	yes	characteristic
58	#14524000	C₈	1	1	yes	characteristic
59	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
61	#14523982	—	2	4	no	—
62	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
63	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
64	C₁₆×D₆₇	—	2	4	no	—
65	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
66	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
67	Dic₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
68	Dic₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
69	Dic₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
70	Dic₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
71	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
72	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
73	(C₂×D₆₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
74	(C₂×D₆₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
75	(C₂×D₆₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
76	(C₂×D₆₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
82	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
86	M₃₂×C₆₇	—	2	4	no	—
87	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
88	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
89	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	#11761628	—	2	4	no	—
94	C₂×Dic₁₃₄	C₂×C₈	1	1	yes	characteristic
95	C₂×D₂₆₈	C₂×C₈	1	1	yes	characteristic
96	C₂×C₂²⋊D₆₇	C₂×C₈	1	1	yes	characteristic
97	C₂×C₂²⋊D₆₇	C₂×C₈	1	1	yes	characteristic
98	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
99	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
108	C₈×D₆₇	—	2	2	no	—
109	C₈×D₆₇	—	2	2	no	—
110	C₈×D₆₇	—	2	2	no	—
111	C₈×D₆₇	—	2	2	no	—
112	C₄⋊Dic₆₇	C₂×C₈	1	1	yes	characteristic
113	C₄⋊Dic₆₇	C₂×C₈	1	1	yes	characteristic
114	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
115	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
116	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
117	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
118	C₂²⋊Dic₆₇	C₂×C₈	1	1	yes	characteristic
119	C₂²⋊Dic₆₇	C₂×C₈	1	1	yes	characteristic
120	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
121	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
122	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
123	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
124	C₄×Dic₆₇	C₂×C₈	1	1	yes	characteristic
125	C₄×Dic₆₇	C₂×C₈	1	1	yes	characteristic
126	C₄×Dic₆₇	C₂×C₈	1	1	yes	characteristic
127	C₄×Dic₆₇	C₂×C₈	1	1	yes	characteristic
128	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
130	C₆₇⋊C₁₆	—	2	2	no	—
131	C₆₇⋊C₁₆	—	2	2	no	—
132	C₂²×C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
133	C₂²×C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
134	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₆₇	—	2	2	no	—
136	C₂×C₈×C₆₇	—	2	2	no	—
137	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
141	C₄²×C₆₇	C₂×C₈	1	1	yes	characteristic
142	C₄²×C₆₇	C₂×C₈	1	1	yes	characteristic
143	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
145	C₁₆×C₆₇	—	2	2	no	—
146	C₁₆×C₆₇	#41	1	4	yes	complemented
147	C₂³×C₆₇	C₂²×C₈	1	1	yes	characteristic
148	C₂²×D₆₇	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₆₇	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₆₇	—	2	1	no	—
151	C₂×C₄×C₆₇	—	2	1	no	—
152	C₂×C₄×C₆₇	—	2	2	no	—
153	C₂×C₄×C₆₇	—	2	2	no	—
154	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
160	C₂²⋊D₆₇	—	2	2	no	—
161	C₂²⋊D₆₇	—	2	2	no	—
162	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
163	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
164	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
165	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
166	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
167	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
168	D₂₆₈	—	2	2	no	—
169	C₄×D₆₇	—	2	1	no	—
170	C₄×D₆₇	—	2	1	no	—
171	C₄×D₆₇	—	2	1	no	—
172	C₄×D₆₇	—	2	1	no	—
173	C₄×D₆₇	—	2	2	no	—
174	C₄×D₆₇	—	2	2	no	—
175	C₄×D₆₇	—	2	2	no	—
176	C₄×D₆₇	M₃₂	1	4	yes	complemented
177	Dic₁₃₄	—	2	2	no	—
178	C₈×C₆₇	—	2	1	no	—
179	C₈×C₆₇	—	2	1	no	—
180	C₈×C₆₇	#131	1	2	yes	—
181	C₈×C₆₇	C₂×#41	1	2	yes	—
182	C₆₇⋊C₈	—	2	1	no	—
183	C₆₇⋊C₈	—	2	1	no	—
184	C₆₇⋊C₈	—	2	1	no	—
185	C₆₇⋊C₈	—	2	1	no	—
186	C₂²×C₆₇	—	2	1	no	—
187	C₂²×C₆₇	—	2	1	no	—
188	C₂²×C₆₇	—	2	1	no	—
189	C₂²×C₆₇	C₂³×C₈	1	1	yes	characteristic
190	C₂×D₆₇	—	2	1	no	—
191	C₂×D₆₇	—	2	1	no	—
192	C₂×D₆₇	—	2	1	no	—
193	C₂×D₆₇	—	2	1	no	—
194	C₂×D₆₇	—	2	1	no	—
195	C₂×D₆₇	C₂×M₃₂	1	2	yes	—
196	C₄×C₆₇	—	2	1	no	—
197	C₄×C₆₇	—	2	1	no	—
198	C₄×C₆₇	—	2	1	no	—
199	C₄×C₆₇	C₂×M₃₂	1	2	yes	—
200	C₄×C₆₇	#504	1	2	yes	—
201	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
202	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
203	Dic₆₇	—	2	1	no	—
204	Dic₆₇	—	2	1	no	—
205	Dic₆₇	—	2	1	no	—
206	Dic₆₇	—	2	1	no	—
207	Dic₆₇	—	2	1	no	—
208	Dic₆₇	C₂×M₃₂	1	2	yes	—
209	#33479	—	67	1	no	maximal, Sylow
210	C₂×C₆₇	—	4	1	no	—
211	C₂×C₆₇	C₈×#41	1	1	yes	characteristic
212	C₂×C₆₇	C₂²×M₃₂	1	1	yes	characteristic
213	C₂×C₆₇	C₂×#504	1	1	yes	characteristic
214	D₆₇	—	2	2	no	—
215	D₆₇	—	4	1	no	—
216	C₈×#41	—	67	1	no	—
217	#2183	—	67	2	no	—
218	#2169	—	67	2	no	—
219	#2168	—	67	2	no	—
220	#2168	—	67	2	no	—
221	#2162	—	67	1	no	—
222	#2162	—	67	1	no	—
223	#2162	—	67	1	no	—
224	C₄×M₃₂	—	67	1	no	—
225	C₄×M₃₂	D₆₇	1	1	yes	characteristic, complemented
226	C₂×C₄×C₁₆	—	67	1	no	—
227	C₆₇	#33479	1	1	yes	characteristic, complemented, Sylow
228	C₄×#41	—	67	1	no	—
229	C₂×M₃₂	—	67	2	no	—
230	C₂×M₃₂	C₂×D₆₇	1	2	yes	—
231	C₂²×C₁₆	—	67	2	no	—
232	C₈×Q₈	—	67	1	no	—
233	C₈×Q₈	—	67	1	no	—
234	C₈×D₄	—	67	1	no	—
235	C₈×D₄	—	67	1	no	—
236	C₈×D₄	—	67	1	no	—
237	C₈×D₄	—	67	1	no	—
238	C₈×D₄	—	67	1	no	—
239	C₈×D₄	—	67	1	no	—
240	#431	—	67	1	no	—
241	#431	—	67	1	no	—
242	#431	—	67	1	no	—
243	C₂×C₄×C₈	—	67	1	no	—
244	C₂×C₄×C₈	—	67	1	no	—
245	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
246	C₄⋊C₁₆	—	67	2	no	—
247	C₄⋊C₁₆	—	67	2	no	—
248	C₄⋊C₁₆	—	67	2	no	—
249	C₂²⋊C₁₆	—	67	2	no	—
250	C₂²⋊C₁₆	—	67	2	no	—
251	C₂²⋊C₁₆	—	67	2	no	—
252	#346	—	67	2	no	—
253	#346	C₂×D₆₇	1	2	yes	—
254	C₄×C₁₆	—	67	2	no	—
255	C₄×C₁₆	—	67	1	no	—
256	C₄×C₁₆	—	67	1	no	—
257	C₄×C₁₆	C₂×D₆₇	1	1	yes	characteristic
258	C₄×C₁₆	C₂×D₆₇	1	1	yes	characteristic
259	C₂×#41	—	67	1	no	—
260	C₂²×C₈	—	67	1	no	—
261	C₂²×C₈	—	67	1	no	—
262	C₂²×C₈	—	67	1	no	—
263	C₂²×C₈	—	67	1	no	—
264	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
266	C₄×Q₈	—	67	1	no	—
267	C₄×Q₈	—	67	1	no	—
268	C₄×D₄	—	67	1	no	—
269	C₄×D₄	—	67	1	no	—
270	C₄×D₄	—	67	1	no	—
271	C₄×D₄	—	67	1	no	—
272	C₄×D₄	—	67	1	no	—
273	C₄×D₄	—	67	1	no	—
274	#117	—	67	1	no	—
275	#117	—	67	1	no	—
276	#117	—	67	1	no	—
277	C₂×C₄²	—	67	1	no	—
278	C₂×C₄²	—	67	1	no	—
279	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
280	M₃₂	—	2	4	no	—
281	M₃₂	—	134	4	no	—
282	C₂×C₁₆	—	67	2	no	—
283	C₂×C₁₆	—	67	2	no	—
284	C₂×C₁₆	—	134	4	no	—
285	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
286	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
287	C₄⋊C₈	—	67	1	no	—
288	C₄⋊C₈	—	67	1	no	—
289	C₄⋊C₈	—	67	1	no	—
290	C₄⋊C₈	—	67	1	no	—
291	C₄⋊C₈	—	67	1	no	—
292	C₄⋊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	C₄×C₈	—	67	1	no	—
300	C₄×C₈	—	67	1	no	—
301	C₄×C₈	—	67	1	no	—
302	C₄×C₈	—	67	1	no	—
303	C₄×C₈	—	67	1	no	—
304	C₄×C₈	—	67	1	no	—
305	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
306	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
307	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
308	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
309	#41	—	134	4	no	—
310	C₂×Q₈	—	67	1	no	—
311	C₂×D₄	—	67	1	no	—
312	C₂×D₄	—	67	1	no	—
313	C₂×D₄	—	67	1	no	—
314	C₂²×C₄	—	67	1	no	—
315	C₂²×C₄	—	67	1	no	—
316	C₂²×C₄	—	67	1	no	—
317	C₂²×C₄	—	67	1	no	—
318	C₂²×C₄	—	67	1	no	—
319	C₂²×C₄	—	67	1	no	—
320	C₂²×C₄	C₈×D₆₇	1	1	yes	characteristic
321	C₂²×C₄	C₈×D₆₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	67	1	no	—
326	C₂×C₈	—	67	1	no	—
327	C₂×C₈	—	67	1	no	—
328	C₂×C₈	—	67	1	no	—
329	C₂×C₈	—	134	2	no	—
330	C₂×C₈	—	134	2	no	—
331	C₂×C₈	—	134	2	no	—
332	C₂×C₈	—	134	2	no	—
333	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
336	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
337	C₄⋊C₄	—	67	1	no	—
338	C₄⋊C₄	—	67	1	no	—
339	C₄⋊C₄	—	67	1	no	—
340	C₄⋊C₄	—	67	1	no	—
341	C₄⋊C₄	—	67	1	no	—
342	C₄⋊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	C₄²	—	67	1	no	—
350	C₄²	—	67	1	no	—
351	C₄²	—	67	1	no	—
352	C₄²	—	67	1	no	—
353	C₄²	—	67	1	no	—
354	C₄²	—	67	1	no	—
355	C₄²	C₈×D₆₇	1	1	yes	characteristic
356	C₄²	C₈×D₆₇	1	1	yes	characteristic
357	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
358	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
359	C₁₆	—	2	2	no	—
360	C₁₆	—	134	2	no	—
361	C₁₆	—	134	2	no	—
362	C₁₆	#11761628	1	4	yes	complemented
363	C₂³	—	67	1	no	—
364	C₂³	—	67	1	no	—
365	C₂³	C₂×C₈×D₆₇	1	1	yes	characteristic
366	Q₈	—	134	2	no	—
367	D₄	—	134	2	no	—
368	D₄	—	134	2	no	—
369	D₄	—	134	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	67	1	no	—
375	C₂×C₄	—	67	4	no	—
376	C₂×C₄	—	67	1	no	—
377	C₂×C₄	—	67	1	no	—
378	C₂×C₄	—	67	1	no	—
379	C₂×C₄	—	67	1	no	—
380	C₂×C₄	—	67	1	no	—
381	C₂×C₄	—	134	2	no	—
382	C₂×C₄	—	134	2	no	—
383	C₂×C₄	—	134	2	no	—
384	C₂×C₄	—	134	1	no	—
385	C₂×C₄	—	134	1	no	—
386	C₂×C₄	—	134	1	no	—
387	C₂×C₄	—	134	1	no	—
388	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
389	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
390	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
391	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
392	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	134	1	no	—
397	C₈	—	134	1	no	—
398	C₈	—	134	1	no	—
399	C₈	—	134	1	no	—
400	C₈	#14524049	1	2	yes	—
401	C₈	C₂×#11761628	1	2	yes	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	67	2	no	—
406	C₂²	—	134	1	no	—
407	C₂²	—	134	1	no	—
408	C₂²	—	134	1	no	—
409	C₂²	—	134	1	no	—
410	C₂²	—	134	1	no	—
411	C₂²	C₂²×C₈×D₆₇	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	67	2	no	—
416	C₄	—	134	1	no	—
417	C₄	—	134	1	no	—
418	C₄	—	134	1	no	—
419	C₄	—	134	1	no	—
420	C₄	—	134	1	no	—
421	C₄	M₃₂×D₆₇	1	2	yes	—
422	C₄	#16863814	1	2	yes	—
423	C₄	C₄×#11761628	1	1	yes	characteristic
424	C₄	C₂×#14524049	1	1	yes	characteristic
425	C₂	—	4	1	no	—
426	C₂	—	268	1	no	—
427	C₂	—	134	2	no	—
428	C₂	C₈×#11761628	1	1	yes	characteristic
429	C₂	C₂×M₃₂×D₆₇	1	1	yes	characteristic
430	C₂	C₂×#16863814	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₆₇
commutator, socle	C₂²×C₆₇	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₄×M₃₂×C₆₇	C₂
prime radical	C₂×#11761628	C₈
cosocle	C₂×C₈×C₆₇	C₂⁴
hypercenter	C₄×M₃₂	D₆₇
hypocenter	C₆₇	#33479
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
2. #22562115	C₂	semidirect
3. #22562039	C₂	semidirect
4. #22562036	C₂	semidirect
5. #22562032	C₂	semidirect
6. #22562008	C₂	semidirect
7. #22562006	C₂	semidirect
8. #22562006	C₂	semidirect
9. C₄×#14523982	C₂	semidirect
10. C₄×C₁₆×D₆₇	C₂	semidirect
11. C₄×M₃₂×C₆₇	C₂	semidirect
146. C₁₆×C₆₇	#41	semidirect
176. C₄×D₆₇	M₃₂	semidirect
225. C₄×M₃₂	D₆₇	semidirect
227. C₆₇	#33479	semidirect
362. C₁₆	#11761628	semidirect

Maximal subgroups

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

subgroup	index
C₈×#11761628	2
#22562115	2
#22562039	2
#22562036	2
#22562032	2
#22562008	2
#22562006	2
C₄×#14523982	2
C₄×C₁₆×D₆₇	2
C₄×M₃₂×C₆₇	2
#33479	67