Subgroups — #31008947

Order 17152.

590 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14524049	C₂	1	1	yes	maximal, characteristic
2	#22562017	C₂	1	2	yes	maximal, complemented
3	#22562013	C₂	1	2	yes	maximal, complemented
4	#22562011	C₂	1	1	yes	maximal, characteristic, complemented
5	#22562008	C₂	1	1	yes	maximal, characteristic, complemented
6	#22562007	C₂	1	1	yes	maximal, characteristic, complemented
7	#22561963	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄⋊C₁₆×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#22561821	C₂	1	2	yes	maximal
10	#22561807	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524049	C₄	1	1	yes	characteristic
13	C₂×#14524049	C₂²	1	1	yes	characteristic
14	C₄×#11761628	C₄	1	1	yes	characteristic
15	C₂×#14523982	C₂²	1	2	yes	—
16	C₂×C₁₆×D₆₇	C₂²	1	2	yes	—
17	#16863351	C₄	1	1	yes	characteristic
18	#16863351	C₂²	1	1	yes	characteristic
19	#16863350	C₄	1	1	yes	characteristic
20	#16863350	C₄	1	1	yes	characteristic
21	#16863350	C₂²	1	1	yes	characteristic
22	#16863350	C₂²	1	1	yes	characteristic
23	C₄×#11761612	C₄	1	1	yes	characteristic
24	C₄×#11761611	C₄	1	1	yes	characteristic
25	C₄×#11761611	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	1	yes	characteristic
29	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	1	yes	characteristic
30	Dic₆₇⋊C₁₆	C₂²	1	2	yes	—
31	Dic₆₇⋊C₁₆	C₂²	1	2	yes	—
32	C₂²⋊(C₆₇⋊C₁₆)	C₂²	1	2	yes	—
33	(C₂×D₆₇)⋊C₁₆	C₂²	1	2	yes	—
34	(C₂×D₆₇)⋊C₁₆	C₂²	1	2	yes	—
35	#16863171	C₂²	1	2	yes	—
36	C₄×C₆₇⋊C₁₆	C₂²	1	2	yes	—
37	C₁₆×Dic₆₇	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₄⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
40	C₄⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²⋊C₁₆×C₆₇	C₂²	1	2	yes	—
42	#346×C₆₇	C₂²	1	2	yes	—
43	C₂×#11761628	C₂×C₄	1	1	yes	characteristic
44	#14524049	—	2	4	no	—
45	#14524049	—	2	2	no	—
46	#14524049	—	2	2	no	—
47	C₂×#11761612	C₂×C₄	1	1	yes	characteristic
48	C₂×#11761612	C₂×C₄	1	1	yes	characteristic
49	C₂×#11761611	C₂×C₄	1	1	yes	characteristic
50	C₂×#11761611	C₂×C₄	1	1	yes	characteristic
51	C₂×#11761611	C₂×C₄	1	1	yes	characteristic
52	C₂×#11761611	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
57	C₄×Dic₁₃₄	C₈	1	1	yes	characteristic
58	C₄×Dic₁₃₄	C₈	1	1	yes	characteristic
59	C₄×D₂₆₈	C₈	1	1	yes	characteristic
60	C₄×D₂₆₈	C₈	1	1	yes	characteristic
61	C₄×C₂²⋊D₆₇	C₈	1	1	yes	characteristic
62	C₄×C₂²⋊D₆₇	C₈	1	1	yes	characteristic
63	C₄×C₂²⋊D₆₇	C₈	1	1	yes	characteristic
64	C₄×C₂²⋊D₆₇	C₈	1	1	yes	characteristic
65	#14524002	C₂×C₄	1	1	yes	characteristic
66	#14524000	C₂×C₄	1	1	yes	characteristic
67	#14524000	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
70	#14523982	—	2	4	no	—
71	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
72	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
73	C₁₆×D₆₇	—	2	4	no	—
74	#14523954	C₂×C₄	1	1	yes	characteristic
75	#14523954	C₂×C₄	1	1	yes	characteristic
76	#14523953	C₂×C₄	1	1	yes	characteristic
77	#14523953	C₂×C₄	1	1	yes	characteristic
78	#14523953	C₂×C₄	1	1	yes	characteristic
79	#14523953	C₂×C₄	1	1	yes	characteristic
80	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
85	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
90	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
91	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	#11761628	—	2	2	no	—
96	#11761628	—	2	2	no	—
97	C₂×Dic₁₃₄	C₂×C₈	1	1	yes	characteristic
98	C₂×D₂₆₈	C₂×C₈	1	1	yes	characteristic
99	C₂×C₂²⋊D₆₇	C₂×C₈	1	1	yes	characteristic
100	C₂×C₂²⋊D₆₇	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₆₇	C₂×C₈	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	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
107	#11761612	—	2	2	no	—
108	#11761612	—	2	2	no	—
109	#11761611	—	2	2	no	—
110	#11761611	—	2	2	no	—
111	#11761611	—	2	2	no	—
112	#11761611	M₁₆	1	4	yes	—
113	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
117	C₈×D₆₇	—	2	2	no	—
118	C₈×D₆₇	—	2	1	no	—
119	C₈×D₆₇	—	2	1	no	—
120	C₈×D₆₇	—	2	2	no	—
121	C₈×D₆₇	#41	1	2	yes	—
122	C₈×D₆₇	#41	1	2	yes	—
123	C₄⋊Dic₆₇	C₂×C₈	1	1	yes	characteristic
124	C₄⋊Dic₆₇	C₂×C₈	1	1	yes	characteristic
125	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
126	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
127	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
128	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
129	C₂²⋊Dic₆₇	C₂×C₈	1	1	yes	characteristic
130	C₂²⋊Dic₆₇	C₂×C₈	1	1	yes	characteristic
131	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
132	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
133	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
134	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₆₇	C₂×C₈	1	1	yes	characteristic
136	C₄×Dic₆₇	C₂×C₈	1	1	yes	characteristic
137	C₄×Dic₆₇	C₂×C₈	1	1	yes	characteristic
138	C₄×Dic₆₇	C₂×C₈	1	1	yes	characteristic
139	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
141	C₆₇⋊C₁₆	—	2	2	no	—
142	C₆₇⋊C₁₆	—	2	2	no	—
143	C₂²×C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
144	C₂²×C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
145	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₆₇	—	2	2	no	—
147	C₂×C₈×C₆₇	—	2	1	no	—
148	C₂×C₈×C₆₇	—	2	1	no	—
149	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
153	C₄²×C₆₇	C₂×C₈	1	1	yes	characteristic
154	C₄²×C₆₇	C₂×C₈	1	1	yes	characteristic
155	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
157	C₁₆×C₆₇	—	2	2	no	—
158	C₁₆×C₆₇	—	2	2	no	—
159	C₂³×C₆₇	C₂²×C₈	1	1	yes	characteristic
160	C₂²×D₆₇	C₂²×C₈	1	1	yes	characteristic
161	C₂²×D₆₇	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₆₇	—	2	1	no	—
163	C₂×C₄×C₆₇	—	2	1	no	—
164	C₂×C₄×C₆₇	—	2	2	no	—
165	C₂×C₄×C₆₇	—	4	1	no	—
166	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
172	C₂²⋊D₆₇	—	2	2	no	—
173	C₂²⋊D₆₇	—	2	2	no	—
174	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
175	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
176	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
177	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
180	D₂₆₈	—	2	2	no	—
181	C₄×D₆₇	—	2	1	no	—
182	C₄×D₆₇	—	2	1	no	—
183	C₄×D₆₇	—	2	2	no	—
184	C₄×D₆₇	—	2	2	no	—
185	C₄×D₆₇	—	4	1	no	—
186	C₄×D₆₇	—	4	1	no	—
187	C₄×D₆₇	#117	1	2	yes	—
188	C₄×D₆₇	C₂×M₁₆	1	2	yes	—
189	Dic₁₃₄	—	2	2	no	—
190	C₈×C₆₇	—	2	1	no	—
191	C₈×C₆₇	—	2	1	no	—
192	C₈×C₆₇	C₂×M₁₆	1	2	yes	—
193	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
194	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
195	C₆₇⋊C₈	—	2	1	no	—
196	C₆₇⋊C₈	—	2	1	no	—
197	C₆₇⋊C₈	#117	1	2	yes	—
198	C₆₇⋊C₈	C₂×M₁₆	1	2	yes	—
199	C₂²×C₆₇	—	2	1	no	—
200	C₂²×C₆₇	—	2	1	no	—
201	C₂²×C₆₇	—	2	1	no	—
202	C₂²×C₆₇	C₂³×C₈	1	1	yes	characteristic
203	C₂×D₆₇	—	2	1	no	—
204	C₂×D₆₇	—	2	1	no	—
205	C₂×D₆₇	—	2	1	no	—
206	C₂×D₆₇	—	2	1	no	—
207	C₂×D₆₇	—	2	1	no	—
208	C₂×D₆₇	#431	1	2	yes	—
209	C₄×C₆₇	—	2	1	no	—
210	C₄×C₆₇	—	2	1	no	—
211	C₄×C₆₇	—	2	1	no	—
212	C₄×C₆₇	—	2	1	no	—
213	C₄×C₆₇	#504	1	2	yes	—
214	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
215	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
216	Dic₆₇	—	2	1	no	—
217	Dic₆₇	—	2	1	no	—
218	Dic₆₇	—	2	1	no	—
219	Dic₆₇	—	2	1	no	—
220	Dic₆₇	—	2	1	no	—
221	Dic₆₇	#431	1	2	yes	—
222	#33423	—	67	1	no	maximal, Sylow
223	C₂×C₆₇	—	4	1	no	—
224	C₂×C₆₇	C₂×#431	1	1	yes	characteristic
225	C₂×C₆₇	C₂×#504	1	1	yes	characteristic
226	C₂×C₆₇	#3407	1	1	yes	characteristic
227	D₆₇	—	2	2	no	—
228	D₆₇	—	4	1	no	—
229	C₄×#131	—	67	1	no	—
230	#2164	—	67	2	no	—
231	#2164	—	67	2	no	—
232	#2163	—	67	1	no	—
233	#2163	D₆₇	1	1	yes	characteristic, complemented
234	#2162	—	67	1	no	—
235	#2162	—	67	1	no	—
236	#2150	—	67	1	no	—
237	C₂×C₄⋊C₁₆	—	67	1	no	—
238	#2113	—	67	2	no	—
239	#2108	—	67	2	no	—
240	C₆₇	#33423	1	1	yes	characteristic, complemented, Sylow
241	C₂×#131	—	67	1	no	—
242	C₂×#131	—	67	1	no	—
243	C₄×#41	—	67	1	no	—
244	C₂×M₃₂	—	67	2	no	—
245	C₂²×C₁₆	—	67	2	no	—
246	#405	—	67	1	no	—
247	#405	—	67	1	no	—
248	#405	—	67	1	no	—
249	#405	—	67	1	no	—
250	#405	—	67	1	no	—
251	#405	—	67	1	no	—
252	C₄×M₁₆	—	67	1	no	—
253	C₄×M₁₆	—	67	1	no	—
254	C₄×M₁₆	—	67	1	no	—
255	C₂×C₄×C₈	—	67	1	no	—
256	C₂×C₄×C₈	—	67	1	no	—
257	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
258	C₄⋊C₁₆	—	67	2	no	—
259	C₄⋊C₁₆	—	67	2	no	—
260	C₄⋊C₁₆	—	67	1	no	—
261	C₄⋊C₁₆	—	67	1	no	—
262	C₄⋊C₁₆	C₂×D₆₇	1	1	yes	characteristic
263	C₄⋊C₁₆	C₂×D₆₇	1	1	yes	characteristic
264	C₂²⋊C₁₆	—	67	2	no	—
265	C₂²⋊C₁₆	—	67	2	no	—
266	C₂²⋊C₁₆	—	67	2	no	—
267	C₂²⋊C₁₆	C₂×D₆₇	1	2	yes	—
268	#346	—	67	2	no	—
269	#346	C₂×D₆₇	1	2	yes	—
270	C₄×C₁₆	—	67	2	no	—
271	C₄×C₁₆	—	67	2	no	—
272	C₂×#41	—	67	1	no	—
273	#131	—	134	2	no	—
274	#131	—	134	2	no	—
275	#131	—	134	4	no	—
276	C₂×M₁₆	—	67	1	no	—
277	C₂×M₁₆	—	67	1	no	—
278	C₂×M₁₆	—	67	1	no	—
279	C₂×M₁₆	—	67	1	no	—
280	C₂×M₁₆	—	67	1	no	—
281	C₂×M₁₆	—	67	1	no	—
282	C₂²×C₈	—	67	1	no	—
283	C₂²×C₈	—	67	1	no	—
284	C₂²×C₈	—	67	1	no	—
285	C₂²×C₈	—	67	1	no	—
286	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
287	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
288	C₄×Q₈	—	67	1	no	—
289	C₄×Q₈	—	67	1	no	—
290	C₄×D₄	—	67	1	no	—
291	C₄×D₄	—	67	1	no	—
292	C₄×D₄	—	67	1	no	—
293	C₄×D₄	—	67	1	no	—
294	C₄×D₄	—	67	1	no	—
295	C₄×D₄	—	67	1	no	—
296	#117	—	67	1	no	—
297	#117	—	67	1	no	—
298	#117	—	67	1	no	—
299	C₂×C₄²	—	67	1	no	—
300	C₂×C₄²	—	67	1	no	—
301	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
302	M₃₂	—	134	4	no	—
303	C₂×C₁₆	—	67	2	no	—
304	C₂×C₁₆	—	67	2	no	—
305	C₂×C₁₆	—	134	4	no	—
306	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
307	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
308	#97	—	67	1	no	—
309	#97	—	67	1	no	—
310	#97	—	67	1	no	—
311	#97	—	67	1	no	—
312	#97	—	67	1	no	—
313	#97	—	67	1	no	—
314	C₄×C₈	—	67	1	no	—
315	C₄×C₈	—	67	1	no	—
316	C₄×C₈	—	67	1	no	—
317	C₄×C₈	—	67	1	no	—
318	C₄×C₈	—	67	1	no	—
319	C₄×C₈	—	67	1	no	—
320	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
321	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
322	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
323	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
324	#41	—	134	2	no	—
325	#41	—	134	2	no	—
326	C₂×Q₈	—	67	1	no	—
327	C₂×D₄	—	67	1	no	—
328	C₂×D₄	—	67	1	no	—
329	C₂×D₄	—	67	1	no	—
330	C₂²×C₄	—	67	1	no	—
331	C₂²×C₄	—	67	1	no	—
332	C₂²×C₄	—	67	1	no	—
333	C₂²×C₄	—	67	1	no	—
334	C₂²×C₄	—	67	1	no	—
335	C₂²×C₄	—	67	1	no	—
336	C₂²×C₄	C₈×D₆₇	1	1	yes	characteristic
337	C₂²×C₄	C₈×D₆₇	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
339	M₁₆	—	67	4	no	—
340	M₁₆	—	134	2	no	—
341	M₁₆	—	134	2	no	—
342	M₁₆	—	134	2	no	—
343	M₁₆	—	134	2	no	—
344	M₁₆	—	134	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	67	1	no	—
349	C₂×C₈	—	67	1	no	—
350	C₂×C₈	—	67	2	no	—
351	C₂×C₈	—	67	2	no	—
352	C₂×C₈	—	67	1	no	—
353	C₂×C₈	—	67	1	no	—
354	C₂×C₈	—	134	2	no	—
355	C₂×C₈	—	134	2	no	—
356	C₂×C₈	—	134	1	no	—
357	C₂×C₈	—	134	1	no	—
358	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
359	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
360	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
361	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
362	C₄⋊C₄	—	67	1	no	—
363	C₄⋊C₄	—	67	1	no	—
364	C₄⋊C₄	—	67	1	no	—
365	C₄⋊C₄	—	67	1	no	—
366	C₄⋊C₄	—	67	1	no	—
367	C₄⋊C₄	—	67	1	no	—
368	C₂²⋊C₄	—	67	1	no	—
369	C₂²⋊C₄	—	67	1	no	—
370	C₂²⋊C₄	—	67	1	no	—
371	C₂²⋊C₄	—	67	1	no	—
372	C₂²⋊C₄	—	67	1	no	—
373	C₂²⋊C₄	—	67	1	no	—
374	C₄²	—	67	1	no	—
375	C₄²	—	67	1	no	—
376	C₄²	—	67	1	no	—
377	C₄²	—	67	1	no	—
378	C₄²	—	67	1	no	—
379	C₄²	—	67	1	no	—
380	C₄²	C₈×D₆₇	1	1	yes	characteristic
381	C₄²	C₈×D₆₇	1	1	yes	characteristic
382	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
383	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
384	C₁₆	—	2	2	no	—
385	C₁₆	—	2	2	no	—
386	C₁₆	—	134	2	no	—
387	C₁₆	—	134	2	no	—
388	C₂³	—	67	1	no	—
389	C₂³	—	67	1	no	—
390	C₂³	C₂×C₈×D₆₇	1	1	yes	characteristic
391	Q₈	—	134	2	no	—
392	D₄	—	134	2	no	—
393	D₄	—	134	2	no	—
394	D₄	—	134	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	268	1	no	—
400	C₂×C₄	—	268	1	no	—
401	C₂×C₄	—	67	1	no	—
402	C₂×C₄	—	67	2	no	—
403	C₂×C₄	—	67	2	no	—
404	C₂×C₄	—	67	1	no	—
405	C₂×C₄	—	67	1	no	—
406	C₂×C₄	—	67	1	no	—
407	C₂×C₄	—	67	1	no	—
408	C₂×C₄	—	67	1	no	—
409	C₂×C₄	—	134	2	no	—
410	C₂×C₄	—	134	2	no	—
411	C₂×C₄	—	134	1	no	—
412	C₂×C₄	—	134	1	no	—
413	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
414	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
415	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
416	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
417	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
418	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	67	2	no	—
422	C₈	—	67	2	no	—
423	C₈	—	134	1	no	—
424	C₈	—	134	1	no	—
425	C₈	M₁₆×D₆₇	1	2	yes	—
426	C₈	#41×D₆₇	1	1	yes	characteristic
427	C₈	#41×D₆₇	1	1	yes	characteristic
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	67	2	no	—
432	C₂²	—	134	1	no	—
433	C₂²	—	134	1	no	—
434	C₂²	—	134	1	no	—
435	C₂²	—	134	1	no	—
436	C₂²	—	134	1	no	—
437	C₂²	C₂²×C₈×D₆₇	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	67	2	no	—
443	C₄	—	134	1	no	—
444	C₄	—	134	1	no	—
445	C₄	—	134	1	no	—
446	C₄	—	134	1	no	—
447	C₄	—	134	1	no	—
448	C₄	#16863814	1	2	yes	—
449	C₄	#117×D₆₇	1	1	yes	characteristic
450	C₄	C₂×M₁₆×D₆₇	1	1	yes	characteristic
451	C₂	—	4	1	no	—
452	C₂	—	268	1	no	—
453	C₂	—	134	2	no	—
454	C₂	#431×D₆₇	1	1	yes	characteristic
455	C₂	C₂×#16863814	1	1	yes	characteristic
456	C₂	#22573311	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₆₇
commutator, socle	C₂²×C₆₇	C₂³×C₈
Fitting	C₆₇×#2163	C₂
prime radical	C₂×#11761628	C₂×C₄
cosocle	C₂×C₈×C₆₇	C₂⁴
hypercenter	#2163	D₆₇
hypocenter	C₆₇	#33423
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ #2163

Complements

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

N	H ≅ G/N	type
2. #22562017	C₂	semidirect
3. #22562013	C₂	semidirect
4. #22562011	C₂	semidirect
5. #22562008	C₂	semidirect
6. #22562007	C₂	semidirect
7. #22561963	C₂	semidirect
8. C₄⋊C₁₆×D₆₇	C₂	semidirect
10. #22561807	C₂	semidirect
11. C₆₇×#2163	C₂	semidirect
233. #2163	D₆₇	semidirect
240. C₆₇	#33423	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14524049	2
#22562017	2
#22562013	2
#22562011	2
#22562008	2
#22562007	2
#22561963	2
C₄⋊C₁₆×D₆₇	2
#22561821	2
#22561807	2
C₆₇×#2163	2
#33423	67