Subgroups — #31008939

Order 17152.

600 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863350	C₂	1	1	yes	maximal, characteristic
2	#22562017	C₂	1	2	yes	maximal, complemented
3	#22562015	C₂	1	2	yes	maximal, complemented
4	#22562009	C₂	1	1	yes	maximal, characteristic, complemented
5	#22562008	C₂	1	1	yes	maximal, characteristic, complemented
6	#22562005	C₂	1	1	yes	maximal, characteristic, complemented
7	#22561966	C₂	1	2	yes	maximal, complemented
8	#22561818	C₂	1	1	yes	maximal, characteristic
9	C₂²⋊C₁₆×D₆₇	C₂	1	1	yes	maximal, characteristic
10	#22561807	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11761611	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
14	C₂×#14524000	C₄	1	1	yes	characteristic
15	C₂×#14523982	C₂²	1	2	yes	—
16	C₂×C₁₆×D₆₇	C₂²	1	2	yes	—
17	#16863350	C₄	1	1	yes	characteristic
18	#16863350	C₄	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	#16863350	C₂²	1	1	yes	characteristic
24	#16863350	C₂²	1	1	yes	characteristic
25	C₂×#14523954	C₄	1	1	yes	characteristic
26	C₂×#14523953	C₄	1	1	yes	characteristic
27	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
28	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	2	yes	complemented
29	Dic₆₇⋊C₁₆	C₂²	1	2	yes	complemented
30	Dic₆₇⋊C₁₆	C₂²	1	2	yes	complemented
31	C₂²⋊(C₆₇⋊C₁₆)	C₂²	1	1	yes	characteristic
32	C₂²⋊(C₆₇⋊C₁₆)	C₂²	1	1	yes	characteristic
33	(C₂×D₆₇)⋊C₁₆	C₂²	1	2	yes	—
34	(C₂×D₆₇)⋊C₁₆	C₂²	1	2	yes	—
35	#16863171	C₂²	1	2	yes	complemented
36	C₄×C₆₇⋊C₁₆	C₂²	1	2	yes	complemented
37	C₁₆×Dic₆₇	C₂²	1	2	yes	complemented
38	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₄⋊C₁₆×C₆₇	C₂²	1	2	yes	complemented
40	C₂²⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
42	#346×C₆₇	C₂²	1	2	yes	complemented
43	C₂²×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
44	C₂×#11761611	—	2	4	no	—
45	C₂×#11761611	C₂×C₄	1	1	yes	characteristic
46	C₂×#11761611	C₂×C₄	1	1	yes	characteristic
47	C₂×#11761611	C₂×C₄	1	1	yes	characteristic
48	C₂×#11761611	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₆₇	—	2	4	no	—
52	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
56	#14524000	C₈	1	1	yes	characteristic
57	#14524000	C₈	1	1	yes	characteristic
58	#14524000	C₈	1	1	yes	characteristic
59	#14524000	C₈	1	1	yes	characteristic
60	#14524000	C₂×C₄	1	1	yes	characteristic
61	#14524000	C₂×C₄	1	1	yes	characteristic
62	#14524000	C₂×C₄	1	1	yes	characteristic
63	#14524000	C₂×C₄	1	1	yes	characteristic
64	C₂×Dic₆₇⋊C₄	C₈	1	1	yes	characteristic
65	C₂×Dic₆₇⋊C₄	C₈	1	1	yes	characteristic
66	C₂×(C₂×D₆₇)⋊C₄	C₈	1	1	yes	characteristic
67	C₂×(C₂×D₆₇)⋊C₄	C₈	1	1	yes	characteristic
68	C₂×C₄×Dic₆₇	C₂×C₄	1	1	yes	characteristic
69	#14523982	—	2	4	no	—
70	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
71	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
72	C₁₆×D₆₇	—	2	4	no	—
73	#14523954	C₂×C₄	1	1	yes	characteristic
74	#14523954	C₂×C₄	1	1	yes	characteristic
75	#14523954	C₂×C₄	1	1	yes	characteristic
76	#14523954	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	#14523953	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
84	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
89	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
90	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂³×D₆₇	C₂×C₈	1	1	yes	characteristic
95	C₂²×Dic₆₇	C₂×C₈	1	1	yes	characteristic
96	C₂²×Dic₆₇	C₂×C₈	1	1	yes	characteristic
97	C₂²×Dic₆₇	C₂×C₈	1	1	yes	characteristic
98	C₂×C₄×D₆₇	—	2	2	no	—
99	C₂×C₄×D₆₇	—	2	2	no	—
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	#11761611	—	2	2	no	—
105	#11761611	—	2	2	no	—
106	#11761611	—	2	2	no	—
107	#11761611	M₁₆	1	4	yes	—
108	C₂×C₆₇⋊C₈	—	2	2	no	—
109	C₂×C₆₇⋊C₈	—	2	2	no	—
110	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
114	C₈×D₆₇	—	2	2	no	—
115	C₈×D₆₇	—	2	2	no	—
116	C₈×D₆₇	—	2	2	no	—
117	C₈×D₆₇	#41	1	4	yes	—
118	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
119	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
120	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
121	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
122	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
123	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
124	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
125	Dic₆₇⋊C₄	C₂×C₈	1	1	yes	characteristic
126	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
127	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
128	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
129	(C₂×D₆₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
130	(C₂×D₆₇)⋊C₄	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	C₄×Dic₆₇	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₆₇	C₂×C₈	1	1	yes	characteristic
136	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
138	C₆₇⋊C₁₆	—	2	2	no	—
139	C₆₇⋊C₁₆	—	2	2	no	—
140	C₂²×C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
141	C₂²×C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
142	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₈×C₆₇	—	2	2	no	—
144	C₂×C₈×C₆₇	—	2	2	no	—
145	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
149	C₄²×C₆₇	C₂×C₈	1	1	yes	characteristic
150	C₄²×C₆₇	C₂×C₈	1	1	yes	characteristic
151	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
153	C₁₆×C₆₇	—	2	2	no	—
154	C₁₆×C₆₇	—	2	2	no	—
155	C₂³×C₆₇	C₂²×C₈	1	1	yes	characteristic
156	C₂²×D₆₇	—	2	2	no	—
157	C₂²×D₆₇	—	2	2	no	—
158	C₂²×D₆₇	—	4	1	no	—
159	C₂²×D₆₇	C₂²×C₈	1	1	yes	characteristic
160	C₂²×D₆₇	C₂²×C₈	1	1	yes	characteristic
161	C₂×C₄×C₆₇	—	2	2	no	—
162	C₂×C₄×C₆₇	—	2	1	no	—
163	C₂×C₄×C₆₇	—	2	1	no	—
164	C₂×C₄×C₆₇	—	4	1	no	—
165	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
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	C₂³×C₄	1	1	yes	characteristic
171	C₂×Dic₆₇	—	2	2	no	—
172	C₂×Dic₆₇	—	2	2	no	—
173	C₂×Dic₆₇	—	4	1	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	C₄×D₆₇	—	2	2	no	—
181	C₄×D₆₇	—	2	1	no	—
182	C₄×D₆₇	—	2	1	no	—
183	C₄×D₆₇	—	2	2	no	—
184	C₄×D₆₇	#117	1	2	yes	—
185	C₄×D₆₇	C₂×M₁₆	1	2	yes	—
186	C₈×C₆₇	—	2	1	no	—
187	C₈×C₆₇	—	2	1	no	—
188	C₈×C₆₇	C₂×M₁₆	1	2	yes	—
189	C₈×C₆₇	C₂×#41	1	2	yes	—
190	C₆₇⋊C₈	—	2	1	no	—
191	C₆₇⋊C₈	—	2	1	no	—
192	C₆₇⋊C₈	#117	1	2	yes	—
193	C₆₇⋊C₈	C₂×M₁₆	1	2	yes	—
194	C₂²×C₆₇	—	2	1	no	—
195	C₂²×C₆₇	—	2	1	no	—
196	C₂²×C₆₇	#504	1	2	yes	—
197	C₂²×C₆₇	C₂³×C₈	1	1	yes	characteristic
198	C₂×D₆₇	—	2	1	no	—
199	C₂×D₆₇	—	2	1	no	—
200	C₂×D₆₇	—	2	1	no	—
201	C₂×D₆₇	—	2	1	no	—
202	C₂×D₆₇	—	2	1	no	—
203	C₂×D₆₇	—	4	4	no	—
204	C₂×D₆₇	#431	1	2	yes	—
205	C₄×C₆₇	—	2	1	no	—
206	C₄×C₆₇	—	2	1	no	—
207	C₄×C₆₇	—	2	1	no	—
208	C₄×C₆₇	—	2	1	no	—
209	C₄×C₆₇	—	2	1	no	—
210	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
211	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
212	Dic₆₇	—	2	1	no	—
213	Dic₆₇	—	2	1	no	—
214	Dic₆₇	—	2	1	no	—
215	Dic₆₇	—	2	1	no	—
216	Dic₆₇	—	2	1	no	—
217	Dic₆₇	#431	1	2	yes	—
218	#33422	—	67	1	no	maximal, Sylow
219	C₂×C₆₇	—	2	2	no	—
220	C₂×C₆₇	C₂×#431	1	1	yes	characteristic
221	C₂×C₆₇	C₂×#504	1	1	yes	characteristic
222	C₂×C₆₇	#3407	1	1	yes	characteristic
223	D₆₇	—	2	2	no	—
224	D₆₇	—	4	1	no	—
225	C₂×#405	—	67	1	no	—
226	#2164	—	67	2	no	—
227	#2164	—	67	2	no	—
228	#2163	—	67	1	no	—
229	#2163	D₆₇	1	1	yes	characteristic, complemented
230	#2162	—	67	1	no	—
231	#2162	—	67	1	no	—
232	#2151	—	67	2	no	—
233	#2112	—	67	1	no	—
234	C₂×C₂²⋊C₁₆	—	67	1	no	—
235	#2108	—	67	2	no	—
236	C₆₇	#33422	1	1	yes	characteristic, complemented, Sylow
237	C₂²×M₁₆	—	67	1	no	—
238	C₂³×C₈	—	67	1	no	—
239	C₂×#117	—	67	1	no	—
240	C₂×M₃₂	—	67	2	no	—
241	C₂²×C₁₆	—	67	2	no	—
242	#405	—	67	1	no	—
243	#405	—	67	1	no	—
244	#405	—	67	1	no	—
245	#405	—	67	1	no	—
246	#405	—	67	1	no	—
247	#405	—	67	1	no	—
248	#405	—	67	1	no	—
249	#405	—	67	1	no	—
250	C₂×#97	—	67	1	no	—
251	C₂×#97	—	67	1	no	—
252	C₂×C₄×C₈	—	67	1	no	—
253	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
254	C₄⋊C₁₆	—	67	2	no	—
255	C₄⋊C₁₆	—	67	2	no	—
256	C₄⋊C₁₆	—	67	2	no	—
257	C₄⋊C₁₆	C₂×D₆₇	1	2	yes	complemented
258	C₂²⋊C₁₆	—	67	1	no	—
259	C₂²⋊C₁₆	—	67	1	no	—
260	C₂²⋊C₁₆	—	67	2	no	—
261	C₂²⋊C₁₆	—	67	2	no	—
262	C₂²⋊C₁₆	C₂×D₆₇	1	1	yes	characteristic
263	C₂²⋊C₁₆	C₂×D₆₇	1	1	yes	characteristic
264	#346	—	67	2	no	—
265	#346	C₂×D₆₇	1	2	yes	complemented
266	C₄×C₁₆	—	67	2	no	—
267	C₄×C₁₆	—	67	2	no	—
268	C₂³×C₄	—	67	1	no	—
269	C₂×M₁₆	—	67	1	no	—
270	C₂×M₁₆	—	67	1	no	—
271	C₂×M₁₆	—	67	1	no	—
272	C₂×M₁₆	—	67	1	no	—
273	C₂×M₁₆	—	134	4	no	—
274	C₂²×C₈	—	67	1	no	—
275	C₂²×C₈	—	67	1	no	—
276	C₂²×C₈	—	67	1	no	—
277	C₂²×C₈	—	67	1	no	—
278	C₂²×C₈	—	67	1	no	—
279	C₂²×C₈	—	67	1	no	—
280	C₂²×C₈	—	134	4	no	—
281	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
282	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
283	#117	—	67	1	no	—
284	#117	—	67	1	no	—
285	#117	—	67	1	no	—
286	#117	—	67	1	no	—
287	#117	—	67	1	no	—
288	#117	—	67	1	no	—
289	#117	—	67	1	no	—
290	#117	—	67	1	no	—
291	C₂×C₄⋊C₄	—	67	1	no	—
292	C₂×C₄⋊C₄	—	67	1	no	—
293	C₂×C₂²⋊C₄	—	67	1	no	—
294	C₂×C₂²⋊C₄	—	67	1	no	—
295	C₂×C₄²	—	67	1	no	—
296	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
297	M₃₂	—	134	4	no	—
298	C₂×C₁₆	—	67	2	no	—
299	C₂×C₁₆	—	67	2	no	—
300	C₂×C₁₆	—	134	4	no	—
301	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
302	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
303	#97	—	67	1	no	—
304	#97	—	67	1	no	—
305	#97	—	67	1	no	—
306	#97	—	67	1	no	—
307	#97	—	67	1	no	—
308	#97	—	67	1	no	—
309	#97	—	67	1	no	—
310	#97	—	67	1	no	—
311	C₄×C₈	—	67	1	no	—
312	C₄×C₈	—	67	1	no	—
313	C₄×C₈	—	67	1	no	—
314	C₄×C₈	—	67	1	no	—
315	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
316	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
319	C₂⁴	—	67	1	no	—
320	C₂²×C₄	—	67	1	no	—
321	C₂²×C₄	—	67	1	no	—
322	C₂²×C₄	—	67	1	no	—
323	C₂²×C₄	—	67	1	no	—
324	C₂²×C₄	—	67	1	no	—
325	C₂²×C₄	—	67	1	no	—
326	C₂²×C₄	—	67	1	no	—
327	C₂²×C₄	—	134	2	no	—
328	C₂²×C₄	—	134	2	no	—
329	C₂²×C₄	C₈×D₆₇	1	1	yes	characteristic
330	C₂²×C₄	C₈×D₆₇	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
332	M₁₆	—	67	4	no	—
333	M₁₆	—	134	2	no	—
334	M₁₆	—	134	2	no	—
335	M₁₆	—	134	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	67	1	no	—
339	C₂×C₈	—	67	1	no	—
340	C₂×C₈	—	67	4	no	—
341	C₂×C₈	—	67	1	no	—
342	C₂×C₈	—	67	1	no	—
343	C₂×C₈	—	134	2	no	—
344	C₂×C₈	—	134	2	no	—
345	C₂×C₈	—	134	2	no	—
346	C₂×C₈	—	134	2	no	—
347	C₂×C₈	—	134	2	no	—
348	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
349	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
350	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
351	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
352	C₄⋊C₄	—	67	1	no	—
353	C₄⋊C₄	—	67	1	no	—
354	C₄⋊C₄	—	67	1	no	—
355	C₄⋊C₄	—	67	1	no	—
356	C₄⋊C₄	—	67	1	no	—
357	C₄⋊C₄	—	67	1	no	—
358	C₄⋊C₄	—	67	1	no	—
359	C₄⋊C₄	—	67	1	no	—
360	C₂²⋊C₄	—	67	1	no	—
361	C₂²⋊C₄	—	67	1	no	—
362	C₂²⋊C₄	—	67	1	no	—
363	C₂²⋊C₄	—	67	1	no	—
364	C₂²⋊C₄	—	67	1	no	—
365	C₂²⋊C₄	—	67	1	no	—
366	C₂²⋊C₄	—	67	1	no	—
367	C₂²⋊C₄	—	67	1	no	—
368	C₄²	—	67	1	no	—
369	C₄²	—	67	1	no	—
370	C₄²	—	67	1	no	—
371	C₄²	—	67	1	no	—
372	C₄²	C₈×D₆₇	1	1	yes	characteristic
373	C₄²	C₈×D₆₇	1	1	yes	characteristic
374	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
375	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
376	C₁₆	—	2	2	no	—
377	C₁₆	—	2	2	no	—
378	C₁₆	—	134	2	no	—
379	C₁₆	—	134	2	no	—
380	C₂³	—	268	1	no	—
381	C₂³	—	67	1	no	—
382	C₂³	—	67	1	no	—
383	C₂³	—	134	2	no	—
384	C₂³	—	134	2	no	—
385	C₂³	C₂×C₈×D₆₇	1	1	yes	characteristic
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	268	1	no	—
391	C₂×C₄	—	67	1	no	—
392	C₂×C₄	—	67	2	no	—
393	C₂×C₄	—	67	2	no	—
394	C₂×C₄	—	67	1	no	—
395	C₂×C₄	—	67	1	no	—
396	C₂×C₄	—	67	1	no	—
397	C₂×C₄	—	67	1	no	—
398	C₂×C₄	—	67	1	no	—
399	C₂×C₄	—	134	2	no	—
400	C₂×C₄	—	134	2	no	—
401	C₂×C₄	—	134	2	no	—
402	C₂×C₄	—	134	2	no	—
403	C₂×C₄	—	134	1	no	—
404	C₂×C₄	—	134	1	no	—
405	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
406	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
407	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
408	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
409	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	67	2	no	—
414	C₈	—	67	2	no	—
415	C₈	—	134	1	no	—
416	C₈	—	134	1	no	—
417	C₈	M₁₆×D₆₇	1	2	yes	—
418	C₈	#41×D₆₇	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	268	4	no	—
422	C₂²	—	67	2	no	—
423	C₂²	—	134	1	no	—
424	C₂²	—	134	1	no	—
425	C₂²	—	134	1	no	—
426	C₂²	—	134	1	no	—
427	C₂²	—	134	1	no	—
428	C₂²	#16863814	1	2	yes	—
429	C₂²	C₂²×C₈×D₆₇	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	67	2	no	—
436	C₄	—	134	1	no	—
437	C₄	—	134	1	no	—
438	C₄	—	134	1	no	—
439	C₄	—	134	1	no	—
440	C₄	—	134	1	no	—
441	C₄	#117×D₆₇	1	1	yes	characteristic
442	C₄	C₂×M₁₆×D₆₇	1	1	yes	characteristic
443	C₂	—	2	2	no	—
444	C₂	—	268	1	no	—
445	C₂	—	134	2	no	—
446	C₂	#431×D₆₇	1	1	yes	characteristic
447	C₂	C₂×#16863814	1	1	yes	characteristic
448	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	C₂³×D₆₇	C₂×C₈
cosocle	C₂×C₈×C₆₇	C₂⁴
hypercenter	#2163	D₆₇
hypocenter	C₆₇	#33422
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. #22562015	C₂	semidirect
4. #22562009	C₂	semidirect
5. #22562008	C₂	semidirect
6. #22562005	C₂	semidirect
7. #22561966	C₂	semidirect
10. #22561807	C₂	semidirect
11. C₆₇×#2163	C₂	semidirect
28. C₄⋊(C₆₇⋊C₁₆)	C₂²	semidirect
29. Dic₆₇⋊C₁₆	C₂²	semidirect
30. Dic₆₇⋊C₁₆	C₂²	semidirect
35. #16863171	C₂²	semidirect
36. C₄×C₆₇⋊C₁₆	C₂²	semidirect
37. C₁₆×Dic₆₇	C₂²	semidirect
39. C₄⋊C₁₆×C₆₇	C₂²	semidirect
42. #346×C₆₇	C₂²	semidirect
229. #2163	D₆₇	semidirect
236. C₆₇	#33422	semidirect
257. C₄⋊C₁₆	C₂×D₆₇	semidirect
265. #346	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863350	2
#22562017	2
#22562015	2
#22562009	2
#22562008	2
#22562005	2
#22561966	2
#22561818	2
C₂²⋊C₁₆×D₆₇	2
#22561807	2
C₆₇×#2163	2
#33422	67