Subgroups — #30824906

Order 17152.

668 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863449	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863449	C₂	1	1	yes	maximal, characteristic
3	#22558990	C₂	1	4	yes	maximal, complemented
4	#22558985	C₂	1	2	yes	maximal, complemented
5	#22558981	C₂	1	2	yes	maximal, complemented
6	#22558955	C₂	1	4	yes	maximal, complemented
7	C₆₇×#2920	C₂	1	1	yes	maximal, characteristic
8	#16863449	—	2	1	no	—
9	#16863449	—	2	1	no	—
10	#16863449	C₄	1	2	yes	—
11	#16863449	C₄	1	2	yes	—
12	#16863449	C₂²	1	2	yes	—
13	#16863449	C₂²	1	2	yes	—
14	#16863449	C₂²	1	1	yes	characteristic
15	#16863449	C₂²	1	1	yes	characteristic
16	#16863449	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₆₇⋊C₈)	C₄	1	2	yes	—
18	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
20	C₂×C₂²⋊(C₆₇⋊C₈)	C₄	1	2	yes	—
21	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
22	C₂×C₄×C₆₇⋊C₈	C₂²	1	2	yes	—
23	#16863148	C₂²	1	8	yes	complemented
24	#16863146	C₂²	1	8	yes	complemented
25	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
26	#432×C₆₇	—	2	1	no	—
27	#432×C₆₇	C₂²	1	2	yes	—
28	#431×C₆₇	—	2	1	no	—
29	#431×C₆₇	C₂²	1	2	yes	—
30	#423×C₆₇	C₂²	1	2	yes	—
31	#407×C₆₇	—	2	1	no	—
32	C₄×M₁₆×C₆₇	—	2	1	no	—
33	C₂²×C₆₇⋊C₈	—	2	2	no	—
34	C₂²×C₆₇⋊C₈	C₂×C₄	1	4	yes	—
35	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
36	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
37	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
38	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
39	C₄⋊(C₆₇⋊C₈)	C₂³	1	4	yes	—
40	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
41	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
43	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
44	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
45	C₄×C₆₇⋊C₈	—	2	2	no	—
46	C₄×C₆₇⋊C₈	—	2	2	no	—
47	C₄×C₆₇⋊C₈	C₂×C₄	1	4	yes	—
48	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
49	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
50	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
53	C₂×M₁₆×C₆₇	—	2	2	no	—
54	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
61	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
62	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
63	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₆₇	—	2	2	no	—
67	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
68	C₂²⋊C₈×C₆₇	—	2	2	no	—
69	C₂²⋊C₈×C₆₇	—	2	2	no	—
70	#97×C₆₇	—	2	2	no	—
71	C₄×C₈×C₆₇	—	2	2	no	—
72	C₂×C₆₇⋊C₈	—	2	8	no	—
73	C₂×C₆₇⋊C₈	—	2	4	no	—
74	C₂×C₆₇⋊C₈	—	4	4	no	—
75	C₂×C₆₇⋊C₈	C₂²×C₄	1	4	yes	—
76	C₂×C₆₇⋊C₈	C₂²×C₄	1	4	yes	—
77	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₇	—	2	4	no	—
79	C₂²×C₄×C₆₇	—	2	4	no	—
80	C₂²×C₄×C₆₇	—	4	2	no	—
81	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
99	M₁₆×C₆₇	—	4	4	no	—
100	C₂×C₈×C₆₇	—	2	4	no	—
101	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
114	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
115	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
116	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
117	C₂³×C₆₇	—	2	2	no	—
118	C₂³×C₆₇	—	2	2	no	—
119	C₂³×C₆₇	—	4	1	no	—
120	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₆₇	—	2	2	no	—
124	C₂×C₄×C₆₇	—	2	2	no	—
125	C₂×C₄×C₆₇	—	2	2	no	—
126	C₂×C₄×C₆₇	—	2	2	no	—
127	C₂×C₄×C₆₇	—	2	2	no	—
128	C₂×C₄×C₆₇	—	2	2	no	—
129	C₂×C₄×C₆₇	—	2	2	no	—
130	C₂×C₄×C₆₇	—	2	2	no	—
131	C₂×C₄×C₆₇	—	2	2	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	—	2	2	no	—
134	C₂×C₄×C₆₇	—	2	2	no	—
135	C₂×C₄×C₆₇	—	2	2	no	—
136	C₂×C₄×C₆₇	—	4	1	no	—
137	C₂×C₄×C₆₇	—	4	1	no	—
138	C₂×C₄×C₆₇	—	4	1	no	—
139	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	#131	1	4	yes	—
149	C₂×C₄×C₆₇	#135	1	4	yes	—
150	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
153	C₈×C₆₇	—	4	4	no	—
154	C₆₇⋊C₈	—	2	4	no	—
155	C₆₇⋊C₈	—	2	4	no	—
156	C₆₇⋊C₈	—	4	4	no	—
157	C₂²×C₆₇	—	2	1	no	—
158	C₂²×C₆₇	—	2	1	no	—
159	C₂²×C₆₇	—	2	1	no	—
160	C₂²×C₆₇	—	2	1	no	—
161	C₂²×C₆₇	—	2	1	no	—
162	C₂²×C₆₇	—	2	1	no	—
163	C₂²×C₆₇	—	2	1	no	—
164	C₂²×C₆₇	—	4	4	no	—
165	C₂²×C₆₇	#424	1	2	yes	—
166	C₂²×C₆₇	#427	1	2	yes	—
167	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
168	C₄×C₆₇	—	2	1	no	—
169	C₄×C₆₇	—	2	1	no	—
170	C₄×C₆₇	—	2	1	no	—
171	C₄×C₆₇	—	2	1	no	—
172	C₄×C₆₇	—	2	1	no	—
173	C₄×C₆₇	—	2	1	no	—
174	C₄×C₆₇	—	2	1	no	—
175	C₄×C₆₇	#424	1	2	yes	—
176	C₄×C₆₇	#427	1	2	yes	—
177	C₄×C₆₇	#430	1	2	yes	—
178	C₄×C₆₇	C₂×#131	1	2	yes	—
179	C₄×C₆₇	C₂×#135	1	2	yes	—
180	#17803	—	67	1	no	maximal, Sylow
181	C₂×C₆₇	—	2	2	no	—
182	C₂×C₆₇	—	2	2	no	—
183	C₂×C₆₇	—	4	1	no	—
184	C₂×C₆₇	C₂×#424	1	1	yes	characteristic
185	C₂×C₆₇	C₂×#427	1	1	yes	characteristic
186	C₂×C₆₇	C₂×#430	1	1	yes	characteristic
187	#2920	D₆₇	1	1	yes	characteristic
188	C₂×#431	—	67	1	no	—
189	C₂×#431	—	67	1	no	—
190	#1572	—	67	4	no	—
191	#1571	—	67	2	no	—
192	#1570	—	67	2	no	—
193	#1564	—	67	4	no	—
194	C₆₇	#17803	1	1	yes	characteristic, complemented, Sylow
195	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
196	#432	—	2	1	no	—
197	#432	C₂×D₆₇	1	2	yes	—
198	#431	—	2	1	no	—
199	#431	—	67	2	no	—
200	#431	—	67	2	no	—
201	#431	—	67	1	no	—
202	#431	—	67	1	no	—
203	#431	—	67	2	no	—
204	#431	—	67	2	no	—
205	#431	—	67	2	no	—
206	#431	—	134	1	no	—
207	#431	—	134	1	no	—
208	#431	C₂×D₆₇	1	2	yes	—
209	#423	C₂×D₆₇	1	2	yes	—
210	C₂×C₄⋊C₈	—	67	2	no	—
211	C₂×C₄⋊C₈	—	67	2	no	—
212	#407	—	2	1	no	—
213	C₂×C₂²⋊C₈	—	67	2	no	—
214	C₂×C₂²⋊C₈	—	134	1	no	—
215	C₄×M₁₆	—	2	1	no	—
216	C₂×C₄×C₈	—	67	2	no	—
217	C₂×C₄×C₈	—	134	1	no	—
218	#335	—	67	8	no	—
219	#334	—	67	8	no	—
220	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
221	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
222	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
223	C₂×M₁₆	—	2	2	no	—
224	C₂²×C₈	—	67	4	no	—
225	C₂²×C₈	—	134	2	no	—
226	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
227	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
228	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
229	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
230	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
231	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
233	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
234	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
236	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
237	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	—	67	2	no	—
240	C₄⋊C₈	—	67	2	no	—
241	C₄⋊C₈	—	67	4	no	—
242	C₄⋊C₈	—	67	4	no	—
243	C₄⋊C₈	—	134	2	no	—
244	C₄⋊C₈	C₂²×D₆₇	1	4	yes	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	67	2	no	—
248	C₂²⋊C₈	—	67	2	no	—
249	C₂²⋊C₈	—	67	4	no	—
250	C₂²⋊C₈	—	134	2	no	—
251	C₂²⋊C₈	—	134	2	no	—
252	#97	—	2	2	no	—
253	C₄×C₈	—	2	2	no	—
254	C₄×C₈	—	67	4	no	—
255	C₄×C₈	—	67	2	no	—
256	C₄×C₈	—	67	2	no	—
257	C₄×C₈	—	134	2	no	—
258	C₄×C₈	—	134	2	no	—
259	C₂⁴	Dic₆₇⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
278	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
279	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
280	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
281	M₁₆	—	4	4	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	268	4	no	—
284	C₂×C₈	—	67	4	no	—
285	C₂×C₈	—	67	4	no	—
286	C₂×C₈	—	134	4	no	—
287	C₂×C₈	—	134	8	no	—
288	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
289	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
290	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
291	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
292	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
293	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
294	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
295	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
296	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
297	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
298	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
299	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
300	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
301	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
302	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
303	C₄²	C₂³×D₆₇	1	1	yes	characteristic
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	4	1	no	—
307	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
308	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
309	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
327	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
328	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
329	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
330	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
335	C₂×C₄	#14524051	1	4	yes	—
336	C₂×C₄	#14524063	1	4	yes	—
337	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
338	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
339	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
340	C₈	—	4	4	no	—
341	C₈	—	268	4	no	—
342	C₈	—	134	4	no	—
343	C₈	—	134	4	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	4	4	no	—
352	C₂²	#16863424	1	2	yes	—
353	C₂²	#16863432	1	2	yes	—
354	C₂²	C₂²×Dic₆₇⋊C₄	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	#16863424	1	2	yes	—
363	C₄	#16863432	1	2	yes	—
364	C₄	#16863444	1	2	yes	—
365	C₄	C₂×#14524051	1	2	yes	—
366	C₄	C₂×#14524063	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	4	1	no	—
370	C₂	C₂×#16863424	1	1	yes	characteristic
371	C₂	C₂×#16863432	1	1	yes	characteristic
372	C₂	C₂×#16863444	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#2920	C₂
socle	C₂²×C₆₇	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₆₇	C₄⋊C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#2920	D₆₇
hypocenter	C₆₇	#17803
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #22558990	C₂	semidirect
4. #22558985	C₂	semidirect
5. #22558981	C₂	semidirect
6. #22558955	C₂	semidirect
23. #16863148	C₂²	semidirect
24. #16863146	C₂²	semidirect
194. C₆₇	#17803	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863449	2
#22558990	2
#22558985	2
#22558981	2
#22558955	2
C₆₇×#2920	2
#17803	67