Subgroups — #30745595

Order 17152.

610 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863453	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863453	C₂	1	1	yes	maximal, characteristic
3	#22558065	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2285	C₂	1	1	yes	maximal, characteristic
5	#16863453	—	2	1	no	—
6	#16863453	—	2	1	no	—
7	#16863453	—	2	1	no	—
8	#16863453	—	2	1	no	—
9	#16863453	C₄	1	2	yes	complemented
10	#16863453	C₄	1	2	yes	complemented
11	#16863453	C₂²	1	2	yes	—
12	#16863453	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
14	C₂×C₄⋊(C₆₇⋊C₈)	C₄	1	2	yes	complemented
15	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
16	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
17	C₂×#14523954	—	2	1	no	—
18	C₂×#14523954	C₄	1	2	yes	complemented
19	C₂×#117×C₆₇	C₄	1	2	yes	—
20	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
21	#384×C₆₇	—	2	1	no	—
22	#382×C₆₇	—	2	1	no	—
23	#380×C₆₇	—	2	1	no	—
24	#380×C₆₇	—	2	1	no	—
25	C₄×C₄⋊C₄×C₆₇	C₄	1	2	yes	—
26	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
27	C₂²×C₆₇⋊C₈	—	2	2	no	—
28	C₂²×C₆₇⋊C₈	—	2	2	no	—
29	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
30	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
31	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
32	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
33	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
34	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
35	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
36	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
37	#14523954	—	2	2	no	—
38	#14523954	—	2	2	no	—
39	#14523954	—	2	2	no	—
40	#14523954	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
44	#117×C₆₇	—	4	4	no	—
45	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
49	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
54	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₇	D₄	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	Q₈	1	1	yes	characteristic
60	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
61	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
62	#95×C₆₇	—	2	2	no	—
63	#95×C₆₇	—	2	2	no	—
64	C₂×C₆₇⋊C₈	—	2	4	no	—
65	C₂×C₆₇⋊C₈	—	2	4	no	—
66	C₂×C₆₇⋊C₈	—	4	4	no	—
67	C₂×C₆₇⋊C₈	—	4	4	no	—
68	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₆₇	—	2	2	no	—
70	C₂²×C₄×C₆₇	—	2	2	no	—
71	C₂²×C₄×C₆₇	—	2	4	no	—
72	C₂²×C₄×C₆₇	—	4	2	no	—
73	C₂²×C₄×C₆₇	—	4	2	no	—
74	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
75	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₇	C₂²⋊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	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
92	C₄⋊C₄×C₆₇	—	4	4	no	—
93	C₄⋊C₄×C₆₇	—	4	4	no	—
94	C₄⋊C₄×C₆₇	—	4	4	no	—
95	C₂²⋊C₄×C₆₇	—	4	4	no	—
96	C₄²×C₆₇	—	4	4	no	—
97	C₄²×C₆₇	C₄²	1	1	yes	characteristic
98	C₄²×C₆₇	C₄²	1	1	yes	characteristic
99	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₆₇	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
113	C₂³×C₆₇	—	4	1	no	—
114	C₂³×C₆₇	—	4	1	no	—
115	C₂³×C₆₇	#95	1	1	yes	characteristic
116	C₂³×C₆₇	#95	1	1	yes	characteristic
117	C₂³×C₆₇	#100	1	2	yes	—
118	C₂³×C₆₇	#101	1	2	yes	—
119	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₆₇	—	2	2	no	—
121	C₂×C₄×C₆₇	—	2	2	no	—
122	C₂×C₄×C₆₇	—	2	2	no	—
123	C₂×C₄×C₆₇	—	2	2	no	—
124	C₂×C₄×C₆₇	—	2	1	no	—
125	C₂×C₄×C₆₇	—	2	1	no	—
126	C₂×C₄×C₆₇	—	2	1	no	—
127	C₂×C₄×C₆₇	—	2	1	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	—	4	1	no	—
135	C₂×C₄×C₆₇	—	4	1	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	—	4	1	no	—
140	C₂×C₄×C₆₇	—	4	4	no	—
141	C₂×C₄×C₆₇	—	4	4	no	—
142	C₂×C₄×C₆₇	—	4	4	no	—
143	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
144	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
145	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
146	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
147	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
148	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₆₇⋊C₈	—	4	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	—	4	2	no	—
164	C₂²×C₆₇	—	4	2	no	—
165	C₂²×C₆₇	#343	1	2	yes	—
166	C₂²×C₆₇	#343	1	2	yes	—
167	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
168	C₂²×C₆₇	C₂×#100	1	1	yes	characteristic
169	C₂²×C₆₇	C₂×#101	1	1	yes	characteristic
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	—	2	1	no	—
176	C₄×C₆₇	—	2	1	no	—
177	C₄×C₆₇	—	2	1	no	—
178	C₄×C₆₇	—	2	1	no	—
179	C₄×C₆₇	—	2	1	no	—
180	C₄×C₆₇	—	8	4	no	—
181	C₄×C₆₇	H(3,ℤ/4)	1	2	yes	—
182	C₄×C₆₇	#421	1	2	yes	—
183	#7952	—	67	1	no	maximal, Sylow
184	C₂×C₆₇	—	2	1	no	—
185	C₂×C₆₇	—	2	2	no	—
186	C₂×C₆₇	—	2	2	no	—
187	C₂×C₆₇	—	2	1	no	—
188	C₂×C₆₇	C₂×H(3,ℤ/4)	1	1	yes	characteristic
189	C₂×C₆₇	#1733	1	1	yes	characteristic
190	C₂×C₆₇	C₂×#343	1	1	yes	characteristic
191	C₂×#432	—	67	1	no	—
192	C₂×#432	—	67	1	no	—
193	#2285	D₆₇	1	1	yes	characteristic
194	#1285	—	67	4	no	—
195	C₆₇	#7952	1	1	yes	characteristic, complemented, Sylow
196	C₂×#117	Dic₆₇	1	2	yes	—
197	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
198	#432	—	67	2	no	—
199	#432	—	67	2	no	—
200	#432	—	67	2	no	—
201	#432	—	67	2	no	—
202	#432	—	134	1	no	—
203	#432	—	134	1	no	—
204	#432	—	134	1	no	—
205	#432	—	134	1	no	—
206	C₂×C₄⋊C₈	—	67	2	no	—
207	C₂×C₄⋊C₈	—	134	1	no	—
208	C₂×C₂²⋊C₈	—	134	1	no	—
209	C₂×C₂²⋊C₈	—	134	1	no	—
210	C₂×#97	—	67	2	no	—
211	C₂×#97	—	134	1	no	—
212	#384	—	2	1	no	—
213	#382	—	2	1	no	—
214	#380	—	2	1	no	—
215	#380	—	2	1	no	—
216	C₄×C₄⋊C₄	Dic₆₇	1	2	yes	—
217	C₄×C₄⋊C₄	C₂×D₆₇	1	2	yes	—
218	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
219	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
220	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
221	C₂²×C₈	—	134	2	no	—
222	C₂²×C₈	—	134	2	no	—
223	#117	—	4	4	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₂²⋊C₄	—	2	2	no	—
228	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
229	C₂×C₄²	Dic₁₃₄	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	C₄×D₆₇	1	1	yes	characteristic
233	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
234	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
235	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
236	C₂×C₄²	C₂×Dic₆₇	1	4	yes	—
237	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
238	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
240	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
241	C₄⋊C₈	—	67	4	no	—
242	C₄⋊C₈	—	134	2	no	—
243	C₄⋊C₈	—	134	2	no	—
244	C₄⋊C₈	—	134	2	no	—
245	C₂²⋊C₈	—	134	2	no	—
246	C₂²⋊C₈	—	134	2	no	—
247	C₂²⋊C₈	—	134	2	no	—
248	C₂²⋊C₈	—	134	2	no	—
249	#97	—	67	4	no	—
250	#97	—	134	2	no	—
251	#97	—	134	2	no	—
252	#97	—	134	2	no	—
253	#95	—	2	2	no	—
254	#95	—	2	2	no	—
255	C₂⁴	C₂²⋊Dic₆₇	1	1	yes	characteristic
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
262	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
263	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
268	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊Dic₆₇	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	Dic₆₇⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
274	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
275	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
276	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
279	C₂×C₈	—	268	4	no	—
280	C₂×C₈	—	268	4	no	—
281	C₂×C₈	—	134	4	no	—
282	C₂×C₈	—	134	4	no	—
283	C₄⋊C₄	—	4	4	no	—
284	C₄⋊C₄	—	4	4	no	—
285	C₄⋊C₄	—	4	4	no	—
286	C₂²⋊C₄	—	4	4	no	—
287	C₄²	—	4	4	no	—
288	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
289	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
290	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
291	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
292	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
293	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
294	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
295	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
296	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
297	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
298	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
299	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
300	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
301	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
302	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
303	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
304	C₂³	—	4	1	no	—
305	C₂³	—	4	1	no	—
306	C₂³	C₆₇⋊#95	1	1	yes	characteristic
307	C₂³	C₆₇⋊#95	1	1	yes	characteristic
308	C₂³	#14523960	1	2	yes	—
309	C₂³	#14523962	1	2	yes	—
310	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	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	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
335	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
336	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
337	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
338	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
339	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄×Dic₆₇	1	1	yes	characteristic
341	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
342	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
346	C₈	—	268	4	no	—
347	C₈	—	268	4	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	#16863165	1	2	yes	—
357	C₂²	#16863165	1	2	yes	—
358	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
359	C₂²	C₂×#14523960	1	1	yes	characteristic
360	C₂²	C₂×#14523962	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	8	4	no	—
372	C₄	#16863152	1	2	yes	—
373	C₄	#16863414	1	2	yes	—
374	C₂	—	2	1	no	—
375	C₂	—	2	1	no	—
376	C₂	—	2	2	no	—
377	C₂	—	2	2	no	—
378	C₂	C₂×#16863152	1	1	yes	characteristic
379	C₂	#22559919	1	1	yes	characteristic
380	C₂	C₂×#16863165	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₆₇⋊#95
commutator	C₂×C₄×C₆₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₆₇×#2285	C₂
socle	C₂²×C₆₇	C₂×#95
prime radical	C₂⁴×C₆₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	#2285	D₆₇
hypocenter	C₆₇	#7952
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ #2285

Complements

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

N	H ≅ G/N	type
3. #22558065	C₂	semidirect
9. #16863453	C₄	semidirect
10. #16863453	C₄	semidirect
14. C₂×C₄⋊(C₆₇⋊C₈)	C₄	semidirect
18. C₂×#14523954	C₄	semidirect
195. C₆₇	#7952	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863453	2
#22558065	2
C₆₇×#2285	2
#7952	67