Subgroups — #30746142

Order 17152.

700 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22568842	C₂	1	1	yes	maximal, characteristic
2	C₄×#14524002	C₂	1	1	yes	maximal, characteristic
3	#22558110	C₂	1	4	yes	maximal, complemented
4	C₂×#423×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#14524002	—	2	1	no	—
6	#16863453	—	2	1	no	—
7	#16863453	C₄	1	2	yes	complemented
8	#16863449	—	2	1	no	—
9	#16863449	C₂²	1	2	yes	—
10	#16863420	C₄	1	2	yes	complemented
11	#16863360	—	2	1	no	—
12	C₄×#11761612	—	2	1	no	—
13	C₄×C₄⋊Dic₆₇	—	2	1	no	—
14	C₄×C₄⋊Dic₆₇	C₂²	1	2	yes	—
15	C₄×C₂²⋊Dic₆₇	—	2	1	no	—
16	C₄×C₂²⋊Dic₆₇	C₄	1	2	yes	—
17	#16863242	C₄	1	2	yes	—
18	C₄²×Dic₆₇	—	2	1	no	—
19	C₂²×M₁₆×C₆₇	—	2	1	no	—
20	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
21	#423×C₆₇	—	2	1	no	—
22	#423×C₆₇	—	2	1	no	—
23	#423×C₆₇	C₄	1	2	yes	complemented
24	#423×C₆₇	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₆₇	—	2	1	no	—
26	C₂×C₄⋊C₈×C₆₇	C₄	1	2	yes	complemented
27	C₂×#11761612	—	2	2	no	—
28	#14524002	—	2	8	no	—
29	C₂×C₄⋊Dic₆₇	—	2	2	no	—
30	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
31	C₂×C₄×Dic₆₇	—	2	2	no	—
32	C₂×C₄×Dic₆₇	—	2	2	no	—
33	C₂×C₄×Dic₆₇	—	2	2	no	—
34	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
35	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
36	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
37	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
38	#14523954	—	2	2	no	—
39	C₄×C₆₇⋊C₈	—	2	2	no	—
40	C₆₇⋊#95	—	2	2	no	—
41	C₆₇⋊#95	C₂×C₄	1	4	yes	—
42	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
45	C₂×M₁₆×C₆₇	—	2	2	no	—
46	C₂×M₁₆×C₆₇	—	2	2	no	—
47	C₂×M₁₆×C₆₇	—	4	4	no	—
48	C₂²×C₈×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	1	yes	characteristic
54	C₂×C₄²×C₆₇	D₄	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	Q₈	1	1	yes	characteristic
59	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
60	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₆₇	—	2	2	no	—
62	C₄⋊C₈×C₆₇	—	2	2	no	—
63	C₄⋊C₈×C₆₇	—	2	2	no	—
64	C₄⋊C₈×C₆₇	C₂×C₄	1	4	yes	—
65	C₂²×Dic₆₇	—	2	4	no	—
66	#11761612	—	4	4	no	—
67	C₂×C₆₇⋊C₈	—	2	4	no	—
68	C₄⋊Dic₆₇	—	2	8	no	—
69	C₂²⋊Dic₆₇	—	2	8	no	—
70	C₄×Dic₆₇	—	2	8	no	—
71	C₄×Dic₆₇	—	4	4	no	—
72	C₄×Dic₆₇	—	4	2	no	—
73	C₄×Dic₆₇	—	4	2	no	—
74	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₇	—	2	4	no	—
76	C₂²×C₄×C₆₇	—	2	2	no	—
77	C₂²×C₄×C₆₇	—	2	2	no	—
78	C₂²×C₄×C₆₇	—	4	2	no	—
79	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
80	C₂²×C₄×C₆₇	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₇	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
97	M₁₆×C₆₇	—	4	4	no	—
98	M₁₆×C₆₇	—	4	4	no	—
99	C₂×C₈×C₆₇	—	2	4	no	—
100	C₂×C₈×C₆₇	—	4	4	no	—
101	C₄²×C₆₇	C₄²	1	1	yes	characteristic
102	C₄²×C₆₇	C₄²	1	1	yes	characteristic
103	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₆₇	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₆₇	C₂×Q₈	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	#95	1	1	yes	characteristic
121	C₂³×C₆₇	#95	1	1	yes	characteristic
122	C₂³×C₆₇	C₂×C₂²⋊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	1	no	—
131	C₂×C₄×C₆₇	—	2	1	no	—
132	C₂×C₄×C₆₇	—	2	1	no	—
133	C₂×C₄×C₆₇	—	2	1	no	—
134	C₂×C₄×C₆₇	—	2	2	no	—
135	C₂×C₄×C₆₇	—	2	2	no	—
136	C₂×C₄×C₆₇	—	2	2	no	—
137	C₂×C₄×C₆₇	—	2	2	no	—
138	C₂×C₄×C₆₇	—	4	1	no	—
139	C₂×C₄×C₆₇	—	4	1	no	—
140	C₂×C₄×C₆₇	—	4	1	no	—
141	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
142	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
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	#104	1	4	yes	—
148	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂×C₄⋊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	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₆₇	#137	1	2	yes	—
156	C₂×Dic₆₇	—	2	8	no	—
157	C₂×Dic₆₇	—	4	4	no	—
158	C₂×Dic₆₇	—	4	4	no	—
159	C₈×C₆₇	—	4	4	no	—
160	C₆₇⋊C₈	—	4	4	no	—
161	C₂²×C₆₇	—	2	1	no	—
162	C₂²×C₆₇	—	2	1	no	—
163	C₂²×C₆₇	—	2	1	no	—
164	C₂²×C₆₇	—	2	1	no	—
165	C₂²×C₆₇	—	2	1	no	—
166	C₂²×C₆₇	—	2	1	no	—
167	C₂²×C₆₇	—	2	1	no	—
168	C₂²×C₆₇	—	4	4	no	—
169	C₂²×C₆₇	#339	1	2	yes	—
170	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
171	C₂²×C₆₇	#417	1	2	yes	—
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	#339	1	2	yes	—
180	C₄×C₆₇	#344	1	2	yes	—
181	C₄×C₆₇	#418	1	1	yes	characteristic
182	C₄×C₆₇	#419	1	1	yes	characteristic
183	C₄×C₆₇	C₂×#104	1	2	yes	—
184	C₄×C₆₇	#428	1	2	yes	—
185	Dic₆₇	—	4	8	no	—
186	#8097	—	67	1	no	maximal, Sylow
187	C₂×C₆₇	—	2	2	no	—
188	C₂×C₆₇	—	2	2	no	—
189	C₂×C₆₇	—	4	1	no	—
190	C₂×C₆₇	C₂×#339	1	1	yes	characteristic
191	C₂×C₆₇	#1736	1	1	yes	characteristic
192	C₂×C₆₇	C₂×#344	1	1	yes	characteristic
193	#2920	—	67	1	no	—
194	C₂×#423	D₆₇	1	1	yes	characteristic
195	C₄×#117	—	67	1	no	—
196	#1303	—	67	4	no	—
197	C₆₇	#8097	1	1	yes	characteristic, complemented, Sylow
198	C₂²×M₁₆	—	2	1	no	—
199	C₂×#117	—	134	1	no	—
200	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
201	#432	—	67	2	no	—
202	#432	—	134	1	no	—
203	#431	—	67	2	no	—
204	#431	—	134	1	no	—
205	#423	—	2	1	no	—
206	#423	—	2	1	no	—
207	#423	—	67	2	no	—
208	#423	Dic₆₇	1	2	yes	complemented
209	#423	C₂×D₆₇	1	2	yes	—
210	C₂×C₄⋊C₈	—	2	1	no	—
211	C₂×C₄⋊C₈	Dic₆₇	1	2	yes	complemented
212	#407	—	134	1	no	—
213	C₄×M₁₆	—	134	1	no	—
214	C₄×C₄⋊C₄	—	67	2	no	—
215	C₄×C₄⋊C₄	—	134	1	no	—
216	C₄×C₂²⋊C₄	—	67	2	no	—
217	C₄×C₂²⋊C₄	—	134	1	no	—
218	#376	—	67	2	no	—
219	C₄³	—	134	1	no	—
220	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
221	C₂³×C₄	D₂₆₈	1	1	yes	characteristic
222	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	4	4	no	—
226	C₂×M₁₆	—	134	2	no	—
227	C₂²×C₈	—	2	2	no	—
228	#117	—	134	8	no	—
229	C₂×C₄⋊C₄	—	134	2	no	—
230	C₂×C₂²⋊C₄	—	134	2	no	—
231	C₂×C₄²	—	134	2	no	—
232	C₂×C₄²	—	134	2	no	—
233	C₂×C₄²	—	134	2	no	—
234	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
235	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
236	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
237	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
238	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
239	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
240	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
241	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
242	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
243	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
244	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
245	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
246	C₄⋊C₈	—	2	2	no	—
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	67	4	no	—
250	C₄⋊C₈	—	134	2	no	—
251	C₄⋊C₈	C₂×Dic₆₇	1	4	yes	—
252	C₂²⋊C₈	—	134	2	no	—
253	C₂²⋊C₈	—	134	2	no	—
254	#97	—	134	2	no	—
255	C₄×C₈	—	134	2	no	—
256	#95	—	67	4	no	—
257	#95	—	134	2	no	—
258	C₂⁴	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	134	4	no	—
264	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
265	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
266	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
272	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
273	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
274	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
275	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
278	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
282	M₁₆	—	4	4	no	—
283	M₁₆	—	4	4	no	—
284	M₁₆	—	268	4	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	4	4	no	—
287	C₂×C₈	—	134	4	no	—
288	C₄⋊C₄	—	134	8	no	—
289	C₂²⋊C₄	—	134	8	no	—
290	C₄²	—	268	4	no	—
291	C₄²	—	268	2	no	—
292	C₄²	—	268	2	no	—
293	C₄²	—	134	8	no	—
294	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
295	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
296	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
297	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
298	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
299	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
300	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
301	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
302	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
303	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
304	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
305	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
306	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
307	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
308	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
309	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
310	C₂³	—	2	2	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	4	1	no	—
313	C₂³	C₆₇⋊#95	1	1	yes	characteristic
314	C₂³	C₆₇⋊#95	1	1	yes	characteristic
315	C₂³	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	268	4	no	—
335	C₂×C₄	—	268	4	no	—
336	C₂×C₄	—	134	8	no	—
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	C₆₇⋊#95	1	1	yes	characteristic
341	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
342	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
343	C₂×C₄	#14523969	1	4	yes	—
344	C₂×C₄	C₂×C₄×Dic₆₇	1	1	yes	characteristic
345	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
346	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
347	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
348	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
350	C₂×C₄	#14524069	1	2	yes	—
351	C₂×C₄	#14524074	1	2	yes	—
352	C₈	—	4	4	no	—
353	C₈	—	268	4	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	4	4	no	—
362	C₂²	#16863157	1	2	yes	—
363	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
364	C₂²	#16863395	1	2	yes	—
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	—	2	1	no	—
372	C₄	—	268	8	no	—
373	C₄	#16863157	1	2	yes	—
374	C₄	#16863167	1	2	yes	—
375	C₄	#16863401	1	1	yes	characteristic
376	C₄	#16863405	1	1	yes	characteristic
377	C₄	C₂×#14523969	1	2	yes	—
378	C₄	#16863436	1	2	yes	—
379	C₂	—	2	2	no	—
380	C₂	—	2	2	no	—
381	C₂	—	4	1	no	—
382	C₂	C₂×#16863157	1	1	yes	characteristic
383	C₂	#22559928	1	1	yes	characteristic
384	C₂	C₂×#16863167	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₆₇
commutator	C₂×C₄×C₆₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₂×#423×C₆₇	C₂
socle	C₂²×C₆₇	C₂×#95
prime radical	C₂⁴×C₆₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	C₂×#423	D₆₇
hypocenter	C₆₇	#8097
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
3. #22558110	C₂	semidirect
7. #16863453	C₄	semidirect
10. #16863420	C₄	semidirect
23. #423×C₆₇	C₄	semidirect
26. C₂×C₄⋊C₈×C₆₇	C₄	semidirect
197. C₆₇	#8097	semidirect
208. #423	Dic₆₇	semidirect
211. C₂×C₄⋊C₈	Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22568842	2
C₄×#14524002	2
#22558110	2
C₂×#423×C₆₇	2
#8097	67