Subgroups — #30824941

Order 17152.

692 conjugacy classes of subgroups.

The subgroup lattice has 392 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	C₂×#16863420	C₂	1	1	yes	maximal, characteristic
3	#22558997	C₂	1	4	yes	maximal, complemented
4	#22558983	C₂	1	2	yes	maximal, complemented
5	#22558979	C₂	1	2	yes	maximal, complemented
6	#22558962	C₂	1	4	yes	maximal, complemented
7	C₂×#431×C₆₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11761612	—	2	1	no	—
9	#16863453	C₄	1	2	yes	—
10	#16863453	C₄	1	2	yes	—
11	#16863449	C₂²	1	2	yes	—
12	#16863449	C₂²	1	2	yes	—
13	#16863420	—	2	1	no	—
14	#16863420	—	2	1	no	—
15	#16863420	C₄	1	2	yes	—
16	#16863420	C₂²	1	2	yes	—
17	#16863420	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
19	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
20	#16863360	C₄	1	2	yes	—
21	C₄×#11761612	C₂²	1	2	yes	—
22	#16863148	C₂²	1	8	yes	complemented
23	#16863146	C₂²	1	8	yes	complemented
24	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
25	#431×C₆₇	—	2	1	no	—
26	#431×C₆₇	—	2	1	no	—
27	#431×C₆₇	C₂²	1	2	yes	—
28	#431×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₆₇	—	2	1	no	—
32	C₂×C₄×C₈×C₆₇	—	2	1	no	—
33	C₂×#11761612	—	2	2	no	—
34	C₂×#11761612	—	2	2	no	—
35	C₂×#11761612	—	4	4	no	—
36	C₂×#11761612	C₂×C₄	1	4	yes	—
37	C₂²×C₆₇⋊C₈	—	2	2	no	—
38	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
39	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
40	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
41	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
42	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
43	C₄⋊(C₆₇⋊C₈)	C₂³	1	4	yes	—
44	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
45	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
46	#14523954	C₂×C₄	1	4	yes	—
47	C₄×C₆₇⋊C₈	C₂³	1	4	yes	—
48	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
51	C₂²×C₈×C₆₇	—	2	1	no	—
52	C₂²×C₈×C₆₇	—	2	1	no	—
53	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₆₇	C₂×C₄	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	Q₈	1	1	yes	characteristic
62	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
65	C₄⋊C₈×C₆₇	—	2	1	no	—
66	C₄⋊C₈×C₆₇	—	2	1	no	—
67	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
68	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
69	C₂²⋊C₈×C₆₇	—	2	2	no	—
70	C₂²⋊C₈×C₆₇	—	2	2	no	—
71	C₄×C₈×C₆₇	—	2	2	no	—
72	C₄×C₈×C₆₇	—	2	2	no	—
73	#11761612	—	2	8	no	—
74	#11761612	—	4	4	no	—
75	#11761612	—	4	4	no	—
76	C₂×C₆₇⋊C₈	—	2	4	no	—
77	C₂×C₆₇⋊C₈	—	4	4	no	—
78	C₂×C₆₇⋊C₈	C₂²×C₄	1	8	yes	—
79	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₆₇	—	2	4	no	—
81	C₂²×C₄×C₆₇	—	2	2	no	—
82	C₂²×C₄×C₆₇	—	2	2	no	—
83	C₂²×C₄×C₆₇	—	4	2	no	—
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	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	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
102	C₂×C₈×C₆₇	—	2	2	no	—
103	C₂×C₈×C₆₇	—	2	2	no	—
104	C₂×C₈×C₆₇	—	4	2	no	—
105	C₂×C₈×C₆₇	—	4	2	no	—
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	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	C₂²×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×D₄	1	1	yes	characteristic
117	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
119	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
120	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
121	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
122	C₂³×C₆₇	—	2	2	no	—
123	C₂³×C₆₇	—	2	2	no	—
124	C₂³×C₆₇	—	4	1	no	—
125	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
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	1	no	—
133	C₂×C₄×C₆₇	—	2	1	no	—
134	C₂×C₄×C₆₇	—	2	1	no	—
135	C₂×C₄×C₆₇	—	2	1	no	—
136	C₂×C₄×C₆₇	—	2	2	no	—
137	C₂×C₄×C₆₇	—	2	2	no	—
138	C₂×C₄×C₆₇	—	2	2	no	—
139	C₂×C₄×C₆₇	—	2	2	no	—
140	C₂×C₄×C₆₇	—	2	2	no	—
141	C₂×C₄×C₆₇	—	2	2	no	—
142	C₂×C₄×C₆₇	—	2	2	no	—
143	C₂×C₄×C₆₇	—	4	1	no	—
144	C₂×C₄×C₆₇	—	4	1	no	—
145	C₂×C₄×C₆₇	—	4	1	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂×C₄⋊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	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₆₇	#131	1	4	yes	—
156	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
157	C₂×C₄×C₆₇	#137	1	2	yes	—
158	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
161	C₈×C₆₇	—	4	2	no	—
162	C₈×C₆₇	—	4	2	no	—
163	C₆₇⋊C₈	—	2	8	no	—
164	C₆₇⋊C₈	—	4	4	no	—
165	C₂²×C₆₇	—	2	1	no	—
166	C₂²×C₆₇	—	2	1	no	—
167	C₂²×C₆₇	—	2	1	no	—
168	C₂²×C₆₇	—	2	1	no	—
169	C₂²×C₆₇	—	2	1	no	—
170	C₂²×C₆₇	—	2	1	no	—
171	C₂²×C₆₇	—	2	1	no	—
172	C₂²×C₆₇	—	4	4	no	—
173	C₂²×C₆₇	#424	1	2	yes	—
174	C₂²×C₆₇	#428	1	2	yes	—
175	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
181	C₄×C₆₇	—	2	1	no	—
182	C₄×C₆₇	—	2	1	no	—
183	C₄×C₆₇	#424	1	2	yes	—
184	C₄×C₆₇	#428	1	2	yes	—
185	C₄×C₆₇	#430	1	2	yes	—
186	C₄×C₆₇	C₂×#131	1	2	yes	—
187	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
189	#17809	—	67	1	no	maximal, Sylow
190	C₂×C₆₇	—	2	2	no	—
191	C₂×C₆₇	—	2	2	no	—
192	C₂×C₆₇	—	4	1	no	—
193	C₂×C₆₇	C₂×#424	1	1	yes	characteristic
194	C₂×C₆₇	C₂×#428	1	1	yes	characteristic
195	C₂×C₆₇	C₂×#430	1	1	yes	characteristic
196	#2920	—	67	1	no	—
197	C₂×#431	D₆₇	1	1	yes	characteristic
198	C₂×#423	—	67	1	no	—
199	#1574	—	67	4	no	—
200	#1571	—	67	2	no	—
201	#1570	—	67	2	no	—
202	#1565	—	67	4	no	—
203	C₆₇	#17809	1	1	yes	characteristic, complemented, Sylow
204	C₂²×M₁₆	—	134	1	no	—
205	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
206	#432	—	67	2	no	—
207	#432	—	67	2	no	—
208	#431	—	2	1	no	—
209	#431	—	2	1	no	—
210	#431	—	67	2	no	—
211	#431	—	67	2	no	—
212	#431	C₂×D₆₇	1	2	yes	—
213	#431	C₂×D₆₇	1	2	yes	—
214	#423	—	67	2	no	—
215	#423	—	67	2	no	—
216	#423	—	67	2	no	—
217	#423	—	134	1	no	—
218	#423	—	134	1	no	—
219	C₂×C₄⋊C₈	—	67	2	no	—
220	C₂×C₄⋊C₈	—	134	1	no	—
221	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
222	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
223	#407	—	67	2	no	—
224	C₂×C₂²⋊C₈	—	2	1	no	—
225	C₄×M₁₆	—	67	2	no	—
226	C₂×C₄×C₈	—	2	1	no	—
227	#335	—	67	8	no	—
228	#334	—	67	8	no	—
229	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
230	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
231	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
232	C₂×M₁₆	—	268	4	no	—
233	C₂×M₁₆	—	67	4	no	—
234	C₂×M₁₆	—	134	2	no	—
235	C₂×M₁₆	—	134	2	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	134	2	no	—
239	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
240	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
241	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
242	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
243	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
244	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
245	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
246	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
247	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
248	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
249	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
250	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	—	67	4	no	—
254	C₄⋊C₈	—	67	4	no	—
255	C₄⋊C₈	—	67	4	no	—
256	C₄⋊C₈	—	134	2	no	—
257	C₄⋊C₈	—	134	2	no	—
258	C₄⋊C₈	—	134	2	no	—
259	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
260	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	—	2	2	no	—
263	C₂²⋊C₈	—	67	4	no	—
264	C₂²⋊C₈	—	67	4	no	—
265	#97	—	67	4	no	—
266	C₄×C₈	—	2	2	no	—
267	C₄×C₈	—	2	2	no	—
268	C₄×C₈	—	67	4	no	—
269	C₂⁴	Dic₆₇⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	4	2	no	—
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	Dic₆₇⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
280	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
281	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
290	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
291	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
292	M₁₆	—	268	4	no	—
293	M₁₆	—	268	4	no	—
294	M₁₆	—	134	8	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	—	268	4	no	—
300	C₂×C₈	—	67	8	no	—
301	C₂×C₈	—	134	4	no	—
302	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
303	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
304	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
305	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
306	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
307	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
308	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
309	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
310	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
311	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
312	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
313	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
314	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
315	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
316	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
317	C₄²	C₂³×D₆₇	1	1	yes	characteristic
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	4	1	no	—
321	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
322	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
323	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
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	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	C₂×Dic₆₇⋊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×Dic₆₇⋊C₄	1	1	yes	characteristic
346	C₂×C₄	C₂×Dic₆₇⋊C₄	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×Dic₆₇⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
351	C₂×C₄	#14524049	1	4	yes	—
352	C₂×C₄	#14524068	1	2	yes	—
353	C₂×C₄	#14524073	1	2	yes	—
354	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
356	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
357	C₈	—	4	2	no	—
358	C₈	—	4	2	no	—
359	C₈	—	268	4	no	—
360	C₈	—	134	8	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	4	4	no	—
369	C₂²	#16863422	1	2	yes	—
370	C₂²	#16863439	1	2	yes	—
371	C₂²	C₂²×Dic₆₇⋊C₄	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	#16863422	1	2	yes	—
380	C₄	#16863439	1	2	yes	—
381	C₄	#16863444	1	2	yes	—
382	C₄	C₂×#14524049	1	2	yes	—
383	C₄	C₂×#14524068	1	1	yes	characteristic
384	C₄	C₂×#14524073	1	1	yes	characteristic
385	C₂	—	2	2	no	—
386	C₂	—	2	2	no	—
387	C₂	—	4	1	no	—
388	C₂	C₂×#16863422	1	1	yes	characteristic
389	C₂	C₂×#16863439	1	1	yes	characteristic
390	C₂	C₂×#16863444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₂×#431×C₆₇	C₂
socle	C₂²×C₆₇	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₆₇	C₄⋊C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	C₂×#431	D₆₇
hypocenter	C₆₇	#17809
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #22558997	C₂	semidirect
4. #22558983	C₂	semidirect
5. #22558979	C₂	semidirect
6. #22558962	C₂	semidirect
22. #16863148	C₂²	semidirect
23. #16863146	C₂²	semidirect
203. C₆₇	#17809	semidirect

Maximal subgroups

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

subgroup	index
#22568842	2
C₂×#16863420	2
#22558997	2
#22558983	2
#22558979	2
#22558962	2
C₂×#431×C₆₇	2
#17809	67