Subgroups — #30745461

Order 17152.

666 conjugacy classes of subgroups.

The subgroup lattice has 376 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×C₄×#11761612	C₂	1	1	yes	maximal, characteristic
3	#22558053	C₂	1	4	yes	maximal, complemented
4	C₂×#431×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11761612	C₄	1	2	yes	—
6	#16863449	—	2	1	no	—
7	#16863449	—	2	1	no	—
8	#16863449	C₄	1	2	yes	—
9	#16863449	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
11	C₂×C₂²⋊(C₆₇⋊C₈)	C₄	1	2	yes	—
12	C₄×#11761612	—	2	1	no	—
13	C₄×#11761612	—	2	1	no	—
14	C₄×#11761612	—	2	1	no	—
15	C₄×#11761612	—	2	1	no	—
16	C₂×#14523954	C₂²	1	2	yes	—
17	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
18	C₂×C₄×C₆₇⋊C₈	C₄	1	2	yes	—
19	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
20	#431×C₆₇	—	2	1	no	—
21	#431×C₆₇	—	2	1	no	—
22	#431×C₆₇	C₄	1	2	yes	—
23	#431×C₆₇	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₆₇	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₆₇	C₄	1	2	yes	—
26	C₂×C₄×C₈×C₆₇	—	2	1	no	—
27	C₂×#11761612	—	2	2	no	—
28	C₂×#11761612	—	2	2	no	—
29	C₂×#11761612	—	2	4	no	—
30	C₂×#11761612	C₈	1	8	yes	complemented
31	C₂²×C₆₇⋊C₈	—	2	2	no	—
32	C₂²×C₆₇⋊C₈	C₂×C₄	1	4	yes	—
33	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
34	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
35	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
36	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
37	#14523954	—	2	2	no	—
38	#14523954	—	2	2	no	—
39	C₄×C₆₇⋊C₈	—	2	2	no	—
40	C₄×C₆₇⋊C₈	—	2	2	no	—
41	C₄×C₆₇⋊C₈	—	2	2	no	—
42	C₄×C₆₇⋊C₈	—	2	2	no	—
43	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₈×C₆₇	—	2	2	no	—
47	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₆₇	D₄	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	Q₈	1	1	yes	characteristic
57	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
58	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₆₇	—	2	2	no	—
60	C₄⋊C₈×C₆₇	—	2	2	no	—
61	C₂²⋊C₈×C₆₇	—	2	2	no	—
62	C₂²⋊C₈×C₆₇	C₂×C₄	1	4	yes	—
63	C₄×C₈×C₆₇	—	2	2	no	—
64	C₄×C₈×C₆₇	—	2	2	no	—
65	#11761612	—	2	8	no	—
66	#11761612	—	2	8	no	—
67	C₂×C₆₇⋊C₈	—	2	4	no	—
68	C₂×C₆₇⋊C₈	—	2	4	no	—
69	C₂×C₆₇⋊C₈	—	2	4	no	—
70	C₂×C₆₇⋊C₈	—	4	4	no	—
71	C₂×C₆₇⋊C₈	C₂×C₈	1	8	yes	complemented
72	C₂⁴×C₆₇	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₆₇	—	4	2	no	—
74	C₂²×C₄×C₆₇	—	4	2	no	—
75	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₆₇	C₄²	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	C₂²⋊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	C₂×C₈	1	4	yes	—
91	C₂²×C₄×C₆₇	M₁₆	1	4	yes	—
92	C₂²×C₄×C₆₇	C₂²×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	C₂×C₈×C₆₇	—	2	4	no	—
96	C₂×C₈×C₆₇	—	4	4	no	—
97	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₆₇	C₂²⋊C₄	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	C₂×D₄	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×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	C₄×C₈	1	2	yes	—
118	C₂³×C₆₇	#97	1	2	yes	—
119	C₂³×C₆₇	C₂×C₄²	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	2	no	—
125	C₂×C₄×C₆₇	—	2	2	no	—
126	C₂×C₄×C₆₇	—	4	1	no	—
127	C₂×C₄×C₆₇	—	4	1	no	—
128	C₂×C₄×C₆₇	—	4	1	no	—
129	C₂×C₄×C₆₇	—	4	1	no	—
130	C₂×C₄×C₆₇	—	4	1	no	—
131	C₂×C₄×C₆₇	—	4	1	no	—
132	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
133	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
134	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
135	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
136	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
137	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
138	C₂×C₄×C₆₇	C₄×C₈	1	2	yes	—
139	C₂×C₄×C₆₇	#97	1	2	yes	—
140	C₂×C₄×C₆₇	C₂²⋊C₈	1	4	yes	—
141	C₂×C₄×C₆₇	C₂²⋊C₈	1	4	yes	—
142	C₂×C₄×C₆₇	C₄⋊C₈	1	4	yes	—
143	C₂×C₄×C₆₇	C₄⋊C₈	1	4	yes	—
144	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₂×C₂²⋊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	C₂²×C₈	1	2	yes	—
151	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
152	C₈×C₆₇	—	4	4	no	—
153	C₆₇⋊C₈	—	2	8	no	—
154	C₆₇⋊C₈	—	4	4	no	—
155	C₂²×C₆₇	—	2	1	no	—
156	C₂²×C₆₇	—	2	1	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	—	4	2	no	—
162	C₂²×C₆₇	—	4	2	no	—
163	C₂²×C₆₇	#336	1	2	yes	—
164	C₂²×C₆₇	#336	1	2	yes	—
165	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
166	C₂²×C₆₇	C₂×C₄×C₈	1	1	yes	characteristic
167	C₂²×C₆₇	C₂×#97	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	#336	1	2	yes	—
175	C₄×C₆₇	#336	1	2	yes	—
176	C₄×C₆₇	#344	1	2	yes	—
177	C₄×C₆₇	#344	1	2	yes	—
178	C₄×C₆₇	C₂×C₂²⋊C₈	1	2	yes	—
179	C₄×C₆₇	C₂×C₄⋊C₈	1	2	yes	—
180	#7918	—	67	1	no	maximal, Sylow
181	C₂×C₆₇	—	2	2	no	—
182	C₂×C₆₇	—	2	2	no	—
183	C₂×C₆₇	—	2	1	no	—
184	C₂×C₆₇	—	2	1	no	—
185	C₂×C₆₇	C₂×#336	1	1	yes	characteristic
186	C₂×C₆₇	C₂×#344	1	1	yes	characteristic
187	C₂×C₆₇	C₂×#344	1	1	yes	characteristic
188	C₂×#431	—	67	1	no	—
189	C₂×#431	D₆₇	1	1	yes	characteristic
190	C₂×C₄×M₁₆	—	67	1	no	—
191	#1281	—	67	4	no	—
192	C₆₇	#7918	1	1	yes	characteristic, complemented, Sylow
193	C₂²×M₁₆	—	67	2	no	—
194	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
195	#431	—	2	1	no	—
196	#431	—	2	1	no	—
197	#431	—	67	2	no	—
198	#431	—	67	2	no	—
199	#431	—	134	1	no	—
200	#431	—	134	1	no	—
201	#431	Dic₆₇	1	2	yes	—
202	#431	C₂×D₆₇	1	2	yes	—
203	C₂×C₄⋊C₈	—	2	1	no	—
204	C₂×C₄⋊C₈	—	134	1	no	—
205	C₂×C₂²⋊C₈	—	67	2	no	—
206	C₂×C₂²⋊C₈	Dic₆₇	1	2	yes	—
207	C₄×M₁₆	—	134	1	no	—
208	C₄×M₁₆	—	134	1	no	—
209	C₄×M₁₆	—	134	1	no	—
210	C₄×M₁₆	—	134	1	no	—
211	C₂×#97	—	67	2	no	—
212	C₂×C₄×C₈	—	2	1	no	—
213	C₂×C₄×C₈	—	67	2	no	—
214	C₂×C₄×C₈	—	134	1	no	—
215	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
216	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
217	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
218	C₂×M₁₆	—	67	8	no	—
219	C₂×M₁₆	—	134	2	no	—
220	C₂×M₁₆	—	134	2	no	—
221	C₂×M₁₆	—	134	4	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	67	4	no	—
224	C₂²×C₈	—	134	2	no	—
225	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
226	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
227	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
228	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
229	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
230	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
231	C₂×C₄²	C₂×Dic₆₇	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	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	—	134	2	no	—
240	C₄⋊C₈	—	134	2	no	—
241	C₂²⋊C₈	—	2	2	no	—
242	C₂²⋊C₈	—	67	4	no	—
243	C₂²⋊C₈	—	134	2	no	—
244	C₂²⋊C₈	C₂×Dic₆₇	1	4	yes	—
245	#97	—	134	2	no	—
246	#97	—	134	2	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	C₄×C₈	—	134	2	no	—
250	C₄×C₈	—	134	2	no	—
251	C₄×C₈	—	134	2	no	—
252	C₄×C₈	—	134	2	no	—
253	C₂⁴	C₄×Dic₆₇	1	1	yes	characteristic
254	C₂²×C₄	—	4	2	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
257	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
258	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
259	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊Dic₆₇	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	C₄⋊Dic₆₇	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
271	C₂²×C₄	C₈×D₆₇	1	4	yes	—
272	C₂²×C₄	#11761611	1	4	yes	—
273	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
275	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
276	M₁₆	—	134	8	no	—
277	M₁₆	—	134	8	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	4	4	no	—
280	C₂×C₈	—	268	4	no	—
281	C₂×C₈	—	67	8	no	—
282	C₂×C₈	—	134	4	no	—
283	C₂×C₈	—	134	4	no	—
284	C₂×C₈	—	134	4	no	—
285	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
286	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
287	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
288	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
289	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
290	C₄²	C₂²⋊Dic₆₇	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	Dic₆₇⋊C₄	1	1	yes	characteristic
295	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
296	C₄²	C₄⋊Dic₆₇	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×D₂₆₈	1	1	yes	characteristic
300	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
301	C₂³	—	4	1	no	—
302	C₂³	—	4	1	no	—
303	C₂³	C₆₇⋊#95	1	1	yes	characteristic
304	C₂³	C₆₇⋊#95	1	1	yes	characteristic
305	C₂³	C₈×Dic₆₇	1	2	yes	—
306	C₂³	#14523953	1	2	yes	—
307	C₂³	C₂×C₄×Dic₆₇	1	1	yes	characteristic
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
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	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
321	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
322	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
323	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
324	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
325	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
326	C₂×C₄	C₈×Dic₆₇	1	2	yes	—
327	C₂×C₄	#14523953	1	2	yes	—
328	C₂×C₄	(C₂×D₆₇)⋊C₈	1	4	yes	—
329	C₂×C₄	(C₂×D₆₇)⋊C₈	1	4	yes	—
330	C₂×C₄	Dic₆₇⋊C₈	1	4	yes	—
331	C₂×C₄	Dic₆₇⋊C₈	1	4	yes	—
332	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
335	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
338	C₂×C₄	C₂×C₈×D₆₇	1	2	yes	—
339	C₂×C₄	C₂×#11761611	1	2	yes	—
340	C₈	—	4	4	no	—
341	C₈	—	268	4	no	—
342	C₈	—	134	8	no	—
343	C₂²	—	2	1	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	—	4	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	#16863150	1	2	yes	—
352	C₂²	#16863150	1	2	yes	—
353	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
354	C₂²	C₂×C₈×Dic₆₇	1	1	yes	characteristic
355	C₂²	C₂×#14523953	1	1	yes	characteristic
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	#16863150	1	2	yes	—
363	C₄	#16863150	1	2	yes	—
364	C₄	#16863166	1	2	yes	—
365	C₄	#16863168	1	2	yes	—
366	C₄	C₂×(C₂×D₆₇)⋊C₈	1	2	yes	—
367	C₄	C₂×Dic₆₇⋊C₈	1	2	yes	—
368	C₂	—	2	1	no	—
369	C₂	—	2	1	no	—
370	C₂	—	2	2	no	—
371	C₂	—	2	2	no	—
372	C₂	C₂×#16863150	1	1	yes	characteristic
373	C₂	C₂×#16863166	1	1	yes	characteristic
374	C₂	C₂×#16863168	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	(C₂×D₆₇)⋊C₄
commutator	C₂²×C₆₇	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₂×#431×C₆₇	C₂
socle	C₂²×C₆₇	C₂×#95
prime radical	C₂⁴×C₆₇	C₄²
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	C₂×#431	D₆₇
hypocenter	C₆₇	#7918
LCS	G ▷ C₂²×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #22558053	C₂	semidirect
30. C₂×#11761612	C₈	semidirect
71. C₂×C₆₇⋊C₈	C₂×C₈	semidirect
192. C₆₇	#7918	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
C₂×C₄×#11761612	2
#22558053	2
C₂×#431×C₆₇	2
#7918	67