Subgroups — #30824975

Order 17152.

730 conjugacy classes of subgroups.

The subgroup lattice has 380 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×#16863420	C₂	1	1	yes	maximal, characteristic
3	#22558981	C₂	1	4	yes	maximal, complemented
4	#22558979	C₂	1	4	yes	maximal, complemented
5	#22558964	C₂	1	4	yes	maximal, complemented
6	C₂×#423×C₆₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×#11761612	—	2	1	no	—
8	#16863449	C₄	1	2	yes	—
9	#16863449	C₄	1	2	yes	—
10	#16863449	C₂²	1	2	yes	—
11	#16863449	C₂²	1	2	yes	—
12	#16863420	—	2	1	no	—
13	#16863420	—	2	1	no	—
14	#16863420	C₂²	1	2	yes	—
15	#16863420	C₂²	1	2	yes	—
16	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
17	C₂×C₄⋊(C₆₇⋊C₈)	C₄	1	2	yes	—
18	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₂²⋊(C₆₇⋊C₈)	C₄	1	2	yes	—
20	C₂×C₄×C₆₇⋊C₈	C₂²	1	2	yes	—
21	#16863146	C₂²	1	16	yes	complemented
22	C₂²×M₁₆×C₆₇	—	2	1	no	—
23	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
24	#423×C₆₇	—	2	1	no	—
25	#423×C₆₇	—	2	1	no	—
26	#423×C₆₇	C₂²	1	2	yes	—
27	#423×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄⋊C₈×C₆₇	—	2	1	no	—
29	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
30	C₂×#11761612	—	2	2	no	—
31	C₂×#11761612	—	2	2	no	—
32	C₂×#11761612	—	4	4	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)	—	2	2	no	—
37	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
38	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
39	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
40	C₄⋊(C₆₇⋊C₈)	C₂³	1	4	yes	—
41	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
42	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
43	C₄×C₆₇⋊C₈	C₂×C₄	1	4	yes	—
44	C₄×C₆₇⋊C₈	C₂³	1	4	yes	—
45	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
48	C₂×M₁₆×C₆₇	—	2	2	no	—
49	C₂×M₁₆×C₆₇	—	2	2	no	—
50	C₂×M₁₆×C₆₇	—	4	4	no	—
51	C₂²×C₈×C₆₇	—	2	2	no	—
52	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
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	Q₈	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	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₆₇	—	2	2	no	—
65	C₄⋊C₈×C₆₇	—	2	2	no	—
66	C₄⋊C₈×C₆₇	—	2	2	no	—
67	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
68	#11761612	—	4	4	no	—
69	#11761612	—	4	4	no	—
70	C₂×C₆₇⋊C₈	—	2	4	no	—
71	C₂×C₆₇⋊C₈	—	4	4	no	—
72	C₂×C₆₇⋊C₈	—	4	4	no	—
73	C₂×C₆₇⋊C₈	C₂²×C₄	1	8	yes	—
74	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₇	—	4	2	no	—
76	C₂²×C₄×C₆₇	—	4	2	no	—
77	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
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	SD₁₆	1	4	yes	—
87	C₂²×C₄×C₆₇	SD₁₆	1	4	yes	—
88	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	C₂×Q₈	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	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	—	4	1	no	—
118	C₂³×C₆₇	—	4	1	no	—
119	C₂³×C₆₇	#106	1	4	yes	—
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	—	4	1	no	—
130	C₂×C₄×C₆₇	—	4	1	no	—
131	C₂×C₄×C₆₇	—	4	1	no	—
132	C₂×C₄×C₆₇	—	4	1	no	—
133	C₂×C₄×C₆₇	—	4	1	no	—
134	C₂×C₄×C₆₇	—	4	1	no	—
135	C₂×C₄×C₆₇	#106	1	4	yes	—
136	C₂×C₄×C₆₇	#106	1	4	yes	—
137	C₂×C₄×C₆₇	#106	1	4	yes	—
138	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
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×SD₁₆	1	2	yes	—
148	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
149	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
150	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
151	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
152	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
153	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
156	C₈×C₆₇	—	4	4	no	—
157	C₆₇⋊C₈	—	2	8	no	—
158	C₆₇⋊C₈	—	4	4	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	—	2	1	no	—
165	C₂²×C₆₇	—	4	4	no	—
166	C₂²×C₆₇	C₂×#106	1	2	yes	—
167	C₂²×C₆₇	C₂×#106	1	2	yes	—
168	C₂²×C₆₇	C₂×#106	1	2	yes	—
169	C₂²×C₆₇	C₂²×C₄⋊C₄	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	C₂×#106	1	2	yes	—
177	C₄×C₆₇	C₂×#106	1	2	yes	—
178	C₄×C₆₇	C₂×#106	1	2	yes	—
179	C₄×C₆₇	#430	1	2	yes	—
180	C₄×C₆₇	#568	1	2	yes	—
181	C₄×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
182	C₄×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
183	#17813	—	67	1	no	maximal, Sylow
184	C₂×C₆₇	—	2	2	no	—
185	C₂×C₆₇	—	2	2	no	—
186	C₂×C₆₇	—	2	2	no	—
187	C₂×C₆₇	#2905	1	1	yes	characteristic
188	C₂×C₆₇	C₂²×#106	1	1	yes	characteristic
189	C₂×C₆₇	C₂×#430	1	1	yes	characteristic
190	C₂×#431	—	67	1	no	—
191	C₂×#423	—	67	1	no	—
192	C₂×#423	D₆₇	1	1	yes	characteristic
193	#1570	—	67	4	no	—
194	#1570	—	67	4	no	—
195	#1566	—	67	4	no	—
196	C₆₇	#17813	1	1	yes	characteristic, complemented, Sylow
197	C₂²×M₁₆	—	2	1	no	—
198	C₂²×M₁₆	—	134	1	no	—
199	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
200	#431	—	67	2	no	—
201	#431	—	67	2	no	—
202	#431	—	67	2	no	—
203	#431	—	67	2	no	—
204	#423	—	2	1	no	—
205	#423	—	2	1	no	—
206	#423	—	67	2	no	—
207	#423	—	67	2	no	—
208	#423	—	134	1	no	—
209	#423	—	134	1	no	—
210	#423	C₂×D₆₇	1	2	yes	—
211	#423	C₂×D₆₇	1	2	yes	—
212	C₂×C₄⋊C₈	—	2	1	no	—
213	C₂×C₄⋊C₈	—	67	2	no	—
214	C₂×C₄⋊C₈	—	67	2	no	—
215	C₂×C₄⋊C₈	—	134	1	no	—
216	C₂×C₄⋊C₈	C₂×D₆₇	1	2	yes	—
217	C₂×C₂²⋊C₈	—	67	2	no	—
218	C₂×C₄×C₈	—	67	2	no	—
219	#334	—	67	16	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	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	4	4	no	—
226	C₂×M₁₆	—	268	4	no	—
227	C₂×M₁₆	—	134	2	no	—
228	C₂×M₁₆	—	134	2	no	—
229	C₂²×C₈	—	2	2	no	—
230	C₂²×C₈	—	67	4	no	—
231	C₂²×C₈	—	134	2	no	—
232	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
233	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
234	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
235	C₂×C₄²	C₄×D₆₇	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	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	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
242	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	—	2	2	no	—
247	C₄⋊C₈	—	67	4	no	—
248	C₄⋊C₈	—	67	4	no	—
249	C₄⋊C₈	—	67	4	no	—
250	C₄⋊C₈	—	134	2	no	—
251	C₄⋊C₈	—	134	2	no	—
252	C₄⋊C₈	—	134	2	no	—
253	C₄⋊C₈	C₂²×D₆₇	1	4	yes	—
254	C₂²⋊C₈	—	67	4	no	—
255	C₂²⋊C₈	—	67	4	no	—
256	C₄×C₈	—	67	4	no	—
257	C₄×C₈	—	67	4	no	—
258	C₂⁴	Dic₆₇⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
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	#11761615	1	4	yes	—
271	C₂²×C₄	#11761616	1	4	yes	—
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	M₁₆	—	4	4	no	—
283	M₁₆	—	268	4	no	—
284	M₁₆	—	268	4	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	4	4	no	—
287	C₂×C₈	—	268	4	no	—
288	C₂×C₈	—	268	4	no	—
289	C₂×C₈	—	67	8	no	—
290	C₂×C₈	—	134	4	no	—
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	Dic₆₇⋊C₄	1	1	yes	characteristic
296	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
297	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
298	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
299	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
300	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
301	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
302	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
303	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
304	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
305	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
306	C₄²	C₂³×D₆₇	1	1	yes	characteristic
307	C₂³	—	4	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	#14523974	1	4	yes	—
310	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
311	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
312	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
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	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	#14523974	1	4	yes	—
326	C₂×C₄	#14523974	1	4	yes	—
327	C₂×C₄	#14523974	1	4	yes	—
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	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×#11761615	1	2	yes	—
338	C₂×C₄	C₂×#11761615	1	2	yes	—
339	C₂×C₄	C₂×#11761615	1	2	yes	—
340	C₂×C₄	C₂×#11761616	1	2	yes	—
341	C₂×C₄	C₂×#11761616	1	2	yes	—
342	C₂×C₄	C₂×#11761616	1	2	yes	—
343	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
345	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
346	C₈	—	4	4	no	—
347	C₈	—	268	4	no	—
348	C₈	—	134	8	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	—	2	1	no	—
355	C₂²	—	4	4	no	—
356	C₂²	C₂×#14523974	1	2	yes	—
357	C₂²	C₂×#14523974	1	2	yes	—
358	C₂²	C₂×#14523974	1	2	yes	—
359	C₂²	C₂²×Dic₆₇⋊C₄	1	1	yes	characteristic
360	C₄	—	2	1	no	—
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	C₂×#14523974	1	2	yes	—
367	C₄	C₂×#14523974	1	2	yes	—
368	C₄	C₂×#14523974	1	2	yes	—
369	C₄	#16863444	1	2	yes	—
370	C₄	#16864162	1	2	yes	—
371	C₄	C₂²×#11761615	1	1	yes	characteristic
372	C₄	C₂²×#11761616	1	1	yes	characteristic
373	C₂	—	2	2	no	—
374	C₂	—	2	2	no	—
375	C₂	—	2	2	no	—
376	C₂	#22568772	1	1	yes	characteristic
377	C₂	C₂²×#14523974	1	1	yes	characteristic
378	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×#423×C₆₇	C₂
socle	C₂²×C₆₇	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₆₇	C₄⋊C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	C₂×#423	D₆₇
hypocenter	C₆₇	#17813
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×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. #22558981	C₂	semidirect
4. #22558979	C₂	semidirect
5. #22558964	C₂	semidirect
21. #16863146	C₂²	semidirect
196. C₆₇	#17813	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×#16863420	2
#22558981	2
#22558979	2
#22558964	2
C₂×#423×C₆₇	2
#17813	67