Subgroups — #30866451

Order 17152.

724 conjugacy classes of subgroups.

The subgroup lattice has 396 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	#22560984	C₂	1	4	yes	maximal, complemented
4	#22560413	C₂	1	4	yes	maximal
5	#22560380	C₂	1	2	yes	maximal, complemented
6	#22560346	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2920	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11761612	C₂²	1	2	yes	—
9	#16863449	C₄	1	2	yes	—
10	#16863449	C₄	1	2	yes	—
11	#16863449	C₄	1	2	yes	—
12	#16863449	C₄	1	2	yes	—
13	C₂×#14523978	C₂²	1	8	yes	—
14	#16863420	—	2	1	no	—
15	#16863420	—	2	1	no	—
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)	—	2	1	no	—
20	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
22	C₂×C₄×C₆₇⋊C₈	C₂²	1	2	yes	—
23	#16863160	C₂²	1	8	yes	—
24	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
25	#432×C₆₇	—	2	1	no	—
26	#432×C₆₇	—	2	1	no	—
27	#431×C₆₇	—	2	1	no	—
28	#431×C₆₇	—	2	1	no	—
29	#423×C₆₇	C₂²	1	1	yes	characteristic
30	#423×C₆₇	C₂²	1	1	yes	characteristic
31	#407×C₆₇	C₂²	1	2	yes	—
32	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
33	C₂×#11761612	—	2	2	no	—
34	C₂×#11761612	—	4	4	no	—
35	C₂×#11761612	C₂³	1	4	yes	—
36	C₂²×C₆₇⋊C₈	—	2	2	no	—
37	C₂²×C₆₇⋊C₈	C₂³	1	4	yes	—
38	#14523978	—	4	8	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	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
44	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
45	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
46	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
47	C₄×C₆₇⋊C₈	C₂×C₄	1	4	yes	—
48	C₄×C₆₇⋊C₈	C₂×C₄	1	4	yes	—
49	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
50	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
51	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
53	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
54	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
63	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
64	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₆₇	—	2	1	no	—
67	C₄⋊C₈×C₆₇	—	2	1	no	—
68	C₄⋊C₈×C₆₇	—	2	1	no	—
69	C₄⋊C₈×C₆₇	—	2	1	no	—
70	C₂²⋊C₈×C₆₇	—	2	2	no	—
71	C₂²⋊C₈×C₆₇	—	2	2	no	—
72	#97×C₆₇	—	2	2	no	—
73	C₄×C₈×C₆₇	—	2	2	no	—
74	#11761612	—	2	8	no	—
75	#11761612	—	4	4	no	—
76	C₂×C₆₇⋊C₈	—	2	4	no	—
77	C₂×C₆₇⋊C₈	—	2	4	no	—
78	C₂×C₆₇⋊C₈	—	2	4	no	—
79	C₂×C₆₇⋊C₈	—	4	4	no	—
80	C₂×C₆₇⋊C₈	C₂²×C₄	1	8	yes	—
81	C₂⁴×C₆₇	C₂×Q₈	1	1	yes	characteristic
82	C₂²×C₄×C₆₇	—	2	4	no	—
83	C₂²×C₄×C₆₇	—	2	2	no	—
84	C₂²×C₄×C₆₇	—	2	2	no	—
85	C₂²×C₄×C₆₇	—	4	2	no	—
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	C₄⋊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×Q₈	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	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
104	M₁₆×C₆₇	—	2	4	no	—
105	M₁₆×C₆₇	—	2	4	no	—
106	C₂×C₈×C₆₇	—	2	2	no	—
107	C₂×C₈×C₆₇	—	2	2	no	—
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	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
124	C₂³×C₆₇	—	2	2	no	—
125	C₂³×C₆₇	—	2	2	no	—
126	C₂³×C₆₇	—	4	1	no	—
127	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂³×C₆₇	C₂²×Q₈	1	1	yes	characteristic
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	—	2	1	no	—
135	C₂×C₄×C₆₇	—	2	1	no	—
136	C₂×C₄×C₆₇	—	2	1	no	—
137	C₂×C₄×C₆₇	—	2	1	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	—	2	2	no	—
144	C₂×C₄×C₆₇	—	2	2	no	—
145	C₂×C₄×C₆₇	—	4	1	no	—
146	C₂×C₄×C₆₇	—	4	1	no	—
147	C₂×C₄×C₆₇	—	4	1	no	—
148	C₂×C₄×C₆₇	#108	1	4	yes	complemented
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	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
162	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
163	C₈×C₆₇	—	4	2	no	—
164	C₈×C₆₇	—	4	2	no	—
165	C₆₇⋊C₈	—	2	8	no	—
166	C₆₇⋊C₈	—	4	4	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	—	2	1	no	—
173	C₂²×C₆₇	—	2	1	no	—
174	C₂²×C₆₇	—	4	4	no	—
175	C₂²×C₆₇	C₂×#108	1	2	yes	—
176	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
177	C₂²×C₆₇	#544	1	2	yes	—
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	—	2	1	no	—
184	C₄×C₆₇	—	2	1	no	—
185	C₄×C₆₇	C₂×#108	1	2	yes	—
186	C₄×C₆₇	C₂×#108	1	2	yes	—
187	C₄×C₆₇	#430	1	2	yes	—
188	C₄×C₆₇	#520	1	2	yes	—
189	C₄×C₆₇	#535	1	1	yes	characteristic
190	C₄×C₆₇	#536	1	1	yes	characteristic
191	#21993	—	67	1	no	maximal, Sylow
192	C₂×C₆₇	—	2	2	no	—
193	C₂×C₆₇	—	2	2	no	—
194	C₂×C₆₇	—	4	1	no	—
195	C₂×C₆₇	#2317	1	1	yes	characteristic
196	C₂×C₆₇	C₂²×#108	1	1	yes	characteristic
197	C₂×C₆₇	C₂×#430	1	1	yes	characteristic
198	#2920	D₆₇	1	1	yes	characteristic
199	C₂×#431	—	67	1	no	—
200	C₂×#423	—	67	1	no	—
201	#1950	—	67	4	no	—
202	#1855	—	67	4	no	—
203	#1848	—	67	2	no	—
204	#1837	—	67	2	no	—
205	C₆₇	#21993	1	1	yes	characteristic, complemented, Sylow
206	C₂²×M₁₆	—	67	2	no	—
207	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
208	#432	—	2	1	no	—
209	#432	—	2	1	no	—
210	#431	—	2	1	no	—
211	#431	—	2	1	no	—
212	#431	—	67	2	no	—
213	#431	—	67	2	no	—
214	#431	—	67	2	no	—
215	#431	—	67	2	no	—
216	C₂×#108	—	67	8	no	—
217	#423	—	67	2	no	—
218	#423	—	67	2	no	—
219	#423	—	134	1	no	—
220	#423	—	134	1	no	—
221	#423	C₂×D₆₇	1	1	yes	characteristic
222	#423	C₂×D₆₇	1	1	yes	characteristic
223	C₂×C₄⋊C₈	—	67	2	no	—
224	C₂×C₄⋊C₈	—	134	1	no	—
225	C₂×C₄⋊C₈	—	134	1	no	—
226	#407	C₂×D₆₇	1	2	yes	—
227	C₂×C₂²⋊C₈	—	67	2	no	—
228	C₄×M₁₆	C₂×D₆₇	1	2	yes	—
229	C₂×C₄×C₈	—	67	2	no	—
230	#341	—	67	8	no	—
231	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
232	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
233	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
234	C₂×M₁₆	—	268	4	no	—
235	C₂×M₁₆	—	67	4	no	—
236	C₂×M₁₆	—	134	2	no	—
237	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
238	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
239	C₂²×C₈	—	67	4	no	—
240	C₂²×C₈	—	134	2	no	—
241	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
242	C₂×C₄²	Dic₁₃₄	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	C₄×D₆₇	1	1	yes	characteristic
246	C₂×C₄²	C₄×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	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
252	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
253	#108	—	268	8	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	—	67	4	no	—
259	C₄⋊C₈	—	67	4	no	—
260	C₄⋊C₈	—	134	2	no	—
261	C₄⋊C₈	—	134	2	no	—
262	C₄⋊C₈	—	134	2	no	—
263	C₄⋊C₈	—	134	2	no	—
264	C₂²⋊C₈	—	2	2	no	—
265	C₂²⋊C₈	—	2	2	no	—
266	C₂²⋊C₈	—	67	4	no	—
267	C₂²⋊C₈	—	67	4	no	—
268	#97	—	2	2	no	—
269	C₄×C₈	—	2	2	no	—
270	C₄×C₈	—	67	4	no	—
271	C₄×C₈	—	67	4	no	—
272	C₂⁴	C₂×Dic₁₃₄	1	1	yes	characteristic
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	2	no	—
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	Dic₆₇⋊C₄	1	1	yes	characteristic
284	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₄×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	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
293	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
294	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
295	M₁₆	—	2	4	no	—
296	M₁₆	—	2	4	no	—
297	M₁₆	—	268	4	no	—
298	M₁₆	—	134	8	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	268	4	no	—
302	C₂×C₈	—	67	8	no	—
303	C₂×C₈	—	134	4	no	—
304	C₂×C₈	—	134	4	no	—
305	C₂×C₈	—	134	4	no	—
306	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
307	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
308	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
309	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
310	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
311	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
312	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
313	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
314	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
315	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
316	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
317	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
318	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
319	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
320	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
321	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	4	1	no	—
325	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
326	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
327	C₂³	C₂²×Dic₁₃₄	1	1	yes	characteristic
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	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	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	#14523978	1	4	yes	complemented
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	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
352	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
353	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
354	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
359	C₂×C₄	#14524089	1	2	yes	—
360	C₂×C₄	#14524090	1	2	yes	—
361	C₈	—	4	2	no	—
362	C₈	—	4	2	no	—
363	C₈	—	268	4	no	—
364	C₈	—	134	8	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	4	4	no	—
373	C₂²	C₂×#14523978	1	2	yes	—
374	C₂²	C₂²×Dic₆₇⋊C₄	1	1	yes	characteristic
375	C₂²	#16864024	1	2	yes	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	C₂×#14523978	1	2	yes	—
384	C₄	C₂×#14523978	1	2	yes	—
385	C₄	#16863444	1	2	yes	—
386	C₄	#16863876	1	2	yes	—
387	C₄	#16863960	1	1	yes	characteristic
388	C₄	#16863967	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	2	2	no	—
391	C₂	—	4	1	no	—
392	C₂	#22562829	1	1	yes	characteristic
393	C₂	C₂²×#14523978	1	1	yes	characteristic
394	C₂	C₂×#16863444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#2920	C₂
socle	C₂²×C₆₇	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₆₇	C₂×Q₈
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#2920	D₆₇
hypocenter	C₆₇	#21993
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #22560984	C₂	semidirect
5. #22560380	C₂	semidirect
6. #22560346	C₂	semidirect
148. C₂×C₄×C₆₇	#108	semidirect
205. C₆₇	#21993	semidirect
346. C₂×C₄	#14523978	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
#22560984	2
#22560413	2
#22560380	2
#22560346	2
C₆₇×#2920	2
#21993	67