Subgroups — #30745280

Order 17152.

684 conjugacy classes of subgroups.

The subgroup lattice has 368 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	C₄×#14524002	C₂	1	1	yes	maximal, characteristic
3	#22558041	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2920	C₂	1	1	yes	maximal, characteristic
5	C₂×#14524002	—	2	1	no	—
6	#16863449	—	2	1	no	—
7	#16863449	—	2	1	no	—
8	#16863449	C₄	1	2	yes	complemented
9	#16863449	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₆₇⋊C₈)	C₄	1	2	yes	complemented
11	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
12	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
13	C₄×C₄⋊Dic₆₇	—	2	1	no	—
14	C₄×C₄⋊Dic₆₇	C₄	1	2	yes	—
15	C₄×C₂²⋊Dic₆₇	—	2	1	no	—
16	C₄×C₂²⋊Dic₆₇	C₄	1	2	yes	—
17	#16863242	—	2	1	no	—
18	C₄²×Dic₆₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
20	#432×C₆₇	—	2	1	no	—
21	#432×C₆₇	C₄	1	2	yes	complemented
22	#431×C₆₇	—	2	1	no	—
23	#431×C₆₇	C₂²	1	2	yes	—
24	#423×C₆₇	C₄	1	2	yes	complemented
25	#407×C₆₇	—	2	1	no	—
26	C₄×M₁₆×C₆₇	—	2	1	no	—
27	C₂²×C₆₇⋊C₈	—	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	C₂×C₄	1	4	yes	—
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	C₄×C₆₇⋊C₈	—	2	2	no	—
39	C₄×C₆₇⋊C₈	—	2	2	no	—
40	C₆₇⋊#95	—	2	2	no	—
41	C₆₇⋊#95	—	2	2	no	—
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×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	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	Q₈	1	1	yes	characteristic
56	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
57	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₆₇	—	2	2	no	—
59	C₄⋊C₈×C₆₇	C₂×C₄	1	4	yes	—
60	C₂²⋊C₈×C₆₇	—	2	2	no	—
61	C₂²⋊C₈×C₆₇	—	2	2	no	—
62	#97×C₆₇	—	2	2	no	—
63	C₄×C₈×C₆₇	—	2	2	no	—
64	C₂²×Dic₆₇	—	2	4	no	—
65	C₂×C₆₇⋊C₈	—	2	4	no	—
66	C₂×C₆₇⋊C₈	—	4	4	no	—
67	C₄⋊Dic₆₇	—	2	8	no	—
68	C₂²⋊Dic₆₇	—	2	8	no	—
69	C₄×Dic₆₇	—	2	8	no	—
70	C₄×Dic₆₇	—	2	8	no	—
71	C₄×Dic₆₇	—	4	4	no	—
72	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₆₇	—	2	4	no	—
74	C₂²×C₄×C₆₇	—	2	4	no	—
75	C₂²×C₄×C₆₇	—	4	2	no	—
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	C₂²⋊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	C₂²×C₄	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	M₁₆×C₆₇	—	4	4	no	—
95	C₂×C₈×C₆₇	—	2	4	no	—
96	C₄²×C₆₇	C₄²	1	1	yes	characteristic
97	C₄²×C₆₇	C₄²	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	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	C₄⋊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×Q₈	1	1	yes	characteristic
112	C₂³×C₆₇	—	2	2	no	—
113	C₂³×C₆₇	—	2	2	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	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₆₇	—	2	2	no	—
119	C₂×C₄×C₆₇	—	2	2	no	—
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	—	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	2	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	#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	#95	1	1	yes	characteristic
139	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
140	C₂×C₄×C₆₇	#104	1	4	yes	—
141	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
142	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₆₇	C₂×C₂²⋊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	#131	1	4	yes	—
148	C₂×Dic₆₇	—	2	8	no	—
149	C₂×Dic₆₇	—	4	4	no	—
150	C₂×Dic₆₇	—	4	4	no	—
151	C₈×C₆₇	—	4	4	no	—
152	C₆₇⋊C₈	—	4	4	no	—
153	C₂²×C₆₇	—	2	1	no	—
154	C₂²×C₆₇	—	2	1	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	—	4	4	no	—
161	C₂²×C₆₇	#339	1	2	yes	—
162	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
163	C₂²×C₆₇	#408	1	2	yes	—
164	C₄×C₆₇	—	2	1	no	—
165	C₄×C₆₇	—	2	1	no	—
166	C₄×C₆₇	—	2	1	no	—
167	C₄×C₆₇	—	2	1	no	—
168	C₄×C₆₇	—	2	1	no	—
169	C₄×C₆₇	—	2	1	no	—
170	C₄×C₆₇	—	2	1	no	—
171	C₄×C₆₇	#339	1	2	yes	—
172	C₄×C₆₇	#405	1	2	yes	—
173	C₄×C₆₇	C₂×#104	1	2	yes	—
174	C₄×C₆₇	#421	1	2	yes	—
175	C₄×C₆₇	#424	1	2	yes	—
176	Dic₆₇	—	4	8	no	—
177	#7869	—	67	1	no	maximal, Sylow
178	C₂×C₆₇	—	2	2	no	—
179	C₂×C₆₇	—	2	2	no	—
180	C₂×C₆₇	—	4	1	no	—
181	C₂×C₆₇	#1729	1	1	yes	characteristic
182	C₂×C₆₇	C₂×#339	1	1	yes	characteristic
183	C₂×C₆₇	#1733	1	1	yes	characteristic
184	#2920	D₆₇	1	1	yes	characteristic
185	C₂×#431	—	67	1	no	—
186	C₄×#117	—	67	1	no	—
187	#1276	—	67	4	no	—
188	C₆₇	#7869	1	1	yes	characteristic, complemented, Sylow
189	C₂×#117	—	134	1	no	—
190	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
191	#432	—	2	1	no	—
192	#432	Dic₆₇	1	2	yes	complemented
193	#431	—	2	1	no	—
194	#431	—	67	2	no	—
195	#431	—	67	2	no	—
196	#431	—	134	1	no	—
197	#431	—	134	1	no	—
198	#431	C₂×D₆₇	1	2	yes	—
199	#423	Dic₆₇	1	2	yes	complemented
200	C₂×C₄⋊C₈	—	67	2	no	—
201	#407	—	2	1	no	—
202	C₂×C₂²⋊C₈	—	134	1	no	—
203	C₄×M₁₆	—	2	1	no	—
204	C₂×C₄×C₈	—	134	1	no	—
205	C₄×C₄⋊C₄	—	67	2	no	—
206	C₄×C₄⋊C₄	—	134	1	no	—
207	C₄×C₂²⋊C₄	—	67	2	no	—
208	C₄×C₂²⋊C₄	—	134	1	no	—
209	#376	—	134	1	no	—
210	C₄³	—	67	2	no	—
211	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
212	C₂³×C₄	D₂₆₈	1	1	yes	characteristic
213	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
214	C₂×M₁₆	—	2	2	no	—
215	C₂²×C₈	—	134	2	no	—
216	#117	—	134	8	no	—
217	C₂×C₄⋊C₄	—	134	2	no	—
218	C₂×C₂²⋊C₄	—	134	2	no	—
219	C₂×C₄²	—	67	4	no	—
220	C₂×C₄²	—	134	2	no	—
221	C₂×C₄²	—	134	2	no	—
222	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
223	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
224	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
225	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
226	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
227	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
228	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
229	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
230	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
233	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
234	C₄⋊C₈	—	2	2	no	—
235	C₄⋊C₈	—	67	4	no	—
236	C₄⋊C₈	—	134	2	no	—
237	C₄⋊C₈	C₂×Dic₆₇	1	4	yes	—
238	C₂²⋊C₈	—	2	2	no	—
239	C₂²⋊C₈	—	2	2	no	—
240	C₂²⋊C₈	—	134	2	no	—
241	C₂²⋊C₈	—	134	2	no	—
242	#97	—	2	2	no	—
243	C₄×C₈	—	2	2	no	—
244	C₄×C₈	—	134	2	no	—
245	C₄×C₈	—	134	2	no	—
246	#95	—	134	2	no	—
247	#95	—	134	2	no	—
248	C₂⁴	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	—	134	4	no	—
253	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
254	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
255	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
256	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊Dic₆₇	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	C₄⋊Dic₆₇	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
271	M₁₆	—	4	4	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	268	4	no	—
274	C₂×C₈	—	134	4	no	—
275	C₄⋊C₄	—	134	8	no	—
276	C₂²⋊C₄	—	134	8	no	—
277	C₄²	—	268	4	no	—
278	C₄²	—	134	8	no	—
279	C₄²	—	134	8	no	—
280	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
281	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
282	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
283	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
284	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
285	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
286	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
287	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
288	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
289	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
290	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
291	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
292	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
293	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
294	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
295	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
296	C₂³	—	2	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	—	4	1	no	—
299	C₂³	C₆₇⋊#95	1	1	yes	characteristic
300	C₂³	C₆₇⋊#95	1	1	yes	characteristic
301	C₂³	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
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	—	2	2	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	268	4	no	—
319	C₂×C₄	—	268	4	no	—
320	C₂×C₄	—	134	8	no	—
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	C₆₇⋊#95	1	1	yes	characteristic
327	C₂×C₄	#14523969	1	4	yes	—
328	C₂×C₄	C₂×C₄×Dic₆₇	1	1	yes	characteristic
329	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
330	C₂×C₄	C₂×C₂²⋊Dic₆₇	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×C₄⋊Dic₆₇	1	1	yes	characteristic
334	C₂×C₄	#14524051	1	4	yes	—
335	C₈	—	4	4	no	—
336	C₈	—	268	4	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	4	4	no	—
345	C₂²	#16863157	1	2	yes	—
346	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
347	C₂²	#16863364	1	2	yes	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	268	8	no	—
356	C₄	#16863157	1	2	yes	—
357	C₄	#16863354	1	2	yes	—
358	C₄	C₂×#14523969	1	2	yes	—
359	C₄	#16863413	1	2	yes	—
360	C₄	#16863424	1	2	yes	—
361	C₂	—	2	2	no	—
362	C₂	—	2	2	no	—
363	C₂	—	4	1	no	—
364	C₂	#22559907	1	1	yes	characteristic
365	C₂	C₂×#16863157	1	1	yes	characteristic
366	C₂	#22559918	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₆₇
commutator	C₂×C₄×C₆₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₆₇×#2920	C₂
socle	C₂²×C₆₇	C₂×#95
prime radical	C₂⁴×C₆₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	#2920	D₆₇
hypocenter	C₆₇	#7869
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #22558041	C₂	semidirect
8. #16863449	C₄	semidirect
10. C₂×C₄⋊(C₆₇⋊C₈)	C₄	semidirect
21. #432×C₆₇	C₄	semidirect
24. #423×C₆₇	C₄	semidirect
188. C₆₇	#7869	semidirect
192. #432	Dic₆₇	semidirect
199. #423	Dic₆₇	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
C₄×#14524002	2
#22558041	2
C₆₇×#2920	2
#7869	67