Subgroups — #30745967

Order 17152.

696 conjugacy classes of subgroups.

The subgroup lattice has 378 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	#22562607	C₂	1	1	yes	maximal, characteristic
3	#22558095	C₂	1	4	yes	maximal
4	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic
5	#16863453	—	2	1	no	—
6	#16863453	—	2	1	no	—
7	#16863449	—	2	1	no	—
8	#16863449	—	2	1	no	—
9	#16863420	C₄	1	2	yes	complemented
10	#16863360	C₂²	1	2	yes	—
11	C₄×#11761612	C₄	1	2	yes	complemented
12	#16863264	C₄	1	2	yes	complemented
13	#16863262	C₄	1	2	yes	complemented
14	#16863259	—	2	1	no	—
15	#16863256	—	2	1	no	—
16	C₄×C₄⋊Dic₆₇	—	2	1	no	—
17	C₄×C₂²⋊Dic₆₇	C₂²	1	2	yes	—
18	#16863242	—	2	1	no	—
19	C₂×#117×C₆₇	—	2	1	no	—
20	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₆₇	—	2	1	no	—
22	C₄×C₄⋊C₄×C₆₇	C₄	1	2	yes	complemented
23	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
24	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
25	#376×C₆₇	C₄	1	2	yes	complemented
26	C₄³×C₆₇	—	2	1	no	—
27	C₂×#11761612	C₂×C₄	1	4	yes	—
28	C₂×C₄⋊Dic₆₇	—	2	2	no	—
29	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
30	C₂×C₄×Dic₆₇	—	2	2	no	—
31	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
32	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
33	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
34	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
35	#14523954	—	2	2	no	—
36	C₄×C₆₇⋊C₈	—	2	2	no	—
37	C₆₇⋊#95	—	2	2	no	—
38	C₆₇⋊#95	—	2	2	no	—
39	C₆₇⋊#95	—	2	2	no	—
40	C₆₇⋊#95	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
44	#117×C₆₇	—	2	8	no	—
45	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
47	C₂×C₄²×C₆₇	—	2	2	no	—
48	C₂×C₄²×C₆₇	—	2	2	no	—
49	C₂×C₄²×C₆₇	—	2	2	no	—
50	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
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	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	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
61	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
62	#95×C₆₇	—	2	2	no	—
63	#95×C₆₇	C₂×C₄	1	4	yes	—
64	C₂²×Dic₆₇	—	2	4	no	—
65	#11761612	—	4	4	no	—
66	C₂×C₆₇⋊C₈	—	2	4	no	—
67	C₄⋊Dic₆₇	—	4	4	no	—
68	C₂²⋊Dic₆₇	—	4	4	no	—
69	C₄×Dic₆₇	—	4	4	no	—
70	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₆₇	—	2	4	no	—
72	C₂²×C₄×C₆₇	—	2	4	no	—
73	C₂²×C₄×C₆₇	—	4	2	no	—
74	C₂²×C₄×C₆₇	—	4	2	no	—
75	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₇	C₂²⋊C₄	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	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	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
93	C₄⋊C₄×C₆₇	—	2	8	no	—
94	C₂²⋊C₄×C₆₇	—	2	8	no	—
95	C₄²×C₆₇	—	2	8	no	—
96	C₄²×C₆₇	—	4	4	no	—
97	C₄²×C₆₇	—	4	4	no	—
98	C₄²×C₆₇	C₄²	1	1	yes	characteristic
99	C₄²×C₆₇	C₄²	1	1	yes	characteristic
100	C₄²×C₆₇	C₄²	1	1	yes	characteristic
101	C₄²×C₆₇	C₄²	1	1	yes	characteristic
102	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₆₇	C₂²⋊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	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	C₂³×C₆₇	—	2	2	no	—
115	C₂³×C₆₇	—	2	2	no	—
116	C₂³×C₆₇	—	4	1	no	—
117	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₆₇	C₂×C₄⋊C₄	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	—	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	8	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	—	4	1	no	—
136	C₂×C₄×C₆₇	—	4	1	no	—
137	C₂×C₄×C₆₇	—	4	1	no	—
138	C₂×C₄×C₆₇	—	4	4	no	—
139	C₂×C₄×C₆₇	—	4	4	no	—
140	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
141	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
142	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
143	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
144	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
145	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
146	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
147	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
148	C₂×C₄×C₆₇	#104	1	4	yes	—
149	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂×C₂²⋊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×Dic₆₇	—	4	4	no	—
154	C₂×Dic₆₇	—	4	4	no	—
155	C₂×Dic₆₇	—	4	4	no	—
156	C₆₇⋊C₈	—	4	4	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	—	2	1	no	—
162	C₂²×C₆₇	—	2	1	no	—
163	C₂²×C₆₇	—	2	1	no	—
164	C₂²×C₆₇	—	4	4	no	—
165	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
166	C₂²×C₆₇	C₂×#104	1	2	yes	—
167	C₂²×C₆₇	#421	1	2	yes	—
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	—	2	1	no	—
175	C₄×C₆₇	—	2	1	no	—
176	C₄×C₆₇	—	2	1	no	—
177	C₄×C₆₇	—	4	8	no	—
178	C₄×C₆₇	#339	1	2	yes	—
179	C₄×C₆₇	#339	1	2	yes	—
180	C₄×C₆₇	#410	1	2	yes	—
181	Dic₆₇	—	8	4	no	—
182	#8052	—	67	1	no	maximal, Sylow
183	C₂×C₆₇	—	2	2	no	—
184	C₂×C₆₇	—	2	2	no	—
185	C₂×C₆₇	—	4	1	no	—
186	C₂×C₆₇	C₂×#339	1	1	yes	characteristic
187	C₂×C₆₇	#1733	1	1	yes	characteristic
188	C₂×C₆₇	#1740	1	1	yes	characteristic
189	#2920	—	67	1	no	—
190	#2283	—	67	1	no	—
191	C₄×#117	D₆₇	1	1	yes	characteristic
192	#1297	—	67	4	no	—
193	C₆₇	#8052	1	1	yes	characteristic, complemented, Sylow
194	C₂×#117	—	2	1	no	—
195	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
196	#432	—	134	1	no	—
197	#432	—	134	1	no	—
198	#431	—	134	1	no	—
199	#431	—	134	1	no	—
200	#423	—	67	2	no	—
201	#407	—	67	2	no	—
202	C₄×M₁₆	—	67	2	no	—
203	#383	—	67	2	no	—
204	#382	—	67	2	no	—
205	#381	—	134	1	no	—
206	#380	—	134	1	no	—
207	C₄×C₄⋊C₄	—	2	1	no	—
208	C₄×C₄⋊C₄	—	134	1	no	—
209	C₄×C₄⋊C₄	Dic₆₇	1	2	yes	complemented
210	C₄×C₂²⋊C₄	—	2	1	no	—
211	C₄×C₂²⋊C₄	—	67	2	no	—
212	C₄×C₂²⋊C₄	C₂×D₆₇	1	2	yes	—
213	#376	—	134	1	no	—
214	#376	Dic₆₇	1	2	yes	complemented
215	C₄³	—	2	1	no	—
216	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
217	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
218	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
219	C₂×M₁₆	—	67	4	no	—
220	#117	—	2	8	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	134	2	no	—
223	C₂×C₂²⋊C₄	—	2	2	no	—
224	C₂×C₂²⋊C₄	—	134	2	no	—
225	C₂×C₄²	—	2	2	no	—
226	C₂×C₄²	—	2	2	no	—
227	C₂×C₄²	—	2	2	no	—
228	C₂×C₄²	—	134	2	no	—
229	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
230	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
231	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
233	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
234	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
235	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
236	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
237	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
238	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
240	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
241	C₄⋊C₈	—	134	2	no	—
242	C₄⋊C₈	—	134	2	no	—
243	C₂²⋊C₈	—	134	2	no	—
244	C₂²⋊C₈	—	134	2	no	—
245	#97	—	134	2	no	—
246	C₄×C₈	—	134	2	no	—
247	#95	—	2	2	no	—
248	#95	—	67	4	no	—
249	#95	—	134	2	no	—
250	#95	—	134	2	no	—
251	#95	—	134	2	no	—
252	#95	C₂×Dic₆₇	1	4	yes	—
253	C₂⁴	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	134	4	no	—
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	C₂²⋊Dic₆₇	1	1	yes	characteristic
266	C₂²×C₄	C₂²⋊Dic₆₇	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	Dic₆₇⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
273	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
276	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
277	M₁₆	—	268	4	no	—
278	C₂×C₈	—	134	4	no	—
279	C₄⋊C₄	—	2	8	no	—
280	C₄⋊C₄	—	268	4	no	—
281	C₂²⋊C₄	—	2	8	no	—
282	C₂²⋊C₄	—	268	4	no	—
283	C₄²	—	2	8	no	—
284	C₄²	—	4	4	no	—
285	C₄²	—	4	4	no	—
286	C₄²	—	268	4	no	—
287	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
288	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
289	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
290	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
291	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
292	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
293	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
294	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
295	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
296	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
297	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
298	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
299	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
300	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
301	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
302	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	4	1	no	—
306	C₂³	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
307	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
308	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
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	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	8	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	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	268	4	no	—
330	C₂×C₄	—	268	4	no	—
331	C₂×C₄	—	268	4	no	—
332	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
333	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
334	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
335	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
336	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
337	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
338	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
339	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
340	C₂×C₄	#14523971	1	4	yes	—
341	C₂×C₄	C₂×C₄×Dic₆₇	1	1	yes	characteristic
342	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
345	C₈	—	268	4	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	4	4	no	—
354	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
355	C₂²	C₂×#14523971	1	2	yes	—
356	C₂²	#16863413	1	2	yes	—
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	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	8	no	—
367	C₄	—	536	4	no	—
368	C₄	#16863156	1	2	yes	—
369	C₄	#16863156	1	2	yes	—
370	C₄	#16863369	1	2	yes	—
371	C₂	—	2	2	no	—
372	C₂	—	2	2	no	—
373	C₂	—	4	1	no	—
374	C₂	C₂×#16863156	1	1	yes	characteristic
375	C₂	#22559918	1	1	yes	characteristic
376	C₂	#22559941	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄
commutator	C₂×C₄×C₆₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₆₇
Fitting	C₄×#117×C₆₇	C₂
socle	C₂²×C₆₇	C₂×#95
prime radical	C₂⁴×C₆₇	C₂×D₄
cosocle	C₂³×C₄×C₆₇	C₂³
hypercenter	C₄×#117	D₆₇
hypocenter	C₆₇	#8052
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
9. #16863420	C₄	semidirect
11. C₄×#11761612	C₄	semidirect
12. #16863264	C₄	semidirect
13. #16863262	C₄	semidirect
22. C₄×C₄⋊C₄×C₆₇	C₄	semidirect
25. #376×C₆₇	C₄	semidirect
193. C₆₇	#8052	semidirect
209. C₄×C₄⋊C₄	Dic₆₇	semidirect
214. #376	Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22568842	2
#22562607	2
#22558095	2
C₄×#117×C₆₇	2
#8052	67