Subgroups — #30825063

Order 17152.

610 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#11761628	C₂	1	1	yes	maximal, characteristic
2	#22568876	C₂	1	2	yes	maximal
3	#22558990	C₂	1	2	yes	maximal, complemented
4	#22558988	C₂	1	2	yes	maximal, complemented
5	#22558982	C₂	1	2	yes	maximal, complemented
6	#22558969	C₂	1	1	yes	maximal, characteristic, complemented
7	#22558963	C₂	1	1	yes	maximal, characteristic, complemented
8	#22558957	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558954	C₂	1	1	yes	maximal, characteristic, complemented
10	#334×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1568	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11761628	C₂²	1	1	yes	characteristic
13	C₈×Dic₁₃₄	C₄	1	1	yes	characteristic
14	C₈×Dic₁₃₄	C₄	1	1	yes	characteristic
15	C₈×D₂₆₈	C₄	1	1	yes	characteristic
16	C₈×D₂₆₈	C₄	1	1	yes	characteristic
17	C₈×C₂²⋊D₆₇	C₄	1	1	yes	characteristic
18	C₈×C₂²⋊D₆₇	C₄	1	1	yes	characteristic
19	C₈×C₂²⋊D₆₇	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₆₇	C₄	1	1	yes	characteristic
21	#16863458	—	2	2	no	—
22	#16863454	—	2	2	no	—
23	#16863452	C₂²	1	2	yes	—
24	#16863449	C₂²	1	2	yes	—
25	#16863449	C₂²	1	1	yes	characteristic
26	#16863448	C₂²	1	2	yes	—
27	#16863447	C₂²	1	1	yes	characteristic
28	#16863447	C₂²	1	1	yes	characteristic
29	#16863418	C₂²	1	2	yes	—
30	C₄⋊C₈×D₆₇	C₂²	1	2	yes	—
31	#16863361	—	2	2	no	—
32	#16863353	—	2	2	no	—
33	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
35	#16863149	C₂²	1	2	yes	—
36	#16863148	C₂²	1	2	yes	—
37	#16863148	C₂²	1	2	yes	—
38	#16863147	C₂²	1	1	yes	characteristic
39	#16863147	C₂²	1	1	yes	characteristic
40	#16863146	C₂²	1	2	yes	—
41	#16863146	C₂²	1	2	yes	—
42	#432×C₆₇	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
44	#335×C₆₇	C₂²	1	2	yes	—
45	#334×C₆₇	C₂²	1	1	yes	characteristic
46	#334×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#11761628	D₄	1	1	yes	characteristic
48	C₂×#11761611	—	2	2	no	—
49	C₂×C₈×D₆₇	—	2	2	no	—
50	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
54	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
55	C₄×Dic₁₃₄	Q₈	1	1	yes	characteristic
56	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
57	C₄×D₂₆₈	Q₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
59	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
60	C₄×C₂²⋊D₆₇	Q₈	1	1	yes	characteristic
61	C₄×C₂²⋊D₆₇	Q₈	1	1	yes	characteristic
62	#14524002	D₄	1	1	yes	characteristic
63	#14524000	D₄	1	1	yes	characteristic
64	#14524000	D₄	1	1	yes	characteristic
65	C₄²×D₆₇	C₂³	1	1	yes	characteristic
66	C₄²×D₆₇	C₂³	1	1	yes	characteristic
67	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
68	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
69	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
70	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
71	Dic₆₇⋊C₈	—	2	2	no	—
72	Dic₆₇⋊C₈	—	2	2	no	—
73	Dic₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
74	Dic₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
75	Dic₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
76	Dic₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
78	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
79	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
80	(C₂×D₆₇)⋊C₈	—	2	2	no	—
81	(C₂×D₆₇)⋊C₈	—	2	2	no	—
82	(C₂×D₆₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
83	(C₂×D₆₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
84	(C₂×D₆₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
85	(C₂×D₆₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
86	#14523953	—	2	2	no	—
87	C₄×C₆₇⋊C₈	—	2	2	no	—
88	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
89	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
90	C₈×Dic₆₇	—	2	2	no	—
91	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
95	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
96	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
99	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
100	C₂²⋊C₈×C₆₇	—	2	2	no	—
101	#97×C₆₇	—	2	2	no	—
102	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
103	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
104	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
105	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
106	#11761628	—	2	4	no	—
107	C₂×Dic₁₃₄	C₄⋊C₄	1	1	yes	characteristic
108	C₂×D₂₆₈	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₂²⋊D₆₇	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₆₇	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₆₇	C₂×Q₈	1	1	yes	characteristic
116	C₂×C₄×D₆₇	C₂×Q₈	1	1	yes	characteristic
117	#11761611	—	4	4	no	—
118	C₂×C₆₇⋊C₈	—	2	2	no	—
119	C₂×C₆₇⋊C₈	—	2	2	no	—
120	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
124	C₈×D₆₇	—	2	2	no	—
125	C₈×D₆₇	—	2	2	no	—
126	C₈×D₆₇	—	4	1	no	—
127	C₈×D₆₇	—	4	1	no	—
128	C₈×D₆₇	—	4	4	no	—
129	C₄⋊Dic₆₇	C₄⋊C₄	1	1	yes	characteristic
130	C₄⋊Dic₆₇	C₄⋊C₄	1	1	yes	characteristic
131	Dic₆₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
132	Dic₆₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
133	Dic₆₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
134	Dic₆₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
135	C₂²⋊Dic₆₇	C₄⋊C₄	1	1	yes	characteristic
136	C₂²⋊Dic₆₇	C₄⋊C₄	1	1	yes	characteristic
137	(C₂×D₆₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
138	(C₂×D₆₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
139	(C₂×D₆₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
140	(C₂×D₆₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
141	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
143	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
144	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
145	C₄×Dic₆₇	C₂×Q₈	1	1	yes	characteristic
146	C₄×Dic₆₇	C₂×Q₈	1	1	yes	characteristic
147	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
150	C₂×C₈×C₆₇	—	2	2	no	—
151	C₂×C₈×C₆₇	—	2	2	no	—
152	C₂×C₈×C₆₇	—	2	2	no	—
153	C₂×C₈×C₆₇	—	4	1	no	—
154	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
161	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
162	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂²×D₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂²×D₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₆₇	—	2	1	no	—
166	C₂×C₄×C₆₇	—	2	1	no	—
167	C₂×C₄×C₆₇	—	2	2	no	—
168	C₂×C₄×C₆₇	—	4	1	no	—
169	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
175	C₂²⋊D₆₇	—	2	2	no	—
176	C₂²⋊D₆₇	—	2	2	no	—
177	C₂×Dic₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×Dic₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×Dic₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×Dic₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×Dic₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
183	D₂₆₈	—	2	2	no	—
184	C₄×D₆₇	—	2	1	no	—
185	C₄×D₆₇	—	2	1	no	—
186	C₄×D₆₇	—	2	1	no	—
187	C₄×D₆₇	—	2	1	no	—
188	C₄×D₆₇	—	2	2	no	—
189	C₄×D₆₇	—	4	1	no	—
190	C₄×D₆₇	—	4	1	no	—
191	C₄×D₆₇	#135	1	4	yes	—
192	Dic₁₃₄	—	2	2	no	—
193	C₈×C₆₇	—	2	1	no	—
194	C₈×C₆₇	—	2	1	no	—
195	C₈×C₆₇	—	2	1	no	—
196	C₈×C₆₇	—	4	2	no	—
197	C₈×C₆₇	—	4	2	no	—
198	C₈×C₆₇	#131	1	2	yes	—
199	C₆₇⋊C₈	—	2	1	no	—
200	C₆₇⋊C₈	—	2	1	no	—
201	C₆₇⋊C₈	—	2	1	no	—
202	C₆₇⋊C₈	—	2	1	no	—
203	C₆₇⋊C₈	—	4	2	no	—
204	C₆₇⋊C₈	—	4	2	no	—
205	C₂²×C₆₇	—	2	1	no	—
206	C₂²×C₆₇	—	2	1	no	—
207	C₂²×C₆₇	—	2	1	no	—
208	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
209	C₂×D₆₇	—	2	1	no	—
210	C₂×D₆₇	—	2	1	no	—
211	C₂×D₆₇	—	2	1	no	—
212	C₂×D₆₇	—	2	1	no	—
213	C₂×D₆₇	—	2	1	no	—
214	C₂×D₆₇	#427	1	2	yes	—
215	C₄×C₆₇	—	2	1	no	—
216	C₄×C₆₇	—	2	1	no	—
217	C₄×C₆₇	—	2	1	no	—
218	C₄×C₆₇	—	2	1	no	—
219	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
220	C₄×C₆₇	#568	1	1	yes	characteristic
221	C₄×C₆₇	C₂×#135	1	2	yes	—
222	Dic₆₇	—	2	1	no	—
223	Dic₆₇	—	2	1	no	—
224	Dic₆₇	—	2	1	no	—
225	Dic₆₇	—	2	1	no	—
226	Dic₆₇	—	2	1	no	—
227	Dic₆₇	#427	1	2	yes	—
228	#17827	—	67	1	no	maximal, Sylow
229	C₂×C₆₇	—	4	1	no	—
230	C₂×C₆₇	#2906	1	1	yes	characteristic
231	C₂×C₆₇	C₂×#427	1	1	yes	characteristic
232	C₂×C₆₇	#2916	1	1	yes	characteristic
233	D₆₇	—	2	2	no	—
234	D₆₇	—	4	1	no	—
235	C₈×#41	—	67	1	no	—
236	#2925	—	67	2	no	—
237	#1572	—	67	2	no	—
238	#1572	—	67	2	no	—
239	#1571	—	67	2	no	—
240	#1568	—	67	1	no	—
241	#1568	D₆₇	1	1	yes	characteristic, complemented
242	#1566	—	67	1	no	—
243	#1564	—	67	1	no	—
244	#1564	—	67	1	no	—
245	C₂×#334	—	67	1	no	—
246	C₆₇	#17827	1	1	yes	characteristic, complemented, Sylow
247	C₄×#41	—	67	1	no	—
248	C₈×Q₈	—	67	1	no	—
249	C₈×Q₈	—	67	1	no	—
250	C₈×D₄	—	67	1	no	—
251	C₈×D₄	—	67	1	no	—
252	C₈×D₄	—	67	1	no	—
253	C₈×D₄	—	67	1	no	—
254	C₈×D₄	—	67	1	no	—
255	C₈×D₄	—	67	1	no	—
256	#433	—	134	2	no	—
257	#433	—	134	2	no	—
258	#432	—	67	2	no	—
259	#432	C₂×D₆₇	1	2	yes	—
260	#431	—	67	1	no	—
261	#431	—	67	1	no	—
262	#431	—	67	1	no	—
263	#431	—	67	2	no	—
264	#431	—	67	2	no	—
265	#423	—	67	2	no	—
266	C₂×C₄⋊C₈	—	67	2	no	—
267	#408	—	134	2	no	—
268	#405	—	134	2	no	—
269	C₂×C₄×C₈	—	67	1	no	—
270	C₂×C₄×C₈	—	67	1	no	—
271	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
272	#335	—	67	2	no	—
273	#335	—	67	2	no	—
274	#335	—	67	2	no	—
275	#335	C₂×D₆₇	1	2	yes	—
276	#334	—	67	2	no	—
277	#334	—	67	2	no	—
278	#334	—	67	1	no	—
279	#334	—	67	1	no	—
280	#334	C₂×D₆₇	1	1	yes	characteristic
281	#334	C₂×D₆₇	1	1	yes	characteristic
282	C₂×#41	—	67	1	no	—
283	C₂×M₁₆	—	134	2	no	—
284	C₂²×C₈	—	67	1	no	—
285	C₂²×C₈	—	67	1	no	—
286	C₂²×C₈	—	67	1	no	—
287	C₂²×C₈	—	67	1	no	—
288	C₂²×C₈	—	134	2	no	—
289	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
290	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
291	C₄×Q₈	—	67	1	no	—
292	C₄×Q₈	—	67	1	no	—
293	C₄×D₄	—	67	1	no	—
294	C₄×D₄	—	67	1	no	—
295	C₄×D₄	—	67	1	no	—
296	C₄×D₄	—	67	1	no	—
297	C₄×D₄	—	67	1	no	—
298	C₄×D₄	—	67	1	no	—
299	#117	—	67	1	no	—
300	#117	—	67	1	no	—
301	#117	—	67	1	no	—
302	C₂×C₄²	—	67	1	no	—
303	C₂×C₄²	—	67	1	no	—
304	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
305	C₄⋊C₈	—	67	1	no	—
306	C₄⋊C₈	—	67	1	no	—
307	C₄⋊C₈	—	67	1	no	—
308	C₄⋊C₈	—	67	1	no	—
309	C₄⋊C₈	—	67	1	no	—
310	C₄⋊C₈	—	67	1	no	—
311	C₄⋊C₈	—	67	2	no	—
312	C₄⋊C₈	—	67	2	no	—
313	C₄⋊C₈	—	134	2	no	—
314	C₄⋊C₈	—	134	2	no	—
315	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
316	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	—	67	1	no	—
319	C₂²⋊C₈	—	67	1	no	—
320	C₂²⋊C₈	—	67	1	no	—
321	C₂²⋊C₈	—	67	1	no	—
322	C₂²⋊C₈	—	67	1	no	—
323	C₂²⋊C₈	—	67	1	no	—
324	C₂²⋊C₈	—	134	2	no	—
325	C₂²⋊C₈	—	134	2	no	—
326	C₂²⋊C₈	—	134	2	no	—
327	#97	—	2	2	no	—
328	#97	—	134	2	no	—
329	C₄×C₈	—	67	1	no	—
330	C₄×C₈	—	67	1	no	—
331	C₄×C₈	—	67	1	no	—
332	C₄×C₈	—	67	1	no	—
333	C₄×C₈	—	67	1	no	—
334	C₄×C₈	—	67	1	no	—
335	C₄×C₈	—	134	2	no	—
336	C₄×C₈	—	134	2	no	—
337	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
338	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
339	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
340	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
341	#41	—	134	4	no	—
342	C₂×Q₈	—	67	1	no	—
343	C₂×D₄	—	67	1	no	—
344	C₂×D₄	—	67	1	no	—
345	C₂×D₄	—	67	1	no	—
346	C₂²×C₄	—	67	1	no	—
347	C₂²×C₄	—	67	1	no	—
348	C₂²×C₄	—	67	1	no	—
349	C₂²×C₄	—	67	1	no	—
350	C₂²×C₄	—	67	1	no	—
351	C₂²×C₄	—	67	1	no	—
352	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
353	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
354	C₂²×C₄	Q₈×D₆₇	1	1	yes	characteristic
355	M₁₆	—	268	4	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	268	1	no	—
361	C₂×C₈	—	268	1	no	—
362	C₂×C₈	—	268	4	no	—
363	C₂×C₈	—	67	1	no	—
364	C₂×C₈	—	67	1	no	—
365	C₂×C₈	—	67	1	no	—
366	C₂×C₈	—	67	1	no	—
367	C₂×C₈	—	134	2	no	—
368	C₂×C₈	—	134	2	no	—
369	C₂×C₈	—	134	2	no	—
370	C₂×C₈	—	134	2	no	—
371	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
372	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
373	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
374	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
375	C₄⋊C₄	—	67	1	no	—
376	C₄⋊C₄	—	67	1	no	—
377	C₄⋊C₄	—	67	1	no	—
378	C₄⋊C₄	—	67	1	no	—
379	C₄⋊C₄	—	67	1	no	—
380	C₄⋊C₄	—	67	1	no	—
381	C₂²⋊C₄	—	67	1	no	—
382	C₂²⋊C₄	—	67	1	no	—
383	C₂²⋊C₄	—	67	1	no	—
384	C₂²⋊C₄	—	67	1	no	—
385	C₂²⋊C₄	—	67	1	no	—
386	C₂²⋊C₄	—	67	1	no	—
387	C₄²	—	67	1	no	—
388	C₄²	—	67	1	no	—
389	C₄²	—	67	1	no	—
390	C₄²	—	67	1	no	—
391	C₄²	—	67	1	no	—
392	C₄²	—	67	1	no	—
393	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
394	C₄²	D₄×D₆₇	1	1	yes	characteristic
395	C₄²	Q₈×D₆₇	1	1	yes	characteristic
396	C₄²	C₂³×D₆₇	1	1	yes	characteristic
397	C₂³	—	67	1	no	—
398	C₂³	—	67	1	no	—
399	C₂³	C₄⋊C₄×D₆₇	1	1	yes	characteristic
400	Q₈	—	134	2	no	—
401	D₄	—	134	2	no	—
402	D₄	—	134	2	no	—
403	D₄	—	134	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	268	1	no	—
409	C₂×C₄	—	268	1	no	—
410	C₂×C₄	—	67	1	no	—
411	C₂×C₄	—	67	4	no	—
412	C₂×C₄	—	67	1	no	—
413	C₂×C₄	—	67	1	no	—
414	C₂×C₄	—	67	1	no	—
415	C₂×C₄	—	67	1	no	—
416	C₂×C₄	—	67	1	no	—
417	C₂×C₄	—	134	1	no	—
418	C₂×C₄	—	134	1	no	—
419	C₂×C₄	—	134	1	no	—
420	C₂×C₄	—	134	1	no	—
421	C₂×C₄	—	134	2	no	—
422	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
423	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
424	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
425	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
426	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
427	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	2	1	no	—
431	C₈	—	4	2	no	—
432	C₈	—	4	2	no	—
433	C₈	—	268	2	no	—
434	C₈	—	268	2	no	—
435	C₈	—	134	1	no	—
436	C₈	—	134	1	no	—
437	C₈	—	134	1	no	—
438	C₈	—	134	1	no	—
439	C₈	#14524051	1	2	yes	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	67	2	no	—
444	C₂²	—	134	1	no	—
445	C₂²	—	134	1	no	—
446	C₂²	—	134	1	no	—
447	C₂²	—	134	1	no	—
448	C₂²	—	134	1	no	—
449	C₂²	C₂×C₄⋊C₄×D₆₇	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	67	2	no	—
455	C₄	—	134	1	no	—
456	C₄	—	134	1	no	—
457	C₄	—	134	1	no	—
458	C₄	—	134	1	no	—
459	C₄	—	134	1	no	—
460	C₄	C₂×#14524051	1	1	yes	characteristic
461	C₄	#16864162	1	1	yes	characteristic
462	C₄	#135×D₆₇	1	2	yes	—
463	C₂	—	4	1	no	—
464	C₂	—	268	1	no	—
465	C₂	—	134	2	no	—
466	C₂	#22568778	1	1	yes	characteristic
467	C₂	#427×D₆₇	1	1	yes	characteristic
468	C₂	#22568817	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#1568	C₂
socle	C₂²×C₆₇	C₂²×C₄⋊C₄
prime radical	C₂×#11761628	D₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#1568	D₆₇
hypocenter	C₆₇	#17827
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
3. #22558990	C₂	semidirect
4. #22558988	C₂	semidirect
5. #22558982	C₂	semidirect
6. #22558969	C₂	semidirect
7. #22558963	C₂	semidirect
8. #22558957	C₂	semidirect
9. #22558954	C₂	semidirect
10. #334×D₆₇	C₂	semidirect
11. C₆₇×#1568	C₂	semidirect
241. #1568	D₆₇	semidirect
246. C₆₇	#17827	semidirect

Maximal subgroups

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

subgroup	index
C₈×#11761628	2
#22568876	2
#22558990	2
#22558988	2
#22558982	2
#22558969	2
#22558963	2
#22558957	2
#22558954	2
#334×D₆₇	2
C₆₇×#1568	2
#17827	67