Subgroups — #30865290

Order 17152.

1194 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14524043	C₂	1	1	yes	maximal, characteristic
2	#22568842	C₂	1	1	yes	maximal, characteristic
3	#22561198	C₂	1	4	yes	maximal, complemented
4	#22561197	C₂	1	4	yes	maximal, complemented
5	#22560287	C₂	1	4	yes	maximal
6	C₆₇×#2920	C₂	1	1	yes	maximal, characteristic
7	C₂³×Dic₁₃₄	C₄	1	2	yes	—
8	C₂×#14524043	—	2	1	no	—
9	C₂×#14524043	—	2	1	no	—
10	C₂×#14524043	—	2	1	no	—
11	C₂×#14524043	—	2	1	no	—
12	C₂×#14524043	—	2	1	no	—
13	C₂×#14524043	—	2	1	no	—
14	C₂×#14524043	—	2	1	no	—
15	C₂×#14524043	—	2	1	no	—
16	C₂×#14524043	C₄	1	2	yes	—
17	C₂×#14524043	C₄	1	2	yes	—
18	C₂×#14524043	C₂²	1	2	yes	—
19	C₂×#14524043	C₂²	1	2	yes	—
20	C₂²×C₄⋊Dic₆₇	C₄	1	2	yes	—
21	C₂²×C₄⋊Dic₆₇	C₂²	1	2	yes	—
22	#16863453	—	2	1	no	—
23	#16863453	—	2	1	no	—
24	#16863449	—	2	1	no	—
25	#16863449	—	2	1	no	—
26	#16863420	C₂²	1	2	yes	—
27	#16863360	C₂²	1	2	yes	—
28	C₄×#11761612	C₂²	1	2	yes	—
29	#16863164	C₂²	1	16	yes	—
30	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
31	#432×C₆₇	—	2	1	no	—
32	#432×C₆₇	—	2	1	no	—
33	#431×C₆₇	—	2	1	no	—
34	#431×C₆₇	—	2	1	no	—
35	#423×C₆₇	C₂²	1	2	yes	—
36	#407×C₆₇	C₂²	1	2	yes	—
37	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
38	C₂²×Dic₁₃₄	—	2	2	no	—
39	C₂²×Dic₁₃₄	—	2	2	no	—
40	C₂²×Dic₁₃₄	—	2	2	no	—
41	C₂²×Dic₁₃₄	—	2	2	no	—
42	C₂²×Dic₁₃₄	—	4	8	no	—
43	C₂²×Dic₁₃₄	C₂×C₄	1	4	yes	—
44	C₂²×Dic₁₃₄	C₂×C₄	1	4	yes	—
45	C₂³×Dic₆₇	C₂×C₄	1	4	yes	—
46	C₂×#11761612	C₂³	1	4	yes	—
47	#14524043	—	2	2	no	—
48	#14524043	—	2	2	no	—
49	#14524043	—	2	2	no	—
50	#14524043	—	2	2	no	—
51	#14524043	—	2	2	no	—
52	#14524043	—	2	2	no	—
53	#14524043	—	2	2	no	—
54	#14524043	—	2	2	no	—
55	#14524043	—	2	2	no	—
56	#14524043	—	2	2	no	—
57	#14524043	—	2	2	no	—
58	#14524043	—	2	2	no	—
59	#14524043	—	2	2	no	—
60	#14524043	—	2	2	no	—
61	#14524043	—	2	2	no	—
62	#14524043	—	2	2	no	—
63	C₂×C₄⋊Dic₆₇	—	2	2	no	—
64	C₂×C₄⋊Dic₆₇	—	2	2	no	—
65	C₂×C₄⋊Dic₆₇	—	2	2	no	—
66	C₂×C₄⋊Dic₆₇	—	2	2	no	—
67	C₂×C₄⋊Dic₆₇	—	2	2	no	—
68	C₂×C₄⋊Dic₆₇	—	2	2	no	—
69	C₂×C₄⋊Dic₆₇	—	2	2	no	—
70	C₂×C₄⋊Dic₆₇	—	2	2	no	—
71	C₂×C₄⋊Dic₆₇	C₂×C₄	1	4	yes	—
72	C₂×C₄⋊Dic₆₇	C₂×C₄	1	4	yes	—
73	C₂×C₄⋊Dic₆₇	C₂×C₄	1	4	yes	—
74	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	—
75	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
76	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
77	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
78	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
79	#14523954	—	2	2	no	—
80	C₄×C₆₇⋊C₈	—	2	2	no	—
81	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
82	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
83	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
85	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₆₇	—	2	2	no	—
98	C₄⋊C₈×C₆₇	—	2	2	no	—
99	C₂²⋊C₈×C₆₇	—	2	2	no	—
100	C₂²⋊C₈×C₆₇	—	2	2	no	—
101	#97×C₆₇	—	2	2	no	—
102	C₄×C₈×C₆₇	—	2	2	no	—
103	C₂×Dic₁₃₄	—	2	4	no	—
104	C₂×Dic₁₃₄	—	2	4	no	—
105	C₂×Dic₁₃₄	—	2	4	no	—
106	C₂×Dic₁₃₄	—	2	4	no	—
107	C₂×Dic₁₃₄	—	4	8	no	—
108	C₂×Dic₁₃₄	—	4	8	no	—
109	C₂×Dic₁₃₄	—	4	8	no	—
110	C₂×Dic₁₃₄	—	4	8	no	—
111	C₂×Dic₁₃₄	—	4	8	no	—
112	C₂×Dic₁₃₄	—	4	8	no	—
113	C₂²×Dic₆₇	—	2	4	no	—
114	C₂²×Dic₆₇	—	2	4	no	—
115	C₂²×Dic₆₇	—	4	8	no	—
116	C₂²×Dic₆₇	C₂²×C₄	1	8	yes	—
117	#11761612	—	2	8	no	—
118	C₂×C₆₇⋊C₈	—	2	4	no	—
119	C₄⋊Dic₆₇	—	2	4	no	—
120	C₄⋊Dic₆₇	—	2	4	no	—
121	C₄⋊Dic₆₇	—	2	4	no	—
122	C₄⋊Dic₆₇	—	2	4	no	—
123	C₄⋊Dic₆₇	—	2	4	no	—
124	C₄⋊Dic₆₇	—	2	4	no	—
125	C₄⋊Dic₆₇	—	2	4	no	—
126	C₄⋊Dic₆₇	—	2	4	no	—
127	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₇	—	2	4	no	—
129	C₂²×C₄×C₆₇	—	2	4	no	—
130	C₂²×C₄×C₆₇	—	2	4	no	—
131	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
149	M₁₆×C₆₇	—	2	8	no	—
150	C₂×C₈×C₆₇	—	2	4	no	—
151	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
152	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
153	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
154	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
155	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
156	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
157	C₄²×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×D₄	1	1	yes	characteristic
161	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
167	C₂³×C₆₇	—	2	2	no	—
168	C₂³×C₆₇	—	2	2	no	—
169	C₂³×C₆₇	—	2	2	no	—
170	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₆₇	—	2	2	no	—
174	C₂×C₄×C₆₇	—	2	2	no	—
175	C₂×C₄×C₆₇	—	2	2	no	—
176	C₂×C₄×C₆₇	—	2	2	no	—
177	C₂×C₄×C₆₇	—	2	2	no	—
178	C₂×C₄×C₆₇	—	2	2	no	—
179	C₂×C₄×C₆₇	—	2	2	no	—
180	C₂×C₄×C₆₇	—	2	2	no	—
181	C₂×C₄×C₆₇	—	2	2	no	—
182	C₂×C₄×C₆₇	—	2	2	no	—
183	C₂×C₄×C₆₇	—	2	2	no	—
184	C₂×C₄×C₆₇	—	2	2	no	—
185	C₂×C₄×C₆₇	—	2	2	no	—
186	C₂×C₄×C₆₇	—	2	2	no	—
187	C₂×C₄×C₆₇	—	2	2	no	—
188	C₂×C₄×C₆₇	#100	1	4	yes	—
189	C₂×C₄×C₆₇	#101	1	4	yes	—
190	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₆₇	2₋¹⁺⁴	1	4	yes	—
203	C₂×Dic₆₇	—	2	8	no	—
204	C₂×Dic₆₇	—	4	8	no	—
205	C₂×Dic₆₇	—	4	8	no	—
206	C₂×Dic₆₇	—	4	8	no	—
207	Dic₁₃₄	—	4	8	no	—
208	Dic₁₃₄	—	4	8	no	—
209	Dic₁₃₄	—	4	8	no	—
210	Dic₁₃₄	—	4	8	no	—
211	C₈×C₆₇	—	4	4	no	—
212	C₆₇⋊C₈	—	4	4	no	—
213	C₂²×C₆₇	—	2	8	no	—
214	C₂²×C₆₇	—	2	1	no	—
215	C₂²×C₆₇	—	2	1	no	—
216	C₂²×C₆₇	—	2	1	no	—
217	C₂²×C₆₇	—	2	1	no	—
218	C₂²×C₆₇	—	2	1	no	—
219	C₂²×C₆₇	—	2	1	no	—
220	C₂²×C₆₇	C₂×#100	1	2	yes	—
221	C₂²×C₆₇	C₂×#101	1	2	yes	—
222	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
223	C₂²×C₆₇	#519	1	2	yes	—
224	C₄×C₆₇	—	2	1	no	—
225	C₄×C₆₇	—	2	1	no	—
226	C₄×C₆₇	—	2	1	no	—
227	C₄×C₆₇	—	2	1	no	—
228	C₄×C₆₇	—	2	1	no	—
229	C₄×C₆₇	—	2	1	no	—
230	C₄×C₆₇	C₂×#100	1	2	yes	—
231	C₄×C₆₇	C₂×#100	1	2	yes	—
232	C₄×C₆₇	C₂×#101	1	2	yes	—
233	C₄×C₆₇	C₂×#101	1	2	yes	—
234	C₄×C₆₇	#536	1	2	yes	—
235	C₄×C₆₇	#536	1	2	yes	—
236	Dic₆₇	—	4	8	no	—
237	#21829	—	67	1	no	maximal, Sylow
238	C₂×C₆₇	—	2	2	no	—
239	C₂×C₆₇	—	2	2	no	—
240	C₂×C₆₇	—	2	2	no	—
241	C₂×C₆₇	#2310	1	1	yes	characteristic
242	C₂×C₆₇	C₂²×#100	1	1	yes	characteristic
243	C₂×C₆₇	C₂²×#101	1	1	yes	characteristic
244	C₂²×C₄⋊Q₈	—	67	1	no	—
245	#2920	—	67	1	no	—
246	#2920	D₆₇	1	1	yes	characteristic
247	#1997	—	67	4	no	—
248	#1997	—	67	4	no	—
249	#1821	—	67	4	no	—
250	C₆₇	#21829	1	1	yes	characteristic, complemented, Sylow
251	C₂³×Q₈	—	67	2	no	—
252	C₂×C₄⋊Q₈	—	67	2	no	—
253	C₂×C₄⋊Q₈	—	67	2	no	—
254	C₂×C₄⋊Q₈	—	67	2	no	—
255	C₂×C₄⋊Q₈	—	67	2	no	—
256	C₂×C₄⋊Q₈	—	134	1	no	—
257	C₂×C₄⋊Q₈	—	134	1	no	—
258	C₂×C₄⋊Q₈	—	134	1	no	—
259	C₂×C₄⋊Q₈	—	134	1	no	—
260	C₂×C₄⋊Q₈	—	134	1	no	—
261	C₂×C₄⋊Q₈	—	134	1	no	—
262	C₂×C₄⋊Q₈	—	134	1	no	—
263	C₂×C₄⋊Q₈	—	134	1	no	—
264	C₂²×C₄⋊C₄	—	67	2	no	—
265	C₂²×C₄⋊C₄	—	67	2	no	—
266	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
267	#432	—	2	1	no	—
268	#432	—	2	1	no	—
269	#432	—	134	1	no	—
270	#432	—	134	1	no	—
271	#431	—	2	1	no	—
272	#431	—	2	1	no	—
273	#431	—	134	1	no	—
274	#431	—	134	1	no	—
275	#423	—	67	2	no	—
276	#423	C₂×D₆₇	1	2	yes	—
277	#407	—	67	2	no	—
278	#407	C₂×D₆₇	1	2	yes	—
279	C₄×M₁₆	—	67	2	no	—
280	C₄×M₁₆	C₂×D₆₇	1	2	yes	—
281	#343	—	67	16	no	—
282	C₂²×Q₈	—	268	8	no	—
283	C₂²×Q₈	—	67	4	no	—
284	C₂²×Q₈	—	67	4	no	—
285	C₂²×Q₈	—	134	2	no	—
286	C₂²×Q₈	—	134	2	no	—
287	C₂²×Q₈	—	134	2	no	—
288	C₂²×Q₈	—	134	2	no	—
289	C₂³×C₄	—	67	4	no	—
290	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
291	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
292	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
293	C₂×M₁₆	—	67	4	no	—
294	C₂×M₁₆	C₂²×D₆₇	1	4	yes	—
295	C₄⋊Q₈	—	134	2	no	—
296	C₄⋊Q₈	—	134	2	no	—
297	C₄⋊Q₈	—	134	2	no	—
298	C₄⋊Q₈	—	134	2	no	—
299	C₄⋊Q₈	—	134	2	no	—
300	C₄⋊Q₈	—	134	2	no	—
301	C₄⋊Q₈	—	134	2	no	—
302	C₄⋊Q₈	—	134	2	no	—
303	C₄⋊Q₈	—	134	2	no	—
304	C₄⋊Q₈	—	134	2	no	—
305	C₄⋊Q₈	—	134	2	no	—
306	C₄⋊Q₈	—	134	2	no	—
307	C₄⋊Q₈	—	134	2	no	—
308	C₄⋊Q₈	—	134	2	no	—
309	C₄⋊Q₈	—	134	2	no	—
310	C₄⋊Q₈	—	134	2	no	—
311	C₂×C₄⋊C₄	—	67	4	no	—
312	C₂×C₄⋊C₄	—	67	4	no	—
313	C₂×C₄⋊C₄	—	67	4	no	—
314	C₂×C₄⋊C₄	—	67	4	no	—
315	C₂×C₄⋊C₄	—	134	2	no	—
316	C₂×C₄⋊C₄	—	134	2	no	—
317	C₂×C₄⋊C₄	—	134	2	no	—
318	C₂×C₄⋊C₄	—	134	2	no	—
319	C₂×C₄⋊C₄	—	134	2	no	—
320	C₂×C₄⋊C₄	—	134	2	no	—
321	C₂×C₄⋊C₄	—	134	2	no	—
322	C₂×C₄⋊C₄	—	134	2	no	—
323	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
324	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
325	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
326	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
327	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
328	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
329	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
330	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
331	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
332	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
333	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
334	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
335	C₄⋊C₈	—	2	2	no	—
336	C₄⋊C₈	—	2	2	no	—
337	C₄⋊C₈	—	134	2	no	—
338	C₄⋊C₈	—	134	2	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	C₂²⋊C₈	—	2	2	no	—
341	C₂²⋊C₈	—	134	2	no	—
342	C₂²⋊C₈	—	134	2	no	—
343	#97	—	2	2	no	—
344	#97	—	134	2	no	—
345	C₄×C₈	—	2	2	no	—
346	C₄×C₈	—	134	2	no	—
347	C₂⁴	C₂×C₄×D₆₇	1	1	yes	characteristic
348	C₂×Q₈	—	268	8	no	—
349	C₂×Q₈	—	268	8	no	—
350	C₂×Q₈	—	268	8	no	—
351	C₂×Q₈	—	268	8	no	—
352	C₂×Q₈	—	268	8	no	—
353	C₂×Q₈	—	268	8	no	—
354	C₂×Q₈	—	134	4	no	—
355	C₂×Q₈	—	134	4	no	—
356	C₂×Q₈	—	134	4	no	—
357	C₂×Q₈	—	134	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	268	8	no	—
362	C₂²×C₄	—	67	8	no	—
363	C₂²×C₄	—	134	4	no	—
364	C₂²×C₄	—	134	4	no	—
365	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
366	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
367	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
368	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
369	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
370	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
371	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
372	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
378	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
382	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
383	M₁₆	—	2	8	no	—
384	M₁₆	—	134	8	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	134	4	no	—
387	C₄⋊C₄	—	134	4	no	—
388	C₄⋊C₄	—	134	4	no	—
389	C₄⋊C₄	—	134	4	no	—
390	C₄⋊C₄	—	134	4	no	—
391	C₄⋊C₄	—	134	4	no	—
392	C₄⋊C₄	—	134	4	no	—
393	C₄⋊C₄	—	134	4	no	—
394	C₄⋊C₄	—	134	4	no	—
395	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
396	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
397	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
398	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
399	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
400	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
401	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
402	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
403	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
404	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
405	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
406	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
407	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
408	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
409	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
410	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
415	C₂³	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
416	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
417	Q₈	—	268	8	no	—
418	Q₈	—	268	8	no	—
419	Q₈	—	268	8	no	—
420	Q₈	—	268	8	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	268	8	no	—
437	C₂×C₄	—	268	8	no	—
438	C₂×C₄	—	268	8	no	—
439	C₂×C₄	—	134	8	no	—
440	C₂×C₄	#14523959	1	4	yes	—
441	C₂×C₄	#14523961	1	4	yes	—
442	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
443	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
444	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
445	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
446	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
447	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
448	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
449	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
450	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
451	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
454	C₂×C₄	#14524090	1	4	yes	—
455	C₈	—	4	4	no	—
456	C₈	—	268	4	no	—
457	C₂²	—	2	8	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	C₂×#14523959	1	2	yes	—
465	C₂²	C₂×#14523961	1	2	yes	—
466	C₂²	C₂²×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
467	C₂²	#16863873	1	2	yes	—
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	268	8	no	—
475	C₄	C₂×#14523959	1	2	yes	—
476	C₄	C₂×#14523959	1	2	yes	—
477	C₄	C₂×#14523961	1	2	yes	—
478	C₄	C₂×#14523961	1	2	yes	—
479	C₄	#16863967	1	2	yes	—
480	C₄	#16863972	1	2	yes	—
481	C₂	—	2	2	no	—
482	C₂	—	2	2	no	—
483	C₂	—	2	2	no	—
484	C₂	#22562793	1	1	yes	characteristic
485	C₂	C₂²×#14523959	1	1	yes	characteristic
486	C₂	C₂²×#14523961	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×(C₂×D₆₇)⋊C₄
commutator	C₂³×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#2920	C₂
socle	C₂²×C₆₇	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₆₇	C₂²×C₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#2920	D₆₇
hypocenter	C₆₇	#21829
LCS	G ▷ C₂³×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #22561198	C₂	semidirect
4. #22561197	C₂	semidirect
250. C₆₇	#21829	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14524043	2
#22568842	2
#22561198	2
#22561197	2
#22560287	2
C₆₇×#2920	2
#21829	67