Subgroups — #30764727

Order 17152.

814 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14523975	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863159	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863159	C₂	1	1	yes	maximal, characteristic
4	C₂×#16863159	C₂	1	1	yes	maximal, characteristic
5	#22558439	C₂	1	1	yes	maximal, characteristic
6	#22558439	C₂	1	1	yes	maximal, characteristic
7	C₂×#336×C₆₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
12	C₂×#14523975	—	2	2	no	—
13	C₂×#14523975	—	2	2	no	—
14	C₂×#14523975	C₄	1	4	yes	complemented
15	C₂×C₆₇⋊#95	—	2	2	no	—
16	C₂×C₆₇⋊#95	—	2	2	no	—
17	#16863159	—	2	2	no	—
18	#16863159	—	2	2	no	—
19	#16863159	—	2	2	no	—
20	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
23	#336×C₆₇	—	2	2	no	—
24	C₂³×Dic₆₇	—	2	1	no	—
25	C₂³×Dic₆₇	—	2	1	no	—
26	C₂³×Dic₆₇	—	2	1	no	—
27	C₂³×Dic₆₇	—	2	1	no	—
28	C₂×C₄⋊Dic₆₇	—	2	1	no	—
29	C₂×C₄⋊Dic₆₇	—	2	1	no	—
30	C₂×C₄⋊Dic₆₇	—	2	1	no	—
31	C₂×C₄⋊Dic₆₇	—	2	1	no	—
32	C₂×C₄⋊Dic₆₇	—	2	1	no	—
33	C₂×C₄⋊Dic₆₇	—	2	1	no	—
34	C₂×C₄⋊Dic₆₇	—	2	1	no	—
35	C₂×C₄⋊Dic₆₇	—	2	1	no	—
36	C₂×C₄⋊Dic₆₇	—	2	1	no	—
37	C₂×C₄⋊Dic₆₇	—	2	1	no	—
38	C₂×C₄⋊Dic₆₇	—	2	1	no	—
39	C₂×C₄⋊Dic₆₇	—	2	1	no	—
40	C₂×C₄⋊Dic₆₇	—	2	1	no	—
41	C₂×C₄⋊Dic₆₇	—	2	1	no	—
42	C₂×C₄⋊Dic₆₇	—	2	1	no	—
43	C₂×C₄⋊Dic₆₇	—	2	1	no	—
44	C₂×C₄⋊Dic₆₇	—	2	1	no	—
45	C₂×C₄⋊Dic₆₇	—	2	1	no	—
46	C₂×C₄⋊Dic₆₇	—	2	1	no	—
47	C₂×C₄⋊Dic₆₇	—	2	1	no	—
48	C₂×C₄⋊Dic₆₇	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊Dic₆₇	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊Dic₆₇	Q₈	1	2	yes	—
51	C₂×C₄⋊Dic₆₇	Q₈	1	2	yes	—
52	#14523975	—	2	8	no	—
53	C₆₇⋊#95	—	4	4	no	—
54	C₆₇⋊#95	—	4	4	no	—
55	C₂³×C₄×C₆₇	D₄	1	2	yes	—
56	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₆₇	—	2	1	no	—
58	C₂²×C₈×C₆₇	—	2	1	no	—
59	C₂²×C₈×C₆₇	—	2	1	no	—
60	C₂²×C₈×C₆₇	—	2	1	no	—
61	C₂²×C₈×C₆₇	—	2	1	no	—
62	C₂²×C₈×C₆₇	—	2	1	no	—
63	C₂²×C₈×C₆₇	—	2	1	no	—
64	C₂²×C₈×C₆₇	—	2	1	no	—
65	C₂²×C₈×C₆₇	—	2	1	no	—
66	C₂²×C₈×C₆₇	—	2	1	no	—
67	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
68	C₂²×C₈×C₆₇	D₄	1	2	yes	—
69	C₂²×C₈×C₆₇	D₄	1	2	yes	—
70	C₂²×C₈×C₆₇	D₄	1	2	yes	—
71	C₂×C₄²×C₆₇	—	2	1	no	—
72	C₂×C₄²×C₆₇	—	2	1	no	—
73	C₂×C₄²×C₆₇	—	2	1	no	—
74	C₂×C₄²×C₆₇	—	2	1	no	—
75	C₂×C₄²×C₆₇	—	2	1	no	—
76	C₂×C₄²×C₆₇	—	2	1	no	—
77	C₂²×Dic₆₇	—	2	2	no	—
78	C₂²×Dic₆₇	—	2	2	no	—
79	C₂²×Dic₆₇	—	2	2	no	—
80	C₂²×Dic₆₇	—	2	2	no	—
81	C₂²×Dic₆₇	—	4	1	no	—
82	C₂²×Dic₆₇	—	4	1	no	—
83	C₂²×Dic₆₇	—	4	1	no	—
84	C₂²×Dic₆₇	—	4	1	no	—
85	C₂²×Dic₆₇	—	4	1	no	—
86	C₂²×Dic₆₇	—	4	1	no	—
87	C₂²×Dic₆₇	—	4	1	no	—
88	C₂²×Dic₆₇	—	4	1	no	—
89	C₂²×Dic₆₇	—	4	2	no	—
90	C₂²×Dic₆₇	—	4	2	no	—
91	C₂²×Dic₆₇	—	4	2	no	—
92	C₂²×Dic₆₇	—	4	2	no	—
93	C₂²×Dic₆₇	—	4	2	no	—
94	C₂²×Dic₆₇	—	4	2	no	—
95	C₂²×Dic₆₇	—	4	2	no	—
96	C₂²×Dic₆₇	—	4	2	no	—
97	C₄⋊Dic₆₇	—	2	2	no	—
98	C₄⋊Dic₆₇	—	2	2	no	—
99	C₄⋊Dic₆₇	—	2	2	no	—
100	C₄⋊Dic₆₇	—	2	2	no	—
101	C₄⋊Dic₆₇	—	2	2	no	—
102	C₄⋊Dic₆₇	—	2	2	no	—
103	C₄⋊Dic₆₇	—	2	2	no	—
104	C₄⋊Dic₆₇	—	2	2	no	—
105	C₄⋊Dic₆₇	—	4	1	no	—
106	C₄⋊Dic₆₇	—	4	1	no	—
107	C₄⋊Dic₆₇	—	4	1	no	—
108	C₄⋊Dic₆₇	—	4	1	no	—
109	C₄⋊Dic₆₇	—	4	1	no	—
110	C₄⋊Dic₆₇	—	4	1	no	—
111	C₄⋊Dic₆₇	—	4	1	no	—
112	C₄⋊Dic₆₇	—	4	1	no	—
113	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₆₇	—	2	2	no	—
115	C₂²×C₄×C₆₇	—	2	2	no	—
116	C₂²×C₄×C₆₇	—	2	2	no	—
117	C₂²×C₄×C₆₇	—	2	2	no	—
118	C₂²×C₄×C₆₇	—	2	2	no	—
119	C₂²×C₄×C₆₇	—	2	2	no	—
120	C₂²×C₄×C₆₇	SD₁₆	1	4	yes	—
121	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
126	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
127	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
128	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
129	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
130	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
131	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
132	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
133	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
134	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
135	C₂×C₈×C₆₇	—	2	2	no	—
136	C₂×C₈×C₆₇	—	2	2	no	—
137	C₂×C₈×C₆₇	—	2	2	no	—
138	C₂×C₈×C₆₇	—	2	2	no	—
139	C₂×C₈×C₆₇	—	2	2	no	—
140	C₂×C₈×C₆₇	—	2	2	no	—
141	C₂×C₈×C₆₇	—	2	2	no	—
142	C₂×C₈×C₆₇	—	2	2	no	—
143	C₂×C₈×C₆₇	—	2	2	no	—
144	C₂×C₈×C₆₇	—	4	1	no	—
145	C₂×C₈×C₆₇	—	4	1	no	—
146	C₂×C₈×C₆₇	—	4	1	no	—
147	C₂×C₈×C₆₇	—	4	1	no	—
148	C₂×C₈×C₆₇	C₂²⋊C₄	1	4	yes	—
149	C₄²×C₆₇	—	4	1	no	—
150	C₄²×C₆₇	—	4	1	no	—
151	C₄²×C₆₇	—	4	1	no	—
152	C₄²×C₆₇	—	4	1	no	—
153	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
154	C₂³×C₆₇	#121	1	1	yes	characteristic
155	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂³×C₆₇	#123	1	1	yes	characteristic
158	C₂³×C₆₇	#123	1	1	yes	characteristic
159	C₂³×C₆₇	#127	1	1	yes	characteristic
160	C₂³×C₆₇	C₂×SD₁₆	1	2	yes	—
161	C₂³×C₆₇	#135	1	2	yes	—
162	C₂³×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
163	C₂³×C₆₇	#137	1	2	yes	—
164	C₂×C₄×C₆₇	—	2	4	no	—
165	C₂×C₄×C₆₇	—	2	4	no	—
166	C₂×C₄×C₆₇	—	2	4	no	—
167	C₂×C₄×C₆₇	—	4	2	no	—
168	C₂×C₄×C₆₇	—	4	2	no	—
169	C₂×C₄×C₆₇	—	4	2	no	—
170	C₂×C₄×C₆₇	—	4	2	no	—
171	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
173	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₆₇	C₄×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₆₇	C₄×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
178	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
179	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
181	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
182	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
183	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
184	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
185	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
186	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
187	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
188	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
189	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
190	C₂×C₄×C₆₇	#125	1	1	yes	characteristic
191	C₂×C₄×C₆₇	#125	1	1	yes	characteristic
192	C₂×C₄×C₆₇	#125	1	1	yes	characteristic
193	C₂×C₄×C₆₇	#125	1	1	yes	characteristic
194	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
195	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
196	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
197	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
198	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
199	C₂×Dic₆₇	—	4	2	no	—
200	C₂×Dic₆₇	—	4	2	no	—
201	C₂×Dic₆₇	—	4	2	no	—
202	C₂×Dic₆₇	—	4	2	no	—
203	C₂×Dic₆₇	—	4	4	no	—
204	C₂×Dic₆₇	—	4	4	no	—
205	C₂×Dic₆₇	—	4	4	no	—
206	C₂×Dic₆₇	—	4	4	no	—
207	C₂×Dic₆₇	—	8	2	no	—
208	C₂×Dic₆₇	—	8	2	no	—
209	C₂×Dic₆₇	—	8	2	no	—
210	C₂×Dic₆₇	—	8	2	no	—
211	C₂×Dic₆₇	—	8	1	no	—
212	C₂×Dic₆₇	—	8	1	no	—
213	C₂×Dic₆₇	—	8	1	no	—
214	C₂×Dic₆₇	—	8	1	no	—
215	C₂×Dic₆₇	—	8	1	no	—
216	C₂×Dic₆₇	—	8	1	no	—
217	C₂×Dic₆₇	—	8	1	no	—
218	C₂×Dic₆₇	—	8	1	no	—
219	C₈×C₆₇	—	2	4	no	—
220	C₈×C₆₇	—	4	2	no	—
221	C₂²×C₆₇	#387	1	1	yes	characteristic
222	C₂²×C₆₇	#387	1	1	yes	characteristic
223	C₂²×C₆₇	#390	1	1	yes	characteristic
224	C₂²×C₆₇	#397	1	1	yes	characteristic
225	C₂²×C₆₇	#398	1	1	yes	characteristic
226	C₂²×C₆₇	#399	1	1	yes	characteristic
227	C₂²×C₆₇	#399	1	1	yes	characteristic
228	C₂²×C₆₇	C₄×SD₁₆	1	2	yes	—
229	C₂²×C₆₇	#440	1	2	yes	—
230	C₂²×C₆₇	#465	1	2	yes	—
231	C₂²×C₆₇	#468	1	2	yes	—
232	C₂²×C₆₇	#475	1	2	yes	—
233	C₂²×C₆₇	#476	1	2	yes	—
234	C₂²×C₆₇	#478	1	2	yes	—
235	C₂²×C₆₇	#479	1	2	yes	—
236	C₂²×C₆₇	#481	1	2	yes	—
237	C₂²×C₆₇	#482	1	2	yes	—
238	C₂²×C₆₇	#483	1	2	yes	—
239	C₂²×C₆₇	#485	1	2	yes	—
240	C₂²×C₆₇	#492	1	1	yes	characteristic
241	C₂²×C₆₇	#495	1	1	yes	characteristic
242	C₂²×C₆₇	#496	1	1	yes	characteristic
243	C₂²×C₆₇	#497	1	1	yes	characteristic
244	C₄×C₆₇	—	4	4	no	—
245	C₄×C₆₇	#381	1	1	yes	characteristic
246	C₄×C₆₇	#387	1	1	yes	characteristic
247	C₄×C₆₇	#387	1	1	yes	characteristic
248	C₄×C₆₇	#391	1	1	yes	characteristic
249	C₄×C₆₇	#397	1	1	yes	characteristic
250	C₄×C₆₇	#398	1	1	yes	characteristic
251	C₄×C₆₇	#400	1	1	yes	characteristic
252	C₄×C₆₇	#400	1	1	yes	characteristic
253	Dic₆₇	—	8	2	no	—
254	Dic₆₇	—	8	2	no	—
255	Dic₆₇	—	8	2	no	—
256	Dic₆₇	—	8	2	no	—
257	#11378	—	67	1	no	maximal, Sylow
258	C₂×C₆₇	#1445	1	1	yes	characteristic
259	C₂×C₆₇	#1919	1	2	yes	—
260	C₂×C₆₇	#1920	1	2	yes	—
261	C₂×C₆₇	#1968	1	1	yes	characteristic
262	C₂×C₆₇	#1973	1	1	yes	characteristic
263	C₂×C₆₇	#2077	1	2	yes	—
264	C₂×C₆₇	#2088	1	2	yes	—
265	C₂×C₆₇	#2092	1	1	yes	characteristic
266	C₂×C₆₇	#2094	1	1	yes	characteristic
267	C₂×C₆₇	#2096	1	1	yes	characteristic
268	C₂×C₆₇	#2097	1	1	yes	characteristic
269	C₂²×#106	—	67	1	no	—
270	C₂×#340	—	67	1	no	—
271	C₂×#340	—	67	1	no	—
272	C₂×#340	—	67	1	no	—
273	C₂×#336	D₆₇	1	1	yes	characteristic
274	C₄⋊#95	—	67	1	no	—
275	C₄⋊#95	—	67	1	no	—
276	C₆₇	#11378	1	1	yes	characteristic, complemented, Sylow
277	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
278	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	—	67	1	no	—
280	C₂²×C₄⋊C₄	—	67	1	no	—
281	C₂²×C₄⋊C₄	—	67	1	no	—
282	C₂²×C₄⋊C₄	—	67	1	no	—
283	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
284	C₂×#106	—	67	4	no	—
285	C₂×#106	—	134	2	no	—
286	C₂×#106	—	134	2	no	—
287	C₂×#95	—	134	2	no	—
288	C₂×#95	—	134	2	no	—
289	#340	—	134	2	no	—
290	#340	—	134	2	no	—
291	#340	—	134	2	no	—
292	#336	—	2	2	no	—
293	C₂³×C₄	—	134	1	no	—
294	C₂³×C₄	—	134	1	no	—
295	C₂³×C₄	—	134	1	no	—
296	C₂³×C₄	—	134	1	no	—
297	C₂³×C₄	D₂₆₈	1	2	yes	—
298	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
299	C₂²×C₈	—	2	1	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₂²×C₈	—	2	1	no	—
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	C₄×D₆₇	1	2	yes	—
310	C₂²×C₈	D₂₆₈	1	2	yes	—
311	C₂²×C₈	D₂₆₈	1	2	yes	—
312	C₂²×C₈	C₂²⋊D₆₇	1	2	yes	—
313	C₂×C₄⋊C₄	—	67	2	no	—
314	C₂×C₄⋊C₄	—	67	2	no	—
315	C₂×C₄⋊C₄	—	67	2	no	—
316	C₂×C₄⋊C₄	—	67	2	no	—
317	C₂×C₄⋊C₄	—	134	1	no	—
318	C₂×C₄⋊C₄	—	134	1	no	—
319	C₂×C₄⋊C₄	—	134	1	no	—
320	C₂×C₄⋊C₄	—	134	1	no	—
321	C₂×C₄⋊C₄	—	134	1	no	—
322	C₂×C₄⋊C₄	—	134	1	no	—
323	C₂×C₄⋊C₄	—	134	1	no	—
324	C₂×C₄⋊C₄	—	134	1	no	—
325	C₂×C₄⋊C₄	—	134	1	no	—
326	C₂×C₄⋊C₄	—	134	1	no	—
327	C₂×C₄⋊C₄	—	134	1	no	—
328	C₂×C₄⋊C₄	—	134	1	no	—
329	C₂×C₄⋊C₄	—	134	1	no	—
330	C₂×C₄⋊C₄	—	134	1	no	—
331	C₂×C₄⋊C₄	—	134	1	no	—
332	C₂×C₄⋊C₄	—	134	1	no	—
333	C₂×C₄⋊C₄	—	134	1	no	—
334	C₂×C₄⋊C₄	—	134	1	no	—
335	C₂×C₄⋊C₄	—	134	1	no	—
336	C₂×C₄⋊C₄	—	134	1	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	—	2	1	no	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	2	1	no	—
343	#106	—	134	8	no	—
344	#95	—	268	4	no	—
345	#95	—	268	4	no	—
346	C₂⁴	C₂×D₂₆₈	1	1	yes	characteristic
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	268	1	no	—
354	C₂²×C₄	—	268	1	no	—
355	C₂²×C₄	—	268	1	no	—
356	C₂²×C₄	—	268	1	no	—
357	C₂²×C₄	—	268	1	no	—
358	C₂²×C₄	—	268	1	no	—
359	C₂²×C₄	—	268	1	no	—
360	C₂²×C₄	—	268	1	no	—
361	C₂²×C₄	—	268	2	no	—
362	C₂²×C₄	—	268	2	no	—
363	C₂²×C₄	—	268	2	no	—
364	C₂²×C₄	—	268	2	no	—
365	C₂²×C₄	—	268	2	no	—
366	C₂²×C₄	—	268	2	no	—
367	C₂²×C₄	—	268	2	no	—
368	C₂²×C₄	—	268	2	no	—
369	C₂²×C₄	—	134	2	no	—
370	C₂²×C₄	—	134	2	no	—
371	C₂²×C₄	—	134	2	no	—
372	C₂²×C₄	—	134	2	no	—
373	C₂²×C₄	#11761617	1	4	yes	—
374	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
378	C₂²×C₄	Q₈×D₆₇	1	1	yes	characteristic
379	C₂²×C₄	Q₈×D₆₇	1	1	yes	characteristic
380	C₂²×C₄	#11761627	1	1	yes	characteristic
381	C₂²×C₄	#11761627	1	1	yes	characteristic
382	C₂²×C₄	#11761627	1	1	yes	characteristic
383	C₂²×C₄	#11761627	1	1	yes	characteristic
384	C₂²×C₄	#11761627	1	1	yes	characteristic
385	C₂²×C₄	#11761627	1	1	yes	characteristic
386	C₂²×C₄	#11761628	1	1	yes	characteristic
387	C₂²×C₄	#11761628	1	1	yes	characteristic
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	4	1	no	—
398	C₂×C₈	—	4	1	no	—
399	C₂×C₈	—	4	1	no	—
400	C₂×C₈	—	4	1	no	—
401	C₂×C₈	(C₂×D₆₇)⋊C₄	1	4	yes	—
402	C₄⋊C₄	—	268	1	no	—
403	C₄⋊C₄	—	268	1	no	—
404	C₄⋊C₄	—	268	1	no	—
405	C₄⋊C₄	—	268	1	no	—
406	C₄⋊C₄	—	268	1	no	—
407	C₄⋊C₄	—	268	1	no	—
408	C₄⋊C₄	—	268	1	no	—
409	C₄⋊C₄	—	268	1	no	—
410	C₄⋊C₄	—	134	2	no	—
411	C₄⋊C₄	—	134	2	no	—
412	C₄⋊C₄	—	134	2	no	—
413	C₄⋊C₄	—	134	2	no	—
414	C₄⋊C₄	—	134	2	no	—
415	C₄⋊C₄	—	134	2	no	—
416	C₄⋊C₄	—	134	2	no	—
417	C₄⋊C₄	—	134	2	no	—
418	C₄²	—	4	1	no	—
419	C₄²	—	4	1	no	—
420	C₄²	—	4	1	no	—
421	C₄²	—	4	1	no	—
422	C₂³	C₄×D₂₆₈	1	1	yes	characteristic
423	C₂³	#14524017	1	1	yes	characteristic
424	C₂³	#14524023	1	1	yes	characteristic
425	C₂³	#14524023	1	1	yes	characteristic
426	C₂³	#14524027	1	1	yes	characteristic
427	C₂³	#14524027	1	1	yes	characteristic
428	C₂³	#14524040	1	1	yes	characteristic
429	C₂³	C₂×#11761617	1	2	yes	—
430	C₂³	#14524065	1	2	yes	—
431	C₂³	#14524071	1	2	yes	—
432	C₂³	#14524076	1	2	yes	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	268	4	no	—
441	C₂×C₄	—	268	2	no	—
442	C₂×C₄	—	268	2	no	—
443	C₂×C₄	—	268	2	no	—
444	C₂×C₄	—	268	2	no	—
445	C₂×C₄	—	268	4	no	—
446	C₂×C₄	—	268	4	no	—
447	C₂×C₄	—	268	4	no	—
448	C₂×C₄	—	536	1	no	—
449	C₂×C₄	—	536	1	no	—
450	C₂×C₄	—	536	1	no	—
451	C₂×C₄	—	536	1	no	—
452	C₂×C₄	—	536	1	no	—
453	C₂×C₄	—	536	1	no	—
454	C₂×C₄	—	536	1	no	—
455	C₂×C₄	—	536	1	no	—
456	C₂×C₄	—	536	2	no	—
457	C₂×C₄	—	536	2	no	—
458	C₂×C₄	—	536	2	no	—
459	C₂×C₄	—	536	2	no	—
460	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
461	C₂×C₄	#14523999	1	1	yes	characteristic
462	C₂×C₄	#14523999	1	1	yes	characteristic
463	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
464	C₂×C₄	#14524008	1	1	yes	characteristic
465	C₂×C₄	#14524008	1	1	yes	characteristic
466	C₂×C₄	#14524017	1	1	yes	characteristic
467	C₂×C₄	#14524023	1	1	yes	characteristic
468	C₂×C₄	#14524023	1	1	yes	characteristic
469	C₂×C₄	#14524023	1	1	yes	characteristic
470	C₂×C₄	#14524023	1	1	yes	characteristic
471	C₂×C₄	#14524024	1	1	yes	characteristic
472	C₂×C₄	#14524024	1	1	yes	characteristic
473	C₂×C₄	#14524027	1	1	yes	characteristic
474	C₂×C₄	#14524027	1	1	yes	characteristic
475	C₂×C₄	#14524027	1	1	yes	characteristic
476	C₂×C₄	#14524027	1	1	yes	characteristic
477	C₂×C₄	#14524030	1	1	yes	characteristic
478	C₂×C₄	#14524031	1	1	yes	characteristic
479	C₂×C₄	#14524033	1	1	yes	characteristic
480	C₂×C₄	#14524033	1	1	yes	characteristic
481	C₂×C₄	#14524033	1	1	yes	characteristic
482	C₂×C₄	#14524033	1	1	yes	characteristic
483	C₂×C₄	#14524036	1	1	yes	characteristic
484	C₂×C₄	#14524036	1	1	yes	characteristic
485	C₂×C₄	#14524036	1	1	yes	characteristic
486	C₂×C₄	#14524036	1	1	yes	characteristic
487	C₂×C₄	#14524041	1	1	yes	characteristic
488	C₈	—	2	4	no	—
489	C₈	—	4	2	no	—
490	C₂²	#16863281	1	1	yes	characteristic
491	C₂²	#16863281	1	1	yes	characteristic
492	C₂²	#16863298	1	1	yes	characteristic
493	C₂²	#16863321	1	1	yes	characteristic
494	C₂²	#16863326	1	1	yes	characteristic
495	C₂²	#16863333	1	1	yes	characteristic
496	C₂²	#16863333	1	1	yes	characteristic
497	C₂²	C₄×#11761617	1	2	yes	—
498	C₂²	#16863498	1	2	yes	—
499	C₂²	#16863625	1	2	yes	—
500	C₂²	#16863642	1	2	yes	—
501	C₂²	#16863682	1	2	yes	—
502	C₂²	#16863687	1	2	yes	—
503	C₂²	#16863697	1	2	yes	—
504	C₂²	#16863704	1	2	yes	—
505	C₂²	#16863715	1	2	yes	—
506	C₂²	#16863721	1	2	yes	—
507	C₂²	#16863727	1	2	yes	—
508	C₂²	#16863738	1	2	yes	—
509	C₂²	#16863769	1	1	yes	characteristic
510	C₂²	#16863780	1	1	yes	characteristic
511	C₂²	#16863785	1	1	yes	characteristic
512	C₂²	#16863790	1	1	yes	characteristic
513	C₄	—	4	4	no	—
514	C₄	—	536	2	no	—
515	C₄	—	536	2	no	—
516	C₄	—	536	2	no	—
517	C₄	—	536	2	no	—
518	C₄	#16863257	1	1	yes	characteristic
519	C₄	#16863281	1	1	yes	characteristic
520	C₄	#16863281	1	1	yes	characteristic
521	C₄	#16863301	1	1	yes	characteristic
522	C₄	#16863321	1	1	yes	characteristic
523	C₄	#16863326	1	1	yes	characteristic
524	C₄	#16863336	1	1	yes	characteristic
525	C₄	#16863336	1	1	yes	characteristic
526	C₂	#22558476	1	1	yes	characteristic
527	C₂	#22560788	1	2	yes	—
528	C₂	#22560795	1	2	yes	—
529	C₂	#22561063	1	1	yes	characteristic
530	C₂	#22561090	1	1	yes	characteristic
531	C₂	#22561642	1	2	yes	—
532	C₂	#22561707	1	2	yes	—
533	C₂	#22561729	1	1	yes	characteristic
534	C₂	#22561741	1	1	yes	characteristic
535	C₂	#22561751	1	1	yes	characteristic
536	C₂	#22561756	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₂₆₈
commutator	C₂²×C₄×C₆₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₆₇
Fitting	C₂×#336×C₆₇	C₂
socle, prime radical	C₂⁴×C₆₇	C₂×D₄
cosocle	C₂³×C₄×C₆₇	C₂³
hypercenter	C₂×#336	D₆₇
hypocenter	C₆₇	#11378
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
14. C₂×#14523975	C₄	semidirect
276. C₆₇	#11378	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14523975	2
C₂×#16863159	2
#22558439	2
C₂×#336×C₆₇	2
#11378	67