Subgroups — #30763346

Order 17152.

950 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863445	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14523959	C₂	1	1	yes	maximal, characteristic
3	C₂²×#14523959	C₂	1	1	yes	maximal, characteristic
4	C₂²×#14523959	C₂	1	1	yes	maximal, characteristic
5	#22559935	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₇⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1738	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic
9	C₂²×#11761612	C₂²	1	1	yes	characteristic
10	C₂²×#11761612	C₂²	1	1	yes	characteristic
11	C₂²×#11761612	C₂²	1	1	yes	characteristic
12	#16863445	—	2	2	no	—
13	#16863445	—	2	2	no	—
14	C₂×#14523979	—	2	2	no	—
15	C₂×#14523959	—	2	2	no	—
16	C₂×#14523959	—	2	2	no	—
17	C₂×#14523959	—	2	2	no	—
18	C₂×#14523959	—	2	2	no	—
19	C₂×#14523959	—	2	2	no	—
20	C₂×#14523959	—	2	2	no	—
21	C₂×#14523959	—	2	2	no	—
22	C₂×#14523959	—	2	2	no	—
23	C₂×#14523959	C₄	1	4	yes	—
24	#16863160	—	2	2	no	—
25	C₆₇⋊#338	—	2	2	no	—
26	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
29	#341×C₆₇	—	2	2	no	—
30	C₂⁴×D₆₇	Q₈	1	2	yes	—
31	C₂²×D₂₆₈	—	2	1	no	—
32	C₂²×D₂₆₈	—	2	1	no	—
33	C₂²×D₂₆₈	—	2	1	no	—
34	C₂²×D₂₆₈	—	2	1	no	—
35	C₂²×D₂₆₈	—	2	1	no	—
36	C₂²×D₂₆₈	—	2	1	no	—
37	C₂²×D₂₆₈	—	2	1	no	—
38	C₂²×D₂₆₈	—	2	1	no	—
39	C₂²×D₂₆₈	—	2	1	no	—
40	C₂²×D₂₆₈	—	2	1	no	—
41	C₂²×D₂₆₈	—	2	1	no	—
42	C₂²×D₂₆₈	—	2	1	no	—
43	C₂²×D₂₆₈	C₂×C₄	1	2	yes	—
44	C₂²×D₂₆₈	D₄	1	2	yes	—
45	C₂×#11761612	—	2	1	no	—
46	C₂×#11761612	—	2	1	no	—
47	C₂×#11761612	—	2	1	no	—
48	C₂×#11761612	—	2	1	no	—
49	C₂×#11761612	—	2	1	no	—
50	C₂×#11761612	—	2	1	no	—
51	C₂×#11761612	—	2	1	no	—
52	C₂×#11761612	—	2	1	no	—
53	C₂×#11761612	—	2	1	no	—
54	C₂×#11761612	—	2	1	no	—
55	C₂×#11761612	—	2	1	no	—
56	C₂×#11761612	—	2	1	no	—
57	C₂×#11761612	—	2	1	no	—
58	C₂×#11761612	—	2	1	no	—
59	C₂×#11761612	—	2	1	no	—
60	C₂×#11761612	C₂×C₄	1	2	yes	—
61	C₂×#11761612	D₄	1	2	yes	—
62	C₂×#11761612	D₄	1	2	yes	—
63	C₂²×C₆₇⋊C₈	—	2	1	no	—
64	C₂²×C₆₇⋊C₈	—	2	1	no	—
65	C₂²×C₆₇⋊C₈	—	2	1	no	—
66	#14523979	—	2	8	no	—
67	#14523959	—	2	8	no	—
68	#14523959	—	2	8	no	—
69	#14523959	—	2	8	no	—
70	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₆₇	—	2	1	no	—
72	C₂×M₁₆×C₆₇	—	2	1	no	—
73	C₂×M₁₆×C₆₇	—	2	1	no	—
74	C₂×M₁₆×C₆₇	—	2	1	no	—
75	C₂×M₁₆×C₆₇	—	2	1	no	—
76	C₂×M₁₆×C₆₇	—	2	1	no	—
77	C₂×M₁₆×C₆₇	—	2	1	no	—
78	C₂×M₁₆×C₆₇	—	2	1	no	—
79	C₂×M₁₆×C₆₇	—	2	1	no	—
80	C₂×M₁₆×C₆₇	—	2	1	no	—
81	C₂×M₁₆×C₆₇	—	2	1	no	—
82	C₂×M₁₆×C₆₇	—	2	1	no	—
83	C₂×M₁₆×C₆₇	—	2	1	no	—
84	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
85	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
86	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
87	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
88	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
89	C₂²×C₈×C₆₇	—	2	1	no	—
90	C₂²×C₈×C₆₇	—	2	1	no	—
91	C₂²×C₈×C₆₇	—	2	1	no	—
92	C₂³×D₆₇	—	2	2	no	—
93	C₂³×D₆₇	—	2	2	no	—
94	C₂³×D₆₇	—	2	2	no	—
95	C₂³×D₆₇	—	2	2	no	—
96	C₂³×D₆₇	—	2	2	no	—
97	C₂³×D₆₇	—	2	2	no	—
98	C₂³×D₆₇	—	8	4	no	—
99	C₂³×D₆₇	C₄⋊C₄	1	4	yes	—
100	C₂×D₂₆₈	—	2	2	no	—
101	C₂×D₂₆₈	—	2	2	no	—
102	C₂×D₂₆₈	—	2	2	no	—
103	C₂×D₂₆₈	—	2	2	no	—
104	C₂×D₂₆₈	—	2	2	no	—
105	C₂×D₂₆₈	—	2	2	no	—
106	C₂×D₂₆₈	—	2	2	no	—
107	C₂×D₂₆₈	—	2	2	no	—
108	C₂×D₂₆₈	—	2	2	no	—
109	C₂×D₂₆₈	—	2	2	no	—
110	C₂×D₂₆₈	—	2	2	no	—
111	C₂×D₂₆₈	—	2	2	no	—
112	C₂×D₂₆₈	—	4	1	no	—
113	C₂×D₂₆₈	—	4	1	no	—
114	C₂×D₂₆₈	—	4	1	no	—
115	C₂×D₂₆₈	—	4	1	no	—
116	C₂×D₂₆₈	—	4	1	no	—
117	C₂×D₂₆₈	—	4	1	no	—
118	C₂×D₂₆₈	—	4	1	no	—
119	C₂×D₂₆₈	—	4	1	no	—
120	C₂×D₂₆₈	—	4	1	no	—
121	C₂×D₂₆₈	—	4	1	no	—
122	C₂×D₂₆₈	—	4	1	no	—
123	C₂×D₂₆₈	—	4	1	no	—
124	C₂×D₂₆₈	—	4	1	no	—
125	C₂×D₂₆₈	—	4	1	no	—
126	C₂×D₂₆₈	—	4	1	no	—
127	C₂×D₂₆₈	—	4	1	no	—
128	#11761612	—	2	2	no	—
129	#11761612	—	2	2	no	—
130	#11761612	—	2	2	no	—
131	#11761612	—	2	2	no	—
132	#11761612	—	2	2	no	—
133	#11761612	—	2	2	no	—
134	#11761612	—	4	1	no	—
135	#11761612	—	4	1	no	—
136	#11761612	—	4	1	no	—
137	#11761612	—	4	1	no	—
138	#11761612	—	4	1	no	—
139	#11761612	—	4	1	no	—
140	C₂×C₆₇⋊C₈	—	2	2	no	—
141	C₂×C₆₇⋊C₈	—	2	2	no	—
142	C₂×C₆₇⋊C₈	—	2	2	no	—
143	C₂×C₆₇⋊C₈	—	4	1	no	—
144	C₂×C₆₇⋊C₈	—	4	1	no	—
145	C₂×C₆₇⋊C₈	—	4	1	no	—
146	C₂×C₆₇⋊C₈	—	4	1	no	—
147	C₂×C₆₇⋊C₈	—	4	1	no	—
148	C₂×C₆₇⋊C₈	—	4	1	no	—
149	C₂⁴×C₆₇	C₂×Q₈	1	1	yes	characteristic
150	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
159	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
160	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
161	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
162	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
163	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
164	M₁₆×C₆₇	—	2	2	no	—
165	M₁₆×C₆₇	—	2	2	no	—
166	M₁₆×C₆₇	—	2	2	no	—
167	M₁₆×C₆₇	—	2	2	no	—
168	M₁₆×C₆₇	—	2	2	no	—
169	M₁₆×C₆₇	—	2	2	no	—
170	M₁₆×C₆₇	—	2	2	no	—
171	M₁₆×C₆₇	—	4	1	no	—
172	M₁₆×C₆₇	—	4	1	no	—
173	M₁₆×C₆₇	—	4	1	no	—
174	M₁₆×C₆₇	—	4	1	no	—
175	M₁₆×C₆₇	C₂²⋊C₄	1	4	yes	—
176	C₂×C₈×C₆₇	—	2	2	no	—
177	C₂×C₈×C₆₇	—	2	2	no	—
178	C₂×C₈×C₆₇	—	2	2	no	—
179	C₂×C₈×C₆₇	—	2	2	no	—
180	C₂×C₈×C₆₇	—	2	2	no	—
181	C₂×C₈×C₆₇	—	4	1	no	—
182	C₂×C₈×C₆₇	—	4	1	no	—
183	C₂×C₈×C₆₇	—	4	1	no	—
184	C₂×C₈×C₆₇	—	4	1	no	—
185	C₂³×C₆₇	—	4	2	no	—
186	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
189	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
190	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
191	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
192	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
193	C₂²×D₆₇	—	2	4	no	—
194	C₂²×D₆₇	—	2	4	no	—
195	C₂²×D₆₇	—	2	4	no	—
196	C₂²×D₆₇	—	4	2	no	—
197	C₂²×D₆₇	—	4	2	no	—
198	C₂²×D₆₇	—	4	2	no	—
199	C₂²×D₆₇	—	4	2	no	—
200	C₂²×D₆₇	—	8	4	no	—
201	C₂²×D₆₇	—	8	4	no	—
202	C₂²×D₆₇	—	8	4	no	—
203	C₂²×D₆₇	—	8	4	no	—
204	C₂²×D₆₇	—	8	4	no	—
205	C₂²×D₆₇	—	8	4	no	—
206	C₂²×D₆₇	—	8	4	no	—
207	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
209	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
214	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
215	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
216	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
217	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
218	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
219	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
220	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
221	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
222	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
223	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
224	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
225	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
226	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
227	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
228	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
229	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
230	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
231	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
232	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
233	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
234	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
235	D₂₆₈	—	4	2	no	—
236	D₂₆₈	—	4	2	no	—
237	D₂₆₈	—	4	2	no	—
238	D₂₆₈	—	4	2	no	—
239	D₂₆₈	—	4	2	no	—
240	D₂₆₈	—	4	2	no	—
241	D₂₆₈	—	4	2	no	—
242	D₂₆₈	—	4	2	no	—
243	C₈×C₆₇	—	2	4	no	—
244	C₈×C₆₇	—	4	2	no	—
245	C₈×C₆₇	—	4	2	no	—
246	C₆₇⋊C₈	—	4	2	no	—
247	C₆₇⋊C₈	—	4	2	no	—
248	C₆₇⋊C₈	—	4	2	no	—
249	C₂²×C₆₇	—	2	2	no	—
250	C₂²×C₆₇	—	2	2	no	—
251	C₂²×C₆₇	—	2	2	no	—
252	C₂²×C₆₇	—	4	1	no	—
253	C₂²×C₆₇	—	4	1	no	—
254	C₂²×C₆₇	—	4	1	no	—
255	C₂²×C₆₇	—	4	1	no	—
256	C₂²×C₆₇	#380	1	1	yes	characteristic
257	C₂²×C₆₇	#385	1	1	yes	characteristic
258	C₂²×C₆₇	#385	1	1	yes	characteristic
259	C₂²×C₆₇	#393	1	1	yes	characteristic
260	C₂²×C₆₇	#396	1	1	yes	characteristic
261	C₂²×C₆₇	#396	1	1	yes	characteristic
262	C₂²×C₆₇	#399	1	1	yes	characteristic
263	C₂×D₆₇	—	4	4	no	—
264	C₂×D₆₇	—	8	4	no	—
265	C₂×D₆₇	—	8	4	no	—
266	C₂×D₆₇	—	8	4	no	—
267	C₂×D₆₇	—	8	4	no	—
268	C₂×D₆₇	—	8	4	no	—
269	C₂×D₆₇	—	8	4	no	—
270	C₂×D₆₇	—	8	4	no	—
271	C₄×C₆₇	#386	1	1	yes	characteristic
272	C₄×C₆₇	#388	1	1	yes	characteristic
273	C₄×C₆₇	#388	1	1	yes	characteristic
274	C₄×C₆₇	#390	1	1	yes	characteristic
275	C₄×C₆₇	#392	1	1	yes	characteristic
276	C₄×C₆₇	#394	1	1	yes	characteristic
277	C₄×C₆₇	#394	1	1	yes	characteristic
278	C₄×C₆₇	#397	1	1	yes	characteristic
279	#11139	—	67	1	no	maximal, Sylow
280	C₂×C₆₇	—	2	1	no	—
281	C₂×C₆₇	—	2	1	no	—
282	C₂×C₆₇	—	2	1	no	—
283	C₂×C₆₇	—	2	1	no	—
284	C₂×C₆₇	—	2	1	no	—
285	C₂×C₆₇	—	2	1	no	—
286	C₂×C₆₇	#1439	1	1	yes	characteristic
287	C₂×C₆₇	#2069	1	2	yes	—
288	D₆₇	—	8	4	no	—
289	C₂×#430	—	67	1	no	—
290	C₂²×#100	—	67	1	no	—
291	C₂²×#100	—	67	1	no	—
292	C₂²×#100	—	67	1	no	—
293	#1738	—	67	1	no	—
294	#1738	D₆₇	1	1	yes	characteristic, complemented
295	C₂×#338	—	67	1	no	—
296	C₆₇	#11139	1	1	yes	characteristic, complemented, Sylow
297	C₂³×D₄	—	67	1	no	—
298	C₂²×M₁₆	—	67	1	no	—
299	C₂²×M₁₆	—	67	1	no	—
300	C₂²×M₁₆	—	67	1	no	—
301	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
302	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
303	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
304	#430	—	134	2	no	—
305	#430	—	134	2	no	—
306	C₂×#108	—	134	2	no	—
307	C₂×#100	—	67	4	no	—
308	C₂×#100	—	134	2	no	—
309	C₂×#100	—	134	2	no	—
310	C₂×#100	—	134	2	no	—
311	C₂×#100	—	134	2	no	—
312	C₂×#100	—	134	2	no	—
313	C₂×#100	—	134	2	no	—
314	C₂×#100	—	134	2	no	—
315	C₂×#100	—	134	2	no	—
316	#341	—	2	2	no	—
317	#341	—	134	2	no	—
318	#338	—	134	2	no	—
319	C₂⁵	—	67	2	no	—
320	C₂²×D₄	—	67	2	no	—
321	C₂²×D₄	—	67	2	no	—
322	C₂²×D₄	—	134	1	no	—
323	C₂²×D₄	—	134	1	no	—
324	C₂²×D₄	—	134	1	no	—
325	C₂²×D₄	—	134	1	no	—
326	C₂²×D₄	—	134	1	no	—
327	C₂²×D₄	—	134	1	no	—
328	C₂²×D₄	—	134	1	no	—
329	C₂²×D₄	—	134	1	no	—
330	C₂²×D₄	—	134	1	no	—
331	C₂²×D₄	—	134	1	no	—
332	C₂²×D₄	—	134	1	no	—
333	C₂²×D₄	—	134	1	no	—
334	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
335	C₂×M₁₆	—	2	1	no	—
336	C₂×M₁₆	—	2	1	no	—
337	C₂×M₁₆	—	2	1	no	—
338	C₂×M₁₆	—	2	1	no	—
339	C₂×M₁₆	—	2	1	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	2	1	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	67	2	no	—
349	C₂×M₁₆	—	67	2	no	—
350	C₂×M₁₆	—	67	2	no	—
351	C₂×M₁₆	—	134	1	no	—
352	C₂×M₁₆	—	134	1	no	—
353	C₂×M₁₆	—	134	1	no	—
354	C₂×M₁₆	—	134	1	no	—
355	C₂×M₁₆	—	134	1	no	—
356	C₂×M₁₆	—	134	1	no	—
357	C₂×M₁₆	—	134	1	no	—
358	C₂×M₁₆	—	134	1	no	—
359	C₂×M₁₆	—	134	1	no	—
360	C₂×M₁₆	—	134	1	no	—
361	C₂×M₁₆	—	134	1	no	—
362	C₂×M₁₆	—	134	1	no	—
363	C₂×M₁₆	—	134	1	no	—
364	C₂×M₁₆	—	134	1	no	—
365	C₂×M₁₆	—	134	1	no	—
366	C₂×M₁₆	C₄×D₆₇	1	2	yes	—
367	C₂×M₁₆	D₂₆₈	1	2	yes	—
368	C₂×M₁₆	D₂₆₈	1	2	yes	—
369	C₂×M₁₆	D₂₆₈	1	2	yes	—
370	C₂×M₁₆	C₂²⋊D₆₇	1	2	yes	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	134	1	no	—
375	C₂²×C₈	—	134	1	no	—
376	C₂²×C₈	—	134	1	no	—
377	#108	—	134	8	no	—
378	#100	—	134	8	no	—
379	#100	—	134	8	no	—
380	#100	—	134	8	no	—
381	C₂⁴	—	536	4	no	—
382	C₂⁴	—	67	4	no	—
383	C₂⁴	—	134	2	no	—
384	C₂⁴	—	134	2	no	—
385	C₂⁴	—	134	2	no	—
386	C₂⁴	—	134	2	no	—
387	C₂⁴	—	134	2	no	—
388	C₂⁴	—	134	2	no	—
389	C₂⁴	Q₈×D₆₇	1	1	yes	characteristic
390	C₂×D₄	—	268	1	no	—
391	C₂×D₄	—	268	1	no	—
392	C₂×D₄	—	268	1	no	—
393	C₂×D₄	—	268	1	no	—
394	C₂×D₄	—	268	1	no	—
395	C₂×D₄	—	268	1	no	—
396	C₂×D₄	—	268	1	no	—
397	C₂×D₄	—	268	1	no	—
398	C₂×D₄	—	268	1	no	—
399	C₂×D₄	—	268	1	no	—
400	C₂×D₄	—	268	1	no	—
401	C₂×D₄	—	268	1	no	—
402	C₂×D₄	—	268	1	no	—
403	C₂×D₄	—	268	1	no	—
404	C₂×D₄	—	268	1	no	—
405	C₂×D₄	—	268	1	no	—
406	C₂×D₄	—	134	2	no	—
407	C₂×D₄	—	134	2	no	—
408	C₂×D₄	—	134	2	no	—
409	C₂×D₄	—	134	2	no	—
410	C₂×D₄	—	134	2	no	—
411	C₂×D₄	—	134	2	no	—
412	C₂×D₄	—	134	2	no	—
413	C₂×D₄	—	134	2	no	—
414	C₂×D₄	—	134	2	no	—
415	C₂×D₄	—	134	2	no	—
416	C₂×D₄	—	134	2	no	—
417	C₂×D₄	—	134	2	no	—
418	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
419	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
420	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
421	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
422	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
426	C₂²×C₄	#11761627	1	1	yes	characteristic
427	C₂²×C₄	#11761627	1	1	yes	characteristic
428	C₂²×C₄	#11761627	1	1	yes	characteristic
429	C₂²×C₄	#11761628	1	1	yes	characteristic
430	C₂²×C₄	#11761628	1	1	yes	characteristic
431	C₂²×C₄	#11761629	1	1	yes	characteristic
432	M₁₆	—	2	2	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	—	2	2	no	—
436	M₁₆	—	2	2	no	—
437	M₁₆	—	2	2	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	4	1	no	—
440	M₁₆	—	4	1	no	—
441	M₁₆	—	4	1	no	—
442	M₁₆	—	4	1	no	—
443	M₁₆	—	268	1	no	—
444	M₁₆	—	268	1	no	—
445	M₁₆	—	268	1	no	—
446	M₁₆	—	268	1	no	—
447	M₁₆	—	268	1	no	—
448	M₁₆	—	268	1	no	—
449	M₁₆	—	134	2	no	—
450	M₁₆	—	134	2	no	—
451	M₁₆	—	134	2	no	—
452	M₁₆	—	134	2	no	—
453	M₁₆	—	134	2	no	—
454	M₁₆	—	134	2	no	—
455	M₁₆	(C₂×D₆₇)⋊C₄	1	4	yes	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	4	1	no	—
462	C₂×C₈	—	4	1	no	—
463	C₂×C₈	—	4	1	no	—
464	C₂×C₈	—	4	1	no	—
465	C₂×C₈	—	268	1	no	—
466	C₂×C₈	—	268	1	no	—
467	C₂×C₈	—	268	1	no	—
468	C₂×C₈	—	268	1	no	—
469	C₂×C₈	—	268	1	no	—
470	C₂×C₈	—	268	1	no	—
471	C₂×C₈	—	134	2	no	—
472	C₂×C₈	—	134	2	no	—
473	C₂×C₈	—	134	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	268	2	no	—
476	C₂³	—	268	2	no	—
477	C₂³	—	268	2	no	—
478	C₂³	—	268	2	no	—
479	C₂³	—	536	4	no	—
480	C₂³	—	536	4	no	—
481	C₂³	—	536	4	no	—
482	C₂³	—	536	4	no	—
483	C₂³	—	536	4	no	—
484	C₂³	—	536	4	no	—
485	C₂³	—	536	4	no	—
486	C₂³	—	134	4	no	—
487	C₂³	—	134	4	no	—
488	C₂³	—	134	4	no	—
489	C₂³	C₄⋊C₄×D₆₇	1	1	yes	characteristic
490	C₂³	#14524019	1	1	yes	characteristic
491	C₂³	#14524021	1	1	yes	characteristic
492	C₂³	#14524021	1	1	yes	characteristic
493	C₂³	#14524023	1	1	yes	characteristic
494	C₂³	#14524023	1	1	yes	characteristic
495	C₂³	#14524023	1	1	yes	characteristic
496	D₄	—	268	2	no	—
497	D₄	—	268	2	no	—
498	D₄	—	268	2	no	—
499	D₄	—	268	2	no	—
500	D₄	—	268	2	no	—
501	D₄	—	268	2	no	—
502	D₄	—	268	2	no	—
503	D₄	—	268	2	no	—
504	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
505	C₂×C₄	#14524001	1	1	yes	characteristic
506	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
507	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
508	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
509	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
510	C₂×C₄	#14524013	1	1	yes	characteristic
511	C₂×C₄	#14524013	1	1	yes	characteristic
512	C₂×C₄	#14524013	1	1	yes	characteristic
513	C₂×C₄	#14524014	1	1	yes	characteristic
514	C₂×C₄	#14524015	1	1	yes	characteristic
515	C₂×C₄	#14524015	1	1	yes	characteristic
516	C₂×C₄	#14524017	1	1	yes	characteristic
517	C₂×C₄	#14524017	1	1	yes	characteristic
518	C₂×C₄	#14524018	1	1	yes	characteristic
519	C₂×C₄	#14524018	1	1	yes	characteristic
520	C₂×C₄	#14524018	1	1	yes	characteristic
521	C₂×C₄	#14524025	1	1	yes	characteristic
522	C₂×C₄	#14524025	1	1	yes	characteristic
523	C₂×C₄	#14524027	1	1	yes	characteristic
524	C₂×C₄	#14524027	1	1	yes	characteristic
525	C₂×C₄	#14524027	1	1	yes	characteristic
526	C₂×C₄	#14524029	1	1	yes	characteristic
527	C₂×C₄	#14524029	1	1	yes	characteristic
528	C₂×C₄	#14524031	1	1	yes	characteristic
529	C₂×C₄	#14524038	1	1	yes	characteristic
530	C₂×C₄	#14524038	1	1	yes	characteristic
531	C₂×C₄	#14524040	1	1	yes	characteristic
532	C₈	—	2	4	no	—
533	C₈	—	4	2	no	—
534	C₈	—	4	2	no	—
535	C₈	—	268	2	no	—
536	C₈	—	268	2	no	—
537	C₈	—	268	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	268	4	no	—
546	C₂²	—	536	4	no	—
547	C₂²	—	536	4	no	—
548	C₂²	—	536	4	no	—
549	C₂²	—	536	4	no	—
550	C₂²	—	536	4	no	—
551	C₂²	—	536	4	no	—
552	C₂²	—	536	4	no	—
553	C₂²	#16863253	1	1	yes	characteristic
554	C₂²	#16863270	1	1	yes	characteristic
555	C₂²	#16863270	1	1	yes	characteristic
556	C₂²	#16863309	1	1	yes	characteristic
557	C₂²	#16863318	1	1	yes	characteristic
558	C₂²	#16863318	1	1	yes	characteristic
559	C₂²	#16863333	1	1	yes	characteristic
560	C₄	#16863273	1	1	yes	characteristic
561	C₄	#16863288	1	1	yes	characteristic
562	C₄	#16863288	1	1	yes	characteristic
563	C₄	#16863298	1	1	yes	characteristic
564	C₄	#16863306	1	1	yes	characteristic
565	C₄	#16863312	1	1	yes	characteristic
566	C₄	#16863312	1	1	yes	characteristic
567	C₄	#16863323	1	1	yes	characteristic
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	—	2	1	no	—
571	C₂	—	2	1	no	—
572	C₂	—	2	1	no	—
573	C₂	—	2	1	no	—
574	C₂	—	536	4	no	—
575	C₂	#22558455	1	1	yes	characteristic
576	C₂	#22561606	1	2	yes	—

	subgroup	G/H
center	C₂²	#16863318
commutator	C₂²×C₄×C₆₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₆₇
Fitting	C₆₇×#1738	C₂
socle	C₂²×C₆₇	#396
prime radical	C₂³×D₂₆₈	C₂²
cosocle	C₂³×C₄×C₆₇	C₂³
hypercenter	#1738	D₆₇
hypocenter	C₆₇	#11139
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #1738

Complements

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

N	H ≅ G/N	type
1. C₂×#16863445	C₂	semidirect
5. #22559935	C₂	semidirect
6. C₂×C₆₇⋊#338	C₂	semidirect
7. C₆₇×#1738	C₂	semidirect
294. #1738	D₆₇	semidirect
296. C₆₇	#11139	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863445	2
C₂²×#14523959	2
#22559935	2
C₂×C₆₇⋊#338	2
C₆₇×#1738	2
#11139	67