Subgroups — #30862287

Order 17152.

910 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863518	C₂	1	2	yes	maximal, complemented
2	#22568921	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14524050	C₂	1	1	yes	maximal, characteristic, complemented
4	#22561129	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560985	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560859	C₂	1	2	yes	maximal, complemented
7	#22560538	C₂	1	2	yes	maximal, complemented
8	#22560229	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560079	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560056	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3035	C₂	1	1	yes	maximal, characteristic
12	C₂×#14524050	C₂²	1	1	yes	characteristic
13	C₂×#14524050	C₂²	1	2	yes	—
14	C₂×#14524050	C₂²	1	1	yes	characteristic
15	#16863518	—	2	8	no	—
16	#16863474	—	2	1	no	—
17	#16863474	—	2	1	no	—
18	D₄×C₆₇⋊C₈	—	2	1	no	—
19	D₄×C₆₇⋊C₈	—	2	1	no	—
20	C₂×#14523979	C₂²	1	2	yes	—
21	#16863420	C₂²	1	1	yes	characteristic
22	C₂×#14523970	C₂²	1	2	yes	—
23	C₂×#14523970	C₂²	1	2	yes	—
24	C₂×#14523970	C₂²	1	2	yes	—
25	#16863363	C₂²	1	2	yes	—
26	#16863352	—	2	1	no	—
27	#16863352	—	2	1	no	—
28	#16863352	C₂²	1	1	yes	characteristic
29	#16863352	C₂²	1	1	yes	characteristic
30	C₄×#11761612	—	2	1	no	—
31	C₄×#11761612	C₂²	1	1	yes	characteristic
32	C₂×#14523953	C₂²	1	2	yes	—
33	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
34	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
36	#16863161	C₂²	1	2	yes	—
37	#16863155	C₂²	1	2	yes	—
38	#16863150	C₂²	1	2	yes	—
39	C₂×#135×C₆₇	C₂²	1	2	yes	—
40	#532×C₆₇	C₂²	1	1	yes	characteristic
41	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
42	#464×C₆₇	C₄	1	2	yes	complemented
43	#463×C₆₇	C₄	1	2	yes	complemented
44	#462×C₆₇	C₄	1	1	yes	characteristic, complemented
45	#461×C₆₇	C₄	1	1	yes	characteristic, complemented
46	#460×C₆₇	C₄	1	1	yes	characteristic, complemented
47	#459×C₆₇	C₄	1	1	yes	characteristic, complemented
48	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
49	#416×C₆₇	C₂²	1	2	yes	—
50	#14524050	—	2	2	no	—
51	#14524050	—	2	2	no	—
52	#14524050	—	2	4	no	—
53	#14524050	—	2	4	no	—
54	#14524050	—	2	2	no	—
55	#14524050	D₄	1	4	yes	complemented
56	C₂×#11761612	—	2	1	no	—
57	C₂×#11761612	—	2	1	no	—
58	C₂×#11761612	—	2	2	no	—
59	C₂×#11761612	C₂³	1	2	yes	—
60	C₂×#11761612	C₂³	1	1	yes	characteristic
61	C₂×#11761612	C₂³	1	1	yes	characteristic
62	C₂²×C₆₇⋊C₈	—	2	1	no	—
63	C₂²×C₆₇⋊C₈	—	2	1	no	—
64	C₂²×C₆₇⋊C₈	—	2	2	no	—
65	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊Dic₆₇	—	2	1	no	—
68	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
69	#14523979	—	2	4	no	—
70	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
71	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
72	#14523970	—	2	4	no	—
73	#14523970	—	2	4	no	—
74	#14523970	—	2	4	no	—
75	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
76	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
77	#14523954	—	2	1	no	—
78	#14523954	—	2	1	no	—
79	#14523954	—	2	1	no	—
80	#14523953	—	2	4	no	—
81	C₄×C₆₇⋊C₈	—	2	1	no	—
82	C₄×C₆₇⋊C₈	—	2	1	no	—
83	C₄×C₆₇⋊C₈	—	2	1	no	—
84	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
85	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
86	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
87	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
88	C₆₇⋊#95	—	2	1	no	—
89	C₂×#41×C₆₇	C₂³	1	2	yes	—
90	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
91	#135×C₆₇	—	2	4	no	—
92	#135×C₆₇	—	2	4	no	—
93	C₂×Q₁₆×C₆₇	C₂×C₄	1	2	yes	—
94	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
95	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
96	C₂×D₈×C₆₇	C₂×C₄	1	2	yes	—
97	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
98	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
99	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
100	#124×C₆₇	C₂×C₄	1	2	yes	—
101	#121×C₆₇	—	2	1	no	—
102	#121×C₆₇	—	2	1	no	—
103	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
104	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₆₇	—	2	1	no	—
106	C₄×D₄×C₆₇	—	2	1	no	—
107	C₄×D₄×C₆₇	—	2	1	no	—
108	C₄×D₄×C₆₇	—	2	1	no	—
109	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
110	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
111	#117×C₆₇	—	2	1	no	—
112	#117×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₆₇	—	2	1	no	—
114	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
115	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
116	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
117	C₄⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
118	#103×C₆₇	C₂×C₄	1	2	yes	—
119	#103×C₆₇	C₂×C₄	1	2	yes	—
120	#102×C₆₇	C₂×C₄	1	2	yes	—
121	#102×C₆₇	C₂×C₄	1	2	yes	—
122	C₂²×Dic₆₇	—	2	2	no	—
123	#11761612	—	2	4	no	—
124	#11761612	—	2	1	no	—
125	#11761612	—	2	1	no	—
126	#11761612	—	2	4	no	—
127	#11761612	—	2	2	no	—
128	#11761612	—	2	2	no	—
129	#11761612	—	4	4	no	—
130	#11761612	C₂×D₄	1	2	yes	—
131	#11761612	#41	1	2	yes	—
132	C₂×C₆₇⋊C₈	—	2	4	no	—
133	C₂×C₆₇⋊C₈	—	2	1	no	—
134	C₂×C₆₇⋊C₈	—	2	1	no	—
135	C₂×C₆₇⋊C₈	—	2	1	no	—
136	C₂×C₆₇⋊C₈	—	2	1	no	—
137	C₂×C₆₇⋊C₈	—	2	4	no	—
138	C₂×C₆₇⋊C₈	—	2	2	no	—
139	C₂×C₆₇⋊C₈	—	4	4	no	—
140	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
141	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
142	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
143	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
145	C₂×C₆₇⋊C₈	#41	1	2	yes	—
146	C₄⋊Dic₆₇	—	4	2	no	—
147	C₄×Dic₆₇	—	2	2	no	—
148	C₄×Dic₆₇	—	2	2	no	—
149	#41×C₆₇	—	2	1	no	—
150	#41×C₆₇	—	2	1	no	—
151	#41×C₆₇	—	2	2	no	—
152	#41×C₆₇	—	2	2	no	—
153	#41×C₆₇	—	2	2	no	—
154	#41×C₆₇	—	2	2	no	—
155	#41×C₆₇	C₂×D₄	1	2	yes	—
156	#41×C₆₇	#41	1	2	yes	—
157	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
158	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
159	C₂×D₄×C₆₇	—	2	1	no	—
160	C₂×D₄×C₆₇	—	2	2	no	—
161	C₂×D₄×C₆₇	—	2	1	no	—
162	C₂×D₄×C₆₇	—	2	1	no	—
163	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
164	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₇	—	2	1	no	—
166	C₂²×C₄×C₆₇	—	2	1	no	—
167	C₂²×C₄×C₆₇	—	2	1	no	—
168	C₂²×C₄×C₆₇	—	2	2	no	—
169	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
170	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
171	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
172	Q₁₆×C₆₇	—	2	4	no	—
173	SD₁₆×C₆₇	—	2	4	no	—
174	SD₁₆×C₆₇	—	2	4	no	—
175	D₈×C₆₇	—	2	4	no	—
176	C₂×C₈×C₆₇	—	2	2	no	—
177	C₂×C₈×C₆₇	—	2	2	no	—
178	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
179	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
180	C₄⋊C₄×C₆₇	—	2	1	no	—
181	C₄⋊C₄×C₆₇	—	2	1	no	—
182	C₄⋊C₄×C₆₇	—	2	1	no	—
183	C₄⋊C₄×C₆₇	—	2	1	no	—
184	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
185	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
186	C₂²⋊C₄×C₆₇	—	2	1	no	—
187	C₂²⋊C₄×C₆₇	—	2	1	no	—
188	C₂²⋊C₄×C₆₇	—	2	1	no	—
189	C₂²⋊C₄×C₆₇	—	2	2	no	—
190	C₂²⋊C₄×C₆₇	—	2	2	no	—
191	C₄²×C₆₇	—	2	1	no	—
192	C₄²×C₆₇	—	2	1	no	—
193	C₄²×C₆₇	—	2	1	no	—
194	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
195	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
196	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
198	C₂³×C₆₇	—	2	1	no	—
199	C₂³×C₆₇	—	2	2	no	—
200	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
201	Q₈×C₆₇	—	2	1	no	—
202	Q₈×C₆₇	—	2	2	no	—
203	Q₈×C₆₇	—	2	2	no	—
204	Q₈×C₆₇	C₄×D₄	1	2	yes	—
205	D₄×C₆₇	—	2	2	no	—
206	D₄×C₆₇	—	2	2	no	—
207	D₄×C₆₇	—	2	2	no	—
208	D₄×C₆₇	—	2	1	no	—
209	D₄×C₆₇	—	2	2	no	—
210	D₄×C₆₇	—	4	2	no	—
211	D₄×C₆₇	—	4	2	no	—
212	D₄×C₆₇	—	4	2	no	—
213	D₄×C₆₇	—	4	2	no	—
214	D₄×C₆₇	C₄×D₄	1	2	yes	—
215	C₂×C₄×C₆₇	—	2	1	no	—
216	C₂×C₄×C₆₇	—	2	2	no	—
217	C₂×C₄×C₆₇	—	2	2	no	—
218	C₂×C₄×C₆₇	—	2	2	no	—
219	C₂×C₄×C₆₇	—	2	1	no	—
220	C₂×C₄×C₆₇	—	2	1	no	—
221	C₂×C₄×C₆₇	—	2	2	no	—
222	C₂×C₄×C₆₇	—	4	1	no	—
223	C₂×C₄×C₆₇	—	4	2	no	—
224	C₂×C₄×C₆₇	—	4	2	no	—
225	C₂×C₄×C₆₇	—	4	2	no	—
226	C₂×C₄×C₆₇	—	4	2	no	—
227	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
237	C₂×Dic₆₇	—	4	2	no	—
238	C₂×Dic₆₇	—	4	2	no	—
239	C₂×Dic₆₇	—	4	2	no	—
240	C₈×C₆₇	—	2	2	no	—
241	C₈×C₆₇	—	2	2	no	—
242	C₆₇⋊C₈	—	2	2	no	—
243	C₆₇⋊C₈	—	2	1	no	—
244	C₆₇⋊C₈	—	2	2	no	—
245	C₆₇⋊C₈	—	2	1	no	—
246	C₆₇⋊C₈	—	4	2	no	—
247	C₆₇⋊C₈	#121	1	2	yes	—
248	C₆₇⋊C₈	#121	1	2	yes	—
249	C₂²×C₆₇	—	2	1	no	—
250	C₂²×C₆₇	—	2	1	no	—
251	C₂²×C₆₇	—	2	2	no	—
252	C₂²×C₆₇	—	4	1	no	—
253	C₂²×C₆₇	—	4	1	no	—
254	C₂²×C₆₇	—	4	2	no	—
255	C₂²×C₆₇	—	4	2	no	—
256	C₂²×C₆₇	—	4	2	no	—
257	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂²×C₆₇	#529	1	1	yes	characteristic
259	C₂²×C₆₇	#532	1	1	yes	characteristic
260	C₄×C₆₇	—	2	1	no	—
261	C₄×C₆₇	—	2	1	no	—
262	C₄×C₆₇	—	2	1	no	—
263	C₄×C₆₇	—	2	2	no	—
264	C₄×C₆₇	—	4	1	no	—
265	C₄×C₆₇	—	4	1	no	—
266	C₄×C₆₇	—	4	2	no	—
267	C₄×C₆₇	#444	1	2	yes	complemented
268	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
269	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
270	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
271	C₄×C₆₇	#525	1	1	yes	characteristic
272	Dic₆₇	—	8	2	no	—
273	#21518	—	67	1	no	maximal, Sylow
274	C₂×C₆₇	—	2	1	no	—
275	C₂×C₆₇	—	2	1	no	—
276	C₂×C₆₇	—	4	2	no	—
277	C₂×C₆₇	—	8	2	no	—
278	C₂×C₆₇	C₄×#121	1	1	yes	characteristic
279	C₂×C₆₇	C₂×#444	1	1	yes	characteristic
280	C₂×C₆₇	#2955	1	1	yes	characteristic
281	#3035	D₆₇	1	1	yes	characteristic
282	C₂×#444	—	67	2	no	—
283	#2931	—	67	1	no	—
284	C₄×#131	—	67	1	no	—
285	#1980	—	67	1	no	—
286	#1950	—	67	1	no	—
287	#1929	—	67	2	no	—
288	#1876	—	67	2	no	—
289	#1806	—	67	1	no	—
290	#1770	—	67	1	no	—
291	#1765	—	67	2	no	—
292	C₆₇	#21518	1	1	yes	characteristic, complemented, Sylow
293	C₂×#135	C₂×D₆₇	1	2	yes	—
294	C₂×#131	—	67	1	no	—
295	C₂×#131	—	67	1	no	—
296	C₂×#131	—	67	2	no	—
297	#532	C₂×D₆₇	1	1	yes	characteristic
298	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
299	#464	Dic₆₇	1	2	yes	complemented
300	#463	Dic₆₇	1	2	yes	complemented
301	#462	Dic₆₇	1	1	yes	characteristic, complemented
302	#461	Dic₆₇	1	1	yes	characteristic, complemented
303	#460	Dic₆₇	1	1	yes	characteristic, complemented
304	#459	Dic₆₇	1	1	yes	characteristic, complemented
305	#444	—	134	8	no	—
306	#436	—	134	1	no	—
307	#436	—	134	1	no	—
308	C₈×D₄	—	134	1	no	—
309	C₈×D₄	—	134	1	no	—
310	C₂×#108	—	67	2	no	—
311	#423	—	67	1	no	—
312	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
313	C₂×#104	—	67	2	no	—
314	C₂×#104	—	67	2	no	—
315	C₂×#104	—	67	2	no	—
316	#416	C₂×D₆₇	1	2	yes	—
317	#408	—	67	2	no	—
318	#405	—	67	1	no	—
319	#405	—	67	1	no	—
320	#405	—	134	1	no	—
321	#405	—	134	1	no	—
322	C₄×M₁₆	—	67	1	no	—
323	C₄×M₁₆	—	134	1	no	—
324	C₂×#97	—	67	2	no	—
325	C₂×C₄×C₈	—	67	1	no	—
326	C₂×C₄×C₈	—	134	1	no	—
327	C₄×C₄⋊C₄	—	67	1	no	—
328	#341	—	67	2	no	—
329	#339	—	67	2	no	—
330	#336	—	67	2	no	—
331	C₂×#41	C₂²×D₆₇	1	2	yes	—
332	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
333	#135	—	2	4	no	—
334	#135	—	2	4	no	—
335	C₂×Q₁₆	C₂×Dic₆₇	1	2	yes	—
336	C₂×SD₁₆	C₂×Dic₆₇	1	2	yes	—
337	C₂×SD₁₆	C₂×Dic₆₇	1	2	yes	—
338	C₂×D₈	C₂×Dic₆₇	1	2	yes	—
339	#131	—	67	4	no	—
340	#131	—	134	4	no	—
341	#131	—	134	4	no	—
342	#131	—	134	2	no	—
343	#131	—	134	2	no	—
344	#131	—	134	2	no	—
345	C₂×M₁₆	—	67	1	no	—
346	C₂×M₁₆	—	67	1	no	—
347	C₂×M₁₆	—	67	2	no	—
348	C₂×M₁₆	—	134	2	no	—
349	C₂×M₁₆	—	134	1	no	—
350	C₂×M₁₆	—	134	1	no	—
351	C₂²×C₈	—	67	1	no	—
352	C₂²×C₈	—	67	1	no	—
353	C₂²×C₈	—	134	2	no	—
354	C₂²×C₈	—	134	1	no	—
355	C₂²×C₈	—	134	1	no	—
356	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
357	C₄⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
358	#127	C₂×Dic₆₇	1	1	yes	characteristic
359	#124	C₂×Dic₆₇	1	2	yes	—
360	#121	—	2	1	no	—
361	#121	—	2	1	no	—
362	C₄×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
363	C₄×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
369	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
370	#117	—	2	1	no	—
371	#117	C₂²×D₆₇	1	1	yes	characteristic
372	C₂×C₄⋊C₄	—	134	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	67	2	no	—
375	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
376	#108	—	134	4	no	—
377	C₄⋊C₈	—	134	1	no	—
378	C₄⋊C₈	—	134	1	no	—
379	C₄⋊C₈	C₂×Dic₆₇	1	1	yes	characteristic
380	C₄⋊C₈	C₂×Dic₆₇	1	1	yes	characteristic
381	C₄⋊C₈	C₂×Dic₆₇	1	2	yes	—
382	#104	—	134	4	no	—
383	#104	—	134	4	no	—
384	#104	—	134	4	no	—
385	#103	C₂×Dic₆₇	1	2	yes	—
386	#103	C₂×Dic₆₇	1	2	yes	—
387	#102	C₂×Dic₆₇	1	2	yes	—
388	#102	C₂×Dic₆₇	1	2	yes	—
389	C₂²⋊C₈	—	134	2	no	—
390	C₂²⋊C₈	—	134	2	no	—
391	#97	—	134	1	no	—
392	#97	—	134	1	no	—
393	#97	—	134	4	no	—
394	#97	—	134	1	no	—
395	C₄×C₈	—	67	1	no	—
396	C₄×C₈	—	67	1	no	—
397	C₄×C₈	—	67	1	no	—
398	C₄×C₈	—	67	1	no	—
399	C₄×C₈	—	134	1	no	—
400	C₄×C₈	—	134	1	no	—
401	C₄×C₈	—	134	1	no	—
402	#95	—	134	1	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	—	2	2	no	—
409	#41	D₄×D₆₇	1	2	yes	—
410	#41	#11761627	1	2	yes	—
411	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
412	C₂×Q₈	C₂²×Dic₆₇	1	1	yes	characteristic
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
418	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	134	2	no	—
424	C₂²×C₄	#11761627	1	1	yes	characteristic
425	C₂²×C₄	#11761627	1	1	yes	characteristic
426	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
427	Q₁₆	—	2	4	no	—
428	SD₁₆	—	2	4	no	—
429	SD₁₆	—	2	4	no	—
430	D₈	—	2	4	no	—
431	M₁₆	—	268	4	no	—
432	M₁₆	—	67	2	no	—
433	M₁₆	—	67	2	no	—
434	M₁₆	—	134	2	no	—
435	M₁₆	—	134	2	no	—
436	M₁₆	—	134	4	no	—
437	M₁₆	—	134	4	no	—
438	M₁₆	—	134	1	no	—
439	M₁₆	—	134	1	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	268	4	no	—
443	C₂×C₈	—	67	2	no	—
444	C₂×C₈	—	67	1	no	—
445	C₂×C₈	—	67	1	no	—
446	C₂×C₈	—	67	2	no	—
447	C₂×C₈	—	67	1	no	—
448	C₂×C₈	—	67	1	no	—
449	C₂×C₈	—	134	2	no	—
450	C₂×C₈	—	134	4	no	—
451	C₂×C₈	—	134	4	no	—
452	C₂×C₈	—	134	1	no	—
453	C₂×C₈	—	134	1	no	—
454	C₂×C₈	—	134	1	no	—
455	C₂×C₈	—	134	1	no	—
456	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
457	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	268	2	no	—
463	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
464	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	134	2	no	—
474	C₄²	—	134	2	no	—
475	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
476	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
477	C₄²	D₄×D₆₇	1	1	yes	characteristic
478	C₄²	D₄×D₆₇	1	1	yes	characteristic
479	C₂³	—	2	1	no	—
480	C₂³	—	2	2	no	—
481	C₂³	C₂×#11761627	1	1	yes	characteristic
482	Q₈	—	2	1	no	—
483	Q₈	—	2	2	no	—
484	Q₈	—	2	2	no	—
485	Q₈	D₄×Dic₆₇	1	2	yes	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	2	1	no	—
490	D₄	—	2	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	2	no	—
495	D₄	D₄×Dic₆₇	1	2	yes	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	268	2	no	—
509	C₂×C₄	—	268	2	no	—
510	C₂×C₄	—	268	2	no	—
511	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
512	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
513	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
514	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
515	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
516	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
517	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
518	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
519	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
520	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
521	C₈	—	2	2	no	—
522	C₈	—	2	2	no	—
523	C₈	—	268	2	no	—
524	C₈	—	67	2	no	—
525	C₈	—	67	2	no	—
526	C₈	—	134	2	no	—
527	C₈	—	134	1	no	—
528	C₈	—	134	1	no	—
529	C₈	—	134	2	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
539	C₂²	#16863927	1	1	yes	characteristic
540	C₂²	#16863941	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	2	no	—
548	C₄	—	536	2	no	—
549	C₄	#16863518	1	2	yes	complemented
550	C₄	C₂×D₄×Dic₆₇	1	1	yes	characteristic
551	C₄	#41×Dic₆₇	1	1	yes	characteristic
552	C₄	#121×D₆₇	1	1	yes	characteristic
553	C₄	#16863906	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	2	no	—
558	C₂	#121×Dic₆₇	1	1	yes	characteristic
559	C₂	C₂×#16863518	1	1	yes	characteristic
560	C₂	#22569112	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting, prime radical	C₆₇×#3035	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#3035	D₆₇
hypocenter	C₆₇	#21518
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3035

Complements

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

N	H ≅ G/N	type
1. C₂×#16863518	C₂	semidirect
2. #22568921	C₂	semidirect
3. C₄×#14524050	C₂	semidirect
4. #22561129	C₂	semidirect
5. #22560985	C₂	semidirect
6. #22560859	C₂	semidirect
7. #22560538	C₂	semidirect
8. #22560229	C₂	semidirect
9. #22560079	C₂	semidirect
10. #22560056	C₂	semidirect
42. #464×C₆₇	C₄	semidirect
43. #463×C₆₇	C₄	semidirect
44. #462×C₆₇	C₄	semidirect
45. #461×C₆₇	C₄	semidirect
46. #460×C₆₇	C₄	semidirect
47. #459×C₆₇	C₄	semidirect
55. #14524050	D₄	semidirect
267. C₄×C₆₇	#444	semidirect
292. C₆₇	#21518	semidirect
299. #464	Dic₆₇	semidirect
300. #463	Dic₆₇	semidirect
301. #462	Dic₆₇	semidirect
302. #461	Dic₆₇	semidirect
303. #460	Dic₆₇	semidirect
304. #459	Dic₆₇	semidirect
549. C₄	#16863518	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863518	2
#22568921	2
C₄×#14524050	2
#22561129	2
#22560985	2
#22560859	2
#22560538	2
#22560229	2
#22560079	2
#22560056	2
C₆₇×#3035	2
#21518	67