Subgroups — #30869034

Order 17152.

782 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22568904	C₂	1	2	yes	maximal, complemented
2	#22560859	C₂	1	2	yes	maximal, complemented
3	#22560810	C₂	1	2	yes	maximal, complemented
4	#22560658	C₂	1	2	yes	maximal, complemented
5	#22560538	C₂	1	2	yes	maximal, complemented
6	#22560486	C₂	1	2	yes	maximal, complemented
7	#22560251	C₂	1	1	yes	maximal, characteristic, complemented
8	#22559907	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3054	C₂	1	1	yes	maximal, characteristic
10	C₂×#14524050	C₂²	1	2	yes	—
11	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×#14524002	C₂²	1	1	yes	characteristic
13	#16863468	—	2	2	no	—
14	#16863468	—	2	2	no	—
15	D₄×C₆₇⋊C₈	—	2	2	no	—
16	D₄×C₆₇⋊C₈	—	2	2	no	—
17	C₂×#14523979	C₂²	1	1	yes	characteristic
18	C₂×#14523979	C₂²	1	1	yes	characteristic
19	#16863423	C₂²	1	2	yes	—
20	C₂×#14523970	C₂²	1	2	yes	—
21	C₂×#14523970	C₂²	1	2	yes	—
22	#16863363	C₂²	1	2	yes	—
23	#16863360	C₂²	1	2	yes	—
24	#16863352	C₂²	1	2	yes	—
25	#16863161	C₂²	1	2	yes	—
26	#16863155	C₂²	1	2	yes	—
27	#16863155	C₂²	1	2	yes	—
28	#16863150	C₂²	1	2	yes	—
29	#16863150	C₂²	1	2	yes	—
30	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
32	#525×C₆₇	C₂²	1	2	yes	—
33	#470×C₆₇	C₄	1	1	yes	characteristic, complemented
34	#470×C₆₇	C₄	1	1	yes	characteristic, complemented
35	#469×C₆₇	C₄	1	1	yes	characteristic, complemented
36	#469×C₆₇	C₄	1	1	yes	characteristic, complemented
37	#468×C₆₇	C₄	1	2	yes	complemented
38	#468×C₆₇	C₄	1	2	yes	complemented
39	#427×C₆₇	C₂²	1	1	yes	characteristic
40	#416×C₆₇	C₂²	1	2	yes	—
41	#14524050	—	4	2	no	—
42	#14524050	—	4	2	no	—
43	C₂×#11761612	—	2	2	no	—
44	C₂×#11761612	C₂³	1	2	yes	—
45	C₂×#11761612	C₂³	1	2	yes	—
46	C₂²×C₆₇⋊C₈	—	2	2	no	—
47	C₂²×C₆₇⋊C₈	—	4	1	no	—
48	C₂²×C₆₇⋊C₈	—	4	1	no	—
49	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
50	C₂²×C₆₇⋊C₈	D₄	1	2	yes	—
51	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
52	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
53	#14524002	—	4	1	no	—
54	#14524002	—	4	1	no	—
55	C₂×C₄⋊Dic₆₇	—	2	1	no	—
56	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
57	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
58	#14523979	—	4	1	no	—
59	#14523979	—	4	1	no	—
60	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
61	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
62	#14523970	—	4	2	no	—
63	#14523970	—	4	2	no	—
64	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
65	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
66	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
67	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
68	#14523954	—	2	2	no	—
69	C₄×C₆₇⋊C₈	—	2	2	no	—
70	C₂×#41×C₆₇	C₂³	1	2	yes	—
71	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
72	#135×C₆₇	—	4	1	no	—
73	#135×C₆₇	—	4	1	no	—
74	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
75	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
76	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
77	C₂×M₁₆×C₆₇	—	4	1	no	—
78	C₂×M₁₆×C₆₇	—	4	1	no	—
79	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
80	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
81	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
82	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
85	#123×C₆₇	—	2	2	no	—
86	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
87	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
88	#121×C₆₇	C₂×C₄	1	2	yes	—
89	#121×C₆₇	C₂×C₄	1	2	yes	—
90	#120×C₆₇	—	2	2	no	—
91	C₄×D₄×C₆₇	—	2	2	no	—
92	C₄×D₄×C₆₇	—	2	2	no	—
93	#117×C₆₇	C₂³	1	2	yes	—
94	#107×C₆₇	C₂×C₄	1	2	yes	—
95	#106×C₆₇	C₂×C₄	1	1	yes	characteristic
96	#106×C₆₇	C₂×C₄	1	1	yes	characteristic
97	#103×C₆₇	C₂×C₄	1	2	yes	—
98	#103×C₆₇	C₂×C₄	1	2	yes	—
99	#102×C₆₇	C₂×C₄	1	2	yes	—
100	#102×C₆₇	C₂×C₄	1	2	yes	—
101	C₂²×Dic₆₇	—	2	2	no	—
102	#11761612	—	2	2	no	—
103	#11761612	—	2	2	no	—
104	#11761612	—	2	2	no	—
105	#11761612	—	2	2	no	—
106	#11761612	—	4	4	no	—
107	C₂×C₆₇⋊C₈	—	2	2	no	—
108	C₂×C₆₇⋊C₈	—	2	2	no	—
109	C₂×C₆₇⋊C₈	—	2	2	no	—
110	C₂×C₆₇⋊C₈	—	2	2	no	—
111	C₂×C₆₇⋊C₈	—	4	1	no	—
112	C₂×C₆₇⋊C₈	—	4	2	no	—
113	C₂×C₆₇⋊C₈	—	4	1	no	—
114	C₂×C₆₇⋊C₈	—	4	4	no	—
115	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
116	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
117	C₄⋊Dic₆₇	—	4	2	no	—
118	C₂²⋊Dic₆₇	—	4	2	no	—
119	C₄×Dic₆₇	—	2	2	no	—
120	C₄×Dic₆₇	—	2	2	no	—
121	C₂⁴×C₆₇	#41	1	1	yes	characteristic
122	#41×C₆₇	—	2	2	no	—
123	#41×C₆₇	—	2	2	no	—
124	#41×C₆₇	—	2	2	no	—
125	#41×C₆₇	—	2	2	no	—
126	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
127	C₂×D₄×C₆₇	—	2	2	no	—
128	C₂×D₄×C₆₇	—	2	2	no	—
129	C₂×D₄×C₆₇	—	2	2	no	—
130	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₆₇	—	2	1	no	—
132	C₂²×C₄×C₆₇	—	2	1	no	—
133	C₂²×C₄×C₆₇	—	2	1	no	—
134	C₂²×C₄×C₆₇	—	2	1	no	—
135	C₂²×C₄×C₆₇	—	2	2	no	—
136	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
141	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
142	Q₁₆×C₆₇	—	4	1	no	—
143	SD₁₆×C₆₇	—	4	2	no	—
144	D₈×C₆₇	—	4	1	no	—
145	M₁₆×C₆₇	—	4	1	no	—
146	M₁₆×C₆₇	—	4	1	no	—
147	M₁₆×C₆₇	—	4	1	no	—
148	M₁₆×C₆₇	—	4	1	no	—
149	C₂×C₈×C₆₇	—	2	1	no	—
150	C₂×C₈×C₆₇	—	2	1	no	—
151	C₂×C₈×C₆₇	—	2	1	no	—
152	C₂×C₈×C₆₇	—	2	1	no	—
153	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
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	C₄⋊C₄×C₆₇	—	2	2	no	—
158	C₄⋊C₄×C₆₇	—	2	2	no	—
159	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
160	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
161	C₂²⋊C₄×C₆₇	—	2	2	no	—
162	C₂²⋊C₄×C₆₇	—	2	2	no	—
163	C₂²⋊C₄×C₆₇	—	2	2	no	—
164	C₂²⋊C₄×C₆₇	—	2	2	no	—
165	C₂²⋊C₄×C₆₇	—	2	2	no	—
166	C₄²×C₆₇	—	2	2	no	—
167	C₂³×C₆₇	—	2	1	no	—
168	C₂³×C₆₇	—	2	1	no	—
169	C₂³×C₆₇	—	2	2	no	—
170	C₂³×C₆₇	—	4	2	no	—
171	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
172	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
173	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
174	Q₈×C₆₇	—	2	2	no	—
175	Q₈×C₆₇	—	2	2	no	—
176	D₄×C₆₇	—	2	2	no	—
177	D₄×C₆₇	—	2	2	no	—
178	D₄×C₆₇	—	4	4	no	—
179	D₄×C₆₇	—	4	4	no	—
180	D₄×C₆₇	—	4	2	no	—
181	D₄×C₆₇	—	4	2	no	—
182	C₂×C₄×C₆₇	—	2	1	no	—
183	C₂×C₄×C₆₇	—	2	1	no	—
184	C₂×C₄×C₆₇	—	2	1	no	—
185	C₂×C₄×C₆₇	—	2	1	no	—
186	C₂×C₄×C₆₇	—	2	1	no	—
187	C₂×C₄×C₆₇	—	2	1	no	—
188	C₂×C₄×C₆₇	—	2	1	no	—
189	C₂×C₄×C₆₇	—	2	1	no	—
190	C₂×C₄×C₆₇	—	2	1	no	—
191	C₂×C₄×C₆₇	—	2	1	no	—
192	C₂×C₄×C₆₇	—	2	2	no	—
193	C₂×C₄×C₆₇	—	2	2	no	—
194	C₂×C₄×C₆₇	—	2	2	no	—
195	C₂×C₄×C₆₇	—	4	2	no	—
196	C₂×C₄×C₆₇	—	4	2	no	—
197	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
205	C₂×Dic₆₇	—	4	4	no	—
206	C₂×Dic₆₇	—	4	2	no	—
207	C₈×C₆₇	—	2	1	no	—
208	C₈×C₆₇	—	2	1	no	—
209	C₈×C₆₇	—	2	1	no	—
210	C₈×C₆₇	—	2	1	no	—
211	C₆₇⋊C₈	—	2	2	no	—
212	C₆₇⋊C₈	—	2	2	no	—
213	C₆₇⋊C₈	—	4	2	no	—
214	C₆₇⋊C₈	—	4	2	no	—
215	C₂²×C₆₇	—	2	2	no	—
216	C₂²×C₆₇	—	2	1	no	—
217	C₂²×C₆₇	—	2	1	no	—
218	C₂²×C₆₇	—	2	2	no	—
219	C₂²×C₆₇	—	2	2	no	—
220	C₂²×C₆₇	—	4	2	no	—
221	C₂²×C₆₇	—	4	2	no	—
222	C₂²×C₆₇	—	4	2	no	—
223	C₂²×C₆₇	—	4	2	no	—
224	C₂²×C₆₇	—	4	2	no	—
225	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
226	C₂²×C₆₇	#538	1	1	yes	characteristic
227	C₂²×C₆₇	#539	1	1	yes	characteristic
228	C₄×C₆₇	—	2	1	no	—
229	C₄×C₆₇	—	2	1	no	—
230	C₄×C₆₇	—	4	2	no	—
231	C₄×C₆₇	—	4	2	no	—
232	C₄×C₆₇	—	4	2	no	—
233	C₄×C₆₇	#518	1	1	yes	characteristic
234	C₄×C₆₇	#520	1	1	yes	characteristic
235	C₄×C₆₇	#534	1	1	yes	characteristic
236	C₄×C₆₇	#537	1	1	yes	characteristic
237	Dic₆₇	—	8	2	no	—
238	#22205	—	67	1	no	maximal, Sylow
239	C₂×C₆₇	—	2	1	no	—
240	C₂×C₆₇	—	2	1	no	—
241	C₂×C₆₇	—	4	1	no	—
242	C₂×C₆₇	—	4	1	no	—
243	C₂×C₆₇	—	8	2	no	—
244	C₂×C₆₇	#2325	1	1	yes	characteristic
245	C₂×C₆₇	#2955	1	2	yes	—
246	#3054	D₆₇	1	1	yes	characteristic
247	#2929	—	67	2	no	—
248	#1929	—	67	2	no	—
249	#1922	—	67	2	no	—
250	#1897	—	67	2	no	—
251	#1876	—	67	2	no	—
252	#1866	—	67	2	no	—
253	#1811	—	67	1	no	—
254	#1729	—	67	1	no	—
255	C₆₇	#22205	1	1	yes	characteristic, complemented, Sylow
256	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
257	C₂×#131	—	67	2	no	—
258	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
259	C₂³×C₈	—	67	1	no	—
260	#525	C₂×D₆₇	1	2	yes	—
261	C₂×#117	—	67	1	no	—
262	#470	Dic₆₇	1	1	yes	characteristic, complemented
263	#470	Dic₆₇	1	1	yes	characteristic, complemented
264	#469	Dic₆₇	1	1	yes	characteristic, complemented
265	#469	Dic₆₇	1	1	yes	characteristic, complemented
266	#468	Dic₆₇	1	2	yes	complemented
267	#468	Dic₆₇	1	2	yes	complemented
268	#435	—	134	2	no	—
269	#435	—	134	2	no	—
270	C₈×D₄	—	134	2	no	—
271	C₈×D₄	—	134	2	no	—
272	C₂×#108	—	67	1	no	—
273	C₂×#108	—	67	1	no	—
274	#427	C₂×D₆₇	1	1	yes	characteristic
275	#424	—	67	2	no	—
276	C₂×#104	—	67	2	no	—
277	C₂×#104	—	67	2	no	—
278	#416	C₂×D₆₇	1	2	yes	—
279	#408	—	67	2	no	—
280	#407	—	67	2	no	—
281	#405	—	67	2	no	—
282	#341	—	67	2	no	—
283	#339	—	67	2	no	—
284	#339	—	67	2	no	—
285	#336	—	67	2	no	—
286	#336	—	67	2	no	—
287	C₂×#41	C₂²×D₆₇	1	2	yes	—
288	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
289	#135	—	4	1	no	—
290	#135	—	4	1	no	—
291	C₂×Q₁₆	C₂×Dic₆₇	1	1	yes	characteristic
292	C₂×SD₁₆	C₂×Dic₆₇	1	2	yes	—
293	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic
294	#131	—	268	2	no	—
295	#131	—	268	2	no	—
296	C₂×M₁₆	—	4	1	no	—
297	C₂×M₁₆	—	4	1	no	—
298	C₂×M₁₆	—	67	2	no	—
299	C₂×M₁₆	—	67	2	no	—
300	C₂×M₁₆	—	134	2	no	—
301	C₂×M₁₆	C₂×Dic₆₇	1	1	yes	characteristic
302	C₂×M₁₆	C₂×Dic₆₇	1	1	yes	characteristic
303	C₂×M₁₆	C₂×Dic₆₇	1	1	yes	characteristic
304	C₂×M₁₆	C₂×Dic₆₇	1	1	yes	characteristic
305	C₂²×C₈	—	268	1	no	—
306	C₂²×C₈	—	268	1	no	—
307	C₂²×C₈	—	67	1	no	—
308	C₂²×C₈	—	67	2	no	—
309	C₂²×C₈	—	67	1	no	—
310	C₂²×C₈	—	67	2	no	—
311	C₂²×C₈	—	134	2	no	—
312	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
313	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
314	#123	—	2	2	no	—
315	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
316	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
317	#121	C₂×Dic₆₇	1	2	yes	—
318	#121	C₂×Dic₆₇	1	2	yes	—
319	#120	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	—	2	2	no	—
322	#117	—	268	1	no	—
323	#117	—	268	1	no	—
324	#117	C₂²×D₆₇	1	2	yes	—
325	C₂×C₄⋊C₄	—	134	1	no	—
326	C₂×C₂²⋊C₄	—	134	1	no	—
327	C₂×C₄²	—	67	2	no	—
328	#108	—	268	1	no	—
329	#108	—	268	1	no	—
330	#107	C₂×Dic₆₇	1	2	yes	—
331	#106	C₂×Dic₆₇	1	1	yes	characteristic
332	#106	C₂×Dic₆₇	1	1	yes	characteristic
333	C₄⋊C₈	—	134	2	no	—
334	C₄⋊C₈	—	134	2	no	—
335	#104	—	268	2	no	—
336	#104	—	268	2	no	—
337	#103	C₂×Dic₆₇	1	2	yes	—
338	#103	C₂×Dic₆₇	1	2	yes	—
339	#102	C₂×Dic₆₇	1	2	yes	—
340	#102	C₂×Dic₆₇	1	2	yes	—
341	C₂²⋊C₈	—	134	2	no	—
342	C₂²⋊C₈	—	134	2	no	—
343	C₂²⋊C₈	—	134	2	no	—
344	C₂²⋊C₈	—	134	2	no	—
345	#97	—	134	2	no	—
346	C₄×C₈	—	134	2	no	—
347	C₂⁴	#11761627	1	1	yes	characteristic
348	#41	—	2	2	no	—
349	#41	—	2	2	no	—
350	#41	—	2	2	no	—
351	#41	—	2	2	no	—
352	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	134	2	no	—
363	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
364	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
365	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
366	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
367	C₂²×C₄	#11761627	1	1	yes	characteristic
368	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
369	Q₁₆	—	4	1	no	—
370	SD₁₆	—	4	2	no	—
371	D₈	—	4	1	no	—
372	M₁₆	—	4	1	no	—
373	M₁₆	—	4	1	no	—
374	M₁₆	—	4	1	no	—
375	M₁₆	—	4	1	no	—
376	M₁₆	—	268	4	no	—
377	M₁₆	—	134	2	no	—
378	M₁₆	—	134	2	no	—
379	M₁₆	—	134	2	no	—
380	M₁₆	—	134	2	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	268	4	no	—
386	C₂×C₈	—	268	1	no	—
387	C₂×C₈	—	268	2	no	—
388	C₂×C₈	—	268	1	no	—
389	C₂×C₈	—	67	2	no	—
390	C₂×C₈	—	67	2	no	—
391	C₂×C₈	—	134	2	no	—
392	C₂×C₈	—	134	2	no	—
393	C₂×C₈	—	134	2	no	—
394	C₂×C₈	—	134	2	no	—
395	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
396	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
397	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
398	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	268	2	no	—
402	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
403	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	268	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	134	2	no	—
412	C₄²	—	134	2	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
418	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
419	C₂³	C₂×#11761627	1	1	yes	characteristic
420	Q₈	—	2	2	no	—
421	Q₈	—	2	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	4	no	—
425	D₄	—	4	4	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	268	4	no	—
444	C₂×C₄	—	268	2	no	—
445	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
446	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
447	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
448	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
449	C₂×C₄	#14524088	1	1	yes	characteristic
450	C₂×C₄	#14524088	1	1	yes	characteristic
451	C₂×C₄	#14524089	1	1	yes	characteristic
452	C₂×C₄	#14524090	1	1	yes	characteristic
453	C₈	—	2	1	no	—
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	268	2	no	—
458	C₈	—	268	2	no	—
459	C₈	—	134	2	no	—
460	C₈	—	134	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
472	C₂²	#16863983	1	1	yes	characteristic
473	C₂²	#16863991	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	536	2	no	—
480	C₄	#16863871	1	1	yes	characteristic
481	C₄	#16863879	1	1	yes	characteristic
482	C₄	#16863954	1	1	yes	characteristic
483	C₄	#16863973	1	1	yes	characteristic
484	C₂	—	2	1	no	—
485	C₂	—	2	1	no	—
486	C₂	—	4	1	no	—
487	C₂	—	4	1	no	—
488	C₂	—	8	2	no	—
489	C₂	#22562914	1	1	yes	characteristic
490	C₂	#22569112	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting, prime radical	C₆₇×#3054	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#3054	D₆₇
hypocenter	C₆₇	#22205
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3054

Complements

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

N	H ≅ G/N	type
1. #22568904	C₂	semidirect
2. #22560859	C₂	semidirect
3. #22560810	C₂	semidirect
4. #22560658	C₂	semidirect
5. #22560538	C₂	semidirect
6. #22560486	C₂	semidirect
7. #22560251	C₂	semidirect
8. #22559907	C₂	semidirect
33. #470×C₆₇	C₄	semidirect
34. #470×C₆₇	C₄	semidirect
35. #469×C₆₇	C₄	semidirect
36. #469×C₆₇	C₄	semidirect
37. #468×C₆₇	C₄	semidirect
38. #468×C₆₇	C₄	semidirect
255. C₆₇	#22205	semidirect
262. #470	Dic₆₇	semidirect
263. #470	Dic₆₇	semidirect
264. #469	Dic₆₇	semidirect
265. #469	Dic₆₇	semidirect
266. #468	Dic₆₇	semidirect
267. #468	Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22568904	2
#22560859	2
#22560810	2
#22560658	2
#22560538	2
#22560486	2
#22560251	2
#22559907	2
C₆₇×#3054	2
#22205	67