Subgroups — #30869025

Order 17152.

838 conjugacy classes of subgroups.

The subgroup lattice has 510 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	#22560653	C₂	1	2	yes	maximal, complemented
5	#22560538	C₂	1	2	yes	maximal, complemented
6	#22560486	C₂	1	2	yes	maximal, complemented
7	#22560247	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16863150	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3050	C₂	1	1	yes	maximal, characteristic
10	C₂×#14524050	C₂²	1	2	yes	—
11	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₆₇	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	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
32	#525×C₆₇	C₂²	1	2	yes	—
33	#467×C₆₇	C₄	1	1	yes	characteristic, complemented
34	#467×C₆₇	C₄	1	1	yes	characteristic, complemented
35	#466×C₆₇	C₄	1	1	yes	characteristic, complemented
36	#466×C₆₇	C₄	1	1	yes	characteristic, complemented
37	#465×C₆₇	C₄	1	2	yes	complemented
38	#465×C₆₇	C₄	1	2	yes	complemented
39	#427×C₆₇	C₂²	1	1	yes	characteristic
40	#416×C₆₇	C₂²	1	2	yes	—
41	C₂³×Dic₆₇	—	2	1	no	—
42	#14524050	—	4	2	no	—
43	#14524050	—	4	2	no	—
44	C₂×#11761612	—	2	2	no	—
45	C₂×#11761612	C₂³	1	2	yes	—
46	C₂×#11761612	C₂³	1	2	yes	—
47	C₂²×C₆₇⋊C₈	—	2	2	no	—
48	C₂²×C₆₇⋊C₈	—	4	1	no	—
49	C₂²×C₆₇⋊C₈	—	4	1	no	—
50	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
51	C₂²×C₆₇⋊C₈	D₄	1	2	yes	—
52	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
53	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
54	C₂×C₄×Dic₆₇	—	2	1	no	—
55	C₂×C₄×Dic₆₇	—	4	1	no	—
56	C₂×C₄×Dic₆₇	—	4	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, complemented
75	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	complemented
76	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
77	C₂²×C₈×C₆₇	—	4	1	no	—
78	C₂²×C₈×C₆₇	—	4	1	no	—
79	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×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	1	yes	characteristic, complemented
95	#107×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
96	#106×C₆₇	C₂×C₄	1	2	yes	complemented
97	#103×C₆₇	C₂×C₄	1	2	yes	complemented
98	#103×C₆₇	C₂×C₄	1	2	yes	complemented
99	#102×C₆₇	C₂×C₄	1	2	yes	complemented
100	#102×C₆₇	C₂×C₄	1	2	yes	complemented
101	C₂²×Dic₆₇	—	2	4	no	—
102	C₂²×Dic₆₇	—	2	2	no	—
103	C₂²×Dic₆₇	—	4	2	no	—
104	C₂²×Dic₆₇	—	4	2	no	—
105	#11761612	—	2	2	no	—
106	#11761612	—	2	2	no	—
107	#11761612	—	2	2	no	—
108	#11761612	—	2	2	no	—
109	#11761612	—	4	4	no	—
110	C₂×C₆₇⋊C₈	—	2	2	no	—
111	C₂×C₆₇⋊C₈	—	2	2	no	—
112	C₂×C₆₇⋊C₈	—	2	2	no	—
113	C₂×C₆₇⋊C₈	—	2	2	no	—
114	C₂×C₆₇⋊C₈	—	4	1	no	—
115	C₂×C₆₇⋊C₈	—	4	2	no	—
116	C₂×C₆₇⋊C₈	—	4	1	no	—
117	C₂×C₆₇⋊C₈	—	4	4	no	—
118	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
119	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
120	C₄×Dic₆₇	—	2	2	no	—
121	C₄×Dic₆₇	—	2	2	no	—
122	C₄×Dic₆₇	—	4	2	no	—
123	C₂⁴×C₆₇	#41	1	1	yes	characteristic
124	#41×C₆₇	—	2	2	no	—
125	#41×C₆₇	—	2	2	no	—
126	#41×C₆₇	—	2	2	no	—
127	#41×C₆₇	—	2	2	no	—
128	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
129	C₂×D₄×C₆₇	—	2	2	no	—
130	C₂×D₄×C₆₇	—	2	2	no	—
131	C₂×D₄×C₆₇	—	2	2	no	—
132	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₆₇	—	2	1	no	—
134	C₂²×C₄×C₆₇	—	2	1	no	—
135	C₂²×C₄×C₆₇	—	2	1	no	—
136	C₂²×C₄×C₆₇	—	2	1	no	—
137	C₂²×C₄×C₆₇	—	2	2	no	—
138	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
143	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
144	Q₁₆×C₆₇	—	4	1	no	—
145	SD₁₆×C₆₇	—	4	2	no	—
146	D₈×C₆₇	—	4	1	no	—
147	C₂×C₈×C₆₇	—	2	1	no	—
148	C₂×C₈×C₆₇	—	2	1	no	—
149	C₂×C₈×C₆₇	—	2	1	no	—
150	C₂×C₈×C₆₇	—	2	1	no	—
151	C₂×C₈×C₆₇	—	4	1	no	—
152	C₂×C₈×C₆₇	—	4	1	no	—
153	C₂×C₈×C₆₇	—	4	1	no	—
154	C₂×C₈×C₆₇	—	4	1	no	—
155	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊C₄×C₆₇	—	2	2	no	—
160	C₄⋊C₄×C₆₇	—	2	2	no	—
161	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
162	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
163	C₂²⋊C₄×C₆₇	—	2	2	no	—
164	C₂²⋊C₄×C₆₇	—	2	2	no	—
165	C₂²⋊C₄×C₆₇	—	2	2	no	—
166	C₂²⋊C₄×C₆₇	—	2	2	no	—
167	C₂²⋊C₄×C₆₇	—	2	2	no	—
168	C₄²×C₆₇	—	2	2	no	—
169	C₂³×C₆₇	—	2	1	no	—
170	C₂³×C₆₇	—	2	1	no	—
171	C₂³×C₆₇	—	2	2	no	—
172	C₂³×C₆₇	—	2	2	no	—
173	C₂³×C₆₇	—	2	2	no	—
174	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
175	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
176	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
177	Q₈×C₆₇	—	2	2	no	—
178	Q₈×C₆₇	—	2	2	no	—
179	D₄×C₆₇	—	2	2	no	—
180	D₄×C₆₇	—	2	2	no	—
181	D₄×C₆₇	—	4	2	no	—
182	D₄×C₆₇	—	4	2	no	—
183	D₄×C₆₇	—	4	4	no	—
184	D₄×C₆₇	—	4	4	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	1	no	—
193	C₂×C₄×C₆₇	—	2	1	no	—
194	C₂×C₄×C₆₇	—	2	1	no	—
195	C₂×C₄×C₆₇	—	2	2	no	—
196	C₂×C₄×C₆₇	—	2	2	no	—
197	C₂×C₄×C₆₇	—	2	2	no	—
198	C₂×C₄×C₆₇	—	4	2	no	—
199	C₂×C₄×C₆₇	—	4	2	no	—
200	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
206	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
208	C₂×Dic₆₇	—	2	4	no	—
209	C₂×Dic₆₇	—	4	8	no	—
210	C₂×Dic₆₇	—	4	2	no	—
211	C₂×Dic₆₇	—	4	2	no	—
212	C₈×C₆₇	—	2	1	no	—
213	C₈×C₆₇	—	2	1	no	—
214	C₈×C₆₇	—	2	1	no	—
215	C₈×C₆₇	—	2	1	no	—
216	C₆₇⋊C₈	—	2	2	no	—
217	C₆₇⋊C₈	—	2	2	no	—
218	C₆₇⋊C₈	—	4	2	no	—
219	C₆₇⋊C₈	—	4	2	no	—
220	C₂²×C₆₇	—	2	4	no	—
221	C₂²×C₆₇	—	2	4	no	—
222	C₂²×C₆₇	—	2	1	no	—
223	C₂²×C₆₇	—	2	1	no	—
224	C₂²×C₆₇	—	2	1	no	—
225	C₂²×C₆₇	—	2	1	no	—
226	C₂²×C₆₇	—	2	1	no	—
227	C₂²×C₆₇	—	2	1	no	—
228	C₂²×C₆₇	—	4	2	no	—
229	C₂²×C₆₇	—	4	2	no	—
230	C₂²×C₆₇	—	4	2	no	—
231	C₂²×C₆₇	#443	1	2	yes	—
232	C₂²×C₆₇	#444	1	2	yes	—
233	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
234	C₂²×C₆₇	#538	1	1	yes	characteristic
235	C₂²×C₆₇	#539	1	1	yes	characteristic
236	C₄×C₆₇	—	2	1	no	—
237	C₄×C₆₇	—	2	1	no	—
238	C₄×C₆₇	—	4	2	no	—
239	C₄×C₆₇	—	4	2	no	—
240	C₄×C₆₇	—	4	2	no	—
241	C₄×C₆₇	#518	1	1	yes	characteristic
242	C₄×C₆₇	#520	1	1	yes	characteristic
243	C₄×C₆₇	#534	1	1	yes	characteristic
244	C₄×C₆₇	#537	1	1	yes	characteristic
245	Dic₆₇	—	4	4	no	—
246	#22204	—	67	1	no	maximal, Sylow
247	C₂×C₆₇	—	2	1	no	—
248	C₂×C₆₇	—	2	1	no	—
249	C₂×C₆₇	—	2	2	no	—
250	C₂×C₆₇	—	2	2	no	—
251	C₂×C₆₇	—	8	2	no	—
252	C₂×C₆₇	#2325	1	1	yes	characteristic
253	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
254	C₂×C₆₇	C₂×#444	1	1	yes	characteristic
255	#3050	D₆₇	1	1	yes	characteristic
256	#2929	—	67	2	no	—
257	#1929	—	67	2	no	—
258	#1922	—	67	2	no	—
259	#1896	—	67	2	no	—
260	#1876	—	67	2	no	—
261	#1866	—	67	2	no	—
262	#1810	—	67	1	no	—
263	C₂×#336	—	67	1	no	—
264	C₆₇	#22204	1	1	yes	characteristic, complemented, Sylow
265	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
266	C₂×#131	—	67	2	no	—
267	C₂³×C₈	—	67	1	no	—
268	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
269	#525	C₂×D₆₇	1	2	yes	—
270	C₂²×C₄²	—	67	1	no	—
271	#467	Dic₆₇	1	1	yes	characteristic, complemented
272	#467	Dic₆₇	1	1	yes	characteristic, complemented
273	#466	Dic₆₇	1	1	yes	characteristic, complemented
274	#466	Dic₆₇	1	1	yes	characteristic, complemented
275	#465	Dic₆₇	1	2	yes	complemented
276	#465	Dic₆₇	1	2	yes	complemented
277	#435	—	134	2	no	—
278	#435	—	134	2	no	—
279	C₈×D₄	—	134	2	no	—
280	C₈×D₄	—	134	2	no	—
281	C₂×#108	—	67	1	no	—
282	C₂×#108	—	67	1	no	—
283	#427	C₂×D₆₇	1	1	yes	characteristic
284	#424	—	67	2	no	—
285	C₂×#104	—	67	2	no	—
286	C₂×#104	—	67	2	no	—
287	#416	C₂×D₆₇	1	2	yes	—
288	#408	—	67	2	no	—
289	#407	—	67	2	no	—
290	#405	—	67	2	no	—
291	#341	—	67	2	no	—
292	#339	—	67	2	no	—
293	#339	—	67	2	no	—
294	#336	—	67	2	no	—
295	#336	—	67	2	no	—
296	C₂×#41	C₂²×D₆₇	1	2	yes	—
297	C₂³×C₄	—	134	1	no	—
298	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
299	#135	—	4	1	no	—
300	#135	—	4	1	no	—
301	C₂×Q₁₆	C₂×Dic₆₇	1	1	yes	characteristic, complemented
302	C₂×SD₁₆	C₂×Dic₆₇	1	2	yes	complemented
303	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic, complemented
304	#131	—	268	2	no	—
305	#131	—	268	2	no	—
306	C₂×M₁₆	—	67	2	no	—
307	C₂×M₁₆	—	67	2	no	—
308	C₂×M₁₆	—	134	2	no	—
309	C₂²×C₈	—	4	1	no	—
310	C₂²×C₈	—	4	1	no	—
311	C₂²×C₈	—	268	1	no	—
312	C₂²×C₈	—	268	1	no	—
313	C₂²×C₈	—	67	1	no	—
314	C₂²×C₈	—	67	2	no	—
315	C₂²×C₈	—	67	1	no	—
316	C₂²×C₈	—	67	2	no	—
317	C₂²×C₈	—	134	2	no	—
318	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
319	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
320	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
321	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
322	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
323	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
324	#123	—	2	2	no	—
325	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
326	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
327	#121	C₂×Dic₆₇	1	2	yes	—
328	#121	C₂×Dic₆₇	1	2	yes	—
329	#120	—	2	2	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	#117	C₂²×D₆₇	1	2	yes	—
333	C₂×C₄²	—	268	1	no	—
334	C₂×C₄²	—	268	1	no	—
335	C₂×C₄²	—	67	2	no	—
336	C₂×C₄²	—	134	1	no	—
337	#108	—	268	1	no	—
338	#108	—	268	1	no	—
339	#107	C₂×Dic₆₇	1	1	yes	characteristic, complemented
340	#107	C₂×Dic₆₇	1	1	yes	characteristic, complemented
341	#106	C₂×Dic₆₇	1	2	yes	complemented
342	C₄⋊C₈	—	134	2	no	—
343	C₄⋊C₈	—	134	2	no	—
344	#104	—	268	2	no	—
345	#104	—	268	2	no	—
346	#103	C₂×Dic₆₇	1	2	yes	complemented
347	#103	C₂×Dic₆₇	1	2	yes	complemented
348	#102	C₂×Dic₆₇	1	2	yes	complemented
349	#102	C₂×Dic₆₇	1	2	yes	complemented
350	C₂²⋊C₈	—	134	2	no	—
351	C₂²⋊C₈	—	134	2	no	—
352	C₂²⋊C₈	—	134	2	no	—
353	C₂²⋊C₈	—	134	2	no	—
354	#97	—	134	2	no	—
355	C₄×C₈	—	134	2	no	—
356	C₂⁴	#11761627	1	1	yes	characteristic
357	#41	—	2	2	no	—
358	#41	—	2	2	no	—
359	#41	—	2	2	no	—
360	#41	—	2	2	no	—
361	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	268	2	no	—
372	C₂²×C₄	—	268	2	no	—
373	C₂²×C₄	—	134	4	no	—
374	C₂²×C₄	—	134	2	no	—
375	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
376	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
377	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
378	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
379	C₂²×C₄	#11761627	1	1	yes	characteristic
380	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
381	Q₁₆	—	4	1	no	—
382	SD₁₆	—	4	2	no	—
383	D₈	—	4	1	no	—
384	M₁₆	—	268	4	no	—
385	M₁₆	—	134	2	no	—
386	M₁₆	—	134	2	no	—
387	M₁₆	—	134	2	no	—
388	M₁₆	—	134	2	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	4	1	no	—
394	C₂×C₈	—	4	1	no	—
395	C₂×C₈	—	4	1	no	—
396	C₂×C₈	—	4	1	no	—
397	C₂×C₈	—	268	4	no	—
398	C₂×C₈	—	268	1	no	—
399	C₂×C₈	—	268	2	no	—
400	C₂×C₈	—	268	1	no	—
401	C₂×C₈	—	67	2	no	—
402	C₂×C₈	—	67	2	no	—
403	C₂×C₈	—	134	2	no	—
404	C₂×C₈	—	134	2	no	—
405	C₂×C₈	—	134	2	no	—
406	C₂×C₈	—	134	2	no	—
407	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
408	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
409	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
410	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
414	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	268	2	no	—
422	C₄²	—	134	2	no	—
423	C₄²	—	134	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	2	no	—
429	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
430	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
431	C₂³	C₂×#11761627	1	1	yes	characteristic
432	Q₈	—	2	2	no	—
433	Q₈	—	2	2	no	—
434	D₄	—	2	2	no	—
435	D₄	—	2	2	no	—
436	D₄	—	4	4	no	—
437	D₄	—	4	4	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	2	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	268	8	no	—
456	C₂×C₄	—	268	2	no	—
457	C₂×C₄	—	268	2	no	—
458	C₂×C₄	—	134	4	no	—
459	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
460	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
461	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
462	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
463	C₂×C₄	#14524088	1	1	yes	characteristic
464	C₂×C₄	#14524088	1	1	yes	characteristic
465	C₂×C₄	#14524089	1	1	yes	characteristic
466	C₂×C₄	#14524090	1	1	yes	characteristic
467	C₈	—	2	1	no	—
468	C₈	—	2	1	no	—
469	C₈	—	2	1	no	—
470	C₈	—	2	1	no	—
471	C₈	—	268	2	no	—
472	C₈	—	268	2	no	—
473	C₈	—	134	2	no	—
474	C₈	—	134	2	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	#16863513	1	2	yes	—
487	C₂²	#16863518	1	2	yes	—
488	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
489	C₂²	#16863983	1	1	yes	characteristic
490	C₂²	#16863991	1	1	yes	characteristic
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	268	4	no	—
497	C₄	#16863871	1	1	yes	characteristic
498	C₄	#16863879	1	1	yes	characteristic
499	C₄	#16863954	1	1	yes	characteristic
500	C₄	#16863973	1	1	yes	characteristic
501	C₂	—	2	1	no	—
502	C₂	—	2	2	no	—
503	C₂	—	2	2	no	—
504	C₂	—	2	1	no	—
505	C₂	—	8	2	no	—
506	C₂	#22562914	1	1	yes	characteristic
507	C₂	C₂×#16863513	1	1	yes	characteristic
508	C₂	C₂×#16863518	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×#3050	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#3050	D₆₇
hypocenter	C₆₇	#22204
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3050

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. #22560653	C₂	semidirect
5. #22560538	C₂	semidirect
6. #22560486	C₂	semidirect
7. #22560247	C₂	semidirect
8. C₂×#16863150	C₂	semidirect
33. #467×C₆₇	C₄	semidirect
34. #467×C₆₇	C₄	semidirect
35. #466×C₆₇	C₄	semidirect
36. #466×C₆₇	C₄	semidirect
37. #465×C₆₇	C₄	semidirect
38. #465×C₆₇	C₄	semidirect
74. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
75. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
76. C₂×D₈×C₆₇	C₂×C₄	semidirect
94. #107×C₆₇	C₂×C₄	semidirect
95. #107×C₆₇	C₂×C₄	semidirect
96. #106×C₆₇	C₂×C₄	semidirect
97. #103×C₆₇	C₂×C₄	semidirect
98. #103×C₆₇	C₂×C₄	semidirect
99. #102×C₆₇	C₂×C₄	semidirect
100. #102×C₆₇	C₂×C₄	semidirect
264. C₆₇	#22204	semidirect
271. #467	Dic₆₇	semidirect
272. #467	Dic₆₇	semidirect
273. #466	Dic₆₇	semidirect
274. #466	Dic₆₇	semidirect
275. #465	Dic₆₇	semidirect
276. #465	Dic₆₇	semidirect
301. C₂×Q₁₆	C₂×Dic₆₇	semidirect
302. C₂×SD₁₆	C₂×Dic₆₇	semidirect
303. C₂×D₈	C₂×Dic₆₇	semidirect
339. #107	C₂×Dic₆₇	semidirect
340. #107	C₂×Dic₆₇	semidirect
341. #106	C₂×Dic₆₇	semidirect
346. #103	C₂×Dic₆₇	semidirect
347. #103	C₂×Dic₆₇	semidirect
348. #102	C₂×Dic₆₇	semidirect
349. #102	C₂×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
#22560653	2
#22560538	2
#22560486	2
#22560247	2
C₂×#16863150	2
C₆₇×#3050	2
#22204	67