Subgroups — #30875293

Order 17152.

752 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	#22568875	C₂	1	1	yes	maximal, characteristic, complemented
2	#22568777	C₂	1	1	yes	maximal, characteristic, complemented
3	#22560915	C₂	1	2	yes	maximal, complemented
4	#22560810	C₂	1	2	yes	maximal, complemented
5	#22560538	C₂	1	2	yes	maximal
6	#22560347	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560229	C₂	1	1	yes	maximal, characteristic, complemented
8	#22560229	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₄⋊Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560049	C₂	1	2	yes	maximal, complemented
11	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#14524050	C₂²	1	2	yes	—
13	#16863457	—	2	2	no	—
14	#16863453	—	2	1	no	—
15	#16863449	—	2	1	no	—
16	#16863423	—	2	2	no	—
17	#16863423	C₂²	1	2	yes	—
18	#16863420	—	2	1	no	—
19	#16863420	C₂²	1	1	yes	characteristic
20	#16863420	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
22	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×#14523970	C₂²	1	2	yes	—
24	C₂×#14523970	C₂²	1	2	yes	—
25	#16863363	C₂²	1	2	yes	—
26	#16863352	C₂²	1	2	yes	—
27	C₂×C₈×Dic₆₇	C₂²	1	2	yes	—
28	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
29	#16863161	C₂²	1	2	yes	—
30	#16863161	C₂²	1	2	yes	—
31	#16863155	C₂²	1	2	yes	—
32	#16863155	C₂²	1	2	yes	—
33	#16863150	C₂²	1	2	yes	—
34	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
35	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
36	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
37	C₄×Q₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
38	C₄×Q₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
39	C₄×SD₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
40	C₄×SD₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
41	C₄×SD₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
42	C₄×SD₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
43	C₄×D₈×C₆₇	C₄	1	1	yes	characteristic, complemented
44	C₄×D₈×C₆₇	C₄	1	1	yes	characteristic, complemented
45	#427×C₆₇	C₂²	1	1	yes	characteristic
46	#416×C₆₇	C₂²	1	1	yes	characteristic
47	#416×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
49	#14524050	—	2	4	no	—
50	#14524050	—	4	2	no	—
51	C₂×#11761612	—	2	2	no	—
52	C₂×#11761612	C₂³	1	2	yes	—
53	C₂×#11761612	C₂³	1	2	yes	—
54	C₂²×C₆₇⋊C₈	—	2	2	no	—
55	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
56	C₂×C₄⋊Dic₆₇	—	2	1	no	—
57	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
58	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
59	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
60	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
61	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
62	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
63	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
64	C₄⋊(C₆₇⋊C₈)	D₄	1	1	yes	characteristic
65	C₄⋊(C₆₇⋊C₈)	D₄	1	1	yes	characteristic
66	C₄⋊(C₆₇⋊C₈)	D₄	1	2	yes	—
67	#14523970	—	2	4	no	—
68	#14523970	—	4	2	no	—
69	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
70	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
71	#14523954	—	2	2	no	—
72	C₄×C₆₇⋊C₈	—	2	2	no	—
73	C₈×Dic₆₇	—	4	2	no	—
74	C₆₇⋊#95	—	2	1	no	—
75	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
76	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
77	#135×C₆₇	—	2	2	no	—
78	#135×C₆₇	—	2	2	no	—
79	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
80	C₂×SD₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
81	C₂×SD₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
82	C₂×D₈×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	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
87	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
88	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
89	C₄×D₄×C₆₇	—	2	1	no	—
90	C₄×D₄×C₆₇	—	2	1	no	—
91	C₄×D₄×C₆₇	—	2	1	no	—
92	C₄×D₄×C₆₇	—	2	1	no	—
93	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
94	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
95	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
96	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
97	#117×C₆₇	—	2	1	no	—
98	#117×C₆₇	—	2	1	no	—
99	#117×C₆₇	C₂³	1	1	yes	characteristic
100	#117×C₆₇	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₆₇	—	2	1	no	—
102	C₂×C₄²×C₆₇	—	2	1	no	—
103	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
104	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
105	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
106	#106×C₆₇	C₂×C₄	1	1	yes	characteristic
107	#106×C₆₇	C₂×C₄	1	1	yes	characteristic
108	#103×C₆₇	C₂×C₄	1	1	yes	characteristic
109	#103×C₆₇	C₂×C₄	1	1	yes	characteristic
110	#103×C₆₇	C₂×C₄	1	1	yes	characteristic
111	#103×C₆₇	C₂×C₄	1	1	yes	characteristic
112	#102×C₆₇	C₂×C₄	1	1	yes	characteristic
113	#102×C₆₇	C₂×C₄	1	1	yes	characteristic
114	#102×C₆₇	C₂×C₄	1	1	yes	characteristic
115	#102×C₆₇	C₂×C₄	1	1	yes	characteristic
116	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
117	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
118	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
119	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
120	C₂²×Dic₆₇	—	2	2	no	—
121	#11761612	—	2	2	no	—
122	#11761612	—	2	2	no	—
123	#11761612	—	2	2	no	—
124	#11761612	—	2	2	no	—
125	#11761612	—	4	4	no	—
126	C₂×C₆₇⋊C₈	—	2	2	no	—
127	C₂×C₆₇⋊C₈	—	2	2	no	—
128	C₂×C₆₇⋊C₈	—	2	2	no	—
129	C₂×C₆₇⋊C₈	—	2	2	no	—
130	C₂×C₆₇⋊C₈	—	4	4	no	—
131	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
132	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
133	C₄⋊Dic₆₇	—	2	4	no	—
134	C₄×Dic₆₇	—	2	2	no	—
135	C₄×Dic₆₇	—	2	2	no	—
136	#41×C₆₇	—	2	1	no	—
137	#41×C₆₇	—	2	1	no	—
138	#41×C₆₇	—	2	1	no	—
139	#41×C₆₇	—	2	1	no	—
140	#41×C₆₇	—	2	1	no	—
141	#41×C₆₇	—	2	1	no	—
142	#41×C₆₇	#41	1	2	yes	—
143	#41×C₆₇	#41	1	2	yes	—
144	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×D₄×C₆₇	—	2	1	no	—
147	C₂×D₄×C₆₇	—	2	1	no	—
148	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
149	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₇	—	2	1	no	—
151	C₂²×C₄×C₆₇	—	2	1	no	—
152	C₂²×C₄×C₆₇	—	2	1	no	—
153	C₂²×C₄×C₆₇	—	2	1	no	—
154	C₂²×C₄×C₆₇	—	2	1	no	—
155	C₂²×C₄×C₆₇	—	2	1	no	—
156	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
157	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
158	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
159	Q₁₆×C₆₇	—	2	2	no	—
160	SD₁₆×C₆₇	—	2	2	no	—
161	SD₁₆×C₆₇	—	2	2	no	—
162	D₈×C₆₇	—	2	2	no	—
163	C₂×C₈×C₆₇	—	2	1	no	—
164	C₂×C₈×C₆₇	—	2	1	no	—
165	C₂×C₈×C₆₇	—	2	1	no	—
166	C₂×C₈×C₆₇	—	2	1	no	—
167	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
171	C₄⋊C₄×C₆₇	—	2	1	no	—
172	C₄⋊C₄×C₆₇	—	2	1	no	—
173	C₄⋊C₄×C₆₇	—	2	1	no	—
174	C₄⋊C₄×C₆₇	—	2	1	no	—
175	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
176	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
177	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
178	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
179	C₂²⋊C₄×C₆₇	—	2	1	no	—
180	C₂²⋊C₄×C₆₇	—	2	1	no	—
181	C₂²⋊C₄×C₆₇	—	2	1	no	—
182	C₂²⋊C₄×C₆₇	—	2	1	no	—
183	C₂²⋊C₄×C₆₇	—	2	1	no	—
184	C₂²⋊C₄×C₆₇	—	2	1	no	—
185	C₄²×C₆₇	—	2	1	no	—
186	C₄²×C₆₇	—	2	1	no	—
187	C₄²×C₆₇	—	2	1	no	—
188	C₄²×C₆₇	—	2	1	no	—
189	C₄²×C₆₇	—	2	1	no	—
190	C₄²×C₆₇	—	2	1	no	—
191	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
192	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
193	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
195	C₂³×C₆₇	—	2	1	no	—
196	C₂³×C₆₇	—	2	1	no	—
197	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
198	Q₈×C₆₇	—	2	1	no	—
199	Q₈×C₆₇	—	2	1	no	—
200	Q₈×C₆₇	—	2	1	no	—
201	Q₈×C₆₇	#117	1	2	yes	—
202	D₄×C₆₇	—	2	2	no	—
203	D₄×C₆₇	—	2	2	no	—
204	D₄×C₆₇	—	2	1	no	—
205	D₄×C₆₇	—	2	1	no	—
206	D₄×C₆₇	—	2	1	no	—
207	D₄×C₆₇	—	4	1	no	—
208	D₄×C₆₇	—	4	1	no	—
209	D₄×C₆₇	#117	1	2	yes	—
210	C₂×C₄×C₆₇	—	2	1	no	—
211	C₂×C₄×C₆₇	—	2	2	no	—
212	C₂×C₄×C₆₇	—	2	2	no	—
213	C₂×C₄×C₆₇	—	2	2	no	—
214	C₂×C₄×C₆₇	—	2	1	no	—
215	C₂×C₄×C₆₇	—	2	1	no	—
216	C₂×C₄×C₆₇	—	2	1	no	—
217	C₂×C₄×C₆₇	—	2	1	no	—
218	C₂×C₄×C₆₇	—	2	1	no	—
219	C₂×C₄×C₆₇	—	4	1	no	—
220	C₂×C₄×C₆₇	—	4	1	no	—
221	C₂×C₄×C₆₇	—	4	1	no	—
222	C₂×C₄×C₆₇	—	4	2	no	—
223	C₂×C₄×C₆₇	—	4	2	no	—
224	C₂×C₄×C₆₇	—	8	1	no	—
225	C₂×C₄×C₆₇	—	8	1	no	—
226	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
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	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
236	C₂×Dic₆₇	—	2	4	no	—
237	C₂×Dic₆₇	—	4	2	no	—
238	C₂×Dic₆₇	—	4	2	no	—
239	C₈×C₆₇	—	2	1	no	—
240	C₈×C₆₇	—	2	1	no	—
241	C₈×C₆₇	—	2	1	no	—
242	C₈×C₆₇	—	2	1	no	—
243	C₆₇⋊C₈	—	2	2	no	—
244	C₆₇⋊C₈	—	2	2	no	—
245	C₆₇⋊C₈	—	4	2	no	—
246	C₆₇⋊C₈	—	4	2	no	—
247	C₂²×C₆₇	—	2	1	no	—
248	C₂²×C₆₇	—	2	1	no	—
249	C₂²×C₆₇	—	2	2	no	—
250	C₂²×C₆₇	—	4	1	no	—
251	C₂²×C₆₇	—	4	1	no	—
252	C₂²×C₆₇	—	4	1	no	—
253	C₂²×C₆₇	—	4	1	no	—
254	C₂²×C₆₇	—	4	1	no	—
255	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
256	C₂²×C₆₇	#552	1	1	yes	characteristic
257	C₂²×C₆₇	#553	1	1	yes	characteristic
258	C₄×C₆₇	—	2	2	no	—
259	C₄×C₆₇	—	2	1	no	—
260	C₄×C₆₇	—	2	1	no	—
261	C₄×C₆₇	—	2	1	no	—
262	C₄×C₆₇	—	4	1	no	—
263	C₄×C₆₇	—	4	1	no	—
264	C₄×C₆₇	—	4	1	no	—
265	C₄×C₆₇	—	4	1	no	—
266	C₄×C₆₇	—	4	1	no	—
267	C₄×C₆₇	#443	1	2	yes	—
268	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
269	C₄×C₆₇	#520	1	1	yes	characteristic
270	C₄×C₆₇	#546	1	1	yes	characteristic
271	C₄×C₆₇	#548	1	1	yes	characteristic
272	Dic₆₇	—	4	4	no	—
273	#22783	—	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	1	no	—
278	C₂×C₆₇	#2352	1	1	yes	characteristic
279	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
280	C₂×C₆₇	#2957	1	1	yes	characteristic
281	C₄×#135	D₆₇	1	1	yes	characteristic
282	#2925	—	67	1	no	—
283	#2906	—	67	1	no	—
284	#1937	—	67	2	no	—
285	#1922	—	67	2	no	—
286	#1876	—	67	2	no	—
287	#1837	—	67	1	no	—
288	#1806	—	67	1	no	—
289	#1806	—	67	1	no	—
290	C₈×C₄⋊C₄	—	67	1	no	—
291	#1764	—	67	2	no	—
292	C₆₇	#22783	1	1	yes	characteristic, complemented, Sylow
293	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
294	C₂×#131	—	67	2	no	—
295	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
296	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
297	C₄×Q₁₆	Dic₆₇	1	1	yes	characteristic, complemented
298	C₄×Q₁₆	Dic₆₇	1	1	yes	characteristic, complemented
299	C₄×SD₁₆	Dic₆₇	1	1	yes	characteristic, complemented
300	C₄×SD₁₆	Dic₆₇	1	1	yes	characteristic, complemented
301	C₄×SD₁₆	Dic₆₇	1	1	yes	characteristic, complemented
302	C₄×SD₁₆	Dic₆₇	1	1	yes	characteristic, complemented
303	C₄×D₈	Dic₆₇	1	1	yes	characteristic, complemented
304	C₄×D₈	Dic₆₇	1	1	yes	characteristic, complemented
305	#433	—	134	2	no	—
306	#432	—	134	1	no	—
307	#431	—	134	1	no	—
308	#427	C₂×D₆₇	1	1	yes	characteristic
309	#424	—	67	2	no	—
310	#424	—	134	2	no	—
311	#423	—	67	1	no	—
312	#423	—	67	1	no	—
313	#423	—	134	1	no	—
314	C₂×C₄⋊C₈	—	67	1	no	—
315	C₂×C₄⋊C₈	—	134	1	no	—
316	C₂×#104	—	67	2	no	—
317	C₂×#104	—	67	2	no	—
318	#416	C₂×D₆₇	1	1	yes	characteristic
319	#416	C₂×D₆₇	1	1	yes	characteristic
320	#408	—	67	2	no	—
321	#405	—	67	2	no	—
322	C₂×C₄×C₈	—	67	2	no	—
323	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
324	C₄×C₄⋊C₄	—	67	1	no	—
325	#341	—	67	2	no	—
326	#341	—	67	2	no	—
327	#339	—	67	2	no	—
328	#339	—	67	2	no	—
329	#336	—	67	2	no	—
330	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
331	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
332	#135	—	2	2	no	—
333	#135	—	2	2	no	—
334	C₂×Q₁₆	C₂×Dic₆₇	1	1	yes	characteristic
335	C₂×SD₁₆	C₂×Dic₆₇	1	1	yes	characteristic
336	C₂×SD₁₆	C₂×Dic₆₇	1	1	yes	characteristic
337	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic
338	#131	—	268	2	no	—
339	#131	—	134	4	no	—
340	C₂×M₁₆	—	67	2	no	—
341	C₂×M₁₆	—	67	2	no	—
342	C₂×M₁₆	—	134	2	no	—
343	C₂²×C₈	—	67	2	no	—
344	C₂²×C₈	—	134	2	no	—
345	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
346	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
347	C₄×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
348	C₄×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
349	C₄×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
350	C₄×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
351	C₄×D₄	—	2	1	no	—
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	—	2	1	no	—
355	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
356	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
357	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
358	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
359	#117	—	2	1	no	—
360	#117	—	2	1	no	—
361	#117	C₂²×D₆₇	1	1	yes	characteristic
362	#117	C₂²×D₆₇	1	1	yes	characteristic
363	C₂×C₄⋊C₄	—	134	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	—	67	2	no	—
367	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
368	#107	C₂×Dic₆₇	1	1	yes	characteristic
369	#107	C₂×Dic₆₇	1	1	yes	characteristic
370	#106	C₂×Dic₆₇	1	1	yes	characteristic
371	#106	C₂×Dic₆₇	1	1	yes	characteristic
372	C₄⋊C₈	—	67	1	no	—
373	C₄⋊C₈	—	67	1	no	—
374	C₄⋊C₈	—	67	2	no	—
375	C₄⋊C₈	—	134	2	no	—
376	C₄⋊C₈	—	134	2	no	—
377	C₄⋊C₈	—	134	1	no	—
378	C₄⋊C₈	—	134	1	no	—
379	C₄⋊C₈	—	134	1	no	—
380	C₄⋊C₈	—	134	1	no	—
381	#104	—	268	2	no	—
382	#104	—	134	4	no	—
383	#103	C₂×Dic₆₇	1	1	yes	characteristic
384	#103	C₂×Dic₆₇	1	1	yes	characteristic
385	#103	C₂×Dic₆₇	1	1	yes	characteristic
386	#103	C₂×Dic₆₇	1	1	yes	characteristic
387	#102	C₂×Dic₆₇	1	1	yes	characteristic
388	#102	C₂×Dic₆₇	1	1	yes	characteristic
389	#102	C₂×Dic₆₇	1	1	yes	characteristic
390	#102	C₂×Dic₆₇	1	1	yes	characteristic
391	C₂²⋊C₈	—	134	2	no	—
392	C₂²⋊C₈	—	134	2	no	—
393	#97	—	134	2	no	—
394	C₄×C₈	—	268	2	no	—
395	C₄×C₈	—	134	2	no	—
396	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
397	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
398	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
399	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
400	#95	—	134	1	no	—
401	#41	—	2	1	no	—
402	#41	—	2	1	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	2	1	no	—
406	#41	—	2	1	no	—
407	#41	#11761628	1	2	yes	—
408	#41	#11761628	1	2	yes	—
409	C₂×Q₈	C₂²×Dic₆₇	1	1	yes	characteristic
410	C₂×Q₈	C₂²×Dic₆₇	1	1	yes	characteristic
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
414	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	134	2	no	—
422	C₂²×C₄	#11761627	1	1	yes	characteristic
423	C₂²×C₄	#11761627	1	1	yes	characteristic
424	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
425	Q₁₆	—	2	2	no	—
426	SD₁₆	—	2	2	no	—
427	SD₁₆	—	2	2	no	—
428	D₈	—	2	2	no	—
429	M₁₆	—	268	4	no	—
430	M₁₆	—	134	2	no	—
431	M₁₆	—	134	2	no	—
432	M₁₆	—	134	2	no	—
433	M₁₆	—	134	2	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	268	4	no	—
439	C₂×C₈	—	67	2	no	—
440	C₂×C₈	—	67	2	no	—
441	C₂×C₈	—	134	2	no	—
442	C₂×C₈	—	134	2	no	—
443	C₂×C₈	—	134	2	no	—
444	C₂×C₈	—	134	2	no	—
445	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
446	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
447	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
448	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	134	4	no	—
454	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
455	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
456	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
457	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	134	2	no	—
471	C₄²	—	134	2	no	—
472	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
473	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
474	C₄²	D₄×D₆₇	1	1	yes	characteristic
475	C₄²	D₄×D₆₇	1	1	yes	characteristic
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	C₂×#11761627	1	1	yes	characteristic
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	2	1	no	—
482	Q₈	#14524002	1	2	yes	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	1	no	—
486	D₄	—	2	1	no	—
487	D₄	—	2	1	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	1	no	—
490	D₄	#14524002	1	2	yes	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	8	1	no	—
506	C₂×C₄	—	8	1	no	—
507	C₂×C₄	—	268	2	no	—
508	C₂×C₄	—	268	2	no	—
509	C₂×C₄	—	134	4	no	—
510	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
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	C₂³×Dic₆₇	1	1	yes	characteristic
515	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
516	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
517	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
518	C₂×C₄	#14524089	1	1	yes	characteristic
519	C₂×C₄	#14524090	1	1	yes	characteristic
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	268	2	no	—
525	C₈	—	268	2	no	—
526	C₈	—	134	2	no	—
527	C₈	—	134	2	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
537	C₂²	#16864086	1	1	yes	characteristic
538	C₂²	#16864092	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	268	4	no	—
549	C₄	#16863513	1	2	yes	—
550	C₄	C₂×#14524002	1	1	yes	characteristic
551	C₄	#16863879	1	1	yes	characteristic
552	C₄	#16864042	1	1	yes	characteristic
553	C₄	#16864055	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	1	no	—
558	C₂	#22563138	1	1	yes	characteristic
559	C₂	C₂×#16863513	1	1	yes	characteristic
560	C₂	#22569126	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	C₄×#135×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#135×C₆₇	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₄×#135	D₆₇
hypocenter	C₆₇	#22783
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #22568875	C₂	semidirect
2. #22568777	C₂	semidirect
3. #22560915	C₂	semidirect
4. #22560810	C₂	semidirect
6. #22560347	C₂	semidirect
7. #22560229	C₂	semidirect
8. #22560229	C₂	semidirect
9. C₈×C₄⋊Dic₆₇	C₂	semidirect
10. #22560049	C₂	semidirect
37. C₄×Q₁₆×C₆₇	C₄	semidirect
38. C₄×Q₁₆×C₆₇	C₄	semidirect
39. C₄×SD₁₆×C₆₇	C₄	semidirect
40. C₄×SD₁₆×C₆₇	C₄	semidirect
41. C₄×SD₁₆×C₆₇	C₄	semidirect
42. C₄×SD₁₆×C₆₇	C₄	semidirect
43. C₄×D₈×C₆₇	C₄	semidirect
44. C₄×D₈×C₆₇	C₄	semidirect
292. C₆₇	#22783	semidirect
297. C₄×Q₁₆	Dic₆₇	semidirect
298. C₄×Q₁₆	Dic₆₇	semidirect
299. C₄×SD₁₆	Dic₆₇	semidirect
300. C₄×SD₁₆	Dic₆₇	semidirect
301. C₄×SD₁₆	Dic₆₇	semidirect
302. C₄×SD₁₆	Dic₆₇	semidirect
303. C₄×D₈	Dic₆₇	semidirect
304. C₄×D₈	Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22568875	2
#22568777	2
#22560915	2
#22560810	2
#22560538	2
#22560347	2
#22560229	2
C₈×C₄⋊Dic₆₇	2
#22560049	2
C₄×#135×C₆₇	2
#22783	67