Subgroups — #30878378

Order 17152.

892 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863513	C₂	1	1	yes	maximal, characteristic, complemented
2	#22568936	C₂	1	2	yes	maximal, complemented
3	C₂²×#14523979	C₂	1	1	yes	maximal, characteristic, complemented
4	#22561098	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560958	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560859	C₂	1	2	yes	maximal, complemented
7	#22560512	C₂	1	2	yes	maximal, complemented
8	#22560486	C₂	1	2	yes	maximal, complemented
9	#22560090	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₂²⋊Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3050	C₂	1	1	yes	maximal, characteristic
12	C₂×#14524050	C₂²	1	2	yes	—
13	C₂²×#11761612	C₂²	1	2	yes	—
14	#16863513	—	2	4	no	—
15	#16863474	—	2	2	no	—
16	#16863468	—	2	2	no	—
17	#16863468	—	2	2	no	—
18	D₄×C₆₇⋊C₈	—	2	2	no	—
19	C₂×#14523979	—	2	4	no	—
20	C₂×#14523979	C₂²	1	1	yes	characteristic
21	C₂×#14523979	C₂²	1	2	yes	—
22	C₂×#14523979	C₂²	1	1	yes	characteristic
23	#16863423	C₂²	1	2	yes	—
24	C₂×#14523970	C₂²	1	2	yes	—
25	C₂×#14523970	C₂²	1	2	yes	—
26	#16863363	C₂²	1	2	yes	—
27	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
28	#16863352	C₂²	1	2	yes	—
29	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
31	C₄×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
32	#16863155	C₂²	1	2	yes	—
33	#16863155	C₂²	1	2	yes	—
34	#16863150	C₂²	1	1	yes	characteristic
35	#16863150	C₂²	1	1	yes	characteristic
36	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
37	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
38	#525×C₆₇	C₂²	1	2	yes	—
39	#467×C₆₇	C₄	1	1	yes	characteristic, complemented
40	#467×C₆₇	C₄	1	1	yes	characteristic, complemented
41	#466×C₆₇	C₄	1	1	yes	characteristic, complemented
42	#466×C₆₇	C₄	1	1	yes	characteristic, complemented
43	#465×C₆₇	C₄	1	2	yes	complemented
44	#465×C₆₇	C₄	1	2	yes	complemented
45	#427×C₆₇	C₂²	1	1	yes	characteristic
46	#416×C₆₇	C₂²	1	2	yes	—
47	#14524050	—	2	4	no	—
48	#14524050	—	4	2	no	—
49	C₂×#11761612	—	2	2	no	—
50	C₂×#11761612	—	2	4	no	—
51	C₂×#11761612	—	2	2	no	—
52	C₂×#11761612	—	4	2	no	—
53	C₂×#11761612	C₂³	1	2	yes	—
54	C₂×#11761612	C₂³	1	2	yes	—
55	C₂²×C₆₇⋊C₈	—	2	2	no	—
56	C₂²×C₆₇⋊C₈	—	2	2	no	—
57	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
60	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
61	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
62	#14523979	—	2	4	no	—
63	#14523979	—	2	2	no	—
64	#14523979	D₄	1	4	yes	complemented
65	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
66	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
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	C₂²⋊(C₆₇⋊C₈)	D₄	1	1	yes	characteristic
72	C₂²⋊(C₆₇⋊C₈)	D₄	1	1	yes	characteristic
73	C₂²⋊(C₆₇⋊C₈)	D₄	1	1	yes	characteristic
74	C₂²⋊(C₆₇⋊C₈)	D₄	1	1	yes	characteristic
75	#14523954	—	2	2	no	—
76	C₄×C₆₇⋊C₈	—	2	2	no	—
77	C₈×Dic₆₇	—	2	2	no	—
78	C₈×Dic₆₇	—	2	2	no	—
79	C₆₇⋊#95	—	2	1	no	—
80	C₂×#41×C₆₇	C₂³	1	2	yes	—
81	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
82	#135×C₆₇	—	2	2	no	—
83	#135×C₆₇	—	2	2	no	—
84	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
85	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
86	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₆₇	—	2	2	no	—
88	C₂²×C₈×C₆₇	—	2	2	no	—
89	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
91	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
92	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
93	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	#123×C₆₇	—	2	2	no	—
96	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
97	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
98	#121×C₆₇	C₂×C₄	1	2	yes	—
99	#121×C₆₇	C₂×C₄	1	2	yes	—
100	#120×C₆₇	—	2	2	no	—
101	C₄×D₄×C₆₇	—	2	2	no	—
102	C₄×D₄×C₆₇	—	2	2	no	—
103	#117×C₆₇	C₂³	1	2	yes	—
104	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
105	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
106	#106×C₆₇	C₂×C₄	1	2	yes	—
107	#103×C₆₇	C₂×C₄	1	2	yes	—
108	#103×C₆₇	C₂×C₄	1	2	yes	—
109	#102×C₆₇	C₂×C₄	1	2	yes	—
110	#102×C₆₇	C₂×C₄	1	2	yes	—
111	C₂²×Dic₆₇	—	2	1	no	—
112	C₂²×Dic₆₇	—	2	1	no	—
113	#11761612	—	2	2	no	—
114	#11761612	—	2	2	no	—
115	#11761612	—	2	2	no	—
116	#11761612	—	4	4	no	—
117	#11761612	—	4	4	no	—
118	#11761612	C₂×D₄	1	4	yes	—
119	C₂×C₆₇⋊C₈	—	2	1	no	—
120	C₂×C₆₇⋊C₈	—	2	2	no	—
121	C₂×C₆₇⋊C₈	—	2	1	no	—
122	C₂×C₆₇⋊C₈	—	2	1	no	—
123	C₂×C₆₇⋊C₈	—	2	1	no	—
124	C₂×C₆₇⋊C₈	—	2	2	no	—
125	C₂×C₆₇⋊C₈	—	4	4	no	—
126	C₂×C₆₇⋊C₈	—	4	4	no	—
127	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
128	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
129	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
130	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
131	C₂²⋊Dic₆₇	—	2	4	no	—
132	C₄×Dic₆₇	—	2	1	no	—
133	C₄×Dic₆₇	—	2	1	no	—
134	C₄×Dic₆₇	—	2	1	no	—
135	C₄×Dic₆₇	—	2	1	no	—
136	C₂⁴×C₆₇	#41	1	1	yes	characteristic
137	#41×C₆₇	—	2	2	no	—
138	#41×C₆₇	—	2	2	no	—
139	#41×C₆₇	—	2	2	no	—
140	#41×C₆₇	—	2	2	no	—
141	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
142	C₂×D₄×C₆₇	—	2	2	no	—
143	C₂×D₄×C₆₇	—	2	2	no	—
144	C₂×D₄×C₆₇	—	2	2	no	—
145	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
146	C₂²×C₄×C₆₇	—	2	1	no	—
147	C₂²×C₄×C₆₇	—	2	1	no	—
148	C₂²×C₄×C₆₇	—	2	1	no	—
149	C₂²×C₄×C₆₇	—	2	1	no	—
150	C₂²×C₄×C₆₇	—	2	2	no	—
151	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₆₇	C₂²×C₄	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	#41	1	1	yes	characteristic
156	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
157	Q₁₆×C₆₇	—	2	2	no	—
158	SD₁₆×C₆₇	—	2	4	no	—
159	D₈×C₆₇	—	2	2	no	—
160	C₂×C₈×C₆₇	—	2	1	no	—
161	C₂×C₈×C₆₇	—	2	1	no	—
162	C₂×C₈×C₆₇	—	2	2	no	—
163	C₂×C₈×C₆₇	—	2	2	no	—
164	C₂×C₈×C₆₇	—	2	2	no	—
165	C₂×C₈×C₆₇	—	2	2	no	—
166	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₆₇	#41	1	2	yes	—
172	C₄⋊C₄×C₆₇	—	2	2	no	—
173	C₄⋊C₄×C₆₇	—	2	2	no	—
174	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
175	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
176	C₂²⋊C₄×C₆₇	—	2	2	no	—
177	C₂²⋊C₄×C₆₇	—	2	2	no	—
178	C₂²⋊C₄×C₆₇	—	2	2	no	—
179	C₂²⋊C₄×C₆₇	—	2	2	no	—
180	C₂²⋊C₄×C₆₇	—	2	2	no	—
181	C₄²×C₆₇	—	2	2	no	—
182	C₂³×C₆₇	—	2	1	no	—
183	C₂³×C₆₇	—	2	1	no	—
184	C₂³×C₆₇	—	2	2	no	—
185	C₂³×C₆₇	—	2	2	no	—
186	C₂³×C₆₇	—	4	1	no	—
187	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
188	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
189	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
190	Q₈×C₆₇	—	2	2	no	—
191	Q₈×C₆₇	—	2	2	no	—
192	D₄×C₆₇	—	2	2	no	—
193	D₄×C₆₇	—	2	2	no	—
194	D₄×C₆₇	—	4	2	no	—
195	D₄×C₆₇	—	4	2	no	—
196	D₄×C₆₇	—	4	4	no	—
197	D₄×C₆₇	—	8	2	no	—
198	C₂×C₄×C₆₇	—	2	1	no	—
199	C₂×C₄×C₆₇	—	2	1	no	—
200	C₂×C₄×C₆₇	—	2	1	no	—
201	C₂×C₄×C₆₇	—	2	1	no	—
202	C₂×C₄×C₆₇	—	2	1	no	—
203	C₂×C₄×C₆₇	—	2	1	no	—
204	C₂×C₄×C₆₇	—	2	1	no	—
205	C₂×C₄×C₆₇	—	2	1	no	—
206	C₂×C₄×C₆₇	—	2	1	no	—
207	C₂×C₄×C₆₇	—	2	1	no	—
208	C₂×C₄×C₆₇	—	2	2	no	—
209	C₂×C₄×C₆₇	—	2	2	no	—
210	C₂×C₄×C₆₇	—	2	2	no	—
211	C₂×C₄×C₆₇	—	4	2	no	—
212	C₂×C₄×C₆₇	—	4	2	no	—
213	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
220	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
221	C₂×Dic₆₇	—	2	2	no	—
222	C₂×Dic₆₇	—	2	2	no	—
223	C₂×Dic₆₇	—	4	1	no	—
224	C₂×Dic₆₇	—	4	1	no	—
225	C₂×Dic₆₇	—	4	1	no	—
226	C₂×Dic₆₇	—	4	1	no	—
227	C₈×C₆₇	—	2	1	no	—
228	C₈×C₆₇	—	2	1	no	—
229	C₈×C₆₇	C₄×D₄	1	2	yes	—
230	C₈×C₆₇	C₄×D₄	1	2	yes	—
231	C₆₇⋊C₈	—	2	1	no	—
232	C₆₇⋊C₈	—	2	1	no	—
233	C₆₇⋊C₈	—	2	4	no	—
234	C₆₇⋊C₈	—	2	1	no	—
235	C₆₇⋊C₈	—	2	1	no	—
236	C₆₇⋊C₈	—	4	2	no	—
237	C₂²×C₆₇	—	2	1	no	—
238	C₂²×C₆₇	—	2	1	no	—
239	C₂²×C₆₇	—	2	1	no	—
240	C₂²×C₆₇	—	2	1	no	—
241	C₂²×C₆₇	—	2	1	no	—
242	C₂²×C₆₇	—	2	1	no	—
243	C₂²×C₆₇	—	2	1	no	—
244	C₂²×C₆₇	—	4	2	no	—
245	C₂²×C₆₇	—	4	2	no	—
246	C₂²×C₆₇	—	4	2	no	—
247	C₂²×C₆₇	—	4	2	no	—
248	C₂²×C₆₇	—	4	2	no	—
249	C₂²×C₆₇	#443	1	2	yes	complemented
250	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂²×C₆₇	#548	1	1	yes	characteristic
252	C₂²×C₆₇	#553	1	1	yes	characteristic
253	C₄×C₆₇	—	2	1	no	—
254	C₄×C₆₇	—	2	1	no	—
255	C₄×C₆₇	—	4	2	no	—
256	C₄×C₆₇	—	4	2	no	—
257	C₄×C₆₇	—	4	2	no	—
258	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
259	C₄×C₆₇	#520	1	1	yes	characteristic
260	C₄×C₆₇	D₄²	1	1	yes	characteristic
261	C₄×C₆₇	#547	1	1	yes	characteristic
262	Dic₆₇	—	4	2	no	—
263	Dic₆₇	—	4	2	no	—
264	#23018	—	67	1	no	maximal, Sylow
265	C₂×C₆₇	—	2	1	no	—
266	C₂×C₆₇	—	2	1	no	—
267	C₂×C₆₇	—	2	2	no	—
268	C₂×C₆₇	—	4	1	no	—
269	C₂×C₆₇	—	8	2	no	—
270	C₂×C₆₇	#2361	1	1	yes	characteristic
271	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
272	C₂×C₆₇	#2957	1	1	yes	characteristic
273	#3050	D₆₇	1	1	yes	characteristic
274	C₂×#443	—	67	1	no	—
275	#2933	—	67	2	no	—
276	C₂²×#108	—	67	1	no	—
277	#1974	—	67	1	no	—
278	#1945	—	67	1	no	—
279	#1929	—	67	2	no	—
280	#1871	—	67	2	no	—
281	#1866	—	67	2	no	—
282	#1772	—	67	1	no	—
283	C₈×C₂²⋊C₄	—	67	1	no	—
284	C₆₇	#23018	1	1	yes	characteristic, complemented, Sylow
285	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
286	C₂×#131	—	67	2	no	—
287	C₂²×M₁₆	—	67	2	no	—
288	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
289	#525	C₂×D₆₇	1	2	yes	—
290	#467	Dic₆₇	1	1	yes	characteristic, complemented
291	#467	Dic₆₇	1	1	yes	characteristic, complemented
292	#466	Dic₆₇	1	1	yes	characteristic, complemented
293	#466	Dic₆₇	1	1	yes	characteristic, complemented
294	#465	Dic₆₇	1	2	yes	complemented
295	#465	Dic₆₇	1	2	yes	complemented
296	#443	—	134	4	no	—
297	#436	—	134	2	no	—
298	#435	—	134	2	no	—
299	#435	—	134	2	no	—
300	C₈×D₄	—	134	2	no	—
301	C₂×#108	—	67	1	no	—
302	C₂×#108	—	67	2	no	—
303	C₂×#108	—	67	1	no	—
304	C₂×#108	—	134	4	no	—
305	#427	C₂×D₆₇	1	1	yes	characteristic
306	#424	—	67	2	no	—
307	C₂×#104	—	67	2	no	—
308	C₂×#104	—	67	2	no	—
309	#416	C₂×D₆₇	1	2	yes	—
310	#408	—	67	2	no	—
311	C₂×C₂²⋊C₈	—	67	1	no	—
312	#405	—	67	2	no	—
313	C₂×C₄×C₈	—	67	1	no	—
314	C₂×C₄×C₈	—	67	1	no	—
315	C₄×C₂²⋊C₄	—	67	1	no	—
316	#339	—	67	2	no	—
317	#339	—	67	2	no	—
318	#336	—	67	1	no	—
319	#336	—	67	1	no	—
320	C₂×#41	C₂²×D₆₇	1	2	yes	—
321	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
322	#135	—	2	2	no	—
323	#135	—	2	2	no	—
324	C₂×Q₁₆	C₂×Dic₆₇	1	1	yes	characteristic
325	C₂×SD₁₆	C₂×Dic₆₇	1	2	yes	—
326	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic
327	#131	—	268	2	no	—
328	#131	—	134	4	no	—
329	C₂×M₁₆	—	268	2	no	—
330	C₂×M₁₆	—	67	2	no	—
331	C₂×M₁₆	—	67	2	no	—
332	C₂×M₁₆	—	134	4	no	—
333	C₂×M₁₆	—	134	2	no	—
334	C₂×M₁₆	—	134	2	no	—
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	—	67	1	no	—
338	C₂²×C₈	—	67	1	no	—
339	C₂²×C₈	—	134	2	no	—
340	C₂²×C₈	—	134	2	no	—
341	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
342	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
343	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
344	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
346	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
347	#123	—	2	2	no	—
348	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
349	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
350	#121	C₂×Dic₆₇	1	2	yes	—
351	#121	C₂×Dic₆₇	1	2	yes	—
352	#120	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	#117	C₂²×D₆₇	1	2	yes	—
356	C₂×C₂²⋊C₄	—	134	1	no	—
357	C₂×C₄²	—	67	1	no	—
358	C₂×C₄²	—	67	1	no	—
359	#108	—	67	4	no	—
360	#108	—	134	4	no	—
361	#108	—	134	2	no	—
362	#107	C₂×Dic₆₇	1	1	yes	characteristic
363	#107	C₂×Dic₆₇	1	1	yes	characteristic
364	#106	C₂×Dic₆₇	1	2	yes	—
365	C₄⋊C₈	—	134	2	no	—
366	C₄⋊C₈	—	134	2	no	—
367	#104	—	268	2	no	—
368	#104	—	134	4	no	—
369	#103	C₂×Dic₆₇	1	2	yes	—
370	#103	C₂×Dic₆₇	1	2	yes	—
371	#102	C₂×Dic₆₇	1	2	yes	—
372	#102	C₂×Dic₆₇	1	2	yes	—
373	C₂²⋊C₈	—	67	1	no	—
374	C₂²⋊C₈	—	67	1	no	—
375	C₂²⋊C₈	—	67	1	no	—
376	C₂²⋊C₈	—	67	1	no	—
377	C₂²⋊C₈	—	134	2	no	—
378	C₂²⋊C₈	—	134	2	no	—
379	#97	—	134	2	no	—
380	C₄×C₈	—	134	2	no	—
381	C₄×C₈	—	134	2	no	—
382	C₄×C₈	—	134	2	no	—
383	#95	—	134	1	no	—
384	C₂⁴	#11761627	1	1	yes	characteristic
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	2	2	no	—
388	#41	—	2	2	no	—
389	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	134	1	no	—
400	C₂²×C₄	—	134	1	no	—
401	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
402	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
403	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
404	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
405	C₂²×C₄	#11761627	1	1	yes	characteristic
406	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
407	Q₁₆	—	2	2	no	—
408	SD₁₆	—	2	4	no	—
409	D₈	—	2	2	no	—
410	M₁₆	—	268	4	no	—
411	M₁₆	—	268	4	no	—
412	M₁₆	—	67	4	no	—
413	M₁₆	—	134	2	no	—
414	M₁₆	—	134	2	no	—
415	M₁₆	—	134	2	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	268	4	no	—
423	C₂×C₈	—	268	4	no	—
424	C₂×C₈	—	67	1	no	—
425	C₂×C₈	—	67	1	no	—
426	C₂×C₈	—	67	1	no	—
427	C₂×C₈	—	67	1	no	—
428	C₂×C₈	—	134	2	no	—
429	C₂×C₈	—	134	1	no	—
430	C₂×C₈	—	134	2	no	—
431	C₂×C₈	—	134	1	no	—
432	C₂×C₈	—	134	1	no	—
433	C₂×C₈	—	134	1	no	—
434	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
435	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
436	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
437	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
438	C₂×C₈	D₄×D₆₇	1	2	yes	—
439	C₂×C₈	#11761627	1	2	yes	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
443	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	134	4	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	134	1	no	—
452	C₄²	—	134	1	no	—
453	C₄²	—	134	1	no	—
454	C₄²	—	134	1	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	4	1	no	—
460	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
461	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
462	C₂³	C₂×#11761627	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	D₄	—	2	2	no	—
466	D₄	—	2	2	no	—
467	D₄	—	4	4	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	8	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	268	1	no	—
487	C₂×C₄	—	268	1	no	—
488	C₂×C₄	—	268	1	no	—
489	C₂×C₄	—	268	1	no	—
490	C₂×C₄	—	134	2	no	—
491	C₂×C₄	—	134	2	no	—
492	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
493	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
494	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
495	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
496	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
497	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
498	C₂×C₄	#14524089	1	1	yes	characteristic
499	C₂×C₄	#14524090	1	1	yes	characteristic
500	C₈	—	2	1	no	—
501	C₈	—	2	1	no	—
502	C₈	—	268	2	no	—
503	C₈	—	134	1	no	—
504	C₈	—	134	4	no	—
505	C₈	—	134	1	no	—
506	C₈	—	134	1	no	—
507	C₈	—	134	1	no	—
508	C₈	D₄×Dic₆₇	1	2	yes	—
509	C₈	D₄×Dic₆₇	1	2	yes	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	#16863513	1	2	yes	complemented
523	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
524	C₂²	#16864052	1	1	yes	characteristic
525	C₂²	#16864098	1	1	yes	characteristic
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	2	no	—
531	C₄	—	268	2	no	—
532	C₄	—	268	2	no	—
533	C₄	C₂×D₄×Dic₆₇	1	1	yes	characteristic
534	C₄	#16863879	1	1	yes	characteristic
535	C₄	#16864030	1	1	yes	characteristic
536	C₄	#16864046	1	1	yes	characteristic
537	C₂	—	2	1	no	—
538	C₂	—	2	1	no	—
539	C₂	—	2	2	no	—
540	C₂	—	4	1	no	—
541	C₂	—	8	2	no	—
542	C₂	#22563229	1	1	yes	characteristic
543	C₂	C₂×#16863513	1	1	yes	characteristic
544	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, prime radical	C₆₇×#3050	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#3050	D₆₇
hypocenter	C₆₇	#23018
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. C₂×#16863513	C₂	semidirect
2. #22568936	C₂	semidirect
3. C₂²×#14523979	C₂	semidirect
4. #22561098	C₂	semidirect
5. #22560958	C₂	semidirect
6. #22560859	C₂	semidirect
7. #22560512	C₂	semidirect
8. #22560486	C₂	semidirect
9. #22560090	C₂	semidirect
10. C₈×C₂²⋊Dic₆₇	C₂	semidirect
39. #467×C₆₇	C₄	semidirect
40. #467×C₆₇	C₄	semidirect
41. #466×C₆₇	C₄	semidirect
42. #466×C₆₇	C₄	semidirect
43. #465×C₆₇	C₄	semidirect
44. #465×C₆₇	C₄	semidirect
64. #14523979	D₄	semidirect
249. C₂²×C₆₇	#443	semidirect
284. C₆₇	#23018	semidirect
290. #467	Dic₆₇	semidirect
291. #467	Dic₆₇	semidirect
292. #466	Dic₆₇	semidirect
293. #466	Dic₆₇	semidirect
294. #465	Dic₆₇	semidirect
295. #465	Dic₆₇	semidirect
522. C₂²	#16863513	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863513	2
#22568936	2
C₂²×#14523979	2
#22561098	2
#22560958	2
#22560859	2
#22560512	2
#22560486	2
#22560090	2
C₈×C₂²⋊Dic₆₇	2
C₆₇×#3050	2
#23018	67