Subgroups — #30763332

Order 17152.

854 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863445	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863378	C₂	1	1	yes	maximal, characteristic
3	#22568653	C₂	1	1	yes	maximal, characteristic
4	C₂×#16863362	C₂	1	1	yes	maximal, characteristic
5	#22559935	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863161	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#341×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11761628	C₂²	1	1	yes	characteristic
9	C₂²×#11761612	C₂²	1	1	yes	characteristic
10	C₂²×#11761612	C₂²	1	1	yes	characteristic
11	C₂²×#11761612	C₂²	1	1	yes	characteristic
12	#16863445	—	2	2	no	—
13	#16863445	—	2	2	no	—
14	C₂×#14523979	—	2	2	no	—
15	#16863378	—	2	2	no	—
16	#16863378	—	2	2	no	—
17	C₂×#14523961	C₄	1	2	yes	—
18	C₂×#14523959	C₄	1	2	yes	—
19	#16863364	—	2	2	no	—
20	#16863362	—	2	2	no	—
21	#16863362	—	2	2	no	—
22	#16863362	—	2	2	no	—
23	#16863359	—	2	2	no	—
24	C₂×(C₂×D₆₇)⋊C₈	—	2	2	no	—
25	#16863161	—	2	2	no	—
26	#16863160	—	2	2	no	—
27	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
29	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
30	#341×C₆₇	—	2	2	no	—
31	C₂×#11761628	—	2	1	no	—
32	C₂×#11761628	—	2	1	no	—
33	C₂×#11761628	—	2	1	no	—
34	C₂×#11761628	—	2	1	no	—
35	C₂×#11761628	—	2	1	no	—
36	C₂×#11761628	—	2	1	no	—
37	C₂×#11761628	—	2	1	no	—
38	C₂×#11761628	—	2	1	no	—
39	C₂×#11761628	—	2	1	no	—
40	C₂×#11761628	—	2	1	no	—
41	C₂×#11761628	—	2	1	no	—
42	C₂×#11761628	—	2	1	no	—
43	C₂²×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₂₆₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₂²⋊D₆₇	Q₈	1	2	yes	—
46	C₂²×C₄×D₆₇	D₄	1	2	yes	—
47	C₂×#11761612	—	2	1	no	—
48	C₂×#11761612	—	2	1	no	—
49	C₂×#11761612	—	2	1	no	—
50	C₂×#11761612	—	2	1	no	—
51	C₂×#11761612	—	2	1	no	—
52	C₂×#11761612	—	2	1	no	—
53	C₂×#11761612	—	2	1	no	—
54	C₂×#11761612	—	2	1	no	—
55	C₂×#11761612	—	2	1	no	—
56	C₂×#11761612	—	2	1	no	—
57	C₂×#11761612	—	2	1	no	—
58	C₂×#11761612	—	2	1	no	—
59	C₂×#11761612	—	2	1	no	—
60	C₂×#11761612	—	2	1	no	—
61	C₂×#11761612	—	2	1	no	—
62	C₂×#11761612	C₂×C₄	1	2	yes	—
63	C₂×#11761612	D₄	1	2	yes	—
64	C₂×#11761612	D₄	1	2	yes	—
65	C₂²×C₆₇⋊C₈	—	2	1	no	—
66	C₂²×C₆₇⋊C₈	—	2	1	no	—
67	C₂²×C₆₇⋊C₈	—	2	1	no	—
68	#14523979	—	2	8	no	—
69	#14523961	—	2	4	no	—
70	#14523959	—	2	4	no	—
71	(C₂×D₆₇)⋊C₈	—	2	8	no	—
72	(C₂×D₆₇)⋊C₈	—	2	8	no	—
73	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₆₇	—	2	1	no	—
75	C₂×M₁₆×C₆₇	—	2	1	no	—
76	C₂×M₁₆×C₆₇	—	2	1	no	—
77	C₂×M₁₆×C₆₇	—	2	1	no	—
78	C₂×M₁₆×C₆₇	—	2	1	no	—
79	C₂×M₁₆×C₆₇	—	2	1	no	—
80	C₂×M₁₆×C₆₇	—	2	1	no	—
81	C₂×M₁₆×C₆₇	—	2	1	no	—
82	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
83	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
84	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
85	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
86	C₂²×C₈×C₆₇	—	2	1	no	—
87	C₂²×C₈×C₆₇	—	2	1	no	—
88	C₂²×C₈×C₆₇	—	2	1	no	—
89	C₂²×C₈×C₆₇	—	2	1	no	—
90	C₂²×C₈×C₆₇	—	2	1	no	—
91	C₂²×C₈×C₆₇	—	2	1	no	—
92	C₂²×C₈×C₆₇	—	2	1	no	—
93	C₂²×C₈×C₆₇	—	2	1	no	—
94	C₂²×C₈×C₆₇	D₄	1	2	yes	—
95	C₂³×D₆₇	C₄⋊C₄	1	2	yes	—
96	#11761628	—	4	1	no	—
97	#11761628	—	4	1	no	—
98	#11761628	—	4	1	no	—
99	#11761628	—	4	1	no	—
100	#11761628	—	4	1	no	—
101	#11761628	—	4	1	no	—
102	#11761628	—	4	1	no	—
103	#11761628	—	4	1	no	—
104	#11761628	—	4	1	no	—
105	#11761628	—	4	1	no	—
106	#11761628	—	4	1	no	—
107	#11761628	—	4	1	no	—
108	#11761628	—	4	1	no	—
109	#11761628	—	4	1	no	—
110	#11761628	—	4	1	no	—
111	#11761628	—	4	1	no	—
112	C₂×Dic₁₃₄	—	2	1	no	—
113	C₂×Dic₁₃₄	—	2	1	no	—
114	C₂×Dic₁₃₄	—	2	1	no	—
115	C₂×Dic₁₃₄	—	2	1	no	—
116	C₂×Dic₁₃₄	—	2	1	no	—
117	C₂×Dic₁₃₄	—	2	1	no	—
118	C₂×D₂₆₈	—	2	1	no	—
119	C₂×D₂₆₈	—	2	1	no	—
120	C₂×D₂₆₈	—	2	1	no	—
121	C₂×D₂₆₈	—	2	1	no	—
122	C₂×D₂₆₈	—	2	1	no	—
123	C₂×D₂₆₈	—	2	1	no	—
124	C₂×C₂²⋊D₆₇	—	2	2	no	—
125	C₂×C₂²⋊D₆₇	—	2	2	no	—
126	C₂×C₂²⋊D₆₇	—	2	2	no	—
127	C₂×C₂²⋊D₆₇	—	2	2	no	—
128	C₂×C₂²⋊D₆₇	—	2	2	no	—
129	C₂×C₂²⋊D₆₇	—	2	2	no	—
130	C₂²×Dic₆₇	C₄⋊C₄	1	2	yes	—
131	C₂×C₄×D₆₇	—	2	2	no	—
132	C₂×C₄×D₆₇	—	2	2	no	—
133	C₂×C₄×D₆₇	—	2	2	no	—
134	C₂×C₄×D₆₇	—	2	2	no	—
135	C₂×C₄×D₆₇	—	2	2	no	—
136	C₂×C₄×D₆₇	—	2	2	no	—
137	#11761612	—	2	2	no	—
138	#11761612	—	2	2	no	—
139	#11761612	—	2	2	no	—
140	#11761612	—	2	2	no	—
141	#11761612	—	2	2	no	—
142	#11761612	—	2	2	no	—
143	#11761612	—	4	1	no	—
144	#11761612	—	4	1	no	—
145	#11761612	—	4	1	no	—
146	#11761612	—	4	1	no	—
147	#11761612	—	4	1	no	—
148	#11761612	—	4	1	no	—
149	C₂×C₆₇⋊C₈	—	2	2	no	—
150	C₂×C₆₇⋊C₈	—	2	2	no	—
151	C₂×C₆₇⋊C₈	—	2	2	no	—
152	C₂×C₆₇⋊C₈	—	4	1	no	—
153	C₂×C₆₇⋊C₈	—	4	1	no	—
154	C₂×C₆₇⋊C₈	—	4	1	no	—
155	C₂×C₆₇⋊C₈	—	4	1	no	—
156	C₂×C₆₇⋊C₈	—	4	1	no	—
157	C₂×C₆₇⋊C₈	—	4	1	no	—
158	C₂⁴×C₆₇	C₂×Q₈	1	1	yes	characteristic
159	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
168	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
169	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
170	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
171	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
172	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
173	M₁₆×C₆₇	—	2	2	no	—
174	M₁₆×C₆₇	—	2	2	no	—
175	M₁₆×C₆₇	—	2	2	no	—
176	M₁₆×C₆₇	—	2	2	no	—
177	M₁₆×C₆₇	—	2	2	no	—
178	M₁₆×C₆₇	—	4	1	no	—
179	M₁₆×C₆₇	—	4	1	no	—
180	M₁₆×C₆₇	C₂²⋊C₄	1	4	yes	—
181	C₂×C₈×C₆₇	—	2	2	no	—
182	C₂×C₈×C₆₇	—	2	2	no	—
183	C₂×C₈×C₆₇	—	2	2	no	—
184	C₂×C₈×C₆₇	—	2	2	no	—
185	C₂×C₈×C₆₇	—	2	2	no	—
186	C₂×C₈×C₆₇	—	2	2	no	—
187	C₂×C₈×C₆₇	—	2	2	no	—
188	C₂×C₈×C₆₇	—	4	1	no	—
189	C₂×C₈×C₆₇	—	4	1	no	—
190	C₂×C₈×C₆₇	—	4	1	no	—
191	C₂×C₈×C₆₇	—	4	1	no	—
192	C₂×C₈×C₆₇	—	4	1	no	—
193	C₂×C₈×C₆₇	—	4	1	no	—
194	C₂³×C₆₇	—	4	2	no	—
195	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
197	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
198	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
199	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
200	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
201	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
202	C₂²×D₆₇	—	2	2	no	—
203	C₂²×D₆₇	—	2	2	no	—
204	C₂²×D₆₇	—	2	2	no	—
205	C₂²×D₆₇	—	4	4	no	—
206	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
208	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
213	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
214	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
215	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
216	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
217	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
218	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
219	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
220	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
221	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
222	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
223	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
224	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
225	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
226	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
227	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
228	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
229	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
230	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
231	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
232	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
233	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
234	C₂²⋊D₆₇	—	4	2	no	—
235	C₂²⋊D₆₇	—	4	2	no	—
236	C₂²⋊D₆₇	—	4	2	no	—
237	C₂²⋊D₆₇	—	4	2	no	—
238	C₂×Dic₆₇	—	2	2	no	—
239	C₂×Dic₆₇	—	2	2	no	—
240	C₂×Dic₆₇	—	2	2	no	—
241	D₂₆₈	—	4	1	no	—
242	D₂₆₈	—	4	1	no	—
243	D₂₆₈	—	4	1	no	—
244	D₂₆₈	—	4	1	no	—
245	C₄×D₆₇	—	4	2	no	—
246	C₄×D₆₇	—	4	2	no	—
247	C₄×D₆₇	—	4	2	no	—
248	C₄×D₆₇	—	4	2	no	—
249	Dic₁₃₄	—	4	1	no	—
250	Dic₁₃₄	—	4	1	no	—
251	Dic₁₃₄	—	4	1	no	—
252	Dic₁₃₄	—	4	1	no	—
253	C₈×C₆₇	—	2	4	no	—
254	C₈×C₆₇	—	4	2	no	—
255	C₈×C₆₇	—	4	2	no	—
256	C₆₇⋊C₈	—	4	2	no	—
257	C₆₇⋊C₈	—	4	2	no	—
258	C₆₇⋊C₈	—	4	2	no	—
259	C₂²×C₆₇	—	2	2	no	—
260	C₂²×C₆₇	—	2	2	no	—
261	C₂²×C₆₇	—	2	2	no	—
262	C₂²×C₆₇	—	4	1	no	—
263	C₂²×C₆₇	—	4	1	no	—
264	C₂²×C₆₇	—	4	1	no	—
265	C₂²×C₆₇	—	4	1	no	—
266	C₂²×C₆₇	#380	1	1	yes	characteristic
267	C₂²×C₆₇	#385	1	1	yes	characteristic
268	C₂²×C₆₇	#385	1	1	yes	characteristic
269	C₂²×C₆₇	#393	1	1	yes	characteristic
270	C₂²×C₆₇	#396	1	1	yes	characteristic
271	C₂²×C₆₇	#396	1	1	yes	characteristic
272	C₂²×C₆₇	#399	1	1	yes	characteristic
273	C₂×D₆₇	—	4	4	no	—
274	C₂×D₆₇	—	4	4	no	—
275	C₂×D₆₇	—	4	2	no	—
276	C₂×D₆₇	—	8	2	no	—
277	C₄×C₆₇	#386	1	1	yes	characteristic
278	C₄×C₆₇	#388	1	1	yes	characteristic
279	C₄×C₆₇	#388	1	1	yes	characteristic
280	C₄×C₆₇	#390	1	1	yes	characteristic
281	C₄×C₆₇	#392	1	1	yes	characteristic
282	C₄×C₆₇	#394	1	1	yes	characteristic
283	C₄×C₆₇	#394	1	1	yes	characteristic
284	C₄×C₆₇	#397	1	1	yes	characteristic
285	Dic₆₇	—	4	2	no	—
286	#11137	—	67	1	no	maximal, Sylow
287	C₂×C₆₇	—	2	1	no	—
288	C₂×C₆₇	—	2	1	no	—
289	C₂×C₆₇	—	2	1	no	—
290	C₂×C₆₇	—	2	1	no	—
291	C₂×C₆₇	—	2	1	no	—
292	C₂×C₆₇	—	2	1	no	—
293	C₂×C₆₇	#1439	1	1	yes	characteristic
294	C₂×C₆₇	#1858	1	2	yes	—
295	D₆₇	—	8	2	no	—
296	C₂×#430	—	67	1	no	—
297	C₂×#413	—	67	1	no	—
298	#2879	—	67	1	no	—
299	C₂×#408	—	67	1	no	—
300	#1738	—	67	1	no	—
301	C₂×#341	—	67	1	no	—
302	C₂×#341	D₆₇	1	1	yes	characteristic, complemented
303	C₆₇	#11137	1	1	yes	characteristic, complemented, Sylow
304	C₂²×#41	—	67	1	no	—
305	C₂²×M₁₆	—	67	1	no	—
306	C₂²×M₁₆	—	67	1	no	—
307	C₂²×M₁₆	—	67	1	no	—
308	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
309	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
310	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
311	#430	—	134	2	no	—
312	#430	—	134	2	no	—
313	C₂×#108	—	134	2	no	—
314	#413	—	134	2	no	—
315	#413	—	134	2	no	—
316	C₂×#101	—	67	2	no	—
317	C₂×#100	—	67	2	no	—
318	#408	—	134	2	no	—
319	#408	—	134	2	no	—
320	#408	—	134	2	no	—
321	#408	—	134	2	no	—
322	#407	—	134	2	no	—
323	C₂×C₂²⋊C₈	—	134	2	no	—
324	#341	—	2	2	no	—
325	#341	—	134	2	no	—
326	#341	—	134	2	no	—
327	C₂×#41	—	134	1	no	—
328	C₂×#41	—	134	1	no	—
329	C₂×#41	—	134	1	no	—
330	C₂×#41	—	134	1	no	—
331	C₂×#41	—	134	1	no	—
332	C₂×#41	—	134	1	no	—
333	C₂×#41	—	134	1	no	—
334	C₂×#41	—	134	1	no	—
335	C₂×#41	—	134	1	no	—
336	C₂×#41	—	134	1	no	—
337	C₂×#41	—	134	1	no	—
338	C₂×#41	—	134	1	no	—
339	C₂²×Q₈	—	67	1	no	—
340	C₂²×D₄	—	67	2	no	—
341	C₂²×D₄	—	67	1	no	—
342	C₂³×C₄	—	67	2	no	—
343	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	67	2	no	—
353	C₂×M₁₆	—	67	2	no	—
354	C₂×M₁₆	—	67	2	no	—
355	C₂×M₁₆	—	134	1	no	—
356	C₂×M₁₆	—	134	1	no	—
357	C₂×M₁₆	—	134	1	no	—
358	C₂×M₁₆	—	134	1	no	—
359	C₂×M₁₆	—	134	1	no	—
360	C₂×M₁₆	—	134	1	no	—
361	C₂×M₁₆	—	134	1	no	—
362	C₂×M₁₆	—	134	1	no	—
363	C₂×M₁₆	—	134	1	no	—
364	C₂×M₁₆	—	134	1	no	—
365	C₂×M₁₆	—	134	1	no	—
366	C₂×M₁₆	—	134	1	no	—
367	C₂×M₁₆	—	134	1	no	—
368	C₂×M₁₆	—	134	1	no	—
369	C₂×M₁₆	—	134	1	no	—
370	C₂×M₁₆	C₄×D₆₇	1	2	yes	—
371	C₂×M₁₆	D₂₆₈	1	2	yes	—
372	C₂×M₁₆	D₂₆₈	1	2	yes	—
373	C₂×M₁₆	C₂²⋊D₆₇	1	2	yes	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	2	1	no	—
382	C₂²×C₈	—	134	1	no	—
383	C₂²×C₈	—	134	1	no	—
384	C₂²×C₈	—	134	1	no	—
385	C₂²×C₈	D₂₆₈	1	2	yes	—
386	#108	—	134	8	no	—
387	#101	—	134	4	no	—
388	#100	—	134	4	no	—
389	C₂²⋊C₈	—	134	8	no	—
390	C₂²⋊C₈	—	134	8	no	—
391	C₂⁴	—	67	2	no	—
392	C₂⁴	Q₈×D₆₇	1	1	yes	characteristic
393	#41	—	268	1	no	—
394	#41	—	268	1	no	—
395	#41	—	268	1	no	—
396	#41	—	268	1	no	—
397	#41	—	268	1	no	—
398	#41	—	268	1	no	—
399	#41	—	268	1	no	—
400	#41	—	268	1	no	—
401	#41	—	268	1	no	—
402	#41	—	268	1	no	—
403	#41	—	268	1	no	—
404	#41	—	268	1	no	—
405	#41	—	268	1	no	—
406	#41	—	268	1	no	—
407	#41	—	268	1	no	—
408	#41	—	268	1	no	—
409	C₂×Q₈	—	134	1	no	—
410	C₂×Q₈	—	134	1	no	—
411	C₂×Q₈	—	134	1	no	—
412	C₂×Q₈	—	134	1	no	—
413	C₂×Q₈	—	134	1	no	—
414	C₂×Q₈	—	134	1	no	—
415	C₂×D₄	—	134	2	no	—
416	C₂×D₄	—	134	2	no	—
417	C₂×D₄	—	134	2	no	—
418	C₂×D₄	—	134	2	no	—
419	C₂×D₄	—	134	2	no	—
420	C₂×D₄	—	134	2	no	—
421	C₂×D₄	—	134	1	no	—
422	C₂×D₄	—	134	1	no	—
423	C₂×D₄	—	134	1	no	—
424	C₂×D₄	—	134	1	no	—
425	C₂×D₄	—	134	1	no	—
426	C₂×D₄	—	134	1	no	—
427	C₂²×C₄	—	67	2	no	—
428	C₂²×C₄	—	134	2	no	—
429	C₂²×C₄	—	134	2	no	—
430	C₂²×C₄	—	134	2	no	—
431	C₂²×C₄	—	134	2	no	—
432	C₂²×C₄	—	134	2	no	—
433	C₂²×C₄	—	134	2	no	—
434	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
435	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
436	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
437	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
442	C₂²×C₄	#11761627	1	1	yes	characteristic
443	C₂²×C₄	#11761627	1	1	yes	characteristic
444	C₂²×C₄	#11761627	1	1	yes	characteristic
445	C₂²×C₄	#11761628	1	1	yes	characteristic
446	C₂²×C₄	#11761628	1	1	yes	characteristic
447	C₂²×C₄	#11761629	1	1	yes	characteristic
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	4	1	no	—
454	M₁₆	—	4	1	no	—
455	M₁₆	—	268	1	no	—
456	M₁₆	—	268	1	no	—
457	M₁₆	—	268	1	no	—
458	M₁₆	—	268	1	no	—
459	M₁₆	—	268	1	no	—
460	M₁₆	—	268	1	no	—
461	M₁₆	—	134	2	no	—
462	M₁₆	—	134	2	no	—
463	M₁₆	—	134	2	no	—
464	M₁₆	—	134	2	no	—
465	M₁₆	—	134	2	no	—
466	M₁₆	—	134	2	no	—
467	M₁₆	(C₂×D₆₇)⋊C₄	1	4	yes	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	4	1	no	—
476	C₂×C₈	—	4	1	no	—
477	C₂×C₈	—	4	1	no	—
478	C₂×C₈	—	4	1	no	—
479	C₂×C₈	—	4	1	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	268	1	no	—
482	C₂×C₈	—	268	1	no	—
483	C₂×C₈	—	268	1	no	—
484	C₂×C₈	—	268	1	no	—
485	C₂×C₈	—	268	1	no	—
486	C₂×C₈	—	268	1	no	—
487	C₂×C₈	—	134	2	no	—
488	C₂×C₈	—	134	2	no	—
489	C₂×C₈	—	134	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	268	4	no	—
492	C₂³	—	134	2	no	—
493	C₂³	—	134	2	no	—
494	C₂³	—	134	2	no	—
495	C₂³	C₄⋊C₄×D₆₇	1	1	yes	characteristic
496	C₂³	#14524019	1	1	yes	characteristic
497	C₂³	#14524021	1	1	yes	characteristic
498	C₂³	#14524021	1	1	yes	characteristic
499	C₂³	#14524023	1	1	yes	characteristic
500	C₂³	#14524023	1	1	yes	characteristic
501	C₂³	#14524023	1	1	yes	characteristic
502	Q₈	—	268	1	no	—
503	Q₈	—	268	1	no	—
504	Q₈	—	268	1	no	—
505	Q₈	—	268	1	no	—
506	D₄	—	268	2	no	—
507	D₄	—	268	2	no	—
508	D₄	—	268	2	no	—
509	D₄	—	268	2	no	—
510	D₄	—	268	1	no	—
511	D₄	—	268	1	no	—
512	D₄	—	268	1	no	—
513	D₄	—	268	1	no	—
514	C₂×C₄	—	268	2	no	—
515	C₂×C₄	—	268	2	no	—
516	C₂×C₄	—	268	2	no	—
517	C₂×C₄	—	268	2	no	—
518	C₂×C₄	—	134	2	no	—
519	C₂×C₄	—	134	2	no	—
520	C₂×C₄	—	134	2	no	—
521	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
522	C₂×C₄	#14524001	1	1	yes	characteristic
523	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
524	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
525	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
526	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
527	C₂×C₄	#14524013	1	1	yes	characteristic
528	C₂×C₄	#14524013	1	1	yes	characteristic
529	C₂×C₄	#14524013	1	1	yes	characteristic
530	C₂×C₄	#14524014	1	1	yes	characteristic
531	C₂×C₄	#14524015	1	1	yes	characteristic
532	C₂×C₄	#14524015	1	1	yes	characteristic
533	C₂×C₄	#14524017	1	1	yes	characteristic
534	C₂×C₄	#14524017	1	1	yes	characteristic
535	C₂×C₄	#14524018	1	1	yes	characteristic
536	C₂×C₄	#14524018	1	1	yes	characteristic
537	C₂×C₄	#14524018	1	1	yes	characteristic
538	C₂×C₄	#14524025	1	1	yes	characteristic
539	C₂×C₄	#14524025	1	1	yes	characteristic
540	C₂×C₄	#14524027	1	1	yes	characteristic
541	C₂×C₄	#14524027	1	1	yes	characteristic
542	C₂×C₄	#14524027	1	1	yes	characteristic
543	C₂×C₄	#14524029	1	1	yes	characteristic
544	C₂×C₄	#14524029	1	1	yes	characteristic
545	C₂×C₄	#14524031	1	1	yes	characteristic
546	C₂×C₄	#14524038	1	1	yes	characteristic
547	C₂×C₄	#14524038	1	1	yes	characteristic
548	C₂×C₄	#14524040	1	1	yes	characteristic
549	C₈	—	2	4	no	—
550	C₈	—	4	2	no	—
551	C₈	—	4	2	no	—
552	C₈	—	268	2	no	—
553	C₈	—	268	2	no	—
554	C₈	—	268	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	268	4	no	—
563	C₂²	—	268	4	no	—
564	C₂²	—	268	2	no	—
565	C₂²	—	536	2	no	—
566	C₂²	#16863253	1	1	yes	characteristic
567	C₂²	#16863270	1	1	yes	characteristic
568	C₂²	#16863270	1	1	yes	characteristic
569	C₂²	#16863309	1	1	yes	characteristic
570	C₂²	#16863318	1	1	yes	characteristic
571	C₂²	#16863318	1	1	yes	characteristic
572	C₂²	#16863333	1	1	yes	characteristic
573	C₄	—	268	2	no	—
574	C₄	#16863273	1	1	yes	characteristic
575	C₄	#16863288	1	1	yes	characteristic
576	C₄	#16863288	1	1	yes	characteristic
577	C₄	#16863298	1	1	yes	characteristic
578	C₄	#16863306	1	1	yes	characteristic
579	C₄	#16863312	1	1	yes	characteristic
580	C₄	#16863312	1	1	yes	characteristic
581	C₄	#16863323	1	1	yes	characteristic
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	536	2	no	—
589	C₂	#22558455	1	1	yes	characteristic
590	C₂	#22560430	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#14524013
commutator	C₂²×C₄×C₆₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₆₇
Fitting	C₂×#341×C₆₇	C₂
socle	C₂²×C₆₇	#385
prime radical	C₂²×#11761628	C₂²
cosocle	C₂³×C₄×C₆₇	C₂³
hypercenter	C₂×#341	D₆₇
hypocenter	C₆₇	#11137
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#341

Complements

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

N	H ≅ G/N	type
1. C₂×#16863445	C₂	semidirect
5. #22559935	C₂	semidirect
6. C₂×#16863161	C₂	semidirect
7. C₂×#341×C₆₇	C₂	semidirect
302. C₂×#341	D₆₇	semidirect
303. C₆₇	#11137	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863445	2
C₂×#16863378	2
#22568653	2
C₂×#16863362	2
#22559935	2
C₂×#16863161	2
C₂×#341×C₆₇	2
#11137	67