Subgroups — C₂×#22561664 #30884754

Order 17152.

906 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863424	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863412	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863390	C₂	1	1	yes	maximal, characteristic
4	C₂×#16863378	C₂	1	1	yes	maximal, characteristic
5	#22561664	C₂	1	8	yes	maximal, direct product factor
6	C₂×#16863160	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863152	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#344×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#11761628	C₂²	1	1	yes	characteristic
10	C₂²×#11761612	C₂²	1	1	yes	characteristic
11	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×#14524002	C₂²	1	1	yes	characteristic
13	#16863424	—	2	2	no	—
14	#16863424	C₂²	1	4	yes	complemented
15	C₂×Dic₆₇⋊C₈	—	2	2	no	—
16	#16863412	—	2	2	no	—
17	#16863412	C₂²	1	4	yes	—
18	C₂×#14523969	—	2	2	no	—
19	#16863390	—	2	2	no	—
20	#16863390	C₂²	1	4	yes	—
21	C₂×#14523966	—	2	1	no	—
22	C₂×#14523963	—	2	1	no	—
23	#16863378	—	2	2	no	—
24	#16863378	C₂²	1	4	yes	—
25	C₂×#14523961	—	2	1	no	—
26	C₂×#14523959	—	2	1	no	—
27	#16863160	C₂²	1	4	yes	complemented
28	#16863152	C₂²	1	4	yes	complemented
29	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
32	#344×C₆₇	C₂²	1	4	yes	complemented
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	C₂×#11761628	D₄	1	2	yes	—
44	C₂×#11761628	C₂³	1	2	yes	—
45	C₂²×Dic₁₃₄	D₄	1	1	yes	characteristic
46	C₂²×D₂₆₈	D₄	1	1	yes	characteristic
47	C₂²×C₂²⋊D₆₇	—	2	1	no	—
48	C₂²×C₄×D₆₇	—	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	C₂³	1	2	yes	—
55	C₂²×C₆₇⋊C₈	—	2	1	no	—
56	C₂²×C₆₇⋊C₈	—	2	1	no	—
57	C₂²×C₆₇⋊C₈	—	2	1	no	—
58	C₂²×C₆₇⋊C₈	—	2	1	no	—
59	C₂²×C₆₇⋊C₈	—	2	1	no	—
60	C₂²×C₆₇⋊C₈	—	2	1	no	—
61	C₂²×C₆₇⋊C₈	—	2	1	no	—
62	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
63	#14524002	—	2	1	no	—
64	#14524002	—	2	1	no	—
65	#14524002	D₄	1	2	yes	—
66	#14524002	C₂³	1	2	yes	—
67	C₂×C₄⋊Dic₆₇	—	2	1	no	—
68	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
69	C₂×C₄×Dic₆₇	D₄	1	2	yes	—
70	Dic₆₇⋊C₈	—	2	8	no	—
71	#14523969	—	2	8	no	—
72	#14523966	—	2	4	no	—
73	#14523963	—	2	4	no	—
74	#14523961	—	2	4	no	—
75	#14523959	—	2	4	no	—
76	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
83	C₂×M₁₆×C₆₇	—	2	1	no	—
84	C₂×M₁₆×C₆₇	—	2	1	no	—
85	C₂×M₁₆×C₆₇	—	2	1	no	—
86	C₂×M₁₆×C₆₇	—	2	1	no	—
87	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
88	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
89	C₂²×C₈×C₆₇	—	2	1	no	—
90	C₂²×C₈×C₆₇	—	2	1	no	—
91	#117×C₆₇	—	2	1	no	—
92	#117×C₆₇	—	2	1	no	—
93	#117×C₆₇	—	2	1	no	—
94	#117×C₆₇	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
97	C₂×C₄²×C₆₇	—	2	1	no	—
98	C₂³×D₆₇	—	2	1	no	—
99	#11761628	—	2	2	no	—
100	#11761628	—	2	2	no	—
101	#11761628	—	2	2	no	—
102	#11761628	—	2	2	no	—
103	#11761628	—	2	2	no	—
104	#11761628	—	2	2	no	—
105	#11761628	—	2	2	no	—
106	#11761628	—	2	2	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	#11761628	—	4	1	no	—
113	#11761628	—	4	1	no	—
114	#11761628	—	4	1	no	—
115	C₂×Dic₁₃₄	—	2	1	no	—
116	C₂×Dic₁₃₄	—	2	1	no	—
117	C₂×Dic₁₃₄	—	2	1	no	—
118	C₂×Dic₁₃₄	—	2	1	no	—
119	C₂×Dic₁₃₄	—	2	1	no	—
120	C₂×Dic₁₃₄	C₂×D₄	1	2	yes	—
121	C₂×D₂₆₈	—	2	1	no	—
122	C₂×D₂₆₈	—	2	1	no	—
123	C₂×D₂₆₈	—	2	1	no	—
124	C₂×D₂₆₈	—	2	1	no	—
125	C₂×D₂₆₈	—	2	1	no	—
126	C₂×D₂₆₈	C₂×D₄	1	2	yes	—
127	C₂×C₂²⋊D₆₇	—	2	2	no	—
128	C₂×C₂²⋊D₆₇	—	2	2	no	—
129	C₂×C₂²⋊D₆₇	—	4	1	no	—
130	C₂×C₂²⋊D₆₇	—	4	1	no	—
131	C₂×C₂²⋊D₆₇	—	4	1	no	—
132	C₂×C₂²⋊D₆₇	—	4	1	no	—
133	C₂²×Dic₆₇	—	2	2	no	—
134	C₂²×Dic₆₇	—	2	1	no	—
135	C₂×C₄×D₆₇	—	2	2	no	—
136	C₂×C₄×D₆₇	—	2	2	no	—
137	C₂×C₄×D₆₇	—	4	1	no	—
138	C₂×C₄×D₆₇	—	4	1	no	—
139	C₂×C₄×D₆₇	—	4	1	no	—
140	C₂×C₄×D₆₇	—	4	1	no	—
141	#11761612	—	2	2	no	—
142	#11761612	—	2	2	no	—
143	#11761612	—	4	1	no	—
144	#11761612	—	4	1	no	—
145	C₂×C₆₇⋊C₈	—	2	2	no	—
146	C₂×C₆₇⋊C₈	—	2	2	no	—
147	C₂×C₆₇⋊C₈	—	2	2	no	—
148	C₂×C₆₇⋊C₈	—	2	2	no	—
149	C₂×C₆₇⋊C₈	—	4	1	no	—
150	C₂×C₆₇⋊C₈	—	4	1	no	—
151	C₂×C₆₇⋊C₈	—	4	1	no	—
152	C₂×C₆₇⋊C₈	—	4	1	no	—
153	C₂×C₆₇⋊C₈	—	4	1	no	—
154	C₂×C₆₇⋊C₈	—	4	1	no	—
155	C₄⋊Dic₆₇	—	2	2	no	—
156	C₄⋊Dic₆₇	—	2	2	no	—
157	C₂²⋊Dic₆₇	—	2	2	no	—
158	C₂²⋊Dic₆₇	—	2	2	no	—
159	C₄×Dic₆₇	—	2	2	no	—
160	C₄×Dic₆₇	C₂×D₄	1	4	yes	—
161	C₂⁴×C₆₇	#41	1	1	yes	characteristic
162	C₂²×C₄×C₆₇	—	4	1	no	—
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	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
174	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
175	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
176	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
177	M₁₆×C₆₇	—	2	2	no	—
178	M₁₆×C₆₇	—	2	2	no	—
179	M₁₆×C₆₇	—	2	2	no	—
180	M₁₆×C₆₇	—	2	2	no	—
181	M₁₆×C₆₇	—	4	1	no	—
182	M₁₆×C₆₇	—	4	1	no	—
183	M₁₆×C₆₇	—	4	1	no	—
184	M₁₆×C₆₇	—	4	1	no	—
185	C₂×C₈×C₆₇	—	2	2	no	—
186	C₂×C₈×C₆₇	—	2	2	no	—
187	C₂×C₈×C₆₇	—	4	1	no	—
188	C₂×C₈×C₆₇	—	4	1	no	—
189	C₂×C₈×C₆₇	—	4	1	no	—
190	C₂×C₈×C₆₇	—	4	1	no	—
191	C₄⋊C₄×C₆₇	—	2	2	no	—
192	C₄⋊C₄×C₆₇	—	4	1	no	—
193	C₂²⋊C₄×C₆₇	—	2	2	no	—
194	C₂²⋊C₄×C₆₇	—	4	1	no	—
195	C₄²×C₆₇	—	2	2	no	—
196	C₄²×C₆₇	—	4	1	no	—
197	C₂³×C₆₇	—	4	2	no	—
198	C₂³×C₆₇	#123	1	1	yes	characteristic
199	C₂³×C₆₇	#123	1	1	yes	characteristic
200	C₂³×C₆₇	#123	1	1	yes	characteristic
201	C₂³×C₆₇	#123	1	1	yes	characteristic
202	C₂³×C₆₇	#126	1	1	yes	characteristic
203	C₂³×C₆₇	#126	1	1	yes	characteristic
204	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
205	C₂²×D₆₇	—	2	2	no	—
206	C₂²×D₆₇	—	4	1	no	—
207	C₂²×D₆₇	—	4	1	no	—
208	C₂²×D₆₇	—	8	2	no	—
209	C₂×C₄×C₆₇	—	4	2	no	—
210	C₂×C₄×C₆₇	—	8	2	no	—
211	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
212	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
213	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
214	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
215	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
216	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
217	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
218	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
219	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
220	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
221	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
222	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
223	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
224	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
225	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
226	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
227	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
228	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
229	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
230	C₂×C₄×C₆₇	#126	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	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
239	C₂²⋊D₆₇	—	4	2	no	—
240	C₂²⋊D₆₇	—	4	2	no	—
241	C₂²⋊D₆₇	—	4	2	no	—
242	C₂²⋊D₆₇	—	4	2	no	—
243	C₂×Dic₆₇	—	2	4	no	—
244	C₂×Dic₆₇	—	2	2	no	—
245	C₂×Dic₆₇	—	4	4	no	—
246	C₂×Dic₆₇	—	4	1	no	—
247	C₂×Dic₆₇	—	4	1	no	—
248	D₂₆₈	—	2	2	no	—
249	D₂₆₈	—	2	2	no	—
250	D₂₆₈	—	4	1	no	—
251	D₂₆₈	—	4	1	no	—
252	C₄×D₆₇	—	4	2	no	—
253	C₄×D₆₇	—	4	2	no	—
254	C₄×D₆₇	—	4	2	no	—
255	C₄×D₆₇	—	4	2	no	—
256	Dic₁₃₄	—	2	2	no	—
257	Dic₁₃₄	—	2	2	no	—
258	Dic₁₃₄	—	4	1	no	—
259	Dic₁₃₄	—	4	1	no	—
260	C₈×C₆₇	—	4	2	no	—
261	C₈×C₆₇	—	4	2	no	—
262	C₆₇⋊C₈	—	4	2	no	—
263	C₆₇⋊C₈	—	4	2	no	—
264	C₂²×C₆₇	—	2	2	no	—
265	C₂²×C₆₇	—	2	2	no	—
266	C₂²×C₆₇	—	2	2	no	—
267	C₂²×C₆₇	—	4	1	no	—
268	C₂²×C₆₇	—	4	1	no	—
269	C₂²×C₆₇	—	4	1	no	—
270	C₂²×C₆₇	—	4	1	no	—
271	C₂²×C₆₇	#397	1	1	yes	characteristic
272	C₂²×C₆₇	#397	1	1	yes	characteristic
273	C₂²×C₆₇	#397	1	1	yes	characteristic
274	C₂²×C₆₇	#397	1	1	yes	characteristic
275	C₂²×C₆₇	C₂×#123	1	1	yes	characteristic
276	C₂²×C₆₇	C₂×#123	1	1	yes	characteristic
277	C₂²×C₆₇	C₂×#126	1	1	yes	characteristic
278	C₂×D₆₇	—	4	2	no	—
279	C₂×D₆₇	—	8	2	no	—
280	C₂×D₆₇	—	8	2	no	—
281	C₂×D₆₇	—	8	2	no	—
282	C₄×C₆₇	—	8	2	no	—
283	C₄×C₆₇	#397	1	1	yes	characteristic
284	C₄×C₆₇	#397	1	1	yes	characteristic
285	C₄×C₆₇	#397	1	1	yes	characteristic
286	C₄×C₆₇	#397	1	1	yes	characteristic
287	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
288	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
289	C₄×C₆₇	C₂×#124	1	1	yes	characteristic
290	C₄×C₆₇	C₂×#126	1	1	yes	characteristic
291	Dic₆₇	—	4	4	no	—
292	Dic₆₇	—	4	2	no	—
293	C₂×#2080	—	67	1	no	maximal, Sylow
294	C₂×C₆₇	—	2	1	no	—
295	C₂×C₆₇	—	2	1	no	—
296	C₂×C₆₇	—	2	1	no	—
297	C₂×C₆₇	—	2	1	no	—
298	C₂×C₆₇	—	2	1	no	—
299	C₂×C₆₇	—	2	1	no	—
300	C₂×C₆₇	#2080	1	2	yes	complemented
301	C₂×C₆₇	C₂×#397	1	1	yes	characteristic
302	D₆₇	—	8	2	no	—
303	C₂×#424	—	67	1	no	—
304	C₂×#421	—	67	1	no	—
305	C₂×#416	—	67	1	no	—
306	C₂×#413	—	67	1	no	—
307	#2080	—	67	8	no	—
308	C₂×#344	D₆₇	1	1	yes	characteristic, complemented
309	C₂×#341	—	67	1	no	—
310	C₂×H(3,ℤ/4)	—	67	1	no	—
311	C₆₇	C₂×#2080	1	1	yes	characteristic, complemented, Sylow
312	C₂²×#41	—	67	1	no	—
313	C₂²×M₁₆	—	67	1	no	—
314	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
315	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
316	C₂³×C₈	—	67	1	no	—
317	C₂×#117	—	67	1	no	—
318	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
319	#424	—	67	4	no	—
320	#424	—	134	2	no	—
321	C₂×C₄⋊C₈	—	134	2	no	—
322	#421	—	67	4	no	—
323	#421	—	134	2	no	—
324	C₂×#104	—	134	2	no	—
325	#416	—	67	4	no	—
326	#416	—	134	2	no	—
327	C₂×#103	—	134	1	no	—
328	C₂×#102	—	134	1	no	—
329	#413	—	67	4	no	—
330	#413	—	134	2	no	—
331	C₂×#101	—	134	1	no	—
332	C₂×#100	—	134	1	no	—
333	#344	C₂×D₆₇	1	4	yes	complemented
334	#341	—	67	4	no	—
335	H(3,ℤ/4)	—	67	4	no	—
336	C₂×#41	—	67	2	no	—
337	C₂×#41	—	67	2	no	—
338	C₂×#41	—	134	1	no	—
339	C₂×#41	—	134	1	no	—
340	C₂×#41	—	134	1	no	—
341	C₂×#41	—	134	1	no	—
342	C₂×#41	—	134	1	no	—
343	C₂×#41	—	134	1	no	—
344	C₂×#41	—	134	1	no	—
345	C₂×#41	—	134	1	no	—
346	C₂×#41	—	134	1	no	—
347	C₂×#41	—	134	1	no	—
348	C₂²×Q₈	—	67	1	no	—
349	C₂²×D₄	—	67	1	no	—
350	C₂²×D₄	—	134	1	no	—
351	C₂³×C₄	—	134	1	no	—
352	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	67	2	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	C₂²×D₆₇	1	2	yes	—
370	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	67	2	no	—
374	C₂²×C₈	—	134	1	no	—
375	C₂²×C₈	—	134	1	no	—
376	C₂²×C₈	—	134	1	no	—
377	C₂²×C₈	—	134	1	no	—
378	C₂²×C₈	—	134	1	no	—
379	C₂²×C₈	—	134	1	no	—
380	C₂²×C₈	—	134	1	no	—
381	#117	—	2	1	no	—
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	#117	—	67	2	no	—
385	#117	—	67	2	no	—
386	#117	—	134	1	no	—
387	#117	—	134	1	no	—
388	#117	C₂²×D₆₇	1	2	yes	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	134	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	134	1	no	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	—	67	2	no	—
395	C₄⋊C₈	—	134	8	no	—
396	#104	—	134	8	no	—
397	#103	—	134	4	no	—
398	#102	—	134	4	no	—
399	#101	—	134	4	no	—
400	#100	—	134	4	no	—
401	C₂⁴	—	134	1	no	—
402	C₂⁴	#11761628	1	1	yes	characteristic
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	#41	—	268	1	no	—
410	#41	—	268	1	no	—
411	#41	—	134	2	no	—
412	#41	—	134	2	no	—
413	#41	—	134	2	no	—
414	#41	—	134	2	no	—
415	#41	—	134	2	no	—
416	#41	—	134	2	no	—
417	#41	—	134	2	no	—
418	#41	—	134	2	no	—
419	C₂×Q₈	—	67	2	no	—
420	C₂×Q₈	—	134	1	no	—
421	C₂×Q₈	—	134	1	no	—
422	C₂×Q₈	—	134	1	no	—
423	C₂×Q₈	—	134	1	no	—
424	C₂×Q₈	—	134	1	no	—
425	C₂×D₄	—	268	1	no	—
426	C₂×D₄	—	268	1	no	—
427	C₂×D₄	—	268	1	no	—
428	C₂×D₄	—	268	1	no	—
429	C₂×D₄	—	67	2	no	—
430	C₂×D₄	—	134	2	no	—
431	C₂×D₄	—	134	2	no	—
432	C₂×D₄	—	134	1	no	—
433	C₂×D₄	—	134	1	no	—
434	C₂×D₄	—	134	1	no	—
435	C₂×D₄	—	134	1	no	—
436	C₂×D₄	—	134	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	—	268	1	no	—
439	C₂²×C₄	—	268	1	no	—
440	C₂²×C₄	—	268	1	no	—
441	C₂²×C₄	—	268	1	no	—
442	C₂²×C₄	—	134	1	no	—
443	C₂²×C₄	—	134	2	no	—
444	C₂²×C₄	—	134	2	no	—
445	C₂²×C₄	—	134	2	no	—
446	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
447	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
448	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
449	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
450	C₂²×C₄	#11761627	1	1	yes	characteristic
451	C₂²×C₄	#11761627	1	1	yes	characteristic
452	C₂²×C₄	#11761628	1	1	yes	characteristic
453	C₂²×C₄	#11761628	1	1	yes	characteristic
454	C₂²×C₄	#11761628	1	1	yes	characteristic
455	C₂²×C₄	#11761628	1	1	yes	characteristic
456	C₂²×C₄	#11761628	1	1	yes	characteristic
457	C₂²×C₄	#11761629	1	1	yes	characteristic
458	C₂²×C₄	#11761629	1	1	yes	characteristic
459	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	2	2	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	—	4	1	no	—
465	M₁₆	—	4	1	no	—
466	M₁₆	—	4	1	no	—
467	M₁₆	—	4	1	no	—
468	M₁₆	—	268	1	no	—
469	M₁₆	—	268	1	no	—
470	M₁₆	—	134	2	no	—
471	M₁₆	—	134	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	4	1	no	—
475	C₂×C₈	—	4	1	no	—
476	C₂×C₈	—	4	1	no	—
477	C₂×C₈	—	4	1	no	—
478	C₂×C₈	—	268	1	no	—
479	C₂×C₈	—	268	1	no	—
480	C₂×C₈	—	268	1	no	—
481	C₂×C₈	—	268	1	no	—
482	C₂×C₈	—	268	1	no	—
483	C₂×C₈	—	268	1	no	—
484	C₂×C₈	—	134	2	no	—
485	C₂×C₈	—	134	2	no	—
486	C₂×C₈	—	134	2	no	—
487	C₂×C₈	—	134	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	—	134	2	no	—
491	C₄⋊C₄	—	134	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	134	2	no	—
495	C₂²⋊C₄	—	134	2	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	4	1	no	—
498	C₄²	—	67	4	no	—
499	C₄²	—	134	2	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	268	1	no	—
502	C₂³	—	268	1	no	—
503	C₂³	—	536	2	no	—
504	C₂³	—	134	2	no	—
505	C₂³	#14524025	1	1	yes	characteristic
506	C₂³	#14524025	1	1	yes	characteristic
507	C₂³	#14524028	1	1	yes	characteristic
508	C₂³	#14524028	1	1	yes	characteristic
509	C₂³	#14524037	1	1	yes	characteristic
510	C₂³	#14524037	1	1	yes	characteristic
511	C₂³	C₂×#11761628	1	1	yes	characteristic
512	Q₈	—	268	1	no	—
513	Q₈	—	268	1	no	—
514	Q₈	—	134	2	no	—
515	Q₈	—	134	2	no	—
516	D₄	—	268	2	no	—
517	D₄	—	268	2	no	—
518	D₄	—	268	2	no	—
519	D₄	—	268	2	no	—
520	D₄	—	268	1	no	—
521	D₄	—	268	1	no	—
522	D₄	—	134	2	no	—
523	D₄	—	134	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	—	268	4	no	—
527	C₂×C₄	—	268	1	no	—
528	C₂×C₄	—	268	1	no	—
529	C₂×C₄	—	268	2	no	—
530	C₂×C₄	—	268	2	no	—
531	C₂×C₄	—	268	2	no	—
532	C₂×C₄	—	268	2	no	—
533	C₂×C₄	—	134	2	no	—
534	C₂×C₄	—	134	4	no	—
535	C₂×C₄	#14524016	1	1	yes	characteristic
536	C₂×C₄	#14524016	1	1	yes	characteristic
537	C₂×C₄	#14524016	1	1	yes	characteristic
538	C₂×C₄	#14524016	1	1	yes	characteristic
539	C₂×C₄	#14524025	1	1	yes	characteristic
540	C₂×C₄	#14524025	1	1	yes	characteristic
541	C₂×C₄	#14524028	1	1	yes	characteristic
542	C₂×C₄	#14524028	1	1	yes	characteristic
543	C₂×C₄	#14524028	1	1	yes	characteristic
544	C₂×C₄	#14524028	1	1	yes	characteristic
545	C₂×C₄	#14524028	1	1	yes	characteristic
546	C₂×C₄	#14524028	1	1	yes	characteristic
547	C₂×C₄	#14524029	1	1	yes	characteristic
548	C₂×C₄	#14524029	1	1	yes	characteristic
549	C₂×C₄	#14524029	1	1	yes	characteristic
550	C₂×C₄	#14524029	1	1	yes	characteristic
551	C₂×C₄	#14524037	1	1	yes	characteristic
552	C₂×C₄	#14524037	1	1	yes	characteristic
553	C₂×C₄	#14524038	1	1	yes	characteristic
554	C₂×C₄	#14524038	1	1	yes	characteristic
555	C₂×C₄	#14524038	1	1	yes	characteristic
556	C₂×C₄	#14524038	1	1	yes	characteristic
557	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
558	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
559	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
560	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
561	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
562	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
563	C₈	—	4	2	no	—
564	C₈	—	4	2	no	—
565	C₈	—	268	2	no	—
566	C₈	—	268	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	268	2	no	—
575	C₂²	—	536	2	no	—
576	C₂²	—	536	2	no	—
577	C₂²	—	536	2	no	—
578	C₂²	#16863325	1	1	yes	characteristic
579	C₂²	#16863325	1	1	yes	characteristic
580	C₂²	#16863325	1	1	yes	characteristic
581	C₂²	#16863325	1	1	yes	characteristic
582	C₂²	C₂×#14524025	1	1	yes	characteristic
583	C₂²	C₂×#14524028	1	1	yes	characteristic
584	C₂²	C₂×#14524037	1	1	yes	characteristic
585	C₄	—	8	2	no	—
586	C₄	—	268	4	no	—
587	C₄	—	268	2	no	—
588	C₄	#16863325	1	1	yes	characteristic
589	C₄	#16863325	1	1	yes	characteristic
590	C₄	#16863325	1	1	yes	characteristic
591	C₄	#16863325	1	1	yes	characteristic
592	C₄	C₂×#14524016	1	1	yes	characteristic
593	C₄	C₂×#14524028	1	1	yes	characteristic
594	C₄	C₂×#14524029	1	1	yes	characteristic
595	C₄	C₂×#14524038	1	1	yes	characteristic
596	C₂	—	2	1	no	—
597	C₂	—	2	1	no	—
598	C₂	—	2	1	no	—
599	C₂	—	2	1	no	—
600	C₂	—	2	1	no	—
601	C₂	—	2	1	no	—
602	C₂	—	536	2	no	—
603	C₂	#22561664	1	2	yes	direct product factor
604	C₂	C₂×#16863325	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14524029
commutator, cosocle	C₂²×C₄×C₆₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂×#344×C₆₇	C₂
socle	C₂²×C₆₇	#397
prime radical	C₂²×#11761628	C₂²
hypercenter	C₂×#344	D₆₇
hypocenter	C₆₇	C₂×#2080
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
1. C₂×#16863424	C₂	semidirect
5. #22561664	C₂	direct (N × H)
6. C₂×#16863160	C₂	semidirect
7. C₂×#16863152	C₂	semidirect
8. C₂×#344×C₆₇	C₂	semidirect
14. #16863424	C₂²	semidirect
27. #16863160	C₂²	semidirect
28. #16863152	C₂²	semidirect
32. #344×C₆₇	C₂²	semidirect
300. C₂×C₆₇	#2080	semidirect
308. C₂×#344	D₆₇	semidirect
311. C₆₇	C₂×#2080	semidirect
333. #344	C₂×D₆₇	semidirect
603. C₂	#22561664	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16863424	2
C₂×#16863412	2
C₂×#16863390	2
C₂×#16863378	2
#22561664	2
C₂×#16863160	2
C₂×#16863152	2
C₂×#344×C₆₇	2
C₂×#2080	67

Subgroups — C2×#22561664 #30884754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22561664 #30884754