Subgroups — C₂×#22561107 #30859805

Order 17152.

1474 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14524065	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863434	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16863412	C₂	1	2	yes	maximal, complemented
4	C₂×#16863369	C₂	1	2	yes	maximal, complemented
5	#22561107	C₂	1	8	yes	maximal, direct product factor
6	C₂×#405×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#11761628	C₂²	1	2	yes	—
8	C₂×#14524065	—	2	1	no	—
9	C₂×#14524065	—	2	1	no	—
10	C₂×#14524065	—	2	2	no	—
11	C₂×#14524065	—	2	1	no	—
12	C₂×#14524065	—	2	1	no	—
13	C₂×#14524065	—	2	2	no	—
14	C₂×#14524065	C₄	1	4	yes	complemented
15	C₂×#14524065	C₂²	1	4	yes	—
16	C₂²×Dic₂₆₈	C₄	1	1	yes	characteristic, complemented
17	C₂²×#11761617	C₄	1	2	yes	complemented
18	C₂²×D₅₃₆	C₄	1	1	yes	characteristic, complemented
19	C₂×#14524002	C₂²	1	2	yes	—
20	#16863434	—	2	2	no	—
21	#16863434	C₂²	1	4	yes	complemented
22	C₂×#14523977	—	2	1	no	—
23	C₂×#14523975	—	2	1	no	—
24	#16863412	—	2	4	no	—
25	#16863412	C₂²	1	8	yes	complemented
26	C₂×#14523969	—	2	4	no	—
27	#16863369	—	2	4	no	—
28	#16863369	C₂²	1	8	yes	complemented
29	C₂×#14523957	—	2	4	no	—
30	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
31	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
33	#405×C₆₇	—	2	2	no	—
34	#405×C₆₇	C₂²	1	4	yes	complemented
35	C₂×#97×C₆₇	—	2	1	no	—
36	C₂×C₄×C₈×C₆₇	—	2	1	no	—
37	C₂×#11761628	—	2	2	no	—
38	C₂×#11761628	—	2	2	no	—
39	C₂×#11761628	—	2	2	no	—
40	C₂×#11761628	—	2	2	no	—
41	C₂×#11761628	—	2	2	no	—
42	C₂×#11761628	—	2	2	no	—
43	C₂×#11761628	—	2	2	no	—
44	C₂×#11761628	—	2	2	no	—
45	C₂×#11761628	—	2	2	no	—
46	C₂×#11761628	—	2	2	no	—
47	C₂×#11761628	C₂×C₄	1	4	yes	—
48	C₂×#11761628	C₂³	1	4	yes	—
49	C₂²×Dic₁₃₄	C₂×C₄	1	2	yes	—
50	C₂²×D₂₆₈	C₂×C₄	1	2	yes	—
51	C₂²×C₂²⋊D₆₇	—	2	2	no	—
52	C₂²×C₄×D₆₇	—	2	2	no	—
53	#14524065	—	2	4	no	—
54	#14524065	—	2	4	no	—
55	#14524065	—	2	4	no	—
56	#14524065	—	2	4	no	—
57	#14524065	—	2	4	no	—
58	#14524065	—	2	4	no	—
59	#14524065	—	2	4	no	—
60	#14524065	—	2	4	no	—
61	C₂×Dic₂₆₈	—	2	1	no	—
62	C₂×Dic₂₆₈	—	2	1	no	—
63	C₂×Dic₂₆₈	—	2	2	no	—
64	C₂×Dic₂₆₈	C₂×C₄	1	4	yes	complemented
65	C₂×#11761617	—	2	2	no	—
66	C₂×#11761617	—	2	2	no	—
67	C₂×#11761617	—	2	4	no	—
68	C₂×#11761617	C₂×C₄	1	8	yes	complemented
69	C₂×D₅₃₆	—	2	1	no	—
70	C₂×D₅₃₆	—	2	1	no	—
71	C₂×D₅₃₆	—	2	2	no	—
72	C₂×D₅₃₆	C₂×C₄	1	4	yes	complemented
73	#14524002	—	2	2	no	—
74	#14524002	—	2	2	no	—
75	#14524002	—	2	2	no	—
76	#14524002	C₂³	1	4	yes	—
77	C₂×C₄⋊Dic₆₇	—	2	2	no	—
78	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
79	C₂×C₄×Dic₆₇	—	2	2	no	—
80	#14523977	—	2	4	no	—
81	#14523975	—	2	4	no	—
82	#14523969	—	2	16	no	—
83	#14523957	—	2	16	no	—
84	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₆₇	—	2	1	no	—
86	C₂×M₁₆×C₆₇	—	2	1	no	—
87	C₂×M₁₆×C₆₇	—	2	1	no	—
88	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
89	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
90	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
91	C₂²×C₈×C₆₇	—	2	1	no	—
92	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
93	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
94	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
95	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
96	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₆₇	D₄	1	2	yes	—
98	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
99	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
100	C₂²×C₈×C₆₇	D₄	1	2	yes	—
101	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
102	#117×C₆₇	—	2	1	no	—
103	#117×C₆₇	—	2	1	no	—
104	#117×C₆₇	D₄	1	2	yes	—
105	#117×C₆₇	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
108	C₂×C₄²×C₆₇	—	2	1	no	—
109	#97×C₆₇	—	2	4	no	—
110	C₄×C₈×C₆₇	—	2	4	no	—
111	C₂³×D₆₇	—	2	2	no	—
112	#11761628	—	2	4	no	—
113	#11761628	—	2	4	no	—
114	#11761628	—	2	4	no	—
115	#11761628	—	2	4	no	—
116	#11761628	—	2	4	no	—
117	#11761628	—	2	4	no	—
118	#11761628	—	2	4	no	—
119	#11761628	—	2	4	no	—
120	#11761628	—	4	2	no	—
121	#11761628	—	4	2	no	—
122	#11761628	—	4	2	no	—
123	#11761628	—	4	2	no	—
124	#11761628	—	4	2	no	—
125	#11761628	—	4	2	no	—
126	#11761628	—	4	2	no	—
127	#11761628	—	4	2	no	—
128	C₂×Dic₁₃₄	—	2	2	no	—
129	C₂×Dic₁₃₄	—	2	2	no	—
130	C₂×Dic₁₃₄	—	2	2	no	—
131	C₂×Dic₁₃₄	—	2	2	no	—
132	C₂×Dic₁₃₄	—	2	2	no	—
133	C₂×Dic₁₃₄	C₂²×C₄	1	4	yes	—
134	C₂×D₂₆₈	—	2	2	no	—
135	C₂×D₂₆₈	—	2	2	no	—
136	C₂×D₂₆₈	—	2	2	no	—
137	C₂×D₂₆₈	—	2	2	no	—
138	C₂×D₂₆₈	—	2	2	no	—
139	C₂×D₂₆₈	C₂²×C₄	1	4	yes	—
140	C₂×C₂²⋊D₆₇	—	2	4	no	—
141	C₂×C₂²⋊D₆₇	—	2	4	no	—
142	C₂×C₂²⋊D₆₇	—	4	2	no	—
143	C₂×C₂²⋊D₆₇	—	4	2	no	—
144	C₂×C₂²⋊D₆₇	—	4	2	no	—
145	C₂×C₂²⋊D₆₇	—	4	2	no	—
146	C₂²×Dic₆₇	—	2	2	no	—
147	C₂²×Dic₆₇	—	4	2	no	—
148	C₂×C₄×D₆₇	—	2	4	no	—
149	C₂×C₄×D₆₇	—	2	4	no	—
150	C₂×C₄×D₆₇	—	4	2	no	—
151	C₂×C₄×D₆₇	—	4	2	no	—
152	C₂×C₄×D₆₇	—	4	2	no	—
153	C₂×C₄×D₆₇	—	4	2	no	—
154	Dic₂₆₈	—	2	4	no	—
155	Dic₂₆₈	—	2	4	no	—
156	#11761617	—	2	8	no	—
157	#11761617	—	2	8	no	—
158	D₅₃₆	—	2	4	no	—
159	D₅₃₆	—	2	4	no	—
160	C₄⋊Dic₆₇	—	2	4	no	—
161	C₄⋊Dic₆₇	—	4	2	no	—
162	C₂²⋊Dic₆₇	—	2	4	no	—
163	C₂²⋊Dic₆₇	—	4	2	no	—
164	C₄×Dic₆₇	—	2	4	no	—
165	C₄×Dic₆₇	—	4	2	no	—
166	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₇	—	2	2	no	—
168	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
178	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
179	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
180	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
181	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
182	M₁₆×C₆₇	—	2	2	no	—
183	M₁₆×C₆₇	—	2	2	no	—
184	M₁₆×C₆₇	—	2	2	no	—
185	M₁₆×C₆₇	C₂×D₄	1	4	yes	—
186	C₂×C₈×C₆₇	—	2	2	no	—
187	C₂×C₈×C₆₇	—	2	2	no	—
188	C₂×C₈×C₆₇	—	2	2	no	—
189	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
192	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
195	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
196	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
197	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
198	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
199	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
200	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
201	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
202	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
203	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
204	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
205	C₄⋊C₄×C₆₇	—	2	2	no	—
206	C₄⋊C₄×C₆₇	—	2	2	no	—
207	C₂²⋊C₄×C₆₇	—	2	2	no	—
208	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
209	C₄²×C₆₇	—	2	2	no	—
210	C₄²×C₆₇	—	2	2	no	—
211	C₂³×C₆₇	—	4	2	no	—
212	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
213	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₆₇	#121	1	1	yes	characteristic
215	C₂³×C₆₇	#121	1	1	yes	characteristic
216	C₂³×C₆₇	#127	1	1	yes	characteristic
217	C₂³×C₆₇	#127	1	1	yes	characteristic
218	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
219	C₂²×D₆₇	—	2	4	no	—
220	C₂²×D₆₇	—	4	2	no	—
221	C₂²×D₆₇	—	4	2	no	—
222	C₂²×D₆₇	—	8	4	no	—
223	C₂×C₄×C₆₇	—	2	4	no	—
224	C₂×C₄×C₆₇	—	4	4	no	—
225	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
236	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
237	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
238	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
239	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
240	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
241	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
242	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
243	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
244	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
245	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
246	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
247	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
253	C₂²⋊D₆₇	—	4	4	no	—
254	C₂²⋊D₆₇	—	4	4	no	—
255	C₂²⋊D₆₇	—	4	4	no	—
256	C₂²⋊D₆₇	—	4	4	no	—
257	C₂×Dic₆₇	—	2	4	no	—
258	C₂×Dic₆₇	—	4	2	no	—
259	C₂×Dic₆₇	—	4	2	no	—
260	C₂×Dic₆₇	—	4	4	no	—
261	C₂×Dic₆₇	—	8	4	no	—
262	D₂₆₈	—	2	4	no	—
263	D₂₆₈	—	2	4	no	—
264	D₂₆₈	—	4	2	no	—
265	D₂₆₈	—	4	2	no	—
266	C₄×D₆₇	—	4	4	no	—
267	C₄×D₆₇	—	4	4	no	—
268	C₄×D₆₇	—	4	4	no	—
269	C₄×D₆₇	—	4	4	no	—
270	Dic₁₃₄	—	2	4	no	—
271	Dic₁₃₄	—	2	4	no	—
272	Dic₁₃₄	—	4	2	no	—
273	Dic₁₃₄	—	4	2	no	—
274	C₈×C₆₇	—	2	4	no	—
275	C₈×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
276	C₈×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
277	C₈×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
278	C₈×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
279	C₂²×C₆₇	—	2	2	no	—
280	C₂²×C₆₇	—	2	2	no	—
281	C₂²×C₆₇	—	2	2	no	—
282	C₂²×C₆₇	—	4	1	no	—
283	C₂²×C₆₇	—	4	1	no	—
284	C₂²×C₆₇	—	4	1	no	—
285	C₂²×C₆₇	—	4	1	no	—
286	C₂²×C₆₇	#390	1	1	yes	characteristic
287	C₂²×C₆₇	#390	1	1	yes	characteristic
288	C₂²×C₆₇	#390	1	1	yes	characteristic
289	C₂²×C₆₇	#390	1	1	yes	characteristic
290	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
292	C₂²×C₆₇	C₂×#127	1	1	yes	characteristic
293	C₂×D₆₇	—	4	4	no	—
294	C₂×D₆₇	—	8	4	no	—
295	C₂×D₆₇	—	8	4	no	—
296	C₂×D₆₇	—	8	4	no	—
297	C₄×C₆₇	—	4	4	no	—
298	C₄×C₆₇	#390	1	1	yes	characteristic
299	C₄×C₆₇	#390	1	1	yes	characteristic
300	C₄×C₆₇	#390	1	1	yes	characteristic
301	C₄×C₆₇	#390	1	1	yes	characteristic
302	C₄×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
303	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
304	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
305	C₄×C₆₇	C₂×#124	1	1	yes	characteristic
306	Dic₆₇	—	4	4	no	—
307	Dic₆₇	—	8	4	no	—
308	C₂×#1976	—	67	1	no	maximal, Sylow
309	C₂×C₆₇	—	2	1	no	—
310	C₂×C₆₇	—	2	1	no	—
311	C₂×C₆₇	—	2	1	no	—
312	C₂×C₆₇	—	2	1	no	—
313	C₂×C₆₇	—	2	1	no	—
314	C₂×C₆₇	—	2	1	no	—
315	C₂×C₆₇	#1976	1	2	yes	complemented
316	C₂×C₆₇	C₂×#390	1	1	yes	characteristic
317	D₆₇	—	8	4	no	—
318	C₂²×#135	—	67	1	no	—
319	C₂×#427	—	67	1	no	—
320	C₂×#421	—	67	2	no	—
321	C₂×#410	—	67	2	no	—
322	C₂×#405	D₆₇	1	1	yes	characteristic, complemented
323	#1976	—	67	8	no	—
324	C₆₇	C₂×#1976	1	1	yes	characteristic, complemented, Sylow
325	C₂²×#41	—	67	2	no	—
326	C₂×#135	—	67	4	no	—
327	C₂×#135	—	67	4	no	—
328	C₂×#135	—	134	1	no	—
329	C₂×#135	—	134	1	no	—
330	C₂×#135	—	134	2	no	—
331	C₂×#135	—	134	1	no	—
332	C₂×#135	—	134	1	no	—
333	C₂×#135	—	134	2	no	—
334	C₂²×Q₁₆	—	67	1	no	—
335	C₂²×SD₁₆	—	67	2	no	—
336	C₂²×D₈	—	67	1	no	—
337	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
338	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
339	C₂×#117	—	67	2	no	—
340	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
341	#427	—	67	4	no	—
342	#427	—	134	2	no	—
343	C₂×#107	—	134	1	no	—
344	C₂×#106	—	134	1	no	—
345	#421	—	67	8	no	—
346	#421	—	134	4	no	—
347	C₂×#104	—	134	4	no	—
348	#410	—	67	8	no	—
349	#410	—	134	4	no	—
350	C₂×#99	—	134	4	no	—
351	#405	—	2	2	no	—
352	#405	C₂×D₆₇	1	4	yes	complemented
353	C₂×#97	—	2	1	no	—
354	C₂×C₄×C₈	—	2	1	no	—
355	C₂×#41	—	67	4	no	—
356	C₂×#41	—	67	4	no	—
357	C₂×#41	—	134	2	no	—
358	C₂×#41	—	134	2	no	—
359	C₂×#41	—	134	2	no	—
360	C₂×#41	—	134	2	no	—
361	C₂×#41	—	134	2	no	—
362	C₂×#41	—	134	2	no	—
363	C₂×#41	—	134	2	no	—
364	C₂×#41	—	134	2	no	—
365	C₂×#41	—	134	2	no	—
366	C₂×#41	—	134	2	no	—
367	C₂²×Q₈	—	67	2	no	—
368	C₂²×D₄	—	67	2	no	—
369	C₂²×D₄	—	134	2	no	—
370	C₂³×C₄	—	134	2	no	—
371	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
372	#135	—	134	4	no	—
373	#135	—	134	4	no	—
374	#135	—	134	4	no	—
375	#135	—	134	4	no	—
376	#135	—	134	4	no	—
377	#135	—	134	4	no	—
378	#135	—	134	4	no	—
379	#135	—	134	4	no	—
380	C₂×Q₁₆	—	67	4	no	—
381	C₂×Q₁₆	—	134	1	no	—
382	C₂×Q₁₆	—	134	1	no	—
383	C₂×Q₁₆	—	134	2	no	—
384	C₂×SD₁₆	—	67	8	no	—
385	C₂×SD₁₆	—	134	2	no	—
386	C₂×SD₁₆	—	134	2	no	—
387	C₂×SD₁₆	—	134	4	no	—
388	C₂×D₈	—	67	4	no	—
389	C₂×D₈	—	134	1	no	—
390	C₂×D₈	—	134	1	no	—
391	C₂×D₈	—	134	2	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	1	no	—
395	C₂×M₁₆	D₂₆₈	1	2	yes	—
396	C₂×M₁₆	D₂₆₈	1	2	yes	—
397	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
398	C₂²×C₈	—	2	1	no	—
399	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
400	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
401	C₂²×C₈	C₄×D₆₇	1	2	yes	—
402	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
403	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
404	C₂²×C₈	D₂₆₈	1	2	yes	—
405	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
406	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
407	C₂²×C₈	C₂²⋊D₆₇	1	2	yes	—
408	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
409	#117	—	2	1	no	—
410	#117	—	2	1	no	—
411	#117	—	67	4	no	—
412	#117	—	134	2	no	—
413	#117	—	134	2	no	—
414	#117	—	134	2	no	—
415	#117	D₂₆₈	1	2	yes	—
416	#117	C₂²×D₆₇	1	2	yes	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	134	2	no	—
419	C₂×C₂²⋊C₄	—	134	2	no	—
420	C₂×C₂²⋊C₄	D₂₆₈	1	2	yes	—
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	—	134	2	no	—
423	#107	—	134	4	no	—
424	#106	—	134	4	no	—
425	#104	—	134	16	no	—
426	#99	—	134	16	no	—
427	#97	—	2	4	no	—
428	C₄×C₈	—	2	4	no	—
429	C₂⁴	—	134	2	no	—
430	C₂⁴	C₂×D₂₆₈	1	1	yes	characteristic
431	#41	—	268	2	no	—
432	#41	—	268	2	no	—
433	#41	—	268	2	no	—
434	#41	—	268	2	no	—
435	#41	—	268	2	no	—
436	#41	—	268	2	no	—
437	#41	—	268	2	no	—
438	#41	—	268	2	no	—
439	#41	—	134	4	no	—
440	#41	—	134	4	no	—
441	#41	—	134	4	no	—
442	#41	—	134	4	no	—
443	#41	—	134	4	no	—
444	#41	—	134	4	no	—
445	#41	—	134	4	no	—
446	#41	—	134	4	no	—
447	C₂×Q₈	—	67	4	no	—
448	C₂×Q₈	—	134	2	no	—
449	C₂×Q₈	—	134	2	no	—
450	C₂×Q₈	—	134	2	no	—
451	C₂×Q₈	—	134	2	no	—
452	C₂×Q₈	—	134	2	no	—
453	C₂×D₄	—	268	2	no	—
454	C₂×D₄	—	268	2	no	—
455	C₂×D₄	—	268	2	no	—
456	C₂×D₄	—	268	2	no	—
457	C₂×D₄	—	67	4	no	—
458	C₂×D₄	—	134	4	no	—
459	C₂×D₄	—	134	4	no	—
460	C₂×D₄	—	134	2	no	—
461	C₂×D₄	—	134	2	no	—
462	C₂×D₄	—	134	2	no	—
463	C₂×D₄	—	134	2	no	—
464	C₂×D₄	—	134	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	268	2	no	—
467	C₂²×C₄	—	268	2	no	—
468	C₂²×C₄	—	268	2	no	—
469	C₂²×C₄	—	268	2	no	—
470	C₂²×C₄	—	268	2	no	—
471	C₂²×C₄	—	134	2	no	—
472	C₂²×C₄	—	134	4	no	—
473	C₂²×C₄	—	134	4	no	—
474	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
476	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
483	C₂²×C₄	#11761628	1	1	yes	characteristic
484	C₂²×C₄	#11761628	1	1	yes	characteristic
485	C₂²×C₄	#11761628	1	1	yes	characteristic
486	C₂²×C₄	#11761628	1	1	yes	characteristic
487	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
488	Q₁₆	—	134	4	no	—
489	Q₁₆	—	134	4	no	—
490	SD₁₆	—	134	8	no	—
491	SD₁₆	—	134	8	no	—
492	D₈	—	134	4	no	—
493	D₈	—	134	4	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	2	2	no	—
497	M₁₆	C₂×D₂₆₈	1	4	yes	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
502	C₂×C₈	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
503	C₂×C₈	(C₂×D₆₇)⋊C₄	1	2	yes	—
504	C₂×C₈	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
505	C₂×C₈	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
506	C₂×C₈	(C₂×D₆₇)⋊C₄	1	2	yes	—
507	C₂×C₈	(C₂×D₆₇)⋊C₄	1	2	yes	—
508	C₂×C₈	(C₂×D₆₇)⋊C₄	1	2	yes	—
509	C₂×C₈	(C₂×D₆₇)⋊C₄	1	2	yes	—
510	C₂×C₈	(C₂×D₆₇)⋊C₄	1	2	yes	—
511	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
512	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
513	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
514	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
515	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
516	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	268	2	no	—
520	C₄⋊C₄	—	134	4	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	268	2	no	—
523	C₂²⋊C₄	—	134	4	no	—
524	C₂²⋊C₄	C₂×D₂₆₈	1	4	yes	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	268	2	no	—
528	C₄²	—	134	4	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	268	2	no	—
531	C₂³	—	268	2	no	—
532	C₂³	—	536	4	no	—
533	C₂³	—	134	4	no	—
534	C₂³	C₄×D₂₆₈	1	1	yes	characteristic
535	C₂³	C₄×D₂₆₈	1	1	yes	characteristic
536	C₂³	#14524017	1	1	yes	characteristic
537	C₂³	#14524017	1	1	yes	characteristic
538	C₂³	#14524040	1	1	yes	characteristic
539	C₂³	#14524040	1	1	yes	characteristic
540	C₂³	C₂²×D₂₆₈	1	1	yes	characteristic
541	Q₈	—	268	2	no	—
542	Q₈	—	268	2	no	—
543	Q₈	—	134	4	no	—
544	Q₈	—	134	4	no	—
545	D₄	—	268	4	no	—
546	D₄	—	268	4	no	—
547	D₄	—	268	4	no	—
548	D₄	—	268	4	no	—
549	D₄	—	268	2	no	—
550	D₄	—	268	2	no	—
551	D₄	—	134	4	no	—
552	D₄	—	134	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	268	2	no	—
556	C₂×C₄	—	268	2	no	—
557	C₂×C₄	—	268	4	no	—
558	C₂×C₄	—	268	4	no	—
559	C₂×C₄	—	268	4	no	—
560	C₂×C₄	—	268	4	no	—
561	C₂×C₄	—	268	4	no	—
562	C₂×C₄	—	536	4	no	—
563	C₂×C₄	—	134	4	no	—
564	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
565	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
566	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
567	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
568	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
569	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
570	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
571	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
572	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
573	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
574	C₂×C₄	#14524017	1	1	yes	characteristic
575	C₂×C₄	#14524017	1	1	yes	characteristic
576	C₂×C₄	#14524017	1	1	yes	characteristic
577	C₂×C₄	#14524017	1	1	yes	characteristic
578	C₂×C₄	#14524017	1	1	yes	characteristic
579	C₂×C₄	#14524017	1	1	yes	characteristic
580	C₂×C₄	#14524031	1	1	yes	characteristic
581	C₂×C₄	#14524031	1	1	yes	characteristic
582	C₂×C₄	#14524031	1	1	yes	characteristic
583	C₂×C₄	#14524031	1	1	yes	characteristic
584	C₂×C₄	#14524040	1	1	yes	characteristic
585	C₂×C₄	#14524040	1	1	yes	characteristic
586	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
587	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
590	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
591	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
592	C₈	—	2	4	no	—
593	C₈	C₂×(C₂×D₆₇)⋊C₄	1	2	yes	—
594	C₈	C₂×(C₂×D₆₇)⋊C₄	1	2	yes	—
595	C₈	C₂×(C₂×D₆₇)⋊C₄	1	2	yes	—
596	C₈	C₂×(C₂×D₆₇)⋊C₄	1	2	yes	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	268	4	no	—
605	C₂²	—	536	4	no	—
606	C₂²	—	536	4	no	—
607	C₂²	—	536	4	no	—
608	C₂²	#16863298	1	1	yes	characteristic
609	C₂²	#16863298	1	1	yes	characteristic
610	C₂²	#16863298	1	1	yes	characteristic
611	C₂²	#16863298	1	1	yes	characteristic
612	C₂²	C₂×C₄×D₂₆₈	1	1	yes	characteristic
613	C₂²	C₂×#14524017	1	1	yes	characteristic
614	C₂²	C₂×#14524040	1	1	yes	characteristic
615	C₄	—	4	4	no	—
616	C₄	—	268	4	no	—
617	C₄	—	536	4	no	—
618	C₄	#16863298	1	1	yes	characteristic
619	C₄	#16863298	1	1	yes	characteristic
620	C₄	#16863298	1	1	yes	characteristic
621	C₄	#16863298	1	1	yes	characteristic
622	C₄	C₂²×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
623	C₄	C₂×C₄×D₂₆₈	1	1	yes	characteristic
624	C₄	C₂×#14524017	1	1	yes	characteristic
625	C₄	C₂×#14524031	1	1	yes	characteristic
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	536	4	no	—
633	C₂	#22561107	1	2	yes	direct product factor
634	C₂	C₂×#16863298	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14524017
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂×#405×C₆₇	C₂
socle	C₂²×C₆₇	#390
prime radical	C₂²×#14524065	C₂
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₂×#405	D₆₇
hypocenter	C₆₇	C₂×#1976
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. C₂×#16863434	C₂	semidirect
3. C₂×#16863412	C₂	semidirect
4. C₂×#16863369	C₂	semidirect
5. #22561107	C₂	direct (N × H)
6. C₂×#405×C₆₇	C₂	semidirect
14. C₂×#14524065	C₄	semidirect
16. C₂²×Dic₂₆₈	C₄	semidirect
17. C₂²×#11761617	C₄	semidirect
18. C₂²×D₅₃₆	C₄	semidirect
21. #16863434	C₂²	semidirect
25. #16863412	C₂²	semidirect
28. #16863369	C₂²	semidirect
34. #405×C₆₇	C₂²	semidirect
64. C₂×Dic₂₆₈	C₂×C₄	semidirect
68. C₂×#11761617	C₂×C₄	semidirect
72. C₂×D₅₃₆	C₂×C₄	semidirect
315. C₂×C₆₇	#1976	semidirect
322. C₂×#405	D₆₇	semidirect
324. C₆₇	C₂×#1976	semidirect
352. #405	C₂×D₆₇	semidirect
633. C₂	#22561107	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14524065	2
C₂×#16863434	2
C₂×#16863412	2
C₂×#16863369	2
#22561107	2
C₂×#405×C₆₇	2
C₂×#1976	67

Subgroups — C2×#22561107 #30859805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22561107 #30859805