Subgroups — C₂×#22560875 #30858409

Order 17152.

1046 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	C₂×#16863444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863413	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863380	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#11761612	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560875	C₂	1	8	yes	maximal, direct product factor
6	C₂×#16863167	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863156	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#104×C₆₇	C₂	1	1	yes	maximal, 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	C₂×#14524002	C₂²	1	1	yes	characteristic
13	#16863444	—	2	2	no	—
14	#16863444	C₂²	1	4	yes	complemented
15	C₂×#14523978	—	2	2	no	—
16	#16863413	—	2	2	no	—
17	#16863413	C₂²	1	4	yes	—
18	C₂×#14523970	—	2	2	no	—
19	#16863380	C₄	1	4	yes	complemented
20	#16863380	C₂²	1	4	yes	—
21	C₂×#14523962	C₄	1	2	yes	complemented
22	C₂×#14523960	C₄	1	2	yes	complemented
23	C₄×#11761612	—	2	2	no	—
24	C₄×#11761612	C₂²	1	4	yes	complemented
25	C₂×#14523954	—	2	1	no	—
26	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
27	#16863167	C₂²	1	4	yes	complemented
28	#16863156	C₂²	1	4	yes	complemented
29	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#104×C₆₇	—	2	1	no	—
33	C₂×#104×C₆₇	—	2	1	no	—
34	C₂×#104×C₆₇	—	2	2	no	—
35	C₂×#104×C₆₇	C₂²	1	4	yes	—
36	C₂×#11761612	—	2	1	no	—
37	C₂×#11761612	—	2	1	no	—
38	C₂×#11761612	—	2	1	no	—
39	C₂×#11761612	—	2	1	no	—
40	C₂×#11761612	—	2	1	no	—
41	C₂×#11761612	—	2	1	no	—
42	C₂×#11761612	—	2	1	no	—
43	C₂×#11761612	—	2	1	no	—
44	C₂×#11761612	—	2	1	no	—
45	C₂×#11761612	C₂×C₄	1	2	yes	—
46	C₂×#11761612	C₂×C₄	1	2	yes	—
47	C₂×#11761612	C₂×C₄	1	2	yes	—
48	C₂×#11761612	C₂×C₄	1	2	yes	—
49	C₂×#11761612	D₄	1	2	yes	—
50	C₂×#11761612	D₄	1	2	yes	—
51	C₂×#11761612	C₂³	1	2	yes	—
52	C₂×#11761612	C₂³	1	2	yes	—
53	C₂×#11761612	C₂³	1	2	yes	—
54	C₂²×C₆₇⋊C₈	—	2	1	no	—
55	C₂²×C₆₇⋊C₈	—	2	1	no	—
56	C₂²×C₆₇⋊C₈	—	2	1	no	—
57	#14524002	—	2	1	no	—
58	#14524002	—	2	1	no	—
59	#14524002	—	2	1	no	—
60	#14524002	C₂³	1	2	yes	—
61	C₂×C₄⋊Dic₆₇	—	2	1	no	—
62	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
63	C₂×C₄×Dic₆₇	—	2	1	no	—
64	#14523978	—	2	8	no	—
65	#14523970	—	2	8	no	—
66	#14523962	C₂×C₄	1	8	yes	complemented
67	#14523960	C₂×C₄	1	8	yes	complemented
68	#14523954	—	2	4	no	—
69	C₄×C₆₇⋊C₈	—	2	4	no	—
70	C₂×#41×C₆₇	—	2	1	no	—
71	C₂×#41×C₆₇	—	2	1	no	—
72	C₂×#41×C₆₇	—	2	1	no	—
73	C₂×#41×C₆₇	—	2	1	no	—
74	C₂×#41×C₆₇	—	2	1	no	—
75	C₂×#41×C₆₇	—	2	1	no	—
76	C₂×#41×C₆₇	—	2	1	no	—
77	C₂×#41×C₆₇	—	2	1	no	—
78	C₂×#41×C₆₇	—	2	1	no	—
79	C₂×#41×C₆₇	—	2	1	no	—
80	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
81	C₂×#41×C₆₇	C₂³	1	2	yes	—
82	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
83	C₂²×D₄×C₆₇	—	2	1	no	—
84	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
85	C₂³×C₄×C₆₇	—	2	1	no	—
86	C₂³×C₄×C₆₇	—	2	1	no	—
87	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₆₇	—	2	1	no	—
89	C₂×M₁₆×C₆₇	—	2	1	no	—
90	C₂×M₁₆×C₆₇	—	2	1	no	—
91	C₂×M₁₆×C₆₇	—	2	1	no	—
92	C₂×M₁₆×C₆₇	—	2	1	no	—
93	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
94	C₂²×C₈×C₆₇	—	2	1	no	—
95	C₂×C₄²×C₆₇	—	2	1	no	—
96	C₂×C₄²×C₆₇	—	2	1	no	—
97	C₂×C₄²×C₆₇	—	2	1	no	—
98	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₆₇	D₄	1	2	yes	—
101	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
102	#104×C₆₇	—	2	4	no	—
103	#104×C₆₇	—	2	4	no	—
104	C₂²×Dic₆₇	—	4	1	no	—
105	#11761612	—	2	2	no	—
106	#11761612	—	2	2	no	—
107	#11761612	—	2	2	no	—
108	#11761612	—	2	2	no	—
109	#11761612	—	2	2	no	—
110	#11761612	—	2	2	no	—
111	#11761612	—	2	2	no	—
112	#11761612	—	2	2	no	—
113	#11761612	—	2	2	no	—
114	#11761612	C₂²×C₄	1	4	yes	—
115	#11761612	C₂²×C₄	1	4	yes	—
116	#11761612	C₂×D₄	1	4	yes	—
117	C₂×C₆₇⋊C₈	—	2	2	no	—
118	C₂×C₆₇⋊C₈	—	2	2	no	—
119	C₂×C₆₇⋊C₈	—	2	2	no	—
120	C₂×C₆₇⋊C₈	—	2	2	no	—
121	C₂×C₆₇⋊C₈	—	2	2	no	—
122	C₂×C₆₇⋊C₈	—	2	2	no	—
123	C₂×C₆₇⋊C₈	—	2	2	no	—
124	C₂×C₆₇⋊C₈	—	2	2	no	—
125	C₂×C₆₇⋊C₈	—	2	2	no	—
126	C₄⋊Dic₆₇	—	2	2	no	—
127	C₄⋊Dic₆₇	—	4	1	no	—
128	C₂²⋊Dic₆₇	—	2	2	no	—
129	C₂²⋊Dic₆₇	—	4	1	no	—
130	C₄×Dic₆₇	—	2	2	no	—
131	C₄×Dic₆₇	—	4	1	no	—
132	C₂⁴×C₆₇	—	2	1	no	—
133	C₂⁴×C₆₇	#41	1	1	yes	characteristic
134	#41×C₆₇	—	2	2	no	—
135	#41×C₆₇	—	2	2	no	—
136	#41×C₆₇	—	2	2	no	—
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	#41×C₆₇	—	2	2	no	—
142	#41×C₆₇	—	4	1	no	—
143	#41×C₆₇	—	4	1	no	—
144	#41×C₆₇	—	4	1	no	—
145	#41×C₆₇	—	4	1	no	—
146	#41×C₆₇	—	4	1	no	—
147	#41×C₆₇	—	4	1	no	—
148	#41×C₆₇	—	4	1	no	—
149	#41×C₆₇	—	4	1	no	—
150	C₂×Q₈×C₆₇	—	2	1	no	—
151	C₂×Q₈×C₆₇	—	2	1	no	—
152	C₂×Q₈×C₆₇	—	2	1	no	—
153	C₂×Q₈×C₆₇	—	2	1	no	—
154	C₂×Q₈×C₆₇	—	2	1	no	—
155	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
156	C₂×D₄×C₆₇	—	2	2	no	—
157	C₂×D₄×C₆₇	—	2	2	no	—
158	C₂×D₄×C₆₇	—	2	1	no	—
159	C₂×D₄×C₆₇	—	2	1	no	—
160	C₂×D₄×C₆₇	—	2	1	no	—
161	C₂×D₄×C₆₇	—	2	1	no	—
162	C₂×D₄×C₆₇	—	2	1	no	—
163	C₂×D₄×C₆₇	—	4	1	no	—
164	C₂×D₄×C₆₇	—	4	1	no	—
165	C₂×D₄×C₆₇	—	4	1	no	—
166	C₂×D₄×C₆₇	—	4	1	no	—
167	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
168	C₂²×C₄×C₆₇	—	2	1	no	—
169	C₂²×C₄×C₆₇	—	2	1	no	—
170	C₂²×C₄×C₆₇	—	2	2	no	—
171	C₂²×C₄×C₆₇	—	2	1	no	—
172	C₂²×C₄×C₆₇	—	2	2	no	—
173	C₂²×C₄×C₆₇	—	2	2	no	—
174	C₂²×C₄×C₆₇	—	2	2	no	—
175	C₂²×C₄×C₆₇	—	4	4	no	—
176	C₂²×C₄×C₆₇	—	4	1	no	—
177	C₂²×C₄×C₆₇	—	4	1	no	—
178	C₂²×C₄×C₆₇	—	4	1	no	—
179	C₂²×C₄×C₆₇	—	4	1	no	—
180	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
187	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
188	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
189	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
190	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
193	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
194	M₁₆×C₆₇	—	2	2	no	—
195	M₁₆×C₆₇	—	2	2	no	—
196	M₁₆×C₆₇	—	4	1	no	—
197	M₁₆×C₆₇	—	4	1	no	—
198	C₂×C₈×C₆₇	—	2	2	no	—
199	C₂×C₈×C₆₇	—	4	1	no	—
200	C₂×C₈×C₆₇	—	4	1	no	—
201	C₄²×C₆₇	—	2	1	no	—
202	C₄²×C₆₇	—	2	2	no	—
203	C₄²×C₆₇	—	2	1	no	—
204	C₄²×C₆₇	—	2	2	no	—
205	C₄²×C₆₇	C₂×D₄	1	2	yes	—
206	C₄²×C₆₇	C₂×D₄	1	2	yes	—
207	C₂³×C₆₇	—	2	2	no	—
208	C₂³×C₆₇	—	4	2	no	—
209	C₂³×C₆₇	—	4	1	no	—
210	C₂³×C₆₇	—	4	1	no	—
211	C₂³×C₆₇	—	8	2	no	—
212	C₂³×C₆₇	#117	1	1	yes	characteristic
213	C₂³×C₆₇	#117	1	1	yes	characteristic
214	C₂³×C₆₇	#123	1	1	yes	characteristic
215	C₂³×C₆₇	#123	1	1	yes	characteristic
216	C₂³×C₆₇	#124	1	1	yes	characteristic
217	C₂³×C₆₇	#124	1	1	yes	characteristic
218	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
219	Q₈×C₆₇	—	2	2	no	—
220	Q₈×C₆₇	—	2	2	no	—
221	Q₈×C₆₇	—	4	1	no	—
222	Q₈×C₆₇	—	4	1	no	—
223	D₄×C₆₇	—	2	2	no	—
224	D₄×C₆₇	—	2	2	no	—
225	D₄×C₆₇	—	4	2	no	—
226	D₄×C₆₇	—	4	2	no	—
227	D₄×C₆₇	—	4	2	no	—
228	D₄×C₆₇	—	4	2	no	—
229	D₄×C₆₇	—	4	1	no	—
230	D₄×C₆₇	—	4	1	no	—
231	C₂×C₄×C₆₇	—	2	4	no	—
232	C₂×C₄×C₆₇	—	2	2	no	—
233	C₂×C₄×C₆₇	—	2	2	no	—
234	C₂×C₄×C₆₇	—	2	2	no	—
235	C₂×C₄×C₆₇	—	4	4	no	—
236	C₂×C₄×C₆₇	—	4	4	no	—
237	C₂×C₄×C₆₇	—	4	2	no	—
238	C₂×C₄×C₆₇	—	4	1	no	—
239	C₂×C₄×C₆₇	—	4	1	no	—
240	C₂×C₄×C₆₇	—	4	2	no	—
241	C₂×C₄×C₆₇	—	4	2	no	—
242	C₂×C₄×C₆₇	—	4	2	no	—
243	C₂×C₄×C₆₇	—	4	2	no	—
244	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
245	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
246	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
255	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
256	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
257	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
258	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
259	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
260	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
261	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
262	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
263	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
264	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
265	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
266	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
267	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
272	C₂×Dic₆₇	—	4	2	no	—
273	C₂×Dic₆₇	—	8	2	no	—
274	C₈×C₆₇	—	4	2	no	—
275	C₆₇⋊C₈	—	2	4	no	—
276	C₆₇⋊C₈	—	2	4	no	—
277	C₆₇⋊C₈	—	2	4	no	—
278	C₂²×C₆₇	—	2	2	no	—
279	C₂²×C₆₇	—	2	2	no	—
280	C₂²×C₆₇	—	2	2	no	—
281	C₂²×C₆₇	—	4	1	no	—
282	C₂²×C₆₇	—	4	1	no	—
283	C₂²×C₆₇	—	4	1	no	—
284	C₂²×C₆₇	—	4	1	no	—
285	C₂²×C₆₇	—	4	2	no	—
286	C₂²×C₆₇	—	8	2	no	—
287	C₂²×C₆₇	—	8	2	no	—
288	C₂²×C₆₇	—	8	2	no	—
289	C₂²×C₆₇	#388	1	1	yes	characteristic
290	C₂²×C₆₇	#388	1	1	yes	characteristic
291	C₂²×C₆₇	#388	1	1	yes	characteristic
292	C₂²×C₆₇	#388	1	1	yes	characteristic
293	C₂²×C₆₇	C₂×#117	1	1	yes	characteristic
294	C₂²×C₆₇	C₂×#123	1	1	yes	characteristic
295	C₂²×C₆₇	C₂×#124	1	1	yes	characteristic
296	C₄×C₆₇	—	2	4	no	—
297	C₄×C₆₇	—	4	2	no	—
298	C₄×C₆₇	—	4	2	no	—
299	C₄×C₆₇	#388	1	1	yes	characteristic
300	C₄×C₆₇	#388	1	1	yes	characteristic
301	C₄×C₆₇	#388	1	1	yes	characteristic
302	C₄×C₆₇	#388	1	1	yes	characteristic
303	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
304	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
305	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
306	C₄×C₆₇	C₂×#126	1	1	yes	characteristic
307	Dic₆₇	—	8	2	no	—
308	C₂×#1932	—	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	—	8	2	no	—
316	C₂×C₆₇	#1932	1	2	yes	complemented
317	C₂×C₆₇	C₂×#388	1	1	yes	characteristic
318	C₂×#430	—	67	1	no	—
319	C₂×#421	—	67	1	no	—
320	C₂²×#104	D₆₇	1	1	yes	characteristic
321	C₂×#413	—	67	1	no	—
322	C₂×C₄×M₁₆	—	67	1	no	—
323	#1932	—	67	8	no	—
324	C₂×#344	—	67	1	no	—
325	C₂×#339	—	67	1	no	—
326	C₆₇	C₂×#1932	1	1	yes	characteristic, complemented, Sylow
327	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
328	C₂²×M₁₆	—	67	1	no	—
329	C₂²×M₁₆	—	67	1	no	—
330	C₂²×M₁₆	—	67	1	no	—
331	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
332	C₂×#117	—	67	1	no	—
333	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
334	#430	—	67	4	no	—
335	#430	—	134	2	no	—
336	C₂×#108	—	134	2	no	—
337	#421	—	67	4	no	—
338	#421	—	134	2	no	—
339	C₂×#104	—	2	1	no	—
340	C₂×#104	—	2	1	no	—
341	C₂×#104	—	2	2	no	—
342	C₂×#104	—	134	2	no	—
343	C₂×#104	C₂×D₆₇	1	4	yes	—
344	#413	—	67	4	no	—
345	#413	—	67	4	no	—
346	C₂×#101	—	67	2	no	—
347	C₂×#100	—	67	2	no	—
348	C₄×M₁₆	—	67	4	no	—
349	C₄×M₁₆	—	134	2	no	—
350	C₂×#97	—	134	1	no	—
351	C₂×C₄×C₈	—	134	1	no	—
352	#344	—	67	4	no	—
353	#339	—	67	4	no	—
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	2	1	no	—
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	C₄×D₆₇	1	2	yes	—
365	C₂×#41	C₂²×D₆₇	1	2	yes	—
366	C₂²×Q₈	C₄×D₆₇	1	1	yes	characteristic
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	C₄×D₆₇	1	1	yes	characteristic
369	C₂³×C₄	—	2	1	no	—
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	67	2	no	—
378	C₂×M₁₆	—	67	2	no	—
379	C₂×M₁₆	—	67	2	no	—
380	C₂×M₁₆	—	67	2	no	—
381	C₂×M₁₆	—	67	2	no	—
382	C₂×M₁₆	—	67	2	no	—
383	C₂×M₁₆	—	67	2	no	—
384	C₂×M₁₆	—	67	2	no	—
385	C₂×M₁₆	—	67	2	no	—
386	C₂×M₁₆	—	134	1	no	—
387	C₂×M₁₆	—	134	1	no	—
388	C₂×M₁₆	—	134	1	no	—
389	C₂×M₁₆	—	134	1	no	—
390	C₂×M₁₆	—	134	1	no	—
391	C₂×M₁₆	—	134	1	no	—
392	C₂×M₁₆	—	134	1	no	—
393	C₂×M₁₆	—	134	1	no	—
394	C₂×M₁₆	—	134	1	no	—
395	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
396	C₂²×C₈	—	2	1	no	—
397	C₂²×C₈	—	134	1	no	—
398	C₂²×C₈	—	134	1	no	—
399	C₂²×C₈	—	134	1	no	—
400	#117	—	67	2	no	—
401	#117	—	134	1	no	—
402	#117	—	134	1	no	—
403	#117	—	134	1	no	—
404	C₂×C₄⋊C₄	—	134	1	no	—
405	C₂×C₂²⋊C₄	—	134	1	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	—	134	1	no	—
410	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
411	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
412	C₂×C₄²	C₂²⋊D₆₇	1	2	yes	—
413	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
414	#108	—	134	8	no	—
415	#104	—	2	4	no	—
416	#104	—	2	4	no	—
417	#104	—	134	8	no	—
418	#101	—	67	8	no	—
419	#100	—	67	8	no	—
420	#97	—	134	4	no	—
421	C₄×C₈	—	134	4	no	—
422	C₂⁴	—	2	1	no	—
423	C₂⁴	#11761627	1	1	yes	characteristic
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	#41	—	2	2	no	—
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	4	1	no	—
433	#41	—	4	1	no	—
434	#41	—	4	1	no	—
435	#41	—	4	1	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	1	no	—
439	#41	—	4	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	C₂×C₄×D₆₇	1	2	yes	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	—	268	1	no	—
471	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
473	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
474	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
476	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
477	C₂²×C₄	#11761627	1	1	yes	characteristic
478	C₂²×C₄	#11761627	1	1	yes	characteristic
479	C₂²×C₄	#11761627	1	1	yes	characteristic
480	C₂²×C₄	#11761627	1	1	yes	characteristic
481	C₂²×C₄	#11761627	1	1	yes	characteristic
482	C₂²×C₄	#11761628	1	1	yes	characteristic
483	C₂²×C₄	#11761628	1	1	yes	characteristic
484	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	4	1	no	—
488	M₁₆	—	4	1	no	—
489	M₁₆	—	67	4	no	—
490	M₁₆	—	67	4	no	—
491	M₁₆	—	67	4	no	—
492	M₁₆	—	134	2	no	—
493	M₁₆	—	134	2	no	—
494	M₁₆	—	134	2	no	—
495	M₁₆	—	134	2	no	—
496	M₁₆	—	134	2	no	—
497	M₁₆	—	134	2	no	—
498	M₁₆	—	134	2	no	—
499	M₁₆	—	134	2	no	—
500	M₁₆	—	134	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	4	1	no	—
503	C₂×C₈	—	4	1	no	—
504	C₂×C₈	—	134	2	no	—
505	C₂×C₈	—	134	2	no	—
506	C₂×C₈	—	134	2	no	—
507	C₂×C₈	—	134	2	no	—
508	C₂×C₈	—	134	2	no	—
509	C₂×C₈	—	134	2	no	—
510	C₂×C₈	—	134	2	no	—
511	C₂×C₈	—	134	2	no	—
512	C₂×C₈	—	134	2	no	—
513	C₄⋊C₄	—	268	1	no	—
514	C₄⋊C₄	—	134	2	no	—
515	C₂²⋊C₄	—	268	1	no	—
516	C₂²⋊C₄	—	134	2	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	268	1	no	—
522	C₄²	—	134	2	no	—
523	C₄²	C₂×C₂²⋊D₆₇	1	2	yes	—
524	C₄²	C₂×C₂²⋊D₆₇	1	2	yes	—
525	C₂³	—	2	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	8	2	no	—
530	C₂³	#14523999	1	1	yes	characteristic
531	C₂³	#14523999	1	1	yes	characteristic
532	C₂³	#14524024	1	1	yes	characteristic
533	C₂³	#14524024	1	1	yes	characteristic
534	C₂³	#14524029	1	1	yes	characteristic
535	C₂³	#14524029	1	1	yes	characteristic
536	C₂³	C₂×#11761627	1	1	yes	characteristic
537	Q₈	—	2	2	no	—
538	Q₈	—	2	2	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	D₄	—	2	2	no	—
542	D₄	—	2	2	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	4	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	268	2	no	—
563	C₂×C₄	—	536	2	no	—
564	C₂×C₄	#14523999	1	1	yes	characteristic
565	C₂×C₄	#14523999	1	1	yes	characteristic
566	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
567	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
568	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
569	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
570	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
571	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
572	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
573	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
574	C₂×C₄	#14524014	1	1	yes	characteristic
575	C₂×C₄	#14524014	1	1	yes	characteristic
576	C₂×C₄	#14524014	1	1	yes	characteristic
577	C₂×C₄	#14524014	1	1	yes	characteristic
578	C₂×C₄	#14524024	1	1	yes	characteristic
579	C₂×C₄	#14524024	1	1	yes	characteristic
580	C₂×C₄	#14524029	1	1	yes	characteristic
581	C₂×C₄	#14524029	1	1	yes	characteristic
582	C₂×C₄	#14524036	1	1	yes	characteristic
583	C₂×C₄	#14524036	1	1	yes	characteristic
584	C₂×C₄	#14524036	1	1	yes	characteristic
585	C₂×C₄	#14524036	1	1	yes	characteristic
586	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
587	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
588	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
589	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
590	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
591	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
592	C₈	—	4	2	no	—
593	C₈	—	134	4	no	—
594	C₈	—	134	4	no	—
595	C₈	—	134	4	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	8	2	no	—
605	C₂²	—	8	2	no	—
606	C₂²	—	8	2	no	—
607	C₂²	#16863284	1	1	yes	characteristic
608	C₂²	#16863284	1	1	yes	characteristic
609	C₂²	#16863284	1	1	yes	characteristic
610	C₂²	#16863284	1	1	yes	characteristic
611	C₂²	C₂×#14523999	1	1	yes	characteristic
612	C₂²	C₂×#14524024	1	1	yes	characteristic
613	C₂²	C₂×#14524029	1	1	yes	characteristic
614	C₄	—	2	4	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	2	no	—
617	C₄	—	536	2	no	—
618	C₄	#16863284	1	1	yes	characteristic
619	C₄	#16863284	1	1	yes	characteristic
620	C₄	#16863284	1	1	yes	characteristic
621	C₄	#16863284	1	1	yes	characteristic
622	C₄	C₂×(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
623	C₄	C₂×C₄×C₂²⋊D₆₇	1	1	yes	characteristic
624	C₄	C₂×#14524014	1	1	yes	characteristic
625	C₄	C₂×#14524036	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	—	8	2	no	—
633	C₂	#22560875	1	2	yes	direct product factor
634	C₂	C₂×#16863284	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14524014
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂²×#104×C₆₇	C₂
socle	C₂²×C₆₇	#388
prime radical	C₂²×#41×C₆₇	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₂²×#104	D₆₇
hypocenter	C₆₇	C₂×#1932
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#104

Complements

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

N	H ≅ G/N	type
1. C₂×#16863444	C₂	semidirect
4. C₂×C₄×#11761612	C₂	semidirect
5. #22560875	C₂	direct (N × H)
6. C₂×#16863167	C₂	semidirect
7. C₂×#16863156	C₂	semidirect
14. #16863444	C₂²	semidirect
19. #16863380	C₄	semidirect
21. C₂×#14523962	C₄	semidirect
22. C₂×#14523960	C₄	semidirect
24. C₄×#11761612	C₂²	semidirect
27. #16863167	C₂²	semidirect
28. #16863156	C₂²	semidirect
66. #14523962	C₂×C₄	semidirect
67. #14523960	C₂×C₄	semidirect
316. C₂×C₆₇	#1932	semidirect
326. C₆₇	C₂×#1932	semidirect
633. C₂	#22560875	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×#16863444	2
C₂×#16863413	2
C₂×#16863380	2
C₂×C₄×#11761612	2
#22560875	2
C₂×#16863167	2
C₂×#16863156	2
C₂²×#104×C₆₇	2
C₂×#1932	67

Subgroups — C2×#22560875 #30858409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22560875 #30858409