Subgroups — C₂×#22561662 #30884752

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×#16863413	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863392	C₂	1	1	yes	maximal, characteristic
4	#22561662	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863168	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863160	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863153	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#413×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11761612	C₂²	1	1	yes	characteristic
10	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×#14524002	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	#16863413	—	2	2	no	—
17	#16863413	C₂²	1	4	yes	—
18	C₂×#14523970	—	2	2	no	—
19	#16863392	—	2	2	no	—
20	#16863392	C₂²	1	4	yes	—
21	C₂×#14523967	—	2	1	no	—
22	C₂×#14523964	—	2	1	no	—
23	#16863168	C₂²	1	4	yes	complemented
24	#16863160	C₂²	1	4	yes	complemented
25	#16863153	C₂²	1	4	yes	complemented
26	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
29	#413×C₆₇	—	2	2	no	—
30	#413×C₆₇	C₂²	1	4	yes	—
31	C₂×#101×C₆₇	—	2	1	no	—
32	C₂×#100×C₆₇	—	2	1	no	—
33	C₂×#11761612	—	2	1	no	—
34	C₂×#11761612	—	2	1	no	—
35	C₂×#11761612	—	2	1	no	—
36	C₂×#11761612	—	2	1	no	—
37	C₂×#11761612	—	2	1	no	—
38	C₂×#11761612	C₂³	1	2	yes	—
39	C₂²×C₆₇⋊C₈	—	2	1	no	—
40	C₂²×C₆₇⋊C₈	—	2	1	no	—
41	C₂²×C₆₇⋊C₈	—	2	1	no	—
42	C₂²×C₆₇⋊C₈	—	2	1	no	—
43	C₂²×C₆₇⋊C₈	—	2	1	no	—
44	C₂²×C₆₇⋊C₈	—	2	1	no	—
45	C₂²×C₆₇⋊C₈	—	2	1	no	—
46	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
47	#14524002	—	2	1	no	—
48	#14524002	—	2	1	no	—
49	#14524002	—	2	1	no	—
50	#14524002	—	2	1	no	—
51	#14524002	—	2	1	no	—
52	#14524002	D₄	1	2	yes	—
53	#14524002	C₂³	1	2	yes	—
54	#14524002	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₆₇	—	2	1	no	—
56	C₂×C₄⋊Dic₆₇	—	2	1	no	—
57	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
58	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
59	C₂×C₄×Dic₆₇	—	2	1	no	—
60	C₂×C₄×Dic₆₇	D₄	1	2	yes	—
61	Dic₆₇⋊C₈	—	2	8	no	—
62	#14523970	—	2	8	no	—
63	#14523967	—	2	4	no	—
64	#14523964	—	2	4	no	—
65	C₂×#41×C₆₇	—	2	1	no	—
66	C₂×#41×C₆₇	—	2	1	no	—
67	C₂×#41×C₆₇	—	2	1	no	—
68	C₂×#41×C₆₇	—	2	1	no	—
69	C₂×#41×C₆₇	—	2	1	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	D₄	1	2	yes	—
76	C₂×#41×C₆₇	C₂³	1	2	yes	—
77	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
78	C₂²×D₄×C₆₇	—	2	1	no	—
79	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
80	C₂³×C₄×C₆₇	—	2	1	no	—
81	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
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	C₂³	1	2	yes	—
93	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
94	C₂²×C₈×C₆₇	—	2	1	no	—
95	C₂²×C₈×C₆₇	—	2	1	no	—
96	#101×C₆₇	—	2	4	no	—
97	#100×C₆₇	—	2	4	no	—
98	C₂²×Dic₆₇	—	2	2	no	—
99	C₂²×Dic₆₇	—	4	1	no	—
100	#11761612	—	2	2	no	—
101	#11761612	—	2	2	no	—
102	#11761612	—	4	1	no	—
103	#11761612	—	4	1	no	—
104	C₂×C₆₇⋊C₈	—	2	2	no	—
105	C₂×C₆₇⋊C₈	—	2	2	no	—
106	C₂×C₆₇⋊C₈	—	2	2	no	—
107	C₂×C₆₇⋊C₈	—	2	2	no	—
108	C₂×C₆₇⋊C₈	—	4	1	no	—
109	C₂×C₆₇⋊C₈	—	4	1	no	—
110	C₂×C₆₇⋊C₈	—	4	1	no	—
111	C₂×C₆₇⋊C₈	—	4	1	no	—
112	C₂×C₆₇⋊C₈	—	4	1	no	—
113	C₂×C₆₇⋊C₈	—	4	1	no	—
114	C₄⋊Dic₆₇	—	2	2	no	—
115	C₄⋊Dic₆₇	—	2	2	no	—
116	C₄⋊Dic₆₇	—	2	2	no	—
117	C₄⋊Dic₆₇	—	4	1	no	—
118	C₂²⋊Dic₆₇	—	2	2	no	—
119	C₂²⋊Dic₆₇	—	2	2	no	—
120	C₂²⋊Dic₆₇	—	2	2	no	—
121	C₂²⋊Dic₆₇	—	4	1	no	—
122	C₄×Dic₆₇	—	2	2	no	—
123	C₄×Dic₆₇	—	2	2	no	—
124	C₄×Dic₆₇	—	4	1	no	—
125	C₄×Dic₆₇	C₂×D₄	1	4	yes	—
126	C₂⁴×C₆₇	—	2	1	no	—
127	C₂⁴×C₆₇	#41	1	1	yes	characteristic
128	#41×C₆₇	—	2	2	no	—
129	#41×C₆₇	—	2	2	no	—
130	#41×C₆₇	—	2	2	no	—
131	#41×C₆₇	—	2	2	no	—
132	#41×C₆₇	—	2	2	no	—
133	#41×C₆₇	—	2	2	no	—
134	#41×C₆₇	—	2	2	no	—
135	#41×C₆₇	—	2	2	no	—
136	#41×C₆₇	—	4	1	no	—
137	#41×C₆₇	—	4	1	no	—
138	#41×C₆₇	—	4	1	no	—
139	#41×C₆₇	—	4	1	no	—
140	#41×C₆₇	—	4	1	no	—
141	#41×C₆₇	—	4	1	no	—
142	#41×C₆₇	—	4	1	no	—
143	#41×C₆₇	—	4	1	no	—
144	C₂×Q₈×C₆₇	—	2	1	no	—
145	C₂×Q₈×C₆₇	—	2	1	no	—
146	C₂×Q₈×C₆₇	—	2	1	no	—
147	C₂×Q₈×C₆₇	—	2	1	no	—
148	C₂×Q₈×C₆₇	—	2	1	no	—
149	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
150	C₂×D₄×C₆₇	—	2	2	no	—
151	C₂×D₄×C₆₇	—	2	2	no	—
152	C₂×D₄×C₆₇	—	2	1	no	—
153	C₂×D₄×C₆₇	—	2	1	no	—
154	C₂×D₄×C₆₇	—	2	1	no	—
155	C₂×D₄×C₆₇	—	2	1	no	—
156	C₂×D₄×C₆₇	—	2	1	no	—
157	C₂×D₄×C₆₇	—	4	1	no	—
158	C₂×D₄×C₆₇	—	4	1	no	—
159	C₂×D₄×C₆₇	—	4	1	no	—
160	C₂×D₄×C₆₇	—	4	1	no	—
161	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₆₇	—	2	1	no	—
163	C₂²×C₄×C₆₇	—	2	2	no	—
164	C₂²×C₄×C₆₇	—	2	2	no	—
165	C₂²×C₄×C₆₇	—	4	1	no	—
166	C₂²×C₄×C₆₇	—	4	1	no	—
167	C₂²×C₄×C₆₇	—	4	1	no	—
168	C₂²×C₄×C₆₇	—	4	1	no	—
169	C₂²×C₄×C₆₇	C₂×D₄	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	#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	#41	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	#41	1	1	yes	characteristic
182	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
183	M₁₆×C₆₇	—	2	2	no	—
184	M₁₆×C₆₇	—	2	2	no	—
185	M₁₆×C₆₇	—	2	2	no	—
186	M₁₆×C₆₇	—	2	2	no	—
187	M₁₆×C₆₇	—	4	1	no	—
188	M₁₆×C₆₇	—	4	1	no	—
189	M₁₆×C₆₇	—	4	1	no	—
190	M₁₆×C₆₇	—	4	1	no	—
191	C₂×C₈×C₆₇	—	2	2	no	—
192	C₂×C₈×C₆₇	—	2	2	no	—
193	C₂×C₈×C₆₇	—	4	1	no	—
194	C₂×C₈×C₆₇	—	4	1	no	—
195	C₂×C₈×C₆₇	—	4	1	no	—
196	C₂×C₈×C₆₇	—	4	1	no	—
197	C₂³×C₆₇	—	2	2	no	—
198	C₂³×C₆₇	—	4	2	no	—
199	C₂³×C₆₇	—	4	1	no	—
200	C₂³×C₆₇	—	4	1	no	—
201	C₂³×C₆₇	—	8	2	no	—
202	C₂³×C₆₇	#123	1	1	yes	characteristic
203	C₂³×C₆₇	#123	1	1	yes	characteristic
204	C₂³×C₆₇	#123	1	1	yes	characteristic
205	C₂³×C₆₇	#123	1	1	yes	characteristic
206	C₂³×C₆₇	#126	1	1	yes	characteristic
207	C₂³×C₆₇	#126	1	1	yes	characteristic
208	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
209	Q₈×C₆₇	—	2	2	no	—
210	Q₈×C₆₇	—	2	2	no	—
211	Q₈×C₆₇	—	4	1	no	—
212	Q₈×C₆₇	—	4	1	no	—
213	D₄×C₆₇	—	2	2	no	—
214	D₄×C₆₇	—	2	2	no	—
215	D₄×C₆₇	—	4	2	no	—
216	D₄×C₆₇	—	4	2	no	—
217	D₄×C₆₇	—	4	2	no	—
218	D₄×C₆₇	—	4	2	no	—
219	D₄×C₆₇	—	4	1	no	—
220	D₄×C₆₇	—	4	1	no	—
221	C₂×C₄×C₆₇	—	2	2	no	—
222	C₂×C₄×C₆₇	—	4	1	no	—
223	C₂×C₄×C₆₇	—	4	1	no	—
224	C₂×C₄×C₆₇	—	4	2	no	—
225	C₂×C₄×C₆₇	—	4	2	no	—
226	C₂×C₄×C₆₇	—	4	2	no	—
227	C₂×C₄×C₆₇	—	4	2	no	—
228	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
229	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
230	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
231	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
232	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
233	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
234	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
235	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
236	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
237	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
238	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
239	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
240	C₂×C₄×C₆₇	#124	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	#126	1	1	yes	characteristic
245	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
246	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
247	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
248	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
249	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
250	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
256	C₂×Dic₆₇	—	2	4	no	—
257	C₂×Dic₆₇	—	4	4	no	—
258	C₂×Dic₆₇	—	4	2	no	—
259	C₂×Dic₆₇	—	8	2	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	—	4	2	no	—
272	C₂²×C₆₇	—	8	2	no	—
273	C₂²×C₆₇	—	8	2	no	—
274	C₂²×C₆₇	—	8	2	no	—
275	C₂²×C₆₇	#397	1	1	yes	characteristic
276	C₂²×C₆₇	#397	1	1	yes	characteristic
277	C₂²×C₆₇	#397	1	1	yes	characteristic
278	C₂²×C₆₇	#397	1	1	yes	characteristic
279	C₂²×C₆₇	C₂×#123	1	1	yes	characteristic
280	C₂²×C₆₇	C₂×#123	1	1	yes	characteristic
281	C₂²×C₆₇	C₂×#126	1	1	yes	characteristic
282	C₄×C₆₇	—	4	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	—	8	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	—	8	2	no	—
301	C₂×C₆₇	#2080	1	2	yes	complemented
302	C₂×C₆₇	C₂×#397	1	1	yes	characteristic
303	C₂×#424	—	67	1	no	—
304	C₂×#421	—	67	1	no	—
305	C₂×#416	—	67	1	no	—
306	C₂×#413	D₆₇	1	1	yes	characteristic
307	#2080	—	67	8	no	—
308	C₂×#344	—	67	1	no	—
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	C₂×D₆₇	1	1	yes	characteristic
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	—	67	1	no	—
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	—	2	2	no	—
330	#413	C₂×D₆₇	1	4	yes	—
331	C₂×#101	—	2	1	no	—
332	C₂×#100	—	2	1	no	—
333	#344	—	67	4	no	—
334	#341	—	67	4	no	—
335	H(3,ℤ/4)	—	67	4	no	—
336	C₂×#41	—	2	1	no	—
337	C₂×#41	—	2	1	no	—
338	C₂×#41	—	2	1	no	—
339	C₂×#41	—	2	1	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	—	2	1	no	—
342	C₂×#41	—	2	1	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	—	2	1	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	C₂²⋊D₆₇	1	2	yes	—
347	C₂×#41	C₂²×D₆₇	1	2	yes	—
348	C₂²×Q₈	C₂²⋊D₆₇	1	1	yes	characteristic
349	C₂²×D₄	—	2	1	no	—
350	C₂²×D₄	C₂²⋊D₆₇	1	1	yes	characteristic
351	C₂³×C₄	—	2	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	—	67	2	no	—
382	#117	—	67	2	no	—
383	#117	—	67	2	no	—
384	#117	—	134	1	no	—
385	#117	—	134	1	no	—
386	#117	—	134	1	no	—
387	#117	—	134	1	no	—
388	#117	—	134	1	no	—
389	C₂×C₄⋊C₄	—	134	1	no	—
390	C₂×C₄⋊C₄	—	134	1	no	—
391	C₂×C₂²⋊C₄	—	134	1	no	—
392	C₂×C₂²⋊C₄	—	134	1	no	—
393	C₂×C₄²	—	67	2	no	—
394	C₂×C₄²	—	134	1	no	—
395	C₄⋊C₈	—	134	8	no	—
396	#104	—	134	8	no	—
397	#103	—	134	4	no	—
398	#102	—	134	4	no	—
399	#101	—	2	4	no	—
400	#100	—	2	4	no	—
401	C₂⁴	—	2	1	no	—
402	C₂⁴	#11761628	1	1	yes	characteristic
403	#41	—	2	2	no	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	—	2	2	no	—
409	#41	—	2	2	no	—
410	#41	—	2	2	no	—
411	#41	—	4	1	no	—
412	#41	—	4	1	no	—
413	#41	—	4	1	no	—
414	#41	—	4	1	no	—
415	#41	—	4	1	no	—
416	#41	—	4	1	no	—
417	#41	—	4	1	no	—
418	#41	—	4	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	C₂×C₂²⋊D₆₇	1	2	yes	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	4	1	no	—
433	C₂×D₄	—	4	1	no	—
434	C₂×D₄	—	4	1	no	—
435	C₂×D₄	—	4	1	no	—
436	C₂×D₄	C₂×C₂²⋊D₆₇	1	2	yes	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	—	4	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	—	268	1	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	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
449	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
450	C₂²×C₄	#11761627	1	1	yes	characteristic
451	C₂²×C₄	#11761627	1	1	yes	characteristic
452	C₂²×C₄	#11761627	1	1	yes	characteristic
453	C₂²×C₄	#11761627	1	1	yes	characteristic
454	C₂²×C₄	#11761627	1	1	yes	characteristic
455	C₂²×C₄	#11761627	1	1	yes	characteristic
456	C₂²×C₄	#11761628	1	1	yes	characteristic
457	C₂²×C₄	#11761628	1	1	yes	characteristic
458	C₂²×C₄	#11761628	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	—	268	1	no	—
489	C₄⋊C₄	—	134	2	no	—
490	C₄⋊C₄	—	134	2	no	—
491	C₄⋊C₄	—	134	2	no	—
492	C₂²⋊C₄	—	268	1	no	—
493	C₂²⋊C₄	—	134	2	no	—
494	C₂²⋊C₄	—	134	2	no	—
495	C₂²⋊C₄	—	134	2	no	—
496	C₄²	—	268	1	no	—
497	C₄²	—	67	4	no	—
498	C₄²	—	134	2	no	—
499	C₄²	—	134	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	8	2	no	—
505	C₂³	#14524025	1	1	yes	characteristic
506	C₂³	#14524025	1	1	yes	characteristic
507	C₂³	#14524026	1	1	yes	characteristic
508	C₂³	#14524026	1	1	yes	characteristic
509	C₂³	#14524036	1	1	yes	characteristic
510	C₂³	#14524036	1	1	yes	characteristic
511	C₂³	C₂×#11761628	1	1	yes	characteristic
512	Q₈	—	2	2	no	—
513	Q₈	—	2	2	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	4	1	no	—
516	D₄	—	2	2	no	—
517	D₄	—	2	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	2	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	268	4	no	—
532	C₂×C₄	—	268	2	no	—
533	C₂×C₄	—	536	2	no	—
534	C₂×C₄	—	134	4	no	—
535	C₂×C₄	#14524015	1	1	yes	characteristic
536	C₂×C₄	#14524015	1	1	yes	characteristic
537	C₂×C₄	#14524015	1	1	yes	characteristic
538	C₂×C₄	#14524015	1	1	yes	characteristic
539	C₂×C₄	#14524024	1	1	yes	characteristic
540	C₂×C₄	#14524024	1	1	yes	characteristic
541	C₂×C₄	#14524024	1	1	yes	characteristic
542	C₂×C₄	#14524024	1	1	yes	characteristic
543	C₂×C₄	#14524025	1	1	yes	characteristic
544	C₂×C₄	#14524025	1	1	yes	characteristic
545	C₂×C₄	#14524026	1	1	yes	characteristic
546	C₂×C₄	#14524026	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	#14524036	1	1	yes	characteristic
552	C₂×C₄	#14524036	1	1	yes	characteristic
553	C₂×C₄	#14524036	1	1	yes	characteristic
554	C₂×C₄	#14524036	1	1	yes	characteristic
555	C₂×C₄	#14524036	1	1	yes	characteristic
556	C₂×C₄	#14524036	1	1	yes	characteristic
557	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
558	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
559	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
560	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
561	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
562	C₂×C₄	C₂×#11761628	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	—	4	2	no	—
575	C₂²	—	8	2	no	—
576	C₂²	—	8	2	no	—
577	C₂²	—	8	2	no	—
578	C₂²	#16863324	1	1	yes	characteristic
579	C₂²	#16863324	1	1	yes	characteristic
580	C₂²	#16863324	1	1	yes	characteristic
581	C₂²	#16863324	1	1	yes	characteristic
582	C₂²	C₂×#14524025	1	1	yes	characteristic
583	C₂²	C₂×#14524026	1	1	yes	characteristic
584	C₂²	C₂×#14524036	1	1	yes	characteristic
585	C₄	—	4	2	no	—
586	C₄	—	268	4	no	—
587	C₄	—	536	2	no	—
588	C₄	#16863324	1	1	yes	characteristic
589	C₄	#16863324	1	1	yes	characteristic
590	C₄	#16863324	1	1	yes	characteristic
591	C₄	#16863324	1	1	yes	characteristic
592	C₄	C₂×#14524015	1	1	yes	characteristic
593	C₄	C₂×#14524024	1	1	yes	characteristic
594	C₄	C₂×#14524029	1	1	yes	characteristic
595	C₄	C₂×#14524036	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	—	8	2	no	—
603	C₂	#22561662	1	2	yes	direct product factor
604	C₂	C₂×#16863324	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14524029
commutator, cosocle	C₂²×C₄×C₆₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂×#413×C₆₇	C₂
socle	C₂²×C₆₇	#397
prime radical	C₂²×#41×C₆₇	C₂²
hypercenter	C₂×#413	D₆₇
hypocenter	C₆₇	C₂×#2080
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#413

Complements

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

N	H ≅ G/N	type
1. C₂×#16863424	C₂	semidirect
4. #22561662	C₂	direct (N × H)
5. C₂×#16863168	C₂	semidirect
6. C₂×#16863160	C₂	semidirect
7. C₂×#16863153	C₂	semidirect
14. #16863424	C₂²	semidirect
23. #16863168	C₂²	semidirect
24. #16863160	C₂²	semidirect
25. #16863153	C₂²	semidirect
301. C₂×C₆₇	#2080	semidirect
311. C₆₇	C₂×#2080	semidirect
603. C₂	#22561662	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×#16863413	2
C₂×#16863392	2
#22561662	2
C₂×#16863168	2
C₂×#16863160	2
C₂×#16863153	2
C₂×#413×C₆₇	2
C₂×#2080	67

Subgroups — C2×#22561662 #30884752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22561662 #30884752