Subgroups — C₂×#22561381 #30883255

Order 17152.

1234 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863953	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863413	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863370	C₂	1	1	yes	maximal, characteristic
4	#22561381	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863168	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863156	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863153	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	#16863953	—	2	2	no	—
11	#16863953	—	2	2	no	—
12	#16863953	—	2	2	no	—
13	#16863953	C₂²	1	4	yes	complemented
14	C₂×#14524043	—	2	1	no	—
15	C₂×#14524035	—	2	1	no	—
16	C₂×#14524022	—	2	2	no	—
17	C₂×C₄×Dic₁₃₄	—	2	2	no	—
18	C₂×#14524002	C₂²	1	1	yes	characteristic
19	C₂×#14524002	C₂²	1	1	yes	characteristic
20	C₂×#14524002	C₂²	1	1	yes	characteristic
21	#16863413	—	2	2	no	—
22	#16863413	C₂²	1	4	yes	—
23	C₂×#14523970	—	2	2	no	—
24	#16863370	—	2	2	no	—
25	#16863370	C₂²	1	4	yes	—
26	C₂×#14523958	—	2	2	no	—
27	#16863168	C₂²	1	4	yes	complemented
28	#16863156	C₂²	1	4	yes	complemented
29	#16863153	C₂²	1	4	yes	complemented
30	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#104×C₆₇	—	2	1	no	—
34	C₂×#104×C₆₇	—	2	1	no	—
35	C₂×#104×C₆₇	—	2	2	no	—
36	C₂×#104×C₆₇	C₂²	1	4	yes	—
37	C₂²×Dic₁₃₄	—	2	2	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	C₂³	1	2	yes	—
44	C₂²×C₆₇⋊C₈	—	2	1	no	—
45	#14524043	—	2	4	no	—
46	#14524043	—	2	4	no	—
47	#14524035	—	2	4	no	—
48	#14524035	—	2	4	no	—
49	#14524022	—	2	8	no	—
50	#14524022	—	2	8	no	—
51	C₄×Dic₁₃₄	—	2	8	no	—
52	C₄×Dic₁₃₄	—	2	8	no	—
53	#14524002	—	2	1	no	—
54	#14524002	—	2	1	no	—
55	#14524002	—	2	1	no	—
56	#14524002	—	2	1	no	—
57	#14524002	—	2	1	no	—
58	#14524002	—	2	1	no	—
59	#14524002	—	2	1	no	—
60	#14524002	D₄	1	2	yes	—
61	#14524002	D₄	1	2	yes	—
62	#14524002	C₂³	1	2	yes	—
63	#14524002	C₂³	1	2	yes	—
64	#14524002	C₂³	1	2	yes	—
65	C₂×C₄⋊Dic₆₇	—	2	2	no	—
66	C₂×C₄⋊Dic₆₇	—	2	1	no	—
67	C₂×C₄⋊Dic₆₇	—	2	1	no	—
68	C₂×C₄⋊Dic₆₇	—	2	1	no	—
69	C₂×Dic₆₇⋊C₄	—	2	4	no	—
70	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
71	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
72	C₂×C₂²⋊Dic₆₇	D₄	1	2	yes	—
73	C₂×C₄×Dic₆₇	—	2	1	no	—
74	C₂×C₄×Dic₆₇	—	2	1	no	—
75	C₂×C₄×Dic₆₇	D₄	1	2	yes	—
76	#14523970	—	2	8	no	—
77	#14523958	—	2	8	no	—
78	C₂×#41×C₆₇	—	2	1	no	—
79	C₂×#41×C₆₇	—	2	1	no	—
80	C₂×#41×C₆₇	—	2	1	no	—
81	C₂×#41×C₆₇	—	2	1	no	—
82	C₂×#41×C₆₇	—	2	1	no	—
83	C₂×#41×C₆₇	—	2	1	no	—
84	C₂×#41×C₆₇	—	2	1	no	—
85	C₂×#41×C₆₇	—	2	1	no	—
86	C₂×#41×C₆₇	—	2	1	no	—
87	C₂×#41×C₆₇	—	2	1	no	—
88	C₂×#41×C₆₇	Q₈	1	2	yes	complemented
89	C₂×#41×C₆₇	C₂³	1	2	yes	—
90	C₂²×Q₈×C₆₇	Q₈	1	1	yes	characteristic, complemented
91	C₂²×D₄×C₆₇	—	2	1	no	—
92	C₂²×D₄×C₆₇	Q₈	1	1	yes	characteristic, complemented
93	C₂³×C₄×C₆₇	—	2	1	no	—
94	C₂³×C₄×C₆₇	—	2	1	no	—
95	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
96	C₂×M₁₆×C₆₇	—	2	1	no	—
97	C₂×M₁₆×C₆₇	—	2	1	no	—
98	C₂×M₁₆×C₆₇	—	2	1	no	—
99	C₂×M₁₆×C₆₇	—	2	1	no	—
100	C₂×M₁₆×C₆₇	—	2	1	no	—
101	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
102	C₂²×C₈×C₆₇	—	2	1	no	—
103	C₂×C₄²×C₆₇	—	2	1	no	—
104	C₂×C₄²×C₆₇	—	2	1	no	—
105	C₂×C₄²×C₆₇	—	2	1	no	—
106	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₆₇	D₄	1	2	yes	—
109	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
110	#104×C₆₇	—	2	4	no	—
111	#104×C₆₇	—	2	4	no	—
112	C₂×Dic₁₃₄	—	2	8	no	—
113	C₂×Dic₁₃₄	—	4	8	no	—
114	C₂²×Dic₆₇	—	2	2	no	—
115	C₂²×Dic₆₇	—	2	2	no	—
116	C₂²×Dic₆₇	—	4	1	no	—
117	#11761612	—	2	2	no	—
118	#11761612	—	2	2	no	—
119	#11761612	—	4	1	no	—
120	#11761612	—	4	1	no	—
121	C₂×C₆₇⋊C₈	—	2	2	no	—
122	C₂×C₆₇⋊C₈	—	4	1	no	—
123	C₂×C₆₇⋊C₈	—	4	1	no	—
124	C₄⋊Dic₆₇	—	2	8	no	—
125	C₄⋊Dic₆₇	—	2	2	no	—
126	C₄⋊Dic₆₇	—	2	2	no	—
127	C₄⋊Dic₆₇	—	2	2	no	—
128	C₄⋊Dic₆₇	—	2	2	no	—
129	C₄⋊Dic₆₇	—	2	2	no	—
130	C₄⋊Dic₆₇	—	4	1	no	—
131	Dic₆₇⋊C₄	—	2	16	no	—
132	C₂²⋊Dic₆₇	—	2	2	no	—
133	C₂²⋊Dic₆₇	—	2	2	no	—
134	C₂²⋊Dic₆₇	—	2	2	no	—
135	C₂²⋊Dic₆₇	—	2	2	no	—
136	C₂²⋊Dic₆₇	—	4	1	no	—
137	C₂²⋊Dic₆₇	C₂×D₄	1	4	yes	—
138	C₄×Dic₆₇	—	2	2	no	—
139	C₄×Dic₆₇	—	2	2	no	—
140	C₄×Dic₆₇	—	2	2	no	—
141	C₄×Dic₆₇	—	2	2	no	—
142	C₄×Dic₆₇	—	4	1	no	—
143	C₄×Dic₆₇	C₂×D₄	1	4	yes	—
144	C₂⁴×C₆₇	—	2	1	no	—
145	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
146	#41×C₆₇	—	2	2	no	—
147	#41×C₆₇	—	2	2	no	—
148	#41×C₆₇	—	2	2	no	—
149	#41×C₆₇	—	2	2	no	—
150	#41×C₆₇	—	2	2	no	—
151	#41×C₆₇	—	2	2	no	—
152	#41×C₆₇	—	2	2	no	—
153	#41×C₆₇	—	2	2	no	—
154	#41×C₆₇	—	4	1	no	—
155	#41×C₆₇	—	4	1	no	—
156	#41×C₆₇	—	4	1	no	—
157	#41×C₆₇	—	4	1	no	—
158	#41×C₆₇	—	4	1	no	—
159	#41×C₆₇	—	4	1	no	—
160	#41×C₆₇	—	4	1	no	—
161	#41×C₆₇	—	4	1	no	—
162	C₂×Q₈×C₆₇	—	2	1	no	—
163	C₂×Q₈×C₆₇	—	2	1	no	—
164	C₂×Q₈×C₆₇	—	2	1	no	—
165	C₂×Q₈×C₆₇	—	2	1	no	—
166	C₂×Q₈×C₆₇	—	2	1	no	—
167	C₂×Q₈×C₆₇	C₂×Q₈	1	2	yes	complemented
168	C₂×D₄×C₆₇	—	2	2	no	—
169	C₂×D₄×C₆₇	—	2	2	no	—
170	C₂×D₄×C₆₇	—	2	1	no	—
171	C₂×D₄×C₆₇	—	2	1	no	—
172	C₂×D₄×C₆₇	—	2	1	no	—
173	C₂×D₄×C₆₇	—	2	1	no	—
174	C₂×D₄×C₆₇	—	2	1	no	—
175	C₂×D₄×C₆₇	—	4	1	no	—
176	C₂×D₄×C₆₇	—	4	1	no	—
177	C₂×D₄×C₆₇	—	4	1	no	—
178	C₂×D₄×C₆₇	—	4	1	no	—
179	C₂×D₄×C₆₇	C₂×Q₈	1	2	yes	complemented
180	C₂²×C₄×C₆₇	—	2	1	no	—
181	C₂²×C₄×C₆₇	—	2	1	no	—
182	C₂²×C₄×C₆₇	—	2	2	no	—
183	C₂²×C₄×C₆₇	—	2	1	no	—
184	C₂²×C₄×C₆₇	—	2	2	no	—
185	C₂²×C₄×C₆₇	—	2	2	no	—
186	C₂²×C₄×C₆₇	—	2	2	no	—
187	C₂²×C₄×C₆₇	—	4	4	no	—
188	C₂²×C₄×C₆₇	—	4	1	no	—
189	C₂²×C₄×C₆₇	—	4	1	no	—
190	C₂²×C₄×C₆₇	—	4	1	no	—
191	C₂²×C₄×C₆₇	—	4	1	no	—
192	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
198	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
199	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
200	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
201	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
202	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
203	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
206	M₁₆×C₆₇	—	2	2	no	—
207	M₁₆×C₆₇	—	2	2	no	—
208	M₁₆×C₆₇	—	4	1	no	—
209	M₁₆×C₆₇	—	4	1	no	—
210	C₂×C₈×C₆₇	—	2	2	no	—
211	C₂×C₈×C₆₇	—	4	1	no	—
212	C₂×C₈×C₆₇	—	4	1	no	—
213	C₄²×C₆₇	—	2	2	no	—
214	C₄²×C₆₇	—	2	1	no	—
215	C₄²×C₆₇	—	2	1	no	—
216	C₄²×C₆₇	—	2	2	no	—
217	C₄²×C₆₇	C₂×D₄	1	2	yes	—
218	C₄²×C₆₇	C₂×D₄	1	2	yes	—
219	C₂³×C₆₇	—	2	2	no	—
220	C₂³×C₆₇	—	4	2	no	—
221	C₂³×C₆₇	—	4	1	no	—
222	C₂³×C₆₇	—	4	1	no	—
223	C₂³×C₆₇	—	8	2	no	—
224	C₂³×C₆₇	#120	1	1	yes	characteristic
225	C₂³×C₆₇	#120	1	1	yes	characteristic
226	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
227	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
228	C₂³×C₆₇	#124	1	1	yes	characteristic
229	C₂³×C₆₇	#124	1	1	yes	characteristic
230	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₆₇	—	2	2	no	—
232	Q₈×C₆₇	—	2	2	no	—
233	Q₈×C₆₇	—	4	1	no	—
234	Q₈×C₆₇	—	4	1	no	—
235	D₄×C₆₇	—	2	2	no	—
236	D₄×C₆₇	—	2	2	no	—
237	D₄×C₆₇	—	4	2	no	—
238	D₄×C₆₇	—	4	2	no	—
239	D₄×C₆₇	—	4	2	no	—
240	D₄×C₆₇	—	4	2	no	—
241	D₄×C₆₇	—	4	1	no	—
242	D₄×C₆₇	—	4	1	no	—
243	C₂×C₄×C₆₇	—	2	4	no	—
244	C₂×C₄×C₆₇	—	2	2	no	—
245	C₂×C₄×C₆₇	—	2	2	no	—
246	C₂×C₄×C₆₇	—	2	2	no	—
247	C₂×C₄×C₆₇	—	4	4	no	—
248	C₂×C₄×C₆₇	—	4	4	no	—
249	C₂×C₄×C₆₇	—	4	2	no	—
250	C₂×C₄×C₆₇	—	4	1	no	—
251	C₂×C₄×C₆₇	—	4	1	no	—
252	C₂×C₄×C₆₇	—	4	2	no	—
253	C₂×C₄×C₆₇	—	4	2	no	—
254	C₂×C₄×C₆₇	—	4	2	no	—
255	C₂×C₄×C₆₇	—	4	2	no	—
256	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
257	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
258	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
259	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
260	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
261	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
262	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
263	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
266	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
267	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
269	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
270	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
271	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
272	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
273	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
274	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
275	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
276	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
277	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
278	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
281	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
284	C₂×Dic₆₇	—	2	4	no	—
285	C₂×Dic₆₇	—	2	4	no	—
286	C₂×Dic₆₇	—	4	4	no	—
287	C₂×Dic₆₇	—	4	4	no	—
288	C₂×Dic₆₇	—	4	2	no	—
289	C₂×Dic₆₇	—	8	2	no	—
290	Dic₁₃₄	—	4	16	no	—
291	C₈×C₆₇	—	4	2	no	—
292	C₆₇⋊C₈	—	4	2	no	—
293	C₂²×C₆₇	—	2	2	no	—
294	C₂²×C₆₇	—	2	2	no	—
295	C₂²×C₆₇	—	2	2	no	—
296	C₂²×C₆₇	—	4	1	no	—
297	C₂²×C₆₇	—	4	1	no	—
298	C₂²×C₆₇	—	4	1	no	—
299	C₂²×C₆₇	—	4	1	no	—
300	C₂²×C₆₇	—	4	2	no	—
301	C₂²×C₆₇	—	8	2	no	—
302	C₂²×C₆₇	—	8	2	no	—
303	C₂²×C₆₇	—	8	2	no	—
304	C₂²×C₆₇	#393	1	1	yes	characteristic
305	C₂²×C₆₇	#393	1	1	yes	characteristic
306	C₂²×C₆₇	#393	1	1	yes	characteristic
307	C₂²×C₆₇	#393	1	1	yes	characteristic
308	C₂²×C₆₇	C₂×#120	1	1	yes	characteristic
309	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
310	C₂²×C₆₇	C₂×#124	1	1	yes	characteristic
311	C₄×C₆₇	—	2	4	no	—
312	C₄×C₆₇	—	4	2	no	—
313	C₄×C₆₇	—	4	2	no	—
314	C₄×C₆₇	#393	1	1	yes	characteristic
315	C₄×C₆₇	#393	1	1	yes	characteristic
316	C₄×C₆₇	#393	1	1	yes	characteristic
317	C₄×C₆₇	#393	1	1	yes	characteristic
318	C₄×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
319	C₄×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
320	C₄×C₆₇	C₂×#124	1	1	yes	characteristic
321	C₄×C₆₇	C₂×#124	1	1	yes	characteristic
322	Dic₆₇	—	4	4	no	—
323	Dic₆₇	—	4	4	no	—
324	Dic₆₇	—	8	2	no	—
325	C₂×#2031	—	67	1	no	maximal, Sylow
326	C₂×C₆₇	—	2	1	no	—
327	C₂×C₆₇	—	2	1	no	—
328	C₂×C₆₇	—	2	1	no	—
329	C₂×C₆₇	—	2	1	no	—
330	C₂×C₆₇	—	2	1	no	—
331	C₂×C₆₇	—	2	1	no	—
332	C₂×C₆₇	—	8	2	no	—
333	C₂×C₆₇	#2031	1	2	yes	complemented
334	C₂×C₆₇	C₂×#393	1	1	yes	characteristic
335	C₂×#533	—	67	1	no	—
336	C₂×#421	—	67	1	no	—
337	C₂²×#104	D₆₇	1	1	yes	characteristic
338	C₂×#410	—	67	1	no	—
339	#2031	—	67	8	no	—
340	C₂×#344	—	67	1	no	—
341	C₂×#339	—	67	1	no	—
342	C₂×H(3,ℤ/4)	—	67	1	no	—
343	C₆₇	C₂×#2031	1	1	yes	characteristic, complemented, Sylow
344	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
345	C₂²×M₁₆	—	67	1	no	—
346	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
347	#533	—	67	4	no	—
348	#533	—	134	2	no	—
349	#533	—	134	2	no	—
350	#533	—	134	2	no	—
351	C₂×C₄⋊Q₈	—	134	1	no	—
352	C₂×#125	—	134	1	no	—
353	C₂×C₂²⋊Q₈	—	134	2	no	—
354	C₂×C₄×Q₈	—	134	2	no	—
355	C₂×#117	—	67	1	no	—
356	C₂×#117	—	67	1	no	—
357	C₂×#117	—	67	1	no	—
358	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
359	#421	—	67	4	no	—
360	#421	—	134	2	no	—
361	C₂×#104	—	2	1	no	—
362	C₂×#104	—	2	1	no	—
363	C₂×#104	—	2	2	no	—
364	C₂×#104	—	134	2	no	—
365	C₂×#104	C₂×D₆₇	1	4	yes	—
366	#410	—	67	4	no	—
367	#410	—	134	2	no	—
368	C₂×#99	—	134	2	no	—
369	#344	—	67	4	no	—
370	#339	—	67	4	no	—
371	H(3,ℤ/4)	—	67	4	no	—
372	C₂×#41	—	2	1	no	—
373	C₂×#41	—	2	1	no	—
374	C₂×#41	—	2	1	no	—
375	C₂×#41	—	2	1	no	—
376	C₂×#41	—	2	1	no	—
377	C₂×#41	—	2	1	no	—
378	C₂×#41	—	2	1	no	—
379	C₂×#41	—	2	1	no	—
380	C₂×#41	—	2	1	no	—
381	C₂×#41	—	2	1	no	—
382	C₂×#41	Dic₁₃₄	1	2	yes	complemented
383	C₂×#41	C₂²×D₆₇	1	2	yes	—
384	C₂²×Q₈	—	134	2	no	—
385	C₂²×Q₈	Dic₁₃₄	1	1	yes	characteristic, complemented
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	Dic₁₃₄	1	1	yes	characteristic, complemented
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	—	2	1	no	—
390	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	1	no	—
395	C₂×M₁₆	—	2	1	no	—
396	C₂×M₁₆	—	67	2	no	—
397	C₂×M₁₆	—	134	1	no	—
398	C₂×M₁₆	—	134	1	no	—
399	C₂×M₁₆	—	134	1	no	—
400	C₂×M₁₆	—	134	1	no	—
401	C₂×M₁₆	—	134	1	no	—
402	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
403	C₂²×C₈	—	2	1	no	—
404	C₂²×C₈	—	134	1	no	—
405	C₄⋊Q₈	—	134	4	no	—
406	C₄⋊Q₈	—	134	4	no	—
407	#125	—	134	4	no	—
408	#125	—	134	4	no	—
409	C₂²⋊Q₈	—	134	8	no	—
410	C₂²⋊Q₈	—	134	8	no	—
411	C₄×Q₈	—	134	8	no	—
412	C₄×Q₈	—	134	8	no	—
413	#117	—	67	2	no	—
414	#117	—	67	2	no	—
415	#117	—	67	2	no	—
416	#117	—	67	2	no	—
417	#117	—	67	2	no	—
418	#117	—	134	1	no	—
419	#117	—	134	1	no	—
420	#117	—	134	1	no	—
421	#117	—	134	1	no	—
422	#117	—	134	1	no	—
423	#117	—	134	1	no	—
424	#117	—	134	1	no	—
425	C₂×C₄⋊C₄	—	134	1	no	—
426	C₂×C₄⋊C₄	—	134	4	no	—
427	C₂×C₄⋊C₄	—	134	2	no	—
428	C₂×C₄⋊C₄	—	134	1	no	—
429	C₂×C₄⋊C₄	—	134	1	no	—
430	C₂×C₂²⋊C₄	—	67	2	no	—
431	C₂×C₂²⋊C₄	—	134	1	no	—
432	C₂×C₂²⋊C₄	—	134	1	no	—
433	C₂×C₄²	—	2	1	no	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	67	2	no	—
437	C₂×C₄²	—	134	1	no	—
438	C₂×C₄²	—	134	1	no	—
439	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
440	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
441	C₂×C₄²	C₂²⋊D₆₇	1	2	yes	—
442	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
443	#104	—	2	4	no	—
444	#104	—	2	4	no	—
445	#104	—	134	8	no	—
446	#99	—	134	8	no	—
447	C₂⁴	—	2	1	no	—
448	C₂⁴	D₄×D₆₇	1	1	yes	characteristic
449	#41	—	2	2	no	—
450	#41	—	2	2	no	—
451	#41	—	2	2	no	—
452	#41	—	2	2	no	—
453	#41	—	2	2	no	—
454	#41	—	2	2	no	—
455	#41	—	2	2	no	—
456	#41	—	2	2	no	—
457	#41	—	4	1	no	—
458	#41	—	4	1	no	—
459	#41	—	4	1	no	—
460	#41	—	4	1	no	—
461	#41	—	4	1	no	—
462	#41	—	4	1	no	—
463	#41	—	4	1	no	—
464	#41	—	4	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	268	8	no	—
471	C₂×Q₈	—	134	8	no	—
472	C₂×Q₈	C₂×Dic₁₃₄	1	2	yes	complemented
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	4	1	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	4	1	no	—
483	C₂×D₄	—	4	1	no	—
484	C₂×D₄	C₂×Dic₁₃₄	1	2	yes	complemented
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	4	4	no	—
493	C₂²×C₄	—	4	1	no	—
494	C₂²×C₄	—	4	1	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	—	4	1	no	—
497	C₂²×C₄	—	268	1	no	—
498	C₂²×C₄	—	134	2	no	—
499	C₂²×C₄	—	134	2	no	—
500	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
501	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
502	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
503	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
505	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
506	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
507	C₂²×C₄	#11761627	1	1	yes	characteristic
508	C₂²×C₄	#11761627	1	1	yes	characteristic
509	C₂²×C₄	#11761627	1	1	yes	characteristic
510	C₂²×C₄	#11761627	1	1	yes	characteristic
511	C₂²×C₄	#11761628	1	1	yes	characteristic
512	C₂²×C₄	#11761628	1	1	yes	characteristic
513	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
514	M₁₆	—	2	2	no	—
515	M₁₆	—	2	2	no	—
516	M₁₆	—	4	1	no	—
517	M₁₆	—	4	1	no	—
518	M₁₆	—	268	1	no	—
519	M₁₆	—	268	1	no	—
520	M₁₆	—	134	2	no	—
521	M₁₆	—	134	2	no	—
522	C₂×C₈	—	2	2	no	—
523	C₂×C₈	—	4	1	no	—
524	C₂×C₈	—	4	1	no	—
525	C₂×C₈	—	268	1	no	—
526	C₂×C₈	—	268	1	no	—
527	C₂×C₈	—	134	2	no	—
528	C₄⋊C₄	—	268	1	no	—
529	C₄⋊C₄	—	134	16	no	—
530	C₄⋊C₄	—	134	8	no	—
531	C₄⋊C₄	—	134	2	no	—
532	C₄⋊C₄	—	134	2	no	—
533	C₄⋊C₄	—	134	2	no	—
534	C₄⋊C₄	—	134	2	no	—
535	C₄⋊C₄	—	134	2	no	—
536	C₂²⋊C₄	—	268	1	no	—
537	C₂²⋊C₄	—	67	4	no	—
538	C₂²⋊C₄	—	134	2	no	—
539	C₂²⋊C₄	—	134	2	no	—
540	C₂²⋊C₄	—	134	2	no	—
541	C₂²⋊C₄	—	134	2	no	—
542	C₄²	—	2	2	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	2	no	—
546	C₄²	—	268	1	no	—
547	C₄²	—	67	4	no	—
548	C₄²	—	134	2	no	—
549	C₄²	—	134	2	no	—
550	C₄²	—	134	2	no	—
551	C₄²	—	134	2	no	—
552	C₄²	C₂×C₂²⋊D₆₇	1	2	yes	—
553	C₄²	C₂×C₂²⋊D₆₇	1	2	yes	—
554	C₂³	—	2	2	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	8	2	no	—
559	C₂³	#14524011	1	1	yes	characteristic
560	C₂³	#14524011	1	1	yes	characteristic
561	C₂³	#14524020	1	1	yes	characteristic
562	C₂³	#14524020	1	1	yes	characteristic
563	C₂³	#14524029	1	1	yes	characteristic
564	C₂³	#14524029	1	1	yes	characteristic
565	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
566	Q₈	—	2	2	no	—
567	Q₈	—	2	2	no	—
568	Q₈	—	4	1	no	—
569	Q₈	—	4	1	no	—
570	Q₈	—	268	16	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	4	2	no	—
574	D₄	—	4	2	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	1	no	—
578	D₄	—	4	1	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	4	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	268	4	no	—
593	C₂×C₄	—	268	4	no	—
594	C₂×C₄	—	268	2	no	—
595	C₂×C₄	—	536	2	no	—
596	C₂×C₄	—	134	4	no	—
597	C₂×C₄	—	134	4	no	—
598	C₂×C₄	#14524011	1	1	yes	characteristic
599	C₂×C₄	#14524011	1	1	yes	characteristic
600	C₂×C₄	#14524020	1	1	yes	characteristic
601	C₂×C₄	#14524020	1	1	yes	characteristic
602	C₂×C₄	#14524020	1	1	yes	characteristic
603	C₂×C₄	#14524020	1	1	yes	characteristic
604	C₂×C₄	#14524020	1	1	yes	characteristic
605	C₂×C₄	#14524020	1	1	yes	characteristic
606	C₂×C₄	#14524022	1	1	yes	characteristic
607	C₂×C₄	#14524022	1	1	yes	characteristic
608	C₂×C₄	#14524022	1	1	yes	characteristic
609	C₂×C₄	#14524022	1	1	yes	characteristic
610	C₂×C₄	#14524029	1	1	yes	characteristic
611	C₂×C₄	#14524029	1	1	yes	characteristic
612	C₂×C₄	#14524029	1	1	yes	characteristic
613	C₂×C₄	#14524029	1	1	yes	characteristic
614	C₂×C₄	#14524029	1	1	yes	characteristic
615	C₂×C₄	#14524029	1	1	yes	characteristic
616	C₂×C₄	#14524030	1	1	yes	characteristic
617	C₂×C₄	#14524030	1	1	yes	characteristic
618	C₂×C₄	#14524030	1	1	yes	characteristic
619	C₂×C₄	#14524030	1	1	yes	characteristic
620	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
621	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
622	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
623	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
624	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
625	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
626	C₈	—	4	2	no	—
627	C₈	—	268	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	8	2	no	—
637	C₂²	—	8	2	no	—
638	C₂²	—	8	2	no	—
639	C₂²	#16863308	1	1	yes	characteristic
640	C₂²	#16863308	1	1	yes	characteristic
641	C₂²	#16863308	1	1	yes	characteristic
642	C₂²	#16863308	1	1	yes	characteristic
643	C₂²	C₂×#14524011	1	1	yes	characteristic
644	C₂²	C₂×#14524020	1	1	yes	characteristic
645	C₂²	C₂×#14524029	1	1	yes	characteristic
646	C₄	—	2	4	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	2	no	—
649	C₄	—	268	4	no	—
650	C₄	—	268	4	no	—
651	C₄	—	536	2	no	—
652	C₄	#16863308	1	1	yes	characteristic
653	C₄	#16863308	1	1	yes	characteristic
654	C₄	#16863308	1	1	yes	characteristic
655	C₄	#16863308	1	1	yes	characteristic
656	C₄	C₂×#14524020	1	1	yes	characteristic
657	C₄	C₂×#14524022	1	1	yes	characteristic
658	C₄	C₂×#14524029	1	1	yes	characteristic
659	C₄	C₂×#14524030	1	1	yes	characteristic
660	C₂	—	2	1	no	—
661	C₂	—	2	1	no	—
662	C₂	—	2	1	no	—
663	C₂	—	2	1	no	—
664	C₂	—	2	1	no	—
665	C₂	—	2	1	no	—
666	C₂	—	8	2	no	—
667	C₂	#22561381	1	2	yes	direct product factor
668	C₂	C₂×#16863308	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14524029
commutator, cosocle	C₂²×C₄×C₆₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂²×#104×C₆₇	C₂
socle	C₂²×C₆₇	#393
prime radical	C₂²×#41×C₆₇	C₂²
hypercenter	C₂²×#104	D₆₇
hypocenter	C₆₇	C₂×#2031
LCS	G ▷ C₂²×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×#16863953	C₂	semidirect
4. #22561381	C₂	direct (N × H)
5. C₂×#16863168	C₂	semidirect
6. C₂×#16863156	C₂	semidirect
7. C₂×#16863153	C₂	semidirect
13. #16863953	C₂²	semidirect
27. #16863168	C₂²	semidirect
28. #16863156	C₂²	semidirect
29. #16863153	C₂²	semidirect
88. C₂×#41×C₆₇	Q₈	semidirect
90. C₂²×Q₈×C₆₇	Q₈	semidirect
92. C₂²×D₄×C₆₇	Q₈	semidirect
167. C₂×Q₈×C₆₇	C₂×Q₈	semidirect
179. C₂×D₄×C₆₇	C₂×Q₈	semidirect
333. C₂×C₆₇	#2031	semidirect
343. C₆₇	C₂×#2031	semidirect
382. C₂×#41	Dic₁₃₄	semidirect
385. C₂²×Q₈	Dic₁₃₄	semidirect
387. C₂²×D₄	Dic₁₃₄	semidirect
472. C₂×Q₈	C₂×Dic₁₃₄	semidirect
484. C₂×D₄	C₂×Dic₁₃₄	semidirect
667. C₂	#22561381	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×#16863953	2
C₂×#16863413	2
C₂×#16863370	2
#22561381	2
C₂×#16863168	2
C₂×#16863156	2
C₂×#16863153	2
C₂²×#104×C₆₇	2
C₂×#2031	67

Subgroups — C2×#22561381 #30883255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22561381 #30883255