Subgroups — C₂×#9634 #203993

Order 512.

626 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1574	C₂	1	2	yes	maximal
2	C₂×#1567	C₂	1	1	yes	maximal, characteristic
3	C₂×#1564	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic
5	#9634	C₂	1	8	yes	maximal, direct product factor
6	C₂×#1299	C₂	1	2	yes	maximal
7	C₂×#431	C₂²	1	2	yes	—
8	C₂×#431	C₂²	1	1	yes	characteristic
9	C₂×#423	C₂²	1	2	yes	—
10	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
12	#1574	—	2	4	no	—
13	#1574	C₂²	1	8	yes	—
14	#1567	—	2	2	no	—
15	#1567	C₂²	1	4	yes	—
16	#1564	C₄	1	4	yes	—
17	#1564	C₂²	1	4	yes	—
18	C₂×#335	—	2	2	no	—
19	C₂×#335	—	2	1	no	—
20	C₂×#335	—	2	1	no	—
21	C₂×#335	C₄	1	2	yes	—
22	C₂×#334	—	2	2	no	—
23	C₂×#334	C₄	1	2	yes	—
24	C₈×M₁₆	—	2	2	no	—
25	C₈×M₁₆	C₂²	1	4	yes	—
26	C₂×#322	—	2	1	no	—
27	C₂×C₈²	—	2	1	no	—
28	#1299	C₂²	1	8	yes	—
29	C₂²×M₁₆	—	2	1	no	—
30	C₂²×M₁₆	—	2	2	no	—
31	C₂³×C₈	Q₈	1	1	yes	characteristic
32	C₂³×C₈	Q₈	1	1	yes	characteristic
33	C₂²×C₄²	C₂³	1	1	yes	characteristic
34	#431	—	2	2	no	—
35	#431	—	2	1	no	—
36	#431	—	2	2	no	—
37	#431	—	2	1	no	—
38	#431	C₂×C₄	1	4	yes	—
39	#431	D₄	1	2	yes	—
40	#431	C₂³	1	4	yes	—
41	#431	C₂³	1	2	yes	—
42	#423	—	2	2	no	—
43	#423	—	2	2	no	—
44	#423	—	2	2	no	—
45	#423	C₂³	1	4	yes	—
46	C₂×C₄⋊C₈	—	2	2	no	—
47	C₂×C₄⋊C₈	—	2	2	no	—
48	C₂×C₄⋊C₈	C₂×C₄	1	4	yes	—
49	C₂×C₄⋊C₈	D₄	1	1	yes	characteristic
50	C₂×C₄⋊C₈	D₄	1	1	yes	characteristic
51	C₂×C₂²⋊C₈	—	2	2	no	—
52	C₂×C₂²⋊C₈	—	2	1	no	—
53	C₄×M₁₆	—	2	1	no	—
54	C₄×M₁₆	—	2	1	no	—
55	C₄×M₁₆	Q₈	1	2	yes	—
56	C₄×M₁₆	C₂³	1	2	yes	—
57	C₂×#97	Q₈	1	2	yes	—
58	C₂×C₄×C₈	—	2	2	no	—
59	C₂×C₄×C₈	—	2	1	no	—
60	C₂×C₄×C₈	—	2	1	no	—
61	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×C₈	C₂×C₄	1	2	yes	—
64	C₂×C₄×C₈	D₄	1	1	yes	characteristic
65	C₂×C₄×C₈	D₄	1	1	yes	characteristic
66	C₂×C₄×C₈	D₄	1	2	yes	—
67	C₂×C₄×C₈	Q₈	1	2	yes	—
68	C₂×C₄×C₈	C₂³	1	2	yes	—
69	#335	—	2	8	no	—
70	#335	—	2	4	no	—
71	#335	—	2	4	no	—
72	#335	C₂×C₄	1	8	yes	—
73	#334	—	2	8	no	—
74	#334	C₂×C₄	1	8	yes	—
75	#322	—	2	4	no	—
76	C₈²	—	2	4	no	—
77	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
78	C₂³×C₄	#41	1	1	yes	characteristic
79	C₂³×C₄	#41	1	1	yes	characteristic
80	C₂×M₁₆	—	2	8	no	—
81	C₂×M₁₆	—	2	2	no	—
82	C₂×M₁₆	—	2	2	no	—
83	C₂×M₁₆	—	2	4	no	—
84	C₂×M₁₆	—	4	2	no	—
85	C₂×M₁₆	—	8	4	no	—
86	C₂²×C₈	—	2	2	no	—
87	C₂²×C₈	—	2	4	no	—
88	C₂²×C₈	—	2	4	no	—
89	C₂²×C₈	—	2	1	no	—
90	C₂²×C₈	—	2	1	no	—
91	C₂²×C₈	—	4	2	no	—
92	C₂²×C₈	—	4	2	no	—
93	C₂²×C₈	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₈	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×C₈	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₈	C₄⋊C₄	1	2	yes	—
97	C₂²×C₈	C₄⋊C₄	1	2	yes	—
98	C₂²×C₈	C₄⋊C₄	1	1	yes	characteristic
99	C₂²×C₈	C₂×Q₈	1	2	yes	—
100	C₂²×C₈	C₂×Q₈	1	2	yes	—
101	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
110	C₂×C₄²	#41	1	1	yes	characteristic
111	C₂×C₄²	#41	1	1	yes	characteristic
112	C₂×C₄²	C₂⁴	1	1	yes	characteristic
113	C₄⋊C₈	—	2	4	no	—
114	C₄⋊C₈	—	2	1	no	—
115	C₄⋊C₈	—	2	1	no	—
116	C₄⋊C₈	—	2	4	no	—
117	C₄⋊C₈	—	2	4	no	—
118	C₄⋊C₈	—	4	2	no	—
119	C₄⋊C₈	—	4	2	no	—
120	C₄⋊C₈	C₂²×C₄	1	8	yes	—
121	C₄⋊C₈	C₂×D₄	1	2	yes	—
122	C₄⋊C₈	C₂×D₄	1	2	yes	—
123	C₂²⋊C₈	—	2	4	no	—
124	C₂²⋊C₈	—	2	2	no	—
125	C₂²⋊C₈	—	2	4	no	—
126	C₂²⋊C₈	—	2	2	no	—
127	#97	—	2	2	no	—
128	#97	C₂×Q₈	1	4	yes	—
129	C₄×C₈	—	2	4	no	—
130	C₄×C₈	—	2	2	no	—
131	C₄×C₈	—	2	2	no	—
132	C₄×C₈	—	2	2	no	—
133	C₄×C₈	—	2	2	no	—
134	C₄×C₈	—	2	4	no	—
135	C₄×C₈	C₄⋊C₄	1	2	yes	—
136	C₄×C₈	C₄⋊C₄	1	2	yes	—
137	C₄×C₈	C₄⋊C₄	1	2	yes	—
138	C₄×C₈	C₄⋊C₄	1	2	yes	—
139	C₄×C₈	C₂²×C₄	1	2	yes	—
140	C₄×C₈	C₂²×C₄	1	2	yes	—
141	C₄×C₈	C₂×D₄	1	2	yes	—
142	C₄×C₈	C₂×D₄	1	2	yes	—
143	C₂⁴	#125	1	1	yes	characteristic
144	C₂²×C₄	—	2	2	no	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	2	4	no	—
147	C₂²×C₄	—	2	2	no	—
148	C₂²×C₄	—	2	2	no	—
149	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
152	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
153	C₂²×C₄	C₄×Q₈	1	1	yes	characteristic
154	C₂²×C₄	C₄×Q₈	1	1	yes	characteristic
155	C₂²×C₄	#121	1	1	yes	characteristic
156	C₂²×C₄	#121	1	1	yes	characteristic
157	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂²×C₄	#125	1	1	yes	characteristic
160	C₂²×C₄	#125	1	1	yes	characteristic
161	C₂²×C₄	#125	1	1	yes	characteristic
162	C₂²×C₄	C₄⋊Q₈	1	1	yes	characteristic
163	C₂²×C₄	C₄⋊Q₈	1	1	yes	characteristic
164	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
165	C₂²×C₄	C₂×#41	1	1	yes	characteristic
166	C₂²×C₄	C₂×#41	1	1	yes	characteristic
167	M₁₆	—	2	8	no	—
168	M₁₆	—	2	8	no	—
169	M₁₆	—	8	4	no	—
170	M₁₆	—	8	4	no	—
171	C₂×C₈	—	2	8	no	—
172	C₂×C₈	—	2	4	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	2	4	no	—
177	C₂×C₈	—	2	4	no	—
178	C₂×C₈	—	2	8	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	4	2	no	—
183	C₂×C₈	—	4	8	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	4	4	no	—
187	C₂×C₈	—	8	4	no	—
188	C₂×C₈	#108	1	4	yes	—
189	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
190	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
191	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
192	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
193	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₄²	C₄×D₄	1	1	yes	characteristic
196	C₄²	C₄×D₄	1	1	yes	characteristic
197	C₄²	C₄×Q₈	1	1	yes	characteristic
198	C₄²	C₄×Q₈	1	1	yes	characteristic
199	C₄²	#121	1	1	yes	characteristic
200	C₄²	#121	1	1	yes	characteristic
201	C₄²	C₂²⋊Q₈	1	1	yes	characteristic
202	C₄²	C₂²⋊Q₈	1	1	yes	characteristic
203	C₄²	C₄⋊Q₈	1	1	yes	characteristic
204	C₄²	C₄⋊Q₈	1	1	yes	characteristic
205	C₄²	C₂³×C₄	1	1	yes	characteristic
206	C₄²	C₂²×D₄	1	1	yes	characteristic
207	C₄²	C₂²×D₄	1	1	yes	characteristic
208	C₄²	C₂²×Q₈	1	1	yes	characteristic
209	C₂³	—	2	2	no	—
210	C₂³	—	2	2	no	—
211	C₂³	—	2	2	no	—
212	C₂³	#389	1	1	yes	characteristic
213	C₂³	#389	1	1	yes	characteristic
214	C₂³	C₂×#125	1	1	yes	characteristic
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	#389	1	1	yes	characteristic
235	C₂×C₄	#389	1	1	yes	characteristic
236	C₂×C₄	#389	1	1	yes	characteristic
237	C₂×C₄	#389	1	1	yes	characteristic
238	C₂×C₄	#389	1	1	yes	characteristic
239	C₂×C₄	#389	1	1	yes	characteristic
240	C₂×C₄	C₂×#108	1	2	yes	—
241	C₂×C₄	#430	1	2	yes	—
242	C₂×C₄	#443	1	4	yes	—
243	C₂×C₄	#472	1	2	yes	—
244	C₂×C₄	#473	1	2	yes	—
245	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
246	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂×C₄	C₂×C₄×Q₈	1	1	yes	characteristic
248	C₂×C₄	C₂×#121	1	1	yes	characteristic
249	C₂×C₄	C₂×C₂²⋊Q₈	1	1	yes	characteristic
250	C₂×C₄	C₂×C₄⋊Q₈	1	1	yes	characteristic
251	C₈	—	2	8	no	—
252	C₈	—	2	2	no	—
253	C₈	—	2	2	no	—
254	C₈	—	2	2	no	—
255	C₈	—	4	8	no	—
256	C₈	—	4	2	no	—
257	C₈	—	4	2	no	—
258	C₈	—	8	4	no	—
259	C₈	C₂×#108	1	4	yes	—
260	C₂²	—	2	1	no	—
261	C₂²	—	2	1	no	—
262	C₂²	—	2	1	no	—
263	C₂²	—	2	1	no	—
264	C₂²	—	2	1	no	—
265	C₂²	—	2	1	no	—
266	C₂²	—	4	4	no	—
267	C₂²	#1945	1	2	yes	—
268	C₂²	#1950	1	2	yes	—
269	C₂²	#1952	1	2	yes	—
270	C₂²	C₂×#389	1	1	yes	characteristic
271	C₄	—	2	1	no	—
272	C₄	—	2	1	no	—
273	C₄	—	2	1	no	—
274	C₄	—	2	1	no	—
275	C₄	—	2	1	no	—
276	C₄	—	2	1	no	—
277	C₄	#1945	1	2	yes	—
278	C₄	#1950	1	2	yes	—
279	C₄	#1952	1	2	yes	—
280	C₄	C₂²×#108	1	1	yes	characteristic
281	C₄	C₂×#430	1	1	yes	characteristic
282	C₄	C₂×#443	1	2	yes	—
283	C₄	C₂×#472	1	1	yes	characteristic
284	C₄	C₂×#473	1	1	yes	characteristic
285	C₂	—	4	1	no	—
286	C₂	—	4	1	no	—
287	C₂	#9634	1	4	yes	direct product factor
288	C₂	C₂×#1945	1	1	yes	characteristic
289	C₂	C₂×#1950	1	1	yes	characteristic
290	C₂	C₂×#1952	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#121
commutator	C₄²	C₂³×C₄
Frattini, cosocle	C₂×C₄²	C₂⁴
socle	C₂³	#389
prime radical	C₂⁴	#125
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
5. #9634	C₂	direct (N × H)
287. C₂	#9634	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×#1574	2
C₂×#1567	2
C₂×#1564	2
C₂×C₈×M₁₆	2
#9634	2
C₂×#1299	2

Subgroups — C2×#9634 #203993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#9634 #203993