Finite Group Databasebeta

← C2×#13131005 #16799328

Subgroups — C2×#13131005 #16799328

Order 3328.

1502 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊#1057C211yesmaximal, characteristic
2C22×C4×#1057C211yesmaximal, characteristic
3#13131005C218yesmaximal, direct product factor
4C2×#11718290C214yesmaximal
5C22×Q8×Dic13C211yesmaximal, characteristic
6C23×Q8×C13C411yescharacteristic
7C23×#1057C2212yes—
8C23×#1057C2212yes—
9C2×Q8×Dic13—24no—
10C2×Q8×Dic13—24no—
11C2×Q8×Dic13C414yes—
12C2×Q8×Dic13C2214yes—
13C22×C4⋊Dic13C411yescharacteristic
14C22×C4⋊Dic13C412yes—
15C22×C4×Dic13C2212yes—
16C22×C4×Dic13C2211yescharacteristic
17C2×C4⋊#1057—24no—
18C2×C4⋊#1057C2214yes—
19C2×C4×#1057—24no—
20C2×C4×#1057C2214yes—
21#11718290C22116yes—
22C22×Q8×C13—24no—
23C22×Q8×C13—24no—
24C22×Q8×C13C818yescomplemented
25C22×Q8×C13C2×C414yes—
26C23×C4×C13C2×C412yes—
27C23×C4×C13C2×C411yescharacteristic
28C23×Dic13C2×C412yes—
29C23×Dic13C2×C411yescharacteristic
30C23×Dic13C2311yescharacteristic
31C22×#1057—24no—
32C22×#1057—24no—
33C22×#1057—24no—
34C22×#1057—28no—
35C22×#1057Q818yescomplemented
36C22×#1057C2314yes—
37C22×#1057C2314yes—
38Q8×Dic13—216no—
39Q8×Dic13—28no—
40Q8×Dic13—28no—
41C2×C4⋊Dic13—24no—
42C2×C4⋊Dic13—28no—
43C2×C4⋊Dic13C2×C414yes—
44C2×C4⋊Dic13C2×C418yes—
45C2×C4×Dic13—24no—
46C2×C4×Dic13—24no—
47C2×C4×Dic13C2×C414yes—
48C2×C4×Dic13C2×C412yes—
49C2×C4×Dic13D414yes—
50C2×C4×Dic13D414yes—
51C2×C4×Dic13C2314yes—
52C2×C4×Dic13C2312yes—
53C4⋊#1057—28no—
54C4×#1057—28no—
55C2×#1984—131nomaximal, Sylow
56C24×C13C22×C411yescharacteristic
57C2×Q8×C13—232no—
58C2×Q8×C13—28no—
59C2×Q8×C13—28no—
60C2×Q8×C13C2×C8116yescomplemented
61C22×C4×C13—24no—
62C22×C4×C13—24no—
63C22×C4×C13C22⋊C414yes—
64C22×C4×C13C2×C818yes—
65C22×C4×C13C2×C814yes—
66C22×C4×C13M1614yes—
67C22×C4×C13C22×C414yes—
68C22×C4×C13C22×C412yes—
69C22×Dic13—24no—
70C22×Dic13—24no—
71C22×Dic13—28no—
72C22×Dic13C22⋊C414yes—
73C22×Dic13C22×C414yes—
74C22×Dic13C22×C412yes—
75C22×Dic13C22×C411yescharacteristic
76C22×Dic13C2×D412yes—
77C22×Dic13C2×D412yes—
78C22×Dic13C2×Q814yes—
79C22×Dic13#4114yes—
80C22×Dic13C2411yescharacteristic
81C2×#1057—216no—
82C2×#1057—24no—
83C2×#1057—24no—
84C2×#1057—24no—
85C2×#1057—28no—
86C2×#1057—48no—
87C2×#1057C2×Q818yescomplemented
88C4⋊Dic13—28no—
89C4⋊Dic13—216no—
90C4×Dic13—28no—
91C4×Dic13—24no—
92C4×Dic13—24no—
93C4×Dic13C22⋊C418yes—
94C4×Dic13C2×D414yes—
95C4×Dic13C2×D414yes—
96C22×C4×Q8—131no—
97C22×C4⋊C8—131no—
98C22×C4×C8—131no—
99#1984—138no—
100C2×#336—134no—
101C23×C13C2×C22⋊C412yes—
102C23×C13C4×Q814yes—
103C23×C13C22×C812yes—
104C23×C13C2×M1612yes—
105C23×C13#13114yes—
106C23×C13C23×C411yescharacteristic
107Q8×C13—232no—
108C2×C4×C13—24no—
109C2×C4×C13—24no—
110C2×C4×C13—216no—
111C2×C4×C13C22⋊C8116yes—
112C2×C4×C13C2×C22⋊C414yes—
113C2×C4×C13C22×C818yes—
114C2×C4×C13C22×C814yes—
115C2×C4×C13C2×M1614yes—
116C2×Dic13—24no—
117C2×Dic13—28no—
118C2×Dic13—24no—
119C2×Dic13—28no—
120C2×Dic13—48no—
121C2×Dic13C2×C22⋊C414yes—
122C2×Dic13C2×C22⋊C412yes—
123C2×Dic13C4×Q814yes—
124C2×Dic13C22⋊Q818yes—
125C2×Dic13#12414yes—
126C2×Dic13C4⋊Q814yes—
127C2×Dic13C22×D411yescharacteristic
128C2×Dic13C22×D411yescharacteristic
129C2×Dic13C22×Q812yes—
130C2×Dic13C2×#4112yes—
131#1057—28no—
132#1057—44no—
133C23×Q8#26111yescharacteristic
134C23×C8—132no—
135C23×C8—132no—
136C2×C4×Q8—134no—
137C2×C4×Q8—134no—
138C2×C4×Q8—264no—
139C2×C4×Q8—264no—
140C22×C4⋊C4—132no—
141C22×C4⋊C4—131no—
142C22×C42—131no—
143C22×C42—132no—
144C2×C4⋊C8—134no—
145C2×C4⋊C8—264no—
146C2×C4×C8—134no—
147C2×C4×C8—264no—
148#336—1316no—
149C22×C13#39114yes—
150C22×C13C2×C22⋊C814yes—
151C22×C13#40814yes—
152C22×C13C8×Q818yes—
153C22×C13#44618yes—
154C22×C13C22×C22⋊C411yescharacteristic
155C22×C13C2×C4×Q812yes—
156C22×C13C23×C811yescharacteristic
157C22×C13C22×M1611yescharacteristic
158C22×C13C2×#13112yes—
159C4×C13—28no—
160C4×C13C2×C22⋊C818yes—
161Dic13—24no—
162Dic13—44no—
163Dic13#39114yes—
164Dic13C2×C22⋊Q812yes—
165Dic13C2×#12411yescharacteristic
166Dic13C2×C4⋊Q811yescharacteristic
167C22×Q8—24no—
168C22×Q8—24no—
169C22×Q8#105718yescomplemented
170C22×Q8C2×#26114yes—
171C23×C4—131no—
172C23×C4—131no—
173C23×C4—132no—
174C23×C4C2×#26112yes—
175C23×C4C2×#26111yescharacteristic
176C22×C8—134no—
177C22×C8—138no—
178C22×C8—134no—
179C22×C8—264no—
180C22×C8—264no—
181C22×C8—264no—
182C22×C8—268no—
183C4×Q8—268no—
184C4×Q8—268no—
185C4×Q8—2616no—
186C2×C4⋊C4—138no—
187C2×C4⋊C4—134no—
188C2×C4⋊C4—268no—
189C2×C4⋊C4—264no—
190C2×C42—134no—
191C2×C42—134no—
192C2×C42—132no—
193C2×C42—132no—
194C2×C42—134no—
195C2×C42—134no—
196C2×C42—264no—
197C2×C42—264no—
198C4⋊C8—268no—
199C4×C8—268no—
200C2×C13#198418yescomplemented
201C2×C13C2×#39111yescharacteristic
202C2×C13C22×C22⋊C811yescharacteristic
203C2×C13C2×#40811yescharacteristic
204C2×C13C2×C8×Q812yes—
205C2×C13C2×#44612yes—
206C24C22×#26111yescharacteristic
207C2×Q8—232no—
208C2×Q8—28no—
209C2×Q8—28no—
210C2×Q8C2×#1057116yescomplemented
211C22×C4—24no—
212C22×C4—24no—
213C22×C4—134no—
214C22×C4—134no—
215C22×C4—132no—
216C22×C4—132no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—134no—
220C22×C4—132no—
221C22×C4—134no—
222C22×C4—264no—
223C22×C4—268no—
224C22×C4—264no—
225C22×C4C2×#105718yes—
226C22×C4C2×#105714yes—
227C22×C4#612214yes—
228C22×C4C22⋊#26114yes—
229C22×C4C22×#26114yes—
230C22×C4C22×#26112yes—
231C2×C8—138no—
232C2×C8—264no—
233C2×C8—264no—
234C2×C8—2616no—
235C2×C8—264no—
236C2×C8—268no—
237C2×C8—528no—
238C4⋊C4—2616no—
239C4⋊C4—268no—
240C42—134no—
241C42—134no—
242C42—138no—
243C42—264no—
244C42—264no—
245C42—268no—
246C13C2×#198411yescharacteristic, complemented, Sylow
247C23#8824014yes—
248C23Q8×#26114yes—
249C23C22×#105712yes—
250C23C2×#612212yes—
251C23C2×C22⋊#26112yes—
252C23C23×#26111yescharacteristic
253Q8—232no—
254C2×C4—216no—
255C2×C4—24no—
256C2×C4—24no—
257C2×C4—132no—
258C2×C4—132no—
259C2×C4—134no—
260C2×C4—131no—
261C2×C4—131no—
262C2×C4—132no—
263C2×C4—138no—
264C2×C4—134no—
265C2×C4—134no—
266C2×C4—134no—
267C2×C4—264no—
268C2×C4—268no—
269C2×C4—268no—
270C2×C4—264no—
271C2×C4—528no—
272C2×C4C22⋊#1057116yes—
273C2×C4C22×#105718yes—
274C2×C4C22×#105714yes—
275C2×C4C2×#612214yes—
276C2×C4C2×C22⋊#26114yes—
277C8—268no—
278C8—524no—
279C22Q8×#105718yes—
280C22#1171915818yes—
281C22#1171915914yes—
282C22(C2×#261)⋊Q814yes—
283C22C2×C22⋊#105714yes—
284C22C2×#8824012yes—
285C22C2×Q8×#26112yes—
286C22C23×#105711yescharacteristic
287C22C22×#612211yescharacteristic
288C22C22×C22⋊#26111yescharacteristic
289C4—28no—
290C4—132no—
291C4—131no—
292C4—131no—
293C4—134no—
294C4—264no—
295C4—524no—
296C4C2×C22⋊#105718yes—
297C2#1313100518yesdirect product factor
298C2C2×(C2×#261)⋊Q811yescharacteristic
299C2C22×C22⋊#105711yescharacteristic
300C2C2×#1171915911yescharacteristic
301C2C2×Q8×#105712yes—
302C2C2×#1171915812yes—
subgroupG/H
centerC24C22×#261
commutatorC22×C13C23×C8
FrattiniC23C23×#261
FittingC23×Q8×C13C4
socle, prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenterC23×Q8#261
hypocenterC13C2×#1984
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
3. #13131005C2direct (N × H)
24. C22×Q8×C13C8semidirect
35. C22×#1057Q8semidirect
60. C2×Q8×C13C2×C8semidirect
87. C2×#1057C2×Q8semidirect
169. C22×Q8#1057semidirect
200. C2×C13#1984semidirect
210. C2×Q8C2×#1057semidirect
246. C13C2×#1984semidirect
297. C2#13131005direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊#10572
C22×C4×#10572
#131310052
C2×#117182902
C22×Q8×Dic132
C2×#198413