Finite Group Databasebeta

← C2×#13129982 #16791319

Subgroups — C2×#13129982 #16791319

Order 3328.

340 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718228C211yesmaximal, characteristic
2C2×#11718226C211yesmaximal, characteristic
3#13129982C214yesmaximal, direct product factor
4C2×#11718729C211yesmaximal, characteristic
5C2×C13×#125C411yescharacteristic, complemented
6C2×#88129C2211yescharacteristic
7C2×#88113—21no—
8C2×#88107—21no—
9#11718729—21no—
10#11718729—21no—
11#11718729C412yescomplemented
12#11718729C2212yes—
13C2×#88050—21no—
14C2×#88049—21no—
15C2×C4×#1055C411yescharacteristic, complemented
16#11718228—21no—
17#11718228C2212yes—
18#11718226—21no—
19#11718226C2212yes—
20C22×D52D411yescharacteristic
21C22×Dic26D411yescharacteristic
22C2×C22⋊#261—41no—
23C2×#6122—41no—
24C13×#125—21no—
25C13×#125—41no—
26C13×#125C2×C412yescomplemented
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—41no—
29C2×C42×C13C2×C411yescharacteristic
30C2×#6103—41no—
31C22×#1055—21no—
32#88129—41no—
33#88129C2×C411yescharacteristic
34#88129D411yescharacteristic
35#88129D411yescharacteristic
36#88129C2311yescharacteristic
37#88113—22no—
38#88113—41no—
39#88107—22no—
40#88107—41no—
41#88050—22no—
42#88050—22no—
43#88049—22no—
44#88049—22no—
45C4×#1055—21no—
46C4×#1055C2×C412yescomplemented
47C2×#1414—131nomaximal, Sylow
48C23×D13—21no—
49C22×#261—81no—
50C22×C4×C13—21no—
51C22×C4×C13—41no—
52C22×C4×C13C22⋊C411yescharacteristic
53C22×Dic13—21no—
54C2×D52—21no—
55C2×D52—41no—
56C2×D52—41no—
57C2×D52C22⋊C411yescharacteristic
58C2×D52C2×D411yescharacteristic
59C2×Dic26—21no—
60C2×Dic26—41no—
61C2×Dic26—41no—
62C2×Dic26C22⋊C411yescharacteristic
63C2×Dic26C2×D411yescharacteristic
64C22⋊#261—42no—
65C22⋊#261—81no—
66#6122—42no—
67#6122—81no—
68C2×#1057—81no—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—41no—
73C42×C13—21no—
74C42×C13C22⋊C411yescharacteristic
75C42×C13C22×C411yescharacteristic
76#6103—41no—
77#6103—41no—
78#6103—41no—
79#6103—41no—
80C2×#1055—22no—
81C2×#1055—41no—
82C2×#1055—41no—
83C2×#488—131no—
84C2×#355—131no—
85C2×#354—131no—
86#1414—134no—
87C23×C13#9911yescharacteristic
88C22×D13—21no—
89C22×D13—21no—
90C22×D13—41no—
91C22×D13—41no—
92C22×D13—82no—
93C2×#261—82no—
94C2×#261—162no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—82no—
102C2×C4×C13#9911yescharacteristic
103C2×C4×C13C2×C22⋊C411yescharacteristic
104C2×Dic13—21no—
105C2×Dic13—21no—
106C2×Dic13—41no—
107C2×Dic13—41no—
108D52—41no—
109D52—41no—
110D52—81no—
111Dic26—41no—
112Dic26—41no—
113Dic26—81no—
114#1057—82no—
115#1055—42no—
116C2×#125#26111yescharacteristic, complemented
117C2×#124—131no—
118#488—132no—
119#488—132no—
120#488—261no—
121#488—261no—
122C2×#103—261no—
123C2×#102—261no—
124C2×#101—261no—
125C2×#99—261no—
126C2×C4×C8—131no—
127#355—132no—
128#355—261no—
129#354—132no—
130#354—261no—
131C22×C13—22no—
132C22×C13#35411yescharacteristic
133C22×C13#35411yescharacteristic
134C22×C13C2×#9911yescharacteristic
135C2×D13—41no—
136C2×D13—41no—
137C2×D13—82no—
138C2×D13—81no—
139C2×D13—81no—
140C2×D13—161no—
141#261—162no—
142C4×C13—21no—
143C4×C13—21no—
144C4×C13—41no—
145C4×C13—41no—
146C4×C13—82no—
147Dic13—41no—
148Dic13—41no—
149C22×Q8—131no—
150C22×D4—131no—
151C2×M16—521no—
152C22×C8—261no—
153#125—21no—
154#125—41no—
155#125C2×#26112yescomplemented
156#124—131no—
157#124—131no—
158#124—131no—
159#124—131no—
160#124—521no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—41no—
163C2×C22⋊C4—521no—
164C2×C22⋊C4—521no—
165C2×C42C2×#26111yescharacteristic
166#103—262no—
167#103—262no—
168#102—262no—
169#102—262no—
170#101—262no—
171#101—521no—
172#99—262no—
173#99—521no—
174C4×C8—132no—
175C4×C8—261no—
176C2×C13—21no—
177C2×C13—21no—
178C2×C13#141412yescomplemented
179C2×C13C2×#35411yescharacteristic
180D13—81no—
181D13—81no—
182C24—261no—
183C2×Q8—131no—
184C2×Q8—131no—
185C2×Q8—261no—
186C2×Q8—521no—
187C2×Q8—521no—
188C2×D4—131no—
189C2×D4—131no—
190C2×D4—261no—
191C2×D4—521no—
192C2×D4—521no—
193C22×C4—21no—
194C22×C4—41no—
195C22×C4—261no—
196C22×C4—1041no—
197C22×C4C22⋊#26111yescharacteristic
198M16—522no—
199M16—1041no—
200C2×C8—262no—
201C2×C8—521no—
202C2×C8—521no—
203C2×C8—1041no—
204C4⋊C4—22no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—41no—
208C22⋊C4—521no—
209C22⋊C4—521no—
210C22⋊C4—521no—
211C22⋊C4—521no—
212C22⋊C4—522no—
213C22⋊C4—1041no—
214C42—21no—
215C42C22⋊#26111yescharacteristic
216C42C22×#26111yescharacteristic
217C13C2×#141411yescharacteristic, complemented, Sylow
218C23—261no—
219C23—261no—
220C23—521no—
221C23—521no—
222C23—1042no—
223C23#8811911yescharacteristic
224Q8—521no—
225Q8—521no—
226Q8—1041no—
227D4—521no—
228D4—521no—
229D4—1041no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—82no—
237C2×C4—261no—
238C2×C4—261no—
239C2×C4—521no—
240C2×C4—521no—
241C2×C4—1042no—
242C2×C4—2082no—
243C2×C4#8811911yescharacteristic
244C2×C4C2×C22⋊#26111yescharacteristic
245C8—522no—
246C8—1042no—
247C22—22no—
248C22—521no—
249C22—521no—
250C22—1041no—
251C22—1041no—
252C22—1042no—
253C22—2081no—
254C22#1171830011yescharacteristic
255C22#1171830011yescharacteristic
256C22C2×#8811911yescharacteristic
257C4—21no—
258C4—21no—
259C4—41no—
260C4—41no—
261C4—82no—
262C4—521no—
263C4—521no—
264C4—2082no—
265C2—21no—
266C2—21no—
267C2—1041no—
268C2—1041no—
269C2#1312998212yesdirect product factor
270C2C2×#1171830011yescharacteristic
subgroupG/H
centerC22#11718300
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC2×C13×#125C4
socleC22×C13#354
prime radicalC22×D52D4
cosocle#88129C23
hypercenterC2×#125#261
hypocenterC13C2×#1414
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
3. #13129982C2direct (N × H)
5. C2×C13×#125C4semidirect
11. #11718729C4semidirect
15. C2×C4×#1055C4semidirect
26. C13×#125C2×C4semidirect
46. C4×#1055C2×C4semidirect
116. C2×#125#261semidirect
155. #125C2×#261semidirect
178. C2×C13#1414semidirect
217. C13C2×#1414semidirect
269. C2#13129982direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117182282
C2×#117182262
#131299822
C2×#117187292
C2×#141413