Finite Group Databasebeta

← C22×#11718304 #16806792

Subgroups — C22×#11718304 #16806792

Order 3328.

1174 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88106C211yesmaximal, characteristic, complemented
2C23×#6092C211yesmaximal, characteristic, complemented
3C2×#11718304C2112yesmaximal, direct product factor
4C22×#88202C211yesmaximal, characteristic
5C22×C13×#41C411yescharacteristic
6C2×#88202—23no—
7C2×#88202—23no—
8C2×#88202C416yes—
9C2×#88202C2216yes—
10C22×#6099—21no—
11C22×#6099C411yescharacteristic
12C23×#1055—21no—
13C23×#1055C2211yescharacteristic
14C2×#88106—23no—
15C2×#88106C2216yescomplemented
16C22×#6092—21no—
17C22×#6092—23no—
18C22×#6092—21no—
19C22×#6092C2216yescomplemented
20#11718304C22116yesdirect product factor
21C2×C13×#41—23no—
22C2×C13×#41—23no—
23C2×C13×#41C816yes—
24C2×C13×#41C2×C416yes—
25C22×Q8×C13C811yescharacteristic
26C22×D4×C13—21no—
27C22×D4×C13C811yescharacteristic
28C23×C4×C13—21no—
29C23×C4×C13C2×C411yescharacteristic
30#88202—212no—
31#88202—26no—
32#88202—26no—
33#88202C2×C4112yes—
34#88202C2314yes—
35C2×#6099—23no—
36C2×#6099—26no—
37C2×#6099—26no—
38C2×#6099C2×C416yes—
39C22×#1055—21no—
40C22×#1055—26no—
41C22×#1055—26no—
42C22×#1055C2×C413yes—
43C22×#1055D411yescharacteristic
44C22×#1055D411yescharacteristic
45C22×#1055D413yes—
46C22×#1055D413yes—
47C22×#1055C2313yes—
48#88106—26no—
49#88106C2314yescomplemented
50C2×#6092—26no—
51C2×#6092—26no—
52C2×#6092—26no—
53C2×#6092C2314yescomplemented
54C22×#350—131nomaximal, Sylow
55C24×C13—21no—
56C24×C13M1611yescharacteristic
57C13×#41—212no—
58C13×#41—26no—
59C13×#41—26no—
60C13×#41C2×C8112yes—
61C13×#41C22×C414yes—
62C2×Q8×C13—23no—
63C2×Q8×C13C2×C816yes—
64C2×D4×C13—26no—
65C2×D4×C13—26no—
66C2×D4×C13—23no—
67C2×D4×C13C2×C816yes—
68C22×C4×C13—21no—
69C22×C4×C13—26no—
70C22×C4×C13—26no—
71C22×C4×C13C22⋊C413yes—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C2×C811yescharacteristic
74C22×C4×C13C2×C813yes—
75C22×C4×C13M1613yes—
76C22×C4×C13C22×C413yes—
77#6099—26no—
78#6099—212no—
79#6099—24no—
80#6099C22×C414yes—
81C2×#1055—26no—
82C2×#1055—212no—
83C2×#1055—24no—
84C2×#1055C22⋊C413yes—
85C2×#1055C22⋊C413yes—
86C2×#1055C22⋊C416yes—
87C2×#1055C22×C413yes—
88C2×#1055C2×D413yes—
89C2×#1055C2×D413yes—
90C2×#1055C2×D413yes—
91C2×#1055C2×D413yes—
92C2×#1055C2411yescharacteristic
93#6092—24no—
94#6092—24no—
95C22×#131—131no—
96C22×M32—131no—
97C23×C16—131no—
98C2×#350—1312no—
99C23×C13—24no—
100C23×C13—26no—
101C23×C13—44no—
102C23×C13C22⋊C813yes—
103C23×C13C22⋊C811yescharacteristic
104C23×C13C2×M1613yes—
105Q8×C13—26no—
106Q8×C13C22×C814yes—
107D4×C13—24no—
108D4×C13—212no—
109D4×C13—26no—
110D4×C13C22×C814yes—
111C2×C4×C13—26no—
112C2×C4×C13—24no—
113C2×C4×C13—212no—
114C2×C4×C13C22⋊C813yes—
115C2×C4×C13C22⋊C813yes—
116C2×C4×C13C22⋊C816yes—
117C2×C4×C13C2×C22⋊C413yes—
118C2×C4×C13C2×C22⋊C413yes—
119C2×C4×C13C22×C813yes—
120C2×C4×C13C22×C813yes—
121C2×C4×C13C2×M1613yes—
122C2×C4×C13C23×C411yescharacteristic
123#1055—24no—
124#1055C2×C22⋊C413yes—
125#1055C2×C22⋊C413yes—
126#1055C22×D411yescharacteristic
127#1055C22×D411yescharacteristic
128C22×#41#26111yescharacteristic
129C2×#131—136no—
130C2×#131—136no—
131C2×#131—263no—
132C2×#131—263no—
133C22×M16—131no—
134C22×M16—261no—
135C23×C8—131no—
136C23×C8—261no—
137C2×M32—136no—
138C2×M32—263no—
139C22×C16—136no—
140C22×C16—263no—
141C22×C16—261no—
142C22×C16—261no—
143#350—1316no—
144C22×C13—26no—
145C22×C13—26no—
146C22×C13—24no—
147C22×C13—412no—
148C22×C13#35014yescomplemented
149C22×C13C2×C22⋊C813yes—
150C22×C13C2×C22⋊C813yes—
151C22×C13C22×M1611yescharacteristic
152C4×C13—24no—
153C4×C13C2×C22⋊C813yes—
154C4×C13C2×C22⋊C813yes—
155C4×C13C22×C22⋊C411yescharacteristic
156C4×C13C23×C811yescharacteristic
157C2×#41—23no—
158C2×#41—23no—
159C2×#41#105716yes—
160C2×#41C2×#26116yes—
161C22×Q8#105711yescharacteristic
162C22×D4—21no—
163C22×D4#105711yescharacteristic
164C23×C4—21no—
165C23×C4C2×#26111yescharacteristic
166#131—134no—
167#131—1312no—
168#131—266no—
169#131—266no—
170#131—2612no—
171C2×M16—136no—
172C2×M16—266no—
173C2×M16—266no—
174C2×M16—263no—
175C22×C8—133no—
176C22×C8—133no—
177C22×C8—131no—
178C22×C8—131no—
179C22×C8—133no—
180C22×C8—133no—
181C22×C8—266no—
182C22×C8—266no—
183C22×C8—261no—
184M32—134no—
185M32—266no—
186C2×C16—134no—
187C2×C16—266no—
188C2×C16—266no—
189C2×C16—266no—
190C2×C13—21no—
191C2×C13—23no—
192C2×C13—44no—
193C2×C13C2×#35016yescomplemented
194C2×C13C22×C22⋊C811yescharacteristic
195C24—21no—
196C24#612211yescharacteristic
197#41—212no—
198#41—26no—
199#41—26no—
200#41C2×#1057112yes—
201#41C22×#26114yes—
202C2×Q8—23no—
203C2×Q8C2×#105716yes—
204C2×D4—26no—
205C2×D4—26no—
206C2×D4—23no—
207C2×D4C2×#105716yes—
208C22×C4—21no—
209C22×C4—26no—
210C22×C4—26no—
211C22×C4C2×#105711yescharacteristic
212C22×C4C2×#105713yes—
213C22×C4#612213yes—
214C22×C4C22⋊#26113yes—
215C22×C4C22⋊#26111yescharacteristic
216C22×C4C22×#26113yes—
217M16—134no—
218M16—264no—
219M16—2612no—
220M16—266no—
221C2×C8—133no—
222C2×C8—133no—
223C2×C8—133no—
224C2×C8—133no—
225C2×C8—133no—
226C2×C8—133no—
227C2×C8—136no—
228C2×C8—131no—
229C2×C8—133no—
230C2×C8—264no—
231C2×C8—2612no—
232C2×C8—266no—
233C16—264no—
234C16—264no—
235C13C22×#35011yescharacteristic, complemented, Sylow
236C23—24no—
237C23—26no—
238C23—44no—
239C23C22⋊#105713yes—
240C23C22⋊#105711yescharacteristic
241C23C2×#612213yes—
242Q8—26no—
243Q8C22×#105714yes—
244D4—212no—
245D4—24no—
246D4—26no—
247D4C22×#105714yes—
248C2×C4—26no—
249C2×C4—212no—
250C2×C4—24no—
251C2×C4C22⋊#105713yes—
252C2×C4C22⋊#105713yes—
253C2×C4C22⋊#105716yes—
254C2×C4C22×#105713yes—
255C2×C4C22×#105713yes—
256C2×C4C2×#612213yes—
257C2×C4C2×C22⋊#26113yes—
258C2×C4C2×C22⋊#26113yes—
259C2×C4C23×#26111yescharacteristic
260C8—131no—
261C8—131no—
262C8—133no—
263C8—133no—
264C8—264no—
265C22—26no—
266C22—26no—
267C22—24no—
268C22—412no—
269C22#1171830414yesdirect product factor
270C22C2×C22⋊#105713yes—
271C22C2×C22⋊#105713yes—
272C22C22×#612211yescharacteristic
273C4—24no—
274C4C2×C22⋊#105713yes—
275C4C2×C22⋊#105713yes—
276C4C23×#105711yescharacteristic
277C4C22×C22⋊#26111yescharacteristic
278C2—23no—
279C2—21no—
280C2—44no—
281C2C2×#1171830416yesdirect product factor
282C2C22×C22⋊#105711yescharacteristic
subgroupG/H
centerC22×C4C22⋊#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
Fitting, prime radicalC22×C13×#41C4
socleC23×C13C22⋊C8
cosocleC2×#1055C24
hypercenterC22×#41#261
hypocenterC13C22×#350
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#88106C2semidirect
2. C23×#6092C2semidirect
3. C2×#11718304C2direct (N × H)
15. C2×#88106C22semidirect
19. C22×#6092C22semidirect
20. #11718304C22direct (N × H)
49. #88106C23semidirect
53. C2×#6092C23semidirect
148. C22×C13#350semidirect
193. C2×C13C2×#350semidirect
235. C13C22×#350semidirect
269. C22#11718304direct (N × H)
281. C2C2×#11718304direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881062
C23×#60922
C2×#117183042
C22×#882022
C22×#35013