Finite Group Databasebeta

← C4×Q8×#1057 #16797448

Subgroups — C4×Q8×#1057 #16797448

Order 3328.

1070 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×#1057C212yesmaximal
2C4⋊C4×#1057C216yesmaximal
3C4×C4⋊#1057C213yesmaximal
4C42×#1057C213yesmaximal
5C4×Q8×Dic13C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×Q8×Dic13C411yescharacteristic
8C2×Q8×Dic13C2211yescharacteristic
9Q8×#1057C4116yesdirect product factor
10C2×C4⋊#1057C2216yes—
11C2×C4×#1057C2213yes—
12C2×C4×#1057C2216yes—
13C2×C4×#1057C2216yes—
14C2×C4×#1057C2211yescharacteristic
15C4⋊C4×Dic13C413yes—
16C4⋊C4×Dic13C2213yes—
17C4×C4⋊Dic13C413yes—
18C42×Dic13C2213yes—
19#11718290C2216yes—
20C22×Q8×C13C2×C411yescharacteristic
21C22×#1057C2316yes—
22C22×#1057C2312yes—
23C4×Q8×C13C818yescomplemented
24C2×C13×C4⋊C4C2×C413yes—
25C2×C42×C13C2×C413yes—
26Q8×Dic13C818yescomplemented
27Q8×Dic13C2×C418yes—
28C2×C4⋊Dic13C2×C413yes—
29C2×C4⋊Dic13C2×C413yes—
30C2×C4×Dic13C2×C413yes—
31C2×C4×Dic13C2×C413yes—
32C2×C4×Dic13C2×C413yes—
33C2×C4×Dic13C2313yes—
34C2×C4×Dic13C2313yes—
35C2×C4×Dic13C2311yescharacteristic
36C4⋊#1057C2×C4124yes—
37C4×#1057—212no—
38C4×#1057—26no—
39C4×#1057C2×C4124yes—
40C4×#1057Q814yesdirect product factor
41#88071C2×C416yes—
42C4×C8×Q8—131nomaximal, Sylow
43C2×Q8×C13C4214yes—
44C2×Q8×C13C2×C814yes—
45C2×Q8×C13C2×C814yes—
46C22×C4×C13C22×C413yes—
47C22×C4×C13C22×C413yes—
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13C22×C413yes—
50C22×Dic13C22×C413yes—
51C22×Dic13C22×C411yescharacteristic
52C22×Dic13C2411yescharacteristic
53C2×#1057—26no—
54C2×#1057—26no—
55C2×#1057C22×C4112yes—
56C2×#1057C22×C414yes—
57C2×#1057C2×Q814yes—
58C2×#1057#4114yes—
59C13×C4⋊C4C2×C8112yes—
60C42×C13C2×C8112yes—
61C4⋊Dic13C42112yes—
62C4⋊Dic13C2×C8112yes—
63C4×Dic13—26no—
64C4×Dic13—26no—
65C4×Dic13—26no—
66C4×Dic13C2×C8112yes—
67C4×Dic13C22×C4112yes—
68C4×Dic13C2×Q812yes—
69C4×Dic13#4112yes—
70C2×C8×Q8—132no—
71C42×Q8—131no—
72C8×C4⋊C4—136no—
73C4×C4⋊C8—133no—
74C42×C8—133no—
75C23×C13C23×C411yescharacteristic
76Q8×C13C4×C8116yescomplemented
77C2×C4×C13—23no—
78C2×C4×C13—23no—
79C2×C4×C13C2×C4216yes—
80C2×C4×C13C4×Q812yes—
81C2×C4×C13C22×C816yes—
82C2×C4×C13C22×C816yes—
83C2×C4×C13C22×C816yes—
84C2×C4×C13C22×C812yes—
85C2×C4×C13#13112yes—
86C2×Dic13—23no—
87C2×Dic13—23no—
88C2×Dic13—23no—
89C2×Dic13—23no—
90C2×Dic13C2×C4216yes—
91C2×Dic13C4×Q812yes—
92C2×Dic13C22×C816yes—
93C2×Dic13C22×C812yes—
94C2×Dic13#13112yes—
95C2×Dic13C23×C412yes—
96C2×Dic13C22×Q811yescharacteristic
97C2×Dic13C2×#4112yes—
98C2×Dic13C2×#4111yescharacteristic
99#1057—212no—
100#1057C4×Q818yesdirect product factor
101C2×C4×Q8—131no—
102C2×C4×Q8—131no—
103C2×C4×Q8#26111yescharacteristic
104C8×Q8—1316no—
105C2×C4⋊C8—136no—
106C2×C4×C8—136no—
107C2×C4×C8—131no—
108C2×C4×C8—133no—
109C2×C4×C8—136no—
110C4×C4⋊C4—133no—
111C4×C4⋊C4—133no—
112C4×C4⋊C4—133no—
113C43—133no—
114#336—136no—
115C22×C13C22×C4211yescharacteristic
116C22×C13C2×C4×Q811yescharacteristic
117C22×C13C4×#4111yescharacteristic
118C22×C13C23×C811yescharacteristic
119C22×C13C23×C811yescharacteristic
120C22×C13C2×#13111yescharacteristic
121C22×C13C2×#13111yescharacteristic
122C4×C13—26no—
123C4×C13C2×C4×C8112yes—
124C4×C13C8×Q814yescomplemented
125Dic13—26no—
126Dic13—26no—
127Dic13C8×Q814yescomplemented
128Dic13C2×C4×Q812yes—
129Dic13C4×#4112yes—
130C22×Q8C2×#26111yescharacteristic
131C22×C8—132no—
132C22×C8—136no—
133C4×Q8—138no—
134C4×Q8—138no—
135C4×Q8#105718yesdirect product factor
136C2×C4⋊C4—133no—
137C2×C4⋊C4—133no—
138C2×C4⋊C4C2×#26113yes—
139C2×C42—133no—
140C2×C42—133no—
141C2×C42—131no—
142C2×C42—133no—
143C2×C42—133no—
144C2×C42—133no—
145C2×C42C2×#26113yes—
146C4⋊C8—1324no—
147C4×C8—1324no—
148C4×C8—134no—
149C4×C8—266no—
150C4×C8—2612no—
151#95—136no—
152C2×C13C42×Q811yescharacteristic
153C2×C13C22×C4×C811yescharacteristic
154C2×C13C4×#13111yescharacteristic
155C2×C13C2×C8×Q811yescharacteristic
156C2×C13C2×C8×Q811yescharacteristic
157C2×C13C8×#4111yescharacteristic
158C2×C13C8×#4111yescharacteristic
159C2×Q8D13⋊C814yes—
160C2×Q8C4×#26114yes—
161C2×Q8C2×#105714yes—
162C22×C4—131no—
163C22×C4—131no—
164C22×C4—133no—
165C22×C4—133no—
166C22×C4C22×#26113yes—
167C22×C4C22×#26113yes—
168C22×C4C22×#26111yescharacteristic
169C2×C8—134no—
170C2×C8—134no—
171C2×C8—134no—
172C2×C8—1312no—
173C2×C8—266no—
174C2×C8—266no—
175C4⋊C4—1312no—
176C4⋊C4—1312no—
177C4⋊C4C2×#1057112yes—
178C42—1312no—
179C42—1312no—
180C42—132no—
181C42—132no—
182C42—266no—
183C42—266no—
184C42—266no—
185C42C2×#1057112yes—
186C13C4×C8×Q811yescharacteristic, complemented, Sylow
187C23C23×#26111yescharacteristic
188Q8C4×#1057116yesdirect product factor
189C2×C4—23no—
190C2×C4—23no—
191C2×C4—132no—
192C2×C4—132no—
193C2×C4—131no—
194C2×C4—131no—
195C2×C4—132no—
196C2×C4—132no—
197C2×C4—132no—
198C2×C4—136no—
199C2×C4—136no—
200C2×C4—263no—
201C2×C4—263no—
202C2×C4—263no—
203C2×C4—263no—
204C2×C4C2×D13⋊C816yes—
205C2×C4C2×C4×#26116yes—
206C2×C4#8824012yes—
207C2×C4Q8×#26112yes—
208C2×C4C22×#105716yes—
209C2×C4C22×#105716yes—
210C2×C4C22×#105712yes—
211C8—138no—
212C8—2612no—
213C22C22×D13⋊C811yescharacteristic
214C22C22×C4×#26111yescharacteristic
215C22C2×#8824011yescharacteristic
216C22C2×Q8×#26111yescharacteristic
217C22D13⋊#13111yescharacteristic
218C22#41×#26111yescharacteristic
219C22C23×#105711yescharacteristic
220C4—26no—
221C4—132no—
222C4—132no—
223C4—134no—
224C4—266no—
225C4—266no—
226C4C2×C4×#1057112yes—
227C4Q8×#105714yesdirect product factor
228C2C4×Q8×#26111yescharacteristic
229C2C22×C4×#105711yescharacteristic
230C2C4×#8824011yescharacteristic
231C2C2×Q8×#105711yescharacteristic
232C2Q8×D13⋊C811yescharacteristic
233C2#41×#105711yescharacteristic
234C2#1313164211yescharacteristic
subgroupG/H
centerC22×C4C22×#261
commutatorC2×C13C22×C4×C8
FrattiniC23C23×#261
FittingC2×C4×Q8×C13C4
socle, prime radicalC23×C13C23×C4
cosocleC22×Dic13C24
hypercenterC2×C4×Q8#261
hypocenterC13C4×C8×Q8
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
9. Q8×#1057C4direct (N × H)
23. C4×Q8×C13C8semidirect
26. Q8×Dic13C8semidirect
40. C4×#1057Q8direct (N × H)
76. Q8×C13C4×C8semidirect
100. #1057C4×Q8direct (N × H)
124. C4×C13C8×Q8semidirect
127. Dic13C8×Q8semidirect
135. C4×Q8#1057direct (N × H)
186. C13C4×C8×Q8semidirect
188. Q8C4×#1057direct (N × H)
227. C4Q8×#1057direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×#10572
C4⋊C4×#10572
C4×C4⋊#10572
C42×#10572
C4×Q8×Dic132
C4×C8×Q813