Finite Group Databasebeta

← C4×#11718140 #15778101

Subgroups — C4×#11718140 #15778101

Order 3328.

500 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 139 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×#11718140C212yesmaximal
2C4×#88076C212yesmaximal
3#13112963C212yesmaximal
4C4×C13×C4⋊Q8C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C2211yescharacteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#391C411yescharacteristic
9C13×#391C2211yescharacteristic
10C13×#389—22no—
11C13×#384C411yescharacteristic
12C4×C13×C4⋊C4—22no—
13C43×C13C411yescharacteristic
14C2×#88076C2214yes—
15C4×#6099—22no—
16#11718140C418yesdirect product factor
17#11718122—22no—
18C22×Q8×C13C2×C411yescharacteristic
19C22×Q8×C13C2311yescharacteristic
20C13×C4⋊Q8—22no—
21C13×C4⋊Q8C2×C414yes—
22C4×Q8×C13—41no—
23C4×Q8×C13—41no—
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4D412yes—
32C2×C42×C13—21no—
33C2×C42×C13—21no—
34C2×C42×C13—21no—
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13D412yes—
39C2×#6099—24no—
40C13×#95—22no—
41C13×#95—22no—
42#88076—24no—
43#88076C2×C418yes—
44#88043—42no—
45C4×#1055—42no—
46C4×#356—131nomaximal, Sylow
47C2×Q8×C13—21no—
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C2×Q8×C13—41no—
51C2×Q8×C13—41no—
52C2×Q8×C13C4212yes—
53C2×Q8×C13C22×C412yes—
54C2×Q8×C13#4112yes—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D412yes—
64C13×C4⋊C4—28no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—44no—
69C13×C4⋊C4—42no—
70C42×C13—24no—
71C42×C13—21no—
72C42×C13—21no—
73C42×C13—22no—
74C42×C13—22no—
75C42×C13—21no—
76C42×C13—41no—
77C42×C13—42no—
78C42×C13—41no—
79C42×C13—41no—
80C42×C13C4212yes—
81#6099—28no—
82#6099—44no—
83C2×#1055—44no—
84C4×C4⋊Q8D1311yescharacteristic
85C2×#356—132no—
86C4×#101—132no—
87#1394—132no—
88C23×C13C2×C22⋊C411yescharacteristic
89Q8×C13—42no—
90Q8×C13—42no—
91Q8×C13—42no—
92Q8×C13—42no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—41no—
113C2×C4×C13#9911yescharacteristic
114C2×C4×C13#9911yescharacteristic
115C2×C4×C13C2×C4211yescharacteristic
116C2×C4×C13#11711yescharacteristic
117C2×C4×C13C4×D414yes—
118#1055—48no—
119C2×C4⋊Q8C2×D1311yescharacteristic
120C2×C4×Q8Dic1311yescharacteristic
121C2×C4×Q8C2×D1311yescharacteristic
122C2×#101—134no—
123C4×M16—262no—
124#391Dic1311yescharacteristic
125#391C2×D1311yescharacteristic
126#389—22no—
127#384Dic1311yescharacteristic
128C4×C4⋊C4—22no—
129C43Dic1311yescharacteristic
130#356—138no—
131#343—262no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13C4×C22⋊C411yescharacteristic
135C22×C13C2×#9911yescharacteristic
136C22×C13#41011yescharacteristic
137C4×C13—24no—
138C4×C13—21no—
139C4×C13—24no—
140C4×C13—21no—
141C4×C13—21no—
142C4×C13—42no—
143C4×C13—41no—
144C4×C13—42no—
145C4×C13—42no—
146C4×C13—81no—
147C4×C13#35612yescomplemented
148C22×Q8C2×Dic1311yescharacteristic
149C22×Q8C22×D1311yescharacteristic
150C2×M16—264no—
151C4⋊Q8—22no—
152C4⋊Q8C4×D1314yes—
153C4×Q8—41no—
154C4×Q8—41no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4C2×Dic1311yescharacteristic
161C2×C4⋊C4C2×Dic1311yescharacteristic
162C2×C4⋊C4C22⋊D1312yes—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42—21no—
166C2×C42C2×Dic1311yescharacteristic
167C2×C42C2×Dic1311yescharacteristic
168C2×C42C2×Dic1311yescharacteristic
169C2×C42C22⋊D1312yes—
170#101—138no—
171#101—264no—
172#97—522no—
173C4×C8—522no—
174#95—22no—
175#95—22no—
176C2×C13—21no—
177C2×C13—21no—
178C2×C13C4×#9911yescharacteristic
179C2×C13C2×#35611yescharacteristic
180C2×C13#213211yescharacteristic
181C2×Q8—21no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8C4×Dic1312yes—
187C2×Q8C2×C4×D1312yes—
188C2×Q8#612712yes—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4C22⋊Dic1312yes—
194C22×C4C22⋊Dic1311yescharacteristic
195C22×C4C22⋊Dic1311yescharacteristic
196C22×C4C22×Dic1311yescharacteristic
197C22×C4C2×C22⋊D1312yes—
198M16—268no—
199M16—524no—
200C2×C8—524no—
201C4⋊C4—28no—
202C4⋊C4—41no—
203C4⋊C4—42no—
204C4⋊C4—41no—
205C4⋊C4—42no—
206C4⋊C4—44no—
207C42—24no—
208C42—22no—
209C42—21no—
210C42—22no—
211C42—21no—
212C42—21no—
213C42—41no—
214C42—42no—
215C42—41no—
216C42—41no—
217C42C4×Dic1312yes—
218C13C4×#35611yescharacteristic, complemented, Sylow
219C23C2×C22⋊Dic1311yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—42no—
223Q8—42no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4#8807411yescharacteristic
245C2×C4#8807411yescharacteristic
246C2×C4C2×C4×Dic1311yescharacteristic
247C2×C4#8818011yescharacteristic
248C2×C4C4×C22⋊D1314yes—
249C8—528no—
250C22—21no—
251C22—21no—
252C22C4×C22⋊Dic1311yescharacteristic
253C22C2×#8807411yescharacteristic
254C22#1171890111yescharacteristic
255C4—24no—
256C4—24no—
257C4—21no—
258C4—21no—
259C4—21no—
260C4—42no—
261C4—42no—
262C4—41no—
263C4—42no—
264C4—81no—
265C4#1171814012yesdirect product factor
266C2—21no—
267C2—21no—
268C2C4×#8807411yescharacteristic
269C2C2×#1171814011yescharacteristic
270C2#1311652111yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC2×C4×C13C2×C42
FrattiniC22×Q8C22×D13
FittingC4×C13×C4⋊Q8C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenterC4×C4⋊Q8D13
hypocenterC13C4×#356
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
16. #11718140C4direct (N × H)
147. C4×C13#356semidirect
218. C13C4×#356semidirect
265. C4#11718140direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117181402
C4×#880762
#131129632
C4×C13×C4⋊Q82
C4×#35613