Finite Group Databasebeta

← #16791297

Subgroups — #16791297

Order 3328.

388 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 60 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×#11718225C212yesmaximal
2#13129976C212yesmaximal, complemented
3#13129975C212yesmaximal, complemented
4#13125212C211yesmaximal, characteristic
5C13×#533C411yescharacteristic, complemented
6C2×#88128C2211yescharacteristic
7C2×#88107—22no—
8#11718749—22no—
9#11718728C411yescharacteristic, complemented
10#11718728C411yescharacteristic, complemented
11#11718728C2211yescharacteristic
12#11718728C2211yescharacteristic
13#11718662—22no—
14C4×#6099C411yescharacteristic, complemented
15#11718225—22no—
16#11718225C2214yes—
17C22×D52—41no—
18C22×D52D412yes—
19C2×C22⋊#261—42no—
20C13×C4⋊Q8—21no—
21C13×#125C2×C411yescharacteristic, complemented
22C13×#125C2×C411yescharacteristic, complemented
23C13×C22⋊Q8—41no—
24C4×Q8×C13—41no—
25C13×#117—21no—
26C2×C42×C13C2×C411yescharacteristic
27C2×#6099—21no—
28#88128—41no—
29#88128C2×C411yescharacteristic
30#88128D412yes—
31#88128C2311yescharacteristic
32#88107—24no—
33#88107—42no—
34#88049—22no—
35#88049—22no—
36#88049—22no—
37#88049—22no—
38#88043C2×C411yescharacteristic, complemented
39#88043C2×C411yescharacteristic, complemented
40C4×#1055—21no—
41#13595—131nomaximal, Sylow
42C23×D13—22no—
43C22×#261—82no—
44C2×Q8×C13—41no—
45C22×C4×C13—21no—
46C22×C4×C13C22⋊C411yescharacteristic
47C2×D52—22no—
48C2×D52—42no—
49C2×D52—42no—
50C2×D52—41no—
51C2×D52—42no—
52C2×D52—41no—
53C2×D52—84no—
54C2×D52C22⋊C412yes—
55C2×D52C2×D412yes—
56C22⋊#261—44no—
57C22⋊#261—82no—
58C13×C4⋊C4—21no—
59C13×C4⋊C4—21no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—41no—
63C13×C22⋊C4—41no—
64C42×C13—21no—
65C42×C13—41no—
66C42×C13C22⋊C411yescharacteristic
67C42×C13C22×C411yescharacteristic
68#6099—42no—
69C2×#1055—21no—
70C2×#1055—21no—
71#3138—131no—
72C2×#353—132no—
73#1412—132no—
74#1412—132no—
75C23×C13#9911yescharacteristic
76C22×D13—22no—
77C22×D13—22no—
78C22×D13—42no—
79C22×D13—42no—
80C22×D13—84no—
81C2×#261—84no—
82C2×#261—164no—
83Q8×C13—82no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—42no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13#9911yescharacteristic
91C2×C4×C13C2×C22⋊C411yescharacteristic
92D52—42no—
93D52—42no—
94D52—82no—
95D52—84no—
96D52—82no—
97D52—82no—
98#1055—41no—
99#1055—41no—
100#533#26111yescharacteristic, complemented
101C2×#127—131no—
102#490—131no—
103#490—131no—
104#490—131no—
105#490—131no—
106#486—262no—
107#418—262no—
108C2×#99—262no—
109C4×M16—131no—
110#353—134no—
111#353—262no—
112C22×C13—41no—
113C22×C13#35412yes—
114C22×C13C2×#9911yescharacteristic
115C2×D13—42no—
116C2×D13—42no—
117C2×D13—84no—
118C2×D13—82no—
119C2×D13—82no—
120C2×D13—162no—
121#261—164no—
122C4×C13—22no—
123C4×C13—21no—
124C4×C13—21no—
125C4×C13—41no—
126C4×C13—81no—
127C4×C13—81no—
128C22×D4—132no—
129C22×D4—521no—
130C2×M16—261no—
131C4⋊Q8—21no—
132#127—132no—
133#127—131no—
134#127—131no—
135#127—521no—
136#125C2×#26111yescharacteristic, complemented
137#125C2×#26111yescharacteristic, complemented
138C22⋊Q8—41no—
139C4×Q8—41no—
140#117—21no—
141C2×C22⋊C4—522no—
142C2×C42C2×#26111yescharacteristic
143#102—262no—
144#102—262no—
145#102—262no—
146#102—262no—
147#99—264no—
148#99—522no—
149#97—131no—
150#97—131no—
151C4×C8—261no—
152C2×C13—21no—
153C2×C13—22no—
154C2×C13C2×#35411yescharacteristic
155D13—82no—
156D13—82no—
157C24—262no—
158C2×Q8—41no—
159C2×D4—132no—
160C2×D4—132no—
161C2×D4—262no—
162C2×D4—522no—
163C2×D4—522no—
164C2×D4—522no—
165C2×D4—521no—
166C2×D4—521no—
167C2×D4—1044no—
168C22×C4—21no—
169C22×C4—1042no—
170C22×C4C22⋊#26111yescharacteristic
171M16—522no—
172C2×C8—261no—
173C2×C8—261no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C22⋊C4—41no—
180C22⋊C4—524no—
181C22⋊C4—1042no—
182C42—21no—
183C42—41no—
184C42C22⋊#26111yescharacteristic
185C42C22×#26111yescharacteristic
186C13#1359511yescharacteristic, complemented, Sylow
187C23—262no—
188C23—262no—
189C23—522no—
190C23—522no—
191C23—1044no—
192C23#8811911yescharacteristic
193Q8—82no—
194D4—522no—
195D4—522no—
196D4—1042no—
197D4—1044no—
198D4—1042no—
199D4—1042no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—1044no—
207C2×C4—2084no—
208C2×C4#8811911yescharacteristic
209C2×C4C2×C22⋊#26111yescharacteristic
210C8—521no—
211C8—521no—
212C22—41no—
213C22—522no—
214C22—522no—
215C22—1042no—
216C22—1042no—
217C22—1044no—
218C22—2082no—
219C22#1171830012yes—
220C22C2×#8811911yescharacteristic
221C4—22no—
222C4—21no—
223C4—21no—
224C4—41no—
225C4—81no—
226C4—81no—
227C4—2084no—
228C2—21no—
229C2—22no—
230C2—1042no—
231C2—1042no—
232C2C2×#1171830011yescharacteristic
subgroupG/H
centerC2C2×#11718300
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#533C4
socleC2×C13C2×#354
prime radicalC2×#88128C22
cosocle#88128C23
hypercenter#533#261
hypocenterC13#13595
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #13129976C2semidirect
3. #13129975C2semidirect
5. C13×#533C4semidirect
9. #11718728C4semidirect
10. #11718728C4semidirect
14. C4×#6099C4semidirect
21. C13×#125C2×C4semidirect
22. C13×#125C2×C4semidirect
38. #88043C2×C4semidirect
39. #88043C2×C4semidirect
100. #533#261semidirect
136. #125C2×#261semidirect
137. #125C2×#261semidirect
186. C13#13595semidirect

Maximal subgroups

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

subgroupindex
C2×#117182252
#131299762
#131299752
#131252122
#1359513