Finite Group Databasebeta

← #15781246

Subgroups — #15781246

Order 3328.

472 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 111 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×#11718140C214yesmaximal
2#13114832C211yesmaximal, characteristic
3C4×#88076C211yesmaximal, characteristic
4C13×#2546C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C13×C4⋊Q8C2212yes—
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#398—21no—
9C13×#398—21no—
10C13×#391C412yes—
11C13×#389—21no—
12C13×#389—21no—
13C4×C13×C4⋊C4C411yescharacteristic
14C2×#88076C2212yes—
15C2×#88076C2212yes—
16#11718585—21no—
17C4×#6099—21no—
18#11718140—28no—
19#11718122—21no—
20#11718122—21no—
21C22×Q8×C13C2×C412yes—
22C22×Q8×C13C2311yescharacteristic
23C13×C4⋊Q8—24no—
24C13×C4⋊Q8—24no—
25C13×C4⋊Q8—41no—
26C13×C4⋊Q8—41no—
27C4×Q8×C13—41no—
28C4×Q8×C13—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C42×C13C2×C412yes—
38C2×C42×C13C2×C411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×#6099—22no—
42C2×#6099—22no—
43C13×#95—21no—
44C13×#95—22no—
45C13×#95—22no—
46#88076—22no—
47#88076—24no—
48#88076D414yes—
49C4⋊#1055—41no—
50C4⋊#1055—41no—
51#88043—41no—
52C4×#1055—41no—
53#13227—131nomaximal, Sylow
54C2×Q8×C13—24no—
55C2×Q8×C13—41no—
56C2×Q8×C13—41no—
57C2×Q8×C13—42no—
58C2×Q8×C13—42no—
59C2×Q8×C13C2×D412yes—
60C2×Q8×C13#4112yes—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C13×C4⋊C4—24no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—44no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—24no—
87#6099—24no—
88#6099—42no—
89#6099—42no—
90#6099—42no—
91C2×#1055—42no—
92C2×#1055—42no—
93#2546D1311yescharacteristic
94C2×#356—134no—
95#1801—131no—
96C4×#101—131no—
97C23×C13C2×C22⋊C411yescharacteristic
98Q8×C13—42no—
99Q8×C13—42no—
100Q8×C13—84no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—24no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13#9911yescharacteristic
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13C4×D412yes—
123C2×C4×C13#12112yes—
124C2×C4×C13#12411yescharacteristic
125C2×C4×C13#12711yescharacteristic
126#1055—44no—
127#1055—82no—
128C2×C4⋊Q8Dic1311yescharacteristic
129C2×C4⋊Q8C2×D1312yes—
130C2×C4×Q8C2×D1311yescharacteristic
131#423—261no—
132C2×#101—132no—
133C2×#101—132no—
134C4×M16—261no—
135#398—21no—
136#398—21no—
137#391Dic1312yes—
138#389—21no—
139#389—21no—
140C4×C4⋊C4Dic1311yescharacteristic
141#356—268no—
142#343—261no—
143#343—261no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13#39011yescharacteristic
147C22×C13C2×#9911yescharacteristic
148C22×C13#41011yescharacteristic
149C4×C13—21no—
150C4×C13—22no—
151C4×C13—21no—
152C4×C13—22no—
153C4×C13—21no—
154C4×C13—44no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13—82no—
159C4×C13#35612yescomplemented
160C22×Q8C2×Dic1312yes—
161C22×Q8C22×D1311yescharacteristic
162C2×M16—262no—
163C2×M16—262no—
164C4⋊Q8—24no—
165C4⋊Q8—24no—
166C4⋊Q8—41no—
167C4⋊Q8—41no—
168C4×Q8—41no—
169C4×Q8—41no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4C2×Dic1311yescharacteristic
176C2×C4⋊C4C22⋊D1311yescharacteristic
177C2×C4⋊C4C22⋊D1311yescharacteristic
178C2×C42C2×Dic1312yes—
179C2×C42C2×Dic1311yescharacteristic
180C2×C42C22⋊D1311yescharacteristic
181C2×C42C22⋊D1311yescharacteristic
182C4⋊C8—521no—
183C4⋊C8—521no—
184#101—134no—
185#101—262no—
186#101—264no—
187#97—521no—
188C4×C8—521no—
189#95—21no—
190#95—22no—
191#95—22no—
192C2×C13—21no—
193C2×C13—21no—
194C2×C13#196411yescharacteristic
195C2×C13C2×#35611yescharacteristic
196C2×C13#213511yescharacteristic
197C2×Q8—24no—
198C2×Q8—41no—
199C2×Q8—41no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8D4×D1312yes—
203C2×Q8#612912yes—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4C22⋊Dic1311yescharacteristic
207C22×C4C22⋊Dic1311yescharacteristic
208C22×C4C22⋊Dic1311yescharacteristic
209C22×C4C22⋊Dic1311yescharacteristic
210C22×C4C22×Dic1311yescharacteristic
211C22×C4C2×C22⋊D1311yescharacteristic
212C22×C4C2×C22⋊D1311yescharacteristic
213M16—264no—
214M16—522no—
215M16—522no—
216M16—522no—
217C2×C8—522no—
218C2×C8—522no—
219C4⋊C4—24no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—44no—
228C4⋊C4—42no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—24no—
236C13#1322711yescharacteristic, complemented, Sylow
237C23C2×C22⋊Dic1311yescharacteristic
238Q8—42no—
239Q8—42no—
240Q8—84no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4#8807411yescharacteristic
261C2×C4#8807411yescharacteristic
262C2×C4D4×Dic1312yes—
263C2×C4#8819011yescharacteristic
264C2×C4#8819212yes—
265C2×C4#8819411yescharacteristic
266C8—524no—
267C8—1042no—
268C22—21no—
269C22—21no—
270C22C2×#8807411yescharacteristic
271C22#1171888211yescharacteristic
272C22#1171890111yescharacteristic
273C4—22no—
274C4—21no—
275C4—22no—
276C4—21no—
277C4—21no—
278C4—44no—
279C4—41no—
280C4—41no—
281C4—41no—
282C4—82no—
283C4#1171814012yescomplemented
284C2—21no—
285C2—21no—
286C2#1311567311yescharacteristic
287C2C2×#1171814011yescharacteristic
288C2#1311653111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#2546C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenter#2546D13
hypocenterC13#13227
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
159. C4×C13#356semidirect
236. C13#13227semidirect
283. C4#11718140semidirect

Maximal subgroups

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

subgroupindex
C2×#117181402
#131148322
C4×#880762
C13×#25462
#1322713