Finite Group Databasebeta

← #15778928

Subgroups — #15778928

Order 3328.

432 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 101 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
1#13117556C211yesmaximal, characteristic
2C2×#11718140C211yesmaximal, characteristic
3#13114830C212yesmaximal
4#13112962C212yesmaximal
5C2×C13×#356C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×Q8×Dic13C411yescharacteristic
8C2×Q8×Dic13C2211yescharacteristic
9C2×C13×#101C2212yes—
10#11718891C411yescharacteristic
11#11718891C2211yescharacteristic
12C2×#88076C2212yes—
13#11718779—22no—
14#11718642—22no—
15#11718642—22no—
16#11718597C411yescharacteristic
17#11718593C411yescharacteristic
18C13×#356—22no—
19#11718146—22no—
20#11718140—22no—
21C22×Q8×C13C2×C411yescharacteristic
22C22×Q8×C13C2311yescharacteristic
23C2×C13×M16—22no—
24C13×C4⋊Q8—22no—
25C13×C4⋊Q8D412yes—
26C13×C4⋊Q8Q812yes—
27C2×C13×C4⋊C4—22no—
28C2×C42×C13C2×C411yescharacteristic
29Q8×Dic13—42no—
30Q8×Dic13—42no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13D412yes—
35C2×C4×Dic13—21no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13D412yes—
39C2×#6099—22no—
40C13×#101—22no—
41C13×#101—22no—
42#88076—22no—
43#88076—22no—
44#88071—22no—
45#88071—21no—
46#88071—21no—
47#88071—22no—
48#88071—22no—
49#88054—44no—
50#12804—131nomaximal, Sylow
51C2×Q8×C13—21no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C2×Q8×C13—41no—
55C2×Q8×C13—41no—
56C2×Q8×C13C4⋊C412yes—
57C2×Q8×C13C2×D411yescharacteristic
58C2×Q8×C13C2×Q811yescharacteristic
59C2×Q8×C13#4112yes—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D412yes—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13C22⋊C412yes—
67C22×Dic13C22⋊C411yescharacteristic
68C22×Dic13C22⋊C411yescharacteristic
69C13×M16—42no—
70C13×M16—42no—
71C2×C8×C13—42no—
72C13×C4⋊C4—24no—
73C13×C4⋊C4—24no—
74C42×C13—21no—
75C42×C13C4⋊C412yes—
76C4⋊Dic13—41no—
77C4⋊Dic13—42no—
78C4⋊Dic13—42no—
79C4⋊Dic13—41no—
80C4×Dic13—22no—
81C4×Dic13—24no—
82C4×Dic13—42no—
83C4×Dic13—41no—
84#6099—42no—
85#6099—42no—
86C2×#1055—42no—
87#2327—131no—
88C2×#356—131no—
89C2×#356D1311yescharacteristic
90#1801—132no—
91#1394—132no—
92C23×C13C2×C22⋊C411yescharacteristic
93Q8×C13—41no—
94Q8×C13—41no—
95Q8×C13—42no—
96Q8×C13—42no—
97Q8×C13—42no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13C2×C4⋊C411yescharacteristic
109C2×C4×C13#11711yescharacteristic
110C2×C4×C13#12112yes—
111C2×C4×C13C22⋊Q812yes—
112C2×Dic13—21no—
113C2×Dic13—22no—
114C2×Dic13—41no—
115C2×Dic13—42no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—42no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13#9912yes—
123C8×C13—82no—
124#1055—82no—
125C2×C4⋊Q8C2×D1311yescharacteristic
126C2×C4×Q8—131no—
127C2×C4×Q8—131no—
128#423—262no—
129C2×#101—132no—
130C2×#101C2×D1312yes—
131#391—131no—
132#391—131no—
133#387—262no—
134#387—262no—
135#382—131no—
136#376—131no—
137#356—22no—
138#356—262no—
139#343—262no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13#38011yescharacteristic
143C22×C13C2×#9911yescharacteristic
144C22×C13#41011yescharacteristic
145C4×C13—22no—
146C4×C13—21no—
147C4×C13—21no—
148C4×C13—22no—
149C4×C13—42no—
150C4×C13—42no—
151Dic13—22no—
152Dic13—41no—
153Dic13—42no—
154Dic13—81no—
155Dic13—81no—
156C22×Q8C4×D1311yescharacteristic
157C22×Q8C22×D1311yescharacteristic
158C2×M16—22no—
159C2×M16—262no—
160C4⋊Q8—22no—
161C4⋊Q8Dic2612yes—
162C4⋊Q8C22⋊D1312yes—
163C4×Q8—522no—
164C4×Q8—522no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—131no—
167C2×C4⋊C4—132no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—261no—
170C2×C42—131no—
171C2×C42—132no—
172C2×C42—131no—
173C2×C42—261no—
174C2×C42C4×D1311yescharacteristic
175C4⋊C8—524no—
176#101—22no—
177#101—22no—
178#101—262no—
179#101—262no—
180#95—261no—
181#95—261no—
182#95—262no—
183#95—262no—
184#95—262no—
185C2×C13—21no—
186C2×C13—21no—
187C2×C13#179911yescharacteristic
188C2×C13#213311yescharacteristic
189C2×C13#213511yescharacteristic
190C2×Q8—21no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8#610112yes—
196C2×Q8C2×Dic2611yescharacteristic
197C2×Q8#612912yes—
198C2×Q8C2×C22⋊D1311yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—131no—
202C22×C4—132no—
203C22×C4—131no—
204C22×C4—261no—
205C22×C4—261no—
206C22×C4C2×C4×D1311yescharacteristic
207C22×C4D4×D1312yes—
208M16—42no—
209M16—42no—
210M16—522no—
211M16—522no—
212C2×C8—42no—
213C2×C8—522no—
214C4⋊C4—24no—
215C4⋊C4—24no—
216C4⋊C4—521no—
217C4⋊C4—522no—
218C4⋊C4—521no—
219C4⋊C4—522no—
220C42—21no—
221C42—264no—
222C42—262no—
223C42—521no—
224C42—522no—
225C42#610112yes—
226C13#1280411yescharacteristic, complemented, Sylow
227C23C22⋊C4×D1311yescharacteristic
228Q8—41no—
229Q8—42no—
230Q8—41no—
231Q8—42no—
232Q8—42no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—132no—
244C2×C4—261no—
245C2×C4—262no—
246C2×C4—521no—
247C2×C4—522no—
248C2×C4—521no—
249C2×C4—521no—
250C2×C4—521no—
251C2×C4—522no—
252C2×C4—521no—
253C2×C4—521no—
254C2×C4#8813111yescharacteristic
255C2×C4#8813212yes—
256C2×C4C2×#610111yescharacteristic
257C2×C4#8819312yes—
258C8—82no—
259C8—1042no—
260C22—21no—
261C22—21no—
262C22#1171840111yescharacteristic
263C22D13×#9911yescharacteristic
264C22#1171860311yescharacteristic
265C4—22no—
266C4—21no—
267C4—22no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—262no—
272C4—521no—
273C4—522no—
274C4—1041no—
275C4—1041no—
276C2—21no—
277C2—21no—
278C2#1311482211yescharacteristic
279C2#1311652411yescharacteristic
280C2#1311652911yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC2×C13×#356C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenterC2×#356D13
hypocenterC13#12804
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
226. C13#12804semidirect

Maximal subgroups

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

subgroupindex
#131175562
C2×#117181402
#131148302
#131129622
C2×C13×#3562
#1280413