Finite Group Databasebeta

← #15772398

Subgroups — #15772398

Order 3328.

412 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 77 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#13117403C211yesmaximal, characteristic
2#13113178C212yesmaximal
3#13112782C211yesmaximal, characteristic
4#13112769C212yesmaximal
5C13×#1325C211yesmaximal, characteristic
6C2×#88141C411yescharacteristic
7C2×#88141C2211yescharacteristic
8C2×#88123C411yescharacteristic
9C13×#384C2211yescharacteristic
10C4⋊C4×Dic13—22no—
11#11718635C411yescharacteristic
12#11718635C2211yescharacteristic
13#11718634—22no—
14C42×Dic13C411yescharacteristic
15#11718380—22no—
16C13×#324C2212yes—
17#11718120C2212yes—
18#11718061—22no—
19C22×Dic26C2×C411yescharacteristic
20C22×Dic26C2×C411yescharacteristic
21C2×C13×C4⋊C4—22no—
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C13×C4⋊C4C2311yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C2×C4⋊Dic13—22no—
26C2×#6101—21no—
27C2×#6101D412yes—
28C2×C4×Dic13—21no—
29C2×C4×Dic13—21no—
30C2×C4×Dic13—21no—
31C2×C4×Dic13C2×C411yescharacteristic
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13D412yes—
34#88141—41no—
35#88141—41no—
36#88141—41no—
37#88141—41no—
38#88123—22no—
39#88123—22no—
40C13×C22⋊C8—22no—
41#88071—22no—
42#88071—22no—
43C22⋊#1055—22no—
44#88055—42no—
45#88054—42no—
46#11532—131nomaximal, Sylow
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13C22×C411yescharacteristic
50C22×C4×C13C2×D412yes—
51C22×Dic13—21no—
52C22×Dic13—21no—
53C22×Dic13C22⋊C412yes—
54C22×Dic13C22⋊C411yescharacteristic
55C22×Dic13C22⋊C411yescharacteristic
56C2×Dic26—21no—
57C2×Dic26—21no—
58C2×Dic26—21no—
59C2×Dic26—41no—
60C2×Dic26—41no—
61C2×Dic26—41no—
62C2×Dic26—41no—
63C2×Dic26M1612yes—
64C2×C8×C13—42no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—44no—
68C42×C13—21no—
69C42×C13M1612yes—
70C4⋊Dic13—28no—
71#6101—42no—
72#6101—42no—
73C4×Dic13—24no—
74C4×Dic13—21no—
75C4×Dic13—21no—
76C4×Dic13—22no—
77C4×Dic13—22no—
78C4×Dic13—42no—
79C4×Dic13—41no—
80C4×Dic13—41no—
81C4×Dic13—41no—
82C2×#1055—42no—
83C4×C4⋊Q8—131no—
84#1467—132no—
85#1325—131no—
86#1325D1311yescharacteristic
87#1319—132no—
88C23×C13C2×C22⋊C411yescharacteristic
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—41no—
98C2×C4×C13C2×M1611yescharacteristic
99C2×C4×C13C2×M1611yescharacteristic
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—21no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—41no—
108C2×Dic13—41no—
109C2×Dic13—41no—
110C2×Dic13—41no—
111C2×Dic13—41no—
112C2×Dic13#9911yescharacteristic
113C2×Dic13#9911yescharacteristic
114Dic26—42no—
115Dic26—42no—
116Dic26—42no—
117Dic26—42no—
118C8×C13—82no—
119#1055—82no—
120C2×C4⋊Q8—131no—
121C2×C4×Q8—131no—
122C2×C4×Q8—131no—
123#432—262no—
124#391—131no—
125#391—131no—
126#389—262no—
127#384C2×D1311yescharacteristic
128C4×C4⋊C4—262no—
129C43—131no—
130#324—132no—
131#324—262no—
132#324C2×D1312yes—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13#40711yescharacteristic
136C22×C13C2×#9911yescharacteristic
137C22×C13#41311yescharacteristic
138C4×C13—24no—
139C4×C13—21no—
140C4×C13—21no—
141C4×C13—42no—
142C4×C13—81no—
143Dic13—21no—
144Dic13—42no—
145Dic13—41no—
146Dic13—42no—
147Dic13—42no—
148Dic13#35612yes—
149C22×Q8—131no—
150C22×Q8—131no—
151C4⋊Q8—262no—
152C4⋊Q8—262no—
153C4×Q8—521no—
154C4×Q8—521no—
155C4×Q8—521no—
156C4×Q8—521no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—132no—
159C2×C4⋊C4—262no—
160C2×C4⋊C4—261no—
161C2×C4⋊C4C4×D1311yescharacteristic
162C2×C4⋊C4C22×D1311yescharacteristic
163C2×C42—131no—
164C2×C42—132no—
165C2×C42—131no—
166C2×C42—261no—
167C2×C42—261no—
168C2×C42—261no—
169C2×C42C4×D1311yescharacteristic
170C4⋊C8—522no—
171C22⋊C8—22no—
172C22⋊C8—262no—
173#97—522no—
174#95—262no—
175#95—262no—
176C2×C13—21no—
177C2×C13—21no—
178C2×C13#146511yescharacteristic
179C2×C13#212611yescharacteristic
180C2×C13C2×#35611yescharacteristic
181C2×Q8—132no—
182C2×Q8—261no—
183C2×Q8—261no—
184C2×Q8—261no—
185C2×Q8—521no—
186C2×Q8—521no—
187C2×Q8—521no—
188C2×Q8—521no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—131no—
192C22×C4—132no—
193C22×C4—131no—
194C22×C4—261no—
195C22×C4—261no—
196C22×C4C2×C4×D1311yescharacteristic
197C22×C4D4×D1312yes—
198C2×C8—42no—
199C2×C8—522no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—44no—
203C4⋊C4—268no—
204C4⋊C4—522no—
205C4⋊C4—522no—
206C42—21no—
207C42—262no—
208C42—262no—
209C42—261no—
210C42—261no—
211C42—264no—
212C42—521no—
213C42—522no—
214C42—521no—
215C42—521no—
216C42#609412yes—
217C13#1153211yescharacteristic, complemented, Sylow
218C23C22⋊C4×D1311yescharacteristic
219Q8—522no—
220Q8—522no—
221Q8—522no—
222Q8—522no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—131no—
233C2×C4—131no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—261no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—521no—
242C2×C4—521no—
243C2×C4—521no—
244C2×C4—521no—
245C2×C4—521no—
246C2×C4C2×#609411yescharacteristic
247C2×C4M16×D1311yescharacteristic
248C8—82no—
249C8—1042no—
250C22—21no—
251C22—21no—
252C22#1171838711yescharacteristic
253C22D13×#9911yescharacteristic
254C22#1171841211yescharacteristic
255C4—24no—
256C4—21no—
257C4—21no—
258C4—42no—
259C4—81no—
260C4—132no—
261C4—261no—
262C4—522no—
263C4—521no—
264C4—522no—
265C4—522no—
266C2—21no—
267C2—21no—
268C2#1311317311yescharacteristic
269C2#1311649811yescharacteristic
270C2D13×#35611yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1325C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1325D13
hypocenterC13#11532
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
217. C13#11532semidirect

Maximal subgroups

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

subgroupindex
#131174032
#131131782
#131127822
#131127692
C13×#13252
#1153213