Finite Group Databasebeta

← #15778929

Subgroups — #15778929

Order 3328.

432 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 93 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#13117554C211yesmaximal, characteristic
2C2×#11718070C212yesmaximal
3#13114830C212yesmaximal
4#13112963C211yesmaximal, characteristic
5C13×#1394C211yesmaximal, characteristic
6C2×Q8×Dic13C2211yescharacteristic
7C2×#88198C2211yescharacteristic
8C2×#88141C411yescharacteristic
9C2×C13×#101C2212yes—
10C13×#391C2211yescharacteristic
11C2×#88076C2212yes—
12#11718779—22no—
13#11718638C411yescharacteristic
14#11718593C411yescharacteristic
15#11718590C411yescharacteristic
16#11718316—22no—
17#11718313—22no—
18#11718146—22no—
19#11718070—24no—
20C22×Q8×C13C2311yescharacteristic
21C22×Dic26C2×C411yescharacteristic
22C2×C13×M16—22no—
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25Q8×Dic13—42no—
26#88198—22no—
27#88198D412yes—
28#88198Q812yes—
29C2×C4⋊Dic13C2×C411yescharacteristic
30C2×C4⋊Dic13D412yes—
31C2×#6101—22no—
32C2×#6101—21no—
33C2×C4×Dic13—21no—
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13D412yes—
37C2×#6099—22no—
38#88141—42no—
39C13×#101—22no—
40C13×#101—22no—
41C13×#95—22no—
42#88076—22no—
43#88076—22no—
44#88071—21no—
45#88071—22no—
46#88071—22no—
47#88071—21no—
48#88054—44no—
49#12804—131nomaximal, Sylow
50C2×Q8×C13—41no—
51C2×Q8×C13—41no—
52C2×Q8×C13C2×D411yescharacteristic
53C2×Q8×C13C2×Q811yescharacteristic
54C2×Q8×C13#4112yes—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D412yes—
59C22×Dic13—21no—
60C22×Dic13—21no—
61C22×Dic13C22⋊C412yes—
62C22×Dic13C22⋊C411yescharacteristic
63C22×Dic13C22⋊C411yescharacteristic
64C2×Dic26—21no—
65C2×Dic26—41no—
66C2×Dic26—41no—
67C2×Dic26C4⋊C412yes—
68C13×M16—42no—
69C13×M16—42no—
70C2×C8×C13—42no—
71C13×C4⋊C4—41no—
72C42×C13—41no—
73C4⋊Dic13—41no—
74C4⋊Dic13—42no—
75#6101—24no—
76#6101—24no—
77#6101—42no—
78C4×Dic13—21no—
79C4×Dic13—22no—
80C4×Dic13—24no—
81C4×Dic13—42no—
82C4×Dic13C4⋊C412yes—
83#6099—42no—
84#6099—42no—
85C2×#1055—42no—
86#2327—131no—
87C2×#356—132no—
88#1801—132no—
89#1394—131no—
90#1394D1311yescharacteristic
91C23×C13C2×C22⋊C411yescharacteristic
92Q8×C13—41no—
93Q8×C13—41no—
94Q8×C13—42no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—22no—
98C2×C4×C13—21no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13C2×C4⋊C411yescharacteristic
105C2×C4×C13#11711yescharacteristic
106C2×C4×C13#12112yes—
107C2×C4×C13C22⋊Q812yes—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—21no—
111C2×Dic13—22no—
112C2×Dic13—41no—
113C2×Dic13—41no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117C2×Dic13—42no—
118C2×Dic13—41no—
119C2×Dic13#9912yes—
120Dic26—42no—
121Dic26—42no—
122C8×C13—82no—
123#1055—82no—
124C2×C4⋊Q8—131no—
125C2×C4×Q8—131no—
126C2×C4×Q8—131no—
127#423—262no—
128C2×#101—132no—
129C2×#101C2×D1312yes—
130#391—131no—
131#391C2×D1311yescharacteristic
132#387—262no—
133#387—262no—
134#382—131no—
135#376—131no—
136#356—264no—
137#343—262no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13#38011yescharacteristic
141C22×C13C2×#9911yescharacteristic
142C22×C13#41011yescharacteristic
143C4×C13—22no—
144C4×C13—21no—
145C4×C13—21no—
146C4×C13—22no—
147C4×C13—81no—
148C4×C13—81no—
149Dic13—22no—
150Dic13—42no—
151Dic13—42no—
152Dic13—41no—
153Dic13—42no—
154C22×Q8—131no—
155C22×Q8C22×D1311yescharacteristic
156C2×M16—22no—
157C2×M16—262no—
158C4⋊Q8—132no—
159C4⋊Q8—132no—
160C4⋊Q8—262no—
161C4×Q8—522no—
162C4×Q8—522no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4—132no—
165C2×C4⋊C4—262no—
166C2×C4⋊C4—261no—
167C2×C4⋊C4C4×D1311yescharacteristic
168C2×C42—131no—
169C2×C42—131no—
170C2×C42—132no—
171C2×C42—261no—
172C2×C42C4×D1311yescharacteristic
173C4⋊C8—524no—
174#101—22no—
175#101—22no—
176#101—262no—
177#101—262no—
178#95—22no—
179#95—261no—
180#95—261no—
181#95—262no—
182#95—262no—
183C2×C13—21no—
184C2×C13—21no—
185C2×C13#179911yescharacteristic
186C2×C13#213311yescharacteristic
187C2×C13#213511yescharacteristic
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8—132no—
191C2×Q8—261no—
192C2×Q8—521no—
193C2×Q8—521no—
194C2×Q8#612712yes—
195C2×Q8D4×D1311yescharacteristic
196C2×Q8Q8×D1311yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—131no—
200C22×C4—132no—
201C22×C4—131no—
202C22×C4—261no—
203C22×C4—261no—
204C22×C4C2×C4×D1311yescharacteristic
205C22×C4D4×D1312yes—
206M16—42no—
207M16—42no—
208M16—522no—
209M16—522no—
210C2×C8—42no—
211C2×C8—522no—
212C4⋊C4—41no—
213C4⋊C4—264no—
214C4⋊C4—264no—
215C4⋊C4—521no—
216C4⋊C4—522no—
217C4⋊C4—522no—
218C42—41no—
219C42—132no—
220C42—264no—
221C42—262no—
222C42—261no—
223C42—522no—
224C13#1280411yescharacteristic, complemented, Sylow
225C23C22⋊C4×D1311yescharacteristic
226Q8—42no—
227Q8—41no—
228Q8—41no—
229Q8—522no—
230Q8—522no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—132no—
241C2×C4—261no—
242C2×C4—262no—
243C2×C4—262no—
244C2×C4—262no—
245C2×C4—521no—
246C2×C4—521no—
247C2×C4—521no—
248C2×C4—521no—
249C2×C4—521no—
250C2×C4—522no—
251C2×C4—521no—
252C2×C4#8812611yescharacteristic
253C2×C4#8813812yes—
254C2×C4C4⋊C4×D1311yescharacteristic
255C2×C4#8815012yes—
256C8—82no—
257C8—1042no—
258C22—21no—
259C22—21no—
260C22#1171832811yescharacteristic
261C22#1171840111yescharacteristic
262C22D13×#9911yescharacteristic
263C4—22no—
264C4—21no—
265C4—21no—
266C4—22no—
267C4—81no—
268C4—81no—
269C4—262no—
270C4—522no—
271C4—521no—
272C4—522no—
273C4—522no—
274C2—21no—
275C2—21no—
276C2#1311482311yescharacteristic
277C2#1311652211yescharacteristic
278C2#1311652911yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#1394C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenter#1394D13
hypocenterC13#12804
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
224. C13#12804semidirect

Maximal subgroups

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

subgroupindex
#131175542
C2×#117180702
#131148302
#131129632
C13×#13942
#1280413