Finite Group Databasebeta

← #15760278

Subgroups — #15760278

Order 3328.

486 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 117 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#13123916C211yesmaximal, characteristic
2#13120044C211yesmaximal, characteristic
3#13114829C211yesmaximal, characteristic
4#13113518C211yesmaximal, characteristic
5#13113516C211yesmaximal, characteristic
6#13112739C211yesmaximal, characteristic
7C13×#1303C211yesmaximal, characteristic
8C2×#88123C2211yescharacteristic
9C2×C4×Dic26C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88064—21no—
14#11718646—22no—
15#11718596—21no—
16#11718590—21no—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19#11718491—22no—
20#11718379—22no—
21C8×Dic26—22no—
22#11718317C414yes—
23#11718146—21no—
24#11718073—22no—
25#11718073—22no—
26C22×Dic26C2×C412yes—
27C22×Dic26D411yescharacteristic
28C2×C13×M16—21no—
29C2×C13×C4⋊C4—21no—
30C2×C42×C13—21no—
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—24no—
35C2×C4⋊Dic13D411yescharacteristic
36C2×#6101C2×C412yes—
37C2×C4×Dic13D412yes—
38C2×#6099—21no—
39#88123—21no—
40#88123—21no—
41#88123—21no—
42#88123—21no—
43C4×Dic26—21no—
44C4×Dic26—21no—
45C4×Dic26—21no—
46C4×Dic26—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8D412yes—
50C13×C22⋊C8—21no—
51C4×C8×C13—21no—
52C13×#95C2×C412yes—
53#88071—24no—
54C22⋊#1055—21no—
55#88064—42no—
56#88054—24no—
57C8×Dic13—24no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055D412yes—
61C4×#1055—21no—
62#9392—131nomaximal, Sylow
63C22×C4×C13—22no—
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×Dic13—22no—
68C22×Dic13C22⋊C412yes—
69C22×Dic13C22⋊C412yes—
70C2×Dic26—21no—
71C2×Dic26—21no—
72C2×Dic26—21no—
73C2×Dic26—21no—
74C2×Dic26—22no—
75C2×Dic26—22no—
76C2×Dic26—82no—
77C2×Dic26SD1612yes—
78C2×Dic26Q1612yes—
79C13×M16—41no—
80C13×M16—41no—
81C2×C8×C13—22no—
82C2×C8×C13—41no—
83C13×C4⋊C4—24no—
84C42×C13—41no—
85C42×C13—41no—
86C42×C13C2×D411yescharacteristic
87C42×C13C2×D411yescharacteristic
88C42×C13#4111yescharacteristic
89C42×C13#4111yescharacteristic
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—41no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96C4⋊Dic13—84no—
97#6101—22no—
98#6101—22no—
99C4×Dic13—22no—
100C4×Dic13—22no—
101#6099—41no—
102#6099—41no—
103C2×#1055—22no—
104C2×#1055—41no—
105#2982—131no—
106#2567—131no—
107#1801—131no—
108#1548—131no—
109#1548—131no—
110#1303—131no—
111#1303D1311yescharacteristic
112C23×C13C2×C22⋊C411yescharacteristic
113C2×C4×C13—22no—
114C2×C4×C13—24no—
115C2×C4×C13—41no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13C4×D411yescharacteristic
119C2×C4×C13C4×D411yescharacteristic
120C2×C4×C13#12011yescharacteristic
121C2×C4×C13#12111yescharacteristic
122C2×C4×C13#12111yescharacteristic
123C2×C4×C13#12311yescharacteristic
124C2×C4×C13C2×SD1611yescharacteristic
125C2×C4×C13C2×Q1611yescharacteristic
126C2×C4×C13#13511yescharacteristic
127C2×C4×C13#13511yescharacteristic
128C2×Dic13—22no—
129C2×Dic13—22no—
130C2×Dic13—22no—
131C2×Dic13—42no—
132C2×Dic13—44no—
133C2×Dic13—42no—
134C2×Dic13#10314yes—
135Dic26—22no—
136Dic26—22no—
137Dic26—22no—
138Dic26—22no—
139Dic26—82no—
140Dic26—82no—
141C8×C13—42no—
142C8×C13—81no—
143#1055—42no—
144#1055—81no—
145C2×C4⋊Q8—131no—
146C2×C4×Q8—131no—
147C8×Q8—262no—
148C8×Q8—262no—
149#431—131no—
150#431—262no—
151#431C2×D1311yescharacteristic
152#423—131no—
153#423C2×D1311yescharacteristic
154C2×#101—261no—
155#395—134no—
156#391—261no—
157#389—262no—
158#384—261no—
159C4×C4⋊C4C2×D1311yescharacteristic
160#343—261no—
161#333—262no—
162#333—262no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13#38611yescharacteristic
166C22×C13C2×#10311yescharacteristic
167C22×C13#41611yescharacteristic
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—44no—
172C4×C13#45612yes—
173C4×C13#46511yescharacteristic
174C4×C13#46511yescharacteristic
175C4×C13#46711yescharacteristic
176C4×C13#46711yescharacteristic
177Dic13—24no—
178Dic13—42no—
179Dic13—82no—
180C22×Q8—131no—
181C22×Q8—132no—
182C2×M16—21no—
183C2×M16—261no—
184C4⋊Q8—261no—
185C4⋊Q8—261no—
186C4⋊Q8—261no—
187C4⋊Q8—261no—
188C4×Q8—261no—
189C4×Q8—261no—
190C4×Q8—261no—
191C4×Q8—261no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—132no—
194C2×C4⋊C4—131no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—264no—
198C2×C42—21no—
199C2×C42—132no—
200C2×C42C22×D1311yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—132no—
204C4⋊C8—264no—
205C4⋊C8—261no—
206C4⋊C8—261no—
207C4⋊C8D5212yes—
208#101—522no—
209C22⋊C8—21no—
210C22⋊C8—261no—
211C4×C8—21no—
212C4×C8—264no—
213C4×C8—261no—
214#95—264no—
215#95C4×D1312yes—
216C2×C13—21no—
217C2×C13—21no—
218C2×C13#188611yescharacteristic
219C2×C13#189211yescharacteristic
220C2×C13#191411yescharacteristic
221C2×Q8—132no—
222C2×Q8—132no—
223C2×Q8—261no—
224C2×Q8—261no—
225C2×Q8—261no—
226C2×Q8—261no—
227C2×Q8—262no—
228C2×Q8—262no—
229C2×Q8—1042no—
230C22×C4—22no—
231C22×C4—132no—
232C22×C4—132no—
233C22×C4—262no—
234C22×C4C2×C4×D1311yescharacteristic
235C22×C4D4×D1311yescharacteristic
236C22×C4D4×D1311yescharacteristic
237M16—41no—
238M16—41no—
239M16—521no—
240M16—521no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—262no—
244C2×C8—521no—
245C4⋊C4—24no—
246C4⋊C4—262no—
247C4⋊C4—261no—
248C4⋊C4—262no—
249C4⋊C4—261no—
250C4⋊C4—521no—
251C4⋊C4—521no—
252C4⋊C4—521no—
253C4⋊C4—521no—
254C4⋊C4—1044no—
255C42—41no—
256C42—41no—
257C42—262no—
258C42—262no—
259C42C2×D5211yescharacteristic
260C42#612711yescharacteristic
261C42D4×D1311yescharacteristic
262C42#613111yescharacteristic
263C13#939211yescharacteristic, complemented, Sylow
264C23C22⋊C4×D1311yescharacteristic
265Q8—262no—
266Q8—262no—
267Q8—262no—
268Q8—262no—
269Q8—1042no—
270Q8—1042no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—134no—
277C2×C4—262no—
278C2×C4—262no—
279C2×C4—262no—
280C2×C4—522no—
281C2×C4—524no—
282C2×C4—522no—
283C2×C4C4×D5211yescharacteristic
284C2×C4#8813611yescharacteristic
285C2×C4#8813811yescharacteristic
286C2×C4#8814711yescharacteristic
287C2×C4#8814811yescharacteristic
288C2×C4#8814911yescharacteristic
289C2×C4#8816611yescharacteristic
290C2×C4SD16×D1311yescharacteristic
291C2×C4#8817011yescharacteristic
292C2×C4Q16×D1311yescharacteristic
293C8—42no—
294C8—81no—
295C8—522no—
296C8—1041no—
297C22—21no—
298C22—21no—
299C22#1171832611yescharacteristic
300C22#1171843311yescharacteristic
301C22D13×#10311yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—44no—
306C4—264no—
307C4—522no—
308C4—1042no—
309C4#1171843911yescharacteristic
310C4#1171847411yescharacteristic
311C4#1171848712yes—
312C4#1171852511yescharacteristic
313C4#1171854811yescharacteristic
314C2—21no—
315C2—21no—
316C2#1311522811yescharacteristic
317C2#1311525811yescharacteristic
318C2#1311538211yescharacteristic
subgroupG/H
centerC22#11718326
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1303C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1303D13
hypocenterC13#9392
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
263. C13#9392semidirect

Maximal subgroups

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

subgroupindex
#131239162
#131200442
#131148292
#131135182
#131135162
#131127392
C13×#13032
#939213