Finite Group Databasebeta

← #15760766

Subgroups — #15760766

Order 3328.

626 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 127 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#13123860C211yesmaximal, characteristic, complemented
2#13119733C211yesmaximal, characteristic
3#13113260C212yesmaximal, complemented
4#13112696C212yesmaximal, complemented
5C13×#1800C211yesmaximal, characteristic, complemented
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88192—21no—
8C2×C4×D52C2211yescharacteristic
9C13×#423C2212yes—
10C2×C13×#100—21no—
11#11718874—22no—
12C2×C22⋊#1055—22no—
13D4×#1055—24no—
14#11718648—21no—
15#11718621C412yes—
16#11718614C412yes—
17#11718597C2211yescharacteristic
18#11718586C2212yes—
19C13×#343—21no—
20#11718075—24no—
21C22×D4×C13D411yescharacteristic
22C23×C4×C13D412yes—
23C22×C22⋊D13—22no—
24C22×D52C2×C411yescharacteristic
25C22×C4×D13—21no—
26C2×C13×M16—22no—
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C22⋊C4C2×C412yes—
31C2×C42×C13C2311yescharacteristic
32C2×C22⋊Dic13—22no—
33#88192—42no—
34#88192—42no—
35C2×#6103—21no—
36C2×#6103—22no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C22×#1055—24no—
40C4×D52—22no—
41C4×D52—22no—
42C13×C4⋊C8—22no—
43C13×C4⋊C8—22no—
44C13×#100—42no—
45#88071—22no—
46#88071—21no—
47#88071C2×C412yes—
48C22⋊#1055—24no—
49C22⋊#1055—22no—
50C4⋊#1055—22no—
51C4×#1055D414yescomplemented
52#9485—131nomaximal, Sylow
53C24×C13C22⋊C412yes—
54C23×D13—21no—
55C2×D4×C13—22no—
56C2×D4×C13—22no—
57C2×D4×C13D812yes—
58C2×D4×C13SD1612yes—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—82no—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C2×C22⋊D13—44no—
67C2×C22⋊D13—44no—
68C2×C22⋊D13—82no—
69C22×Dic13—22no—
70C22×Dic13—21no—
71C2×D52—22no—
72C2×D52—42no—
73C2×C4×D13—42no—
74C2×C4×D13—41no—
75C2×C4×D13—41no—
76C2×C4×D13—42no—
77C13×M16—42no—
78C13×M16—42no—
79C2×C8×C13—42no—
80C13×C4⋊C4—22no—
81C13×C22⋊C4—24no—
82C42×C13C2×D412yes—
83C42×C13#4112yes—
84C22⋊Dic13—44no—
85#6103—41no—
86#6103—41no—
87#6103—82no—
88C4⋊Dic13—22no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91C2×#1055—24no—
92C2×#1055—84no—
93#2972—131no—
94#2535—131no—
95#1800D1311yescharacteristic, complemented
96#1486—132no—
97#1286—132no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13#10214yes—
103C23×C13C2×C22⋊C411yescharacteristic
104C22×D13—22no—
105C22×D13—41no—
106C22×D13—41no—
107C22×D13—41no—
108C22×D13—41no—
109C22×D13—41no—
110C22×D13—41no—
111D4×C13—24no—
112D4×C13—24no—
113C2×C4×C13—22no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—44no—
117C2×C4×C13—42no—
118C2×C4×C13—82no—
119C2×C4×C13C4×D412yes—
120C2×C4×C13#12011yescharacteristic
121C2×C4×C13#12112yes—
122C2×C4×C13#12311yescharacteristic
123C2×C4×C13C2×D811yescharacteristic
124C2×C4×C13C2×SD1611yescharacteristic
125C2×C4×C13#13512yes—
126C22⋊D13—88no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13—41no—
130C2×Dic13—42no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133D52—24no—
134D52—42no—
135C4×D13—82no—
136C4×D13—82no—
137C8×C13—82no—
138#1055—44no—
139C2×#121—261no—
140C2×C4×D4—131no—
141C2×C4×D4C2×D1311yescharacteristic
142C8×D4—264no—
143#431—132no—
144#423C2×D1312yes—
145C2×#100—21no—
146C2×C22⋊C8—262no—
147#397—132no—
148#392—132no—
149#386—262no—
150#382—131no—
151#380—261no—
152#343—21no—
153D4⋊C8—264no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—24no—
157C22×C13—44no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—82no—
161C22×C13#38611yescharacteristic
162C22×C13C2×#10211yescharacteristic
163C22×C13#41611yescharacteristic
164C2×D13—42no—
165C2×D13—42no—
166C2×D13—42no—
167C2×D13—81no—
168C2×D13—81no—
169C2×D13—81no—
170C2×D13—81no—
171C4×C13—22no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—42no—
175C4×C13#46512yes—
176C4×C13#46612yes—
177Dic13—82no—
178Dic13—81no—
179C22×D4—131no—
180C22×D4—262no—
181C22×D4C22⋊D1311yescharacteristic
182C23×C4—261no—
183C23×C4D5212yes—
184C2×M16—22no—
185C22×C8—264no—
186#121—522no—
187#121—522no—
188C4×D4—22no—
189C4×D4—22no—
190C4×D4—262no—
191C4×D4—262no—
192C2×C4⋊C4—131no—
193C2×C4⋊C4—261no—
194C2×C4⋊C4C22⋊D1311yescharacteristic
195C2×C22⋊C4—262no—
196C2×C22⋊C4—261no—
197C2×C22⋊C4—262no—
198C2×C22⋊C4C4×D1312yes—
199C2×C42C22×D1311yescharacteristic
200C4⋊C8—22no—
201C4⋊C8—22no—
202C4⋊C8—262no—
203#100—42no—
204C22⋊C8—264no—
205C22⋊C8—262no—
206C4×C8—134no—
207#95—132no—
208#95—262no—
209#95—261no—
210C2×C13—21no—
211C2×C13—21no—
212C2×C13—44no—
213C2×C13#189111yescharacteristic
214C2×C13#189311yescharacteristic
215C2×C13#191111yescharacteristic
216D13—82no—
217C24—261no—
218C24#610312yes—
219C2×D4—22no—
220C2×D4—22no—
221C2×D4—262no—
222C2×D4—522no—
223C2×D4—524no—
224C2×D4—524no—
225C2×D4—1042no—
226C2×D4#610412yes—
227C2×D4#610612yes—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—82no—
231C22×C4—262no—
232C22×C4—261no—
233C22×C4—521no—
234C22×C4—522no—
235C22×C4—521no—
236C22×C4—522no—
237C22×C4#610312yes—
238C22×C4C2×C4×D1311yescharacteristic
239C22×C4C2×D5211yescharacteristic
240C22×C4C2×C22⋊D1311yescharacteristic
241M16—42no—
242M16—42no—
243C2×C8—42no—
244C2×C8—264no—
245C2×C8—1044no—
246C4⋊C4—22no—
247C4⋊C4—262no—
248C4⋊C4—521no—
249C4⋊C4—521no—
250C22⋊C4—24no—
251C22⋊C4—524no—
252C22⋊C4—521no—
253C22⋊C4—521no—
254C22⋊C4—1042no—
255C42D4×D1312yes—
256C42#612912yes—
257C13#948511yescharacteristic, complemented, Sylow
258C23—22no—
259C23—22no—
260C23—42no—
261C23—42no—
262C23—262no—
263C23—521no—
264C23—521no—
265C23—521no—
266C23—521no—
267C23—521no—
268C23—521no—
269C23#8804914yes—
270C23C2×#610311yescharacteristic
271D4—24no—
272D4—24no—
273D4—264no—
274D4—522no—
275D4—1048no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—42no—
281C2×C4—82no—
282C2×C4—522no—
283C2×C4—522no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—522no—
288C2×C4—1042no—
289C2×C4—1042no—
290C2×C4#8813512yes—
291C2×C4#8813611yescharacteristic
292C2×C4#8814011yescharacteristic
293C2×C4C2×#610411yescharacteristic
294C2×C4#8819312yes—
295C2×C4C2×#610611yescharacteristic
296C2×C4#8820412yes—
297C8—82no—
298C8—524no—
299C22—21no—
300C22—21no—
301C22—24no—
302C22—44no—
303C22—42no—
304C22—42no—
305C22—82no—
306C22—522no—
307C22—522no—
308C22—522no—
309C22—1041no—
310C22—1041no—
311C22—1041no—
312C22—1041no—
313C22#1171861911yescharacteristic
314C22C2×#8804911yescharacteristic
315C22#1171866311yescharacteristic
316C4—22no—
317C4—21no—
318C4—21no—
319C4—42no—
320C4—1042no—
321C4—1041no—
322C4#1171869912yes—
323C4#1171870912yes—
324C2—21no—
325C2—21no—
326C2—44no—
327C2—1042no—
328C2#1311525211yescharacteristic
329C2#1311526211yescharacteristic
330C2#1311536611yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1800C2
socleC22×C13#386
prime radical#13119733C2
cosocleC2×C42×C13C23
hypercenter#1800D13
hypocenterC13#9485
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
1. #13123860C2semidirect
3. #13113260C2semidirect
4. #13112696C2semidirect
5. C13×#1800C2semidirect
51. C4×#1055D4semidirect
95. #1800D13semidirect
257. C13#9485semidirect

Maximal subgroups

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

subgroupindex
#131238602
#131197332
#131132602
#131126962
C13×#18002
#948513