Finite Group Databasebeta

← #15758662

Subgroups — #15758662

Order 3328.

756 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 135 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#13123167C211yesmaximal, characteristic
2C2×#11718593C211yesmaximal, characteristic, complemented
3C2×#11718062C212yesmaximal
4#13112716C212yesmaximal, complemented
5C13×#1817C211yesmaximal, characteristic, complemented
6C22×C42×C13C2211yescharacteristic
7C2×#88184C2211yescharacteristic
8C2×#88183—21no—
9C22×C4×Dic13—21no—
10C2×C13×C22⋊C8C2212yes—
11#11718874—21no—
12#11718873C2211yescharacteristic
13C2×#88071—21no—
14C2×#88071C2212yes—
15#11718601—22no—
16#11718600C412yescomplemented
17#11718593—24no—
18#11718589C412yescomplemented
19C13×#336—22no—
20#11718062—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C22×C22⋊D13—21no—
25C23×Dic13—22no—
26C22×D52C2×C411yescharacteristic
27C22×C8×C13—22no—
28C2×C42×C13—22no—
29C2×C42×C13—22no—
30C2×C42×C13C2×C412yes—
31C2×C42×C13D412yes—
32C2×C22⋊Dic13—21no—
33#88184—22no—
34#88184—22no—
35#88183—44no—
36C2×#6103—22no—
37C2×#6103—22no—
38C2×#6103—21no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13C2×C412yes—
41C2×#6101—22no—
42C2×C4×Dic13—28no—
43C2×C4×Dic13—24no—
44C13×C22⋊C8—22no—
45C13×C22⋊C8—22no—
46#88071—24no—
47#88071—22no—
48#88071—22no—
49#88071—21no—
50#88071D414yes—
51#9149—131nomaximal, Sylow
52C24×C13C2×D411yescharacteristic
53C23×D13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—24no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—42no—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13C22⋊C412yes—
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D412yes—
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13#4112yes—
68C2×C22⋊D13—41no—
69C2×C22⋊D13—41no—
70C2×C22⋊D13—42no—
71C2×C22⋊D13—42no—
72C22×Dic13—28no—
73C22×Dic13—24no—
74C22×Dic13—21no—
75C22×Dic13—22no—
76C22×Dic13—44no—
77C22×Dic13—42no—
78C22×Dic13—42no—
79C2×D52—22no—
80C2×D52—42no—
81C2×C8×C13—44no—
82C2×C8×C13—42no—
83C42×C13—24no—
84C42×C13—24no—
85C22⋊Dic13—42no—
86#6103—44no—
87#6103—44no—
88#6103—42no—
89C4⋊Dic13—22no—
90C4⋊Dic13—42no—
91#6101—44no—
92C4×Dic13—216no—
93#2854—131no—
94C2×#376—131no—
95#1817D1311yescharacteristic, complemented
96C2×#327—132no—
97#1294—132no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13C2×C22⋊C411yescharacteristic
101C23×C13#12011yescharacteristic
102C23×C13#12311yescharacteristic
103C23×C13#13512yes—
104C23×C13AGL(1,ℤ/8)12yes—
105C22×D13—41no—
106C22×D13—42no—
107C22×D13—41no—
108C22×D13—41no—
109C22×D13—42no—
110C2×C4×C13—24no—
111C2×C4×C13—24no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13#10414yes—
124C2×C4×C13C4×D412yes—
125C2×C4×C13#12112yes—
126C22⋊D13—82no—
127C22⋊D13—82no—
128C2×Dic13—28no—
129C2×Dic13—44no—
130C2×Dic13—48no—
131C2×Dic13—48no—
132C2×Dic13—44no—
133C2×Dic13—41no—
134C2×Dic13—42no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139D52—82no—
140C8×C13—82no—
141C2×#123—261no—
142C2×#121—131no—
143C22×C42—261no—
144C22×C42C2×D1311yescharacteristic
145C2×C22⋊C8C2×D1312yes—
146#390—132no—
147#389—132no—
148#388—262no—
149#386—261no—
150#380—131no—
151#376—264no—
152C2×#95—132no—
153C2×#95—261no—
154#336—22no—
155#327—264no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—24no—
161C22×C13—24no—
162C22×C13#38611yescharacteristic
163C22×C13#41012yes—
164C22×C13#41611yescharacteristic
165C22×C13#41811yescharacteristic
166C22×C13C2×#10412yes—
167C22×C13#44912yes—
168C22×C13#48212yes—
169C2×D13—81no—
170C2×D13—81no—
171C2×D13—81no—
172C2×D13—82no—
173C2×D13—82no—
174C4×C13—24no—
175C4×C13—22no—
176C4×C13—22no—
177C4×C13—42no—
178Dic13—48no—
179Dic13—81no—
180Dic13—82no—
181C22×D4—131no—
182C22×D4—261no—
183C23×C4—262no—
184C23×C4D5211yescharacteristic
185C23×C4D5211yescharacteristic
186C23×C4C22×D1311yescharacteristic
187C22×C8—22no—
188#123—524no—
189#121—262no—
190#121—262no—
191C2×C4⋊C4—131no—
192C2×C4⋊C4—132no—
193C2×C4⋊C4—262no—
194C2×C22⋊C4—261no—
195C2×C22⋊C4—262no—
196C2×C22⋊C4—262no—
197C2×C22⋊C4—261no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—264no—
201C2×C42—268no—
202C2×C42C4×D1312yes—
203C2×C42C22⋊D1312yes—
204C22⋊C8—22no—
205C22⋊C8—22no—
206#95—134no—
207#95—264no—
208#95—262no—
209#95—262no—
210#95—261no—
211C2×C13—22no—
212C2×C13—22no—
213C2×C13#150012yes—
214C2×C13#150512yes—
215C2×C13#187511yescharacteristic
216C2×C13#189611yescharacteristic
217C2×C13#189911yescharacteristic
218D13—161no—
219C24—261no—
220C24C2×D5211yescharacteristic
221C2×D4—262no—
222C2×D4—522no—
223C2×D4—521no—
224C2×D4—521no—
225C2×D4—522no—
226C2×D4—522no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—24no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—42no—
235C22×C4—268no—
236C22×C4—264no—
237C22×C4—262no—
238C22×C4—261no—
239C22×C4—524no—
240C22×C4—522no—
241C22×C4—522no—
242C22×C4#610312yes—
243C22×C4#610312yes—
244C22×C4C2×C4×D1311yescharacteristic
245C22×C4D4×D1312yes—
246C22×C4#612912yes—
247C22×C4C2×C22⋊D1311yescharacteristic
248C2×C8—44no—
249C2×C8—42no—
250C4⋊C4—262no—
251C4⋊C4—522no—
252C4⋊C4—524no—
253C22⋊C4—524no—
254C22⋊C4—522no—
255C22⋊C4—524no—
256C22⋊C4—522no—
257C42—24no—
258C42—24no—
259C42—2616no—
260C13#914911yescharacteristic, complemented, Sylow
261C23—22no—
262C23—22no—
263C23—522no—
264C23—521no—
265C23—521no—
266C23—522no—
267C23—521no—
268C23#8813611yescharacteristic
269C23#8814011yescharacteristic
270C23#8815812yes—
271C23#8816212yes—
272C23C2×#610311yescharacteristic
273D4—1042no—
274D4—1042no—
275D4—1042no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—268no—
290C2×C4—528no—
291C2×C4—524no—
292C2×C4—528no—
293C2×C4—524no—
294C2×C4—522no—
295C2×C4—521no—
296C2×C4—522no—
297C2×C4—521no—
298C2×C4—522no—
299C2×C4—521no—
300C2×C4#8806514yes—
301C2×C4#8813512yes—
302C2×C4#8819312yes—
303C8—82no—
304C22—24no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—24no—
310C22—1042no—
311C22—1041no—
312C22—1041no—
313C22—1041no—
314C22—1042no—
315C22#1171839512yes—
316C22#1171839812yes—
317C22#1171861911yescharacteristic
318C22#1171866712yes—
319C22#1171877411yescharacteristic
320C22#1171879211yescharacteristic
321C22C2×#8806512yes—
322C4—24no—
323C4—22no—
324C4—22no—
325C4—42no—
326C4—528no—
327C4—1042no—
328C4—1041no—
329C2—22no—
330C2—22no—
331C2—2081no—
332C2#1311332312yes—
333C2#1311334512yes—
334C2#1311515611yescharacteristic
335C2#1311527711yescharacteristic
336C2#1311529211yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1817C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenter#1817D13
hypocenterC13#9149
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. C2×#11718593C2semidirect
4. #13112716C2semidirect
5. C13×#1817C2semidirect
16. #11718600C4semidirect
18. #11718589C4semidirect
95. #1817D13semidirect
260. C13#9149semidirect

Maximal subgroups

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

subgroupindex
#131231672
C2×#117185932
C2×#117180622
#131127162
C13×#18172
#914913