Finite Group Databasebeta

← #15758942

Subgroups — #15758942

Order 3328.

524 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120602C211yesmaximal, characteristic
2#13113509C212yesmaximal, complemented
3#13113150C211yesmaximal, characteristic
4#13112696C212yesmaximal, complemented
5C13×#2905C211yesmaximal, characteristic
6C22×C13×M16—21no—
7C2×C13×#117C2211yescharacteristic
8C2×#88178—21no—
9C2×#88123C2211yescharacteristic
10C13×#424—24no—
11C13×#423—21no—
12C13×#423C2212yes—
13#11718644—21no—
14#11718644C412yes—
15#11718614—21no—
16#11718614C412yes—
17#11718597C2211yescharacteristic
18#11718590—21no—
19#11718586C2212yes—
20#11718120—21no—
21#11718117—21no—
22#11718074—24no—
23C23×C4×C13D411yescharacteristic
24C22×Dic26—21no—
25C2×C13×M16—22no—
26C2×C13×M16—22no—
27C2×C13×M16—42no—
28C2×C13×M16—42no—
29C22×C8×C13—22no—
30C13×#117—22no—
31C13×#117—22no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C22⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×C42×C13C2311yescharacteristic
38C2×C22⋊Dic13—22no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13C2×C412yes—
42#88178—42no—
43#88178—42no—
44C2×#6101—22no—
45#88123—22no—
46#88123—22no—
47C13×C4⋊C8—24no—
48C13×C4⋊C8—22no—
49C13×C4⋊C8D414yes—
50#88071—22no—
51#88071—22no—
52#88071—21no—
53#88071C2×C412yes—
54C22⋊#1055—22no—
55C4⋊#1055—22no—
56C4×#1055—22no—
57#9195—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13D812yes—
67C22×C4×C13SD1612yes—
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—22no—
72C22×Dic13—22no—
73C2×Dic26—41no—
74C2×Dic26—41no—
75C2×Dic26—41no—
76C2×Dic26—41no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C13×M16—44no—
80C13×M16—42no—
81C13×M16—42no—
82C2×C8×C13—24no—
83C2×C8×C13—44no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—22no—
86C13×C22⋊C4—22no—
87C13×C22⋊C4—22no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13C2×D412yes—
91C42×C13#4112yes—
92C22⋊Dic13—44no—
93C4⋊Dic13—24no—
94C4⋊Dic13—42no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97#6101—44no—
98C2×#1055—42no—
99#2905D1311yescharacteristic
100#2621—131no—
101#1546—132no—
102#1458—131no—
103#1286—132no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13#10212yes—
109C23×C13C2×C22⋊C411yescharacteristic
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13#10212yes—
123C2×C4×C13C4×D412yes—
124C2×C4×C13#12011yescharacteristic
125C2×C4×C13#12112yes—
126C2×C4×C13#12311yescharacteristic
127C2×C4×C13C2×D811yescharacteristic
128C2×C4×C13C2×SD1611yescharacteristic
129C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C13#13711yescharacteristic
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137Dic26—81no—
138Dic26—81no—
139Dic26—81no—
140Dic26—81no—
141C8×C13—44no—
142#1055—82no—
143C22×M16—21no—
144C2×C4⋊Q8—131no—
145C2×C22⋊Q8—261no—
146C2×#117C2×D1311yescharacteristic
147#431—132no—
148#424—24no—
149#423—21no—
150#423C2×D1312yes—
151#398—132no—
152#398—261no—
153#397—132no—
154#397—261no—
155#391—261no—
156#382—131no—
157#332—264no—
158#324—261no—
159#323—261no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—22no—
163C22×C13—42no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—81no—
167C22×C13#38611yescharacteristic
168C22×C13C2×#10211yescharacteristic
169C22×C13#41711yescharacteristic
170C4×C13—22no—
171C4×C13—22no—
172C4×C13—22no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13#44711yescharacteristic
176C4×C13#44811yescharacteristic
177C4×C13#48011yescharacteristic
178C4×C13#48111yescharacteristic
179Dic13—82no—
180Dic13—82no—
181C22×Q8—261no—
182C23×C4C22⋊D1311yescharacteristic
183C2×M16—22no—
184C2×M16—22no—
185C2×M16—42no—
186C2×M16—42no—
187C22×C8—22no—
188C4⋊Q8—262no—
189C4⋊Q8—262no—
190C22⋊Q8—522no—
191C22⋊Q8—522no—
192#117—22no—
193#117—22no—
194C2×C4⋊C4—132no—
195C2×C4⋊C4—262no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4C4×D1311yescharacteristic
199C2×C4⋊C4D5211yescharacteristic
200C2×C22⋊C4—262no—
201C2×C22⋊C4C4×D1311yescharacteristic
202C2×C22⋊C4D5211yescharacteristic
203C2×C42C22⋊D1311yescharacteristic
204C2×C42C22×D1311yescharacteristic
205C4⋊C8—24no—
206C4⋊C8—22no—
207C4⋊C8—262no—
208C4⋊C8C22⋊D1314yes—
209C22⋊C8—262no—
210C4×C8—262no—
211#95—132no—
212#95—262no—
213#95—262no—
214#95—261no—
215C2×C13—21no—
216C2×C13—21no—
217C2×C13—42no—
218C2×C13#187411yescharacteristic
219C2×C13#190911yescharacteristic
220C2×C13#191511yescharacteristic
221C24#610311yescharacteristic
222C2×Q8—521no—
223C2×Q8—521no—
224C2×Q8—521no—
225C2×Q8—521no—
226C2×Q8—521no—
227C2×Q8—521no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—262no—
233C22×C4—262no—
234C22×C4#610311yescharacteristic
235C22×C4#610311yescharacteristic
236C22×C4#610311yescharacteristic
237C22×C4#610412yes—
238C22×C4#610612yes—
239C22×C4C2×C4×D1311yescharacteristic
240C22×C4C2×D5211yescharacteristic
241C22×C4C2×C22⋊D1311yescharacteristic
242M16—44no—
243M16—42no—
244M16—42no—
245C2×C8—24no—
246C2×C8—44no—
247C2×C8—522no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—264no—
251C4⋊C4—522no—
252C4⋊C4—521no—
253C4⋊C4—521no—
254C4⋊C4—524no—
255C22⋊C4—22no—
256C22⋊C4—22no—
257C22⋊C4—524no—
258C42—21no—
259C42—21no—
260C42#612712yes—
261C42C2×C22⋊D1312yes—
262C13#919511yescharacteristic, complemented, Sylow
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23#8804912yes—
268C23C2×#610311yescharacteristic
269Q8—1041no—
270Q8—1041no—
271Q8—1041no—
272Q8—1041no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—522no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—522no—
289C2×C4—522no—
290C2×C4—522no—
291C2×C4#8804912yes—
292C2×C4C4×C22⋊D1312yes—
293C2×C4#8818311yescharacteristic
294C2×C4#8818412yes—
295C2×C4C2×#610411yescharacteristic
296C2×C4#8818611yescharacteristic
297C2×C4C2×#610611yescharacteristic
298C2×C4#8819611yescharacteristic
299C2×C4#8820711yescharacteristic
300C8—44no—
301C8—1042no—
302C22—21no—
303C22—21no—
304C22—22no—
305C22—42no—
306C22—41no—
307C22—41no—
308C22—81no—
309C22C2×#8804911yescharacteristic
310C22#1171862711yescharacteristic
311C22#1171887411yescharacteristic
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—1042no—
318C4—1042no—
319C4#1171862811yescharacteristic
320C4#1171862911yescharacteristic
321C4#1171887811yescharacteristic
322C4#1171888811yescharacteristic
323C2—21no—
324C2—21no—
325C2—42no—
326C2#1311515311yescharacteristic
327C2#1311535811yescharacteristic
328C2#1311538811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2905C2
socleC22×C13#386
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2905D13
hypocenterC13#9195
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2905

Complements

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

NH ≅ G/Ntype
2. #13113509C2semidirect
4. #13112696C2semidirect
262. C13#9195semidirect

Maximal subgroups

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

subgroupindex
#131206022
#131135092
#131131502
#131126962
C13×#29052
#919513