Finite Group Databasebeta

← #15846044

Subgroups — #15846044

Order 3328.

638 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13126153C212yesmaximal
2#13125350C211yesmaximal, characteristic, complemented
3#13123549C211yesmaximal, characteristic
4#13114360C212yesmaximal, complemented
5#13114350C212yesmaximal, complemented
6#13114212C214yesmaximal, complemented
7#13113524C212yesmaximal, complemented
8C2×C13×#334C211yesmaximal, characteristic, complemented
9C2×#88155—21no—
10#11719182C2211yescharacteristic
11#11719175C2212yes—
12C2×C13×C4⋊C8C2212yes—
13C2×C4×C8×C13C2211yescharacteristic
14#11718775—24no—
15#11718771—21no—
16#11718767—21no—
17#11718767—21no—
18#11718585C2211yescharacteristic
19#11718512—22no—
20#11718509—22no—
21#11718503C2214yes—
22#11718502C2214yes—
23#11718349—21no—
24#11718349C2212yes—
25C8×D52—21no—
26C8×D52C2212yes—
27#11718344—21no—
28#11718344—21no—
29#11718343C2211yescharacteristic
30#11718343C2211yescharacteristic
31#11718341C2212yes—
32C13×#334C2212yes—
33C13×#334C2212yes—
34#11718074C2214yes—
35#11718073C2214yes—
36C2×#6127—21no—
37C22×C8×C13—22no—
38C22×C8×C13D411yescharacteristic
39C22×C8×C13D411yescharacteristic
40C2×C42×C13C2311yescharacteristic
41#88184—21no—
42#88184D412yes—
43#88180—22no—
44#88178—22no—
45#88178—22no—
46C2×#6099—21no—
47C2×#6095—24no—
48#88155—44no—
49C2×#6094—22no—
50C2×C8×D13—22no—
51#88129—21no—
52#88128D411yescharacteristic
53C4×D52—21no—
54C4×D52C2312yes—
55#88124—22no—
56#88123D411yescharacteristic
57#88123C2312yes—
58#88123C2312yes—
59C4×Dic26—22no—
60C4×Dic26—22no—
61C13×C4⋊C8—22no—
62C13×C4⋊C8C2314yes—
63C4×C8×C13D411yescharacteristic
64C4×C8×C13D411yescharacteristic
65C4×C8×C13C2311yescharacteristic
66C4×C8×C13C2311yescharacteristic
67#88061—24no—
68#88060—22no—
69#88060—22no—
70#88058—21no—
71#88058—21no—
72#88058—21no—
73#88058—21no—
74#88057—22no—
75#88057—22no—
76#88057—24no—
77#88056—24no—
78C4⋊#1055—21no—
79C4⋊#1055C2312yes—
80#19194—131nomaximal, Sylow
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13#4111yescharacteristic
84C2×C22⋊D13—22no—
85#6127—42no—
86#6127—42no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52C2×D412yes—
90C2×C4×D13—22no—
91C2×Dic26—21no—
92C2×Dic26—22no—
93C2×Dic26—22no—
94C2×C8×C13—22no—
95C2×C8×C13—24no—
96C2×C8×C13—82no—
97C2×C8×C13SD1614yescomplemented
98C2×C8×C13C2×D411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×D411yescharacteristic
102C42×C13C2×D411yescharacteristic
103C42×C13C2×D411yescharacteristic
104C42×C13#4111yescharacteristic
105C42×C13C2411yescharacteristic
106C22⋊Dic13—42no—
107#6103—22no—
108#6103—22no—
109C4⋊Dic13—21no—
110C4⋊Dic13—22no—
111C4⋊Dic13—22no—
112C4⋊Dic13—22no—
113C4⋊Dic13—22no—
114C4⋊Dic13C2×D412yes—
115#6101—42no—
116#6101—42no—
117C4×Dic13—42no—
118#6099—42no—
119C2×#1055—22no—
120#6095—84no—
121#6094—44no—
122C8×D13—44no—
123#3246—132no—
124#3160—131no—
125#2931—131no—
126#1695—132no—
127#1693—132no—
128#1671—134no—
129C2×#334D1311yescharacteristic, complemented
130#1550—132no—
131C23×C13#12111yescharacteristic
132C22×D13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—41no—
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13#12111yescharacteristic
138C2×C4×C13C2×SD1612yes—
139C2×C4×C13#13712yes—
140C2×C4×C13C22×D411yescharacteristic
141C2×C4×C13C22×D411yescharacteristic
142C2×C4×C13C2×#4111yescharacteristic
143C22⋊D13—44no—
144C2×Dic13—22no—
145C2×Dic13—42no—
146C2×Dic13—42no—
147D52—24no—
148D52—42no—
149D52—42no—
150C4×D13—42no—
151C4×D13—42no—
152Dic26—42no—
153Dic26—42no—
154Dic26—42no—
155Dic26—82no—
156C8×C13—21no—
157C8×C13—21no—
158C8×C13—44no—
159C8×C13C2×SD1612yes—
160C8×C13C2×SD1612yes—
161#1055—42no—
162C2×#131—261no—
163#533—132no—
164#532—131no—
165#500—131no—
166#500—131no—
167#499—261no—
168#499—261no—
169#498—132no—
170#476—134no—
171#475—262no—
172#465—264no—
173#461—134no—
174#460—262no—
175#436—132no—
176#436—261no—
177C8×D4—132no—
178C8×D4—261no—
179#427—261no—
180#427—261no—
181#423—131no—
182C2×C4⋊C8C2×D1312yes—
183#408—261no—
184C2×C4×C8C2×D1311yescharacteristic
185#334C2×D1312yes—
186#334C2×D1312yes—
187#333—134no—
188#332—134no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13#46112yes—
192C22×C13C2×#12111yescharacteristic
193C2×D13—42no—
194C2×D13—42no—
195C2×D13—42no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13#46112yes—
200C4×C13C22×SD1611yescharacteristic
201C4×C13C2×#13711yescharacteristic
202C4×C13#57712yes—
203Dic13—42no—
204Dic13—82no—
205Dic13—82no—
206C2×#41—261no—
207C2×SD16—264no—
208#131—524no—
209C2×M16—261no—
210C2×M16—262no—
211C22×C8—22no—
212C22×C8—262no—
213C22×C8D5211yescharacteristic
214C22×C8D5211yescharacteristic
215C4⋊Q8—131no—
216C4⋊Q8—132no—
217C4⋊Q8—132no—
218#127—131no—
219#125—262no—
220#124—261no—
221C22⋊Q8—262no—
222C22⋊Q8—262no—
223#121—132no—
224#121—261no—
225C4×Q8—262no—
226C4×Q8—262no—
227C4×D4—132no—
228C4×D4—261no—
229#117—262no—
230C2×C42C22×D1311yescharacteristic
231#107—261no—
232#107—261no—
233#107—261no—
234#107—261no—
235#106—264no—
236#106—262no—
237#106—262no—
238C4⋊C8—22no—
239C4⋊C8—132no—
240C4⋊C8—261no—
241C4⋊C8C22×D1314yes—
242#103—264no—
243#102—264no—
244C22⋊C8—262no—
245C22⋊C8—262no—
246C4×C8D5211yescharacteristic
247C4×C8D5211yescharacteristic
248C4×C8C22×D1311yescharacteristic
249C4×C8C22×D1311yescharacteristic
250C2×C13—22no—
251C2×C13C2×#46111yescharacteristic
252C2×C13#306011yescharacteristic
253C2×C13#306711yescharacteristic
254D13—82no—
255#41—522no—
256#41—522no—
257C2×Q8—261no—
258C2×Q8—262no—
259C2×Q8—262no—
260C2×D4—132no—
261C2×D4—262no—
262C2×D4—261no—
263C2×D4—261no—
264C22×C4—262no—
265C22×C4C2×D5211yescharacteristic
266C22×C4D4×D1311yescharacteristic
267C22×C4#613111yescharacteristic
268SD16—1044no—
269M16—522no—
270M16—524no—
271C2×C8—22no—
272C2×C8—24no—
273C2×C8—82no—
274C2×C8—262no—
275C2×C8—524no—
276C2×C8#609514yescomplemented
277C2×C8C2×D5211yescharacteristic
278C2×C8C2×D5211yescharacteristic
279C2×C8C2×D5211yescharacteristic
280C2×C8C2×D5211yescharacteristic
281C4⋊C4—132no—
282C4⋊C4—261no—
283C4⋊C4—262no—
284C4⋊C4—262no—
285C4⋊C4—262no—
286C4⋊C4—262no—
287C4⋊C4—522no—
288C4⋊C4—522no—
289C22⋊C4—262no—
290C22⋊C4—262no—
291C22⋊C4—522no—
292C42—522no—
293C42C2×D5211yescharacteristic
294C42D4×D1311yescharacteristic
295C42#613111yescharacteristic
296C42C23×D1311yescharacteristic
297C13#1919411yescharacteristic, complemented, Sylow
298C23—262no—
299C23#8814911yescharacteristic
300Q8—522no—
301Q8—522no—
302Q8—522no—
303Q8—1042no—
304D4—264no—
305D4—522no—
306D4—524no—
307D4—522no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—262no—
311C2×C4—522no—
312C2×C4—522no—
313C2×C4—522no—
314C2×C4—522no—
315C2×C4#8814911yescharacteristic
316C2×C4#8814911yescharacteristic
317C2×C4#8814911yescharacteristic
318C2×C4C2×#609512yes—
319C2×C4#8816312yes—
320C2×C4C22×D5211yescharacteristic
321C2×C4C2×D4×D1311yescharacteristic
322C2×C4C2×#613111yescharacteristic
323C8—21no—
324C8—21no—
325C8—44no—
326C8—522no—
327C8C2×#609512yes—
328C8C2×#609512yes—
329C22—21no—
330C22—21no—
331C22—522no—
332C22—522no—
333C22—522no—
334C22#1171850212yes—
335C22C2×#8814911yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—522no—
340C4—1042no—
341C4—1042no—
342C4#1171850212yes—
343C4C22×#609511yescharacteristic
344C4C2×#8816311yescharacteristic
345C4#1171946712yes—
346C2—22no—
347C2—1042no—
348C2C2×#1171850211yescharacteristic
349C2#1312449911yescharacteristic
350C2#1312455711yescharacteristic
subgroupG/H
centerC22C2×#88149
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#334C2
socleC22×C13C2×#121
prime radical#11719182C22
hypercenterC2×#334D13
hypocenterC13#19194
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. #13125350C2semidirect
4. #13114360C2semidirect
5. #13114350C2semidirect
6. #13114212C2semidirect
7. #13113524C2semidirect
8. C2×C13×#334C2semidirect
97. C2×C8×C13SD16semidirect
129. C2×#334D13semidirect
276. C2×C8#6095semidirect
297. C13#19194semidirect

Maximal subgroups

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

subgroupindex
#131261532
#131253502
#131235492
#131143602
#131143502
#131142122
#131135242
C2×C13×#3342
#1919413