Finite Group Databasebeta

← #15848268

Subgroups — #15848268

Order 3328.

676 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125957C211yesmaximal, characteristic
2#13124308C211yesmaximal, characteristic
3#13123917C211yesmaximal, characteristic, complemented
4#13114282C214yesmaximal, complemented
5#13114228C214yesmaximal, complemented
6#13113610C211yesmaximal, characteristic, complemented
7#13113508C211yesmaximal, characteristic, complemented
8#13113486C211yesmaximal, characteristic
9C2×C13×#462C211yesmaximal, characteristic, complemented
10C22×C13×Q16—21no—
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×C4×Q8×C13C2211yescharacteristic
13C2×#88196—21no—
14#11719182C2211yescharacteristic
15C13×#462—22no—
16C13×#462C2214yes—
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×#103—21no—
19#11718749C2212yes—
20#11718748—22no—
21#11718739C2212yes—
22#11718692C2212yes—
23#11718689—22no—
24#11718688C2212yes—
25Q8×#1055—22no—
26Q8×#1055C2214yes—
27#11718628—22no—
28#11718627—21no—
29#11718586—22no—
30#11718586C2211yescharacteristic
31#11718586C2211yescharacteristic
32#11718585C2211yescharacteristic
33#11718139C2214yes—
34#11718077C2212yes—
35#11718074C2212yes—
36#11718071C2214yes—
37C22×Q8×C13—21no—
38C22×Q8×C13D411yescharacteristic
39C2×#6127—21no—
40C2×C13×Q16—24no—
41C2×C13×Q16—44no—
42C22×C8×C13—21no—
43C13×C4⋊Q8—21no—
44C13×C4⋊Q8—21no—
45C13×C4⋊Q8—21no—
46C13×C4⋊Q8C2312yes—
47C4×Q8×C13—21no—
48C4×Q8×C13—21no—
49C4×Q8×C13D412yes—
50C4×Q8×C13C2312yes—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4D411yescharacteristic
55C2×C42×C13—21no—
56C2×C42×C13C2311yescharacteristic
57C2×#6107—22no—
58#88196—44no—
59C2×#6106—22no—
60#88184—21no—
61#88184—21no—
62C2×#6099—21no—
63#88129—21no—
64#88128C2311yescharacteristic
65C4×D52—21no—
66C4×D52—21no—
67#88123C2311yescharacteristic
68C13×C4⋊C8—21no—
69C13×C4⋊C8C2312yes—
70C13×#103—24no—
71C22⋊#1055—21no—
72C22⋊#1055D412yes—
73#88050—22no—
74#88049—22no—
75#88049—24no—
76#88047—24no—
77C4⋊#1055—21no—
78C4⋊#1055—24no—
79C4⋊#1055D412yes—
80C4⋊#1055C2312yes—
81C4⋊#1055C2312yes—
82C4×#1055—21no—
83C4×#1055—24no—
84C4×#1055C2312yes—
85#19404—131nomaximal, Sylow
86C2×Q8×C13—21no—
87C2×Q8×C13—22no—
88C2×Q8×C13—22no—
89C2×Q8×C13—41no—
90C2×Q8×C13—42no—
91C2×Q8×C13—42no—
92C2×Q8×C13D814yes—
93C2×Q8×C13C2×D412yes—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—41no—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13#4111yescharacteristic
100C2×C22⋊D13—41no—
101#6127—42no—
102#6127—42no—
103C2×D52—21no—
104C2×D52—21no—
105C2×D52—21no—
106C2×C4×D13—41no—
107C2×Dic26—21no—
108C13×Q16—48no—
109C2×C8×C13—22no—
110C2×C8×C13—42no—
111C13×C4⋊C4—22no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—22no—
115C13×C4⋊C4—22no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4C2×D412yes—
119C42×C13—22no—
120C42×C13—22no—
121C42×C13C2×D411yescharacteristic
122C42×C13C2×D411yescharacteristic
123C42×C13#4111yescharacteristic
124C42×C13C2411yescharacteristic
125#6107—44no—
126#6106—44no—
127#6103—41no—
128#6103—41no—
129C4⋊Dic13—21no—
130C4⋊Dic13—21no—
131#6099—42no—
132C2×#1055—22no—
133C2×#1055—22no—
134C2×#1055C2×D414yes—
135#3226—131no—
136#3037—131no—
137C2×#462D1311yescharacteristic, complemented
138#2982—131no—
139#1682—134no—
140#1674—134no—
141#1571—131no—
142#1546—131no—
143#1540—131no—
144C23×C13#12111yescharacteristic
145C22×D13—41no—
146Q8×C13—22no—
147Q8×C13—24no—
148Q8×C13—42no—
149Q8×C13—42no—
150Q8×C13—82no—
151Q8×C13C2×D814yes—
152C2×C4×C13—22no—
153C2×C4×C13—24no—
154C2×C4×C13—22no—
155C2×C4×C13—22no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—81no—
159C2×C4×C13—82no—
160C2×C4×C13#12111yescharacteristic
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13C2×D812yes—
164C2×C4×C13#13512yes—
165C2×C4×C13C22×D411yescharacteristic
166C2×C4×C13C22×D411yescharacteristic
167C2×C4×C13C2×#4111yescharacteristic
168C22⋊D13—82no—
169C2×Dic13—41no—
170D52—41no—
171D52—41no—
172D52—42no—
173D52—81no—
174C4×D13—82no—
175Dic26—41no—
176Dic26—41no—
177C8×C13—42no—
178#1055—24no—
179#1055—42no—
180#1055—42no—
181C2×#137—261no—
182C22×Q16—21no—
183#532—131no—
184C2×C4⋊Q8C2×D1311yescharacteristic
185C2×C4×Q8C2×D1311yescharacteristic
186#500—132no—
187#486—132no—
188#480—262no—
189#474—262no—
190#464—262no—
191#462—22no—
192#462—132no—
193#462C2×D1314yes—
194#460—132no—
195C8×Q8—134no—
196C8×Q8—262no—
197#431—131no—
198#431—131no—
199#431—262no—
200#423—131no—
201C2×C4⋊C8C2×D1311yescharacteristic
202#417—261no—
203C2×#103—21no—
204#335—134no—
205#332—134no—
206#332—132no—
207#331—132no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13#46612yes—
211C22×C13C2×#12111yescharacteristic
212C2×D13—81no—
213C2×D13—81no—
214C2×D13—81no—
215C4×C13—21no—
216C4×C13—24no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—42no—
220C4×C13—82no—
221C4×C13#46612yes—
222C4×C13C22×D811yescharacteristic
223C4×C13C2×#13511yescharacteristic
224C4×C13#57812yes—
225Dic13—81no—
226C2×#41—261no—
227C22×Q8—21no—
228C22×Q8C22⋊D1311yescharacteristic
229#137—524no—
230C2×Q16—24no—
231C2×Q16—44no—
232C2×Q16—262no—
233C2×SD16—262no—
234C2×M16—261no—
235C22×C8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—131no—
240C4⋊Q8C22×D1312yes—
241#127—131no—
242#124—261no—
243#121—261no—
244#121—261no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8C22⋊D1312yes—
248C4×Q8C22×D1312yes—
249C4×D4—261no—
250C4×D4—261no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4C22⋊D1311yescharacteristic
255C2×C42—21no—
256C2×C42C22×D1311yescharacteristic
257#107—264no—
258C4⋊C8—21no—
259C4⋊C8—132no—
260C4⋊C8—132no—
261C4⋊C8—132no—
262C4⋊C8—264no—
263C4⋊C8—261no—
264C4⋊C8C22×D1312yes—
265#103—24no—
266#103—262no—
267#102—264no—
268#102—262no—
269C22⋊C8—132no—
270C22⋊C8—261no—
271C4×C8—132no—
272C4×C8—264no—
273C4×C8—261no—
274C2×C13—22no—
275C2×C13#304411yescharacteristic
276C2×C13C2×#46611yescharacteristic
277C2×C13#306911yescharacteristic
278D13—161no—
279#41—522no—
280#41—522no—
281C2×Q8—21no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—42no—
286C2×Q8—42no—
287C2×Q8—261no—
288C2×Q8#610414yes—
289C2×Q8C2×C22⋊D1312yes—
290C2×D4—261no—
291C2×D4—261no—
292C2×D4—261no—
293C2×D4—521no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—41no—
297C22×C4—521no—
298C22×C4D4×D1311yescharacteristic
299C22×C4#612911yescharacteristic
300C22×C4C2×C22⋊D1311yescharacteristic
301Q16—48no—
302Q16—524no—
303SD16—524no—
304M16—522no—
305C2×C8—22no—
306C2×C8—42no—
307C2×C8—134no—
308C2×C8—262no—
309C2×C8—262no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—261no—
318C4⋊C4—261no—
319C4⋊C4C2×C22⋊D1312yes—
320C22⋊C4—521no—
321C22⋊C4—521no—
322C42—22no—
323C42—22no—
324C42D4×D1311yescharacteristic
325C42#612911yescharacteristic
326C42C2×C22⋊D1311yescharacteristic
327C42C23×D1311yescharacteristic
328C13#1940411yescharacteristic, complemented, Sylow
329C23—521no—
330C23#8819311yescharacteristic
331Q8—24no—
332Q8—22no—
333Q8—42no—
334Q8—42no—
335Q8—82no—
336Q8—521no—
337Q8—521no—
338Q8C2×#610414yes—
339D4—522no—
340D4—521no—
341D4—521no—
342D4—1041no—
343D4—1042no—
344C2×C4—24no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—81no—
351C2×C4—82no—
352C2×C4—521no—
353C2×C4—1042no—
354C2×C4C2×#610412yes—
355C2×C4#8819311yescharacteristic
356C2×C4#8819311yescharacteristic
357C2×C4#8819311yescharacteristic
358C2×C4#8820412yes—
359C2×C4C2×D4×D1311yescharacteristic
360C2×C4C2×#612911yescharacteristic
361C2×C4C22×C22⋊D1311yescharacteristic
362C8—42no—
363C8—264no—
364C8—522no—
365C8—522no—
366C22—21no—
367C22—21no—
368C22—1041no—
369C22—1041no—
370C22—1041no—
371C22#1171869912yes—
372C22C2×#8819311yescharacteristic
373C4—21no—
374C4—24no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—82no—
379C4—1041no—
380C4#1171869912yes—
381C4#1171947112yes—
382C4C22×#610411yescharacteristic
383C4C2×#8820411yescharacteristic
384C2—22no—
385C2—2081no—
386C2#1312436311yescharacteristic
387C2C2×#1171869911yescharacteristic
388C2#1312457011yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#462C2
socleC22×C13C2×#121
prime radical#11719182C22
hypercenterC2×#462D13
hypocenterC13#19404
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #13123917C2semidirect
4. #13114282C2semidirect
5. #13114228C2semidirect
6. #13113610C2semidirect
7. #13113508C2semidirect
9. C2×C13×#462C2semidirect
137. C2×#462D13semidirect
328. C13#19404semidirect

Maximal subgroups

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

subgroupindex
#131259572
#131243082
#131239172
#131142822
#131142282
#131136102
#131135082
#131134862
C2×C13×#4622
#1940413