Finite Group Databasebeta

← #15764182

Subgroups — #15764182

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718748C211yesmaximal, characteristic
2#13119790C211yesmaximal, characteristic
3#13115760C211yesmaximal, characteristic, complemented
4C2×#11718139C211yesmaximal, characteristic, complemented
5C2×#11718051C211yesmaximal, characteristic
6#13112676C211yesmaximal, characteristic, complemented
7C2×C13×#500C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×#88200—22no—
11C2×C4×D52C2211yescharacteristic
12C13×#500—22no—
13C13×#500—22no—
14C2×C13×#107—22no—
15C2×C4×C8×C13C2211yescharacteristic
16C2×#88075—22no—
17#11718748—22no—
18#11718748—22no—
19#11718653—22no—
20#11718649—21no—
21#11718637—21no—
22C2×#88049—21no—
23C2×#88047—21no—
24C4×C4⋊Dic13C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26C2×C4⋊#1055C2211yescharacteristic
27#11718139—22no—
28#11718051—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13—21no—
31C22×D52D411yescharacteristic
32C22×C4×D13—21no—
33C22×C8×C13—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8D412yes—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4D412yes—
46C2×C42×C13C2311yescharacteristic
47#88200—44no—
48#88200—44no—
49C2×#6103—24no—
50C2×#6103—21no—
51C2×C4⋊Dic13D411yescharacteristic
52C2×C4⋊Dic13D412yes—
53C2×#6101—24no—
54C2×C4×Dic13—21no—
55C22×#1055—21no—
56C22×#1055—21no—
57C4×D52—21no—
58C4×D52—21no—
59C4×D52—21no—
60C4×D52—21no—
61C13×#107—28no—
62C4×C8×C13—21no—
63C4×C8×C13D412yes—
64#88075—44no—
65#88071—21no—
66#88049—24no—
67#88047—24no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4⋊#1055D412yes—
72#10076—131nomaximal, Sylow
73C23×D13—21no—
74C2×Q8×C13—22no—
75C2×Q8×C13—41no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C2×Q8×C13—42no—
79C2×Q8×C13—42no—
80C2×Q8×C13—42no—
81C2×Q8×C13—42no—
82C22×C4×C13—22no—
83C22×C4×C13—41no—
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C22×Dic13—22no—
88C22×Dic13—21no—
89C2×D52—21no—
90C2×D52—21no—
91C2×D52—21no—
92C2×D52—21no—
93C2×D52—21no—
94C2×D52Q1612yes—
95C2×C4×D13—41no—
96C2×C4×D13—41no—
97C2×C4×D13—42no—
98C2×C4×D13—42no—
99C2×C8×C13—24no—
100C2×C8×C13—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13C2×D411yescharacteristic
112C42×C13#4111yescharacteristic
113#6103—48no—
114#6103—41no—
115#6103—41no—
116C4⋊Dic13—22no—
117C4⋊Dic13—21no—
118C4⋊Dic13—21no—
119C4⋊Dic13D814yes—
120#6101—48no—
121C4×Dic13—41no—
122C4×Dic13—41no—
123C2×#1055—22no—
124C2×#1055—41no—
125C2×#1055—41no—
126C2×#1055—41no—
127C2×#1055—42no—
128C2×#500D1311yescharacteristic, complemented
129C2×#474—131no—
130#2542—131no—
131#1981—131no—
132C2×#332—131no—
133C2×D4⋊C8—131no—
134#1279—131no—
135C23×C13#12011yescharacteristic
136C22×D13—22no—
137C22×D13—41no—
138C22×D13—42no—
139C22×D13—41no—
140C22×D13—42no—
141Q8×C13—44no—
142Q8×C13—82no—
143Q8×C13—81no—
144Q8×C13—81no—
145Q8×C13—81no—
146Q8×C13—81no—
147C2×C4×C13—22no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—44no—
151C2×C4×C13—82no—
152C2×C4×C13#12011yescharacteristic
153C2×C4×C13#12011yescharacteristic
154C2×C4×C13#12111yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13#12111yescharacteristic
157C2×C4×C13#12711yescharacteristic
158C2×C4×C13C2×D812yes—
159C2×C4×C13C2×Q1611yescharacteristic
160C2×C4×C13#13511yescharacteristic
161C2×C4×C13AGL(1,ℤ/8)12yes—
162C2×C4×C13#13711yescharacteristic
163C2×C4×C13#13711yescharacteristic
164C2×Dic13—24no—
165C2×Dic13—42no—
166C2×Dic13—42no—
167C2×Dic13—41no—
168C2×Dic13—42no—
169D52—22no—
170D52—22no—
171D52—41no—
172D52—41no—
173C4×D13—82no—
174C4×D13—81no—
175C4×D13—81no—
176C8×C13—24no—
177#1055—42no—
178#1055—81no—
179C2×C4⋊Q8C2×D1311yescharacteristic
180C2×C4⋊Q8C2×D1311yescharacteristic
181C2×C22⋊Q8—262no—
182C2×C4×D4—131no—
183#500—22no—
184#500—22no—
185#474—262no—
186#474—262no—
187C2×#107—22no—
188C2×#107—261no—
189C2×C4⋊C8—131no—
190C2×C4⋊C8—131no—
191C2×#103—262no—
192C2×#102—261no—
193C2×C4×C8C2×D1311yescharacteristic
194#399—262no—
195#390—261no—
196#384—261no—
197C4×C4⋊C4—131no—
198#332—262no—
199D4⋊C8—262no—
200C22×C13#39211yescharacteristic
201C22×C13#44712yes—
202C22×C13#45111yescharacteristic
203C22×C13#45211yescharacteristic
204C22×C13#45612yes—
205C2×D13—44no—
206C2×D13—42no—
207C2×D13—82no—
208C2×D13—81no—
209C2×D13—81no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—82no—
213C4×C13—82no—
214C4×C13#45111yescharacteristic
215C4×C13#45211yescharacteristic
216C4×C13#45912yes—
217C4×C13#46711yescharacteristic
218C4×C13#47011yescharacteristic
219C4×C13#49311yescharacteristic
220C4×C13#49611yescharacteristic
221Dic13—44no—
222Dic13—81no—
223C22×Q8—21no—
224C22×Q8—21no—
225C22×D4—131no—
226C23×C4—261no—
227C22×C8—21no—
228C22×C8—261no—
229C22×C8—261no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8C22⋊D1312yes—
238C22⋊Q8—524no—
239C22⋊Q8—524no—
240C4×D4—261no—
241C4×D4—261no—
242C4×D4—261no—
243C4×D4—261no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—132no—
248C2×C4⋊C4—131no—
249C2×C4⋊C4—264no—
250C2×C4⋊C4C22⋊D1312yes—
251C2×C22⋊C4—264no—
252C2×C22⋊C4—261no—
253C2×C42—261no—
254C2×C42C22×D1311yescharacteristic
255#107—28no—
256#107—264no—
257C4⋊C8—132no—
258C4⋊C8—261no—
259C4⋊C8—261no—
260C4⋊C8—261no—
261#103—524no—
262#102—264no—
263C4×C8—21no—
264C4×C8C22⋊D1312yes—
265#95—261no—
266C2×C13#164712yes—
267C2×C13#164912yes—
268C2×C13#200111yescharacteristic
269C2×C13#200511yescharacteristic
270C2×C13#201111yescharacteristic
271D13—82no—
272C24—261no—
273C2×Q8—22no—
274C2×Q8—42no—
275C2×Q8—42no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—42no—
280C2×Q8—42no—
281C2×D4—132no—
282C2×D4—261no—
283C2×D4—261no—
284C2×D4—261no—
285C2×D4—261no—
286C2×D4—261no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4—262no—
290C22×C4—261no—
291C22×C4—522no—
292C22×C4—522no—
293C22×C4—521no—
294C22×C4—521no—
295C22×C4D4×D1311yescharacteristic
296C22×C4D4×D1311yescharacteristic
297C22×C4C2×C22⋊D1311yescharacteristic
298C2×C8—24no—
299C2×C8—22no—
300C2×C8—262no—
301C2×C8—521no—
302C2×C8—521no—
303C2×C8—522no—
304C2×C8—521no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—134no—
314C4⋊C4—262no—
315C4⋊C4—261no—
316C4⋊C4—261no—
317C4⋊C4—528no—
318C22⋊C4—528no—
319C22⋊C4—521no—
320C22⋊C4—521no—
321C42—521no—
322C42—521no—
323C42D4×D1311yescharacteristic
324C42#612911yescharacteristic
325C42C2×C22⋊D1311yescharacteristic
326C42C2×C22⋊D1311yescharacteristic
327C13#1007611yescharacteristic, complemented, Sylow
328C23—262no—
329C23—522no—
330C23—522no—
331C23—521no—
332C23—521no—
333C23#8819111yescharacteristic
334Q8—44no—
335Q8—82no—
336Q8—81no—
337Q8—81no—
338Q8—81no—
339Q8—81no—
340D4—262no—
341D4—262no—
342D4—521no—
343D4—521no—
344C2×C4—22no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—82no—
349C2×C4—264no—
350C2×C4—522no—
351C2×C4—522no—
352C2×C4—522no—
353C2×C4—521no—
354C2×C4—1042no—
355C2×C4—1041no—
356C2×C4—1041no—
357C2×C4D8×D1312yes—
358C2×C4#8816512yes—
359C2×C4Q16×D1311yescharacteristic
360C2×C4#8817211yescharacteristic
361C2×C4#8817211yescharacteristic
362C2×C4#8817311yescharacteristic
363C2×C4#8819111yescharacteristic
364C2×C4#8819211yescharacteristic
365C2×C4#8819311yescharacteristic
366C2×C4#8819311yescharacteristic
367C2×C4#8819411yescharacteristic
368C2×C4#8820711yescharacteristic
369C8—24no—
370C8—522no—
371C8—1041no—
372C22—522no—
373C22—524no—
374C22—1041no—
375C22—1042no—
376C22—1041no—
377C22#1171875612yes—
378C22#1171881712yes—
379C22#1171884711yescharacteristic
380C22#1171884811yescharacteristic
381C22#1171888411yescharacteristic
382C4—21no—
383C4—21no—
384C4—82no—
385C4—82no—
386C4—524no—
387C4—1041no—
388C4#1171881112yes—
389C4#1171881211yescharacteristic
390C4#1171881511yescharacteristic
391C4#1171884711yescharacteristic
392C4#1171884811yescharacteristic
393C4#1171884911yescharacteristic
394C4#1171885011yescharacteristic
395C2—1042no—
396C2#1311406812yes—
397C2#1311408212yes—
398C2#1311584311yescharacteristic
399C2#1311587211yescharacteristic
400C2#1311590511yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#500C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenterC2×#500D13
hypocenterC13#10076
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
3. #13115760C2semidirect
4. C2×#11718139C2semidirect
6. #13112676C2semidirect
7. C2×C13×#500C2semidirect
128. C2×#500D13semidirect
327. C13#10076semidirect

Maximal subgroups

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

subgroupindex
C2×#117187482
#131197902
#131157602
C2×#117181392
C2×#117180512
#131126762
C2×C13×#5002
#1007613