Finite Group Databasebeta

← #15758812

Subgroups — #15758812

Order 3328.

562 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124316C211yesmaximal, characteristic
2#13113505C211yesmaximal, characteristic, complemented
3C2×#11718077C211yesmaximal, characteristic, complemented
4#13113223C211yesmaximal, characteristic, complemented
5#13112733C211yesmaximal, characteristic, complemented
6#13112710C211yesmaximal, characteristic, complemented
7C13×#2906C211yesmaximal, characteristic, complemented
8C2×C13×#131—21no—
9C4×C13×#41C2211yescharacteristic
10C2×#88203—21no—
11C2×#88128C2211yescharacteristic
12C13×#424—21no—
13C13×#424—22no—
14C13×#423—21no—
15C13×#423C2211yescharacteristic
16C2×C13×C4⋊C8—21no—
17C2×C13×C4⋊C8C2211yescharacteristic
18#11718688—21no—
19#11718688C412yes—
20#11718676—21no—
21#11718676C412yes—
22#11718662—21no—
23#11718586C2211yescharacteristic
24#11718585C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26Q8⋊#1055—21no—
27D4⋊#1055—21no—
28#11718077—21no—
29#11718077—21no—
30#11718077—22no—
31C2×C13×#41D411yescharacteristic
32C22×D52—21no—
33C22×D52—21no—
34C22×D52—21no—
35C13×#131—42no—
36C13×#131—42no—
37C2×C13×M16—22no—
38C2×C13×M16—21no—
39C22×C8×C13—22no—
40C22×C8×C13—21no—
41C4×Q8×C13C2×C411yescharacteristic
42C4×Q8×C13D411yescharacteristic
43C4×D4×C13—21no—
44C4×D4×C13—21no—
45C4×D4×C13C2×C411yescharacteristic
46C4×D4×C13D411yescharacteristic
47C13×#117—21no—
48C13×#117D411yescharacteristic
49C2×C42×C13—21no—
50C2×C42×C13C2311yescharacteristic
51#88203—42no—
52#88203—42no—
53C2×#6106—22no—
54C2×#6104—22no—
55C2×#6099—21no—
56C22×#1055—21no—
57#88128—21no—
58#88128—21no—
59#88128—21no—
60#88128C2×C412yes—
61C13×C4⋊C8—22no—
62C13×C4⋊C8—22no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8D411yescharacteristic
66C13×C4⋊C8D411yescharacteristic
67C13×C4⋊C8D412yes—
68C22⋊#1055—21no—
69#88049—22no—
70#88049—22no—
71C4⋊#1055—21no—
72C4⋊#1055—21no—
73C4⋊#1055—21no—
74C4⋊#1055—21no—
75C4⋊#1055C2×C412yes—
76C4×#1055—21no—
77#9173—131nomaximal, Sylow
78C23×D13—41no—
79C13×#41—21no—
80C13×#41—21no—
81C13×#41D812yes—
82C13×#41SD1612yes—
83C2×Q8×C13C22⋊C411yescharacteristic
84C2×D4×C13—21no—
85C2×D4×C13C22⋊C411yescharacteristic
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13#4111yescharacteristic
91C22×C4×C13#4111yescharacteristic
92C2×D52—22no—
93C2×D52—22no—
94C2×D52—22no—
95C2×D52—41no—
96C2×D52—41no—
97C2×D52—41no—
98C2×D52—41no—
99C2×D52—41no—
100C2×D52—41no—
101C2×D52—41no—
102C2×D52—82no—
103C2×D52—81no—
104C2×D52—81no—
105C13×M16—44no—
106C13×M16—41no—
107C13×M16—41no—
108C2×C8×C13—21no—
109C2×C8×C13—22no—
110C2×C8×C13—21no—
111C2×C8×C13—44no—
112C2×C8×C13—41no—
113C2×C8×C13—41no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4C22⋊C411yescharacteristic
117C13×C4⋊C4C22⋊C411yescharacteristic
118C13×C22⋊C4—21no—
119C13×C22⋊C4—21no—
120C13×C22⋊C4—21no—
121C42×C13—21no—
122C42×C13—21no—
123C42×C13—21no—
124C42×C13C22×C411yescharacteristic
125C42×C13C2×D411yescharacteristic
126C42×C13C2×D411yescharacteristic
127C42×C13C2×D411yescharacteristic
128#6106—44no—
129#6104—44no—
130#6099—41no—
131#6099—41no—
132C2×#1055—22no—
133C2×#1055—41no—
134C2×#1055—41no—
135C2×#1055—81no—
136#3038—131no—
137#2906D1311yescharacteristic, complemented
138#1545—131no—
139C2×#331—131no—
140#1477—131no—
141#1301—131no—
142#1292—131no—
143C23×C13—21no—
144C23×C13#12311yescharacteristic
145C22×D13—42no—
146C22×D13—82no—
147C22×D13—82no—
148C22×D13—81no—
149C22×D13—81no—
150Q8×C13—21no—
151Q8×C13#10212yes—
152D4×C13—22no—
153D4×C13—22no—
154D4×C13—21no—
155D4×C13#10212yes—
156C2×C4×C13—21no—
157C2×C4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—81no—
167C2×C4×C13C2×C22⋊C411yescharacteristic
168C2×C4×C13C4×D411yescharacteristic
169C2×C4×C13C4×D411yescharacteristic
170C2×C4×C13#12011yescharacteristic
171C2×C4×C13#12111yescharacteristic
172C2×C4×C13#12111yescharacteristic
173C2×C4×C13C2×D811yescharacteristic
174C2×C4×C13C2×SD1611yescharacteristic
175C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C13#13711yescharacteristic
177D52—42no—
178D52—42no—
179D52—82no—
180D52—82no—
181D52—82no—
182D52—81no—
183D52—81no—
184D52—81no—
185D52—81no—
186C8×C13—41no—
187C8×C13—42no—
188C8×C13—41no—
189#1055—42no—
190#1055—81no—
191#1055—81no—
192C2×AGL(1,ℤ/8)—261no—
193C2×#131—21no—
194C2×#127—131no—
195C4×#41C2×D1311yescharacteristic
196#460—132no—
197#460—261no—
198#459—132no—
199#459—261no—
200#431—131no—
201#424—21no—
202#424—22no—
203#423—21no—
204#423—131no—
205#423C2×D1311yescharacteristic
206C2×C4⋊C8—21no—
207C2×C4⋊C8—131no—
208C2×C4⋊C8C2×D1311yescharacteristic
209#418—261no—
210#331—261no—
211#331—261no—
212#331—262no—
213Q8⋊C8—261no—
214D4⋊C8—261no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—22no—
218C22×C13—41no—
219C22×C13—41no—
220C22×C13#38611yescharacteristic
221C22×C13#48011yescharacteristic
222C22×C13#48111yescharacteristic
223C2×D13—82no—
224C2×D13—82no—
225C2×D13—82no—
226C2×D13—162no—
227C2×D13—162no—
228C4×C13—22no—
229C4×C13—21no—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—41no—
233C4×C13—41no—
234C4×C13C2×#10211yescharacteristic
235C4×C13#41711yescharacteristic
236C4×C13#44711yescharacteristic
237C4×C13#44811yescharacteristic
238C4×C13#47111yescharacteristic
239C4×C13#47211yescharacteristic
240C2×#41C22⋊D1311yescharacteristic
241C22×D4—261no—
242C22×D4—261no—
243C22×D4—261no—
244AGL(1,ℤ/8)—522no—
245AGL(1,ℤ/8)—522no—
246C2×SD16—262no—
247C2×D8—262no—
248#131—42no—
249#131—42no—
250C2×M16—22no—
251C2×M16—21no—
252C2×M16—261no—
253C22×C8—22no—
254C22×C8—21no—
255C22×C8—261no—
256#127—132no—
257#127—261no—
258#127—261no—
259#127—261no—
260C4×Q8C4×D1311yescharacteristic
261C4×Q8D5211yescharacteristic
262C4×D4—21no—
263C4×D4—21no—
264C4×D4C4×D1311yescharacteristic
265C4×D4D5211yescharacteristic
266#117—21no—
267#117C22⋊D1311yescharacteristic
268C2×C42—21no—
269C2×C42C22×D1311yescharacteristic
270C4⋊C8—22no—
271C4⋊C8—22no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—132no—
275C4⋊C8—261no—
276C4⋊C8—261no—
277C4⋊C8—261no—
278C4⋊C8—261no—
279C4⋊C8C22⋊D1311yescharacteristic
280C4⋊C8C22⋊D1311yescharacteristic
281C4⋊C8C22⋊D1312yes—
282#102—262no—
283#102—262no—
284C22⋊C8—261no—
285C4×C8—261no—
286C2×C13—21no—
287C2×C13—21no—
288C2×C13—42no—
289C2×C13#187411yescharacteristic
290C2×C13#190311yescharacteristic
291C2×C13#190711yescharacteristic
292D13—162no—
293C24—521no—
294#41—21no—
295#41—21no—
296#41#610412yes—
297#41#610612yes—
298C2×Q8#610311yescharacteristic
299C2×D4—21no—
300C2×D4—262no—
301C2×D4—262no—
302C2×D4—262no—
303C2×D4—521no—
304C2×D4—521no—
305C2×D4—521no—
306C2×D4—521no—
307C2×D4—521no—
308C2×D4—521no—
309C2×D4—521no—
310C2×D4—1041no—
311C2×D4—1041no—
312C2×D4—1042no—
313C2×D4#610311yescharacteristic
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4#612711yescharacteristic
318C22×C4#612711yescharacteristic
319C22×C4C2×C22⋊D1311yescharacteristic
320SD16—524no—
321D8—524no—
322M16—44no—
323M16—41no—
324M16—41no—
325M16—521no—
326M16—521no—
327C2×C8—21no—
328C2×C8—22no—
329C2×C8—21no—
330C2×C8—44no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—262no—
334C2×C8—521no—
335C2×C8—521no—
336C2×C8—1041no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4#610311yescharacteristic
340C4⋊C4#610311yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C42—21no—
345C42—21no—
346C42—21no—
347C42C2×C4×D1311yescharacteristic
348C42C2×D5211yescharacteristic
349C42C2×C22⋊D1311yescharacteristic
350C42C2×C22⋊D1311yescharacteristic
351C13#917311yescharacteristic, complemented, Sylow
352C23—21no—
353C23—522no—
354C23—1042no—
355C23—1042no—
356C23—1041no—
357C23—1041no—
358C23#8818311yescharacteristic
359Q8—21no—
360Q8#8804912yes—
361D4—22no—
362D4—22no—
363D4—21no—
364D4—522no—
365D4—522no—
366D4—1042no—
367D4—1042no—
368D4—1042no—
369D4—1041no—
370D4—1041no—
371D4—1041no—
372D4—1041no—
373D4#8804912yes—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4C2×#610311yescharacteristic
386C2×C4C4×C22⋊D1311yescharacteristic
387C2×C4C4×C22⋊D1311yescharacteristic
388C2×C4#8818411yescharacteristic
389C2×C4#8818411yescharacteristic
390C2×C4C2×#610411yescharacteristic
391C2×C4#8818611yescharacteristic
392C2×C4C2×#610611yescharacteristic
393C2×C4#8819611yescharacteristic
394C2×C4#8820711yescharacteristic
395C8—41no—
396C8—42no—
397C8—41no—
398C8—522no—
399C8—1041no—
400C8—1041no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—41no—
405C22—41no—
406C22—1042no—
407C22—1042no—
408C22—1042no—
409C22—2082no—
410C22—2082no—
411C22#1171862811yescharacteristic
412C22#1171862911yescharacteristic
413C22#1171887411yescharacteristic
414C4—22no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4C2×#8804911yescharacteristic
421C4#1171862711yescharacteristic
422C4#1171880211yescharacteristic
423C4#1171880311yescharacteristic
424C4#1171887811yescharacteristic
425C4#1171888811yescharacteristic
426C2—21no—
427C2—21no—
428C2—42no—
429C2—2082no—
430C2#1311515311yescharacteristic
431C2#1311531611yescharacteristic
432C2#1311534411yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2906C2
socleC22×C13#386
prime radical#13124316C2
cosocleC2×C42×C13C23
hypercenter#2906D13
hypocenterC13#9173
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #13113505C2semidirect
3. C2×#11718077C2semidirect
4. #13113223C2semidirect
5. #13112733C2semidirect
6. #13112710C2semidirect
7. C13×#2906C2semidirect
137. #2906D13semidirect
351. C13#9173semidirect

Maximal subgroups

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

subgroupindex
#131243162
#131135052
C2×#117180772
#131132232
#131127332
#131127102
C13×#29062
#917313