Finite Group Databasebeta

← #15758821

Subgroups — #15758821

Order 3328.

516 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123502C211yesmaximal, characteristic, complemented
2#13113504C211yesmaximal, characteristic, complemented
3C2×#11718136C211yesmaximal, characteristic, complemented
4#13113223C211yesmaximal, characteristic, complemented
5#13112731C211yesmaximal, characteristic, complemented
6#13112710C211yesmaximal, characteristic, complemented
7C13×#3038C211yesmaximal, characteristic
8C2×C13×AGL(1,ℤ/8)—21no—
9C2×C13×#127C2211yescharacteristic
10C4×C13×#41C2211yescharacteristic
11C13×#460—21no—
12C13×#460C412yes—
13C13×#459—21no—
14C13×#459C412yes—
15C13×#423C2211yescharacteristic
16C13×#418—21no—
17#11718895—21no—
18#11718661—22no—
19#11718658—21no—
20#11718587—21no—
21#11718586—21no—
22#11718586C2211yescharacteristic
23#11718585C2211yescharacteristic
24C2×C4⋊#1055C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26#11718136—21no—
27#11718136—21no—
28#11718136—22no—
29Q8⋊#1055—21no—
30D4⋊#1055—21no—
31C2×C13×#41D411yescharacteristic
32C22×D4×C13—21no—
33C22×D4×C13—21no—
34C22×D4×C13—21no—
35C13×AGL(1,ℤ/8)—42no—
36C13×AGL(1,ℤ/8)—42no—
37C2×C13×SD16—22no—
38C2×C13×D8—22no—
39C2×C13×M16—21no—
40C13×#127—21no—
41C13×#127—21no—
42C13×#127—21no—
43C13×#127C2×C412yes—
44C4×Q8×C13C2×C411yescharacteristic
45C4×Q8×C13D411yescharacteristic
46C4×D4×C13—21no—
47C4×D4×C13—21no—
48C4×D4×C13C2×C411yescharacteristic
49C4×D4×C13D411yescharacteristic
50C13×#117—21no—
51C13×#117D411yescharacteristic
52C2×C42×C13—21no—
53C2×C42×C13C2311yescharacteristic
54C2×#6099—21no—
55C22×#1055—21no—
56C22×#1055—21no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8C2×C412yes—
59C13×#102—22no—
60C13×#102—22no—
61C22⋊#1055—22no—
62C22⋊#1055—22no—
63C22⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055D412yes—
70C4⋊#1055D411yescharacteristic
71C4⋊#1055D411yescharacteristic
72#88043—22no—
73C4×#1055—22no—
74C4×#1055—21no—
75#9174—131nomaximal, Sylow
76C24×C13—41no—
77C13×#41—21no—
78C13×#41—21no—
79C13×#41—21no—
80C13×#41—21no—
81C2×Q8×C13C22⋊C411yescharacteristic
82C2×D4×C13—21no—
83C2×D4×C13—22no—
84C2×D4×C13—22no—
85C2×D4×C13—22no—
86C2×D4×C13—41no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—81no—
94C2×D4×C13—81no—
95C2×D4×C13—82no—
96C2×D4×C13C22⋊C411yescharacteristic
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13#4111yescharacteristic
102C22×C4×C13#4111yescharacteristic
103C13×SD16—44no—
104C13×D8—44no—
105C13×M16—41no—
106C13×M16—41no—
107C2×C8×C13—22no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4C22⋊C411yescharacteristic
111C13×C4⋊C4C22⋊C411yescharacteristic
112C13×C22⋊C4—21no—
113C13×C22⋊C4—21no—
114C13×C22⋊C4—21no—
115C42×C13—21no—
116C42×C13—21no—
117C42×C13—21no—
118C42×C13C22×C411yescharacteristic
119C42×C13C2×D411yescharacteristic
120C42×C13C2×D411yescharacteristic
121C42×C13C2×D411yescharacteristic
122#6099—41no—
123#6099—41no—
124C2×#1055—21no—
125C2×#1055—21no—
126C2×#1055—22no—
127C2×#1055—41no—
128C2×#1055—41no—
129C2×#1055—41no—
130C2×#1055—41no—
131C2×#1055—81no—
132#3038D1311yescharacteristic
133#2925—131no—
134#1545—131no—
135C2×#331—131no—
136#1477—131no—
137#1301—131no—
138#1292—131no—
139C23×C13—21no—
140C23×C13—42no—
141C23×C13—82no—
142C23×C13—82no—
143C23×C13—81no—
144C23×C13—81no—
145C23×C13#12311yescharacteristic
146Q8×C13—21no—
147Q8×C13—21no—
148D4×C13—21no—
149D4×C13—21no—
150D4×C13—41no—
151D4×C13—41no—
152D4×C13—42no—
153D4×C13—42no—
154D4×C13—82no—
155D4×C13—82no—
156D4×C13—82no—
157D4×C13—81no—
158D4×C13—81no—
159D4×C13—81no—
160D4×C13—81no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—81no—
172C2×C4×C13C2×C22⋊C411yescharacteristic
173C2×C4×C13C4×D411yescharacteristic
174C2×C4×C13C4×D411yescharacteristic
175C2×C4×C13#12011yescharacteristic
176C2×C4×C13#12111yescharacteristic
177C2×C4×C13#12111yescharacteristic
178C2×C4×C13#13511yescharacteristic
179C2×C4×C13#13511yescharacteristic
180C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
182C8×C13—42no—
183#1055—41no—
184#1055—41no—
185#1055—42no—
186#1055—81no—
187#1055—81no—
188C2×AGL(1,ℤ/8)—21no—
189C2×#127C2×D1311yescharacteristic
190C4×#41C2×D1311yescharacteristic
191#460—21no—
192#460Dic1312yes—
193#459—21no—
194#459Dic1312yes—
195#433—262no—
196#432—261no—
197#431—131no—
198#431—261no—
199#423—131no—
200#423C2×D1311yescharacteristic
201C2×C4⋊C8—131no—
202C2×C4⋊C8—131no—
203#418—21no—
204#408—261no—
205#405—261no—
206#331—261no—
207#331—261no—
208#331—262no—
209Q8⋊C8—261no—
210D4⋊C8—261no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—41no—
214C22×C13—41no—
215C22×C13—41no—
216C22×C13—82no—
217C22×C13—82no—
218C22×C13—82no—
219C22×C13—162no—
220C22×C13—162no—
221C22×C13#38611yescharacteristic
222C22×C13#48211yescharacteristic
223C22×C13#48211yescharacteristic
224C4×C13—21no—
225C4×C13—21no—
226C4×C13—21no—
227C4×C13—41no—
228C4×C13—41no—
229C4×C13—41no—
230C4×C13#41611yescharacteristic
231C4×C13#41811yescharacteristic
232C4×C13#44911yescharacteristic
233C4×C13#44911yescharacteristic
234C4×C13#47111yescharacteristic
235C4×C13#47211yescharacteristic
236C2×#41C22⋊D1311yescharacteristic
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—21no—
240AGL(1,ℤ/8)—42no—
241AGL(1,ℤ/8)—42no—
242C2×SD16—22no—
243C2×D8—22no—
244C2×M16—21no—
245C2×M16—261no—
246C22×C8—261no—
247C22×C8—261no—
248#127—21no—
249#127—21no—
250#127—21no—
251#127C2×Dic1312yes—
252C4×Q8C2×Dic1311yescharacteristic
253C4×Q8C22⋊D1311yescharacteristic
254C4×D4—21no—
255C4×D4—21no—
256C4×D4C2×Dic1311yescharacteristic
257C4×D4C22⋊D1311yescharacteristic
258#117—21no—
259#117C22⋊D1311yescharacteristic
260C2×C42—21no—
261C2×C42C22×D1311yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—131no—
264C4⋊C8—131no—
265C4⋊C8—132no—
266C4⋊C8—261no—
267C4⋊C8—261no—
268C4⋊C8—261no—
269C4⋊C8—261no—
270C4⋊C8—261no—
271C4⋊C8C2×Dic1312yes—
272#102—22no—
273#102—22no—
274C22⋊C8—262no—
275C22⋊C8—262no—
276C22⋊C8—261no—
277#97—262no—
278C4×C8—262no—
279C4×C8—261no—
280C2×C13—21no—
281C2×C13—21no—
282C2×C13—81no—
283C2×C13—162no—
284C2×C13#187511yescharacteristic
285C2×C13#190311yescharacteristic
286C2×C13#190711yescharacteristic
287C24—41no—
288#41—21no—
289#41—21no—
290#41—21no—
291#41—21no—
292C2×Q8C22⋊Dic1311yescharacteristic
293C2×D4—21no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—81no—
305C2×D4—81no—
306C2×D4—82no—
307C2×D4C22⋊Dic1311yescharacteristic
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4#612911yescharacteristic
312C22×C4#612911yescharacteristic
313C22×C4C2×C22⋊D1311yescharacteristic
314SD16—44no—
315D8—44no—
316M16—41no—
317M16—41no—
318M16—521no—
319M16—521no—
320C2×C8—22no—
321C2×C8—261no—
322C2×C8—262no—
323C2×C8—261no—
324C2×C8—521no—
325C2×C8—521no—
326C2×C8—521no—
327C2×C8—521no—
328C2×C8—1041no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4C22⋊Dic1311yescharacteristic
332C4⋊C4C22⋊Dic1311yescharacteristic
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C42—21no—
337C42—21no—
338C42—21no—
339C42D4×D1311yescharacteristic
340C42D4×D1311yescharacteristic
341C42C22×Dic1311yescharacteristic
342C42C2×C22⋊D1311yescharacteristic
343C13#917411yescharacteristic, complemented, Sylow
344C23—21no—
345C23—42no—
346C23—82no—
347C23—82no—
348C23—81no—
349C23—81no—
350C23#8818911yescharacteristic
351Q8—21no—
352Q8—21no—
353D4—21no—
354D4—21no—
355D4—41no—
356D4—41no—
357D4—42no—
358D4—42no—
359D4—82no—
360D4—82no—
361D4—82no—
362D4—81no—
363D4—81no—
364D4—81no—
365D4—81no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4#8818611yescharacteristic
378C2×C4#8818611yescharacteristic
379C2×C4D4×Dic1311yescharacteristic
380C2×C4D4×Dic1311yescharacteristic
381C2×C4#8819111yescharacteristic
382C2×C4#8819311yescharacteristic
383C2×C4#8819311yescharacteristic
384C2×C4#8820411yescharacteristic
385C2×C4#8820411yescharacteristic
386C2×C4C2×C22⋊Dic1311yescharacteristic
387C8—42no—
388C8—521no—
389C8—521no—
390C8—522no—
391C8—1041no—
392C8—1041no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—82no—
399C22—82no—
400C22—82no—
401C22—162no—
402C22—162no—
403C22#1171869611yescharacteristic
404C22#1171869611yescharacteristic
405C22#1171888111yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4#1171869811yescharacteristic
413C4#1171869811yescharacteristic
414C4#1171886011yescharacteristic
415C4#1171886111yescharacteristic
416C4#1171887611yescharacteristic
417C4#1171889411yescharacteristic
418C2—21no—
419C2—21no—
420C2—81no—
421C2—162no—
422C2#1311515911yescharacteristic
423C2#1311531811yescharacteristic
424C2#1311534611yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#3038C2
socleC22×C13#386
cosocleC2×C42×C13C23
hypercenter#3038D13
hypocenterC13#9174
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. #13123502C2semidirect
2. #13113504C2semidirect
3. C2×#11718136C2semidirect
4. #13113223C2semidirect
5. #13112731C2semidirect
6. #13112710C2semidirect
343. C13#9174semidirect

Maximal subgroups

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

subgroupindex
#131235022
#131135042
C2×#117181362
#131132232
#131127312
#131127102
C13×#30382
#917413