Finite Group Databasebeta

← #15758814

Subgroups — #15758814

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#13123404C211yesmaximal, 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
11C2×#88202—21no—
12C13×#460—21no—
13C13×#460C412yes—
14C13×#459—21no—
15C13×#459C412yes—
16C13×#423C2211yescharacteristic
17C13×#418—21no—
18#11718660—22no—
19#11718660—21no—
20#11718586C2211yescharacteristic
21#11718585—21no—
22#11718585C2211yescharacteristic
23C2×C4⋊#1055—21no—
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
54#88202—42no—
55#88202—42no—
56C2×#6099—22no—
57C2×#6099—21no—
58C22×#1055—22no—
59C22×#1055—21no—
60C22×#1055—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8C2×C412yes—
63C13×#102—22no—
64C13×#102—22no—
65C22⋊#1055—21no—
66C4⋊#1055—22no—
67C4⋊#1055—22no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4⋊#1055—21no—
72C4⋊#1055—21no—
73C4⋊#1055D412yes—
74C4⋊#1055D411yescharacteristic
75C4⋊#1055D411yescharacteristic
76C4×#1055—21no—
77#9173—131nomaximal, Sylow
78C24×C13—41no—
79C13×#41—21no—
80C13×#41—21no—
81C13×#41D812yes—
82C13×#41SD1612yes—
83C2×Q8×C13C22⋊C411yescharacteristic
84C2×D4×C13—21no—
85C2×D4×C13—22no—
86C2×D4×C13—22no—
87C2×D4×C13—22no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C2×D4×C13—81no—
96C2×D4×C13—81no—
97C2×D4×C13—82no—
98C2×D4×C13C22⋊C411yescharacteristic
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13#4111yescharacteristic
104C22×C4×C13#4111yescharacteristic
105C13×SD16—44no—
106C13×D8—44no—
107C13×M16—41no—
108C13×M16—41no—
109C2×C8×C13—22no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4C22⋊C411yescharacteristic
113C13×C4⋊C4C22⋊C411yescharacteristic
114C13×C22⋊C4—21no—
115C13×C22⋊C4—21no—
116C13×C22⋊C4—21no—
117C42×C13—21no—
118C42×C13—21no—
119C42×C13—21no—
120C42×C13C22×C411yescharacteristic
121C42×C13C2×D411yescharacteristic
122C42×C13C2×D411yescharacteristic
123C42×C13C2×D411yescharacteristic
124#6099—44no—
125#6099—41no—
126#6099—41no—
127C2×#1055—21no—
128C2×#1055—22no—
129C2×#1055—21no—
130C2×#1055—44no—
131C2×#1055—41no—
132C2×#1055—41no—
133C2×#1055—41no—
134C2×#1055—41no—
135C2×#1055—81no—
136#3038D1311yescharacteristic
137#2906—131no—
138#1545—131no—
139C2×#331—131no—
140#1477—131no—
141#1301—131no—
142#1292—131no—
143C23×C13—21no—
144C23×C13—42no—
145C23×C13—82no—
146C23×C13—82no—
147C23×C13—81no—
148C23×C13—81no—
149C23×C13#12311yescharacteristic
150Q8×C13—21no—
151Q8×C13#10212yes—
152D4×C13—22no—
153D4×C13—22no—
154D4×C13—21no—
155D4×C13—42no—
156D4×C13—42no—
157D4×C13—82no—
158D4×C13—82no—
159D4×C13—82no—
160D4×C13—81no—
161D4×C13—81no—
162D4×C13—81no—
163D4×C13—81no—
164D4×C13#10212yes—
165C2×C4×C13—21no—
166C2×C4×C13—22no—
167C2×C4×C13—22no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—81no—
176C2×C4×C13C2×C22⋊C411yescharacteristic
177C2×C4×C13C4×D411yescharacteristic
178C2×C4×C13C4×D411yescharacteristic
179C2×C4×C13#12011yescharacteristic
180C2×C4×C13#12111yescharacteristic
181C2×C4×C13#12111yescharacteristic
182C2×C4×C13C2×D811yescharacteristic
183C2×C4×C13C2×SD1611yescharacteristic
184C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C13#13711yescharacteristic
186C8×C13—42no—
187#1055—41no—
188#1055—42no—
189#1055—41no—
190#1055—81no—
191#1055—81no—
192C2×AGL(1,ℤ/8)—21no—
193C2×#131—261no—
194C2×#127C2×D1311yescharacteristic
195C4×#41C2×D1311yescharacteristic
196#460—21no—
197#460Dic1312yes—
198#459—21no—
199#459Dic1312yes—
200#431—131no—
201#424—262no—
202#424—261no—
203#423—131no—
204#423—261no—
205#423C2×D1311yescharacteristic
206C2×C4⋊C8—131no—
207C2×C4⋊C8—131no—
208C2×C4⋊C8—261no—
209#418—21no—
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—82no—
221C22×C13—82no—
222C22×C13—82no—
223C22×C13—162no—
224C22×C13—162no—
225C22×C13#38611yescharacteristic
226C22×C13#48011yescharacteristic
227C22×C13#48111yescharacteristic
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—21no—
242C22×D4—21no—
243C22×D4—21no—
244AGL(1,ℤ/8)—42no—
245AGL(1,ℤ/8)—42no—
246C2×SD16—22no—
247C2×D8—22no—
248#131—522no—
249#131—522no—
250C2×M16—21no—
251C2×M16—262no—
252C2×M16—261no—
253C22×C8—262no—
254C22×C8—261no—
255C22×C8—261no—
256#127—21no—
257#127—21no—
258#127—21no—
259#127C2×Dic1312yes—
260C4×Q8C2×Dic1311yescharacteristic
261C4×Q8C22⋊D1311yescharacteristic
262C4×D4—21no—
263C4×D4—21no—
264C4×D4C2×Dic1311yescharacteristic
265C4×D4C22⋊D1311yescharacteristic
266#117—21no—
267#117C22⋊D1311yescharacteristic
268C2×C42—21no—
269C2×C42C22×D1311yescharacteristic
270C4⋊C8—21no—
271C4⋊C8—131no—
272C4⋊C8—131no—
273C4⋊C8—132no—
274C4⋊C8—262no—
275C4⋊C8—262no—
276C4⋊C8—261no—
277C4⋊C8—261no—
278C4⋊C8—261no—
279C4⋊C8—261no—
280C4⋊C8—261no—
281C4⋊C8C2×Dic1312yes—
282#102—22no—
283#102—22no—
284C22⋊C8—261no—
285C4×C8—261no—
286C2×C13—21no—
287C2×C13—21no—
288C2×C13—42no—
289C2×C13—162no—
290C2×C13#187411yescharacteristic
291C2×C13#190311yescharacteristic
292C2×C13#190711yescharacteristic
293C24—41no—
294#41—21no—
295#41—21no—
296#41#610412yes—
297#41#610512yes—
298C2×Q8C22⋊Dic1311yescharacteristic
299C2×D4—21no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—81no—
311C2×D4—81no—
312C2×D4—82no—
313C2×D4C22⋊Dic1311yescharacteristic
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4#612911yescharacteristic
318C22×C4#612911yescharacteristic
319C22×C4C2×C22⋊D1311yescharacteristic
320SD16—44no—
321D8—44no—
322M16—41no—
323M16—41no—
324M16—524no—
325M16—521no—
326M16—521no—
327C2×C8—22no—
328C2×C8—261no—
329C2×C8—261no—
330C2×C8—262no—
331C2×C8—524no—
332C2×C8—521no—
333C2×C8—521no—
334C2×C8—521no—
335C2×C8—521no—
336C2×C8—1041no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4C22⋊Dic1311yescharacteristic
340C4⋊C4C22⋊Dic1311yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C42—21no—
345C42—21no—
346C42—21no—
347C42D4×D1311yescharacteristic
348C42D4×D1311yescharacteristic
349C42C22×Dic1311yescharacteristic
350C42C2×C22⋊D1311yescharacteristic
351C13#917311yescharacteristic, complemented, Sylow
352C23—21no—
353C23—42no—
354C23—82no—
355C23—82no—
356C23—81no—
357C23—81no—
358C23#8818911yescharacteristic
359Q8—21no—
360Q8#8807212yes—
361D4—22no—
362D4—22no—
363D4—21no—
364D4—42no—
365D4—42no—
366D4—82no—
367D4—82no—
368D4—82no—
369D4—81no—
370D4—81no—
371D4—81no—
372D4—81no—
373D4#8807212yes—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4C2×#610411yescharacteristic
386C2×C4C2×#610511yescharacteristic
387C2×C4D4×Dic1311yescharacteristic
388C2×C4D4×Dic1311yescharacteristic
389C2×C4#8819111yescharacteristic
390C2×C4#8819311yescharacteristic
391C2×C4#8819311yescharacteristic
392C2×C4#8820311yescharacteristic
393C2×C4#8820511yescharacteristic
394C2×C4C2×C22⋊Dic1311yescharacteristic
395C8—42no—
396C8—521no—
397C8—522no—
398C8—521no—
399C8—1041no—
400C8—1041no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—41no—
405C22—41no—
406C22—82no—
407C22—82no—
408C22—82no—
409C22—162no—
410C22—162no—
411C22#1171869411yescharacteristic
412C22#1171869511yescharacteristic
413C22#1171888111yescharacteristic
414C4—22no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4#1171869711yescharacteristic
421C4#1171870111yescharacteristic
422C4#1171886011yescharacteristic
423C4#1171886111yescharacteristic
424C4C2×#8807211yescharacteristic
425C4#1171889311yescharacteristic
426C2—21no—
427C2—21no—
428C2—42no—
429C2—162no—
430C2#1311515411yescharacteristic
431C2#1311531811yescharacteristic
432C2#1311534611yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#3038C2
socleC22×C13#386
cosocleC2×C42×C13C23
hypercenter#3038D13
hypocenterC13#9173
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. #13123404C2semidirect
2. #13113504C2semidirect
3. C2×#11718136C2semidirect
4. #13113223C2semidirect
5. #13112731C2semidirect
6. #13112710C2semidirect
351. C13#9173semidirect

Maximal subgroups

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

subgroupindex
#131234042
#131135042
C2×#117181362
#131132232
#131127312
#131127102
C13×#30382
#917313