Finite Group Databasebeta

← #15758349

Subgroups — #15758349

Order 3328.

512 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123917C211yesmaximal, characteristic, complemented
2C2×#11718687C211yesmaximal, characteristic
3#13113226C211yesmaximal, characteristic
4#13113156C211yesmaximal, characteristic
5#13112680C211yesmaximal, characteristic, complemented
6#13112666C211yesmaximal, characteristic, complemented
7C13×#1479C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C13C2211yescharacteristic
9C22×#6106C411yescharacteristic
10C2×C4×D52C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#431C2211yescharacteristic
13C2×#88075C411yescharacteristic
14#11718687—22no—
15#11718687—22no—
16Q8×#1055—22no—
17Q8×#1055—22no—
18C2×#88049C411yescharacteristic
19C2×#88047C411yescharacteristic
20#11718586—22no—
21#11718586C2211yescharacteristic
22#11718586C2211yescharacteristic
23C2×#88043C2211yescharacteristic
24C13×Q8⋊C8—22no—
25#11718075—22no—
26#11718060—22no—
27C22×Q8×C13C2×C411yescharacteristic
28C22×D52C2×C411yescharacteristic
29C22×C4×D13—21no—
30C4×Q8×C13—21no—
31C4×Q8×C13—21no—
32C4×Q8×C13D412yes—
33C4×Q8×C13D412yes—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C42×C13—21no—
37C2×C42×C13C2311yescharacteristic
38C2×#6106—22no—
39C2×#6106—22no—
40C2×#6106C814yescomplemented
41C2×#6103—21no—
42C2×C4⋊Dic13C2×C411yescharacteristic
43C22×#1055C2×C411yescharacteristic
44C22×#1055C2×C411yescharacteristic
45C4×D52—21no—
46C4×D52—21no—
47C4×D52—21no—
48C4×D52—21no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C22⋊C8—21no—
52C13×C22⋊C8—21no—
53C4×C8×C13—21no—
54C4×C8×C13—21no—
55#88075—22no—
56C22⋊#1055—21no—
57C22⋊#1055D412yes—
58#88049—22no—
59#88047—22no—
60C4⋊#1055—24no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63#88043—21no—
64#88043—21no—
65C4×#1055—24no—
66C4×#1055—21no—
67C4×#1055D412yes—
68#9090—131nomaximal, Sylow
69C23×D13—21no—
70C2×Q8×C13—21no—
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13C22⋊C412yes—
74C2×Q8×C13C2×C812yes—
75C2×Q8×C13M1612yes—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C22×Dic13—21no—
82C2×D52—21no—
83C2×D52—21no—
84C2×D52—21no—
85C2×D52—21no—
86C2×D52—21no—
87C2×D52C2×C812yes—
88C2×C4×D13—41no—
89C2×C4×D13—41no—
90C2×C4×D13—82no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4C22⋊C412yes—
97C42×C13—22no—
98C42×C13—22no—
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13C2×D411yescharacteristic
102C42×C13#4111yescharacteristic
103#6106—28no—
104#6103—41no—
105#6103—41no—
106C4⋊Dic13—21no—
107C4⋊Dic13—21no—
108C2×#1055—21no—
109C2×#1055—21no—
110C2×#1055—21no—
111C2×#1055—22no—
112C2×#1055—22no—
113C2×#1055—21no—
114C2×#1055—21no—
115C2×#1055C2×C812yes—
116#2982—131no—
117C2×#440—131no—
118#1479D1311yescharacteristic, complemented
119#1478—131no—
120#1460—131no—
121#1281—131no—
122#1275—131no—
123C23×C13C4×D411yescharacteristic
124C22×D13—22no—
125C22×D13—41no—
126C22×D13—41no—
127C22×D13—81no—
128C22×D13—81no—
129Q8×C13—22no—
130Q8×C13—22no—
131Q8×C13—22no—
132Q8×C13C22⋊C814yes—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—22no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—81no—
140C2×C4×C13C2×C22⋊C411yescharacteristic
141C2×C4×C13C4×D411yescharacteristic
142C2×C4×C13#12011yescharacteristic
143C2×C4×C13#12111yescharacteristic
144C2×C4×C13#12111yescharacteristic
145C2×C4×C13#12311yescharacteristic
146C2×C4×C13C22×C811yescharacteristic
147C2×C4×C13C2×M1611yescharacteristic
148C2×C4×C13#13111yescharacteristic
149C2×C4×C13#13111yescharacteristic
150C2×Dic13—41no—
151C2×Dic13—81no—
152D52—22no—
153D52—22no—
154D52—41no—
155D52—41no—
156C4×D13—82no—
157C4×D13—82no—
158C8×C13—81no—
159C8×C13—81no—
160#1055—22no—
161#1055—42no—
162#1055—42no—
163#1055—41no—
164C22×SD16—131no—
165C2×C4×Q8C2×D1311yescharacteristic
166C2×C4×D4—131no—
167C8×Q8—262no—
168C8×Q8—262no—
169#440—262no—
170#440—262no—
171#431—131no—
172#431—131no—
173#431—262no—
174#431C2×D1311yescharacteristic
175#431C2×D1311yescharacteristic
176C2×#107—131no—
177C2×#103—131no—
178C2×#102—131no—
179C2×#97—131no—
180Q8⋊C8—22no—
181D4⋊C8—262no—
182#323—262no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13#38611yescharacteristic
186C22×C13C8×D411yescharacteristic
187C22×C13#43511yescharacteristic
188C2×D13—42no—
189C2×D13—82no—
190C2×D13—81no—
191C2×D13—81no—
192C2×D13—82no—
193C4×C13—24no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—42no—
199C4×C13C2×C22⋊C811yescharacteristic
200C4×C13#40811yescharacteristic
201C4×C13C8×D411yescharacteristic
202C4×C13#43511yescharacteristic
203Dic13—81no—
204C22×Q8C4×D1311yescharacteristic
205C22×D4—131no—
206C23×C4—261no—
207C2×SD16—134no—
208C2×SD16—262no—
209C2×SD16—262no—
210C22×C8—131no—
211C22×C8—131no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8D5212yes—
215C4×Q8C22⋊D1312yes—
216C4×D4—261no—
217C4×D4—261no—
218C4×D4—261no—
219C4×D4—261no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—131no—
222C2×C4⋊C4C4×D1311yescharacteristic
223C2×C22⋊C4—261no—
224C2×C42—21no—
225C2×C42C22×D1311yescharacteristic
226#107—262no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—264no—
230C4⋊C8—261no—
231C4⋊C8—261no—
232#103—262no—
233#102—262no—
234C22⋊C8—21no—
235C22⋊C8—21no—
236C22⋊C8—132no—
237C22⋊C8—261no—
238#97—261no—
239#97—261no—
240C4×C8—21no—
241C4×C8—21no—
242C4×C8—132no—
243C4×C8—264no—
244C4×C8—261no—
245C2×C13—21no—
246C2×C13—21no—
247C2×C13#186911yescharacteristic
248C2×C13#190311yescharacteristic
249C2×C13#190511yescharacteristic
250D13—82no—
251C24—261no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8C8×D1312yes—
256C2×Q8#609412yes—
257C2×Q8#610312yes—
258C2×D4—132no—
259C2×D4—261no—
260C2×D4—261no—
261C2×D4—261no—
262C2×D4—261no—
263C2×D4—261no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—261no—
267C22×C4—521no—
268C22×C4—521no—
269C22×C4—1042no—
270C22×C4C2×C4×D1311yescharacteristic
271C22×C4D4×D1311yescharacteristic
272C22×C4#612911yescharacteristic
273SD16—268no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—132no—
277C2×C8—261no—
278C2×C8—261no—
279C2×C8—262no—
280C2×C8—262no—
281C2×C8—261no—
282C2×C8—261no—
283C2×C8—261no—
284C4⋊C4—21no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—261no—
288C4⋊C4—261no—
289C4⋊C4#610312yes—
290C22⋊C4—521no—
291C22⋊C4—521no—
292C42—22no—
293C42—22no—
294C42C2×D5211yescharacteristic
295C42D4×D1311yescharacteristic
296C42#612911yescharacteristic
297C42C2×C22⋊D1311yescharacteristic
298C13#909011yescharacteristic, complemented, Sylow
299C23—262no—
300C23—521no—
301C23—521no—
302C23—1041no—
303C23—1041no—
304C23#8813511yescharacteristic
305Q8—22no—
306Q8—22no—
307Q8—22no—
308Q8#8806014yes—
309D4—262no—
310D4—262no—
311D4—521no—
312D4—521no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—521no—
321C2×C4—1042no—
322C2×C4—1042no—
323C2×C4—1041no—
324C2×C4#8813511yescharacteristic
325C2×C4#8813611yescharacteristic
326C2×C4#8814011yescharacteristic
327C2×C4C2×C8×D1311yescharacteristic
328C2×C4C2×#609411yescharacteristic
329C2×C4#8816111yescharacteristic
330C2×C4#8816111yescharacteristic
331C2×C4C2×#610311yescharacteristic
332C2×C4#8819311yescharacteristic
333C2×C4#8819311yescharacteristic
334C8—81no—
335C8—81no—
336C8—262no—
337C8—522no—
338C8—522no—
339C8—521no—
340C22—21no—
341C22—21no—
342C22—522no—
343C22—1042no—
344C22—1042no—
345C22—1041no—
346C22—1041no—
347C22#1171838611yescharacteristic
348C22#1171839111yescharacteristic
349C22#1171861911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—24no—
355C4—42no—
356C4—1041no—
357C4#1171838611yescharacteristic
358C4#1171839111yescharacteristic
359C4C2×#8806011yescharacteristic
360C4#1171879011yescharacteristic
361C2—21no—
362C2—21no—
363C2—1042no—
364C2#1311512611yescharacteristic
365C2#1311531411yescharacteristic
366C2#1311532811yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1479C2
socleC22×C13#386
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1479D13
hypocenterC13#9090
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
1. #13123917C2semidirect
5. #13112680C2semidirect
6. #13112666C2semidirect
7. C13×#1479C2semidirect
40. C2×#6106C8semidirect
118. #1479D13semidirect
298. C13#9090semidirect

Maximal subgroups

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

subgroupindex
#131239172
C2×#117186872
#131132262
#131131562
#131126802
#131126662
C13×#14792
#909013