Finite Group Databasebeta

← #15758333

Subgroups — #15758333

Order 3328.

532 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123859C211yesmaximal, characteristic
2C2×#11718687C211yesmaximal, characteristic
3#13113231C211yesmaximal, characteristic, complemented
4#13113226C211yesmaximal, characteristic
5#13112680C211yesmaximal, characteristic, complemented
6#13112666C211yesmaximal, characteristic, complemented
7C13×#1461C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C13C2211yescharacteristic
9C22×#6106C411yescharacteristic
10C2×C4×D52C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#431C2211yescharacteristic
13C2×#88075C411yescharacteristic
14#11718687—22no—
15#11718687—22no—
16C2×#88049C411yescharacteristic
17C2×#88047C411yescharacteristic
18#11718586C2211yescharacteristic
19#11718586C2211yescharacteristic
20C2×#88043C2211yescharacteristic
21#11718495—22no—
22D13×C22⋊C8—22no—
23C8×D52—22no—
24C13×#324—22no—
25Q8⋊#1055—22no—
26#11718075—22no—
27C22×Q8×C13C2×C411yescharacteristic
28C22×D52C2×C411yescharacteristic
29C22×C4×D13—21no—
30C4×Q8×C13—21no—
31C4×Q8×C13—21no—
32C4×Q8×C13—21no—
33C4×Q8×C13—21no—
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
45C2×C8×D13—24no—
46C4×D52—21no—
47C4×D52—21no—
48C4×D52D412yes—
49C4×D52D412yes—
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C22⋊C8—21no—
53C13×C22⋊C8D412yes—
54C4×C8×C13—21no—
55C4×C8×C13—21no—
56#88075—22no—
57C22⋊#1055—21no—
58C22⋊#1055—21no—
59#88060—24no—
60#88049—22no—
61#88047—22no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64#88043—21no—
65#88043—21no—
66C4×#1055—21no—
67C4×#1055D412yes—
68#9087—131nomaximal, Sylow
69C23×D13—21no—
70C2×Q8×C13—21no—
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13—21no—
74C2×Q8×C13—21no—
75C2×Q8×C13C2×C812yescomplemented
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×D52C22⋊C412yes—
86C2×D52C2×C812yes—
87C2×D52M1612yes—
88C2×C4×D13—22no—
89C2×C4×D13—22no—
90C2×C4×D13—82no—
91C2×C8×C13—22no—
92C2×C8×C13—41no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C42×C13—41no—
98C42×C13—41no—
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13C2×D411yescharacteristic
102C42×C13#4111yescharacteristic
103#6106—28no—
104#6103—22no—
105#6103—22no—
106C4⋊Dic13—21no—
107C4⋊Dic13C22⋊C412yes—
108C2×#1055—21no—
109C2×#1055—21no—
110C2×#1055—21no—
111C2×#1055—22no—
112C2×#1055—21no—
113C2×#1055—21no—
114C2×#1055—41no—
115C2×#1055C2×C812yescomplemented
116C8×D13—84no—
117#2972—131no—
118C2×#440—131no—
119#1479—131no—
120#1478—131no—
121#1461D1311yescharacteristic, complemented
122#1281—131no—
123#1275—131no—
124C23×C13C4×D411yescharacteristic
125C22×D13—22no—
126C22×D13—22no—
127C22×D13—22no—
128C22×D13—81no—
129C22×D13—81no—
130Q8×C13—22no—
131Q8×C13—22no—
132Q8×C13—41no—
133Q8×C13—41no—
134C2×C4×C13—22no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—81no—
141C2×C4×C13C2×C22⋊C411yescharacteristic
142C2×C4×C13C4×D411yescharacteristic
143C2×C4×C13#12011yescharacteristic
144C2×C4×C13#12111yescharacteristic
145C2×C4×C13#12111yescharacteristic
146C2×C4×C13#12311yescharacteristic
147C2×C4×C13C22×C811yescharacteristic
148C2×C4×C13C2×M1611yescharacteristic
149C2×C4×C13#13111yescharacteristic
150C2×C4×C13#13111yescharacteristic
151C2×Dic13—22no—
152C2×Dic13—81no—
153D52—22no—
154D52—22no—
155D52—22no—
156D52C22⋊C814yes—
157C4×D13—44no—
158C4×D13—82no—
159C8×C13—42no—
160C8×C13—81no—
161#1055—22no—
162#1055—42no—
163#1055—41no—
164#1055—81no—
165C22×SD16—131no—
166C2×C4×Q8C2×D1311yescharacteristic
167C2×C4×D4—131no—
168#440—262no—
169#440—262no—
170C8×D4—262no—
171C8×D4—262no—
172#431—131no—
173#431—131no—
174#431C2×D1311yescharacteristic
175#431C2×D1311yescharacteristic
176C2×#107—131no—
177C2×#103—131no—
178C2×#102—131no—
179C2×C22⋊C8—262no—
180C2×#97—131no—
181Q8⋊C8—262no—
182D4⋊C8—262no—
183#324—22no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13#38611yescharacteristic
187C22×C13C8×D411yescharacteristic
188C22×C13#43511yescharacteristic
189C2×D13—24no—
190C2×D13—42no—
191C2×D13—42no—
192C2×D13—82no—
193C2×D13—82no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—42no—
199C4×C13—81no—
200C4×C13C2×C22⋊C811yescharacteristic
201C4×C13#40811yescharacteristic
202C4×C13C8×D411yescharacteristic
203C4×C13#43511yescharacteristic
204Dic13—42no—
205C22×Q8C4×D1311yescharacteristic
206C22×D4—131no—
207C23×C4—261no—
208C2×SD16—134no—
209C2×SD16—262no—
210C2×SD16—262no—
211C22×C8—131no—
212C22×C8—131no—
213C22×C8—264no—
214C4×Q8—21no—
215C4×Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×D4—132no—
219C4×D4—132no—
220C4×D4—261no—
221C4×D4—261no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4C4×D1311yescharacteristic
225C2×C22⋊C4—261no—
226C2×C42—21no—
227C2×C42C22×D1311yescharacteristic
228#107—262no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—261no—
232C4⋊C8—261no—
233#103—262no—
234#102—262no—
235C22⋊C8—21no—
236C22⋊C8—264no—
237C22⋊C8—261no—
238C22⋊C8—261no—
239C22⋊C8C22⋊D1312yes—
240#97—261no—
241#97—261no—
242C4×C8—21no—
243C4×C8—21no—
244C4×C8—132no—
245C4×C8—261no—
246C2×C13—21no—
247C2×C13—21no—
248C2×C13#186911yescharacteristic
249C2×C13#190211yescharacteristic
250C2×C13#190411yescharacteristic
251D13—44no—
252C24—261no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8C8×D1312yescomplemented
259C2×D4—132no—
260C2×D4—132no—
261C2×D4—132no—
262C2×D4—261no—
263C2×D4—261no—
264C2×D4—261no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—261no—
268C22×C4—262no—
269C22×C4—262no—
270C22×C4—1042no—
271C22×C4C2×C4×D1311yescharacteristic
272C22×C4#612711yescharacteristic
273C22×C4C2×C22⋊D1311yescharacteristic
274SD16—268no—
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—132no—
278C2×C8—261no—
279C2×C8—261no—
280C2×C8—261no—
281C2×C8—261no—
282C2×C8—261no—
283C2×C8—262no—
284C2×C8—521no—
285C2×C8—1044no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—132no—
291C4⋊C4—261no—
292C22⋊C4—262no—
293C22⋊C4—262no—
294C42—41no—
295C42—41no—
296C42D4×D1311yescharacteristic
297C42D4×D1311yescharacteristic
298C42D4×D1311yescharacteristic
299C42#612911yescharacteristic
300C13#908711yescharacteristic, complemented, Sylow
301C23—262no—
302C23—262no—
303C23—262no—
304C23—1041no—
305C23—1041no—
306C23C4×C22⋊D1311yescharacteristic
307Q8—22no—
308Q8—22no—
309Q8—41no—
310Q8—41no—
311D4—134no—
312D4—262no—
313D4—262no—
314D4—262no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—262no—
323C2×C4—524no—
324C2×C4—1042no—
325C2×C4—1041no—
326C2×C4C22⋊C4×D1311yescharacteristic
327C2×C4#8813511yescharacteristic
328C2×C4#8813711yescharacteristic
329C2×C4#8813811yescharacteristic
330C2×C4C2×C8×D1311yescharacteristic
331C2×C4#8815511yescharacteristic
332C2×C4M16×D1311yescharacteristic
333C2×C4#8816111yescharacteristic
334C2×C4#8819111yescharacteristic
335C2×C4#8819211yescharacteristic
336C8—42no—
337C8—81no—
338C8—262no—
339C8—522no—
340C8—521no—
341C8—1041no—
342C22—21no—
343C22—21no—
344C22—264no—
345C22—522no—
346C22—522no—
347C22—1042no—
348C22—1042no—
349C22#1171861711yescharacteristic
350C22C8×C22⋊D1311yescharacteristic
351C22#1171878811yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—42no—
357C4—81no—
358C4—522no—
359C4D13×C22⋊C811yescharacteristic
360C4#1171838611yescharacteristic
361C4#1171838811yescharacteristic
362C4#1171838911yescharacteristic
363C2—21no—
364C2—21no—
365C2—524no—
366C2#1311512511yescharacteristic
367C2#1311531211yescharacteristic
368C2#1311532611yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1461C2
socleC22×C13#386
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1461D13
hypocenterC13#9087
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
3. #13113231C2semidirect
5. #13112680C2semidirect
6. #13112666C2semidirect
7. C13×#1461C2semidirect
40. C2×#6106C8semidirect
75. C2×Q8×C13C2×C8semidirect
115. C2×#1055C2×C8semidirect
121. #1461D13semidirect
258. C2×Q8C8×D13semidirect
300. C13#9087semidirect

Maximal subgroups

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

subgroupindex
#131238592
C2×#117186872
#131132312
#131132262
#131126802
#131126662
C13×#14612
#908713