Finite Group Databasebeta

← #15781121

Subgroups — #15781121

Order 3328.

438 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123530C211yesmaximal, characteristic
2#13116601C211yesmaximal, characteristic, complemented
3#13116465C211yesmaximal, characteristic, complemented
4#13116463C211yesmaximal, characteristic, complemented
5#13116447C211yesmaximal, characteristic, complemented
6#13116440C211yesmaximal, characteristic, complemented
7C13×#2112C211yesmaximal, characteristic, complemented
8C23×C8×C13C2211yescharacteristic
9#11719496C411yescharacteristic
10C2×#88155C2211yescharacteristic
11C2×C13×M32C2211yescharacteristic
12C2×C13×M32C2211yescharacteristic
13#11718868C411yescharacteristic
14#11718772—22no—
15#11718771C411yescharacteristic
16C8×C22⋊D13—22no—
17#11718763C411yescharacteristic
18#11718762C2211yescharacteristic
19C2×#88052C2211yescharacteristic
20C2×#88052C2211yescharacteristic
21C13×C22⋊C16—22no—
22C22⋊#6090—22no—
23#11718107—22no—
24#11718104—22no—
25#11718103—22no—
26#11718100—22no—
27C23×C4×C13C2×C411yescharacteristic
28C2×#6127C2×C411yescharacteristic
29C22×C8×C13—21no—
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C22×C8×C13—21no—
33C22×C8×C13—21no—
34C22×C8×C13—21no—
35C22×C8×C13C2×C411yescharacteristic
36C22×C8×C13C2311yescharacteristic
37#88207—21no—
38#88184—21no—
39#88183—21no—
40C4×C22⋊D13—22no—
41#88180C2×C411yescharacteristic
42#88178—21no—
43C2×#6099C2×C411yescharacteristic
44C2×#6099C2×C411yescharacteristic
45#88155—21no—
46#88155—21no—
47#88155—21no—
48#88155—21no—
49C2×#6094—21no—
50C2×C8×D13—21no—
51C13×M32—21no—
52C13×M32—21no—
53C13×M32—21no—
54C13×M32—21no—
55C2×C13×C16—21no—
56C2×C13×C16D412yescomplemented
57C22⋊#1055—22no—
58#88060—22no—
59#88055D412yes—
60#88054—22no—
61C8×Dic13D412yes—
62#88052—21no—
63#88052—21no—
64#88052—21no—
65#88052—21no—
66C2×#6090—21no—
67C2×#6090D412yescomplemented
68#13200—131nomaximal, Sylow
69C24×C13M1611yescharacteristic
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13M1611yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C2×C22⋊D13—22no—
79C2×C22⋊D13—21no—
80#6127—21no—
81#6127—21no—
82#6127—21no—
83#6127—21no—
84C2×D52M1611yescharacteristic
85C2×C4×D13—21no—
86C2×Dic26M1611yescharacteristic
87C2×C8×C13—21no—
88C2×C8×C13—21no—
89C2×C8×C13—21no—
90C2×C8×C13—41no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C2×C8×C13—41no—
94C2×C8×C13C2×D411yescharacteristic
95C2×C8×C13C2×D411yescharacteristic
96C2×C8×C13C2×D411yescharacteristic
97C2×C8×C13C2×D411yescharacteristic
98C2×C8×C13#4111yescharacteristic
99C2×C8×C13#4111yescharacteristic
100C22⋊Dic13—22no—
101C22⋊Dic13—21no—
102#6103—22no—
103C4⋊Dic13—21no—
104#6101—22no—
105C4×Dic13C22⋊C412yes—
106#6099—21no—
107#6099—21no—
108#6099—21no—
109#6099—21no—
110C2×#1055—21no—
111C2×#1055C22⋊C412yes—
112#6094—41no—
113#6094—41no—
114C8×D13—41no—
115C8×D13—41no—
116C13×C16—22no—
117C13×C16—41no—
118#6090—22no—
119#6090—41no—
120#2929—131no—
121#2153—131no—
122#2117—131no—
123#2117—131no—
124#2112—131no—
125#2112D1311yescharacteristic, complemented
126#2110—131no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—21no—
130C23×C13—42no—
131C23×C13C2×M1611yescharacteristic
132C22×D13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13C2×C22⋊C411yescharacteristic
141C2×C4×C13C4×D411yescharacteristic
142C2×C4×C13C4×D411yescharacteristic
143C2×C4×C13C2×M1611yescharacteristic
144C2×C4×C13#13111yescharacteristic
145C2×C4×C13#13111yescharacteristic
146C22⋊D13—44no—
147C22⋊D13—41no—
148C22⋊D13—41no—
149C2×Dic13—22no—
150C2×Dic13—21no—
151D52—21no—
152D52—21no—
153C4×D13—41no—
154C4×D13—41no—
155Dic26—21no—
156Dic26—21no—
157C8×C13—41no—
158C8×C13#12111yescharacteristic
159C8×C13#12111yescharacteristic
160C8×C13#12411yescharacteristic
161C8×C13#12711yescharacteristic
162#1055—22no—
163#1055—41no—
164C2×#131—131no—
165C23×C8C2×D1311yescharacteristic
166#525—131no—
167C2×M32—131no—
168C2×M32—131no—
169C2×M32C2×D1311yescharacteristic
170C2×M32C2×D1311yescharacteristic
171#435—262no—
172C8×D4—262no—
173#424—131no—
174#408—131no—
175#407—131no—
176#405—131no—
177#364—262no—
178#350—262no—
179#350—262no—
180C22⋊C16—22no—
181C22⋊C16—262no—
182#347—262no—
183C22×C13—22no—
184C22×C13—22no—
185C22×C13—22no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13#40711yescharacteristic
192C22×C13#43511yescharacteristic
193C22×C13#43511yescharacteristic
194C2×D13—42no—
195C2×D13—41no—
196C4×C13—41no—
197C4×C13#39011yescharacteristic
198C4×C13#40811yescharacteristic
199C4×C13#43511yescharacteristic
200C4×C13#43511yescharacteristic
201Dic13—42no—
202Dic13—41no—
203C2×#41—131no—
204C23×C4C4×D1311yescharacteristic
205#131—261no—
206#131—261no—
207#131—261no—
208#131—261no—
209C2×M16—131no—
210C2×M16—131no—
211C2×M16—261no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—261no—
219C22×C8C4×D1311yescharacteristic
220C22×C8C22×D1311yescharacteristic
221#123—261no—
222C22⋊Q8—261no—
223#121—261no—
224#120—261no—
225C4×D4—262no—
226#117—131no—
227M32—21no—
228M32—21no—
229M32—21no—
230M32—21no—
231M32—261no—
232M32—261no—
233M32—261no—
234M32—261no—
235C2×C16—21no—
236C2×C16—132no—
237C2×C16—261no—
238C2×C16C22⋊D1312yescomplemented
239C4⋊C8—262no—
240C22⋊C8—262no—
241C22⋊C8—262no—
242#97—132no—
243C4×C8—132no—
244C2×C13—21no—
245C2×C13—21no—
246C2×C13—21no—
247C2×C13—42no—
248C2×C13#195511yescharacteristic
249D13—81no—
250C24#609411yescharacteristic
251#41—261no—
252#41—261no—
253#41—261no—
254#41—261no—
255C2×Q8—131no—
256C2×D4—131no—
257C2×D4—262no—
258C2×D4—261no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—261no—
266C22×C4#609411yescharacteristic
267C22×C4C2×C4×D1311yescharacteristic
268M16—261no—
269M16—261no—
270M16—261no—
271M16—261no—
272M16—521no—
273M16—521no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—132no—
282C2×C8—261no—
283C2×C8—521no—
284C2×C8—521no—
285C2×C8#612711yescharacteristic
286C2×C8D4×D1311yescharacteristic
287C2×C8D4×D1311yescharacteristic
288C2×C8D4×D1311yescharacteristic
289C2×C8#612911yescharacteristic
290C2×C8C2×C22⋊D1311yescharacteristic
291C4⋊C4—262no—
292C4⋊C4—261no—
293C22⋊C4—262no—
294C22⋊C4—262no—
295C22⋊C4—261no—
296C42—132no—
297C16—22no—
298C16—41no—
299C16—262no—
300C16—521no—
301C13#1320011yescharacteristic, complemented, Sylow
302C23—21no—
303C23—21no—
304C23—21no—
305C23—42no—
306C23—261no—
307C23C2×#609411yescharacteristic
308Q8—261no—
309Q8—261no—
310D4—261no—
311D4—261no—
312D4—524no—
313D4—521no—
314D4—521no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—262no—
323C2×C4—261no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4C22⋊C4×D1311yescharacteristic
327C2×C4#8813511yescharacteristic
328C2×C4#8815511yescharacteristic
329C2×C4M16×D1311yescharacteristic
330C2×C4#8816111yescharacteristic
331C2×C4C4×C22⋊D1311yescharacteristic
332C8—41no—
333C8—262no—
334C8—521no—
335C8#8813811yescharacteristic
336C8#8813911yescharacteristic
337C8#8819311yescharacteristic
338C8#8819411yescharacteristic
339C22—22no—
340C22—22no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—522no—
348C22—521no—
349C22#1171838711yescharacteristic
350C22#1171839111yescharacteristic
351C22#1171877211yescharacteristic
352C4—41no—
353C4—522no—
354C4—521no—
355C4#1171838811yescharacteristic
356C4#1171838911yescharacteristic
357C4#1171861811yescharacteristic
358C4#1171878811yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—1041no—
364C2#1311563211yescharacteristic
subgroupG/H
centerC8#88194
commutatorC22×C4×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#2112C2
socleC2×C13#1955
prime radical#11719496C4
cosocleC22×C8×C13C23
hypercenter#2112D13
hypocenterC13#13200
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
2. #13116601C2semidirect
3. #13116465C2semidirect
4. #13116463C2semidirect
5. #13116447C2semidirect
6. #13116440C2semidirect
7. C13×#2112C2semidirect
56. C2×C13×C16D4semidirect
67. C2×#6090D4semidirect
125. #2112D13semidirect
238. C2×C16C22⋊D13semidirect
301. C13#13200semidirect

Maximal subgroups

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

subgroupindex
#131235302
#131166012
#131164652
#131164632
#131164472
#131164402
C13×#21122
#1320013