Finite Group Databasebeta

← #15776441

Subgroups — #15776441

Order 3328.

322 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117093C211yesmaximal, characteristic
2#13116876C211yesmaximal, characteristic
3#13114196C211yesmaximal, characteristic
4#13112885C211yesmaximal, characteristic, complemented
5Q8⋊#6090C211yesmaximal, characteristic, complemented
6#13112800C211yesmaximal, characteristic, complemented
7C13×#3395C211yesmaximal, characteristic, complemented
8C13×#557—21no—
9C13×#494—21no—
10C13×#494C2211yescharacteristic
11C13×#462—22no—
12C13×#462—21no—
13C8×Q8×C13C2211yescharacteristic
14C4×C13×Q16—21no—
15C4×C13×Q16C2211yescharacteristic
16C2×#88068—22no—
17C2×#88068—21no—
18#11718688—21no—
19#11718356C2211yescharacteristic
20#11718083—21no—
21#11718077—21no—
22C4⋊#6090C2211yescharacteristic
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×Q16—22no—
26C2×C13×Q16—21no—
27C2×C13×Q16D411yescharacteristic
28C2×C13×Q16D412yes—
29C13×C4⋊Q8—22no—
30C13×C4⋊Q8—21no—
31C13×#125—42no—
32C13×#125—41no—
33C4×Q8×C13—22no—
34C4×Q8×C13—21no—
35C4×Q8×C13—41no—
36C4×Q8×C13D411yescharacteristic
37C2×#6106—41no—
38C2×D104—21no—
39C2×D104—21no—
40#88128—21no—
41C13×#107D411yescharacteristic
42C13×C4⋊C8—21no—
43C13×C4⋊C8D411yescharacteristic
44C13×#103—22no—
45C13×#103—21no—
46C4×C8×C13—21no—
47C4×C8×C13C2311yescharacteristic
48#88068—44no—
49#88068—42no—
50C2×#6090—21no—
51C2×#6090—21no—
52#88049—41no—
53C4⋊#1055—21no—
54#12330—131nomaximal, Sylow
55C2×Q8×C13—21no—
56C2×Q8×C13—22no—
57C2×Q8×C13D811yescharacteristic
58C2×D52—41no—
59C2×D52—41no—
60C2×D52—41no—
61C13×Q16—21no—
62C13×Q16—21no—
63C13×Q16—42no—
64C13×Q16—41no—
65C13×Q16—41no—
66C13×Q16—82no—
67C2×C8×C13—21no—
68C2×C8×C13C2×D411yescharacteristic
69C2×C8×C13C2×D411yescharacteristic
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4D811yescharacteristic
79C42×C13—21no—
80C42×C13—42no—
81C42×C13—41no—
82C42×C13C2×D411yescharacteristic
83#6106—82no—
84C2×#1055—41no—
85D104—42no—
86D104—41no—
87D104—41no—
88#6090—22no—
89#6090—41no—
90#3395D1311yescharacteristic, complemented
91#2248—131no—
92#2207—131no—
93#1668—131no—
94#1362—131no—
95Q8⋊C16—131no—
96#1332—131no—
97C22×D13—81no—
98Q8×C13—21no—
99Q8×C13—41no—
100Q8×C13—42no—
101Q8×C13—42no—
102Q8×C13—41no—
103Q8×C13SD3212yescomplemented
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—41no—
109C2×C4×C13#12011yescharacteristic
110C2×C4×C13C2×D811yescharacteristic
111C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
112D52—81no—
113D52—81no—
114D52—81no—
115D52—81no—
116D52—161no—
117C8×C13—21no—
118C8×C13—41no—
119C8×C13#13511yescharacteristic
120C8×C13AGL(1,ℤ/8)11yescharacteristic
121#1055—81no—
122#557—21no—
123C2×SD32—261no—
124C2×SD32—262no—
125#494—21no—
126#494C2×D1311yescharacteristic
127#493—131no—
128#462—22no—
129#462—21no—
130#460—261no—
131C8×Q8C2×D1311yescharacteristic
132C4×Q16—21no—
133C4×Q16C2×D1311yescharacteristic
134C4⋊C16—131no—
135#357—261no—
136C4×C16—131no—
137#335—131no—
138#331—261no—
139C22×C13#44711yescharacteristic
140C2×D13—161no—
141C2×D13—161no—
142C2×D13—161no—
143C4×C13—22no—
144C4×C13—21no—
145C4×C13—41no—
146C4×C13—81no—
147C4×C13—82no—
148C4×C13—81no—
149C4×C13#44911yescharacteristic
150C4×C13#45311yescharacteristic
151C4×C13C2×SD3211yescharacteristic
152C4×C13#51011yescharacteristic
153C2×Q16—22no—
154C2×Q16—21no—
155C2×Q16C22⋊D1311yescharacteristic
156C2×Q16C22⋊D1312yes—
157C2×SD16—521no—
158C2×D8—261no—
159C2×D8—261no—
160C4⋊Q8—22no—
161C4⋊Q8—21no—
162#127—261no—
163#125—42no—
164#125—41no—
165C4×Q8—22no—
166C4×Q8—21no—
167C4×Q8—41no—
168C4×Q8C22⋊D1311yescharacteristic
169SD32—524no—
170SD32—522no—
171C2×C16—261no—
172C2×C16—261no—
173#107C22⋊D1311yescharacteristic
174C4⋊C8—21no—
175C4⋊C8—261no—
176C4⋊C8C22⋊D1311yescharacteristic
177#103—22no—
178#103—21no—
179#102—521no—
180C4×C8—21no—
181C4×C8C22×D1311yescharacteristic
182C2×C13#162111yescharacteristic
183C2×C13#218511yescharacteristic
184C2×C13#219311yescharacteristic
185D13—321no—
186C2×Q8—21no—
187C2×Q8—22no—
188C2×Q8#610411yescharacteristic
189C2×D4—521no—
190C2×D4—521no—
191C2×D4—521no—
192Q16—21no—
193Q16—21no—
194Q16—42no—
195Q16—41no—
196Q16—41no—
197Q16—82no—
198SD16—1042no—
199D8—522no—
200D8—521no—
201D8—521no—
202C2×C8—21no—
203C2×C8—521no—
204C2×C8C2×C22⋊D1311yescharacteristic
205C2×C8C2×C22⋊D1311yescharacteristic
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4#610411yescharacteristic
215C42—21no—
216C42—42no—
217C42—41no—
218C42C2×C22⋊D1311yescharacteristic
219C16—262no—
220C16—521no—
221C13#1233011yescharacteristic, complemented, Sylow
222C23—1041no—
223Q8—21no—
224Q8—41no—
225Q8—42no—
226Q8—42no—
227Q8—41no—
228Q8#8806812yescomplemented
229D4—1041no—
230D4—1041no—
231D4—1041no—
232D4—1041no—
233D4—2081no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4C2×#610411yescharacteristic
240C2×C4#8818611yescharacteristic
241C2×C4#8820711yescharacteristic
242C8—21no—
243C8—41no—
244C8—1041no—
245C8#8820311yescharacteristic
246C8#8820411yescharacteristic
247C22—2081no—
248C22—2081no—
249C22—2081no—
250C22#1171887811yescharacteristic
251C4—22no—
252C4—21no—
253C4—41no—
254C4—81no—
255C4—82no—
256C4—81no—
257C4C2×#8806811yescharacteristic
258C4#1171884011yescharacteristic
259C4#1171889911yescharacteristic
260C4#1171890211yescharacteristic
261C2—4161no—
262C2#1311390111yescharacteristic
263C2#1311675311yescharacteristic
264C2#1311680011yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#3395C2
socleC22×C13#447
prime radical#11718356C22
hypercenter#3395D13
hypocenterC13#12330
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3395

Complements

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

NH ≅ G/Ntype
4. #13112885C2semidirect
5. Q8⋊#6090C2semidirect
6. #13112800C2semidirect
7. C13×#3395C2semidirect
90. #3395D13semidirect
103. Q8×C13SD32semidirect
221. C13#12330semidirect
228. Q8#88068semidirect

Maximal subgroups

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

subgroupindex
#131170932
#131168762
#131141962
#131128852
Q8⋊#60902
#131128002
C13×#33952
#1233013