Finite Group Databasebeta

← #15776469

Subgroups — #15776469

Order 3328.

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

normal subgroups only

This group has 306 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#13117088C211yesmaximal, characteristic
2#13116886C211yesmaximal, characteristic
3#13114206C211yesmaximal, characteristic
4#13112885C211yesmaximal, characteristic
5Q8⋊#6090C211yesmaximal, characteristic
6#13112800C211yesmaximal, characteristic
7C13×#3395C211yesmaximal, characteristic
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×#88069—22no—
17C2×#88069—21no—
18#11718681—21no—
19#11718360C2211yescharacteristic
20#11718084—21no—
21#11718074—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×Dic52—21no—
38C2×Dic52—21no—
39#88123—21no—
40C13×#107D411yescharacteristic
41C13×C4⋊C8—21no—
42C13×C4⋊C8D411yescharacteristic
43C13×#103—22no—
44C13×#103—21no—
45C4×C8×C13—21no—
46C4×C8×C13C2311yescharacteristic
47#88075—41no—
48#88069—44no—
49#88069—42no—
50C2×#6090—21no—
51C2×#6090—21no—
52#88048—41no—
53C4⋊#1055—21no—
54#12334—131nomaximal, Sylow
55C2×Q8×C13—21no—
56C2×Q8×C13—22no—
57C2×Q8×C13D811yescharacteristic
58C2×Dic26—41no—
59C13×Q16—21no—
60C13×Q16—21no—
61C13×Q16—42no—
62C13×Q16—41no—
63C13×Q16—41no—
64C13×Q16—82no—
65C2×C8×C13—21no—
66C2×C8×C13C2×D411yescharacteristic
67C2×C8×C13C2×D411yescharacteristic
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4D811yescharacteristic
77C42×C13—21no—
78C42×C13—42no—
79C42×C13—41no—
80C42×C13C2×D411yescharacteristic
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83C2×#1055—41no—
84Dic52—42no—
85Dic52—41no—
86Dic52—41no—
87#6090—22no—
88#6090—41no—
89#3395D1311yescharacteristic
90#2247—131no—
91#2209—131no—
92#1670—131no—
93#1362—131no—
94Q8⋊C16—131no—
95#1332—131no—
96Q8×C13—21no—
97Q8×C13—41no—
98Q8×C13—42no—
99Q8×C13—42no—
100Q8×C13—41no—
101Q8×C13Q3212yescomplemented
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—41no—
105C2×C4×C13—42no—
106C2×C4×C13—41no—
107C2×C4×C13#12011yescharacteristic
108C2×C4×C13C2×D811yescharacteristic
109C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
110C2×Dic13—81no—
111Dic26—81no—
112Dic26—81no—
113C8×C13—21no—
114C8×C13—41no—
115C8×C13#13511yescharacteristic
116C8×C13AGL(1,ℤ/8)11yescharacteristic
117#1055—81no—
118#557—21no—
119C2×Q32—261no—
120C2×Q32—262no—
121#494—21no—
122#494—131no—
123#494C2×D1311yescharacteristic
124#475—261no—
125#462—22no—
126#462—21no—
127C8×Q8C2×D1311yescharacteristic
128C4×Q16—21no—
129C4×Q16C2×D1311yescharacteristic
130C4⋊C16—131no—
131#358—261no—
132C4×C16—131no—
133#335—131no—
134#332—261no—
135C22×C13#44711yescharacteristic
136C4×C13—22no—
137C4×C13—21no—
138C4×C13—41no—
139C4×C13—81no—
140C4×C13—82no—
141C4×C13—81no—
142C4×C13#44911yescharacteristic
143C4×C13#45311yescharacteristic
144C4×C13C2×Q3211yescharacteristic
145C4×C13#51011yescharacteristic
146Dic13—161no—
147C2×Q16—22no—
148C2×Q16—21no—
149C2×Q16—261no—
150C2×Q16—261no—
151C2×Q16C22⋊D1311yescharacteristic
152C2×Q16C22⋊D1312yes—
153C4⋊Q8—22no—
154C4⋊Q8—21no—
155C4⋊Q8—261no—
156#125—42no—
157#125—41no—
158C4×Q8—22no—
159C4×Q8—21no—
160C4×Q8—41no—
161C4×Q8C22⋊D1311yescharacteristic
162Q32—524no—
163Q32—522no—
164C2×C16—261no—
165C2×C16—261no—
166#107C22⋊D1311yescharacteristic
167#106—521no—
168C4⋊C8—21no—
169C4⋊C8—261no—
170C4⋊C8C22⋊D1311yescharacteristic
171#103—22no—
172#103—21no—
173#103—521no—
174C4×C8—21no—
175C4×C8C22×D1311yescharacteristic
176C2×C13#162111yescharacteristic
177C2×C13#218811yescharacteristic
178C2×C13#219511yescharacteristic
179C2×Q8—21no—
180C2×Q8—22no—
181C2×Q8—521no—
182C2×Q8#610411yescharacteristic
183Q16—21no—
184Q16—21no—
185Q16—42no—
186Q16—41no—
187Q16—41no—
188Q16—82no—
189Q16—522no—
190Q16—521no—
191Q16—521no—
192C2×C8—21no—
193C2×C8—521no—
194C2×C8C2×C22⋊D1311yescharacteristic
195C2×C8C2×C22⋊D1311yescharacteristic
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—521no—
205C4⋊C4—521no—
206C4⋊C4#610411yescharacteristic
207C42—21no—
208C42—42no—
209C42—41no—
210C42C2×C22⋊D1311yescharacteristic
211C16—262no—
212C16—521no—
213C13#1233411yescharacteristic, complemented, Sylow
214Q8—21no—
215Q8—41no—
216Q8—42no—
217Q8—42no—
218Q8—41no—
219Q8—1041no—
220Q8—1041no—
221Q8#8806912yescomplemented
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—1041no—
228C2×C4C2×#610411yescharacteristic
229C2×C4#8818611yescharacteristic
230C2×C4#8820711yescharacteristic
231C8—21no—
232C8—41no—
233C8—1041no—
234C8#8820311yescharacteristic
235C8#8820411yescharacteristic
236C22#1171887811yescharacteristic
237C4—22no—
238C4—21no—
239C4—41no—
240C4—81no—
241C4—82no—
242C4—81no—
243C4—2081no—
244C4#1171884011yescharacteristic
245C4C2×#8806911yescharacteristic
246C4#1171889911yescharacteristic
247C4#1171890211yescharacteristic
248C2#1311390111yescharacteristic
249C2#1311677011yescharacteristic
250C2#1311681411yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#3395C2
socle, prime radicalC22×C13#447
hypercenter#3395D13
hypocenterC13#12334
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
101. Q8×C13Q32semidirect
213. C13#12334semidirect
221. Q8#88069semidirect

Maximal subgroups

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

subgroupindex
#131170882
#131168862
#131142062
#131128852
Q8⋊#60902
#131128002
C13×#33952
#1233413