Finite Group Databasebeta

← #15776644

Subgroups — #15776644

Order 3328.

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

normal subgroups only

This group has 296 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#13117065C211yesmaximal, characteristic, complemented
2#13116881C211yesmaximal, characteristic
3#13114206C211yesmaximal, characteristic, complemented
4#13112894C211yesmaximal, characteristic, complemented
5Q8⋊#6090C211yesmaximal, characteristic, complemented
6#13112797C211yesmaximal, characteristic
7C13×#3380C211yesmaximal, characteristic
8C13×#554—21no—
9C13×#500C2211yescharacteristic
10C13×#499—21no—
11C13×#478—22no—
12C13×#476—21no—
13C8×Q8×C13C2211yescharacteristic
14C4×C13×D8—21no—
15C4×C13×D8C2211yescharacteristic
16C2×#88067—21no—
17#11718681—21no—
18#11718360C2211yescharacteristic
19#11718084—22no—
20#11718084—21no—
21#11718074—21no—
22C4⋊#6090C2211yescharacteristic
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×D8D411yescharacteristic
26C13×C4⋊Q8—21no—
27C13×#125—22no—
28C13×C22⋊Q8—42no—
29C13×C22⋊Q8—41no—
30C4×Q8×C13D411yescharacteristic
31C4×D4×C13—22no—
32C4×D4×C13—21no—
33C2×C13×C4⋊C4—41no—
34C2×Dic52—21no—
35C2×Dic52—21no—
36#88123—21no—
37C13×#107—21no—
38C13×#107D411yescharacteristic
39C13×#107D412yes—
40C13×#106—22no—
41C13×C4⋊C8—21no—
42C13×C4⋊C8D411yescharacteristic
43C13×#102—22no—
44C13×#102—21no—
45C4×C8×C13—21no—
46C4×C8×C13C2311yescharacteristic
47#88075—41no—
48#88067—42no—
49C2×#6090—21no—
50C2×#6090—21no—
51#88048—41no—
52C4⋊#1055—21no—
53#12359—131nomaximal, Sylow
54C2×Q8×C13—41no—
55C2×Q8×C13D811yescharacteristic
56C2×D4×C13—21no—
57C22×C4×C13—42no—
58C22×C4×C13—41no—
59C2×Dic26—41no—
60C13×D8—21no—
61C13×D8SD1612yes—
62C2×C8×C13—21no—
63C2×C8×C13C2×D411yescharacteristic
64C2×C8×C13C2×D411yescharacteristic
65C13×C4⋊C4—21no—
66C13×C4⋊C4—21no—
67C13×C4⋊C4—22no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4D811yescharacteristic
72C13×C22⋊C4—42no—
73C13×C22⋊C4—41no—
74C42×C13—21no—
75C42×C13C2×D411yescharacteristic
76C4⋊Dic13—41no—
77C4⋊Dic13—41no—
78C2×#1055—41no—
79Dic52—42no—
80Dic52—41no—
81Dic52—41no—
82#6090—41no—
83#6090—41no—
84#3380D1311yescharacteristic
85#2241—131no—
86#2208—131no—
87#1670—131no—
88#1365—131no—
89Q8⋊C16—131no—
90#1331—131no—
91C23×C13—41no—
92Q8×C13—21no—
93Q8×C13—21no—
94Q8×C13—161no—
95D4×C13—22no—
96D4×C13—41no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13—81no—
102C2×C4×C13—81no—
103C2×C4×C13—162no—
104C2×C4×C13#12011yescharacteristic
105C2×C4×C13C2×D811yescharacteristic
106C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
107C2×Dic13—81no—
108Dic26—81no—
109Dic26—81no—
110C8×C13—21no—
111C8×C13—41no—
112C8×C13C2×SD1611yescharacteristic
113C8×C13#13711yescharacteristic
114#1055—81no—
115#554—21no—
116C2×SD32—261no—
117#500C2×D1311yescharacteristic
118#499—21no—
119#494—131no—
120#478—22no—
121#476—21no—
122#475—261no—
123C8×Q8C2×D1311yescharacteristic
124C4×D8—21no—
125C4×D8C2×D1311yescharacteristic
126C4⋊C16—131no—
127#358—261no—
128#358—262no—
129C4×C16—131no—
130#335—131no—
131#332—261no—
132C22×C13—42no—
133C22×C13—81no—
134C22×C13—81no—
135C22×C13#44711yescharacteristic
136C4×C13—21no—
137C4×C13—41no—
138C4×C13—41no—
139C4×C13—81no—
140C4×C13—82no—
141C4×C13#44811yescharacteristic
142C4×C13#45411yescharacteristic
143C4×C13#50811yescharacteristic
144C4×C13#51011yescharacteristic
145Dic13—161no—
146C2×Q16—261no—
147C2×Q16—261no—
148C2×D8C22⋊D1311yescharacteristic
149C4⋊Q8—21no—
150C4⋊Q8—261no—
151#125—22no—
152C22⋊Q8—42no—
153C22⋊Q8—41no—
154C4×Q8C22⋊D1311yescharacteristic
155C4×D4—22no—
156C4×D4—21no—
157C2×C4⋊C4—41no—
158SD32—522no—
159C2×C16—261no—
160C2×C16—261no—
161#107—21no—
162#107C22⋊D1311yescharacteristic
163#107C22⋊D1312yes—
164#106—22no—
165#106—521no—
166C4⋊C8—21no—
167C4⋊C8—261no—
168C4⋊C8C22⋊D1311yescharacteristic
169#103—521no—
170#102—22no—
171#102—21no—
172C4×C8—21no—
173C4×C8C22×D1311yescharacteristic
174C2×C13—82no—
175C2×C13#162711yescharacteristic
176C2×C13#218911yescharacteristic
177C2×C13#219411yescharacteristic
178C2×Q8—41no—
179C2×Q8—521no—
180C2×Q8#610411yescharacteristic
181C2×D4—21no—
182C22×C4—42no—
183C22×C4—41no—
184Q16—522no—
185Q16—521no—
186Q16—521no—
187D8—21no—
188D8#610612yes—
189C2×C8—21no—
190C2×C8—521no—
191C2×C8C2×C22⋊D1311yescharacteristic
192C2×C8C2×C22⋊D1311yescharacteristic
193C4⋊C4—21no—
194C4⋊C4—21no—
195C4⋊C4—22no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—41no—
199C4⋊C4—521no—
200C4⋊C4—521no—
201C4⋊C4#610411yescharacteristic
202C22⋊C4—42no—
203C22⋊C4—41no—
204C42—21no—
205C42C2×C22⋊D1311yescharacteristic
206C16—521no—
207C16—521no—
208C13#1235911yescharacteristic, complemented, Sylow
209C23—41no—
210Q8—21no—
211Q8—21no—
212Q8—161no—
213Q8—1041no—
214Q8—1041no—
215D4—22no—
216D4—41no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4—162no—
224C2×C4—1041no—
225C2×C4C2×#610411yescharacteristic
226C2×C4#8818611yescharacteristic
227C2×C4#8820711yescharacteristic
228C8—21no—
229C8—41no—
230C8—1041no—
231C8C2×#610611yescharacteristic
232C8#8819611yescharacteristic
233C22—42no—
234C22—81no—
235C22—81no—
236C22#1171887811yescharacteristic
237C4—21no—
238C4—41no—
239C4—41no—
240C4—81no—
241C4—82no—
242C4—2081no—
243C4#1171885511yescharacteristic
244C4#1171885611yescharacteristic
245C4#1171888811yescharacteristic
246C4#1171890611yescharacteristic
247C2—82no—
248C2#1311393911yescharacteristic
249C2#1311677611yescharacteristic
250C2#1311680711yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#3380C2
socleC22×C13#447
prime radicalC2×C13×D8D4
hypercenter#3380D13
hypocenterC13#12359
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3380

Complements

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

NH ≅ G/Ntype
1. #13117065C2semidirect
3. #13114206C2semidirect
4. #13112894C2semidirect
5. Q8⋊#6090C2semidirect
208. C13#12359semidirect

Maximal subgroups

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

subgroupindex
#131170652
#131168812
#131142062
#131128942
Q8⋊#60902
#131127972
C13×#33802
#1235913