Finite Group Databasebeta

← #15776602

Subgroups — #15776602

Order 3328.

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

normal subgroups only

This group has 298 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#13117061C211yesmaximal, characteristic
2#13116876C211yesmaximal, characteristic
3#13114196C211yesmaximal, characteristic
4#13112891C211yesmaximal, characteristic, complemented
5Q8⋊#6090C211yesmaximal, characteristic, complemented
6#13112800C211yesmaximal, characteristic, complemented
7C13×#3383C211yesmaximal, characteristic, complemented
8C13×#557—21no—
9C13×#500C2211yescharacteristic
10C13×#499—21no—
11C13×#479—22no—
12C13×#475—21no—
13C8×Q8×C13C2211yescharacteristic
14C4×C13×Q16—21no—
15C4×C13×Q16C2211yescharacteristic
16C2×#88068—21no—
17#11718688—21no—
18#11718356C2211yescharacteristic
19#11718083—22no—
20#11718083—21no—
21#11718077—21no—
22C4⋊#6090C2211yescharacteristic
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×Q16D411yescharacteristic
26C13×C4⋊Q8—21no—
27C13×C4⋊Q8—41no—
28C13×#125—22no—
29C13×#125—42no—
30C4×Q8×C13—22no—
31C4×Q8×C13—21no—
32C4×Q8×C13—41no—
33C4×Q8×C13D411yescharacteristic
34C2×#6106—41no—
35C2×D104—21no—
36C2×D104—21no—
37#88128—21no—
38C13×#107—21no—
39C13×#107D411yescharacteristic
40C13×#107D412yes—
41C13×#106—22no—
42C13×C4⋊C8—21no—
43C13×C4⋊C8D411yescharacteristic
44C13×#103—22no—
45C13×#103—21no—
46C4×C8×C13—21no—
47C4×C8×C13C2311yescharacteristic
48#88068—42no—
49C2×#6090—21no—
50C2×#6090—21no—
51#88049—41no—
52C4⋊#1055—21no—
53#12353—131nomaximal, Sylow
54C2×Q8×C13—21no—
55C2×Q8×C13—41no—
56C2×Q8×C13D811yescharacteristic
57C2×D52—41no—
58C2×D52—41no—
59C2×D52—41no—
60C13×Q16—21no—
61C13×Q16SD1612yescomplemented
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—42no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4D811yescharacteristic
74C42×C13—21no—
75C42×C13—42no—
76C42×C13—41no—
77C42×C13C2×D411yescharacteristic
78#6106—82no—
79C2×#1055—41no—
80D104—42no—
81D104—41no—
82D104—41no—
83#6090—41no—
84#6090—41no—
85#3383D1311yescharacteristic, complemented
86#2240—131no—
87#2207—131no—
88#1668—131no—
89#1364—131no—
90Q8⋊C16—131no—
91#1332—131no—
92C22×D13—81no—
93Q8×C13—22no—
94Q8×C13—21no—
95Q8×C13—21no—
96Q8×C13—41no—
97Q8×C13—81no—
98Q8×C13—81no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—42no—
104C2×C4×C13#12011yescharacteristic
105C2×C4×C13C2×D811yescharacteristic
106C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
107D52—81no—
108D52—81no—
109D52—81no—
110D52—81no—
111D52—161no—
112C8×C13—21no—
113C8×C13—41no—
114C8×C13C2×SD1611yescharacteristic
115C8×C13#13711yescharacteristic
116#1055—81no—
117#557—21no—
118C2×SD32—261no—
119#500C2×D1311yescharacteristic
120#499—21no—
121#493—131no—
122#479—22no—
123#475—21no—
124#460—261no—
125C8×Q8C2×D1311yescharacteristic
126C4×Q16—21no—
127C4×Q16C2×D1311yescharacteristic
128C4⋊C16—131no—
129#357—261no—
130#357—262no—
131C4×C16—131no—
132#335—131no—
133#331—261no—
134C22×C13#44711yescharacteristic
135C2×D13—161no—
136C2×D13—161no—
137C2×D13—161no—
138C4×C13—21no—
139C4×C13—42no—
140C4×C13—41no—
141C4×C13—41no—
142C4×C13—82no—
143C4×C13—81no—
144C4×C13#44811yescharacteristic
145C4×C13#45411yescharacteristic
146C4×C13#50811yescharacteristic
147C4×C13#50911yescharacteristic
148C2×Q16C22⋊D1311yescharacteristic
149C2×SD16—521no—
150C2×D8—261no—
151C2×D8—261no—
152C4⋊Q8—21no—
153C4⋊Q8—41no—
154#127—261no—
155#125—22no—
156#125—42no—
157C4×Q8—22no—
158C4×Q8—21no—
159C4×Q8—41no—
160C4×Q8C22⋊D1311yescharacteristic
161SD32—522no—
162C2×C16—261no—
163C2×C16—261no—
164#107—21no—
165#107C22⋊D1311yescharacteristic
166#107C22⋊D1312yes—
167#106—22no—
168C4⋊C8—21no—
169C4⋊C8—261no—
170C4⋊C8C22⋊D1311yescharacteristic
171#103—22no—
172#103—21no—
173#102—521no—
174C4×C8—21no—
175C4×C8C22×D1311yescharacteristic
176C2×C13#162711yescharacteristic
177C2×C13#218611yescharacteristic
178C2×C13#219311yescharacteristic
179D13—321no—
180C2×Q8—21no—
181C2×Q8—41no—
182C2×Q8#610411yescharacteristic
183C2×D4—521no—
184C2×D4—521no—
185C2×D4—521no—
186Q16—21no—
187Q16#610612yescomplemented
188SD16—1042no—
189D8—522no—
190D8—521no—
191D8—521no—
192C2×C8—21no—
193C2×C8—521no—
194C2×C8C2×C22⋊D1311yescharacteristic
195C2×C8C2×C22⋊D1311yescharacteristic
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—22no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4#610411yescharacteristic
205C42—21no—
206C42—42no—
207C42—41no—
208C42C2×C22⋊D1311yescharacteristic
209C16—521no—
210C16—521no—
211C13#1235311yescharacteristic, complemented, Sylow
212C23—1041no—
213Q8—21no—
214Q8—21no—
215Q8—22no—
216Q8—41no—
217Q8—81no—
218Q8—81no—
219D4—1041no—
220D4—1041no—
221D4—1041no—
222D4—1041no—
223D4—2081no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4C2×#610411yescharacteristic
230C2×C4#8818611yescharacteristic
231C2×C4#8820711yescharacteristic
232C8—21no—
233C8—41no—
234C8—1041no—
235C8C2×#610611yescharacteristic
236C8#8819611yescharacteristic
237C22—2081no—
238C22—2081no—
239C22—2081no—
240C22#1171887811yescharacteristic
241C4—21no—
242C4—42no—
243C4—41no—
244C4—41no—
245C4—82no—
246C4—81no—
247C4#1171885411yescharacteristic
248C4#1171885511yescharacteristic
249C4#1171888811yescharacteristic
250C4#1171890611yescharacteristic
251C2—4161no—
252C2#1311393911yescharacteristic
253C2#1311675911yescharacteristic
254C2#1311680011yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#3383C2
socleC22×C13#447
prime radical#11718356C22
hypercenter#3383D13
hypocenterC13#12353
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3383

Complements

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

NH ≅ G/Ntype
4. #13112891C2semidirect
5. Q8⋊#6090C2semidirect
6. #13112800C2semidirect
7. C13×#3383C2semidirect
61. C13×Q16SD16semidirect
85. #3383D13semidirect
187. Q16#6106semidirect
211. C13#12353semidirect

Maximal subgroups

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

subgroupindex
#131170612
#131168762
#131141962
#131128912
Q8⋊#60902
#131128002
C13×#33832
#1235313