Finite Group Databasebeta

← #15776788

Subgroups — #15776788

Order 3328.

306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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#13127849C211yesmaximal, characteristic
2#13117061C211yesmaximal, characteristic
3#13116975C211yesmaximal, characteristic, complemented
4#13112881C211yesmaximal, characteristic
5Q8⋊#6090C211yesmaximal, characteristic, complemented
6#13112799C211yesmaximal, characteristic, complemented
7C13×#1674C211yesmaximal, characteristic, complemented
8#11719290—21no—
9C13×#500C2211yescharacteristic
10C13×#462—21no—
11C8×Q8×C13C2211yescharacteristic
12#11718509—21no—
13#11718505—22no—
14C4×Dic52C2211yescharacteristic
15#11718357—21no—
16#11718356C2211yescharacteristic
17C4×D104—21no—
18C13×#335C2211yescharacteristic
19C13×#332—21no—
20#11718084—21no—
21#11718083—22no—
22#11718082—21no—
23C4⋊#6090C2211yescharacteristic
24C4×#6090C2211yescharacteristic
25C2×C13×Q16—41no—
26C13×C4⋊Q8—21no—
27C4×Q8×C13D411yescharacteristic
28#88201—41no—
29C2×Dic52D411yescharacteristic
30C2×D104—21no—
31C2×D104D412yes—
32C2×#6095—22no—
33#88148—42no—
34#88147—41no—
35#88129—22no—
36#88128—21no—
37C4×D52—22no—
38C4×Dic26—21no—
39C13×#107—21no—
40C13×#107—21no—
41C13×C4⋊C8—21no—
42C13×C4⋊C8—21no—
43C13×C4⋊C8D411yescharacteristic
44C13×#103—41no—
45C4×C8×C13—21no—
46C4×C8×C13C2311yescharacteristic
47#88061—22no—
48#88058D411yescharacteristic
49#88056—21no—
50C2×#6090—21no—
51C2×#6090—21no—
52#12381—131nomaximal, Sylow
53C2×Q8×C13—41no—
54C2×Q8×C13D811yescharacteristic
55C2×D52—22no—
56C2×D52—41no—
57C2×D52—41no—
58C2×C4×D13—42no—
59C2×Dic26—21no—
60C13×Q16—82no—
61C2×C8×C13—21no—
62C2×C8×C13—41no—
63C2×C8×C13C2×D411yescharacteristic
64C2×C8×C13C2×D411yescharacteristic
65C13×C4⋊C4—21no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4D811yescharacteristic
69C42×C13—21no—
70C42×C13C2×D411yescharacteristic
71#6103—42no—
72#6103—42no—
73#6103—42no—
74C4⋊Dic13—21no—
75#6101—41no—
76C4×Dic13—41no—
77Dic52—21no—
78Dic52—21no—
79D104—42no—
80D104—41no—
81D104—41no—
82#6095—82no—
83#6090—41no—
84#6090—41no—
85#3396—131no—
86#2240—131no—
87#2225—131no—
88#1674D1311yescharacteristic, complemented
89#1361—131no—
90Q8⋊C16—131no—
91#1332—131no—
92C22×D13—42no—
93Q8×C13—21no—
94Q8×C13—21no—
95Q8×C13—81no—
96Q8×C13—81no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—81no—
100C2×C4×C13#12011yescharacteristic
101C2×C4×C13C2×D811yescharacteristic
102C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
103C2×Dic13—41no—
104C2×Dic13—41no—
105D52—42no—
106D52—42no—
107D52—81no—
108D52—81no—
109D52—161no—
110C4×D13—162no—
111Dic26—41no—
112Dic26—41no—
113C8×C13—21no—
114C8×C13—41no—
115C8×C13—81no—
116C8×C13#13511yescharacteristic
117C8×C13#13711yescharacteristic
118#559—261no—
119#500C2×D1311yescharacteristic
120#495—261no—
121#493—131no—
122#463—262no—
123#462—21no—
124#460—261no—
125C8×Q8C2×D1311yescharacteristic
126C4×Q16—131no—
127C4×D8—261no—
128#367—261no—
129C4⋊C16—131no—
130#358—261no—
131#357—262no—
132C4×C16—131no—
133#335C2×D1311yescharacteristic
134#332—21no—
135C22×C13#44711yescharacteristic
136C2×D13—82no—
137C2×D13—82no—
138C2×D13—82no—
139C4×C13—21no—
140C4×C13—41no—
141C4×C13—41no—
142C4×C13—161no—
143C4×C13#45211yescharacteristic
144C4×C13#45511yescharacteristic
145C4×C13#50811yescharacteristic
146C4×C13#50911yescharacteristic
147Dic13—81no—
148Dic13—81no—
149C2×Q16—41no—
150C2×Q16—131no—
151C2×SD16—262no—
152C2×D8—132no—
153C2×D8—261no—
154C4⋊Q8—21no—
155#127—261no—
156#124—262no—
157#124—521no—
158#123—522no—
159C4×Q8—261no—
160C4×Q8C22⋊D1311yescharacteristic
161C4×D4—262no—
162C4×D4—521no—
163C2×C16—261no—
164C2×C16—261no—
165#107—21no—
166#107—21no—
167#107—131no—
168C4⋊C8—21no—
169C4⋊C8—21no—
170C4⋊C8C22⋊D1311yescharacteristic
171#103—41no—
172#103—261no—
173#102—262no—
174C4×C8—21no—
175C4×C8C22×D1311yescharacteristic
176C2×C13#164111yescharacteristic
177C2×C13#218611yescharacteristic
178C2×C13#219411yescharacteristic
179D13—162no—
180C2×Q8—41no—
181C2×Q8—261no—
182C2×Q8#610411yescharacteristic
183C2×D4—262no—
184C2×D4—521no—
185C2×D4—521no—
186C22×C4—522no—
187Q16—82no—
188Q16—261no—
189Q16—261no—
190SD16—1042no—
191D8—522no—
192D8—521no—
193D8—521no—
194C2×C8—21no—
195C2×C8—41no—
196C2×C8D4×D1311yescharacteristic
197C2×C8D4×D1311yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—261no—
202C4⋊C4—521no—
203C4⋊C4#610411yescharacteristic
204C22⋊C4—522no—
205C22⋊C4—522no—
206C22⋊C4—522no—
207C42—21no—
208C42—521no—
209C42C2×C22⋊D1311yescharacteristic
210C16—521no—
211C16—521no—
212C13#1238111yescharacteristic, complemented, Sylow
213C23—522no—
214Q8—21no—
215Q8—21no—
216Q8—81no—
217Q8—81no—
218Q8—521no—
219Q8—521no—
220D4—522no—
221D4—522no—
222D4—1041no—
223D4—1041no—
224D4—2081no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—81no—
228C2×C4—521no—
229C2×C4—521no—
230C2×C4—2082no—
231C2×C4C2×#610411yescharacteristic
232C2×C4#8819111yescharacteristic
233C2×C4#8820311yescharacteristic
234C8—21no—
235C8—41no—
236C8—81no—
237C8#8817211yescharacteristic
238C8#8817311yescharacteristic
239C22—1042no—
240C22—1042no—
241C22—1042no—
242C22#1171869711yescharacteristic
243C4—21no—
244C4—41no—
245C4—41no—
246C4—161no—
247C4—1041no—
248C4—1041no—
249C4#1171880811yescharacteristic
250C4#1171884811yescharacteristic
251C4#1171885511yescharacteristic
252C4#1171886311yescharacteristic
253C2—2082no—
254C2#1311402711yescharacteristic
255C2#1311675711yescharacteristic
256C2#1311680511yescharacteristic
subgroupG/H
centerC22#11718697
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1674C2
socleC22×C13#447
prime radical#11718356C22
hypercenter#1674D13
hypocenterC13#12381
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1674

Complements

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

NH ≅ G/Ntype
3. #13116975C2semidirect
5. Q8⋊#6090C2semidirect
6. #13112799C2semidirect
7. C13×#1674C2semidirect
88. #1674D13semidirect
212. C13#12381semidirect

Maximal subgroups

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

subgroupindex
#131278492
#131170612
#131169752
#131128812
Q8⋊#60902
#131127992
C13×#16742
#1238113