Finite Group Databasebeta

← #15777336

Subgroups — #15777336

Order 3328.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#13117060C211yesmaximal, characteristic, complemented
2#13114225C211yesmaximal, characteristic, complemented
3#13114191C211yesmaximal, characteristic
4#13112908C211yesmaximal, characteristic, complemented
5#13112890C211yesmaximal, characteristic, complemented
6#13112883C211yesmaximal, characteristic, complemented
7D4×C13×C16C211yesmaximal, characteristic, complemented
8C22×C13×C16—21no—
9C8×D4×C13C2211yescharacteristic
10#11718680—21no—
11#11718676—21no—
12#11718356C2211yescharacteristic
13#11718343C2211yescharacteristic
14C13×C4⋊C16C2211yescharacteristic
15C13×C22⋊C16—21no—
16C4×C13×C16C2211yescharacteristic
17#11718101—21no—
18#11718101—21no—
19#11718078—21no—
20#11718077—21no—
21#11718050C2211yescharacteristic
22#11718050C2211yescharacteristic
23C22×C8×C13—21no—
24C4×D4×C13D411yescharacteristic
25C2×#6105—41no—
26C2×#6104—41no—
27C2×D104—21no—
28C2×D104—21no—
29#88128—21no—
30#88123—21no—
31C2×C13×C16—21no—
32C2×C13×C16—42no—
33C2×C13×C16D411yescharacteristic
34C2×C13×C16D411yescharacteristic
35C13×C4⋊C8D411yescharacteristic
36C13×C22⋊C8—21no—
37C4×C8×C13C2311yescharacteristic
38#88058—21no—
39#88058—21no—
40#88050—41no—
41#88049—41no—
42C4⋊#1055—21no—
43C4⋊#1055—21no—
44#12467—131nomaximal, Sylow
45C2×D4×C13D811yescharacteristic
46C22×C4×C13—21no—
47C2×D52—41no—
48C2×D52—41no—
49C2×D52—41no—
50C2×Dic26—41no—
51C2×C8×C13—21no—
52C2×C8×C13—41no—
53C2×C8×C13—41no—
54C2×C8×C13C2×D411yescharacteristic
55C2×C8×C13#4111yescharacteristic
56C13×C4⋊C4D811yescharacteristic
57C13×C22⋊C4—21no—
58C42×C13C2×D411yescharacteristic
59#6105—82no—
60#6104—82no—
61C4⋊Dic13—41no—
62C4⋊Dic13—41no—
63C2×#1055—41no—
64C2×#1055—41no—
65D104—41no—
66D104—41no—
67D104—81no—
68C13×C16—21no—
69C13×C16—21no—
70C13×C16—41no—
71#2240—131no—
72D4×C16D1311yescharacteristic, complemented
73#1673—131no—
74#1667—131no—
75#1371—131no—
76#1364—131no—
77#1361—131no—
78C23×C13—21no—
79C22×D13—81no—
80D4×C13—21no—
81D4×C13D1612yes—
82C2×C4×C13—21no—
83C2×C4×C13—41no—
84C2×C4×C13—41no—
85C2×C4×C13#12111yescharacteristic
86C2×C4×C13C2×D811yescharacteristic
87C2×C4×C13#13511yescharacteristic
88C2×Dic13—81no—
89D52—81no—
90D52—81no—
91D52—81no—
92D52—81no—
93D52—161no—
94Dic26—81no—
95Dic26—81no—
96C8×C13—21no—
97C8×C13—41no—
98C8×C13#13511yescharacteristic
99C8×C13AGL(1,ℤ/8)11yescharacteristic
100#1055—81no—
101#1055—81no—
102C22×C16—21no—
103#500—131no—
104#493—131no—
105#461—261no—
106#459—261no—
107C8×D4C2×D1311yescharacteristic
108C4⋊C16C2×D1311yescharacteristic
109#357—261no—
110#357—261no—
111C22⋊C16—21no—
112C4×C16C2×D1311yescharacteristic
113#335—131no—
114#335—131no—
115#332—261no—
116#331—261no—
117C22×C13—22no—
118C22×C13—41no—
119C22×C13—41no—
120C22×C13#46611yescharacteristic
121C2×D13—161no—
122C2×D13—161no—
123C2×D13—161no—
124C4×C13—21no—
125C4×C13—41no—
126C4×C13#46311yescharacteristic
127C4×C13#47111yescharacteristic
128C4×C13C2×D1611yescharacteristic
129C4×C13#50811yescharacteristic
130Dic13—161no—
131C2×SD16—521no—
132C2×D8—261no—
133C2×D8—261no—
134C2×D8—521no—
135C22×C8—21no—
136C4⋊Q8—261no—
137#127—261no—
138C4×D4D5211yescharacteristic
139C2×C16—21no—
140C2×C16—42no—
141C2×C16C22⋊D1311yescharacteristic
142C2×C16C22⋊D1311yescharacteristic
143#107—261no—
144#107—261no—
145C4⋊C8—261no—
146C4⋊C8—261no—
147C4⋊C8D5211yescharacteristic
148#103—521no—
149#102—521no—
150C22⋊C8—21no—
151C4×C8C22×D1311yescharacteristic
152C2×C13—42no—
153C2×C13#168111yescharacteristic
154C2×C13#221511yescharacteristic
155C2×C13#222311yescharacteristic
156D13—321no—
157C2×Q8—521no—
158C2×D4—521no—
159C2×D4—521no—
160C2×D4—521no—
161C2×D4D10411yescharacteristic
162C22×C4—21no—
163SD16—1042no—
164D8—521no—
165D8—521no—
166D8—1041no—
167D8—1042no—
168C2×C8—21no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—521no—
172C2×C8—521no—
173C2×C8#612711yescharacteristic
174C2×C8C2×C22⋊D1311yescharacteristic
175C4⋊C4—521no—
176C4⋊C4—521no—
177C4⋊C4D10411yescharacteristic
178C22⋊C4—21no—
179C42C2×D5211yescharacteristic
180C16—21no—
181C16—21no—
182C16—41no—
183C13#1246711yescharacteristic, complemented, Sylow
184C23—21no—
185C23—1041no—
186Q8—1041no—
187Q8—1041no—
188D4—21no—
189D4—1041no—
190D4—1041no—
191D4—1041no—
192D4—1041no—
193D4—2081no—
194D4D20812yes—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—1041no—
199C2×C4C2×D10411yescharacteristic
200C2×C4#8815811yescharacteristic
201C2×C4#8818411yescharacteristic
202C8—21no—
203C8—41no—
204C8—1041no—
205C8—1041no—
206C8#8818611yescharacteristic
207C8#8820411yescharacteristic
208C22—22no—
209C22—41no—
210C22—41no—
211C22—2081no—
212C22—2081no—
213C22—2081no—
214C22#1171877611yescharacteristic
215C4—21no—
216C4—41no—
217C4—2081no—
218C4C2×D20811yescharacteristic
219C4#1171856511yescharacteristic
220C4#1171867711yescharacteristic
221C4#1171880211yescharacteristic
222C2—42no—
223C2—4161no—
224C2#1311427311yescharacteristic
225C2#1311692211yescharacteristic
226C2#1311696611yescharacteristic
subgroupG/H
centerC22#11718776
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingD4×C13×C16C2
socleC22×C13#466
prime radical#13114191C2
hypercenterD4×C16D13
hypocenterC13#12467
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
1. #13117060C2semidirect
2. #13114225C2semidirect
4. #13112908C2semidirect
5. #13112890C2semidirect
6. #13112883C2semidirect
7. D4×C13×C16C2semidirect
72. D4×C16D13semidirect
183. C13#12467semidirect

Maximal subgroups

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

subgroupindex
#131170602
#131142252
#131141912
#131129082
#131128902
#131128832
D4×C13×C162
#1246713