Finite Group Databasebeta

← #15749598

Subgroups — #15749598

Order 3328.

286 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 51 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#13112760C211yesmaximal, characteristic
2#13112704C211yesmaximal, characteristic
3C13×#2001C211yesmaximal, characteristic
4C22×C13×Q16C411yescharacteristic, complemented
5C2×C13×C22⋊Q8—21no—
6C2×C13×#103—21no—
7C2×C13×C22⋊C8C2211yescharacteristic
8#11718873—21no—
9C13×#340C411yescharacteristic, complemented
10C22⋊#6090—21no—
11C22×Q8×C13—21no—
12C23×C4×C13D411yescharacteristic
13C2×C13×Q16—41no—
14C2×C13×Q16—42no—
15C22×C8×C13C2×C411yescharacteristic
16C22×C8×C13D411yescharacteristic
17C13×C22⋊Q8—42no—
18C13×C22⋊Q8—42no—
19C2×C13×C4⋊C4—21no—
20C2×C13×C4⋊C4—41no—
21C2×C13×C22⋊C4—41no—
22C2×C22⋊Dic13—41no—
23C2×C4⋊Dic13—41no—
24C13×#103—42no—
25C13×C22⋊C8—41no—
26#88071—22no—
27C2×#6090—41no—
28#7078—131nomaximal, Sylow
29C24×C13D811yescharacteristic
30C2×Q8×C13—22no—
31C2×Q8×C13—41no—
32C2×Q8×C13—41no—
33C2×Q8×C13—41no—
34C2×Q8×C13—41no—
35C2×Q8×C13—41no—
36C22×C4×C13—21no—
37C22×C4×C13—21no—
38C22×C4×C13—41no—
39C22×C4×C13—41no—
40C22×C4×C13—41no—
41C22×C4×C13—41no—
42C22×C4×C13C22⋊C411yescharacteristic
43C22×C4×C13SD1611yescharacteristic
44C22×Dic13—42no—
45C13×Q16—42no—
46C13×Q16—42no—
47C2×C8×C13—21no—
48C2×C8×C13—21no—
49C2×C8×C13—41no—
50C2×C8×C13—41no—
51C13×C4⋊C4—22no—
52C13×C4⋊C4—41no—
53C13×C4⋊C4—44no—
54C13×C22⋊C4—44no—
55C22⋊Dic13—81no—
56C22⋊Dic13—81no—
57C4⋊Dic13—81no—
58C4⋊Dic13—81no—
59#6090—81no—
60#2001D1311yescharacteristic
61#1314—131no—
62#1289—131no—
63C23×C13—21no—
64C23×C13—21no—
65C23×C13—41no—
66C23×C13—41no—
67C23×C13#10211yescharacteristic
68C23×C13SD3211yescharacteristic
69C23×C13Q3211yescharacteristic
70Q8×C13—42no—
71Q8×C13—42no—
72Q8×C13—81no—
73Q8×C13—81no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—41no—
78C2×C4×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—81no—
83C2×C4×C13—81no—
84C2×C4×C13—81no—
85C2×C4×C13—81no—
86C2×C4×C13—81no—
87C2×C4×C13#9911yescharacteristic
88C2×C4×C13#10411yescharacteristic
89C2×Dic13—82no—
90C2×Dic13—82no—
91C2×Dic13—82no—
92C8×C13—41no—
93C8×C13—41no—
94C22×Q16Dic1311yescharacteristic, complemented
95C2×C22⋊Q8—21no—
96C2×#103—21no—
97C2×C22⋊C8C2×D1311yescharacteristic
98#380—261no—
99C22⋊C16—261no—
100#340Dic1311yescharacteristic, complemented
101C22×C13—21no—
102C22×C13—21no—
103C22×C13—21no—
104C22×C13—21no—
105C22×C13—41no—
106C22×C13—41no—
107C22×C13—41no—
108C22×C13—41no—
109C22×C13—81no—
110C22×C13#32711yescharacteristic
111C22×C13#35811yescharacteristic
112C22×C13#36011yescharacteristic
113C4×C13—21no—
114C4×C13—41no—
115C4×C13—82no—
116C4×C13—82no—
117C4×C13AΣL(1,𝔽16)11yescharacteristic
118C4×C13#35311yescharacteristic
119Dic13—162no—
120C22×Q8—21no—
121C23×C4C22⋊D1311yescharacteristic
122C2×Q16—41no—
123C2×Q16—42no—
124C22×C8C2×Dic1311yescharacteristic
125C22×C8C22⋊D1311yescharacteristic
126C22⋊Q8—42no—
127C22⋊Q8—42no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—41no—
130C2×C4⋊C4—521no—
131C2×C22⋊C4—41no—
132C2×C22⋊C4—521no—
133C2×C16—521no—
134#103—42no—
135C22⋊C8—41no—
136#95—262no—
137C2×C13—21no—
138C2×C13—21no—
139C2×C13—41no—
140C2×C13—41no—
141C2×C13#134011yescharacteristic
142C2×C13#134311yescharacteristic
143C2×C13#134811yescharacteristic
144C24#610411yescharacteristic
145C2×Q8—22no—
146C2×Q8—41no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—41no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—522no—
158C22×C4#610511yescharacteristic
159C22×C4C22⋊Dic1311yescharacteristic
160Q16—42no—
161Q16—42no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—41no—
165C2×C8—41no—
166C4⋊C4—22no—
167C4⋊C4—41no—
168C4⋊C4—44no—
169C4⋊C4—1041no—
170C4⋊C4—1041no—
171C22⋊C4—44no—
172C22⋊C4—1041no—
173C22⋊C4—1041no—
174C16—1041no—
175C13#707811yescharacteristic, complemented, Sylow
176C23—21no—
177C23—21no—
178C23—41no—
179C23—41no—
180C23#8806811yescharacteristic
181C23#8806911yescharacteristic
182C23#8807211yescharacteristic
183Q8—42no—
184Q8—42no—
185Q8—81no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—1042no—
201C2×C4—1042no—
202C2×C4—1042no—
203C2×C4#8807411yescharacteristic
204C2×C4#8807711yescharacteristic
205C8—41no—
206C8—41no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—41no—
215C22—81no—
216C22#1171812911yescharacteristic
217C22#1171815611yescharacteristic
218C22#1171815811yescharacteristic
219C4—21no—
220C4—41no—
221C4—82no—
222C4—82no—
223C4—2082no—
224C4#1171812811yescharacteristic
225C4#1171813711yescharacteristic
226C2—21no—
227C2—21no—
228C2—41no—
229C2—41no—
230C2#1311282411yescharacteristic
231C2#1311283311yescharacteristic
232C2#1311284811yescharacteristic
subgroupG/H
centerC22#11718129
commutatorC22×C8×C13C2×C4
FrattiniC2×C22⋊C8C2×D13
FittingC13×#2001C2
socleC22×C13#327
prime radicalC24×C13D8
cosocleC2×C13×C22⋊C8C22
hypercenter#2001D13
hypocenterC13#7078
LCSG ▷ C22×C8×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #2001

Complements

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

NH ≅ G/Ntype
4. C22×C13×Q16C4semidirect
9. C13×#340C4semidirect
94. C22×Q16Dic13semidirect
100. #340Dic13semidirect
175. C13#7078semidirect

Maximal subgroups

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

subgroupindex
#131127602
#131127042
C13×#20012
#707813