Finite Group Databasebeta

← #15772127

Subgroups — #15772127

Order 3328.

314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 89 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#13123476C211yesmaximal, characteristic
2#13116632C212yesmaximal, complemented
3#13112777C212yesmaximal, complemented
4#13112762C211yesmaximal, characteristic
5C13×#1315C211yesmaximal, characteristic
6#41×Dic13C411yescharacteristic
7C13×#408C2211yescharacteristic
8#11718895C411yescharacteristic
9#11718780C411yescharacteristic
10M16×Dic13C411yescharacteristic
11#11718763C2211yescharacteristic
12C2×C8×Dic13C2211yescharacteristic
13#11718381—22no—
14#11718379—22no—
15C13×C22⋊C16C2212yes—
16C22⋊#6090C2212yes—
17#11718093—22no—
18C16×Dic13—22no—
19C2×C13×#41C2×C411yescharacteristic
20C2×C13×M16C2×C411yescharacteristic
21C22×C8×C13C2311yescharacteristic
22Q8×Dic13C812yes—
23D4×Dic13—22no—
24D4×Dic13C812yes—
25#88180—21no—
26#88180C2×C411yescharacteristic
27C2×C4×Dic13—21no—
28C2×C4×Dic13C2×C411yescharacteristic
29C2×#6099C2×C411yescharacteristic
30C22×#1055C2×C411yescharacteristic
31C2×C13×C16—22no—
32C13×C22⋊C8—22no—
33C22⋊#1055—22no—
34#88055—21no—
35#88054—22no—
36#88054—22no—
37C8×Dic13—21no—
38C8×Dic13D412yes—
39C8×Dic13D412yes—
40C2×#6090—22no—
41#11462—131nomaximal, Sylow
42C13×#41—41no—
43C13×#41—41no—
44C2×Q8×C13C2×C811yescharacteristic
45C2×D4×C13—21no—
46C2×D4×C13C2×C811yescharacteristic
47C22×C4×C13—21no—
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13—22no—
50C22×Dic13M1612yes—
51C13×M16—41no—
52C2×C8×C13—21no—
53C2×C8×C13—41no—
54C2×C8×C13C2×D412yes—
55C22⋊Dic13—21no—
56C22⋊Dic13—22no—
57C4⋊Dic13—22no—
58C4⋊Dic13C2×C812yes—
59C4×Dic13—21no—
60C4×Dic13—22no—
61C4×Dic13C22⋊C411yescharacteristic
62C4×Dic13C22⋊C411yescharacteristic
63C4×Dic13C2×C812yes—
64#6099—41no—
65C2×#1055—21no—
66C2×#1055—41no—
67C2×#1055C22⋊C412yes—
68C13×C16—42no—
69#6090—42no—
70#2922—131no—
71#2162—132no—
72#1323—132no—
73#1315—131no—
74#1315D1311yescharacteristic
75C23×C13—21no—
76C23×C13C2×M1611yescharacteristic
77Q8×C13—41no—
78D4×C13—41no—
79D4×C13—42no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—41no—
84C2×C4×C13—41no—
85C2×C4×C13C2×C22⋊C411yescharacteristic
86C2×C4×C13C22×C811yescharacteristic
87C2×Dic13—24no—
88C2×Dic13—22no—
89C2×Dic13—44no—
90C2×Dic13C22⋊C812yes—
91C2×Dic13C22⋊C812yes—
92C8×C13—22no—
93C8×C13—41no—
94#1055—22no—
95#1055—41no—
96C4×#41—131no—
97#433—262no—
98#431—262no—
99#424—131no—
100#424—131no—
101#408—131no—
102#408C2×D1311yescharacteristic
103C4×M16—131no—
104C2×C4×C8—131no—
105C4⋊C16—262no—
106C22⋊C16—132no—
107C22⋊C16C2×D1312yes—
108C4×C16—262no—
109C22×C13—22no—
110C22×C13—21no—
111C22×C13—42no—
112C22×C13—41no—
113C22×C13C2×C22⋊C811yescharacteristic
114C4×C13—21no—
115C4×C13—41no—
116C4×C13#41011yescharacteristic
117C4×C13#41311yescharacteristic
118Dic13—22no—
119Dic13—42no—
120Dic13#35014yes—
121C2×#41C4×D1311yescharacteristic
122C2×M16—131no—
123C2×M16C4×D1311yescharacteristic
124C22×C8—131no—
125C22×C8C22×D1311yescharacteristic
126C4×Q8—132no—
127C4×D4—132no—
128C4×D4—262no—
129#117—131no—
130#117—261no—
131C2×C42—131no—
132C2×C42—261no—
133C2×C16—22no—
134C2×C16—262no—
135C4⋊C8—262no—
136C4⋊C8—262no—
137C22⋊C8—22no—
138C22⋊C8—262no—
139#97—261no—
140C4×C8—132no—
141C4×C8—132no—
142C4×C8—261no—
143C2×C13—41no—
144C2×C13—81no—
145C2×C13#145811yescharacteristic
146C2×C13C2×#35012yes—
147#41—41no—
148#41—41no—
149C2×Q8C8×D1311yescharacteristic
150C2×D4—21no—
151C2×D4C8×D1311yescharacteristic
152C22×C4—21no—
153C22×C4—132no—
154C22×C4—262no—
155C22×C4C2×C4×D1311yescharacteristic
156M16—41no—
157M16—521no—
158C2×C8—21no—
159C2×C8—41no—
160C2×C8—132no—
161C2×C8—261no—
162C2×C8—521no—
163C2×C8D4×D1312yes—
164C4⋊C4—132no—
165C4⋊C4—262no—
166C22⋊C4—262no—
167C22⋊C4—261no—
168C42—131no—
169C42—131no—
170C42—132no—
171C42—262no—
172C42—261no—
173C16—42no—
174C16—522no—
175C13#1146211yescharacteristic, complemented, Sylow
176C23—21no—
177C23M16×D1311yescharacteristic
178Q8—41no—
179D4—41no—
180D4—42no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—132no—
187C2×C4—132no—
188C2×C4—264no—
189C2×C4—262no—
190C2×C4—524no—
191C2×C4C22⋊C4×D1311yescharacteristic
192C2×C4C2×C8×D1311yescharacteristic
193C8—22no—
194C8—41no—
195C8—262no—
196C8—521no—
197C22—22no—
198C22—21no—
199C22—42no—
200C22—41no—
201C22D13×C22⋊C811yescharacteristic
202C4—21no—
203C4—41no—
204C4—134no—
205C4—262no—
206C4—522no—
207C4#1171840111yescharacteristic
208C4#1171840611yescharacteristic
209C2—41no—
210C2—81no—
211C2#1311314711yescharacteristic
212C2D13×#35012yes—
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC2×C4×C13C22×C8
FrattiniC22×C8C22×D13
FittingC13×#1315C2
socleC22×C13C2×C22⋊C8
prime radicalC2×C13×#41C2×C4
cosocleC22×C8×C13C23
hypercenter#1315D13
hypocenterC13#11462
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1315

Complements

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

NH ≅ G/Ntype
2. #13116632C2semidirect
3. #13112777C2semidirect
175. C13#11462semidirect

Maximal subgroups

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

subgroupindex
#131234762
#131166322
#131127772
#131127622
C13×#13152
#1146213