Finite Group Databasebeta

← #15772153

Subgroups — #15772153

Order 3328.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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#13123533C211yesmaximal, characteristic
2D13×C22⋊C16C212yesmaximal, complemented
3#13112777C212yesmaximal, complemented
4#13112762C211yesmaximal, characteristic, complemented
5C13×#1315C211yesmaximal, characteristic, complemented
6#11719533C411yescharacteristic
7C2×#88202C411yescharacteristic
8C22×C8×D13C2211yescharacteristic
9C13×#408C2211yescharacteristic
10#11718787C411yescharacteristic
11#11718783C411yescharacteristic
12#11718763C2211yescharacteristic
13C2×C16×D13—22no—
14#11718389—22no—
15#11718386—22no—
16C13×C22⋊C16C2212yes—
17C22⋊#6090C2212yes—
18#11718099—22no—
19C2×C13×#41C2×C411yescharacteristic
20C22×C4×D13C2×C411yescharacteristic
21C2×C13×M16C2×C411yescharacteristic
22C22×C8×C13C2311yescharacteristic
23#88202—42no—
24#88200C812yes—
25#88192C812yes—
26#88191—21no—
27#88189—21no—
28C4×C22⋊D13—22no—
29#88180C2×C411yescharacteristic
30C2×#6099—21no—
31C2×#6099C2×C411yescharacteristic
32C22×#1055—21no—
33C22×#1055C2×C411yescharacteristic
34C2×C8×D13—42no—
35C2×C8×D13D412yes—
36C2×C8×D13D412yes—
37C2×C13×C16—22no—
38C13×C22⋊C8—22no—
39#88060—22no—
40#88055—21no—
41#88054—22no—
42C8×Dic13—21no—
43C2×#6090—22no—
44C16×D13—44no—
45#11468—131nomaximal, Sylow
46C23×D13M1611yescharacteristic
47C13×#41—41no—
48C13×#41—41no—
49C2×Q8×C13C2×C811yescharacteristic
50C2×D4×C13—21no—
51C2×D4×C13C2×C811yescharacteristic
52C22×C4×C13—21no—
53C22×C4×C13C22×C411yescharacteristic
54C2×C22⋊D13—22no—
55C22×Dic13M1611yescharacteristic
56C2×C4×D13—41no—
57C2×C4×D13—41no—
58C2×C4×D13C22⋊C412yes—
59C2×C4×D13C2×C812yes—
60C13×M16—41no—
61C2×C8×C13—21no—
62C2×C8×C13—41no—
63C2×C8×C13C2×D412yes—
64C22⋊Dic13—21no—
65C22⋊Dic13—22no—
66#6103—22no—
67C4⋊Dic13C2×C812yes—
68#6101—22no—
69C4×Dic13—21no—
70#6099—42no—
71#6099—41no—
72C2×#1055—22no—
73C2×#1055—21no—
74C2×#1055—42no—
75C2×#1055C22⋊C411yescharacteristic
76C2×#1055C22⋊C411yescharacteristic
77C8×D13—24no—
78C8×D13—42no—
79C13×C16—42no—
80#6090—42no—
81#2929—131no—
82C2×C22⋊C16—132no—
83#1323—132no—
84#1315—131no—
85#1315D1311yescharacteristic, complemented
86C23×C13—21no—
87C23×C13C2×M1611yescharacteristic
88C22×D13—24no—
89C22×D13—41no—
90C22×D13C22⋊C812yes—
91Q8×C13—41no—
92D4×C13—41no—
93D4×C13—42no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13C2×C22⋊C411yescharacteristic
100C2×C4×C13C22×C811yescharacteristic
101C22⋊D13—44no—
102C2×Dic13—22no—
103C2×Dic13—41no—
104C2×Dic13C22⋊C812yes—
105C4×D13—22no—
106C4×D13—22no—
107C4×D13—42no—
108C8×C13—22no—
109C8×C13—41no—
110#1055—21no—
111#1055—41no—
112#1055#9912yes—
113C2×#131—131no—
114C23×C8—131no—
115#525—131no—
116C22×C16—262no—
117#435—262no—
118C8×D4—262no—
119#424—131no—
120#408C2×D1311yescharacteristic
121#407—131no—
122#405—131no—
123C22⋊C16—132no—
124C22⋊C16—262no—
125C22⋊C16C2×D1312yes—
126C22×C13—22no—
127C22×C13—21no—
128C22×C13—42no—
129C22×C13—41no—
130C22×C13C2×C22⋊C811yescharacteristic
131C2×D13—22no—
132C2×D13—22no—
133C2×D13—44no—
134C2×D13#35014yes—
135C4×C13—21no—
136C4×C13—41no—
137C4×C13C2×#9911yescharacteristic
138C4×C13#41311yescharacteristic
139Dic13—22no—
140Dic13—42no—
141C2×#41C4×D1311yescharacteristic
142C23×C4—131no—
143#131—522no—
144C2×M16—131no—
145C2×M16—261no—
146C2×M16C4×D1311yescharacteristic
147C22×C8—131no—
148C22×C8—132no—
149C22×C8—132no—
150C22×C8—261no—
151C22×C8—522no—
152C22×C8C22×D1311yescharacteristic
153#123—261no—
154C22⋊Q8—132no—
155#121—132no—
156#120—261no—
157C4×D4—262no—
158#117—131no—
159C2×C16—22no—
160C2×C16—262no—
161C2×C16—524no—
162C4⋊C8—262no—
163C22⋊C8—22no—
164C22⋊C8—262no—
165#97—261no—
166C4×C8—261no—
167C2×C13—41no—
168C2×C13—81no—
169C2×C13#145911yescharacteristic
170C2×C13C2×#35012yes—
171D13—24no—
172C24—131no—
173#41—41no—
174#41—41no—
175C2×Q8C8×D1311yescharacteristic
176C2×D4—21no—
177C2×D4—262no—
178C2×D4C8×D1311yescharacteristic
179C22×C4—21no—
180C22×C4—131no—
181C22×C4—132no—
182C22×C4—132no—
183C22×C4—521no—
184C22×C4—521no—
185C22×C4C2×C4×D1311yescharacteristic
186M16—41no—
187M16—522no—
188M16—521no—
189C2×C8—21no—
190C2×C8—41no—
191C2×C8—131no—
192C2×C8—131no—
193C2×C8—264no—
194C2×C8—262no—
195C2×C8—261no—
196C2×C8—522no—
197C2×C8—522no—
198C2×C8D4×D1312yes—
199C4⋊C4—132no—
200C4⋊C4—262no—
201C22⋊C4—262no—
202C22⋊C4—262no—
203C22⋊C4—261no—
204C42—261no—
205C16—42no—
206C16—522no—
207C13#1146811yescharacteristic, complemented, Sylow
208C23—21no—
209C23—132no—
210C23—264no—
211C23—521no—
212C23M16×D1311yescharacteristic
213Q8—41no—
214D4—41no—
215D4—42no—
216D4—524no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—132no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—522no—
227C2×C4—521no—
228C2×C4C22⋊C4×D1311yescharacteristic
229C2×C4C2×C8×D1311yescharacteristic
230C8—22no—
231C8—41no—
232C8—132no—
233C8—261no—
234C8—521no—
235C22—22no—
236C22—21no—
237C22—42no—
238C22—41no—
239C22—134no—
240C22—262no—
241C22—262no—
242C22—524no—
243C22D13×C22⋊C811yescharacteristic
244C4—21no—
245C4—41no—
246C4—262no—
247C4—522no—
248C4D13×#9911yescharacteristic
249C4#1171840611yescharacteristic
250C2—41no—
251C2—81no—
252C2—264no—
253C2#1311315111yescharacteristic
254C2D13×#35012yes—
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC2×C4×C13C22×C8
FrattiniC22×C8C22×D13
FittingC13×#1315C2
socleC22×C13C2×C22⋊C8
prime radical#11719533C4
cosocleC22×C8×C13C23
hypercenter#1315D13
hypocenterC13#11468
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. D13×C22⋊C16C2semidirect
3. #13112777C2semidirect
4. #13112762C2semidirect
5. C13×#1315C2semidirect
85. #1315D13semidirect
207. C13#11468semidirect

Maximal subgroups

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

subgroupindex
#131235332
D13×C22⋊C162
#131127772
#131127622
C13×#13152
#1146813