Finite Group Databasebeta

← #16786951

Subgroups — #16786951

Order 3328.

364 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 90 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#13131194C212yesmaximal, complemented
2#13129759C212yesmaximal, complemented
3#13129758C212yesmaximal, complemented
4#13123546C211yesmaximal, characteristic
5C2×C13×#131C411yescharacteristic
6#11719537C411yescharacteristic
7C2×#88155C411yescharacteristic
8#11718895C2211yescharacteristic
9#11718790C2211yescharacteristic
10#11718789—22no—
11#11718779C411yescharacteristic
12C8×C22⋊D13—22no—
13C2×C8×Dic13C2211yescharacteristic
14C22⋊#6092C2214yes—
15#11718260—22no—
16#11718257—22no—
17C2×C13×#41C2×C411yescharacteristic
18C2×#6127C2×C411yescharacteristic
19C13×#131—42no—
20C2×C13×M16—21no—
21C2×C13×M16C2×C411yescharacteristic
22C22×C8×C13—21no—
23C22×C8×C13C2×C411yescharacteristic
24#88201C811yescharacteristic
25#88198C811yescharacteristic
26#88194C811yescharacteristic
27#88193—22no—
28#88190C811yescharacteristic
29C4×C22⋊D13—22no—
30C2×C4×Dic13C2×C411yescharacteristic
31C2×#6099C2×C411yescharacteristic
32C22×#1055C2311yescharacteristic
33#88155—42no—
34C2×#6094—21no—
35C2×C8×D13—21no—
36C2×#6092—24no—
37C22⋊#1055—22no—
38#88060—22no—
39#88054—22no—
40C8×Dic13D412yes—
41C8×Dic13D412yes—
42#11490—131nomaximal, Sylow
43C13×#41—41no—
44C13×#41—41no—
45C2×Q8×C13C2×C811yescharacteristic
46C2×D4×C13—21no—
47C2×D4×C13C2×C811yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13C22×C411yescharacteristic
50C2×C22⋊D13—21no—
51C2×C22⋊D13—22no—
52C22×Dic13M1612yes—
53#6127—41no—
54#6127—41no—
55C2×D52C2×C811yescharacteristic
56C2×C4×D13—21no—
57C2×Dic26C2×C811yescharacteristic
58C13×M16—42no—
59C13×M16—41no—
60C2×C8×C13—22no—
61C2×C8×C13—21no—
62C2×C8×C13—42no—
63C2×C8×C13C22⋊C411yescharacteristic
64C2×C8×C13C22⋊C411yescharacteristic
65C22⋊Dic13—22no—
66#6103—22no—
67#6101—22no—
68C4×Dic13C22⋊C412yes—
69C4×Dic13C2×C811yescharacteristic
70C4×Dic13C2×C811yescharacteristic
71#6099—41no—
72C2×#1055—21no—
73C2×#1055—41no—
74C2×#1055C2×D412yes—
75#6094—42no—
76C8×D13—42no—
77#6092—44no—
78#2931—131no—
79#2162—132no—
80#1315—132no—
81#1315—132no—
82C23×C13—21no—
83C23×C13C2×M1611yescharacteristic
84C22×D13—21no—
85Q8×C13—41no—
86D4×C13—41no—
87D4×C13—42no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13C2×C22⋊C411yescharacteristic
94C2×C4×C13C22×C811yescharacteristic
95C22⋊D13—42no—
96C22⋊D13—44no—
97C2×Dic13—24no—
98C2×Dic13—21no—
99C2×Dic13C22⋊C812yes—
100C2×Dic13C22⋊C812yes—
101D52—41no—
102C4×D13—41no—
103C4×D13—41no—
104Dic26—41no—
105C8×C13—21no—
106C8×C13—41no—
107C8×C13#10012yes—
108#1055—22no—
109#1055—41no—
110C2×#131—131no—
111C2×#131#26111yescharacteristic
112#532—131no—
113#436—262no—
114C8×D4—262no—
115#423—131no—
116#408—131no—
117#408—131no—
118C2×C4×C8—131no—
119C4⋊C16—262no—
120C22⋊C16—134no—
121C4×C16—262no—
122C22×C13—22no—
123C22×C13—21no—
124C22×C13—42no—
125C22×C13—41no—
126C22×C13C2×C22⋊C811yescharacteristic
127C2×D13—42no—
128C2×D13—41no—
129C4×C13—21no—
130C4×C13—41no—
131C4×C13#41011yescharacteristic
132C4×C13C2×#10011yescharacteristic
133Dic13—22no—
134Dic13—41no—
135Dic13#35014yes—
136C2×#41—131no—
137C2×#41C2×#26111yescharacteristic
138#131—42no—
139#131—522no—
140C2×M16—21no—
141C2×M16—131no—
142C2×M16—261no—
143C2×M16C2×#26111yescharacteristic
144C22×C8—21no—
145C22×C8—131no—
146C22×C8—261no—
147C22×C8C2×#26111yescharacteristic
148C4⋊Q8—131no—
149#127—131no—
150#124—131no—
151#124—131no—
152#121—262no—
153C4×D4—262no—
154C2×C42—131no—
155C2×C16—264no—
156C4⋊C8—262no—
157C22⋊C8—262no—
158C22⋊C8—262no—
159C4×C8—132no—
160C4×C8—132no—
161C2×C13—41no—
162C2×C13—81no—
163C2×C13#146011yescharacteristic
164C2×C13C2×#35012yes—
165D13—81no—
166#41—41no—
167#41—41no—
168#41—521no—
169#41—521no—
170C2×Q8—131no—
171C2×Q8D13⋊C811yescharacteristic
172C2×D4—21no—
173C2×D4—131no—
174C2×D4—262no—
175C2×D4—261no—
176C2×D4D13⋊C811yescharacteristic
177C22×C4—21no—
178C22×C4—132no—
179C22×C4—261no—
180C22×C4C22×#26111yescharacteristic
181M16—42no—
182M16—41no—
183M16—522no—
184M16—521no—
185C2×C8—22no—
186C2×C8—21no—
187C2×C8—42no—
188C2×C8—132no—
189C2×C8—261no—
190C2×C8—521no—
191C2×C8—522no—
192C2×C8C22⋊#26111yescharacteristic
193C2×C8C22⋊#26111yescharacteristic
194C4⋊C4—262no—
195C22⋊C4—262no—
196C22⋊C4—262no—
197C42—131no—
198C42—131no—
199C42—132no—
200C16—524no—
201C13#1149011yescharacteristic, complemented, Sylow
202C23—21no—
203C23—261no—
204C23D13⋊M1611yescharacteristic
205Q8—41no—
206Q8—521no—
207D4—41no—
208D4—42no—
209D4—521no—
210D4—524no—
211D4—522no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—132no—
218C2×C4—132no—
219C2×C4—264no—
220C2×C4—261no—
221C2×C4—521no—
222C2×C4—521no—
223C2×C4C2×D13⋊C811yescharacteristic
224C2×C4C2×C22⋊#26111yescharacteristic
225C8—21no—
226C8—41no—
227C8—262no—
228C8—521no—
229C8#8812112yes—
230C22—22no—
231C22—21no—
232C22—42no—
233C22—41no—
234C22—522no—
235C22—521no—
236C22D13⋊(C22⋊C8)11yescharacteristic
237C4—21no—
238C4—41no—
239C4—134no—
240C4—262no—
241C4—521no—
242C4#1171911611yescharacteristic
243C4C2×#8812111yescharacteristic
244C2—41no—
245C2—81no—
246C2—1041no—
247C2#1313007511yescharacteristic
248C2D13⋊#35012yes—
subgroupG/H
centerC2×C8C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#131C4
socleC22×C13C2×C22⋊C8
prime radical#11719537C4
cosocleC22×#1055C23
hypercenterC2×#131#261
hypocenterC13#11490
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #13131194C2semidirect
2. #13129759C2semidirect
3. #13129758C2semidirect
201. C13#11490semidirect

Maximal subgroups

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

subgroupindex
#131311942
#131297592
#131297582
#131235462
#1149013