Finite Group Databasebeta

← #16786796

Subgroups — #16786796

Order 3328.

454 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C2×#11718285C212yesmaximal
2#13129778C212yesmaximal, complemented
3#13129776C212yesmaximal, complemented
4#13117459C211yesmaximal, characteristic
5C2×C13×#117C411yescharacteristic
6C2×#88180C411yescharacteristic
7C22×C4⋊Dic13C2211yescharacteristic
8C2×C22⋊#1057—22no—
9#11718646—22no—
10#11718611—22no—
11#11718597C411yescharacteristic
12#11718597C2211yescharacteristic
13#11718596C411yescharacteristic
14#11718596C2211yescharacteristic
15#11718285—22no—
16#11718285C2214yes—
17C23×C4×C13C2×C411yescharacteristic
18C23×Dic13D412yes—
19C22×#1057—42no—
20C13×#117—22no—
21C13×#117C814yescomplemented
22C2×C13×C4⋊C4—21no—
23C2×C13×C22⋊C4—21no—
24C2×C42×C13C2×C411yescharacteristic
25C2×C42×C13C2×C411yescharacteristic
26C2×C22⋊Dic13—21no—
27#88180—42no—
28C2×C4⋊Dic13—22no—
29C2×C4⋊Dic13—22no—
30C2×C4⋊Dic13—42no—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13D412yes—
35C2×C4⋊Dic13C2311yescharacteristic
36C2×C4×Dic13—21no—
37C22⋊#1057—24no—
38C22⋊#1057—42no—
39#88071—22no—
40#88071—22no—
41#11448—131nomaximal, Sylow
42C24×C13C22⋊C411yescharacteristic
43C22×C4×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C22⋊C411yescharacteristic
48C22×C4×C13C2×C812yes—
49C22×C4×C13M1612yes—
50C22×C4×C13C22×C411yescharacteristic
51C22×Dic13—22no—
52C22×Dic13—22no—
53C22×Dic13—21no—
54C22×Dic13—21no—
55C22×Dic13—82no—
56C22×Dic13C22⋊C412yes—
57C22×Dic13C2×D412yes—
58C2×#1057—44no—
59C2×#1057—84no—
60C13×C4⋊C4—24no—
61C13×C22⋊C4—24no—
62C42×C13—21no—
63C42×C13—21no—
64C42×C13C2×C812yescomplemented
65C42×C13C2×C812yescomplemented
66C22⋊Dic13—42no—
67C4⋊Dic13—41no—
68C4⋊Dic13—42no—
69C4⋊Dic13—41no—
70C4⋊Dic13—41no—
71C4⋊Dic13—41no—
72C4⋊Dic13—82no—
73C4⋊Dic13—82no—
74C4×Dic13—42no—
75#2317—131no—
76C2×#324—132no—
77#1325—132no—
78#1324—132no—
79C23×C13—41no—
80C23×C13—41no—
81C23×C13C22⋊C812yes—
82C23×C13#9912yes—
83C23×C13#10112yes—
84C23×C13C2×C22⋊C411yescharacteristic
85C2×C4×C13—24no—
86C2×C4×C13—24no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13C22⋊C812yes—
98C2×C4×C13C22×C811yescharacteristic
99C2×C4×C13C2×M1611yescharacteristic
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—44no—
103C2×Dic13—42no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13—41no—
108C2×Dic13—41no—
109C2×Dic13—82no—
110#1057—84no—
111C2×#117—131no—
112C2×#117#26111yescharacteristic
113C22×C4⋊C4—131no—
114C2×C22⋊C8—262no—
115#389—262no—
116#385—262no—
117#384—131no—
118#384—131no—
119#382—131no—
120#382—131no—
121#324—134no—
122#324—262no—
123C22×C13—21no—
124C22×C13—22no—
125C22×C13—21no—
126C22×C13—22no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13#32414yes—
130C22×C13C2×C22⋊C811yescharacteristic
131C22×C13C2×#9911yescharacteristic
132C22×C13C2×#10111yescharacteristic
133C4×C13—22no—
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—42no—
137C4×C13—42no—
138Dic13—42no—
139Dic13—42no—
140Dic13—81no—
141Dic13—81no—
142C23×C4—132no—
143C23×C4C2×#26111yescharacteristic
144C22×C8—522no—
145#117—22no—
146#117—522no—
147#117#105714yescomplemented
148C2×C4⋊C4—21no—
149C2×C4⋊C4—132no—
150C2×C4⋊C4—131no—
151C2×C4⋊C4—131no—
152C2×C4⋊C4—131no—
153C2×C4⋊C4—131no—
154C2×C4⋊C4—262no—
155C2×C4⋊C4—262no—
156C2×C4⋊C4—522no—
157C2×C22⋊C4—21no—
158C2×C22⋊C4—261no—
159C2×C42—261no—
160C2×C42C2×#26111yescharacteristic
161C2×C42C2×#26111yescharacteristic
162C22⋊C8—264no—
163C22⋊C8—522no—
164#95—262no—
165#95—262no—
166C2×C13—21no—
167C2×C13—24no—
168C2×C13—21no—
169C2×C13C2×#32411yescharacteristic
170C2×C13#212711yescharacteristic
171C2×C13#213311yescharacteristic
172C24C22⋊#26111yescharacteristic
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—132no—
178C22×C4—132no—
179C22×C4—262no—
180C22×C4—262no—
181C22×C4—261no—
182C22×C4—261no—
183C22×C4—1042no—
184C22×C4C2×#105712yes—
185C22×C4#612212yes—
186C22×C4C22⋊#26111yescharacteristic
187C22×C4C22×#26111yescharacteristic
188C2×C8—524no—
189C2×C8—1044no—
190C4⋊C4—24no—
191C4⋊C4—522no—
192C4⋊C4—521no—
193C4⋊C4—521no—
194C4⋊C4—521no—
195C4⋊C4—521no—
196C4⋊C4—1042no—
197C4⋊C4—1042no—
198C22⋊C4—24no—
199C22⋊C4—522no—
200C42—21no—
201C42—21no—
202C42—522no—
203C42C2×#105712yescomplemented
204C42C2×#105712yescomplemented
205C13#1144811yescharacteristic, complemented, Sylow
206C23—41no—
207C23—41no—
208C23#8810712yes—
209C23#8811312yes—
210C23C22⋊#105712yes—
211C23C2×C22⋊#26111yescharacteristic
212C2×C4—24no—
213C2×C4—24no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—524no—
227C2×C4—522no—
228C2×C4—522no—
229C2×C4—522no—
230C2×C4—522no—
231C2×C4—521no—
232C2×C4—521no—
233C2×C4—1042no—
234C2×C4C22⋊#105712yes—
235C2×C4C22×#105711yescharacteristic
236C2×C4C2×#612211yescharacteristic
237C8—1044no—
238C22—21no—
239C22—22no—
240C22—21no—
241C22—22no—
242C22—42no—
243C22—42no—
244C22#1171828514yes—
245C22C2×#8810711yescharacteristic
246C22C2×#8811311yescharacteristic
247C22C2×C22⋊#105711yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—522no—
254C4—522no—
255C4—1041no—
256C4—1041no—
257C2—21no—
258C2—24no—
259C2—21no—
260C2C2×#1171828511yescharacteristic
261C2#1313111311yescharacteristic
262C2#1313113311yescharacteristic
subgroupG/H
centerC22C2×#88107
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC2×#117#261
hypocenterC13#11448
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #13129778C2semidirect
3. #13129776C2semidirect
21. C13×#117C8semidirect
64. C42×C13C2×C8semidirect
65. C42×C13C2×C8semidirect
147. #117#1057semidirect
203. C42C2×#1057semidirect
204. C42C2×#1057semidirect
205. C13#11448semidirect

Maximal subgroups

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

subgroupindex
C2×#117182852
#131297782
#131297762
#131174592
#1144813