Finite Group Databasebeta

← #16788343

Subgroups — #16788343

Order 3328.

412 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 82 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#13131064C211yesmaximal, characteristic
2#13130712C211yesmaximal, characteristic
3#13129825C214yesmaximal, complemented
4C2×#11718548C211yesmaximal, characteristic
5C22×Dic52C411yescharacteristic, complemented
6C22×C8×D13C2211yescharacteristic
7C2×#88151—21no—
8#11719136—21no—
9C2×#88101—21no—
10C2×#88098—21no—
11C2×C13×#107C411yescharacteristic, complemented
12C2×#88050—21no—
13#11718548—21no—
14#11718548—21no—
15#11718548C412yescomplemented
16#11718548C2212yes—
17C22⋊#6092—21no—
18#11718265C2212yes—
19#11718259C2212yes—
20C22×C4×D13D411yescharacteristic
21C22×Dic26—21no—
22C2×C22⋊#261—41no—
23C2×C4⋊#261—22no—
24C22×C8×C13C2×C411yescharacteristic
25C2×C13×C4⋊C4—21no—
26C2×#6103—41no—
27C2×C4⋊Dic13—41no—
28C22×#1055D411yescharacteristic
29C2×Dic52—21no—
30C2×Dic52—42no—
31C2×Dic52C2×C412yes—
32C2×C8×D13—42no—
33C2×C8×D13C2×C411yescharacteristic
34C2×C8×D13D411yescharacteristic
35C2×C8×D13D411yescharacteristic
36C2×C8×D13C2311yescharacteristic
37#88151—22no—
38#88151—22no—
39#88151—41no—
40#88151—41no—
41(C2×#261)⋊C4—41no—
42C2×#6092—22no—
43#88101—42no—
44#88098—42no—
45C13×#107—21no—
46C13×#107C2×C412yes—
47#88050—22no—
48#88050—22no—
49#11889—131nomaximal, Sylow
50C23×D13D811yescharacteristic
51C22×#261—42no—
52C22×C4×C13—41no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×Dic13—41no—
55C22×Dic13SD1611yescharacteristic
56C2×C4×D13—41no—
57C2×C4×D13—41no—
58C2×C4×D13C22⋊C411yescharacteristic
59C2×C4×D13D811yescharacteristic
60C2×C4×D13SD1611yescharacteristic
61C2×C4×D13C2×D411yescharacteristic
62C2×Dic26—22no—
63C2×Dic26—42no—
64C2×Dic26—42no—
65C2×Dic26—41no—
66C22⋊#261—82no—
67C4⋊#261—42no—
68C4⋊#261—42no—
69C2×C8×C13—22no—
70C2×C8×C13C22⋊C411yescharacteristic
71C2×C8×C13C22×C411yescharacteristic
72C13×C4⋊C4—22no—
73C13×C4⋊C4—41no—
74#6103—42no—
75#6103—42no—
76C4⋊Dic13—42no—
77C4⋊Dic13—42no—
78C2×#1055—41no—
79C2×#1055C22⋊C411yescharacteristic
80C2×#1055C2×D411yescharacteristic
81Dic52—42no—
82Dic52—42no—
83C8×D13—22no—
84C8×D13—22no—
85C8×D13—41no—
86C8×D13—41no—
87#6092—42no—
88C2×#467—131no—
89#2112—131no—
90#1807—131no—
91#1348—134no—
92C23×C13#10211yescharacteristic
93C22×D13—22no—
94C22×D13—22no—
95C22×D13—41no—
96C22×D13#10211yescharacteristic
97C22×D13C2×D811yescharacteristic
98C2×#261—82no—
99C2×#261—82no—
100C2×#261—82no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—42no—
104C2×C4×C13—82no—
105C2×C4×C13#10211yescharacteristic
106C2×C4×C13C2×C22⋊C411yescharacteristic
107C2×Dic13—41no—
108C2×Dic13—42no—
109C2×Dic13—82no—
110C2×Dic13#10211yescharacteristic
111C2×Dic13C2×SD1611yescharacteristic
112C4×D13—21no—
113C4×D13—21no—
114C4×D13—21no—
115C4×D13—21no—
116C4×D13—41no—
117C4×D13—41no—
118Dic26—42no—
119Dic26—42no—
120Dic26—82no—
121C8×C13—21no—
122C8×C13#9912yes—
123#1055—21no—
124#1055—21no—
125C22×Q16—131no—
126C23×C8—131no—
127C2×C22⋊Q8—261no—
128C2×M32—261no—
129#467—132no—
130#467—132no—
131#467—261no—
132#467—261no—
133C2×#107#26111yescharacteristic, complemented
134C2×#106—261no—
135C2×#103—261no—
136#380—261no—
137C22⋊C16—132no—
138C22⋊C16—261no—
139#340—132no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13#36012yes—
143C22×C13C2×#10211yescharacteristic
144C2×D13—21no—
145C2×D13—21no—
146C2×D13—21no—
147C2×D13—21no—
148C2×D13—21no—
149C2×D13—44no—
150C2×D13#51012yes—
151#261—162no—
152C4×C13—21no—
153C4×C13—82no—
154C4×C13C2×#9911yescharacteristic
155C4×C13#42111yescharacteristic
156Dic13—21no—
157Dic13—21no—
158Dic13—82no—
159C22×Q8—261no—
160C23×C4—131no—
161C2×Q16—132no—
162C2×Q16—261no—
163C2×Q16—522no—
164C22×C8—131no—
165C22×C8—131no—
166C22×C8—131no—
167C22×C8—131no—
168C22×C8—131no—
169C22×C8—522no—
170C22×C8C2×#26111yescharacteristic
171C22⋊Q8—262no—
172C22⋊Q8—262no—
173C22⋊Q8—521no—
174C22⋊Q8—521no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—262no—
177C2×C4⋊C4—521no—
178C2×C22⋊C4—521no—
179C2×C22⋊C4—521no—
180M32—522no—
181C2×C16—262no—
182#107—21no—
183#107C2×#26112yes—
184#106—522no—
185#103—262no—
186#103—262no—
187#95—521no—
188C2×C13—22no—
189C2×C13#151911yescharacteristic
190C2×C13#214111yescharacteristic
191C2×C13C2×#36011yescharacteristic
192D13—22no—
193D13—41no—
194C24—131no—
195C2×Q8—262no—
196C2×Q8—522no—
197C2×Q8—522no—
198C2×Q8—521no—
199C22×C4—41no—
200C22×C4—131no—
201C22×C4—131no—
202C22×C4—131no—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4—521no—
206C22×C4—521no—
207C22×C4—521no—
208C22×C4—522no—
209C22×C4C22⋊#26111yescharacteristic
210Q16—522no—
211Q16—522no—
212C2×C8—22no—
213C2×C8—131no—
214C2×C8—131no—
215C2×C8—262no—
216C2×C8—262no—
217C2×C8—521no—
218C2×C8—521no—
219C2×C8—521no—
220C2×C8C22⋊#26111yescharacteristic
221C2×C8C22×#26111yescharacteristic
222C4⋊C4—22no—
223C4⋊C4—41no—
224C4⋊C4—522no—
225C4⋊C4—522no—
226C4⋊C4—522no—
227C4⋊C4—522no—
228C22⋊C4—522no—
229C22⋊C4—522no—
230C22⋊C4—1042no—
231C16—522no—
232C13#1188911yescharacteristic, complemented, Sylow
233C23—131no—
234C23—131no—
235C23—262no—
236C23—262no—
237C23—521no—
238C23#8811511yescharacteristic
239Q8—522no—
240Q8—522no—
241Q8—1042no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—82no—
246C2×C4—131no—
247C2×C4—131no—
248C2×C4—261no—
249C2×C4—261no—
250C2×C4—261no—
251C2×C4—261no—
252C2×C4—521no—
253C2×C4—521no—
254C2×C4—521no—
255C2×C4—522no—
256C2×C4—1042no—
257C2×C4—1042no—
258C2×C4—1042no—
259C2×C4—1042no—
260C2×C4#8811511yescharacteristic
261C2×C4C2×C22⋊#26111yescharacteristic
262C8—21no—
263C8—261no—
264C8—261no—
265C8#8810712yes—
266C22—21no—
267C22—21no—
268C22—132no—
269C22—261no—
270C22—261no—
271C22—261no—
272C22—261no—
273C22—261no—
274C22—524no—
275C22#1171827512yes—
276C22C2×#8811511yescharacteristic
277C4—21no—
278C4—82no—
279C4—261no—
280C4—261no—
281C4—1042no—
282C4—2082no—
283C4C2×#8810711yescharacteristic
284C4#1171915511yescharacteristic
285C2—22no—
286C2—262no—
287C2—521no—
288C2#1313027311yescharacteristic
289C2#1313114611yescharacteristic
290C2C2×#1171827511yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC2×C13×#107C4
socleC22×C13C2×#102
prime radicalC23×D13D8
cosocleC2×C8×D13C23
hypercenterC2×#107#261
hypocenterC13#11889
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #13129825C2semidirect
5. C22×Dic52C4semidirect
11. C2×C13×#107C4semidirect
15. #11718548C4semidirect
133. C2×#107#261semidirect
232. C13#11889semidirect

Maximal subgroups

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

subgroupindex
#131310642
#131307122
#131298252
C2×#117185482
#1188913