Finite Group Databasebeta

← #16778678

Subgroups — #16778678

Order 3328.

562 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 116 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
1C4×#88111C211yesmaximal, characteristic
2#13130500C211yesmaximal, characteristic
3#13129654C214yesmaximal, complemented
4#13123189C211yesmaximal, characteristic
5C22×#6118—21no—
6C2×#88151—21no—
7C2×C42×D13C2211yescharacteristic
8C2×#88123C411yescharacteristic
9C2×#88111—21no—
10C2×C4×#1057—21no—
11C13×#384C411yescharacteristic
12#11718648—21no—
13#11718648C412yes—
14#11718646—21no—
15#11718646C2212yes—
16#11718635—21no—
17#11718290—21no—
18#11718290C2212yes—
19#11718290C2212yes—
20C22×C4×D13C2×C411yescharacteristic
21C22×C4×D13D411yescharacteristic
22C22×C4×D13D411yescharacteristic
23C22×Dic26—21no—
24C22×#1057—22no—
25C22×#1057—22no—
26C2×#6118—24no—
27C2×#6118—42no—
28C2×#6118—42no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C42×C13C2×C411yescharacteristic
33C2×#6103—22no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—22no—
36C2×C4⋊Dic13C2×C412yes—
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13C2311yescharacteristic
40#88151—42no—
41#88151—42no—
42C42×D13—42no—
43#88123—42no—
44#88111—24no—
45C4×#1057—42no—
46#88071—22no—
47#88071—22no—
48#7685—131nomaximal, Sylow
49C23×D13C22⋊C411yescharacteristic
50C22×C4×C13—22no—
51C22×C4×C13C22⋊C411yescharacteristic
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22×C411yescharacteristic
54C22×Dic13—22no—
55C22×Dic13C22⋊C411yescharacteristic
56C22×Dic13C2×D411yescharacteristic
57C22×Dic13C2×D411yescharacteristic
58C2×C4×D13—22no—
59C2×C4×D13—22no—
60C2×C4×D13—22no—
61C2×C4×D13—22no—
62C2×C4×D13—22no—
63C2×C4×D13—22no—
64C2×C4×D13—41no—
65C2×C4×D13—41no—
66C2×C4×D13D812yes—
67C2×C4×D13SD1612yes—
68C2×Dic26—42no—
69C2×Dic26—42no—
70C2×Dic26—42no—
71C2×#1057—24no—
72C2×#1057—24no—
73C2×#1057—42no—
74C2×#1057—42no—
75C2×#1057—42no—
76C2×#1057—42no—
77#6118—48no—
78C13×C4⋊C4—24no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C42×C13—22no—
82#6103—44no—
83C4⋊Dic13—42no—
84C4⋊Dic13—42no—
85C4⋊Dic13—42no—
86C4⋊Dic13—42no—
87C4×Dic13—22no—
88C4×Dic13—41no—
89C4×Dic13—41no—
90#2857—131no—
91C4×C22⋊C8—131no—
92#1728—131no—
93#1271—134no—
94C23×C13C2×C22⋊C411yescharacteristic
95C22×D13—21no—
96C22×D13—21no—
97C22×D13—21no—
98C22×D13—21no—
99C22×D13—21no—
100C22×D13—21no—
101C22×D13#10212yes—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13#9912yes—
110C2×C4×C13#10212yes—
111C2×C4×C13#10412yes—
112C2×C4×C13#10412yes—
113C2×C4×C13#13112yes—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13#10112yes—
124C2×Dic13C2×D811yescharacteristic
125C2×Dic13C2×SD1611yescharacteristic
126C2×Dic13#13712yes—
127C4×D13—24no—
128C4×D13—24no—
129C4×D13—44no—
130C4×D13—44no—
131Dic26—84no—
132#1057—44no—
133#1057—44no—
134C22×M16—261no—
135C2×C4⋊Q8—131no—
136C2×C22⋊Q8—261no—
137C22×C42—131no—
138C2×C22⋊C8—261no—
139C2×C4×C8—261no—
140#391—261no—
141#389—132no—
142#389—261no—
143#384#26111yescharacteristic
144#380—132no—
145#380—261no—
146#336—132no—
147#336—132no—
148#336—261no—
149C22×C13#40811yescharacteristic
150C22×C13C2×#9911yescharacteristic
151C22×C13C2×#10111yescharacteristic
152C22×C13C2×#10211yescharacteristic
153C22×C13#41911yescharacteristic
154C22×C13C2×#10411yescharacteristic
155C22×C13C2×#10411yescharacteristic
156C2×D13—22no—
157C2×D13—22no—
158C2×D13—22no—
159C2×D13—41no—
160C2×D13—41no—
161C2×D13—41no—
162C2×D13—41no—
163C4×C13—22no—
164C4×C13—22no—
165C4×C13—82no—
166C4×C13#32714yes—
167Dic13—22no—
168Dic13—21no—
169Dic13—21no—
170Dic13—22no—
171Dic13—82no—
172C22×Q8—261no—
173C23×C4—131no—
174C23×C4—131no—
175C23×C4—131no—
176C2×M16—264no—
177C2×M16—522no—
178C2×M16—522no—
179C22×C8—262no—
180C22×C8—262no—
181C4⋊Q8—522no—
182C22⋊Q8—522no—
183C22⋊Q8—522no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—132no—
187C2×C4⋊C4—262no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4C2×#26112yes—
190C2×C22⋊C4—262no—
191C2×C42—131no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—522no—
195C2×C42C2×#26111yescharacteristic
196C22⋊C8—264no—
197C4×C8—522no—
198#95—262no—
199#95—262no—
200C2×C13#147211yescharacteristic
201C2×C13#148511yescharacteristic
202C2×C13#149211yescharacteristic
203C2×C13C2×#32711yescharacteristic
204C2×C13#150811yescharacteristic
205C2×C13#152611yescharacteristic
206C2×C13#154611yescharacteristic
207D13—42no—
208C24—131no—
209C2×Q8—522no—
210C2×Q8—522no—
211C2×Q8—522no—
212C22×C4—22no—
213C22×C4—131no—
214C22×C4—131no—
215C22×C4—131no—
216C22×C4—132no—
217C22×C4—132no—
218C22×C4—262no—
219C22×C4—262no—
220C22×C4—262no—
221C22×C4—262no—
222C22×C4—262no—
223C22×C4—262no—
224C22×C4—262no—
225C22×C4—521no—
226C22×C4—521no—
227C22×C4C22⋊#26111yescharacteristic
228C22×C4C22⋊#26111yescharacteristic
229C22×C4C22×#26111yescharacteristic
230M16—528no—
231C2×C8—264no—
232C2×C8—264no—
233C2×C8—522no—
234C2×C8—522no—
235C2×C8—522no—
236C2×C8—522no—
237C4⋊C4—24no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—522no—
241C4⋊C4—522no—
242C4⋊C4—522no—
243C4⋊C4—522no—
244C22⋊C4—524no—
245C42—22no—
246C42—262no—
247C42—521no—
248C42—521no—
249C13#768511yescharacteristic, complemented, Sylow
250C23—132no—
251C23—261no—
252C23—261no—
253C23—261no—
254C23—261no—
255C23—261no—
256C23—261no—
257C23C2×C22⋊#26111yescharacteristic
258Q8—1044no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—131no—
267C2×C4—131no—
268C2×C4—132no—
269C2×C4—132no—
270C2×C4—261no—
271C2×C4—261no—
272C2×C4—261no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—264no—
277C2×C4—264no—
278C2×C4—524no—
279C2×C4—524no—
280C2×C4—522no—
281C2×C4—522no—
282C2×C4—522no—
283C2×C4#8810712yes—
284C2×C4#8811512yes—
285C2×C4#8811612yes—
286C2×C4#8811812yes—
287C2×C4#8823812yes—
288C8—524no—
289C8—524no—
290C22—262no—
291C22—262no—
292C22—262no—
293C22—521no—
294C22—521no—
295C22—521no—
296C22—521no—
297C22C2×#8810711yescharacteristic
298C22C2×#8811511yescharacteristic
299C22C2×#8811611yescharacteristic
300C22#1171914711yescharacteristic
301C22#1171915311yescharacteristic
302C22C2×#8811811yescharacteristic
303C22D13⋊#10111yescharacteristic
304C4—22no—
305C4—22no—
306C4—82no—
307C4—262no—
308C4—261no—
309C4—261no—
310C4—262no—
311C4—1042no—
312C4#1171824014yes—
313C2—522no—
314C2#1313011411yescharacteristic
315C2#1313015911yescharacteristic
316C2#1313018211yescharacteristic
317C2C2×#1171824011yescharacteristic
318C2#1313023511yescharacteristic
319C2#1313029411yescharacteristic
320C2#1313034611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#384C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#384#261
hypocenterC13#7685
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
3. #13129654C2semidirect
249. C13#7685semidirect

Maximal subgroups

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

subgroupindex
C4×#881112
#131305002
#131296542
#131231892
#768513