Finite Group Databasebeta

← #16790009

Subgroups — #16790009

Order 3328.

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

normal subgroups only

This group has 544 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
1C2×#11718300C212yesmaximal
2#13130697C212yesmaximal
3#13129931C212yesmaximal
4C4×#88201C211yesmaximal, characteristic
5C2×C4×Q8×C13C411yescharacteristic, complemented
6C2×#88201C2211yescharacteristic
7C2×C4×D52C2211yescharacteristic
8#11719136—22no—
9C2×#88107C2214yes—
10#11718891C411yescharacteristic, complemented
11#11718651—22no—
12#11718649C2211yescharacteristic
13#11718638C411yescharacteristic, complemented
14C4×#6103—22no—
15C42×Dic13C411yescharacteristic, complemented
16#11718300—24no—
17#11718289—22no—
18C22×Q8×C13C2×C411yescharacteristic
19C22×D52C2311yescharacteristic
20C22×C4×D13D412yes—
21C2×C22⋊#261—24no—
22C2×C4⋊#261—42no—
23C4×Q8×C13—41no—
24C4×Q8×C13—41no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C42×C13—21no—
28C2×C42×C13C2×C411yescharacteristic
29#88201—22no—
30#88201D412yes—
31#88201Q812yes—
32C2×#6103—22no—
33C2×#6103—22no—
34C2×#6103D412yes—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13C2×C411yescharacteristic
40C4×D52—41no—
41C4×D52—41no—
42(C2×#261)⋊C4—42no—
43#88107—24no—
44#88107—24no—
45#88071—22no—
46#88071—22no—
47#12798—131nomaximal, Sylow
48C23×D13C2×D412yes—
49C22×#261—44no—
50C2×Q8×C13—21no—
51C2×Q8×C13—41no—
52C2×Q8×C13—41no—
53C2×Q8×C13C4⋊C412yescomplemented
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22×C411yescharacteristic
59C22×Dic13—21no—
60C22×Dic13—21no—
61C22×Dic13C22⋊C412yes—
62C2×D52—41no—
63C2×D52—41no—
64C2×D52C2×D411yescharacteristic
65C2×D52C2×Q811yescharacteristic
66C2×D52#4112yes—
67C2×C4×D13—22no—
68C2×C4×D13—22no—
69C2×C4×D13—44no—
70C22⋊#261—44no—
71C22⋊#261—44no—
72C4⋊#261—84no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—42no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—41no—
78C42×C13—41no—
79#6103—24no—
80#6103—24no—
81#6103—42no—
82#6103—44no—
83C4⋊Dic13—41no—
84C4×Dic13—21no—
85C4×Dic13—42no—
86C4×Dic13—42no—
87C4×Dic13—41no—
88C4×Dic13C4⋊C412yescomplemented
89C4×#124—131no—
90C2×#354—132no—
91#1799—132no—
92#1393—132no—
93C23×C13C2×C22⋊C411yescharacteristic
94C22×D13—22no—
95C22×D13—22no—
96C22×D13—42no—
97C22×D13—42no—
98C22×D13#12112yes—
99C22×D13C22⋊Q812yes—
100C2×#261—84no—
101C2×#261—84no—
102C2×#261—84no—
103Q8×C13—42no—
104Q8×C13—42no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—21no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13#9911yescharacteristic
116C2×C4×C13#9911yescharacteristic
117C2×C4×C13C2×C4⋊C411yescharacteristic
118C2×C4×C13#11711yescharacteristic
119C2×Dic13—22no—
120C2×Dic13—22no—
121C2×Dic13—22no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—42no—
127D52—41no—
128D52—41no—
129D52—42no—
130C4×D13—44no—
131C4×D13—82no—
132C2×#124—131no—
133C2×C4×Q8#26111yescharacteristic, complemented
134C2×C4×D4—131no—
135C2×#99—134no—
136#391—131no—
137#390—131no—
138#388—262no—
139#382—131no—
140#380—262no—
141C4×C22⋊C4—262no—
142C43—131no—
143#354—264no—
144#342—262no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13#38011yescharacteristic
148C22×C13C2×#9911yescharacteristic
149C22×C13#41011yescharacteristic
150C2×D13—22no—
151C2×D13—22no—
152C2×D13—42no—
153C2×D13—42no—
154C2×D13—42no—
155C2×D13—42no—
156C2×D13—82no—
157#261—164no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—42no—
162C4×C13—41no—
163C4×C13—81no—
164C4×C13#35412yescomplemented
165Dic13—42no—
166Dic13—42no—
167Dic13—42no—
168C22×Q8C2×#26111yescharacteristic
169C22×D4—131no—
170C23×C4—132no—
171#124—132no—
172#124—132no—
173#124—262no—
174C4×Q8—41no—
175C4×Q8—41no—
176C4×D4—521no—
177C4×D4—521no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—131no—
180C2×C4⋊C4—522no—
181C2×C4⋊C4C2×#26111yescharacteristic
182C2×C22⋊C4—132no—
183C2×C22⋊C4—262no—
184C2×C22⋊C4—262no—
185C2×C22⋊C4—264no—
186C2×C42—21no—
187C2×C42—131no—
188C2×C42—131no—
189C2×C42—261no—
190C2×C42—261no—
191C2×C42C2×#26111yescharacteristic
192#99—264no—
193#99—264no—
194#95—262no—
195#95—262no—
196#95—522no—
197C2×C13—21no—
198C2×C13—21no—
199C2×C13#179911yescharacteristic
200C2×C13C2×#35411yescharacteristic
201C2×C13#212611yescharacteristic
202D13—42no—
203D13—42no—
204C24—132no—
205C2×Q8—21no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8C4⋊#26112yescomplemented
209C2×D4—131no—
210C2×D4—131no—
211C2×D4—132no—
212C2×D4—521no—
213C2×D4—521no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—132no—
217C22×C4—261no—
218C22×C4—261no—
219C22×C4—262no—
220C22×C4—262no—
221C22×C4—524no—
222C22×C4—524no—
223C22×C4C22⋊#26111yescharacteristic
224C22×C4C22⋊#26111yescharacteristic
225C22×C4C22×#26111yescharacteristic
226C4⋊C4—41no—
227C4⋊C4—42no—
228C4⋊C4—521no—
229C4⋊C4—1044no—
230C22⋊C4—264no—
231C22⋊C4—264no—
232C22⋊C4—522no—
233C22⋊C4—524no—
234C22⋊C4—524no—
235C22⋊C4—524no—
236C42—21no—
237C42—21no—
238C42—41no—
239C42—41no—
240C42—132no—
241C42—261no—
242C42—521no—
243C42—522no—
244C42—522no—
245C13#1279811yescharacteristic, complemented, Sylow
246C23—132no—
247C23—132no—
248C23—262no—
249C23—262no—
250C23—522no—
251C23—522no—
252C23C2×C22⋊#26111yescharacteristic
253Q8—42no—
254Q8—42no—
255D4—521no—
256D4—521no—
257D4—522no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—262no—
269C2×C4—262no—
270C2×C4—262no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4—524no—
276C2×C4—522no—
277C2×C4—1042no—
278C2×C4—1044no—
279C2×C4—1044no—
280C2×C4—1044no—
281C2×C4#8811911yescharacteristic
282C2×C4#8811911yescharacteristic
283C2×C4C2×C4⋊#26111yescharacteristic
284C2×C4#8823711yescharacteristic
285C22—21no—
286C22—21no—
287C22—262no—
288C22—262no—
289C22—522no—
290C22—522no—
291C22—522no—
292C22—522no—
293C22—1042no—
294C22#1171911611yescharacteristic
295C22#1171913611yescharacteristic
296C22C2×#8811911yescharacteristic
297C4—21no—
298C4—21no—
299C4—21no—
300C4—41no—
301C4—42no—
302C4—81no—
303C4—522no—
304C4—522no—
305C4—522no—
306C4—2084no—
307C4#1171830012yescomplemented
308C2—21no—
309C2—21no—
310C2—522no—
311C2—522no—
312C2#1313069611yescharacteristic
313C2C2×#1171830011yescharacteristic
314C2#1313110711yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socleC22×C13C2×#99
prime radical, cosocleC22×D52C23
hypercenterC2×C4×Q8#261
hypocenterC13#12798
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
5. C2×C4×Q8×C13C4semidirect
10. #11718891C4semidirect
13. #11718638C4semidirect
15. C42×Dic13C4semidirect
53. C2×Q8×C13C4⋊C4semidirect
88. C4×Dic13C4⋊C4semidirect
133. C2×C4×Q8#261semidirect
164. C4×C13#354semidirect
208. C2×Q8C4⋊#261semidirect
245. C13#12798semidirect
307. C4#11718300semidirect

Maximal subgroups

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

subgroupindex
C2×#117183002
#131306972
#131299312
C4×#882012
#1279813