Finite Group Databasebeta

← #16786748

Subgroups — #16786748

Order 3328.

594 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 104 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, complemented
2#13129767C212yesmaximal, complemented
3#13129765C212yesmaximal, complemented
4#13117424C211yesmaximal, characteristic
5C22×#6127C411yescharacteristic
6C2×C13×#117C411yescharacteristic
7C22×C4⋊Dic13C2211yescharacteristic
8C2×C22⋊#1057—22no—
9#11718648—22no—
10#11718619—22no—
11#11718600C411yescharacteristic
12#11718600C2211yescharacteristic
13#11718590C411yescharacteristic
14#11718590C2211yescharacteristic
15#11718285—22no—
16#11718285C2214yes—
17C23×C4×C13C2×C411yescharacteristic
18C22×C22⋊D13—21no—
19C23×Dic13D412yes—
20C2×#6127—22no—
21C2×#6127—42no—
22C2×#6127—42no—
23C2×#6127C814yescomplemented
24C22×D52C2×C411yescharacteristic
25C22×C4×D13—21no—
26C22×Dic26C2×C411yescharacteristic
27C22×#1057—42no—
28C13×#117—42no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C22⋊C4—21no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×#6103—22no—
34C2×#6103—22no—
35C2×C4⋊Dic13—42no—
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×C4⋊Dic13D412yes—
38C2×C4⋊Dic13C2311yescharacteristic
39C22⋊#1057—24no—
40C22⋊#1057—42no—
41#88071—22no—
42#88071—22no—
43#11432—131nomaximal, Sylow
44C24×C13C22⋊C411yescharacteristic
45C23×D13—21no—
46C22×C4×C13—22no—
47C22×C4×C13—22no—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13C22⋊C411yescharacteristic
51C22×C4×C13C2×C812yes—
52C22×C4×C13M1612yes—
53C22×C4×C13C22×C411yescharacteristic
54C2×C22⋊D13—24no—
55C2×C22⋊D13—42no—
56C2×C22⋊D13—42no—
57C22×Dic13—22no—
58C22×Dic13—21no—
59C22×Dic13—22no—
60C22×Dic13—82no—
61C22×Dic13C22⋊C412yes—
62C22×Dic13C2×D412yes—
63#6127—48no—
64#6127—48no—
65C2×D52—21no—
66C2×D52—41no—
67C2×D52—41no—
68C2×D52C2×C812yescomplemented
69C2×C4×D13—24no—
70C2×C4×D13—42no—
71C2×C4×D13—42no—
72C2×Dic26—21no—
73C2×Dic26—41no—
74C2×Dic26—41no—
75C2×Dic26C2×C812yescomplemented
76C2×#1057—44no—
77C2×#1057—84no—
78C13×C4⋊C4—42no—
79C13×C22⋊C4—42no—
80C42×C13—41no—
81C42×C13—41no—
82#6103—82no—
83#6103—82no—
84C4⋊Dic13—41no—
85C4⋊Dic13—42no—
86C4⋊Dic13—41no—
87#2311—131no—
88C2×#324—132no—
89#1319—132no—
90#1318—132no—
91C23×C13—41no—
92C23×C13—41no—
93C23×C13C22⋊C812yes—
94C23×C13#9912yes—
95C23×C13#10012yes—
96C23×C13C2×C22⋊C411yescharacteristic
97C22×D13—22no—
98C22×D13—42no—
99C22×D13—42no—
100C22×D13—41no—
101C22×D13—41no—
102C2×C4×C13—24no—
103C2×C4×C13—24no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13C22⋊C812yes—
115C2×C4×C13C22×C811yescharacteristic
116C2×C4×C13C2×M1611yescharacteristic
117C22⋊D13—48no—
118C2×Dic13—22no—
119C2×Dic13—22no—
120C2×Dic13—22no—
121C2×Dic13—44no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—82no—
127D52—42no—
128D52—42no—
129C4×D13—48no—
130Dic26—42no—
131Dic26—42no—
132#1057—84no—
133C22×#41—131no—
134C2×#117#26111yescharacteristic
135C22×C4⋊C4—131no—
136C2×C22⋊C8—262no—
137#391—131no—
138#391—131no—
139#390—131no—
140#390—131no—
141#386—262no—
142#380—262no—
143#324—134no—
144#324—262no—
145C22×C13—21no—
146C22×C13—22no—
147C22×C13—21no—
148C22×C13—22no—
149C22×C13—42no—
150C22×C13—42no—
151C22×C13#32314yes—
152C22×C13C2×C22⋊C811yescharacteristic
153C22×C13C2×#9911yescharacteristic
154C22×C13C2×#10011yescharacteristic
155C2×D13—44no—
156C2×D13—42no—
157C2×D13—82no—
158C2×D13—81no—
159C2×D13—81no—
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—22no—
163C4×C13—81no—
164C4×C13—81no—
165Dic13—42no—
166Dic13—42no—
167Dic13—42no—
168C2×#41—134no—
169C2×#41—262no—
170C2×#41—522no—
171C2×#41—522no—
172C22×Q8—131no—
173C22×D4—131no—
174C22×D4—261no—
175C23×C4—132no—
176C23×C4—261no—
177C23×C4C2×#26111yescharacteristic
178C22×C8—522no—
179#117—42no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—132no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—522no—
185C2×C22⋊C4—21no—
186C2×C22⋊C4—262no—
187C2×C22⋊C4—262no—
188C2×C42C2×#26111yescharacteristic
189C2×C42C2×#26111yescharacteristic
190C22⋊C8—264no—
191C22⋊C8—522no—
192#95—262no—
193#95—262no—
194C2×C13—21no—
195C2×C13—21no—
196C2×C13—24no—
197C2×C13C2×#32311yescharacteristic
198C2×C13#212711yescharacteristic
199C2×C13#213311yescharacteristic
200D13—82no—
201C24—261no—
202C24C22⋊#26111yescharacteristic
203#41—528no—
204#41—528no—
205C2×Q8—132no—
206C2×Q8—261no—
207C2×Q8—521no—
208C2×Q8—521no—
209C2×D4—132no—
210C2×D4—264no—
211C2×D4—261no—
212C2×D4—521no—
213C2×D4—521no—
214C2×D4—522no—
215C2×D4—522no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—132no—
221C22×C4—132no—
222C22×C4—262no—
223C22×C4—261no—
224C22×C4—262no—
225C22×C4—264no—
226C22×C4—522no—
227C22×C4—522no—
228C22×C4—1042no—
229C22×C4D13⋊C812yes—
230C22×C4#611812yes—
231C22×C4C22⋊#26111yescharacteristic
232C22×C4C22×#26111yescharacteristic
233C2×C8—524no—
234C2×C8—1044no—
235C4⋊C4—42no—
236C4⋊C4—522no—
237C4⋊C4—521no—
238C4⋊C4—521no—
239C22⋊C4—42no—
240C22⋊C4—1042no—
241C22⋊C4—1042no—
242C42—41no—
243C42—41no—
244C13#1143211yescharacteristic, complemented, Sylow
245C23—41no—
246C23—41no—
247C23—262no—
248C23—522no—
249C23—522no—
250C23—521no—
251C23—521no—
252C23#8810712yes—
253C23#8811112yes—
254C23#8812112yes—
255C23C2×C22⋊#26111yescharacteristic
256Q8—522no—
257Q8—522no—
258D4—522no—
259D4—522no—
260D4—528no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—262no—
274C2×C4—262no—
275C2×C4—262no—
276C2×C4—528no—
277C2×C4—524no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4—522no—
281C2×C4—522no—
282C2×C4—1042no—
283C2×C4#8811112yes—
284C2×C4C2×D13⋊C811yescharacteristic
285C2×C4C2×#611811yescharacteristic
286C8—1044no—
287C22—21no—
288C22—22no—
289C22—21no—
290C22—22no—
291C22—42no—
292C22—42no—
293C22—524no—
294C22—522no—
295C22—1042no—
296C22—1041no—
297C22—1041no—
298C22#1171828714yes—
299C22C2×#8810711yescharacteristic
300C22C2×#8811111yescharacteristic
301C22C2×#8812111yescharacteristic
302C4—22no—
303C4—21no—
304C4—21no—
305C4—81no—
306C4—81no—
307C4—522no—
308C4—522no—
309C4—522no—
310C2—21no—
311C2—21no—
312C2—24no—
313C2—1042no—
314C2C2×#1171828711yescharacteristic
315C2#1313111311yescharacteristic
316C2#1313113311yescharacteristic
subgroupG/H
centerC22C2×#88107
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC22×C13C2×#99
prime radicalC22×#6127C4
cosocleC2×C4⋊Dic13C23
hypercenterC2×#117#261
hypocenterC13#11432
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
1. C2×#11718285C2semidirect
2. #13129767C2semidirect
3. #13129765C2semidirect
23. C2×#6127C8semidirect
68. C2×D52C2×C8semidirect
75. C2×Dic26C2×C8semidirect
244. C13#11432semidirect

Maximal subgroups

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

subgroupindex
C2×#117182852
#131297672
#131297652
#131174242
#1143213