Finite Group Databasebeta

← #16786746

Subgroups — #16786746

Order 3328.

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

normal subgroups only

This group has 594 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, complemented
2#13129766C212yesmaximal, complemented
3#13129764C212yesmaximal, complemented
4#13117428C211yesmaximal, characteristic
5C22×C13×#41C411yescharacteristic
6C2×#88180C411yescharacteristic
7C22×C4⋊Dic13C2211yescharacteristic
8C2×C22⋊#1057—22no—
9#11718891C411yescharacteristic
10#11718891C2211yescharacteristic
11#11718882C411yescharacteristic
12#11718882C2211yescharacteristic
13#11718881—22no—
14#11718873—22no—
15#11718285—22no—
16#11718285C2214yes—
17C2×C13×#41—22no—
18C2×C13×#41—42no—
19C2×C13×#41—42no—
20C2×C13×#41C814yescomplemented
21C22×Q8×C13C2×C411yescharacteristic
22C22×D4×C13—21no—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13—21no—
25C23×C4×C13C2×C411yescharacteristic
26C23×Dic13D412yes—
27C22×#1057—42no—
28C2×C22⋊Dic13—21no—
29C2×C22⋊Dic13—22no—
30C2×C22⋊Dic13—22no—
31#88180—42no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—42no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13D412yes—
36C2×C4⋊Dic13C2311yescharacteristic
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13C2×C411yescharacteristic
39C22⋊#1057—24no—
40C22⋊#1057—42no—
41#88071—22no—
42#88071—22no—
43#11432—131nomaximal, Sylow
44C24×C13—21no—
45C24×C13C22⋊C411yescharacteristic
46C13×#41—48no—
47C13×#41—48no—
48C2×Q8×C13—21no—
49C2×Q8×C13—41no—
50C2×Q8×C13—41no—
51C2×Q8×C13C2×C812yescomplemented
52C2×D4×C13—24no—
53C2×D4×C13—21no—
54C2×D4×C13—41no—
55C2×D4×C13—41no—
56C2×D4×C13—42no—
57C2×D4×C13—42no—
58C2×D4×C13C2×C812yescomplemented
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—21no—
62C22×C4×C13—24no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C2×C812yes—
67C22×C4×C13M1612yes—
68C22×C4×C13C22×C411yescharacteristic
69C22×Dic13—22no—
70C22×Dic13—22no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13—82no—
74C22×Dic13C22⋊C412yes—
75C22×Dic13C2×D412yes—
76C2×#1057—44no—
77C2×#1057—84no—
78C22⋊Dic13—42no—
79C22⋊Dic13—82no—
80C22⋊Dic13—82no—
81C4⋊Dic13—41no—
82C4⋊Dic13—42no—
83C4⋊Dic13—41no—
84C4⋊Dic13—42no—
85C4×Dic13—41no—
86C4×Dic13—41no—
87#2311—131no—
88C2×#324—132no—
89#1319—132no—
90#1318—132no—
91C23×C13—22no—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13C22⋊C812yes—
99C23×C13#9912yes—
100C23×C13#10012yes—
101C23×C13C2×C22⋊C411yescharacteristic
102Q8×C13—42no—
103Q8×C13—42no—
104D4×C13—42no—
105D4×C13—42no—
106D4×C13—48no—
107C2×C4×C13—24no—
108C2×C4×C13—24no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—22no—
114C2×C4×C13—48no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13C22⋊C812yes—
118C2×C4×C13C22×C811yescharacteristic
119C2×C4×C13C2×M1611yescharacteristic
120C2×Dic13—22no—
121C2×Dic13—22no—
122C2×Dic13—44no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—82no—
132#1057—84no—
133C22×#41#26111yescharacteristic
134C2×#117—131no—
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—44no—
152C22×C13—42no—
153C22×C13—82no—
154C22×C13—81no—
155C22×C13—81no—
156C22×C13#32314yes—
157C22×C13C2×C22⋊C811yescharacteristic
158C22×C13C2×#9911yescharacteristic
159C22×C13C2×#10011yescharacteristic
160C4×C13—22no—
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—42no—
164Dic13—42no—
165Dic13—42no—
166Dic13—81no—
167Dic13—81no—
168C2×#41—22no—
169C2×#41—42no—
170C2×#41—42no—
171C2×#41#105714yescomplemented
172C22×Q8C2×#26111yescharacteristic
173C22×D4—21no—
174C22×D4C2×#26111yescharacteristic
175C23×C4—21no—
176C23×C4—132no—
177C23×C4C2×#26111yescharacteristic
178C22×C8—522no—
179#117—522no—
180C2×C4⋊C4—132no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—522no—
185C2×C22⋊C4—261no—
186C2×C22⋊C4—262no—
187C2×C22⋊C4—262no—
188C2×C42—131no—
189C2×C42—131no—
190C22⋊C8—264no—
191C22⋊C8—522no—
192#95—262no—
193#95—262no—
194C2×C13—21no—
195C2×C13—21no—
196C2×C13—24no—
197C2×C13—82no—
198C2×C13C2×#32311yescharacteristic
199C2×C13#212711yescharacteristic
200C2×C13#213311yescharacteristic
201C24—21no—
202C24C22⋊#26111yescharacteristic
203#41—48no—
204#41—48no—
205C2×Q8—21no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8C2×#105712yescomplemented
209C2×D4—24no—
210C2×D4—21no—
211C2×D4—41no—
212C2×D4—41no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4C2×#105712yescomplemented
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—24no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—132no—
223C22×C4—132no—
224C22×C4—262no—
225C22×C4—262no—
226C22×C4—261no—
227C22×C4—261no—
228C22×C4—1042no—
229C22×C4C2×#105712yes—
230C22×C4#612212yes—
231C22×C4C22⋊#26111yescharacteristic
232C22×C4C22×#26111yescharacteristic
233C2×C8—524no—
234C2×C8—1044no—
235C4⋊C4—522no—
236C4⋊C4—521no—
237C4⋊C4—521no—
238C4⋊C4—522no—
239C22⋊C4—522no—
240C22⋊C4—1042no—
241C22⋊C4—1042no—
242C42—521no—
243C42—521no—
244C13#1143211yescharacteristic, complemented, Sylow
245C23—22no—
246C23—41no—
247C23—41no—
248C23—42no—
249C23—42no—
250C23—41no—
251C23—41no—
252C23#8811912yes—
253C23C22⋊#105712yes—
254C23#8812112yes—
255C23C2×C22⋊#26111yescharacteristic
256Q8—42no—
257Q8—42no—
258D4—42no—
259D4—42no—
260D4—48no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—48no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—262no—
272C2×C4—262no—
273C2×C4—524no—
274C2×C4—522no—
275C2×C4—522no—
276C2×C4—521no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4—1042no—
283C2×C4C22⋊#105712yes—
284C2×C4C22×#105711yescharacteristic
285C2×C4C2×#612211yescharacteristic
286C8—1044no—
287C22—21no—
288C22—22no—
289C22—21no—
290C22—22no—
291C22—42no—
292C22—42no—
293C22—44no—
294C22—42no—
295C22—82no—
296C22—81no—
297C22—81no—
298C22#1171830514yes—
299C22C2×#8811911yescharacteristic
300C22C2×C22⋊#105711yescharacteristic
301C22C2×#8812111yescharacteristic
302C4—22no—
303C4—21no—
304C4—21no—
305C4—42no—
306C4—522no—
307C4—522no—
308C4—1041no—
309C4—1041no—
310C2—21no—
311C2—21no—
312C2—24no—
313C2—82no—
314C2C2×#1171830511yescharacteristic
315C2#1313111111yescharacteristic
316C2#1313113111yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
Fitting, prime radicalC22×C13×#41C4
socleC22×C13C2×#99
cosocleC2×C4⋊Dic13C23
hypercenterC22×#41#261
hypocenterC13#11432
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#11718285C2semidirect
2. #13129766C2semidirect
3. #13129764C2semidirect
20. C2×C13×#41C8semidirect
51. C2×Q8×C13C2×C8semidirect
58. C2×D4×C13C2×C8semidirect
171. C2×#41#1057semidirect
208. C2×Q8C2×#1057semidirect
215. C2×D4C2×#1057semidirect
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
#131297662
#131297642
#131174282
#1143213