Finite Group Databasebeta

← C2×#13129763 #16786721

Subgroups — C2×#13129763 #16786721

Order 3328.

726 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 120 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×#11718305C212yesmaximal
2#13129763C214yesmaximal, direct product factor
3C2×#11718604C211yesmaximal, characteristic
4C24×Dic13C411yescharacteristic
5C22×C13×C22⋊C4C411yescharacteristic
6C22×C22⋊Dic13C2211yescharacteristic
7C2×C22⋊#1057—22no—
8C2×#88071—22no—
9#11718604—22no—
10#11718604C412yes—
11#11718604C2212yes—
12#11718305—22no—
13#11718305C2214yes—
14C25×C13C2×C411yescharacteristic
15C23×C4×C13—21no—
16C23×Dic13—21no—
17C23×Dic13—21no—
18C23×Dic13—22no—
19C23×Dic13—41no—
20C23×Dic13—41no—
21C23×Dic13—42no—
22C23×Dic13C814yescomplemented
23C23×Dic13C2×C412yes—
24C23×Dic13D412yes—
25C22×#1057—42no—
26C2×C13×C22⋊C4—21no—
27C2×C13×C22⋊C4—42no—
28C2×C13×C22⋊C4C2×C412yes—
29C2×C22⋊Dic13—41no—
30C2×C22⋊Dic13—41no—
31C2×C22⋊Dic13C2×C411yescharacteristic
32C2×C22⋊Dic13D412yes—
33C2×C22⋊Dic13C2311yescharacteristic
34C22⋊#1057—24no—
35C22⋊#1057—42no—
36#88071—24no—
37#88071—24no—
38C2×#1317—131nomaximal, Sylow
39C24×C13—21no—
40C24×C13—21no—
41C24×C13—22no—
42C24×C13—44no—
43C24×C13C22⋊C411yescharacteristic
44C24×C13C22⋊C411yescharacteristic
45C24×C13C2×C812yes—
46C24×C13M1612yes—
47C24×C13C22×C411yescharacteristic
48C22×C4×C13—22no—
49C22×C4×C13—44no—
50C22×C4×C13—42no—
51C22×Dic13—24no—
52C22×Dic13—24no—
53C22×Dic13—22no—
54C22×Dic13—22no—
55C22×Dic13—22no—
56C22×Dic13—22no—
57C22×Dic13—44no—
58C22×Dic13—44no—
59C22×Dic13—42no—
60C22×Dic13—42no—
61C22×Dic13—41no—
62C22×Dic13—41no—
63C22×Dic13—42no—
64C22×Dic13—44no—
65C22×Dic13—44no—
66C22×Dic13—42no—
67C22×Dic13—42no—
68C22×Dic13—44no—
69C22×Dic13C22⋊C412yes—
70C22×Dic13C2×C814yescomplemented
71C22×Dic13C2×D412yes—
72C2×#1057—44no—
73C2×#1057—84no—
74C13×C22⋊C4—42no—
75C13×C22⋊C4—42no—
76C22⋊Dic13—41no—
77C22⋊Dic13—42no—
78C22⋊Dic13—41no—
79C2×#381—131no—
80C2×#323—132no—
81#1317—134no—
82C23×C13—24no—
83C23×C13—22no—
84C23×C13—22no—
85C23×C13—22no—
86C23×C13—22no—
87C23×C13—21no—
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—48no—
92C23×C13—44no—
93C23×C13—42no—
94C23×C13—44no—
95C23×C13—44no—
96C23×C13—42no—
97C23×C13—44no—
98C23×C13C22⋊C812yes—
99C23×C13C22⋊C812yes—
100C23×C13#9911yescharacteristic
101C23×C13#9911yescharacteristic
102C23×C13#10012yes—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13C22×C811yescharacteristic
105C23×C13C2×M1611yescharacteristic
106C2×C4×C13—44no—
107C2×C4×C13—42no—
108C2×C4×C13—84no—
109C2×Dic13—24no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—48no—
113C2×Dic13—44no—
114C2×Dic13—44no—
115C2×Dic13—44no—
116C2×Dic13—44no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—44no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—82no—
123#1057—84no—
124C24×C4—131no—
125C22×C22⋊C4—131no—
126C22×C22⋊C4#26111yescharacteristic
127C2×C22⋊C8—262no—
128#381—132no—
129#381—132no—
130#381—262no—
131C2×#95—262no—
132#323—134no—
133#323—262no—
134C22×C13—24no—
135C22×C13—24no—
136C22×C13—22no—
137C22×C13—22no—
138C22×C13—22no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—42no—
142C22×C13—41no—
143C22×C13—41no—
144C22×C13—42no—
145C22×C13—42no—
146C22×C13—44no—
147C22×C13—44no—
148C22×C13—44no—
149C22×C13—44no—
150C22×C13—42no—
151C22×C13—42no—
152C22×C13#32312yes—
153C22×C13#32312yes—
154C22×C13#35214yes—
155C22×C13C2×C22⋊C811yescharacteristic
156C22×C13C2×#9911yescharacteristic
157C22×C13C2×#10011yescharacteristic
158C4×C13—82no—
159Dic13—42no—
160Dic13—42no—
161Dic13—44no—
162C25C2×#26111yescharacteristic
163C23×C4—21no—
164C23×C4—134no—
165C23×C4—132no—
166C23×C4—132no—
167C23×C4—262no—
168C23×C4—261no—
169C23×C4—261no—
170C23×C4—521no—
171C23×C4—521no—
172C23×C4—522no—
173C22×C8—522no—
174C2×C22⋊C4—21no—
175C2×C22⋊C4—42no—
176C2×C22⋊C4—132no—
177C2×C22⋊C4—131no—
178C2×C22⋊C4—131no—
179C2×C22⋊C4—521no—
180C2×C22⋊C4—521no—
181C2×C22⋊C4C2×#26112yes—
182C22⋊C8—264no—
183C22⋊C8—522no—
184#95—264no—
185#95—264no—
186C2×C13—21no—
187C2×C13—22no—
188C2×C13—21no—
189C2×C13—42no—
190C2×C13—41no—
191C2×C13—41no—
192C2×C13#131714yescomplemented
193C2×C13C2×#32311yescharacteristic
194C2×C13C2×#35212yes—
195C24—21no—
196C24—21no—
197C24—22no—
198C24—44no—
199C24D13⋊C812yes—
200C24#611812yes—
201C24C22⋊#26111yescharacteristic
202C24C22⋊#26111yescharacteristic
203C24C22×#26111yescharacteristic
204C22×C4—22no—
205C22×C4—44no—
206C22×C4—42no—
207C22×C4—134no—
208C22×C4—132no—
209C22×C4—132no—
210C22×C4—262no—
211C22×C4—264no—
212C22×C4—264no—
213C22×C4—262no—
214C22×C4—262no—
215C22×C4—262no—
216C22×C4—522no—
217C22×C4—524no—
218C22×C4—524no—
219C22×C4—522no—
220C22×C4—521no—
221C22×C4—521no—
222C22×C4—522no—
223C22×C4—522no—
224C22×C4—524no—
225C22×C4—524no—
226C22×C4—522no—
227C22×C4—524no—
228C2×C8—524no—
229C2×C8—1044no—
230C22⋊C4—42no—
231C22⋊C4—42no—
232C22⋊C4—521no—
233C22⋊C4—522no—
234C22⋊C4—521no—
235C13C2×#131711yescharacteristic, complemented, Sylow
236C23—24no—
237C23—21no—
238C23—21no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—21no—
244C23—21no—
245C23—44no—
246C23—44no—
247C23—42no—
248C23—42no—
249C23—48no—
250C23—44no—
251C23—44no—
252C23#8810711yescharacteristic
253C23#8810711yescharacteristic
254C23#8811112yes—
255C23#8811112yes—
256C23#8812112yes—
257C23C2×D13⋊C811yescharacteristic
258C23C2×#611811yescharacteristic
259C23C2×C22⋊#26111yescharacteristic
260C2×C4—44no—
261C2×C4—42no—
262C2×C4—84no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4—264no—
266C2×C4—528no—
267C2×C4—524no—
268C2×C4—522no—
269C2×C4—524no—
270C2×C4—524no—
271C2×C4—524no—
272C2×C4—522no—
273C2×C4—522no—
274C2×C4—522no—
275C2×C4—524no—
276C2×C4—1042no—
277C8—1044no—
278C22—24no—
279C22—24no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—21no—
284C22—21no—
285C22—42no—
286C22—41no—
287C22—41no—
288C22—42no—
289C22—42no—
290C22—44no—
291C22—44no—
292C22—44no—
293C22—44no—
294C22—42no—
295C22—42no—
296C22#1171823714yes—
297C22#1171828712yes—
298C22#1171828712yes—
299C22C2×#8810711yescharacteristic
300C22C2×#8811111yescharacteristic
301C22C2×#8812111yescharacteristic
302C4—82no—
303C4—522no—
304C4—522no—
305C4—524no—
306C2—21no—
307C2—22no—
308C2—21no—
309C2—42no—
310C2—41no—
311C2—41no—
312C2#1312976314yesdirect product factor
313C2C2×#1171828711yescharacteristic
314C2C2×#1171823712yes—
subgroupG/H
centerC23#88107
commutatorC23×C13C22×C8
FrattiniC24C22×#261
FittingC22×C13×C22⋊C4C4
socleC23×C13#99
prime radicalC25×C13C2×C4
cosocleC2×C22⋊Dic13C23
hypercenterC22×C22⋊C4#261
hypocenterC13C2×#1317
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13129763C2direct (N × H)
22. C23×Dic13C8semidirect
70. C22×Dic13C2×C8semidirect
192. C2×C13#1317semidirect
235. C13C2×#1317semidirect
312. C2#13129763direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117183052
#131297632
C2×#117186042
C2×#131713