Finite Group Databasebeta

← C2×#13129824 #16787675

Subgroups — C2×#13129824 #16787675

Order 3328.

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

normal subgroups only

This group has 506 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×#11718259C211yesmaximal, characteristic
2C2×#11718265C211yesmaximal, characteristic
3#13129824C214yesmaximal, direct product factor
4C2×#11718849C211yesmaximal, characteristic
5C22×C4⋊#261—21no—
6C22×C13×Q16C411yescharacteristic, complemented
7C2×#88200—21no—
8C22×C8×D13C2211yescharacteristic
9C22×#6092—21no—
10C2×#88075—21no—
11#11718849—21no—
12#11718849—21no—
13#11718849C412yescomplemented
14#11718849C2212yes—
15C2×#88058C411yescharacteristic, complemented
16#11718265—21no—
17#11718265C2212yes—
18#11718259—21no—
19#11718259C2212yes—
20C23×#261—41no—
21C22×Q8×C13—21no—
22C22×C4×D13D411yescharacteristic
23C2×C4⋊#261—24no—
24C2×C4⋊#261—22no—
25C2×C4⋊#261—42no—
26C2×C4⋊#261—41no—
27C2×C13×Q16—21no—
28C2×C13×Q16—42no—
29C2×C13×Q16C2×C412yescomplemented
30C22×C8×C13C2×C411yescharacteristic
31#88200—22no—
32#88200—22no—
33#88200—41no—
34#88200—41no—
35C2×#6103—41no—
36C2×C4⋊Dic13—21no—
37C2×#6101—41no—
38C22×#1055D411yescharacteristic
39C2×C8×D13—42no—
40C2×C8×D13C2×C411yescharacteristic
41C2×C8×D13D411yescharacteristic
42C2×C8×D13D411yescharacteristic
43C2×C8×D13C2311yescharacteristic
44C2×#6092—22no—
45C2×#6092—42no—
46#88075—22no—
47#88075—22no—
48#88058—21no—
49#88058C2×C412yescomplemented
50C2×#1348—131nomaximal, Sylow
51C23×D13D811yescharacteristic
52C22×#261—44no—
53C22×#261—42no—
54C22×#261—82no—
55C22×#261—82no—
56C2×Q8×C13—22no—
57C2×Q8×C13—41no—
58C2×Q8×C13—42no—
59C2×Q8×C13—42no—
60C22×C4×C13—41no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×Dic13—41no—
63C22×Dic13SD1611yescharacteristic
64C2×C4×D13—22no—
65C2×C4×D13—22no—
66C2×C4×D13C22⋊C411yescharacteristic
67C2×C4×D13D811yescharacteristic
68C2×C4×D13SD1611yescharacteristic
69C2×C4×D13C2×D411yescharacteristic
70C4⋊#261—24no—
71C4⋊#261—44no—
72C4⋊#261—42no—
73C13×Q16—42no—
74C13×Q16—42no—
75C2×C8×C13—22no—
76C2×C8×C13C22⋊C411yescharacteristic
77C2×C8×C13C22×C411yescharacteristic
78#6103—42no—
79#6103—42no—
80C4⋊Dic13—22no—
81C4⋊Dic13—41no—
82#6101—42no—
83#6101—42no—
84C2×#1055—22no—
85C2×#1055C22⋊C411yescharacteristic
86C2×#1055C2×D411yescharacteristic
87C8×D13—41no—
88C8×D13—41no—
89C8×D13—41no—
90C8×D13—41no—
91#6092—42no—
92C2×#467—131no—
93C2×C22⋊C16—131no—
94C2×#340—131no—
95#1348—134no—
96C23×C13#10211yescharacteristic
97C22×D13—22no—
98C22×D13—22no—
99C22×D13#10211yescharacteristic
100C22×D13SD3212yes—
101C22×D13Q3212yes—
102C22×D13C2×D811yescharacteristic
103C2×#261—44no—
104C2×#261—88no—
105C2×#261—82no—
106C2×#261—82no—
107Q8×C13—42no—
108Q8×C13—42no—
109Q8×C13—82no—
110C2×C4×C13—42no—
111C2×C4×C13—82no—
112C2×C4×C13#9912yes—
113C2×C4×C13#10211yescharacteristic
114C2×C4×C13#10412yes—
115C2×C4×C13C2×C22⋊C411yescharacteristic
116C2×Dic13—22no—
117C2×Dic13—42no—
118C2×Dic13—82no—
119C2×Dic13#10211yescharacteristic
120C2×Dic13C2×SD1611yescharacteristic
121C4×D13—22no—
122C4×D13—22no—
123C4×D13—21no—
124C4×D13—21no—
125C4×D13—21no—
126C4×D13—21no—
127C8×C13—21no—
128C8×C13—21no—
129#1055—21no—
130#1055—21no—
131C22×Q16#26111yescharacteristic, complemented
132C23×C8—131no—
133C2×C22⋊Q8—261no—
134C22×C4⋊C4—261no—
135C22×C16—261no—
136#467—132no—
137#467—132no—
138#467—261no—
139#467—261no—
140C2×#107—131no—
141C2×#103—261no—
142C22⋊C16—132no—
143C22⋊C16—261no—
144#340—132no—
145#340—261no—
146C22×C13#32712yes—
147C22×C13#35812yes—
148C22×C13#36012yes—
149C22×C13C2×#10211yescharacteristic
150C2×D13—24no—
151C2×D13—24no—
152C2×D13—21no—
153C2×D13—21no—
154C2×D13—21no—
155C2×D13—21no—
156C2×D13#35812yes—
157C2×D13C2×SD3211yescharacteristic
158C2×D13C2×Q3211yescharacteristic
159#261—84no—
160C4×C13—82no—
161C4×C13#32712yes—
162C4×C13C2×#9911yescharacteristic
163C4×C13C2×#10411yescharacteristic
164Dic13—21no—
165Dic13—21no—
166Dic13—82no—
167C22×Q8—21no—
168C23×C4—131no—
169C23×C4—521no—
170C2×Q16—21no—
171C2×Q16—42no—
172C2×Q16C2×#26112yescomplemented
173C22×C8—131no—
174C22×C8—131no—
175C22×C8—131no—
176C22×C8—131no—
177C22×C8—131no—
178C22×C8—522no—
179C22×C8C2×#26111yescharacteristic
180C22⋊Q8—262no—
181C22⋊Q8—262no—
182C22⋊Q8—521no—
183C22⋊Q8—521no—
184C2×C4⋊C4—262no—
185C2×C4⋊C4—264no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—521no—
188C2×C4⋊C4—521no—
189C2×C4⋊C4—522no—
190C2×C22⋊C4—521no—
191C2×C16—262no—
192C2×C16—522no—
193#107—132no—
194#107—261no—
195#103—262no—
196#103—262no—
197C2×C13#134814yescomplemented
198C2×C13C2×#32711yescharacteristic
199C2×C13C2×#35811yescharacteristic
200C2×C13C2×#36011yescharacteristic
201D13—21no—
202D13—22no—
203D13—21no—
204C24—131no—
205C2×Q8—22no—
206C2×Q8—41no—
207C2×Q8—42no—
208C2×Q8—42no—
209C22×C4—41no—
210C22×C4—131no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—131no—
214C22×C4—131no—
215C22×C4—262no—
216C22×C4—262no—
217C22×C4—522no—
218C22×C4—524no—
219C22×C4—521no—
220C22×C4—1042no—
221C22×C4—1042no—
222C22×C4C22⋊#26111yescharacteristic
223Q16—42no—
224Q16—42no—
225C2×C8—22no—
226C2×C8—131no—
227C2×C8—131no—
228C2×C8—262no—
229C2×C8—521no—
230C2×C8—521no—
231C2×C8—521no—
232C2×C8—521no—
233C2×C8C22⋊#26111yescharacteristic
234C2×C8C22×#26111yescharacteristic
235C4⋊C4—264no—
236C4⋊C4—262no—
237C4⋊C4—522no—
238C4⋊C4—522no—
239C4⋊C4—524no—
240C4⋊C4—522no—
241C4⋊C4—521no—
242C22⋊C4—522no—
243C22⋊C4—522no—
244C16—522no—
245C13C2×#134811yescharacteristic, complemented, Sylow
246C23—132no—
247C23—132no—
248C23—131no—
249C23—131no—
250C23—262no—
251C23—262no—
252C23#8811511yescharacteristic
253Q8—42no—
254Q8—42no—
255Q8—82no—
256C2×C4—42no—
257C2×C4—82no—
258C2×C4—131no—
259C2×C4—131no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—262no—
263C2×C4—261no—
264C2×C4—261no—
265C2×C4—261no—
266C2×C4—261no—
267C2×C4—524no—
268C2×C4—522no—
269C2×C4—1042no—
270C2×C4—1048no—
271C2×C4—1042no—
272C2×C4—1042no—
273C2×C4#8811511yescharacteristic
274C2×C4#8811612yes—
275C2×C4#8811912yes—
276C2×C4C2×C22⋊#26111yescharacteristic
277C8—21no—
278C8—21no—
279C8—261no—
280C8—261no—
281C22—132no—
282C22—131no—
283C22—131no—
284C22—264no—
285C22—264no—
286C22—261no—
287C22—261no—
288C22—261no—
289C22—261no—
290C22#1171827912yes—
291C22#1171828012yes—
292C22#1171829212yes—
293C22C2×#8811511yescharacteristic
294C4—82no—
295C4—261no—
296C4—261no—
297C4—1044no—
298C4—1042no—
299C4#1171829212yes—
300C4C2×#8811611yescharacteristic
301C4C2×#8811911yescharacteristic
302C2—261no—
303C2—262no—
304C2—261no—
305C2#1312982414yesdirect product factor
306C2C2×#1171829211yescharacteristic
307C2C2×#1171828011yescharacteristic
308C2C2×#1171827911yescharacteristic
subgroupG/H
centerC23#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC22×C13×Q16C4
socleC23×C13#102
prime radicalC23×D13D8
cosocleC2×C8×D13C23
hypercenterC22×Q16#261
hypocenterC13C2×#1348
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
3. #13129824C2direct (N × H)
6. C22×C13×Q16C4semidirect
13. #11718849C4semidirect
15. C2×#88058C4semidirect
29. C2×C13×Q16C2×C4semidirect
49. #88058C2×C4semidirect
131. C22×Q16#261semidirect
172. C2×Q16C2×#261semidirect
197. C2×C13#1348semidirect
245. C13C2×#1348semidirect
305. C2#13129824direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117182592
C2×#117182652
#131298242
C2×#117188492
C2×#134813