Finite Group Databasebeta

← C2×#13129907 #16789131

Subgroups — C2×#13129907 #16789131

Order 3328.

630 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88098C211yesmaximal, characteristic
2C22×#88101C211yesmaximal, characteristic
3#13129907C214yesmaximal, direct product factor
4C2×#11718541C211yesmaximal, characteristic
5C22×C4⋊#261—21no—
6C22×C8×D13C2211yescharacteristic
7C2×#88146—21no—
8C22×#6092—21no—
9C2×#88101—21no—
10C2×#88101—22no—
11C2×#88101C414yescomplemented
12C2×#88101C2212yes—
13C2×#88098—21no—
14C2×#88098—22no—
15C2×#88098C414yescomplemented
16C2×#88098C2212yes—
17C2×C13×#107C411yescharacteristic, complemented
18C2×#88058C411yescharacteristic, complemented
19C2×#88048—21no—
20#11718541—21no—
21#11718541—21no—
22#11718541C412yescomplemented
23#11718541C2212yes—
24C23×#261—41no—
25C22×C4×D13D411yescharacteristic
26C2×C4⋊#261—24no—
27C2×C4⋊#261—22no—
28C2×C4⋊#261—41no—
29C2×C4⋊#261—42no—
30C22×C8×C13C2×C411yescharacteristic
31C2×C13×C4⋊C4—21no—
32C2×#6103—41no—
33C2×C4⋊Dic13—21no—
34C2×C4×Dic13—41no—
35C22×#1055D411yescharacteristic
36C2×C8×D13C2×C411yescharacteristic
37C2×C8×D13C2×C412yes—
38C2×C8×D13C2×C412yes—
39C2×C8×D13D411yescharacteristic
40C2×C8×D13D411yescharacteristic
41C2×C8×D13D412yes—
42C2×C8×D13Q812yes—
43C2×C8×D13C2311yescharacteristic
44#88146—22no—
45#88146—22no—
46#88146—41no—
47#88146—41no—
48C2×#6092—24no—
49C2×#6092—22no—
50#88101—24no—
51#88101—22no—
52#88101C2×C414yescomplemented
53#88098—24no—
54#88098—22no—
55#88098C2×C414yescomplemented
56C13×#107—21no—
57C13×#107C2×C412yescomplemented
58#88058—21no—
59#88058C2×C412yescomplemented
60#88048—22no—
61#88048—22no—
62C2×#1386—131nomaximal, Sylow
63C23×D13D811yescharacteristic
64C22×#261—44no—
65C22×#261—42no—
66C22×#261—82no—
67C22×#261—82no—
68C22×C4×C13—41no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×Dic13—41no—
71C22×Dic13SD1611yescharacteristic
72C2×C4×D13C22⋊C411yescharacteristic
73C2×C4×D13C22⋊C412yes—
74C2×C4×D13C4⋊C412yes—
75C2×C4×D13D811yescharacteristic
76C2×C4×D13SD1612yes—
77C2×C4×D13SD1611yescharacteristic
78C2×C4×D13Q1612yes—
79C2×C4×D13C2×D411yescharacteristic
80C4⋊#261—24no—
81C4⋊#261—44no—
82C4⋊#261—42no—
83C2×C8×C13C4212yes—
84C2×C8×C13C22⋊C411yescharacteristic
85C2×C8×C13C4⋊C412yes—
86C2×C8×C13C22×C411yescharacteristic
87C13×C4⋊C4—22no—
88C13×C4⋊C4—41no—
89#6103—42no—
90#6103—42no—
91C4⋊Dic13—22no—
92C4⋊Dic13—41no—
93C4×Dic13—42no—
94C4×Dic13—42no—
95C2×#1055C22⋊C411yescharacteristic
96C2×#1055C22⋊C412yes—
97C2×#1055C4⋊C412yes—
98C2×#1055C2×D411yescharacteristic
99C8×D13C4212yes—
100C8×D13C22⋊C412yes—
101C8×D13C22⋊C412yes—
102C8×D13C4⋊C412yes—
103C8×D13C4⋊C412yes—
104C8×D13C4⋊C412yes—
105C8×D13C22×C411yescharacteristic
106C8×D13C22×C411yescharacteristic
107C8×D13C2×D411yescharacteristic
108C8×D13C2×Q811yescharacteristic
109#6092—24no—
110C22×M32—131no—
111C2×#427—131no—
112C22×#106—131no—
113#1386—134no—
114C23×C13#10211yescharacteristic
115C22×D13—22no—
116C22×D13—22no—
117C22×D13#10211yescharacteristic
118C22×D13#10212yes—
119C22×D13#10712yes—
120C22×D13C2×D811yescharacteristic
121C2×#261—44no—
122C2×#261—82no—
123C2×#261—82no—
124C2×#261—88no—
125C2×C4×C13—42no—
126C2×C4×C13—82no—
127C2×C4×C13#9512yes—
128C2×C4×C13#10211yescharacteristic
129C2×C4×C13#10312yes—
130C2×C4×C13C2×C22⋊C411yescharacteristic
131C2×Dic13—42no—
132C2×Dic13—82no—
133C2×Dic13#10211yescharacteristic
134C2×Dic13#10312yes—
135C2×Dic13#10612yes—
136C2×Dic13C2×SD1611yescharacteristic
137C4×D13#9512yes—
138C4×D13#10212yes—
139C4×D13#10312yes—
140C4×D13#10312yes—
141C4×D13#10612yes—
142C4×D13#10712yes—
143C4×D13C2×C22⋊C411yescharacteristic
144C4×D13C2×C4⋊C411yescharacteristic
145C4×D13C2×SD1611yescharacteristic
146C4×D13C2×Q1611yescharacteristic
147C8×C13#9512yes—
148C8×C13C2×C4211yescharacteristic
149C8×C13C2×C4⋊C411yescharacteristic
150#1055#9512yes—
151#1055C2×C22⋊C411yescharacteristic
152#1055C2×C4⋊C411yescharacteristic
153C23×C8—131no—
154C2×#117—261no—
155C22×C4⋊C4—261no—
156C2×M32—132no—
157C2×M32—134no—
158C2×M32—262no—
159C2×M32—261no—
160C22×C16—261no—
161#427—132no—
162#427—132no—
163#427—261no—
164#427—261no—
165C2×#107—131no—
166C2×#107#26111yescharacteristic, complemented
167C2×#106—132no—
168C2×#106—134no—
169C2×#106—261no—
170C2×#106—262no—
171C2×#106—261no—
172C22×C13#34012yes—
173C22×C13#36012yes—
174C22×C13#36012yes—
175C22×C13C2×#10211yescharacteristic
176C2×D13—21no—
177C2×D13—21no—
178C2×D13—21no—
179C2×D13—21no—
180C2×D13—24no—
181C2×D13—24no—
182C2×D13#34012yes—
183C2×D13C2×#10211yescharacteristic
184C2×D13C2×#10711yescharacteristic
185#261—84no—
186C4×C13—82no—
187C4×C13#34012yes—
188C4×C13C2×#9511yescharacteristic
189C4×C13C2×#10311yescharacteristic
190Dic13—82no—
191Dic13#34012yes—
192Dic13C2×#10311yescharacteristic
193Dic13C2×#10611yescharacteristic
194C23×C4—131no—
195C23×C4—521no—
196C22×C8—131no—
197C22×C8—132no—
198C22×C8—132no—
199C22×C8—132no—
200C22×C8—132no—
201C22×C8—131no—
202C22×C8—131no—
203C22×C8—131no—
204C22×C8—131no—
205C22×C8C2×#26111yescharacteristic
206#117—262no—
207#117—262no—
208#117—521no—
209#117—521no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—264no—
212C2×C4⋊C4—262no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—521no—
215C2×C4⋊C4—522no—
216C2×C22⋊C4—521no—
217C2×C42—521no—
218M32—134no—
219M32—264no—
220M32—262no—
221C2×C16—264no—
222C2×C16—262no—
223#107—21no—
224#107—132no—
225#107—261no—
226#107C2×#26112yescomplemented
227#106—134no—
228#106—262no—
229#106—262no—
230#106—264no—
231#106—262no—
232C2×C13#138614yescomplemented
233C2×C13C2×#34011yescharacteristic
234C2×C13C2×#36011yescharacteristic
235C2×C13C2×#36011yescharacteristic
236D13—21no—
237D13—22no—
238D13—21no—
239C24—131no—
240C22×C4—41no—
241C22×C4—131no—
242C22×C4—132no—
243C22×C4—132no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—132no—
247C22×C4—132no—
248C22×C4—131no—
249C22×C4—131no—
250C22×C4—524no—
251C22×C4—522no—
252C22×C4—521no—
253C22×C4—1042no—
254C22×C4—1042no—
255C22×C4C22⋊#26111yescharacteristic
256C2×C8—132no—
257C2×C8—132no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—132no—
261C2×C8—132no—
262C2×C8—132no—
263C2×C8—132no—
264C2×C8—131no—
265C2×C8—131no—
266C2×C8—132no—
267C2×C8—131no—
268C2×C8—132no—
269C2×C8—131no—
270C2×C8C4×#26112yes—
271C2×C8C4⋊#26112yes—
272C2×C8C22⋊#26111yescharacteristic
273C2×C8C22×#26111yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—264no—
277C4⋊C4—262no—
278C4⋊C4—524no—
279C4⋊C4—522no—
280C4⋊C4—521no—
281C22⋊C4—522no—
282C22⋊C4—522no—
283C42—522no—
284C42—522no—
285C16—264no—
286C13C2×#138611yescharacteristic, complemented, Sylow
287C23—132no—
288C23—132no—
289C23—131no—
290C23—131no—
291C23—262no—
292C23—262no—
293C23#8811511yescharacteristic
294C2×C4—42no—
295C2×C4—82no—
296C2×C4—132no—
297C2×C4—132no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—132no—
301C2×C4—132no—
302C2×C4—132no—
303C2×C4—132no—
304C2×C4—131no—
305C2×C4—132no—
306C2×C4—131no—
307C2×C4—131no—
308C2×C4—132no—
309C2×C4—131no—
310C2×C4—524no—
311C2×C4—522no—
312C2×C4—1042no—
313C2×C4—1042no—
314C2×C4—1048no—
315C2×C4—1042no—
316C2×C4(C2×#261)⋊C412yes—
317C2×C4#8811511yescharacteristic
318C2×C4#8811712yes—
319C2×C4C2×C22⋊#26111yescharacteristic
320C8—131no—
321C8—132no—
322C8—131no—
323C8(C2×#261)⋊C412yes—
324C8C2×C4×#26111yescharacteristic
325C8C2×C4⋊#26111yescharacteristic
326C22—132no—
327C22—131no—
328C22—131no—
329C22—261no—
330C22—261no—
331C22—261no—
332C22—261no—
333C22—264no—
334C22—264no—
335C22#1171824612yes—
336C22#1171827512yes—
337C22#1171827912yes—
338C22C2×#8811511yescharacteristic
339C4—82no—
340C4—132no—
341C4—131no—
342C4—131no—
343C4—1044no—
344C4—1042no—
345C4#1171824612yes—
346C4C2×(C2×#261)⋊C411yescharacteristic
347C4C2×#8811711yescharacteristic
348C2—261no—
349C2—262no—
350C2—261no—
351C2#1312990714yesdirect product factor
352C2C2×#1171824611yescharacteristic
353C2C2×#1171827511yescharacteristic
354C2C2×#1171827911yescharacteristic
subgroupG/H
centerC23#88115
commutatorC8×C13C2×C42
FrattiniC2×C8C22×#261
FittingC2×C13×#107C4
socleC23×C13#102
prime radicalC23×D13D8
cosocleC2×C8×D13C23
hypercenterC2×#107#261
hypocenterC13C2×#1386
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #13129907C2direct (N × H)
11. C2×#88101C4semidirect
15. C2×#88098C4semidirect
17. C2×C13×#107C4semidirect
18. C2×#88058C4semidirect
22. #11718541C4semidirect
52. #88101C2×C4semidirect
55. #88098C2×C4semidirect
57. C13×#107C2×C4semidirect
59. #88058C2×C4semidirect
166. C2×#107#261semidirect
226. #107C2×#261semidirect
232. C2×C13#1386semidirect
286. C13C2×#1386semidirect
351. C2#13129907direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880982
C22×#881012
#131299072
C2×#117185412
C2×#138613