Finite Group Databasebeta

← C2×#13130942 #16799046

Subgroups — C2×#13130942 #16799046

Order 3328.

1142 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88102C211yesmaximal, characteristic
2C22×#88100C211yesmaximal, characteristic
3C2×#11719083C212yesmaximal
4#13130942C218yesmaximal, direct product factor
5C2×#11718246C212yesmaximal
6C2×D13×#106C211yesmaximal, characteristic
7C22×C4⋊#261—22no—
8C22×C4⋊#261C2212yes—
9C22×C4×#261C2211yescharacteristic
10C22×D13⋊C8C2211yescharacteristic
11C22×C8×D13C2211yescharacteristic
12C2×C4⋊C4×D13C2212yes—
13C2×(C2×#261)⋊C4—22no—
14C2×#88102—24no—
15C2×#88102C2214yes—
16C2×#88100—24no—
17C2×#88100C2214yes—
18#11719083—24no—
19#11719083C2218yes—
20C2×C13×#106C411yescharacteristic, complemented
21C2×#88057C411yescharacteristic, complemented
22C2×#88048C412yescomplemented
23D13×#106C414yescomplemented
24D13×#106C2214yes—
25#11718246C2218yes—
26C23×#261—22no—
27C23×#261D411yescharacteristic
28C23×#261D411yescharacteristic
29C22×C4×D13—22no—
30C22×C4×D13C2311yescharacteristic
31C22×#1057—21no—
32C2×C4⋊#261—24no—
33C2×C4⋊#261—24no—
34C2×C4⋊#261—28no—
35C2×C4⋊#261—22no—
36C2×C4⋊#261—48no—
37C2×C4⋊#261C2314yes—
38C2×C4×#261—22no—
39C2×C4×#261—22no—
40C2×C4×#261D412yes—
41C2×C4×#261C2312yes—
42C2×D13⋊C8—22no—
43C2×D13⋊C8—21no—
44C2×D13⋊C8Q814yes—
45C2×D13⋊C8C2312yes—
46C22×C8×C13C2×C411yescharacteristic
47C2×C13×C4⋊C4C2×C412yes—
48C2×C4⋊Dic13C2×C412yes—
49C2×#6101—22no—
50C22×#1055C2×C411yescharacteristic
51C2×C8×D13C2×C412yes—
52C2×C8×D13D414yes—
53C2×C8×D13Q814yes—
54C2×C8×D13C2312yes—
55C4⋊C4×D13—22no—
56C4⋊C4×D13—22no—
57C4⋊C4×D13C2×C414yes—
58C4⋊C4×D13C2314yes—
59(C2×#261)⋊C4—28no—
60#88102—28no—
61#88100—28no—
62C13×#106C2×C414yescomplemented
63#88057C2×C414yescomplemented
64#88048C2×C418yescomplemented
65C2×#1944—131nomaximal, Sylow
66C23×D13C2×D411yescharacteristic
67C22×#261—22no—
68C22×#261—22no—
69C22×#261—24no—
70C22×#261—24no—
71C22×#261—24no—
72C22×#261—44no—
73C22×#261—44no—
74C22×#261—44no—
75C22×#261C2×D412yes—
76C22×#261C2×D412yes—
77C22×C4×C13—22no—
78C22×C4×C13C22×C411yescharacteristic
79C22×Dic13—22no—
80C22×Dic13#4111yescharacteristic
81C2×C4×D13—24no—
82C2×C4×D13—24no—
83C2×C4×D13—44no—
84C2×C4×D13—44no—
85C2×C4×D13C22×C411yescharacteristic
86C2×C4×D13C2×D412yes—
87C2×C4×D13C2×D411yescharacteristic
88C2×C4×D13C2×Q812yes—
89C2×C4×D13C2×Q812yes—
90C2×C4×D13#4112yes—
91C2×C4×D13#4111yescharacteristic
92C2×C4×D13C2411yescharacteristic
93C2×#1057—24no—
94C2×#1057—22no—
95C4⋊#261—24no—
96C4⋊#261—24no—
97C4⋊#261—416no—
98C4⋊#261—44no—
99C4×#261—24no—
100C4×#261—22no—
101C4×#261—22no—
102D13⋊C8—24no—
103D13⋊C8—22no—
104D13⋊C8C2×Q814yes—
105C2×C8×C13C4⋊C414yescomplemented
106C2×C8×C13C22×C412yes—
107C13×C4⋊C4—22no—
108C13×C4⋊C4C22×C414yes—
109C4⋊Dic13—22no—
110C4⋊Dic13C22×C414yes—
111#6101—24no—
112#6101—24no—
113C2×#1055C4⋊C414yescomplemented
114C2×#1055C22×C412yes—
115C8×D13C4⋊C418yescomplemented
116C8×D13C2×D414yes—
117C8×D13C2×Q814yes—
118C22×#107—131no—
119C22×#106—131no—
120C22×#97—131no—
121C2×#389—132no—
122#1944—138no—
123C2×#340—132no—
124C23×C13C4×D411yescharacteristic
125C22×D13C4×D411yescharacteristic
126C22×D13#12112yes—
127C22×D13C4⋊Q812yes—
128C22×D13AGL(1,ℤ/8)14yes—
129C22×D13#13714yes—
130C22×D13C22×D411yescharacteristic
131C2×#261—22no—
132C2×#261—22no—
133C2×#261—24no—
134C2×#261—24no—
135C2×#261—44no—
136C2×#261—44no—
137C2×#261—44no—
138C2×#261—44no—
139C2×#261—44no—
140C2×#261—88no—
141C2×C4×C13—24no—
142C2×C4×C13—44no—
143C2×C4×C13C2×C4⋊C412yes—
144C2×C4×C13C4×D411yescharacteristic
145C2×C4×C13C4×Q812yes—
146C2×C4×C13C23×C411yescharacteristic
147C2×Dic13—24no—
148C2×Dic13—44no—
149C2×Dic13C4×D411yescharacteristic
150C2×Dic13C22⋊Q812yes—
151C2×Dic13#12512yes—
152C2×Dic13C2×#4111yescharacteristic
153C4×D13—44no—
154C4×D13—44no—
155C4×D13—48no—
156C4×D13C2×C4⋊C412yes—
157C4×D13C4×Q812yes—
158C4×D13#12112yes—
159C4×D13C22⋊Q812yes—
160C4×D13#12512yes—
161C4×D13C4⋊Q812yes—
162C4×D13C22×D411yescharacteristic
163C4×D13C22×Q811yescharacteristic
164C4×D13C22×Q811yescharacteristic
165C4×D13C2×#4111yescharacteristic
166#1057—24no—
167C8×C13C2×C4⋊C414yescomplemented
168#1055C2×C4⋊C414yescomplemented
169C23×C8—131no—
170C23×C8—131no—
171C22×C4⋊C4—132no—
172C22×C4⋊C4—132no—
173C22×C4⋊C4—262no—
174C22×C42—131no—
175C2×#107—134no—
176C2×#107—264no—
177C2×#106—131no—
178C2×#106—132no—
179C2×#106—134no—
180C2×#106—134no—
181C2×#106#26111yescharacteristic, complemented
182C2×#97—134no—
183C2×#97—264no—
184#389—138no—
185#389—264no—
186C2×#95—262no—
187#340—138no—
188C22×C13#38912yes—
189C22×C13#44014yes—
190C22×C13C2×C4×D411yescharacteristic
191C2×D13#38912yes—
192C2×D13#44014yes—
193C2×D13#46914yes—
194C2×D13#47014yes—
195C2×D13#50118yes—
196C2×D13C2×#12111yescharacteristic
197C2×D13C2×C4⋊Q811yescharacteristic
198C2×D13C2×AGL(1,ℤ/8)12yes—
199C2×D13C2×#13712yes—
200#261—42no—
201#261—42no—
202#261—84no—
203C4×C13—44no—
204C4×C13#38912yes—
205C4×C13C22×C4⋊C411yescharacteristic
206C4×C13C2×C4×Q811yescharacteristic
207Dic13—44no—
208Dic13#38912yes—
209Dic13C2×C22⋊Q811yescharacteristic
210Dic13C2×#12511yescharacteristic
211C23×C4—131no—
212C23×C4—131no—
213C23×C4—131no—
214C23×C4—262no—
215C23×C4—262no—
216C22×C8—131no—
217C22×C8—134no—
218C22×C8—134no—
219C22×C8—132no—
220C22×C8—132no—
221C22×C8—132no—
222C22×C8—134no—
223C22×C8—262no—
224C22×C8—261no—
225C22×C8—261no—
226C22×C8C2×#26111yescharacteristic
227C2×C4⋊C4—132no—
228C2×C4⋊C4—134no—
229C2×C4⋊C4—134no—
230C2×C4⋊C4—134no—
231C2×C4⋊C4—262no—
232C2×C4⋊C4—262no—
233C2×C4⋊C4—262no—
234C2×C4⋊C4—264no—
235C2×C4⋊C4—264no—
236C2×C4⋊C4—262no—
237C2×C4⋊C4—268no—
238C2×C4⋊C4—528no—
239C2×C4⋊C4C2×#26112yes—
240C2×C42—132no—
241C2×C42—132no—
242C2×C42—262no—
243C2×C42—262no—
244#107—268no—
245#106—134no—
246#106—138no—
247#106C2×#26114yescomplemented
248#97—268no—
249#95—268no—
250C2×C13#194414yescomplemented
251C2×C13C2×#38911yescharacteristic
252C2×C13C2×#44012yes—
253D13#194414yescomplemented
254D13C2×#46911yescharacteristic
255D13C2×#47011yescharacteristic
256D13C2×#50112yes—
257C24—131no—
258C22×C4—22no—
259C22×C4—131no—
260C22×C4—132no—
261C22×C4—132no—
262C22×C4—131no—
263C22×C4—131no—
264C22×C4—132no—
265C22×C4—132no—
266C22×C4—131no—
267C22×C4—131no—
268C22×C4—132no—
269C22×C4—132no—
270C22×C4—264no—
271C22×C4—264no—
272C22×C4—262no—
273C22×C4—262no—
274C22×C4—264no—
275C22×C4—264no—
276C22×C4—262no—
277C22×C4—264no—
278C22×C4—524no—
279C22×C4—524no—
280C22×C4—524no—
281C22×C4—524no—
282C22×C4—524no—
283C22×C4C22×#26111yescharacteristic
284C2×C8—134no—
285C2×C8—132no—
286C2×C8—134no—
287C2×C8—138no—
288C2×C8—134no—
289C2×C8—134no—
290C2×C8—262no—
291C2×C8—264no—
292C2×C8—264no—
293C2×C8—262no—
294C2×C8C4⋊#26114yescomplemented
295C2×C8C22×#26112yes—
296C4⋊C4—22no—
297C4⋊C4—134no—
298C4⋊C4—264no—
299C4⋊C4—264no—
300C4⋊C4—264no—
301C4⋊C4—264no—
302C4⋊C4—262no—
303C4⋊C4—524no—
304C4⋊C4—5216no—
305C4⋊C4C22×#26114yes—
306C42—262no—
307C42—264no—
308C42—262no—
309C13C2×#194411yescharacteristic, complemented, Sylow
310C23—132no—
311C23—132no—
312C23—134no—
313C23—134no—
314C23—131no—
315C23—131no—
316C23D4×#26111yescharacteristic
317C2×C4—24no—
318C2×C4—44no—
319C2×C4—132no—
320C2×C4—132no—
321C2×C4—131no—
322C2×C4—131no—
323C2×C4—132no—
324C2×C4—132no—
325C2×C4—132no—
326C2×C4—132no—
327C2×C4—131no—
328C2×C4—132no—
329C2×C4—131no—
330C2×C4—131no—
331C2×C4—131no—
332C2×C4—132no—
333C2×C4—262no—
334C2×C4—262no—
335C2×C4—264no—
336C2×C4—264no—
337C2×C4—264no—
338C2×C4—524no—
339C2×C4—524no—
340C2×C4—528no—
341C2×C4—524no—
342C2×C4—524no—
343C2×C4—524no—
344C2×C4—524no—
345C2×C4—524no—
346C2×C4—524no—
347C2×C4—1048no—
348C2×C4C2×C4⋊#26112yes—
349C2×C4D4×#26111yescharacteristic
350C2×C4Q8×#26112yes—
351C2×C4C23×#26111yescharacteristic
352C8—134no—
353C8—264no—
354C8C2×C4⋊#26114yescomplemented
355C22—131no—
356C22—131no—
357C22—132no—
358C22—132no—
359C22—132no—
360C22—134no—
361C22—134no—
362C22—134no—
363C22—138no—
364C22#1171908312yes—
365C22#1171910614yes—
366C22C2×D4×#26111yescharacteristic
367C4—44no—
368C4—131no—
369C4—131no—
370C4—132no—
371C4—522no—
372C4—522no—
373C4—524no—
374C4—1044no—
375C4#1171908312yes—
376C4C22×C4⋊#26111yescharacteristic
377C4C2×Q8×#26111yescharacteristic
378C2—131no—
379C2—131no—
380C2—132no—
381C2—134no—
382C2#1313094214yesdirect product factor
383C2C2×#1171908311yescharacteristic
384C2C2×#1171910612yes—
subgroupG/H
centerC23D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#106C4
socleC23×C13C4×D4
prime radicalC23×D13C2×D4
cosocleC2×C4×D13C24
hypercenterC2×#106#261
hypocenterC13C2×#1944
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
4. #13130942C2direct (N × H)
20. C2×C13×#106C4semidirect
21. C2×#88057C4semidirect
22. C2×#88048C4semidirect
23. D13×#106C4semidirect
62. C13×#106C2×C4semidirect
63. #88057C2×C4semidirect
64. #88048C2×C4semidirect
105. C2×C8×C13C4⋊C4semidirect
113. C2×#1055C4⋊C4semidirect
115. C8×D13C4⋊C4semidirect
167. C8×C13C2×C4⋊C4semidirect
168. #1055C2×C4⋊C4semidirect
181. C2×#106#261semidirect
247. #106C2×#261semidirect
250. C2×C13#1944semidirect
253. D13#1944semidirect
294. C2×C8C4⋊#261semidirect
309. C13C2×#1944semidirect
354. C8C2×C4⋊#261semidirect
382. C2#13130942direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881022
C22×#881002
C2×#117190832
#131309422
C2×#117182462
C2×D13×#1062
C2×#194413