Finite Group Databasebeta

← C2×#13129925 #16789183

Subgroups — C2×#13129925 #16789183

Order 3328.

782 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719116C212yesmaximal
2#13129925C214yesmaximal, direct product factor
3C2×#11718790C211yesmaximal, characteristic
4C22×#6127C2211yescharacteristic
5C2×#88237—22no—
6C22×C13×M16C411yescharacteristic, complemented
7C23×#1055C411yescharacteristic, complemented
8C2×#88119C414yescomplemented
9#11719116—22no—
10#11719116—22no—
11#11719116C414yescomplemented
12#11719116C2214yes—
13C2×#88107—22no—
14#11718790—22no—
15#11718790C412yescomplemented
16#11718790C2212yes—
17C2×#88060—22no—
18C23×C4×C13C2×C411yescharacteristic
19C22×C22⋊D13C2×C412yes—
20C2×#6127—41no—
21C2×#6127—41no—
22C2×#6127—41no—
23C2×#6127—41no—
24C2×#6127C2×C411yescharacteristic
25C2×#6127C2×C412yes—
26C2×#6127D411yescharacteristic
27C2×#6127D412yes—
28C2×#6127Q811yescharacteristic
29C2×#6127C2311yescharacteristic
30C22×D52D411yescharacteristic
31C22×C4×D13D412yes—
32C22×Dic26Q811yescharacteristic
33C2×C22⋊#261—24no—
34#88237—24no—
35#88237—24no—
36#88237—42no—
37#88237—42no—
38C2×C4⋊#261—42no—
39C2×C4×#261—42no—
40C2×C13×M16—21no—
41C2×C13×M16—41no—
42C2×C13×M16—41no—
43C2×C13×M16C2×C412yescomplemented
44C22×C8×C13—21no—
45C22×#1055—21no—
46C22×#1055—21no—
47C22×#1055—41no—
48C22×#1055—41no—
49C22×#1055C2×C412yescomplemented
50#88119—24no—
51#88119C2×C418yescomplemented
52#88107—24no—
53#88107—24no—
54#88060—24no—
55#88060—24no—
56C2×#1391—131nomaximal, Sylow
57C24×C13C4211yescharacteristic
58C23×D13C22⋊C412yes—
59C22×#261—44no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13C4211yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C4⋊C411yescharacteristic
68C22×C4×C13C4⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C2×C22⋊D13—42no—
71C2×C22⋊D13—42no—
72C2×C22⋊D13C4212yes—
73C2×C22⋊D13C22⋊C412yes—
74C2×C22⋊D13C4⋊C412yes—
75C2×C22⋊D13C22×C412yes—
76C22×Dic13C4⋊C412yes—
77#6127—42no—
78#6127—42no—
79#6127—41no—
80#6127—41no—
81#6127—41no—
82#6127—41no—
83#6127—42no—
84#6127—42no—
85#6127—41no—
86#6127—41no—
87#6127—41no—
88#6127—41no—
89C2×D52—41no—
90C2×D52—41no—
91C2×D52C22⋊C412yes—
92C2×D52C4⋊C411yescharacteristic
93C2×D52C2×D411yescharacteristic
94C2×C4×D13—22no—
95C2×C4×D13—22no—
96C2×C4×D13—22no—
97C2×C4×D13—22no—
98C2×C4×D13C22⋊C412yes—
99C2×C4×D13C22⋊C412yes—
100C2×C4×D13C4⋊C412yes—
101C2×C4×D13C2×D412yes—
102C2×Dic26—41no—
103C2×Dic26—41no—
104C2×Dic26C4⋊C411yescharacteristic
105C2×Dic26C4⋊C412yes—
106C2×Dic26C2×Q811yescharacteristic
107C22⋊#261—28no—
108C22⋊#261—44no—
109C4⋊#261—44no—
110C4⋊#261—44no—
111C4×#261—44no—
112C4×#261—44no—
113C13×M16—42no—
114C13×M16—42no—
115C2×C8×C13—22no—
116C2×C8×C13—41no—
117C2×C8×C13—41no—
118C2×#1055—22no—
119C2×#1055—42no—
120C2×#1055—41no—
121C2×#1055—41no—
122C2×#1055—42no—
123C2×#410—132no—
124C2×#408—131no—
125#1391—134no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—42no—
129C23×C13#9511yescharacteristic
130C23×C13#9511yescharacteristic
131C23×C13C2×C4211yescharacteristic
132C22×D13—22no—
133C22×D13—22no—
134C22×D13—44no—
135C22×D13#9512yes—
136C22×D13C2×C22⋊C412yes—
137C2×#261—48no—
138C2×#261—88no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13#9511yescharacteristic
150C2×C4×C13#9511yescharacteristic
151C2×C4×C13#9911yescharacteristic
152C2×C4×C13#9911yescharacteristic
153C2×C4×C13#9911yescharacteristic
154C2×C4×C13#9911yescharacteristic
155C2×C4×C13C2×C22⋊C411yescharacteristic
156C2×C4×C13C2×C4⋊C411yescharacteristic
157C22⋊D13—42no—
158C22⋊D13—42no—
159C22⋊D13—42no—
160C22⋊D13—42no—
161C2×Dic13—22no—
162C2×Dic13—22no—
163C2×Dic13#9512yes—
164C2×Dic13C2×C4⋊C412yes—
165D52—42no—
166D52—41no—
167D52—41no—
168C4×D13—22no—
169C4×D13—22no—
170C4×D13—22no—
171C4×D13—22no—
172C4×D13—22no—
173C4×D13—22no—
174C4×D13—22no—
175C4×D13—22no—
176Dic26—41no—
177Dic26—42no—
178Dic26—41no—
179C8×C13—42no—
180#1055—42no—
181C22×#41—131no—
182C22×M16#26111yescharacteristic, complemented
183C23×C8—131no—
184C2×#117—262no—
185#410—134no—
186#410—134no—
187#410—262no—
188#410—262no—
189C2×#99—134no—
190C2×#99—262no—
191#408—132no—
192#408—132no—
193#408—262no—
194C2×C22⋊C8—262no—
195C22×C13—22no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—42no—
201C22×C13—42no—
202C22×C13#34211yescharacteristic
203C22×C13#34211yescharacteristic
204C22×C13C2×#9511yescharacteristic
205C2×D13—22no—
206C2×D13—22no—
207C2×D13—44no—
208C2×D13—42no—
209C2×D13—42no—
210C2×D13—82no—
211#261—88no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13#34211yescharacteristic
215C4×C13#34211yescharacteristic
216C4×C13C2×#9911yescharacteristic
217C4×C13C2×#9911yescharacteristic
218Dic13—22no—
219Dic13—22no—
220C2×#41—132no—
221C2×#41—131no—
222C2×#41—131no—
223C2×#41—132no—
224C2×#41—131no—
225C2×#41—131no—
226C2×#41—521no—
227C2×#41—521no—
228C2×#41—521no—
229C2×#41—521no—
230C22×Q8—131no—
231C22×D4—132no—
232C22×D4—131no—
233C23×C4—132no—
234C23×C4C2×#26111yescharacteristic
235C2×M16—21no—
236C2×M16—41no—
237C2×M16—41no—
238C2×M16C2×#26112yescomplemented
239C22×C8—21no—
240C22×C8—132no—
241C22×C8—261no—
242C22×C8—261no—
243C22×C8—521no—
244C22×C8—521no—
245#117—264no—
246#117—264no—
247#117—522no—
248#117—522no—
249C2×C4⋊C4—522no—
250C2×C22⋊C4—264no—
251C2×C42—522no—
252#99—138no—
253#99—264no—
254#99—264no—
255#99—264no—
256C22⋊C8—264no—
257C22⋊C8—264no—
258C2×C13—21no—
259C2×C13—21no—
260C2×C13—41no—
261C2×C13—41no—
262C2×C13#139112yescomplemented
263C2×C13C2×#34211yescharacteristic
264D13—42no—
265D13—42no—
266C24—132no—
267C24C4×#26111yescharacteristic
268#41—522no—
269#41—522no—
270#41—521no—
271#41—521no—
272#41—521no—
273#41—521no—
274#41—522no—
275#41—521no—
276#41—521no—
277#41—522no—
278#41—521no—
279#41—521no—
280C2×Q8—132no—
281C2×Q8—131no—
282C2×Q8—131no—
283C2×Q8—521no—
284C2×Q8—521no—
285C2×D4—132no—
286C2×D4—132no—
287C2×D4—132no—
288C2×D4—132no—
289C2×D4—132no—
290C2×D4—131no—
291C2×D4—131no—
292C2×D4—521no—
293C2×D4—521no—
294C2×D4—522no—
295C2×D4—522no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—132no—
301C22×C4—132no—
302C22×C4—132no—
303C22×C4—132no—
304C22×C4—132no—
305C22×C4—262no—
306C22×C4—262no—
307C22×C4—262no—
308C22×C4—262no—
309C22×C4—524no—
310C22×C4C4×#26111yescharacteristic
311C22×C4C4⋊#26111yescharacteristic
312C22×C4C4⋊#26111yescharacteristic
313C22×C4C22⋊#26111yescharacteristic
314C22×C4C22⋊#26111yescharacteristic
315C22×C4C22×#26111yescharacteristic
316M16—42no—
317M16—42no—
318C2×C8—22no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—262no—
322C2×C8—522no—
323C2×C8—521no—
324C2×C8—521no—
325C2×C8—522no—
326C4⋊C4—524no—
327C4⋊C4—524no—
328C22⋊C4—268no—
329C22⋊C4—524no—
330C42—524no—
331C42—524no—
332C13C2×#139111yescharacteristic, complemented, Sylow
333C23—21no—
334C23—21no—
335C23—42no—
336C23—132no—
337C23—132no—
338C23—262no—
339C23—262no—
340C23—524no—
341C23(C2×#261)⋊C411yescharacteristic
342C23(C2×#261)⋊C411yescharacteristic
343C23C2×C4×#26111yescharacteristic
344Q8—522no—
345Q8—521no—
346Q8—521no—
347D4—522no—
348D4—521no—
349D4—521no—
350D4—522no—
351D4—522no—
352D4—522no—
353D4—522no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—132no—
365C2×C4—132no—
366C2×C4—262no—
367C2×C4—262no—
368C2×C4—262no—
369C2×C4—262no—
370C2×C4—262no—
371C2×C4—262no—
372C2×C4—262no—
373C2×C4—262no—
374C2×C4—262no—
375C2×C4—262no—
376C2×C4—528no—
377C2×C4—1048no—
378C2×C4#8810711yescharacteristic
379C2×C4#8810711yescharacteristic
380C2×C4(C2×#261)⋊C411yescharacteristic
381C2×C4(C2×#261)⋊C411yescharacteristic
382C2×C4#8811911yescharacteristic
383C2×C4#8811911yescharacteristic
384C2×C4C2×C4⋊#26111yescharacteristic
385C2×C4C2×C22⋊#26111yescharacteristic
386C8—42no—
387C8—522no—
388C22—22no—
389C22—21no—
390C22—21no—
391C22—41no—
392C22—41no—
393C22—42no—
394C22—42no—
395C22—262no—
396C22—262no—
397C22—522no—
398C22—522no—
399C22—524no—
400C22—1042no—
401C22#1171828911yescharacteristic
402C22#1171828911yescharacteristic
403C22C2×(C2×#261)⋊C411yescharacteristic
404C4—21no—
405C4—21no—
406C4—262no—
407C4—262no—
408C4—1048no—
409C4#1171828911yescharacteristic
410C4#1171828911yescharacteristic
411C4C2×#8810711yescharacteristic
412C4C2×#8811911yescharacteristic
413C2—21no—
414C2—21no—
415C2—41no—
416C2—41no—
417C2—522no—
418C2—522no—
419C2#1312992512yesdirect product factor
420C2C2×#1171828911yescharacteristic
subgroupG/H
centerC2×C4#88107
commutatorC23×C13C2×C42
FrattiniC22×C4C22×#261
FittingC22×C13×M16C4
socleC22×C13#342
prime radicalC22×#6127C22
cosocleC2×#6127C23
hypercenterC22×M16#261
hypocenterC13C2×#1391
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. #13129925C2direct (N × H)
6. C22×C13×M16C4semidirect
7. C23×#1055C4semidirect
8. C2×#88119C4semidirect
11. #11719116C4semidirect
15. #11718790C4semidirect
43. C2×C13×M16C2×C4semidirect
49. C22×#1055C2×C4semidirect
51. #88119C2×C4semidirect
182. C22×M16#261semidirect
238. C2×M16C2×#261semidirect
262. C2×C13#1391semidirect
332. C13C2×#1391semidirect
419. C2#13129925direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191162
#131299252
C2×#117187902
C2×#139113