Finite Group Databasebeta

← C2×#13130539 #16796814

Subgroups — C2×#13130539 #16796814

Order 3328.

2494 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D13⋊M16C212yesmaximal
2#13130539C218yesmaximal, direct product factor
3C2×#11718291C214yesmaximal, complemented
4C22×C4⋊C4×D13C211yesmaximal, characteristic
5C23×C4×D13C412yes—
6C23×C4×D13C2211yescharacteristic
7C22×#6122C2214yes—
8C2×D13⋊M16—28no—
9C2×D13⋊M16—24no—
10C2×D13⋊M16C4116yescomplemented
11C2×D13⋊M16C2218yes—
12C22×#6118—22no—
13C22×D13⋊C8—22no—
14C22×C13×C4⋊C4C411yescharacteristic
15C22×C4⋊Dic13C411yescharacteristic
16C22×#6101C2212yes—
17C2×C4⋊C4×D13—22no—
18C2×C4⋊C4×D13—22no—
19C2×C4⋊C4×D13—24no—
20C2×C4⋊C4×D13C414yes—
21C2×C4⋊C4×D13C2214yes—
22#11718291C22116yescomplemented
23C24×D13C2×C411yescharacteristic
24C23×C4×C13C2×C412yes—
25C23×C4×C13C2×C411yescharacteristic
26C23×Dic13C2×C412yes—
27C23×Dic13C2311yescharacteristic
28C22×C4×D13—24no—
29C22×C4×D13—22no—
30C22×C4×D13—22no—
31C22×C4×D13—48no—
32C22×C4×D13C2×C418yes—
33C22×C4×D13C2×C412yes—
34C22×C4×D13C2×C418yes—
35C22×C4×D13D414yes—
36C22×C4×D13D412yes—
37C22×C4×D13D412yes—
38C22×C4×D13D414yes—
39C22×C4×D13Q814yes—
40C22×C4×D13C2312yes—
41C2×#6122—28no—
42C2×#6122—24no—
43C2×#6122C2×C4116yescomplemented
44C2×#6122C2318yes—
45C22×#1057—24no—
46D13⋊M16—232no—
47D13⋊M16—216no—
48D13⋊M16C2×C4132yescomplemented
49C2×#6118—216no—
50C2×#6118—28no—
51C2×D13⋊C8—216no—
52C2×D13⋊C8—28no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4C2×C414yes—
56C2×C4⋊Dic13—22no—
57C2×C4⋊Dic13—22no—
58C2×C4⋊Dic13C2×C414yes—
59C2×#6101—24no—
60C2×#6101—24no—
61C2×#6101C2×C414yes—
62C2×#6101C2314yes—
63C4⋊C4×D13—28no—
64C4⋊C4×D13—28no—
65C4⋊C4×D13—28no—
66C4⋊C4×D13—28no—
67C22×#343—131nomaximal, Sylow
68C24×C13C22×C411yescharacteristic
69C23×D13—24no—
70C23×D13—24no—
71C23×D13C4214yes—
72C23×D13C22⋊C412yes—
73C23×D13C22⋊C411yescharacteristic
74C23×D13C22⋊C411yescharacteristic
75C23×D13C4⋊C414yes—
76C23×D13C22×C412yes—
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—44no—
80C22×C4×C13C4214yes—
81C22×C4×C13C22⋊C412yes—
82C22×C4×C13C22⋊C412yes—
83C22×C4×C13C4⋊C414yes—
84C22×C4×C13C22×C414yes—
85C22×C4×C13C22×C412yes—
86C22×Dic13—22no—
87C22×Dic13—22no—
88C22×Dic13—44no—
89C22×Dic13C22×C414yes—
90C22×Dic13C22×C411yescharacteristic
91C22×Dic13C22×C414yes—
92C22×Dic13C2×D412yes—
93C22×Dic13C2×D412yes—
94C22×Dic13C2×D412yes—
95C22×Dic13C2×Q812yes—
96C22×Dic13C2411yescharacteristic
97C2×C4×D13—28no—
98C2×C4×D13—28no—
99C2×C4×D13—48no—
100C2×C4×D13—416no—
101C2×C4×D13—48no—
102C2×C4×D13—416no—
103C2×C4×D13C4218yes—
104C2×C4×D13C22⋊C414yes—
105C2×C4×D13C22⋊C414yes—
106C2×C4×D13C22⋊C418yes—
107C2×C4×D13C22⋊C418yes—
108C2×C4×D13C22⋊C4116yes—
109C2×C4×D13C4⋊C418yes—
110C2×C4×D13C4⋊C418yes—
111C2×C4×D13C4⋊C4116yes—
112C2×C4×D13C4⋊C418yes—
113C2×C4×D13C22×C418yes—
114C2×C4×D13C2×D414yes—
115C2×C4×D13C2×D414yes—
116C2×C4×D13C2×D414yes—
117C2×C4×D13C2×Q814yes—
118#6122—216no—
119#6122—28no—
120#6122C22×C4116yescomplemented
121C2×#1057—216no—
122C2×#1057—28no—
123#6118—232no—
124D13⋊C8—232no—
125C13×C4⋊C4—28no—
126C4⋊Dic13—28no—
127#6101—28no—
128#6101—28no—
129C23×M16—132no—
130C23×C4⋊C4—131no—
131C2×#343—134no—
132C2×#343—138no—
133C23×C13—22no—
134C23×C13—22no—
135C23×C13C2×C4212yes—
136C23×C13C2×C22⋊C411yescharacteristic
137C23×C13C2×C22⋊C411yescharacteristic
138C23×C13C2×C4⋊C412yes—
139C23×C13C23×C411yescharacteristic
140C22×D13—22no—
141C22×D13—22no—
142C22×D13—216no—
143C22×D13—216no—
144C22×D13—24no—
145C22×D13—24no—
146C22×D13—24no—
147C22×D13—24no—
148C22×D13#9514yes—
149C22×D13#9518yes—
150C22×D13#9514yes—
151C22×D13#10014yes—
152C22×D13#10114yes—
153C22×D13C2×C4214yes—
154C22×D13C2×C22⋊C412yes—
155C22×D13C2×C22⋊C412yes—
156C22×D13C2×C4⋊C414yes—
157C2×C4×C13—24no—
158C2×C4×C13—44no—
159C2×C4×C13—44no—
160C2×C4×C13—44no—
161C2×C4×C13#9518yes—
162C2×C4×C13#9518yes—
163C2×C4×C13C2×C4214yes—
164C2×C4×C13C2×C22⋊C414yes—
165C2×C4×C13C2×C4⋊C414yes—
166C2×Dic13—24no—
167C2×Dic13—44no—
168C2×Dic13—44no—
169C2×Dic13—44no—
170C2×Dic13C2×C4212yes—
171C2×Dic13C2×C22⋊C414yes—
172C2×Dic13C2×C22⋊C414yes—
173C2×Dic13C2×C22⋊C412yes—
174C2×Dic13C2×C4⋊C414yes—
175C2×Dic13C2×C4⋊C414yes—
176C2×Dic13C2×C4⋊C412yes—
177C2×Dic13C23×C412yes—
178C2×Dic13C22×D411yescharacteristic
179C2×Dic13C22×D412yes—
180C2×Dic13C22×Q811yescharacteristic
181C4×D13—416no—
182C4×D13—416no—
183C4×D13#95116yes—
184C4×D13#95116yes—
185C4×D13C2×C22⋊C418yes—
186C4×D13C2×C22⋊C418yes—
187C4×D13C2×C4⋊C418yes—
188C4×D13C2×C4⋊C418yes—
189#1057—216no—
190C24×C4—131no—
191C24×C4—132no—
192C22×M16—1316no—
193C22×M16—138no—
194C22×M16—134no—
195C22×M16—262no—
196C22×M16—268no—
197C22×M16—264no—
198C23×C8—262no—
199C22×C4⋊C4—132no—
200C22×C4⋊C4—131no—
201C22×C4⋊C4—134no—
202C22×C4⋊C4—134no—
203C22×C4⋊C4—262no—
204C22×C4⋊C4—264no—
205C22×C4⋊C4—262no—
206C22×C4⋊C4#26111yescharacteristic
207#343—1316no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—24no—
213C22×C13—24no—
214C22×C13C2×#9512yes—
215C22×C13C2×#9512yes—
216C22×C13C2×#10012yes—
217C22×C13C2×#10112yes—
218C22×C13C22×C4211yescharacteristic
219C22×C13C22×C22⋊C411yescharacteristic
220C22×C13C22×C4⋊C411yescharacteristic
221C2×D13—22no—
222C2×D13—22no—
223C2×D13—28no—
224C2×D13—216no—
225C2×D13—28no—
226C2×D13—28no—
227C2×D13#343116yescomplemented
228C2×D13C2×#9514yes—
229C2×D13C2×#9514yes—
230C2×D13C2×#10014yes—
231C2×D13C2×#10114yes—
232C4×C13—44no—
233C4×C13C2×#9518yes—
234Dic13—44no—
235Dic13C2×#9514yes—
236Dic13C22×C22⋊C412yes—
237Dic13C22×C4⋊C412yes—
238C25—131no—
239C23×C4—131no—
240C23×C4—138no—
241C23×C4—134no—
242C23×C4—134no—
243C23×C4—132no—
244C23×C4—134no—
245C23×C4—132no—
246C23×C4—132no—
247C23×C4—132no—
248C23×C4—132no—
249C23×C4—138no—
250C23×C4—264no—
251C23×C4—262no—
252C23×C4—262no—
253C23×C4—528no—
254C23×C4C2×#26112yes—
255C23×C4C2×#26111yescharacteristic
256C2×M16—138no—
257C2×M16—1332no—
258C2×M16—1316no—
259C2×M16—2616no—
260C2×M16—268no—
261C2×M16—2632no—
262C2×M16—2616no—
263C2×M16—268no—
264C2×M16—264no—
265C22×C8—2616no—
266C22×C8—268no—
267C22×C8—264no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—134no—
271C2×C4⋊C4—134no—
272C2×C4⋊C4—134no—
273C2×C4⋊C4—268no—
274C2×C4⋊C4—268no—
275C2×C4⋊C4—268no—
276C2×C4⋊C4—268no—
277C2×C4⋊C4—264no—
278C2×C4⋊C4—264no—
279C2×C4⋊C4—262no—
280C2×C4⋊C4—262no—
281C2×C4⋊C4C2×#26114yes—
282C2×C13—21no—
283C2×C13—22no—
284C2×C13—21no—
285C2×C13C2×#34314yescomplemented
286C2×C13C22×#9511yescharacteristic
287C2×C13C22×#10011yescharacteristic
288C2×C13C22×#10111yescharacteristic
289D13—24no—
290D13C2×#34318yescomplemented
291C24—131no—
292C24—134no—
293C24—134no—
294C24—132no—
295C24—131no—
296C24—132no—
297C24—264no—
298C24—264no—
299C24C22×#26111yescharacteristic
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—44no—
303C22×C4—134no—
304C22×C4—132no—
305C22×C4—132no—
306C22×C4—132no—
307C22×C4—132no—
308C22×C4—131no—
309C22×C4—131no—
310C22×C4—138no—
311C22×C4—138no—
312C22×C4—1316no—
313C22×C4—138no—
314C22×C4—1316no—
315C22×C4—138no—
316C22×C4—138no—
317C22×C4—138no—
318C22×C4—134no—
319C22×C4—138no—
320C22×C4—134no—
321C22×C4—134no—
322C22×C4—134no—
323C22×C4—134no—
324C22×C4—134no—
325C22×C4—134no—
326C22×C4—268no—
327C22×C4—268no—
328C22×C4—262no—
329C22×C4—262no—
330C22×C4—528no—
331C22×C4—5216no—
332C22×C4—528no—
333C22×C4—5216no—
334C22×C4—524no—
335C22×C4C4×#26114yes—
336C22×C4C4⋊#26114yes—
337C22×C4C22⋊#26112yes—
338C22×C4C22⋊#26112yes—
339C22×C4C22×#26114yes—
340C22×C4C22×#26112yes—
341M16—1316no—
342M16—2632no—
343M16—268no—
344M16—2616no—
345C2×C8—2632no—
346C2×C8—268no—
347C2×C8—2616no—
348C4⋊C4—28no—
349C4⋊C4—268no—
350C4⋊C4—268no—
351C4⋊C4—268no—
352C13C22×#34311yescharacteristic, complemented, Sylow
353C23—22no—
354C23—22no—
355C23—132no—
356C23—134no—
357C23—134no—
358C23—134no—
359C23—134no—
360C23—134no—
361C23—132no—
362C23—138no—
363C23—134no—
364C23—264no—
365C23—264no—
366C23—2616no—
367C23—2616no—
368C23—264no—
369C23—264no—
370C23—262no—
371C23—262no—
372C23C2×C4×#26112yes—
373C23C2×C4⋊#26112yes—
374C23C2×C22⋊#26111yescharacteristic
375C23C2×C22⋊#26111yescharacteristic
376C23C23×#26111yescharacteristic
377C2×C4—24no—
378C2×C4—44no—
379C2×C4—44no—
380C2×C4—44no—
381C2×C4—132no—
382C2×C4—132no—
383C2×C4—131no—
384C2×C4—132no—
385C2×C4—131no—
386C2×C4—132no—
387C2×C4—132no—
388C2×C4—134no—
389C2×C4—134no—
390C2×C4—134no—
391C2×C4—134no—
392C2×C4—138no—
393C2×C4—138no—
394C2×C4—1316no—
395C2×C4—1316no—
396C2×C4—138no—
397C2×C4—138no—
398C2×C4—264no—
399C2×C4—5216no—
400C2×C4—5216no—
401C2×C4—524no—
402C2×C4—524no—
403C2×C4—524no—
404C2×C4(C2×#261)⋊C418yes—
405C2×C4(C2×#261)⋊C418yes—
406C2×C4C2×C4×#26114yes—
407C2×C4C2×C4⋊#26114yes—
408C2×C4C2×C22⋊#26114yes—
409C8—2616no—
410C22—24no—
411C22—24no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—1316no—
417C22—134no—
418C22—134no—
419C22—134no—
420C22—134no—
421C22—268no—
422C22—268no—
423C22—2616no—
424C22—268no—
425C22—262no—
426C22—262no—
427C22C2×(C2×#261)⋊C412yes—
428C22C2×(C2×#261)⋊C412yes—
429C22D13⋊#10012yes—
430C22D13⋊#10112yes—
431C22C22×C4×#26111yescharacteristic
432C22C22×C4⋊#26111yescharacteristic
433C22C22×C22⋊#26111yescharacteristic
434C4—44no—
435C4—132no—
436C4—132no—
437C4—134no—
438C4—524no—
439C4C2×(C2×#261)⋊C418yes—
440C2—21no—
441C2—21no—
442C2—22no—
443C2—138no—
444C2—264no—
445C2#1313053914yesdirect product factor
446C2C22×(C2×#261)⋊C411yescharacteristic
447C2C2×D13⋊#10011yescharacteristic
448C2C2×D13⋊#10111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×D13C2×C4
cosocleC22×Dic13C24
hypercenterC22×C4⋊C4#261
hypocenterC13C22×#343
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13130539C2direct (N × H)
3. C2×#11718291C2semidirect
10. C2×D13⋊M16C4semidirect
22. #11718291C22semidirect
43. C2×#6122C2×C4semidirect
48. D13⋊M16C2×C4semidirect
120. #6122C22×C4semidirect
227. C2×D13#343semidirect
285. C2×C13C2×#343semidirect
290. D13C2×#343semidirect
352. C13C22×#343semidirect
445. C2#13130539direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D13⋊M162
#131305392
C2×#117182912
C22×C4⋊C4×D132
C22×#34313