Finite Group Databasebeta

← C2×#13114006 #15838671

Subgroups — C2×#13114006 #15838671

Order 3328.

946 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719247C211yesmaximal, characteristic
2C2×#11718742C211yesmaximal, characteristic, complemented
3C2×#11718752C211yesmaximal, characteristic, complemented
4#13114006C218yesmaximal, direct product factor
5C2×#11718074C211yesmaximal, characteristic, complemented
6C2×#11718076C211yesmaximal, characteristic, complemented
7C2×D4⋊#1055C211yesmaximal, characteristic
8C2×C13×#476C211yesmaximal, characteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C13C2211yescharacteristic
11C2×#88190—21no—
12C2×#88180—21no—
13C2×#88178—21no—
14#11719247—22no—
15#11719247—22no—
16#11719247—22no—
17#11719247C2214yes—
18C2×#88141—21no—
19C2×#88133—22no—
20C2×#88123C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C13×#476—22no—
23C13×#476C2214yes—
24C2×C13×#106—21no—
25C2×C13×C4⋊C8C2211yescharacteristic
26C2×C13×#102—21no—
27C2×#88075—22no—
28#11718752—22no—
29#11718752C2214yescomplemented
30#11718742—22no—
31#11718742C2214yescomplemented
32C2×#88050—21no—
33C2×#88047—21no—
34C2×C4⋊#1055C2211yescharacteristic
35C2×C4×#1055C2211yescharacteristic
36D4⋊#1055C2214yes—
37#11718076C2214yescomplemented
38#11718074C2214yescomplemented
39C22×Q8×C13—21no—
40C22×D4×C13D411yescharacteristic
41C23×C4×C13—21no—
42C22×Dic26—21no—
43C22×Dic26D411yescharacteristic
44C22×C8×C13—21no—
45C13×C4⋊Q8—21no—
46C13×C4⋊Q8—21no—
47C13×C4⋊Q8—21no—
48C13×C4⋊Q8C2312yes—
49C4×D4×C13—21no—
50C4×D4×C13—21no—
51C4×D4×C13D412yes—
52C4×D4×C13C2312yes—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4D411yescharacteristic
56C2×C13×C22⋊C4—21no—
57C2×C42×C13C2311yescharacteristic
58C2×C22⋊Dic13—22no—
59C2×C22⋊Dic13—22no—
60#88190—24no—
61#88190—24no—
62#88180—24no—
63#88180—24no—
64C2×C4⋊Dic13—21no—
65C2×C4⋊Dic13D411yescharacteristic
66C2×C4⋊Dic13D412yes—
67#88178—24no—
68#88178—24no—
69C2×#6101—22no—
70C2×#6101—21no—
71C2×C4×Dic13—22no—
72C2×C4×Dic13—21no—
73C22×#1055—21no—
74C22×#1055—21no—
75#88141—24no—
76#88141—24no—
77#88133—28no—
78#88133—28no—
79#88123—21no—
80#88123—21no—
81#88123D412yes—
82#88123C2312yes—
83C4×Dic26—21no—
84C4×Dic26—21no—
85C4×Dic26D412yes—
86C4×Dic26C2312yes—
87C13×#106—24no—
88C13×C4⋊C8—21no—
89C13×C4⋊C8C2312yes—
90C13×#102—24no—
91#88075—28no—
92#88050—24no—
93#88047—24no—
94C4⋊#1055—21no—
95C4⋊#1055C2312yes—
96C4×#1055—21no—
97C4×#1055C2312yes—
98C2×#1638—131nomaximal, Sylow
99C24×C13—21no—
100C2×Q8×C13—22no—
101C2×Q8×C13—44no—
102C2×Q8×C13—41no—
103C2×D4×C13—21no—
104C2×D4×C13—22no—
105C2×D4×C13—22no—
106C2×D4×C13C2×D412yes—
107C22×C4×C13—21no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—42no—
111C22×C4×C13—42no—
112C22×C4×C13—41no—
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13C2×D411yescharacteristic
116C22×Dic13—21no—
117C22×Dic13—21no—
118C22×Dic13—22no—
119C2×Dic26—22no—
120C2×Dic26—22no—
121C2×Dic26—21no—
122C2×Dic26—22no—
123C2×Dic26—22no—
124C2×Dic26—42no—
125C2×Dic26—42no—
126C2×Dic26C2×D412yes—
127C2×C8×C13—22no—
128C2×C8×C13—42no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—22no—
131C13×C4⋊C4—22no—
132C13×C4⋊C4—41no—
133C13×C4⋊C4—41no—
134C13×C4⋊C4C2×D412yes—
135C13×C22⋊C4—22no—
136C13×C22⋊C4—22no—
137C42×C13C2×D411yescharacteristic
138C42×C13C2×D411yescharacteristic
139C42×C13C2×D411yescharacteristic
140C42×C13C2411yescharacteristic
141C22⋊Dic13—28no—
142C22⋊Dic13—28no—
143C4⋊Dic13—21no—
144C4⋊Dic13—22no—
145C4⋊Dic13—22no—
146C4⋊Dic13—22no—
147C4⋊Dic13C2×D414yes—
148C4⋊Dic13C2×D412yes—
149#6101—28no—
150#6101—22no—
151#6101—22no—
152C4×Dic13—28no—
153C4×Dic13—22no—
154C4×Dic13—22no—
155C2×#1055—22no—
156C2×#1055—22no—
157C2×#1055—42no—
158C2×#1055—42no—
159C2×#556—131no—
160C2×#487—131no—
161C2×#477—131no—
162C2×#476D1311yescharacteristic
163#1638—138no—
164C2×#332—131no—
165C2×Q8⋊C8—131no—
166C2×D4⋊C8—131no—
167C23×C13—22no—
168C23×C13—42no—
169C23×C13—42no—
170C23×C13—42no—
171C23×C13#12011yescharacteristic
172Q8×C13—44no—
173Q8×C13—82no—
174D4×C13—22no—
175D4×C13—22no—
176D4×C13—42no—
177C2×C4×C13—22no—
178C2×C4×C13—22no—
179C2×C4×C13—42no—
180C2×C4×C13—42no—
181C2×C4×C13—42no—
182C2×C4×C13—44no—
183C2×C4×C13—42no—
184C2×C4×C13—82no—
185C2×C4×C13#12011yescharacteristic
186C2×C4×C13#12011yescharacteristic
187C2×C4×C13#12011yescharacteristic
188C2×C4×C13#13512yes—
189C2×C4×C13#13512yes—
190C2×C4×C13#13712yes—
191C2×C4×C13#13712yes—
192C2×C4×C13C22×D411yescharacteristic
193C2×C4×C13C22×D411yescharacteristic
194C2×C4×C13C22×D411yescharacteristic
195C2×Dic13—22no—
196C2×Dic13—22no—
197C2×Dic13—24no—
198C2×Dic13—42no—
199C2×Dic13—44no—
200C2×Dic13—42no—
201Dic26—22no—
202Dic26—22no—
203Dic26—42no—
204Dic26—42no—
205Dic26—42no—
206Dic26—44no—
207C8×C13—42no—
208#1055—42no—
209#1055—42no—
210#556—134no—
211#556—262no—
212#556—262no—
213#556—262no—
214C2×C4⋊Q8—131no—
215C2×C4⋊Q8C2×D1311yescharacteristic
216C2×#126—262no—
217C2×#124—261no—
218C2×C22⋊Q8—261no—
219C2×C4×Q8—131no—
220C2×C4×Q8—261no—
221C2×C4×D4C2×D1311yescharacteristic
222C2×#117—261no—
223#487—134no—
224#487—262no—
225#477—134no—
226#477—262no—
227#476—22no—
228#476C2×D1314yes—
229C2×#107—261no—
230C2×#106—21no—
231C2×C4⋊C8—131no—
232C2×C4⋊C8C2×D1311yescharacteristic
233C2×#103—261no—
234C2×#103—262no—
235C2×#102—21no—
236C2×C4×C8—131no—
237#332—134no—
238Q8⋊C8—134no—
239D4⋊C8—134no—
240C22×C13—42no—
241C22×C13—42no—
242C22×C13—42no—
243C22×C13—84no—
244C22×C13#45212yes—
245C22×C13#45212yes—
246C22×C13#45412yes—
247C22×C13C2×#12011yescharacteristic
248C4×C13—21no—
249C4×C13—21no—
250C4×C13—42no—
251C4×C13—82no—
252C4×C13#45212yes—
253C4×C13#45212yes—
254C4×C13C2×#13511yescharacteristic
255C4×C13C2×#13511yescharacteristic
256C4×C13C2×#13711yescharacteristic
257C4×C13C2×#13711yescharacteristic
258Dic13—42no—
259Dic13—44no—
260Dic13—42no—
261C22×Q8—21no—
262C22×Q8—131no—
263C22×Q8—261no—
264C22×D4C22⋊D1311yescharacteristic
265C23×C4—21no—
266C22×C8—21no—
267C22×C8—261no—
268C22×C8—261no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8—21no—
272C4⋊Q8—132no—
273C4⋊Q8—132no—
274C4⋊Q8—261no—
275C4⋊Q8—261no—
276C4⋊Q8C22×D1312yes—
277#126—268no—
278#126—268no—
279#124—264no—
280#124—264no—
281C22⋊Q8—264no—
282C22⋊Q8—264no—
283C4×Q8—132no—
284C4×Q8—132no—
285C4×Q8—264no—
286C4×Q8—264no—
287C4×Q8—261no—
288C4×Q8—261no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4C22⋊D1312yes—
292C4×D4C22×D1312yes—
293#117—264no—
294#117—264no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—131no—
298C2×C4⋊C4—132no—
299C2×C4⋊C4—262no—
300C2×C4⋊C4—261no—
301C2×C4⋊C4—261no—
302C2×C4⋊C4C22⋊D1311yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—262no—
305C2×C22⋊C4—262no—
306C2×C42—262no—
307C2×C42—261no—
308C2×C42C22×D1311yescharacteristic
309#107—264no—
310#106—24no—
311C4⋊C8—21no—
312C4⋊C8—132no—
313C4⋊C8—261no—
314C4⋊C8C22×D1312yes—
315#103—264no—
316#103—268no—
317#102—24no—
318C4×C8—132no—
319C4×C8—261no—
320C2×C13—82no—
321C2×C13#163814yescomplemented
322C2×C13C2×#45211yescharacteristic
323C2×C13C2×#45211yescharacteristic
324C2×C13C2×#45411yescharacteristic
325C24—21no—
326C2×Q8—22no—
327C2×Q8—44no—
328C2×Q8—41no—
329C2×Q8—132no—
330C2×Q8—261no—
331C2×Q8—262no—
332C2×Q8—262no—
333C2×Q8—262no—
334C2×Q8—262no—
335C2×Q8—522no—
336C2×Q8—522no—
337C2×D4—21no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4C2×C22⋊D1312yes—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—41no—
347C22×C4—261no—
348C22×C4—262no—
349C22×C4—261no—
350C22×C4D4×D1311yescharacteristic
351C22×C4D4×D1311yescharacteristic
352C22×C4C2×C22⋊D1311yescharacteristic
353C2×C8—22no—
354C2×C8—42no—
355C2×C8—262no—
356C2×C8—262no—
357C2×C8—522no—
358C2×C8—522no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—134no—
365C4⋊C4—132no—
366C4⋊C4—268no—
367C4⋊C4—261no—
368C4⋊C4—262no—
369C4⋊C4—262no—
370C4⋊C4—262no—
371C4⋊C4—262no—
372C4⋊C4—262no—
373C4⋊C4C2×C22⋊D1312yes—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—268no—
377C22⋊C4—268no—
378C42—268no—
379C42—262no—
380C42—262no—
381C42D4×D1311yescharacteristic
382C42D4×D1311yescharacteristic
383C42C2×C22⋊D1311yescharacteristic
384C42C23×D1311yescharacteristic
385C13C2×#163811yescharacteristic, complemented, Sylow
386C23—22no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23#8819111yescharacteristic
391Q8—44no—
392Q8—82no—
393Q8—262no—
394Q8—262no—
395Q8—524no—
396Q8—522no—
397Q8—522no—
398Q8—522no—
399D4—22no—
400D4—22no—
401D4—42no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—82no—
410C2×C4—262no—
411C2×C4—264no—
412C2×C4—262no—
413C2×C4—524no—
414C2×C4—522no—
415C2×C4—522no—
416C2×C4#8816912yes—
417C2×C4#8817012yes—
418C2×C4#8819111yescharacteristic
419C2×C4#8819111yescharacteristic
420C2×C4#8819111yescharacteristic
421C2×C4#8819612yes—
422C2×C4#8820412yes—
423C2×C4C2×D4×D1311yescharacteristic
424C2×C4C2×D4×D1311yescharacteristic
425C2×C4C22×C22⋊D1311yescharacteristic
426C8—42no—
427C8—522no—
428C8—522no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—84no—
433C22#1171870812yes—
434C22#1171883412yes—
435C22#1171886212yes—
436C22C2×#8819111yescharacteristic
437C4—21no—
438C4—21no—
439C4—42no—
440C4—82no—
441C4—522no—
442C4—522no—
443C4—524no—
444C4#1171870812yes—
445C4#1171883412yes—
446C4C2×#8816911yescharacteristic
447C4C2×#8817011yescharacteristic
448C4C2×#8819611yescharacteristic
449C4C2×#8820411yescharacteristic
450C2—82no—
451C2#1311400614yesdirect product factor
452C2C2×#1171883411yescharacteristic
453C2C2×#1171870811yescharacteristic
454C2C2×#1171886211yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#476C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenterC2×#476D13
hypocenterC13C2×#1638
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
2. C2×#11718742C2semidirect
3. C2×#11718752C2semidirect
4. #13114006C2direct (N × H)
5. C2×#11718074C2semidirect
6. C2×#11718076C2semidirect
29. #11718752C22semidirect
31. #11718742C22semidirect
37. #11718076C22semidirect
38. #11718074C22semidirect
321. C2×C13#1638semidirect
385. C13C2×#1638semidirect
451. C2#13114006direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192472
C2×#117187422
C2×#117187522
#131140062
C2×#117180742
C2×#117180762
C2×D4⋊#10552
C2×C13×#4762
C2×#163813