Finite Group Databasebeta

← C2×#13131652 #16808467

Subgroups — C2×#13131652 #16808467

Order 3328.

2070 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131652C2116yesmaximal, direct product factor
2C2×#11719158C211yesmaximal, characteristic, complemented
3C2×Q8×#1057C211yesmaximal, characteristic, complemented
4C2×#11719076C211yesmaximal, characteristic, complemented
5C2×#11719064C212yesmaximal, complemented
6C2×#11719073C211yesmaximal, characteristic, complemented
7C2×#11719063C212yesmaximal, complemented
8C2×#11719077C212yesmaximal, complemented
9C2×#11719130C211yesmaximal, characteristic, complemented
10C2×#11719072C212yesmaximal, complemented
11C22×C4×#1057C211yesmaximal, characteristic, complemented
12C2×#11719329C211yesmaximal, characteristic
13C23×#1057C2211yescharacteristic
14C23×#1057C2211yescharacteristic
15C22×#6118C2212yes—
16C22×D13⋊C8C2212yes—
17C2×C13×C22⋊Q8C411yescharacteristic
18C2×#88201C411yescharacteristic
19C2×Q8×Dic13C2211yescharacteristic
20C2×#88184C411yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22#11719329C418yes—
23#11719329C2218yes—
24C2×#88152C412yes—
25C2×#88147C2211yescharacteristic
26C2×#88146C2212yes—
27C2×#88144C411yescharacteristic
28C2×#88140C412yes—
29C2×#88135C2212yes—
30C2×C22⋊#1057C2212yes—
31#11719158C2218yescomplemented
32Q8×#1057C2218yescomplemented
33#11719130C2218yescomplemented
34C2×#88112C2212yes—
35C2×#88111C2212yes—
36C2×#88111C2212yes—
37C2×#88110C2212yes—
38C2×#88110C2212yes—
39C2×C4⋊#1057C2211yescharacteristic
40C2×C4⋊#1057C2212yes—
41C2×C4⋊#1057C2211yescharacteristic
42C2×C4×#1057C2212yes—
43C2×C4×#1057C2211yescharacteristic
44C2×C4×#1057C2211yescharacteristic
45C2×C4×#1057C2211yescharacteristic
46C2×C4×#1057C2211yescharacteristic
47C2×C4×#1057C2218yescomplemented
48#11719077C22116yescomplemented
49#11719076C2218yescomplemented
50#11719073C2218yescomplemented
51#11719072C22116yescomplemented
52#11719064C22116yescomplemented
53#11719063C22116yescomplemented
54C22×Q8×C13C2×C411yescharacteristic
55C23×C4×C13C2×C411yescharacteristic
56C22×C22⋊D13C2×C412yes—
57C23×Dic13C2×C411yescharacteristic
58C23×Dic13C2311yescharacteristic
59C22×D52C2×C411yescharacteristic
60C22×C4×D13C2312yes—
61C22×#1057—24no—
62C22×#1057—24no—
63C22×#1057C2312yes—
64C22×#1057C2312yes—
65C22×#1057C2314yes—
66C22×#1057C2314yes—
67C22×#1057C2311yescharacteristic
68C22×#1057C2311yescharacteristic
69C22×#1057C2311yescharacteristic
70C22×#1057C2311yescharacteristic
71C2×#6118—28no—
72C2×#6118C2318yes—
73C2×D13⋊C8—28no—
74C2×D13⋊C8C2318yes—
75C13×C22⋊Q8C2×C418yes—
76C2×C13×C4⋊C4C2×C411yescharacteristic
77C2×C13×C4⋊C4C2×C412yes—
78C2×C13×C22⋊C4C2×C412yes—
79#88201C2×C418yes—
80Q8×Dic13C2×C414yes—
81Q8×Dic13C2314yes—
82#88184C2×C418yes—
83C2×#6103C2×C412yes—
84C2×#6103C2×C412yes—
85C2×#6103C2×C412yes—
86C2×#6103C2×C412yes—
87C2×C4⋊Dic13C2×C412yes—
88C2×C4⋊Dic13C2×C412yes—
89C2×C4⋊Dic13C2×C411yescharacteristic
90C2×#6101C2×C412yes—
91C2×C4×Dic13C2×C411yescharacteristic
92C2×C4×Dic13C2×C411yescharacteristic
93C2×C4×Dic13C2×C414yes—
94C2×C4×Dic13C2312yes—
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C2×C4×Dic13C2314yes—
98#88152C2×C4116yes—
99#88147C2×C414yes—
100#88147C2314yes—
101#88146C2×C418yes—
102#88146C2318yes—
103#88144C2×C418yes—
104#88140C2×C4116yes—
105#88135C2×C418yes—
106#88135C2318yes—
107C22⋊#1057C2318yes—
108#88112C2318yes—
109#88111C2318yes—
110#88111C2318yes—
111#88110C2318yes—
112#88110C2318yes—
113C4⋊#1057C2318yes—
114C4⋊#1057C2314yes—
115C4⋊#1057C2314yes—
116C4×#1057C2318yes—
117C4×#1057C2314yes—
118C4×#1057C2314yes—
119C4×#1057C2314yes—
120C4×#1057C2314yes—
121C2×#2966—131nomaximal, Sylow
122C24×C13C22×C411yescharacteristic
123C23×D13C22×C412yes—
124C2×Q8×C13—24no—
125C2×Q8×C13C22×C414yes—
126C22×C4×C13—24no—
127C22×C4×C13C22×C411yescharacteristic
128C22×C4×C13C22×C414yes—
129C22×C4×C13C22×C412yes—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C22×C411yescharacteristic
132C2×C22⋊D13—28no—
133C2×C22⋊D13C22×C418yes—
134C22×Dic13—24no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13C22×C412yes—
138C22×Dic13C22×C414yes—
139C22×Dic13C22×C411yescharacteristic
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142C22×Dic13C22×C412yes—
143C22×Dic13C2412yes—
144C22×Dic13C2411yescharacteristic
145C2×D52—24no—
146C2×D52C22×C414yes—
147C2×C4×D13—24no—
148C2×C4×D13—24no—
149C2×C4×D13C22×C414yes—
150C2×C4×D13C2414yes—
151C2×#1057—24no—
152C2×#1057—24no—
153C2×#1057—22no—
154C2×#1057—22no—
155C2×#1057—28no—
156C2×#1057—28no—
157C2×#1057#4114yes—
158C2×#1057#4114yes—
159C2×#1057C2412yes—
160C2×#1057C2412yes—
161C2×#1057C2414yes—
162C2×#1057C2414yes—
163C2×#1057C2412yes—
164C2×#1057C2412yes—
165#6118—216no—
166D13⋊C8—216no—
167C13×C4⋊C4C22×C414yes—
168C13×C4⋊C4C22×C418yes—
169C13×C22⋊C4C22×C418yes—
170#6103C22×C418yes—
171#6103C22×C418yes—
172#6103C22×C418yes—
173#6103C22×C418yes—
174C4⋊Dic13C22×C418yes—
175C4⋊Dic13C22×C418yes—
176C4⋊Dic13C22×C414yes—
177#6101C22×C418yes—
178C4×Dic13C22×C414yes—
179C4×Dic13C22×C414yes—
180C4×Dic13C22×C412yes—
181C4×Dic13C22×C412yes—
182C4×Dic13C22×C414yes—
183C4×Dic13C2412yes—
184C4×Dic13C2412yes—
185C4×Dic13C2414yes—
186C2×#529—131no—
187#2966—1316no—
188C2×#446—131no—
189C2×C8×Q8—131no—
190C2×#436—131no—
191C2×#435—132no—
192C2×C8×D4—132no—
193C2×C8×D4—131no—
194C2×#433—132no—
195C2×#432—131no—
196C2×#405—132no—
197C22×C4×C8—131no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13#13114yes—
201C23×C13C23×C412yes—
202C23×C13C23×C411yescharacteristic
203C22×D13—24no—
204C22×D13—24no—
205C22×D13—24no—
206C22×D13C23×C414yes—
207Q8×C13—28no—
208C2×C4×C13—24no—
209C2×C4×C13—22no—
210C2×C4×C13—24no—
211C2×C4×C13—28no—
212C2×C4×C13#13114yes—
213C2×C4×C13C23×C412yes—
214C2×C4×C13C23×C414yes—
215C2×C4×C13C23×C414yes—
216C2×C4×C13C23×C412yes—
217C22⋊D13—216no—
218C2×Dic13—22no—
219C2×Dic13—28no—
220C2×Dic13—22no—
221C2×Dic13—22no—
222C2×Dic13—24no—
223C2×Dic13—24no—
224C2×Dic13—22no—
225C2×Dic13—22no—
226C2×Dic13C23×C412yes—
227C2×Dic13C23×C412yes—
228C2×Dic13C23×C412yes—
229C2×Dic13C23×C414yes—
230C2×Dic13C23×C411yescharacteristic
231C2×Dic13C2×#4112yes—
232C2×Dic13C2×#4112yes—
233C2×Dic13C2511yescharacteristic
234D52—28no—
235C4×D13—28no—
236C4×D13—24no—
237C4×D13—24no—
238#1057—24no—
239#1057—24no—
240#1057—22no—
241#1057—22no—
242#1057C2×#4114yes—
243#1057C2×#4114yes—
244C22×M16—132no—
245C23×C8—131no—
246C23×C8—131no—
247C23×C8—132no—
248#529—138no—
249#529—138no—
250C2×#126—132no—
251C2×#125—131no—
252C2×#124—131no—
253C2×#123—132no—
254C2×C22⋊Q8#26111yescharacteristic
255C2×#121—131no—
256C2×C4×Q8—131no—
257C2×C4×D4—131no—
258C2×C4×D4—132no—
259C2×#117—132no—
260C22×C42—131no—
261#446—138no—
262C8×Q8—138no—
263#436—138no—
264#435—1316no—
265C8×D4—1316no—
266C8×D4—138no—
267#433—1316no—
268#432—138no—
269C2×C4⋊C8—131no—
270C2×C4⋊C8—131no—
271C2×C4⋊C8—132no—
272C2×C4⋊C8—132no—
273C2×C22⋊C8—132no—
274C2×C22⋊C8—132no—
275C2×C22⋊C8—132no—
276#405—1316no—
277C2×#97—132no—
278C2×#97—132no—
279C2×C4×C8—131no—
280C2×C4×C8—131no—
281C2×C4×C8—131no—
282C2×C4×C8—131no—
283C2×C4×C8—138no—
284C2×C4×C8—132no—
285C22×C13—22no—
286C22×C13—28no—
287C22×C13—22no—
288C22×C13C4×#4112yes—
289C22×C13C2×#13112yes—
290C22×C13C2×#13114yes—
291C22×C13C2×#13112yes—
292C22×C13C24×C411yescharacteristic
293C2×D13—24no—
294C2×D13—24no—
295C2×D13—24no—
296C2×D13—48no—
297C4×C13—24no—
298C4×C13—22no—
299C4×C13—24no—
300C4×C13C2×#13114yes—
301Dic13—22no—
302Dic13—22no—
303Dic13—22no—
304Dic13—24no—
305Dic13C4×#4112yes—
306Dic13C22×#4111yescharacteristic
307Dic13C22×#4111yescharacteristic
308C22×Q8C2×#26111yescharacteristic
309C22×D4—132no—
310C22×D4—131no—
311C23×C4—131no—
312C23×C4—131no—
313C23×C4—132no—
314C23×C4C2×#26111yescharacteristic
315C2×M16—138no—
316C2×M16—268no—
317C22×C8—131no—
318C22×C8—131no—
319C22×C8—131no—
320C22×C8—131no—
321C22×C8—134no—
322C22×C8—134no—
323C22×C8—132no—
324C22×C8—138no—
325C22×C8—132no—
326C22×C8—268no—
327C22×C8—264no—
328C22×C8—264no—
329#126—1316no—
330#125—138no—
331#124—138no—
332#123—1316no—
333C22⋊Q8C2×#26118yes—
334#121—138no—
335C4×Q8—134no—
336C4×Q8—134no—
337C4×D4—134no—
338C4×D4—134no—
339C4×D4—138no—
340C4×D4—138no—
341#117—138no—
342#117—138no—
343C2×C4⋊C4—132no—
344C2×C4⋊C4—132no—
345C2×C4⋊C4—131no—
346C2×C4⋊C4—132no—
347C2×C4⋊C4C2×#26112yes—
348C2×C4⋊C4C2×#26111yescharacteristic
349C2×C22⋊C4—132no—
350C2×C22⋊C4—132no—
351C2×C22⋊C4—132no—
352C2×C22⋊C4—132no—
353C2×C22⋊C4C2×#26112yes—
354C2×C42—131no—
355C2×C42—132no—
356C2×C42—131no—
357C2×C42—131no—
358C2×C42—131no—
359C2×C42—134no—
360C2×C42—134no—
361C4⋊C8—134no—
362C4⋊C8—134no—
363C4⋊C8—138no—
364C4⋊C8—138no—
365C22⋊C8—138no—
366C22⋊C8—138no—
367C22⋊C8—138no—
368#97—138no—
369#97—138no—
370C4×C8—134no—
371C4×C8—134no—
372C4×C8—134no—
373C4×C8—134no—
374C4×C8—138no—
375C2×C13—24no—
376C2×C13#296614yescomplemented
377C2×C13C2×C4×#4111yescharacteristic
378C2×C13C22×#13111yescharacteristic
379C2×C13C22×#13111yescharacteristic
380D13—44no—
381C24—132no—
382C24C22×#26111yescharacteristic
383C2×Q8—24no—
384C2×Q8C22×#26114yes—
385C2×D4—138no—
386C2×D4—134no—
387C2×D4—268no—
388C2×D4—264no—
389C22×C4—24no—
390C22×C4—131no—
391C22×C4—132no—
392C22×C4—132no—
393C22×C4—134no—
394C22×C4—131no—
395C22×C4—131no—
396C22×C4—131no—
397C22×C4—132no—
398C22×C4—134no—
399C22×C4—134no—
400C22×C4—264no—
401C22×C4—264no—
402C22×C4—262no—
403C22×C4—262no—
404C22×C4—264no—
405C22×C4C22×#26114yes—
406C22×C4C22×#26111yescharacteristic
407C22×C4C22×#26112yes—
408C22×C4C22×#26112yes—
409C22×C4C22×#26111yescharacteristic
410M16—2616no—
411C2×C8—132no—
412C2×C8—132no—
413C2×C8—134no—
414C2×C8—134no—
415C2×C8—132no—
416C2×C8—132no—
417C2×C8—134no—
418C2×C8—134no—
419C2×C8—2616no—
420C2×C8—268no—
421C2×C8—268no—
422C2×C8—262no—
423C2×C8—262no—
424C2×C8—264no—
425C2×C8—264no—
426C4⋊C4—138no—
427C4⋊C4—138no—
428C4⋊C4—134no—
429C4⋊C4—138no—
430C4⋊C4C22×#26118yes—
431C4⋊C4C22×#26114yes—
432C22⋊C4—138no—
433C22⋊C4—138no—
434C22⋊C4—138no—
435C22⋊C4—138no—
436C22⋊C4C22×#26118yes—
437C42—132no—
438C42—132no—
439C42—134no—
440C42—132no—
441C42—132no—
442C42—134no—
443C42—134no—
444C42—134no—
445C13C2×#296611yescharacteristic, complemented, Sylow
446C23—22no—
447C23—22no—
448C23—134no—
449C23—264no—
450C23—264no—
451C23—264no—
452C23#8824014yes—
453C23C23×#26112yes—
454C23C23×#26111yescharacteristic
455Q8—28no—
456D4—2616no—
457D4—268no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—28no—
462C2×C4—132no—
463C2×C4—132no—
464C2×C4—131no—
465C2×C4—131no—
466C2×C4—132no—
467C2×C4—132no—
468C2×C4—132no—
469C2×C4—134no—
470C2×C4—264no—
471C2×C4—264no—
472C2×C4—268no—
473C2×C4—262no—
474C2×C4—262no—
475C2×C4—264no—
476C2×C4—268no—
477C2×C4—262no—
478C2×C4—262no—
479C2×C4—264no—
480C2×C4—262no—
481C2×C4#8823814yes—
482C2×C4C23×#26112yes—
483C2×C4C23×#26114yes—
484C2×C4C23×#26114yes—
485C2×C4C23×#26112yes—
486C8—134no—
487C8—134no—
488C8—262no—
489C8—262no—
490C8—264no—
491C8—264no—
492C22—22no—
493C22—22no—
494C22—28no—
495C22—264no—
496C22—264no—
497C22—264no—
498C22—528no—
499C22C2×#8823812yes—
500C22C2×#8824014yes—
501C22C2×#8824012yes—
502C22#41×#26112yes—
503C22C24×#26111yescharacteristic
504C4—24no—
505C4—22no—
506C4—24no—
507C4—132no—
508C4—131no—
509C4—131no—
510C4—262no—
511C4—262no—
512C4—262no—
513C4—264no—
514C4C2×#8823814yes—
515C2—24no—
516C2—524no—
517C2#1313165214yesdirect product factor
518C2C2×#41×#26111yescharacteristic
519C2C22×#8823811yescharacteristic
520C2C22×#8824011yescharacteristic
subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×C22⋊Q8C4
socleC23×C13C23×C4
prime radicalC2×#88184C4
cosocleC2×Dic13C25
hypercenterC2×C22⋊Q8#261
hypocenterC13C2×#2966
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #13131652C2direct (N × H)
2. C2×#11719158C2semidirect
3. C2×Q8×#1057C2semidirect
4. C2×#11719076C2semidirect
5. C2×#11719064C2semidirect
6. C2×#11719073C2semidirect
7. C2×#11719063C2semidirect
8. C2×#11719077C2semidirect
9. C2×#11719130C2semidirect
10. C2×#11719072C2semidirect
11. C22×C4×#1057C2semidirect
31. #11719158C22semidirect
32. Q8×#1057C22semidirect
33. #11719130C22semidirect
47. C2×C4×#1057C22semidirect
48. #11719077C22semidirect
49. #11719076C22semidirect
50. #11719073C22semidirect
51. #11719072C22semidirect
52. #11719064C22semidirect
53. #11719063C22semidirect
376. C2×C13#2966semidirect
445. C13C2×#2966semidirect
517. C2#13131652direct (N × H)

Maximal subgroups

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

subgroupindex
#131316522
C2×#117191582
C2×Q8×#10572
C2×#117190762
C2×#117190642
C2×#117190732
C2×#117190632
C2×#117190772
C2×#117191302
C2×#117190722
C22×C4×#10572
C2×#117193292
C2×#296613