Finite Group Databasebeta

← C2×#13131025 #16799393

Subgroups — C2×#13131025 #16799393

Order 3328.

1698 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719136C211yesmaximal, characteristic
2C2×C4×C22⋊#261C211yesmaximal, characteristic
3#13131025C218yesmaximal, direct product factor
4C2×#11718289C214yesmaximal
5C22×#88200C211yesmaximal, characteristic
6C23×Q8×C13C411yescharacteristic, complemented
7C23×C4×D13C2211yescharacteristic
8C22×C22⋊#261C2212yes—
9C22×C22⋊#261C2212yes—
10C22×C4⋊#261—21no—
11C22×C4×#261—21no—
12C2×#88200—21no—
13C2×#88200—21no—
14C2×#88200—21no—
15C2×#88200—21no—
16C2×#88200—22no—
17C2×#88200—22no—
18C2×#88200C414yescomplemented
19C2×#88200C2214yes—
20C22×#6103C2212yes—
21C22×C4⋊Dic13C411yescharacteristic, complemented
22C22×#6101C412yescomplemented
23#11719136—22no—
24#11719136C2214yes—
25C4×C22⋊#261—22no—
26C4×C22⋊#261C2214yes—
27C2×(C2×#261)⋊C4—21no—
28C2×(C2×#261)⋊C4—21no—
29#11718289C22116yes—
30C24×D13C2311yescharacteristic
31C23×#261—22no—
32C23×#261—22no—
33C22×Q8×C13—22no—
34C22×Q8×C13—21no—
35C22×Q8×C13—21no—
36C22×Q8×C13—44no—
37C22×Q8×C13C2×C414yescomplemented
38C23×C4×C13C2×C412yes—
39C23×C4×C13C2×C411yescharacteristic
40C23×Dic13C2×C412yes—
41C23×Dic13C2×C411yescharacteristic
42C22×C4×D13—44no—
43C22×C4×D13C2×C412yes—
44C22×C4×D13D411yescharacteristic
45C22×C4×D13D411yescharacteristic
46C22×C4×D13D411yescharacteristic
47C22×C4×D13D411yescharacteristic
48C22×C4×D13D412yes—
49C22×C4×D13D412yes—
50C22×C4×D13C2312yes—
51C2×C22⋊#261—22no—
52C2×C22⋊#261—24no—
53C2×C22⋊#261—28no—
54C2×C22⋊#261—22no—
55C2×C22⋊#261Q818yescomplemented
56C2×C22⋊#261C2314yes—
57C2×C22⋊#261C2314yes—
58C2×C4⋊#261—24no—
59C2×C4⋊#261—44no—
60C2×C4×#261—24no—
61C2×C4×#261—44no—
62#88200—24no—
63#88200—24no—
64#88200—24no—
65#88200—24no—
66#88200—24no—
67#88200—24no—
68#88200—24no—
69#88200—24no—
70C2×#6103—22no—
71C2×#6103—22no—
72C2×#6103—22no—
73C2×#6103—22no—
74C2×#6103C2×C414yes—
75C2×#6103C2314yes—
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13C2×C414yescomplemented
80C2×#6101—22no—
81C2×#6101—22no—
82C2×#6101—24no—
83C2×#6101C2×C418yescomplemented
84(C2×#261)⋊C4—24no—
85(C2×#261)⋊C4—24no—
86C2×#1996—131nomaximal, Sylow
87C24×C13C22×C411yescharacteristic
88C23×D13—42no—
89C23×D13—42no—
90C23×D13C22×C411yescharacteristic
91C23×D13C2×D411yescharacteristic
92C23×D13C2×D411yescharacteristic
93C23×D13C2×D411yescharacteristic
94C23×D13C2×D411yescharacteristic
95C23×D13C2×Q814yes—
96C23×D13#4114yes—
97C23×D13C2411yescharacteristic
98C22×#261—28no—
99C22×#261—24no—
100C22×#261—24no—
101C22×#261—44no—
102C22×#261—44no—
103C22×#261—44no—
104C22×#261—44no—
105C22×#261—44no—
106C2×Q8×C13—24no—
107C2×Q8×C13—24no—
108C2×Q8×C13—48no—
109C2×Q8×C13—44no—
110C2×Q8×C13—48no—
111C2×Q8×C13—44no—
112C22×C4×C13—24no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—44no—
116C22×C4×C13C22⋊C412yes—
117C22×C4×C13C22⋊C411yescharacteristic
118C22×C4×C13C22⋊C411yescharacteristic
119C22×C4×C13C22×C412yes—
120C22×C4×C13C22×C414yes—
121C22×Dic13—22no—
122C22×Dic13—22no—
123C22×Dic13—42no—
124C22×Dic13—44no—
125C22×Dic13C22⋊C411yescharacteristic
126C22×Dic13C22⋊C411yescharacteristic
127C22×Dic13C22⋊C412yes—
128C22×Dic13C22×C414yes—
129C22×Dic13C22×C412yes—
130C2×C4×D13—24no—
131C2×C4×D13—24no—
132C2×C4×D13—44no—
133C2×C4×D13—44no—
134C2×C4×D13—44no—
135C2×C4×D13—44no—
136C2×C4×D13—42no—
137C2×C4×D13—42no—
138C2×C4×D13C22⋊C412yes—
139C2×C4×D13C22⋊C412yes—
140C2×C4×D13C22⋊C412yes—
141C2×C4×D13C22⋊C412yes—
142C2×C4×D13C2×D412yes—
143C2×C4×D13C2×D412yes—
144C2×C4×D13C2×D412yes—
145C2×C4×D13C2×D412yes—
146C22⋊#261—28no—
147C22⋊#261—24no—
148C22⋊#261—28no—
149C22⋊#261—44no—
150C22⋊#261C2×Q818yescomplemented
151C4⋊#261—48no—
152C4×#261—48no—
153#6103—24no—
154#6103—24no—
155#6103—24no—
156#6103—24no—
157C4⋊Dic13—24no—
158C4⋊Dic13—24no—
159#6101—28no—
160#6101—28no—
161C22×C22⋊Q8—131no—
162C2×#380—131no—
163C2×C4×C22⋊C4—131no—
164#1996—138no—
165C2×#342—134no—
166C23×C13—22no—
167C23×C13—22no—
168C23×C13C2×C22⋊C411yescharacteristic
169C23×C13C2×C22⋊C411yescharacteristic
170C23×C13C4×Q814yes—
171C23×C13C23×C411yescharacteristic
172C22×D13—22no—
173C22×D13—22no—
174C22×D13—22no—
175C22×D13—22no—
176C22×D13—41no—
177C22×D13—41no—
178C22×D13—41no—
179C22×D13—41no—
180C22×D13—41no—
181C22×D13—41no—
182C22×D13—41no—
183C22×D13—48no—
184C22×D13—48no—
185C22×D13—41no—
186C22×D13C2×C22⋊C411yescharacteristic
187C22×D13C2×C22⋊C411yescharacteristic
188C22×D13C4×Q814yes—
189C22×D13C22⋊Q814yes—
190C22×D13C22⋊Q814yes—
191C22×D13#12412yes—
192C22×D13#12412yes—
193C22×D13C4⋊Q812yes—
194C22×D13C4⋊Q812yes—
195C22×D13C22×D411yescharacteristic
196C22×D13C22×D411yescharacteristic
197C22×D13C22×Q812yes—
198C22×D13C2×#4112yes—
199C2×#261—28no—
200C2×#261—44no—
201C2×#261—44no—
202C2×#261—416no—
203C2×#261—44no—
204C2×#261—44no—
205C2×#261—44no—
206C2×#261—88no—
207Q8×C13—48no—
208Q8×C13—48no—
209C2×C4×C13—22no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—44no—
214C2×C4×C13—44no—
215C2×C4×C13—44no—
216C2×C4×C13#9914yes—
217C2×C4×C13C2×C22⋊C412yes—
218C2×C4×C13C2×C22⋊C412yes—
219C2×Dic13—22no—
220C2×Dic13—22no—
221C2×Dic13—24no—
222C2×Dic13—42no—
223C2×Dic13—42no—
224C2×Dic13—44no—
225C2×Dic13—44no—
226C2×Dic13—44no—
227C2×Dic13C2×C22⋊C412yes—
228C2×Dic13C2×C22⋊C412yes—
229C4×D13—24no—
230C4×D13—24no—
231C4×D13—24no—
232C4×D13—24no—
233C4×D13—42no—
234C4×D13—42no—
235C4×D13—42no—
236C4×D13—42no—
237C23×Q8#26111yescharacteristic, complemented
238C24×C4—131no—
239C2×C22⋊Q8—134no—
240C2×C22⋊Q8—134no—
241C2×C22⋊Q8—261no—
242C2×C22⋊Q8—261no—
243C2×C22⋊Q8—261no—
244C2×C22⋊Q8—261no—
245C2×C22⋊Q8—262no—
246C2×C22⋊Q8—262no—
247C22×C4⋊C4—132no—
248C22×C4⋊C4—131no—
249C22×C4⋊C4—261no—
250C22×C22⋊C4—132no—
251C22×C22⋊C4—132no—
252C22×C22⋊C4—132no—
253C22×C42—261no—
254#380—134no—
255#380—262no—
256C4×C22⋊C4—134no—
257C4×C22⋊C4—262no—
258C2×#95—261no—
259C2×#95—261no—
260#342—1316no—
261C22×C13—21no—
262C22×C13—21no—
263C22×C13—21no—
264C22×C13—21no—
265C22×C13—28no—
266C22×C13#39112yes—
267C22×C13#39112yes—
268C22×C13C2×#9912yes—
269C22×C13#41012yes—
270C22×C13C22×C22⋊C411yescharacteristic
271C22×C13C2×C4×Q812yes—
272C2×D13—21no—
273C2×D13—21no—
274C2×D13—21no—
275C2×D13—21no—
276C2×D13—21no—
277C2×D13—21no—
278C2×D13—21no—
279C2×D13—21no—
280C2×D13—28no—
281C2×D13—24no—
282C2×D13—24no—
283C2×D13—44no—
284C2×D13—44no—
285C2×D13—42no—
286C2×D13—42no—
287C2×D13—42no—
288C2×D13—42no—
289C2×D13#39112yes—
290C2×D13#39112yes—
291C2×D13C2×C22⋊Q812yes—
292C2×D13C2×#12411yescharacteristic
293C2×D13C2×C4⋊Q811yescharacteristic
294#261—48no—
295#261—84no—
296C4×C13—22no—
297C4×C13—44no—
298C4×C13C2×#9914yes—
299Dic13—22no—
300Dic13—22no—
301Dic13—44no—
302C25—131no—
303C22×Q8—22no—
304C22×Q8—21no—
305C22×Q8—21no—
306C22×Q8—44no—
307C22×Q8C2×#26114yescomplemented
308C23×C4—131no—
309C23×C4—131no—
310C23×C4—131no—
311C23×C4—131no—
312C23×C4—131no—
313C23×C4—132no—
314C23×C4—132no—
315C23×C4—132no—
316C23×C4—132no—
317C23×C4—132no—
318C23×C4—262no—
319C23×C4—262no—
320C23×C4—524no—
321C23×C4C2×#26112yes—
322C23×C4C2×#26111yescharacteristic
323C22⋊Q8—264no—
324C22⋊Q8—264no—
325C22⋊Q8—264no—
326C22⋊Q8—264no—
327C22⋊Q8—264no—
328C22⋊Q8—264no—
329C22⋊Q8—264no—
330C22⋊Q8—264no—
331C2×C4⋊C4—138no—
332C2×C4⋊C4—134no—
333C2×C4⋊C4—264no—
334C2×C4⋊C4—262no—
335C2×C4⋊C4—262no—
336C2×C4⋊C4—262no—
337C2×C4⋊C4—261no—
338C2×C4⋊C4—261no—
339C2×C4⋊C4—264no—
340C2×C4⋊C4—524no—
341C2×C22⋊C4—134no—
342C2×C22⋊C4—138no—
343C2×C22⋊C4—134no—
344C2×C22⋊C4—134no—
345C2×C22⋊C4—134no—
346C2×C22⋊C4—262no—
347C2×C22⋊C4—262no—
348C2×C22⋊C4—262no—
349C2×C22⋊C4—262no—
350C2×C22⋊C4—262no—
351C2×C22⋊C4—264no—
352C2×C22⋊C4—268no—
353C2×C22⋊C4—262no—
354C2×C42—264no—
355C2×C42—524no—
356#95—264no—
357#95—264no—
358C2×C13—22no—
359C2×C13—22no—
360C2×C13#199614yescomplemented
361C2×C13C2×#39111yescharacteristic
362C2×C13C22×#9911yescharacteristic
363C2×C13C2×#41011yescharacteristic
364D13—22no—
365D13—21no—
366D13—21no—
367D13—22no—
368D13—22no—
369C24—131no—
370C24—131no—
371C24—134no—
372C24—134no—
373C24—131no—
374C24—131no—
375C24—131no—
376C24—131no—
377C24—522no—
378C24—522no—
379C24C22×#26111yescharacteristic
380C2×Q8—24no—
381C2×Q8—24no—
382C2×Q8—48no—
383C2×Q8—44no—
384C2×Q8—48no—
385C2×Q8—44no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—44no—
390C22×C4—131no—
391C22×C4—131no—
392C22×C4—132no—
393C22×C4—132no—
394C22×C4—132no—
395C22×C4—132no—
396C22×C4—132no—
397C22×C4—132no—
398C22×C4—132no—
399C22×C4—132no—
400C22×C4—132no—
401C22×C4—132no—
402C22×C4—134no—
403C22×C4—264no—
404C22×C4—264no—
405C22×C4—264no—
406C22×C4—268no—
407C22×C4—262no—
408C22×C4—262no—
409C22×C4—264no—
410C22×C4—524no—
411C22×C4—524no—
412C22×C4—524no—
413C22×C4—524no—
414C22×C4—522no—
415C22×C4—522no—
416C22×C4—522no—
417C22×C4—524no—
418C22×C4—524no—
419C22×C4—524no—
420C22×C4—524no—
421C22×C4—524no—
422C22×C4—524no—
423C22×C4C22⋊#26112yes—
424C22×C4C22⋊#26111yescharacteristic
425C22×C4C22⋊#26111yescharacteristic
426C22×C4C22×#26112yes—
427C22×C4C22×#26114yes—
428C4⋊C4—268no—
429C4⋊C4—268no—
430C4⋊C4—264no—
431C4⋊C4—264no—
432C4⋊C4—528no—
433C22⋊C4—138no—
434C22⋊C4—264no—
435C22⋊C4—264no—
436C22⋊C4—264no—
437C22⋊C4—264no—
438C22⋊C4—264no—
439C22⋊C4—268no—
440C22⋊C4—268no—
441C22⋊C4—524no—
442C42—528no—
443C13C2×#199611yescharacteristic, complemented, Sylow
444C23—22no—
445C23—22no—
446C23—131no—
447C23—131no—
448C23—131no—
449C23—131no—
450C23—134no—
451C23—132no—
452C23—132no—
453C23—132no—
454C23—132no—
455C23—134no—
456C23—134no—
457C23—132no—
458C23—132no—
459C23—262no—
460C23—262no—
461C23—262no—
462C23—262no—
463C23—521no—
464C23—521no—
465C23—521no—
466C23—521no—
467C23—528no—
468C23—528no—
469C23—521no—
470C23—521no—
471C23—521no—
472C23—521no—
473C23Q8×#26114yes—
474C23C2×C22⋊#26111yescharacteristic
475C23C2×C22⋊#26111yescharacteristic
476C23C23×#26111yescharacteristic
477Q8—48no—
478Q8—48no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—44no—
484C2×C4—44no—
485C2×C4—44no—
486C2×C4—132no—
487C2×C4—132no—
488C2×C4—262no—
489C2×C4—262no—
490C2×C4—264no—
491C2×C4—264no—
492C2×C4—264no—
493C2×C4—264no—
494C2×C4—268no—
495C2×C4—264no—
496C2×C4—522no—
497C2×C4—522no—
498C2×C4—522no—
499C2×C4—522no—
500C2×C4—522no—
501C2×C4—522no—
502C2×C4—524no—
503C2×C4—524no—
504C2×C4—5216no—
505C2×C4—524no—
506C2×C4—524no—
507C2×C4—524no—
508C2×C4—524no—
509C2×C4—524no—
510C2×C4—524no—
511C2×C4—1048no—
512C2×C4#8811914yes—
513C2×C4C2×C22⋊#26112yes—
514C2×C4C2×C22⋊#26112yes—
515C22—28no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—132no—
521C22—131no—
522C22—131no—
523C22—132no—
524C22—132no—
525C22—268no—
526C22—264no—
527C22—264no—
528C22—261no—
529C22—261no—
530C22—261no—
531C22—261no—
532C22—261no—
533C22—261no—
534C22—261no—
535C22—261no—
536C22—522no—
537C22—522no—
538C22—524no—
539C22—524no—
540C22—522no—
541C22—522no—
542C22#1171915612yes—
543C22(C2×#261)⋊Q812yes—
544C22(C2×#261)⋊Q812yes—
545C22C2×#8811912yes—
546C22C2×Q8×#26112yes—
547C22C22×C22⋊#26111yescharacteristic
548C4—22no—
549C4—44no—
550C4—262no—
551C4—262no—
552C4—528no—
553C4—524no—
554C4—1044no—
555C4C2×#8811914yes—
556C2—22no—
557C2—22no—
558C2—262no—
559C2—261no—
560C2—261no—
561C2—262no—
562C2—262no—
563C2#1313102514yesdirect product factor
564C2C2×(C2×#261)⋊Q811yescharacteristic
565C2C22×#8811911yescharacteristic
566C2C2×#1171915611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC23×Q8×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC24×D13C23
cosocleC23×D13C24
hypercenterC23×Q8#261
hypocenterC13C2×#1996
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
3. #13131025C2direct (N × H)
6. C23×Q8×C13C4semidirect
18. C2×#88200C4semidirect
21. C22×C4⋊Dic13C4semidirect
22. C22×#6101C4semidirect
37. C22×Q8×C13C2×C4semidirect
55. C2×C22⋊#261Q8semidirect
79. C2×C4⋊Dic13C2×C4semidirect
83. C2×#6101C2×C4semidirect
150. C22⋊#261C2×Q8semidirect
237. C23×Q8#261semidirect
307. C22×Q8C2×#261semidirect
360. C2×C13#1996semidirect
443. C13C2×#1996semidirect
563. C2#13131025direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191362
C2×C4×C22⋊#2612
#131310252
C2×#117182892
C22×#882002
C2×#199613