Finite Group Databasebeta

← C2×#13131026 #16799394

Subgroups — C2×#13131026 #16799394

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#13131026C218yesmaximal, direct product factor
4C2×#11718289C214yesmaximal
5C22×#88151C211yesmaximal, characteristic
6C23×C4×D13C2211yescharacteristic
7C23×Dic26C411yescharacteristic, complemented
8C22×C22⋊#261C2212yes—
9C22×C22⋊#261C2212yes—
10C22×C4⋊#261—21no—
11C22×C4×#261—21no—
12C22×C13×C4⋊C4C411yescharacteristic, complemented
13C22×#6103C2212yes—
14C22×C4⋊Dic13C412yescomplemented
15C2×#88151—21no—
16C2×#88151—21no—
17C2×#88151—21no—
18C2×#88151—21no—
19C2×#88151—22no—
20C2×#88151—22no—
21C2×#88151C414yescomplemented
22C2×#88151C2214yes—
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—
33C23×C4×C13C2×C412yes—
34C23×C4×C13C2×C411yescharacteristic
35C23×Dic13C2×C412yes—
36C23×Dic13C2×C411yescharacteristic
37C22×C4×D13—44no—
38C22×C4×D13C2×C412yes—
39C22×C4×D13D411yescharacteristic
40C22×C4×D13D411yescharacteristic
41C22×C4×D13D411yescharacteristic
42C22×C4×D13D411yescharacteristic
43C22×C4×D13D412yes—
44C22×C4×D13D412yes—
45C22×C4×D13C2312yes—
46C22×Dic26—22no—
47C22×Dic26—21no—
48C22×Dic26—21no—
49C22×Dic26—44no—
50C22×Dic26C2×C414yescomplemented
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—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4C2×C414yescomplemented
66C2×#6103—22no—
67C2×#6103—22no—
68C2×#6103—22no—
69C2×#6103—22no—
70C2×#6103C2×C414yes—
71C2×#6103C2314yes—
72C2×C4⋊Dic13—22no—
73C2×C4⋊Dic13—22no—
74C2×C4⋊Dic13—24no—
75C2×C4⋊Dic13C2×C418yescomplemented
76#88151—24no—
77#88151—24no—
78#88151—24no—
79#88151—24no—
80#88151—24no—
81#88151—24no—
82#88151—24no—
83#88151—24no—
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—
106C22×C4×C13—24no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—44no—
110C22×C4×C13C22⋊C412yes—
111C22×C4×C13C22⋊C411yescharacteristic
112C22×C4×C13C22⋊C411yescharacteristic
113C22×C4×C13C22×C412yes—
114C22×C4×C13C22×C414yes—
115C22×Dic13—22no—
116C22×Dic13—22no—
117C22×Dic13—42no—
118C22×Dic13—44no—
119C22×Dic13C22⋊C411yescharacteristic
120C22×Dic13C22⋊C411yescharacteristic
121C22×Dic13C22⋊C412yes—
122C22×Dic13C22×C414yes—
123C22×Dic13C22×C412yes—
124C2×C4×D13—24no—
125C2×C4×D13—24no—
126C2×C4×D13—44no—
127C2×C4×D13—44no—
128C2×C4×D13—44no—
129C2×C4×D13—44no—
130C2×C4×D13—42no—
131C2×C4×D13—42no—
132C2×C4×D13C22⋊C412yes—
133C2×C4×D13C22⋊C412yes—
134C2×C4×D13C22⋊C412yes—
135C2×C4×D13C22⋊C412yes—
136C2×C4×D13C2×D412yes—
137C2×C4×D13C2×D412yes—
138C2×C4×D13C2×D412yes—
139C2×C4×D13C2×D412yes—
140C2×Dic26—24no—
141C2×Dic26—24no—
142C2×Dic26—44no—
143C2×Dic26—48no—
144C2×Dic26—44no—
145C2×Dic26—48no—
146C22⋊#261—28no—
147C22⋊#261—24no—
148C22⋊#261—28no—
149C22⋊#261—44no—
150C22⋊#261C2×Q818yescomplemented
151C4⋊#261—48no—
152C4×#261—48no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—24no—
155#6103—24no—
156#6103—24no—
157#6103—24no—
158#6103—24no—
159C4⋊Dic13—28no—
160C4⋊Dic13—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—
207C2×C4×C13—22no—
208C2×C4×C13—24no—
209C2×C4×C13—24no—
210C2×C4×C13—24no—
211C2×C4×C13—44no—
212C2×C4×C13—44no—
213C2×C4×C13—44no—
214C2×C4×C13#9914yes—
215C2×C4×C13C2×C22⋊C412yes—
216C2×C4×C13C2×C22⋊C412yes—
217C2×Dic13—22no—
218C2×Dic13—22no—
219C2×Dic13—24no—
220C2×Dic13—42no—
221C2×Dic13—42no—
222C2×Dic13—44no—
223C2×Dic13—44no—
224C2×Dic13—44no—
225C2×Dic13C2×C22⋊C412yes—
226C2×Dic13C2×C22⋊C412yes—
227C4×D13—24no—
228C4×D13—24no—
229C4×D13—24no—
230C4×D13—24no—
231C4×D13—42no—
232C4×D13—42no—
233C4×D13—42no—
234C4×D13—42no—
235Dic26—48no—
236Dic26—48no—
237C23×Q8—131no—
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—261no—
249C22×C4⋊C4#26111yescharacteristic, complemented
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—134no—
304C22×Q8—262no—
305C22×Q8—261no—
306C22×Q8—261no—
307C22×Q8—524no—
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—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—138no—
335C2×C4⋊C4—264no—
336C2×C4⋊C4—262no—
337C2×C4⋊C4—262no—
338C2×C4⋊C4—264no—
339C2×C4⋊C4—524no—
340C2×C4⋊C4C2×#26114yescomplemented
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—264no—
381C2×Q8—264no—
382C2×Q8—528no—
383C2×Q8—524no—
384C2×Q8—528no—
385C2×Q8—524no—
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—24no—
429C4⋊C4—24no—
430C4⋊C4—268no—
431C4⋊C4—268no—
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—528no—
478Q8—528no—
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#8810714yes—
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—
542C22C2×#8810712yes—
543C22#1171914212yes—
544C22(C2×#261)⋊Q812yes—
545C22(C2×#261)⋊Q812yes—
546C22C2×Q8×#26112yes—
547C22C22×C22⋊#26111yescharacteristic
548C4—22no—
549C4—44no—
550C4—262no—
551C4—262no—
552C4—528no—
553C4—524no—
554C4—1044no—
555C4C2×#8810714yes—
556C2—22no—
557C2—22no—
558C2—262no—
559C2—261no—
560C2—261no—
561C2—262no—
562C2—262no—
563C2#1313102614yesdirect product factor
564C2C2×(C2×#261)⋊Q811yescharacteristic
565C2C22×#8810711yescharacteristic
566C2C2×#1171914211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×D13C23
cosocleC23×D13C24
hypercenterC22×C4⋊C4#261
hypocenterC13C2×#1996
LCSG ▷ C23×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
3. #13131026C2direct (N × H)
7. C23×Dic26C4semidirect
12. C22×C13×C4⋊C4C4semidirect
14. C22×C4⋊Dic13C4semidirect
21. C2×#88151C4semidirect
50. C22×Dic26C2×C4semidirect
55. C2×C22⋊#261Q8semidirect
65. C2×C13×C4⋊C4C2×C4semidirect
75. C2×C4⋊Dic13C2×C4semidirect
150. C22⋊#261C2×Q8semidirect
249. C22×C4⋊C4#261semidirect
340. C2×C4⋊C4C2×#261semidirect
360. C2×C13#1996semidirect
443. C13C2×#1996semidirect
563. C2#13131026direct (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
#131310262
C2×#117182892
C22×#881512
C2×#199613