Finite Group Databasebeta

← C2×#13130916 #16798815

Subgroups — C2×#13130916 #16798815

Order 3328.

1238 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88102C211yesmaximal, characteristic
2C22×#88117C211yesmaximal, characteristic
3C2×(C2×#261)⋊Q8C211yesmaximal, characteristic
4C2×C4⋊C4×#261C211yesmaximal, characteristic
5#13130916C218yesmaximal, direct product factor
6C2×#11718246C211yesmaximal, characteristic
7C2×(C2×#261)⋊C8C211yesmaximal, characteristic
8C2×D13×#103C211yesmaximal, characteristic
9C22×Q8×D13C2211yescharacteristic
10C22×C4⋊#261C2211yescharacteristic
11C22×C4⋊#261C2211yescharacteristic
12C22×C4×#261—21no—
13C22×C4×#261C2211yescharacteristic
14C22×D13⋊C8C2211yescharacteristic
15C22×C8×D13C2211yescharacteristic
16C2×C4⋊C4×D13C2211yescharacteristic
17(C2×#261)⋊Q8—22no—
18(C2×#261)⋊Q8C2214yes—
19C2×#88117—24no—
20C2×#88117C2214yes—
21C2×(C2×#261)⋊C4—21no—
22C2×(C2×#261)⋊C4—21no—
23C2×(C2×#261)⋊C4—21no—
24C2×#88102—24no—
25C2×#88102C2214yes—
26C4⋊C4×#261—22no—
27C4⋊C4×#261C2214yes—
28C2×C13×#103C411yescharacteristic, complemented
29C2×#88075C411yescharacteristic, complemented
30C2×#88056C411yescharacteristic, complemented
31C2×#88050C411yescharacteristic, complemented
32D13×#103C414yescomplemented
33D13×#103C2214yes—
34(C2×#261)⋊C8C2214yes—
35#11718246C2214yes—
36C23×#261—21no—
37C23×#261—21no—
38C23×#261D411yescharacteristic
39C23×#261D411yescharacteristic
40C22×Q8×C13C2×C411yescharacteristic
41C2×Q8×D13—21no—
42C2×Q8×D13—21no—
43C2×Q8×D13—22no—
44C2×Q8×D13—22no—
45C2×Q8×D13—22no—
46C2×Q8×D13—22no—
47C2×Q8×D13C2×C412yes—
48C2×Q8×D13C2312yes—
49C22×C4×D13—21no—
50C22×C4×D13—21no—
51C22×C4×D13C2311yescharacteristic
52C22×Dic26—21no—
53C22×Dic26C2×C411yescharacteristic
54C22×#1057—21no—
55C2×C4⋊#261—21no—
56C2×C4⋊#261—22no—
57C2×C4⋊#261—22no—
58C2×C4⋊#261—22no—
59C2×C4⋊#261—21no—
60C2×C4⋊#261D414yes—
61C2×C4⋊#261C2312yes—
62C2×C4⋊#261C2312yes—
63C2×C4×#261—22no—
64C2×C4×#261—22no—
65C2×C4×#261—24no—
66C2×C4×#261—44no—
67C2×C4×#261D412yes—
68C2×C4×#261C2312yes—
69C2×D13⋊C8—22no—
70C2×D13⋊C8—22no—
71C2×D13⋊C8—21no—
72C2×D13⋊C8C2312yes—
73C22×C8×C13C2×C411yescharacteristic
74C2×C13×C4⋊C4C2×C411yescharacteristic
75C2×C4⋊Dic13C2×C411yescharacteristic
76C2×#6101—21no—
77C22×#1055C2×C411yescharacteristic
78C2×C8×D13—22no—
79C2×C8×D13—22no—
80C2×C8×D13C2×C412yes—
81C2×C8×D13C2312yes—
82C4⋊C4×D13—21no—
83C4⋊C4×D13—21no—
84C4⋊C4×D13C2×C412yes—
85C4⋊C4×D13C2312yes—
86#88117—28no—
87(C2×#261)⋊C4—24no—
88(C2×#261)⋊C4—24no—
89(C2×#261)⋊C4—24no—
90#88102—28no—
91C13×#103C2×C414yescomplemented
92#88075C2×C414yescomplemented
93#88056C2×C414yescomplemented
94#88050C2×C414yescomplemented
95C2×#1928—131nomaximal, Sylow
96C23×D13C2×D411yescharacteristic
97C22×#261—22no—
98C22×#261—22no—
99C22×#261—24no—
100C22×#261—22no—
101C22×#261—22no—
102C22×#261—22no—
103C22×#261—22no—
104C22×#261—22no—
105C22×#261—42no—
106C22×#261—42no—
107C22×#261—42no—
108C22×#261—42no—
109C22×#261—42no—
110C22×#261Q1614yes—
111C22×#261C2×D412yes—
112C22×#261C2×D412yes—
113C2×Q8×C13—21no—
114C2×Q8×C13—22no—
115C2×Q8×C13—22no—
116C2×Q8×C13C22×C412yes—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13C22×C411yescharacteristic
120C22×Dic13—21no—
121C22×Dic13—21no—
122C22×Dic13#4111yescharacteristic
123Q8×D13—24no—
124Q8×D13—24no—
125Q8×D13—22no—
126Q8×D13—22no—
127Q8×D13—22no—
128Q8×D13—22no—
129Q8×D13—42no—
130Q8×D13—42no—
131Q8×D13—42no—
132Q8×D13—42no—
133C2×C4×D13—22no—
134C2×C4×D13—22no—
135C2×C4×D13—22no—
136C2×C4×D13—22no—
137C2×C4×D13—42no—
138C2×C4×D13—42no—
139C2×C4×D13—42no—
140C2×C4×D13—42no—
141C2×C4×D13C22×C411yescharacteristic
142C2×C4×D13C2×D412yes—
143C2×C4×D13C2×D411yescharacteristic
144C2×C4×D13#4112yes—
145C2×C4×D13#4112yes—
146C2×C4×D13#4112yes—
147C2×C4×D13#4111yescharacteristic
148C2×C4×D13C2411yescharacteristic
149C2×Dic26—22no—
150C2×Dic26—22no—
151C2×Dic26—21no—
152C2×Dic26—22no—
153C2×Dic26—22no—
154C2×Dic26—42no—
155C2×Dic26—42no—
156C2×Dic26C22×C412yes—
157C2×#1057—22no—
158C2×#1057—42no—
159C4⋊#261—24no—
160C4⋊#261—22no—
161C4⋊#261—22no—
162C4⋊#261—22no—
163C4⋊#261—42no—
164C4⋊#261C2×D414yes—
165C4×#261—24no—
166C4×#261—22no—
167C4×#261—22no—
168C4×#261—48no—
169D13⋊C8—22no—
170D13⋊C8—22no—
171D13⋊C8—42no—
172C2×C8×C13—22no—
173C2×C8×C13C22×C412yes—
174C13×C4⋊C4—21no—
175C13×C4⋊C4C22×C412yes—
176C4⋊Dic13—21no—
177C4⋊Dic13C22×C412yes—
178#6101—22no—
179#6101—22no—
180C2×#1055—22no—
181C2×#1055C22×C412yes—
182C8×D13—24no—
183C8×D13—22no—
184C8×D13—22no—
185C22×#107—131no—
186C22×#103—131no—
187C22×#103—131no—
188C2×#391—131no—
189C2×C4×C4⋊C4—131no—
190#1928—138no—
191C2×#340—131no—
192C2×#336—131no—
193C23×C13C4×D411yescharacteristic
194C22×D13C4×D411yescharacteristic
195C22×D13#12112yes—
196C22×D13#12312yes—
197C22×D13C2×Q1612yes—
198C22×D13#13512yes—
199C22×D13AGL(1,ℤ/8)12yes—
200C22×D13#13712yes—
201C22×D13C22×D411yescharacteristic
202C2×#261—22no—
203C2×#261—22no—
204C2×#261—28no—
205C2×#261—24no—
206C2×#261—22no—
207C2×#261—22no—
208C2×#261—22no—
209C2×#261—42no—
210C2×#261—42no—
211C2×#261—48no—
212C2×#261—44no—
213C2×#261—42no—
214C2×#261—42no—
215C2×#261—42no—
216C2×#261—84no—
217C2×#261C2×Q1614yes—
218Q8×C13—22no—
219Q8×C13—22no—
220Q8×C13—42no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13#11712yes—
226C2×C4×C13C4×D412yes—
227C2×C4×C13C4×D411yescharacteristic
228C2×C4×C13C23×C411yescharacteristic
229C2×Dic13—22no—
230C2×Dic13—22no—
231C2×Dic13—42no—
232C2×Dic13—42no—
233C2×Dic13C4×D411yescharacteristic
234C2×Dic13#12412yes—
235C2×Dic13#12612yes—
236C2×Dic13C2×#4111yescharacteristic
237C4×D13—42no—
238C4×D13—42no—
239C4×D13—42no—
240C4×D13—42no—
241C4×D13—44no—
242C4×D13—44no—
243C4×D13#11712yes—
244C4×D13C4×D412yes—
245C4×D13#12112yes—
246C4×D13#12312yes—
247C4×D13#12412yes—
248C4×D13#12612yes—
249C4×D13C22×D411yescharacteristic
250C4×D13C2×#4111yescharacteristic
251C4×D13C2×#4111yescharacteristic
252C4×D13C2×#4111yescharacteristic
253Dic26—22no—
254Dic26—22no—
255Dic26—42no—
256Dic26—42no—
257Dic26—42no—
258Dic26—44no—
259#1057—42no—
260C8×C13—22no—
261#1055—22no—
262C23×Q8—131no—
263C23×C8—131no—
264C23×C8—131no—
265C22×C4⋊C4—131no—
266C22×C4⋊C4—131no—
267C22×C4⋊C4—131no—
268C22×C42—131no—
269C22×C42—261no—
270C2×#107—134no—
271C2×#107—264no—
272C2×#103—131no—
273C2×#103—131no—
274C2×#103—131no—
275C2×#103—134no—
276C2×#103—134no—
277C2×#103—134no—
278C2×#103—264no—
279C2×#103#26111yescharacteristic, complemented
280#391—134no—
281#391—262no—
282C4×C4⋊C4—134no—
283C4×C4⋊C4—262no—
284C2×#95—261no—
285C2×#95—261no—
286C2×#95—261no—
287#340—134no—
288#336—134no—
289C22×C13#38812yes—
290C22×C13C4×Q1612yes—
291C22×C13#44012yes—
292C22×C13C2×C4×D411yescharacteristic
293C2×D13#38812yes—
294C2×D13C4×Q1612yes—
295C2×D13#44012yes—
296C2×D13#46214yes—
297C2×D13#46314yes—
298C2×D13#48414yes—
299C2×D13#48514yes—
300C2×D13C2×#12111yescharacteristic
301C2×D13C2×#12311yescharacteristic
302C2×D13C22×Q1611yescharacteristic
303C2×D13C2×#13511yescharacteristic
304C2×D13C2×AGL(1,ℤ/8)11yescharacteristic
305C2×D13C2×#13711yescharacteristic
306#261—24no—
307#261—42no—
308#261—44no—
309#261—82no—
310C4×C13—42no—
311C4×C13—42no—
312C4×C13#38812yes—
313C4×C13C2×#11711yescharacteristic
314C4×C13C2×C4×D411yescharacteristic
315Dic13—42no—
316Dic13—42no—
317Dic13#38812yes—
318Dic13C2×#12411yescharacteristic
319Dic13C2×#12611yescharacteristic
320C22×Q8—132no—
321C22×Q8—132no—
322C22×Q8—131no—
323C22×Q8—261no—
324C22×Q8—261no—
325C22×Q8—261no—
326C22×Q8—262no—
327C22×Q8—262no—
328C22×Q8—262no—
329C22×Q8—262no—
330C22×Q8C2×#26111yescharacteristic
331C23×C4—131no—
332C23×C4—131no—
333C23×C4—131no—
334C23×C4—261no—
335C23×C4—261no—
336C23×C4—261no—
337C23×C4—261no—
338C22×C8—131no—
339C22×C8—132no—
340C22×C8—132no—
341C22×C8—132no—
342C22×C8—262no—
343C22×C8—262no—
344C22×C8—262no—
345C22×C8—262no—
346C22×C8—261no—
347C22×C8—261no—
348C22×C8C2×#26111yescharacteristic
349C2×C4⋊C4—132no—
350C2×C4⋊C4—134no—
351C2×C4⋊C4—131no—
352C2×C4⋊C4—132no—
353C2×C4⋊C4—132no—
354C2×C4⋊C4—132no—
355C2×C4⋊C4—261no—
356C2×C4⋊C4—261no—
357C2×C4⋊C4—261no—
358C2×C4⋊C4—261no—
359C2×C4⋊C4—262no—
360C2×C4⋊C4—262no—
361C2×C4⋊C4—262no—
362C2×C4⋊C4—261no—
363C2×C4⋊C4C2×#26111yescharacteristic
364C2×C42—132no—
365C2×C42—132no—
366C2×C42—262no—
367C2×C42—262no—
368C2×C42—264no—
369C2×C42—524no—
370#107—268no—
371#103—134no—
372#103—134no—
373#103—134no—
374#103—268no—
375#103C2×#26114yescomplemented
376#95—264no—
377#95—264no—
378#95—264no—
379C2×C13#192814yescomplemented
380C2×C13C2×#38811yescharacteristic
381C2×C13C2×C4×Q1611yescharacteristic
382C2×C13C2×#44011yescharacteristic
383D13#192814yescomplemented
384D13C2×#46311yescharacteristic
385D13C2×#46211yescharacteristic
386D13C2×#48511yescharacteristic
387D13C2×#48411yescharacteristic
388C24—131no—
389C2×Q8—21no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—132no—
393C2×Q8—262no—
394C2×Q8—262no—
395C2×Q8—262no—
396C2×Q8—262no—
397C2×Q8—262no—
398C2×Q8—264no—
399C2×Q8—262no—
400C2×Q8—264no—
401C2×Q8—261no—
402C2×Q8—262no—
403C2×Q8—262no—
404C2×Q8—522no—
405C2×Q8—522no—
406C2×Q8—522no—
407C2×Q8—522no—
408C2×Q8—522no—
409C2×Q8—522no—
410C2×Q8C22×#26112yes—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—131no—
414C22×C4—132no—
415C22×C4—132no—
416C22×C4—131no—
417C22×C4—132no—
418C22×C4—132no—
419C22×C4—131no—
420C22×C4—131no—
421C22×C4—131no—
422C22×C4—132no—
423C22×C4—134no—
424C22×C4—132no—
425C22×C4—262no—
426C22×C4—262no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—264no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—262no—
439C22×C4—522no—
440C22×C4—522no—
441C22×C4—522no—
442C22×C4—522no—
443C22×C4—522no—
444C22×C4—522no—
445C22×C4—522no—
446C22×C4—522no—
447C22×C4—522no—
448C22×C4C22×#26111yescharacteristic
449C2×C8—22no—
450C2×C8—132no—
451C2×C8—262no—
452C2×C8—262no—
453C2×C8—264no—
454C2×C8—262no—
455C2×C8—262no—
456C2×C8—262no—
457C2×C8—262no—
458C2×C8—522no—
459C2×C8—522no—
460C2×C8C22×#26112yes—
461C4⋊C4—21no—
462C4⋊C4—134no—
463C4⋊C4—132no—
464C4⋊C4—262no—
465C4⋊C4—262no—
466C4⋊C4—264no—
467C4⋊C4—262no—
468C4⋊C4—262no—
469C4⋊C4—262no—
470C4⋊C4—261no—
471C4⋊C4—522no—
472C4⋊C4C22×#26112yes—
473C42—264no—
474C42—262no—
475C42—262no—
476C42—528no—
477C13C2×#192811yescharacteristic, complemented, Sylow
478C23—132no—
479C23—132no—
480C23—132no—
481C23—132no—
482C23—132no—
483C23—132no—
484C23—131no—
485C23—131no—
486C23D4×#26111yescharacteristic
487Q8—22no—
488Q8—22no—
489Q8—42no—
490Q8—262no—
491Q8—262no—
492Q8—522no—
493Q8—522no—
494Q8—524no—
495Q8—522no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—132no—
501C2×C4—132no—
502C2×C4—131no—
503C2×C4—131no—
504C2×C4—132no—
505C2×C4—132no—
506C2×C4—132no—
507C2×C4—132no—
508C2×C4—131no—
509C2×C4—131no—
510C2×C4—132no—
511C2×C4—131no—
512C2×C4—131no—
513C2×C4—132no—
514C2×C4—134no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—268no—
518C2×C4—262no—
519C2×C4—264no—
520C2×C4—262no—
521C2×C4—262no—
522C2×C4—262no—
523C2×C4—262no—
524C2×C4—522no—
525C2×C4—522no—
526C2×C4—524no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4—524no—
530C2×C4—522no—
531C2×C4—524no—
532C2×C4—522no—
533C2×C4—528no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—1044no—
540C2×C4#8823712yes—
541C2×C4D4×#26111yescharacteristic
542C2×C4D4×#26112yes—
543C2×C4C23×#26111yescharacteristic
544C8—22no—
545C8—262no—
546C8—522no—
547C22—131no—
548C22—131no—
549C22—132no—
550C22—131no—
551C22—131no—
552C22—132no—
553C22—131no—
554C22—131no—
555C22—132no—
556C22—134no—
557C22—134no—
558C22—134no—
559C22—134no—
560C22#1171907112yes—
561C22#1171910612yes—
562C22Q16×#26112yes—
563C22C2×D4×#26111yescharacteristic
564C4—42no—
565C4—42no—
566C4—131no—
567C4—131no—
568C4—132no—
569C4—264no—
570C4—522no—
571C4—524no—
572C4—522no—
573C4—522no—
574C4—1042no—
575C4#1171907112yes—
576C4C2×#8823711yescharacteristic
577C4C2×D4×#26111yescharacteristic
578C2—131no—
579C2—131no—
580C2—131no—
581C2—134no—
582C2—131no—
583C2#1313091614yesdirect product factor
584C2C2×#1171907111yescharacteristic
585C2C2×Q16×#26111yescharacteristic
586C2C2×#1171910611yescharacteristic
subgroupG/H
centerC23D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#103C4
socleC23×C13C4×D4
prime radicalC23×D13C2×D4
cosocleC2×C4×D13C24
hypercenterC2×#103#261
hypocenterC13C2×#1928
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
5. #13130916C2direct (N × H)
28. C2×C13×#103C4semidirect
29. C2×#88075C4semidirect
30. C2×#88056C4semidirect
31. C2×#88050C4semidirect
32. D13×#103C4semidirect
91. C13×#103C2×C4semidirect
92. #88075C2×C4semidirect
93. #88056C2×C4semidirect
94. #88050C2×C4semidirect
279. C2×#103#261semidirect
375. #103C2×#261semidirect
379. C2×C13#1928semidirect
383. D13#1928semidirect
477. C13C2×#1928semidirect
583. C2#13130916direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881022
C22×#881172
C2×(C2×#261)⋊Q82
C2×C4⋊C4×#2612
#131309162
C2×#117182462
C2×(C2×#261)⋊C82
C2×D13×#1032
C2×#192813