Finite Group Databasebeta

← #16797377

Subgroups — #16797377

Order 3328.

1246 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719064C212yesmaximal
2C2×C4×#6118C211yesmaximal, characteristic, complemented
3C22×#88110C211yesmaximal, characteristic, complemented
4#13130635C212yesmaximal, complemented
5#13130622C211yesmaximal, characteristic, complemented
6#13130577C212yesmaximal, complemented
7C22⋊C4×#1057C212yesmaximal, complemented
8#13130563C211yesmaximal, characteristic, complemented
9#13130562C211yesmaximal, characteristic, complemented
10C4×#88110C211yesmaximal, characteristic, complemented
11C4×#88135C211yesmaximal, characteristic
12C23×#1057C2212yes—
13C22×#6118C2212yes—
14C2×C4×C22⋊D13C411yescharacteristic
15C22×C4×Dic13C2211yescharacteristic
16C2×#88135C411yescharacteristic
17C2×#88135C2211yescharacteristic
18C2×C42×D13C2211yescharacteristic
19C2×C22⋊#1057C2212yes—
20C2×#88111C2212yes—
21C2×#88110—24no—
22C2×#88110C2211yescharacteristic
23C2×#88110C2211yescharacteristic
24C2×#88110C2211yescharacteristic
25C2×#88110C2212yes—
26C2×#88110C2212yes—
27C2×#88110C2211yescharacteristic
28C2×C4⋊#1057C2212yes—
29C2×C4×#1057C2212yes—
30C2×C4×#1057C2212yes—
31#11719064C4116yescomplemented
32C4×#6118—24no—
33C4×C13×C22⋊C4C411yescharacteristic
34C22⋊C4×Dic13C411yescharacteristic
35C22⋊C4×Dic13C2211yescharacteristic
36C4×#6103C411yescharacteristic
37C4×#6101C411yescharacteristic
38C42×Dic13C2211yescharacteristic
39#11718327C411yescharacteristic
40#11718327C2211yescharacteristic
41#11718310C411yescharacteristic
42#11718310C2211yescharacteristic
43#11718290C2212yes—
44#11718290C2212yes—
45#11718290C2212yes—
46C23×C4×C13C2×C411yescharacteristic
47C22×C22⋊D13C2×C411yescharacteristic
48C23×Dic13C2×C411yescharacteristic
49C23×Dic13C2311yescharacteristic
50C22×C4×D13C2×C411yescharacteristic
51C22×C4×D13C2×C411yescharacteristic
52C22×C4×D13C2311yescharacteristic
53C22×#1057—24no—
54C22×#1057—24no—
55C22×#1057C2×C418yescomplemented
56C22×#1057C2312yes—
57C22×#1057C2312yes—
58C22×#1057C2312yes—
59C22×#1057C2312yes—
60C2×#6118—24no—
61C2×#6118—24no—
62C2×#6118C2×C418yescomplemented
63C2×C13×C22⋊C4C2×C411yescharacteristic
64C2×C13×C22⋊C4C2×C411yescharacteristic
65C2×C42×C13C2×C411yescharacteristic
66C2×C42×C13C2×C411yescharacteristic
67C2×C22⋊Dic13C2×C411yescharacteristic
68C4×C22⋊D13—24no—
69C2×#6103C2×C411yescharacteristic
70C2×#6103C2×C411yescharacteristic
71C2×#6103C2×C411yescharacteristic
72C2×#6101C2×C411yescharacteristic
73C2×#6101C2×C411yescharacteristic
74C2×#6101C2×C411yescharacteristic
75C2×C4×Dic13—22no—
76C2×C4×Dic13—22no—
77C2×C4×Dic13C2×C411yescharacteristic
78C2×C4×Dic13C2×C411yescharacteristic
79C2×C4×Dic13C2×C411yescharacteristic
80C2×C4×Dic13C2×C411yescharacteristic
81C2×C4×Dic13C2×C411yescharacteristic
82C2×C4×Dic13C2×C411yescharacteristic
83C2×C4×Dic13C2311yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C2×C4×Dic13C2311yescharacteristic
86C2×C4×Dic13C2311yescharacteristic
87C2×C4×Dic13C2311yescharacteristic
88#88135—24no—
89#88135C2×C418yes—
90C42×D13—22no—
91C42×D13—22no—
92C22⋊#1057C2×C418yescomplemented
93#88111C2×C418yescomplemented
94#88110—24no—
95#88110—22no—
96#88110—22no—
97#88110—22no—
98#88110C2×C418yescomplemented
99#88110D414yescomplemented
100C4⋊#1057C2×C418yescomplemented
101C4×#1057—24no—
102C4×#1057—24no—
103C13×#95C2×C411yescharacteristic
104C13×#95C2×C411yescharacteristic
105#88071C2×C411yescharacteristic
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108#88071C2×C411yescharacteristic
109#20491—131nomaximal, Sylow
110C24×C13C22×C411yescharacteristic
111C23×D13C22×C411yescharacteristic
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—41no—
115C22×C4×C13C22×C411yescharacteristic
116C22×C4×C13C22×C411yescharacteristic
117C22×C4×C13C22×C411yescharacteristic
118C22×C4×C13C22×C411yescharacteristic
119C22×C4×C13C22×C411yescharacteristic
120C22×C4×C13C22×C411yescharacteristic
121C2×C22⋊D13—22no—
122C2×C22⋊D13—22no—
123C2×C22⋊D13C4214yes—
124C22×Dic13—21no—
125C22×Dic13—21no—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—41no—
130C22×Dic13C22×C411yescharacteristic
131C22×Dic13C22×C411yescharacteristic
132C22×Dic13C22×C411yescharacteristic
133C22×Dic13C22×C414yes—
134C22×Dic13C22×C411yescharacteristic
135C22×Dic13C22×C411yescharacteristic
136C22×Dic13C22×C411yescharacteristic
137C22×Dic13C2411yescharacteristic
138C2×C4×D13—21no—
139C2×C4×D13—21no—
140C2×C4×D13—22no—
141C2×C4×D13—22no—
142C2×C4×D13—22no—
143C2×C4×D13—22no—
144C2×C4×D13—22no—
145C2×C4×D13—41no—
146C2×C4×D13—41no—
147C2×C4×D13C22×C414yes—
148C2×#1057—22no—
149C2×#1057—22no—
150C2×#1057—22no—
151C2×#1057—22no—
152C2×#1057—22no—
153C2×#1057—22no—
154C2×#1057—216no—
155C2×#1057C22×C414yes—
156C2×#1057C22×C414yes—
157C2×#1057C22×C414yes—
158C2×#1057C22×C414yes—
159C2×#1057C2×D414yes—
160C2×#1057#4114yes—
161#6118—216no—
162C13×C22⋊C4C4214yes—
163C13×C22⋊C4M1614yescomplemented
164C42×C13—22no—
165C42×C13—41no—
166C22⋊Dic13M1614yescomplemented
167#6103—22no—
168#6103—22no—
169#6103C4214yes—
170#6101—22no—
171#6101—22no—
172#6101C4214yes—
173C4×Dic13—22no—
174C4×Dic13—22no—
175C4×Dic13—22no—
176C4×Dic13—22no—
177C4×Dic13—22no—
178C4×Dic13—21no—
179C4×Dic13—21no—
180C4×Dic13—22no—
181C4×Dic13—21no—
182C4×Dic13—21no—
183C4×Dic13—41no—
184C4×Dic13C22×C414yes—
185C4×Dic13C2×D412yes—
186C4×Dic13#4112yes—
187C2×#435—132no—
188C2×C4×M16—131no—
189C22×#97—131no—
190C42×D4—131no—
191#1771—132no—
192#1767—131no—
193#1753—132no—
194C8×C22⋊C4—132no—
195#1749—131no—
196#1749—131no—
197C4×#97—131no—
198C23×C13—21no—
199C23×C13—21no—
200C23×C13—21no—
201C23×C13—21no—
202C23×C13C2×C4212yes—
203C23×C13C2×M1612yes—
204C23×C13C2×M1612yes—
205C23×C13C23×C411yescharacteristic
206C22×D13—21no—
207C22×D13—21no—
208C22×D13—21no—
209C22×D13—21no—
210C22×D13—21no—
211C22×D13—21no—
212C22×D13C2×C4212yes—
213C2×C4×C13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—44no—
227C2×C4×C13C2×C4212yes—
228C2×C4×C13C2×C4212yes—
229C2×C4×C13C4×D412yes—
230C2×C4×C13C2×M1612yes—
231C2×C4×C13C2×M1612yes—
232C22⋊D13—28no—
233C2×Dic13—21no—
234C2×Dic13—21no—
235C2×Dic13—21no—
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—24no—
244C2×Dic13—24no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—44no—
249C2×Dic13C2×C4212yes—
250C2×Dic13C2×C4212yes—
251C2×Dic13C4×D412yes—
252C2×Dic13C2×M1612yes—
253C2×Dic13C2×M1612yes—
254C2×Dic13C23×C412yes—
255C2×Dic13C22×D411yescharacteristic
256C2×Dic13C2×#4112yes—
257C2×Dic13C2×#4111yescharacteristic
258C4×D13—24no—
259C4×D13—24no—
260C4×D13—44no—
261C4×D13—44no—
262#1057—24no—
263#1057—24no—
264#1057—24no—
265#1057C4×D418yescomplemented
266C22×M16—132no—
267C23×C8—132no—
268C2×C4×D4—131no—
269C2×C4×D4—131no—
270C2×C4×D4—131no—
271C22×C42—131no—
272C22×C42—131no—
273#435—1316no—
274C2×C4⋊C8—132no—
275C2×C22⋊C8—132no—
276C2×C22⋊C8—132no—
277C4×M16—264no—
278C2×#97—131no—
279C2×#97—132no—
280C2×#97—131no—
281C2×#97—132no—
282C2×#97—131no—
283C2×#97—131no—
284C2×#97—264no—
285C2×C4×C8—132no—
286C2×C4×C8—132no—
287C4×C4⋊C4—131no—
288C4×C4⋊C4—131no—
289C4×C4⋊C4—131no—
290C4×C22⋊C4—131no—
291C4×C22⋊C4—131no—
292C4×C22⋊C4—131no—
293C4×C22⋊C4—131no—
294C4×C22⋊C4—131no—
295C4×C22⋊C4#26111yescharacteristic
296C43—131no—
297#336—132no—
298#336—132no—
299#336—132no—
300C22×C13—22no—
301C22×C13—22no—
302C22×C13—22no—
303C22×C13—22no—
304C22×C13—22no—
305C22×C13—22no—
306C22×C13C4×M1614yescomplemented
307C22×C13C22×C4211yescharacteristic
308C22×C13C2×C4×D411yescharacteristic
309C22×C13C4×#4111yescharacteristic
310C22×C13C22×M1611yescharacteristic
311C22×C13C22×M1611yescharacteristic
312C22×C13#56811yescharacteristic
313C22×C13#56811yescharacteristic
314C2×D13—22no—
315C2×D13—22no—
316C2×D13—22no—
317C2×D13—41no—
318C2×D13—41no—
319C2×D13—41no—
320C2×D13—41no—
321C4×C13—22no—
322C4×C13—22no—
323C4×C13—22no—
324C4×C13—22no—
325C4×C13—22no—
326C4×C13—41no—
327Dic13—22no—
328Dic13—22no—
329Dic13—22no—
330Dic13—22no—
331Dic13—22no—
332Dic13—41no—
333Dic13C2×C4×D412yes—
334Dic13C4×#4112yes—
335C22×D4—131no—
336C23×C4—131no—
337C23×C4—131no—
338C23×C4—131no—
339C23×C4—131no—
340C23×C4—131no—
341C23×C4C2×#26111yescharacteristic
342C2×M16—138no—
343C2×M16—264no—
344C2×M16—264no—
345C22×C8—132no—
346C22×C8—132no—
347C22×C8—138no—
348C22×C8—132no—
349C22×C8—132no—
350C22×C8—264no—
351C22×C8—264no—
352C4×D4—138no—
353C4×D4—264no—
354C4×D4—264no—
355C2×C4⋊C4—131no—
356C2×C4⋊C4—131no—
357C2×C4⋊C4—131no—
358C2×C22⋊C4—131no—
359C2×C22⋊C4—131no—
360C2×C22⋊C4—131no—
361C2×C22⋊C4—131no—
362C2×C22⋊C4C2×#26111yescharacteristic
363C2×C22⋊C4C2×#26111yescharacteristic
364C2×C42—131no—
365C2×C42—131no—
366C2×C42—131no—
367C2×C42—131no—
368C2×C42—131no—
369C2×C42—131no—
370C2×C42—131no—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—131no—
375C2×C42—262no—
376C2×C42—262no—
377C2×C42—262no—
378C2×C42—262no—
379C2×C42C2×#26111yescharacteristic
380C2×C42C2×#26111yescharacteristic
381C4⋊C8—138no—
382C22⋊C8—138no—
383C22⋊C8—138no—
384#97—138no—
385#97—134no—
386#97—262no—
387#97—262no—
388#97—262no—
389#97—264no—
390C4×C8—264no—
391C4×C8—264no—
392#95—131no—
393#95—131no—
394#95—131no—
395#95—131no—
396#95C2×#26111yescharacteristic
397#95C2×#26111yescharacteristic
398C2×C13—24no—
399C2×C13C42×D411yescharacteristic
400C2×C13C2×C4×M1611yescharacteristic
401C2×C13#287511yescharacteristic
402C2×C13D4×M1611yescharacteristic
403C2×C13D4×M1611yescharacteristic
404C2×C13#297011yescharacteristic
405C2×C13#297011yescharacteristic
406D13—42no—
407C24—131no—
408C24C22×#26111yescharacteristic
409C2×D4—134no—
410C2×D4—262no—
411C2×D4—262no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—41no—
415C22×C4—131no—
416C22×C4—134no—
417C22×C4—131no—
418C22×C4—131no—
419C22×C4—131no—
420C22×C4—131no—
421C22×C4—131no—
422C22×C4—134no—
423C22×C4—131no—
424C22×C4—261no—
425C22×C4—261no—
426C22×C4—262no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—521no—
437C22×C4—521no—
438C22×C4—521no—
439C22×C4C22×#26111yescharacteristic
440C22×C4C22×#26111yescharacteristic
441C22×C4C22×#26111yescharacteristic
442C22×C4C22×#26111yescharacteristic
443C22×C4C22×#26111yescharacteristic
444C22×C4C22×#26111yescharacteristic
445M16—2616no—
446C2×C8—134no—
447C2×C8—134no—
448C2×C8—134no—
449C2×C8—134no—
450C2×C8—134no—
451C2×C8—134no—
452C2×C8—2616no—
453C2×C8—262no—
454C2×C8—262no—
455C2×C8—262no—
456C2×C8—262no—
457C2×C8—262no—
458C2×C8—262no—
459C4⋊C4—134no—
460C4⋊C4—262no—
461C4⋊C4—262no—
462C22⋊C4—134no—
463C22⋊C4—134no—
464C22⋊C4—262no—
465C22⋊C4—262no—
466C22⋊C4#611814yescomplemented
467C22⋊C4C4×#26114yes—
468C42—22no—
469C42—41no—
470C42—134no—
471C42—132no—
472C42—132no—
473C42—261no—
474C42—262no—
475C42—261no—
476C42—261no—
477C42—262no—
478C42—261no—
479C42—262no—
480C42—262no—
481C42—262no—
482C42—262no—
483C42—521no—
484C13#2049111yescharacteristic, complemented, Sylow
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—132no—
490C23—261no—
491C23—261no—
492C23—261no—
493C23—261no—
494C23—261no—
495C23—261no—
496C23C2×#611812yes—
497C23D13⋊M1612yes—
498C23C2×C4×#26112yes—
499C23C23×#26111yescharacteristic
500D4—268no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—44no—
515C2×C4—132no—
516C2×C4—131no—
517C2×C4—131no—
518C2×C4—132no—
519C2×C4—132no—
520C2×C4—132no—
521C2×C4—132no—
522C2×C4—132no—
523C2×C4—132no—
524C2×C4—264no—
525C2×C4—264no—
526C2×C4—264no—
527C2×C4—264no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—524no—
542C2×C4—524no—
543C2×C4—524no—
544C2×C4C2×#611812yes—
545C2×C4C2×#611812yes—
546C2×C4C2×C4×#26112yes—
547C2×C4C2×C4×#26112yes—
548C2×C4D4×#26112yes—
549C8—138no—
550C8—264no—
551C8—264no—
552C8—264no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—262no—
560C22—262no—
561C22—262no—
562C22—521no—
563C22—521no—
564C22—521no—
565C22—521no—
566C22C4×#611814yescomplemented
567C22C22×#611811yescharacteristic
568C22C2×D13⋊M1611yescharacteristic
569C22C22×C4×#26111yescharacteristic
570C22#1171962111yescharacteristic
571C22C2×D4×#26111yescharacteristic
572C22#1171962911yescharacteristic
573C22#41×#26111yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—22no—
578C4—22no—
579C4—41no—
580C4—132no—
581C4—132no—
582C4—262no—
583C4—262no—
584C4—262no—
585C4—262no—
586C4—262no—
587C4—521no—
588C2—24no—
589C2—522no—
590C2C4×D4×#26111yescharacteristic
591C2C2×C4×#611811yescharacteristic
592C2#1313140711yescharacteristic
593C2D4×#611811yescharacteristic
594C2#1313157411yescharacteristic
595C2#1313167411yescharacteristic
596C2#1313167511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC4×C13×C22⋊C4C4
socleC23×C13C23×C4
prime radicalC22×C22⋊D13C2×C4
cosocleC22×Dic13C24
hypercenterC4×C22⋊C4#261
hypocenterC13#20491
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6118C2semidirect
3. C22×#88110C2semidirect
4. #13130635C2semidirect
5. #13130622C2semidirect
6. #13130577C2semidirect
7. C22⋊C4×#1057C2semidirect
8. #13130563C2semidirect
9. #13130562C2semidirect
10. C4×#88110C2semidirect
31. #11719064C4semidirect
55. C22×#1057C2×C4semidirect
62. C2×#6118C2×C4semidirect
92. C22⋊#1057C2×C4semidirect
93. #88111C2×C4semidirect
98. #88110C2×C4semidirect
99. #88110D4semidirect
100. C4⋊#1057C2×C4semidirect
163. C13×C22⋊C4M16semidirect
166. C22⋊Dic13M16semidirect
265. #1057C4×D4semidirect
306. C22×C13C4×M16semidirect
466. C22⋊C4#6118semidirect
484. C13#20491semidirect
566. C22C4×#6118semidirect

Maximal subgroups

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

subgroupindex
C2×#117190642
C2×C4×#61182
C22×#881102
#131306352
#131306222
#131305772
C22⋊C4×#10572
#131305632
#131305622
C4×#881102
C4×#881352
#2049113