Finite Group Databasebeta

← #15770783

Subgroups — #15770783

Order 3328.

1042 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718868C211yesmaximal, characteristic
2C2×#11718873C211yesmaximal, characteristic
3C2×#11718146C212yesmaximal, complemented
4C2×#11718146C212yesmaximal, complemented
5C2×C13×#407C211yesmaximal, characteristic
6C24×C4×C13C2211yescharacteristic
7C22×C13×M16C2212yes—
8C22×C22⋊Dic13C412yes—
9C22×C4⋊Dic13C2211yescharacteristic
10C22×C4⋊Dic13C2211yescharacteristic
11C22×#6099C2212yes—
12C13×#407—24no—
13C2×C13×C22⋊C8—21no—
14C2×C13×C22⋊C8—21no—
15#11718873—21no—
16#11718873—21no—
17#11718873—21no—
18#11718873—21no—
19C2×#88071C412yes—
20#11718868—24no—
21C2×C22⋊#1055—21no—
22C2×C22⋊#1055—21no—
23#11718146—24no—
24#11718146—24no—
25C25×C13C2×C411yescharacteristic
26C23×C4×C13—22no—
27C23×C4×C13—22no—
28C23×C4×C13—22no—
29C23×C4×C13—22no—
30C23×C4×C13—22no—
31C23×C4×C13—22no—
32C23×C4×C13C2×C411yescharacteristic
33C23×C4×C13D411yescharacteristic
34C23×C4×C13D411yescharacteristic
35C23×C4×C13D411yescharacteristic
36C23×C4×C13D411yescharacteristic
37C23×C4×C13C2311yescharacteristic
38C23×Dic13C2×C412yes—
39C23×Dic13C2×C412yes—
40C2×C13×M16—22no—
41C2×C13×M16—22no—
42C2×C13×M16—22no—
43C2×C13×M16—22no—
44C2×C13×M16—22no—
45C2×C13×M16D414yes—
46C22×C8×C13—22no—
47C2×C22⋊Dic13—22no—
48C2×C22⋊Dic13—22no—
49C2×C22⋊Dic13—44no—
50C2×C4⋊Dic13—22no—
51C2×C4⋊Dic13—22no—
52C2×C4⋊Dic13—21no—
53C2×C4⋊Dic13—21no—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13—21no—
56C2×C4⋊Dic13—22no—
57C2×C4⋊Dic13—22no—
58C2×#6099—22no—
59C2×#6099—22no—
60C2×#6099—22no—
61C2×#6099—22no—
62C2×#6099—22no—
63C2×#6099D414yes—
64C22×#1055—22no—
65C13×C22⋊C8—24no—
66C13×C22⋊C8—24no—
67#88071—22no—
68#88071—22no—
69C22⋊#1055—24no—
70C22⋊#1055—24no—
71#11198—131nomaximal, Sylow
72C24×C13—22no—
73C24×C13—22no—
74C24×C13—21no—
75C24×C13—21no—
76C24×C13—22no—
77C24×C13—22no—
78C24×C13—41no—
79C24×C13—41no—
80C24×C13C22⋊C411yescharacteristic
81C24×C13C22⋊C411yescharacteristic
82C24×C13C22×C411yescharacteristic
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—22no—
86C22×C4×C13—22no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—42no—
104C22×C4×C13—42no—
105C22×C4×C13—42no—
106C22×C4×C13—42no—
107C22×C4×C13—42no—
108C22×C4×C13—42no—
109C22×C4×C13—42no—
110C22×C4×C13—42no—
111C22×C4×C13C22⋊C411yescharacteristic
112C22×C4×C13C22⋊C411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D412yes—
115C22×C4×C13C2×D412yes—
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13#4112yes—
118C22×C4×C13#4112yes—
119C22×C4×C13#4112yes—
120C22×C4×C13#4112yes—
121C22×Dic13—22no—
122C22×Dic13—22no—
123C22×Dic13—24no—
124C22×Dic13—24no—
125C22×Dic13—42no—
126C22×Dic13—42no—
127C22×Dic13—42no—
128C22×Dic13—42no—
129C13×M16—24no—
130C13×M16—24no—
131C13×M16—42no—
132C13×M16—42no—
133C2×C8×C13—24no—
134C2×C8×C13—42no—
135C2×C8×C13—42no—
136C22⋊Dic13—44no—
137C22⋊Dic13—44no—
138C4⋊Dic13—41no—
139C4⋊Dic13—41no—
140C4⋊Dic13—42no—
141C4⋊Dic13—42no—
142C4⋊Dic13—41no—
143C4⋊Dic13—41no—
144#6099—24no—
145#6099—24no—
146#6099—42no—
147#6099—42no—
148C2×#1055—24no—
149C2×#1055—42no—
150C2×#1055—42no—
151C2×#407—131no—
152C2×#407D1311yescharacteristic
153C2×#380—131no—
154C2×#343—132no—
155C2×#343—132no—
156C23×C13—21no—
157C23×C13—21no—
158C23×C13—21no—
159C23×C13—21no—
160C23×C13—24no—
161C23×C13—24no—
162C23×C13—21no—
163C23×C13—21no—
164C23×C13—21no—
165C23×C13—21no—
166C23×C13—21no—
167C23×C13—21no—
168C23×C13—21no—
169C23×C13—21no—
170C23×C13—21no—
171C23×C13—21no—
172C23×C13—21no—
173C23×C13—21no—
174C23×C13—44no—
175C23×C13—44no—
176C23×C13—44no—
177C23×C13—44no—
178C23×C13—42no—
179C23×C13—42no—
180C23×C13—42no—
181C23×C13—42no—
182C23×C13#10012yes—
183C23×C13#10112yes—
184C23×C13C2×C22⋊C411yescharacteristic
185C23×C13#11711yescharacteristic
186C23×C13#11711yescharacteristic
187C23×C13C4×D412yes—
188C23×C13C4×D412yes—
189C2×C4×C13—21no—
190C2×C4×C13—21no—
191C2×C4×C13—21no—
192C2×C4×C13—21no—
193C2×C4×C13—21no—
194C2×C4×C13—21no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—42no—
199C2×C4×C13—42no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13#12011yescharacteristic
206C2×C4×C13#12011yescharacteristic
207C2×C4×C13#12112yes—
208C2×C4×C13#12112yes—
209C2×C4×C13#12112yes—
210C2×C4×C13#12112yes—
211C2×C4×C13#12312yes—
212C2×C4×C13#12312yes—
213C2×C4×C13#12312yes—
214C2×C4×C13#12312yes—
215C2×C4×C13#12311yescharacteristic
216C2×C4×C13#12311yescharacteristic
217C2×C4×C13#12412yes—
218C2×C4×C13#12412yes—
219C2×C4×C13#12612yes—
220C2×C4×C13#12612yes—
221C2×Dic13—42no—
222C2×Dic13—42no—
223C2×Dic13—42no—
224C2×Dic13—42no—
225C2×Dic13—42no—
226C2×Dic13—42no—
227C2×Dic13—84no—
228C2×Dic13—84no—
229C8×C13—44no—
230#1055—44no—
231C24×C4C2×D1311yescharacteristic
232C22×M16—132no—
233C22×M16C2×D1312yes—
234C22×C4⋊C4—131no—
235C22×C4⋊C4—131no—
236C22×C22⋊C4—132no—
237#407—24no—
238#407—264no—
239C2×C22⋊C8—21no—
240C2×C22⋊C8—21no—
241C2×C22⋊C8—261no—
242C2×C22⋊C8—261no—
243#380—261no—
244#380—261no—
245#380—261no—
246#380—261no—
247C2×#95—132no—
248#343—264no—
249#343—264no—
250C22×C13—21no—
251C22×C13—21no—
252C22×C13—21no—
253C22×C13—21no—
254C22×C13—22no—
255C22×C13—22no—
256C22×C13—22no—
257C22×C13—22no—
258C22×C13—22no—
259C22×C13—22no—
260C22×C13—22no—
261C22×C13—22no—
262C22×C13—22no—
263C22×C13—22no—
264C22×C13—48no—
265C22×C13—48no—
266C22×C13—41no—
267C22×C13—41no—
268C22×C13—41no—
269C22×C13—41no—
270C22×C13—41no—
271C22×C13—41no—
272C22×C13—41no—
273C22×C13—41no—
274C22×C13#38111yescharacteristic
275C22×C13#38611yescharacteristic
276C22×C13#38611yescharacteristic
277C22×C13#38812yes—
278C22×C13#38812yes—
279C22×C13C2×#10011yescharacteristic
280C22×C13C2×#10111yescharacteristic
281C22×C13#41311yescharacteristic
282C22×C13#41311yescharacteristic
283C4×C13—41no—
284C4×C13—41no—
285C4×C13#39412yes—
286C4×C13#39412yes—
287C4×C13#39712yes—
288C4×C13#39712yes—
289Dic13—82no—
290Dic13—82no—
291C25C4×D1311yescharacteristic
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—132no—
299C23×C4—132no—
300C23×C4C4×D1311yescharacteristic
301C23×C4D5211yescharacteristic
302C23×C4D5211yescharacteristic
303C23×C4C22⋊D1311yescharacteristic
304C23×C4C22⋊D1311yescharacteristic
305C23×C4C22×D1311yescharacteristic
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—22no—
311C2×M16—134no—
312C2×M16—262no—
313C2×M16—262no—
314C2×M16—262no—
315C2×M16—262no—
316C2×M16—262no—
317C2×M16C22⋊D1314yes—
318C22×C8—22no—
319C22×C8—262no—
320C2×C4⋊C4—261no—
321C2×C4⋊C4—261no—
322C2×C4⋊C4—262no—
323C2×C4⋊C4—262no—
324C2×C4⋊C4—262no—
325C2×C4⋊C4—262no—
326C2×C4⋊C4—261no—
327C2×C4⋊C4—261no—
328C2×C22⋊C4—262no—
329C2×C22⋊C4—262no—
330C2×C22⋊C4—524no—
331C22⋊C8—24no—
332C22⋊C8—24no—
333C22⋊C8—264no—
334C22⋊C8—264no—
335#95—262no—
336#95—262no—
337C2×C13—22no—
338C2×C13—22no—
339C2×C13—42no—
340C2×C13—42no—
341C2×C13#144011yescharacteristic
342C2×C13#182111yescharacteristic
343C2×C13#182211yescharacteristic
344C2×C13#190011yescharacteristic
345C2×C13#190011yescharacteristic
346C2×C13#190111yescharacteristic
347C2×C13#190111yescharacteristic
348C24—22no—
349C24—21no—
350C24—21no—
351C24—22no—
352C24—22no—
353C24—22no—
354C24—41no—
355C24—41no—
356C24#610311yescharacteristic
357C24#610311yescharacteristic
358C24C2×C4×D1311yescharacteristic
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—262no—
388C22×C4—262no—
389C22×C4—264no—
390C22×C4—264no—
391C22×C4—522no—
392C22×C4—522no—
393C22×C4—522no—
394C22×C4—522no—
395C22×C4#610311yescharacteristic
396C22×C4#610311yescharacteristic
397C22×C4C2×D5211yescharacteristic
398C22×C4#612712yes—
399C22×C4D4×D1312yes—
400C22×C4#612912yes—
401C22×C4#612912yes—
402C22×C4#612912yes—
403C22×C4C2×C22⋊D1311yescharacteristic
404C22×C4C2×C22⋊D1312yes—
405M16—24no—
406M16—24no—
407M16—42no—
408M16—42no—
409M16—264no—
410M16—264no—
411M16—522no—
412M16—522no—
413C2×C8—24no—
414C2×C8—42no—
415C2×C8—42no—
416C2×C8—264no—
417C2×C8—522no—
418C2×C8—522no—
419C4⋊C4—521no—
420C4⋊C4—521no—
421C4⋊C4—521no—
422C4⋊C4—522no—
423C4⋊C4—522no—
424C4⋊C4—521no—
425C22⋊C4—524no—
426C22⋊C4—524no—
427C13#1119811yescharacteristic, complemented, Sylow
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—24no—
433C23—24no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—44no—
447C23—44no—
448C23—44no—
449C23—44no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23#8806312yes—
455C23#8806412yes—
456C23#8813111yescharacteristic
457C23#8813111yescharacteristic
458C23#8813512yes—
459C23C2×#610311yescharacteristic
460C23C4×C22⋊D1312yes—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—522no—
478C2×C4—522no—
479C2×C4—522no—
480C2×C4—522no—
481C2×C4—522no—
482C2×C4—522no—
483C2×C4—1044no—
484C2×C4—1044no—
485C2×C4#8813312yes—
486C2×C4#8813312yes—
487C2×C4#8813611yescharacteristic
488C2×C4#8813712yes—
489C2×C4#8813912yes—
490C2×C4#8814011yescharacteristic
491C2×C4#8814012yes—
492C2×C4#8818311yescharacteristic
493C2×C4#8818412yes—
494C2×C4#8818912yes—
495C2×C4#8818912yes—
496C2×C4#8819012yes—
497C2×C4#8819212yes—
498C2×C4#8819312yes—
499C2×C4#8819312yes—
500C2×C4#8820711yescharacteristic
501C8—44no—
502C8—524no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—22no—
508C22—22no—
509C22—22no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—48no—
518C22—48no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22#1171860411yescharacteristic
528C22#1171860512yes—
529C22#1171860612yes—
530C22#1171861911yescharacteristic
531C22C2×#8806311yescharacteristic
532C22#1171879311yescharacteristic
533C22#1171879311yescharacteristic
534C22C2×#8806411yescharacteristic
535C22#1171887411yescharacteristic
536C4—41no—
537C4—41no—
538C4—1042no—
539C4—1042no—
540C4#1171861312yes—
541C4#1171861412yes—
542C4#1171862212yes—
543C4#1171888312yes—
544C2—22no—
545C2—22no—
546C2—42no—
547C2—42no—
548C2#1311308311yescharacteristic
549C2#1311491411yescharacteristic
550C2#1311491711yescharacteristic
551C2#1311529711yescharacteristic
552C2#1311529911yescharacteristic
553C2#1311530211yescharacteristic
554C2#1311530411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#407C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC23×C4×C13C23
hypercenterC2×#407D13
hypocenterC13#11198
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
3. C2×#11718146C2semidirect
4. C2×#11718146C2semidirect
427. C13#11198semidirect

Maximal subgroups

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

subgroupindex
C2×#117188682
C2×#117188732
C2×#117181462
C2×C13×#4072
#1119813