Finite Group Databasebeta

← #15770810

Subgroups — #15770810

Order 3328.

1194 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718871C211yesmaximal, characteristic
2C2×#11718873C211yesmaximal, characteristic
3C2×#11718119C212yesmaximal
4C2×#11718119C212yesmaximal
5C13×C22⋊#95C211yesmaximal, characteristic
6C24×C4×C13C2211yescharacteristic
7C22×C13×C22⋊C4C2212yes—
8C22×C22⋊Dic13C2211yescharacteristic
9C22×C22⋊Dic13C2212yes—
10C22×C22⋊Dic13C2211yescharacteristic
11C22×C4⋊Dic13—21no—
12C22×#6101C412yescomplemented
13C2×C13×#95—22no—
14#11718873—24no—
15#11718871—21no—
16#11718871—21no—
17#11718871—22no—
18C2×#88071—21no—
19C2×#88071C412yescomplemented
20#11718119—24no—
21#11718119—24no—
22C25×C13C2311yescharacteristic
23C23×C4×C13—22no—
24C23×C4×C13—22no—
25C23×C4×C13—22no—
26C23×C4×C13—44no—
27C23×C4×C13C2×C412yes—
28C23×C4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C23×C4×C13D412yes—
31C23×Dic13—22no—
32C23×Dic13C2×C411yescharacteristic
33C23×Dic13C2×C411yescharacteristic
34C23×Dic13C2×C412yes—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4Q814yes—
41C2×C22⋊Dic13—21no—
42C2×C22⋊Dic13—21no—
43C2×C22⋊Dic13—21no—
44C2×C22⋊Dic13—21no—
45C2×C22⋊Dic13—22no—
46C2×C22⋊Dic13—22no—
47C2×C22⋊Dic13—22no—
48C2×C22⋊Dic13—22no—
49C2×C22⋊Dic13—21no—
50C2×C22⋊Dic13—21no—
51C2×C22⋊Dic13—22no—
52C2×C22⋊Dic13—22no—
53C2×C22⋊Dic13—22no—
54C2×C22⋊Dic13D414yes—
55C2×C22⋊Dic13D412yes—
56C2×C22⋊Dic13Q812yes—
57C2×C4⋊Dic13—24no—
58C2×C4⋊Dic13—44no—
59C2×#6101—22no—
60C2×#6101—22no—
61C2×#6101—44no—
62C13×#95—44no—
63#88071—24no—
64#88071—22no—
65#88071—22no—
66#11203—131nomaximal, Sylow
67C24×C13—42no—
68C24×C13—42no—
69C24×C13C22×C411yescharacteristic
70C24×C13C2×D411yescharacteristic
71C24×C13C2×D411yescharacteristic
72C24×C13C2×D412yes—
73C24×C13C2×D411yescharacteristic
74C24×C13C2×Q812yes—
75C24×C13C2×Q811yescharacteristic
76C24×C13#4112yes—
77C24×C13#4111yescharacteristic
78C24×C13#4112yes—
79C24×C13#4111yescharacteristic
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—24no—
83C22×C4×C13—24no—
84C22×C4×C13—21no—
85C22×C4×C13—24no—
86C22×C4×C13—21no—
87C22×C4×C13—24no—
88C22×C4×C13—24no—
89C22×C4×C13—24no—
90C22×C4×C13—42no—
91C22×C4×C13—42no—
92C22×C4×C13—42no—
93C22×C4×C13—48no—
94C22×C4×C13—48no—
95C22×C4×C13—44no—
96C22×C4×C13—44no—
97C22×C4×C13—42no—
98C22×C4×C13—42no—
99C22×C4×C13C22⋊C412yes—
100C22×C4×C13C22⋊C412yes—
101C22×Dic13—22no—
102C22×Dic13—22no—
103C22×Dic13—21no—
104C22×Dic13—21no—
105C22×Dic13—24no—
106C22×Dic13—22no—
107C22×Dic13—22no—
108C22×Dic13—42no—
109C22×Dic13—42no—
110C22×Dic13—44no—
111C22×Dic13—44no—
112C22×Dic13—42no—
113C22×Dic13—42no—
114C22×Dic13—42no—
115C22×Dic13—42no—
116C22×Dic13C4⋊C414yescomplemented
117C13×C22⋊C4—24no—
118C13×C22⋊C4—24no—
119C13×C22⋊C4—42no—
120C13×C22⋊C4—42no—
121C22⋊Dic13—22no—
122C22⋊Dic13—22no—
123C22⋊Dic13—22no—
124C22⋊Dic13—22no—
125C22⋊Dic13—24no—
126C22⋊Dic13—24no—
127C22⋊Dic13—41no—
128C22⋊Dic13—42no—
129C22⋊Dic13—42no—
130C22⋊Dic13—41no—
131C22⋊Dic13—42no—
132C4⋊Dic13—48no—
133#6101—44no—
134#6101—44no—
135C2×#385—131no—
136C2×#380—131no—
137C2×#342—132no—
138C2×#342—132no—
139C22⋊#95D1311yescharacteristic
140C23×C13—22no—
141C23×C13—22no—
142C23×C13—22no—
143C23×C13—22no—
144C23×C13—22no—
145C23×C13—22no—
146C23×C13—42no—
147C23×C13—42no—
148C23×C13—42no—
149C23×C13—42no—
150C23×C13—42no—
151C23×C13—44no—
152C23×C13—42no—
153C23×C13—42no—
154C23×C13—42no—
155C23×C13—44no—
156C23×C13C2×C22⋊C411yescharacteristic
157C23×C13C2×C4⋊C411yescharacteristic
158C23×C13#11711yescharacteristic
159C23×C13C4×D412yes—
160C23×C13C4×Q812yes—
161C23×C13#12011yescharacteristic
162C23×C13#12111yescharacteristic
163C23×C13#12111yescharacteristic
164C23×C13#12112yes—
165C23×C13#12112yes—
166C23×C13C22⋊Q811yescharacteristic
167C23×C13C22⋊Q811yescharacteristic
168C23×C13C22⋊Q812yes—
169C23×C13C22⋊Q812yes—
170C23×C13C22⋊Q812yes—
171C23×C13#12311yescharacteristic
172C23×C13#12312yes—
173C23×C13#12411yescharacteristic
174C23×C13#12512yes—
175C23×C13#12512yes—
176C23×C13#12612yes—
177C23×C13C4⋊Q811yescharacteristic
178C23×C13C4⋊Q812yes—
179C2×C4×C13—24no—
180C2×C4×C13—24no—
181C2×C4×C13—22no—
182C2×C4×C13—22no—
183C2×C4×C13—22no—
184C2×C4×C13—22no—
185C2×C4×C13—22no—
186C2×C4×C13—48no—
187C2×C4×C13—48no—
188C2×C4×C13—42no—
189C2×C4×C13—42no—
190C2×C4×C13—48no—
191C2×C4×C13—44no—
192C2×C4×C13—84no—
193C2×C4×C13—82no—
194C2×C4×C13—82no—
195C2×C4×C13#9914yes—
196C2×Dic13—24no—
197C2×Dic13—44no—
198C2×Dic13—42no—
199C2×Dic13—42no—
200C2×Dic13—44no—
201C2×Dic13—44no—
202C2×Dic13—44no—
203C2×Dic13—41no—
204C2×Dic13—41no—
205C2×Dic13—44no—
206C2×Dic13—42no—
207C2×Dic13—42no—
208C2×Dic13—84no—
209C2×Dic13—84no—
210C2×Dic13—82no—
211C2×Dic13—82no—
212C24×C4C2×D1311yescharacteristic
213C22×C4⋊C4—132no—
214C22×C4⋊C4—261no—
215C22×C22⋊C4—131no—
216C22×C22⋊C4—132no—
217C22×C22⋊C4—131no—
218C22×C22⋊C4C2×D1312yes—
219#385—261no—
220#385—261no—
221#385—262no—
222#380—264no—
223C2×#95—22no—
224C2×#95—132no—
225C2×#95—261no—
226#342—264no—
227#342—264no—
228C22×C13—22no—
229C22×C13—22no—
230C22×C13—22no—
231C22×C13—22no—
232C22×C13—22no—
233C22×C13—22no—
234C22×C13—21no—
235C22×C13—22no—
236C22×C13—21no—
237C22×C13—22no—
238C22×C13—21no—
239C22×C13—22no—
240C22×C13—22no—
241C22×C13—21no—
242C22×C13—22no—
243C22×C13—24no—
244C22×C13—24no—
245C22×C13—22no—
246C22×C13—42no—
247C22×C13—42no—
248C22×C13—42no—
249C22×C13—42no—
250C22×C13—42no—
251C22×C13—42no—
252C22×C13—42no—
253C22×C13—42no—
254C22×C13#38011yescharacteristic
255C22×C13#38611yescharacteristic
256C22×C13#38712yes—
257C22×C13#38912yes—
258C22×C13#39111yescharacteristic
259C22×C13#39411yescharacteristic
260C22×C13#39511yescharacteristic
261C22×C13#39612yes—
262C22×C13#39811yescharacteristic
263C22×C13#39812yes—
264C22×C13#40011yescharacteristic
265C22×C13C2×#9912yes—
266C22×C13#41012yes—
267C4×C13—24no—
268C4×C13—42no—
269C4×C13—84no—
270Dic13—44no—
271Dic13—84no—
272Dic13—81no—
273Dic13—81no—
274C25C22×D1311yescharacteristic
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—44no—
279C23×C4—132no—
280C23×C4—131no—
281C23×C4—131no—
282C23×C4—262no—
283C23×C4C4×D1312yes—
284C23×C4D5211yescharacteristic
285C23×C4D5211yescharacteristic
286C23×C4C22⋊D1312yes—
287C2×C4⋊C4—264no—
288C2×C4⋊C4—262no—
289C2×C4⋊C4—262no—
290C2×C4⋊C4—524no—
291C2×C4⋊C4—524no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—132no—
298C2×C22⋊C4—132no—
299C2×C22⋊C4—134no—
300C2×C22⋊C4—261no—
301C2×C22⋊C4—261no—
302C2×C22⋊C4—261no—
303C2×C22⋊C4—261no—
304C2×C22⋊C4—262no—
305C2×C22⋊C4—262no—
306C2×C22⋊C4—262no—
307C2×C22⋊C4—262no—
308C2×C22⋊C4—261no—
309C2×C22⋊C4—262no—
310C2×C22⋊C4—262no—
311C2×C22⋊C4—262no—
312C2×C22⋊C4—261no—
313C2×C22⋊C4Dic2614yes—
314#95—44no—
315#95—264no—
316#95—262no—
317#95—262no—
318C2×C13—21no—
319C2×C13—22no—
320C2×C13—22no—
321C2×C13—22no—
322C2×C13—21no—
323C2×C13—21no—
324C2×C13—22no—
325C2×C13—21no—
326C2×C13#144111yescharacteristic
327C2×C13#179912yes—
328C2×C13#189811yescharacteristic
329C2×C13#189911yescharacteristic
330C2×C13#199612yes—
331C24—42no—
332C24—42no—
333C24C2×Dic2612yes—
334C24C2×C4×D1311yescharacteristic
335C24C2×D5211yescharacteristic
336C24#612712yes—
337C24D4×D1311yescharacteristic
338C24D4×D1312yes—
339C24#612911yescharacteristic
340C24#612912yes—
341C24Q8×D1311yescharacteristic
342C24#613111yescharacteristic
343C24C2×C22⋊D1311yescharacteristic
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—48no—
358C22×C4—48no—
359C22×C4—44no—
360C22×C4—44no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—134no—
364C22×C4—262no—
365C22×C4—262no—
366C22×C4—264no—
367C22×C4—261no—
368C22×C4—261no—
369C22×C4—262no—
370C22×C4—262no—
371C22×C4—522no—
372C22×C4—522no—
373C22×C4—524no—
374C22×C4—524no—
375C22×C4—522no—
376C22×C4—522no—
377C22×C4—522no—
378C22×C4—522no—
379C22×C4#610312yes—
380C22×C4#610312yes—
381C4⋊C4—524no—
382C4⋊C4—528no—
383C4⋊C4—524no—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—42no—
387C22⋊C4—42no—
388C22⋊C4—262no—
389C22⋊C4—262no—
390C22⋊C4—262no—
391C22⋊C4—262no—
392C22⋊C4—264no—
393C22⋊C4—264no—
394C22⋊C4—521no—
395C22⋊C4—522no—
396C22⋊C4—521no—
397C22⋊C4—522no—
398C22⋊C4—522no—
399C13#1120311yescharacteristic, complemented, Sylow
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23—42no—
407C23—42no—
408C23—44no—
409C23—44no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23—42no—
416C23C4×Dic2612yes—
417C23#8812311yescharacteristic
418C23#8812911yescharacteristic
419C23#8813212yes—
420C23#8813212yes—
421C23#8813312yes—
422C23#8813512yes—
423C23#8813611yescharacteristic
424C23#8813812yes—
425C23#8814011yescharacteristic
426C23#8814212yes—
427C23#8814312yes—
428C23#8814412yes—
429C23C4⋊C4×D1311yescharacteristic
430C23#8814611yescharacteristic
431C23#8814812yes—
432C23#8814911yescharacteristic
433C23#8815111yescharacteristic
434C23#8817812yes—
435C23C2×#610311yescharacteristic
436C23#8819211yescharacteristic
437C23#8819312yes—
438C23#8820011yescharacteristic
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—48no—
447C2×C4—48no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—48no—
451C2×C4—44no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4—84no—
455C2×C4—264no—
456C2×C4—524no—
457C2×C4—522no—
458C2×C4—522no—
459C2×C4—524no—
460C2×C4—524no—
461C2×C4—524no—
462C2×C4—522no—
463C2×C4—524no—
464C2×C4—522no—
465C2×C4—521no—
466C2×C4—521no—
467C2×C4—1044no—
468C2×C4—1044no—
469C2×C4—1042no—
470C2×C4—1042no—
471C2×C4#8804614yes—
472C22—21no—
473C22—21no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—21no—
478C22—22no—
479C22—21no—
480C22—24no—
481C22—22no—
482C22—24no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22#1171830812yes—
499C22#1171831612yes—
500C22#1171831711yescharacteristic
501C22#1171832011yescharacteristic
502C22#1171832211yescharacteristic
503C22#1171833311yescharacteristic
504C22#1171859011yescharacteristic
505C22#1171860912yes—
506C22C2×#8804612yes—
507C22#1171861911yescharacteristic
508C22#1171864512yes—
509C22#1171864811yescharacteristic
510C22#1171866712yes—
511C4—24no—
512C4—42no—
513C4—84no—
514C4—524no—
515C4—1044no—
516C4—1041no—
517C4—1041no—
518C2—22no—
519C2—21no—
520C2—22no—
521C2—22no—
522C2—21no—
523C2—21no—
524C2—21no—
525C2—22no—
526C2#1311309011yescharacteristic
527C2#1311482112yes—
528C2#1311528711yescharacteristic
529C2#1311529211yescharacteristic
530C2#1311582112yes—
subgroupG/H
centerC23C2×#6103
commutatorC24×C13C22×C4
FrattiniC25C22×D13
FittingC13×C22⋊#95C2
socleC23×C13C2×C22⋊C4
prime radical, cosocleC25×C13C23
hypercenterC22⋊#95D13
hypocenterC13#11203
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
12. C22×#6101C4semidirect
19. C2×#88071C4semidirect
116. C22×Dic13C4⋊C4semidirect
399. C13#11203semidirect

Maximal subgroups

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

subgroupindex
C2×#117188712
C2×#117188732
C2×#117181192
C13×C22⋊#952
#1120313