Finite Group Databasebeta

← #15780449

Subgroups — #15780449

Order 3328.

910 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88074C211yesmaximal, characteristic
2C2×#11718133C212yesmaximal, complemented
3#13114751C211yesmaximal, characteristic
4#13112961C212yesmaximal, complemented
5C13×#2435C211yesmaximal, characteristic
6C23×D4×C13C2211yescharacteristic
7C2×C13×#124C411yescharacteristic, complemented
8C2×C13×#124C2211yescharacteristic
9C2×C13×C22⋊Q8C411yescharacteristic, complemented
10C22×C22⋊Dic13—21no—
11C13×#394—21no—
12C13×#394—21no—
13C13×#390C411yescharacteristic, complemented
14C13×#390C2211yescharacteristic
15C13×#379—21no—
16C13×#379—21no—
17C4×C13×C22⋊C4C411yescharacteristic, complemented
18#11718908—21no—
19C2×#88074—21no—
20C2×#88074—24no—
21C2×#88074—21no—
22C2×#88074C2212yes—
23C2×#88074C2212yes—
24#11718133—24no—
25C25×C13D411yescharacteristic
26C25×C13D411yescharacteristic
27C22×Q8×C13C2×C411yescharacteristic, complemented
28C22×D4×C13—22no—
29C22×D4×C13—22no—
30C22×D4×C13—41no—
31C22×D4×C13—41no—
32C22×D4×C13—42no—
33C22×D4×C13C2×C411yescharacteristic
34C22×D4×C13D411yescharacteristic
35C22×D4×C13D411yescharacteristic
36C22×D4×C13C2311yescharacteristic
37C23×C4×C13C2×C411yescharacteristic
38C23×Dic13—41no—
39C13×#124—22no—
40C13×#124—22no—
41C13×#124—42no—
42C13×C22⋊Q8—41no—
43C13×C22⋊Q8—41no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C42×C13C2×C411yescharacteristic, complemented
57C2×C42×C13C2×C411yescharacteristic, complemented
58C2×C22⋊Dic13—24no—
59C2×C22⋊Dic13—22no—
60C2×C22⋊Dic13—22no—
61C2×C22⋊Dic13—41no—
62C2×C22⋊Dic13—42no—
63C2×C22⋊Dic13—41no—
64C2×C22⋊Dic13—41no—
65C13×#95—21no—
66#88074—24no—
67#88074—22no—
68#88074—22no—
69#88074—22no—
70#88074—42no—
71#88074D414yes—
72#13090—131nomaximal, Sylow
73C24×C13—21no—
74C24×C13—22no—
75C24×C13—21no—
76C24×C13—21no—
77C24×C13—21no—
78C24×C13—21no—
79C24×C13—21no—
80C24×C13—22no—
81C24×C13—41no—
82C24×C13—42no—
83C24×C13—42no—
84C24×C13—81no—
85C24×C13—81no—
86C24×C13C22⋊C411yescharacteristic
87C24×C13C22⋊C411yescharacteristic
88C24×C13C22⋊C411yescharacteristic
89C24×C13C2×D411yescharacteristic
90C24×C13C2×D411yescharacteristic
91C2×Q8×C13—22no—
92C2×Q8×C13—41no—
93C2×Q8×C13—41no—
94C2×D4×C13—22no—
95C2×D4×C13—22no—
96C2×D4×C13—21no—
97C2×D4×C13—22no—
98C2×D4×C13—21no—
99C2×D4×C13—22no—
100C2×D4×C13—41no—
101C2×D4×C13—41no—
102C2×D4×C13—41no—
103C2×D4×C13—41no—
104C2×D4×C13—41no—
105C2×D4×C13—41no—
106C2×D4×C13—44no—
107C2×D4×C13—44no—
108C2×D4×C13—44no—
109C2×D4×C13—44no—
110C2×D4×C13C2×D412yes—
111C2×D4×C13#4112yes—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—41no—
120C22×C4×C13C22⋊C411yescharacteristic
121C22×C4×C13C22×C411yescharacteristic
122C22×Dic13—44no—
123C22×Dic13—42no—
124C22×Dic13—42no—
125C22×Dic13—82no—
126C22×Dic13—82no—
127C13×C4⋊C4—41no—
128C13×C4⋊C4—42no—
129C13×C22⋊C4—42no—
130C13×C22⋊C4—42no—
131C13×C22⋊C4—41no—
132C13×C22⋊C4—41no—
133C13×C22⋊C4—42no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—42no—
136C13×C22⋊C4—41no—
137C13×C22⋊C4—81no—
138C13×C22⋊C4—81no—
139C13×C22⋊C4—81no—
140C13×C22⋊C4—81no—
141C42×C13—22no—
142C42×C13—41no—
143C22⋊Dic13—24no—
144C22⋊Dic13—44no—
145C22⋊Dic13—42no—
146C22⋊Dic13—42no—
147C22⋊Dic13—42no—
148C22⋊Dic13—82no—
149C22⋊Dic13—82no—
150C22×#99—131no—
151#2435D1311yescharacteristic
152C2×#354—132no—
153#1781—131no—
154#1393—132no—
155C23×C13—22no—
156C23×C13—22no—
157C23×C13—22no—
158C23×C13—22no—
159C23×C13—22no—
160C23×C13—21no—
161C23×C13—21no—
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—41no—
172C23×C13—42no—
173C23×C13—42no—
174C23×C13—42no—
175C23×C13—41no—
176C23×C13—41no—
177C23×C13—41no—
178C23×C13—41no—
179C23×C13—41no—
180C23×C13—41no—
181C23×C13—41no—
182C23×C13—41no—
183C23×C13—42no—
184C23×C13—42no—
185C23×C13—42no—
186C23×C13—81no—
187C23×C13—81no—
188C23×C13—81no—
189C23×C13—81no—
190C23×C13—84no—
191C23×C13—82no—
192C23×C13—82no—
193C23×C13—84no—
194C23×C13—84no—
195C23×C13#9911yescharacteristic
196C23×C13#9911yescharacteristic
197C23×C13#9912yes—
198C23×C13C2×C22⋊C411yescharacteristic
199C23×C13#12011yescharacteristic
200C23×C13#12112yes—
201C23×C13#12311yescharacteristic
202Q8×C13—82no—
203D4×C13—42no—
204D4×C13—42no—
205D4×C13—44no—
206D4×C13—44no—
207D4×C13—42no—
208D4×C13—42no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13C4×D412yes—
229C2×Dic13—44no—
230C2×Dic13—88no—
231C2×Dic13—82no—
232C2×Dic13—82no—
233C2×Dic13—82no—
234C2×Dic13—82no—
235C2×Dic13—82no—
236C23×D4C2×D1311yescharacteristic
237C2×#124Dic1311yescharacteristic, complemented
238C2×#124C2×D1311yescharacteristic
239C2×C22⋊Q8Dic1311yescharacteristic, complemented
240C22×C22⋊C4—261no—
241C2×#99—132no—
242C2×#99—132no—
243C2×#99—264no—
244C2×#99—261no—
245C2×#99—261no—
246#394—21no—
247#394—21no—
248#390Dic1311yescharacteristic, complemented
249#390C2×D1311yescharacteristic
250#379—21no—
251#379—21no—
252#379—261no—
253C4×C22⋊C4Dic1311yescharacteristic, complemented
254#354—264no—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13—21no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—22no—
263C22×C13—21no—
264C22×C13—22no—
265C22×C13—21no—
266C22×C13—42no—
267C22×C13—42no—
268C22×C13—42no—
269C22×C13—41no—
270C22×C13—42no—
271C22×C13—41no—
272C22×C13—44no—
273C22×C13—44no—
274C22×C13—42no—
275C22×C13—41no—
276C22×C13—41no—
277C22×C13—41no—
278C22×C13—41no—
279C22×C13—41no—
280C22×C13—41no—
281C22×C13—41no—
282C22×C13—41no—
283C22×C13—41no—
284C22×C13—81no—
285C22×C13—81no—
286C22×C13—81no—
287C22×C13—84no—
288C22×C13—81no—
289C22×C13—82no—
290C22×C13—82no—
291C22×C13—84no—
292C22×C13#35412yescomplemented
293C22×C13#38611yescharacteristic
294C22×C13C2×#9911yescharacteristic
295C22×C13C2×#9911yescharacteristic
296C4×C13—22no—
297C4×C13—41no—
298C4×C13—81no—
299C4×C13—81no—
300C4×C13—81no—
301C4×C13—81no—
302Dic13—84no—
303Dic13—162no—
304C25C22⋊D1311yescharacteristic
305C25C22⋊D1311yescharacteristic
306C22×Q8C2×Dic1311yescharacteristic, complemented
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—41no—
310C22×D4—41no—
311C22×D4—42no—
312C22×D4C2×Dic1311yescharacteristic
313C22×D4C22⋊D1311yescharacteristic
314C22×D4C22⋊D1311yescharacteristic
315C22×D4C22×D1311yescharacteristic
316C23×C4—521no—
317C23×C4C2×Dic1311yescharacteristic
318#124—22no—
319#124—22no—
320#124—42no—
321C22⋊Q8—41no—
322C22⋊Q8—41no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4C2×Dic1311yescharacteristic, complemented
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—264no—
336C2×C22⋊C4—262no—
337C2×C22⋊C4—262no—
338C2×C22⋊C4—521no—
339C2×C22⋊C4—522no—
340C2×C22⋊C4—521no—
341C2×C22⋊C4—521no—
342C2×C42C2×Dic1311yescharacteristic, complemented
343C2×C42C2×Dic1311yescharacteristic, complemented
344#99—134no—
345#99—264no—
346#99—262no—
347#99—262no—
348#99—262no—
349#99—522no—
350#95—21no—
351C2×C13—21no—
352C2×C13—21no—
353C2×C13—22no—
354C2×C13—41no—
355C2×C13—42no—
356C2×C13—41no—
357C2×C13—42no—
358C2×C13—41no—
359C2×C13—81no—
360C2×C13#189811yescharacteristic
361C2×C13C2×#35411yescharacteristic
362C2×C13#212711yescharacteristic
363C24—21no—
364C24—22no—
365C24—21no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—22no—
371C24—41no—
372C24—42no—
373C24—42no—
374C24—81no—
375C24—81no—
376C24C22⋊Dic1311yescharacteristic
377C24C22⋊Dic1311yescharacteristic
378C24C22⋊Dic1311yescharacteristic
379C24C2×C22⋊D1311yescharacteristic
380C24C2×C22⋊D1311yescharacteristic
381C2×Q8—22no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—44no—
397C2×D4—44no—
398C2×D4—44no—
399C2×D4—44no—
400C2×D4D4×D1312yes—
401C2×D4#612912yes—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—41no—
410C22×C4—524no—
411C22×C4—522no—
412C22×C4—522no—
413C22×C4—1042no—
414C22×C4—1042no—
415C22×C4C22⋊Dic1311yescharacteristic
416C22×C4C22×Dic1311yescharacteristic
417C4⋊C4—41no—
418C4⋊C4—42no—
419C22⋊C4—42no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—42no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—42no—
427C22⋊C4—81no—
428C22⋊C4—81no—
429C22⋊C4—81no—
430C22⋊C4—81no—
431C22⋊C4—264no—
432C22⋊C4—524no—
433C22⋊C4—522no—
434C22⋊C4—522no—
435C22⋊C4—522no—
436C22⋊C4—1042no—
437C22⋊C4—1042no—
438C42—22no—
439C42—41no—
440C13#1309011yescharacteristic, complemented, Sylow
441C23—22no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—22no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—41no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—81no—
473C23—81no—
474C23—81no—
475C23—81no—
476C23—84no—
477C23—82no—
478C23—82no—
479C23—84no—
480C23—84no—
481C23#8807411yescharacteristic
482C23#8807411yescharacteristic
483C23#8807412yes—
484C23#8818911yescharacteristic
485C23#8819111yescharacteristic
486C23#8819312yes—
487C23C2×C22⋊Dic1311yescharacteristic
488Q8—82no—
489D4—42no—
490D4—42no—
491D4—44no—
492D4—44no—
493D4—42no—
494D4—42no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—524no—
515C2×C4—1048no—
516C2×C4—1042no—
517C2×C4—1042no—
518C2×C4—1042no—
519C2×C4—1042no—
520C2×C4—1042no—
521C2×C4D4×Dic1312yes—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—22no—
531C22—22no—
532C22—21no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22—41no—
538C22—42no—
539C22—44no—
540C22—44no—
541C22—42no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—84no—
555C22—81no—
556C22—82no—
557C22—82no—
558C22—84no—
559C22#1171813312yescomplemented
560C22C2×#8807411yescharacteristic
561C22C2×#8807411yescharacteristic
562C22#1171888111yescharacteristic
563C4—22no—
564C4—41no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—1044no—
570C4—2082no—
571C2—21no—
572C2—21no—
573C2—22no—
574C2—41no—
575C2—42no—
576C2—41no—
577C2—42no—
578C2—41no—
579C2—81no—
580C2#1311529011yescharacteristic
581C2C2×#1171813311yescharacteristic
582C2#1311650511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2435C2
socleC22×C13C2×#99
prime radicalC23×D4×C13C22
cosocleC22×D4×C13C23
hypercenter#2435D13
hypocenterC13#13090
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ #2435

Complements

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

NH ≅ G/Ntype
2. C2×#11718133C2semidirect
4. #13112961C2semidirect
7. C2×C13×#124C4semidirect
9. C2×C13×C22⋊Q8C4semidirect
13. C13×#390C4semidirect
17. C4×C13×C22⋊C4C4semidirect
27. C22×Q8×C13C2×C4semidirect
45. C2×C13×C4⋊C4C2×C4semidirect
56. C2×C42×C13C2×C4semidirect
57. C2×C42×C13C2×C4semidirect
237. C2×#124Dic13semidirect
239. C2×C22⋊Q8Dic13semidirect
248. #390Dic13semidirect
253. C4×C22⋊C4Dic13semidirect
292. C22×C13#354semidirect
306. C22×Q8C2×Dic13semidirect
324. C2×C4⋊C4C2×Dic13semidirect
342. C2×C42C2×Dic13semidirect
343. C2×C42C2×Dic13semidirect
440. C13#13090semidirect
559. C22#11718133semidirect

Maximal subgroups

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

subgroupindex
C22×#880742
C2×#117181332
#131147512
#131129612
C13×#24352
#1309013