Finite Group Databasebeta

← #15780419

Subgroups — #15780419

Order 3328.

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

normal subgroups only

This group has 894 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×#11718131C212yesmaximal, complemented
3#13114757C211yesmaximal, characteristic
4#13112954C212yesmaximal, complemented
5C13×#2405C211yesmaximal, characteristic
6C23×D4×C13C2211yescharacteristic
7C2×C13×#123C411yescharacteristic, complemented
8C2×C13×#123C2211yescharacteristic
9C22×C13×C22⋊C4C411yescharacteristic, complemented
10C22×C22⋊Dic13—21no—
11C13×#394—21no—
12C13×#394—21no—
13C13×#386C411yescharacteristic, complemented
14C13×#386C2211yescharacteristic
15C13×#385—21no—
16C13×#379—21no—
17C13×#379C411yescharacteristic, complemented
18C2×#88074—21no—
19C2×#88074—24no—
20C2×#88074C2212yes—
21C2×#88073—21no—
22C2×#88073C2212yes—
23#11718868—21no—
24#11718131—24no—
25C25×C13C2×C411yescharacteristic
26C25×C13D411yescharacteristic
27C22×D4×C13—22no—
28C22×D4×C13—22no—
29C22×D4×C13—41no—
30C22×D4×C13—41no—
31C22×D4×C13—42no—
32C22×D4×C13C2×C411yescharacteristic
33C22×D4×C13D411yescharacteristic
34C22×D4×C13D411yescharacteristic
35C22×D4×C13C2311yescharacteristic
36C23×C4×C13C2×C411yescharacteristic, complemented
37C23×C4×C13C2×C411yescharacteristic, complemented
38C23×C4×C13D411yescharacteristic
39C23×Dic13—41no—
40C13×#123—22no—
41C13×#123—22no—
42C13×#123—42no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C22⋊C4—21no—
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—41no—
54C2×C13×C22⋊C4—41no—
55C2×C13×C22⋊C4C2×C411yescharacteristic, complemented
56C2×C13×C22⋊C4C2×C411yescharacteristic, complemented
57C2×C22⋊Dic13—24no—
58C2×C22⋊Dic13—22no—
59C2×C22⋊Dic13—41no—
60C2×C22⋊Dic13—42no—
61C2×#6099—22no—
62C13×#95—21no—
63C13×#95—21no—
64#88074—24no—
65#88074—22no—
66#88074D414yes—
67#88073—22no—
68#88073—22no—
69#88073—42no—
70C22⋊#1055—41no—
71C22⋊#1055—41no—
72#13084—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×C13C22×C411yescharacteristic
90C24×C13C2×D411yescharacteristic
91C2×D4×C13—22no—
92C2×D4×C13—22no—
93C2×D4×C13—22no—
94C2×D4×C13—21no—
95C2×D4×C13—21no—
96C2×D4×C13—22no—
97C2×D4×C13—41no—
98C2×D4×C13—41no—
99C2×D4×C13—41no—
100C2×D4×C13—41no—
101C2×D4×C13—41no—
102C2×D4×C13—41no—
103C2×D4×C13—44no—
104C2×D4×C13—44no—
105C2×D4×C13—44no—
106C2×D4×C13—44no—
107C2×D4×C13C2×D412yes—
108C2×D4×C13#4112yes—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—22no—
117C22×C4×C13—41no—
118C22×C4×C13—41no—
119C22×C4×C13—41no—
120C22×C4×C13—41no—
121C22×C4×C13—81no—
122C22×C4×C13C22⋊C411yescharacteristic
123C22×C4×C13C2×D411yescharacteristic
124C22×Dic13—44no—
125C22×Dic13—42no—
126C22×Dic13—82no—
127C22×Dic13—82no—
128C13×C4⋊C4—42no—
129C13×C4⋊C4—42no—
130C13×C22⋊C4—22no—
131C13×C22⋊C4—42no—
132C13×C22⋊C4—42no—
133C13×C22⋊C4—41no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—42no—
136C13×C22⋊C4—41no—
137C13×C22⋊C4—41no—
138C13×C22⋊C4—41no—
139C13×C22⋊C4—81no—
140C13×C22⋊C4—81no—
141C13×C22⋊C4—81no—
142C22⋊Dic13—24no—
143C22⋊Dic13—44no—
144C22⋊Dic13—42no—
145#6099—42no—
146#6099—42no—
147C2×#1055—42no—
148C22×#99—131no—
149#2405D1311yescharacteristic
150C2×#352—132no—
151#1783—131no—
152#1390—132no—
153C23×C13—22no—
154C23×C13—22no—
155C23×C13—22no—
156C23×C13—22no—
157C23×C13—22no—
158C23×C13—21no—
159C23×C13—21no—
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—41no—
170C23×C13—42no—
171C23×C13—42no—
172C23×C13—42no—
173C23×C13—41no—
174C23×C13—41no—
175C23×C13—41no—
176C23×C13—41no—
177C23×C13—41no—
178C23×C13—41no—
179C23×C13—42no—
180C23×C13—41no—
181C23×C13—41no—
182C23×C13—42no—
183C23×C13—42no—
184C23×C13—81no—
185C23×C13—81no—
186C23×C13—81no—
187C23×C13—81no—
188C23×C13—84no—
189C23×C13—82no—
190C23×C13—82no—
191C23×C13—84no—
192C23×C13—84no—
193C23×C13#9911yescharacteristic
194C23×C13#9911yescharacteristic
195C23×C13#9912yes—
196C23×C13C2×C22⋊C411yescharacteristic
197C23×C13C4×D412yes—
198C23×C13#12011yescharacteristic
199C23×C13#12311yescharacteristic
200D4×C13—42no—
201D4×C13—42no—
202D4×C13—44no—
203D4×C13—44no—
204D4×C13—42no—
205D4×C13—42no—
206C2×C4×C13—21no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
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—82no—
226C2×C4×C13—82no—
227C2×C4×C13#12112yes—
228C2×Dic13—44no—
229C2×Dic13—88no—
230C2×Dic13—82no—
231C2×Dic13—82no—
232#1055—82no—
233C23×D4C2×D1311yescharacteristic
234C2×#123Dic1311yescharacteristic, complemented
235C2×#123C2×D1311yescharacteristic
236C22×C22⋊C4—261no—
237C22×C22⋊C4Dic1311yescharacteristic, complemented
238C2×#100—132no—
239C2×#100—261no—
240C2×#99—132no—
241C2×#99—264no—
242C2×#99—261no—
243#407—261no—
244#394—21no—
245#394—21no—
246#386Dic1311yescharacteristic, complemented
247#386C2×D1311yescharacteristic
248#385—21no—
249#379—21no—
250#379Dic1311yescharacteristic, complemented
251#352—264no—
252C22×C13—21no—
253C22×C13—21no—
254C22×C13—21no—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13—21no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—22no—
261C22×C13—22no—
262C22×C13—21no—
263C22×C13—42no—
264C22×C13—42no—
265C22×C13—42no—
266C22×C13—42no—
267C22×C13—41no—
268C22×C13—41no—
269C22×C13—44no—
270C22×C13—42no—
271C22×C13—44no—
272C22×C13—41no—
273C22×C13—41no—
274C22×C13—41no—
275C22×C13—41no—
276C22×C13—41no—
277C22×C13—41no—
278C22×C13—41no—
279C22×C13—41no—
280C22×C13—41no—
281C22×C13—81no—
282C22×C13—81no—
283C22×C13—84no—
284C22×C13—81no—
285C22×C13—81no—
286C22×C13—82no—
287C22×C13—82no—
288C22×C13—84no—
289C22×C13#35212yescomplemented
290C22×C13#38611yescharacteristic
291C22×C13C2×#9911yescharacteristic
292C22×C13C2×#9911yescharacteristic
293C4×C13—22no—
294C4×C13—41no—
295C4×C13—81no—
296C4×C13—81no—
297C4×C13—81no—
298C4×C13—81no—
299Dic13—84no—
300C25C2×Dic1311yescharacteristic
301C25C22⋊D1311yescharacteristic
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—41no—
305C22×D4—41no—
306C22×D4—42no—
307C22×D4C2×Dic1311yescharacteristic
308C22×D4C22⋊D1311yescharacteristic
309C22×D4C22⋊D1311yescharacteristic
310C22×D4C22×D1311yescharacteristic
311C23×C4—521no—
312C23×C4C2×Dic1311yescharacteristic, complemented
313C23×C4C2×Dic1311yescharacteristic, complemented
314C23×C4C22⋊D1311yescharacteristic
315C2×M16—262no—
316#123—22no—
317#123—22no—
318#123—42no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—41no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—264no—
332C2×C22⋊C4—262no—
333C2×C22⋊C4—521no—
334C2×C22⋊C4—522no—
335C2×C22⋊C4C2×Dic1311yescharacteristic, complemented
336C2×C22⋊C4C2×Dic1311yescharacteristic, complemented
337#100—262no—
338#100—262no—
339#100—522no—
340#99—134no—
341#99—264no—
342#99—262no—
343C22⋊C8—521no—
344C22⋊C8—521no—
345#95—21no—
346#95—21no—
347C2×C13—21no—
348C2×C13—21no—
349C2×C13—22no—
350C2×C13—41no—
351C2×C13—41no—
352C2×C13—42no—
353C2×C13—41no—
354C2×C13—42no—
355C2×C13—81no—
356C2×C13#189811yescharacteristic
357C2×C13C2×#35211yescharacteristic
358C2×C13#212111yescharacteristic
359C24—21no—
360C24—22no—
361C24—21no—
362C24—21no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—22no—
367C24—41no—
368C24—42no—
369C24—42no—
370C24—81no—
371C24—81no—
372C24C22⋊Dic1311yescharacteristic
373C24C22⋊Dic1311yescharacteristic
374C24C22⋊Dic1311yescharacteristic
375C24C22×Dic1311yescharacteristic
376C24C2×C22⋊D1311yescharacteristic
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—44no—
390C2×D4—44no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4D4×D1312yes—
394C2×D4#612912yes—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—81no—
408C22×C4—524no—
409C22×C4—522no—
410C22×C4—1042no—
411C22×C4—1042no—
412C22×C4C22⋊Dic1311yescharacteristic
413C22×C4C2×C22⋊D1311yescharacteristic
414M16—522no—
415M16—522no—
416C2×C8—522no—
417C4⋊C4—42no—
418C4⋊C4—42no—
419C22⋊C4—22no—
420C22⋊C4—42no—
421C22⋊C4—42no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—42no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—81no—
429C22⋊C4—81no—
430C22⋊C4—81no—
431C22⋊C4—264no—
432C22⋊C4—524no—
433C22⋊C4—522no—
434C13#1308411yescharacteristic, complemented, Sylow
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—22no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—41no—
452C23—42no—
453C23—42no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—42no—
462C23—41no—
463C23—41no—
464C23—42no—
465C23—42no—
466C23—81no—
467C23—81no—
468C23—81no—
469C23—81no—
470C23—84no—
471C23—82no—
472C23—82no—
473C23—84no—
474C23—84no—
475C23#8807411yescharacteristic
476C23#8807411yescharacteristic
477C23#8807412yes—
478C23D4×Dic1312yes—
479C23#8818911yescharacteristic
480C23#8819111yescharacteristic
481C23C2×C22⋊Dic1311yescharacteristic
482D4—42no—
483D4—42no—
484D4—44no—
485D4—44no—
486D4—42no—
487D4—42no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—82no—
508C2×C4—82no—
509C2×C4—524no—
510C2×C4—1048no—
511C2×C4—1042no—
512C2×C4—1042no—
513C2×C4#8819312yes—
514C8—1042no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—22no—
523C22—21no—
524C22—22no—
525C22—21no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—41no—
531C22—41no—
532C22—44no—
533C22—42no—
534C22—44no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—81no—
545C22—81no—
546C22—84no—
547C22—81no—
548C22—81no—
549C22—82no—
550C22—82no—
551C22—84no—
552C22#1171813112yescomplemented
553C22C2×#8807411yescharacteristic
554C22C2×#8807411yescharacteristic
555C22#1171888111yescharacteristic
556C4—22no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—1044no—
563C2—21no—
564C2—21no—
565C2—22no—
566C2—41no—
567C2—41no—
568C2—42no—
569C2—41no—
570C2—42no—
571C2—81no—
572C2#1311529011yescharacteristic
573C2C2×#1171813111yescharacteristic
574C2#1311648211yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2405C2
socleC22×C13C2×#99
prime radicalC23×D4×C13C22
cosocleC22×D4×C13C23
hypercenter#2405D13
hypocenterC13#13084
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ #2405

Complements

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

NH ≅ G/Ntype
2. C2×#11718131C2semidirect
4. #13112954C2semidirect
7. C2×C13×#123C4semidirect
9. C22×C13×C22⋊C4C4semidirect
13. C13×#386C4semidirect
17. C13×#379C4semidirect
36. C23×C4×C13C2×C4semidirect
37. C23×C4×C13C2×C4semidirect
55. C2×C13×C22⋊C4C2×C4semidirect
56. C2×C13×C22⋊C4C2×C4semidirect
234. C2×#123Dic13semidirect
237. C22×C22⋊C4Dic13semidirect
246. #386Dic13semidirect
250. #379Dic13semidirect
289. C22×C13#352semidirect
312. C23×C4C2×Dic13semidirect
313. C23×C4C2×Dic13semidirect
335. C2×C22⋊C4C2×Dic13semidirect
336. C2×C22⋊C4C2×Dic13semidirect
434. C13#13084semidirect
552. C22#11718131semidirect

Maximal subgroups

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

subgroupindex
C22×#880742
C2×#117181312
#131147572
#131129542
C13×#24052
#1308413