Finite Group Databasebeta

← #15870627

Subgroups — #15870627

Order 3328.

868 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718552C211yesmaximal, characteristic
2#13117573C211yesmaximal, characteristic, complemented
3#13117196C211yesmaximal, characteristic
4#13115792C211yesmaximal, characteristic, complemented
5#13115596C211yesmaximal, characteristic, complemented
6#13115412C211yesmaximal, characteristic, complemented
7#13115409C211yesmaximal, characteristic, complemented
8#13115098C211yesmaximal, characteristic
9#13115094C211yesmaximal, characteristic
10#13114835C211yesmaximal, characteristic
11C4×#88048C211yesmaximal, characteristic, complemented
12#13114696C211yesmaximal, characteristic, complemented
13#13114662C211yesmaximal, characteristic
14C4×#88049C211yesmaximal, characteristic
15C13×#1776C211yesmaximal, characteristic, complemented
16C2×#88147C2211yescharacteristic
17C2×#88147C2211yescharacteristic
18C2×#88144C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C2×C13×#107C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C2×C13×#97C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C4×C13×C4⋊C4C2211yescharacteristic
25C2×#88061C2211yescharacteristic
26C2×#88061C2211yescharacteristic
27C2×#88054C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29#11718646C2211yescharacteristic
30#11718637C2211yescharacteristic
31C4⋊C4×Dic13C2211yescharacteristic
32C4⋊C4×Dic13C2211yescharacteristic
33#11718634C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C4×#6103—21no—
39C4×#6103—21no—
40C4×C4⋊Dic13C2211yescharacteristic
41#11718594—21no—
42#11718593C2211yescharacteristic
43#11718589—21no—
44C2×C4×#1055C2211yescharacteristic
45#11718552C418yescomplemented
46#11718327—21no—
47D13×#95—21no—
48#11718315—21no—
49#11718308—21no—
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C22×C4×D13—21no—
63C22×C4×D13—21no—
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C42×C13—21no—
71C2×C42×C13—21no—
72C2×C42×C13C2311yescharacteristic
73C2×#6103—21no—
74C2×#6103—21no—
75C2×#6103—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×#6101—21no—
82C2×#6101—21no—
83C2×#6101—21no—
84C2×#6101—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13C2311yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92#88147—22no—
93#88147—22no—
94#88147—22no—
95#88147C2×C414yes—
96#88144—22no—
97#88144C2×C414yescomplemented
98C4×D52—22no—
99C4×D52Q814yes—
100C13×#107C2×C414yescomplemented
101C13×#106—22no—
102C13×#97—22no—
103C13×#95—21no—
104C13×#95—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071D411yescharacteristic
111#88071D411yescharacteristic
112#88071D411yescharacteristic
113#88071D411yescharacteristic
114#88061—22no—
115#88061C2×C414yes—
116#88054—22no—
117#88054C2×C414yescomplemented
118#88049—22no—
119#88049C2×C414yes—
120#88048—22no—
121#88048C2×C414yescomplemented
122C4×#1055—22no—
123#21619—131nomaximal, Sylow
124C23×D13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2411yescharacteristic
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13C2×D411yescharacteristic
136C22×Dic13C2×D411yescharacteristic
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×D411yescharacteristic
139C2×D52—21no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52C22×C412yes—
143C2×D52C2×Q812yes—
144C2×D52#4112yes—
145C2×C4×D13—24no—
146C2×C4×D13—24no—
147C2×C4×D13—24no—
148C2×C4×D13—81no—
149C2×C4×D13—81no—
150C2×C4×D13—81no—
151C2×C4×D13—81no—
152C2×C4×D13—81no—
153C2×C4×D13—81no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13C22×C412yes—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4C22×C412yes—
166C13×C4⋊C4C22×C412yes—
167C13×C4⋊C4#4112yes—
168C42×C13—81no—
169C42×C13—81no—
170C42×C13C2×Q812yes—
171C42×C13#4112yes—
172#6103—24no—
173#6103—24no—
174#6103—24no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—24no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—81no—
181C4⋊Dic13C22×C412yes—
182C4⋊Dic13C2×Q812yes—
183#6101—24no—
184#6101—81no—
185#6101—81no—
186#6101—81no—
187C4×Dic13—21no—
188C4×Dic13—21no—
189C4×Dic13—81no—
190C4×Dic13—81no—
191C4×Dic13—81no—
192C4×Dic13C22×C412yes—
193C4×Dic13#4112yes—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C22×C412yes—
200C2×#478—131no—
201#2330—131no—
202#2275—131no—
203#1989—131no—
204#1948—131no—
205#1919—131no—
206#1918—131no—
207#1864—131no—
208#1864—131no—
209#1802—131no—
210#1776D1311yescharacteristic, complemented
211C4×#106—131no—
212#1768—131no—
213#1762—131no—
214C4×#102—131no—
215C23×C13C22×D411yescharacteristic
216C22×D13—22no—
217C22×D13—22no—
218C22×D13—22no—
219C22×D13—41no—
220C22×D13—41no—
221C22×D13—41no—
222C22×D13—41no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13C22⋊Q812yes—
240C2×C4×C13C22⋊Q812yes—
241C2×C4×C13C23×C411yescharacteristic
242C2×C4×C13C22×Q811yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13C4×D412yes—
267C2×Dic13C4×D412yes—
268D52—22no—
269D52—22no—
270D52—22no—
271D52C4×Q814yes—
272C4×D13—84no—
273C4×D13—84no—
274C4×D13—84no—
275C8×C13—22no—
276C8×C13—41no—
277#1055—22no—
278#1055—41no—
279C2×#125—131no—
280C2×C4×D4—131no—
281C2×C4×D4—131no—
282C2×C4×D4—131no—
283#478—138no—
284C2×#107C2×D1311yescharacteristic
285C2×#106—131no—
286C2×#106—131no—
287C2×#106C2×D1311yescharacteristic
288C2×C4⋊C8—131no—
289C2×C4⋊C8—131no—
290C2×#102—131no—
291C2×#102—131no—
292C2×#102—131no—
293C2×#102—131no—
294C2×#97C2×D1311yescharacteristic
295C2×C4×C8—131no—
296#389—131no—
297#389—131no—
298#389—261no—
299#389—261no—
300#387—261no—
301#387—261no—
302#384—131no—
303C4×C4⋊C4—131no—
304C4×C4⋊C4—131no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4C2×D1311yescharacteristic
307C4×C4⋊C4C2×D1311yescharacteristic
308C4×C22⋊C4—261no—
309C4×C22⋊C4—261no—
310C4×C22⋊C4—261no—
311#376—131no—
312C2×#95—261no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340C2×D1311yescharacteristic
320#340C2×D1311yescharacteristic
321#336—131no—
322#336—131no—
323C22×C13C2×C4×D411yescharacteristic
324C22×C13C2×C22⋊Q811yescharacteristic
325C22×C13#52511yescharacteristic
326C22×C13#57611yescharacteristic
327C22×C13#57711yescharacteristic
328C22×C13#57711yescharacteristic
329C22×C13#57711yescharacteristic
330C2×D13—24no—
331C2×D13—42no—
332C2×D13—42no—
333C2×D13—42no—
334C2×D13—42no—
335C2×D13—42no—
336C2×D13—42no—
337C4×C13—22no—
338C4×C13—22no—
339C4×C13—42no—
340C4×C13—42no—
341C4×C13—42no—
342C4×C13—81no—
343C4×C13C2×C4×Q811yescharacteristic
344C4×C13C4×#4111yescharacteristic
345C4×C13#52911yescharacteristic
346C4×C13#53311yescharacteristic
347Dic13—22no—
348Dic13—22no—
349Dic13—42no—
350Dic13—41no—
351Dic13—41no—
352Dic13—42no—
353Dic13—81no—
354C22×D4—131no—
355C23×C4—261no—
356C23×C4—261no—
357C23×C4—261no—
358C22×C8—131no—
359C22×C8—131no—
360C22×C8C22×D1311yescharacteristic
361C22×C8C22×D1311yescharacteristic
362#125—134no—
363#125—262no—
364C4×D4—134no—
365C4×D4—134no—
366C4×D4—262no—
367C4×D4—262no—
368C4×D4—262no—
369C4×D4—262no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—261no—
391C2×C42—261no—
392C2×C42—261no—
393C2×C42C22×D1311yescharacteristic
394#107C4×D1314yescomplemented
395#106—22no—
396#106—134no—
397#106—262no—
398C4⋊C8—134no—
399C4⋊C8—262no—
400#102—134no—
401#102—134no—
402#102—262no—
403#102—262no—
404#97—22no—
405C4×C8—262no—
406#95—21no—
407#95—21no—
408#95—131no—
409#95—131no—
410#95—131no—
411#95—131no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417C2×C13C4×C22⋊Q811yescharacteristic
418C2×C13#294611yescharacteristic
419C2×C13#295211yescharacteristic
420C2×C13#308111yescharacteristic
421C2×C13#308411yescharacteristic
422C2×C13#311911yescharacteristic
423C2×C13#312311yescharacteristic
424D13—44no—
425C24—261no—
426C2×D4—132no—
427C2×D4—132no—
428C2×D4—132no—
429C2×D4—261no—
430C2×D4—261no—
431C2×D4—261no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—264no—
441C22×C4—264no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—264no—
445C22×C4—261no—
446C22×C4—1041no—
447C22×C4—1041no—
448C22×C4—1041no—
449C22×C4—1041no—
450C22×C4—1041no—
451C22×C4—1041no—
452C22×C4D4×D1311yescharacteristic
453C22×C4D4×D1311yescharacteristic
454C22×C4C23×D1311yescharacteristic
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—132no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8C2×C4×D1312yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—132no—
473C4⋊C4—132no—
474C4⋊C4—264no—
475C4⋊C4—264no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—1041no—
481C4⋊C4—1041no—
482C4⋊C4—1041no—
483C4⋊C4—1041no—
484C4⋊C4C2×C4×D1312yes—
485C4⋊C4C2×C4×D1312yes—
486C4⋊C4#612712yes—
487C22⋊C4—264no—
488C22⋊C4—264no—
489C22⋊C4—264no—
490C42—81no—
491C42—81no—
492C42—132no—
493C42—132no—
494C42—261no—
495C42—261no—
496C42—1041no—
497C42—1041no—
498C42—1041no—
499C42#612712yes—
500C42Q8×D1312yes—
501C13#2161911yescharacteristic, complemented, Sylow
502C23—262no—
503C23—262no—
504C23—262no—
505C23—521no—
506C23—521no—
507C23—521no—
508C23—521no—
509C23C2×D4×D1311yescharacteristic
510D4—134no—
511D4—262no—
512D4—262no—
513D4—262no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—132no—
531C2×C4—132no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—262no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—262no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—1044no—
552C2×C4—1044no—
553C2×C4—1044no—
554C2×C4#8815012yes—
555C2×C4#8815012yes—
556C2×C4C22×C4×D1311yescharacteristic
557C2×C4C2×#612711yescharacteristic
558C2×C4C2×#612711yescharacteristic
559C2×C4C2×Q8×D1311yescharacteristic
560C2×C4#41×D1311yescharacteristic
561C2×C4#41×D1311yescharacteristic
562C8—22no—
563C8—41no—
564C8—262no—
565C8—521no—
566C22—264no—
567C22—522no—
568C22—522no—
569C22—522no—
570C22—522no—
571C22—522no—
572C22—522no—
573C22C2×#8815011yescharacteristic
574C22C4×D4×D1311yescharacteristic
575C22#1171925211yescharacteristic
576C22#1171947911yescharacteristic
577C22#1171948011yescharacteristic
578C22#1171948311yescharacteristic
579C22#1171948311yescharacteristic
580C4—22no—
581C4—22no—
582C4—42no—
583C4—42no—
584C4—42no—
585C4—81no—
586C4—262no—
587C4—262no—
588C4—522no—
589C4—522no—
590C4—521no—
591C4—521no—
592C4—1041no—
593C4C4×#612711yescharacteristic
594C4#1171923311yescharacteristic
595C4C4×Q8×D1311yescharacteristic
596C4#1171928311yescharacteristic
597C2—524no—
598C2C4×#8815011yescharacteristic
599C2#1312366511yescharacteristic
600C2#1312371611yescharacteristic
601C2#1312466511yescharacteristic
602C2#1312469711yescharacteristic
603C2#1312503311yescharacteristic
604C2#1312508711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1776C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1776D13
hypocenterC13#21619
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
2. #13117573C2semidirect
4. #13115792C2semidirect
5. #13115596C2semidirect
6. #13115412C2semidirect
7. #13115409C2semidirect
11. C4×#88048C2semidirect
12. #13114696C2semidirect
15. C13×#1776C2semidirect
45. #11718552C4semidirect
97. #88144C2×C4semidirect
100. C13×#107C2×C4semidirect
117. #88054C2×C4semidirect
121. #88048C2×C4semidirect
210. #1776D13semidirect
394. #107C4×D13semidirect
501. C13#21619semidirect

Maximal subgroups

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

subgroupindex
C2×#117185522
#131175732
#131171962
#131157922
#131155962
#131154122
#131154092
#131150982
#131150942
#131148352
C4×#880482
#131146962
#131146622
C4×#880492
C13×#17762
#2161913