Finite Group Databasebeta

← #15884763

Subgroups — #15884763

Order 3328.

846 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#13117937C211yesmaximal, characteristic, complemented
3#13117745C211yesmaximal, characteristic
4#13115799C211yesmaximal, characteristic, complemented
5#13115601C211yesmaximal, characteristic, complemented
6#13115563C211yesmaximal, characteristic, complemented
7#13115430C211yesmaximal, characteristic, complemented
8#13115418C211yesmaximal, characteristic, complemented
9#13115096C211yesmaximal, characteristic
10#13115080C211yesmaximal, characteristic
11C8×#6101C211yesmaximal, characteristic, complemented
12C4×#88061C211yesmaximal, characteristic
13#13114650C211yesmaximal, characteristic
14#13114650C211yesmaximal, characteristic
15C13×#1942C211yesmaximal, characteristic, complemented
16C2×#88147C2211yescharacteristic
17C2×#88147C2211yescharacteristic
18C2×#88144C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C2×C13×#107C2211yescharacteristic
21C2×C13×#107C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C2×#88061C2211yescharacteristic
26C2×#88061C2211yescharacteristic
27C2×#88054C2211yescharacteristic
28C2×C8×Dic13C2211yescharacteristic
29C2×C8×Dic13C2211yescharacteristic
30#11718650—21no—
31#11718648—21no—
32#11718646C2211yescharacteristic
33#11718639—21no—
34#11718638C2211yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36C4⋊C4×Dic13C2211yescharacteristic
37#11718634—21no—
38#11718634C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88049C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44C4×#6101C2211yescharacteristic
45#11718552C418yescomplemented
46#11718329—21no—
47D13×#95—21no—
48#11718314—21no—
49#11718310—21no—
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C22×C4×D13—21no—
63C22×C4×D13—21no—
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
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×#6101D411yescharacteristic
84C2×#6101D411yescharacteristic
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—41no—
95#88147C2×C414yes—
96#88144—22no—
97#88144C2×C414yescomplemented
98C4×D52—22no—
99C4×D52—41no—
100C13×#107—41no—
101C13×#107C2×C414yescomplemented
102C4×C8×C13—41no—
103C13×#95—21no—
104C13×#95—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071D411yescharacteristic
113#88071D411yescharacteristic
114#88061C2×C414yes—
115#88061Q814yes—
116#88054C2×C414yescomplemented
117C8×Dic13—22no—
118C8×Dic13—41no—
119#88049—22no—
120#88049C2×C414yes—
121#88048—41no—
122#88048C2×C414yescomplemented
123#22966—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—42no—
147C2×C4×D13—42no—
148C2×C4×D13—42no—
149C2×C4×D13—42no—
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×C13C22×C412yes—
159C2×C8×C13C2×Q812yes—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—81no—
167C13×C4⋊C4—81no—
168C13×C4⋊C4C22×C412yes—
169C13×C4⋊C4C22×C412yes—
170C42×C13—21no—
171C42×C13—21no—
172#6103—24no—
173#6103—42no—
174#6103—42no—
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—22no—
184#6101—24no—
185#6101—22no—
186#6101—42no—
187C4×Dic13—21no—
188C4×Dic13—21no—
189C4×Dic13—42no—
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#2370—131no—
202#2349—131no—
203#1991—131no—
204#1949—131no—
205#1942D1311yescharacteristic, complemented
206#1941—131no—
207#1921—131no—
208#1920—131no—
209#1864—131no—
210#1862—131no—
211C8×C4⋊C4—131no—
212C4×#102—131no—
213C4×#102—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—22no—
226C2×C4×C13—22no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
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×C13—41no—
240C2×C4×C13#13512yes—
241C2×C4×C13C23×C411yescharacteristic
242C2×C4×C13C22×Q811yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13H(5,𝔽2)11yescharacteristic
246C2×C4×C132−1+411yescharacteristic
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—22no—
254C2×Dic13—21no—
255C2×Dic13—22no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13C4×D412yes—
266C2×Dic13C4×D412yes—
267C2×Dic13#13512yes—
268D52—22no—
269D52—22no—
270D52—22no—
271D52C4×Q814yes—
272C4×D13—84no—
273C4×D13—84no—
274C4×D13—84no—
275C8×C13—22no—
276C8×C13—22no—
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×#107C2×D1311yescharacteristic
286C2×#106—131no—
287C2×#106—131no—
288C2×C4⋊C8—131no—
289C2×#102—131no—
290C2×#102—131no—
291C2×#102—131no—
292C2×#102—131no—
293C2×C4×C8—131no—
294C2×C4×C8—131no—
295C2×C4×C8C2×D1311yescharacteristic
296#389—131no—
297#389—131no—
298#389—261no—
299#389C2×D1311yescharacteristic
300#389C2×D1311yescharacteristic
301#387—261no—
302#387—261no—
303#385—261no—
304#385—261no—
305#382—131no—
306#380—261no—
307C4×C4⋊C4—131no—
308C4×C4⋊C4—131no—
309C4×C4⋊C4—131no—
310C4×C4⋊C4—131no—
311C4×C4⋊C4—261no—
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×C13#54611yescharacteristic
325C22×C13D4×Q811yescharacteristic
326C22×C13C2×#13511yescharacteristic
327C22×C13C2×#13511yescharacteristic
328C22×C13#57611yescharacteristic
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—42no—
339C4×C13—42no—
340C4×C13—41no—
341C4×C13—81no—
342C4×C13—81no—
343C4×C13C2×C4×Q811yescharacteristic
344C4×C13#52011yescharacteristic
345C4×C13#55211yescharacteristic
346C4×C13#55411yescharacteristic
347Dic13—22no—
348Dic13—22no—
349Dic13—22no—
350Dic13—42no—
351Dic13—42no—
352Dic13—41no—
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—262no—
366C4×D4—262no—
367C4×D4—262no—
368C4×D4—521no—
369C4×D4—521no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C4⋊C4C22×D1311yescharacteristic
385C2×C22⋊C4—261no—
386C2×C22⋊C4—261no—
387C2×C22⋊C4—261no—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—261no—
391C2×C42—261no—
392C2×C42—261no—
393C2×C42C22×D1311yescharacteristic
394#107—41no—
395#107C4×D1314yescomplemented
396#106—134no—
397#106—521no—
398C4⋊C8—134no—
399#102—134no—
400#102—134no—
401#102—134no—
402#102—262no—
403C4×C8—41no—
404C4×C8—262no—
405C4×C8—521no—
406#95—21no—
407#95—21no—
408#95—131no—
409#95—131no—
410#95—261no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417C2×C13#236011yescharacteristic
418C2×C13C4×#13511yescharacteristic
419C2×C13#294611yescharacteristic
420C2×C13#329611yescharacteristic
421C2×C13#329711yescharacteristic
422C2×C13#338011yescharacteristic
423C2×C13#338111yescharacteristic
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—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—522no—
445C22×C4—522no—
446C22×C4—522no—
447C22×C4—522no—
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—132no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8C2×C4×D1312yes—
466C2×C8Q8×D1312yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—132no—
476C4⋊C4—132no—
477C4⋊C4—262no—
478C4⋊C4—264no—
479C4⋊C4—264no—
480C4⋊C4—262no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—522no—
486C4⋊C4—1041no—
487C4⋊C4C2×C4×D1312yes—
488C4⋊C4C2×C4×D1312yes—
489C22⋊C4—264no—
490C22⋊C4—522no—
491C22⋊C4—522no—
492C42—21no—
493C42—21no—
494C42—132no—
495C42—132no—
496C42—261no—
497C42—261no—
498C42—522no—
499C42—1041no—
500C42—1041no—
501C13#2296611yescharacteristic, 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—21no—
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—41no—
531C2×C4—132no—
532C2×C4—132no—
533C2×C4—132no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—262no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—262no—
544C2×C4—261no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—1044no—
553C2×C4—1044no—
554C2×C4—1044no—
555C2×C4#8817312yes—
556C2×C4C22×C4×D1311yescharacteristic
557C2×C4#8825111yescharacteristic
558C2×C4C2×Q8×D1311yescharacteristic
559C2×C4#8825411yescharacteristic
560C2×C4#41×D1311yescharacteristic
561C2×C4#41×D1311yescharacteristic
562C8—22no—
563C8—22no—
564C8—262no—
565C8—521no—
566C22—264no—
567C22—522no—
568C22—522no—
569C22—522no—
570C22—522no—
571C22—522no—
572C22—522no—
573C22C4×D4×D1311yescharacteristic
574C22#1171931511yescharacteristic
575C22#1171943211yescharacteristic
576C22#1171946211yescharacteristic
577C22C2×#8817311yescharacteristic
578C22D13×#13511yescharacteristic
579C22#1171947511yescharacteristic
580C4—22no—
581C4—41no—
582C4—42no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—262no—
587C4—262no—
588C4—262no—
589C4—521no—
590C4—522no—
591C4—522no—
592C4—1041no—
593C4#1171920911yescharacteristic
594C4C4×Q8×D1311yescharacteristic
595C4#1171934111yescharacteristic
596C4#1171939811yescharacteristic
597C2—524no—
598C2#1311783811yescharacteristic
599C2C4×#8817311yescharacteristic
600C2#1312366111yescharacteristic
601C2#1312667711yescharacteristic
602C2#1312668111yescharacteristic
603C2#1312770511yescharacteristic
604C2#1312770811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1942C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1942D13
hypocenterC13#22966
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1942

Complements

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

NH ≅ G/Ntype
2. #13117937C2semidirect
4. #13115799C2semidirect
5. #13115601C2semidirect
6. #13115563C2semidirect
7. #13115430C2semidirect
8. #13115418C2semidirect
11. C8×#6101C2semidirect
15. C13×#1942C2semidirect
45. #11718552C4semidirect
97. #88144C2×C4semidirect
101. C13×#107C2×C4semidirect
116. #88054C2×C4semidirect
122. #88048C2×C4semidirect
205. #1942D13semidirect
395. #107C4×D13semidirect
501. C13#22966semidirect

Maximal subgroups

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

subgroupindex
C2×#117185522
#131179372
#131177452
#131157992
#131156012
#131155632
#131154302
#131154182
#131150962
#131150802
C8×#61012
C4×#880612
#131146502
C13×#19422
#2296613