Finite Group Databasebeta

← #15873321

Subgroups — #15873321

Order 3328.

786 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718498C211yesmaximal, characteristic
2#13117232C211yesmaximal, characteristic
3#13117229C211yesmaximal, characteristic
4#13115607C211yesmaximal, characteristic, complemented
5#13115606C211yesmaximal, characteristic, complemented
6#13115605C211yesmaximal, characteristic, complemented
7#13115604C211yesmaximal, characteristic, complemented
8#13115603C211yesmaximal, characteristic, complemented
9#13115602C211yesmaximal, characteristic, complemented
10#13115601C211yesmaximal, characteristic, complemented
11#13114870C211yesmaximal, characteristic
12#13114868C211yesmaximal, characteristic
13#13114868C211yesmaximal, characteristic
14#13114866C211yesmaximal, characteristic
15C13×#1949C211yesmaximal, characteristic, complemented
16C22×#6094C2211yescharacteristic
17C22×#6094C2211yescharacteristic
18C2×C42×D13C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C2×C13×#106C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C13×#382C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C2×#88058C2211yescharacteristic
25C2×#88057C2211yescharacteristic
26C2×#88054C2211yescharacteristic
27C2×#88054C2211yescharacteristic
28#11718648C2211yescharacteristic
29#11718648C2211yescharacteristic
30#11718648C2211yescharacteristic
31#11718648C2211yescharacteristic
32#11718638C2211yescharacteristic
33#11718638C2211yescharacteristic
34C4⋊C4×Dic13C2211yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C4×#6103—21no—
41#11718597C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43#11718593—21no—
44C2×C4⋊#1055C2211yescharacteristic
45#11718498C418yescomplemented
46#11718327—21no—
47#11718325—21no—
48#11718325—21no—
49#11718312—21no—
50#11718312—21no—
51#11718309—21no—
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×C4×D13D411yescharacteristic
61C22×C4×D13D411yescharacteristic
62C22×C4×D13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C42×C13—21no—
70C2×C42×C13C2311yescharacteristic
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×C4⋊Dic13C2311yescharacteristic
76C2×C4⋊Dic13C2311yescharacteristic
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4×Dic13—21no—
80C2×C4×Dic13—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13D411yescharacteristic
83C2×C4×Dic13D411yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C22×#1055C2311yescharacteristic
86C22×#1055C2311yescharacteristic
87C2×#6094—41no—
88C2×#6094—41no—
89C2×#6094—41no—
90C2×#6094—41no—
91C2×#6094C2×C414yes—
92C2×#6094C2×C414yes—
93C42×D13C2×C414yes—
94C42×D13Q814yes—
95C13×#107—41no—
96C13×#106—41no—
97C13×C4⋊C8C2×C414yes—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101#88071—21no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88058—41no—
115#88057—41no—
116#88054C2×C414yes—
117#88054C2×C414yes—
118#88048—41no—
119#88048—41no—
120#88047—41no—
121#88047—41no—
122C4⋊#1055C2×C414yes—
123#21965—131nomaximal, Sylow
124C23×D13C2×D411yescharacteristic
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×Dic13—21no—
136C22×Dic13C2×D411yescharacteristic
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×D411yescharacteristic
139C2×C4×D13—21no—
140C2×C4×D13—21no—
141C2×C4×D13—21no—
142C2×C4×D13—21no—
143C2×C4×D13—41no—
144C2×C4×D13—41no—
145C2×C4×D13—41no—
146C2×C4×D13—41no—
147C2×C4×D13C4⋊C414yes—
148C2×C4×D13C4⋊C414yes—
149C2×C4×D13C22×C412yes—
150C2×C4×D13C2×Q812yes—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13C22×C412yes—
156C2×C8×C13C22×C412yes—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C42×C13—42no—
166C42×C13C22×C412yes—
167C42×C13C2×Q812yes—
168#6103—42no—
169#6103—42no—
170#6103—42no—
171#6103—42no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4×Dic13—42no—
181C4×Dic13—42no—
182C4×Dic13—42no—
183C4×Dic13C4⋊C414yes—
184C4×Dic13C4⋊C414yes—
185C4×Dic13C22×C412yes—
186C4×Dic13C2×Q812yes—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055C22×C412yes—
192C2×#1055C22×C412yes—
193#6094—44no—
194#6094—44no—
195C2×#423—131no—
196#2283—131no—
197#2283—131no—
198#1949—131no—
199#1949—131no—
200#1949—131no—
201#1949—131no—
202#1949—131no—
203#1949—131no—
204#1949—131no—
205#1949D1311yescharacteristic, complemented
206#1809—131no—
207#1809—131no—
208#1809—131no—
209#1809—131no—
210C23×C13C22×D411yescharacteristic
211C22×D13—21no—
212C22×D13—21no—
213C22×D13—21no—
214C22×D13—21no—
215C22×D13—21no—
216C22×D13—21no—
217C22×D13C2×C4⋊C412yes—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
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×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13C2×C4⋊C412yes—
235C2×C4×C13C2×C4⋊C412yes—
236C2×C4×C13C23×C411yescharacteristic
237C2×C4×C13C22×Q811yescharacteristic
238C2×C4×C13H(5,𝔽2)11yescharacteristic
239C2×C4×C13H(5,𝔽2)11yescharacteristic
240C2×C4×C132−1+411yescharacteristic
241C2×C4×C132−1+411yescharacteristic
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13C2×C4⋊C412yes—
261C2×Dic13C2×C4⋊C412yes—
262C2×Dic13C2×C4⋊C412yes—
263C4×D13—22no—
264C4×D13—22no—
265C4×D13—22no—
266C4×D13—22no—
267C4×D13—44no—
268C4×D13—44no—
269C8×C13—22no—
270C8×C13—22no—
271#1055—22no—
272#1055—22no—
273C22×M16—131no—
274C22×M16—131no—
275C22×C42—131no—
276C2×#107—131no—
277C2×#107—131no—
278C2×#107—131no—
279C2×#107C2×D1311yescharacteristic
280C2×#106—131no—
281C2×#106—131no—
282C2×#106—131no—
283C2×#106C2×D1311yescharacteristic
284#423—138no—
285C2×C4⋊C8—131no—
286C2×C4⋊C8—131no—
287C2×C4⋊C8—131no—
288C2×C4⋊C8C2×D1311yescharacteristic
289#383—261no—
290#383—261no—
291#382—131no—
292#382—131no—
293#382—131no—
294#382C2×D1311yescharacteristic
295#381—261no—
296#381—261no—
297#380—131no—
298#380—131no—
299#380—131no—
300#380—131no—
301C4×C4⋊C4—131no—
302C4×C4⋊C4—131no—
303C4×C4⋊C4—131no—
304C4×C4⋊C4C2×D1311yescharacteristic
305C4×C22⋊C4—261no—
306C4×C22⋊C4—261no—
307#376—261no—
308#376—261no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340C2×D1311yescharacteristic
316#340C2×D1311yescharacteristic
317C22×C13C22×C4⋊C411yescharacteristic
318C22×C13#53711yescharacteristic
319C22×C13#53711yescharacteristic
320C22×C13#57511yescharacteristic
321C22×C13#57511yescharacteristic
322C22×C13#57511yescharacteristic
323C22×C13#57511yescharacteristic
324C2×D13—22no—
325C2×D13—22no—
326C2×D13—22no—
327C2×D13—41no—
328C2×D13—41no—
329C2×D13—41no—
330C2×D13—41no—
331C4×C13—22no—
332C4×C13—22no—
333C4×C13—81no—
334C4×C13—81no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13#51811yescharacteristic
338C4×C13#51911yescharacteristic
339C4×C13#54411yescharacteristic
340C4×C13#54411yescharacteristic
341Dic13—22no—
342Dic13—22no—
343Dic13—22no—
344Dic13—81no—
345Dic13—81no—
346Dic13—81no—
347Dic13—81no—
348C23×C4—131no—
349C23×C4—131no—
350C23×C4—131no—
351C2×M16—134no—
352C2×M16—134no—
353C2×M16—521no—
354C2×M16—521no—
355C2×M16—521no—
356C2×M16—521no—
357C22×C8—131no—
358C22×C8—131no—
359C22×C8C22×D1311yescharacteristic
360C22×C8C22×D1311yescharacteristic
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4C22×D1311yescharacteristic
366C2×C4⋊C4C22×D1311yescharacteristic
367C2×C4⋊C4C22×D1311yescharacteristic
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C22⋊C4—261no—
370C2×C22⋊C4—261no—
371C2×C22⋊C4—261no—
372C2×C22⋊C4—261no—
373C2×C42—21no—
374C2×C42—131no—
375C2×C42—131no—
376C2×C42—131no—
377C2×C42—134no—
378C2×C42—134no—
379C2×C42—261no—
380C2×C42—261no—
381C2×C42—261no—
382C2×C42C22×D1311yescharacteristic
383#107—41no—
384#107—521no—
385#107—521no—
386#107—521no—
387#106—41no—
388#106—521no—
389#106—521no—
390#106—521no—
391C4⋊C8—134no—
392C4⋊C8—134no—
393C4⋊C8—134no—
394C4⋊C8C4×D1314yes—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—261no—
399#95—261no—
400#95—261no—
401#95—261no—
402#95—261no—
403#95—261no—
404#95—261no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411C2×C13#231611yescharacteristic
412C2×C13#291111yescharacteristic
413C2×C13#291111yescharacteristic
414C2×C13#325611yescharacteristic
415C2×C13#325611yescharacteristic
416C2×C13#325611yescharacteristic
417C2×C13#325611yescharacteristic
418D13—42no—
419C24—131no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—132no—
428C22×C4—132no—
429C22×C4—134no—
430C22×C4—134no—
431C22×C4—261no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—521no—
440C22×C4—521no—
441C22×C4—521no—
442C22×C4—521no—
443C22×C4D4×D1311yescharacteristic
444C22×C4D4×D1311yescharacteristic
445C22×C4C23×D1311yescharacteristic
446M16—524no—
447M16—524no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—132no—
453C2×C8—132no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8C2×C4×D1312yes—
459C2×C8C2×C4×D1312yes—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C22⋊C4—522no—
477C22⋊C4—522no—
478C22⋊C4—522no—
479C22⋊C4—522no—
480C42—42no—
481C42—134no—
482C42—134no—
483C42—132no—
484C42—132no—
485C42—522no—
486C42—522no—
487C42—522no—
488C42C2×C4×D1312yes—
489C42Q8×D1312yes—
490C13#2196511yescharacteristic, complemented, Sylow
491C23—132no—
492C23—261no—
493C23—261no—
494C23—261no—
495C23—261no—
496C23—261no—
497C23—261no—
498C23C2×D4×D1311yescharacteristic
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
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—41no—
515C2×C4—132no—
516C2×C4—132no—
517C2×C4—132no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—262no—
528C2×C4—524no—
529C2×C4—524no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4C4⋊C4×D1312yes—
543C2×C4C4⋊C4×D1312yes—
544C2×C4C22×C4×D1311yescharacteristic
545C2×C4#8825111yescharacteristic
546C2×C4C2×Q8×D1311yescharacteristic
547C2×C4#8825411yescharacteristic
548C2×C4#8825611yescharacteristic
549C2×C4#8825711yescharacteristic
550C8—22no—
551C8—22no—
552C8—262no—
553C8—262no—
554C22—262no—
555C22—262no—
556C22—262no—
557C22—521no—
558C22—521no—
559C22—521no—
560C22—521no—
561C22C2×C4⋊C4×D1311yescharacteristic
562C22#1171931311yescharacteristic
563C22#1171933411yescharacteristic
564C22#1171947311yescharacteristic
565C22#1171947311yescharacteristic
566C22#1171947811yescharacteristic
567C22#1171948211yescharacteristic
568C4—22no—
569C4—22no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—262no—
575C4—262no—
576C4—262no—
577C4—1041no—
578C4—1041no—
579C4—1041no—
580C4—1041no—
581C4#1171925011yescharacteristic
582C4#1171927711yescharacteristic
583C4#1171939411yescharacteristic
584C4#1171943411yescharacteristic
585C2—522no—
586C2#1311745111yescharacteristic
587C2#1312342311yescharacteristic
588C2#1312342411yescharacteristic
589C2#1312623411yescharacteristic
590C2#1312623511yescharacteristic
591C2#1312623611yescharacteristic
592C2#1312623911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1949C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1949D13
hypocenterC13#21965
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #13115607C2semidirect
5. #13115606C2semidirect
6. #13115605C2semidirect
7. #13115604C2semidirect
8. #13115603C2semidirect
9. #13115602C2semidirect
10. #13115601C2semidirect
15. C13×#1949C2semidirect
45. #11718498C4semidirect
205. #1949D13semidirect
490. C13#21965semidirect

Maximal subgroups

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

subgroupindex
C2×#117184982
#131172322
#131172292
#131156072
#131156062
#131156052
#131156042
#131156032
#131156022
#131156012
#131148702
#131148682
#131148662
C13×#19492
#2196513