Finite Group Databasebeta

← #15880568

Subgroups — #15880568

Order 3328.

822 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×#107C211yesmaximal, characteristic
2#13117712C211yesmaximal, characteristic
3#13117709C211yesmaximal, characteristic
4#13115568C211yesmaximal, characteristic, complemented
5#13115566C211yesmaximal, characteristic, complemented
6#13115430C211yesmaximal, characteristic, complemented
7#13115429C211yesmaximal, characteristic, complemented
8#13115427C211yesmaximal, characteristic, complemented
9#13114925C211yesmaximal, characteristic
10#13114925C211yesmaximal, characteristic
11#13114864C211yesmaximal, characteristic
12C4×#88047C211yesmaximal, characteristic, complemented
13#13114728C211yesmaximal, characteristic, complemented
14#13114606C211yesmaximal, characteristic
15C13×#1921C211yesmaximal, characteristic, complemented
16C22×C8×D13C2211yescharacteristic
17C2×C4⋊C4×D13C2211yescharacteristic
18C2×C4⋊C4×D13C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C13×#389C2211yescharacteristic
21C4×C13×C4⋊C4C2211yescharacteristic
22C2×#88060C2211yescharacteristic
23C2×#88058C2211yescharacteristic
24C2×C8×Dic13C2211yescharacteristic
25#11718648—21no—
26#11718648C2211yescharacteristic
27#11718648C2211yescharacteristic
28#11718646C2211yescharacteristic
29#11718639—21no—
30C4⋊C4×Dic13C2211yescharacteristic
31C4⋊C4×Dic13C2211yescharacteristic
32#11718634C2211yescharacteristic
33C2×#88047C2211yescharacteristic
34C2×#88047C2211yescharacteristic
35C2×#88047C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37C4×#6103—21no—
38C4×#6103C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40#11718594—21no—
41#11718589C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43D13×#107C418yescomplemented
44#11718328—21no—
45#11718327—21no—
46#11718316—21no—
47#11718313—21no—
48C13×#340C2211yescharacteristic
49C13×#340C2211yescharacteristic
50C13×#340C2211yescharacteristic
51C13×#336C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×C4×D13—21no—
61C22×C4×D13—21no—
62C22×C4×D13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C42×C13—21no—
71C2×C42×C13C2311yescharacteristic
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103D411yescharacteristic
75C2×#6103D411yescharacteristic
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13C2311yescharacteristic
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
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C2×C8×D13—22no—
92C2×C8×D13—22no—
93C2×C8×D13C2×C414yes—
94C4⋊C4×D13—22no—
95C4⋊C4×D13—22no—
96C4⋊C4×D13C2×C414yes—
97C4⋊C4×D13C2×C414yes—
98C13×#107C2×C414yes—
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#88071D411yescharacteristic
110#88071D411yescharacteristic
111#88060—22no—
112#88058C2×C414yes—
113C8×Dic13—22no—
114#88047—22no—
115#88047—22no—
116#88047C2×C414yes—
117#88047C2×C414yes—
118C4×#1055—22no—
119#22612—131nomaximal, Sylow
120C23×D13C2×D411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2411yescharacteristic
128C22×Dic13—21no—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13C2×D411yescharacteristic
133C22×Dic13C2×D411yescharacteristic
134C22×Dic13C2×D411yescharacteristic
135C2×C4×D13—21no—
136C2×C4×D13—21no—
137C2×C4×D13—21no—
138C2×C4×D13—21no—
139C2×C4×D13—24no—
140C2×C4×D13—24no—
141C2×C4×D13—81no—
142C2×C4×D13—81no—
143C2×C4×D13—81no—
144C2×C4×D13—81no—
145C2×C4×D13C22×C412yes—
146C2×C4×D13#4112yes—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13C22×C412yes—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—81no—
160C13×C4⋊C4C22×C412yes—
161C13×C4⋊C4C22×C412yes—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13—81no—
165#6103—22no—
166#6103—42no—
167#6103—42no—
168#6103Q1614yes—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—81no—
176C4⋊Dic13C22×C412yes—
177C4⋊Dic13C22×C412yes—
178#6101—24no—
179#6101—24no—
180#6101—81no—
181#6101—81no—
182C4×Dic13—21no—
183C4×Dic13—21no—
184C4×Dic13—81no—
185C4×Dic13—81no—
186C4×Dic13—81no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055C22×C412yes—
191C2×#1055#4112yes—
192C2×#1055#4112yes—
193C8×D13—28no—
194C22×#107—131no—
195#2345—131no—
196#2345—131no—
197#1942—131no—
198#1942—131no—
199#1921—131no—
200#1921—131no—
201#1921—131no—
202#1921D1311yescharacteristic, complemented
203#1824—131no—
204#1824—131no—
205#1808—131no—
206C4×#107—131no—
207C4×#107—131no—
208C8×C22⋊C4—131no—
209C23×C13C22×D411yescharacteristic
210C22×D13—21no—
211C22×D13—21no—
212C22×D13—21no—
213C22×D13—21no—
214C22×D13C4×D412yes—
215C22×D13C2×Q1612yes—
216C22×D13#13512yes—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
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×Q1612yes—
235C2×C4×C13C23×C411yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C132−1+411yescharacteristic
240C2×C4×C132−1+411yescharacteristic
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
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×Dic13C4×D412yes—
261C2×Dic13C2×Q1612yes—
262C4×D13—22no—
263C4×D13—22no—
264C4×D13—22no—
265C4×D13—22no—
266C4×D13—84no—
267C4×D13—84no—
268C8×C13—22no—
269C8×C13—41no—
270#1055—41no—
271#1055#11714yes—
272C23×C8—131no—
273C22×C4⋊C4—131no—
274C22×C4⋊C4—131no—
275C2×#107—131no—
276C2×#107—131no—
277C2×#107—131no—
278C2×#107—138no—
279C2×#107—131no—
280C2×#107—131no—
281C2×#107C2×D1311yescharacteristic
282C2×C22⋊C8—131no—
283C2×C4×C8—131no—
284C2×C4×C8—131no—
285#389—131no—
286#389—131no—
287#389—131no—
288#389C2×D1311yescharacteristic
289#387—261no—
290#387—261no—
291#387—261no—
292#387—261no—
293#380—131no—
294#380—131no—
295#380—261no—
296#380—261no—
297C4×C4⋊C4—131no—
298C4×C4⋊C4—131no—
299C4×C4⋊C4—131no—
300C4×C4⋊C4C2×D1311yescharacteristic
301C4×C22⋊C4—131no—
302C4×C22⋊C4—261no—
303C4×C22⋊C4—261no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340C2×D1311yescharacteristic
312#340C2×D1311yescharacteristic
313#340C2×D1311yescharacteristic
314#336—131no—
315#336C2×D1311yescharacteristic
316C22×C13C2×C4×D411yescharacteristic
317C22×C13#54711yescharacteristic
318C22×C13#54711yescharacteristic
319C22×C13C22×Q1611yescharacteristic
320C22×C13C2×#13511yescharacteristic
321C22×C13#57611yescharacteristic
322C22×C13#57611yescharacteristic
323C2×D13—22no—
324C2×D13—22no—
325C2×D13—22no—
326C2×D13—22no—
327C2×D13—22no—
328C2×D13—22no—
329C2×D13C4×Q1614yes—
330C4×C13—22no—
331C4×C13—41no—
332C4×C13—42no—
333C4×C13—42no—
334C4×C13—81no—
335C4×C13—81no—
336C4×C13C2×#11711yescharacteristic
337C4×C13#51911yescharacteristic
338C4×C13#55211yescharacteristic
339C4×C13#55211yescharacteristic
340Dic13—22no—
341Dic13—22no—
342Dic13—41no—
343Dic13—42no—
344Dic13—42no—
345Dic13—81no—
346Dic13—81no—
347C23×C4—131no—
348C23×C4—261no—
349C23×C4—261no—
350C22×C8—131no—
351C22×C8—134no—
352C22×C8—131no—
353C22×C8—262no—
354C22×C8—262no—
355C22×C8C22×D1311yescharacteristic
356C22×C8C22×D1311yescharacteristic
357C2×C4⋊C4—21no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—134no—
361C2×C4⋊C4—134no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—262no—
365C2×C4⋊C4—262no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4C22×D1311yescharacteristic
372C2×C4⋊C4C22×D1311yescharacteristic
373C2×C4⋊C4C22×D1311yescharacteristic
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C22⋊C4—131no—
376C2×C22⋊C4—131no—
377C2×C22⋊C4—261no—
378C2×C22⋊C4—261no—
379C2×C42—21no—
380C2×C42—131no—
381C2×C42—261no—
382C2×C42—261no—
383C2×C42—261no—
384C2×C42C22×D1311yescharacteristic
385#107—134no—
386#107—134no—
387#107—134no—
388#107—262no—
389#107—262no—
390#107C4×D1314yes—
391C22⋊C8—262no—
392C4×C8—262no—
393C4×C8—262no—
394#95—21no—
395#95—21no—
396#95—131no—
397#95—131no—
398#95—261no—
399#95—261no—
400#95—261no—
401#95—261no—
402#95—261no—
403#95—261no—
404#95—261no—
405#95—261no—
406C2×C13#234411yescharacteristic
407C2×C13C2×C4×Q1611yescharacteristic
408C2×C13#294811yescharacteristic
409C2×C13#333811yescharacteristic
410C2×C13#333811yescharacteristic
411C2×C13#333911yescharacteristic
412C2×C13#333911yescharacteristic
413D13—24no—
414C24—131no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—131no—
420C22×C4—131no—
421C22×C4—132no—
422C22×C4—132no—
423C22×C4—131no—
424C22×C4—264no—
425C22×C4—264no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—261no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4—1041no—
435C22×C4—1041no—
436C22×C4—1041no—
437C22×C4—1041no—
438C22×C4D4×D1311yescharacteristic
439C22×C4D4×D1311yescharacteristic
440C22×C4C23×D1311yescharacteristic
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—132no—
447C2×C8—132no—
448C2×C8—132no—
449C2×C8—268no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8C2×C4×D1312yes—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—81no—
461C4⋊C4—132no—
462C4⋊C4—132no—
463C4⋊C4—264no—
464C4⋊C4—264no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—1041no—
472C4⋊C4—1041no—
473C4⋊C4—1041no—
474C4⋊C4C2×C4×D1312yes—
475C4⋊C4C2×C4×D1312yes—
476C22⋊C4—134no—
477C22⋊C4—262no—
478C22⋊C4—522no—
479C22⋊C4—522no—
480C42—21no—
481C42—21no—
482C42—81no—
483C42—261no—
484C42—261no—
485C42—1041no—
486C42—1041no—
487C42—1041no—
488C13#2261211yescharacteristic, complemented, Sylow
489C23—132no—
490C23—132no—
491C23—132no—
492C23—261no—
493C23—261no—
494C23—261no—
495C23—261no—
496C23C2×D4×D1311yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
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—132no—
515C2×C4—132no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—262no—
521C2×C4—262no—
522C2×C4—262no—
523C2×C4—262no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—262no—
527C2×C4—262no—
528C2×C4—261no—
529C2×C4—521no—
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—1044no—
540C2×C4—1044no—
541C2×C4Q16×D1312yes—
542C2×C4C22×C4×D1311yescharacteristic
543C2×C4#8825411yescharacteristic
544C2×C4#41×D1311yescharacteristic
545C2×C4#41×D1311yescharacteristic
546C2×C4#41×D1311yescharacteristic
547C2×C4#8825711yescharacteristic
548C8—22no—
549C8—41no—
550C8—134no—
551C8—521no—
552C22—134no—
553C22—262no—
554C22—262no—
555C22—262no—
556C22—262no—
557C22—262no—
558C22—262no—
559C22C4×D4×D1311yescharacteristic
560C22#1171933611yescharacteristic
561C22#1171936011yescharacteristic
562C22C2×Q16×D1311yescharacteristic
563C22D13×#13511yescharacteristic
564C22#1171947911yescharacteristic
565C22#1171947911yescharacteristic
566C4—22no—
567C4—41no—
568C4—42no—
569C4—42no—
570C4—81no—
571C4—81no—
572C4—262no—
573C4—262no—
574C4—521no—
575C4—522no—
576C4—522no—
577C4—1041no—
578C4—1041no—
579C4D13×#11711yescharacteristic
580C4#1171927711yescharacteristic
581C4#1171939811yescharacteristic
582C4#1171941311yescharacteristic
583C2—264no—
584C2#1311770211yescharacteristic
585C2C4×Q16×D1311yescharacteristic
586C2#1312368511yescharacteristic
587C2#1312722311yescharacteristic
588C2#1312722711yescharacteristic
589C2#1312723111yescharacteristic
590C2#1312723511yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1921C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1921D13
hypocenterC13#22612
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
4. #13115568C2semidirect
5. #13115566C2semidirect
6. #13115430C2semidirect
7. #13115429C2semidirect
8. #13115427C2semidirect
12. C4×#88047C2semidirect
13. #13114728C2semidirect
15. C13×#1921C2semidirect
43. D13×#107C4semidirect
202. #1921D13semidirect
488. C13#22612semidirect

Maximal subgroups

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

subgroupindex
C2×D13×#1072
#131177122
#131177092
#131155682
#131155662
#131154302
#131154292
#131154272
#131149252
#131148642
C4×#880472
#131147282
#131146062
C13×#19212
#2261213