Finite Group Databasebeta

← #15880679

Subgroups — #15880679

Order 3328.

782 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718522C211yesmaximal, characteristic
2#13117728C211yesmaximal, characteristic
3#13117712C211yesmaximal, characteristic
4#13115580C211yesmaximal, characteristic, complemented
5#13115425C211yesmaximal, characteristic, complemented
6#13115424C211yesmaximal, characteristic, complemented
7#13115411C211yesmaximal, characteristic, complemented
8#13115410C211yesmaximal, characteristic, complemented
9#13114930C211yesmaximal, characteristic
10#13114921C211yesmaximal, characteristic
11#13114866C211yesmaximal, characteristic
12#13114736C211yesmaximal, characteristic, complemented
13C4×#88058C211yesmaximal, characteristic, complemented
14#13114619C211yesmaximal, characteristic
15C13×#1941C211yesmaximal, characteristic, complemented
16C22×#6094C2211yescharacteristic
17C2×#88146C2211yescharacteristic
18C2×C4⋊C4×D13C2211yescharacteristic
19C2×C13×#106C2211yescharacteristic
20C2×C13×#106C2211yescharacteristic
21C2×C4×C8×C13C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C2×#88060C2211yescharacteristic
25C2×#88058C2211yescharacteristic
26C2×#88058C2211yescharacteristic
27C2×#88055C2211yescharacteristic
28#11718651—21no—
29#11718648—21no—
30#11718648C2211yescharacteristic
31#11718648C2211yescharacteristic
32#11718646C2211yescharacteristic
33#11718646C2211yescharacteristic
34#11718639—21no—
35C4⋊C4×Dic13—21no—
36C4⋊C4×Dic13C2211yescharacteristic
37C4⋊C4×Dic13C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C4×#6103C2211yescharacteristic
41C4×C4⋊Dic13C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43#11718522C418yescomplemented
44#11718331—21no—
45#11718327—21no—
46#11718316—21no—
47#11718312—21no—
48C13×#340C2211yescharacteristic
49C13×#340C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×C4×D13—21no—
61C22×C4×D13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103D411yescharacteristic
75C2×#6103D411yescharacteristic
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×#6101—21no—
83C2×C4×Dic13—21no—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C2×#6094—22no—
92C2×#6094—22no—
93C2×#6094C2×C414yes—
94#88146—22no—
95#88146C2×C414yes—
96C4⋊C4×D13—22no—
97C4⋊C4×D13C2×C414yes—
98C13×#106—22no—
99C13×#106C2×C414yes—
100C4×C8×C13—22no—
101C13×#95—21no—
102C13×#95—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#88071D411yescharacteristic
112#88071D411yescharacteristic
113#88060—22no—
114#88058—22no—
115#88058C2×C414yes—
116#88055—22no—
117#88048C2×C414yes—
118#88047C2×C414yes—
119#22623—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—81no—
141C2×C4×D13—81no—
142C2×C4×D13C22×C412yes—
143C2×C4×D13#4112yes—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13C22×C412yes—
148C2×C8×C13#4112yes—
149C2×C8×C13#4112yes—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—42no—
157C13×C4⋊C4—81no—
158C13×C4⋊C4C22×C412yes—
159C13×C4⋊C4C22×C412yes—
160C42×C13—21no—
161C42×C13—21no—
162#6103—24no—
163#6103—22no—
164#6103—41no—
165#6103—42no—
166#6103—81no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—42no—
174C4⋊Dic13—81no—
175C4⋊Dic13C22×C412yes—
176C4⋊Dic13C22×C412yes—
177#6101—24no—
178C4×Dic13—21no—
179C4×Dic13—21no—
180C4×Dic13—24no—
181C4×Dic13—81no—
182C4×Dic13—81no—
183C4×Dic13—81no—
184C4×Dic13—81no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055C22×C412yes—
191#6094—28no—
192C2×#428—131no—
193#2347—131no—
194#2345—131no—
195#1944—131no—
196#1941D1311yescharacteristic, complemented
197#1921—131no—
198#1920—131no—
199#1919—131no—
200#1918—131no—
201#1825—131no—
202#1823—131no—
203#1809—131no—
204#1776—131no—
205C4×#107—131no—
206#1753—131no—
207C23×C13C22×D411yescharacteristic
208C22×D13—21no—
209C22×D13—21no—
210C22×D13—21no—
211C22×D13—21no—
212C22×D13—21no—
213C22×D13—21no—
214C22×D13C4×D412yes—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
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#13712yes—
233C2×C4×C13C23×C411yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C132−1+411yescharacteristic
238C2×C4×C132−1+411yescharacteristic
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
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×Dic13C4×D412yes—
260C4×D13—22no—
261C4×D13—22no—
262C4×D13—22no—
263C4×D13—22no—
264C4×D13—84no—
265C8×C13—41no—
266C8×C13#11714yes—
267#1055—22no—
268#1055—41no—
269C22×M16—131no—
270C2×#117—131no—
271C22×C4⋊C4—131no—
272#428—138no—
273C2×#107—131no—
274C2×#107—131no—
275C2×#107—131no—
276C2×#106—131no—
277C2×#106C2×D1311yescharacteristic
278C2×#106C2×D1311yescharacteristic
279C2×C22⋊C8—131no—
280C2×#97—131no—
281C2×C4×C8C2×D1311yescharacteristic
282#389—131no—
283#389—131no—
284#389C2×D1311yescharacteristic
285#389C2×D1311yescharacteristic
286#388—261no—
287#388—261no—
288#387—261no—
289#387—261no—
290#383—261no—
291#380—131no—
292#380—131no—
293#380—261no—
294C4×C4⋊C4—131no—
295C4×C4⋊C4—131no—
296C4×C4⋊C4—131no—
297C4×C4⋊C4—131no—
298C4×C4⋊C4—261no—
299C4×C22⋊C4—131no—
300C4×C22⋊C4—261no—
301#340—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340C2×D1311yescharacteristic
310#340C2×D1311yescharacteristic
311#336—131no—
312#336—131no—
313C22×C13C2×C4×D411yescharacteristic
314C22×C13#54711yescharacteristic
315C22×C13#54711yescharacteristic
316C22×C13C2×#13711yescharacteristic
317C22×C13#57511yescharacteristic
318C22×C13#57611yescharacteristic
319C22×C13#57711yescharacteristic
320C2×D13—22no—
321C2×D13—22no—
322C2×D13—22no—
323C2×D13—41no—
324C2×D13—41no—
325C2×D13—41no—
326C2×D13—41no—
327C4×C13—22no—
328C4×C13—41no—
329C4×C13—42no—
330C4×C13—42no—
331C4×C13—81no—
332C4×C13—81no—
333C4×C13C2×#11711yescharacteristic
334C4×C13#51911yescharacteristic
335C4×C13#55211yescharacteristic
336C4×C13#55211yescharacteristic
337Dic13—22no—
338Dic13—41no—
339Dic13—41no—
340Dic13—42no—
341Dic13—42no—
342Dic13—81no—
343Dic13—81no—
344C23×C4—131no—
345C23×C4—261no—
346C2×M16—134no—
347C2×M16—262no—
348C2×M16—262no—
349C22×C8—131no—
350C22×C8—131no—
351C22×C8C22×D1311yescharacteristic
352C22×C8C22×D1311yescharacteristic
353#117—134no—
354#117—262no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—134no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—262no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4C22×D1311yescharacteristic
367C2×C4⋊C4C22×D1311yescharacteristic
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C22⋊C4—131no—
371C2×C22⋊C4—131no—
372C2×C22⋊C4—261no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C42—131no—
376C2×C42—261no—
377C2×C42—261no—
378C2×C42—261no—
379C2×C42—261no—
380C2×C42—261no—
381C2×C42C22×D1311yescharacteristic
382#107—134no—
383#107—134no—
384#107—262no—
385#106—22no—
386#106—134no—
387#106C4×D1314yes—
388C22⋊C8—262no—
389#97—262no—
390C4×C8—22no—
391#95—21no—
392#95—21no—
393#95—131no—
394#95—131no—
395#95—261no—
396#95—261no—
397#95—261no—
398#95—261no—
399#95—261no—
400#95—261no—
401#95—261no—
402#95—261no—
403C2×C13#234411yescharacteristic
404C2×C13C4×#13711yescharacteristic
405C2×C13#294611yescharacteristic
406C2×C13#334611yescharacteristic
407C2×C13#335011yescharacteristic
408C2×C13#335511yescharacteristic
409C2×C13#335611yescharacteristic
410D13—42no—
411C24—131no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—131no—
417C22×C4—132no—
418C22×C4—132no—
419C22×C4—131no—
420C22×C4—131no—
421C22×C4—264no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—261no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—1041no—
431C22×C4—1041no—
432C22×C4D4×D1311yescharacteristic
433C22×C4D4×D1311yescharacteristic
434C22×C4C23×D1311yescharacteristic
435M16—268no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—132no—
440C2×C8—261no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8C2×C4×D1312yes—
446C2×C8#612912yes—
447C2×C8#613112yes—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—42no—
455C4⋊C4—81no—
456C4⋊C4—132no—
457C4⋊C4—132no—
458C4⋊C4—264no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—522no—
466C4⋊C4—1041no—
467C4⋊C4C2×C4×D1312yes—
468C4⋊C4C2×C4×D1312yes—
469C22⋊C4—264no—
470C22⋊C4—262no—
471C22⋊C4—521no—
472C22⋊C4—522no—
473C22⋊C4—1041no—
474C42—21no—
475C42—21no—
476C42—264no—
477C42—261no—
478C42—261no—
479C42—1041no—
480C42—1041no—
481C42—1041no—
482C42—1041no—
483C13#2262311yescharacteristic, complemented, Sylow
484C23—132no—
485C23—261no—
486C23—261no—
487C23—261no—
488C23—261no—
489C23—261no—
490C23—261no—
491C23C2×D4×D1311yescharacteristic
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—21no—
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—41no—
508C2×C4—41no—
509C2×C4—132no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—262no—
513C2×C4—262no—
514C2×C4—262no—
515C2×C4—262no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—262no—
523C2×C4—262no—
524C2×C4—521no—
525C2×C4—521no—
526C2×C4—521no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—1044no—
535C2×C4#8816912yes—
536C2×C4C22×C4×D1311yescharacteristic
537C2×C4C2×#612911yescharacteristic
538C2×C4C2×#613111yescharacteristic
539C2×C4#8825411yescharacteristic
540C2×C4#41×D1311yescharacteristic
541C2×C4#8825711yescharacteristic
542C8—41no—
543C8—262no—
544C8—521no—
545C8#8814614yes—
546C22—262no—
547C22—262no—
548C22—262no—
549C22—521no—
550C22—521no—
551C22—521no—
552C22—521no—
553C22C4×D4×D1311yescharacteristic
554C22#1171931611yescharacteristic
555C22#1171943111yescharacteristic
556C22C2×#8816911yescharacteristic
557C22#1171946711yescharacteristic
558C22#1171947311yescharacteristic
559C22#1171947411yescharacteristic
560C4—22no—
561C4—42no—
562C4—42no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—262no—
567C4—521no—
568C4—521no—
569C4—522no—
570C4—522no—
571C4—1041no—
572C4—1041no—
573C4C2×#8814611yescharacteristic
574C4#1171927711yescharacteristic
575C4#1171934411yescharacteristic
576C4#1171939911yescharacteristic
577C2—522no—
578C2#1311770411yescharacteristic
579C2C4×#8816911yescharacteristic
580C2#1312366311yescharacteristic
581C2#1312732711yescharacteristic
582C2#1312738711yescharacteristic
583C2#1312744011yescharacteristic
584C2#1312745011yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1941C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1941D13
hypocenterC13#22623
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1941

Complements

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

NH ≅ G/Ntype
4. #13115580C2semidirect
5. #13115425C2semidirect
6. #13115424C2semidirect
7. #13115411C2semidirect
8. #13115410C2semidirect
12. #13114736C2semidirect
13. C4×#88058C2semidirect
15. C13×#1941C2semidirect
43. #11718522C4semidirect
196. #1941D13semidirect
483. C13#22623semidirect

Maximal subgroups

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

subgroupindex
C2×#117185222
#131177282
#131177122
#131155802
#131154252
#131154242
#131154112
#131154102
#131149302
#131149212
#131148662
#131147362
C4×#880582
#131146192
C13×#19412
#2262313