Finite Group Databasebeta

← #15863497

Subgroups — #15863497

Order 3328.

810 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718369C211yesmaximal, characteristic
2#13117446C211yesmaximal, characteristic
3#13117444C211yesmaximal, characteristic
4#13115004C211yesmaximal, characteristic, complemented
5#13114966C211yesmaximal, characteristic, complemented
6#13114963C211yesmaximal, characteristic, complemented
7#13114870C211yesmaximal, characteristic
8#13114866C211yesmaximal, characteristic
9#13114862C211yesmaximal, characteristic
10#13114858C211yesmaximal, characteristic
11#13114736C211yesmaximal, characteristic, complemented
12#13114735C211yesmaximal, characteristic, complemented
13#107×Dic13C211yesmaximal, characteristic, complemented
14#106×Dic13C211yesmaximal, characteristic, complemented
15C13×#1847C211yesmaximal, characteristic, complemented
16C22×#6094C2211yescharacteristic
17C22×C8×D13C2211yescharacteristic
18C2×#88126C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C2×C13×#107C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C2×C13×#106C2211yescharacteristic
23C2×C13×#97C2211yescharacteristic
24C13×#384C2211yescharacteristic
25C13×#382C2211yescharacteristic
26C2×#88058C2211yescharacteristic
27C2×#88058C2211yescharacteristic
28C2×#88057C2211yescharacteristic
29C2×#88057C2211yescharacteristic
30C2×#88055C2211yescharacteristic
31C2×C8×Dic13C2211yescharacteristic
32#11718651—21no—
33#11718651—21no—
34#11718648C2211yescharacteristic
35#11718648C2211yescharacteristic
36#11718648C2211yescharacteristic
37#11718648C2211yescharacteristic
38#11718639—21no—
39#11718639—21no—
40C4⋊C4×Dic13C2211yescharacteristic
41C4⋊C4×Dic13C2211yescharacteristic
42C4⋊C4×Dic13C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44#11718597C2211yescharacteristic
45#11718596C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718369C418yescomplemented
48#11718331—21no—
49#11718331—21no—
50#11718316—21no—
51#11718316—21no—
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×C4×D13C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C42×C13C2311yescharacteristic
70C2×#6103—21no—
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×#6101D411yescharacteristic
83C2×#6101D411yescharacteristic
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—
94C2×C8×D13—22no—
95C2×C8×D13—22no—
96C2×C8×D13C2×C414yes—
97#88126C2×C414yes—
98#88126Q814yes—
99C13×#107—22no—
100C13×#107—22no—
101C13×#106—22no—
102C13×#106—22no—
103C13×#97C2×C414yes—
104C13×#95—21no—
105C13×#95—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#88071—21no—
115#88071—21no—
116#88058—22no—
117#88058—22no—
118#88057—22no—
119#88057—22no—
120#88055C2×C414yes—
121C8×Dic13C2×C414yes—
122C4×#1055C2×C414yes—
123#20822—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×D13C22×C412yes—
144C2×C4×D13C2×Q812yes—
145C2×C8×C13C22×C412yes—
146C2×C8×C13C22×C412yes—
147C2×C8×C13#4112yes—
148C2×C8×C13#4112yes—
149C2×C8×C13#4112yes—
150C2×C8×C13#4112yes—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
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⋊C4—81no—
161C42×C13C22×C412yes—
162C42×C13C2×Q812yes—
163#6103—81no—
164#6103—81no—
165#6103—81no—
166#6103—81no—
167#6103C4⋊C414yes—
168#6103C4⋊C414yes—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—81no—
178C4⋊Dic13—81no—
179#6101C4⋊C414yes—
180#6101C4⋊C414yes—
181C4×Dic13—81no—
182C4×Dic13—81no—
183C4×Dic13—81no—
184C4×Dic13—81no—
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—28no—
194C8×D13—28no—
195C2×#405—131no—
196#2314—131no—
197#2314—131no—
198#1847—131no—
199#1847D1311yescharacteristic, complemented
200#1835—131no—
201#1834—131no—
202#1809—131no—
203#1809—131no—
204#1808—131no—
205#1807—131no—
206#1776—131no—
207#1776—131no—
208C4×#107—131no—
209C4×#106—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×C13C2×#4111yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C2×C4×C13C2×#4111yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
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—
267C8×C13#11714yes—
268C8×C13#11714yes—
269#1055—22no—
270#1055—22no—
271C22×M16—131no—
272C23×C8—131no—
273C2×#117—131no—
274C2×#107—131no—
275C2×#107—131no—
276C2×#107C2×D1311yescharacteristic
277C2×#107C2×D1311yescharacteristic
278C2×#106—131no—
279C2×#106—131no—
280C2×#106C2×D1311yescharacteristic
281C2×#106C2×D1311yescharacteristic
282#405—138no—
283C2×#97—131no—
284C2×#97C2×D1311yescharacteristic
285C2×C4×C8—131no—
286C2×C4×C8—131no—
287#388—261no—
288#388—261no—
289#388—261no—
290#388—261no—
291#387—261no—
292#387—261no—
293#387—261no—
294#387—261no—
295#384—131no—
296#384C2×D1311yescharacteristic
297#382—131no—
298#382C2×D1311yescharacteristic
299#380—131no—
300#380—131no—
301#380—131no—
302#380—131no—
303C4×C4⋊C4—131no—
304C4×C4⋊C4—131no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315C22×C13C22×C4⋊C411yescharacteristic
316C22×C13#53211yescharacteristic
317C22×C13#53211yescharacteristic
318C22×C13#57611yescharacteristic
319C22×C13#57711yescharacteristic
320C22×C13#57711yescharacteristic
321C22×C13#57811yescharacteristic
322C2×D13—22no—
323C2×D13—22no—
324C2×D13—22no—
325C2×D13—41no—
326C2×D13—41no—
327C2×D13—41no—
328C2×D13—41no—
329C4×C13—22no—
330C4×C13—22no—
331C4×C13—81no—
332C4×C13—81no—
333C4×C13—81no—
334C4×C13—81no—
335C4×C13C2×#11711yescharacteristic
336C4×C13C2×#11711yescharacteristic
337C4×C13#53311yescharacteristic
338C4×C13#53311yescharacteristic
339Dic13—22no—
340Dic13—22no—
341Dic13—22no—
342Dic13—81no—
343Dic13—81no—
344Dic13—81no—
345Dic13—81no—
346C23×C4—131no—
347C2×M16—134no—
348C2×M16—262no—
349C2×M16—262no—
350C22×C8—131no—
351C22×C8—131no—
352C22×C8—134no—
353C22×C8—262no—
354C22×C8—262no—
355C22×C8C22×D1311yescharacteristic
356C22×C8C22×D1311yescharacteristic
357#117—134no—
358#117—134no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C4⋊C4C22×D1311yescharacteristic
372C2×C4⋊C4C22×D1311yescharacteristic
373C2×C22⋊C4—131no—
374C2×C22⋊C4—131no—
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C22⋊C4—261no—
378C2×C22⋊C4—261no—
379C2×C42—131no—
380C2×C42—261no—
381C2×C42—261no—
382C2×C42—261no—
383C2×C42—261no—
384C2×C42C22×D1311yescharacteristic
385#107—22no—
386#107—22no—
387#107—262no—
388#107—262no—
389#106—22no—
390#106—22no—
391#106—262no—
392#106—262no—
393#97—134no—
394#97C4×D1314yes—
395C4×C8—134no—
396C4×C8—134no—
397#95—21no—
398#95—21no—
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—
409C2×C13#228511yescharacteristic
410C2×C13#291211yescharacteristic
411C2×C13#291311yescharacteristic
412C2×C13#317811yescharacteristic
413C2×C13#317811yescharacteristic
414C2×C13#317911yescharacteristic
415C2×C13#317911yescharacteristic
416D13—42no—
417C24—131no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—131no—
423C22×C4—131no—
424C22×C4—131no—
425C22×C4—132no—
426C22×C4—132no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—261no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4D4×D1311yescharacteristic
436C22×C4D4×D1311yescharacteristic
437C22×C4C23×D1311yescharacteristic
438M16—268no—
439C2×C8—132no—
440C2×C8—132no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—268no—
446C2×C8C2×C4×D1312yes—
447C2×C8C2×C4×D1312yes—
448C2×C8#612912yes—
449C2×C8#612912yes—
450C2×C8#613112yes—
451C2×C8#613112yes—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C4⋊C4—134no—
463C4⋊C4—134no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—1041no—
473C4⋊C4—1041no—
474C22⋊C4—134no—
475C22⋊C4—134no—
476C22⋊C4—1041no—
477C22⋊C4—1041no—
478C22⋊C4—1041no—
479C22⋊C4—1041no—
480C42—132no—
481C42—132no—
482C42—1041no—
483C42—1041no—
484C42—1041no—
485C42—1041no—
486C42C2×C4×D1312yes—
487C42Q8×D1312yes—
488C13#2082211yescharacteristic, complemented, Sylow
489C23—132no—
490C23—261no—
491C23—261no—
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—41no—
502C2×C4—41no—
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—132no—
514C2×C4—132no—
515C2×C4—132no—
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—262no—
525C2×C4—262no—
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—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4C4⋊C4×D1312yes—
539C2×C4C4⋊C4×D1312yes—
540C2×C4C22×C4×D1311yescharacteristic
541C2×C4C2×#612911yescharacteristic
542C2×C4C2×#612911yescharacteristic
543C2×C4C2×Q8×D1311yescharacteristic
544C2×C4C2×#613111yescharacteristic
545C2×C4C2×#613111yescharacteristic
546C8—262no—
547C8—262no—
548C8#8814614yes—
549C8#8814614yes—
550C22—262no—
551C22—262no—
552C22—262no—
553C22—521no—
554C22—521no—
555C22—521no—
556C22—521no—
557C22C2×C4⋊C4×D1311yescharacteristic
558C22#1171942111yescharacteristic
559C22#1171943011yescharacteristic
560C22#1171947911yescharacteristic
561C22#1171948011yescharacteristic
562C22#1171948311yescharacteristic
563C22#1171948411yescharacteristic
564C4—22no—
565C4—22no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—262no—
571C4—262no—
572C4—262no—
573C4—1041no—
574C4—1041no—
575C4—1041no—
576C4—1041no—
577C4C2×#8814611yescharacteristic
578C4C2×#8814611yescharacteristic
579C4#1171943311yescharacteristic
580C4#1171943311yescharacteristic
581C2—522no—
582C2#1311724111yescharacteristic
583C2#1312343011yescharacteristic
584C2#1312343511yescharacteristic
585C2#1312550111yescharacteristic
586C2#1312550911yescharacteristic
587C2#1312551611yescharacteristic
588C2#1312552411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1847C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1847D13
hypocenterC13#20822
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
4. #13115004C2semidirect
5. #13114966C2semidirect
6. #13114963C2semidirect
11. #13114736C2semidirect
12. #13114735C2semidirect
13. #107×Dic13C2semidirect
14. #106×Dic13C2semidirect
15. C13×#1847C2semidirect
47. #11718369C4semidirect
199. #1847D13semidirect
488. C13#20822semidirect

Maximal subgroups

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

subgroupindex
C2×#117183692
#131174462
#131174442
#131150042
#131149662
#131149632
#131148702
#131148662
#131148622
#131148582
#131147362
#131147352
#107×Dic132
#106×Dic132
C13×#18472
#2082213