Finite Group Databasebeta

← #15834914

Subgroups — #15834914

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125400C211yesmaximal, characteristic
2#13123996C211yesmaximal, characteristic, complemented
3#13123992C211yesmaximal, characteristic, complemented
4#13113730C211yesmaximal, characteristic, complemented
5#13113718C211yesmaximal, characteristic, complemented
6#13113717C211yesmaximal, characteristic, complemented
7#13113711C211yesmaximal, characteristic, complemented
8#13113696C211yesmaximal, characteristic, complemented
9#13113690C211yesmaximal, characteristic, complemented
10#13113640C211yesmaximal, characteristic, complemented
11#13113628C211yesmaximal, characteristic, complemented
12C2×#11718071C211yesmaximal, characteristic, complemented
13#13113250C211yesmaximal, characteristic, complemented
14M16×#1055C211yesmaximal, characteristic, complemented
15C13×#1483C211yesmaximal, characteristic, complemented
16C13×#529C2211yescharacteristic
17#11719184C2211yescharacteristic
18C2×C13×C4⋊C8C2211yescharacteristic
19C4×C13×M16C2211yescharacteristic
20#11718772—21no—
21C8×C22⋊D13—21no—
22#11718729C411yescharacteristic
23#11718725C411yescharacteristic
24#11718720C411yescharacteristic
25#11718717C411yescharacteristic
26#11718712C411yescharacteristic
27#11718709C411yescharacteristic
28#11718702C411yescharacteristic
29#11718699C411yescharacteristic
30C4×#6107C2211yescharacteristic
31C4×#6106C2211yescharacteristic
32#11718685C2211yescharacteristic
33Q8×#1055C2211yescharacteristic
34C4×#6105C2211yescharacteristic
35C4×#6104C2211yescharacteristic
36#11718673C2211yescharacteristic
37#11718672—21no—
38D4×#1055—21no—
39D4×#1055C2211yescharacteristic
40#11718661—21no—
41#11718660—21no—
42#11718586C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×C4×#1055C2211yescharacteristic
45#11718501—21no—
46#11718500—21no—
47#11718499C2211yescharacteristic
48#11718495C2211yescharacteristic
49#11718492C2211yescharacteristic
50#11718491C2211yescharacteristic
51C13×Q8⋊C8C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊C8C2211yescharacteristic
55#11718071C2211yescharacteristic
56#11718071C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718047C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×M16—21no—
68C22×C8×C13—21no—
69C13×#126—21no—
70C13×#125C2×C411yescharacteristic
71C13×#124C2×C411yescharacteristic
72C13×#123—21no—
73C13×C22⋊Q8C2×C411yescharacteristic
74C13×#121C2×C411yescharacteristic
75C4×Q8×C13C2311yescharacteristic
76C4×D4×C13—21no—
77C4×D4×C13C2311yescharacteristic
78C13×#117—21no—
79C2×C42×C13C2311yescharacteristic
80C2×#6107C2×C411yescharacteristic
81C2×#6106C2×C411yescharacteristic
82C2×#6105C2×C411yescharacteristic
83C2×#6104C2×C411yescharacteristic
84#88184C2×C411yescharacteristic
85#88183—21no—
86C4×C22⋊D13—21no—
87#88178C2×C411yescharacteristic
88C2×#6099—21no—
89C22×#1055—21no—
90C22×#1055—21no—
91C22×#1055C2×C411yescharacteristic
92C22×#1055C2×C411yescharacteristic
93C2×#6094—21no—
94C2×C8×D13—21no—
95#88130—21no—
96#88129C2×C411yescharacteristic
97C4×D52C2311yescharacteristic
98#88126—21no—
99#88124C2×C411yescharacteristic
100C4×Dic26C2311yescharacteristic
101C13×C4⋊C8—21no—
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×#97—21no—
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107#88075C2×C411yescharacteristic
108#88075C2×C411yescharacteristic
109#88072C2×C411yescharacteristic
110#88072C2×C411yescharacteristic
111C22⋊#1055—21no—
112C22⋊#1055—21no—
113C22⋊#1055D411yescharacteristic
114C22⋊#1055D411yescharacteristic
115#88060—21no—
116#88060—21no—
117#88055—21no—
118#88054—21no—
119#88054—21no—
120C8×Dic13—21no—
121#88050C2×C411yescharacteristic
122#88050C2×C411yescharacteristic
123#88049C2×C411yescharacteristic
124#88049C2×C411yescharacteristic
125#88048C2×C411yescharacteristic
126#88048C2×C411yescharacteristic
127#88047C2×C411yescharacteristic
128#88047C2×C411yescharacteristic
129C4⋊#1055—21no—
130C4⋊#1055—21no—
131C4⋊#1055—21no—
132C4⋊#1055D411yescharacteristic
133C4⋊#1055D411yescharacteristic
134C4⋊#1055C2311yescharacteristic
135C4⋊#1055C2311yescharacteristic
136#88043—21no—
137C4×#1055—21no—
138C4×#1055C2×C411yescharacteristic
139C4×#1055C2×C411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18087—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13—21no—
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13#4111yescharacteristic
152C2×C22⋊D13—21no—
153C2×D52C22×C411yescharacteristic
154C2×C4×D13—21no—
155C2×Dic26C22×C411yescharacteristic
156C13×M16—24no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—81no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4C22×C411yescharacteristic
167C13×C4⋊C4C22×C411yescharacteristic
168C13×C22⋊C4—21no—
169C13×C22⋊C4—21no—
170C13×C22⋊C4—21no—
171C13×C22⋊C4—21no—
172C13×C22⋊C4—21no—
173C42×C13—21no—
174C42×C13C22×C411yescharacteristic
175C42×C13C2×D411yescharacteristic
176C42×C13#4111yescharacteristic
177C42×C13C2411yescharacteristic
178C22⋊Dic13—21no—
179#6107—22no—
180#6106—41no—
181#6105—41no—
182#6104—22no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187C4⋊Dic13C22×C411yescharacteristic
188C4⋊Dic13C22×C411yescharacteristic
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193C4×Dic13—21no—
194#6099—81no—
195C2×#1055—22no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—41no—
199C2×#1055—81no—
200C2×#1055—81no—
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209#6094—81no—
210C8×D13—81no—
211#3168—131no—
212#2994—131no—
213#2994—131no—
214#1591—131no—
215#1589—131no—
216#1588—131no—
217#1588—131no—
218#1585—131no—
219#1585—131no—
220C8×Q16—131no—
221C8×D8—131no—
222C2×#335—131no—
223#1483—131no—
224#1483D1311yescharacteristic, complemented
225C8×M16—131no—
226C23×C13—21no—
227C23×C13C4×D411yescharacteristic
228C22×D13—21no—
229Q8×C13—21no—
230Q8×C13—21no—
231D4×C13—21no—
232D4×C13—21no—
233D4×C13—42no—
234C2×C4×C13—22no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C4×D411yescharacteristic
247C2×C4×C13C23×C411yescharacteristic
248C2×C4×C13C22×D411yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C22⋊D13—42no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254D52—21no—
255D52—21no—
256C4×D13—41no—
257C4×D13—41no—
258Dic26—21no—
259Dic26—21no—
260C8×C13—22no—
261C8×C13—22no—
262C8×C13—41no—
263C8×C13—41no—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—21no—
269#1055—21no—
270#1055—21no—
271#1055—41no—
272#1055—41no—
273#1055#13112yes—
274#529—131no—
275#529C2×D1311yescharacteristic
276#499—131no—
277#495—131no—
278#488—131no—
279#488—131no—
280#467—131no—
281#466—131no—
282#465—131no—
283#465—131no—
284#446—131no—
285#446—131no—
286C8×Q8—131no—
287C8×Q8—131no—
288C4×Q16—131no—
289C4×SD16—131no—
290C4×SD16—131no—
291C4×D8—131no—
292#436—131no—
293#436—131no—
294#435—261no—
295#435—261no—
296C8×D4—131no—
297C8×D4—131no—
298C8×D4—261no—
299C8×D4—261no—
300#433—261no—
301#433—261no—
302#431—131no—
303#424—261no—
304#424—261no—
305C2×C4⋊C8—131no—
306C2×C4⋊C8C2×D1311yescharacteristic
307C4×M16C2×D1311yescharacteristic
308C2×C4×C8—131no—
309#335—131no—
310#335—131no—
311#335—131no—
312#335—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8C2×D1311yescharacteristic
316Q8⋊C8C2×D1311yescharacteristic
317D4⋊C8—131no—
318D4⋊C8—131no—
319D4⋊C8C2×D1311yescharacteristic
320D4⋊C8C2×D1311yescharacteristic
321#322—131no—
322#322—131no—
323C82—131no—
324C82—131no—
325C22×C13—21no—
326C22×C13—21no—
327C22×C13—41no—
328C22×C13—41no—
329C22×C13—41no—
330C22×C13#44312yes—
331C22×C13C2×C4×D411yescharacteristic
332C2×D13—41no—
333C2×D13—41no—
334C2×D13—41no—
335C4×C13—21no—
336C4×C13—21no—
337C4×C13—21no—
338C4×C13—21no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13C2×#13111yescharacteristic
343C4×C13#56811yescharacteristic
344C4×C13#57611yescharacteristic
345C4×C13#57811yescharacteristic
346Dic13—41no—
347Dic13—41no—
348Dic13—41no—
349C2×Q16—131no—
350C2×SD16—131no—
351C2×SD16—131no—
352C2×D8—131no—
353C2×M16—21no—
354C2×M16—261no—
355C2×M16—261no—
356C22×C8—21no—
357C22×C8—131no—
358C22×C8—131no—
359C22×C8—261no—
360C22×C8—261no—
361C22×C8—261no—
362#126—21no—
363#126—261no—
364#125—131no—
365#125C4×D1311yescharacteristic
366#124—131no—
367#124C4×D1311yescharacteristic
368#123—21no—
369#123—261no—
370C22⋊Q8—131no—
371C22⋊Q8C4×D1311yescharacteristic
372#121—131no—
373#121C4×D1311yescharacteristic
374C4×Q8—131no—
375C4×Q8C22×D1311yescharacteristic
376C4×D4—21no—
377C4×D4—131no—
378C4×D4—261no—
379C4×D4C22×D1311yescharacteristic
380#117—21no—
381#117—261no—
382C2×C42C22×D1311yescharacteristic
383#107—131no—
384#107—131no—
385#106—131no—
386#106—131no—
387C4⋊C8—21no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—131no—
392C4⋊C8—261no—
393C4⋊C8—261no—
394C4⋊C8—261no—
395C4⋊C8—261no—
396C4⋊C8—261no—
397C4⋊C8C22×D1311yescharacteristic
398C4⋊C8C22×D1311yescharacteristic
399#103—131no—
400#103—131no—
401#103—131no—
402#103—131no—
403#102—131no—
404#102—131no—
405#102—131no—
406#102—131no—
407C22⋊C8—131no—
408C22⋊C8—131no—
409C22⋊C8—261no—
410C22⋊C8—261no—
411C22⋊C8—261no—
412C22⋊C8—261no—
413#97—21no—
414#97—261no—
415#97—261no—
416C4×C8—131no—
417C4×C8—131no—
418C4×C8—131no—
419C4×C8—131no—
420C4×C8—131no—
421C4×C8—131no—
422C4×C8—261no—
423C4×C8—261no—
424C4×C8C22×D1311yescharacteristic
425C4×C8C22×D1311yescharacteristic
426C2×C13—22no—
427C2×C13—81no—
428C2×C13#293511yescharacteristic
429C2×C13#295111yescharacteristic
430C2×C13C2×#44311yescharacteristic
431D13—81no—
432C2×Q8—131no—
433C2×Q8C2×C4×D1311yescharacteristic
434C2×D4—21no—
435C2×D4—131no—
436C2×D4—261no—
437C2×D4C2×C4×D1311yescharacteristic
438C22×C4—21no—
439C22×C4—261no—
440C22×C4C2×C4×D1311yescharacteristic
441C22×C4D4×D1311yescharacteristic
442C22×C4#612911yescharacteristic
443Q16—262no—
444SD16—521no—
445SD16—521no—
446D8—262no—
447M16—24no—
448M16—1041no—
449M16—1041no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—81no—
455C2×C8—131no—
456C2×C8—131no—
457C2×C8—131no—
458C2×C8—131no—
459C2×C8—131no—
460C2×C8—131no—
461C2×C8—131no—
462C2×C8—131no—
463C2×C8—262no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—521no—
467C2×C8—1041no—
468C2×C8—1041no—
469C2×C8—1041no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—131no—
475C4⋊C4—131no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4C2×C4×D1311yescharacteristic
481C4⋊C4C2×C4×D1311yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—261no—
488C22⋊C4—261no—
489C22⋊C4—261no—
490C22⋊C4—261no—
491C22⋊C4—261no—
492C42—21no—
493C42—261no—
494C42C2×C4×D1311yescharacteristic
495C42D4×D1311yescharacteristic
496C42#612911yescharacteristic
497C42C23×D1311yescharacteristic
498C13#1808711yescharacteristic, complemented, Sylow
499C23—21no—
500C23—261no—
501C23#8813511yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—261no—
505Q8—261no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—261no—
510D4—261no—
511D4—522no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—521no—
526C2×C4—521no—
527C2×C4#8813511yescharacteristic
528C2×C4#8813511yescharacteristic
529C2×C4#8813511yescharacteristic
530C2×C4C22×C4×D1311yescharacteristic
531C2×C4C2×D4×D1311yescharacteristic
532C2×C4C2×#612911yescharacteristic
533C8—22no—
534C8—22no—
535C8—41no—
536C8—41no—
537C8—132no—
538C8—261no—
539C8—261no—
540C8—261no—
541C8—261no—
542C8—261no—
543C8—261no—
544C8—261no—
545C8—521no—
546C8—521no—
547C22—21no—
548C22—21no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—521no—
553C22—521no—
554C22—521no—
555C22#1171848512yes—
556C22C2×#8813511yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—521no—
565C4—521no—
566C4—521no—
567C4D13×#13111yescharacteristic
568C4#1171945511yescharacteristic
569C4#1171947911yescharacteristic
570C4#1171948411yescharacteristic
571C2—22no—
572C2—81no—
573C2—1041no—
574C2#1312357611yescharacteristic
575C2#1312370711yescharacteristic
576C2C2×#1171848511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1483C2
socleC22×C13C2×C4×D4
prime radical#11718699C4
cosocleC42×C13C24
hypercenter#1483D13
hypocenterC13#18087
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1483

Complements

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

NH ≅ G/Ntype
2. #13123996C2semidirect
3. #13123992C2semidirect
4. #13113730C2semidirect
5. #13113718C2semidirect
6. #13113717C2semidirect
7. #13113711C2semidirect
8. #13113696C2semidirect
9. #13113690C2semidirect
10. #13113640C2semidirect
11. #13113628C2semidirect
12. C2×#11718071C2semidirect
13. #13113250C2semidirect
14. M16×#1055C2semidirect
15. C13×#1483C2semidirect
224. #1483D13semidirect
498. C13#18087semidirect

Maximal subgroups

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

subgroupindex
#131254002
#131239962
#131239922
#131137302
#131137182
#131137172
#131137112
#131136962
#131136902
#131136402
#131136282
C2×#117180712
#131132502
M16×#10552
C13×#14832
#1808713