Finite Group Databasebeta

← #16795859

Subgroups — #16795859

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131649C211yesmaximal, characteristic
2#13131624C211yesmaximal, characteristic, complemented
3#13130482C211yesmaximal, characteristic, complemented
4#13130481C211yesmaximal, characteristic, complemented
5#13130479C211yesmaximal, characteristic, complemented
6#13130477C211yesmaximal, characteristic, complemented
7#13130424C211yesmaximal, characteristic, complemented
8#13130423C211yesmaximal, characteristic, complemented
9#13130419C211yesmaximal, characteristic, complemented
10SD16×#1057C211yesmaximal, characteristic, complemented
11#13130400C211yesmaximal, characteristic, complemented
12#13130198C211yesmaximal, characteristic, complemented
13#13130191C211yesmaximal, characteristic
14M16×#1057C211yesmaximal, characteristic, complemented
15#13125435C211yesmaximal, characteristic
16#11719327C2211yescharacteristic
17#11719305C2211yescharacteristic
18#11719158C2211yescharacteristic
19Q8×#1057C2211yescharacteristic
20#11719145C2211yescharacteristic
21#11719144—21no—
22D4×#1057—21no—
23D4×#1057C2211yescharacteristic
24#11719130C2211yescharacteristic
25#11719129C2211yescharacteristic
26#11719119C2211yescharacteristic
27C2×C4×#1057C2211yescharacteristic
28#11719080C2211yescharacteristic
29#11719080C2211yescharacteristic
30#11719078—21no—
31#11719074—21no—
32#11719074C2211yescharacteristic
33#11719074C2211yescharacteristic
34#11719068—21no—
35#11719067—21no—
36#11719062—21no—
37#11719062—21no—
38C13×#468C411yescharacteristic
39#11718828C411yescharacteristic
40SD16×Dic13C2211yescharacteristic
41#11718798C411yescharacteristic
42M16×Dic13C2211yescharacteristic
43#11718713C411yescharacteristic
44#11718703C411yescharacteristic
45#11718537C411yescharacteristic
46#11718534C2211yescharacteristic
47#11718458C411yescharacteristic
48#11718451C2211yescharacteristic
49#11718426C411yescharacteristic
50#11718419C2211yescharacteristic
51Q8⋊#1057C2211yescharacteristic
52Q8⋊#1057C2211yescharacteristic
53D4⋊#1057C2211yescharacteristic
54D4⋊#1057C2211yescharacteristic
55#11718256C2211yescharacteristic
56#11718255C2211yescharacteristic
57#11718254C2211yescharacteristic
58#11718253C2211yescharacteristic
59#11718251C2211yescharacteristic
60#11718251C2211yescharacteristic
61C8×#1057C2211yescharacteristic
62C8×#1057C2211yescharacteristic
63#11718244C2211yescharacteristic
64#11718244C2211yescharacteristic
65#11718244C2211yescharacteristic
66#11718244C2211yescharacteristic
67C2×#6122—21no—
68C2×#6122—21no—
69C22×#1057—21no—
70C22×#1057D411yescharacteristic
71C22×#1057D411yescharacteristic
72C2×C13×SD16C2×C411yescharacteristic
73C2×C13×M16C2×C411yescharacteristic
74C13×C22⋊Q8C2×C411yescharacteristic
75C13×#121C2×C411yescharacteristic
76Q8×Dic13C2311yescharacteristic
77#88198C2×C411yescharacteristic
78C2×#6107C2×C411yescharacteristic
79#88190C2×C411yescharacteristic
80#88189—21no—
81D4×Dic13—21no—
82D4×Dic13C2311yescharacteristic
83C2×#6105C2×C411yescharacteristic
84#88178C2×C411yescharacteristic
85#88178C2×C411yescharacteristic
86C2×C4×Dic13C2311yescharacteristic
87C2×#6099C2×C411yescharacteristic
88C2×Dic52C2×C411yescharacteristic
89#88144C2×C411yescharacteristic
90#88143—21no—
91#88142C2×C411yescharacteristic
92#88141—21no—
93#88141C2311yescharacteristic
94#88141C2311yescharacteristic
95#88133—21no—
96#88132—21no—
97#88131—21no—
98#88131—21no—
99C22⋊#1057—21no—
100C22⋊#1057—21no—
101C22⋊#1057—21no—
102C22⋊#1057—21no—
103#88112—21no—
104#88112—21no—
105#88112—21no—
106#88112—21no—
107#88110—21no—
108#88110—21no—
109#88110—21no—
110#88110—21no—
111C4⋊#1057—21no—
112C4⋊#1057—21no—
113C4⋊#1057—21no—
114C4⋊#1057—21no—
115C4⋊#1057C2311yescharacteristic
116C4⋊#1057C2311yescharacteristic
117C4⋊#1057C2311yescharacteristic
118C4⋊#1057C2311yescharacteristic
119C4×#1057—21no—
120C4×#1057—21no—
121C4×#1057—21no—
122C4×#1057D411yescharacteristic
123C4×#1057D411yescharacteristic
124C4×#1057C2311yescharacteristic
125C4×#1057C2311yescharacteristic
126C4×#1057C2311yescharacteristic
127C4×#1057C2311yescharacteristic
128C13×#107C2×C411yescharacteristic
129C13×#103C2×C411yescharacteristic
130C13×#102C2×C411yescharacteristic
131#88075C2×C411yescharacteristic
132#88072C2×C411yescharacteristic
133#88057C2×C411yescharacteristic
134#88056C2×C411yescharacteristic
135#88056C2×C411yescharacteristic
136#88055C2×C411yescharacteristic
137#88055C2×C411yescharacteristic
138C8×Dic13C2311yescharacteristic
139C8×Dic13C2311yescharacteristic
140#88050C2×C411yescharacteristic
141#88050C2×C411yescharacteristic
142#88048C2×C411yescharacteristic
143#88047C2×C411yescharacteristic
144#17965—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13—21no—
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13C22×C411yescharacteristic
149C22×Dic13—21no—
150C22×Dic13C2×D411yescharacteristic
151C22×Dic13#4111yescharacteristic
152C2×Dic26—21no—
153C2×Dic26C22×C411yescharacteristic
154C2×Dic26C22×C411yescharacteristic
155#6122—42no—
156#6122—42no—
157C2×#1057—22no—
158C2×#1057—21no—
159C2×#1057—21no—
160C2×#1057—21no—
161C2×#1057—21no—
162C2×#1057—21no—
163C2×#1057—21no—
164C2×#1057—41no—
165C2×#1057—42no—
166C2×#1057C2×D411yescharacteristic
167C2×#1057C2×D411yescharacteristic
168C2×#1057C2×D411yescharacteristic
169C2×#1057C2×D411yescharacteristic
170C13×SD16—22no—
171C13×M16—22no—
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C13×C4⋊C4—21no—
175C13×C4⋊C4C22×C411yescharacteristic
176C13×C4⋊C4C22×C411yescharacteristic
177C13×C22⋊C4—21no—
178C13×C22⋊C4—21no—
179C22⋊Dic13—21no—
180C22⋊Dic13—21no—
181C22⋊Dic13—21no—
182C22⋊Dic13—21no—
183C22⋊Dic13—21no—
184#6107—22no—
185#6105—22no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13C22×C411yescharacteristic
189C4⋊Dic13C22×C411yescharacteristic
190#6101—21no—
191#6101—21no—
192#6101—21no—
193#6101—21no—
194#6101—21no—
195#6101—21no—
196#6101—21no—
197#6101—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13C22×C411yescharacteristic
202C4×Dic13C2×D411yescharacteristic
203C4×Dic13#4111yescharacteristic
204C4×Dic13C2411yescharacteristic
205#6099—22no—
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208Dic52—22no—
209#3172—131no—
210#2966—131no—
211#2960—131no—
212#1593—131no—
213#1593—131no—
214#1592—131no—
215#1592—131no—
216C8×Q16—131no—
217C8×Q16—131no—
218C8×SD16—131no—
219C8×SD16—131no—
220#1569—131no—
221#1497—131no—
222#1495—131no—
223C8×M16—131no—
224C23×C13—21no—
225C23×C13C4×D411yescharacteristic
226Q8×C13—21no—
227Q8×C13—21no—
228D4×C13—21no—
229D4×C13—21no—
230D4×C13—42no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13C4×D411yescharacteristic
237C2×C4×C13C23×C411yescharacteristic
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—41no—
245C2×Dic13—41no—
246C2×Dic13—41no—
247C2×Dic13C4×D411yescharacteristic
248C2×Dic13C4×D411yescharacteristic
249C2×Dic13C22×D411yescharacteristic
250C2×Dic13C2×#4111yescharacteristic
251Dic26—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—21no—
255Dic26—42no—
256#1057—21no—
257#1057—21no—
258#1057—21no—
259#1057—41no—
260#1057—41no—
261#1057—41no—
262#1057—41no—
263#1057—41no—
264#1057—41no—
265#1057#13712yes—
266C8×C13—21no—
267C8×C13#13112yes—
268#1055—21no—
269#1055#13112yes—
270#533—131no—
271#529—131no—
272#501—131no—
273#497—131no—
274#491—131no—
275#489—131no—
276#470—131no—
277#470—131no—
278#468—131no—
279#468#26111yescharacteristic
280#446—131no—
281#446—131no—
282#446—131no—
283#446—261no—
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—131no—
287C8×Q8—261no—
288C4×Q16—131no—
289C4×Q16—131no—
290C4×SD16—131no—
291C4×SD16—131no—
292#436—131no—
293#435—261no—
294C8×D4—131no—
295C8×D4—261no—
296#433—261no—
297#432—131no—
298#431—131no—
299#424—261no—
300#423—131no—
301#405—261no—
302#405—261no—
303C4×M16—131no—
304C2×C4×C8—131no—
305#335—131no—
306#335—131no—
307#334—131no—
308#334—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315D4⋊C8—131no—
316D4⋊C8—131no—
317#322—131no—
318#322—131no—
319C82—131no—
320C82—131no—
321C22×C13—21no—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—41no—
325C22×C13—41no—
326C22×C13—41no—
327C22×C13C2×C4×D411yescharacteristic
328C4×C13—21no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13C2×#13111yescharacteristic
333C4×C13C2×#13111yescharacteristic
334Dic13—21no—
335Dic13—21no—
336Dic13—21no—
337Dic13—41no—
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341Dic13C2×#13711yescharacteristic
342Dic13#57511yescharacteristic
343C2×Q16—131no—
344C2×Q16—131no—
345C2×SD16—131no—
346C2×SD16C2×#26111yescharacteristic
347C2×M16—131no—
348C2×M16—261no—
349C2×M16—261no—
350C2×M16C2×#26111yescharacteristic
351C22×C8—131no—
352C22×C8—131no—
353C22×C8—261no—
354C4⋊Q8—131no—
355C4⋊Q8—131no—
356#126—261no—
357#125—131no—
358#125—261no—
359#124—131no—
360#123—261no—
361C22⋊Q8—131no—
362C22⋊Q8—131no—
363C22⋊Q8—261no—
364C22⋊Q8C2×#26111yescharacteristic
365#121C2×#26111yescharacteristic
366C4×Q8—131no—
367C4×Q8—131no—
368C4×Q8—131no—
369C4×Q8—261no—
370C4×D4—131no—
371C4×D4—261no—
372#117—261no—
373#117—261no—
374C2×C42—131no—
375#107—131no—
376#107C2×#26111yescharacteristic
377#106—131no—
378#106—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103C2×#26111yescharacteristic
397#102—131no—
398#102C2×#26111yescharacteristic
399C22⋊C8—261no—
400C22⋊C8—261no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403#97—131no—
404#97—131no—
405#97—261no—
406#97—261no—
407#97—261no—
408#97—261no—
409C4×C8—131no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8—261no—
420C2×C13—41no—
421C2×C13—81no—
422C2×C13#293111yescharacteristic
423C2×C13C4×#13711yescharacteristic
424C2×C13#295511yescharacteristic
425C2×Q8—131no—
426C2×Q8—131no—
427C2×Q8—261no—
428C2×Q8C22×#26111yescharacteristic
429C2×D4—21no—
430C2×D4C22×#26111yescharacteristic
431C22×C4—131no—
432C22×C4—131no—
433C22×C4—261no—
434C22×C4C22×#26111yescharacteristic
435Q16—262no—
436Q16—262no—
437SD16—22no—
438SD16—262no—
439M16—22no—
440M16—262no—
441M16—522no—
442M16—522no—
443C2×C8—131no—
444C2×C8—131no—
445C2×C8—131no—
446C2×C8—131no—
447C2×C8—131no—
448C2×C8—131no—
449C2×C8—262no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—522no—
457C2×C8—521no—
458C2×C8C22×#26111yescharacteristic
459C2×C8C22×#26111yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—131no—
462C4⋊C4—131no—
463C4⋊C4—261no—
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—261no—
473C4⋊C4C22×#26111yescharacteristic
474C4⋊C4C22×#26111yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C42—131no—
483C42—131no—
484C42—131no—
485C42—131no—
486C42—261no—
487C42—261no—
488C42—261no—
489C13#1796511yescharacteristic, complemented, Sylow
490C23—21no—
491C23D4×#26111yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—261no—
495Q8—261no—
496Q8—261no—
497Q8—261no—
498Q8—522no—
499D4—21no—
500D4—21no—
501D4—42no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—131no—
508C2×C4—131no—
509C2×C4—131no—
510C2×C4—131no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—521no—
518C2×C4—521no—
519C2×C4—521no—
520C2×C4D4×#26111yescharacteristic
521C2×C4C23×#26111yescharacteristic
522C8—21no—
523C8—132no—
524C8—132no—
525C8—261no—
526C8—261no—
527C8—261no—
528C8—261no—
529C8—521no—
530C8—521no—
531C8—521no—
532C8—521no—
533C8—521no—
534C8—521no—
535C8#8823812yes—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22C2×D4×#26111yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—131no—
548C4—131no—
549C4—261no—
550C4—261no—
551C4—261no—
552C4—521no—
553C4—521no—
554C4—521no—
555C4—521no—
556C4C2×#8823811yescharacteristic
557C4D13⋊#13111yescharacteristic
558C2—41no—
559C2—81no—
560C2#1313155911yescharacteristic
561C2#137×#26111yescharacteristic
562C2#1313160811yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#468C4
socleC22×C13C2×C4×D4
prime radicalC13×#121C2×C4
cosocleC4×Dic13C24
hypercenter#468#261
hypocenterC13#17965
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. #13131624C2semidirect
3. #13130482C2semidirect
4. #13130481C2semidirect
5. #13130479C2semidirect
6. #13130477C2semidirect
7. #13130424C2semidirect
8. #13130423C2semidirect
9. #13130419C2semidirect
10. SD16×#1057C2semidirect
11. #13130400C2semidirect
12. #13130198C2semidirect
14. M16×#1057C2semidirect
489. C13#17965semidirect

Maximal subgroups

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

subgroupindex
#131316492
#131316242
#131304822
#131304812
#131304792
#131304772
#131304242
#131304232
#131304192
SD16×#10572
#131304002
#131301982
#131301912
M16×#10572
#131254352
#1796513