Finite Group Databasebeta

← #16792790

Subgroups — #16792790

Order 3328.

688 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#13131644C211yesmaximal, characteristic
2#13131521C211yesmaximal, characteristic
3#13130060C211yesmaximal, characteristic, complemented
4#13130058C211yesmaximal, characteristic, complemented
5#13130058C211yesmaximal, characteristic, complemented
6#13130056C211yesmaximal, characteristic, complemented
7#13130054C211yesmaximal, characteristic, complemented
8#13130054C211yesmaximal, characteristic, complemented
9#13130052C211yesmaximal, characteristic, complemented
10#13130050C211yesmaximal, characteristic, complemented
11#13130048C211yesmaximal, characteristic, complemented
12#13130046C211yesmaximal, characteristic, complemented
13#13130044C211yesmaximal, characteristic, complemented
14#13130044C211yesmaximal, characteristic, complemented
15#13123801C211yesmaximal, characteristic
16C4×#6131C2211yescharacteristic
17#11719159C412yes—
18#11719158C412yes—
19#11719079C412yes—
20#11719077C412yes—
21#11719077C412yes—
22#11719076C412yes—
23#11719075C412yes—
24#11719075C412yes—
25#11719051C2211yescharacteristic
26#11719051C2211yescharacteristic
27#11719051C2211yescharacteristic
28#11719049C2211yescharacteristic
29#11719049C2211yescharacteristic
30#11719049C2211yescharacteristic
31#11719049C2211yescharacteristic
32C4×#6118C2211yescharacteristic
33C4×#6118C2211yescharacteristic
34C4×#6118C2211yescharacteristic
35C4×D13⋊C8C2211yescharacteristic
36C4×D13⋊C8C2211yescharacteristic
37C13×#446C411yescharacteristic
38#11718685C411yescharacteristic
39#11718499C411yescharacteristic
40#11718497C411yescharacteristic
41#11718497C411yescharacteristic
42#11718494C2211yescharacteristic
43#11718494C2211yescharacteristic
44#11718494C2211yescharacteristic
45#11718368C2211yescharacteristic
46#11718368C2211yescharacteristic
47#11718367C411yescharacteristic
48#11718367C411yescharacteristic
49#11718349C411yescharacteristic
50C4×C8×D13C2211yescharacteristic
51#1057⋊C8C2211yescharacteristic
52#1057⋊C8C2211yescharacteristic
53#1057⋊C8C2211yescharacteristic
54#1057⋊C8C2211yescharacteristic
55#1057⋊C8C2211yescharacteristic
56#1057⋊C8C2211yescharacteristic
57#1057⋊C8C2211yescharacteristic
58#1057⋊C8C2211yescharacteristic
59#1057⋊C8C2211yescharacteristic
60#1057⋊C8C2211yescharacteristic
61#11718251C2211yescharacteristic
62#11718251C2211yescharacteristic
63#11718251C2211yescharacteristic
64#11718251C2211yescharacteristic
65C8×#1057C2211yescharacteristic
66C8×#1057C2211yescharacteristic
67C2×#6131C2×C411yescharacteristic
68C2×#6118C2×C412yes—
69C2×#6118C2×C412yes—
70C2×#6118C2×C412yes—
71C2×D13⋊C8C2×C412yes—
72C2×D13⋊C8C2×C412yes—
73C4×Q8×C13C2×C411yescharacteristic
74Q8×Dic13C2×C411yescharacteristic
75C2×#6094C2×C411yescharacteristic
76C2×#6094C2×C411yescharacteristic
77C2×#6094C2×C411yescharacteristic
78C2×#6094C2×C411yescharacteristic
79C2×C8×D13C2×C411yescharacteristic
80C2×C8×D13C2×C411yescharacteristic
81#88147C2×C411yescharacteristic
82#88147C2×C411yescharacteristic
83#88147C2×C411yescharacteristic
84#88146C2×C411yescharacteristic
85#88146C2×C411yescharacteristic
86#88146C2×C411yescharacteristic
87C4×D52C2×C411yescharacteristic
88C4×D52C2×C411yescharacteristic
89C4×D52C2×C411yescharacteristic
90C42×D13C2311yescharacteristic
91C42×D13C2311yescharacteristic
92C42×D13C2311yescharacteristic
93#88112C2×C412yes—
94#88112C2×C412yes—
95#88112C2×C412yes—
96#88112C2×C412yes—
97#88111C2×C412yes—
98#88111C2×C412yes—
99#88111C2×C412yes—
100#88111C2×C412yes—
101#88111C2×C412yes—
102#88111C2×C412yes—
103#88111C2×C412yes—
104#88110C2×C412yes—
105#88110C2×C412yes—
106#88110C2×C412yes—
107C4⋊#1057C2×C412yes—
108C4⋊#1057C2×C412yes—
109C4⋊#1057C2×C412yes—
110C4×#1057C2×C412yes—
111C4×#1057C2×C412yes—
112C4×#1057C2311yescharacteristic
113C4×#1057C2311yescharacteristic
114C4×#1057C2311yescharacteristic
115C4×#1057C2311yescharacteristic
116C4×#1057C2311yescharacteristic
117C4×#1057C2311yescharacteristic
118C4×#1057C2311yescharacteristic
119C4×#1057C2311yescharacteristic
120C13×C4⋊C8C2×C411yescharacteristic
121C13×C4⋊C8C2×C411yescharacteristic
122C13×C4⋊C8C2×C411yescharacteristic
123C13×#97C2×C411yescharacteristic
124C13×#97C2×C411yescharacteristic
125C4×C8×C13C2×C411yescharacteristic
126#88060C2×C411yescharacteristic
127#88060C2×C411yescharacteristic
128#88060C2×C411yescharacteristic
129#88060C2×C411yescharacteristic
130#88060C2×C411yescharacteristic
131#88060C2×C411yescharacteristic
132C8×Dic13C2311yescharacteristic
133C8×Dic13C2311yescharacteristic
134C8×Dic13C2311yescharacteristic
135C8×Dic13C2311yescharacteristic
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2×C411yescharacteristic
138C4⋊#1055C2×C411yescharacteristic
139#88043C2×C411yescharacteristic
140#88043C2×C411yescharacteristic
141C4×#1055C2×C411yescharacteristic
142#17342—131nomaximal, Sylow
143C2×Q8×C13C4211yescharacteristic
144#6131—42no—
145C2×D52C4211yescharacteristic
146C2×D52C4211yescharacteristic
147C2×D52C4211yescharacteristic
148C2×C4×D13C22×C411yescharacteristic
149C2×C4×D13C22×C411yescharacteristic
150C2×C4×D13C22×C411yescharacteristic
151C2×C4×D13C22×C411yescharacteristic
152C2×C4×D13C22×C411yescharacteristic
153C2×C4×D13C22×C411yescharacteristic
154C2×C4×D13C22×C411yescharacteristic
155C2×C4×D13C22×C411yescharacteristic
156C2×C4×D13C22×C411yescharacteristic
157C2×#1057C22×C412yes—
158C2×#1057C22×C412yes—
159C2×#1057C22×C412yes—
160C2×#1057C22×C412yes—
161C2×#1057C22×C412yes—
162C2×#1057C22×C412yes—
163C2×#1057C22×C412yes—
164C2×#1057C22×C412yes—
165#6118—42no—
166#6118—42no—
167#6118—42no—
168D13⋊C8—42no—
169D13⋊C8—42no—
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C13×C4⋊C4C4211yescharacteristic
175C13×C4⋊C4C4211yescharacteristic
176C13×C4⋊C4C4211yescharacteristic
177C42×C13C22×C411yescharacteristic
178C42×C13C22×C411yescharacteristic
179C42×C13C22×C411yescharacteristic
180#6103C4211yescharacteristic
181#6103C4211yescharacteristic
182#6103C4211yescharacteristic
183#6103C4211yescharacteristic
184#6103C4211yescharacteristic
185#6103C4211yescharacteristic
186C4⋊Dic13C4211yescharacteristic
187C4⋊Dic13C4211yescharacteristic
188C4⋊Dic13C4211yescharacteristic
189C4×Dic13C22×C411yescharacteristic
190C4×Dic13C22×C411yescharacteristic
191C4×Dic13C22×C411yescharacteristic
192C4×Dic13C22×C411yescharacteristic
193C4×Dic13C22×C411yescharacteristic
194C4×Dic13C22×C411yescharacteristic
195C4×Dic13C2411yescharacteristic
196C2×#1055C22×C411yescharacteristic
197C2×#1055C22×C411yescharacteristic
198C2×#1055C22×C411yescharacteristic
199C2×#1055C22×C411yescharacteristic
200#6094—41no—
201#6094—41no—
202#6094—41no—
203#6094—41no—
204C8×D13—41no—
205C8×D13—41no—
206#2965—131no—
207#2965—131no—
208#2922—131no—
209#1455—131no—
210#1454—131no—
211#1454—131no—
212#1453—131no—
213#1453—131no—
214#1453—131no—
215#1452—131no—
216#1452—131no—
217#1451—131no—
218#1451—131no—
219#1451—131no—
220#1451—131no—
221C22×D13C2×C4211yescharacteristic
222C22×D13C2×C4211yescharacteristic
223C22×D13C2×C4211yescharacteristic
224Q8×C13—41no—
225C2×C4×C13C2×C4211yescharacteristic
226C2×C4×C13C2×C4211yescharacteristic
227C2×C4×C13C2×C4211yescharacteristic
228C2×C4×C13C2×C4211yescharacteristic
229C2×C4×C13C2×C4211yescharacteristic
230C2×C4×C13C2×C4211yescharacteristic
231C2×C4×C13C23×C411yescharacteristic
232C2×Dic13C2×C4211yescharacteristic
233C2×Dic13C2×C4211yescharacteristic
234C2×Dic13C2×C4211yescharacteristic
235C2×Dic13C23×C411yescharacteristic
236C2×Dic13C23×C411yescharacteristic
237D52—41no—
238D52—41no—
239D52—41no—
240C4×D13—21no—
241C4×D13—21no—
242C4×D13—21no—
243C4×D13—21no—
244C4×D13—21no—
245C4×D13—21no—
246C4×D13—22no—
247C4×D13—22no—
248C4×D13—22no—
249C4×D13—22no—
250C4×D13—22no—
251C4×D13—22no—
252#1057—22no—
253#1057—22no—
254#1057—22no—
255#1057—22no—
256#1057—22no—
257#1057—22no—
258#1057—22no—
259#1057—22no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—21no—
263C8×C13—21no—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268C4×#41—131no—
269#446—132no—
270#446—131no—
271#446#26111yescharacteristic
272#436—132no—
273#436—131no—
274#436—131no—
275#435—132no—
276#435—132no—
277#435—131no—
278#435—131no—
279#435—131no—
280#435—131no—
281#433—132no—
282#433—132no—
283#431—131no—
284#431—131no—
285#431—131no—
286#431—131no—
287#431—131no—
288#431—131no—
289#431—131no—
290#431—131no—
291#431—131no—
292#431—131no—
293#424—132no—
294#408—132no—
295C4×M16—131no—
296C4×M16—131no—
297C4×M16—131no—
298C4×M16—131no—
299C4×M16—131no—
300C2×C4×C8—131no—
301C2×C4×C8—131no—
302C2×C4×C8—131no—
303#322—131no—
304#322—131no—
305#322—131no—
306#322—131no—
307#322—131no—
308#322—131no—
309#322—131no—
310#322—131no—
311#322—131no—
312#322—131no—
313#322—131no—
314#322—131no—
315#322—131no—
316#322—131no—
317C82—131no—
318C82—131no—
319C22×C13C22×C4211yescharacteristic
320C2×D13—21no—
321C2×D13—21no—
322C2×D13—21no—
323C2×D13—21no—
324C2×D13—21no—
325C2×D13—21no—
326C2×D13—21no—
327C2×D13—21no—
328C2×D13—21no—
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13#56811yescharacteristic
336C4×C13#56811yescharacteristic
337Dic13—21no—
338Dic13—21no—
339Dic13—21no—
340Dic13#56812yes—
341Dic13#56812yes—
342C2×#41—131no—
343C2×M16—132no—
344C2×M16—132no—
345C2×M16—132no—
346C2×M16—131no—
347C2×M16—131no—
348C2×M16—131no—
349C2×M16—131no—
350C22×C8—132no—
351C22×C8—132no—
352C22×C8—131no—
353C22×C8—131no—
354C4×Q8—131no—
355C4×Q8C2×#26111yescharacteristic
356C4×D4—131no—
357C4×D4—131no—
358C4×D4—131no—
359C4×D4—131no—
360C4×D4—131no—
361C4×D4—131no—
362#117—131no—
363#117—131no—
364#117—131no—
365C2×C42—131no—
366C2×C42—131no—
367C2×C42—131no—
368C4⋊C8—132no—
369C4⋊C8—132no—
370C4⋊C8—132no—
371C4⋊C8—132no—
372C4⋊C8—132no—
373C4⋊C8—132no—
374C4⋊C8—132no—
375C4⋊C8—131no—
376C4⋊C8—131no—
377C4⋊C8—131no—
378C4⋊C8C2×#26111yescharacteristic
379C4⋊C8C2×#26111yescharacteristic
380C4⋊C8C2×#26111yescharacteristic
381C22⋊C8—132no—
382C22⋊C8—132no—
383C22⋊C8—132no—
384C22⋊C8—132no—
385C22⋊C8—132no—
386C22⋊C8—132no—
387C22⋊C8—132no—
388C22⋊C8—131no—
389C22⋊C8—131no—
390C22⋊C8—131no—
391C22⋊C8—131no—
392C22⋊C8—131no—
393C22⋊C8—131no—
394#97—132no—
395#97—132no—
396#97—132no—
397#97—131no—
398#97—131no—
399#97C2×#26111yescharacteristic
400#97C2×#26111yescharacteristic
401C4×C8—132no—
402C4×C8—132no—
403C4×C8—131no—
404C4×C8—131no—
405C4×C8—131no—
406C4×C8—131no—
407C4×C8—131no—
408C4×C8—131no—
409C4×C8—131no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8C2×#26111yescharacteristic
417C2×C13#287311yescharacteristic
418C2×C13#287511yescharacteristic
419C2×C13#287511yescharacteristic
420D13—41no—
421D13—41no—
422D13—41no—
423#41—522no—
424C2×Q8C4×#26111yescharacteristic
425C2×D4—131no—
426C2×D4—131no—
427C2×D4—131no—
428C22×C4—131no—
429C22×C4—131no—
430C22×C4—131no—
431C22×C4—131no—
432C22×C4—131no—
433C22×C4—131no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—131no—
437M16—521no—
438M16—521no—
439M16—521no—
440M16—521no—
441M16—522no—
442M16—522no—
443M16—522no—
444C2×C8—132no—
445C2×C8—132no—
446C2×C8—132no—
447C2×C8—132no—
448C2×C8—132no—
449C2×C8—132no—
450C2×C8—132no—
451C2×C8—132no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—521no—
457C2×C8—521no—
458C2×C8—522no—
459C2×C8—522no—
460C2×C8C22×#26111yescharacteristic
461C2×C8C22×#26111yescharacteristic
462C2×C8C22×#26111yescharacteristic
463C2×C8C22×#26111yescharacteristic
464C4⋊C4—131no—
465C4⋊C4—131no—
466C4⋊C4—131no—
467C4⋊C4C4×#26111yescharacteristic
468C4⋊C4C4×#26111yescharacteristic
469C4⋊C4C4×#26111yescharacteristic
470C22⋊C4—131no—
471C22⋊C4—131no—
472C22⋊C4—131no—
473C22⋊C4—131no—
474C22⋊C4—131no—
475C22⋊C4—131no—
476C42—131no—
477C42—131no—
478C42—131no—
479C42—131no—
480C42—131no—
481C42—131no—
482C42—131no—
483C42C22×#26111yescharacteristic
484C42C22×#26111yescharacteristic
485C42C22×#26111yescharacteristic
486C13#1734211yescharacteristic, complemented, Sylow
487C23—131no—
488C23—131no—
489C23—131no—
490Q8—41no—
491D4—521no—
492D4—521no—
493D4—521no—
494C2×C4—131no—
495C2×C4—131no—
496C2×C4—131no—
497C2×C4—131no—
498C2×C4—131no—
499C2×C4—262no—
500C2×C4—262no—
501C2×C4—262no—
502C2×C4—262no—
503C2×C4—262no—
504C2×C4—262no—
505C2×C4—261no—
506C2×C4—261no—
507C2×C4—261no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4C2×C4×#26111yescharacteristic
512C2×C4C2×C4×#26111yescharacteristic
513C2×C4C2×C4×#26111yescharacteristic
514C2×C4C2×C4×#26111yescharacteristic
515C2×C4C2×C4×#26111yescharacteristic
516C2×C4C2×C4×#26111yescharacteristic
517C2×C4C23×#26111yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—262no—
523C8—262no—
524C8—262no—
525C8—262no—
526C8—262no—
527C8—262no—
528C8—262no—
529C8—262no—
530C8—261no—
531C8—261no—
532C8—261no—
533C8—261no—
534C22—261no—
535C22—261no—
536C22—261no—
537C22—261no—
538C22—261no—
539C22—261no—
540C22—261no—
541C22—261no—
542C22—261no—
543C22C22×C4×#26111yescharacteristic
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—132no—
551C4—132no—
552C4—261no—
553C4—261no—
554C4—261no—
555C4#1171962511yescharacteristic
556C4#1171962911yescharacteristic
557C2—521no—
558C2—521no—
559C2—521no—
560C2#1313139911yescharacteristic
561C2#1313140611yescharacteristic
562C2#1313140811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×#261
commutator, socleC22×C13C22×C42
FittingC13×#446C4
prime radicalC2×#6131C2×C4
cosocleC4×Dic13C24
hypercenter#446#261
hypocenterC13#17342
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #446

Complements

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

NH ≅ G/Ntype
3. #13130060C2semidirect
4. #13130058C2semidirect
5. #13130058C2semidirect
6. #13130056C2semidirect
7. #13130054C2semidirect
8. #13130054C2semidirect
9. #13130052C2semidirect
10. #13130050C2semidirect
11. #13130048C2semidirect
12. #13130046C2semidirect
13. #13130044C2semidirect
14. #13130044C2semidirect
486. C13#17342semidirect

Maximal subgroups

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

subgroupindex
#131316442
#131315212
#131300602
#131300582
#131300562
#131300542
#131300522
#131300502
#131300482
#131300462
#131300442
#131238012
#1734213