Finite Group Databasebeta

← #16795109

Subgroups — #16795109

Order 3328.

588 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131532C211yesmaximal, characteristic
2#13131531C211yesmaximal, characteristic
3#13130414C211yesmaximal, characteristic, complemented
4#13130412C211yesmaximal, characteristic, complemented
5#13130411C211yesmaximal, characteristic, complemented
6#13130410C211yesmaximal, characteristic, complemented
7#13130407C211yesmaximal, characteristic, complemented
8#13130407C211yesmaximal, characteristic, complemented
9#13130401C211yesmaximal, characteristic, complemented
10#13130400C211yesmaximal, characteristic, complemented
11#13130398C211yesmaximal, characteristic, complemented
12#13130388C211yesmaximal, characteristic, complemented
13#13130387C211yesmaximal, characteristic, complemented
14#13130383C211yesmaximal, characteristic, complemented
15#13123796C211yesmaximal, characteristic
16C4×#6129C2211yescharacteristic
17#11719147—21no—
18#11719146—21no—
19#11719130C2211yescharacteristic
20#11719130C2211yescharacteristic
21#11719130C2211yescharacteristic
22#11719129C2211yescharacteristic
23#11719119C2211yescharacteristic
24#11719119C2211yescharacteristic
25#11719119C2211yescharacteristic
26C2×C4⋊#1057C2211yescharacteristic
27#11719077—21no—
28#11719072—21no—
29#11719068—21no—
30#11719068—21no—
31#11719068—21no—
32#11719062—21no—
33#11719054C2211yescharacteristic
34#11719052C2211yescharacteristic
35#11719051C2211yescharacteristic
36D13⋊(C4⋊C8)C2211yescharacteristic
37C13×#435C411yescharacteristic
38#11718789C411yescharacteristic
39M16×Dic13C2211yescharacteristic
40#11718772C411yescharacteristic
41C2×C8×Dic13C2211yescharacteristic
42#11718672C411yescharacteristic
43#11718494C2211yescharacteristic
44#11718489C411yescharacteristic
45#11718391C411yescharacteristic
46#11718390C411yescharacteristic
47#11718379C2211yescharacteristic
48#11718379C2211yescharacteristic
49#11718368C2211yescharacteristic
50#11718362C411yescharacteristic
51#11718256C2211yescharacteristic
52#11718256C2211yescharacteristic
53#11718255C2211yescharacteristic
54#11718255C2211yescharacteristic
55#11718255C2211yescharacteristic
56#11718255C2211yescharacteristic
57#11718254C2211yescharacteristic
58#11718254C2211yescharacteristic
59#11718254C2211yescharacteristic
60#11718254C2211yescharacteristic
61#11718254C2211yescharacteristic
62#11718254C2211yescharacteristic
63#11718253C2211yescharacteristic
64#11718253C2211yescharacteristic
65#11718253C2211yescharacteristic
66#11718253C2211yescharacteristic
67C2×#6129D411yescharacteristic
68C2×#6122—21no—
69C22×#1057—21no—
70C2×#6118—21no—
71C2×D13⋊C8—21no—
72C2×C13×M16C2×C411yescharacteristic
73C22×C8×C13C2×C411yescharacteristic
74C4×D4×C13C2×C411yescharacteristic
75D4×Dic13Q811yescharacteristic
76C4×C22⋊D13C2×C411yescharacteristic
77C4×C22⋊D13C2×C411yescharacteristic
78C2×C4×Dic13C2311yescharacteristic
79C2×C4×Dic13C2311yescharacteristic
80C2×#6099C2×C411yescharacteristic
81C22×#1055C2×C411yescharacteristic
82C2×#6094C2×C411yescharacteristic
83C2×#6094C2×C411yescharacteristic
84#88146D411yescharacteristic
85#88141Q811yescharacteristic
86#88135Q811yescharacteristic
87#88135Q811yescharacteristic
88#88131D411yescharacteristic
89#88131D411yescharacteristic
90C42×D13C2311yescharacteristic
91C4×Dic26C2×C411yescharacteristic
92C22⋊#1057—21no—
93C22⋊#1057—21no—
94C22⋊#1057—21no—
95C22⋊#1057—21no—
96C22⋊#1057—21no—
97C22⋊#1057—21no—
98#88112—21no—
99#88112—21no—
100#88111—21no—
101#88111—21no—
102#88110—21no—
103#88110—21no—
104#88110—21no—
105#88110—21no—
106C4⋊#1057—21no—
107C4⋊#1057—21no—
108C4⋊#1057C2311yescharacteristic
109C4⋊#1057C2311yescharacteristic
110C4⋊#1057C2311yescharacteristic
111C4⋊#1057C2311yescharacteristic
112C4⋊#1057C2311yescharacteristic
113C4⋊#1057C2311yescharacteristic
114C4⋊#1057C2311yescharacteristic
115C4⋊#1057C2311yescharacteristic
116C4×#1057—21no—
117C4×#1057—21no—
118C4×#1057—21no—
119C4×#1057—21no—
120C13×C4⋊C8C2×C411yescharacteristic
121C13×C22⋊C8C2×C411yescharacteristic
122C13×C22⋊C8C2×C411yescharacteristic
123C13×#97C2×C411yescharacteristic
124C22⋊#1055C2×C411yescharacteristic
125C22⋊#1055C2×C411yescharacteristic
126#88060C2×C411yescharacteristic
127#88060C2×C411yescharacteristic
128#88055C2×C411yescharacteristic
129#88055C2×C411yescharacteristic
130#88054C2×C411yescharacteristic
131#88054C2×C411yescharacteristic
132#88054C2×C411yescharacteristic
133#88054C2×C411yescharacteristic
134C8×Dic13C2×C411yescharacteristic
135C8×Dic13C2×C411yescharacteristic
136C8×Dic13C2311yescharacteristic
137C8×Dic13C2311yescharacteristic
138C8×Dic13C2311yescharacteristic
139C8×Dic13C2311yescharacteristic
140C4⋊#1055C2×C411yescharacteristic
141#88043C2×C411yescharacteristic
142#17831—131nomaximal, Sylow
143C2×D4×C13C4⋊C411yescharacteristic
144C22×C4×C13C22×C411yescharacteristic
145C22×C4×C13C22×C411yescharacteristic
146C2×C22⋊D13C4⋊C411yescharacteristic
147C2×C22⋊D13C4⋊C411yescharacteristic
148C22×Dic13C2×D411yescharacteristic
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13C2×Q811yescharacteristic
151C22×Dic13C2×Q811yescharacteristic
152#6129—41no—
153#6129—41no—
154C2×C4×D13C22×C411yescharacteristic
155C2×C4×D13C2×D411yescharacteristic
156C2×C4×D13C2×Q811yescharacteristic
157C2×Dic26C4⋊C411yescharacteristic
158#6122—42no—
159C2×#1057—21no—
160C2×#1057—21no—
161C2×#1057—21no—
162C2×#1057—21no—
163C2×#1057—21no—
164C2×#1057—21no—
165C2×#1057—21no—
166C2×#1057—21no—
167C2×#1057—42no—
168#6118—42no—
169D13⋊C8—42no—
170C13×M16—22no—
171C2×C8×C13—22no—
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C2×C8×C13C22×C411yescharacteristic
175C2×C8×C13C22×C411yescharacteristic
176C13×C4⋊C4C4⋊C411yescharacteristic
177C13×C22⋊C4C4⋊C411yescharacteristic
178C13×C22⋊C4C4⋊C411yescharacteristic
179C42×C13C22×C411yescharacteristic
180C22⋊Dic13C4⋊C411yescharacteristic
181C22⋊Dic13C4⋊C411yescharacteristic
182#6103C4⋊C411yescharacteristic
183#6103C4⋊C411yescharacteristic
184C4⋊Dic13C4⋊C411yescharacteristic
185#6101C4⋊C411yescharacteristic
186#6101C4⋊C411yescharacteristic
187#6101C4⋊C411yescharacteristic
188#6101C4⋊C411yescharacteristic
189C4×Dic13C22×C411yescharacteristic
190C4×Dic13C22×C411yescharacteristic
191C4×Dic13C2×D411yescharacteristic
192C4×Dic13C2×D411yescharacteristic
193C4×Dic13C2×D411yescharacteristic
194C4×Dic13C2×Q811yescharacteristic
195C4×Dic13C2×Q811yescharacteristic
196C4×Dic13C2×Q811yescharacteristic
197C4×Dic13C2411yescharacteristic
198#6099—41no—
199C2×#1055—41no—
200C2×#1055C22×C411yescharacteristic
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204#6094—22no—
205#6094—41no—
206#2965—131no—
207#2925—131no—
208#2925—131no—
209#1574—131no—
210#1574—131no—
211#1573—131no—
212#1573—131no—
213#1572—131no—
214#1572—131no—
215#1569—131no—
216#1569—131no—
217#1568—131no—
218#1565—131no—
219#1565—131no—
220#1564—131no—
221C23×C13C2×C4⋊C411yescharacteristic
222C23×C13C2×C4⋊C411yescharacteristic
223C22×D13C2×C4⋊C411yescharacteristic
224D4×C13—41no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13C2×C4⋊C411yescharacteristic
230C2×C4×C13C2×C4⋊C411yescharacteristic
231C2×C4×C13C2×C4⋊C411yescharacteristic
232C2×C4×C13C2×C4⋊C411yescharacteristic
233C2×C4×C13C23×C411yescharacteristic
234C22⋊D13—41no—
235C22⋊D13—41no—
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—41no—
241C2×Dic13—41no—
242C2×Dic13C2×C4⋊C411yescharacteristic
243C2×Dic13C2×C4⋊C411yescharacteristic
244C2×Dic13C2×C4⋊C411yescharacteristic
245C2×Dic13C2×C4⋊C411yescharacteristic
246C2×Dic13C2×C4⋊C411yescharacteristic
247C2×Dic13C22×D411yescharacteristic
248C2×Dic13C22×Q811yescharacteristic
249C4×D13—21no—
250C4×D13—21no—
251C4×D13—21no—
252C4×D13—21no—
253C4×D13—41no—
254Dic26—41no—
255#1057—41no—
256#1057—41no—
257#1057—41no—
258#1057—41no—
259#1057—41no—
260#1057—41no—
261#1057—41no—
262#1057—41no—
263C8×C13—21no—
264C8×C13—21no—
265C8×C13—21no—
266C8×C13#13112yes—
267#1055—21no—
268#1055—21no—
269#1055—21no—
270#1055—21no—
271C4×#41—131no—
272#446—131no—
273#446—131no—
274#436—131no—
275#436—131no—
276#435—131no—
277#435—131no—
278#435—131no—
279#435#26111yescharacteristic
280#433—261no—
281#433—261no—
282#433—261no—
283#433—261no—
284#432—131no—
285#432—131no—
286#432—131no—
287#432—131no—
288#431—131no—
289#431—131no—
290#431—131no—
291#431—131no—
292#431—131no—
293#431—131no—
294#431—131no—
295#423—131no—
296#423—131no—
297C2×C4⋊C8—131no—
298C2×C4⋊C8—131no—
299#408—261no—
300#408—261no—
301#405—261no—
302#405—261no—
303C4×M16—131no—
304C4×M16—131no—
305C2×C4×C8—131no—
306#335—131no—
307#335—131no—
308#335—131no—
309#335—131no—
310#335—131no—
311#335—131no—
312#335—131no—
313#335—131no—
314#334—131no—
315#334—131no—
316#334—131no—
317#334—131no—
318#334—131no—
319#334—131no—
320#334—131no—
321#334—131no—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13—21no—
327C22×C13—21no—
328C22×C13C22×C4⋊C411yescharacteristic
329C2×D13—21no—
330C2×D13—21no—
331C2×D13—21no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13—21no—
336C4×C13C2×#13111yescharacteristic
337C4×C13#56811yescharacteristic
338Dic13—21no—
339Dic13—21no—
340Dic13—21no—
341Dic13—21no—
342Dic13—21no—
343Dic13—21no—
344Dic13#57511yescharacteristic
345Dic13#57511yescharacteristic
346C2×#41—131no—
347C2×M16—131no—
348C2×M16—131no—
349C2×M16—131no—
350C2×M16—261no—
351C2×M16—261no—
352C2×M16C2×#26111yescharacteristic
353C22×C8—131no—
354C22×C8—261no—
355C22×C8—261no—
356C22×C8C2×#26111yescharacteristic
357C4×Q8—131no—
358C4×Q8—131no—
359C4×D4—131no—
360C4×D4—131no—
361C4×D4—131no—
362C4×D4—131no—
363C4×D4—131no—
364C4×D4C2×#26111yescharacteristic
365#117—131no—
366#117—131no—
367#117—131no—
368C2×C42—131no—
369C2×C42—131no—
370C2×C42—131no—
371C4⋊C8—131no—
372C4⋊C8—131no—
373C4⋊C8—131no—
374C4⋊C8—131no—
375C4⋊C8—131no—
376C4⋊C8—131no—
377C4⋊C8—131no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8C2×#26111yescharacteristic
389C22⋊C8—131no—
390C22⋊C8—131no—
391C22⋊C8—131no—
392C22⋊C8—131no—
393C22⋊C8—261no—
394C22⋊C8—261no—
395C22⋊C8—261no—
396C22⋊C8—261no—
397C22⋊C8—261no—
398C22⋊C8—261no—
399C22⋊C8—261no—
400C22⋊C8—261no—
401C22⋊C8C2×#26111yescharacteristic
402C22⋊C8C2×#26111yescharacteristic
403#97—131no—
404#97—131no—
405#97—131no—
406#97—261no—
407#97—261no—
408#97—261no—
409#97—261no—
410#97C2×#26111yescharacteristic
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—
420C4×C8—261no—
421C2×C13—41no—
422C2×C13—41no—
423C2×C13#290611yescharacteristic
424C2×C13#291111yescharacteristic
425C2×C13#291611yescharacteristic
426D13—41no—
427#41—521no—
428#41—521no—
429C2×Q8—131no—
430C2×D4—131no—
431C2×D4—131no—
432C2×D4C4⋊#26111yescharacteristic
433C22×C4—131no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4C22×#26111yescharacteristic
441C22×C4C22×#26111yescharacteristic
442M16—22no—
443M16—262no—
444M16—521no—
445M16—521no—
446M16—522no—
447M16—522no—
448C2×C8—22no—
449C2×C8—131no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—521no—
462C2×C8—522no—
463C2×C8—522no—
464C2×C8C22×#26111yescharacteristic
465C2×C8C22×#26111yescharacteristic
466C2×C8C22×#26111yescharacteristic
467C2×C8C22×#26111yescharacteristic
468C4⋊C4—131no—
469C4⋊C4—131no—
470C4⋊C4—131no—
471C4⋊C4—131no—
472C4⋊C4—131no—
473C4⋊C4C4⋊#26111yescharacteristic
474C22⋊C4—131no—
475C22⋊C4—131no—
476C22⋊C4—131no—
477C22⋊C4—131no—
478C22⋊C4C4⋊#26111yescharacteristic
479C22⋊C4C4⋊#26111yescharacteristic
480C42—131no—
481C42—131no—
482C42—131no—
483C42—131no—
484C42—131no—
485C42—131no—
486C42—131no—
487C42—131no—
488C42—131no—
489C42C22×#26111yescharacteristic
490C13#1783111yescharacteristic, complemented, Sylow
491C23—131no—
492C23C2×C4⋊#26111yescharacteristic
493C23C2×C4⋊#26111yescharacteristic
494Q8—521no—
495D4—41no—
496D4—521no—
497D4—521no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—131no—
503C2×C4—131no—
504C2×C4—131no—
505C2×C4—131no—
506C2×C4—131no—
507C2×C4—131no—
508C2×C4—131no—
509C2×C4—261no—
510C2×C4—261no—
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×C4C2×C4⋊#26111yescharacteristic
521C2×C4C2×C4⋊#26111yescharacteristic
522C2×C4C2×C4⋊#26111yescharacteristic
523C2×C4C2×C4⋊#26111yescharacteristic
524C2×C4C23×#26111yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—261no—
529C8—261no—
530C8—261no—
531C8—261no—
532C8—521no—
533C8—521no—
534C8—521no—
535C8—521no—
536C8—521no—
537C8—521no—
538C8—521no—
539C8—521no—
540C8#8823812yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—261no—
548C22—261no—
549C22—261no—
550C22C22×C4⋊#26111yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—131no—
556C4—131no—
557C4—261no—
558C4—261no—
559C4—261no—
560C4—261no—
561C4—261no—
562C4—261no—
563C4C2×#8823811yescharacteristic
564C4#1171962911yescharacteristic
565C2—41no—
566C2—41no—
567C2—521no—
568C2#1313148111yescharacteristic
569C2#1313148911yescharacteristic
570C2#1313149811yescharacteristic
subgroupG/H
centerC22C22×C4⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#435C4
socleC22×C13C22×C4⋊C4
prime radicalC2×#6129D4
cosocleC4×Dic13C24
hypercenter#435#261
hypocenterC13#17831
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
3. #13130414C2semidirect
4. #13130412C2semidirect
5. #13130411C2semidirect
6. #13130410C2semidirect
7. #13130407C2semidirect
8. #13130407C2semidirect
9. #13130401C2semidirect
10. #13130400C2semidirect
11. #13130398C2semidirect
12. #13130388C2semidirect
13. #13130387C2semidirect
14. #13130383C2semidirect
490. C13#17831semidirect

Maximal subgroups

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

subgroupindex
#131315322
#131315312
#131304142
#131304122
#131304112
#131304102
#131304072
#131304012
#131304002
#131303982
#131303882
#131303872
#131303832
#131237962
#1783113