Finite Group Databasebeta

← #16795103

Subgroups — #16795103

Order 3328.

634 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131531C211yesmaximal, characteristic
2#13131481C211yesmaximal, characteristic
3#13130413C211yesmaximal, characteristic, complemented
4#13130412C211yesmaximal, characteristic, complemented
5#13130410C211yesmaximal, characteristic, complemented
6#13130409C211yesmaximal, characteristic, complemented
7#13130405C211yesmaximal, characteristic, complemented
8#13130403C211yesmaximal, characteristic, complemented
9#13130401C211yesmaximal, characteristic, complemented
10#13130400C211yesmaximal, characteristic, complemented
11#13130393C211yesmaximal, characteristic, complemented
12#13130388C211yesmaximal, characteristic, complemented
13#13130387C211yesmaximal, characteristic, complemented
14C2×#11718253C211yesmaximal, characteristic, complemented
15#13123796C211yesmaximal, characteristic
16C2×#88238—21no—
17C4×#6129C2211yescharacteristic
18#11719146—21no—
19#11719130C2211yescharacteristic
20#11719129C2211yescharacteristic
21#11719129C2211yescharacteristic
22#11719129C2211yescharacteristic
23#11719119C2211yescharacteristic
24C2×C4⋊#1057C2211yescharacteristic
25C2×C4⋊#1057C2211yescharacteristic
26C2×C4⋊#1057C2211yescharacteristic
27#11719079—21no—
28#11719077—21no—
29#11719068—21no—
30#11719067—21no—
31#11719067—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#11718256C2211yescharacteristic
54#11718256C2211yescharacteristic
55#11718255C2211yescharacteristic
56#11718255C2211yescharacteristic
57#11718254C2211yescharacteristic
58#11718254C2211yescharacteristic
59#11718254C2211yescharacteristic
60#11718254C2211yescharacteristic
61#11718253C2211yescharacteristic
62#11718253C2211yescharacteristic
63#11718253C2211yescharacteristic
64#11718253C2211yescharacteristic
65#11718253C2211yescharacteristic
66#11718253C2211yescharacteristic
67C2×#6129D411yescharacteristic
68C2×#6122—21no—
69C2×#6122—21no—
70C2×#6122—21no—
71C22×#1057—21no—
72C22×#1057—21no—
73C22×#1057—21no—
74#88238—44no—
75C2×#6118—21no—
76C2×D13⋊C8—21no—
77C2×C13×M16C2×C411yescharacteristic
78C22×C8×C13C2×C411yescharacteristic
79C4×D4×C13C2×C411yescharacteristic
80D4×Dic13Q811yescharacteristic
81C4×C22⋊D13C2×C411yescharacteristic
82C4×C22⋊D13C2×C411yescharacteristic
83C2×C4×Dic13C2311yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C2×#6099C2×C411yescharacteristic
86C22×#1055C2×C411yescharacteristic
87C2×#6094C2×C411yescharacteristic
88C2×#6094C2×C411yescharacteristic
89#88146D411yescharacteristic
90#88141Q811yescharacteristic
91#88135Q811yescharacteristic
92#88135Q811yescharacteristic
93#88131D411yescharacteristic
94#88131D411yescharacteristic
95C42×D13C2311yescharacteristic
96C4×Dic26C2×C411yescharacteristic
97C22⋊#1057—21no—
98C22⋊#1057—21no—
99#88112—21no—
100#88112—21no—
101#88112—21no—
102#88112—21no—
103#88111—21no—
104#88111—21no—
105#88110—21no—
106#88110—21no—
107C4⋊#1057—21no—
108C4⋊#1057—21no—
109C4⋊#1057—21no—
110C4⋊#1057—21no—
111C4⋊#1057C2311yescharacteristic
112C4⋊#1057C2311yescharacteristic
113C4⋊#1057C2311yescharacteristic
114C4⋊#1057C2311yescharacteristic
115C4⋊#1057C2311yescharacteristic
116C4⋊#1057C2311yescharacteristic
117C4⋊#1057C2311yescharacteristic
118C4⋊#1057C2311yescharacteristic
119C4×#1057—21no—
120C4×#1057—21no—
121C13×C4⋊C8C2×C411yescharacteristic
122C13×C22⋊C8C2×C411yescharacteristic
123C13×C22⋊C8C2×C411yescharacteristic
124C13×#97C2×C411yescharacteristic
125C22⋊#1055C2×C411yescharacteristic
126C22⋊#1055C2×C411yescharacteristic
127#88060C2×C411yescharacteristic
128#88060C2×C411yescharacteristic
129#88055C2×C411yescharacteristic
130#88055C2×C411yescharacteristic
131#88054C2×C411yescharacteristic
132#88054C2×C411yescharacteristic
133#88054C2×C411yescharacteristic
134#88054C2×C411yescharacteristic
135C8×Dic13C2×C411yescharacteristic
136C8×Dic13C2×C411yescharacteristic
137C8×Dic13C2311yescharacteristic
138C8×Dic13C2311yescharacteristic
139C8×Dic13C2311yescharacteristic
140C8×Dic13C2311yescharacteristic
141C4⋊#1055C2×C411yescharacteristic
142#88043C2×C411yescharacteristic
143#17830—131nomaximal, Sylow
144C2×D4×C13C4⋊C411yescharacteristic
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C22×C411yescharacteristic
147C2×C22⋊D13C4⋊C411yescharacteristic
148C2×C22⋊D13C4⋊C411yescharacteristic
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13C2×D411yescharacteristic
151C22×Dic13C2×Q811yescharacteristic
152C22×Dic13C2×Q811yescharacteristic
153#6129—22no—
154#6129—22no—
155C2×C4×D13C22×C411yescharacteristic
156C2×C4×D13C2×D411yescharacteristic
157C2×C4×D13C2×Q811yescharacteristic
158C2×Dic26C4⋊C411yescharacteristic
159#6122—42no—
160#6122—42no—
161#6122—42no—
162C2×#1057—21no—
163C2×#1057—21no—
164C2×#1057—21no—
165C2×#1057—21no—
166C2×#1057—21no—
167C2×#1057—21no—
168C2×#1057—21no—
169C2×#1057—21no—
170C2×#1057—42no—
171C2×#1057—42no—
172C2×#1057—42no—
173#6118—42no—
174D13⋊C8—42no—
175C13×M16—22no—
176C2×C8×C13—22no—
177C2×C8×C13C22×C411yescharacteristic
178C2×C8×C13C22×C411yescharacteristic
179C2×C8×C13C22×C411yescharacteristic
180C2×C8×C13C22×C411yescharacteristic
181C13×C4⋊C4C4⋊C411yescharacteristic
182C13×C22⋊C4C4⋊C411yescharacteristic
183C13×C22⋊C4C4⋊C411yescharacteristic
184C42×C13C22×C411yescharacteristic
185C22⋊Dic13C4⋊C411yescharacteristic
186C22⋊Dic13C4⋊C411yescharacteristic
187#6103C4⋊C411yescharacteristic
188#6103C4⋊C411yescharacteristic
189C4⋊Dic13C4⋊C411yescharacteristic
190#6101C4⋊C411yescharacteristic
191#6101C4⋊C411yescharacteristic
192#6101C4⋊C411yescharacteristic
193#6101C4⋊C411yescharacteristic
194C4×Dic13C22×C411yescharacteristic
195C4×Dic13C22×C411yescharacteristic
196C4×Dic13C2×D411yescharacteristic
197C4×Dic13C2×D411yescharacteristic
198C4×Dic13C2×D411yescharacteristic
199C4×Dic13C2×Q811yescharacteristic
200C4×Dic13C2×Q811yescharacteristic
201C4×Dic13C2×Q811yescharacteristic
202C4×Dic13C2411yescharacteristic
203#6099—41no—
204C2×#1055—41no—
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209#6094—22no—
210#6094—41no—
211#2965—131no—
212#2925—131no—
213#2906—131no—
214#1574—131no—
215#1574—131no—
216#1573—131no—
217#1573—131no—
218#1571—131no—
219#1570—131no—
220#1569—131no—
221#1569—131no—
222#1567—131no—
223#1565—131no—
224#1565—131no—
225C2×#334—131no—
226C23×C13C2×C4⋊C411yescharacteristic
227C23×C13C2×C4⋊C411yescharacteristic
228C22×D13C2×C4⋊C411yescharacteristic
229D4×C13—22no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13C2×C4⋊C411yescharacteristic
235C2×C4×C13C2×C4⋊C411yescharacteristic
236C2×C4×C13C2×C4⋊C411yescharacteristic
237C2×C4×C13C2×C4⋊C411yescharacteristic
238C2×C4×C13C23×C411yescharacteristic
239C22⋊D13—22no—
240C22⋊D13—22no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—41no—
244C2×Dic13—41no—
245C2×Dic13C2×C4⋊C411yescharacteristic
246C2×Dic13C2×C4⋊C411yescharacteristic
247C2×Dic13C2×C4⋊C411yescharacteristic
248C2×Dic13C2×C4⋊C411yescharacteristic
249C2×Dic13C2×C4⋊C411yescharacteristic
250C2×Dic13AGL(1,ℤ/8)12yes—
251C2×Dic13#13712yes—
252C2×Dic13C22×D411yescharacteristic
253C2×Dic13C22×Q811yescharacteristic
254C4×D13—21no—
255C4×D13—21no—
256C4×D13—21no—
257C4×D13—21no—
258C4×D13—41no—
259Dic26—22no—
260#1057—41no—
261#1057—41no—
262#1057—41no—
263#1057—41no—
264#1057—41no—
265#1057—41no—
266#1057—41no—
267#1057—41no—
268C8×C13—21no—
269C8×C13—21no—
270C8×C13—21no—
271C8×C13#13112yescomplemented
272#1055—21no—
273#1055—21no—
274#1055—21no—
275#1055—21no—
276C2×#131—261no—
277C4×#41—131no—
278#446—131no—
279#446—131no—
280#436—131no—
281#436—131no—
282#435—131no—
283#435—131no—
284#435—131no—
285#435#26111yescharacteristic
286#433—261no—
287#433—261no—
288#432—131no—
289#432—131no—
290#431—131no—
291#431—131no—
292#431—131no—
293#431—131no—
294#431—131no—
295#424—261no—
296#424—261no—
297#424—261no—
298#423—131no—
299#423—131no—
300#423—131no—
301#423—131no—
302C2×C4⋊C8—131no—
303C2×C4⋊C8—131no—
304C2×C4⋊C8—131no—
305C2×C4⋊C8—131no—
306#408—261no—
307#405—261no—
308C4×M16—131no—
309C4×M16—131no—
310C2×C4×C8—131no—
311#335—131no—
312#335—131no—
313#335—131no—
314#335—131no—
315#335—131no—
316#335—131no—
317#335—131no—
318#335—131no—
319#334—131no—
320#334—131no—
321#334—131no—
322#334—131no—
323#334—131no—
324#334—131no—
325#334—131no—
326#334—131no—
327C22×C13—21no—
328C22×C13—21no—
329C22×C13—21no—
330C22×C13—21no—
331C22×C13—21no—
332C22×C13#42812yes—
333C22×C13C22×C4⋊C411yescharacteristic
334C2×D13—21no—
335C2×D13—21no—
336C2×D13—21no—
337C4×C13—21no—
338C4×C13—21no—
339C4×C13—21no—
340C4×C13—21no—
341C4×C13C2×#13111yescharacteristic
342C4×C13#56811yescharacteristic
343Dic13—21no—
344Dic13—21no—
345Dic13—21no—
346Dic13—21no—
347Dic13—21no—
348Dic13#42812yes—
349Dic13C2×AGL(1,ℤ/8)11yescharacteristic
350Dic13C2×#13711yescharacteristic
351C2×#41—131no—
352#131—524no—
353C2×M16—131no—
354C2×M16—131no—
355C2×M16—131no—
356C2×M16—261no—
357C2×M16—261no—
358C2×M16—261no—
359C2×M16—261no—
360C2×M16C2×#26111yescharacteristic
361C22×C8—131no—
362C22×C8—261no—
363C22×C8—261no—
364C22×C8—261no—
365C22×C8—261no—
366C22×C8C2×#26111yescharacteristic
367C4×Q8—131no—
368C4×Q8—131no—
369C4×D4—131no—
370C4×D4—131no—
371C4×D4—131no—
372C4×D4—131no—
373C4×D4—131no—
374C4×D4C2×#26111yescharacteristic
375#117—131no—
376#117—131no—
377#117—131no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—131no—
385C4⋊C8—131no—
386C4⋊C8—131no—
387C4⋊C8—131no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—131no—
392C4⋊C8—131no—
393C4⋊C8—131no—
394C4⋊C8—261no—
395C4⋊C8—261no—
396C4⋊C8—261no—
397C4⋊C8—261no—
398C4⋊C8—261no—
399C4⋊C8—261no—
400C4⋊C8—261no—
401C4⋊C8—261no—
402C4⋊C8C2×#26111yescharacteristic
403C22⋊C8—131no—
404C22⋊C8—131no—
405C22⋊C8—131no—
406C22⋊C8—131no—
407C22⋊C8—261no—
408C22⋊C8—261no—
409C22⋊C8—261no—
410C22⋊C8—261no—
411C22⋊C8C2×#26111yescharacteristic
412C22⋊C8C2×#26111yescharacteristic
413#97—131no—
414#97—131no—
415#97—131no—
416#97—261no—
417#97—261no—
418#97C2×#26111yescharacteristic
419C4×C8—131no—
420C4×C8—131no—
421C4×C8—131no—
422C4×C8—131no—
423C4×C8—131no—
424C4×C8—131no—
425C4×C8—261no—
426C4×C8—261no—
427C2×C13—22no—
428C2×C13—41no—
429C2×C13#290611yescharacteristic
430C2×C13C2×#42811yescharacteristic
431C2×C13#291611yescharacteristic
432D13—41no—
433#41—262no—
434#41—262no—
435C2×Q8—131no—
436C2×D4—131no—
437C2×D4—131no—
438C2×D4C4⋊#26111yescharacteristic
439C22×C4—131no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—131no—
443C22×C4—131no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4C22×#26111yescharacteristic
447C22×C4C22×#26111yescharacteristic
448M16—22no—
449M16—262no—
450M16—521no—
451M16—521no—
452M16—522no—
453M16—522no—
454M16—522no—
455M16—522no—
456C2×C8—22no—
457C2×C8—131no—
458C2×C8—131no—
459C2×C8—131no—
460C2×C8—131no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—521no—
470C2×C8—522no—
471C2×C8—522no—
472C2×C8—522no—
473C2×C8—522no—
474C2×C8C22×#26111yescharacteristic
475C2×C8C22×#26111yescharacteristic
476C2×C8C22×#26111yescharacteristic
477C2×C8C22×#26111yescharacteristic
478C4⋊C4—131no—
479C4⋊C4—131no—
480C4⋊C4—131no—
481C4⋊C4—131no—
482C4⋊C4—131no—
483C4⋊C4C4⋊#26111yescharacteristic
484C22⋊C4—131no—
485C22⋊C4—131no—
486C22⋊C4—131no—
487C22⋊C4—131no—
488C22⋊C4C4⋊#26111yescharacteristic
489C22⋊C4C4⋊#26111yescharacteristic
490C42—131no—
491C42—131no—
492C42—131no—
493C42—131no—
494C42—131no—
495C42—131no—
496C42—131no—
497C42—131no—
498C42—131no—
499C42C22×#26111yescharacteristic
500C13#1783011yescharacteristic, complemented, Sylow
501C23—131no—
502C23C2×C4⋊#26111yescharacteristic
503C23C2×C4⋊#26111yescharacteristic
504Q8—262no—
505D4—22no—
506D4—262no—
507D4—262no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—132no—
513C2×C4—132no—
514C2×C4—131no—
515C2×C4—131no—
516C2×C4—131no—
517C2×C4—131no—
518C2×C4—131no—
519C2×C4—131no—
520C2×C4—131no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4C2×C4⋊#26111yescharacteristic
531C2×C4C2×C4⋊#26111yescharacteristic
532C2×C4C2×C4⋊#26111yescharacteristic
533C2×C4C2×C4⋊#26111yescharacteristic
534C2×C4C23×#26111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—261no—
539C8—261no—
540C8—261no—
541C8—261no—
542C8—521no—
543C8—521no—
544C8—521no—
545C8—521no—
546C8—521no—
547C8—521no—
548C8—521no—
549C8—521no—
550C8#8823812yescomplemented
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—261no—
557C22—261no—
558C22—261no—
559C22#1171909812yes—
560C22C22×C4⋊#26111yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—131no—
566C4—131no—
567C4—132no—
568C4—261no—
569C4—261no—
570C4—261no—
571C4—261no—
572C4—261no—
573C4C2×#8823811yescharacteristic
574C4#1171962911yescharacteristic
575C2—22no—
576C2—41no—
577C2—521no—
578C2#1313148111yescharacteristic
579C2C2×#1171909811yescharacteristic
580C2#1313149711yescharacteristic
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#17830
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. #13130413C2semidirect
4. #13130412C2semidirect
5. #13130410C2semidirect
6. #13130409C2semidirect
7. #13130405C2semidirect
8. #13130403C2semidirect
9. #13130401C2semidirect
10. #13130400C2semidirect
11. #13130393C2semidirect
12. #13130388C2semidirect
13. #13130387C2semidirect
14. C2×#11718253C2semidirect
271. C8×C13#131semidirect
500. C13#17830semidirect
550. C8#88238semidirect

Maximal subgroups

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

subgroupindex
#131315312
#131314812
#131304132
#131304122
#131304102
#131304092
#131304052
#131304032
#131304012
#131304002
#131303932
#131303882
#131303872
C2×#117182532
#131237962
#1783013