Finite Group Databasebeta

← #16795027

Subgroups — #16795027

Order 3328.

602 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#13131758C211yesmaximal, characteristic
2#13131753C211yesmaximal, characteristic
3#13130414C211yesmaximal, characteristic, complemented
4#13130412C211yesmaximal, characteristic, complemented
5#13130411C211yesmaximal, characteristic, complemented
6#13130410C211yesmaximal, characteristic, complemented
7#13130408C211yesmaximal, characteristic, complemented
8#13130407C211yesmaximal, characteristic, complemented
9#13130406C211yesmaximal, characteristic, complemented
10#13130405C211yesmaximal, characteristic, complemented
11#13130388C211yesmaximal, characteristic, complemented
12#13130388C211yesmaximal, characteristic, complemented
13#13130386C211yesmaximal, characteristic, complemented
14D13⋊#335C211yesmaximal, characteristic, complemented
15#13123477C211yesmaximal, characteristic
16#11719227C2211yescharacteristic
17#11719130C2211yescharacteristic
18#11719129C2211yescharacteristic
19#11719119C2211yescharacteristic
20C2×C4⋊#1057C2211yescharacteristic
21#11719078—21no—
22#11719075—21no—
23#11719074—21no—
24#11719073—21no—
25#11719066—21no—
26#11719065—21no—
27#11719063—21no—
28#11719063—21no—
29#11719054C2211yescharacteristic
30#11719052C2211yescharacteristic
31#11719051C2211yescharacteristic
32#11719051C2211yescharacteristic
33#11719051C2211yescharacteristic
34D13⋊(C4⋊C8)C2211yescharacteristic
35D13⋊(C4⋊C8)C2211yescharacteristic
36D13⋊(C4⋊C8)C2211yescharacteristic
37C13×#433C411yescharacteristic
38#11718661C411yescharacteristic
39#11718500C411yescharacteristic
40#11718500C411yescharacteristic
41#11718494C2211yescharacteristic
42#11718494C2211yescharacteristic
43#11718388C411yescharacteristic
44#11718388C411yescharacteristic
45#11718379C2211yescharacteristic
46#11718379C2211yescharacteristic
47#11718370C411yescharacteristic
48#11718368C2211yescharacteristic
49#11718351C411yescharacteristic
50C4×C8×D13C2211yescharacteristic
51#11718256C2211yescharacteristic
52#11718256C2211yescharacteristic
53#11718256C2211yescharacteristic
54#11718256C2211yescharacteristic
55#11718255C2211yescharacteristic
56#11718255C2211yescharacteristic
57#11718255C2211yescharacteristic
58#11718255C2211yescharacteristic
59#11718254C2211yescharacteristic
60#11718254C2211yescharacteristic
61#11718254C2211yescharacteristic
62#11718254C2211yescharacteristic
63#11718254C2211yescharacteristic
64#11718254C2211yescharacteristic
65#11718253C2211yescharacteristic
66#11718253C2211yescharacteristic
67C2×#6127C2×C411yescharacteristic
68C2×#6122—21no—
69C22×#1057—21no—
70C2×#6118—21no—
71C2×D13⋊C8—21no—
72C2×D13⋊C8—21no—
73C2×D13⋊C8—21no—
74C13×#117C2×C411yescharacteristic
75C2×C4×Dic13C2311yescharacteristic
76C2×#6094C2×C411yescharacteristic
77C2×#6094C2×C411yescharacteristic
78C2×C8×D13C2×C411yescharacteristic
79C2×C8×D13C2×C411yescharacteristic
80#88147D411yescharacteristic
81#88147Q811yescharacteristic
82#88141D411yescharacteristic
83#88141Q811yescharacteristic
84#88135D411yescharacteristic
85#88135D411yescharacteristic
86#88135Q811yescharacteristic
87#88135Q811yescharacteristic
88#88126C2×C411yescharacteristic
89#88126C2×C411yescharacteristic
90C42×D13C2311yescharacteristic
91C42×D13C2311yescharacteristic
92C22⋊#1057—21no—
93C22⋊#1057—21no—
94#88112—21no—
95#88112—21no—
96#88112—21no—
97#88112—21no—
98#88111—21no—
99#88111—21no—
100#88111—21no—
101#88111—21no—
102#88110—21no—
103#88110—21no—
104C4⋊#1057—21no—
105C4⋊#1057—21no—
106C4⋊#1057C2311yescharacteristic
107C4⋊#1057C2311yescharacteristic
108C4⋊#1057C2311yescharacteristic
109C4⋊#1057C2311yescharacteristic
110C4⋊#1057C2311yescharacteristic
111C4⋊#1057C2311yescharacteristic
112C4⋊#1057C2311yescharacteristic
113C4⋊#1057C2311yescharacteristic
114C4×#1057—21no—
115C4×#1057—21no—
116C4×#1057—21no—
117C4×#1057—21no—
118C13×C4⋊C8C2×C411yescharacteristic
119C13×C4⋊C8C2×C411yescharacteristic
120C13×C22⋊C8C2×C411yescharacteristic
121C13×C22⋊C8C2×C411yescharacteristic
122C13×#97C2×C411yescharacteristic
123C4×C8×C13C2×C411yescharacteristic
124C22⋊#1055C2×C411yescharacteristic
125C22⋊#1055C2×C411yescharacteristic
126#88060C2×C411yescharacteristic
127#88060C2×C411yescharacteristic
128#88060C2×C411yescharacteristic
129#88060C2×C411yescharacteristic
130#88054C2×C411yescharacteristic
131#88054C2×C411yescharacteristic
132#88054C2×C411yescharacteristic
133#88054C2×C411yescharacteristic
134C8×Dic13C2311yescharacteristic
135C8×Dic13C2311yescharacteristic
136C8×Dic13C2311yescharacteristic
137C8×Dic13C2311yescharacteristic
138C4⋊#1055C2×C411yescharacteristic
139C4⋊#1055C2×C411yescharacteristic
140#88043C2×C411yescharacteristic
141C4×#1055C2×C411yescharacteristic
142#17812—131nomaximal, Sylow
143C22×C4×C13C22×C411yescharacteristic
144C2×C22⋊D13C4⋊C411yescharacteristic
145C2×C22⋊D13C4⋊C411yescharacteristic
146C22×Dic13C2×D411yescharacteristic
147C22×Dic13C2×Q811yescharacteristic
148#6127—22no—
149#6127—22no—
150C2×D52C4⋊C411yescharacteristic
151C2×C4×D13C22×C411yescharacteristic
152C2×C4×D13C22×C411yescharacteristic
153C2×C4×D13C2×D411yescharacteristic
154C2×C4×D13C2×D411yescharacteristic
155C2×C4×D13C2×Q811yescharacteristic
156C2×C4×D13C2×Q811yescharacteristic
157C2×Dic26C4⋊C411yescharacteristic
158#6122—81no—
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—81no—
168#6118—81no—
169D13⋊C8—81no—
170D13⋊C8—81no—
171D13⋊C8—81no—
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C2×C8×C13C22×C411yescharacteristic
175C2×C8×C13C22×C411yescharacteristic
176C13×C4⋊C4C4⋊C411yescharacteristic
177C13×C4⋊C4C4⋊C411yescharacteristic
178C13×C22⋊C4C4⋊C411yescharacteristic
179C13×C22⋊C4C4⋊C411yescharacteristic
180C42×C13C22×C411yescharacteristic
181C42×C13C22×C411yescharacteristic
182#6103C4⋊C411yescharacteristic
183#6103C4⋊C411yescharacteristic
184#6103C4⋊C411yescharacteristic
185#6103C4⋊C411yescharacteristic
186#6101C4⋊C411yescharacteristic
187#6101C4⋊C411yescharacteristic
188#6101C4⋊C411yescharacteristic
189#6101C4⋊C411yescharacteristic
190C4×Dic13C22×C411yescharacteristic
191C4×Dic13C2×D411yescharacteristic
192C4×Dic13C2×D411yescharacteristic
193C4×Dic13C2×D411yescharacteristic
194C4×Dic13C2×Q811yescharacteristic
195C4×Dic13C2×Q811yescharacteristic
196C4×Dic13C2×Q811yescharacteristic
197C4×Dic13C2411yescharacteristic
198C2×#1055C22×C411yescharacteristic
199C2×#1055C22×C411yescharacteristic
200C2×#1055C22×C411yescharacteristic
201C2×#1055C22×C411yescharacteristic
202#6094—22no—
203#6094—22no—
204C8×D13—22no—
205C8×D13—22no—
206#2989—131no—
207#2988—131no—
208#2922—131no—
209#1574—131no—
210#1574—131no—
211#1573—131no—
212#1573—131no—
213#1572—131no—
214#1572—131no—
215#1571—131no—
216#1571—131no—
217#1565—131no—
218#1565—131no—
219#1564—131no—
220C2×#335—131no—
221C23×C13C2×C4⋊C411yescharacteristic
222C22×D13C2×C4⋊C411yescharacteristic
223C22×D13C2×C4⋊C411yescharacteristic
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13C2×C4⋊C411yescharacteristic
227C2×C4×C13C2×C4⋊C411yescharacteristic
228C2×C4×C13C2×C4⋊C411yescharacteristic
229C2×C4×C13C2×C4⋊C411yescharacteristic
230C2×C4×C13C2×C4⋊C411yescharacteristic
231C2×C4×C13C23×C411yescharacteristic
232C22⋊D13—22no—
233C22⋊D13—22no—
234C2×Dic13—21no—
235C2×Dic13—21no—
236C2×Dic13—41no—
237C2×Dic13C2×C4⋊C411yescharacteristic
238C2×Dic13C2×C4⋊C411yescharacteristic
239C2×Dic13C2×C4⋊C411yescharacteristic
240C2×Dic13C2×C4⋊C411yescharacteristic
241C2×Dic13C22×D411yescharacteristic
242C2×Dic13C22×Q811yescharacteristic
243D52—22no—
244C4×D13—21no—
245C4×D13—21no—
246C4×D13—21no—
247C4×D13—21no—
248C4×D13—21no—
249C4×D13—21no—
250C4×D13—41no—
251C4×D13—41no—
252C4×D13#13112yes—
253C4×D13#13112yes—
254Dic26—22no—
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—21no—
267#1055—21no—
268#1055—21no—
269#1055—21no—
270#1055—21no—
271C4×#41—131no—
272#446—261no—
273C8×Q8—261no—
274#436—261no—
275#435—261no—
276#435—261no—
277C8×D4—261no—
278C8×D4—261no—
279C8×D4—261no—
280#433—131no—
281#433—131no—
282#433—131no—
283#433#26111yescharacteristic
284#432—131no—
285#432—131no—
286#431—131no—
287#431—131no—
288#431—131no—
289#431—131no—
290#431—131no—
291#431—131no—
292#431—131no—
293#431—131no—
294#424—131no—
295#424—131no—
296#423—131no—
297#423—131no—
298C2×C4⋊C8—131no—
299C2×C4⋊C8—131no—
300C2×C4⋊C8—131no—
301C2×C4⋊C8—131no—
302#408—131no—
303#408—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#335—131no—
315#335—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×C13C22×C4⋊C411yescharacteristic
326C2×D13—21no—
327C2×D13—21no—
328C2×D13—21no—
329C2×D13—21no—
330C2×D13—21no—
331C2×D13#42412yes—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13—21no—
336C4×C13—21no—
337C4×C13C2×#13111yescharacteristic
338C4×C13C2×#13111yescharacteristic
339Dic13—21no—
340Dic13—21no—
341Dic13—21no—
342Dic13—21no—
343Dic13#42412yes—
344Dic13#57611yescharacteristic
345Dic13#57811yescharacteristic
346C2×#41—131no—
347C2×M16—131no—
348C2×M16—131no—
349C2×M16—261no—
350C2×M16—261no—
351C22×C8—131no—
352C22×C8—131no—
353C22×C8—261no—
354C22×C8—261no—
355C22×C8—261no—
356C22×C8—261no—
357C4×Q8—131no—
358C4×Q8—131no—
359C4×D4—131no—
360C4×D4—131no—
361C4×D4—131no—
362C4×D4—131no—
363C4×D4—131no—
364C4×D4—131no—
365#117—131no—
366#117—131no—
367#117C2×#26111yescharacteristic
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—131no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8C2×#26111yescharacteristic
392C4⋊C8C2×#26111yescharacteristic
393C22⋊C8—131no—
394C22⋊C8—131no—
395C22⋊C8—131no—
396C22⋊C8—131no—
397C22⋊C8—131no—
398C22⋊C8—131no—
399C22⋊C8—261no—
400C22⋊C8—261no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403C22⋊C8—261no—
404C22⋊C8—261no—
405C22⋊C8C2×#26111yescharacteristic
406C22⋊C8C2×#26111yescharacteristic
407#97—131no—
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—261no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8—261no—
420C4×C8C2×#26111yescharacteristic
421C2×C13—41no—
422C2×C13C2×#42411yescharacteristic
423C2×C13#291311yescharacteristic
424C2×C13#291611yescharacteristic
425D13—22no—
426D13—41no—
427#41—262no—
428#41—262no—
429C2×Q8—131no—
430C2×D4—131no—
431C2×D4—131no—
432C2×D4—131no—
433C22×C4—131no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—131no—
441C22×C4C22×#26111yescharacteristic
442M16—262no—
443M16—262no—
444M16—1041no—
445M16—1041no—
446C2×C8—131no—
447C2×C8—131no—
448C2×C8—131no—
449C2×C8—131no—
450C2×C8—262no—
451C2×C8—262no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—1041no—
461C2×C8—1041no—
462C2×C8—1041no—
463C2×C8—1041no—
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⋊C4C4⋊#26111yescharacteristic
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—
488C42C22×#26111yescharacteristic
489C42C22×#26111yescharacteristic
490C13#1781211yescharacteristic, complemented, Sylow
491C23—131no—
492C23—131no—
493C23C2×C4⋊#26111yescharacteristic
494Q8—262no—
495D4—262no—
496D4—262no—
497D4—262no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—131no—
501C2×C4—131no—
502C2×C4—132no—
503C2×C4—132no—
504C2×C4—131no—
505C2×C4—131no—
506C2×C4—131no—
507C2×C4—131no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—521no—
517C2×C4—521no—
518C2×C4—521no—
519C2×C4C2×C4⋊#26111yescharacteristic
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—21no—
529C8—261no—
530C8—261no—
531C8—261no—
532C8—261no—
533C8—521no—
534C8—521no—
535C8—521no—
536C8—521no—
537C8—521no—
538C8—521no—
539C8—521no—
540C8—521no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—132no—
545C22—261no—
546C22—261no—
547C22—261no—
548C22—261no—
549C22—261no—
550C22C22×C4⋊#26111yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—21no—
556C4—132no—
557C4—131no—
558C4—131no—
559C4—261no—
560C4—261no—
561C4—261no—
562C4—261no—
563C4D13⋊#13111yescharacteristic
564C4D13⋊#13111yescharacteristic
565C2—41no—
566C2—262no—
567C2—521no—
568C2D13⋊#42411yescharacteristic
569C2#1313149111yescharacteristic
570C2#1313149811yescharacteristic
subgroupG/H
centerC22C22×C4⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#433C4
socleC22×C13C22×C4⋊C4
prime radicalC2×#6127C2×C4
cosocleC4×Dic13C24
hypercenter#433#261
hypocenterC13#17812
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
3. #13130414C2semidirect
4. #13130412C2semidirect
5. #13130411C2semidirect
6. #13130410C2semidirect
7. #13130408C2semidirect
8. #13130407C2semidirect
9. #13130406C2semidirect
10. #13130405C2semidirect
11. #13130388C2semidirect
12. #13130388C2semidirect
13. #13130386C2semidirect
14. D13⋊#335C2semidirect
490. C13#17812semidirect

Maximal subgroups

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

subgroupindex
#131317582
#131317532
#131304142
#131304122
#131304112
#131304102
#131304082
#131304072
#131304062
#131304052
#131303882
#131303862
D13⋊#3352
#131234772
#1781213