Finite Group Databasebeta

← #15832182

Subgroups — #15832182

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#13123800C211yesmaximal, characteristic
2#13123504C211yesmaximal, characteristic
3#13123497C211yesmaximal, characteristic
4#13113623C211yesmaximal, characteristic, complemented
5#13113621C211yesmaximal, characteristic, complemented
6#13113620C211yesmaximal, characteristic, complemented
7#13113615C211yesmaximal, characteristic, complemented
8#13113613C211yesmaximal, characteristic, complemented
9#13113601C211yesmaximal, characteristic, complemented
10#13113600C211yesmaximal, characteristic, complemented
11#13113596C211yesmaximal, characteristic, complemented
12#13113589C211yesmaximal, characteristic, complemented
13#13113587C211yesmaximal, characteristic, complemented
14#13113583C211yesmaximal, characteristic, complemented
15C13×#1574C211yesmaximal, characteristic, complemented
16C4×#6127C2211yescharacteristic
17C13×#431C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#423C2211yescharacteristic
20#11718790—21no—
21#11718783—21no—
22#11718587C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24C4×#6099C2211yescharacteristic
25#11718501—21no—
26#11718501—21no—
27#11718498C2211yescharacteristic
28#11718497C411yescharacteristic
29#11718497C411yescharacteristic
30#11718496C2211yescharacteristic
31#11718496C2211yescharacteristic
32#11718496C2211yescharacteristic
33#11718494C2211yescharacteristic
34#11718494C2211yescharacteristic
35#11718494C2211yescharacteristic
36D13×C4⋊C8C2211yescharacteristic
37#11718489C411yescharacteristic
38#11718489C411yescharacteristic
39#11718390C411yescharacteristic
40#11718390C411yescharacteristic
41#11718389C411yescharacteristic
42#11718389C411yescharacteristic
43#11718388—21no—
44#11718381—21no—
45#11718351—21no—
46#11718350—21no—
47C4×#6094C2211yescharacteristic
48#11718346C2211yescharacteristic
49#11718346C2211yescharacteristic
50C4×C8×D13C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×#335C2211yescharacteristic
53C13×#334C2211yescharacteristic
54C13×#334C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718072C2211yescharacteristic
58#11718072C2211yescharacteristic
59#11718071C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718050C2211yescharacteristic
64#11718050C2211yescharacteristic
65#11718049C2211yescharacteristic
66#11718049C2211yescharacteristic
67C2×#6127D411yescharacteristic
68C2×C13×M16—21no—
69C2×C42×C13C2311yescharacteristic
70C4×C22⋊D13C2×C411yescharacteristic
71C4×C22⋊D13C2×C411yescharacteristic
72C4×C22⋊D13Q811yescharacteristic
73C4×C22⋊D13Q811yescharacteristic
74#88180D411yescharacteristic
75C2×#6099C2×C411yescharacteristic
76C2×#6099C2×C411yescharacteristic
77C22×#1055—21no—
78C2×#6094—21no—
79C2×#6094C2×C411yescharacteristic
80C2×#6094C2×C411yescharacteristic
81C2×C8×D13—21no—
82C2×C8×D13C2×C411yescharacteristic
83C2×C8×D13C2×C411yescharacteristic
84C4×D52C2×C411yescharacteristic
85C4×D52Q811yescharacteristic
86#88126D411yescharacteristic
87#88126D411yescharacteristic
88C42×D13C2311yescharacteristic
89C42×D13C2311yescharacteristic
90C4×Dic26C2×C411yescharacteristic
91C4×Dic26Q811yescharacteristic
92C13×C4⋊C8—21no—
93C13×C4⋊C8C2×C411yescharacteristic
94C13×C4⋊C8C2×C411yescharacteristic
95C13×C4⋊C8C2311yescharacteristic
96C13×C4⋊C8C2311yescharacteristic
97C13×C4⋊C8C2311yescharacteristic
98C13×C4⋊C8C2311yescharacteristic
99C13×C22⋊C8—21no—
100C13×C22⋊C8C2×C411yescharacteristic
101C13×C22⋊C8C2×C411yescharacteristic
102C4×C8×C13—21no—
103C4×C8×C13C2311yescharacteristic
104C4×C8×C13C2311yescharacteristic
105C22⋊#1055—21no—
106#88060—21no—
107#88060—21no—
108#88060—21no—
109#88060—21no—
110#88060—21no—
111#88060—21no—
112#88060C2×C411yescharacteristic
113#88060C2×C411yescharacteristic
114#88060C2×C411yescharacteristic
115#88060C2×C411yescharacteristic
116#88055—21no—
117#88055—21no—
118#88055—21no—
119#88055C2×C411yescharacteristic
120#88055C2×C411yescharacteristic
121#88054—21no—
122#88054—21no—
123#88054C2×C411yescharacteristic
124#88054C2×C411yescharacteristic
125#88054C2×C411yescharacteristic
126#88054C2×C411yescharacteristic
127C8×Dic13—21no—
128C8×Dic13—21no—
129C8×Dic13—21no—
130C8×Dic13C2×C411yescharacteristic
131C8×Dic13C2×C411yescharacteristic
132C4⋊#1055—21no—
133C4⋊#1055C2311yescharacteristic
134C4⋊#1055C2311yescharacteristic
135C4⋊#1055C2311yescharacteristic
136C4⋊#1055C2311yescharacteristic
137#88043—21no—
138#88043C2×C411yescharacteristic
139#88043C2×C411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142#17831—131nomaximal, Sylow
143C22×C4×C13C22×C411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×Q811yescharacteristic
146C2×C22⋊D13C4⋊C411yescharacteristic
147C2×C22⋊D13C4⋊C411yescharacteristic
148#6127—41no—
149#6127—41no—
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
158C13×M16—42no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C2×C8×C13C22×C411yescharacteristic
167C42×C13C22×C411yescharacteristic
168C42×C13C2×D411yescharacteristic
169C42×C13C2×Q811yescharacteristic
170C42×C13C2411yescharacteristic
171C22⋊Dic13C4⋊C411yescharacteristic
172C22⋊Dic13C4⋊C411yescharacteristic
173#6103C4⋊C411yescharacteristic
174#6103C4⋊C411yescharacteristic
175#6103C4⋊C411yescharacteristic
176#6103C4⋊C411yescharacteristic
177C4⋊Dic13C4⋊C411yescharacteristic
178C4⋊Dic13C4⋊C411yescharacteristic
179#6101C4⋊C411yescharacteristic
180#6101C4⋊C411yescharacteristic
181#6101C4⋊C411yescharacteristic
182#6101C4⋊C411yescharacteristic
183C4×Dic13C22×C411yescharacteristic
184C4×Dic13C22×C411yescharacteristic
185C4×Dic13C2×D411yescharacteristic
186C4×Dic13C2×D411yescharacteristic
187C4×Dic13C2×Q811yescharacteristic
188C4×Dic13C2×Q811yescharacteristic
189#6099—22no—
190#6099—41no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—42no—
196C2×#1055C22×C411yescharacteristic
197C2×#1055C22×C411yescharacteristic
198C2×#1055C22×C411yescharacteristic
199C2×#1055C22×C411yescharacteristic
200#6094—22no—
201#6094—41no—
202#6094—42no—
203C8×D13—22no—
204C8×D13—41no—
205C8×D13—42no—
206#2965—131no—
207#2925—131no—
208#2925—131no—
209#1574—131no—
210#1574D1311yescharacteristic, complemented
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
222C22×D13C2×C4⋊C411yescharacteristic
223C22×D13C2×C4⋊C411yescharacteristic
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—41no—
229C2×C4×C13C2×C4⋊C411yescharacteristic
230C2×C4×C13C2×C4⋊C411yescharacteristic
231C2×C4×C13C2×C4⋊C411yescharacteristic
232C2×C4×C13C23×C411yescharacteristic
233C2×C4×C13C22×D411yescharacteristic
234C2×C4×C13C22×Q811yescharacteristic
235C22⋊D13—41no—
236C22⋊D13—41no—
237C2×Dic13C2×C4⋊C411yescharacteristic
238C2×Dic13C2×C4⋊C411yescharacteristic
239C2×Dic13C2×C4⋊C411yescharacteristic
240C2×Dic13C2×C4⋊C411yescharacteristic
241C2×Dic13C2×C4⋊C411yescharacteristic
242C2×Dic13C2×C4⋊C411yescharacteristic
243D52—41no—
244C4×D13—21no—
245C4×D13—21no—
246C4×D13—21no—
247C4×D13—21no—
248C4×D13—21no—
249C4×D13—21no—
250C4×D13—21no—
251C4×D13—21no—
252C4×D13—41no—
253C4×D13—41no—
254Dic26—41no—
255C8×C13—21no—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—41no—
260C8×C13—41no—
261C8×C13—41no—
262C8×C13—41no—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—41no—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270#1055#13112yes—
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—131no—
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#431C2×D1311yescharacteristic
294#431C2×D1311yescharacteristic
295#423—131no—
296#423C2×D1311yescharacteristic
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#335C2×D1311yescharacteristic
313#335C2×D1311yescharacteristic
314#334—131no—
315#334—131no—
316#334—131no—
317#334—131no—
318#334—131no—
319#334—131no—
320#334C2×D1311yescharacteristic
321#334C2×D1311yescharacteristic
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—21no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13—21no—
336C4×C13C2×#13111yescharacteristic
337C4×C13#56811yescharacteristic
338C4×C13#57511yescharacteristic
339C4×C13#57511yescharacteristic
340Dic13—21no—
341Dic13—21no—
342Dic13—21no—
343Dic13—21no—
344Dic13—21no—
345Dic13—21no—
346C2×#41—131no—
347C2×M16—21no—
348C2×M16—131no—
349C2×M16—131no—
350C2×M16—131no—
351C2×M16—131no—
352C2×M16—261no—
353C22×C8—131no—
354C22×C8—131no—
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#117—131no—
368C2×C42—131no—
369C2×C42—131no—
370C2×C42C22×D1311yescharacteristic
371C4⋊C8—21no—
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—261no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8C4×D1311yescharacteristic
384C4⋊C8C4×D1311yescharacteristic
385C4⋊C8C22×D1311yescharacteristic
386C4⋊C8C22×D1311yescharacteristic
387C4⋊C8C22×D1311yescharacteristic
388C4⋊C8C22×D1311yescharacteristic
389C22⋊C8—21no—
390C22⋊C8—131no—
391C22⋊C8—131no—
392C22⋊C8—131no—
393C22⋊C8—131no—
394C22⋊C8—261no—
395C22⋊C8—261no—
396C22⋊C8—261no—
397C22⋊C8—261no—
398C22⋊C8—261no—
399C22⋊C8—261no—
400C22⋊C8—261no—
401C22⋊C8C4×D1311yescharacteristic
402C22⋊C8C4×D1311yescharacteristic
403#97—131no—
404#97—131no—
405#97—131no—
406#97—131no—
407#97—261no—
408#97—261no—
409#97—261no—
410#97—261no—
411C4×C8—21no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8C22×D1311yescharacteristic
420C4×C8C22×D1311yescharacteristic
421C2×C13—41no—
422C2×C13#290611yescharacteristic
423C2×C13#291111yescharacteristic
424C2×C13#291611yescharacteristic
425D13—41no—
426D13—41no—
427#41—521no—
428#41—521no—
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×C4C2×C4×D1311yescharacteristic
440C22×C4D4×D1311yescharacteristic
441C22×C4Q8×D1311yescharacteristic
442M16—42no—
443M16—262no—
444M16—262no—
445M16—521no—
446M16—522no—
447M16—521no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—262no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—521no—
462C2×C8—522no—
463C2×C8—522no—
464C2×C8C2×C4×D1311yescharacteristic
465C2×C8C2×C4×D1311yescharacteristic
466C2×C8C2×C4×D1311yescharacteristic
467C2×C8C2×C4×D1311yescharacteristic
468C4⋊C4—131no—
469C4⋊C4—131no—
470C4⋊C4—131no—
471C4⋊C4—131no—
472C4⋊C4—131no—
473C4⋊C4—131no—
474C22⋊C4—131no—
475C22⋊C4—131no—
476C22⋊C4—131no—
477C22⋊C4—131no—
478C22⋊C4—131no—
479C22⋊C4—131no—
480C42—131no—
481C42—131no—
482C42—131no—
483C42—131no—
484C42—131no—
485C42—131no—
486C42C2×C4×D1311yescharacteristic
487C42D4×D1311yescharacteristic
488C42Q8×D1311yescharacteristic
489C42C23×D1311yescharacteristic
490C13#1783111yescharacteristic, complemented, Sylow
491C23—131no—
492C23—131no—
493C23C4⋊C4×D1311yescharacteristic
494Q8—521no—
495D4—521no—
496D4—521no—
497D4—521no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
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×C4C4⋊C4×D1311yescharacteristic
520C2×C4C4⋊C4×D1311yescharacteristic
521C2×C4C4⋊C4×D1311yescharacteristic
522C2×C4C22×C4×D1311yescharacteristic
523C2×C4C2×D4×D1311yescharacteristic
524C2×C4C2×Q8×D1311yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—132no—
534C8—261no—
535C8—261no—
536C8—261no—
537C8—521no—
538C8—521no—
539C8—521no—
540C8—521no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—261no—
545C22—261no—
546C22—261no—
547C22—261no—
548C22—261no—
549C22—261no—
550C22C2×C4⋊C4×D1311yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—261no—
556C4—261no—
557C4—261no—
558C4—261no—
559C4—261no—
560C4—261no—
561C4D13×#13111yescharacteristic
562C4#1171945511yescharacteristic
563C4#1171947811yescharacteristic
564C4#1171948211yescharacteristic
565C2—41no—
566C2—521no—
567C2—521no—
568C2#1312340311yescharacteristic
569C2#1312342311yescharacteristic
570C2#1312344411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1574C2
socleC22×C13C22×C4⋊C4
prime radicalC2×#6127D4
cosocleC42×C13C24
hypercenter#1574D13
hypocenterC13#17831
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
4. #13113623C2semidirect
5. #13113621C2semidirect
6. #13113620C2semidirect
7. #13113615C2semidirect
8. #13113613C2semidirect
9. #13113601C2semidirect
10. #13113600C2semidirect
11. #13113596C2semidirect
12. #13113589C2semidirect
13. #13113587C2semidirect
14. #13113583C2semidirect
15. C13×#1574C2semidirect
210. #1574D13semidirect
490. C13#17831semidirect

Maximal subgroups

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

subgroupindex
#131238002
#131235042
#131234972
#131136232
#131136212
#131136202
#131136152
#131136132
#131136012
#131136002
#131135962
#131135892
#131135872
#131135832
C13×#15742
#1783113