Finite Group Databasebeta

← #15832136

Subgroups — #15832136

Order 3328.

572 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123955C211yesmaximal, characteristic
2#13123950C211yesmaximal, characteristic
3#13123481C211yesmaximal, characteristic
4#13113626C211yesmaximal, characteristic, complemented
5#13113623C211yesmaximal, characteristic, complemented
6#13113620C211yesmaximal, characteristic, complemented
7#13113618C211yesmaximal, characteristic, complemented
8#13113613C211yesmaximal, characteristic, complemented
9#13113613C211yesmaximal, characteristic, complemented
10#13113609C211yesmaximal, characteristic, complemented
11#13113609C211yesmaximal, characteristic, complemented
12#13113603C211yesmaximal, characteristic, complemented
13#13113597C211yesmaximal, characteristic, complemented
14#13113594C211yesmaximal, characteristic, complemented
15C13×#1569C211yesmaximal, characteristic, complemented
16C4×#6127C2211yescharacteristic
17C13×#432C2211yescharacteristic
18C13×#423C2211yescharacteristic
19C4×C13×M16C2211yescharacteristic
20#11718790C412yes—
21#11718789—21no—
22#11718788—21no—
23#11718780C412yes—
24#11718587C2211yescharacteristic
25#11718585C2211yescharacteristic
26C2×C4×#1055C2211yescharacteristic
27#11718498C2211yescharacteristic
28#11718498C2211yescharacteristic
29#11718497—21no—
30#11718496C2211yescharacteristic
31#11718496C2211yescharacteristic
32#11718494C2211yescharacteristic
33#11718494C2211yescharacteristic
34D13×C4⋊C8C2211yescharacteristic
35D13×C4⋊C8C2211yescharacteristic
36#11718489—21no—
37#11718390—21no—
38#11718389—21no—
39#11718370C412yes—
40#11718370C412yes—
41#11718367—21no—
42#11718362—21no—
43#11718346C2211yescharacteristic
44#11718346C2211yescharacteristic
45#11718346C2211yescharacteristic
46#11718346C2211yescharacteristic
47C13×#335C2211yescharacteristic
48C13×#335C2211yescharacteristic
49C13×#334C2211yescharacteristic
50C13×#334C2211yescharacteristic
51#11718072C2211yescharacteristic
52#11718072C2211yescharacteristic
53#11718071C2211yescharacteristic
54#11718071C2211yescharacteristic
55#11718071C2211yescharacteristic
56#11718071C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718050C2211yescharacteristic
60#11718050C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718049C2211yescharacteristic
63C2×#6127C2×C411yescharacteristic
64C2×C13×M16—21no—
65C2×C13×M16C2×C412yes—
66C2×C42×C13C2311yescharacteristic
67C4×C22⋊D13D411yescharacteristic
68C4×C22⋊D13D411yescharacteristic
69C4×C22⋊D13Q811yescharacteristic
70C4×C22⋊D13Q811yescharacteristic
71#88180C2×C411yescharacteristic
72C2×#6099—21no—
73C22×#1055C2×C412yes—
74C2×#6094—21no—
75C2×#6094—21no—
76C2×C8×D13—21no—
77C2×C8×D13—21no—
78C4×D52D411yescharacteristic
79C4×D52Q811yescharacteristic
80#88126C2×C411yescharacteristic
81#88126C2×C411yescharacteristic
82C42×D13C2311yescharacteristic
83C42×D13C2311yescharacteristic
84C4×Dic26D411yescharacteristic
85C4×Dic26Q811yescharacteristic
86C13×C4⋊C8—21no—
87C13×C4⋊C8C2311yescharacteristic
88C13×C4⋊C8C2311yescharacteristic
89C13×C4⋊C8C2311yescharacteristic
90C13×C4⋊C8C2311yescharacteristic
91C13×C22⋊C8—21no—
92C13×#97—21no—
93C13×#97C2×C412yes—
94C4×C8×C13C2311yescharacteristic
95C4×C8×C13C2311yescharacteristic
96C22⋊#1055—21no—
97#88060—21no—
98#88060—21no—
99#88060—21no—
100#88060—21no—
101#88060C2×C412yes—
102#88060C2×C412yes—
103#88060C2×C412yes—
104#88060C2×C412yes—
105#88055—21no—
106#88055—21no—
107#88054—21no—
108#88054—21no—
109#88054—21no—
110#88054—21no—
111#88054C2×C412yes—
112#88054C2×C412yes—
113#88054C2×C412yes—
114#88054C2×C412yes—
115C8×Dic13—21no—
116C8×Dic13—21no—
117C4⋊#1055—21no—
118C4⋊#1055C2311yescharacteristic
119C4⋊#1055C2311yescharacteristic
120C4⋊#1055C2311yescharacteristic
121C4⋊#1055C2311yescharacteristic
122#88043—21no—
123C4×#1055C2×C412yes—
124C4×#1055C2311yescharacteristic
125C4×#1055C2311yescharacteristic
126#17825—131nomaximal, Sylow
127C22×C4×C13C22×C411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×Q811yescharacteristic
130C2×C22⋊D13C4⋊C411yescharacteristic
131C2×C22⋊D13C4⋊C411yescharacteristic
132#6127—42no—
133C2×D52C4⋊C411yescharacteristic
134C2×C4×D13C22×C411yescharacteristic
135C2×C4×D13C22×C411yescharacteristic
136C2×C4×D13C2×D411yescharacteristic
137C2×C4×D13C2×D411yescharacteristic
138C2×C4×D13C2×Q811yescharacteristic
139C2×C4×D13C2×Q811yescharacteristic
140C2×Dic26C4⋊C411yescharacteristic
141C13×M16—42no—
142C13×M16—81no—
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13C22×C412yes—
148C2×C8×C13C22×C412yes—
149C42×C13C22×C411yescharacteristic
150C42×C13C2×D411yescharacteristic
151C42×C13C2×Q811yescharacteristic
152C42×C13C2411yescharacteristic
153C22⋊Dic13C4⋊C411yescharacteristic
154C22⋊Dic13C4⋊C411yescharacteristic
155#6103C4⋊C411yescharacteristic
156#6103C4⋊C411yescharacteristic
157#6103C4⋊C411yescharacteristic
158#6103C4⋊C411yescharacteristic
159C4⋊Dic13C4⋊C411yescharacteristic
160C4⋊Dic13C4⋊C411yescharacteristic
161#6101C4⋊C411yescharacteristic
162#6101C4⋊C411yescharacteristic
163#6101C4⋊C411yescharacteristic
164#6101C4⋊C411yescharacteristic
165C4×Dic13C22×C411yescharacteristic
166C4×Dic13C22×C411yescharacteristic
167C4×Dic13C2×D411yescharacteristic
168C4×Dic13C2×D411yescharacteristic
169C4×Dic13C2×Q811yescharacteristic
170C4×Dic13C2×Q811yescharacteristic
171#6099—81no—
172C2×#1055—21no—
173C2×#1055—21no—
174C2×#1055—21no—
175C2×#1055—21no—
176C2×#1055—42no—
177C2×#1055C22×C412yes—
178C2×#1055C22×C412yes—
179#6094—81no—
180#6094—81no—
181C8×D13—81no—
182C8×D13—81no—
183#2989—131no—
184#2989—131no—
185#2922—131no—
186#1574—131no—
187#1574—131no—
188#1573—131no—
189#1573—131no—
190#1572—131no—
191#1572—131no—
192#1571—131no—
193#1571—131no—
194#1569—131no—
195#1569D1311yescharacteristic, complemented
196#1568—131no—
197#1567—131no—
198C23×C13C2×C4⋊C411yescharacteristic
199C22×D13C2×C4⋊C411yescharacteristic
200C22×D13C2×C4⋊C411yescharacteristic
201C2×C4×C13—22no—
202C2×C4×C13—21no—
203C2×C4×C13—21no—
204C2×C4×C13—41no—
205C2×C4×C13C2×C4⋊C411yescharacteristic
206C2×C4×C13C2×C4⋊C411yescharacteristic
207C2×C4×C13C2×C4⋊C411yescharacteristic
208C2×C4×C13C23×C411yescharacteristic
209C2×C4×C13C22×D411yescharacteristic
210C2×C4×C13C22×Q811yescharacteristic
211C22⋊D13—41no—
212C22⋊D13—41no—
213C2×Dic13C2×C4⋊C411yescharacteristic
214C2×Dic13C2×C4⋊C411yescharacteristic
215C2×Dic13C2×C4⋊C411yescharacteristic
216C2×Dic13C2×C4⋊C411yescharacteristic
217C2×Dic13C2×C4⋊C411yescharacteristic
218C2×Dic13C2×C4⋊C411yescharacteristic
219D52—41no—
220C4×D13—22no—
221C4×D13—22no—
222C4×D13—21no—
223C4×D13—21no—
224C4×D13—21no—
225C4×D13—21no—
226C4×D13—41no—
227C4×D13—41no—
228Dic26—41no—
229C8×C13—22no—
230C8×C13—22no—
231C8×C13—41no—
232C8×C13—41no—
233C8×C13—41no—
234C8×C13—41no—
235#1055—22no—
236#1055—22no—
237#1055—41no—
238#1055—41no—
239#1055—41no—
240#1055—41no—
241C4×#41—131no—
242#446—261no—
243#446—261no—
244#436—261no—
245#436—261no—
246#435—261no—
247#435—261no—
248#435—261no—
249#435—261no—
250#433—132no—
251#433—132no—
252#432—131no—
253#432—131no—
254#432—131no—
255#432C2×D1311yescharacteristic
256#431—131no—
257#431—131no—
258#431—131no—
259#431—131no—
260#431—131no—
261#431—131no—
262#424—132no—
263#423—131no—
264#423—131no—
265#423—131no—
266#423C2×D1311yescharacteristic
267C2×C4⋊C8—131no—
268C2×C4⋊C8—131no—
269#408—132no—
270C4×M16C2×D1311yescharacteristic
271C2×C4×C8—131no—
272#335—131no—
273#335—131no—
274#335—131no—
275#335—131no—
276#335—131no—
277#335—131no—
278#335—131no—
279#335—131no—
280#335C2×D1311yescharacteristic
281#335C2×D1311yescharacteristic
282#334—131no—
283#334—131no—
284#334—131no—
285#334—131no—
286#334C2×D1311yescharacteristic
287#334C2×D1311yescharacteristic
288C22×C13—21no—
289C22×C13—21no—
290C22×C13—21no—
291C22×C13C22×C4⋊C411yescharacteristic
292C2×D13—21no—
293C2×D13—21no—
294C2×D13—21no—
295C2×D13—21no—
296C2×D13—21no—
297C2×D13—21no—
298C4×C13—21no—
299C4×C13—21no—
300C4×C13—21no—
301C4×C13—21no—
302C4×C13#56812yes—
303C4×C13#57611yescharacteristic
304C4×C13#57811yescharacteristic
305Dic13—21no—
306Dic13—21no—
307Dic13—21no—
308Dic13—21no—
309Dic13—21no—
310Dic13—21no—
311C2×#41—131no—
312C2×M16—21no—
313C2×M16—261no—
314C2×M16—261no—
315C2×M16—261no—
316C2×M16C4×D1312yes—
317C22×C8—132no—
318C22×C8—261no—
319C22×C8—261no—
320C4×Q8—131no—
321C4×Q8—131no—
322C4×D4—131no—
323C4×D4—131no—
324C4×D4—131no—
325C4×D4—131no—
326C4×D4—131no—
327C4×D4—131no—
328#117—131no—
329#117—131no—
330#117—131no—
331C2×C42—131no—
332C2×C42—131no—
333C2×C42C22×D1311yescharacteristic
334C4⋊C8—21no—
335C4⋊C8—132no—
336C4⋊C8—132no—
337C4⋊C8—132no—
338C4⋊C8—132no—
339C4⋊C8—131no—
340C4⋊C8—131no—
341C4⋊C8—131no—
342C4⋊C8—131no—
343C4⋊C8—261no—
344C4⋊C8—261no—
345C4⋊C8—261no—
346C4⋊C8—261no—
347C4⋊C8—261no—
348C4⋊C8C22×D1311yescharacteristic
349C4⋊C8C22×D1311yescharacteristic
350C4⋊C8C22×D1311yescharacteristic
351C4⋊C8C22×D1311yescharacteristic
352C22⋊C8—21no—
353C22⋊C8—132no—
354C22⋊C8—132no—
355C22⋊C8—132no—
356C22⋊C8—132no—
357C22⋊C8—261no—
358C22⋊C8—261no—
359C22⋊C8—261no—
360C22⋊C8—261no—
361C22⋊C8—261no—
362#97—21no—
363#97—261no—
364#97—261no—
365#97—261no—
366#97C4×D1312yes—
367C4×C8—132no—
368C4×C8—131no—
369C4×C8—131no—
370C4×C8—261no—
371C4×C8—261no—
372C4×C8C22×D1311yescharacteristic
373C4×C8C22×D1311yescharacteristic
374C2×C13—41no—
375C2×C13#290511yescharacteristic
376C2×C13#291311yescharacteristic
377C2×C13#291611yescharacteristic
378D13—41no—
379D13—41no—
380#41—522no—
381C2×Q8—131no—
382C2×D4—131no—
383C2×D4—131no—
384C2×D4—131no—
385C22×C4—131no—
386C22×C4—131no—
387C22×C4—131no—
388C22×C4—131no—
389C22×C4—131no—
390C22×C4—131no—
391C22×C4C2×C4×D1311yescharacteristic
392C22×C4D4×D1311yescharacteristic
393C22×C4Q8×D1311yescharacteristic
394M16—42no—
395M16—81no—
396M16—1041no—
397M16—1041no—
398M16—1041no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—132no—
404C2×C8—132no—
405C2×C8—261no—
406C2×C8—261no—
407C2×C8—261no—
408C2×C8—261no—
409C2×C8—522no—
410C2×C8—1041no—
411C2×C8—1041no—
412C2×C8C2×C4×D1312yes—
413C2×C8C2×C4×D1312yes—
414C4⋊C4—131no—
415C4⋊C4—131no—
416C4⋊C4—131no—
417C4⋊C4—131no—
418C4⋊C4—131no—
419C4⋊C4—131no—
420C22⋊C4—131no—
421C22⋊C4—131no—
422C22⋊C4—131no—
423C22⋊C4—131no—
424C22⋊C4—131no—
425C22⋊C4—131no—
426C42—131no—
427C42—131no—
428C42—131no—
429C42—131no—
430C42—131no—
431C42—131no—
432C42C2×C4×D1311yescharacteristic
433C42D4×D1311yescharacteristic
434C42Q8×D1311yescharacteristic
435C42C23×D1311yescharacteristic
436C13#1782511yescharacteristic, complemented, Sylow
437C23—131no—
438C23—131no—
439C23C4⋊C4×D1311yescharacteristic
440Q8—521no—
441D4—521no—
442D4—521no—
443D4—521no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—41no—
448C2×C4—131no—
449C2×C4—131no—
450C2×C4—131no—
451C2×C4—131no—
452C2×C4—131no—
453C2×C4—131no—
454C2×C4—262no—
455C2×C4—262no—
456C2×C4—261no—
457C2×C4—261no—
458C2×C4—261no—
459C2×C4—261no—
460C2×C4—521no—
461C2×C4—521no—
462C2×C4C4⋊C4×D1311yescharacteristic
463C2×C4C4⋊C4×D1311yescharacteristic
464C2×C4C4⋊C4×D1311yescharacteristic
465C2×C4C22×C4×D1311yescharacteristic
466C2×C4C2×D4×D1311yescharacteristic
467C2×C4C2×Q8×D1311yescharacteristic
468C8—22no—
469C8—22no—
470C8—41no—
471C8—41no—
472C8—41no—
473C8—41no—
474C8—262no—
475C8—262no—
476C8—521no—
477C8—521no—
478C8—521no—
479C8—521no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—261no—
484C22—261no—
485C22—261no—
486C22—261no—
487C22—261no—
488C22—261no—
489C22C2×C4⋊C4×D1311yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—261no—
495C4—261no—
496C4—261no—
497C4—261no—
498C4—261no—
499C4—261no—
500C4#1171945012yes—
501C4#1171947911yescharacteristic
502C4#1171948411yescharacteristic
503C2—41no—
504C2—521no—
505C2—521no—
506C2#1312339811yescharacteristic
507C2#1312343511yescharacteristic
508C2#1312344611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1569C2
socleC22×C13C22×C4⋊C4
prime radicalC2×#6127C2×C4
cosocleC42×C13C24
hypercenter#1569D13
hypocenterC13#17825
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
4. #13113626C2semidirect
5. #13113623C2semidirect
6. #13113620C2semidirect
7. #13113618C2semidirect
8. #13113613C2semidirect
9. #13113613C2semidirect
10. #13113609C2semidirect
11. #13113609C2semidirect
12. #13113603C2semidirect
13. #13113597C2semidirect
14. #13113594C2semidirect
15. C13×#1569C2semidirect
195. #1569D13semidirect
436. C13#17825semidirect

Maximal subgroups

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

subgroupindex
#131239552
#131239502
#131234812
#131136262
#131136232
#131136202
#131136182
#131136132
#131136092
#131136032
#131135972
#131135942
C13×#15692
#1782513