Finite Group Databasebeta

← #15834665

Subgroups — #15834665

Order 3328.

652 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#13123962C211yesmaximal, characteristic, complemented
2#13123961C211yesmaximal, characteristic, complemented
3C4×#88204C211yesmaximal, characteristic
4#13113742C212yesmaximal, complemented
5#13113675C212yesmaximal, complemented
6#13113669C212yesmaximal, complemented
7#13113657C212yesmaximal, complemented
8#13113591C211yesmaximal, characteristic, complemented
9#13113276C211yesmaximal, characteristic, complemented
10#13113123C211yesmaximal, characteristic, complemented
11C13×#1489C211yesmaximal, characteristic, complemented
12C4×C13×#41C2211yescharacteristic
13C2×#88204C411yescharacteristic
14C4×#6127C2211yescharacteristic
15C13×#423C2211yescharacteristic
16C4×C13×M16C2211yescharacteristic
17#11718894C411yescharacteristic
18#11718788—22no—
19C4×#6107C411yescharacteristic
20C4×#6107C2211yescharacteristic
21C4×#6106C411yescharacteristic
22C4×#6106C2211yescharacteristic
23#11718685C2212yes—
24C4×#6105C411yescharacteristic
25C4×#6105C2211yescharacteristic
26C4×#6104C411yescharacteristic
27C4×#6104C2211yescharacteristic
28#11718672—22no—
29D4×#1055C2212yes—
30#11718663C411yescharacteristic
31#11718659C411yescharacteristic
32#11718587—21no—
33#11718586C2211yescharacteristic
34#11718585C2211yescharacteristic
35C2×C4⋊#1055—21no—
36C2×C4×#1055C2211yescharacteristic
37#11718496—21no—
38#11718495C2212yes—
39D13×C4⋊C8—21no—
40#11718492C2212yes—
41C13×Q8⋊C8C2212yes—
42C13×D4⋊C8C2212yes—
43#11718072C2212yes—
44#11718072C2212yes—
45#11718051C2212yes—
46#11718048C2212yes—
47#11718046C2212yes—
48#11718046C2212yes—
49C2×C13×#41C2×C411yescharacteristic
50C2×#6127C2×C411yescharacteristic
51C2×C13×M16—21no—
52C2×C13×M16—21no—
53C4×Q8×C13C2×C411yescharacteristic
54C4×Q8×C13C2311yescharacteristic
55C4×D4×C13—21no—
56C4×D4×C13—21no—
57C4×D4×C13C2×C411yescharacteristic
58C4×D4×C13C2311yescharacteristic
59C13×#117—21no—
60C13×#117C2×C411yescharacteristic
61C2×C42×C13—21no—
62C2×C42×C13C2311yescharacteristic
63#88204—24no—
64C2×#6107C2×C411yescharacteristic
65C2×#6106C2×C411yescharacteristic
66C2×#6105C2×C411yescharacteristic
67C2×#6104C2×C411yescharacteristic
68C4×C22⋊D13—21no—
69C4×C22⋊D13—21no—
70#88180C2×C411yescharacteristic
71C2×#6099—21no—
72C22×#1055—22no—
73C22×#1055C2×C411yescharacteristic
74C22×#1055C2×C411yescharacteristic
75C2×C8×D13—22no—
76C4×D52C2×C411yescharacteristic
77C4×D52C2311yescharacteristic
78#88126—21no—
79C42×D13—21no—
80C4×Dic26C2×C411yescharacteristic
81C4×Dic26C2311yescharacteristic
82C13×C4⋊C8—21no—
83C13×C4⋊C8C2312yes—
84C13×#97—21no—
85C4×C8×C13C2312yes—
86#88075C2×C411yescharacteristic
87#88075C2×C411yescharacteristic
88#88072C2×C411yescharacteristic
89#88072C2×C411yescharacteristic
90C22⋊#1055—22no—
91C22⋊#1055D412yes—
92#88060—22no—
93#88055—22no—
94#88054—22no—
95#88050C2×C411yescharacteristic
96#88050C2×C411yescharacteristic
97#88049C2×C411yescharacteristic
98#88049C2×C411yescharacteristic
99#88048C2×C411yescharacteristic
100#88048C2×C411yescharacteristic
101#88047C2×C411yescharacteristic
102#88047C2×C411yescharacteristic
103C4⋊#1055—21no—
104C4⋊#1055—22no—
105C4⋊#1055D411yescharacteristic
106C4⋊#1055D411yescharacteristic
107C4⋊#1055C2312yes—
108#88043—22no—
109C4×#1055C2×C411yescharacteristic
110C4×#1055C2×C411yescharacteristic
111C4×#1055C2311yescharacteristic
112C4×#1055C2311yescharacteristic
113C4×#1055C2312yes—
114#18065—131nomaximal, Sylow
115C13×#41—22no—
116C13×#41—41no—
117C2×Q8×C13C22×C411yescharacteristic
118C2×D4×C13—21no—
119C2×D4×C13C22×C411yescharacteristic
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13#4111yescharacteristic
126C2×C22⋊D13—21no—
127#6127—22no—
128#6127—41no—
129C2×D52C22×C411yescharacteristic
130C2×C4×D13—21no—
131C2×C4×D13—21no—
132C2×C4×D13—21no—
133C2×Dic26C22×C411yescharacteristic
134C13×M16—42no—
135C13×M16—81no—
136C2×C8×C13—22no—
137C2×C8×C13—22no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—21no—
140C13×C4⋊C4C22×C411yescharacteristic
141C13×C4⋊C4C22×C411yescharacteristic
142C13×C22⋊C4—21no—
143C13×C22⋊C4—21no—
144C13×C22⋊C4—21no—
145C42×C13—21no—
146C42×C13—21no—
147C42×C13—21no—
148C42×C13C22×C411yescharacteristic
149C42×C13C2×D411yescharacteristic
150C42×C13#4111yescharacteristic
151C42×C13C2411yescharacteristic
152C22⋊Dic13—21no—
153#6107—22no—
154#6106—22no—
155#6105—22no—
156#6104M1614yescomplemented
157#6103—21no—
158#6103—21no—
159C4⋊Dic13C22×C411yescharacteristic
160C4⋊Dic13C22×C411yescharacteristic
161#6101—21no—
162#6101—21no—
163C4×Dic13—21no—
164C4×Dic13—21no—
165C4×Dic13—21no—
166#6099—81no—
167C2×#1055—22no—
168C2×#1055—22no—
169C2×#1055—41no—
170C2×#1055—82no—
171C2×#1055C22×C411yescharacteristic
172C2×#1055C22×C411yescharacteristic
173C2×#1055C22×C411yescharacteristic
174C2×#1055C22×C411yescharacteristic
175C2×#1055C2×D412yes—
176C2×#1055C2×D412yes—
177C8×D13—82no—
178#2990—131no—
179#2990—131no—
180C4×#135—131no—
181#1593—132no—
182#1582—132no—
183#1582—132no—
184#1580—132no—
185#1566—131no—
186#1489—131no—
187#1489D1311yescharacteristic, complemented
188#1451—131no—
189C23×C13—21no—
190C23×C13C4×D411yescharacteristic
191C22×D13—21no—
192Q8×C13—21no—
193Q8×C13—21no—
194D4×C13—21no—
195D4×C13—42no—
196D4×C13C2×M1612yes—
197C2×C4×C13—21no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—22no—
202C2×C4×C13—21no—
203C2×C4×C13—21no—
204C2×C4×C13—21no—
205C2×C4×C13—42no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—42no—
209C2×C4×C13C4×D411yescharacteristic
210C2×C4×C13C4×D411yescharacteristic
211C2×C4×C13C4×D411yescharacteristic
212C2×C4×C13C23×C411yescharacteristic
213C2×C4×C13C22×D411yescharacteristic
214C2×C4×C13C2×#4111yescharacteristic
215C22⋊D13—42no—
216C2×Dic13—21no—
217C2×Dic13—21no—
218C2×Dic13—21no—
219D52—21no—
220D52C2×M1612yes—
221C4×D13—42no—
222C4×D13—41no—
223C4×D13—41no—
224C4×D13—42no—
225Dic26—21no—
226Dic26—21no—
227C8×C13—42no—
228C8×C13—42no—
229#1055—21no—
230#1055—21no—
231#1055—21no—
232#1055—22no—
233#1055—22no—
234#1055—42no—
235#1055C2×M1612yes—
236C2×#135—131no—
237C4×#41—131no—
238C4×#41C2×D1311yescharacteristic
239#446—132no—
240#446—132no—
241C4×Q16—131no—
242C4×Q16—131no—
243C4×SD16—131no—
244C4×SD16—131no—
245C4×SD16—131no—
246C4×SD16—131no—
247C4×D8—131no—
248C4×D8—131no—
249#435—262no—
250#435—262no—
251C8×D4—132no—
252C8×D4—132no—
253#432—261no—
254#432—261no—
255#431—131no—
256#427—131no—
257#423—131no—
258#423C2×D1311yescharacteristic
259C2×C4⋊C8—261no—
260C2×C4⋊C8—261no—
261#416—131no—
262#416—131no—
263C4×M16C2×D1311yescharacteristic
264C2×C4×C8—131no—
265#334—132no—
266#334—132no—
267Q8⋊C8—132no—
268Q8⋊C8C2×D1312yes—
269D4⋊C8—132no—
270D4⋊C8C2×D1312yes—
271#322—132no—
272#322—132no—
273C22×C13—21no—
274C22×C13—22no—
275C22×C13—21no—
276C22×C13—21no—
277C22×C13—41no—
278C22×C13—41no—
279C22×C13C2×C4×D411yescharacteristic
280C2×D13—22no—
281C2×D13—41no—
282C2×D13—41no—
283C4×C13—21no—
284C4×C13—21no—
285C4×C13—21no—
286C4×C13—41no—
287C4×C13—41no—
288C4×C13—41no—
289C4×C13#44412yes—
290C4×C13C22×M1611yescharacteristic
291C4×C13#56811yescharacteristic
292C4×C13#57711yescharacteristic
293C4×C13#57711yescharacteristic
294Dic13—41no—
295Dic13—41no—
296Dic13—41no—
297C2×#41—131no—
298C2×#41C4×D1311yescharacteristic
299#135—264no—
300C2×Q16—131no—
301C2×SD16—131no—
302C2×SD16—131no—
303C2×D8—131no—
304C2×M16—21no—
305C2×M16—21no—
306C2×M16—261no—
307C22×C8—131no—
308C22×C8—131no—
309C22×C8—262no—
310C22×C8—262no—
311C4×Q8—131no—
312C4×Q8—131no—
313C4×Q8C4×D1311yescharacteristic
314C4×Q8C22×D1311yescharacteristic
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—131no—
318C4×D4—131no—
319C4×D4—261no—
320C4×D4—261no—
321C4×D4C4×D1311yescharacteristic
322C4×D4C22×D1311yescharacteristic
323#117—21no—
324#117—131no—
325#117—261no—
326#117C4×D1311yescharacteristic
327C2×C42—21no—
328C2×C42—261no—
329C2×C42C22×D1311yescharacteristic
330#107—131no—
331#107—131no—
332#106—131no—
333#106—131no—
334C4⋊C8—21no—
335C4⋊C8—131no—
336C4⋊C8—131no—
337C4⋊C8—132no—
338C4⋊C8—262no—
339C4⋊C8—262no—
340C4⋊C8—261no—
341C4⋊C8C22×D1312yes—
342#103—131no—
343#103—131no—
344#103—131no—
345#103—131no—
346#102—131no—
347#102—131no—
348#102—131no—
349#102—131no—
350C22⋊C8—132no—
351C22⋊C8—262no—
352C22⋊C8—262no—
353#97—21no—
354#97—262no—
355#97—262no—
356C4×C8—131no—
357C4×C8—131no—
358C4×C8—131no—
359C4×C8—131no—
360C4×C8—132no—
361C4×C8C22×D1312yes—
362C2×C13—41no—
363C2×C13—42no—
364C2×C13D4×M1611yescharacteristic
365C2×C13#295211yescharacteristic
366C2×C13C2×#44411yescharacteristic
367D13—42no—
368#41—22no—
369#41—41no—
370#41—262no—
371#41—521no—
372C2×Q8—131no—
373C2×Q8C2×C4×D1311yescharacteristic
374C2×D4—21no—
375C2×D4—131no—
376C2×D4—261no—
377C2×D4C2×C4×D1311yescharacteristic
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—261no—
382C22×C4—261no—
383C22×C4—261no—
384C22×C4C2×C4×D1311yescharacteristic
385C22×C4D4×D1311yescharacteristic
386C22×C4#612911yescharacteristic
387Q16—262no—
388SD16—262no—
389SD16—262no—
390D8—134no—
391M16—42no—
392M16—81no—
393M16—1041no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—131no—
397C2×C8—131no—
398C2×C8—131no—
399C2×C8—131no—
400C2×C8—132no—
401C2×C8—132no—
402C2×C8—262no—
403C2×C8—262no—
404C2×C8—521no—
405C2×C8—1042no—
406C2×C8—1042no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—131no—
410C4⋊C4—131no—
411C4⋊C4—261no—
412C4⋊C4—261no—
413C4⋊C4C2×C4×D1311yescharacteristic
414C4⋊C4C2×C4×D1311yescharacteristic
415C22⋊C4—21no—
416C22⋊C4—21no—
417C22⋊C4—21no—
418C22⋊C4—261no—
419C22⋊C4—261no—
420C22⋊C4—261no—
421C42—21no—
422C42—21no—
423C42—21no—
424C42—261no—
425C42—261no—
426C42—261no—
427C42C2×C4×D1311yescharacteristic
428C42D4×D1311yescharacteristic
429C42#612911yescharacteristic
430C42C23×D1311yescharacteristic
431C13#1806511yescharacteristic, complemented, Sylow
432C23—21no—
433C23—261no—
434C23#8813511yescharacteristic
435Q8—21no—
436Q8—21no—
437Q8—261no—
438Q8—261no—
439D4—21no—
440D4—42no—
441D4—132no—
442D4—261no—
443D4—522no—
444D4M16×D1312yes—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—261no—
458C2×C4—261no—
459C2×C4—261no—
460C2×C4—522no—
461C2×C4—521no—
462C2×C4—521no—
463C2×C4—522no—
464C2×C4#8813511yescharacteristic
465C2×C4#8813511yescharacteristic
466C2×C4#8813511yescharacteristic
467C2×C4C22×C4×D1311yescharacteristic
468C2×C4C2×D4×D1311yescharacteristic
469C2×C4C2×#612911yescharacteristic
470C8—42no—
471C8—42no—
472C8—132no—
473C8—261no—
474C8—261no—
475C8—261no—
476C8—262no—
477C8—262no—
478C8—522no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—262no—
486C22—521no—
487C22—521no—
488C22C2×#8813511yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—521no—
496C4—521no—
497C4—521no—
498C4#1171848412yes—
499C4C2×M16×D1311yescharacteristic
500C4#1171945011yescharacteristic
501C4#1171948011yescharacteristic
502C4#1171948311yescharacteristic
503C2—41no—
504C2—42no—
505C2—522no—
506C2#1312356811yescharacteristic
507C2#1312371511yescharacteristic
508C2C2×#1171848411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1489C2
socleC22×C13C2×C4×D4
prime radicalC2×#88204C4
cosocleC42×C13C24
hypercenter#1489D13
hypocenterC13#18065
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
1. #13123962C2semidirect
2. #13123961C2semidirect
4. #13113742C2semidirect
5. #13113675C2semidirect
6. #13113669C2semidirect
7. #13113657C2semidirect
8. #13113591C2semidirect
9. #13113276C2semidirect
10. #13113123C2semidirect
11. C13×#1489C2semidirect
156. #6104M16semidirect
187. #1489D13semidirect
431. C13#18065semidirect

Maximal subgroups

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

subgroupindex
#131239622
#131239612
C4×#882042
#131137422
#131136752
#131136692
#131136572
#131135912
#131132762
#131131232
C13×#14892
#1806513