Finite Group Databasebeta

← #15832775

Subgroups — #15832775

Order 3328.

646 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123954C211yesmaximal, characteristic, complemented
2#13123953C211yesmaximal, characteristic, complemented
3C4×#88204C211yesmaximal, characteristic
4#13113747C212yesmaximal, complemented
5#13113742C212yesmaximal, complemented
6#13113729C212yesmaximal, complemented
7#13113723C212yesmaximal, complemented
8C2×#11718072C211yesmaximal, characteristic, complemented
9#13113224C211yesmaximal, characteristic, complemented
10#13113120C211yesmaximal, characteristic, complemented
11C13×#1477C211yesmaximal, characteristic, complemented
12C4×C13×#41C2211yescharacteristic
13C2×#88204C411yescharacteristic
14C4×#6127C2211yescharacteristic
15C13×#431C2211yescharacteristic
16C2×C13×C4⋊C8C2211yescharacteristic
17#11718894C411yescharacteristic
18#11718772—22no—
19C4×#6107C411yescharacteristic
20C4×#6107C2211yescharacteristic
21C4×#6106C411yescharacteristic
22C4×#6106C2211yescharacteristic
23#11718685C2212yes—
24C4×#6105C411yescharacteristic
25C4×#6105C2211yescharacteristic
26C4×#6104C411yescharacteristic
27C4×#6104C2211yescharacteristic
28#11718673C2212yes—
29#11718672—22no—
30#11718663C411yescharacteristic
31#11718659C411yescharacteristic
32#11718587—21no—
33#11718586C2211yescharacteristic
34#11718585—21no—
35C2×C4⋊#1055C2211yescharacteristic
36C2×C4×#1055C2211yescharacteristic
37#11718499C2212yes—
38#11718498—21no—
39#11718496—21no—
40#11718492C2212yes—
41C13×Q8⋊C8C2212yes—
42C13×D4⋊C8C2212yes—
43#11718072C2212yes—
44#11718072C2212yes—
45#11718051C2212yes—
46#11718048C2212yes—
47#11718046C2212yes—
48C8×#1055C2212yes—
49C2×C13×#41C2×C411yescharacteristic
50C2×#6127C2×C411yescharacteristic
51C22×C8×C13—21no—
52C4×Q8×C13C2×C411yescharacteristic
53C4×Q8×C13C2311yescharacteristic
54C4×D4×C13—21no—
55C4×D4×C13—21no—
56C4×D4×C13C2×C411yescharacteristic
57C4×D4×C13C2311yescharacteristic
58C13×#117—21no—
59C13×#117C2×C411yescharacteristic
60C2×C42×C13—21no—
61C2×C42×C13C2311yescharacteristic
62#88204—24no—
63C2×#6107C2×C411yescharacteristic
64C2×#6106C2×C411yescharacteristic
65C2×#6105C2×C411yescharacteristic
66C2×#6104C2×C411yescharacteristic
67C4×C22⋊D13—21no—
68C4×C22⋊D13—21no—
69#88180C2×C411yescharacteristic
70C2×#6099—22no—
71C22×#1055—21no—
72C22×#1055C2×C411yescharacteristic
73C22×#1055C2×C411yescharacteristic
74C2×#6094—22no—
75C4×D52C2×C411yescharacteristic
76C4×D52C2311yescharacteristic
77#88126—21no—
78C42×D13—21no—
79C4×Dic26C2×C411yescharacteristic
80C4×Dic26C2311yescharacteristic
81C13×C4⋊C8—21no—
82C13×C4⋊C8—21no—
83C13×C4⋊C8C2312yes—
84C13×C22⋊C8—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#17899—131nomaximal, Sylow
115C13×#41—22no—
116C13×#41—22no—
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—22no—
129C2×D52C22×C411yescharacteristic
130C2×C4×D13—21no—
131C2×C4×D13—21no—
132C2×C4×D13—21no—
133C2×Dic26C22×C411yescharacteristic
134C2×C8×C13—22no—
135C2×C8×C13—22no—
136C2×C8×C13—81no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4C22×C411yescharacteristic
140C13×C4⋊C4C22×C411yescharacteristic
141C13×C22⋊C4—21no—
142C13×C22⋊C4—21no—
143C13×C22⋊C4—21no—
144C42×C13—21no—
145C42×C13—21no—
146C42×C13—21no—
147C42×C13C22×C411yescharacteristic
148C42×C13C2×D411yescharacteristic
149C42×C13#4111yescharacteristic
150C42×C13C2411yescharacteristic
151C22⋊Dic13—21no—
152#6107—22no—
153#6106—22no—
154#6105—22no—
155#6104—22no—
156#6103—21no—
157#6103—21no—
158C4⋊Dic13C22×C411yescharacteristic
159C4⋊Dic13C22×C411yescharacteristic
160#6101—21no—
161#6101—21no—
162C4×Dic13—21no—
163C4×Dic13—21no—
164C4×Dic13—21no—
165#6099—82no—
166C2×#1055—22no—
167C2×#1055—22no—
168C2×#1055—81no—
169C2×#1055M1614yescomplemented
170C2×#1055C22×C411yescharacteristic
171C2×#1055C22×C411yescharacteristic
172C2×#1055C22×C411yescharacteristic
173C2×#1055C22×C411yescharacteristic
174C2×#1055C2×D412yes—
175C2×#1055C2×D412yes—
176#6094—82no—
177#2989—131no—
178#2989—131no—
179C4×#135—131no—
180#1594—132no—
181#1593—132no—
182#1590—132no—
183#1590—132no—
184C2×#334—131no—
185#1477—131no—
186#1477D1311yescharacteristic, complemented
187#1450—131no—
188C23×C13—21no—
189C23×C13C4×D411yescharacteristic
190C22×D13—21no—
191Q8×C13—21no—
192Q8×C13—21no—
193D4×C13—21no—
194D4×C13—21no—
195D4×C13—42no—
196C2×C4×C13—21no—
197C2×C4×C13—21no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—41no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—42no—
205C2×C4×C13—81no—
206C2×C4×C13C4×D411yescharacteristic
207C2×C4×C13C4×D411yescharacteristic
208C2×C4×C13C4×D411yescharacteristic
209C2×C4×C13C2×M1612yes—
210C2×C4×C13#13112yes—
211C2×C4×C13C23×C411yescharacteristic
212C2×C4×C13C22×D411yescharacteristic
213C2×C4×C13C2×#4111yescharacteristic
214C22⋊D13—42no—
215C2×Dic13—21no—
216C2×Dic13—21no—
217C2×Dic13—21no—
218D52—21no—
219D52—21no—
220C4×D13—41no—
221C4×D13—41no—
222C4×D13—42no—
223C4×D13—81no—
224Dic26—21no—
225Dic26—21no—
226C8×C13—42no—
227C8×C13—42no—
228#1055—21no—
229#1055—21no—
230#1055—22no—
231#1055—22no—
232#1055—42no—
233#1055C2×M1612yes—
234#1055C2×M1612yes—
235C2×#135—131no—
236C4×#41—131no—
237C4×#41C2×D1311yescharacteristic
238#446—132no—
239#446—132no—
240C4×Q16—131no—
241C4×Q16—131no—
242C4×SD16—131no—
243C4×SD16—131no—
244C4×SD16—131no—
245C4×SD16—131no—
246C4×D8—131no—
247C4×D8—131no—
248#436—132no—
249#436—132no—
250#435—262no—
251#435—262no—
252#432—261no—
253#432—261no—
254#431—131no—
255#431C2×D1311yescharacteristic
256#427—131no—
257#423—261no—
258#423—261no—
259C2×C4⋊C8—131no—
260C2×C4⋊C8C2×D1311yescharacteristic
261#416—131no—
262#416—131no—
263C2×C4×C8—131no—
264#334—132no—
265#334—132no—
266Q8⋊C8—132no—
267Q8⋊C8C2×D1312yes—
268D4⋊C8—132no—
269D4⋊C8C2×D1312yes—
270#322—132no—
271C82—132no—
272C22×C13—21no—
273C22×C13—21no—
274C22×C13—41no—
275C22×C13—41no—
276C22×C13—41no—
277C22×C13#43612yes—
278C22×C13C2×C4×D411yescharacteristic
279C2×D13—41no—
280C2×D13—41no—
281C2×D13—41no—
282C4×C13—21no—
283C4×C13—21no—
284C4×C13—21no—
285C4×C13—41no—
286C4×C13—41no—
287C4×C13—41no—
288C4×C13#43612yes—
289C4×C13C22×M1611yescharacteristic
290C4×C13C2×#13111yescharacteristic
291C4×C13#57711yescharacteristic
292C4×C13#57711yescharacteristic
293Dic13—41no—
294Dic13—41no—
295Dic13—41no—
296C2×#41—131no—
297C2×#41C4×D1311yescharacteristic
298#135—264no—
299C2×Q16—131no—
300C2×SD16—131no—
301C2×SD16—131no—
302C2×D8—131no—
303C2×M16—262no—
304C2×M16—262no—
305C22×C8—21no—
306C22×C8—131no—
307C22×C8—131no—
308C22×C8—261no—
309C4×Q8—131no—
310C4×Q8—131no—
311C4×Q8C4×D1311yescharacteristic
312C4×Q8C22×D1311yescharacteristic
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—131no—
316C4×D4—131no—
317C4×D4—261no—
318C4×D4—261no—
319C4×D4C4×D1311yescharacteristic
320C4×D4C22×D1311yescharacteristic
321#117—21no—
322#117—131no—
323#117—261no—
324#117C4×D1311yescharacteristic
325C2×C42—21no—
326C2×C42—261no—
327C2×C42C22×D1311yescharacteristic
328#107—131no—
329#107—131no—
330#106—131no—
331#106—131no—
332C4⋊C8—21no—
333C4⋊C8—21no—
334C4⋊C8—131no—
335C4⋊C8—131no—
336C4⋊C8—132no—
337C4⋊C8—262no—
338C4⋊C8—262no—
339C4⋊C8—261no—
340C4⋊C8C22×D1312yes—
341#103—131no—
342#103—131no—
343#103—131no—
344#103—131no—
345#102—131no—
346#102—131no—
347#102—131no—
348#102—131no—
349C22⋊C8—21no—
350C22⋊C8—132no—
351C22⋊C8—262no—
352C22⋊C8—262no—
353#97—262no—
354#97—262no—
355C4×C8—131no—
356C4×C8—131no—
357C4×C8—131no—
358C4×C8—132no—
359C4×C8—131no—
360C4×C8C22×D1312yes—
361C2×C13—22no—
362C2×C13—81no—
363C2×C13C2×#43611yescharacteristic
364C2×C13#295211yescharacteristic
365C2×C13#295711yescharacteristic
366D13—81no—
367#41—22no—
368#41—22no—
369#41—262no—
370#41—262no—
371C2×Q8—131no—
372C2×Q8C2×C4×D1311yescharacteristic
373C2×D4—21no—
374C2×D4—131no—
375C2×D4—261no—
376C2×D4C2×C4×D1311yescharacteristic
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—261no—
381C22×C4—261no—
382C22×C4—261no—
383C22×C4C2×C4×D1311yescharacteristic
384C22×C4D4×D1311yescharacteristic
385C22×C4#612911yescharacteristic
386Q16—262no—
387SD16—262no—
388SD16—262no—
389D8—262no—
390M16—1042no—
391M16—1042no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—81no—
395C2×C8—134no—
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—1041no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—131no—
408C4⋊C4—131no—
409C4⋊C4—261no—
410C4⋊C4—261no—
411C4⋊C4C2×C4×D1311yescharacteristic
412C4⋊C4C2×C4×D1311yescharacteristic
413C22⋊C4—21no—
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—261no—
417C22⋊C4—261no—
418C22⋊C4—261no—
419C42—21no—
420C42—21no—
421C42—21no—
422C42—261no—
423C42—261no—
424C42—261no—
425C42C2×C4×D1311yescharacteristic
426C42D4×D1311yescharacteristic
427C42#612911yescharacteristic
428C42C23×D1311yescharacteristic
429C13#1789911yescharacteristic, complemented, Sylow
430C23—21no—
431C23—261no—
432C23#8813511yescharacteristic
433Q8—21no—
434Q8—21no—
435Q8—261no—
436Q8—261no—
437D4—21no—
438D4—21no—
439D4—42no—
440D4—261no—
441D4—261no—
442D4—522no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—81no—
453C2×C4—261no—
454C2×C4—261no—
455C2×C4—261no—
456C2×C4—521no—
457C2×C4—521no—
458C2×C4—522no—
459C2×C4—1041no—
460C2×C4#8813511yescharacteristic
461C2×C4#8813511yescharacteristic
462C2×C4#8813511yescharacteristic
463C2×C4#8815512yes—
464C2×C4M16×D1312yes—
465C2×C4C22×C4×D1311yescharacteristic
466C2×C4C2×D4×D1311yescharacteristic
467C2×C4C2×#612911yescharacteristic
468C8—42no—
469C8—42no—
470C8—132no—
471C8—132no—
472C8—261no—
473C8—261no—
474C8—262no—
475C8—262no—
476C8—522no—
477C22—21no—
478C22—21no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—521no—
483C22—521no—
484C22—521no—
485C22#1171839012yes—
486C22C2×#8813511yescharacteristic
487C4—21no—
488C4—21no—
489C4—21no—
490C4—41no—
491C4—41no—
492C4—41no—
493C4—521no—
494C4—521no—
495C4—521no—
496C4#1171839012yes—
497C4C2×#8815511yescharacteristic
498C4C2×M16×D1311yescharacteristic
499C4#1171948011yescharacteristic
500C4#1171948311yescharacteristic
501C2—22no—
502C2—81no—
503C2—1041no—
504C2C2×#1171839011yescharacteristic
505C2#1312371511yescharacteristic
506C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1477C2
socleC22×C13C2×C4×D4
prime radicalC2×#88204C4
cosocleC42×C13C24
hypercenter#1477D13
hypocenterC13#17899
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
1. #13123954C2semidirect
2. #13123953C2semidirect
4. #13113747C2semidirect
5. #13113742C2semidirect
6. #13113729C2semidirect
7. #13113723C2semidirect
8. C2×#11718072C2semidirect
9. #13113224C2semidirect
10. #13113120C2semidirect
11. C13×#1477C2semidirect
169. C2×#1055M16semidirect
186. #1477D13semidirect
429. C13#17899semidirect

Maximal subgroups

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

subgroupindex
#131239542
#131239532
C4×#882042
#131137472
#131137422
#131137292
#131137232
C2×#117180722
#131132242
#131131202
C13×#14772
#1789913