Finite Group Databasebeta

← #16017716

Subgroups — #16017716

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124413C211yesmaximal, characteristic
2D13×#427C211yesmaximal, characteristic, complemented
3#13117043C211yesmaximal, characteristic, complemented
4#13117042C211yesmaximal, characteristic, complemented
5#13117037C211yesmaximal, characteristic, complemented
6#13117032C211yesmaximal, characteristic, complemented
7#13117026C211yesmaximal, characteristic, complemented
8#13117025C211yesmaximal, characteristic, complemented
9#13117020C211yesmaximal, characteristic, complemented
10#13117015C211yesmaximal, characteristic, complemented
11#13116620C211yesmaximal, characteristic, complemented
12#13116618C211yesmaximal, characteristic, complemented
13#13116543C211yesmaximal, characteristic, complemented
14C2×#11718099C211yesmaximal, characteristic, complemented
15C13×#2138C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic
17#11719533—21no—
18C22×C8×D13C2211yescharacteristic
19D13×#117—21no—
20C22×C13×C16C2211yescharacteristic
21C13×#427C2211yescharacteristic
22#11718894—21no—
23#11718849C2211yescharacteristic
24#11718849C2211yescharacteristic
25#11718832—21no—
26#11718832—21no—
27#11718818C2211yescharacteristic
28#11718818C2211yescharacteristic
29#11718767C2211yescharacteristic
30#11718767C2211yescharacteristic
31C22×#6090C2211yescharacteristic
32#11718659—21no—
33#11718541C2211yescharacteristic
34#11718541C2211yescharacteristic
35D13×#107C2211yescharacteristic
36D13×#107C2211yescharacteristic
37#11718521—21no—
38D13×#106—21no—
39C13×#358C2211yescharacteristic, complemented
40C13×#358C2211yescharacteristic, complemented
41C13×#357C2211yescharacteristic, complemented
42C13×#357C2211yescharacteristic, complemented
43#11718156C2211yescharacteristic, complemented
44#11718156C2211yescharacteristic, complemented
45#11718154C2211yescharacteristic, complemented
46#11718154C2211yescharacteristic, complemented
47#11718099C2211yescharacteristic
48#11718099C2211yescharacteristic
49#11718099C2211yescharacteristic
50#11718099C2211yescharacteristic
51#11718097C2211yescharacteristic, complemented
52#11718097C2211yescharacteristic, complemented
53#11718096C2211yescharacteristic, complemented
54#11718096C2211yescharacteristic, complemented
55#11718082C2211yescharacteristic, complemented
56#11718082C2211yescharacteristic, complemented
57#11718081C2211yescharacteristic, complemented
58#11718081C2211yescharacteristic, complemented
59C2×C13×#41—21no—
60C22×C4×D13D411yescharacteristic
61C13×#135—22no—
62C13×#135—22no—
63C2×C13×Q16C2311yescharacteristic
64C2×C13×SD16—21no—
65C2×C13×D8C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C13×#117—21no—
68#88200—21no—
69#88200—21no—
70#88192—21no—
71#88192—21no—
72#88191—41no—
73#88189—41no—
74C4×C22⋊D13—41no—
75C4×C22⋊D13—41no—
76#88180—21no—
77#88180—21no—
78C22×#1055D411yescharacteristic
79C2×C8×D13—22no—
80C2×C8×D13—22no—
81C2×C8×D13D411yescharacteristic
82C2×C8×D13D411yescharacteristic
83C2×C8×D13C2311yescharacteristic
84C2×C8×D13C2311yescharacteristic
85#88146—21no—
86#88146—21no—
87C4⋊C4×D13—21no—
88C4⋊C4×D13—21no—
89C22⋊C4×D13—41no—
90#88131—41no—
91#88126—41no—
92C42×D13—41no—
93C2×C13×C16—22no—
94C2×C13×C16C2311yescharacteristic
95C2×C13×C16C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#106—21no—
99#88075—21no—
100#88075—21no—
101#88072—21no—
102#88072—21no—
103#88058C2311yescharacteristic
104#88058C2311yescharacteristic
105#88058C2311yescharacteristic
106#88058C2311yescharacteristic
107#88057—21no—
108#88057—21no—
109C2×#6090—22no—
110C2×#6090C2311yescharacteristic
111C2×#6090C2311yescharacteristic
112#88048—21no—
113#88048—21no—
114#88047—21no—
115#88047—21no—
116#33645—131nomaximal, Sylow
117C23×D13D811yescharacteristic
118C13×#41—42no—
119C13×#41—42no—
120C2×Q8×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—41no—
123C22×C4×C13—41no—
124C22×C4×C13C2×D411yescharacteristic
125C2×C22⋊D13—41no—
126C2×C22⋊D13—41no—
127C22×Dic13D811yescharacteristic
128C2×C4×D13—22no—
129C2×C4×D13—22no—
130C2×C4×D13—41no—
131C2×C4×D13—41no—
132C2×C4×D13D811yescharacteristic
133C2×C4×D13D811yescharacteristic
134C2×C4×D13C2×D411yescharacteristic
135C2×C4×D13C2×D411yescharacteristic
136C13×Q16—21no—
137C13×Q16—21no—
138C13×SD16—42no—
139C13×D8—21no—
140C13×D8—21no—
141C2×C8×C13C2×D411yescharacteristic
142C2×C8×C13#4112yes—
143C2×C8×C13#4112yes—
144C2×C8×C13C2411yescharacteristic
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C22⋊C4—41no—
148C42×C13—41no—
149C22⋊Dic13—41no—
150C22⋊Dic13—41no—
151C22⋊Dic13—41no—
152C22⋊Dic13—41no—
153#6103—41no—
154#6103—41no—
155#6103—41no—
156#6103—41no—
157C4⋊Dic13—21no—
158C4⋊Dic13—21no—
159C4⋊Dic13—21no—
160C4⋊Dic13—21no—
161#6101—41no—
162#6101—41no—
163#6101—41no—
164#6101—41no—
165C4×Dic13—41no—
166C4×Dic13—41no—
167C4×Dic13—41no—
168C4×Dic13—41no—
169C2×#1055—22no—
170C2×#1055C2×D411yescharacteristic
171C2×#1055C2×D411yescharacteristic
172C8×D13—22no—
173C8×D13—22no—
174C8×D13—21no—
175C8×D13—21no—
176C8×D13—21no—
177C8×D13—21no—
178C13×C16—21no—
179C13×C16—21no—
180#6090—21no—
181#6090—21no—
182#3050—131no—
183C2×#427—131no—
184#2237—131no—
185#2237—131no—
186#2236—131no—
187#2235—131no—
188#2234—131no—
189#2234—131no—
190#2233—131no—
191#2232—131no—
192#2158—131no—
193#2158—131no—
194#2138—131no—
195#2138D1311yescharacteristic, complemented
196C2×C22⋊C16—131no—
197C23×C13—41no—
198C23×C13C2×D811yescharacteristic
199C22×D13—22no—
200C22×D13—22no—
201C22×D13—41no—
202C22×D13C2×D811yescharacteristic
203C22×D13C2×D811yescharacteristic
204Q8×C13—41no—
205Q8×C13—41no—
206D4×C13—41no—
207D4×C13—41no—
208D4×C13—82no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—82no—
213C2×C4×C13#12312yes—
214C2×C4×C13C2×D811yescharacteristic
215C2×C4×C13#13712yes—
216C2×C4×C13C22×D411yescharacteristic
217C22⋊D13—82no—
218C22⋊D13—82no—
219C2×Dic13—22no—
220C2×Dic13—41no—
221C2×Dic13—41no—
222C2×Dic13—41no—
223C2×Dic13—41no—
224C2×Dic13C2×D811yescharacteristic
225C2×Dic13C2×D811yescharacteristic
226C4×D13—21no—
227C4×D13—21no—
228C4×D13—21no—
229C4×D13—21no—
230C4×D13—22no—
231C4×D13—22no—
232C4×D13—82no—
233C4×D13—82no—
234C8×C13#12312yes—
235C8×C13C2×#4111yescharacteristic
236C8×C13C2×#4111yescharacteristic
237#1055—21no—
238#1055—21no—
239C2×#135C2×D1311yescharacteristic
240C23×C8—131no—
241#525—261no—
242C2×#117—261no—
243C22×C16—131no—
244C22×C16C2×D1311yescharacteristic
245#467—131no—
246#467—131no—
247#466—131no—
248#466—131no—
249#465—261no—
250#465—261no—
251#427—131no—
252#427—131no—
253#427—131no—
254#427—131no—
255#427—261no—
256#427—261no—
257#427C2×D1311yescharacteristic
258C2×#107—131no—
259C2×#107—131no—
260C2×#106—261no—
261#416—261no—
262#367—131no—
263#367—131no—
264#367—131no—
265#367—131no—
266#366—131no—
267#366—131no—
268#366—131no—
269#366—131no—
270#358—131no—
271#358—131no—
272#358C2×D1311yescharacteristic, complemented
273#358C2×D1311yescharacteristic, complemented
274#357—131no—
275#357—131no—
276#357C2×D1311yescharacteristic, complemented
277#357C2×D1311yescharacteristic, complemented
278C22⋊C16—131no—
279C22⋊C16—131no—
280C22⋊C16—131no—
281C22⋊C16—131no—
282C22×C13—21no—
283C22×C13—21no—
284C22×C13—81no—
285C22×C13—81no—
286C22×C13—81no—
287C22×C13#48012yes—
288C22×C13C22×D811yescharacteristic
289C2×D13—21no—
290C2×D13—21no—
291C2×D13—21no—
292C2×D13—21no—
293C2×D13—21no—
294C2×D13—44no—
295C2×D13#50812yes—
296C4×C13—81no—
297C4×C13—81no—
298C4×C13—81no—
299C4×C13#48012yes—
300C4×C13C2×#12311yescharacteristic
301C4×C13C2×#13711yescharacteristic
302Dic13—21no—
303Dic13—21no—
304Dic13—81no—
305Dic13—81no—
306Dic13—81no—
307Dic13—81no—
308C2×#41—21no—
309C23×C4—131no—
310#135—22no—
311#135—22no—
312C2×Q16C22×D1311yescharacteristic
313C2×SD16—21no—
314C2×D8C22×D1311yescharacteristic
315C22×C8—131no—
316C22×C8—131no—
317C22×C8—131no—
318C22×C8—131no—
319C22×C8—131no—
320C22×C8—262no—
321C22×C8—262no—
322C22×C8C22×D1311yescharacteristic
323#123—521no—
324C22⋊Q8—261no—
325C22⋊Q8—261no—
326#121—261no—
327#121—261no—
328#120—521no—
329C4×D4—521no—
330C4×D4—521no—
331#117—21no—
332#117—261no—
333#117—261no—
334#117—261no—
335#117—261no—
336#117—521no—
337#117—521no—
338C2×C4⋊C4—261no—
339C2×C4⋊C4—261no—
340C2×C22⋊C4—521no—
341C2×C42—521no—
342C2×C16—22no—
343C2×C16—131no—
344C2×C16—131no—
345C2×C16—262no—
346C2×C16C22×D1311yescharacteristic
347C2×C16C22×D1311yescharacteristic
348#107—131no—
349#107—131no—
350#107—131no—
351#107—131no—
352#107—261no—
353#107—261no—
354#107C22×D1311yescharacteristic
355#107C22×D1311yescharacteristic
356#106—21no—
357#106—261no—
358#106—261no—
359#106—261no—
360#106—261no—
361#103—261no—
362#103—261no—
363#102—261no—
364#102—261no—
365C2×C13—22no—
366C2×C13—161no—
367C2×C13C2×#48011yescharacteristic
368C2×C13C2×#50811yescharacteristic
369C2×C13#341411yescharacteristic
370D13—22no—
371D13—41no—
372C24—131no—
373#41—42no—
374#41—42no—
375C2×Q8—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—521no—
379C2×D4—521no—
380C22×C4—41no—
381C22×C4—131no—
382C22×C4—131no—
383C22×C4—131no—
384C22×C4—131no—
385C22×C4—131no—
386C22×C4—262no—
387C22×C4—262no—
388C22×C4—521no—
389C22×C4—521no—
390C22×C4D4×D1311yescharacteristic
391Q16—21no—
392Q16—21no—
393SD16—42no—
394D8—21no—
395D8—21no—
396C2×C8—131no—
397C2×C8—131no—
398C2×C8—262no—
399C2×C8—262no—
400C2×C8—262no—
401C2×C8—261no—
402C2×C8—261no—
403C2×C8—261no—
404C2×C8—261no—
405C2×C8#612712yes—
406C2×C8D4×D1311yescharacteristic
407C2×C8#612912yes—
408C2×C8C23×D1311yescharacteristic
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—261no—
412C4⋊C4—261no—
413C4⋊C4—261no—
414C4⋊C4—261no—
415C4⋊C4—521no—
416C4⋊C4—521no—
417C4⋊C4—521no—
418C4⋊C4—521no—
419C22⋊C4—41no—
420C22⋊C4—521no—
421C22⋊C4—521no—
422C22⋊C4—521no—
423C22⋊C4—521no—
424C22⋊C4—521no—
425C22⋊C4—521no—
426C22⋊C4—521no—
427C22⋊C4—521no—
428C42—41no—
429C42—521no—
430C42—521no—
431C42—521no—
432C42—521no—
433C16—21no—
434C16—21no—
435C16—261no—
436C16—261no—
437C13#3364511yescharacteristic, complemented, Sylow
438C23—41no—
439C23—131no—
440C23—131no—
441C23—262no—
442C23—262no—
443C23—521no—
444C23D8×D1311yescharacteristic
445Q8—41no—
446Q8—41no—
447D4—41no—
448D4—41no—
449D4—82no—
450D4—1042no—
451D4—1042no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—82no—
456C2×C4—131no—
457C2×C4—131no—
458C2×C4—262no—
459C2×C4—261no—
460C2×C4—261no—
461C2×C4—262no—
462C2×C4—262no—
463C2×C4—261no—
464C2×C4—261no—
465C2×C4—521no—
466C2×C4—521no—
467C2×C4—521no—
468C2×C4—521no—
469C2×C4—1042no—
470C2×C4—1042no—
471C2×C4#8813712yes—
472C2×C4D8×D1311yescharacteristic
473C2×C4#8816912yes—
474C2×C4C2×D4×D1311yescharacteristic
475C8—261no—
476C8—261no—
477C8#8813712yes—
478C8C2×#612711yescharacteristic
479C8C2×#612911yescharacteristic
480C22—21no—
481C22—21no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—132no—
486C22—261no—
487C22—261no—
488C22—261no—
489C22—261no—
490C22—261no—
491C22—524no—
492C22#1171843512yes—
493C22C2×D8×D1311yescharacteristic
494C4—81no—
495C4—81no—
496C4—81no—
497C4—261no—
498C4—261no—
499C4—1041no—
500C4—1041no—
501C4—1041no—
502C4—1041no—
503C4#1171843512yes—
504C4C2×#8813711yescharacteristic
505C4C2×#8816911yescharacteristic
506C2—22no—
507C2—161no—
508C2—262no—
509C2—521no—
510C2C2×#1171843511yescharacteristic
511C2D13×#50811yescharacteristic
512C2#1312796911yescharacteristic
subgroupG/H
centerC2×C4D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2138C2
socleC22×C13C22×D8
prime radical#13124413C2
hypercenter#2138D13
hypocenterC13#33645
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2138

Complements

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

NH ≅ G/Ntype
2. D13×#427C2semidirect
3. #13117043C2semidirect
4. #13117042C2semidirect
5. #13117037C2semidirect
6. #13117032C2semidirect
7. #13117026C2semidirect
8. #13117025C2semidirect
9. #13117020C2semidirect
10. #13117015C2semidirect
11. #13116620C2semidirect
12. #13116618C2semidirect
13. #13116543C2semidirect
14. C2×#11718099C2semidirect
15. C13×#2138C2semidirect
39. C13×#358C22semidirect
40. C13×#358C22semidirect
41. C13×#357C22semidirect
42. C13×#357C22semidirect
43. #11718156C22semidirect
44. #11718156C22semidirect
45. #11718154C22semidirect
46. #11718154C22semidirect
51. #11718097C22semidirect
52. #11718097C22semidirect
53. #11718096C22semidirect
54. #11718096C22semidirect
55. #11718082C22semidirect
56. #11718082C22semidirect
57. #11718081C22semidirect
58. #11718081C22semidirect
195. #2138D13semidirect
272. #358C2×D13semidirect
273. #358C2×D13semidirect
276. #357C2×D13semidirect
277. #357C2×D13semidirect
437. C13#33645semidirect

Maximal subgroups

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

subgroupindex
#131244132
D13×#4272
#131170432
#131170422
#131170372
#131170322
#131170262
#131170252
#131170202
#131170152
#131166202
#131166182
#131165432
C2×#117180992
C13×#21382
#3364513