Finite Group Databasebeta

← #16017403

Subgroups — #16017403

Order 3328.

686 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718840C211yesmaximal, characteristic, complemented
2C22×#88052C211yesmaximal, characteristic, complemented
3#13124417C211yesmaximal, characteristic
4#13116951C212yesmaximal, complemented
5#13116942C212yesmaximal, complemented
6#13116934C212yesmaximal, complemented
7#13116925C212yesmaximal, complemented
8#13116622C211yesmaximal, characteristic, complemented
9#13116556C211yesmaximal, characteristic, complemented
10#13116546C211yesmaximal, characteristic, complemented
11C2×C13×#467C211yesmaximal, characteristic, complemented
12C22×C13×Q16C2211yescharacteristic
13C23×C8×C13C2211yescharacteristic
14C2×C13×C22⋊Q8—21no—
15#11719496—21no—
16C2×#88158C2211yescharacteristic
17C13×#467—21no—
18C13×#467—21no—
19C13×#467C2212yes—
20C13×#467C2212yes—
21C2×C13×#107C2211yescharacteristic
22C2×C13×#103—21no—
23C2×#88069C2212yescomplemented
24#11718840—24no—
25C2×#88068C2212yescomplemented
26#11718777C2211yescharacteristic
27#11718777C2211yescharacteristic
28#11718776C2211yescharacteristic
29#11718776C2211yescharacteristic
30#11718775—21no—
31#11718775—21no—
32#11718774—21no—
33#11718767C2211yescharacteristic
34C2×#88052—24no—
35C2×#88052C2212yes—
36C2×#88052C2211yescharacteristic
37C2×#88052C2211yescharacteristic
38C22×#6090C2212yes—
39#11718156C2212yescomplemented
40#11718156C2212yescomplemented
41#11718084C2212yescomplemented
42#11718083C2212yescomplemented
43#11718082C2212yescomplemented
44#11718081C2212yescomplemented
45C22×Q8×C13—21no—
46C23×C4×C13D411yescharacteristic
47C2×#6127—21no—
48C2×C13×Q16—22no—
49C2×C13×Q16—21no—
50C2×C13×Q16—22no—
51C2×C13×Q16C2312yes—
52C22×C8×C13—22no—
53C22×C8×C13—22no—
54C22×C8×C13D411yescharacteristic
55C22×C8×C13D411yescharacteristic
56C22×C8×C13D411yescharacteristic
57C22×C8×C13C2311yescharacteristic
58C22×C8×C13C2311yescharacteristic
59C22×C8×C13C2311yescharacteristic
60C13×C22⋊Q8—22no—
61C13×C22⋊Q8—22no—
62C13×C22⋊Q8—41no—
63C13×C22⋊Q8—41no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—41no—
66C2×C13×C22⋊C4—41no—
67#88207—41no—
68#88184—21no—
69#88184—21no—
70#88183—41no—
71C4×C22⋊D13—41no—
72C4×C22⋊D13—41no—
73#88180—21no—
74#88178—21no—
75#88178—21no—
76C2×Dic52C2311yescharacteristic
77#88158—22no—
78#88158—22no—
79C2×D104C2311yescharacteristic
80C2×#6095—21no—
81C13×#107—21no—
82C13×#107C2312yes—
83C13×#103—22no—
84C13×#103—22no—
85#88069—24no—
86#88068—24no—
87#88061—21no—
88#88061—21no—
89#88058C2311yescharacteristic
90#88058C2311yescharacteristic
91#88057—21no—
92#88056—21no—
93#88056—21no—
94#88052—22no—
95#88052—24no—
96#88052D414yescomplemented
97C2×#6090—24no—
98C2×#6090C2312yes—
99C2×#6090C2312yes—
100#33606—131nomaximal, Sylow
101C24×C13D811yescharacteristic
102C2×Q8×C13—22no—
103C2×Q8×C13—41no—
104C2×Q8×C13—42no—
105C2×Q8×C13—42no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—41no—
109C22×C4×C13—41no—
110C22×C4×C13D811yescharacteristic
111C22×C4×C13D811yescharacteristic
112C22×C4×C13D811yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13C2×D411yescharacteristic
116C2×C22⋊D13—41no—
117C2×C22⋊D13—41no—
118C2×C22⋊D13—41no—
119#6127—42no—
120#6127—42no—
121C2×D52—21no—
122C2×C4×D13—41no—
123C2×Dic26—21no—
124C13×Q16—22no—
125C13×Q16—22no—
126C13×Q16—42no—
127C2×C8×C13—22no—
128C2×C8×C13—22no—
129C2×C8×C13—22no—
130C2×C8×C13—21no—
131C2×C8×C13—21no—
132C2×C8×C13—21no—
133C2×C8×C13—21no—
134C2×C8×C13C2×D411yescharacteristic
135C2×C8×C13C2×D411yescharacteristic
136C2×C8×C13C2×D411yescharacteristic
137C2×C8×C13C2×D412yes—
138C2×C8×C13#4112yes—
139C2×C8×C13C2411yescharacteristic
140C13×C4⋊C4—22no—
141C13×C4⋊C4—41no—
142C13×C4⋊C4—42no—
143C13×C4⋊C4—42no—
144C13×C22⋊C4—42no—
145C13×C22⋊C4—42no—
146C22⋊Dic13—41no—
147C22⋊Dic13—41no—
148C22⋊Dic13—41no—
149#6103—41no—
150#6103—41no—
151C4⋊Dic13—21no—
152C4⋊Dic13—21no—
153#6101—41no—
154#6101—41no—
155C4×Dic13—41no—
156Dic52—21no—
157Dic52—21no—
158D104—21no—
159D104—21no—
160#6095—42no—
161#6090—22no—
162#6090C2×D414yes—
163C2×#510—131no—
164C22×M32—131no—
165#3050—131no—
166C2×#467D1311yescharacteristic, complemented
167#2220—132no—
168#2219—132no—
169#2217—132no—
170#2216—132no—
171#2159—131no—
172#2141—131no—
173#2139—131no—
174C23×C13—22no—
175C23×C13—22no—
176C23×C13—41no—
177C23×C13C2×D811yescharacteristic
178C23×C13C2×D811yescharacteristic
179C23×C13C2×D811yescharacteristic
180C22×D13—41no—
181Q8×C13—42no—
182Q8×C13—42no—
183Q8×C13—82no—
184C2×C4×C13—22no—
185C2×C4×C13—21no—
186C2×C4×C13—21no—
187C2×C4×C13—21no—
188C2×C4×C13—21no—
189C2×C4×C13—22no—
190C2×C4×C13—22no—
191C2×C4×C13—42no—
192C2×C4×C13—42no—
193C2×C4×C13—82no—
194C2×C4×C13—82no—
195C2×C4×C13#12112yes—
196C2×C4×C13C2×D811yescharacteristic
197C2×C4×C13C2×D811yescharacteristic
198C2×C4×C13C2×D811yescharacteristic
199C2×C4×C13#13512yes—
200C2×C4×C13C22×D411yescharacteristic
201C22⋊D13—82no—
202C22⋊D13—82no—
203C22⋊D13—82no—
204C2×Dic13—41no—
205C2×Dic13—41no—
206C2×Dic13—41no—
207D52—41no—
208D52—41no—
209C4×D13—82no—
210Dic26—41no—
211Dic26—41no—
212C8×C13—21no—
213C8×C13—21no—
214C8×C13#12112yes—
215C8×C13C22×D411yescharacteristic
216C8×C13C2×#4111yescharacteristic
217C2×#135—131no—
218C22×Q16C2×D1311yescharacteristic
219C23×C8C2×D1311yescharacteristic
220#525—261no—
221C2×C22⋊Q8—21no—
222#510—264no—
223C2×Q32—132no—
224C2×SD32—132no—
225C2×M32—131no—
226C2×M32—131no—
227C2×M32—132no—
228C2×M32—264no—
229C22×C16—132no—
230#467—21no—
231#467—21no—
232#467—131no—
233#467—131no—
234#467C2×D1312yes—
235#467C2×D1312yes—
236#466—131no—
237#466—131no—
238#465—261no—
239#465—261no—
240#427—131no—
241C2×#107C2×D1311yescharacteristic
242#416—261no—
243C2×#103—21no—
244#367—132no—
245#366—132no—
246#358—132no—
247#358—132no—
248#358—132no—
249#357—132no—
250C22×C13—21no—
251C22×C13—21no—
252C22×C13—21no—
253C22×C13—21no—
254C22×C13—21no—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13—44no—
258C22×C13#46612yes—
259C22×C13#51012yescomplemented
260C22×C13C22×D811yescharacteristic
261C2×D13—81no—
262C2×D13—81no—
263C2×D13—81no—
264C4×C13—21no—
265C4×C13—21no—
266C4×C13—82no—
267C4×C13—82no—
268C4×C13#46612yes—
269C4×C13C2×#12111yescharacteristic
270C4×C13C2×#13511yescharacteristic
271Dic13—81no—
272Dic13—81no—
273Dic13—81no—
274C2×#41—261no—
275C22×Q8—21no—
276C23×C4C22⋊D1311yescharacteristic
277#135—262no—
278#135—262no—
279C2×Q16—22no—
280C2×Q16—22no—
281C2×Q16—21no—
282C2×Q16—131no—
283C2×Q16C22×D1312yes—
284C2×SD16—261no—
285C2×D8—131no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8C22⋊D1311yescharacteristic
289C22×C8C22⋊D1311yescharacteristic
290C22×C8C22⋊D1311yescharacteristic
291C22×C8C22×D1311yescharacteristic
292C22×C8C22×D1311yescharacteristic
293C22×C8C22×D1311yescharacteristic
294#123—521no—
295C22⋊Q8—22no—
296C22⋊Q8—22no—
297C22⋊Q8—41no—
298C22⋊Q8—41no—
299C22⋊Q8—261no—
300C22⋊Q8—261no—
301#121—261no—
302#121—261no—
303#120—521no—
304C4×D4—521no—
305C4×D4—521no—
306#117—261no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—41no—
309C2×C22⋊C4—41no—
310Q32—264no—
311SD32—264no—
312M32—134no—
313M32—264no—
314M32—262no—
315C2×C16—132no—
316C2×C16—132no—
317C2×C16—264no—
318#107—21no—
319#107—131no—
320#107—131no—
321#107C22×D1312yes—
322#106—261no—
323#103—22no—
324#103—22no—
325#103—261no—
326#103—261no—
327#102—261no—
328#102—261no—
329C2×C13—22no—
330C2×C13—22no—
331C2×C13—41no—
332C2×C13C2×#46611yescharacteristic
333C2×C13C2×#51011yescharacteristic
334C2×C13#341411yescharacteristic
335D13—161no—
336C24#610411yescharacteristic
337#41—522no—
338#41—522no—
339C2×Q8—22no—
340C2×Q8—41no—
341C2×Q8—42no—
342C2×Q8—42no—
343C2×Q8—261no—
344C2×D4—261no—
345C2×D4—521no—
346C2×D4—521no—
347C2×D4—521no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—521no—
353C22×C4#610411yescharacteristic
354C22×C4#610411yescharacteristic
355C22×C4#610411yescharacteristic
356C22×C4C2×C22⋊D1311yescharacteristic
357C22×C4C2×C22⋊D1311yescharacteristic
358C22×C4C2×C22⋊D1311yescharacteristic
359Q16—22no—
360Q16—22no—
361Q16—42no—
362Q16—261no—
363Q16—261no—
364SD16—522no—
365D8—261no—
366D8—261no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8D4×D1312yes—
375C2×C8#612912yes—
376C2×C8C2×C22⋊D1311yescharacteristic
377C2×C8C2×C22⋊D1311yescharacteristic
378C2×C8C2×C22⋊D1311yescharacteristic
379C2×C8C23×D1311yescharacteristic
380C4⋊C4—22no—
381C4⋊C4—41no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—261no—
385C4⋊C4—261no—
386C4⋊C4—521no—
387C4⋊C4—521no—
388C22⋊C4—42no—
389C22⋊C4—42no—
390C22⋊C4—521no—
391C22⋊C4—521no—
392C22⋊C4—521no—
393C22⋊C4—521no—
394C22⋊C4—521no—
395C42—521no—
396C16—134no—
397C16—262no—
398C13#3360611yescharacteristic, complemented, Sylow
399C23—22no—
400C23—22no—
401C23—41no—
402C23—521no—
403C23C2×#610411yescharacteristic
404C23C2×#610411yescharacteristic
405C23C2×#610411yescharacteristic
406Q8—42no—
407Q8—42no—
408Q8—82no—
409Q8—521no—
410Q8—521no—
411D4—521no—
412D4—521no—
413D4—1042no—
414D4—1042no—
415D4—1042no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—521no—
428C2×C4—521no—
429C2×C4—521no—
430C2×C4—1042no—
431C2×C4C2×#610411yescharacteristic
432C2×C4C2×#610411yescharacteristic
433C2×C4C2×#610411yescharacteristic
434C2×C4#8819312yes—
435C2×C4#8820412yes—
436C2×C4C22×C22⋊D1311yescharacteristic
437C8—21no—
438C8—21no—
439C8#8819312yes—
440C8C2×D4×D1311yescharacteristic
441C8C2×#612911yescharacteristic
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—44no—
450C22—1041no—
451C22—1041no—
452C22—1041no—
453C22#1171869912yes—
454C22#1171884012yescomplemented
455C22C22×#610411yescharacteristic
456C4—21no—
457C4—21no—
458C4—82no—
459C4—82no—
460C4—1041no—
461C4—1041no—
462C4—1041no—
463C4#1171869912yes—
464C4C2×#8819311yescharacteristic
465C4C2×#8820411yescharacteristic
466C2—22no—
467C2—22no—
468C2—41no—
469C2—2081no—
470C2C2×#1171869911yescharacteristic
471C2C2×#1171884011yescharacteristic
472C2#1312797011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#467C2
socleC22×C13C22×D8
prime radical#13124417C2
hypercenterC2×#467D13
hypocenterC13#33606
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#11718840C2semidirect
2. C22×#88052C2semidirect
4. #13116951C2semidirect
5. #13116942C2semidirect
6. #13116934C2semidirect
7. #13116925C2semidirect
8. #13116622C2semidirect
9. #13116556C2semidirect
10. #13116546C2semidirect
11. C2×C13×#467C2semidirect
23. C2×#88069C22semidirect
25. C2×#88068C22semidirect
39. #11718156C22semidirect
40. #11718156C22semidirect
41. #11718084C22semidirect
42. #11718083C22semidirect
43. #11718082C22semidirect
44. #11718081C22semidirect
96. #88052D4semidirect
166. C2×#467D13semidirect
259. C22×C13#510semidirect
398. C13#33606semidirect
454. C22#11718840semidirect

Maximal subgroups

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

subgroupindex
C2×#117188402
C22×#880522
#131244172
#131169512
#131169422
#131169342
#131169252
#131166222
#131165562
#131165462
C2×C13×#4672
#3360613