Finite Group Databasebeta

← #16017409

Subgroups — #16017409

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×#11718856C211yesmaximal, characteristic, complemented
2C22×#88052C211yesmaximal, characteristic, complemented
3C2×#11718777C211yesmaximal, characteristic, complemented
4#13116947C212yesmaximal, complemented
5#13116942C212yesmaximal, complemented
6#13116930C212yesmaximal, complemented
7#13116925C212yesmaximal, complemented
8#13116625C211yesmaximal, characteristic, complemented
9#13116555C211yesmaximal, characteristic, complemented
10#13116548C211yesmaximal, characteristic, complemented
11C13×#3050C211yesmaximal, characteristic
12C2×C13×#135C2211yescharacteristic
13C23×C8×C13C2211yescharacteristic
14C13×#525—21no—
15C2×#88178—21no—
16C22×Dic52C2211yescharacteristic
17C13×#467C2211yescharacteristic
18C13×#467C2211yescharacteristic
19C13×#466C2211yescharacteristic
20C13×#466C2211yescharacteristic
21C13×#465—21no—
22C13×#465—21no—
23C13×#427C2211yescharacteristic
24C13×#416—21no—
25#11718856—24no—
26C2×#88069C2212yescomplemented
27C2×#88067C2212yescomplemented
28#11718777—21no—
29#11718777—21no—
30#11718777C2212yes—
31#11718777C2212yes—
32C2×#88058C2211yescharacteristic
33C2×#88056—21no—
34C2×#88052—24no—
35C2×#88052C2212yes—
36C2×#88052C2211yescharacteristic
37C2×#88052C2211yescharacteristic
38C22×#6090C2212yes—
39#11718156C2212yescomplemented
40#11718154C2212yescomplemented
41#11718084C2212yescomplemented
42#11718084C2212yescomplemented
43#11718082C2212yescomplemented
44#11718081C2212yescomplemented
45C2×C13×#41—21no—
46C23×C4×C13D411yescharacteristic
47C22×Dic26—21no—
48C13×#135—22no—
49C13×#135—22no—
50C2×C13×Q16C2311yescharacteristic
51C2×C13×SD16—21no—
52C2×C13×D8C2311yescharacteristic
53C22×C8×C13—22no—
54C22×C8×C13—22no—
55C22×C8×C13D411yescharacteristic
56C22×C8×C13D411yescharacteristic
57C22×C8×C13D411yescharacteristic
58C22×C8×C13C2311yescharacteristic
59C22×C8×C13C2311yescharacteristic
60C22×C8×C13C2311yescharacteristic
61C13×#123—41no—
62C13×C22⋊Q8—21no—
63C13×C22⋊Q8—21no—
64C13×#121—21no—
65C13×#121—21no—
66C13×#120—41no—
67C4×D4×C13—41no—
68C4×D4×C13—41no—
69C13×#117—21no—
70C2×C22⋊Dic13—41no—
71C2×C4⋊Dic13—21no—
72#88178—22no—
73#88178—22no—
74#88178—41no—
75#88178—41no—
76C2×#6101—41no—
77C2×Dic52—22no—
78C2×Dic52—22no—
79C2×Dic52—21no—
80C2×Dic52C2312yes—
81C13×#107C2311yescharacteristic
82C13×#107C2311yescharacteristic
83C13×#106—21no—
84C13×#103—21no—
85C13×#103—21no—
86C13×#102—21no—
87C13×#102—21no—
88#88069—24no—
89#88067—24no—
90#88058—21no—
91#88058C2312yes—
92#88056—22no—
93#88056—22no—
94#88052—22no—
95#88052—24no—
96#88052D414yescomplemented
97C2×#6090—24no—
98C2×#6090C2312yes—
99C2×#6090C2312yes—
100#33606—131nomaximal, Sylow
101C24×C13D811yescharacteristic
102C13×#41—42no—
103C13×#41—42no—
104C2×Q8×C13—21no—
105C2×D4×C13—21no—
106C2×D4×C13—41no—
107C2×D4×C13—41no—
108C2×D4×C13—41no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—41no—
112C22×C4×C13D811yescharacteristic
113C22×C4×C13D811yescharacteristic
114C22×C4×C13D811yescharacteristic
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2×D411yescharacteristic
118C22×Dic13—41no—
119C22×Dic13—41no—
120C2×Dic26—22no—
121C2×Dic26—42no—
122C2×Dic26—42no—
123C2×Dic26—41no—
124C13×Q16—21no—
125C13×Q16—21no—
126C13×SD16—42no—
127C13×D8—21no—
128C13×D8—21no—
129C2×C8×C13—22no—
130C2×C8×C13—22no—
131C2×C8×C13—22no—
132C2×C8×C13—21no—
133C2×C8×C13—21no—
134C2×C8×C13—21no—
135C2×C8×C13—21no—
136C2×C8×C13C2×D411yescharacteristic
137C2×C8×C13C2×D411yescharacteristic
138C2×C8×C13C2×D411yescharacteristic
139C2×C8×C13C2×D412yes—
140C2×C8×C13#4112yes—
141C2×C8×C13C2411yescharacteristic
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—41no—
145C13×C4⋊C4—41no—
146C13×C22⋊C4—41no—
147C13×C22⋊C4—41no—
148C13×C22⋊C4—41no—
149C13×C22⋊C4—41no—
150C13×C22⋊C4—41no—
151C42×C13—41no—
152C22⋊Dic13—42no—
153C22⋊Dic13—42no—
154C4⋊Dic13—22no—
155C4⋊Dic13—41no—
156#6101—42no—
157#6101—42no—
158Dic52—22no—
159Dic52—22no—
160Dic52—42no—
161#6090—22no—
162#6090C2×D414yes—
163C2×#510—131no—
164C22×M32—131no—
165#3050D1311yescharacteristic
166C2×#467—131no—
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×C13—41no—
178C23×C13C2×D811yescharacteristic
179C23×C13C2×D811yescharacteristic
180C23×C13C2×D811yescharacteristic
181Q8×C13—41no—
182Q8×C13—41no—
183D4×C13—41no—
184D4×C13—41no—
185D4×C13—82no—
186D4×C13—82no—
187D4×C13—82no—
188C2×C4×C13—22no—
189C2×C4×C13—21no—
190C2×C4×C13—21no—
191C2×C4×C13—21no—
192C2×C4×C13—21no—
193C2×C4×C13—22no—
194C2×C4×C13—22no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—82no—
199C2×C4×C13#12112yes—
200C2×C4×C13C2×D811yescharacteristic
201C2×C4×C13C2×D811yescharacteristic
202C2×C4×C13C2×D811yescharacteristic
203C2×C4×C13#13512yes—
204C2×C4×C13C22×D411yescharacteristic
205C2×Dic13—42no—
206C2×Dic13—42no—
207C2×Dic13—82no—
208C2×Dic13—82no—
209Dic26—42no—
210Dic26—42no—
211Dic26—82no—
212C8×C13—21no—
213C8×C13—21no—
214C8×C13#12112yes—
215C8×C13C22×D411yescharacteristic
216C8×C13C2×#4111yescharacteristic
217C2×#135C2×D1311yescharacteristic
218C22×Q16—131no—
219C23×C8C2×D1311yescharacteristic
220#525—21no—
221C2×C22⋊Q8—261no—
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—132no—
231#467—132no—
232#467—261no—
233#467—261no—
234#467C2×D1311yescharacteristic
235#467C2×D1311yescharacteristic
236#466C2×D1311yescharacteristic
237#466C2×D1311yescharacteristic
238#465—21no—
239#465—21no—
240#427C2×D1311yescharacteristic
241C2×#107—131no—
242#416—21no—
243C2×#103—261no—
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—81no—
259C22×C13—81no—
260C22×C13—81no—
261C22×C13#46612yes—
262C22×C13#51012yescomplemented
263C22×C13C22×D811yescharacteristic
264C4×C13—21no—
265C4×C13—21no—
266C4×C13—81no—
267C4×C13—81no—
268C4×C13—81no—
269C4×C13#46612yes—
270C4×C13C2×#12111yescharacteristic
271C4×C13C2×#13511yescharacteristic
272Dic13—82no—
273Dic13—82no—
274C2×#41—21no—
275C22×Q8—261no—
276C23×C4C22⋊D1311yescharacteristic
277#135—22no—
278#135—22no—
279C2×Q16—132no—
280C2×Q16—262no—
281C2×Q16—262no—
282C2×Q16—261no—
283C2×Q16C22×D1311yescharacteristic
284C2×SD16—21no—
285C2×D8C22×D1311yescharacteristic
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—41no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—262no—
298C22⋊Q8—262no—
299C22⋊Q8—521no—
300C22⋊Q8—521no—
301#121—21no—
302#121—21no—
303#120—41no—
304C4×D4—41no—
305C4×D4—41no—
306#117—21no—
307C2×C4⋊C4—261no—
308C2×C4⋊C4—521no—
309C2×C22⋊C4—521no—
310Q32—264no—
311SD32—264no—
312M32—134no—
313M32—264no—
314M32—262no—
315C2×C16—132no—
316C2×C16—132no—
317C2×C16—264no—
318#107—132no—
319#107—261no—
320#107C22×D1311yescharacteristic
321#107C22×D1311yescharacteristic
322#106—21no—
323#103—21no—
324#103—21no—
325#103—262no—
326#103—262no—
327#102—21no—
328#102—21no—
329C2×C13—22no—
330C2×C13—22no—
331C2×C13—41no—
332C2×C13—161no—
333C2×C13C2×#46611yescharacteristic
334C2×C13C2×#51011yescharacteristic
335C2×C13#341411yescharacteristic
336C24#610411yescharacteristic
337#41—42no—
338#41—42no—
339C2×Q8—21no—
340C2×Q8—262no—
341C2×Q8—521no—
342C2×Q8—522no—
343C2×Q8—522no—
344C2×D4—21no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—41no—
351C22×C4—521no—
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—21no—
360Q16—21no—
361Q16—262no—
362Q16—262no—
363Q16—522no—
364SD16—42no—
365D8—21no—
366D8—21no—
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—21no—
381C4⋊C4—21no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—262no—
385C4⋊C4—521no—
386C4⋊C4—522no—
387C4⋊C4—522no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—522no—
394C22⋊C4—522no—
395C42—41no—
396C16—134no—
397C16—262no—
398C13#3360611yescharacteristic, complemented, Sylow
399C23—22no—
400C23—22no—
401C23—41no—
402C23—41no—
403C23C2×#610411yescharacteristic
404C23C2×#610411yescharacteristic
405C23C2×#610411yescharacteristic
406Q8—41no—
407Q8—41no—
408Q8—522no—
409Q8—522no—
410Q8—1042no—
411D4—41no—
412D4—41no—
413D4—82no—
414D4—82no—
415D4—82no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—82no—
427C2×C4—522no—
428C2×C4—522no—
429C2×C4—1042no—
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—81no—
451C22—81no—
452C22—81no—
453C22#1171869912yes—
454C22#1171885612yescomplemented
455C22C22×#610411yescharacteristic
456C4—21no—
457C4—21no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—1042no—
462C4—1042no—
463C4#1171869912yes—
464C4C2×#8819311yescharacteristic
465C4C2×#8820411yescharacteristic
466C2—22no—
467C2—22no—
468C2—41no—
469C2—161no—
470C2C2×#1171869911yescharacteristic
471C2C2×#1171885611yescharacteristic
472C2#1312797011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
Fitting, prime radicalC13×#3050C2
socleC22×C13C22×D8
hypercenter#3050D13
hypocenterC13#33606
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C2×#11718856C2semidirect
2. C22×#88052C2semidirect
3. C2×#11718777C2semidirect
4. #13116947C2semidirect
5. #13116942C2semidirect
6. #13116930C2semidirect
7. #13116925C2semidirect
8. #13116625C2semidirect
9. #13116555C2semidirect
10. #13116548C2semidirect
26. C2×#88069C22semidirect
27. C2×#88067C22semidirect
39. #11718156C22semidirect
40. #11718154C22semidirect
41. #11718084C22semidirect
42. #11718084C22semidirect
43. #11718082C22semidirect
44. #11718081C22semidirect
96. #88052D4semidirect
262. C22×C13#510semidirect
398. C13#33606semidirect
454. C22#11718856semidirect

Maximal subgroups

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

subgroupindex
C2×#117188562
C22×#880522
C2×#117187772
#131169472
#131169422
#131169302
#131169252
#131166252
#131165552
#131165482
C13×#30502
#3360613