Finite Group Databasebeta

← #15758212

Subgroups — #15758212

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718354C211yesmaximal, characteristic
2#13117900C211yesmaximal, characteristic
3#13115784C211yesmaximal, characteristic, complemented
4#13115783C211yesmaximal, characteristic, complemented
5C2×#11718077C211yesmaximal, characteristic
6#13112676C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C22×#6095—22no—
9C2×#88147—21no—
10C2×#88128C2211yescharacteristic
11C2×C4×D52—21no—
12C2×#88123C2211yescharacteristic
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×C4×C8×C13C2211yescharacteristic
15C4×C13×C4⋊C4C2211yescharacteristic
16#11718649—21no—
17#11718600—21no—
18C4×C4⋊Dic13C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20#11718354—22no—
21#11718354C414yescomplemented
22#11718326—22no—
23#11718143—21no—
24#11718143—21no—
25#11718121—21no—
26#11718121—21no—
27#11718077—22no—
28C22×D52—21no—
29C22×D52—21no—
30C22×D52D412yes—
31C22×C4×D13—22no—
32C22×Dic26—21no—
33C22×C8×C13—21no—
34C22×C8×C13—21no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C42×C13—21no—
38C2×C42×C13C2311yescharacteristic
39C2×#6103—22no—
40C2×#6103—22no—
41C2×#6103—22no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13D411yescharacteristic
45C2×C4⋊Dic13D411yescharacteristic
46C2×C4×Dic13—21no—
47C22×#1055—21no—
48C2×#6095—28no—
49C2×#6095—44no—
50C2×#6095—44no—
51#88147—42no—
52#88147—42no—
53#88128—21no—
54#88128—21no—
55#88128C2×C412yes—
56#88128D412yes—
57C4×D52—42no—
58C4×D52—42no—
59#88123—21no—
60#88123—21no—
61#88123—21no—
62#88123C2×C412yescomplemented
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C4×C8×C13—21no—
66C4×C8×C13C2×C412yescomplemented
67C13×#95—21no—
68#88071—21no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71#9064—131nomaximal, Sylow
72C23×D13—22no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—41no—
81C2×D52—22no—
82C2×D52—22no—
83C2×D52—22no—
84C2×D52—22no—
85C2×D52—22no—
86C2×D52—41no—
87C2×D52—41no—
88C2×D52—41no—
89C2×D52—41no—
90C2×D52—41no—
91C2×D52—41no—
92C2×D52—41no—
93C2×D52—41no—
94C2×D52—42no—
95C2×D52—42no—
96C2×D52C22⋊C414yes—
97C2×C4×D13—44no—
98C2×C4×D13—44no—
99C2×C4×D13—82no—
100C2×Dic26—22no—
101C2×Dic26—42no—
102C2×Dic26—42no—
103C2×Dic26—41no—
104C2×C8×C13—22no—
105C2×C8×C13—22no—
106C2×C8×C13—22no—
107C2×C8×C13—41no—
108C2×C8×C13—41no—
109C2×C8×C13—41no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4SD1612yescomplemented
114C42×C13—41no—
115C42×C13—41no—
116C42×C13C22×C411yescharacteristic
117C42×C13C2×D411yescharacteristic
118C42×C13#4111yescharacteristic
119C42×C13#4111yescharacteristic
120#6103—44no—
121#6103—44no—
122#6103—82no—
123C4⋊Dic13—21no—
124C4⋊Dic13—22no—
125C4⋊Dic13—22no—
126C4⋊Dic13—21no—
127C4⋊Dic13—21no—
128C4⋊Dic13—41no—
129C4⋊Dic13—41no—
130C4⋊Dic13SD1612yescomplemented
131C4×Dic13—41no—
132C4×Dic13—41no—
133C2×#1055—41no—
134C2×#1055—41no—
135C2×#1055—41no—
136#6095—416no—
137C2×#492—131no—
138#2366—131no—
139#1987—131no—
140#1987—131no—
141C2×#331—131no—
142#1279—131no—
143#1279D1311yescharacteristic, complemented
144C23×C13#12011yescharacteristic
145C22×D13—24no—
146C22×D13—42no—
147C22×D13—42no—
148C22×D13—42no—
149C22×D13—42no—
150C22×D13—42no—
151C22×D13—42no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—22no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13C2×C22⋊C411yescharacteristic
161C2×C4×C13C4×D411yescharacteristic
162C2×C4×C13C4×D411yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#12111yescharacteristic
165C2×C4×C13#12311yescharacteristic
166C2×C4×C13C2×SD1611yescharacteristic
167C2×C4×C13C2×SD1611yescharacteristic
168C2×C4×C13#13511yescharacteristic
169C2×C4×C13#13511yescharacteristic
170C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C13#13711yescharacteristic
173C2×C4×C13#13711yescharacteristic
174C2×Dic13—22no—
175C2×Dic13—41no—
176C2×Dic13—41no—
177C2×Dic13—42no—
178C2×Dic13—41no—
179C2×Dic13—41no—
180C2×Dic13—41no—
181C2×Dic13—81no—
182C2×Dic13—81no—
183D52—44no—
184D52—42no—
185D52—42no—
186D52—42no—
187D52—42no—
188D52—42no—
189D52—42no—
190D52—42no—
191D52—42no—
192D52—82no—
193C4×D13—88no—
194Dic26—44no—
195Dic26—82no—
196C8×C13—24no—
197C8×C13—81no—
198#1055—81no—
199C22×SD16—262no—
200C2×C4⋊Q8—131no—
201C2×#127—131no—
202C2×C4×D4—261no—
203C2×C4×D4—261no—
204#492—134no—
205#492—262no—
206C2×C4⋊C8—131no—
207C2×C4⋊C8C2×D1311yescharacteristic
208C2×C4×C8C2×D1311yescharacteristic
209#390—261no—
210#390—261no—
211#386—262no—
212C4×C4⋊C4—131no—
213C4×C4⋊C4C2×D1311yescharacteristic
214#340—261no—
215#340—261no—
216#340—261no—
217#340—261no—
218#331—262no—
219C22×C13#38611yescharacteristic
220C22×C13#45011yescharacteristic
221C22×C13#45011yescharacteristic
222C22×C13#45211yescharacteristic
223C22×C13#45211yescharacteristic
224C22×C13#45311yescharacteristic
225C22×C13#45311yescharacteristic
226C2×D13—44no—
227C2×D13—44no—
228C2×D13—44no—
229C2×D13—82no—
230C2×D13—82no—
231C2×D13—82no—
232C2×D13—82no—
233C4×C13—21no—
234C4×C13—21no—
235C4×C13—42no—
236C4×C13—81no—
237C4×C13C4×SD1611yescharacteristic
238C4×C13C4×SD1611yescharacteristic
239C4×C13#44011yescharacteristic
240C4×C13#44011yescharacteristic
241C4×C13#46111yescharacteristic
242C4×C13#46111yescharacteristic
243C4×C13#46311yescharacteristic
244C4×C13#46311yescharacteristic
245Dic13—42no—
246Dic13—81no—
247Dic13—82no—
248C22×Q8—261no—
249C22×D4—132no—
250C22×D4—261no—
251C22×D4—261no—
252C23×C4—262no—
253C2×SD16—268no—
254C2×SD16—524no—
255C2×SD16—524no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—261no—
259C4⋊Q8—132no—
260C4⋊Q8—261no—
261C4⋊Q8—261no—
262C4⋊Q8—261no—
263#127—132no—
264#127—132no—
265#127—261no—
266#127—261no—
267C4×D4—522no—
268C4×D4—522no—
269C4×D4—522no—
270C4×D4—522no—
271C2×C4⋊C4—131no—
272C2×C4⋊C4—131no—
273C2×C4⋊C4—261no—
274C2×C4⋊C4—261no—
275C2×C4⋊C4D5211yescharacteristic
276C2×C4⋊C4D5211yescharacteristic
277C2×C22⋊C4—262no—
278C2×C22⋊C4—262no—
279C2×C22⋊C4—262no—
280C2×C42—21no—
281C2×C42—261no—
282C2×C42C22×D1311yescharacteristic
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—261no—
286C4⋊C8—261no—
287C4×C8—21no—
288C4×C8C4×D1312yescomplemented
289#95—21no—
290#95—261no—
291C2×C13#162911yescharacteristic
292C2×C13#163011yescharacteristic
293C2×C13#163111yescharacteristic
294C2×C13#163111yescharacteristic
295C2×C13#187711yescharacteristic
296C2×C13#187711yescharacteristic
297C2×C13#188711yescharacteristic
298D13—84no—
299C24—262no—
300C2×Q8—262no—
301C2×Q8—522no—
302C2×Q8—522no—
303C2×Q8—521no—
304C2×D4—134no—
305C2×D4—262no—
306C2×D4—262no—
307C2×D4—262no—
308C2×D4—262no—
309C2×D4—262no—
310C2×D4—522no—
311C2×D4—522no—
312C2×D4—521no—
313C2×D4—521no—
314C2×D4—521no—
315C2×D4—521no—
316C2×D4—521no—
317C2×D4—521no—
318C2×D4—521no—
319C2×D4—521no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—261no—
323C22×C4—261no—
324C22×C4—524no—
325C22×C4—524no—
326C22×C4—521no—
327C22×C4—1042no—
328C22×C4C2×D5211yescharacteristic
329C22×C4D4×D1311yescharacteristic
330C22×C4D4×D1311yescharacteristic
331SD16—5216no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—521no—
339C2×C8—521no—
340C2×C8—521no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—132no—
345C4⋊C4—261no—
346C4⋊C4—262no—
347C4⋊C4—262no—
348C4⋊C4—261no—
349C4⋊C4—261no—
350C4⋊C4—521no—
351C4⋊C4—521no—
352C4⋊C4#609512yescomplemented
353C22⋊C4—524no—
354C22⋊C4—524no—
355C22⋊C4—1042no—
356C42—41no—
357C42—41no—
358C42—521no—
359C42—521no—
360C42C2×C4×D1311yescharacteristic
361C42#612711yescharacteristic
362C42D4×D1311yescharacteristic
363C42#613111yescharacteristic
364C13#906411yescharacteristic, complemented, Sylow
365C23—264no—
366C23—522no—
367C23—522no—
368C23—522no—
369C23—522no—
370C23—522no—
371C23—522no—
372C23#8813611yescharacteristic
373Q8—524no—
374Q8—1042no—
375D4—524no—
376D4—522no—
377D4—522no—
378D4—522no—
379D4—522no—
380D4—522no—
381D4—522no—
382D4—522no—
383D4—522no—
384D4—1042no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—262no—
394C2×C4—521no—
395C2×C4—521no—
396C2×C4—521no—
397C2×C4—521no—
398C2×C4—522no—
399C2×C4—521no—
400C2×C4—1048no—
401C2×C4—1041no—
402C2×C4—1041no—
403C2×C4C4×D5211yescharacteristic
404C2×C4C22⋊C4×D1311yescharacteristic
405C2×C4#8813811yescharacteristic
406C2×C4#8814711yescharacteristic
407C2×C4#8814811yescharacteristic
408C2×C4#8814911yescharacteristic
409C2×C4C2×#609511yescharacteristic
410C2×C4#8815811yescharacteristic
411C2×C4#8816211yescharacteristic
412C2×C4#8816311yescharacteristic
413C2×C4#8816511yescharacteristic
414C2×C4SD16×D1311yescharacteristic
415C2×C4#8817011yescharacteristic
416C2×C4#8817211yescharacteristic
417C8—24no—
418C8—81no—
419C8—1041no—
420C22—524no—
421C22—524no—
422C22—524no—
423C22—1042no—
424C22—1042no—
425C22—1042no—
426C22—1042no—
427C22#1171832611yescharacteristic
428C22#1171839211yescharacteristic
429C22#1171839411yescharacteristic
430C22#1171843711yescharacteristic
431C22#1171847111yescharacteristic
432C22#1171848311yescharacteristic
433C22#1171848311yescharacteristic
434C4—21no—
435C4—21no—
436C4—42no—
437C4—81no—
438C4—522no—
439C4—1042no—
440C4—1041no—
441C4C4×#609511yescharacteristic
442C4#1171837111yescharacteristic
443C4#1171844811yescharacteristic
444C4#1171847911yescharacteristic
445C4#1171850211yescharacteristic
446C4#1171850511yescharacteristic
447C4#1171851311yescharacteristic
448C4#1171855011yescharacteristic
449C2—1044no—
450C2#1311395411yescharacteristic
451C2#1311395911yescharacteristic
452C2#1311396511yescharacteristic
453C2#1311396611yescharacteristic
454C2#1311516911yescharacteristic
455C2#1311517111yescharacteristic
456C2#1311523311yescharacteristic
subgroupG/H
centerC23#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socleC23×C13#120
prime radicalC2×#88128C22
cosocleC2×C42×C13C23
hypercenter#1279D13
hypocenterC13#9064
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
3. #13115784C2semidirect
4. #13115783C2semidirect
6. #13112676C2semidirect
7. C13×#1279C2semidirect
21. #11718354C4semidirect
62. #88123C2×C4semidirect
66. C4×C8×C13C2×C4semidirect
113. C13×C4⋊C4SD16semidirect
130. C4⋊Dic13SD16semidirect
143. #1279D13semidirect
288. C4×C8C4×D13semidirect
352. C4⋊C4#6095semidirect
364. C13#9064semidirect

Maximal subgroups

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

subgroupindex
C2×#117183542
#131179002
#131157842
#131157832
C2×#117180772
#131126762
C13×#12792
#906413