Finite Group Databasebeta

← #15758169

Subgroups — #15758169

Order 3328.

690 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718355C211yesmaximal, characteristic
2#13117900C211yesmaximal, characteristic
3#13115787C211yesmaximal, characteristic, complemented
4#13115759C211yesmaximal, characteristic, complemented
5C2×#11718077C211yesmaximal, characteristic
6#13112676C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×#88147—21no—
9C2×#88128C2211yescharacteristic
10C2×C4×D52—21no—
11C2×#88123C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C13C2211yescharacteristic
14C4×C13×C4⋊C4C2211yescharacteristic
15C2×#88061—22no—
16#11718649—21no—
17C2×#88050—21no—
18C2×#88050—21no—
19#11718600—21no—
20C4×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22#11718355—22no—
23#11718355C414yescomplemented
24#11718326—22no—
25#11718143—21no—
26#11718143—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—
48#88147—42no—
49#88147—42no—
50#88128—21no—
51#88128—21no—
52#88128C2×C412yes—
53#88128D412yes—
54C4×D52—42no—
55C4×D52—42no—
56#88123—21no—
57#88123—21no—
58#88123—21no—
59#88123C2×C412yescomplemented
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62C4×C8×C13—21no—
63C4×C8×C13C2×C412yescomplemented
64C13×#95—21no—
65#88071—21no—
66#88061—28no—
67#88050—42no—
68#88050—42no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71#9057—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—41no—
102C2×Dic26—41no—
103C2×Dic26—41no—
104C2×Dic26—41no—
105C2×Dic26—41no—
106C2×C8×C13—22no—
107C2×C8×C13—41no—
108C2×C8×C13—41no—
109C2×C8×C13—41no—
110C2×C8×C13—41no—
111C2×C8×C13—41no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4D812yes—
116C42×C13—41no—
117C42×C13—41no—
118C42×C13C22×C411yescharacteristic
119C42×C13C2×D411yescharacteristic
120C42×C13#4111yescharacteristic
121C42×C13#4111yescharacteristic
122#6103—44no—
123#6103—44no—
124#6103—82no—
125C4⋊Dic13—21no—
126C4⋊Dic13—22no—
127C4⋊Dic13—22no—
128C4⋊Dic13—21no—
129C4⋊Dic13—21no—
130C4⋊Dic13—41no—
131C4⋊Dic13—41no—
132C4⋊Dic13SD1612yes—
133C4×Dic13—41no—
134C4×Dic13—41no—
135C2×#1055—41no—
136C2×#1055—41no—
137C2×#1055—41no—
138C2×#486—131no—
139#2366—131no—
140#1988—131no—
141#1981—131no—
142C2×#331—131no—
143#1279—131no—
144#1279D1311yescharacteristic, complemented
145C23×C13#12011yescharacteristic
146C22×D13—24no—
147C22×D13—42no—
148C22×D13—42no—
149C22×D13—42no—
150C22×D13—42no—
151C22×D13—42no—
152C22×D13—42no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—22no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13C2×C22⋊C411yescharacteristic
162C2×C4×C13C4×D411yescharacteristic
163C2×C4×C13C4×D411yescharacteristic
164C2×C4×C13#12111yescharacteristic
165C2×C4×C13#12111yescharacteristic
166C2×C4×C13#12311yescharacteristic
167C2×C4×C13C2×D811yescharacteristic
168C2×C4×C13C2×SD1611yescharacteristic
169C2×C4×C13#13511yescharacteristic
170C2×C4×C13#13511yescharacteristic
171C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C13#13711yescharacteristic
175C2×Dic13—22no—
176C2×Dic13—41no—
177C2×Dic13—41no—
178C2×Dic13—42no—
179C2×Dic13—41no—
180C2×Dic13—41no—
181C2×Dic13—41no—
182C2×Dic13—81no—
183C2×Dic13—81no—
184D52—44no—
185D52—42no—
186D52—42no—
187D52—42no—
188D52—42no—
189D52—42no—
190D52—42no—
191D52—42no—
192D52—42no—
193D52—82no—
194C4×D13—88no—
195Dic26—42no—
196Dic26—42no—
197Dic26—81no—
198Dic26—81no—
199C8×C13—42no—
200C8×C13—81no—
201#1055—81no—
202C2×C4⋊Q8—131no—
203C2×#127—131no—
204C2×C4×D4—261no—
205C2×C4×D4—261no—
206#486—134no—
207#486—262no—
208C2×C4⋊C8—131no—
209C2×C4⋊C8C2×D1311yescharacteristic
210C2×#103—261no—
211C2×#103—261no—
212C2×#102—262no—
213C2×C4×C8C2×D1311yescharacteristic
214#390—261no—
215#390—261no—
216#386—262no—
217C4×C4⋊C4—131no—
218C4×C4⋊C4C2×D1311yescharacteristic
219#340—261no—
220#340—261no—
221#331—262no—
222C22×C13#38611yescharacteristic
223C22×C13#44711yescharacteristic
224C22×C13#44911yescharacteristic
225C22×C13#45011yescharacteristic
226C22×C13#45211yescharacteristic
227C22×C13#45511yescharacteristic
228C22×C13#45511yescharacteristic
229C2×D13—44no—
230C2×D13—44no—
231C2×D13—44no—
232C2×D13—82no—
233C2×D13—82no—
234C2×D13—82no—
235C2×D13—82no—
236C4×C13—21no—
237C4×C13—21no—
238C4×C13—42no—
239C4×C13—81no—
240C4×C13C4×D811yescharacteristic
241C4×C13C4×SD1611yescharacteristic
242C4×C13#44011yescharacteristic
243C4×C13#44211yescharacteristic
244C4×C13#45911yescharacteristic
245C4×C13#46111yescharacteristic
246C4×C13#46311yescharacteristic
247C4×C13#46311yescharacteristic
248Dic13—42no—
249Dic13—82no—
250Dic13—81no—
251C22×Q8—261no—
252C22×D4—132no—
253C22×D4—261no—
254C22×D4—261no—
255C23×C4—262no—
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—
287#103—522no—
288#103—522no—
289#102—268no—
290C4×C8—21no—
291C4×C8C4×D1312yescomplemented
292#95—21no—
293#95—261no—
294C2×C13#163911yescharacteristic
295C2×C13#164011yescharacteristic
296C2×C13#164111yescharacteristic
297C2×C13#164211yescharacteristic
298C2×C13#187711yescharacteristic
299C2×C13#187911yescharacteristic
300C2×C13#188511yescharacteristic
301D13—84no—
302C24—262no—
303C2×Q8—262no—
304C2×Q8—521no—
305C2×Q8—521no—
306C2×Q8—521no—
307C2×Q8—521no—
308C2×Q8—521no—
309C2×D4—134no—
310C2×D4—262no—
311C2×D4—262no—
312C2×D4—262no—
313C2×D4—262no—
314C2×D4—262no—
315C2×D4—522no—
316C2×D4—522no—
317C2×D4—521no—
318C2×D4—521no—
319C2×D4—521no—
320C2×D4—521no—
321C2×D4—521no—
322C2×D4—521no—
323C2×D4—521no—
324C2×D4—521no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—261no—
328C22×C4—261no—
329C22×C4—524no—
330C22×C4—524no—
331C22×C4—521no—
332C22×C4—1042no—
333C22×C4C2×D5211yescharacteristic
334C22×C4D4×D1311yescharacteristic
335C22×C4D4×D1311yescharacteristic
336C2×C8—22no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—521no—
343C2×C8—521no—
344C2×C8—521no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—132no—
349C4⋊C4—261no—
350C4⋊C4—262no—
351C4⋊C4—262no—
352C4⋊C4—261no—
353C4⋊C4—261no—
354C4⋊C4—521no—
355C4⋊C4—521no—
356C4⋊C4D10412yes—
357C22⋊C4—524no—
358C22⋊C4—524no—
359C22⋊C4—1042no—
360C42—41no—
361C42—41no—
362C42—521no—
363C42—521no—
364C42C2×C4×D1311yescharacteristic
365C42#612711yescharacteristic
366C42D4×D1311yescharacteristic
367C42#613111yescharacteristic
368C13#905711yescharacteristic, complemented, Sylow
369C23—264no—
370C23—522no—
371C23—522no—
372C23—522no—
373C23—522no—
374C23—522no—
375C23—522no—
376C23#8813611yescharacteristic
377Q8—522no—
378Q8—522no—
379Q8—1041no—
380Q8—1041no—
381D4—524no—
382D4—522no—
383D4—522no—
384D4—522no—
385D4—522no—
386D4—522no—
387D4—522no—
388D4—522no—
389D4—522no—
390D4—1042no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—262no—
400C2×C4—521no—
401C2×C4—521no—
402C2×C4—521no—
403C2×C4—521no—
404C2×C4—522no—
405C2×C4—521no—
406C2×C4—1048no—
407C2×C4—1041no—
408C2×C4—1041no—
409C2×C4C4×D5211yescharacteristic
410C2×C4C22⋊C4×D1311yescharacteristic
411C2×C4#8813811yescharacteristic
412C2×C4#8814711yescharacteristic
413C2×C4#8814811yescharacteristic
414C2×C4#8814911yescharacteristic
415C2×C4C2×D10411yescharacteristic
416C2×C4#8815811yescharacteristic
417C2×C4#8816211yescharacteristic
418C2×C4#8816211yescharacteristic
419C2×C4#8816511yescharacteristic
420C2×C4SD16×D1311yescharacteristic
421C2×C4#8817011yescharacteristic
422C2×C4#8817211yescharacteristic
423C8—42no—
424C8—81no—
425C8—1041no—
426C22—524no—
427C22—524no—
428C22—524no—
429C22—1042no—
430C22—1042no—
431C22—1042no—
432C22—1042no—
433C22#1171832611yescharacteristic
434C22#1171839311yescharacteristic
435C22#1171839511yescharacteristic
436C22#1171843711yescharacteristic
437C22#1171847111yescharacteristic
438C22#1171848611yescharacteristic
439C22#1171848611yescharacteristic
440C4—21no—
441C4—21no—
442C4—42no—
443C4—81no—
444C4—522no—
445C4—1042no—
446C4—1041no—
447C4C4×D10411yescharacteristic
448C4#1171837211yescharacteristic
449C4#1171844811yescharacteristic
450C4#1171847911yescharacteristic
451C4#1171850411yescharacteristic
452C4#1171850511yescharacteristic
453C4#1171851311yescharacteristic
454C4#1171855011yescharacteristic
455C2—1044no—
456C2#1311401711yescharacteristic
457C2#1311402411yescharacteristic
458C2#1311403111yescharacteristic
459C2#1311403811yescharacteristic
460C2#1311517111yescharacteristic
461C2#1311518311yescharacteristic
462C2#1311522311yescharacteristic
subgroupG/H
centerC23#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socleC23×C13#120
prime radicalC2×#88128C22
cosocleC2×C42×C13C23
hypercenter#1279D13
hypocenterC13#9057
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. #13115787C2semidirect
4. #13115759C2semidirect
6. #13112676C2semidirect
7. C13×#1279C2semidirect
23. #11718355C4semidirect
59. #88123C2×C4semidirect
63. C4×C8×C13C2×C4semidirect
144. #1279D13semidirect
291. C4×C8C4×D13semidirect
368. C13#9057semidirect

Maximal subgroups

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

subgroupindex
C2×#117183552
#131179002
#131157872
#131157592
C2×#117180772
#131126762
C13×#12792
#905713