Finite Group Databasebeta

← #15759161

Subgroups — #15759161

Order 3328.

570 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718688C211yesmaximal, characteristic
2C2×#11718685C211yesmaximal, characteristic, complemented
3#13115641C211yesmaximal, characteristic
4C2×#11718077C211yesmaximal, characteristic
5#13112719C211yesmaximal, characteristic, complemented
6#13112670C211yesmaximal, characteristic, complemented
7C13×#1803C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C13C2211yescharacteristic
9C22×#6106—21no—
10C2×#88128C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×#103—21no—
13C13×#384C2211yescharacteristic
14#11718688—22no—
15#11718688C414yescomplemented
16#11718685—22no—
17#11718685—22no—
18C2×#88049—21no—
19C2×#88049—21no—
20C2×#88049—21no—
21C2×C4⋊#1055—21no—
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24C2×#88043—21no—
25C2×C4×#1055C2211yescharacteristic
26C13×#340—21no—
27#11718077—22no—
28C22×Q8×C13D411yescharacteristic
29C22×D52—21no—
30C22×D52—21no—
31C22×D52—21no—
32C22×C8×C13—21no—
33C4×Q8×C13—21no—
34C4×Q8×C13—21no—
35C4×Q8×C13C2×C412yes—
36C4×Q8×C13D412yes—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4D411yescharacteristic
42C2×C42×C13—21no—
43C2×C42×C13C2311yescharacteristic
44C2×#6106—24no—
45C2×#6106—42no—
46C2×#6106—42no—
47C22×#1055—21no—
48C22×#1055—21no—
49C22×#1055D411yescharacteristic
50C22×#1055D411yescharacteristic
51#88128—21no—
52#88128—21no—
53#88128—21no—
54#88128C2×C412yes—
55C13×C4⋊C8—21no—
56C13×C4⋊C8—21no—
57C13×#103—42no—
58#88049—24no—
59#88049—42no—
60#88049—42no—
61C4⋊#1055—24no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055C2×C412yes—
65C4⋊#1055D412yes—
66#88043—24no—
67C4×#1055—21no—
68C4×#1055—21no—
69#9230—131nomaximal, Sylow
70C23×D13—41no—
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13—21no—
74C2×Q8×C13—21no—
75C2×Q8×C13—21no—
76C2×Q8×C13C22⋊C412yes—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—41no—
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13#4111yescharacteristic
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—41no—
95C2×D52—41no—
96C2×D52—41no—
97C2×D52—81no—
98C2×D52—81no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C2×C8×C13—41no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—81no—
110C13×C4⋊C4C22⋊C412yes—
111C42×C13—22no—
112C42×C13—22no—
113C42×C13C22×C411yescharacteristic
114C42×C13C2×D411yescharacteristic
115C42×C13C2×D411yescharacteristic
116C42×C13#4111yescharacteristic
117#6106—48no—
118C2×#1055—21no—
119C2×#1055—21no—
120C2×#1055—22no—
121C2×#1055—22no—
122C2×#1055—21no—
123C2×#1055—21no—
124C2×#1055—21no—
125C2×#1055—41no—
126C2×#1055—41no—
127C2×#1055—41no—
128C2×#1055—41no—
129C2×#1055SD1612yescomplemented
130C2×#460—131no—
131C2×#446—131no—
132#1957—131no—
133#1803D1311yescharacteristic, complemented
134C2×#331—131no—
135#1296—131no—
136#1277—131no—
137C23×C13#12111yescharacteristic
138C22×D13—42no—
139C22×D13—81no—
140C22×D13—81no—
141C22×D13—81no—
142C22×D13—81no—
143C22×D13—81no—
144C22×D13—81no—
145Q8×C13—22no—
146Q8×C13—22no—
147Q8×C13—41no—
148Q8×C13—41no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—81no—
158C2×C4×C13—81no—
159C2×C4×C13—81no—
160C2×C4×C13C2×C22⋊C411yescharacteristic
161C2×C4×C13C4×D411yescharacteristic
162C2×C4×C13C4×D411yescharacteristic
163C2×C4×C13#12011yescharacteristic
164C2×C4×C13#12111yescharacteristic
165C2×C4×C13#12311yescharacteristic
166C2×C4×C13C2×SD1611yescharacteristic
167C2×C4×C13#13511yescharacteristic
168C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C13#13711yescharacteristic
173C2×C4×C13#13711yescharacteristic
174D52—42no—
175D52—42no—
176D52—42no—
177D52—42no—
178D52—82no—
179D52—82no—
180D52—81no—
181D52—81no—
182D52—81no—
183D52—81no—
184C8×C13—81no—
185#1055—22no—
186#1055—42no—
187#1055—41no—
188#1055—42no—
189C22×SD16—261no—
190C2×#127—131no—
191C2×C4×Q8C2×D1311yescharacteristic
192#460—134no—
193#460—262no—
194#446—262no—
195#446—262no—
196C2×C4⋊C8—131no—
197C2×C4⋊C8—131no—
198C2×C4⋊C8—261no—
199C2×C4⋊C8C2×D1311yescharacteristic
200C2×#103—21no—
201C2×#102—261no—
202C2×#102—261no—
203C2×#102—261no—
204C2×#97—261no—
205C2×C4×C8—131no—
206#384C2×D1311yescharacteristic
207#340—21no—
208#331—262no—
209C22×C13#38611yescharacteristic
210C22×C13#46011yescharacteristic
211C22×C13#46411yescharacteristic
212C22×C13#46811yescharacteristic
213C22×C13#46911yescharacteristic
214C22×C13#47111yescharacteristic
215C22×C13#47211yescharacteristic
216C2×D13—82no—
217C2×D13—82no—
218C2×D13—82no—
219C2×D13—161no—
220C2×D13—161no—
221C2×D13—161no—
222C2×D13—161no—
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—42no—
226C4×C13—42no—
227C4×C13—161no—
228C4×C13#41711yescharacteristic
229C4×C13#41811yescharacteristic
230C4×C13C4×SD1611yescharacteristic
231C4×C13#44011yescharacteristic
232C4×C13#44811yescharacteristic
233C4×C13#44911yescharacteristic
234C4×C13#46811yescharacteristic
235C4×C13#46911yescharacteristic
236C22×Q8C22⋊D1311yescharacteristic
237C22×D4—261no—
238C22×D4—261no—
239C22×D4—261no—
240C2×SD16—264no—
241C2×SD16—522no—
242C2×SD16—522no—
243C22×C8—21no—
244C22×C8—131no—
245C22×C8—131no—
246C22×C8—261no—
247C22×C8—261no—
248#127—132no—
249#127—261no—
250#127—261no—
251#127—261no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8C4×D1312yes—
255C4×Q8D5212yes—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4C22⋊D1311yescharacteristic
261C2×C42—21no—
262C2×C42C22×D1311yescharacteristic
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—132no—
266C4⋊C8—132no—
267C4⋊C8—264no—
268C4⋊C8—261no—
269C4⋊C8—261no—
270#103—42no—
271#102—264no—
272#102—522no—
273#102—522no—
274#97—264no—
275C4×C8—261no—
276C4×C8—261no—
277C2×C13#168611yescharacteristic
278C2×C13#168811yescharacteristic
279C2×C13#169811yescharacteristic
280C2×C13#170211yescharacteristic
281C2×C13#188011yescharacteristic
282C2×C13#189511yescharacteristic
283C2×C13#190711yescharacteristic
284D13—162no—
285C24—521no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8#610312yes—
292C2×D4—262no—
293C2×D4—262no—
294C2×D4—262no—
295C2×D4—521no—
296C2×D4—521no—
297C2×D4—521no—
298C2×D4—521no—
299C2×D4—521no—
300C2×D4—521no—
301C2×D4—521no—
302C2×D4—521no—
303C2×D4—521no—
304C2×D4—521no—
305C2×D4—521no—
306C2×D4—1041no—
307C2×D4—1041no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—41no—
311C22×C4D4×D1311yescharacteristic
312C22×C4#612911yescharacteristic
313C22×C4C2×C22⋊D1311yescharacteristic
314SD16—528no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—132no—
319C2×C8—261no—
320C2×C8—261no—
321C2×C8—261no—
322C2×C8—262no—
323C2×C8—261no—
324C2×C8—261no—
325C2×C8—262no—
326C2×C8—521no—
327C2×C8—521no—
328C2×C8—521no—
329C2×C8—521no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—81no—
338C4⋊C4#610312yes—
339C42—22no—
340C42—22no—
341C42C2×C4×D1311yescharacteristic
342C42C2×D5211yescharacteristic
343C42D4×D1311yescharacteristic
344C42#612911yescharacteristic
345C13#923011yescharacteristic, complemented, Sylow
346C23—522no—
347C23—1041no—
348C23—1041no—
349C23—1041no—
350C23—1041no—
351C23—1041no—
352C23—1041no—
353C23#8819311yescharacteristic
354Q8—22no—
355Q8—22no—
356Q8—41no—
357Q8—41no—
358D4—522no—
359D4—522no—
360D4—522no—
361D4—522no—
362D4—1042no—
363D4—1042no—
364D4—1041no—
365D4—1041no—
366D4—1041no—
367D4—1041no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4#8813511yescharacteristic
380C2×C4#8813511yescharacteristic
381C2×C4#8813611yescharacteristic
382C2×C4#8814011yescharacteristic
383C2×C4SD16×D1311yescharacteristic
384C2×C4#8816811yescharacteristic
385C2×C4#8817211yescharacteristic
386C2×C4#8817311yescharacteristic
387C2×C4C2×#610311yescharacteristic
388C2×C4#8818611yescharacteristic
389C2×C4#8819311yescharacteristic
390C2×C4#8819611yescharacteristic
391C2×C4#8820311yescharacteristic
392C2×C4#8820311yescharacteristic
393C8—81no—
394C8—262no—
395C8—522no—
396C8—521no—
397C8—522no—
398C22—1042no—
399C22—1042no—
400C22—1042no—
401C22—2081no—
402C22—2081no—
403C22—2081no—
404C22—2081no—
405C22#1171861911yescharacteristic
406C22#1171870011yescharacteristic
407C22#1171871011yescharacteristic
408C22#1171882411yescharacteristic
409C22#1171884611yescharacteristic
410C22#1171886011yescharacteristic
411C22#1171886411yescharacteristic
412C4—21no—
413C4—21no—
414C4—42no—
415C4—42no—
416C4—161no—
417C4#1171844911yescharacteristic
418C4#1171846711yescharacteristic
419C4#1171847211yescharacteristic
420C4#1171847811yescharacteristic
421C4#1171862711yescharacteristic
422C4#1171866211yescharacteristic
423C4#1171870011yescharacteristic
424C4#1171871011yescharacteristic
425C2—2082no—
426C2#1311431011yescharacteristic
427C2#1311431811yescharacteristic
428C2#1311437811yescharacteristic
429C2#1311440611yescharacteristic
430C2#1311518911yescharacteristic
431C2#1311527211yescharacteristic
432C2#1311534211yescharacteristic
subgroupG/H
centerC23#88193
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1803C2
socleC23×C13#121
prime radicalC2×#88128C22
cosocleC2×C42×C13C23
hypercenter#1803D13
hypocenterC13#9230
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. C2×#11718685C2semidirect
5. #13112719C2semidirect
6. #13112670C2semidirect
7. C13×#1803C2semidirect
15. #11718688C4semidirect
129. C2×#1055SD16semidirect
133. #1803D13semidirect
345. C13#9230semidirect

Maximal subgroups

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

subgroupindex
C2×#117186882
C2×#117186852
#131156412
C2×#117180772
#131127192
#131126702
C13×#18032
#923013