Finite Group Databasebeta

← #15757760

Subgroups — #15757760

Order 3328.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718744C211yesmaximal, characteristic
2#13117783C211yesmaximal, characteristic
3#13115798C211yesmaximal, characteristic, complemented
4C2×#11718075C211yesmaximal, characteristic
5#13112720C211yesmaximal, characteristic, complemented
6#13112677C211yesmaximal, characteristic, complemented
7C13×#1988C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C22×#6106—21no—
10C2×#88146—21no—
11C2×C4×D52C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C4×C13×C4⋊C4C2211yescharacteristic
14C2×#88075—21no—
15#11718744—22no—
16#11718744C414yescomplemented
17#11718648—21no—
18#11718600—21no—
19#11718596C2211yescharacteristic
20C4×C4⋊Dic13—21no—
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4×#1055C2211yescharacteristic
23#11718331—22no—
24C13×#340—21no—
25C13×#340—21no—
26#11718121—22no—
27#11718075—22no—
28C22×Q8×C13—21no—
29C22×D52D411yescharacteristic
30C22×C4×D13—21no—
31C22×C8×C13—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8C2×C412yes—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C42×C13—21no—
41C2×C42×C13C2311yescharacteristic
42C2×#6106—24no—
43C2×#6106—42no—
44C2×#6106—42no—
45C2×#6103—21no—
46C2×#6103—22no—
47C2×#6103—22no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13—21no—
50C2×C4⋊Dic13D411yescharacteristic
51C2×C4⋊Dic13D412yes—
52C2×C4×Dic13—22no—
53C22×#1055—21no—
54C22×#1055—21no—
55#88146—42no—
56#88146—42no—
57C4×D52—21no—
58C4×D52—21no—
59C4×D52C2×C412yes—
60C4×D52D412yes—
61C13×C4⋊C8—21no—
62C13×C4⋊C8—21no—
63C13×#95—21no—
64#88075—24no—
65#88071—22no—
66C4⋊#1055—21no—
67C4⋊#1055C2×C412yes—
68C4×#1055—21no—
69C4×#1055—21no—
70#8988—131nomaximal, Sylow
71C23×D13—21no—
72C2×Q8×C13—22no—
73C2×Q8×C13—41no—
74C2×Q8×C13—41no—
75C2×Q8×C13—41no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—41no—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×Dic13—21no—
85C22×Dic13—22no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52—21no—
90C2×D52—21no—
91C2×D52C22⋊C412yes—
92C2×C4×D13—22no—
93C2×C4×D13—22no—
94C2×C4×D13—41no—
95C2×C4×D13—41no—
96C2×C4×D13—41no—
97C2×C4×D13—41no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4SD1612yescomplemented
109C42×C13—41no—
110C42×C13—41no—
111C42×C13C22×C411yescharacteristic
112C42×C13C2×D411yescharacteristic
113C42×C13#4111yescharacteristic
114C42×C13#4111yescharacteristic
115#6106—48no—
116#6103—22no—
117#6103—22no—
118#6103—44no—
119#6103—82no—
120C4⋊Dic13—21no—
121C4⋊Dic13—41no—
122C4⋊Dic13—41no—
123C4⋊Dic13—41no—
124C4⋊Dic13—41no—
125C4⋊Dic13—42no—
126C4⋊Dic13C22⋊C412yes—
127C4×Dic13—44no—
128C2×#1055—22no—
129C2×#1055—22no—
130C2×#1055—41no—
131C2×#1055—41no—
132C2×#1055—41no—
133C2×#1055—41no—
134C2×#461—131no—
135#2354—131no—
136#1990—131no—
137#1988D1311yescharacteristic, complemented
138C2×D4⋊C8—131no—
139#1296—131no—
140#1279—131no—
141C23×C13#12011yescharacteristic
142C22×D13—22no—
143C22×D13—41no—
144C22×D13—41no—
145C22×D13—41no—
146C22×D13—41no—
147C22×D13—41no—
148C22×D13—41no—
149Q8×C13—42no—
150Q8×C13—42no—
151Q8×C13—81no—
152Q8×C13—81no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—22no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—42no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—81no—
163C2×C4×C13—81no—
164C2×C4×C13C2×C22⋊C411yescharacteristic
165C2×C4×C13C4×D411yescharacteristic
166C2×C4×C13C4×D411yescharacteristic
167C2×C4×C13#12111yescharacteristic
168C2×C4×C13#12111yescharacteristic
169C2×C4×C13#12311yescharacteristic
170C2×C4×C13C2×SD1611yescharacteristic
171C2×C4×C13#13511yescharacteristic
172C2×C4×C13#13511yescharacteristic
173C2×C4×C13#13511yescharacteristic
174C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C13#13711yescharacteristic
178C2×Dic13—22no—
179C2×Dic13—41no—
180C2×Dic13—41no—
181C2×Dic13—42no—
182C2×Dic13—42no—
183C2×Dic13—42no—
184D52—22no—
185D52—22no—
186D52—41no—
187D52—41no—
188C4×D13—42no—
189C4×D13—42no—
190C4×D13—42no—
191C4×D13—42no—
192C8×C13—81no—
193#1055—42no—
194#1055—42no—
195C22×SD16—261no—
196C2×C4⋊Q8C2×D1311yescharacteristic
197C2×C4×D4—131no—
198C2×#117—261no—
199#461—134no—
200#461—262no—
201C2×C4⋊C8—131no—
202C2×C4⋊C8C2×D1311yescharacteristic
203C2×#103—261no—
204C2×C4×C8—131no—
205#390—261no—
206#388—262no—
207#384—131no—
208#380—261no—
209C4×C4⋊C4—261no—
210C4×C4⋊C4C2×D1311yescharacteristic
211#340—21no—
212#340—21no—
213#340—262no—
214D4⋊C8—262no—
215C22×C13#38611yescharacteristic
216C22×C13#44911yescharacteristic
217C22×C13#44911yescharacteristic
218C22×C13#45011yescharacteristic
219C22×C13#45211yescharacteristic
220C22×C13#45511yescharacteristic
221C22×C13#45611yescharacteristic
222C2×D13—42no—
223C2×D13—42no—
224C2×D13—42no—
225C2×D13—81no—
226C2×D13—81no—
227C2×D13—81no—
228C2×D13—81no—
229C4×C13—21no—
230C4×C13—21no—
231C4×C13—42no—
232C4×C13—82no—
233C4×C13—81no—
234C4×C13#41611yescharacteristic
235C4×C13#41811yescharacteristic
236C4×C13C4×SD1611yescharacteristic
237C4×C13#44011yescharacteristic
238C4×C13#46111yescharacteristic
239C4×C13#46311yescharacteristic
240C4×C13#48211yescharacteristic
241C4×C13#48211yescharacteristic
242Dic13—42no—
243Dic13—82no—
244C22×Q8—21no—
245C22×D4—131no—
246C23×C4—261no—
247C2×SD16—264no—
248C2×SD16—522no—
249C2×SD16—522no—
250C22×C8—21no—
251C22×C8—261no—
252C22×C8—261no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8C4×D1312yes—
257C4×D4—132no—
258C4×D4—132no—
259C4×D4—261no—
260C4×D4—261no—
261#117—522no—
262#117—522no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—131no—
266C2×C4⋊C4—132no—
267C2×C4⋊C4—261no—
268C2×C4⋊C4—261no—
269C2×C4⋊C4C22⋊D1311yescharacteristic
270C2×C4⋊C4C22⋊D1311yescharacteristic
271C2×C22⋊C4—261no—
272C2×C22⋊C4—262no—
273C2×C22⋊C4—262no—
274C2×C42—21no—
275C2×C42—262no—
276C2×C42C22×D1311yescharacteristic
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—132no—
280C4⋊C8—261no—
281#103—264no—
282C4×C8—261no—
283C4×C8—261no—
284#95—21no—
285#95—262no—
286C2×C13#164211yescharacteristic
287C2×C13#164611yescharacteristic
288C2×C13#165011yescharacteristic
289C2×C13#165411yescharacteristic
290C2×C13#187511yescharacteristic
291C2×C13#187711yescharacteristic
292C2×C13#188211yescharacteristic
293D13—82no—
294C24—261no—
295C2×Q8—22no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×D4—132no—
302C2×D4—261no—
303C2×D4—261no—
304C2×D4—261no—
305C2×D4—261no—
306C2×D4—261no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—261no—
311C22×C4—262no—
312C22×C4—262no—
313C22×C4—262no—
314C22×C4—521no—
315C22×C4—521no—
316C22×C4—521no—
317C22×C4—521no—
318C22×C4D4×D1311yescharacteristic
319C22×C4D4×D1311yescharacteristic
320C22×C4C2×C22⋊D1311yescharacteristic
321SD16—528no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—262no—
326C2×C8—262no—
327C2×C8—521no—
328C2×C8—521no—
329C2×C8—521no—
330C2×C8—521no—
331C4⋊C4—21no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—132no—
339C4⋊C4—261no—
340C4⋊C4—522no—
341C4⋊C4—521no—
342C4⋊C4—521no—
343C4⋊C4—521no—
344C4⋊C4—521no—
345C4⋊C4#610612yescomplemented
346C22⋊C4—262no—
347C22⋊C4—262no—
348C22⋊C4—524no—
349C22⋊C4—1042no—
350C42—41no—
351C42—41no—
352C42—524no—
353C42C2×C4×D1311yescharacteristic
354C42#612711yescharacteristic
355C42D4×D1311yescharacteristic
356C42#612911yescharacteristic
357C13#898811yescharacteristic, complemented, Sylow
358C23—262no—
359C23—521no—
360C23—521no—
361C23—521no—
362C23—521no—
363C23—521no—
364C23—521no—
365C23#8819111yescharacteristic
366Q8—42no—
367Q8—42no—
368Q8—81no—
369Q8—81no—
370D4—262no—
371D4—262no—
372D4—521no—
373D4—521no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—262no—
386C2×C4—521no—
387C2×C4—521no—
388C2×C4—522no—
389C2×C4—522no—
390C2×C4—522no—
391C2×C4—522no—
392C2×C4—522no—
393C2×C4—522no—
394C2×C4—522no—
395C2×C4C22⋊C4×D1311yescharacteristic
396C2×C4#8813511yescharacteristic
397C2×C4#8813711yescharacteristic
398C2×C4#8813811yescharacteristic
399C2×C4#8816511yescharacteristic
400C2×C4#8816611yescharacteristic
401C2×C4#8816811yescharacteristic
402C2×C4#8817011yescharacteristic
403C2×C4C4×C22⋊D1311yescharacteristic
404C2×C4#8819211yescharacteristic
405C2×C4C2×#610611yescharacteristic
406C2×C4#8819611yescharacteristic
407C2×C4#8820311yescharacteristic
408C2×C4#8820411yescharacteristic
409C8—81no—
410C8—522no—
411C8—522no—
412C22—522no—
413C22—522no—
414C22—522no—
415C22—1041no—
416C22—1041no—
417C22—1041no—
418C22—1041no—
419C22#1171861711yescharacteristic
420C22#1171870711yescharacteristic
421C22#1171870811yescharacteristic
422C22#1171881911yescharacteristic
423C22#1171883311yescharacteristic
424C22#1171886311yescharacteristic
425C22#1171886611yescharacteristic
426C4—21no—
427C4—21no—
428C4—42no—
429C4—82no—
430C4—81no—
431C4—522no—
432C4—1042no—
433C4#1171843111yescharacteristic
434C4#1171843311yescharacteristic
435C4#1171844011yescharacteristic
436C4#1171844511yescharacteristic
437C4C4×#610611yescharacteristic
438C4#1171868711yescharacteristic
439C4#1171871811yescharacteristic
440C4#1171874411yescharacteristic
441C2—1042no—
442C2#1311403511yescharacteristic
443C2#1311406311yescharacteristic
444C2#1311409111yescharacteristic
445C2#1311411911yescharacteristic
446C2#1311515511yescharacteristic
447C2#1311517311yescharacteristic
448C2#1311520211yescharacteristic
subgroupG/H
centerC23#88191
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1988C2
socleC23×C13#120
prime radicalC22×D52D4
cosocleC2×C42×C13C23
hypercenter#1988D13
hypocenterC13#8988
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
3. #13115798C2semidirect
5. #13112720C2semidirect
6. #13112677C2semidirect
7. C13×#1988C2semidirect
16. #11718744C4semidirect
108. C13×C4⋊C4SD16semidirect
137. #1988D13semidirect
345. C4⋊C4#6106semidirect
357. C13#8988semidirect

Maximal subgroups

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

subgroupindex
C2×#117187442
#131177832
#131157982
C2×#117180752
#131127202
#131126772
C13×#19882
#898813