Finite Group Databasebeta

← #15753469

Subgroups — #15753469

Order 3328.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718391C211yesmaximal, characteristic
2C4×#88046C211yesmaximal, characteristic
3#13114615C211yesmaximal, characteristic, complemented
4C22⋊C4×#1055C211yesmaximal, characteristic, complemented
5#13113152C211yesmaximal, characteristic
6#13112683C211yesmaximal, characteristic, complemented
7C13×#1282C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D13C2211yescharacteristic
9C23×#1055C2211yescharacteristic
10C22×#6094C411yescharacteristic, complemented
11C2×C13×C22⋊C8C2211yescharacteristic
12C2×C13×C22⋊C8C2211yescharacteristic
13C4×C13×C22⋊C4C2211yescharacteristic
14C4×C22⋊Dic13C2211yescharacteristic
15C2×C22⋊#1055C2211yescharacteristic
16C2×#88060C411yescharacteristic, complemented
17C2×#88055—21no—
18C2×#88055C411yescharacteristic, complemented
19C2×#88054C411yescharacteristic, complemented
20C2×#88046C412yes—
21C2×C4×#1055—21no—
22#11718391—21no—
23#11718391—21no—
24#11718391—21no—
25#11718391—21no—
26#11718142—21no—
27#11718119C412yes—
28#11718116—21no—
29#11718061C412yescomplemented
30#11718060C412yescomplemented
31C23×C4×C13C2311yescharacteristic
32C22×C22⋊D13C2×C411yescharacteristic
33C22×C4×D13C2×C411yescharacteristic
34C22×C8×C13—21no—
35C22×C8×C13C2×C411yescharacteristic
36C22×C8×C13C2×C411yescharacteristic
37C2×C13×C22⋊C4C2×C412yes—
38C2×C42×C13—21no—
39C2×C22⋊Dic13C2×C412yes—
40C2×C22⋊Dic13C2×C411yescharacteristic
41C4×C22⋊D13—21no—
42C4×C22⋊D13—21no—
43C4×C22⋊D13—21no—
44C4×C22⋊D13—21no—
45C2×#6103C2×C411yescharacteristic
46C2×#6101C2×C411yescharacteristic
47C2×C4×Dic13—21no—
48C2×C4×Dic13C2×C411yescharacteristic
49C22×#1055—21no—
50C22×#1055—42no—
51C22×#1055C2×C411yescharacteristic
52C22×#1055C2×C411yescharacteristic
53C22×#1055D411yescharacteristic
54C22×#1055D411yescharacteristic
55C22×#1055D411yescharacteristic
56C22×#1055D411yescharacteristic
57C2×#6094—21no—
58C2×#6094—21no—
59C2×#6094—42no—
60C13×C22⋊C8—21no—
61C13×C22⋊C8—21no—
62C13×C22⋊C8—21no—
63C13×C22⋊C8C2×C412yes—
64C13×#95—21no—
65#88071—21no—
66C22⋊#1055—21no—
67C22⋊#1055C2×C412yes—
68#88060—21no—
69#88060—21no—
70#88055—21no—
71#88055—21no—
72#88055—42no—
73#88054—21no—
74#88054—21no—
75#88046—24no—
76C4×#1055—42no—
77#8161—131nomaximal, Sylow
78C24×C13C22×C411yescharacteristic
79C23×D13C4211yescharacteristic
80C22×C4×C13—22no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C22×C411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13#4111yescharacteristic
88C22×C4×C13#4111yescharacteristic
89C2×C22⋊D13—21no—
90C2×C22⋊D13—21no—
91C2×C22⋊D13—22no—
92C2×C22⋊D13—22no—
93C22×Dic13—22no—
94C22×Dic13C4211yescharacteristic
95C22×Dic13C4211yescharacteristic
96C22×Dic13C4211yescharacteristic
97C2×C4×D13—21no—
98C2×C4×D13—21no—
99C2×C4×D13—41no—
100C2×C4×D13—41no—
101C2×C8×C13—21no—
102C2×C8×C13—21no—
103C2×C8×C13—22no—
104C2×C8×C13—41no—
105C2×C8×C13—41no—
106C2×C8×C13—41no—
107C2×C8×C13—41no—
108C13×C22⋊C4—22no—
109C13×C22⋊C4M1614yescomplemented
110C42×C13—41no—
111C42×C13—41no—
112C22⋊Dic13—21no—
113C22⋊Dic13—21no—
114C22⋊Dic13—22no—
115C22⋊Dic13—22no—
116#6103—21no—
117#6103—21no—
118#6101—21no—
119#6101—21no—
120C4×Dic13—21no—
121C4×Dic13—21no—
122C4×Dic13—41no—
123C4×Dic13—41no—
124C2×#1055—22no—
125C2×#1055—22no—
126C2×#1055—22no—
127C2×#1055—22no—
128C2×#1055—41no—
129C2×#1055—41no—
130C2×#1055—41no—
131C2×#1055—41no—
132C2×#1055—41no—
133C2×#1055C22⋊C411yescharacteristic
134C2×#1055C22⋊C411yescharacteristic
135C2×#1055C22⋊C411yescharacteristic
136C2×#1055C22⋊C411yescharacteristic
137#6094—42no—
138#6094—42no—
139C2×#435—131no—
140C4×#99—131no—
141#1752—131no—
142C8×C22⋊C4—131no—
143#1459—131no—
144#1282—131no—
145#1282D1311yescharacteristic, complemented
146C23×C13—41no—
147C23×C13—41no—
148C23×C13C2×C4211yescharacteristic
149C23×C13C4×D411yescharacteristic
150C23×C13C4×D411yescharacteristic
151C23×C13C2×M1612yes—
152C23×C13#13112yes—
153C22×D13—21no—
154C22×D13—21no—
155C22×D13—21no—
156C22×D13—41no—
157C22×D13—41no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—24no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—42no—
169C2×C4×C13—42no—
170C2×C4×C13C2×C22⋊C411yescharacteristic
171C2×C4×C13#11711yescharacteristic
172C2×C4×C13C4×D411yescharacteristic
173C2×C4×C13C4×D411yescharacteristic
174C22⋊D13—42no—
175C22⋊D13—42no—
176C2×Dic13—21no—
177C2×Dic13—21no—
178C2×Dic13—21no—
179C2×Dic13—21no—
180C2×Dic13—21no—
181C2×Dic13—41no—
182C2×Dic13—41no—
183C2×Dic13—42no—
184C2×Dic13—42no—
185C2×Dic13—42no—
186C4×D13—42no—
187C4×D13—41no—
188C4×D13—41no—
189C8×C13—42no—
190C8×C13—41no—
191C8×C13—41no—
192#1055—21no—
193#1055—21no—
194#1055—21no—
195#1055—42no—
196#1055#9912yescomplemented
197C22×M16—131no—
198C23×C8—131no—
199C2×C4×D4—131no—
200#435—261no—
201#435—261no—
202#435—261no—
203#435—261no—
204C2×C4⋊C8—131no—
205C2×#99—132no—
206C2×C22⋊C8—131no—
207C2×C22⋊C8—131no—
208C2×C22⋊C8C2×D1311yescharacteristic
209C2×C22⋊C8C2×D1311yescharacteristic
210C2×#97—131no—
211C2×#97—261no—
212C2×C4×C8—261no—
213C4×C22⋊C4—131no—
214C4×C22⋊C4C2×D1311yescharacteristic
215#342—132no—
216#336—261no—
217#336—261no—
218#324—132no—
219#323—132no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—42no—
227C22×C13—42no—
228C22×C13C4×C22⋊C411yescharacteristic
229C22×C13C4×M1611yescharacteristic
230C22×C13#40511yescharacteristic
231C22×C13#43512yes—
232C22×C13#43612yes—
233C2×D13—41no—
234C2×D13—41no—
235C2×D13—41no—
236C2×D13—81no—
237C2×D13—81no—
238C4×C13—21no—
239C4×C13—21no—
240C4×C13—21no—
241C4×C13—44no—
242C4×C13C2×#9911yescharacteristic
243C4×C13#41011yescharacteristic
244Dic13—41no—
245Dic13—41no—
246Dic13—41no—
247Dic13—82no—
248C22×D4—131no—
249C23×C4—131no—
250C23×C4C22×D1311yescharacteristic
251C2×M16—261no—
252C2×M16—261no—
253C2×M16—522no—
254C22×C8—21no—
255C22×C8—131no—
256C22×C8—131no—
257C22×C8—131no—
258C22×C8—131no—
259C22×C8—131no—
260C22×C8—131no—
261C22×C8—261no—
262C22×C8—522no—
263C22×C8C4×D1311yescharacteristic
264C22×C8C4×D1311yescharacteristic
265C4×D4—261no—
266C4×D4—261no—
267C4×D4—261no—
268C4×D4—261no—
269C2×C4⋊C4—131no—
270C2×C22⋊C4—131no—
271C2×C22⋊C4—131no—
272C2×C22⋊C4—132no—
273C2×C22⋊C4C4×D1312yes—
274C2×C42—21no—
275C2×C42—131no—
276C2×C42—261no—
277C4⋊C8—261no—
278C4⋊C8—261no—
279#99—264no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—132no—
284C22⋊C8—261no—
285C22⋊C8—261no—
286C22⋊C8—261no—
287C22⋊C8C4×D1312yes—
288#97—261no—
289#97—261no—
290#97—522no—
291C4×C8—522no—
292#95—21no—
293#95—261no—
294C2×C13—22no—
295C2×C13—22no—
296C2×C13—21no—
297C2×C13—21no—
298C2×C13#175311yescharacteristic
299C2×C13C4×#9911yescharacteristic
300C2×C13#175711yescharacteristic
301D13—81no—
302C24—131no—
303C24C2×C4×D1311yescharacteristic
304C2×D4—261no—
305C2×D4—261no—
306C2×D4—262no—
307C2×D4—262no—
308C22×C4—22no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—131no—
312C22×C4—131no—
313C22×C4—131no—
314C22×C4—261no—
315C22×C4—261no—
316C22×C4—262no—
317C22×C4—521no—
318C22×C4—521no—
319C22×C4C2×C4×D1311yescharacteristic
320C22×C4C2×C4×D1311yescharacteristic
321C22×C4D4×D1311yescharacteristic
322C22×C4D4×D1311yescharacteristic
323C22×C4#612911yescharacteristic
324C22×C4#613111yescharacteristic
325M16—522no—
326M16—522no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—131no—
335C2×C8—131no—
336C2×C8—131no—
337C2×C8—131no—
338C2×C8—262no—
339C2×C8—262no—
340C2×C8—262no—
341C2×C8—262no—
342C2×C8—521no—
343C2×C8—521no—
344C2×C8—521no—
345C2×C8—521no—
346C2×C8—521no—
347C4⋊C4—261no—
348C4⋊C4—261no—
349C22⋊C4—22no—
350C22⋊C4—261no—
351C22⋊C4—261no—
352C22⋊C4—261no—
353C22⋊C4—261no—
354C22⋊C4—262no—
355C22⋊C4—262no—
356C22⋊C4#609414yescomplemented
357C42—41no—
358C42—41no—
359C42—261no—
360C42—261no—
361C42—521no—
362C42—521no—
363C13#816111yescharacteristic, complemented, Sylow
364C23—41no—
365C23—41no—
366C23—261no—
367C23—261no—
368C23—261no—
369C23—521no—
370C23—521no—
371C23C42×D1311yescharacteristic
372C23#8813511yescharacteristic
373C23#8814711yescharacteristic
374C23C2×#609412yes—
375C23#8816112yes—
376D4—522no—
377D4—522no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—24no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—261no—
391C2×C4—261no—
392C2×C4—261no—
393C2×C4—261no—
394C2×C4—261no—
395C2×C4—522no—
396C2×C4—521no—
397C2×C4—521no—
398C2×C4—521no—
399C2×C4—521no—
400C2×C4—522no—
401C2×C4—522no—
402C2×C4—522no—
403C2×C4C22⋊C4×D1311yescharacteristic
404C2×C4#8813511yescharacteristic
405C2×C4#8814611yescharacteristic
406C2×C4#8814711yescharacteristic
407C8—42no—
408C8—41no—
409C8—41no—
410C8—132no—
411C8—261no—
412C8—261no—
413C8—261no—
414C8—522no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—42no—
422C22—42no—
423C22—521no—
424C22—521no—
425C22—521no—
426C22—1041no—
427C22—1041no—
428C22#1171832711yescharacteristic
429C22C4×#609411yescharacteristic
430C22#1171836911yescharacteristic
431C22#1171839112yes—
432C22#1171849912yes—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—44no—
437C4—521no—
438C4—521no—
439C4—521no—
440C4—1042no—
441C4#1171840111yescharacteristic
442C4D13×#9911yescharacteristic
443C2—22no—
444C2—22no—
445C2—21no—
446C2—21no—
447C2—1041no—
448C2#1311461611yescharacteristic
449C2#1311462311yescharacteristic
450C2#1311463511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC23×C13C2×C42
FrattiniC23×C4C22×D13
FittingC13×#1282C2
socleC22×C13C4×C22⋊C4
prime radicalC22×C22⋊D13C2×C4
cosocleC23×C4×C13C23
hypercenter#1282D13
hypocenterC13#8161
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
3. #13114615C2semidirect
4. C22⋊C4×#1055C2semidirect
6. #13112683C2semidirect
7. C13×#1282C2semidirect
10. C22×#6094C4semidirect
16. C2×#88060C4semidirect
18. C2×#88055C4semidirect
19. C2×#88054C4semidirect
29. #11718061C4semidirect
30. #11718060C4semidirect
109. C13×C22⋊C4M16semidirect
145. #1282D13semidirect
196. #1055#99semidirect
356. C22⋊C4#6094semidirect
363. C13#8161semidirect

Maximal subgroups

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

subgroupindex
C2×#117183912
C4×#880462
#131146152
C22⋊C4×#10552
#131131522
#131126832
C13×#12822
#816113