Finite Group Databasebeta

← #15753919

Subgroups — #15753919

Order 3328.

522 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123530C211yesmaximal, characteristic
2C8×C22⋊Dic13C211yesmaximal, characteristic, complemented
3#13113328C211yesmaximal, characteristic
4#13113325C211yesmaximal, characteristic
5#13112724C211yesmaximal, characteristic, complemented
6#13112722C211yesmaximal, characteristic, complemented
7C13×#1752C211yesmaximal, characteristic, complemented
8C23×C8×C13C2211yescharacteristic
9#11719496C2211yescharacteristic
10C2×#88155C411yescharacteristic, complemented
11C2×C13×C22⋊C8C2211yescharacteristic
12C2×C13×#97—21no—
13C4×C13×C22⋊C4C2211yescharacteristic
14C4×C22⋊Dic13C2211yescharacteristic
15#11718868C2211yescharacteristic
16C2×C22⋊#1055C2211yescharacteristic
17#11718772—21no—
18#11718772—21no—
19#11718771C411yescharacteristic, complemented
20C8×C22⋊D13—21no—
21C8×C22⋊D13—21no—
22#11718763C411yescharacteristic, complemented
23#11718762C411yescharacteristic, complemented
24C2×C8×Dic13—21no—
25C13×#336—21no—
26#11718142—21no—
27#11718062C412yescomplemented
28#11718059C412yescomplemented
29#11718044C412yescomplemented
30#11718043C412yescomplemented
31C23×C4×C13C2311yescharacteristic
32C2×#6127C2×C411yescharacteristic
33C22×C8×C13—21no—
34C22×C8×C13—42no—
35C22×C8×C13C2×C411yescharacteristic
36C22×C8×C13C2×C411yescharacteristic
37C22×C8×C13D411yescharacteristic
38C22×C8×C13D411yescharacteristic
39C22×C8×C13D411yescharacteristic
40C22×C8×C13D411yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C42×C13—21no—
43#88207—21no—
44C2×C22⋊Dic13—21no—
45#88184C2×C411yescharacteristic
46#88184C2×C411yescharacteristic
47#88183—21no—
48C4×C22⋊D13—21no—
49C4×C22⋊D13—21no—
50#88180C2×C411yescharacteristic
51#88178C2×C411yescharacteristic
52#88178C2×C411yescharacteristic
53C2×C4×Dic13—21no—
54C2×#6099C2×C411yescharacteristic
55C2×#6099C2×C411yescharacteristic
56C22×#1055—21no—
57#88155—42no—
58C2×#6094—21no—
59C2×C8×D13—21no—
60C13×C22⋊C8—21no—
61C13×C22⋊C8C2×C412yes—
62C13×#97—42no—
63C13×#95C2×C412yes—
64#88071C2×C412yes—
65C22⋊#1055—21no—
66C22⋊#1055—21no—
67C22⋊#1055—21no—
68C22⋊#1055C2×C412yes—
69#88060—21no—
70#88060—21no—
71#88055—21no—
72#88054—21no—
73#88054—21no—
74C8×Dic13—21no—
75C8×Dic13—42no—
76#8240—131nomaximal, Sylow
77C24×C13#4111yescharacteristic
78C22×C4×C13—22no—
79C22×C4×C13—41no—
80C22×C4×C13—41no—
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13#4111yescharacteristic
87C2×C22⋊D13—21no—
88C2×C22⋊D13—21no—
89C2×C22⋊D13—21no—
90C22×Dic13—22no—
91#6127—41no—
92#6127—41no—
93C2×D52C4211yescharacteristic
94C2×C4×D13—21no—
95C2×Dic26C4211yescharacteristic
96C2×C8×C13—22no—
97C2×C8×C13—22no—
98C2×C8×C13—22no—
99C2×C8×C13—22no—
100C2×C8×C13—41no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C2×C8×C13—41no—
104C2×C8×C13—41no—
105C2×C8×C13C22⋊C411yescharacteristic
106C2×C8×C13C22⋊C411yescharacteristic
107C2×C8×C13C22⋊C411yescharacteristic
108C2×C8×C13C22⋊C411yescharacteristic
109C13×C22⋊C4—42no—
110C42×C13—41no—
111C42×C13—41no—
112C22⋊Dic13—24no—
113C22⋊Dic13—21no—
114C22⋊Dic13—21no—
115C22⋊Dic13—21no—
116#6103—21no—
117#6103—21no—
118C4⋊Dic13C4211yescharacteristic
119C4⋊Dic13C4211yescharacteristic
120#6101—21no—
121#6101—21no—
122C4×Dic13—21no—
123C4×Dic13—41no—
124C4×Dic13—41no—
125#6099—41no—
126#6099—41no—
127C2×#1055—21no—
128C2×#1055—21no—
129C2×#1055—22no—
130C2×#1055—41no—
131C2×#1055—41no—
132#6094—42no—
133C8×D13—42no—
134#2929—131no—
135#1752D1311yescharacteristic, complemented
136C8×C22⋊C4—131no—
137#1501—131no—
138#1501—131no—
139#1298—131no—
140#1297—131no—
141C23×C13—22no—
142C23×C13—22no—
143C23×C13—41no—
144C23×C13#11711yescharacteristic
145C23×C13C4×D411yescharacteristic
146C23×C13C4×D411yescharacteristic
147C22×D13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13C2×C4211yescharacteristic
161C2×C4×C13C2×C22⋊C411yescharacteristic
162C2×C4×C13C4×D411yescharacteristic
163C2×C4×C13C4×D411yescharacteristic
164C22⋊D13—42no—
165C22⋊D13—42no—
166C22⋊D13—42no—
167C2×Dic13—24no—
168C2×Dic13—21no—
169C2×Dic13—21no—
170C2×Dic13—21no—
171C2×Dic13—42no—
172C2×Dic13—42no—
173D52—41no—
174C4×D13—41no—
175C4×D13—41no—
176Dic26—41no—
177C8×C13—21no—
178C8×C13—21no—
179C8×C13—21no—
180C8×C13—42no—
181C8×C13#9912yes—
182#1055—42no—
183#1055—41no—
184#1055—41no—
185C2×#131—131no—
186C23×C8C2×D1311yescharacteristic
187#525—131no—
188#435—261no—
189#435—261no—
190C8×D4—261no—
191C8×D4—261no—
192#424—131no—
193#408—131no—
194#407—131no—
195C2×C22⋊C8—131no—
196C2×C22⋊C8C2×D1311yescharacteristic
197#405—131no—
198C2×#97—21no—
199C2×C4×C8—261no—
200C4×C22⋊C4—131no—
201C4×C22⋊C4C2×D1311yescharacteristic
202#336—21no—
203#336—261no—
204#328—132no—
205#328—132no—
206#327—132no—
207#327—132no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—44no—
216C22×C13C4×C22⋊C411yescharacteristic
217C22×C13#44312yes—
218C22×C13#44412yes—
219C2×D13—41no—
220C2×D13—41no—
221C2×D13—41no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—82no—
226C4×C13C2×#9911yescharacteristic
227C4×C13#41011yescharacteristic
228Dic13—44no—
229Dic13—41no—
230Dic13—41no—
231Dic13—41no—
232C2×#41—131no—
233C23×C4C22×D1311yescharacteristic
234#131—522no—
235C2×M16—131no—
236C2×M16—131no—
237C2×M16—261no—
238C22×C8—21no—
239C22×C8—42no—
240C22×C8—261no—
241C22×C8—261no—
242C22×C8C4×D1311yescharacteristic
243C22×C8C4×D1311yescharacteristic
244C22×C8D5211yescharacteristic
245C22×C8D5211yescharacteristic
246C22×C8C22⋊D1311yescharacteristic
247C22×C8C22⋊D1311yescharacteristic
248#123—261no—
249C22⋊Q8—131no—
250C22⋊Q8—131no—
251#121—131no—
252#121—131no—
253#120—261no—
254C4×D4—261no—
255C4×D4—261no—
256#117—131no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—261no—
259C2×C42—21no—
260C2×C42—261no—
261C4⋊C8—261no—
262C4⋊C8—261no—
263C22⋊C8—21no—
264C22⋊C8—132no—
265C22⋊C8—261no—
266C22⋊C8—261no—
267C22⋊C8—261no—
268C22⋊C8—261no—
269C22⋊C8—261no—
270C22⋊C8C4×D1312yes—
271#97—42no—
272#97—261no—
273C4×C8—261no—
274C4×C8—522no—
275#95—132no—
276#95C4×D1312yes—
277C2×C13—22no—
278C2×C13—22no—
279C2×C13—41no—
280C2×C13C4×#9911yescharacteristic
281C2×C13#176411yescharacteristic
282C2×C13#176511yescharacteristic
283D13—81no—
284C24#612711yescharacteristic
285#41—521no—
286#41—521no—
287C2×Q8—131no—
288C2×D4—131no—
289C2×D4—261no—
290C2×D4—261no—
291C2×D4—261no—
292C22×C4—22no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—262no—
296C22×C4—261no—
297C22×C4C2×C4×D1311yescharacteristic
298C22×C4C2×C4×D1311yescharacteristic
299C22×C4C2×C4×D1311yescharacteristic
300C22×C4C2×D5211yescharacteristic
301C22×C4#612711yescharacteristic
302C22×C4C2×C22⋊D1311yescharacteristic
303M16—522no—
304M16—521no—
305M16—521no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—262no—
316C2×C8—261no—
317C2×C8—261no—
318C2×C8—522no—
319C2×C8—521no—
320C2×C8—521no—
321C2×C8#610311yescharacteristic
322C2×C8#610311yescharacteristic
323C2×C8#610311yescharacteristic
324C2×C8#610311yescharacteristic
325C4⋊C4—131no—
326C4⋊C4—131no—
327C4⋊C4—261no—
328C4⋊C4—261no—
329C22⋊C4—42no—
330C22⋊C4—264no—
331C22⋊C4—261no—
332C22⋊C4—261no—
333C22⋊C4—261no—
334C22⋊C4—261no—
335C22⋊C4—261no—
336C42—41no—
337C42—41no—
338C42—261no—
339C42—521no—
340C42—521no—
341C13#824011yescharacteristic, complemented, Sylow
342C23—22no—
343C23—22no—
344C23—41no—
345C23—261no—
346C23#8812611yescharacteristic
347C23C4×D5211yescharacteristic
348C23C4×C22⋊D1311yescharacteristic
349Q8—521no—
350D4—521no—
351D4—522no—
352D4—522no—
353D4—522no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—264no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—522no—
371C2×C4—522no—
372C2×C4—521no—
373C2×C4—521no—
374C2×C4C42×D1311yescharacteristic
375C2×C4C4×D5211yescharacteristic
376C2×C4C2×#610311yescharacteristic
377C2×C4C4×C22⋊D1311yescharacteristic
378C8—21no—
379C8—21no—
380C8—21no—
381C8—42no—
382C8—522no—
383C8—521no—
384C8—521no—
385C8#8804612yes—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—521no—
395C22—521no—
396C22—521no—
397C22#1171837812yes—
398C22C4×#610311yescharacteristic
399C22#1171880512yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—82no—
404C4—524no—
405C4—521no—
406C4—521no—
407C4—521no—
408C4C2×#8804611yescharacteristic
409C4#1171866711yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—1041no—
414C2C4×#8804611yescharacteristic
415C2#1311467511yescharacteristic
416C2#1311468011yescharacteristic
subgroupG/H
centerC2×C4C2×#6103
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC13×#1752C2
socleC22×C13C4×C22⋊C4
prime radical#11719496C22
cosocleC23×C4×C13C23
hypercenter#1752D13
hypocenterC13#8240
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. C8×C22⋊Dic13C2semidirect
5. #13112724C2semidirect
6. #13112722C2semidirect
7. C13×#1752C2semidirect
10. C2×#88155C4semidirect
19. #11718771C4semidirect
22. #11718763C4semidirect
23. #11718762C4semidirect
27. #11718062C4semidirect
28. #11718059C4semidirect
29. #11718044C4semidirect
30. #11718043C4semidirect
135. #1752D13semidirect
341. C13#8240semidirect

Maximal subgroups

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

subgroupindex
#131235302
C8×C22⋊Dic132
#131133282
#131133252
#131127242
#131127222
C13×#17522
#824013