Finite Group Databasebeta

← #15761181

Subgroups — #15761181

Order 3328.

466 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115629C211yesmaximal, characteristic
2#13115552C211yesmaximal, characteristic, complemented
3C4×#88061C211yesmaximal, characteristic
4C2×#11718075C211yesmaximal, characteristic
5C2×C8×#1055C211yesmaximal, characteristic, complemented
6#13112675C211yesmaximal, characteristic, complemented
7C13×#1277C211yesmaximal, characteristic, complemented
8C2×C4×D52C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C2×#88061C411yescharacteristic
13C2×#88061C411yescharacteristic
14C2×#88060—21no—
15C2×#88060—21no—
16C2×#88054—21no—
17C4×C4⋊Dic13C2211yescharacteristic
18C2×C4×#1055C2211yescharacteristic
19C2×C4×#1055C2211yescharacteristic
20#11718143C411yescharacteristic
21#11718143C411yescharacteristic
22#11718142—21no—
23#11718075—22no—
24C8×#1055—22no—
25C22×D52C2×C411yescharacteristic
26C22×C4×D13—21no—
27C22×C8×C13—21no—
28C22×C8×C13—21no—
29C22×C8×C13C2×C411yescharacteristic
30C22×C8×C13C2×C411yescharacteristic
31C2×C42×C13C2311yescharacteristic
32C2×#6103—21no—
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4×Dic13—21no—
37C22×#1055—21no—
38C22×#1055D411yescharacteristic
39C22×#1055D411yescharacteristic
40C4×D52—21no—
41C4×D52—21no—
42C4×D52—21no—
43C4×D52—21no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C4×C8×C13—21no—
49C4×C8×C13—21no—
50#88071—21no—
51#88061—22no—
52#88061C814yescomplemented
53#88060—42no—
54#88060—42no—
55#88054—42no—
56C4×#1055—21no—
57C4×#1055—21no—
58C4×#1055—21no—
59C4×#1055D412yes—
60#9554—131nomaximal, Sylow
61C23×D13—21no—
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13#4111yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C2×D52—21no—
69C2×D52—21no—
70C2×D52—21no—
71C2×D52—21no—
72C2×D52—21no—
73C2×D52C2×C812yes—
74C2×C4×D13—41no—
75C2×C4×D13—41no—
76C2×C4×D13—41no—
77C2×C4×D13—41no—
78C2×C4×D13—41no—
79C2×C4×D13—41no—
80C2×C8×C13—21no—
81C2×C8×C13—21no—
82C2×C8×C13—21no—
83C2×C8×C13—21no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C2×C8×C13—41no—
90C2×C8×C13C2×C812yes—
91C2×C8×C13M1612yes—
92C42×C13C2×D411yescharacteristic
93C42×C13#4111yescharacteristic
94C42×C13#4111yescharacteristic
95C42×C13#4111yescharacteristic
96#6103—41no—
97#6103—41no—
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102C4⋊Dic13—21no—
103C4⋊Dic13C2×C812yes—
104C4×Dic13—41no—
105C4×Dic13—41no—
106C2×#1055—22no—
107C2×#1055—22no—
108C2×#1055—21no—
109C2×#1055—21no—
110C2×#1055—22no—
111C2×#1055—21no—
112C2×#1055—21no—
113C2×#1055D812yes—
114C2×#1055SD1612yes—
115#1954—131no—
116#1939—131no—
117C4×#102—131no—
118C2×D4⋊C8—131no—
119C2×C82—131no—
120#1279—131no—
121#1277D1311yescharacteristic, complemented
122C23×C13C4×D411yescharacteristic
123C22×D13—22no—
124C22×D13—41no—
125C22×D13—41no—
126C22×D13—41no—
127C22×D13—41no—
128C22×D13—41no—
129C22×D13—41no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13#11711yescharacteristic
133C2×C4×C13C4×D411yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12311yescharacteristic
136C2×C4×C13#12411yescharacteristic
137C2×C4×C13#12611yescharacteristic
138C2×C4×C13C22×C811yescharacteristic
139C2×C4×C13C2×M1611yescharacteristic
140C2×C4×C13#13111yescharacteristic
141C2×C4×C13#13111yescharacteristic
142C2×C4×C13C2×D811yescharacteristic
143C2×C4×C13C2×SD1611yescharacteristic
144C2×C4×C13#13511yescharacteristic
145C2×C4×C13#13511yescharacteristic
146C2×Dic13—22no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155D52—22no—
156D52—22no—
157D52—41no—
158D52—41no—
159C4×D13—81no—
160C4×D13—81no—
161C4×D13—81no—
162C4×D13—81no—
163C8×C13—22no—
164C8×C13—22no—
165C8×C13—81no—
166C8×C13—81no—
167#1055—24no—
168#1055—22no—
169#1055—22no—
170C2×C4×D4—131no—
171C2×C4⋊C8—261no—
172C2×C4⋊C8C2×D1311yescharacteristic
173C2×C4⋊C8C2×D1311yescharacteristic
174C2×#102—131no—
175C2×#102—131no—
176C2×C22⋊C8—261no—
177C2×C22⋊C8—261no—
178C2×C4×C8—131no—
179C2×C4×C8—131no—
180C2×C4×C8C2×D1311yescharacteristic
181C4×C4⋊C4—131no—
182#340—131no—
183#340—131no—
184#336—261no—
185D4⋊C8—262no—
186C82—262no—
187C22×C13#38811yescharacteristic
188C22×C13C8×D411yescharacteristic
189C22×C13#43611yescharacteristic
190C22×C13C4×D811yescharacteristic
191C22×C13C4×SD1611yescharacteristic
192C22×C13#44311yescharacteristic
193C22×C13#44311yescharacteristic
194C2×D13—42no—
195C2×D13—42no—
196C2×D13—42no—
197C2×D13—81no—
198C2×D13—81no—
199C2×D13—81no—
200C2×D13—81no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13#43111yescharacteristic
204C4×C13#43311yescharacteristic
205C4×C13C8×D411yescharacteristic
206C4×C13#43511yescharacteristic
207C4×C13#46511yescharacteristic
208C4×C13#46611yescharacteristic
209C4×C13#48611yescharacteristic
210C4×C13#48811yescharacteristic
211Dic13—42no—
212Dic13—81no—
213Dic13—81no—
214C22×D4—131no—
215C23×C4—261no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—131no—
219C22×C8—131no—
220C22×C8—261no—
221C22×C8C4×D1311yescharacteristic
222C22×C8C4×D1311yescharacteristic
223C4×D4—261no—
224C4×D4—261no—
225C4×D4—261no—
226C4×D4—261no—
227C2×C4⋊C4—131no—
228C2×C4⋊C4—131no—
229C2×C4⋊C4—131no—
230C2×C22⋊C4—261no—
231C2×C42—261no—
232C2×C42C22×D1311yescharacteristic
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—522no—
238#102—134no—
239#102—262no—
240C22⋊C8—522no—
241C22⋊C8—522no—
242C4×C8—21no—
243C4×C8—21no—
244C4×C8—132no—
245C4×C8—261no—
246C4×C8—261no—
247C4×C8—261no—
248#95—261no—
249C2×C13C8×D811yescharacteristic
250C2×C13C8×SD1611yescharacteristic
251C2×C13#158911yescharacteristic
252C2×C13#159011yescharacteristic
253C2×C13#192311yescharacteristic
254C2×C13#193411yescharacteristic
255C2×C13#193711yescharacteristic
256D13—82no—
257C24—261no—
258C2×D4—132no—
259C2×D4—261no—
260C2×D4—261no—
261C2×D4—261no—
262C2×D4—261no—
263C2×D4—261no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4—521no—
268C22×C4—521no—
269C22×C4—521no—
270C22×C4—521no—
271C22×C4—521no—
272C22×C4—521no—
273C22×C4C2×C4×D1311yescharacteristic
274C22×C4D4×D1311yescharacteristic
275C22×C4#613111yescharacteristic
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—132no—
287C2×C8—132no—
288C2×C8—262no—
289C2×C8—262no—
290C2×C8—261no—
291C2×C8—261no—
292C2×C8—262no—
293C2×C8—261no—
294C2×C8—261no—
295C2×C8C8×D1312yes—
296C2×C8#609412yes—
297C4⋊C4—132no—
298C4⋊C4—261no—
299C4⋊C4—261no—
300C4⋊C4—261no—
301C4⋊C4—261no—
302C4⋊C4—261no—
303C22⋊C4—521no—
304C22⋊C4—521no—
305C42—521no—
306C42—521no—
307C42#612711yescharacteristic
308C42#612711yescharacteristic
309C42D4×D1311yescharacteristic
310C42#612911yescharacteristic
311C13#955411yescharacteristic, complemented, Sylow
312C23—262no—
313C23—521no—
314C23—521no—
315C23—521no—
316C23—521no—
317C23—521no—
318C23—521no—
319C23#8814711yescharacteristic
320D4—262no—
321D4—262no—
322D4—521no—
323D4—521no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—262no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4—1041no—
336C2×C4—1041no—
337C2×C4—1041no—
338C2×C4—1041no—
339C2×C4#8812611yescharacteristic
340C2×C4#8813511yescharacteristic
341C2×C4#8813811yescharacteristic
342C2×C4#8813911yescharacteristic
343C2×C4#8814811yescharacteristic
344C2×C4#8815211yescharacteristic
345C2×C4C2×C8×D1311yescharacteristic
346C2×C4C2×#609411yescharacteristic
347C2×C4#8816111yescharacteristic
348C2×C4#8816111yescharacteristic
349C2×C4D8×D1311yescharacteristic
350C2×C4SD16×D1311yescharacteristic
351C2×C4#8817011yescharacteristic
352C2×C4#8817311yescharacteristic
353C8—22no—
354C8—22no—
355C8—81no—
356C8—81no—
357C8—264no—
358C8—262no—
359C8—262no—
360C22—522no—
361C22—522no—
362C22—522no—
363C22—1041no—
364C22—1041no—
365C22—1041no—
366C22—1041no—
367C22#1171833011yescharacteristic
368C22#1171849511yescharacteristic
369C22#1171849911yescharacteristic
370C22#1171851311yescharacteristic
371C22#1171853311yescharacteristic
372C22#1171855611yescharacteristic
373C22#1171855611yescharacteristic
374C4—21no—
375C4—21no—
376C4—522no—
377C4—1041no—
378C4—1041no—
379C4#1171834611yescharacteristic
380C4#1171837011yescharacteristic
381C4#1171838611yescharacteristic
382C4#1171839111yescharacteristic
383C4#1171842111yescharacteristic
384C4#1171843611yescharacteristic
385C4#1171846111yescharacteristic
386C4#1171846811yescharacteristic
387C2—1042no—
388C2#1311363011yescharacteristic
389C2#1311363511yescharacteristic
390C2#1311372011yescharacteristic
391C2#1311372511yescharacteristic
392C2#1311544011yescharacteristic
393C2#1311551711yescharacteristic
394C2#1311553811yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1277C2
socleC23×C13C4×D4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1277D13
hypocenterC13#9554
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. #13115552C2semidirect
5. C2×C8×#1055C2semidirect
6. #13112675C2semidirect
7. C13×#1277C2semidirect
52. #88061C8semidirect
121. #1277D13semidirect
311. C13#9554semidirect

Maximal subgroups

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

subgroupindex
#131156292
#131155522
C4×#880612
C2×#117180752
C2×C8×#10552
#131126752
C13×#12772
#955413