Finite Group Databasebeta

← #15832210

Subgroups — #15832210

Order 3328.

616 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123962C211yesmaximal, characteristic
2#13123957C211yesmaximal, characteristic
3#13123792C211yesmaximal, characteristic
4#13113625C211yesmaximal, characteristic, complemented
5#13113620C212yesmaximal, complemented
6#13113618C212yesmaximal, complemented
7#13113598C212yesmaximal, complemented
8#13113591C211yesmaximal, characteristic, complemented
9#13113582C211yesmaximal, characteristic, complemented
10D13×#334C212yesmaximal, complemented
11C13×#1574C211yesmaximal, characteristic, complemented
12C4×#6127C2211yescharacteristic
13C13×#431C2211yescharacteristic
14C13×#431C2211yescharacteristic
15C13×#423C2211yescharacteristic
16#11718788—22no—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19C2×C4×#1055C2211yescharacteristic
20#11718496C2212yes—
21#11718496C2212yes—
22#11718495—21no—
23#11718495C411yescharacteristic
24#11718495C411yescharacteristic
25D13×C4⋊C8C2212yes—
26D13×C4⋊C8C2212yes—
27#11718492—21no—
28#11718491C411yescharacteristic
29#11718491C411yescharacteristic
30#11718389—22no—
31#11718386C412yes—
32#11718386C412yes—
33C8×D52—21no—
34#11718346C2212yes—
35C4×C8×D13C2212yes—
36#11718340—21no—
37C13×#335C2212yes—
38C13×#334C2212yes—
39#11718072C2212yes—
40#11718072C2211yescharacteristic
41#11718072C2212yes—
42#11718072C2211yescharacteristic
43#11718071C2211yescharacteristic
44#11718071C2211yescharacteristic
45#11718050C2212yes—
46#11718049C2212yes—
47C2×#6127Q811yescharacteristic
48C2×C13×M16—21no—
49C2×C42×C13C2311yescharacteristic
50C4×C22⋊D13C2×C412yes—
51C4×C22⋊D13D412yes—
52#88180Q811yescharacteristic
53C2×#6099—21no—
54C22×#1055C2×C411yescharacteristic
55C22×#1055C2×C411yescharacteristic
56C2×C8×D13—22no—
57C2×C8×D13—22no—
58C2×C8×D13C2×C412yes—
59C2×C8×D13C2×C412yes—
60C4×D52C2×C411yescharacteristic
61C4×D52D411yescharacteristic
62#88126Q812yes—
63C42×D13C2312yes—
64C4×Dic26C2×C411yescharacteristic
65C4×Dic26D411yescharacteristic
66C13×C4⋊C8—21no—
67C13×C4⋊C8C2×C411yescharacteristic
68C13×C4⋊C8C2×C411yescharacteristic
69C13×C4⋊C8C2311yescharacteristic
70C13×C4⋊C8C2312yes—
71C13×C4⋊C8C2311yescharacteristic
72C13×C22⋊C8—21no—
73C13×C22⋊C8C2×C412yes—
74C4×C8×C13—21no—
75C4×C8×C13C2312yes—
76C22⋊#1055—21no—
77#88060—22no—
78#88060—22no—
79#88060C2×C412yes—
80#88060C2×C412yes—
81#88055—22no—
82#88055—22no—
83#88054—22no—
84#88054—22no—
85#88054C2×C412yes—
86#88054C2×C412yes—
87C8×Dic13C2×C412yes—
88C8×Dic13C2×C412yes—
89C4⋊#1055—21no—
90C4⋊#1055C2311yescharacteristic
91C4⋊#1055C2312yes—
92C4⋊#1055C2311yescharacteristic
93C4×#1055—21no—
94C4×#1055C2×C411yescharacteristic
95C4×#1055C2×C411yescharacteristic
96C4×#1055C2311yescharacteristic
97C4×#1055C2311yescharacteristic
98#17834—131nomaximal, Sylow
99C22×C4×C13C22×C411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×Q811yescharacteristic
102C2×C22⋊D13C4⋊C412yes—
103#6127—24no—
104C2×D52C4⋊C411yescharacteristic
105C2×C4×D13C22×C412yes—
106C2×C4×D13C2×D412yes—
107C2×C4×D13C2×Q812yes—
108C2×Dic26C4⋊C411yescharacteristic
109C13×M16—81no—
110C2×C8×C13—21no—
111C2×C8×C13—21no—
112C2×C8×C13—22no—
113C2×C8×C13C22×C412yes—
114C2×C8×C13C22×C412yes—
115C42×C13C22×C411yescharacteristic
116C42×C13C2×D411yescharacteristic
117C42×C13C2×Q811yescharacteristic
118C42×C13C2411yescharacteristic
119C22⋊Dic13C4⋊C412yes—
120#6103C4⋊C412yes—
121#6103C4⋊C412yes—
122C4⋊Dic13C4⋊C411yescharacteristic
123C4⋊Dic13C4⋊C411yescharacteristic
124#6101C4⋊C412yes—
125#6101C4⋊C412yes—
126C4×Dic13C22×C412yes—
127C4×Dic13C2×D412yes—
128C4×Dic13C2×Q812yes—
129#6099—81no—
130C2×#1055—22no—
131C2×#1055—21no—
132C2×#1055—21no—
133C2×#1055—22no—
134C2×#1055—41no—
135C2×#1055C22×C411yescharacteristic
136C2×#1055C22×C411yescharacteristic
137C2×#1055C22×C411yescharacteristic
138C2×#1055C22×C411yescharacteristic
139C8×D13—24no—
140C8×D13—42no—
141C8×D13—82no—
142C8×D13—82no—
143#2990—131no—
144#2990—131no—
145C8×#41—131no—
146#1574—131no—
147#1574D1311yescharacteristic, complemented
148#1573—132no—
149#1573—132no—
150#1568—132no—
151#1566—131no—
152#1564—131no—
153C2×#334—132no—
154C23×C13C2×C4⋊C411yescharacteristic
155C22×D13C2×C4⋊C412yes—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—22no—
161C2×C4×C13C2×C4⋊C411yescharacteristic
162C2×C4×C13C2×C4⋊C411yescharacteristic
163C2×C4×C13C2×C4⋊C411yescharacteristic
164C2×C4×C13C23×C411yescharacteristic
165C2×C4×C13C22×D411yescharacteristic
166C2×C4×C13C22×Q811yescharacteristic
167C22⋊D13—24no—
168C2×Dic13C2×C4⋊C412yes—
169C2×Dic13C2×C4⋊C412yes—
170C2×Dic13C2×C4⋊C412yes—
171D52#10814yes—
172C4×D13—24no—
173C4×D13—22no—
174C4×D13—22no—
175C4×D13—22no—
176C4×D13—22no—
177Dic26—22no—
178C8×C13—22no—
179C8×C13—22no—
180C8×C13—41no—
181C8×C13—42no—
182C8×C13—41no—
183#1055—21no—
184#1055—21no—
185#1055—21no—
186#1055—41no—
187#1055—42no—
188#1055—41no—
189#1055#13112yes—
190C4×#41—131no—
191#446—261no—
192#446—261no—
193C8×Q8—131no—
194C8×Q8—131no—
195#435—262no—
196#435—262no—
197C8×D4—131no—
198C8×D4—131no—
199C8×D4—132no—
200C8×D4—132no—
201C8×D4—261no—
202C8×D4—261no—
203#432—132no—
204#432—132no—
205#431—132no—
206#431—131no—
207#431C2×D1311yescharacteristic
208#431C2×D1311yescharacteristic
209#423—131no—
210#423C2×D1311yescharacteristic
211C2×C4⋊C8—132no—
212C2×C4⋊C8—132no—
213C2×C4×C8—131no—
214C2×C4×C8—132no—
215#335—131no—
216#335—131no—
217#335—132no—
218#335C2×D1312yes—
219#334—131no—
220#334—132no—
221#334—131no—
222#334—132no—
223#334—132no—
224#334C2×D1312yes—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—21no—
228C22×C13C22×C4⋊C411yescharacteristic
229C2×D13—22no—
230C2×D13—22no—
231C2×D13C2×#10814yes—
232C4×C13—21no—
233C4×C13—21no—
234C4×C13—21no—
235C4×C13C2×#10812yes—
236C4×C13C2×#13111yescharacteristic
237C4×C13#56811yescharacteristic
238C4×C13#57711yescharacteristic
239C4×C13#57711yescharacteristic
240Dic13—22no—
241Dic13—22no—
242Dic13—22no—
243C2×#41—131no—
244C2×M16—21no—
245C2×M16—261no—
246C22×C8—131no—
247C22×C8—131no—
248C22×C8—132no—
249C22×C8—132no—
250C22×C8—262no—
251C22×C8—262no—
252C4×Q8—131no—
253C4×Q8—131no—
254C4×D4—132no—
255C4×D4—132no—
256C4×D4—131no—
257C4×D4—131no—
258#117—131no—
259#117—132no—
260C2×C42—132no—
261C2×C42C22×D1311yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—132no—
264C4⋊C8—132no—
265C4⋊C8—131no—
266C4⋊C8—132no—
267C4⋊C8—131no—
268C4⋊C8—262no—
269C4⋊C8—262no—
270C4⋊C8—261no—
271C4⋊C8C4×D1311yescharacteristic
272C4⋊C8C4×D1311yescharacteristic
273C4⋊C8C22×D1312yes—
274C4⋊C8C22×D1311yescharacteristic
275C4⋊C8C22×D1311yescharacteristic
276C22⋊C8—21no—
277C22⋊C8—132no—
278C22⋊C8—132no—
279C22⋊C8—262no—
280C22⋊C8—262no—
281C22⋊C8—261no—
282C22⋊C8C4×D1312yes—
283#97—262no—
284#97—262no—
285C4×C8—21no—
286C4×C8—132no—
287C4×C8—132no—
288C4×C8—131no—
289C4×C8—131no—
290C4×C8—131no—
291C4×C8—131no—
292C4×C8—261no—
293C4×C8C22×D1312yes—
294C2×C13—41no—
295C2×C13#290611yescharacteristic
296C2×C13#291211yescharacteristic
297C2×C13C22×#10811yescharacteristic
298D13—24no—
299#41—264no—
300C2×Q8—131no—
301C2×D4—132no—
302C2×D4—131no—
303C22×C4—132no—
304C22×C4—132no—
305C22×C4—132no—
306C22×C4C2×C4×D1311yescharacteristic
307C22×C4D4×D1311yescharacteristic
308C22×C4Q8×D1311yescharacteristic
309M16—81no—
310M16—1041no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—22no—
314C2×C8—131no—
315C2×C8—131no—
316C2×C8—131no—
317C2×C8—131no—
318C2×C8—264no—
319C2×C8—262no—
320C2×C8—261no—
321C2×C8—261no—
322C2×C8—262no—
323C2×C8—522no—
324C2×C8—521no—
325C2×C8—1042no—
326C2×C8—1042no—
327C2×C8C2×C4×D1312yes—
328C2×C8C2×C4×D1312yes—
329C4⋊C4—132no—
330C4⋊C4—132no—
331C4⋊C4—131no—
332C4⋊C4—131no—
333C22⋊C4—132no—
334C22⋊C4—132no—
335C22⋊C4—132no—
336C42—132no—
337C42—132no—
338C42—132no—
339C42C2×C4×D1311yescharacteristic
340C42D4×D1311yescharacteristic
341C42Q8×D1311yescharacteristic
342C42C23×D1311yescharacteristic
343C13#1783411yescharacteristic, complemented, Sylow
344C23—132no—
345C23C4⋊C4×D1311yescharacteristic
346Q8—262no—
347D4—134no—
348D4—264no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—22no—
354C2×C4—132no—
355C2×C4—132no—
356C2×C4—132no—
357C2×C4—264no—
358C2×C4—262no—
359C2×C4—262no—
360C2×C4—262no—
361C2×C4—262no—
362C2×C4C4⋊C4×D1311yescharacteristic
363C2×C4C4⋊C4×D1311yescharacteristic
364C2×C4C4⋊C4×D1311yescharacteristic
365C2×C4C22×C4×D1311yescharacteristic
366C2×C4C2×D4×D1311yescharacteristic
367C2×C4C2×Q8×D1311yescharacteristic
368C8—22no—
369C8—22no—
370C8—41no—
371C8—42no—
372C8—41no—
373C8—132no—
374C8—261no—
375C8—261no—
376C8—261no—
377C8—521no—
378C8—521no—
379C8—522no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—134no—
384C22—262no—
385C22—262no—
386C22C2×C4⋊C4×D1311yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—262no—
391C4—262no—
392C4—262no—
393C4D13×#10812yes—
394C4D13×#13111yescharacteristic
395C4#1171945511yescharacteristic
396C4#1171948011yescharacteristic
397C4#1171948311yescharacteristic
398C2—41no—
399C2—264no—
400C2#1312340311yescharacteristic
401C2#1312343011yescharacteristic
402C2C2×D13×#10811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1574C2
socleC22×C13C22×C4⋊C4
prime radicalC2×#6127Q8
cosocleC42×C13C24
hypercenter#1574D13
hypocenterC13#17834
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
4. #13113625C2semidirect
5. #13113620C2semidirect
6. #13113618C2semidirect
7. #13113598C2semidirect
8. #13113591C2semidirect
9. #13113582C2semidirect
10. D13×#334C2semidirect
11. C13×#1574C2semidirect
147. #1574D13semidirect
343. C13#17834semidirect

Maximal subgroups

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

subgroupindex
#131239622
#131239572
#131237922
#131136252
#131136202
#131136182
#131135982
#131135912
#131135822
D13×#3342
C13×#15742
#1783413