Finite Group Databasebeta

← #14722900

Subgroups — #14722900

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077733C211yesmaximal, characteristic
2#13077727C211yesmaximal, characteristic
3#13067405C212yesmaximal, complemented
4#13067401C212yesmaximal, complemented
5#13067396C212yesmaximal, complemented
6#13067387C212yesmaximal, complemented
7#13067368C211yesmaximal, characteristic, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067364C211yesmaximal, characteristic, complemented
10C2×#10622095C211yesmaximal, characteristic, complemented
11C11×#2922C211yesmaximal, characteristic
12C4×C11×#41C2211yescharacteristic
13C11×#433C414yes—
14C11×#431C2212yes—
15C11×#431C2212yes—
16C11×#424C412yes—
17C11×#408C412yes—
18C4×C11×M16C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20#10622637—21no—
21Q8×C11⋊C8—21no—
22#10622625—21no—
23#10622624—22no—
24D4×C11⋊C8—22no—
25D4×C11⋊C8—21no—
26#10622539C2212yes—
27#10622538C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622538C2212yes—
30#10622537C2212yes—
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2212yes—
34#10622096C2211yescharacteristic
35#10622096C2211yescharacteristic
36#10622096C2212yes—
37#10622096C2212yes—
38#10622095C2212yes—
39#10622095C2212yes—
40#10622095C2211yescharacteristic
41#10622095C2211yescharacteristic
42#10622095C2212yes—
43#10622095C2212yes—
44C2×C11×#41C2×C411yescharacteristic
45C2×C11×M16C2×C412yes—
46C22×C8×C11C2×C412yes—
47C4×Q8×C11D411yescharacteristic
48C4×Q8×C11Q811yescharacteristic
49C4×D4×C11D412yes—
50C4×D4×C11D411yescharacteristic
51C4×D4×C11Q812yes—
52C4×D4×C11Q811yescharacteristic
53C11×#117C2×C411yescharacteristic
54C11×#117C2×C412yes—
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2312yes—
57C2×#4318—22no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—22no—
60C22×C11⋊C8—21no—
61C11×C4⋊C8C2×C414yes—
62C11×C4⋊C8C2×C414yes—
63C11×C22⋊C8C2×C414yes—
64C11×C22⋊C8C2×C414yes—
65C11×#97C2×C412yes—
66C4×C8×C11C2×C412yes—
67C4×C8×C11C2311yescharacteristic
68C4×C8×C11C2311yescharacteristic
69C4×C8×C11C2312yes—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—22no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—22no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—22no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—22no—
78C4⋊(C11⋊C8)C2312yes—
79C4⋊(C11⋊C8)C2311yescharacteristic
80C4⋊(C11⋊C8)C2312yes—
81C4⋊(C11⋊C8)C2311yescharacteristic
82C4⋊(C11⋊C8)C2311yescharacteristic
83C4⋊(C11⋊C8)C2311yescharacteristic
84#66867—22no—
85C4×C11⋊C8—21no—
86C4×C11⋊C8—22no—
87C4×C11⋊C8—21no—
88#17811—111nomaximal, Sylow
89C11×#41—24no—
90C2×Q8×C11C4⋊C411yescharacteristic
91C2×D4×C11C4⋊C412yes—
92C2×D4×C11C4⋊C411yescharacteristic
93C22×C4×C11C22×C412yes—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×Q812yes—
98C22×C4×C11C2×Q811yescharacteristic
99C11×M16—24no—
100C2×C8×C11—24no—
101C2×C8×C11C22×C412yes—
102C2×C8×C11C22×C412yes—
103C2×C8×C11C22×C414yes—
104C11×C4⋊C4C4⋊C412yes—
105C11×C4⋊C4C4⋊C411yescharacteristic
106C11×C4⋊C4C4⋊C412yes—
107C11×C4⋊C4C4⋊C411yescharacteristic
108C11×C22⋊C4C4⋊C412yes—
109C11×C22⋊C4C4⋊C412yes—
110C11×C22⋊C4C4⋊C412yes—
111C42×C11C22×C411yescharacteristic
112C42×C11C22×C412yes—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D412yes—
115C42×C11C2×Q812yes—
116C42×C11C2×Q811yescharacteristic
117C42×C11C2411yescharacteristic
118#4318—82no—
119C2×C11⋊C8—21no—
120C2×C11⋊C8—21no—
121C2×C11⋊C8—21no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—81no—
126C2×C11⋊C8—82no—
127C2×C11⋊C8—81no—
128#2989—111no—
129#2988—111no—
130#2922D1111yescharacteristic
131#1574—112no—
132#1573—112no—
133#1572—112no—
134#1570—112no—
135#1565—111no—
136#1565—111no—
137#1564—111no—
138C2×#334—111no—
139C23×C11C2×C4⋊C412yes—
140C23×C11C2×C4⋊C411yescharacteristic
141Q8×C11—22no—
142D4×C11—24no—
143D4×C11—22no—
144C2×C4×C11—24no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11C2×C4⋊C411yescharacteristic
152C2×C4×C11C2×C4⋊C412yes—
153C2×C4×C11C2×C4⋊C411yescharacteristic
154C2×C4×C11C2×C4⋊C412yes—
155C2×C4×C11C2×C4⋊C412yes—
156C2×C4×C11C2×C4⋊C411yescharacteristic
157C2×C4×C11#13114yes—
158C2×C4×C11C23×C411yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11C22×Q811yescharacteristic
161C8×C11—22no—
162C8×C11—22no—
163C8×C11—24no—
164C11⋊C8—41no—
165C11⋊C8—41no—
166C11⋊C8—41no—
167C11⋊C8—42no—
168C11⋊C8—42no—
169C11⋊C8—41no—
170C4×#41C2×D1111yescharacteristic
171#446—221no—
172C8×Q8—221no—
173#436—221no—
174#435—222no—
175C8×D4—222no—
176C8×D4—221no—
177#433Dic1114yes—
178#432—112no—
179#431—111no—
180#431—111no—
181#431—112no—
182#431C2×D1112yes—
183#431C2×D1112yes—
184#424Dic1112yes—
185#423—112no—
186C2×C4⋊C8—111no—
187C2×C4⋊C8—111no—
188C2×C4⋊C8—112no—
189#408Dic1112yes—
190C4×M16C2×D1111yescharacteristic
191C2×C4×C8C2×D1111yescharacteristic
192#335—111no—
193#335—111no—
194#335—112no—
195#335—112no—
196#334—112no—
197#334—112no—
198#334—111no—
199#334—111no—
200#334—112no—
201#334—112no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11#42412yes—
208C22×C11C22×C4⋊C411yescharacteristic
209C4×C11—22no—
210C4×C11—21no—
211C4×C11—22no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—22no—
215C4×C11#42412yes—
216C4×C11C2×#13112yes—
217C4×C11#57711yescharacteristic
218C4×C11#57711yescharacteristic
219C2×#41C2×Dic1111yescharacteristic
220C2×M16—222no—
221C2×M16C2×Dic1112yes—
222C22×C8—221no—
223C22×C8—222no—
224C22×C8—221no—
225C22×C8C2×Dic1112yes—
226C4×Q8Dic2211yescharacteristic
227C4×Q8D4411yescharacteristic
228C4×D4Dic2212yes—
229C4×D4Dic2211yescharacteristic
230C4×D4D4412yes—
231C4×D4D4411yescharacteristic
232#117C2×Dic1111yescharacteristic
233#117C2×Dic1112yes—
234C2×C42C22×D1111yescharacteristic
235C2×C42C22×D1112yes—
236C4⋊C8—112no—
237C4⋊C8—111no—
238C4⋊C8—112no—
239C4⋊C8—111no—
240C4⋊C8—111no—
241C4⋊C8—111no—
242C4⋊C8—221no—
243C4⋊C8—222no—
244C4⋊C8—221no—
245C4⋊C8—222no—
246C4⋊C8C2×Dic1114yes—
247C4⋊C8C2×Dic1114yes—
248C22⋊C8—221no—
249C22⋊C8—222no—
250C22⋊C8—221no—
251C22⋊C8—222no—
252C22⋊C8C2×Dic1114yes—
253C22⋊C8C2×Dic1114yes—
254#97—222no—
255#97C2×Dic1112yes—
256C4×C8—221no—
257C4×C8—222no—
258C4×C8—221no—
259C4×C8C2×Dic1112yes—
260C4×C8C22×D1111yescharacteristic
261C4×C8C22×D1111yescharacteristic
262C4×C8C22×D1112yes—
263C2×C11—22no—
264C2×C11—42no—
265C2×C11C2×#42411yescharacteristic
266C2×C11#291211yescharacteristic
267C2×C11#291611yescharacteristic
268#41—24no—
269C2×Q8C4⋊Dic1111yescharacteristic
270C2×D4C4⋊Dic1112yes—
271C2×D4C4⋊Dic1111yescharacteristic
272C22×C4C2×Dic2212yes—
273C22×C4C2×Dic2211yescharacteristic
274C22×C4C2×D4411yescharacteristic
275C22×C4C2×D4412yes—
276C22×C4C22×Dic1112yes—
277C22×C4C22×Dic1111yescharacteristic
278M16—24no—
279M16—882no—
280C2×C8—24no—
281C2×C8—221no—
282C2×C8—221no—
283C2×C8—221no—
284C2×C8—222no—
285C2×C8—221no—
286C2×C8—222no—
287C2×C8—881no—
288C2×C8—882no—
289C2×C8—881no—
290C2×C8C22×Dic1112yes—
291C2×C8C22×Dic1112yes—
292C2×C8C22×Dic1114yes—
293C4⋊C4C4⋊Dic1112yes—
294C4⋊C4C4⋊Dic1111yescharacteristic
295C4⋊C4C4⋊Dic1112yes—
296C4⋊C4C4⋊Dic1111yescharacteristic
297C22⋊C4C4⋊Dic1112yes—
298C22⋊C4C4⋊Dic1112yes—
299C22⋊C4C4⋊Dic1112yes—
300C42C2×Dic2212yes—
301C42C2×Dic2211yescharacteristic
302C42C2×D4411yescharacteristic
303C42C2×D4412yes—
304C42C22×Dic1111yescharacteristic
305C42C22×Dic1112yes—
306C42C23×D1111yescharacteristic
307C11#1781111yescharacteristic, complemented, Sylow
308C23C2×C4⋊Dic1112yes—
309C23C2×C4⋊Dic1111yescharacteristic
310Q8—22no—
311D4—24no—
312D4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4C2×C4⋊Dic1112yes—
321C2×C4C2×C4⋊Dic1111yescharacteristic
322C2×C4C2×C4⋊Dic1112yes—
323C2×C4C2×C4⋊Dic1111yescharacteristic
324C2×C4C2×C4⋊Dic1112yes—
325C2×C4C2×C4⋊Dic1111yescharacteristic
326C2×C4#6700114yes—
327C2×C4C22×Dic2211yescharacteristic
328C2×C4C22×D4411yescharacteristic
329C2×C4C23×Dic1111yescharacteristic
330C8—22no—
331C8—22no—
332C8—24no—
333C8—441no—
334C8—442no—
335C8—442no—
336C8—441no—
337C8—441no—
338C8—441no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22#1062261212yes—
345C22C22×C4⋊Dic1111yescharacteristic
346C4—22no—
347C4—21no—
348C4—22no—
349C4—21no—
350C4—21no—
351C4—22no—
352C4#1062261212yes—
353C4#1062328211yescharacteristic
354C4#1062328211yescharacteristic
355C4C2×#6700112yes—
356C2—22no—
357C2—42no—
358C2C2×#1062261211yescharacteristic
359C2#1307721111yescharacteristic
360C2#1307722711yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2922C2
socleC22×C11C22×C4⋊C4
prime radicalC2×C11×#41C2×C4
cosocleC42×C11C24
hypercenter#2922D11
hypocenterC11#17811
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2922

Complements

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

NH ≅ G/Ntype
3. #13067405C2semidirect
4. #13067401C2semidirect
5. #13067396C2semidirect
6. #13067387C2semidirect
7. #13067368C2semidirect
8. #13067368C2semidirect
9. #13067364C2semidirect
10. C2×#10622095C2semidirect
307. C11#17811semidirect

Maximal subgroups

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

subgroupindex
#130777332
#130777272
#130674052
#130674012
#130673962
#130673872
#130673682
#130673642
C2×#106220952
C11×#29222
#1781111