Finite Group Databasebeta

← #14723970

Subgroups — #14723970

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078647C211yesmaximal, characteristic
2C2×#10622637C211yesmaximal, characteristic, complemented
3#13077327C211yesmaximal, characteristic
4#13067503C214yesmaximal, complemented
5#13067455C214yesmaximal, complemented
6#13067388C211yesmaximal, characteristic, complemented
7#13067016C211yesmaximal, characteristic
8#13066900C211yesmaximal, characteristic, complemented
9C11×#1487C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66960—21no—
12#10623008C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#423C2211yescharacteristic
15#10622840C412yes—
16#10622742—21no—
17#10622640C412yes—
18C4×#4325C2214yes—
19#10622637—21no—
20#10622637—21no—
21#10622637C2212yes—
22#10622637C2212yes—
23#10622633C412yes—
24#10622581C412yes—
25#10622538C2211yescharacteristic
26C2×C4⋊(C11⋊C8)—21no—
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C2×#66867—21no—
29C2×C4×C11⋊C8C2211yescharacteristic
30#10622451—21no—
31#10622451C2212yes—
32#10622447—21no—
33#10622447C2212yes—
34C11×Q8⋊C8C2214yes—
35#10622118C2214yes—
36#10622097C2214yes—
37#10622092C2212yes—
38C8×C11⋊C8C2212yes—
39C22×Q8×C11C2×C411yescharacteristic
40C2×#4339—21no—
41C2×C11×M16—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11C2×C412yes—
45C4×Q8×C11C2312yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50C2×#4325C2×C414yes—
51#66983—21no—
52#66983C2×C412yes—
53C22×C11⋊C8—21no—
54C22×C11⋊C8D411yescharacteristic
55C22×C11⋊C8D411yescharacteristic
56#66960—44no—
57C2×#4313—22no—
58C2×C8×D11—22no—
59#66928—21no—
60#66927C2×C411yescharacteristic
61C4×D44—21no—
62C4×D44C2312yes—
63#66922C2×C411yescharacteristic
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8C2312yes—
67C11×C22⋊C8—21no—
68C4×C8×C11C2312yes—
69#66899C2×C414yes—
70C22⋊(C11⋊C8)C2×C412yes—
71(C2×D11)⋊C8—22no—
72(C2×D11)⋊C8—22no—
73#66873C2×C414yes—
74#66872C2×C414yes—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—22no—
77C4⋊(C11⋊C8)—22no—
78C4⋊(C11⋊C8)C2×C412yes—
79C4⋊(C11⋊C8)C2312yes—
80#66867—22no—
81#66867—22no—
82C4×C11⋊C8D411yescharacteristic
83C4×C11⋊C8D411yescharacteristic
84C4×C11⋊C8C2312yes—
85C4×C11⋊C8C2311yescharacteristic
86C4×C11⋊C8C2311yescharacteristic
87#17929—111nomaximal, Sylow
88C2×Q8×C11—21no—
89C2×Q8×C11—42no—
90C2×Q8×C11C22×C412yes—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C2×C22⋊D11—22no—
97#4339—42no—
98#4339—42no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44C22×C412yes—
102C2×C4×D11—22no—
103C2×Dic22—21no—
104C11×M16—42no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4C22×C412yes—
111C42×C11—22no—
112C42×C11—22no—
113C42×C11C22×C411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11C2411yescharacteristic
117#4325—44no—
118(C2×D11)⋊C4—22no—
119(C2×D11)⋊C4—22no—
120C4⋊Dic11—21no—
121C4⋊Dic11C22×C412yes—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—42no—
125C2×C11⋊C8SD1614yescomplemented
126C2×C11⋊C8C22×C414yes—
127C2×C11⋊C8C2×D411yescharacteristic
128C2×C11⋊C8C2×D411yescharacteristic
129C2×C11⋊C8C2×D411yescharacteristic
130C2×C11⋊C8C2×D411yescharacteristic
131#4313—44no—
132C8×D11—44no—
133#3103—111no—
134C2×#446—111no—
135#2931—111no—
136#1590—114no—
137#1582—114no—
138#1570—111no—
139#1487D1111yescharacteristic, complemented
140#1480—111no—
141#1450—111no—
142C23×C11C4×D411yescharacteristic
143C22×D11—22no—
144Q8×C11—22no—
145Q8×C11—22no—
146Q8×C11—42no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11C4×D411yescharacteristic
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11C2×SD1612yes—
157C2×C4×C11#13512yes—
158C2×C4×C11C23×C411yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11C2×#4111yescharacteristic
161C22⋊D11—44no—
162C2×Dic11—22no—
163D44—24no—
164D44—42no—
165D44—42no—
166C4×D11—42no—
167C4×D11—42no—
168Dic22—42no—
169C8×C11—42no—
170C8×C11—42no—
171C11⋊C8—24no—
172C11⋊C8—21no—
173C11⋊C8—21no—
174C11⋊C8—42no—
175C11⋊C8C2×SD1612yes—
176C11⋊C8C2×SD1612yes—
177C2×#131—221no—
178#532—111no—
179C2×C4×Q8C2×D1111yescharacteristic
180#481—112no—
181#475—112no—
182#460—112no—
183#448—112no—
184#446—112no—
185#446—112no—
186#446—221no—
187#446—221no—
188C4×SD16—114no—
189#436—112no—
190#436—221no—
191C8×D4—112no—
192C8×D4—221no—
193#431—111no—
194#431C2×D1111yescharacteristic
195#423C2×D1111yescharacteristic
196C2×C4⋊C8—111no—
197C2×C4⋊C8—221no—
198#408—221no—
199C2×#97—221no—
200C2×C4×C8—111no—
201#334—114no—
202Q8⋊C8C2×D1114yes—
203D4⋊C8—114no—
204#322—112no—
205C82—112no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11C4×SD1612yes—
209C22×C11C2×C4×D411yescharacteristic
210C2×D11—42no—
211C2×D11—42no—
212C2×D11—42no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—42no—
217C4×C11—42no—
218C4×C11C4×SD1612yes—
219C4×C11#56812yes—
220C4×C11C22×SD1611yescharacteristic
221C4×C11C2×#13511yescharacteristic
222Dic11—42no—
223C2×#41—221no—
224C22×Q8C4×D1111yescharacteristic
225C2×SD16—114no—
226#131—444no—
227C2×M16—21no—
228C2×M16—222no—
229C22×C8—111no—
230C22×C8—111no—
231C22×C8—222no—
232C22×C8—221no—
233C4⋊Q8—111no—
234#127—111no—
235#124—221no—
236#121—112no—
237#121—221no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8C4×D1112yes—
241C4×Q8C22×D1112yes—
242C4×D4—112no—
243C4×D4—221no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4C4×D1111yescharacteristic
246C2×C42—21no—
247C2×C42C22×D1111yescharacteristic
248#106—114no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—112no—
252C4⋊C8—112no—
253C4⋊C8—222no—
254C4⋊C8—222no—
255C4⋊C8—221no—
256C4⋊C8C22×D1112yes—
257#103—114no—
258#102—114no—
259C22⋊C8—21no—
260C22⋊C8—112no—
261C22⋊C8—222no—
262C22⋊C8—222no—
263#97—222no—
264#97—222no—
265C4×C8—111no—
266C4×C8—111no—
267C4×C8—111no—
268C4×C8—112no—
269C4×C8—111no—
270C4×C8C22×D1112yes—
271C2×C11—22no—
272C2×C11#293011yescharacteristic
273C2×C11C2×C4×SD1611yescharacteristic
274C2×C11#295511yescharacteristic
275D11—82no—
276#41—442no—
277#41—442no—
278C2×Q8—21no—
279C2×Q8—42no—
280C2×Q8—221no—
281C2×Q8C2×C4×D1112yes—
282C2×D4—112no—
283C2×D4—222no—
284C2×D4—221no—
285C2×D4—221no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—222no—
289C22×C4C2×C4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291C22×C4#434111yescharacteristic
292SD16—444no—
293M16—42no—
294M16—444no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—114no—
298C2×C8—111no—
299C2×C8—111no—
300C2×C8—114no—
301C2×C8—111no—
302C2×C8—111no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8—444no—
306C2×C8—442no—
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—112no—
311C4⋊C4—221no—
312C4⋊C4C2×C4×D1112yes—
313C22⋊C4—222no—
314C22⋊C4—222no—
315C42—22no—
316C42—22no—
317C42C2×C4×D1111yescharacteristic
318C42D4×D1111yescharacteristic
319C42#434111yescharacteristic
320C42C23×D1111yescharacteristic
321C11#1792911yescharacteristic, complemented, Sylow
322C23—222no—
323C23(C22⋊D11)⋊C411yescharacteristic
324Q8—22no—
325Q8—22no—
326Q8—42no—
327Q8—442no—
328D4—224no—
329D4—442no—
330D4—444no—
331D4—442no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—222no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4(C22⋊D11)⋊C411yescharacteristic
342C2×C4(C22⋊D11)⋊C411yescharacteristic
343C2×C4(C22⋊D11)⋊C411yescharacteristic
344C2×C4SD16×D1112yes—
345C2×C4#6697212yes—
346C2×C4C22×C4×D1111yescharacteristic
347C2×C4C2×D4×D1111yescharacteristic
348C2×C4C2×#434111yescharacteristic
349C8—42no—
350C8—42no—
351C8—112no—
352C8—112no—
353C8—224no—
354C8—221no—
355C8—221no—
356C8—442no—
357C22—21no—
358C22—21no—
359C22—442no—
360C22—442no—
361C22—442no—
362C22#1062240112yes—
363C22C2×(C22⋊D11)⋊C411yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—42no—
368C4—42no—
369C4—442no—
370C4#1062240112yes—
371C4#1062327612yes—
372C4C2×SD16×D1111yescharacteristic
373C4C2×#6697211yescharacteristic
374C2—22no—
375C2—882no—
376C2#1307731511yescharacteristic
377C2C2×#1062240111yescharacteristic
378C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1487C2
socleC22×C11C2×C4×D4
prime radical#10623008C22
cosocleC42×C11C24
hypercenter#1487D11
hypocenterC11#17929
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
2. C2×#10622637C2semidirect
4. #13067503C2semidirect
5. #13067455C2semidirect
6. #13067388C2semidirect
8. #13066900C2semidirect
9. C11×#1487C2semidirect
125. C2×C11⋊C8SD16semidirect
139. #1487D11semidirect
321. C11#17929semidirect

Maximal subgroups

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

subgroupindex
#130786472
C2×#106226372
#130773272
#130675032
#130674552
#130673882
#130670162
#130669002
C11×#14872
#1792911