Finite Group Databasebeta

← #14656840

Subgroups — #14656840

Order 2816.

452 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073651C211yesmaximal, characteristic
2#13069578C211yesmaximal, characteristic
3#13069569C211yesmaximal, characteristic
4#13066500C211yesmaximal, characteristic
5#13066457C211yesmaximal, characteristic
6#13066455C211yesmaximal, characteristic
7C11×#1981C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66923—21no—
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×#103—21no—
12C2×C11×#103—21no—
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622589—21no—
15#10622586—21no—
16#10622548C2211yescharacteristic
17C4×C4⋊Dic11C2211yescharacteristic
18#10622541—21no—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21#10622270—22no—
22#10622167—21no—
23#10622167—21no—
24#10622167—22no—
25C22×Q8×C11—21no—
26C22×C8×C11—21no—
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8Q812yes—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×C4⋊Dic11D412yes—
42C2×Dic11⋊C4—22no—
43C2×Dic11⋊C4—22no—
44C2×Dic11⋊C4—22no—
45C2×C4×Dic11—21no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48#66923—42no—
49#66923—42no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×#103—42no—
53C11×#103—42no—
54C11×#95—21no—
55C11⋊#95—22no—
56C11⋊#95—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4×C11⋊C8—21no—
60C4×C11⋊C8—21no—
61#10357—111nomaximal, Sylow
62C2×Q8×C11—22no—
63C2×Q8×C11—41no—
64C2×Q8×C11—41no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—22no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C42×C11—41no—
89C42×C11—41no—
90C42×C11C2×Q811yescharacteristic
91C42×C11#4111yescharacteristic
92C42×C11#4111yescharacteristic
93C42×C11#4111yescharacteristic
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—42no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11SD1612yes—
102C4⋊Dic11Q1612yes—
103Dic11⋊C4—44no—
104Dic11⋊C4—44no—
105Dic11⋊C4—82no—
106C4×Dic11—41no—
107C4×Dic11—41no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#2552—111no—
115#1990—111no—
116#1988—111no—
117#1981D1111yescharacteristic
118#1296—111no—
119#1279—111no—
120#1279—111no—
121C23×C11#12011yescharacteristic
122Q8×C11—42no—
123Q8×C11—42no—
124Q8×C11—81no—
125Q8×C11—81no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11C22⋊Q811yescharacteristic
138C2×C4×C11C22⋊Q811yescharacteristic
139C2×C4×C11C22⋊Q811yescharacteristic
140C2×C4×C11#12411yescharacteristic
141C2×C4×C11#12411yescharacteristic
142C2×C4×C11#12411yescharacteristic
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11C2×Q1611yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11#13511yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C2×Dic11—22no—
152C2×Dic11—22no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C8×C11—81no—
161C11⋊C8—42no—
162C11⋊C8—81no—
163C2×C4⋊Q8C2×D1111yescharacteristic
164C2×#125—221no—
165C2×C4⋊C8—111no—
166C2×C4⋊C8C2×D1111yescharacteristic
167C2×#103—21no—
168C2×#103—21no—
169C2×C4×C8—111no—
170#398—222no—
171#389—221no—
172#389—221no—
173#384—111no—
174#384—221no—
175C4×C4⋊C4—111no—
176C4×C4⋊C4C2×D1111yescharacteristic
177#340—221no—
178#340—221no—
179#340—222no—
180C22×C11#39311yescharacteristic
181C22×C11#44911yescharacteristic
182C22×C11#44911yescharacteristic
183C22×C11#45011yescharacteristic
184C22×C11#45111yescharacteristic
185C22×C11#45511yescharacteristic
186C22×C11#45611yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—81no—
190C4×C11—81no—
191C4×C11—82no—
192C4×C11#47511yescharacteristic
193C4×C11#47711yescharacteristic
194C4×C11#47811yescharacteristic
195C4×C11#47811yescharacteristic
196C4×C11#48711yescharacteristic
197C4×C11#48811yescharacteristic
198C4×C11#48911yescharacteristic
199C4×C11#49011yescharacteristic
200Dic11—42no—
201Dic11—42no—
202Dic11—82no—
203C22×Q8—21no—
204C22×C8—21no—
205C22×C8—221no—
206C22×C8—221no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8Dic2212yes—
211#125—442no—
212#125—442no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—112no—
218C2×C4⋊C4—222no—
219C2×C4⋊C4—222no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—222no—
223C2×C4⋊C4C22⋊D1111yescharacteristic
224C2×C4⋊C4C22⋊D1111yescharacteristic
225C2×C42—21no—
226C2×C42—221no—
227C2×C42C22×D1111yescharacteristic
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—221no—
231C4⋊C8—221no—
232#103—42no—
233#103—42no—
234C4×C8—221no—
235C4×C8—221no—
236#95—21no—
237#95—222no—
238#95—221no—
239C2×C11#164211yescharacteristic
240C2×C11#164411yescharacteristic
241C2×C11#164811yescharacteristic
242C2×C11#165411yescharacteristic
243C2×C11#202411yescharacteristic
244C2×C11#202511yescharacteristic
245C2×C11#202811yescharacteristic
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4—222no—
258C22×C4D4×D1111yescharacteristic
259C22×C4D4×D1111yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—222no—
265C2×C8—441no—
266C2×C8—441no—
267C2×C8—441no—
268C2×C8—441no—
269C2×C8—441no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—112no—
279C4⋊C4—112no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—442no—
283C4⋊C4—444no—
284C4⋊C4—444no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—882no—
290C42—41no—
291C42—41no—
292C42—441no—
293C42—441no—
294C42C2×Dic2211yescharacteristic
295C42#433911yescharacteristic
296C42#434111yescharacteristic
297C42#434111yescharacteristic
298C11#1035711yescharacteristic, complemented, Sylow
299C23#6699011yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—81no—
303Q8—81no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—222no—
316C2×C4—222no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4#6693111yescharacteristic
325C2×C4#6693111yescharacteristic
326C2×C4#6693811yescharacteristic
327C2×C4#6693811yescharacteristic
328C2×C4SD16×D1111yescharacteristic
329C2×C4#6696711yescharacteristic
330C2×C4Q16×D1111yescharacteristic
331C2×C4#6697111yescharacteristic
332C2×C4#6697711yescharacteristic
333C2×C4#6698511yescharacteristic
334C2×C4#6698511yescharacteristic
335C2×C4#6698911yescharacteristic
336C2×C4#6700311yescharacteristic
337C2×C4#6700311yescharacteristic
338C8—81no—
339C8—442no—
340C8—881no—
341C22#1062256011yescharacteristic
342C22#1062265011yescharacteristic
343C22#1062265011yescharacteristic
344C22#1062278211yescharacteristic
345C22#1062279911yescharacteristic
346C22#1062281511yescharacteristic
347C22#1062281811yescharacteristic
348C4—21no—
349C4—21no—
350C4—81no—
351C4—81no—
352C4—82no—
353C4—442no—
354C4—442no—
355C4—882no—
356C4#1062240411yescharacteristic
357C4#1062240511yescharacteristic
358C4#1062240711yescharacteristic
359C4#1062240811yescharacteristic
360C4#1062262211yescharacteristic
361C4#1062262211yescharacteristic
362C4#1062266911yescharacteristic
363C4#1062268411yescharacteristic
364C2#1306781411yescharacteristic
365C2#1306782811yescharacteristic
366C2#1306785611yescharacteristic
367C2#1306789811yescharacteristic
368C2#1306975511yescharacteristic
369C2#1306976211yescharacteristic
370C2#1306977511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1981C2
socle, prime radicalC23×C11#120
hypercenter#1981D11
hypocenterC11#10357
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
298. C11#10357semidirect

Maximal subgroups

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

subgroupindex
#130736512
#130695782
#130695692
#130665002
#130664572
#130664552
C11×#19812
#1035711