Finite Group Databasebeta

← #14650433

Subgroups — #14650433

Order 2816.

490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079541C211yesmaximal, characteristic
2#13077335C211yesmaximal, characteristic
3#13067301C211yesmaximal, characteristic, complemented
4#13067175C211yesmaximal, characteristic
5#13066474C211yesmaximal, characteristic, complemented
6#13066447C211yesmaximal, characteristic, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66954—21no—
10#10623008C2211yescharacteristic
11C2×C11×#97C2211yescharacteristic
12C11×#382C2211yescharacteristic
13#10622840—22no—
14#10622723—21no—
15#10622698C412yescomplemented
16#10622696—22no—
17#10622694C412yescomplemented
18#10622538C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21#10622319—22no—
22#10622319—22no—
23C11×#340—21no—
24C11×#340—21no—
25#10622185—22no—
26#10622089—22no—
27C22×Q8×C11—21no—
28C2×#4339—21no—
29C22×C8×C11D411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8C2×C412yes—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C42×C11C2311yescharacteristic
39C2×#4325—24no—
40#66983—21no—
41#66983D412yes—
42C2×#4318—21no—
43#66954—42no—
44#66954—42no—
45C2×#4313—22no—
46C2×C8×D11—22no—
47#66928—21no—
48#66927C2×C411yescharacteristic
49C4×D44—21no—
50C4×D44D412yes—
51#66922C2×C411yescharacteristic
52C11×#97—21no—
53C11×#97—21no—
54C11×#95—21no—
55C11×#95—21no—
56#66899—24no—
57C22⋊(C11⋊C8)—21no—
58C22⋊(C11⋊C8)—21no—
59(C2×D11)⋊C8—24no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)D412yes—
64C4×C11⋊C8—21no—
65C4×C11⋊C8C2×C412yes—
66#9289—111nomaximal, Sylow
67C2×Q8×C11—22no—
68C2×Q8×C11—41no—
69C2×Q8×C11—82no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C2×C22⋊D11—22no—
76#4339—41no—
77#4339—41no—
78#4339—41no—
79#4339—41no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44C22⋊C412yes—
83C2×C4×D11—22no—
84C2×Dic22—21no—
85C2×C8×C11—21no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11SD1612yescomplemented
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C42×C11C22×C411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101#4325—84no—
102(C2×D11)⋊C4—22no—
103(C2×D11)⋊C4—22no—
104C4⋊Dic11—21no—
105C4⋊Dic11C22⋊C412yes—
106#4318—41no—
107#4318—41no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—41no—
111#4313—44no—
112C8×D11—44no—
113#3206—111no—
114#2932—111no—
115#1993D1111yescharacteristic, complemented
116#1549—111no—
117#1517—111no—
118#1286—111no—
119#1275—111no—
120C23×C11#12111yescharacteristic
121C22×D11—22no—
122Q8×C11—44no—
123Q8×C11—82no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—82no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11—81no—
131C2×C4×C11C2×C22⋊C411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C22⋊D11—42no—
142C22⋊D11—42no—
143C2×Dic11—22no—
144D44—42no—
145D44—41no—
146D44—41no—
147D44—81no—
148C4×D11—42no—
149C4×D11—42no—
150Dic22—41no—
151Dic22—41no—
152C8×C11—22no—
153C8×C11—41no—
154C11⋊C8—42no—
155C11⋊C8—42no—
156C11⋊C8—81no—
157C2×#131—221no—
158#532—111no—
159C2×C4⋊Q8C2×D1111yescharacteristic
160#492—112no—
161#487—112no—
162#461—222no—
163#448—222no—
164#435—222no—
165#435—222no—
166#431—111no—
167#431—111no—
168#423—111no—
169#408—221no—
170C2×#97C2×D1111yescharacteristic
171#382C2×D1111yescharacteristic
172#340—21no—
173#340—21no—
174#332—222no—
175#327—222no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#38611yescharacteristic
179C22×C11#46111yescharacteristic
180C22×C11#46311yescharacteristic
181C2×D11—42no—
182C2×D11—42no—
183C2×D11—42no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—82no—
189C4×C11—161no—
190C4×C11C4×SD1611yescharacteristic
191C4×C11#44011yescharacteristic
192C4×C11#45011yescharacteristic
193C4×C11#45211yescharacteristic
194Dic11—42no—
195C2×#41—221no—
196C22×Q8—21no—
197C2×SD16—224no—
198#131—442no—
199#131—442no—
200C2×M16—222no—
201C2×M16—221no—
202C22×C8—222no—
203C22×C8C22⋊D1111yescharacteristic
204C22×C8C22⋊D1111yescharacteristic
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—111no—
209C4⋊Q8C4×D1112yes—
210#127—111no—
211#124—221no—
212#121—112no—
213#121—221no—
214C4×D4—112no—
215C4×D4—221no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C42C22×D1111yescharacteristic
220C4⋊C8—112no—
221C4⋊C8—221no—
222C4⋊C8—221no—
223C4⋊C8—221no—
224#103—224no—
225C22⋊C8—224no—
226C22⋊C8—221no—
227C22⋊C8—221no—
228#97—21no—
229#97—21no—
230C4×C8—112no—
231C4×C8—221no—
232#95—21no—
233#95—21no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11#187711yescharacteristic
237C2×C11#190211yescharacteristic
238C2×C11#191011yescharacteristic
239D11—82no—
240#41—441no—
241#41—441no—
242#41—441no—
243#41—441no—
244C2×Q8—22no—
245C2×Q8—41no—
246C2×Q8—82no—
247C2×Q8—221no—
248C2×D4—112no—
249C2×D4—222no—
250C2×D4—221no—
251C2×D4—221no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—222no—
255C22×C4D4×D1111yescharacteristic
256C22×C4#434111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258SD16—884no—
259M16—444no—
260M16—441no—
261M16—441no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—222no—
268C2×C8—222no—
269C2×C8—444no—
270C2×C8—441no—
271C2×C8#432512yescomplemented
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—112no—
279C4⋊C4—221no—
280C22⋊C4—222no—
281C22⋊C4—222no—
282C42C2×C4×D1111yescharacteristic
283C42#433911yescharacteristic
284C42D4×D1111yescharacteristic
285C42D4×D1111yescharacteristic
286C11#928911yescharacteristic, complemented, Sylow
287C23—222no—
288C23#6699111yescharacteristic
289Q8—44no—
290Q8—82no—
291Q8—441no—
292Q8—441no—
293D4—442no—
294D4—442no—
295D4—442no—
296D4—441no—
297D4—441no—
298D4—881no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—82no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—222no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4C22⋊C4×D1111yescharacteristic
310C2×C4(C22⋊D11)⋊C411yescharacteristic
311C2×C4#6693611yescharacteristic
312C2×C4#6693711yescharacteristic
313C2×C4C4×C22⋊D1111yescharacteristic
314C2×C4#6699011yescharacteristic
315C2×C4C2×#432511yescharacteristic
316C2×C4#6699511yescharacteristic
317C2×C4#6700211yescharacteristic
318C2×C4#6700311yescharacteristic
319C8—22no—
320C8—41no—
321C8—442no—
322C8—442no—
323C8—881no—
324C22—21no—
325C22—21no—
326C22—442no—
327C22—442no—
328C22—442no—
329C22#1062256911yescharacteristic
330C22#1062267011yescharacteristic
331C22#1062269611yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—161no—
338C4—442no—
339C4C4×#432511yescharacteristic
340C4#1062263911yescharacteristic
341C4#1062265911yescharacteristic
342C4#1062266011yescharacteristic
343C2—21no—
344C2—21no—
345C2—882no—
346C2#1306895311yescharacteristic
347C2#1306908611yescharacteristic
348C2#1306914011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1993C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1993D11
hypocenterC11#9289
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
3. #13067301C2semidirect
5. #13066474C2semidirect
6. #13066447C2semidirect
7. C11×#1993C2semidirect
15. #10622698C4semidirect
17. #10622694C4semidirect
90. C2×C8×C11SD16semidirect
115. #1993D11semidirect
271. C2×C8#4325semidirect
286. C11#9289semidirect

Maximal subgroups

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

subgroupindex
#130795412
#130773352
#130673012
#130671752
#130664742
#130664472
C11×#19932
#928911