Finite Group Databasebeta

← #14657528

Subgroups — #14657528

Order 2816.

420 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 93 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#13078088C211yesmaximal, characteristic
2#13067386C211yesmaximal, characteristic, complemented
3#13067266C211yesmaximal, characteristic
4#13067175C211yesmaximal, characteristic
5#13066940C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#1805C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66995—21no—
10#10623008C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×#103—21no—
13C11×#382C2211yescharacteristic
14#10622644—21no—
15#10622641—22no—
16#10622640—21no—
17#10622579—21no—
18#10622538C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21C11×#340—21no—
22#10622166—22no—
23#10622123—21no—
24#10622120—21no—
25#10622118—22no—
26#10622089—22no—
27C22×Q8×C11D411yescharacteristic
28C2×#4339—21no—
29C22×C8×C11—21no—
30C4×Q8×C11—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C42×C11—21no—
38C2×C42×C11C2311yescharacteristic
39C2×#4326—22no—
40#66995—42no—
41#66995—42no—
42C2×#4325—22no—
43#66983—21no—
44#66983—21no—
45C2×#4318—21no—
46#66928—21no—
47#66927D411yescharacteristic
48C4×D44—21no—
49C4×D44—21no—
50#66922D411yescharacteristic
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×#103—42no—
54C11×#95—21no—
55C11×#95—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)D412yes—
58#66874—22no—
59#66873—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)D412yes—
64C4×C11⋊C8—21no—
65C4×C11⋊C8—21no—
66#10467—111nomaximal, Sylow
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11SD1612yes—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C2×C22⋊D11—41no—
80#4339—41no—
81#4339—41no—
82#4339—41no—
83#4339—41no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×C4×D11—41no—
88C2×Dic22—21no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11—41no—
99C42×C11—41no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103C42×C11#4111yescharacteristic
104#4326—44no—
105#4325—44no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110#4318—41no—
111#4318—41no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—41no—
115#3037—111no—
116#1805D1111yescharacteristic, complemented
117#1570—111no—
118#1540—111no—
119#1517—111no—
120#1461—111no—
121#1286—111no—
122C23×C11#12111yescharacteristic
123C22×D11—41no—
124Q8×C11—22no—
125Q8×C11—22no—
126Q8×C11—41no—
127Q8×C11—41no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—81no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12311yescharacteristic
142C2×C4×C11#12311yescharacteristic
143C2×C4×C11#12411yescharacteristic
144C2×C4×C11C2×SD1611yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C22⋊D11—81no—
149C22⋊D11—81no—
150C2×Dic11—41no—
151D44—41no—
152D44—41no—
153D44—81no—
154D44—81no—
155C4×D11—81no—
156C4×D11—81no—
157Dic22—41no—
158Dic22—41no—
159C8×C11—81no—
160C11⋊C8—42no—
161C11⋊C8—42no—
162C11⋊C8—81no—
163C2×#137—221no—
164#532—111no—
165C2×C4×Q8C2×D1111yescharacteristic
166#464—222no—
167#462—221no—
168#460—221no—
169#431—111no—
170#431—111no—
171#423—111no—
172C2×C4⋊C8C2×D1111yescharacteristic
173#417—221no—
174C2×#103—21no—
175#382C2×D1111yescharacteristic
176#340—21no—
177#334—222no—
178#332—221no—
179#331—221no—
180#327—222no—
181#324—222no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11#39411yescharacteristic
185C22×C11#46511yescharacteristic
186C22×C11#46911yescharacteristic
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—42no—
195C4×C11—81no—
196C4×C11—161no—
197C4×C11#44911yescharacteristic
198C4×C11#45011yescharacteristic
199C4×C11#48111yescharacteristic
200C4×C11#48211yescharacteristic
201Dic11—81no—
202C2×#41—221no—
203C22×Q8C22⋊D1111yescharacteristic
204#137—442no—
205#137—442no—
206C2×Q16—222no—
207C2×SD16—222no—
208C2×M16—221no—
209C22×C8—21no—
210C4⋊Q8—111no—
211#127—111no—
212#124—221no—
213#121—221no—
214#121—221no—
215C4×Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×D4—221no—
220C4×D4—221no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4C22⋊D1111yescharacteristic
224C2×C42—21no—
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—112no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231C4⋊C8—221no—
232#103—42no—
233#103—222no—
234#102—222no—
235C22⋊C8—112no—
236C22⋊C8—221no—
237C4×C8—221no—
238C4×C8—221no—
239#95—21no—
240#95—21no—
241C2×C11—21no—
242C2×C11—21no—
243C2×C11#203411yescharacteristic
244C2×C11#204911yescharacteristic
245C2×C11#205311yescharacteristic
246D11—161no—
247#41—441no—
248#41—441no—
249#41—441no—
250#41—441no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—221no—
257C2×Q8#432512yes—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—441no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—441no—
266C22×C4D4×D1111yescharacteristic
267C22×C4#434111yescharacteristic
268C22×C4C2×C22⋊D1111yescharacteristic
269Q16—444no—
270SD16—444no—
271M16—441no—
272M16—441no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—222no—
277C2×C8—222no—
278C2×C8—441no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C22⋊C4—441no—
288C22⋊C4—441no—
289C42—41no—
290C42—41no—
291C42#433911yescharacteristic
292C42#433911yescharacteristic
293C42D4×D1111yescharacteristic
294C42D4×D1111yescharacteristic
295C11#1046711yescharacteristic, complemented, Sylow
296C23—441no—
297C23#6699211yescharacteristic
298Q8—22no—
299Q8—22no—
300Q8—41no—
301Q8—41no—
302Q8—441no—
303Q8—441no—
304D4—441no—
305D4—441no—
306D4—881no—
307D4—881no—
308D4—881no—
309D4—881no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—441no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4#6693611yescharacteristic
324C2×C4#6693711yescharacteristic
325C2×C4#6693711yescharacteristic
326C2×C4#6693811yescharacteristic
327C2×C4#6698211yescharacteristic
328C2×C4#6698511yescharacteristic
329C2×C4#6699011yescharacteristic
330C2×C4C2×#432511yescharacteristic
331C2×C4#6700211yescharacteristic
332C2×C4#6700311yescharacteristic
333C8—81no—
334C8—442no—
335C8—442no—
336C8—881no—
337C22—21no—
338C22—21no—
339C22—881no—
340C22—881no—
341C22—881no—
342C22#1062257211yescharacteristic
343C22#1062265211yescharacteristic
344C22#1062266111yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—42no—
350C4—81no—
351C4—161no—
352C4—881no—
353C4#1062258111yescharacteristic
354C4#1062261611yescharacteristic
355C4#1062265011yescharacteristic
356C4#1062265911yescharacteristic
357C2—21no—
358C2—21no—
359C2—1761no—
360C2#1306980511yescharacteristic
361C2#1306989411yescharacteristic
362C2#1306992011yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1805C2
socleC22×C11#394
prime radical#10623008C22
hypercenter#1805D11
hypocenterC11#10467
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
2. #13067386C2semidirect
5. #13066940C2semidirect
6. #13066474C2semidirect
7. C11×#1805C2semidirect
116. #1805D11semidirect
295. C11#10467semidirect

Maximal subgroups

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

subgroupindex
#130780882
#130673862
#130672662
#130671752
#130669402
#130664742
C11×#18052
#1046711