Finite Group Databasebeta

← #14657427

Subgroups — #14657427

Order 2816.

408 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 101 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#13068608C211yesmaximal, characteristic
2#13067390C211yesmaximal, characteristic, complemented
3#13067301C211yesmaximal, characteristic, complemented
4#13067297C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic
6#13066513C211yesmaximal, characteristic, complemented
7C2×C11×#476C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C11×#476—22no—
11C11×#476—22no—
12C2×C11×#106—21no—
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×#102—21no—
15C2×#66897—21no—
16#10622538C2211yescharacteristic
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622537C2211yescharacteristic
20#10622185—22no—
21#10622184—22no—
22D4⋊(C11⋊C8)—22no—
23#10622168—21no—
24#10622117—22no—
25C22×Q8×C11—21no—
26C22×D4×C11D411yescharacteristic
27C23×C4×C11—21no—
28C22×C8×C11—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8D412yes—
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4318—21no—
43C2×#4318—21no—
44C11×#106—24no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8D412yes—
47C11×#102—24no—
48#66897—42no—
49C22⋊(C11⋊C8)—21no—
50C22⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)D412yes—
57C4×C11⋊C8—21no—
58C4×C11⋊C8—21no—
59#10453—111nomaximal, Sylow
60C24×C11—21no—
61C2×Q8×C11—22no—
62C2×Q8×C11—41no—
63C2×Q8×C11—82no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11Q1612yes—
70C22×C4×C11—21no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—82no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11#4111yescharacteristic
93#4318—41no—
94#4318—41no—
95#4318—41no—
96#4318—41no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×#476D1111yescharacteristic
102#1800—111no—
103#1571—111no—
104#1549—111no—
105#1548—111no—
106#1478—111no—
107#1301—111no—
108C23×C11—22no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—81no—
112C23×C11—81no—
113C23×C11#12311yescharacteristic
114Q8×C11—82no—
115Q8×C11—82no—
116D4×C11—22no—
117D4×C11—22no—
118D4×C11—41no—
119D4×C11—41no—
120C2×C4×C11—22no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—42no—
124C2×C4×C11—82no—
125C2×C4×C11—82no—
126C2×C4×C11—82no—
127C2×C4×C11—81no—
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11#12411yescharacteristic
134C2×C4×C11C2×Q1611yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C8×C11—42no—
139C11⋊C8—42no—
140C11⋊C8—81no—
141C11⋊C8—81no—
142C11⋊C8—81no—
143C2×C4⋊Q8C2×D1111yescharacteristic
144C2×C4×D4C2×D1111yescharacteristic
145#476—22no—
146#476—22no—
147#431—111no—
148#431—111no—
149C2×#106—21no—
150#423—111no—
151#423—111no—
152C2×C4⋊C8C2×D1111yescharacteristic
153C2×#102—21no—
154C2×#100—221no—
155#343—221no—
156#335—222no—
157#333—222no—
158#332—222no—
159D4⋊C8—222no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—42no—
163C22×C11—82no—
164C22×C11—82no—
165C22×C11—81no—
166C22×C11—81no—
167C22×C11#39411yescharacteristic
168C22×C11#48411yescharacteristic
169C22×C11#48511yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—82no—
174C4×C11—81no—
175C4×C11#44911yescharacteristic
176C4×C11#45111yescharacteristic
177C4×C11#46711yescharacteristic
178C4×C11#46811yescharacteristic
179C4×C11#47112yes—
180C22×Q8—21no—
181C22×D4C22⋊D1111yescharacteristic
182C23×C4—21no—
183C2×M16—221no—
184C2×M16—221no—
185C22×C8—21no—
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4⋊Q8—21no—
189C4⋊Q8C22⋊D1112yes—
190C4×D4—21no—
191C4×D4—21no—
192C4×D4—21no—
193C4×D4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4C22⋊D1111yescharacteristic
197C2×C22⋊C4—21no—
198C2×C42C22×D1111yescharacteristic
199#106—24no—
200C4⋊C8—21no—
201C4⋊C8—112no—
202C4⋊C8—221no—
203C4⋊C8—221no—
204C4⋊C8—221no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8C22⋊D1112yes—
208#102—24no—
209#100—442no—
210C22⋊C8—221no—
211C22⋊C8—221no—
212C4×C8—221no—
213C4×C8—221no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11—82no—
217C2×C11#203611yescharacteristic
218C2×C11#204611yescharacteristic
219C2×C11#204811yescharacteristic
220C24—21no—
221C2×Q8—22no—
222C2×Q8—41no—
223C2×Q8—82no—
224C2×D4—21no—
225C2×D4—21no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4#432612yes—
230C22×C4—21no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—82no—
235C22×C4#434111yescharacteristic
236C22×C4#434111yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238M16—441no—
239M16—441no—
240M16—441no—
241M16—441no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—222no—
246C2×C8—441no—
247C2×C8—441no—
248C2×C8—441no—
249C4⋊C4—22no—
250C4⋊C4—21no—
251C4⋊C4—22no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C42D4×D1111yescharacteristic
258C42#434111yescharacteristic
259C42C2×C22⋊D1111yescharacteristic
260C42C2×C22⋊D1111yescharacteristic
261C11#1045311yescharacteristic, complemented, Sylow
262C23—22no—
263C23—41no—
264C23—41no—
265C23—81no—
266C23—81no—
267C23#6698811yescharacteristic
268Q8—82no—
269Q8—82no—
270D4—22no—
271D4—22no—
272D4—41no—
273D4—41no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4—82no—
281C2×C4—81no—
282C2×C4#6698811yescharacteristic
283C2×C4#6698911yescharacteristic
284C2×C4#6699111yescharacteristic
285C2×C4#6699211yescharacteristic
286C2×C4#6699211yescharacteristic
287C2×C4#6699511yescharacteristic
288C2×C4C2×#432611yescharacteristic
289C2×C4#6700211yescharacteristic
290C2×C4#6700311yescharacteristic
291C2×C4#6700611yescharacteristic
292C8—42no—
293C8—442no—
294C8—881no—
295C8—881no—
296C8—881no—
297C22—21no—
298C22—21no—
299C22—42no—
300C22—82no—
301C22—82no—
302C22—81no—
303C22—81no—
304C22#1062265711yescharacteristic
305C22#1062265811yescharacteristic
306C22#1062283511yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—81no—
311C4—82no—
312C4#1062266211yescharacteristic
313C4#1062266411yescharacteristic
314C4#1062279012yes—
315C4#1062284111yescharacteristic
316C4#1062285111yescharacteristic
317C2—21no—
318C2—21no—
319C2—82no—
320C2#1306981611yescharacteristic
321C2#1306987411yescharacteristic
322C2#1306988611yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#476C2
socleC22×C11#394
prime radicalC22×D4×C11D4
hypercenterC2×#476D11
hypocenterC11#10453
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
2. #13067390C2semidirect
3. #13067301C2semidirect
4. #13067297C2semidirect
6. #13066513C2semidirect
261. C11#10453semidirect

Maximal subgroups

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

subgroupindex
#130686082
#130673902
#130673012
#130672972
#130670072
#130665132
C2×C11×#4762
#1045311