Finite Group Databasebeta

← #14657397

Subgroups — #14657397

Order 2816.

408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#10622459C211yesmaximal, characteristic
2#13068605C211yesmaximal, characteristic
3#13067300C211yesmaximal, characteristic, complemented
4#13067298C211yesmaximal, characteristic, complemented
5#13067006C211yesmaximal, characteristic
6#13066513C211yesmaximal, characteristic, complemented
7C11×#1570C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×#66887—21no—
14C2×#66885—21no—
15C2×#66882—21no—
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18#10622459—22no—
19#10622459—22no—
20C11×#334—22no—
21#10622192—21no—
22#10622121—22no—
23#10622120—22no—
24#10622119—22no—
25C22×D44D411yescharacteristic
26C22×C4×D11—21no—
27C22×Dic22—21no—
28C2×C11×M16—21no—
29C22×C8×C11—21no—
30C2×C42×C11C2311yescharacteristic
31C2×(C2×D11)⋊C4—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11D411yescharacteristic
35C2×#4318—21no—
36C4×D44—21no—
37C4×D44—21no—
38C4×D44—21no—
39C4×D44—21no—
40#66922—21no—
41#66922—21no—
42#66922—21no—
43#66922D412yes—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8D412yes—
48C11×C4⋊C8D412yes—
49C11×C22⋊C8—21no—
50C4×C8×C11—21no—
51C22⋊(C11⋊C8)—21no—
52#66887—42no—
53#66885—24no—
54#66882—24no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4×C11⋊C8—21no—
59#10448—111nomaximal, Sylow
60C23×D11—21no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11#4111yescharacteristic
63C22×C4×C11#4111yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—41no—
66C2×D44—21no—
67C2×D44—21no—
68C2×D44—21no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44SD1612yes—
72C2×C4×D11—41no—
73C2×C4×D11—41no—
74C2×C4×D11—82no—
75C2×Dic22—22no—
76C2×Dic22—41no—
77C2×Dic22—82no—
78C11×M16—41no—
79C11×M16—41no—
80C2×C8×C11—22no—
81C2×C8×C11—22no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C42×C11C2×D411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11#4111yescharacteristic
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91C4⋊Dic11—21no—
92C4⋊Dic11—22no—
93C4⋊Dic11—22no—
94C4⋊Dic11—21no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97#4318—41no—
98#4318—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×#474—111no—
102#1800—111no—
103#1570D1111yescharacteristic, complemented
104#1549—111no—
105#1548—111no—
106#1478—111no—
107#1301—111no—
108C23×C11#12311yescharacteristic
109C22×D11—22no—
110C22×D11—41no—
111C22×D11—41no—
112C22×D11—81no—
113C22×D11—81no—
114C2×C4×C11—22no—
115C2×C4×C11—41no—
116C2×C4×C11#12011yescharacteristic
117C2×C4×C11#12111yescharacteristic
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12111yescharacteristic
120C2×C4×C11#12311yescharacteristic
121C2×C4×C11#12411yescharacteristic
122C2×C4×C11C2×SD1611yescharacteristic
123C2×C4×C11#13511yescharacteristic
124C2×C4×C11#13711yescharacteristic
125C2×C4×C11#13711yescharacteristic
126C2×Dic11—42no—
127C2×Dic11—41no—
128C2×Dic11—82no—
129C2×Dic11—81no—
130D44—22no—
131D44—22no—
132D44—41no—
133D44—41no—
134C4×D11—82no—
135C4×D11—82no—
136Dic22—82no—
137Dic22—82no—
138C8×C11—42no—
139C8×C11—42no—
140C8×C11—81no—
141C11⋊C8—81no—
142C11⋊C8—81no—
143C2×C4⋊Q8—111no—
144C2×C4×D4—111no—
145#474—222no—
146#474—222no—
147#431—111no—
148#431C2×D1111yescharacteristic
149C2×#107—221no—
150#423—111no—
151#423C2×D1111yescharacteristic
152C2×C4⋊C8C2×D1111yescharacteristic
153C2×#102—221no—
154C2×#100—221no—
155#343—221no—
156#334—22no—
157#333—222no—
158#332—222no—
159D4⋊C8—222no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11#39411yescharacteristic
163C22×C11#48311yescharacteristic
164C22×C11#48511yescharacteristic
165C2×D11—42no—
166C2×D11—82no—
167C2×D11—81no—
168C2×D11—81no—
169C2×D11—82no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11#44811yescharacteristic
174C4×C11#45211yescharacteristic
175C4×C11#46511yescharacteristic
176C4×C11#47011yescharacteristic
177C4×C11#47212yes—
178Dic11—82no—
179Dic11—81no—
180C22×Q8—221no—
181C22×D4—111no—
182C23×C4—221no—
183C2×M16—21no—
184C2×M16—221no—
185C22×C8—21no—
186C4⋊Q8—112no—
187C4⋊Q8—221no—
188C4⋊Q8—221no—
189C4⋊Q8—221no—
190C4×D4—221no—
191C4×D4—221no—
192C4×D4—221no—
193C4×D4—221no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C22⋊C4—221no—
198C2×C42C22×D1111yescharacteristic
199#107—224no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—221no—
204C4⋊C8—221no—
205C4⋊C8—221no—
206C4⋊C8D4412yes—
207C4⋊C8C22⋊D1112yes—
208#102—224no—
209#100—442no—
210C22⋊C8—21no—
211C22⋊C8—221no—
212C4×C8—21no—
213C4×C8—221no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11#203511yescharacteristic
217C2×C11#204511yescharacteristic
218C2×C11#204911yescharacteristic
219D11—82no—
220C24—221no—
221C2×Q8—222no—
222C2×Q8—441no—
223C2×Q8—882no—
224C2×D4—112no—
225C2×D4—221no—
226C2×D4—221no—
227C2×D4—221no—
228C2×D4—221no—
229C2×D4—221no—
230C22×C4—221no—
231C22×C4—441no—
232C22×C4—441no—
233C22×C4—441no—
234C22×C4—882no—
235C22×C4#433911yescharacteristic
236C22×C4D4×D1111yescharacteristic
237C22×C4#434311yescharacteristic
238M16—41no—
239M16—41no—
240M16—441no—
241M16—441no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—441no—
248C2×C8—441no—
249C4⋊C4—221no—
250C4⋊C4—222no—
251C4⋊C4—222no—
252C4⋊C4—221no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C22⋊C4—441no—
256C22⋊C4—441no—
257C42C2×D4411yescharacteristic
258C42D4×D1111yescharacteristic
259C42#434311yescharacteristic
260C42C2×C22⋊D1111yescharacteristic
261C11#1044811yescharacteristic, complemented, Sylow
262C23—222no—
263C23—441no—
264C23—441no—
265C23—881no—
266C23—881no—
267C23#6694711yescharacteristic
268Q8—882no—
269Q8—882no—
270D4—222no—
271D4—222no—
272D4—441no—
273D4—441no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—441no—
277C2×C4—442no—
278C2×C4—882no—
279C2×C4—882no—
280C2×C4—882no—
281C2×C4—881no—
282C2×C4#6694711yescharacteristic
283C2×C4#6694811yescharacteristic
284C2×C4#6694811yescharacteristic
285C2×C4SD16×D1111yescharacteristic
286C2×C4#6696811yescharacteristic
287C2×C4#6696811yescharacteristic
288C2×C4#6696911yescharacteristic
289C2×C4#6698311yescharacteristic
290C2×C4#6699011yescharacteristic
291C2×C4#6700011yescharacteristic
292C8—42no—
293C8—42no—
294C8—81no—
295C8—881no—
296C8—881no—
297C22—21no—
298C22—21no—
299C22—442no—
300C22—882no—
301C22—882no—
302C22—881no—
303C22—881no—
304C22#1062247511yescharacteristic
305C22#1062248011yescharacteristic
306C22#1062260411yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—881no—
311C4—882no—
312C4#1062247711yescharacteristic
313C4#1062248111yescharacteristic
314C4#1062275512yes—
315C4#1062278311yescharacteristic
316C4#1062278611yescharacteristic
317C2—21no—
318C2—21no—
319C2—882no—
320C2#1306981411yescharacteristic
321C2#1306987211yescharacteristic
322C2#1306989811yescharacteristic
subgroupG/H
centerC22#10622604
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1570C2
socleC22×C11#394
prime radicalC22×D44D4
hypercenter#1570D11
hypocenterC11#10448
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
3. #13067300C2semidirect
4. #13067298C2semidirect
6. #13066513C2semidirect
7. C11×#1570C2semidirect
103. #1570D11semidirect
261. C11#10448semidirect

Maximal subgroups

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

subgroupindex
C2×#106224592
#130686052
#130673002
#130672982
#130670062
#130665132
C11×#15702
#1044811