Finite Group Databasebeta

← #14658598

Subgroups — #14658598

Order 2816.

330 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 89 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#13068626C211yesmaximal, characteristic
2#13067392C211yesmaximal, characteristic, complemented
3#13067007C211yesmaximal, characteristic
4#13066511C211yesmaximal, characteristic, complemented
5#13066476C211yesmaximal, characteristic, complemented
6#13066476C211yesmaximal, characteristic, complemented
7C11×#1800C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C11×#423C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C11×#100—21no—
12C2×#66896—21no—
13#10622549C2211yescharacteristic
14#10622538C2211yescharacteristic
15#10622538C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C11×#343—21no—
18D4⋊(C11⋊C8)—22no—
19#10622167—21no—
20#10622117—22no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11—21no—
23C2×C11×M16—21no—
24C2×C11×M16—21no—
25C4×D4×C11—21no—
26C4×D4×C11—21no—
27C4×D4×C11—21no—
28C4×D4×C11—21no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C22⋊C4—21no—
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11—21no—
33C22×C11⋊C8—21no—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C4⋊C8—21no—
38C11×#100—42no—
39#66896—42no—
40C11⋊#95—21no—
41C11⋊#95—21no—
42C22⋊(C11⋊C8)—21no—
43C22⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4×C11⋊C8—21no—
49C4×C11⋊C8D412yes—
50#10637—111nomaximal, Sylow
51C24×C11—21no—
52C2×D4×C11—21no—
53C2×D4×C11—21no—
54C2×D4×C11—21no—
55C2×D4×C11—21no—
56C2×D4×C11—21no—
57C2×D4×C11D812yes—
58C22×C4×C11—21no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—82no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11#4111yescharacteristic
64C22×C4×C11#4111yescharacteristic
65C22×Dic11—41no—
66C11×M16—41no—
67C11×M16—41no—
68C11×M16—41no—
69C11×M16—41no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C22⋊C4—41no—
75C11×C22⋊C4—41no—
76C42×C11C2×D411yescharacteristic
77C42×C11#4111yescharacteristic
78C42×C11#4111yescharacteristic
79C42×C11#4111yescharacteristic
80C4⋊Dic11—41no—
81C4⋊Dic11—41no—
82C2×C11⋊C8—22no—
83C2×C11⋊C8—41no—
84C2×C11⋊C8—41no—
85C2×C11⋊C8—41no—
86C2×C11⋊C8—41no—
87#1804—111no—
88#1800D1111yescharacteristic
89#1571—111no—
90#1478—111no—
91#1301—111no—
92#1286—111no—
93#1286—111no—
94C23×C11—22no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11—81no—
98C23×C11—81no—
99C23×C11#12311yescharacteristic
100D4×C11—22no—
101D4×C11—22no—
102D4×C11—41no—
103D4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—82no—
108C2×C4×C11—82no—
109C2×C4×C11—81no—
110C2×C4×C11#12111yescharacteristic
111C2×C4×C11#12311yescharacteristic
112C2×C4×C11#12311yescharacteristic
113C2×C4×C11#12411yescharacteristic
114C2×C4×C11#12611yescharacteristic
115C2×C4×C11#12611yescharacteristic
116C2×C4×C11C2×D811yescharacteristic
117C2×C4×C11#13511yescharacteristic
118C2×C4×C11#13711yescharacteristic
119C2×C4×C11#13711yescharacteristic
120C2×Dic11—81no—
121C2×Dic11—81no—
122C2×Dic11—81no—
123C8×C11—81no—
124C8×C11—81no—
125C11⋊C8—42no—
126C11⋊C8—81no—
127C11⋊C8—81no—
128C2×C4×D4C2×D1111yescharacteristic
129#431—111no—
130#431—111no—
131#423C2×D1111yescharacteristic
132#423C2×D1111yescharacteristic
133C2×C4⋊C8—111no—
134C2×#102—221no—
135C2×#100—21no—
136#382—111no—
137#343—21no—
138#340—221no—
139#335—222no—
140D4⋊C8—222no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—42no—
144C22×C11—82no—
145C22×C11—82no—
146C22×C11—81no—
147C22×C11—81no—
148C22×C11#39711yescharacteristic
149C22×C11#48011yescharacteristic
150C22×C11#48511yescharacteristic
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—81no—
156C4×C11#46611yescharacteristic
157C4×C11#47011yescharacteristic
158C4×C11#48011yescharacteristic
159C4×C11#48511yescharacteristic
160Dic11—161no—
161C22×D4C22⋊D1111yescharacteristic
162C23×C4—21no—
163C2×M16—21no—
164C2×M16—21no—
165C22×C8—221no—
166C4×D4—21no—
167C4×D4—21no—
168C4×D4—21no—
169C4×D4—21no—
170C2×C4⋊C4—221no—
171C2×C4⋊C4C22⋊D1111yescharacteristic
172C2×C22⋊C4—21no—
173C2×C42C22×D1111yescharacteristic
174C4⋊C8—21no—
175C4⋊C8—21no—
176C4⋊C8—21no—
177C4⋊C8—21no—
178C4⋊C8—221no—
179C4⋊C8—221no—
180C4⋊C8—221no—
181C4⋊C8—221no—
182#102—442no—
183#100—42no—
184C22⋊C8—221no—
185C22⋊C8—221no—
186C4×C8—112no—
187C4×C8—221no—
188#95—221no—
189#95—221no—
190C2×C11—21no—
191C2×C11—21no—
192C2×C11—82no—
193C2×C11#207511yescharacteristic
194C2×C11#208011yescharacteristic
195C2×C11#208111yescharacteristic
196C24—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—21no—
202C2×D4#432312yes—
203C22×C4—21no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—82no—
207C22×C4—441no—
208C22×C4#433911yescharacteristic
209C22×C4#433911yescharacteristic
210C22×C4C2×C22⋊D1111yescharacteristic
211M16—41no—
212M16—41no—
213M16—41no—
214M16—41no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—222no—
218C2×C8—441no—
219C2×C8—441no—
220C2×C8—441no—
221C2×C8—441no—
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—441no—
225C4⋊C4—441no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C42D4×D1111yescharacteristic
229C42#434111yescharacteristic
230C42#434111yescharacteristic
231C42#434111yescharacteristic
232C11#1063711yescharacteristic, complemented, Sylow
233C23—22no—
234C23—41no—
235C23—41no—
236C23—81no—
237C23—81no—
238C23#6698211yescharacteristic
239D4—22no—
240D4—22no—
241D4—41no—
242D4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—82no—
247C2×C4—82no—
248C2×C4—81no—
249C2×C4—881no—
250C2×C4—881no—
251C2×C4—881no—
252C2×C4#6693211yescharacteristic
253C2×C4#6693211yescharacteristic
254C2×C4#6693611yescharacteristic
255C2×C4#6693811yescharacteristic
256C2×C4C2×#432311yescharacteristic
257C2×C4#6698811yescharacteristic
258C2×C4#6699211yescharacteristic
259C2×C4#6699511yescharacteristic
260C2×C4#6700311yescharacteristic
261C2×C4#6700411yescharacteristic
262C8—81no—
263C8—81no—
264C8—442no—
265C8—881no—
266C8—881no—
267C22—21no—
268C22—21no—
269C22—42no—
270C22—82no—
271C22—82no—
272C22—81no—
273C22—81no—
274C22#1062256511yescharacteristic
275C22#1062258011yescharacteristic
276C22#1062260911yescharacteristic
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—81no—
282C4—1761no—
283C4#1062264611yescharacteristic
284C4#1062265111yescharacteristic
285C4#1062265811yescharacteristic
286C4#1062266511yescharacteristic
287C2—21no—
288C2—21no—
289C2—82no—
290C2#1307004211yescharacteristic
291C2#1307006911yescharacteristic
292C2#1307007611yescharacteristic
subgroupG/H
centerC22#10622565
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1800C2
socleC22×C11#397
prime radicalC22×D4×C11D4
hypercenter#1800D11
hypocenterC11#10637
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
2. #13067392C2semidirect
4. #13066511C2semidirect
5. #13066476C2semidirect
6. #13066476C2semidirect
232. C11#10637semidirect

Maximal subgroups

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

subgroupindex
#130686262
#130673922
#130670072
#130665112
#130664762
C11×#18002
#1063711