Finite Group Databasebeta

← #14657384

Subgroups — #14657384

Order 2816.

408 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 95 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×#10622462C211yesmaximal, characteristic
2#13068609C211yesmaximal, characteristic
3#13067390C211yesmaximal, characteristic
4#13067289C211yesmaximal, characteristic
5#13067287C211yesmaximal, characteristic
6#13067012C211yesmaximal, characteristic
7C11×#1301C211yesmaximal, characteristic
8C22×Dic44—21no—
9C2×#66922C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×#66888—21no—
15C2×#66880—21no—
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18#10622462—22no—
19#10622462—22no—
20#10622192—21no—
21#10622124—22no—
22#10622120—22no—
23#10622117—22no—
24#10622094—22no—
25C22×Dic22—21no—
26C22×Dic22D411yescharacteristic
27C2×C11×M16—21no—
28C22×C8×C11—21no—
29C2×C42×C11C2311yescharacteristic
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11D411yescharacteristic
33C2×Dic11⋊C4—21no—
34C2×C4×Dic11—21no—
35C2×#4318—21no—
36C2×Dic44—24no—
37C2×Dic44—42no—
38C2×Dic44—42no—
39#66922—21no—
40#66922—21no—
41#66922—21no—
42#66922D412yes—
43C4×Dic22—21no—
44C4×Dic22—21no—
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8D412yes—
52C11×C22⋊C8—21no—
53C4×C8×C11—21no—
54C22⋊(C11⋊C8)—21no—
55#66888—42no—
56#66880—24no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)D412yes—
60C4×C11⋊C8—21no—
61#10446—111nomaximal, Sylow
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11#4111yescharacteristic
64C22×C4×C11#4111yescharacteristic
65C22×Dic11—21no—
66C22×Dic11—21no—
67C22×Dic11—41no—
68C2×Dic22—21no—
69C2×Dic22—22no—
70C2×Dic22—21no—
71C2×Dic22—21no—
72C2×Dic22—21no—
73C2×Dic22—21no—
74C2×Dic22—41no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22D812yes—
80C11×M16—41no—
81C11×M16—41no—
82C2×C8×C11—22no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11#4111yescharacteristic
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—22no—
94C4⋊Dic11—22no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99C4×Dic11—41no—
100C4×Dic11—41no—
101#4318—41no—
102#4318—41no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—41no—
105Dic44—48no—
106C2×#462—111no—
107#1801—111no—
108#1571—111no—
109#1546—111no—
110#1546—111no—
111#1479—111no—
112#1301D1111yescharacteristic
113C23×C11#12311yescharacteristic
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×D811yescharacteristic
123C2×C4×C11#13511yescharacteristic
124C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C11#13711yescharacteristic
126C2×Dic11—22no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—42no—
131C2×Dic11—81no—
132C2×Dic11—81no—
133C2×Dic11—81no—
134Dic22—22no—
135Dic22—22no—
136Dic22—41no—
137Dic22—41no—
138Dic22—42no—
139Dic22—42no—
140Dic22—81no—
141Dic22—81no—
142C8×C11—42no—
143C8×C11—81no—
144C8×C11—81no—
145C11⋊C8—42no—
146C11⋊C8—81no—
147C22×Q16—221no—
148C2×C4⋊Q8—111no—
149C2×C4×Q8—111no—
150#462—222no—
151#462—222no—
152#431—111no—
153#431C2×D1111yescharacteristic
154#423—111no—
155#423C2×D1111yescharacteristic
156C2×C4⋊C8C2×D1111yescharacteristic
157C2×#103—221no—
158C2×#101—221no—
159#343—221no—
160#335—222no—
161#332—222no—
162#332—222no—
163Q8⋊C8—222no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11#39411yescharacteristic
167C22×C11#48011yescharacteristic
168C22×C11#48211yescharacteristic
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11#44711yescharacteristic
173C4×C11#45211yescharacteristic
174C4×C11#46611yescharacteristic
175C4×C11#46811yescharacteristic
176C4×C11#47312yes—
177Dic11—42no—
178Dic11—81no—
179Dic11—82no—
180C22×Q8—111no—
181C22×Q8—221no—
182C2×Q16—224no—
183C2×Q16—442no—
184C2×Q16—442no—
185C2×M16—21no—
186C2×M16—221no—
187C22×C8—21no—
188C4⋊Q8—112no—
189C4⋊Q8—221no—
190C4⋊Q8—221no—
191C4⋊Q8—221no—
192C4×Q8—221no—
193C4×Q8—221no—
194C4×Q8—221no—
195C4×Q8—221no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C42—221no—
201C2×C42C22×D1111yescharacteristic
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—112no—
207C4⋊C8—221no—
208C4⋊C8—221no—
209C4⋊C8D4412yes—
210#103—224no—
211#101—442no—
212C22⋊C8—21no—
213C22⋊C8—221no—
214C4×C8—21no—
215C4×C8—221no—
216C2×C11—21no—
217C2×C11—21no—
218C2×C11#203311yescharacteristic
219C2×C11#204711yescharacteristic
220C2×C11#204911yescharacteristic
221C2×Q8—112no—
222C2×Q8—221no—
223C2×Q8—221no—
224C2×Q8—222no—
225C2×Q8—221no—
226C2×Q8—221no—
227C2×Q8—221no—
228C2×Q8—441no—
229C2×Q8—441no—
230C2×Q8—441no—
231C2×Q8—441no—
232C2×Q8—441no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—441no—
236C22×C4#433911yescharacteristic
237C22×C4D4×D1111yescharacteristic
238C22×C4#434311yescharacteristic
239Q16—448no—
240M16—41no—
241M16—41no—
242M16—441no—
243M16—441no—
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—222no—
250C2×C8—441no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—222no—
254C4⋊C4—222no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C42—441no—
260C42—441no—
261C42C2×D4411yescharacteristic
262C42#433911yescharacteristic
263C42D4×D1111yescharacteristic
264C42D4×D1111yescharacteristic
265C11#1044611yescharacteristic, complemented, Sylow
266C23#6694711yescharacteristic
267Q8—222no—
268Q8—222no—
269Q8—441no—
270Q8—441no—
271Q8—442no—
272Q8—442no—
273Q8—881no—
274Q8—881no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—222no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—442no—
282C2×C4—881no—
283C2×C4—881no—
284C2×C4—881no—
285C2×C4#6692811yescharacteristic
286C2×C4#6693511yescharacteristic
287C2×C4#6693711yescharacteristic
288C2×C4#6693711yescharacteristic
289C2×C4#6694711yescharacteristic
290C2×C4#6694811yescharacteristic
291C2×C4D8×D1111yescharacteristic
292C2×C4#6696711yescharacteristic
293C2×C4#6696911yescharacteristic
294C2×C4#6697111yescharacteristic
295C8—42no—
296C8—81no—
297C8—81no—
298C8—442no—
299C8—881no—
300C22—21no—
301C22—21no—
302C22#1062228511yescharacteristic
303C22#1062247911yescharacteristic
304C22#1062249511yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—442no—
309C4—881no—
310C4—882no—
311C4#1062238611yescharacteristic
312C4#1062238811yescharacteristic
313C4#1062242311yescharacteristic
314C4#1062242511yescharacteristic
315C4#1062250912yes—
316C2—21no—
317C2—21no—
318C2#1306980111yescharacteristic
319C2#1306988511yescharacteristic
320C2#1306989911yescharacteristic
subgroupG/H
centerC22#10622285
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1301C2
socleC22×C11#394
prime radicalC23×C11#123
hypercenter#1301D11
hypocenterC11#10446
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
265. C11#10446semidirect

Maximal subgroups

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

subgroupindex
C2×#106224622
#130686092
#130673902
#130672892
#130672872
#130670122
C11×#13012
#1044611