Finite Group Databasebeta

← #14657388

Subgroups — #14657388

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×#10622644C211yesmaximal, characteristic
2#13067388C211yesmaximal, characteristic
3#13067289C211yesmaximal, characteristic
4#13067289C211yesmaximal, characteristic
5#13067011C211yesmaximal, characteristic
6#13066511C211yesmaximal, characteristic
7C11×#1801C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C22×#4326—21no—
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×#101—21no—
14#10622644—22no—
15#10622644—22no—
16C2×#66874—21no—
17#10622538C2211yescharacteristic
18#10622538C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×#343—21no—
21Q8⋊(C11⋊C8)—22no—
22#10622120—22no—
23#10622120—22no—
24#10622118—22no—
25C22×Q8×C11D411yescharacteristic
26C22×Dic22—21no—
27C2×C11×M16—21no—
28C2×C11×M16—21no—
29C4×Q8×C11—21no—
30C4×Q8×C11—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C2×#4326—24no—
38C2×#4326—42no—
39C2×#4326—42no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C22×C11⋊C8—21no—
43#66922—21no—
44#66922—21no—
45#66922—21no—
46#66922D412yes—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×#101—42no—
52C22⋊(C11⋊C8)—21no—
53C22⋊(C11⋊C8)—21no—
54#66874—24no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)D412yes—
58C4⋊(C11⋊C8)D412yes—
59C4×C11⋊C8—21no—
60C4×C11⋊C8—21no—
61#10447—111nomaximal, Sylow
62C2×Q8×C11—21no—
63C2×Q8×C11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11SD1612yes—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—41no—
74C2×Dic22—22no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C11×M16—41no—
81C11×M16—41no—
82C11×M16—41no—
83C11×M16—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C42×C11—41no—
91C42×C11—41no—
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11#4111yescharacteristic
96#4326—48no—
97C4⋊Dic11—22no—
98C4⋊Dic11—22no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×#462—111no—
107#1801D1111yescharacteristic
108#1570—111no—
109#1546—111no—
110#1546—111no—
111#1479—111no—
112#1301—111no—
113C23×C11#12311yescharacteristic
114Q8×C11—22no—
115Q8×C11—22no—
116Q8×C11—41no—
117Q8×C11—41no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—81no—
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12311yescharacteristic
130C2×C4×C11#12411yescharacteristic
131C2×C4×C11C2×SD1611yescharacteristic
132C2×C4×C11#13511yescharacteristic
133C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
135C2×Dic11—42no—
136C2×Dic11—81no—
137C2×Dic11—81no—
138Dic22—42no—
139Dic22—42no—
140Dic22—81no—
141Dic22—81no—
142C8×C11—81no—
143C8×C11—81no—
144C11⋊C8—42no—
145C11⋊C8—42no—
146C11⋊C8—81no—
147C22×Q16—221no—
148C2×C4⋊Q8—111no—
149C2×C4×Q8C2×D1111yescharacteristic
150#462—222no—
151#462—222no—
152#431—111no—
153#431—111no—
154#423C2×D1111yescharacteristic
155#423C2×D1111yescharacteristic
156C2×C4⋊C8—111no—
157C2×#103—221no—
158C2×#101—21no—
159#343—21no—
160#334—222no—
161#332—222no—
162#332—222no—
163Q8⋊C8—222no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11#39411yescharacteristic
167C22×C11#48111yescharacteristic
168C22×C11#48211yescharacteristic
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—42no—
173C4×C11—81no—
174C4×C11#44911yescharacteristic
175C4×C11#45011yescharacteristic
176C4×C11#46511yescharacteristic
177C4×C11#46911yescharacteristic
178C4×C11#47312yes—
179Dic11—82no—
180C22×Q8—221no—
181C22×Q8C22⋊D1111yescharacteristic
182C2×Q16—224no—
183C2×Q16—442no—
184C2×Q16—442no—
185C2×M16—21no—
186C2×M16—21no—
187C22×C8—221no—
188C4⋊Q8—112no—
189C4⋊Q8—221no—
190C4⋊Q8—221no—
191C4⋊Q8—221no—
192C4×Q8—21no—
193C4×Q8—21no—
194C4×Q8—21no—
195C4×Q8—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4C22⋊D1111yescharacteristic
200C2×C42—21no—
201C2×C42C22×D1111yescharacteristic
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—112no—
207C4⋊C8—112no—
208C4⋊C8—221no—
209C4⋊C8—221no—
210#103—224no—
211#101—42no—
212C22⋊C8—221no—
213C22⋊C8—221no—
214C4×C8—221no—
215C4×C8—221no—
216C2×C11—21no—
217C2×C11—21no—
218C2×C11#203411yescharacteristic
219C2×C11#204711yescharacteristic
220C2×C11#204911yescharacteristic
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—21no—
226C2×Q8—222no—
227C2×Q8—441no—
228C2×Q8—441no—
229C2×Q8—441no—
230C2×Q8—441no—
231C2×Q8—441no—
232C2×Q8#432512yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—441no—
236C22×C4#433911yescharacteristic
237C22×C4#433911yescharacteristic
238C22×C4C2×C22⋊D1111yescharacteristic
239Q16—448no—
240M16—41no—
241M16—41no—
242M16—41no—
243M16—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—222no—
247C2×C8—222no—
248C2×C8—441no—
249C2×C8—441no—
250C2×C8—441no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—222no—
256C4⋊C4—222no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C42—41no—
260C42—41no—
261C42D4×D1111yescharacteristic
262C42D4×D1111yescharacteristic
263C42D4×D1111yescharacteristic
264C42#434111yescharacteristic
265C11#1044711yescharacteristic, complemented, Sylow
266C23#6698211yescharacteristic
267Q8—22no—
268Q8—22no—
269Q8—41no—
270Q8—41no—
271Q8—442no—
272Q8—442no—
273Q8—881no—
274Q8—881no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—81no—
282C2×C4—442no—
283C2×C4—881no—
284C2×C4—881no—
285C2×C4#6693611yescharacteristic
286C2×C4#6693711yescharacteristic
287C2×C4#6693711yescharacteristic
288C2×C4#6693811yescharacteristic
289C2×C4#6698511yescharacteristic
290C2×C4#6699011yescharacteristic
291C2×C4#6699211yescharacteristic
292C2×C4C2×#432511yescharacteristic
293C2×C4#6700211yescharacteristic
294C2×C4#6700311yescharacteristic
295C8—81no—
296C8—81no—
297C8—442no—
298C8—442no—
299C8—881no—
300C22—21no—
301C22—21no—
302C22#1062257211yescharacteristic
303C22#1062258111yescharacteristic
304C22#1062261611yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—42no—
309C4—81no—
310C4—882no—
311C4#1062236812yes—
312C4#1062265011yescharacteristic
313C4#1062265211yescharacteristic
314C4#1062265911yescharacteristic
315C4#1062266111yescharacteristic
316C2—21no—
317C2—21no—
318C2#1306980511yescharacteristic
319C2#1306988211yescharacteristic
320C2#1306989611yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1801C2
socleC22×C11#394
prime radicalC23×C11#123
hypercenter#1801D11
hypocenterC11#10447
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
265. C11#10447semidirect

Maximal subgroups

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

subgroupindex
C2×#106226442
#130673882
#130672892
#130670112
#130665112
C11×#18012
#1044711