Finite Group Databasebeta

← #14657694

Subgroups — #14657694

Order 2816.

366 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 81 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#13079741C211yesmaximal, characteristic
2#13069604C211yesmaximal, characteristic, complemented
3#13067407C211yesmaximal, characteristic, complemented
4#13067289C211yesmaximal, characteristic, complemented
5#13067033C211yesmaximal, characteristic
6#13066505C211yesmaximal, characteristic, complemented
7C11×#1560C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622692—21no—
13#10622683—21no—
14#10622647—22no—
15#10622621—21no—
16#10622621—21no—
17#10622538C2211yescharacteristic
18#10622538C2211yescharacteristic
19C4×#4318C2211yescharacteristic
20C11×#333—21no—
21C11×#331—21no—
22#10622192—22no—
23D4⋊(C11⋊C8)—22no—
24#10622120—22no—
25#10622118—21no—
26#10622117—21no—
27C2×C11×#41—21no—
28C22×Dic22—21no—
29C2×C11×M16—21no—
30C2×C11×M16—21no—
31C11×C4⋊Q8D411yescharacteristic
32C11×#127D411yescharacteristic
33C11×#124—21no—
34C11×#121—21no—
35C11×#121—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C2×C42×C11C2311yescharacteristic
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11D412yes—
41C2×#4318—21no—
42#66922—21no—
43#66922—21no—
44#66922—21no—
45#66922—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50#66896—22no—
51#66896—22no—
52C22⋊(C11⋊C8)—21no—
53C22⋊(C11⋊C8)—21no—
54#66872—22no—
55#66872—22no—
56C4⋊(C11⋊C8)D411yescharacteristic
57C4⋊(C11⋊C8)D411yescharacteristic
58C4⋊(C11⋊C8)D412yes—
59#66867—21no—
60C4×C11⋊C8—21no—
61C4×C11⋊C8—21no—
62C4×C11⋊C8—21no—
63#10491—111nomaximal, Sylow
64C11×#41—82no—
65C2×Q8×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×Dic11—22no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—81no—
78C2×Dic22—81no—
79C11×M16—42no—
80C11×M16—81no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11#4111yescharacteristic
91C4⋊Dic11—22no—
92C4⋊Dic11—22no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95#4318—22no—
96#4318—41no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—41no—
101#3227—111no—
102#1997—111no—
103#1574—111no—
104#1560D1111yescharacteristic
105#1546—111no—
106#1484—111no—
107#1299—111no—
108C23×C11—41no—
109C23×C11#12311yescharacteristic
110Q8×C11—81no—
111D4×C11—41no—
112D4×C11—41no—
113D4×C11—41no—
114D4×C11—41no—
115D4×C11—81no—
116D4×C11—82no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—82no—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12311yescharacteristic
129C2×C4×C11#12411yescharacteristic
130C2×Dic11—42no—
131C2×Dic11—82no—
132Dic22—82no—
133Dic22—81no—
134Dic22—81no—
135C8×C11—81no—
136C8×C11—81no—
137C11⋊C8—42no—
138C11⋊C8—41no—
139C11⋊C8—41no—
140C11⋊C8—42no—
141#532C2×D1111yescharacteristic
142C2×C4⋊Q8—111no—
143#498—221no—
144#486—221no—
145#481—222no—
146#476—221no—
147#476—221no—
148#431—111no—
149#431—111no—
150#423C2×D1111yescharacteristic
151#423C2×D1111yescharacteristic
152C4×M16—111no—
153#343—222no—
154#335—221no—
155#334—221no—
156#333—21no—
157#332—222no—
158#331—21no—
159D4⋊C8—222no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—81no—
164C22×C11—81no—
165C22×C11—81no—
166C22×C11#39411yescharacteristic
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—81no—
171C4×C11#45411yescharacteristic
172C4×C11#45611yescharacteristic
173C4×C11#47111yescharacteristic
174C4×C11#47112yes—
175C4×C11#47211yescharacteristic
176Dic11—82no—
177C2×#41—21no—
178C22×Q8—221no—
179C2×M16—21no—
180C2×M16—21no—
181C2×M16—221no—
182C4⋊Q8—221no—
183C4⋊Q8—221no—
184C4⋊Q8—221no—
185C4⋊Q8—221no—
186C4⋊Q8C22⋊D1111yescharacteristic
187#127C22⋊D1111yescharacteristic
188#124—21no—
189#121—21no—
190#121—21no—
191C4×D4—21no—
192C4×D4—21no—
193C2×C4⋊C4—112no—
194C2×C4⋊C4—221no—
195C2×C42C22×D1111yescharacteristic
196#106—222no—
197#106—222no—
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—112no—
203C4⋊C8—111no—
204C4⋊C8—111no—
205#102—222no—
206#102—222no—
207C22⋊C8—221no—
208C22⋊C8—221no—
209#97—221no—
210C4×C8—221no—
211C4×C8—221no—
212C4×C8—221no—
213C2×C11—41no—
214C2×C11—161no—
215C2×C11#203811yescharacteristic
216C2×C11#204611yescharacteristic
217C2×C11#205111yescharacteristic
218#41—82no—
219C2×Q8—21no—
220C2×Q8—441no—
221C2×Q8—441no—
222C2×Q8—881no—
223C2×Q8—881no—
224C2×D4—21no—
225C2×D4—21no—
226C2×D4—21no—
227C2×D4—41no—
228C22×C4—41no—
229C22×C4—222no—
230C22×C4#433911yescharacteristic
231C22×C4D4×D1111yescharacteristic
232C22×C4#434111yescharacteristic
233M16—42no—
234M16—81no—
235M16—222no—
236M16—441no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—222no—
240C2×C8—221no—
241C2×C8—221no—
242C2×C8—441no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—222no—
246C4⋊C4—222no—
247C4⋊C4—441no—
248C4⋊C4—441no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C42#433911yescharacteristic
252C42D4×D1111yescharacteristic
253C42D4×D1111yescharacteristic
254C42C2×C22⋊D1111yescharacteristic
255C11#1049111yescharacteristic, complemented, Sylow
256C23—41no—
257C23#6693611yescharacteristic
258Q8—81no—
259Q8—882no—
260Q8—881no—
261Q8—881no—
262D4—41no—
263D4—41no—
264D4—41no—
265D4—41no—
266D4—81no—
267D4—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—82no—
275C2×C4—442no—
276C2×C4—882no—
277C2×C4#6693711yescharacteristic
278C2×C4#6693711yescharacteristic
279C2×C4#6693811yescharacteristic
280C2×C4#6698211yescharacteristic
281C2×C4#6699011yescharacteristic
282C2×C4#6699211yescharacteristic
283C8—81no—
284C8—81no—
285C8—442no—
286C8—441no—
287C8—441no—
288C8—442no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—81no—
293C22—81no—
294C22—81no—
295C22#1062257211yescharacteristic
296C4—21no—
297C4—21no—
298C4—21no—
299C4—81no—
300C4—882no—
301C4#1062236112yes—
302C4#1062281211yescharacteristic
303C4#1062281411yescharacteristic
304C4#1062281611yescharacteristic
305C4#1062281811yescharacteristic
306C2—41no—
307C2—161no—
308C2#1306983111yescharacteristic
309C2#1306987711yescharacteristic
310C2#1306990611yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1560C2
socleC22×C11#394
prime radicalC11×#532C22
hypercenter#1560D11
hypocenterC11#10491
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1560

Complements

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

NH ≅ G/Ntype
2. #13069604C2semidirect
3. #13067407C2semidirect
4. #13067289C2semidirect
6. #13066505C2semidirect
255. C11#10491semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130696042
#130674072
#130672892
#130670332
#130665052
C11×#15602
#1049111