Finite Group Databasebeta

← #14664141

Subgroups — #14664141

Order 2816.

434 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 73 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#13071905C211yesmaximal, characteristic
2#13068411C211yesmaximal, characteristic, complemented
3#13066938C211yesmaximal, characteristic, complemented
4#13066643C211yesmaximal, characteristic, complemented
5#13066620C211yesmaximal, characteristic
6#13066618C211yesmaximal, characteristic
7C11×#1353C211yesmaximal, characteristic, complemented
8C2×#66946C411yescharacteristic
9C2×#66940C2211yescharacteristic
10C11×#400C2211yescharacteristic
11C2×#66888—21no—
12M16×Dic11—21no—
13#10622604C2211yescharacteristic
14#10622595C411yescharacteristic
15#10622331—21no—
16#10622288—21no—
17#10622286—21no—
18#10622285C411yescharacteristic
19#10622279—21no—
20#10622279—21no—
21#10622261C411yescharacteristic
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×D44C2×C411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22D411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×Dic11⋊C4C2×C411yescharacteristic
39C2×Dic11⋊C4D411yescharacteristic
40C2×C4×Dic11—21no—
41C2×C4×Dic11C2×C411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×#4318—21no—
45#66946—41no—
46#66946—41no—
47#66940—41no—
48#66940—41no—
49C11×C22⋊C8—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95C2×C411yescharacteristic
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C22⋊(C11⋊C8)—21no—
58#66888—24no—
59#66879—41no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62C8×Dic11—41no—
63#11734—111nomaximal, Sylow
64C23×D11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C2×D44—41no—
76C2×D44—42no—
77C2×C4×D11—42no—
78C2×C4×D11—42no—
79C2×C4×D11—41no—
80C2×C4×D11—41no—
81C2×Dic22—22no—
82C2×Dic22—21no—
83C2×Dic22—21no—
84C2×Dic22—41no—
85C11×M16—22no—
86C11×M16—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91(C2×D11)⋊C4—42no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—42no—
106#4318—22no—
107#4318—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110#2398—111no—
111C4×#101—111no—
112#1461—111no—
113#1353—111no—
114#1353D1111yescharacteristic, complemented
115#1345—111no—
116#1345—111no—
117C23×C11C2×C22⋊C411yescharacteristic
118C22×D11—22no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11#13511yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—22no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11#9911yescharacteristic
151C2×Dic11#9911yescharacteristic
152C2×Dic11#10412yes—
153D44—42no—
154D44—42no—
155C4×D11—82no—
156C4×D11—82no—
157Dic22—42no—
158Dic22—42no—
159C8×C11—42no—
160C8×C11—81no—
161C11⋊C8—42no—
162C11⋊C8—81no—
163C2×C4×Q8—111no—
164C2×C4×D4—111no—
165#431—221no—
166C2×#101—221no—
167C4×M16—221no—
168#400—111no—
169#400C2×D1111yescharacteristic
170#397—221no—
171#394—111no—
172#394—111no—
173#393—221no—
174C4×C22⋊C4—221no—
175C4×C22⋊C4—221no—
176#376—111no—
177#343—111no—
178#343C2×D1111yescharacteristic
179#324—111no—
180#324—221no—
181#324C2×D1111yescharacteristic
182C22×C11—21no—
183C22×C11—21no—
184C22×C11C2×#9911yescharacteristic
185C22×C11#41611yescharacteristic
186C22×C11C2×#10411yescharacteristic
187C2×D11—42no—
188C2×D11—42no—
189C2×D11—42no—
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—81no—
199C4×C11—81no—
200Dic11—21no—
201Dic11—22no—
202Dic11—41no—
203Dic11—41no—
204Dic11—81no—
205Dic11#35512yes—
206C22×Q8—111no—
207C22×D4—111no—
208C23×C4—221no—
209C2×M16—21no—
210C2×M16—221no—
211C4×Q8—441no—
212C4×Q8—441no—
213C4×D4—441no—
214C4×D4—441no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4C4×D1111yescharacteristic
218C2×C4⋊C4C22×D1111yescharacteristic
219C2×C22⋊C4—221no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C42—111no—
225C2×C42—111no—
226C2×C42—111no—
227C2×C42—221no—
228C4⋊C8—441no—
229#101—224no—
230C22⋊C8—21no—
231C22⋊C8—221no—
232#97—441no—
233C4×C8—441no—
234C4×C8—441no—
235#95—21no—
236#95—21no—
237#95—111no—
238#95—221no—
239#95—221no—
240#95—221no—
241#95C4×D1111yescharacteristic
242C2×C11—21no—
243C2×C11—21no—
244C2×C11#150111yescharacteristic
245C2×C11#212011yescharacteristic
246C2×C11C2×#35511yescharacteristic
247D11—82no—
248C24—221no—
249C2×Q8—222no—
250C2×Q8—221no—
251C2×Q8—221no—
252C2×Q8—441no—
253C2×D4—441no—
254C2×D4—442no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—221no—
262C22×C4—441no—
263C22×C4—441no—
264C22×C4—442no—
265C22×C4—442no—
266C22×C4C2×C4×D1111yescharacteristic
267C22×C4D4×D1111yescharacteristic
268C22×C4D4×D1111yescharacteristic
269M16—22no—
270M16—41no—
271M16—222no—
272M16—441no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—441no—
276C2×C8—441no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C22⋊C4—442no—
282C22⋊C4—442no—
283C22⋊C4—442no—
284C22⋊C4—442no—
285C22⋊C4—441no—
286C22⋊C4—441no—
287C42—221no—
288C42—221no—
289C42—221no—
290C42—221no—
291C42—221no—
292C42—221no—
293C42—442no—
294C11#1173411yescharacteristic, complemented, Sylow
295C23—222no—
296C23—441no—
297C23—441no—
298C23—441no—
299C23—441no—
300C23—441no—
301C23—441no—
302C23C22⋊C4×D1111yescharacteristic
303Q8—442no—
304Q8—442no—
305D4—442no—
306D4—442no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—111no—
320C2×C4—111no—
321C2×C4—112no—
322C2×C4—222no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—882no—
334C2×C4—882no—
335C2×C4#6696911yescharacteristic
336C2×C4#6697211yescharacteristic
337C8—42no—
338C8—81no—
339C8—442no—
340C8—881no—
341C22—21no—
342C22—21no—
343C22—442no—
344C22—442no—
345C22—442no—
346C22—881no—
347C22—881no—
348C22—881no—
349C22—881no—
350C22D11×#9911yescharacteristic
351C22#1062241711yescharacteristic
352C22D11×#10411yescharacteristic
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—112no—
360C4—222no—
361C4—221no—
362C4—441no—
363C4—441no—
364C4—881no—
365C2—21no—
366C2—21no—
367C2—882no—
368C2#1306710611yescharacteristic
369C2#1307025611yescharacteristic
370C2D11×#35511yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1353C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1353D11
hypocenterC11#11734
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
2. #13068411C2semidirect
3. #13066938C2semidirect
4. #13066643C2semidirect
7. C11×#1353C2semidirect
114. #1353D11semidirect
294. C11#11734semidirect

Maximal subgroups

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

subgroupindex
#130719052
#130684112
#130669382
#130666432
#130666202
#130666182
C11×#13532
#1173411