Finite Group Databasebeta

← #14646757

Subgroups — #14646757

Order 2816.

456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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#13077310C211yesmaximal, characteristic
2#13068654C211yesmaximal, characteristic, complemented
3#13067157C212yesmaximal
4#13066522C212yesmaximal, complemented
5C11×#1807C211yesmaximal, characteristic, complemented
6C23×C8×C11C2211yescharacteristic
7#10623322C2211yescharacteristic
8C2×#66954C411yescharacteristic, complemented
9C2×C11×#106—21no—
10C11×#380C2212yes—
11#10622820C2212yes—
12#10622820C2211yescharacteristic
13#10622724—21no—
14#10622724—21no—
15#10622723C411yescharacteristic, complemented
16C8×C22⋊D11—21no—
17C8×C22⋊D11—21no—
18C2×#66883—21no—
19#10622715C411yescharacteristic, complemented
20#10622714C411yescharacteristic, complemented
21C11×#340—21no—
22#10622190—21no—
23#10622090—22no—
24#10622089—22no—
25C23×C4×C11C2311yescharacteristic
26C2×#4339C2×C411yescharacteristic
27C22×C8×C11—42no—
28C22×C8×C11C2×C411yescharacteristic
29C22×C8×C11C2×C411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C22×C8×C11D411yescharacteristic
32C22×C8×C11D411yescharacteristic
33C22×C8×C11D411yescharacteristic
34C2×C11×C4⋊C4—22no—
35C2×C11×C22⋊C4—22no—
36#67006—21no—
37#66983D411yescharacteristic
38#66983Q811yescharacteristic
39#66982—21no—
40C4×C22⋊D11—21no—
41C4×C22⋊D11—21no—
42#66979C2×C411yescharacteristic
43#66977D411yescharacteristic
44#66977Q811yescharacteristic
45C2×#4318—22no—
46C2×#4318C2×C411yescharacteristic
47C2×#4318C2×C411yescharacteristic
48#66954—42no—
49C2×#4313—21no—
50C2×C8×D11—21no—
51C11×#106—42no—
52C11×#95—22no—
53C22⋊(C11⋊C8)—21no—
54C22⋊(C11⋊C8)—21no—
55C22⋊(C11⋊C8)—22no—
56C22⋊(C11⋊C8)—22no—
57(C2×D11)⋊C8—21no—
58(C2×D11)⋊C8—21no—
59#66883—42no—
60#66879—21no—
61Dic11⋊C8—21no—
62Dic11⋊C8—21no—
63C8×Dic11—21no—
64#8629—111nomaximal, Sylow
65C24×C11#4111yescharacteristic
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11—42no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×Q811yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C2×C22⋊D11—21no—
76C2×C22⋊D11—21no—
77C2×C22⋊D11—21no—
78#4339—41no—
79#4339—41no—
80C2×D44C4⋊C411yescharacteristic
81C2×C4×D11—21no—
82C2×Dic22C4⋊C411yescharacteristic
83C2×C8×C11—22no—
84C2×C8×C11—22no—
85C2×C8×C11—22no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C2×C8×C11C22⋊C411yescharacteristic
90C2×C8×C11C22⋊C411yescharacteristic
91C2×C8×C11C22⋊C411yescharacteristic
92C2×C8×C11C22⋊C411yescharacteristic
93C11×C4⋊C4—42no—
94C11×C4⋊C4—42no—
95C11×C22⋊C4—82no—
96C22⋊Dic11—21no—
97C22⋊Dic11—21no—
98C22⋊Dic11—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101C4⋊Dic11C4⋊C411yescharacteristic
102C4⋊Dic11C4⋊C411yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105C4×Dic11—21no—
106#4318—41no—
107#4318—41no—
108#4318—42no—
109#4318—42no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—42no—
113#4313—42no—
114C8×D11—42no—
115#2929—111no—
116#1810—111no—
117#1807D1111yescharacteristic, complemented
118#1513—112no—
119#1305—112no—
120C23×C11—22no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11#11711yescharacteristic
124C23×C11#12111yescharacteristic
125C23×C11C22⋊Q811yescharacteristic
126C22×D11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—82no—
137C2×C4×C11—82no—
138C2×C4×C11—82no—
139C2×C4×C11C2×C22⋊C411yescharacteristic
140C2×C4×C11C2×C4⋊C411yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11C22⋊Q811yescharacteristic
143C22⋊D11—42no—
144C22⋊D11—42no—
145C22⋊D11—42no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149D44—41no—
150C4×D11—41no—
151C4×D11—41no—
152Dic22—41no—
153C8×C11—21no—
154C8×C11—21no—
155C8×C11—21no—
156C8×C11#9912yes—
157C11⋊C8—41no—
158C11⋊C8—41no—
159C11⋊C8—82no—
160C2×#131—111no—
161C23×C8C2×D1111yescharacteristic
162#525—111no—
163#435—221no—
164#435—221no—
165C8×D4—221no—
166C8×D4—221no—
167C2×#108—221no—
168C2×#106—21no—
169#424—111no—
170#408—111no—
171#407—111no—
172#407—112no—
173#405—111no—
174#380C2×D1112yes—
175#341—221no—
176#340—21no—
177#328—222no—
178#327—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—44no—
188C22×C11#38011yescharacteristic
189C22×C11#47112yes—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—162no—
197C4×C11C2×#9911yescharacteristic
198C4×C11#41011yescharacteristic
199Dic11—41no—
200Dic11—41no—
201Dic11—41no—
202C2×#41—111no—
203C23×C4C22×D1111yescharacteristic
204#131—442no—
205C2×M16—111no—
206C2×M16—111no—
207C2×M16—221no—
208C2×M16—222no—
209C22×C8—42no—
210C22×C8—221no—
211C22×C8C4×D1111yescharacteristic
212C22×C8C4×D1111yescharacteristic
213C22×C8D4411yescharacteristic
214C22×C8D4411yescharacteristic
215C22×C8C22⋊D1111yescharacteristic
216C22×C8C22⋊D1111yescharacteristic
217#123—221no—
218C22⋊Q8—111no—
219C22⋊Q8—111no—
220#121—111no—
221#121—111no—
222#120—221no—
223C4×D4—221no—
224C4×D4—221no—
225#117—111no—
226C2×C4⋊C4—22no—
227C2×C22⋊C4—22no—
228#108—442no—
229#106—42no—
230C4⋊C8—221no—
231C4⋊C8—221no—
232C22⋊C8—221no—
233C22⋊C8—221no—
234C22⋊C8—221no—
235C22⋊C8—221no—
236C22⋊C8—222no—
237C22⋊C8—222no—
238#97—221no—
239C4×C8—221no—
240#95—22no—
241C2×C11—22no—
242C2×C11—41no—
243C2×C11—41no—
244C2×C11#179911yescharacteristic
245C2×C11#181411yescharacteristic
246C2×C11#181511yescharacteristic
247D11—81no—
248C24#434111yescharacteristic
249#41—441no—
250#41—441no—
251C2×Q8—111no—
252C2×D4—111no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—42no—
259C22×C4—221no—
260C22×C4C2×C4×D1111yescharacteristic
261C22×C4C2×D4411yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4Q8×D1111yescharacteristic
264C22×C4#434311yescharacteristic
265C22×C4C2×C22⋊D1111yescharacteristic
266M16—442no—
267M16—441no—
268M16—441no—
269M16—442no—
270M16—442no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—221no—
278C2×C8—221no—
279C2×C8—442no—
280C2×C8—442no—
281C2×C8(C2×D11)⋊C411yescharacteristic
282C2×C8(C2×D11)⋊C411yescharacteristic
283C2×C8(C2×D11)⋊C411yescharacteristic
284C2×C8(C2×D11)⋊C411yescharacteristic
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—111no—
288C4⋊C4—111no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C22⋊C4—82no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C42—221no—
298C11#862911yescharacteristic, complemented, Sylow
299C23—22no—
300C23—41no—
301C23—41no—
302C23—221no—
303C23#6694511yescharacteristic
304C23#6695011yescharacteristic
305C23#6699111yescharacteristic
306Q8—441no—
307D4—441no—
308D4—442no—
309D4—442no—
310D4—442no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4C4⋊C4×D1111yescharacteristic
329C2×C4#6694811yescharacteristic
330C2×C4C2×(C2×D11)⋊C411yescharacteristic
331C2×C4#6699911yescharacteristic
332C8—21no—
333C8—21no—
334C8—21no—
335C8—441no—
336C8—441no—
337C8—882no—
338C8#6687012yes—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—44no—
348C22—441no—
349C22—441no—
350C22—441no—
351C22#1062260011yescharacteristic
352C22#1062279012yes—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—162no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4C2×#6687011yescharacteristic
361C4#1062261911yescharacteristic
362C2—22no—
363C2—41no—
364C2—41no—
365C2—881no—
366C2#1306860111yescharacteristic
367C2#1306866711yescharacteristic
368C2#1306867611yescharacteristic
subgroupG/H
centerC22#10622600
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1807C2
socleC22×C11#380
prime radical#10623322C22
cosocleC23×C4×C11C23
hypercenter#1807D11
hypocenterC11#8629
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1807

Complements

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

NH ≅ G/Ntype
2. #13068654C2semidirect
4. #13066522C2semidirect
5. C11×#1807C2semidirect
8. C2×#66954C4semidirect
15. #10622723C4semidirect
19. #10622715C4semidirect
20. #10622714C4semidirect
117. #1807D11semidirect
298. C11#8629semidirect

Maximal subgroups

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

subgroupindex
#130773102
#130686542
#130671572
#130665222
C11×#18072
#862911