Finite Group Databasebeta

← #14663255

Subgroups — #14663255

Order 2816.

504 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 83 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#13071338C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic, complemented
3#13066559C212yesmaximal, complemented
4#13066547C212yesmaximal, complemented
5C11×#1465C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66993C411yescharacteristic
8C2×C4×D44C411yescharacteristic
9C11×#407—21no—
10#10622834C411yescharacteristic
11#10622826—21no—
12#10622826—21no—
13#10622820—21no—
14#10622601C2211yescharacteristic
15#10622590C2211yescharacteristic
16#10622569—21no—
17#10622569—21no—
18#10622545C411yescharacteristic
19C11×#324C2212yes—
20C11×#323—21no—
21#10622166C2212yes—
22#10622163—21no—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C22×D44C2×C411yescharacteristic
29C22×C4×D11—21no—
30C2×C11×M16—41no—
31C4×D4×C11—41no—
32C4×D4×C11—41no—
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39#66993—22no—
40#66993—22no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×C4⋊Dic11C2×C411yescharacteristic
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11C2×C411yescharacteristic
47C2×#4318—41no—
48C4×D44—41no—
49C4×D44—41no—
50C11×C22⋊C8—22no—
51C11×C22⋊C8—41no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58#11533—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C24×C11C22⋊C411yescharacteristic
61C23×D11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—81no—
71C22×C4×C11—81no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—24no—
78C2×C22⋊D11—24no—
79C2×C22⋊D11—81no—
80C2×C22⋊D11—81no—
81C2×C22⋊D11—81no—
82C2×C22⋊D11—81no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C2×D44—21no—
87C2×D44—41no—
88C2×D44—41no—
89C2×D44M1612yescomplemented
90C2×C4×D11—42no—
91C2×C4×D11—81no—
92C2×C4×D11—81no—
93C11×M16—82no—
94C2×C8×C11—42no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11—21no—
99C42×C11—21no—
100C22⋊Dic11—81no—
101C22⋊Dic11—81no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—81no—
105(C2×D11)⋊C4—81no—
106C4⋊Dic11—41no—
107C4×Dic11—21no—
108C4×Dic11—41no—
109C4×Dic11M1612yescomplemented
110#4318—82no—
111C2×C11⋊C8—42no—
112#2328—111no—
113#1465—111no—
114#1465D1111yescharacteristic, complemented
115#1324—112no—
116#1318—112no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11C2×C22⋊C411yescharacteristic
128C22×D11—22no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135D4×C11—42no—
136D4×C11—42no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11#9911yescharacteristic
151C2×C4×C11#9911yescharacteristic
152C2×C4×C11C2×M1611yescharacteristic
153C2×C4×C11C2×M1611yescharacteristic
154C22⋊D11—84no—
155C22⋊D11—84no—
156C2×Dic11—22no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165D44—42no—
166D44—42no—
167C4×D11—84no—
168C8×C11—82no—
169C11⋊C8—82no—
170C2×#127—111no—
171C2×C4×D4—111no—
172C2×C4×D4C2×D1111yescharacteristic
173#407—21no—
174#407—221no—
175#390—111no—
176#390—111no—
177#386—221no—
178#386—221no—
179#386—221no—
180#386—221no—
181#382—111no—
182#376—111no—
183#324—112no—
184#324C2×D1112yes—
185#323—21no—
186#323—221no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—42no—
190C22×C11—42no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11#40711yescharacteristic
200C22×C11C2×#9911yescharacteristic
201C22×C11#41311yescharacteristic
202C2×D11—42no—
203C2×D11—42no—
204C2×D11—42no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C2×D11—81no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—41no—
214C4×C11—41no—
215C4×C11—41no—
216Dic11—42no—
217Dic11—81no—
218Dic11—81no—
219C22×D4—111no—
220C22×D4—221no—
221C22×D4—221no—
222C22×D4C4×D1111yescharacteristic
223C23×C4—221no—
224C23×C4D4411yescharacteristic
225C23×C4C22⋊D1111yescharacteristic
226C2×M16—41no—
227C2×M16—441no—
228#127—222no—
229#127—222no—
230C4×D4—41no—
231C4×D4—41no—
232C4×D4—441no—
233C4×D4—441no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4C22×D1111yescharacteristic
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4D4411yescharacteristic
242C2×C22⋊C4C22⋊D1111yescharacteristic
243C2×C42—111no—
244C2×C42—111no—
245C2×C42C4×D1111yescharacteristic
246C22⋊C8—22no—
247C22⋊C8—41no—
248C22⋊C8—222no—
249C22⋊C8—441no—
250#95—221no—
251#95—221no—
252#95—221no—
253#95—221no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11—81no—
257C2×C11—81no—
258C2×C11#146511yescharacteristic
259C2×C11#212711yescharacteristic
260C2×C11#213411yescharacteristic
261D11—82no—
262C24—221no—
263C24(C2×D11)⋊C411yescharacteristic
264C24(C2×D11)⋊C411yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—112no—
270C2×D4—224no—
271C2×D4—224no—
272C2×D4—221no—
273C2×D4—441no—
274C2×D4—441no—
275C2×D4—881no—
276C2×D4—881no—
277C2×D4—881no—
278C2×D4—881no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—81no—
284C22×C4—81no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—442no—
289C22×C4—881no—
290C22×C4—881no—
291C22×C4(C2×D11)⋊C411yescharacteristic
292C22×C4(C2×D11)⋊C411yescharacteristic
293C22×C4C2×C4×D1111yescharacteristic
294C22×C4C2×D4411yescharacteristic
295C22×C4C2×C22⋊D1111yescharacteristic
296M16—82no—
297M16—882no—
298C2×C8—42no—
299C2×C8—442no—
300C4⋊C4—41no—
301C4⋊C4—441no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—881no—
307C22⋊C4—881no—
308C22⋊C4—881no—
309C22⋊C4—881no—
310C42—21no—
311C42—21no—
312C42—112no—
313C42—221no—
314C42—441no—
315C11#1153311yescharacteristic, complemented, Sylow
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—222no—
327C23—441no—
328C23—441no—
329C23—441no—
330C23—441no—
331C23—441no—
332C23—441no—
333C23C2×(C2×D11)⋊C411yescharacteristic
334D4—42no—
335D4—42no—
336D4—442no—
337D4—442no—
338D4—884no—
339D4—884no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—222no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—884no—
363C2×C4#6687011yescharacteristic
364C2×C4#6687011yescharacteristic
365C2×C4M16×D1111yescharacteristic
366C2×C4M16×D1111yescharacteristic
367C8—82no—
368C8—882no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—42no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—81no—
380C22—81no—
381C22—442no—
382C22—442no—
383C22—442no—
384C22—881no—
385C22—881no—
386C22—881no—
387C22—881no—
388C22C2×#6687011yescharacteristic
389C22#1062273911yescharacteristic
390C22#1062274511yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—442no—
399C4—881no—
400C4—881no—
401C2—21no—
402C2—21no—
403C2—81no—
404C2—81no—
405C2—882no—
406C2#1306695211yescharacteristic
407C2#1307028311yescharacteristic
408C2#1307030711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1465C2
socleC22×C11C2×#99
prime radicalC2×#66993C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1465D11
hypocenterC11#11533
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #13066954C2semidirect
3. #13066559C2semidirect
4. #13066547C2semidirect
5. C11×#1465C2semidirect
89. C2×D44M16semidirect
109. C4×Dic11M16semidirect
114. #1465D11semidirect
315. C11#11533semidirect

Maximal subgroups

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

subgroupindex
#130713382
#130669542
#130665592
#130665472
C11×#14652
#1153311