Finite Group Databasebeta

← #14642359

Subgroups — #14642359

Order 2816.

570 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 111 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#13076917C211yesmaximal, characteristic
2#13068310C211yesmaximal, characteristic, complemented
3#13066441C212yesmaximal, complemented
4#13066436C212yesmaximal, complemented
5C11×#1797C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983C411yescharacteristic
8C2×#66977C411yescharacteristic
9C22×#4318—21no—
10C2×#66928C411yescharacteristic
11C2×C11×C4⋊C8—21no—
12C2×C11×C22⋊C8—21no—
13#10622826—21no—
14#10622826—21no—
15#10622553—21no—
16#10622553—21no—
17#10622552C2211yescharacteristic
18#10622549C411yescharacteristic
19#10622542C2211yescharacteristic
20C11×#336C2212yes—
21#10622162—21no—
22#10622162C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×D44C2×C411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C22×C8×C11—22no—
30C2×C42×C11—42no—
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×C22⋊Dic11—21no—
36#66983—42no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×C4⋊Dic11C2×C411yescharacteristic
44#66977—42no—
45C2×Dic11⋊C4—21no—
46C2×#4318—24no—
47C2×#4318—42no—
48C2×#4318—42no—
49C22×C11⋊C8—22no—
50#66928—42no—
51C11×C4⋊C8—42no—
52C11×C22⋊C8—42no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57#7710—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C23×D11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C2×D44—22no—
84C2×D44—41no—
85C2×D44—41no—
86C2×Dic22—22no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C2×C8×C11—42no—
90C2×C8×C11—42no—
91C2×C8×C11—42no—
92C42×C11—22no—
93C42×C11—22no—
94C42×C11—41no—
95C42×C11—41no—
96C22⋊Dic11—42no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106Dic11⋊C4—42no—
107#4318—48no—
108C2×C11⋊C8—24no—
109C2×C11⋊C8—42no—
110C2×C11⋊C8—42no—
111#2850—111no—
112#1797D1111yescharacteristic, complemented
113#1728—111no—
114#1272—112no—
115#1270—112no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11#10412yes—
123C23×C11C2×C22⋊C411yescharacteristic
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—44no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11#9912yes—
150C2×C4×C11#10012yes—
151C2×C4×C11#13112yes—
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C11#13711yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C22⋊D11—84no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166D44—82no—
167Dic22—82no—
168C8×C11—82no—
169C11⋊C8—44no—
170C22×M16—221no—
171C2×#124—111no—
172C2×C22⋊Q8—111no—
173C2×#121—111no—
174C22×C42C2×D1111yescharacteristic
175C2×C4⋊C8—21no—
176C2×C22⋊C8—21no—
177#391—111no—
178#390—111no—
179#388—221no—
180#388—221no—
181#386—221no—
182#386—221no—
183#382—111no—
184#336—112no—
185#336—221no—
186#336C2×D1112yes—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11#40811yescharacteristic
195C22×C11C2×#9911yescharacteristic
196C22×C11C2×#10011yescharacteristic
197C22×C11#41711yescharacteristic
198C22×C11#41711yescharacteristic
199C22×C11C2×#10411yescharacteristic
200C22×C11#42111yescharacteristic
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—22no—
209C4×C11—22no—
210C4×C11—22no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—41no—
216Dic11—81no—
217Dic11—81no—
218Dic11—81no—
219C22×Q8—111no—
220C22×D4—111no—
221C22×D4—221no—
222C23×C4C4×D1111yescharacteristic
223C23×C4D4411yescharacteristic
224C23×C4C22⋊D1111yescharacteristic
225C2×M16—224no—
226C2×M16—442no—
227C2×M16—442no—
228C22×C8—22no—
229C22×C8—222no—
230#124—442no—
231C22⋊Q8—442no—
232#121—442no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C42—42no—
243C2×C42C4×D1111yescharacteristic
244C2×C42D4411yescharacteristic
245C2×C42C22⋊D1111yescharacteristic
246C2×C42C22×D1111yescharacteristic
247C4⋊C8—42no—
248C22⋊C8—42no—
249#95—221no—
250#95—221no—
251#95—221no—
252#95—221no—
253C2×C11—42no—
254C2×C11#147111yescharacteristic
255C2×C11#148311yescharacteristic
256C2×C11#149511yescharacteristic
257C2×C11#150411yescharacteristic
258C2×C11#151311yescharacteristic
259C2×C11#152711yescharacteristic
260C2×C11#156011yescharacteristic
261D11—161no—
262C24—221no—
263C24(C2×D11)⋊C411yescharacteristic
264C2×Q8—222no—
265C2×Q8—441no—
266C2×Q8—441no—
267C2×D4—222no—
268C2×D4—441no—
269C2×D4—441no—
270C2×D4—442no—
271C2×D4—442no—
272C2×D4—442no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4(C2×D11)⋊C411yescharacteristic
288C22×C4(C2×D11)⋊C411yescharacteristic
289C22×C4(C2×D11)⋊C411yescharacteristic
290C22×C4C2×C4×D1111yescharacteristic
291C22×C4C2×D4411yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293M16—448no—
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—42no—
297C2×C8—224no—
298C2×C8—442no—
299C2×C8—442no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C4⋊C4—442no—
303C22⋊C4—442no—
304C22⋊C4—442no—
305C22⋊C4—442no—
306C22⋊C4—442no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C42—22no—
312C42—22no—
313C42—41no—
314C42—41no—
315C11#771011yescharacteristic, complemented, Sylow
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—441no—
323C23—441no—
324C23—441no—
325C23—441no—
326C23—441no—
327C23—441no—
328C23—441no—
329C23#6688912yes—
330C23C2×(C2×D11)⋊C411yescharacteristic
331Q8—882no—
332D4—882no—
333D4—884no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4#6687012yes—
362C2×C4#6688712yes—
363C2×C4#6695412yes—
364C2×C4#6696111yescharacteristic
365C2×C4#6696211yescharacteristic
366C2×C4#6698511yescharacteristic
367C2×C4#6699511yescharacteristic
368C8—82no—
369C8—444no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—881no—
378C22—881no—
379C22—881no—
380C22—881no—
381C22—881no—
382C22—881no—
383C22—881no—
384C22C2×#6687011yescharacteristic
385C22#1062257911yescharacteristic
386C22#1062261811yescharacteristic
387C22#1062272311yescharacteristic
388C22C2×#6688711yescharacteristic
389C22#1062274611yescharacteristic
390C22C2×#6688911yescharacteristic
391C4—21no—
392C4—22no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—22no—
397C4—22no—
398C4—41no—
399C4—881no—
400C4—881no—
401C4—881no—
402C2—42no—
403C2—1761no—
404C2#1306697511yescharacteristic
405C2#1306702711yescharacteristic
406C2#1306708211yescharacteristic
407C2#1306712111yescharacteristic
408C2#1306715711yescharacteristic
409C2#1306721511yescharacteristic
410C2#1306734911yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C4
cosocleC2×C42×C11C23
hypercenter#1797D11
hypocenterC11#7710
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. #13068310C2semidirect
3. #13066441C2semidirect
4. #13066436C2semidirect
5. C11×#1797C2semidirect
112. #1797D11semidirect
315. C11#7710semidirect

Maximal subgroups

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

subgroupindex
#130769172
#130683102
#130664412
#130664362
C11×#17972
#771011