Finite Group Databasebeta

← #14651772

Subgroups — #14651772

Order 2816.

628 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 103 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#13073502C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic, complemented
3#13066942C212yesmaximal, complemented
4#13066523C212yesmaximal, complemented
5C11×#2973C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66990C411yescharacteristic
8C2×#66988C411yescharacteristic
9C22×(C2×D11)⋊C4C2211yescharacteristic
10C11×#435—24no—
11C11×#432—21no—
12C11×#407C2212yes—
13C2×C11×C22⋊C8—21no—
14#10622826—21no—
15#10622825C2211yescharacteristic
16#10622820C2212yes—
17#10622607—21no—
18#10622574—21no—
19#10622568C411yescharacteristic
20#10622556C411yescharacteristic
21#10622553—21no—
22#10622166—21no—
23#10622163—21no—
24#10622106—24no—
25C24×D11C2×C411yescharacteristic
26C22×D4×C11C2×C411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C23×C4×C11C2311yescharacteristic
29C22×C22⋊D11—21no—
30C23×Dic11C2×C411yescharacteristic
31C2×C11×M16—22no—
32C22×C8×C11—22no—
33C4×D4×C11—22no—
34C4×D4×C11—22no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11C2×C411yescharacteristic
41C2×C22⋊Dic11C2×C411yescharacteristic
42#66990—42no—
43#66988—42no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—22no—
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4—21no—
51C2×C4⋊Dic11—21no—
52C2×Dic11⋊C4—21no—
53C2×#4318—22no—
54C11×C4⋊C8—22no—
55C11×C22⋊C8—22no—
56C11×C22⋊C8—22no—
57C11×C22⋊C8D414yescomplemented
58C11×#97—22no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C22⋊(C11⋊C8)—22no—
63C22⋊(C11⋊C8)—22no—
64#9515—111nomaximal, Sylow
65C24×C11C22⋊C411yescharacteristic
66C24×C11C22×C411yescharacteristic
67C23×D11—21no—
68C23×D11—22no—
69C23×D11—42no—
70C23×D11—41no—
71C23×D11—41no—
72C23×D11—81no—
73C2×D4×C11—22no—
74C2×D4×C11—22no—
75C2×D4×C11—41no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—81no—
79C22×C4×C11—81no—
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4112yes—
87C2×C22⋊D11—42no—
88C2×C22⋊D11—42no—
89C2×C22⋊D11—81no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—22no—
94C22×Dic11—41no—
95C22×Dic11—41no—
96C11×M16—82no—
97C2×C8×C11—24no—
98C2×C8×C11—82no—
99C11×C4⋊C4—22no—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—22no—
102C42×C11—21no—
103C42×C11—21no—
104C22⋊Dic11—41no—
105C22⋊Dic11—41no—
106C22⋊Dic11—42no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—81no—
113C4⋊Dic11—81no—
114Dic11⋊C4—42no—
115#4318—82no—
116C2×C11⋊C8—42no—
117#2973D1111yescharacteristic, complemented
118#2534—111no—
119#1465—111no—
120#1462—112no—
121#1305—112no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11#10012yes—
131C23×C11C2×C22⋊C411yescharacteristic
132C23×C11C4×D412yes—
133C22×D11—22no—
134C22×D11—24no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—42no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—84no—
143C22×D11—84no—
144C22×D11—82no—
145C22×D11—82no—
146D4×C11—44no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—81no—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12112yes—
162C2×C4×C11#12311yescharacteristic
163C22⋊D11—84no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—82no—
174C8×C11—44no—
175C11⋊C8—82no—
176C2×#123—111no—
177C2×#120—111no—
178C2×C4×D4C2×D1111yescharacteristic
179C22×C22⋊C4—111no—
180#435—24no—
181#432—21no—
182#407—112no—
183#407C2×D1112yes—
184C2×C22⋊C8—21no—
185#396—221no—
186#394—221no—
187#388—221no—
188#386—221no—
189#381—111no—
190#380—111no—
191#379—111no—
192#324—221no—
193#323—221no—
194#323—224no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11—42no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—81no—
207C22×C11#38611yescharacteristic
208C22×C11C2×#10011yescharacteristic
209C22×C11#41311yescharacteristic
210C2×D11—42no—
211C2×D11—42no—
212C2×D11—42no—
213C2×D11—81no—
214C2×D11—81no—
215C2×D11—84no—
216C2×D11—81no—
217C2×D11—81no—
218C2×D11—84no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—22no—
222C4×C11—41no—
223C4×C11—41no—
224C4×C11—41no—
225Dic11—81no—
226Dic11—81no—
227Dic11—81no—
228C25—111no—
229C22×D4—221no—
230C22×D4C4×D1111yescharacteristic
231C23×C4—111no—
232C23×C4C22⋊D1111yescharacteristic
233C23×C4C22×D1111yescharacteristic
234C2×M16—22no—
235C2×M16—222no—
236C22×C8—22no—
237#123—442no—
238#120—442no—
239C4×D4—22no—
240C4×D4—22no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4D4411yescharacteristic
244C2×C22⋊C4—111no—
245C2×C22⋊C4—111no—
246C2×C22⋊C4—221no—
247C2×C22⋊C4—221no—
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—222no—
251C2×C22⋊C4—222no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—221no—
254C2×C22⋊C4C4×D1111yescharacteristic
255C2×C22⋊C4D4411yescharacteristic
256C2×C42C22⋊D1111yescharacteristic
257C4⋊C8—22no—
258C22⋊C8—22no—
259C22⋊C8—22no—
260C22⋊C8—222no—
261C22⋊C8—222no—
262C22⋊C8C22⋊D1114yescomplemented
263#97—22no—
264#95—221no—
265#95—221no—
266#95—221no—
267C2×C11—21no—
268C2×C11—21no—
269C2×C11—42no—
270C2×C11—42no—
271C2×C11#189111yescharacteristic
272C2×C11#190011yescharacteristic
273C2×C11#191311yescharacteristic
274D11—82no—
275C24—221no—
276C24—222no—
277C24—441no—
278C24—441no—
279C24—442no—
280C24—881no—
281C24(C2×D11)⋊C411yescharacteristic
282C24C2×C4×D1111yescharacteristic
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—41no—
286C2×D4—442no—
287C2×D4—442no—
288C2×D4—881no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—81no—
292C22×C4—81no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—222no—
297C22×C4—441no—
298C22×C4—441no—
299C22×C4(C2×D11)⋊C411yescharacteristic
300C22×C4(C2×D11)⋊C411yescharacteristic
301C22×C4(C2×D11)⋊C411yescharacteristic
302C22×C4C2×D4411yescharacteristic
303C22×C4#433912yes—
304C22×C4C2×C22⋊D1111yescharacteristic
305C22×C4C2×C22⋊D1112yes—
306M16—82no—
307M16—882no—
308C2×C8—24no—
309C2×C8—82no—
310C2×C8—442no—
311C4⋊C4—22no—
312C4⋊C4—442no—
313C4⋊C4—881no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—442no—
317C22⋊C4—442no—
318C22⋊C4—442no—
319C22⋊C4—441no—
320C22⋊C4—442no—
321C22⋊C4—441no—
322C22⋊C4—441no—
323C22⋊C4—441no—
324C22⋊C4—881no—
325C42—21no—
326C42—21no—
327C11#951511yescharacteristic, complemented, Sylow
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—222no—
337C23—224no—
338C23—441no—
339C23—441no—
340C23—441no—
341C23—442no—
342C23—441no—
343C23—441no—
344C23—441no—
345C23—882no—
346C23—882no—
347C23—884no—
348C23—884no—
349C23#6688712yes—
350C23C2×(C2×D11)⋊C411yescharacteristic
351C23C4×C22⋊D1112yes—
352D4—44no—
353D4—884no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—882no—
377C2×C4#6698211yescharacteristic
378C2×C4#6698312yes—
379C2×C4#6700611yescharacteristic
380C8—44no—
381C8—882no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—41no—
392C22—41no—
393C22—81no—
394C22—442no—
395C22—442no—
396C22—442no—
397C22—881no—
398C22—881no—
399C22—884no—
400C22—884no—
401C22—881no—
402C22—881no—
403C22C2×#6688711yescharacteristic
404C22#1062274511yescharacteristic
405C22#1062282611yescharacteristic
406C4—21no—
407C4—22no—
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—881no—
413C4—881no—
414C4—881no—
415C2—21no—
416C2—21no—
417C2—42no—
418C2—42no—
419C2—882no—
420C2#1306903411yescharacteristic
421C2#1306907911yescharacteristic
422C2#1306915811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2973C2
socleC22×C11#386
prime radicalC2×#66990C4
cosocleC23×C4×C11C23
hypercenter#2973D11
hypocenterC11#9515
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #13066954C2semidirect
3. #13066942C2semidirect
4. #13066523C2semidirect
5. C11×#2973C2semidirect
57. C11×C22⋊C8D4semidirect
117. #2973D11semidirect
262. C22⋊C8C22⋊D11semidirect
327. C11#9515semidirect

Maximal subgroups

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

subgroupindex
#130735022
#130669542
#130669422
#130665232
C11×#29732
#951511