Finite Group Databasebeta

← #14651389

Subgroups — #14651389

Order 2816.

490 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079005C211yesmaximal, characteristic
2#13071726C211yesmaximal, characteristic
3#13067239C211yesmaximal, characteristic
4#13067128C211yesmaximal, characteristic, complemented
5#13066509C211yesmaximal, characteristic, complemented
6#13066508C211yesmaximal, characteristic, complemented
7C11×#1506C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×#66928C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#376C2211yescharacteristic
12#10622702C412yescomplemented
13#10622702C412yescomplemented
14#10622681—22no—
15#10622617—21no—
16#10622614—21no—
17#10622553—21no—
18C4×(C2×D11)⋊C4—21no—
19#10622545C2211yescharacteristic
20#10622539C2211yescharacteristic
21C4×#4318C2211yescharacteristic
22#10622282—21no—
23#10622279—21no—
24#10622278—21no—
25#10622259—21no—
26C11×#328—21no—
27C11×#328—21no—
28#10622176—21no—
29#10622176—21no—
30#10622102—22no—
31C22×D44D411yescharacteristic
32C22×C4×D11—21no—
33C22×Dic22D411yescharacteristic
34C11×C4⋊Q8C2×C411yescharacteristic, complemented
35C11×C4⋊Q8C2×C411yescharacteristic, complemented
36C11×#125—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C11×#117—21no—
42C2×C42×C11—21no—
43C2×C42×C11C2311yescharacteristic
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11—21no—
51C2×C4×Dic11—21no—
52C2×#4318—21no—
53#66928—21no—
54#66928—21no—
55#66928C2×C412yes—
56#66928D412yes—
57C11×C4⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#97—21no—
60C11×#95—21no—
61C11×#95D411yescharacteristic
62C11×#95D411yescharacteristic
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95D411yescharacteristic
67C11⋊#95D411yescharacteristic
68C22⋊(C11⋊C8)—21no—
69#66874—22no—
70#66874—22no—
71#66873—22no—
72#66873—22no—
73C4⋊(C11⋊C8)—21no—
74#66867—21no—
75#66867C2×C412yescomplemented
76C4×C11⋊C8—21no—
77#9439—111nomaximal, Sylow
78C23×D11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C2×D44—21no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44C22⋊C412yes—
93C2×C4×D11—42no—
94C2×C4×D11—42no—
95C2×C4×D11—81no—
96C2×Dic22—21no—
97C2×Dic22—41no—
98C2×Dic22—41no—
99C2×Dic22C22⋊C412yes—
100C2×C8×C11—41no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11—42no—
109C42×C11—41no—
110C42×C11C22×C411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113C42×C11#4111yescharacteristic
114(C2×D11)⋊C4—22no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—22no—
117(C2×D11)⋊C4—22no—
118(C2×D11)⋊C4—42no—
119(C2×D11)⋊C4—42no—
120(C2×D11)⋊C4—81no—
121Dic11⋊C4—81no—
122C4×Dic11—42no—
123C4×Dic11—81no—
124#4318—41no—
125#4318—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128#3140—111no—
129#2372—111no—
130#1533—111no—
131#1506—111no—
132#1506D1111yescharacteristic, complemented
133#1300—111no—
134#1300—111no—
135C23×C11#12011yescharacteristic
136C22×D11—22no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143Q8×C11—81no—
144Q8×C11—81no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11C2×C22⋊C411yescharacteristic
158C2×C4×C11C4×D411yescharacteristic
159C2×C4×C11C4×D411yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12311yescharacteristic
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172D44—42no—
173D44—81no—
174C4×D11—84no—
175Dic22—42no—
176Dic22—81no—
177C8×C11—81no—
178C11⋊C8—42no—
179C11⋊C8—81no—
180#533C2×D1111yescharacteristic
181C2×#124—111no—
182#489—112no—
183#489—112no—
184#488—222no—
185#432—111no—
186#432C2×D1111yescharacteristic
187#419—221no—
188#418—221no—
189C4×M16—111no—
190#391—221no—
191#388—221no—
192#388—221no—
193#386—221no—
194C4×C22⋊C4—221no—
195C4×C22⋊C4—221no—
196#376—111no—
197#376C2×D1111yescharacteristic
198#329—222no—
199#328—21no—
200#328—21no—
201#328—221no—
202#328—221no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11#38611yescharacteristic
206C22×C11#45511yescharacteristic
207C22×C11#45511yescharacteristic
208C2×D11—42no—
209C2×D11—42no—
210C2×D11—42no—
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—42no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11—81no—
225Dic11—42no—
226Dic11—42no—
227Dic11—81no—
228C22×Q8—111no—
229C22×D4—111no—
230C23×C4—221no—
231C2×M16—221no—
232C4⋊Q8C4×D1111yescharacteristic, complemented
233C4⋊Q8C4×D1111yescharacteristic, complemented
234#125—21no—
235#124—112no—
236#124—112no—
237#124—221no—
238#124—221no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243#117—21no—
244C2×C4⋊C4—221no—
245C2×C22⋊C4—221no—
246C2×C22⋊C4—221no—
247C2×C22⋊C4—221no—
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C42—21no—
251C2×C42—221no—
252C2×C42—221no—
253C2×C42C22×D1111yescharacteristic
254C4⋊C8—21no—
255C4⋊C8—221no—
256#103—222no—
257#103—222no—
258#102—222no—
259#102—222no—
260C22⋊C8—21no—
261C22⋊C8—221no—
262#97—21no—
263#97—112no—
264#97—221no—
265C4×C8—221no—
266#95—21no—
267#95—111no—
268#95—111no—
269#95—221no—
270#95—221no—
271#95—221no—
272#95C22⋊D1111yescharacteristic
273#95C22⋊D1111yescharacteristic
274C2×C11—21no—
275C2×C11—21no—
276C2×C11#188511yescharacteristic
277C2×C11#190611yescharacteristic
278C2×C11#190611yescharacteristic
279D11—82no—
280C24—221no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—112no—
284C2×Q8—221no—
285C2×Q8—441no—
286C2×Q8—441no—
287C2×D4—112no—
288C2×D4—221no—
289C2×D4—441no—
290C2×D4—441no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—442no—
297C22×C4—442no—
298C22×C4—881no—
299C22×C4D4×D1111yescharacteristic
300C22×C4D4×D1111yescharacteristic
301C22×C4C2×C22⋊D1111yescharacteristic
302M16—441no—
303M16—441no—
304C2×C8—41no—
305C2×C8—222no—
306C2×C8—441no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—881no—
314C22⋊C4—41no—
315C22⋊C4—222no—
316C22⋊C4—222no—
317C22⋊C4—222no—
318C22⋊C4—222no—
319C22⋊C4—442no—
320C22⋊C4—442no—
321C22⋊C4—881no—
322C42—42no—
323C42—41no—
324C42—442no—
325C42—881no—
326C42C2×C4×D1111yescharacteristic
327C42#433911yescharacteristic
328C42D4×D1111yescharacteristic
329C42#434111yescharacteristic
330C11#943911yescharacteristic, complemented, Sylow
331C23—222no—
332C23—441no—
333C23—441no—
334C23—441no—
335C23—441no—
336C23—441no—
337C23—441no—
338C23#6699011yescharacteristic
339Q8—81no—
340Q8—81no—
341Q8—442no—
342Q8—881no—
343D4—442no—
344D4—881no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—884no—
367C2×C4C22⋊C4×D1111yescharacteristic
368C2×C4(C22⋊D11)⋊C411yescharacteristic
369C2×C4#6693611yescharacteristic
370C2×C4#6693711yescharacteristic
371C2×C4C4×C22⋊D1111yescharacteristic
372C2×C4#6699111yescharacteristic
373C8—81no—
374C8—442no—
375C8—881no—
376C22—21no—
377C22—21no—
378C22—442no—
379C22—442no—
380C22—442no—
381C22—881no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22#1062256911yescharacteristic
386C22#1062281511yescharacteristic
387C22#1062281511yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—442no—
399C4—442no—
400C4—881no—
401C2—21no—
402C2—21no—
403C2—882no—
404C2#1306900111yescharacteristic
405C2#1306911411yescharacteristic
406C2#1306912011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1506C2
socleC22×C11#386
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1506D11
hypocenterC11#9439
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
4. #13067128C2semidirect
5. #13066509C2semidirect
6. #13066508C2semidirect
7. C11×#1506C2semidirect
12. #10622702C4semidirect
13. #10622702C4semidirect
34. C11×C4⋊Q8C2×C4semidirect
35. C11×C4⋊Q8C2×C4semidirect
75. #66867C2×C4semidirect
132. #1506D11semidirect
232. C4⋊Q8C4×D11semidirect
233. C4⋊Q8C4×D11semidirect
330. C11#9439semidirect

Maximal subgroups

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

subgroupindex
#130790052
#130717262
#130672392
#130671282
#130665092
#130665082
C11×#15062
#943911