Finite Group Databasebeta

← #14651086

Subgroups — #14651086

Order 2816.

570 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 127 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#13077640C211yesmaximal, characteristic
2#13073792C211yesmaximal, characteristic
3#13067187C212yesmaximal, complemented
4#13066494C212yesmaximal, complemented
5C11×#1799C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977C2211yescharacteristic
8C2×C11×#99—21no—
9C11×#380C2212yes—
10#10622833—21no—
11#10622823—21no—
12C2×C11⋊#95C2211yescharacteristic
13C2×C22⋊(C11⋊C8)—21no—
14C2×C22⋊(C11⋊C8)C2212yes—
15D4×C11⋊C8—24no—
16#10622599C411yescharacteristic, complemented
17#10622592C411yescharacteristic, complemented
18#10622562C411yescharacteristic, complemented
19#10622560C411yescharacteristic, complemented
20#10622555—21no—
21#10622546—21no—
22#10622538—21no—
23C11×#342—21no—
24#10622090—24no—
25C22×D4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C23×Dic11—21no—
29C22×Dic22C2×C411yescharacteristic
30C4×D4×C11—22no—
31C4×D4×C11—22no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42#66977—22no—
43#66977—22no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C22×C11⋊C8—22no—
48C22×C11⋊C8—22no—
49C11×#99—42no—
50C11×#95—22no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C11⋊#95C2×C411yescharacteristic
58C22⋊(C11⋊C8)—22no—
59C22⋊(C11⋊C8)—22no—
60C22⋊(C11⋊C8)D414yes—
61C4⋊(C11⋊C8)—22no—
62C4×C11⋊C8—22no—
63#9383—111nomaximal, Sylow
64C24×C11C22⋊C411yescharacteristic
65C24×C11C2×D411yescharacteristic
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11SD1612yes—
69C2×D4×C11Q1612yes—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—42no—
73C22×C4×C11—81no—
74C22×C4×C11—81no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4112yes—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—42no—
87C22×Dic11—42no—
88C22×Dic11—81no—
89C2×Dic22—22no—
90C2×Dic22—81no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—82no—
93C11×C22⋊C4—22no—
94C11×C22⋊C4—22no—
95C11×C22⋊C4—42no—
96C11×C22⋊C4—42no—
97C42×C11—21no—
98C42×C11—21no—
99C22⋊Dic11—42no—
100C22⋊Dic11—42no—
101C22⋊Dic11—81no—
102C4⋊Dic11—22no—
103Dic11⋊C4—42no—
104Dic11⋊C4—41no—
105Dic11⋊C4—41no—
106Dic11⋊C4—81no—
107C2×C11⋊C8—24no—
108C2×C11⋊C8—82no—
109C2×C11⋊C8—82no—
110#2972—111no—
111#2564—111no—
112#1799D1111yescharacteristic
113#1520—112no—
114#1294—112no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11#10312yes—
122C23×C11C2×C22⋊C411yescharacteristic
123C23×C11#12112yes—
124C23×C11C2×SD1611yescharacteristic
125C23×C11C2×Q1611yescharacteristic
126C23×C11#13512yes—
127D4×C11—24no—
128D4×C11—24no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—81no—
141C2×C4×C11—82no—
142C2×C4×C11—82no—
143C2×C4×C11—82no—
144C2×C4×C11#10312yes—
145C2×C4×C11C4×D412yes—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12311yescharacteristic
148C2×Dic11—22no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—84no—
161Dic22—82no—
162C11⋊C8—44no—
163C2×C22⋊Q8—111no—
164C2×C4×D4C2×D1111yescharacteristic
165C8×D4—224no—
166#431—221no—
167C2×#99—21no—
168C2×C22⋊C8—112no—
169C2×C22⋊C8—221no—
170#400—111no—
171#399—111no—
172#395—111no—
173#393—111no—
174#387—221no—
175#386—221no—
176#385—221no—
177#380—221no—
178#380C2×D1112yes—
179C2×#95—111no—
180#342—21no—
181#328—224no—
182C22×C11—21no—
183C22×C11—22no—
184C22×C11—21no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—42no—
190C22×C11—42no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—81no—
194C22×C11#38611yescharacteristic
195C22×C11C2×#10311yescharacteristic
196C22×C11#41611yescharacteristic
197C22×C11#46512yes—
198C22×C11#46712yes—
199C4×C11—22no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—22no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—162no—
206Dic11—42no—
207Dic11—81no—
208Dic11—81no—
209Dic11—81no—
210C22×Q8—111no—
211C22×D4C22⋊D1111yescharacteristic
212C23×C4—221no—
213C23×C4D4411yescharacteristic
214C23×C4C22×D1111yescharacteristic
215C22×C8—222no—
216C22×C8—222no—
217C22⋊Q8—222no—
218C22⋊Q8—222no—
219C4×D4—22no—
220C4×D4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4C4×D1111yescharacteristic
227C2×C22⋊C4—22no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4C4×D1111yescharacteristic
232C2×C22⋊C4C22⋊D1111yescharacteristic
233C2×C42D4411yescharacteristic
234C4⋊C8—222no—
235#99—42no—
236C22⋊C8—114no—
237C22⋊C8—222no—
238C22⋊C8—222no—
239C4×C8—222no—
240#95—22no—
241#95—111no—
242#95—111no—
243#95—221no—
244#95—221no—
245#95—221no—
246#95—221no—
247#95—221no—
248C2×C11—21no—
249C2×C11—22no—
250C2×C11—21no—
251C2×C11—22no—
252C2×C11—42no—
253C2×C11#188411yescharacteristic
254C2×C11#189211yescharacteristic
255C2×C11#191311yescharacteristic
256C24(C2×D11)⋊C411yescharacteristic
257C24C2×C22⋊D1111yescharacteristic
258C2×Q8—222no—
259C2×Q8—881no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4#432412yes—
263C2×D4#432612yes—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—42no—
267C22×C4—81no—
268C22×C4—81no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—442no—
274C22×C4—442no—
275C22×C4—881no—
276C22×C4(C2×D11)⋊C411yescharacteristic
277C22×C4(C2×D11)⋊C411yescharacteristic
278C22×C4(C2×D11)⋊C411yescharacteristic
279C22×C4C2×C4×D1111yescharacteristic
280C22×C4C2×D4411yescharacteristic
281C22×C4D4×D1112yes—
282C22×C4#434112yes—
283C2×C8—224no—
284C2×C8—882no—
285C2×C8—882no—
286C4⋊C4—22no—
287C4⋊C4—82no—
288C4⋊C4—222no—
289C4⋊C4—442no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—881no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—442no—
298C22⋊C4—442no—
299C22⋊C4—881no—
300C42—21no—
301C42—21no—
302C11#938311yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#6687412yes—
310C23C2×(C2×D11)⋊C411yescharacteristic
311C23C2×#432411yescharacteristic
312C23#6699212yes—
313C23C2×#432611yescharacteristic
314C23#6700312yes—
315Q8—882no—
316D4—24no—
317D4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—222no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—884no—
346C2×C4#6687412yes—
347C2×C4(C22⋊D11)⋊C412yes—
348C2×C4#6693511yescharacteristic
349C2×C4#6693911yescharacteristic
350C8—444no—
351C22—21no—
352C22—22no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—42no—
357C22—41no—
358C22—41no—
359C22—42no—
360C22—41no—
361C22—41no—
362C22—81no—
363C22#1062257111yescharacteristic
364C22C2×#6687411yescharacteristic
365C22#1062261511yescharacteristic
366C22#1062265412yes—
367C22#1062266412yes—
368C4—21no—
369C4—21no—
370C4—22no—
371C4—22no—
372C4—41no—
373C4—41no—
374C4—162no—
375C4—442no—
376C4—881no—
377C4—881no—
378C4—881no—
379C2—22no—
380C2—21no—
381C2—21no—
382C2—22no—
383C2—42no—
384C2#1306899711yescharacteristic
385C2#1306903711yescharacteristic
386C2#1306915611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1799C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC23×C4×C11C23
hypercenter#1799D11
hypocenterC11#9383
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #13067187C2semidirect
4. #13066494C2semidirect
16. #10622599C4semidirect
17. #10622592C4semidirect
18. #10622562C4semidirect
19. #10622560C4semidirect
302. C11#9383semidirect

Maximal subgroups

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

subgroupindex
#130776402
#130737922
#130671872
#130664942
C11×#17992
#938311