Finite Group Databasebeta

← #14651459

Subgroups — #14651459

Order 2816.

498 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 95 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#13077644C211yesmaximal, characteristic
2#13073790C211yesmaximal, characteristic
3#13067333C211yesmaximal, characteristic, complemented
4#13066956C211yesmaximal, characteristic
5#13066473C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#1556C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12#10622844—21no—
13#10622844—21no—
14#10622601C412yes—
15#10622600—21no—
16#10622600—21no—
17#10622590C412yes—
18C4×C4⋊Dic11C2211yescharacteristic
19#10622539C2211yescharacteristic
20#10622539C2211yescharacteristic
21#10622449—22no—
22#10622339—21no—
23D11×C22⋊C8—21no—
24#10622319—22no—
25C11×#332—22no—
26#10622185—22no—
27#10622106—21no—
28#10622106—21no—
29C22×Q8×C11—21no—
30C22×D44C2×C411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4C2×C412yes—
39C2×C42×C11C2311yescharacteristic
40C2×(C2×D11)⋊C4—22no—
41C2×(C2×D11)⋊C4—22no—
42C2×(C2×D11)⋊C4D411yescharacteristic
43C2×(C2×D11)⋊C4D411yescharacteristic
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×C4×Dic11C2×C412yes—
47C2×#4313—22no—
48C2×C8×D11—22no—
49C4×D44—21no—
50C4×D44—21no—
51C4×D44—21no—
52C4×D44—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8D412yes—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×#97—21no—
58C11×#97—21no—
59C11⋊#95—21no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)—21no—
64(C2×D11)⋊C8—22no—
65(C2×D11)⋊C8—22no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)D412yes—
68#66867—21no—
69#66867—21no—
70#9453—111nomaximal, Sylow
71C23×D11C22⋊C411yescharacteristic
72C23×D11C22⋊C411yescharacteristic
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—82no—
76C22×C4×C11—22no—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×Dic11—22no—
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C2×D44—22no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—41no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—42no—
92C2×C4×D11—42no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—82no—
108(C2×D11)⋊C4—82no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—42no—
112C4×Dic11—42no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—41no—
115#4313—82no—
116C8×D11—82no—
117#2973—111no—
118#2563—111no—
119#1556—111no—
120#1556D1111yescharacteristic, complemented
121#1466—111no—
122#1285—111no—
123#1285—111no—
124C23×C11C2×C22⋊C411yescharacteristic
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11#10112yes—
135Q8×C11—82no—
136Q8×C11—82no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157D44—42no—
158D44—42no—
159C4×D11—42no—
160C4×D11—42no—
161C4×D11—81no—
162C4×D11—81no—
163C8×C11—42no—
164C8×C11—81no—
165C11⋊C8—42no—
166C11⋊C8—81no—
167C2×C4⋊Q8C2×D1111yescharacteristic
168C2×C4×D4—111no—
169#435—222no—
170#435—222no—
171#432—111no—
172#432—111no—
173#432C2×D1111yescharacteristic
174#432C2×D1111yescharacteristic
175#407—221no—
176C2×C22⋊C8—221no—
177#393—221no—
178#393—221no—
179#390—112no—
180#382—112no—
181#380—221no—
182#380—221no—
183C4×C4⋊C4—111no—
184#332—22no—
185#332—222no—
186#323—221no—
187#323—221no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11#38611yescharacteristic
191C22×C11C2×#10111yescharacteristic
192C22×C11#41311yescharacteristic
193C2×D11—22no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—42no—
197C2×D11—42no—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—82no—
209C4×C11#45512yes—
210Dic11—41no—
211Dic11—41no—
212Dic11—82no—
213C22×Q8—21no—
214C22×D4—111no—
215C23×C4—111no—
216C23×C4—111no—
217C2×M16—222no—
218C22×C8—222no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4×D4—221no—
224C4×D4—221no—
225C4×D4—221no—
226C4×D4—221no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4C4×D1112yes—
231C2×C22⋊C4—111no—
232C2×C22⋊C4—111no—
233C2×C22⋊C4—222no—
234C2×C22⋊C4—222no—
235C2×C42—112no—
236C2×C42C22×D1111yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—112no—
239C4⋊C8—221no—
240C4⋊C8C22⋊D1112yes—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8—222no—
244C22⋊C8—222no—
245C22⋊C8—221no—
246C22⋊C8—221no—
247#97—21no—
248#97—21no—
249#97—221no—
250#97—221no—
251#95—222no—
252#95—222no—
253#95—221no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11#188511yescharacteristic
257C2×C11#190111yescharacteristic
258C2×C11#191011yescharacteristic
259D11—42no—
260D11—81no—
261C24—111no—
262C24—111no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—82no—
266C2×D4—222no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—441no—
270C22×C4—22no—
271C22×C4—111no—
272C22×C4—111no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—222no—
278C22×C4—442no—
279C22×C4—442no—
280C22×C4C2×C4×D1111yescharacteristic
281C22×C4D4×D1111yescharacteristic
282C22×C4D4×D1111yescharacteristic
283M16—882no—
284C2×C8—22no—
285C2×C8—41no—
286C2×C8—222no—
287C2×C8—441no—
288C2×C8—882no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—442no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C22⋊C4—882no—
301C22⋊C4—882no—
302C42—442no—
303C42#433911yescharacteristic
304C42D4×D1111yescharacteristic
305C42#434111yescharacteristic
306C42C2×C22⋊D1111yescharacteristic
307C11#945311yescharacteristic, complemented, Sylow
308C23—112no—
309C23—221no—
310C23—221no—
311C23—221no—
312C23—221no—
313C23—221no—
314C23—441no—
315C23—441no—
316C23—441no—
317C23—441no—
318C23C22⋊C4×D1111yescharacteristic
319Q8—82no—
320Q8—82no—
321D4—442no—
322D4—442no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—442no—
333C2×C4—442no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4(C22⋊D11)⋊C411yescharacteristic
342C2×C4#6693611yescharacteristic
343C2×C4#6693711yescharacteristic
344C2×C4C4×C22⋊D1111yescharacteristic
345C2×C4#6699011yescharacteristic
346C2×C4#6699111yescharacteristic
347C8—42no—
348C8—81no—
349C8—442no—
350C8—881no—
351C22—21no—
352C22—21no—
353C22—222no—
354C22—442no—
355C22—442no—
356C22—441no—
357C22—441no—
358C22—441no—
359C22—441no—
360C22—441no—
361C22—881no—
362C22—881no—
363C22D11×#10111yescharacteristic
364C22#1062236411yescharacteristic
365C22#1062256911yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—82no—
372C4—441no—
373C4—441no—
374C4—882no—
375C4#1062281512yes—
376C2—21no—
377C2—21no—
378C2—442no—
379C2—881no—
380C2#1306900111yescharacteristic
381C2#1306908111yescharacteristic
382C2#1306914011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1556C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1556D11
hypocenterC11#9453
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1556

Complements

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

NH ≅ G/Ntype
3. #13067333C2semidirect
5. #13066473C2semidirect
6. #13066471C2semidirect
7. C11×#1556C2semidirect
120. #1556D11semidirect
307. C11#9453semidirect

Maximal subgroups

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

subgroupindex
#130776442
#130737902
#130673332
#130669562
#130664732
#130664712
C11×#15562
#945311