Finite Group Databasebeta

← #14663388

Subgroups — #14663388

Order 2816.

444 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 73 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#13072923C211yesmaximal, characteristic
2#13066951C211yesmaximal, characteristic
3#13066935C211yesmaximal, characteristic
4#13066546C211yesmaximal, characteristic, complemented
5#13066545C211yesmaximal, characteristic, complemented
6#13066545C211yesmaximal, characteristic, complemented
7C11×#1317C211yesmaximal, characteristic, complemented
8C2×#66982C411yescharacteristic
9C22×Dic11⋊C4C411yescharacteristic
10C2×#66939C411yescharacteristic
11C2×(C22⋊D11)⋊C4C2211yescharacteristic
12C11×#381C2211yescharacteristic
13#10622556C2211yescharacteristic
14#10622555C411yescharacteristic
15#10622339—21no—
16#10622331—21no—
17#10622288—21no—
18#10622280—21no—
19#10622270—21no—
20#10622260—21no—
21C11×#323C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622107—21no—
26#10622106—21no—
27C23×C4×C11C2×C411yescharacteristic
28C22×C22⋊D11C2×C411yescharacteristic
29C23×Dic11C2×C411yescharacteristic
30C23×Dic11C2×C411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4C2311yescharacteristic
34C2×C22⋊Dic11C2×C411yescharacteristic
35#66982—42no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4D411yescharacteristic
39C2×C4⋊Dic11—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—41no—
45C2×Dic11⋊C4—41no—
46C2×Dic11⋊C4D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×#4313—41no—
49#66939—42no—
50(C22⋊D11)⋊C4—41no—
51(C22⋊D11)⋊C4—41no—
52C11×C22⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C22⋊(C11⋊C8)—21no—
60C22⋊(C11⋊C8)—21no—
61(C2×D11)⋊C8—41no—
62Dic11⋊C8—41no—
63C8×Dic11—41no—
64#11562—111nomaximal, Sylow
65C24×C11C22×C411yescharacteristic
66C23×D11C22⋊C411yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C2×C22⋊D11—22no—
76C2×C22⋊D11—21no—
77C2×C22⋊D11—21no—
78C2×C22⋊D11—41no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—41no—
86C22×Dic11—41no—
87C22×Dic11—42no—
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C22×Dic11C22⋊C411yescharacteristic
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—42no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C22⋊Dic11—41no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102C4⋊Dic11—42no—
103Dic11⋊C4—41no—
104Dic11⋊C4—42no—
105Dic11⋊C4—42no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—42no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#4313—82no—
114#2486—111no—
115#1465—111no—
116#1460—111no—
117#1317—111no—
118#1317—111no—
119#1317—111no—
120#1317D1111yescharacteristic, complemented
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11C2×C22⋊C411yescharacteristic
126C23×C11#13111yescharacteristic
127C23×C11#13111yescharacteristic
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—41no—
132C22×D11—41no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C22⋊D11—42no—
146C22⋊D11—42no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—22no—
150C2×Dic11—21no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—81no—
161C2×Dic11—81no—
162C2×Dic11#9911yescharacteristic
163C2×Dic11#9911yescharacteristic
164C2×Dic11#10012yes—
165C4×D11—42no—
166C4×D11—81no—
167C8×C11—81no—
168C8×C11—81no—
169C11⋊C8—81no—
170C11⋊C8—81no—
171C2×#123—111no—
172C2×#123—111no—
173C2×C4×D4—111no—
174C22×C4⋊C4—111no—
175#431—221no—
176#407—221no—
177#398—221no—
178#397—221no—
179#389—221no—
180#381—111no—
181#381C2×D1111yescharacteristic
182#380—111no—
183#380—221no—
184#324—221no—
185#323—111no—
186#323—111no—
187#323—221no—
188#323C2×D1111yescharacteristic
189#323C2×D1111yescharacteristic
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—42no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11#40811yescharacteristic
200C22×C11C2×#9911yescharacteristic
201C22×C11C2×#10011yescharacteristic
202C2×D11—42no—
203C2×D11—41no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—81no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—81no—
210C4×C11—81no—
211Dic11—21no—
212Dic11—22no—
213Dic11—41no—
214Dic11—81no—
215Dic11—81no—
216Dic11#35212yes—
217C22×D4—111no—
218C23×C4—111no—
219C23×C4—111no—
220C23×C4—111no—
221C23×C4C4×D1111yescharacteristic
222C2×M16—441no—
223#123—442no—
224#123—442no—
225C4×D4—441no—
226C4×D4—441no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—441no—
234C2×C4⋊C4—441no—
235C2×C22⋊C4—111no—
236C2×C22⋊C4—111no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4C4×D1111yescharacteristic
240C2×C22⋊C4C22×D1111yescharacteristic
241C2×C42—111no—
242C4⋊C8—441no—
243C22⋊C8—21no—
244C22⋊C8—21no—
245C22⋊C8—221no—
246C22⋊C8—221no—
247C22⋊C8—441no—
248C4×C8—441no—
249#95—21no—
250#95—21no—
251#95—221no—
252#95—221no—
253#95—221no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11—41no—
257C2×C11—41no—
258C2×C11#147111yescharacteristic
259C2×C11C2×#35211yescharacteristic
260C2×C11#212311yescharacteristic
261D11—81no—
262C24—111no—
263C24C2×C4×D1111yescharacteristic
264C2×D4—222no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—441no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—442no—
286C22×C4—442no—
287C22×C4—441no—
288C22×C4—441no—
289C22×C4D4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291M16—882no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—441no—
295C2×C8—441no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C4⋊C4—442no—
300C4⋊C4—442no—
301C4⋊C4—442no—
302C4⋊C4—442no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—441no—
306C22⋊C4—442no—
307C22⋊C4—442no—
308C22⋊C4—441no—
309C42—221no—
310C42—221no—
311C11#1156211yescharacteristic, complemented, Sylow
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—221no—
317C23—221no—
318C23—221no—
319C23—441no—
320C23—441no—
321C23C22⋊C4×D1111yescharacteristic
322C23#6695411yescharacteristic
323C23#6696011yescharacteristic
324D4—442no—
325D4—442no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—111no—
339C2×C4—111no—
340C2×C4—112no—
341C2×C4—222no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—881no—
356C2×C4—881no—
357C2×C4—881no—
358C8—81no—
359C8—81no—
360C8—881no—
361C8—881no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—42no—
369C22—41no—
370C22—41no—
371C22—442no—
372C22—441no—
373C22—441no—
374C22—441no—
375C22—881no—
376C22#1062234011yescharacteristic
377C22D11×#9911yescharacteristic
378C22D11×#10011yescharacteristic
379C4—41no—
380C4—41no—
381C4—81no—
382C4—81no—
383C4—112no—
384C4—221no—
385C4—222no—
386C4—441no—
387C4—881no—
388C4—881no—
389C2—21no—
390C2—21no—
391C2—41no—
392C2—41no—
393C2—881no—
394C2#1306697411yescharacteristic
395C2D11×#35211yescharacteristic
396C2#1307026811yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1317C2
socleC22×C11C2×#99
prime radicalC22×C22⋊D11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1317D11
hypocenterC11#11562
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
4. #13066546C2semidirect
5. #13066545C2semidirect
6. #13066545C2semidirect
7. C11×#1317C2semidirect
120. #1317D11semidirect
311. C11#11562semidirect

Maximal subgroups

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

subgroupindex
#130729232
#130669512
#130669352
#130665462
#130665452
C11×#13172
#1156211