Finite Group Databasebeta

← #14663225

Subgroups — #14663225

Order 2816.

470 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 77 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#13071135C211yesmaximal, characteristic
2#13066955C211yesmaximal, characteristic
3#13066951C211yesmaximal, characteristic
4#13066564C211yesmaximal, characteristic, complemented
5#13066545C211yesmaximal, characteristic, complemented
6#13066545C211yesmaximal, characteristic, complemented
7C11×#1326C211yesmaximal, characteristic, complemented
8C22×C4×Dic11C411yescharacteristic
9C2×#66939C411yescharacteristic
10C2×(C22⋊D11)⋊C4C2211yescharacteristic
11C11×#385C2211yescharacteristic
12#10622826C411yescharacteristic
13#10622603—21no—
14C4⋊C4×Dic11—21no—
15#10622556C2211yescharacteristic
16C22⋊C4×Dic11C411yescharacteristic
17#10622339—21no—
18#10622332—21no—
19#10622279—21no—
20#10622267—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×C4⋊C4—21no—
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4C2311yescharacteristic
35C2×C22⋊Dic11C2×C411yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4D411yescharacteristic
39C2×C4⋊Dic11—21no—
40C2×Dic11⋊C4D411yescharacteristic
41C2×C4×Dic11—21no—
42C2×C4×Dic11—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11—41no—
45C2×C4×Dic11—41no—
46C2×C4×Dic11D411yescharacteristic
47C2×#4313—41no—
48#66939—22no—
49#66939—22no—
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—
62#66879—41no—
63Dic11⋊C8—41no—
64#11526—111nomaximal, Sylow
65C24×C11C22×C411yescharacteristic
66C23×D11C22⋊C411yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—42no—
70C22×C4×C11—41no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—21no—
74C2×C22⋊D11—21no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11—41no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—41no—
83C22×Dic11—41no—
84C22×Dic11—42no—
85C22×Dic11C22⋊C411yescharacteristic
86C22×Dic11C22⋊C411yescharacteristic
87C22×Dic11C22⋊C411yescharacteristic
88C22×Dic11M1612yescomplemented
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—42no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C11×C4⋊C4—42no—
95C11×C22⋊C4—21no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4M1612yescomplemented
98C22⋊Dic11—41no—
99(C2×D11)⋊C4—24no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—42no—
102C4⋊Dic11—24no—
103Dic11⋊C4—41no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—42no—
107C4×Dic11—42no—
108C4×Dic11—41no—
109C4×Dic11—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112#4313—82no—
113C4×#123—111no—
114#1466—111no—
115#1465—111no—
116#1326—111no—
117#1326D1111yescharacteristic, complemented
118#1317—111no—
119#1317—111no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11C2×C22⋊C411yescharacteristic
125C23×C11C2×M1611yescharacteristic
126C23×C11C2×M1611yescharacteristic
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—41no—
131C22×D11—41no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C22⋊D11—42no—
145C22⋊D11—42no—
146C2×Dic11—22no—
147C2×Dic11—21no—
148C2×Dic11—22no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—42no—
157C2×Dic11—41no—
158C2×Dic11—42no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11#9911yescharacteristic
163C2×Dic11#9911yescharacteristic
164C4×D11—42no—
165C4×D11—81no—
166C8×C11—81no—
167C8×C11—81no—
168C11⋊C8—81no—
169C11⋊C8—81no—
170C2×#123—111no—
171C2×C4×D4—111no—
172C22×C42—111no—
173#432—221no—
174#407—221no—
175#388—221no—
176#387—221no—
177#386—111no—
178#385C2×D1111yescharacteristic
179#381—111no—
180C4×C4⋊C4—221no—
181C4×C22⋊C4—111no—
182C4×C22⋊C4—221no—
183#324—221no—
184#323—111no—
185#323—111no—
186#323—221no—
187#323C2×D1111yescharacteristic
188#323C2×D1111yescharacteristic
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—42no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11#40711yescharacteristic
199C22×C11C2×#9911yescharacteristic
200C22×C11#41311yescharacteristic
201C2×D11—42no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—41no—
205C2×D11—81no—
206C4×C11—42no—
207C4×C11—41no—
208C4×C11—42no—
209C4×C11—41no—
210Dic11—21no—
211Dic11—41no—
212Dic11—41no—
213Dic11—42no—
214Dic11—81no—
215Dic11#35212yes—
216C22×D4—111no—
217C23×C4—111no—
218C23×C4—111no—
219C23×C4—111no—
220C23×C4C4×D1111yescharacteristic
221C2×M16—441no—
222#123—222no—
223#123—222no—
224C4×D4—441no—
225C4×D4—441no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—221no—
229C2×C22⋊C4—111no—
230C2×C22⋊C4—111no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4C4×D1111yescharacteristic
234C2×C22⋊C4C22×D1111yescharacteristic
235C2×C42—111no—
236C2×C42—221no—
237C2×C42—221no—
238C2×C42—221no—
239C2×C42—441no—
240C2×C42—441no—
241C4⋊C8—441no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C22⋊C8—221no—
245C22⋊C8—221no—
246C22⋊C8—441no—
247#97—441no—
248#95—21no—
249#95—221no—
250#95—221no—
251#95—221no—
252#95—221no—
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—41no—
256C2×C11—41no—
257C2×C11#146511yescharacteristic
258C2×C11C2×#35211yescharacteristic
259C2×C11#212011yescharacteristic
260D11—81no—
261C24—111no—
262C24C2×C4×D1111yescharacteristic
263C2×D4—221no—
264C2×D4—221no—
265C2×D4—441no—
266C2×D4—441no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4—111no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—112no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—442no—
283C22×C4—442no—
284C22×C4—441no—
285C22×C4—441no—
286C22×C4D4×D1111yescharacteristic
287C22×C4D4×D1111yescharacteristic
288M16—882no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—441no—
292C2×C8—441no—
293C4⋊C4—42no—
294C4⋊C4—224no—
295C4⋊C4—441no—
296C22⋊C4—21no—
297C22⋊C4—41no—
298C22⋊C4—224no—
299C22⋊C4—441no—
300C22⋊C4—442no—
301C22⋊C4—441no—
302C22⋊C4#431312yescomplemented
303C42—221no—
304C42—221no—
305C42—441no—
306C42—441no—
307C42—442no—
308C42—442no—
309C11#1152611yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—41no—
313C23—41no—
314C23—221no—
315C23—221no—
316C23—221no—
317C23—441no—
318C23—441no—
319C23C22⋊C4×D1111yescharacteristic
320C23C2×#431311yescharacteristic
321C23M16×D1111yescharacteristic
322D4—442no—
323D4—442no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—111no—
337C2×C4—111no—
338C2×C4—222no—
339C2×C4—222no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—442no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—881no—
356C8—81no—
357C8—81no—
358C8—881no—
359C8—881no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—41no—
365C22—41no—
366C22—42no—
367C22—41no—
368C22—41no—
369C22—442no—
370C22—441no—
371C22—441no—
372C22—441no—
373C22—881no—
374C22#1062233911yescharacteristic
375C22D11×#9911yescharacteristic
376C22#1062236411yescharacteristic
377C4—42no—
378C4—41no—
379C4—41no—
380C4—42no—
381C4—112no—
382C4—221no—
383C4—441no—
384C4—441no—
385C4—442no—
386C4—881no—
387C2—21no—
388C2—21no—
389C2—41no—
390C2—41no—
391C2—881no—
392C2#1306695311yescharacteristic
393C2D11×#35211yescharacteristic
394C2#1307025411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1326C2
socleC22×C11C2×#99
prime radicalC22×C22⋊D11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1326D11
hypocenterC11#11526
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1326

Complements

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

NH ≅ G/Ntype
4. #13066564C2semidirect
5. #13066545C2semidirect
6. #13066545C2semidirect
7. C11×#1326C2semidirect
88. C22×Dic11M16semidirect
97. C11×C22⋊C4M16semidirect
117. #1326D11semidirect
302. C22⋊C4#4313semidirect
309. C11#11526semidirect

Maximal subgroups

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

subgroupindex
#130711352
#130669552
#130669512
#130665642
#130665452
C11×#13262
#1152611