Finite Group Databasebeta

← #14651516

Subgroups — #14651516

Order 2816.

610 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 93 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#13073087C211yesmaximal, characteristic
2#13071217C211yesmaximal, characteristic, complemented
3#13068694C211yesmaximal, characteristic, complemented
4#13067146C211yesmaximal, characteristic
5#13067144C211yesmaximal, characteristic
6#13066469C211yesmaximal, characteristic, complemented
7C11×#1284C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C22×C4⋊Dic11C2211yescharacteristic
10C2×#66939—21no—
11C2×#66939—21no—
12C11×#407C2211yescharacteristic
13C11×#381C2211yescharacteristic
14C4×C11×C22⋊C4C2211yescharacteristic
15#10622824C2211yescharacteristic
16#10622820C2211yescharacteristic
17#10622555—21no—
18C22⋊C4×Dic11—21no—
19#10622552C412yescomplemented
20#10622548C412yescomplemented
21#10622290—22no—
22#10622267—22no—
23#10622266—22no—
24#10622192—22no—
25#10622108—22no—
26#10622089—22no—
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C23×Dic11D411yescharacteristic
30C23×Dic11D411yescharacteristic
31C22×D44C2×C411yescharacteristic
32C2×C11×M16—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C42×C11C2×C412yes—
36C2×C22⋊Dic11—21no—
37#66983—21no—
38#66983—21no—
39#66983—21no—
40#66983—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—22no—
43C2×(C2×D11)⋊C4—22no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—22no—
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11C2×C411yescharacteristic
51C2×C4⋊Dic11C2×C412yes—
52C2×C4⋊Dic11D412yes—
53C2×Dic11⋊C4—22no—
54C2×C4×Dic11—22no—
55C2×#4318—21no—
56#66939—44no—
57#66939—44no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95D412yes—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95—21no—
66C11⋊#95D412yes—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#9464—111nomaximal, Sylow
70C24×C11C2×D411yescharacteristic
71C23×D11—21no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—42no—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C2×C22⋊D11—42no—
82C2×C22⋊D11—42no—
83C2×C22⋊D11—41no—
84C2×C22⋊D11—41no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—22no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—42no—
92C22×Dic11—42no—
93C22×Dic11C22⋊C412yes—
94C22×Dic11C22⋊C412yes—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—42no—
98C11×M16—42no—
99C2×C8×C11—41no—
100C11×C22⋊C4—24no—
101C11×C22⋊C4—42no—
102C42×C11—42no—
103C22⋊Dic11—42no—
104(C2×D11)⋊C4—44no—
105(C2×D11)⋊C4—44no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114C4⋊Dic11—44no—
115C4⋊Dic11—44no—
116Dic11⋊C4—82no—
117C4×Dic11—82no—
118#4318—42no—
119C2×C11⋊C8—41no—
120#2501—111no—
121#2313—111no—
122#1821—111no—
123#1510—111no—
124#1510—111no—
125#1284—111no—
126#1284D1111yescharacteristic, complemented
127C23×C11—22no—
128C23×C11—22no—
129C23×C11—41no—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11#12011yescharacteristic
132C23×C11#12311yescharacteristic
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—42no—
136C22×D11—41no—
137C22×D11—42no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—24no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11C4×D411yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C22⋊D11—82no—
155C22⋊D11—82no—
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167C2×Dic11—42no—
168C2×Dic11—81no—
169C2×Dic11—81no—
170D44—81no—
171D44—81no—
172C8×C11—81no—
173C11⋊C8—81no—
174C2×#123—221no—
175C2×#123—221no—
176C2×#121—111no—
177C22×C4⋊C4—111no—
178#407—111no—
179#407C2×D1111yescharacteristic
180#399—222no—
181#390—112no—
182#387—222no—
183#387—222no—
184#384—112no—
185#381—111no—
186#381C2×D1111yescharacteristic
187#380—221no—
188C4×C22⋊C4—221no—
189C4×C22⋊C4C2×D1111yescharacteristic
190#343—222no—
191#327—222no—
192#327—222no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—44no—
201C22×C11#38611yescharacteristic
202C22×C11#41012yes—
203C22×C11#45312yes—
204C2×D11—82no—
205C2×D11—82no—
206C2×D11—81no—
207C2×D11—81no—
208C2×D11—81no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—44no—
214C4×C11—82no—
215Dic11—42no—
216Dic11—42no—
217Dic11—82no—
218Dic11—81no—
219C22×D4—111no—
220C22×D4—221no—
221C23×C4—111no—
222C23×C4—111no—
223C23×C4C22×D1111yescharacteristic
224C2×M16—21no—
225C2×M16—221no—
226#123—444no—
227#123—444no—
228#121—221no—
229#121—221no—
230#121—221no—
231#121—221no—
232C2×C4⋊C4—112no—
233C2×C4⋊C4—112no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—222no—
240C2×C4⋊C4—222no—
241C2×C4⋊C4—222no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—222no—
245C2×C22⋊C4—222no—
246C2×C22⋊C4—221no—
247C2×C22⋊C4—221no—
248C2×C42—222no—
249C2×C42C4×D1112yes—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—221no—
253C22⋊C8—221no—
254#95—21no—
255#95—21no—
256#95—112no—
257#95—222no—
258#95—222no—
259#95—221no—
260#95D4412yes—
261C2×C11—22no—
262C2×C11—22no—
263C2×C11—41no—
264C2×C11#188711yescharacteristic
265C2×C11#189911yescharacteristic
266C2×C11#191211yescharacteristic
267D11—161no—
268C24—221no—
269C24D4×D1111yescharacteristic
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—442no—
273C2×D4—442no—
274C2×D4—442no—
275C2×D4—441no—
276C2×D4—441no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—42no—
280C22×C4—112no—
281C22×C4—112no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—222no—
288C22×C4—442no—
289C22×C4—442no—
290C22×C4C2×C4×D1111yescharacteristic
291C22×C4C2×D4411yescharacteristic
292C22×C4#433911yescharacteristic
293C22×C4D4×D1111yescharacteristic
294C22×C4D4×D1111yescharacteristic
295C22×C4#434311yescharacteristic
296M16—42no—
297M16—442no—
298C2×C8—41no—
299C2×C8—441no—
300C4⋊C4—222no—
301C4⋊C4—222no—
302C4⋊C4—222no—
303C4⋊C4—222no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—444no—
307C4⋊C4—444no—
308C4⋊C4—882no—
309C22⋊C4—24no—
310C22⋊C4—42no—
311C22⋊C4—444no—
312C22⋊C4—444no—
313C22⋊C4—442no—
314C22⋊C4—441no—
315C22⋊C4—441no—
316C42—42no—
317C42—882no—
318C11#946411yescharacteristic, complemented, Sylow
319C23—22no—
320C23—22no—
321C23—41no—
322C23—441no—
323C23—441no—
324C23—442no—
325C23—441no—
326C23—442no—
327C23C22⋊C4×D1111yescharacteristic
328C23#6693511yescharacteristic
329C23#6694711yescharacteristic
330D4—881no—
331D4—881no—
332D4—882no—
333D4—882no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—222no—
347C2×C4—222no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4—442no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—442no—
356C2×C4—441no—
357C2×C4—442no—
358C2×C4—881no—
359C2×C4—881no—
360C2×C4C4×D4411yescharacteristic
361C2×C4#6693711yescharacteristic
362C2×C4#6694611yescharacteristic
363C2×C4#6694811yescharacteristic
364C8—81no—
365C8—881no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—44no—
374C22—882no—
375C22—882no—
376C22—881no—
377C22—881no—
378C22—881no—
379C22#1062227811yescharacteristic
380C22#1062235312yes—
381C22#1062243512yes—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—44no—
387C4—82no—
388C4—442no—
389C4—442no—
390C4—882no—
391C4—881no—
392C2—22no—
393C2—22no—
394C2—41no—
395C2—1761no—
396C2#1306901311yescharacteristic
397C2#1306907311yescharacteristic
398C2#1306915211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1284C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1284D11
hypocenterC11#9464
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
2. #13071217C2semidirect
3. #13068694C2semidirect
6. #13066469C2semidirect
7. C11×#1284C2semidirect
19. #10622552C4semidirect
20. #10622548C4semidirect
126. #1284D11semidirect
318. C11#9464semidirect

Maximal subgroups

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

subgroupindex
#130730872
#130712172
#130686942
#130671462
#130671442
#130664692
C11×#12842
#946411