Finite Group Databasebeta

← #14651237

Subgroups — #14651237

Order 2816.

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

normal subgroups only

This group has 720 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#13073542C211yesmaximal, characteristic
2#13071211C211yesmaximal, characteristic, complemented
3#13067133C211yesmaximal, characteristic, complemented
4#13067131C211yesmaximal, characteristic, complemented
5#13066942C211yesmaximal, characteristic, complemented
6#13066502C211yesmaximal, characteristic, complemented
7C11×#1297C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C22×(C2×D11)⋊C4C2211yescharacteristic
10C2×#66939—21no—
11C2×#66935—21no—
12C11×#407C2211yescharacteristic
13C4×C11×C22⋊C4C2211yescharacteristic
14C4×C11×C22⋊C4C2211yescharacteristic
15C4×C22⋊Dic11C2211yescharacteristic
16#10622820C2211yescharacteristic
17#10622568—21no—
18#10622555—21no—
19#10622553—22no—
20#10622552—22no—
21#10622290C412yescomplemented
22#10622284C412yescomplemented
23#10622282—22no—
24#10622108—22no—
25#10622106—22no—
26#10622089—22no—
27C24×D11D411yescharacteristic
28C23×C4×C11C2311yescharacteristic
29C22×C22⋊D11—21no—
30C23×Dic11D411yescharacteristic
31C22×D44—22no—
32C22×D44C2×C411yescharacteristic
33C2×C11×M16—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C42×C11—21no—
37C2×C42×C11—21no—
38C2×C22⋊Dic11—21no—
39#66983—21no—
40#66983—21no—
41#66983—21no—
42#66983—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—22no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4—22no—
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4C2×C412yes—
53C2×(C2×D11)⋊C4D412yes—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11C2×C411yescharacteristic
56C2×Dic11⋊C4—22no—
57C2×C4×Dic11—21no—
58C2×#4318—21no—
59#66939—44no—
60#66935—44no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×#95C2×C412yes—
64C11×#95D412yescomplemented
65C11⋊#95—22no—
66C11⋊#95D412yescomplemented
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#9413—111nomaximal, Sylow
70C24×C11C2×D411yescharacteristic
71C23×D11—21no—
72C23×D11—21no—
73C23×D11—21no—
74C23×D11—42no—
75C23×D11—42no—
76C23×D11—81no—
77C23×D11C22⋊C412yes—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—81no—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C2×C22⋊D11—42no—
88C2×C22⋊D11—42no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—41no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—22no—
94C22×Dic11—21no—
95C22×Dic11—42no—
96C22×Dic11C22⋊C412yes—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—44no—
100C2×D44—44no—
101C2×D44—81no—
102C2×D44—82no—
103C11×M16—81no—
104C2×C8×C11—41no—
105C11×C22⋊C4—24no—
106C11×C22⋊C4—42no—
107C42×C11—81no—
108C42×C11—81no—
109C22⋊Dic11—42no—
110(C2×D11)⋊C4—22no—
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—22no—
113(C2×D11)⋊C4—22no—
114(C2×D11)⋊C4—44no—
115(C2×D11)⋊C4—44no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—82no—
119(C2×D11)⋊C4—82no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—44no—
123Dic11⋊C4—82no—
124C4×Dic11—81no—
125#4318—81no—
126C2×C11⋊C8—41no—
127#2539—111no—
128#2312—111no—
129#1507—111no—
130#1507—111no—
131#1462—111no—
132#1297—111no—
133#1297D1111yescharacteristic, complemented
134C23×C11—22no—
135C23×C11—22no—
136C23×C11—41no—
137C23×C11C2×C22⋊C411yescharacteristic
138C23×C11#12011yescharacteristic
139C23×C11#12311yescharacteristic
140C22×D11—22no—
141C22×D11—22no—
142C22×D11—22no—
143C22×D11—42no—
144C22×D11—42no—
145C22×D11—42no—
146C22×D11—42no—
147C22×D11—42no—
148C22×D11—42no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—42no—
152C22×D11—41no—
153C22×D11—42no—
154C22×D11—81no—
155C22×D11—81no—
156C22×D11—88no—
157C2×C4×C11—24no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11C4×D411yescharacteristic
170C2×C4×C11C4×D411yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C22⋊D11—82no—
174C22⋊D11—82no—
175C2×Dic11—22no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—42no—
182C2×Dic11—41no—
183C2×Dic11—42no—
184C2×Dic11—81no—
185D44—81no—
186D44—81no—
187D44—88no—
188C8×C11—81no—
189C11⋊C8—81no—
190C2×#123—221no—
191C2×#121—111no—
192C2×#120—221no—
193C22×C22⋊C4—111no—
194#407—111no—
195#407C2×D1111yescharacteristic
196#399—112no—
197#392—112no—
198#390—222no—
199#388—222no—
200#388—222no—
201#380—221no—
202#379—221no—
203C4×C22⋊C4—111no—
204C4×C22⋊C4C2×D1111yescharacteristic
205C4×C22⋊C4C2×D1111yescharacteristic
206#327—222no—
207#327—222no—
208#323—222no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—44no—
217C22×C11#38611yescharacteristic
218C22×C11#42112yes—
219C22×C11#45312yes—
220C2×D11—44no—
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—42no—
224C2×D11—84no—
225C2×D11—84no—
226C2×D11—82no—
227C2×D11—82no—
228C2×D11—82no—
229C2×D11—81no—
230C2×D11—81no—
231C2×D11—81no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—44no—
237C4×C11—82no—
238Dic11—42no—
239Dic11—82no—
240Dic11—81no—
241C25—111no—
242C22×D4—111no—
243C22×D4—222no—
244C22×D4—221no—
245C23×C4—111no—
246C23×C4C22×D1111yescharacteristic
247C2×M16—21no—
248C2×M16—221no—
249#123—444no—
250#121—221no—
251#121—221no—
252#121—221no—
253#121—221no—
254#120—444no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—222no—
257C2×C4⋊C4—222no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—112no—
261C2×C22⋊C4—112no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—222no—
267C2×C22⋊C4—222no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—222no—
272C2×C42—21no—
273C2×C42—21no—
274C2×C42—221no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—221no—
278C22⋊C8—221no—
279#95—112no—
280#95—222no—
281#95C4×D1112yes—
282#95D4412yescomplemented
283C2×C11—22no—
284C2×C11—22no—
285C2×C11—41no—
286C2×C11#188711yescharacteristic
287C2×C11#189711yescharacteristic
288C2×C11#191311yescharacteristic
289D11—82no—
290D11—161no—
291C24—112no—
292C24—221no—
293C24—221no—
294C24—221no—
295C24—442no—
296C24—442no—
297C24—881no—
298C24D4×D1111yescharacteristic
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—444no—
302C2×D4—444no—
303C2×D4—442no—
304C2×D4—442no—
305C2×D4—441no—
306C2×D4—441no—
307C2×D4—882no—
308C2×D4—881no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—81no—
312C22×C4—112no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—222no—
317C22×C4—442no—
318C22×C4C2×C4×D1111yescharacteristic
319C22×C4C2×D4411yescharacteristic
320C22×C4#433911yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C22×C4#434311yescharacteristic
324M16—81no—
325M16—881no—
326C2×C8—41no—
327C2×C8—441no—
328C4⋊C4—221no—
329C4⋊C4—221no—
330C4⋊C4—444no—
331C4⋊C4—882no—
332C22⋊C4—24no—
333C22⋊C4—42no—
334C22⋊C4—222no—
335C22⋊C4—222no—
336C22⋊C4—222no—
337C22⋊C4—222no—
338C22⋊C4—444no—
339C22⋊C4—444no—
340C22⋊C4—442no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—882no—
344C22⋊C4—882no—
345C42—81no—
346C42—81no—
347C42—881no—
348C11#941311yescharacteristic, complemented, Sylow
349C23—22no—
350C23—22no—
351C23—41no—
352C23—222no—
353C23—222no—
354C23—222no—
355C23—442no—
356C23—442no—
357C23—442no—
358C23—442no—
359C23—442no—
360C23—441no—
361C23—441no—
362C23—442no—
363C23—442no—
364C23—441no—
365C23—442no—
366C23—881no—
367C23—881no—
368C23—888no—
369C23C22⋊C4×D1111yescharacteristic
370C23#6693511yescharacteristic
371C23#6694711yescharacteristic
372D4—881no—
373D4—881no—
374D4—888no—
375D4—882no—
376D4—882no—
377C2×C4—24no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—222no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—441no—
394C2×C4—442no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—442no—
398C2×C4—881no—
399C2×C4C4×D4411yescharacteristic
400C2×C4#6693711yescharacteristic
401C2×C4#6694611yescharacteristic
402C2×C4#6694811yescharacteristic
403C8—81no—
404C8—881no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—44no—
413C22—444no—
414C22—442no—
415C22—442no—
416C22—442no—
417C22—882no—
418C22—884no—
419C22—882no—
420C22—882no—
421C22—884no—
422C22—881no—
423C22—881no—
424C22—881no—
425C22#1062227811yescharacteristic
426C22#1062243412yes—
427C22#1062243512yes—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—44no—
433C4—82no—
434C4—442no—
435C4—882no—
436C4—881no—
437C2—22no—
438C2—22no—
439C2—41no—
440C2—882no—
441C2—1761no—
442C2#1306901311yescharacteristic
443C2#1306906311yescharacteristic
444C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1297C2
socleC22×C11#386
prime radical#13073542C2
cosocleC23×C4×C11C23
hypercenter#1297D11
hypocenterC11#9413
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. #13071211C2semidirect
3. #13067133C2semidirect
4. #13067131C2semidirect
5. #13066942C2semidirect
6. #13066502C2semidirect
7. C11×#1297C2semidirect
21. #10622290C4semidirect
22. #10622284C4semidirect
64. C11×#95D4semidirect
66. C11⋊#95D4semidirect
133. #1297D11semidirect
282. #95D44semidirect
348. C11#9413semidirect

Maximal subgroups

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

subgroupindex
#130735422
#130712112
#130671332
#130671312
#130669422
#130665022
C11×#12972
#941311