Finite Group Databasebeta

← #14663228

Subgroups — #14663228

Order 2816.

530 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 75 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#13071271C211yesmaximal, characteristic
2#13066955C211yesmaximal, characteristic, complemented
3#13066951C211yesmaximal, characteristic, complemented
4#13066565C211yesmaximal, characteristic, complemented
5#13066563C211yesmaximal, characteristic, complemented
6#13066544C211yesmaximal, characteristic, complemented
7C11×#1316C211yesmaximal, characteristic, complemented
8C2×#67006C411yescharacteristic
9C22×C22⋊Dic11C411yescharacteristic
10C2×(C22⋊D11)⋊C4C2211yescharacteristic
11C11×#379C2211yescharacteristic
12#10622571C411yescharacteristic
13#10622570—21no—
14#10622569—21no—
15#10622559C2211yescharacteristic
16#10622558—21no—
17#10622557—21no—
18C22⋊C4×Dic11C411yescharacteristic
19#10622339—21no—
20#10622332—21no—
21C11×#323C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622107—21no—
26#10622106—21no—
27C25×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11C2×C411yescharacteristic
30C23×Dic11C2×C411yescharacteristic
31C23×Dic11C2×C411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4C2311yescharacteristic
37#67006—22no—
38#67006—22no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—41no—
43C2×C22⋊Dic11—41no—
44C2×C22⋊Dic11C2×C411yescharacteristic
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4D411yescharacteristic
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4D411yescharacteristic
49C2×C4×Dic11—21no—
50C2×C4×Dic11D411yescharacteristic
51C2×#4313—41no—
52(C22⋊D11)⋊C4—41no—
53(C22⋊D11)⋊C4—41no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—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#11527—111nomaximal, Sylow
65C24×C11—21no—
66C24×C11—21no—
67C24×C11—41no—
68C24×C11—41no—
69C24×C11—81no—
70C24×C11—81no—
71C24×C11M1612yescomplemented
72C24×C11C22×C411yescharacteristic
73C23×D11C22⋊C411yescharacteristic
74C22×C4×C11—21no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—24no—
78C2×C22⋊D11—21no—
79C2×C22⋊D11—21no—
80C2×C22⋊D11—41no—
81C2×C22⋊D11—41no—
82C2×C22⋊D11—81no—
83C2×C22⋊D11—81no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—41no—
89C22×Dic11—81no—
90C22×Dic11—81no—
91C22×Dic11C22⋊C411yescharacteristic
92C22×Dic11C22⋊C411yescharacteristic
93C22×Dic11C22⋊C411yescharacteristic
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—81no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—81no—
102C11×C22⋊C4—81no—
103C22⋊Dic11—24no—
104C22⋊Dic11—21no—
105C22⋊Dic11—42no—
106C22⋊Dic11—41no—
107C22⋊Dic11—41no—
108C22⋊Dic11M1612yescomplemented
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—81no—
111Dic11⋊C4—41no—
112Dic11⋊C4—81no—
113C4×Dic11—21no—
114C4×Dic11—21no—
115C4×Dic11—81no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118#4313—82no—
119#2321—111no—
120#1466—111no—
121#1465—111no—
122#1326—111no—
123#1326—111no—
124#1316—111no—
125#1316D1111yescharacteristic, complemented
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—22no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—82no—
140C23×C11—82no—
141C23×C11—82no—
142C23×C11—82no—
143C23×C11—84no—
144C23×C11C2×C22⋊C411yescharacteristic
145C23×C11C2×M1611yescharacteristic
146C23×C11C2×M1611yescharacteristic
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—41no—
151C22×D11—41no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C22⋊D11—42no—
160C22⋊D11—42no—
161C22⋊D11—84no—
162C2×Dic11—21no—
163C2×Dic11—22no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—81no—
175C2×Dic11—81no—
176C2×Dic11—82no—
177C2×Dic11#9911yescharacteristic
178C2×Dic11#9911yescharacteristic
179C4×D11—42no—
180C4×D11—81no—
181C8×C11—81no—
182C8×C11—81no—
183C11⋊C8—81no—
184C11⋊C8—81no—
185C2×#120—111no—
186C2×C4×D4—111no—
187C22×C22⋊C4—111no—
188#432—221no—
189#407—221no—
190#390—221no—
191#388—221no—
192#388—221no—
193#386—111no—
194#386—221no—
195#385—111no—
196#379C2×D1111yescharacteristic
197C4×C22⋊C4—111no—
198#324—221no—
199#323—111no—
200#323—111no—
201#323—221no—
202#323C2×D1111yescharacteristic
203#323C2×D1111yescharacteristic
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—42no—
211C22×C11—42no—
212C22×C11—42no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—42no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—84no—
219C22×C11—84no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11#40711yescharacteristic
223C22×C11C2×#9911yescharacteristic
224C22×C11#41311yescharacteristic
225C2×D11—42no—
226C2×D11—41no—
227C2×D11—41no—
228C2×D11—41no—
229C2×D11—81no—
230C4×C11—41no—
231C4×C11—41no—
232C4×C11—81no—
233Dic11—21no—
234Dic11—21no—
235Dic11—42no—
236Dic11—41no—
237Dic11—41no—
238Dic11—81no—
239C25C4×D1111yescharacteristic
240C22×D4—111no—
241C22×D4—221no—
242C23×C4—111no—
243C23×C4—111no—
244C23×C4—111no—
245C2×M16—441no—
246#120—222no—
247#120—222no—
248C4×D4—441no—
249C4×D4—441no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—221no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—111no—
255C2×C22⋊C4—111no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—441no—
261C2×C22⋊C4—441no—
262C2×C22⋊C4C4×D1111yescharacteristic
263C2×C22⋊C4C22×D1111yescharacteristic
264C2×C42—111no—
265C2×C42—221no—
266C4⋊C8—441no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C22⋊C8—221no—
270C22⋊C8—221no—
271C22⋊C8—441no—
272#97—441no—
273#95—221no—
274#95—221no—
275#95—221no—
276C2×C11—21no—
277C2×C11—21no—
278C2×C11—41no—
279C2×C11—41no—
280C2×C11—82no—
281C2×C11#146511yescharacteristic
282C2×C11#212111yescharacteristic
283C2×C11#212211yescharacteristic
284D11—81no—
285C24—21no—
286C24—21no—
287C24—41no—
288C24—41no—
289C24—81no—
290C24—81no—
291C24—111no—
292C24#431312yescomplemented
293C24C2×C4×D1111yescharacteristic
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—224no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—881no—
300C2×D4—881no—
301C22×C4—21no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—111no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—221no—
311C22×C4—441no—
312C22×C4—881no—
313C22×C4—881no—
314C22×C4—881no—
315C22×C4D4×D1111yescharacteristic
316C22×C4D4×D1111yescharacteristic
317M16—882no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—441no—
321C2×C8—441no—
322C4⋊C4—441no—
323C4⋊C4—881no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—81no—
327C22⋊C4—81no—
328C22⋊C4—112no—
329C22⋊C4—224no—
330C22⋊C4—221no—
331C22⋊C4—441no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C22⋊C4—442no—
335C22⋊C4—881no—
336C42—221no—
337C42—221no—
338C42—881no—
339C11#1152711yescharacteristic, complemented, Sylow
340C23—21no—
341C23—21no—
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—42no—
350C23—42no—
351C23—41no—
352C23—41no—
353C23—82no—
354C23—82no—
355C23—82no—
356C23—82no—
357C23—84no—
358C23—221no—
359C23—221no—
360C23—221no—
361C23—441no—
362C23—441no—
363C23C22⋊C4×D1111yescharacteristic
364C23C2×#431311yescharacteristic
365C23M16×D1111yescharacteristic
366D4—442no—
367D4—442no—
368D4—884no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—111no—
377C2×C4—111no—
378C2×C4—222no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—442no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—881no—
392C2×C4—881no—
393C2×C4—881no—
394C2×C4—882no—
395C8—81no—
396C8—81no—
397C8—881no—
398C8—881no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—42no—
406C22—42no—
407C22—42no—
408C22—41no—
409C22—41no—
410C22—42no—
411C22—81no—
412C22—81no—
413C22—84no—
414C22—84no—
415C22—81no—
416C22—81no—
417C22—442no—
418C22—441no—
419C22—441no—
420C22—441no—
421C22—881no—
422C22#1062233911yescharacteristic
423C22D11×#9911yescharacteristic
424C22#1062235811yescharacteristic
425C4—41no—
426C4—41no—
427C4—81no—
428C4—221no—
429C4—221no—
430C4—442no—
431C4—441no—
432C4—441no—
433C4—881no—
434C2—21no—
435C2—21no—
436C2—41no—
437C2—41no—
438C2—82no—
439C2—881no—
440C2#1306695111yescharacteristic
441C2#1307025911yescharacteristic
442C2#1307026411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1316C2
socleC22×C11C2×#99
prime radicalC2×#67006C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1316D11
hypocenterC11#11527
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1316

Complements

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

NH ≅ G/Ntype
2. #13066955C2semidirect
3. #13066951C2semidirect
4. #13066565C2semidirect
5. #13066563C2semidirect
6. #13066544C2semidirect
7. C11×#1316C2semidirect
71. C24×C11M16semidirect
108. C22⋊Dic11M16semidirect
125. #1316D11semidirect
292. C24#4313semidirect
339. C11#11527semidirect

Maximal subgroups

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

subgroupindex
#130712712
#130669552
#130669512
#130665652
#130665632
#130665442
C11×#13162
#1152711