Finite Group Databasebeta

← #14663222

Subgroups — #14663222

Order 2816.

738 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C4×#66990C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic, complemented
3#13066565C212yesmaximal, complemented
4#13066543C212yesmaximal, complemented
5C11×#1466C211yesmaximal, characteristic, complemented
6C23×C4×D11C411yescharacteristic
7C2×C4×D4×C11C2211yescharacteristic
8C2×#66990C411yescharacteristic
9C2×C4×C22⋊D11—21no—
10C11×#432—21no—
11#10622833C411yescharacteristic
12C4×C22⋊Dic11C411yescharacteristic
13#10622820—21no—
14#10622602—21no—
15#10622569—21no—
16#10622568C2211yescharacteristic
17#10622559C2211yescharacteristic
18C4×(C2×D11)⋊C4—21no—
19C11×#323—21no—
20C11×#323C2212yes—
21#10622166—21no—
22#10622163C2212yes—
23C24×D11C2×C411yescharacteristic
24C22×D4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C22×C22⋊D11—21no—
28C23×Dic11C2×C411yescharacteristic
29C22×C4×D11—21no—
30C22×C4×D11—21no—
31C22×C4×D11—44no—
32C22×C4×D11—41no—
33C22×C4×D11—41no—
34C4×D4×C11—41no—
35C4×D4×C11—41no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C11×C22⋊C4C2311yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11C2×C411yescharacteristic
42C2×C22⋊Dic11C2×C411yescharacteristic
43#66990—22no—
44#66990—22no—
45C4×C22⋊D11—44no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11—21no—
51C2×#4318—41no—
52C11×C4⋊C8—41no—
53C11×C22⋊C8—22no—
54C11×#97—41no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C22⋊(C11⋊C8)—22no—
59C22⋊(C11⋊C8)—41no—
60#11525—111nomaximal, Sylow
61C24×C11C22⋊C411yescharacteristic
62C24×C11C22×C411yescharacteristic
63C23×D11—21no—
64C23×D11—21no—
65C23×D11—42no—
66C23×D11—42no—
67C23×D11—41no—
68C23×D11—41no—
69C23×D11M1612yescomplemented
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C2×C22⋊D11—24no—
86C2×C22⋊D11—42no—
87C2×C22⋊D11—42no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—41no—
92C22×Dic11—42no—
93C2×C4×D11—24no—
94C2×C4×D11—42no—
95C2×C4×D11—42no—
96C2×C4×D11—42no—
97C2×C4×D11—42no—
98C2×C4×D11—44no—
99C2×C4×D11—44no—
100C2×C4×D11—44no—
101C2×C4×D11—44no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×C8×C11—42no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11—21no—
109C42×C11—21no—
110C22⋊Dic11—21no—
111C22⋊Dic11—41no—
112C22⋊Dic11—42no—
113C22⋊Dic11M1612yescomplemented
114(C2×D11)⋊C4—24no—
115(C2×D11)⋊C4—42no—
116(C2×D11)⋊C4—42no—
117Dic11⋊C4—42no—
118C4×Dic11—42no—
119#4318—82no—
120C2×C11⋊C8—42no—
121C4×#120—111no—
122#1466D1111yescharacteristic, complemented
123#1465—111no—
124#1326—112no—
125#1316—112no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11C2×C22⋊C411yescharacteristic
136C23×C11C2×M1611yescharacteristic
137C23×C11C2×M1611yescharacteristic
138C22×D11—22no—
139C22×D11—22no—
140C22×D11—22no—
141C22×D11—44no—
142C22×D11—44no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—42no—
146C22×D11—42no—
147C22×D11—48no—
148C22×D11—42no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—42no—
152C22×D11—42no—
153C22×D11—42no—
154D4×C11—42no—
155D4×C11—42no—
156C2×C4×C11—22no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—81no—
170C2×C4×C11#9911yescharacteristic
171C2×C4×C11#9911yescharacteristic
172C22⋊D11—48no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—42no—
179C2×Dic11—41no—
180C2×Dic11—42no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C4×D11—44no—
185C4×D11—48no—
186C4×D11—44no—
187C8×C11—82no—
188C11⋊C8—82no—
189C24×C4—111no—
190C2×#120—111no—
191C2×C4×D4—221no—
192C2×C4×D4C2×D1111yescharacteristic
193#432—21no—
194#407—221no—
195#386—111no—
196#386—221no—
197#385—111no—
198#385—221no—
199#379—111no—
200C4×C22⋊C4—111no—
201C4×C22⋊C4—221no—
202#324—221no—
203#323—21no—
204#323—112no—
205#323C2×D1112yes—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—42no—
213C22×C11—42no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—81no—
220C22×C11#40711yescharacteristic
221C22×C11C2×#9911yescharacteristic
222C22×C11#41311yescharacteristic
223C2×D11—24no—
224C2×D11—42no—
225C2×D11—42no—
226C2×D11—42no—
227C2×D11—44no—
228C2×D11—44no—
229C2×D11—44no—
230C2×D11—42no—
231C2×D11—42no—
232C2×D11—42no—
233C2×D11—44no—
234C4×C11—21no—
235C4×C11—41no—
236C4×C11—41no—
237C4×C11—41no—
238C4×C11—41no—
239C4×C11AΣL(1,𝔽16)12yes—
240Dic11—42no—
241Dic11—42no—
242Dic11—81no—
243C25—111no—
244C22×D4—221no—
245C22×D4C4×D1111yescharacteristic
246C23×C4—111no—
247C23×C4—221no—
248C23×C4—221no—
249C23×C4—441no—
250C23×C4—441no—
251C23×C4—444no—
252C23×C4C4×D1111yescharacteristic
253C23×C4D4411yescharacteristic
254C2×M16—441no—
255#120—222no—
256#120—222no—
257C4×D4—41no—
258C4×D4—41no—
259C4×D4—444no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4D4411yescharacteristic
262C2×C22⋊C4—111no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4C22⋊D1111yescharacteristic
269C2×C22⋊C4C22×D1111yescharacteristic
270C2×C42—221no—
271C2×C42C22⋊D1111yescharacteristic
272C4⋊C8—41no—
273C22⋊C8—22no—
274C22⋊C8—222no—
275C22⋊C8—441no—
276#97—41no—
277#95—221no—
278#95—221no—
279#95—221no—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11—41no—
283C2×C11—41no—
284C2×C11—81no—
285C2×C11#146511yescharacteristic
286C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
287C2×C11#212011yescharacteristic
288D11—44no—
289C24—112no—
290C24—221no—
291C24—221no—
292C24—441no—
293C24—441no—
294C24—442no—
295C24—442no—
296C24(C2×D11)⋊C411yescharacteristic
297C24C2×C4×D1111yescharacteristic
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—224no—
303C2×D4—442no—
304C2×D4—442no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—224no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—442no—
316C22×C4—442no—
317C22×C4—442no—
318C22×C4—442no—
319C22×C4—444no—
320C22×C4—444no—
321C22×C4—444no—
322C22×C4—444no—
323C22×C4—442no—
324C22×C4—441no—
325C22×C4—441no—
326C22×C4—441no—
327C22×C4(C2×D11)⋊C411yescharacteristic
328C22×C4(C2×D11)⋊C411yescharacteristic
329C22×C4(C2×D11)⋊C411yescharacteristic
330C22×C4C2×D4411yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332M16—882no—
333C2×C8—42no—
334C2×C8—442no—
335C4⋊C4—41no—
336C4⋊C4—442no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—112no—
340C22⋊C4—224no—
341C22⋊C4—221no—
342C22⋊C4—442no—
343C22⋊C4—442no—
344C22⋊C4—442no—
345C22⋊C4—441no—
346C42—21no—
347C42—21no—
348C42—442no—
349C11#1152511yescharacteristic, complemented, Sylow
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—222no—
360C23—222no—
361C23—222no—
362C23—442no—
363C23—441no—
364C23—441no—
365C23—442no—
366C23—444no—
367C23—444no—
368C23—442no—
369C23—442no—
370C23—442no—
371C23—448no—
372C23—442no—
373C23—441no—
374C23—441no—
375C23M16×D1111yescharacteristic
376C23M16×D1111yescharacteristic
377C23C2×(C2×D11)⋊C411yescharacteristic
378D4—42no—
379D4—42no—
380D4—448no—
381C2×C4—22no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—444no—
398C2×C4—448no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—442no—
403C2×C4—441no—
404C2×C4—444no—
405C2×C4—442no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4#6687011yescharacteristic
410C2×C4#6687011yescharacteristic
411C8—82no—
412C8—882no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—41no—
418C22—41no—
419C22—42no—
420C22—42no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—81no—
427C22—224no—
428C22—442no—
429C22—442no—
430C22—442no—
431C22—444no—
432C22—444no—
433C22—444no—
434C22—444no—
435C22—442no—
436C22—442no—
437C22—442no—
438C22C2×#6687011yescharacteristic
439C22#1062273911yescharacteristic
440C22#1062274511yescharacteristic
441C4—21no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—41no—
446C4—442no—
447C4—442no—
448C4—881no—
449C4#1062211312yes—
450C2—21no—
451C2—21no—
452C2—41no—
453C2—41no—
454C2—81no—
455C2—444no—
456C2#1306695211yescharacteristic
457C2C2×#1062211311yescharacteristic
458C2#1307025511yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1466C2
socleC22×C11C2×#99
prime radicalC2×#66990C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1466D11
hypocenterC11#11525
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. #13066954C2semidirect
3. #13066565C2semidirect
4. #13066543C2semidirect
5. C11×#1466C2semidirect
69. C23×D11M16semidirect
113. C22⋊Dic11M16semidirect
122. #1466D11semidirect
349. C11#11525semidirect

Maximal subgroups

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

subgroupindex
C4×#669902
#130669542
#130665652
#130665432
C11×#14662
#1152511