Finite Group Databasebeta

← #14664444

Subgroups — #14664444

Order 2816.

574 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 79 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#13074350C211yesmaximal, characteristic
2#13068690C211yesmaximal, characteristic, complemented
3#13066617C212yesmaximal, complemented
4#13066614C212yesmaximal, complemented
5C11×#1462C211yesmaximal, characteristic, complemented
6C22×C11×C22⋊C4C2211yescharacteristic
7C2×#67006—21no—
8C2×#66983C411yescharacteristic, complemented
9C11×#407—21no—
10#10622860—21no—
11#10622826—21no—
12#10622825C411yescharacteristic, complemented
13#10622574—21no—
14#10622574—21no—
15#10622573C411yescharacteristic, complemented
16#10622573C2211yescharacteristic
17#10622566C411yescharacteristic, complemented
18#10622566C2211yescharacteristic
19C11×#323—21no—
20C11×#323C2212yes—
21#10622164—21no—
22#10622164C2212yes—
23C25×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C22×C22⋊D11—21no—
29C22×D44C2×C411yescharacteristic
30C2×C11×M16—41no—
31C2×C11×C22⋊C4—41no—
32C2×C11×C22⋊C4—41no—
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C11×C22⋊C4C2311yescharacteristic
37#67006—44no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—22no—
42C2×C22⋊Dic11—41no—
43C2×C22⋊Dic11—41no—
44#66983—41no—
45#66983—41no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11C2×C411yescharacteristic
51C11×C22⋊C8—22no—
52C11×C22⋊C8—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95C2×C411yescharacteristic
56C11⋊#95C2×C411yescharacteristic
57#11799—111nomaximal, Sylow
58C24×C11—21no—
59C24×C11—21no—
60C24×C11—22no—
61C24×C11—41no—
62C24×C11—81no—
63C24×C11—81no—
64C24×C11C22⋊C411yescharacteristic
65C24×C11C22⋊C411yescharacteristic
66C24×C11C2×D411yescharacteristic
67C23×D11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—81no—
73C22×C4×C11—81no—
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—42no—
81C2×C22⋊D11—41no—
82C2×C22⋊D11—41no—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—81no—
85C2×C22⋊D11—81no—
86C2×C22⋊D11—81no—
87C2×C22⋊D11—81no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—42no—
92C2×D44—41no—
93C2×D44—81no—
94C11×M16—82no—
95C2×C8×C11—42no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C22⋊Dic11—42no—
101C22⋊Dic11—42no—
102C22⋊Dic11—42no—
103C22⋊Dic11—42no—
104C22⋊Dic11—42no—
105C22⋊Dic11—82no—
106C22⋊Dic11—82no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—81no—
109(C2×D11)⋊C4—81no—
110C4⋊Dic11—41no—
111C4⋊Dic11—81no—
112#2617—111no—
113#1819—111no—
114#1462D1111yescharacteristic, complemented
115#1344—112no—
116#1343—112no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—42no—
133C23×C11—42no—
134C23×C11—81no—
135C23×C11—81no—
136C23×C11—84no—
137C23×C11—84no—
138C23×C11#9911yescharacteristic
139C23×C11#9911yescharacteristic
140C23×C11C2×C22⋊C411yescharacteristic
141C23×C11AGL(1,ℤ/8)12yes—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—41no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C22⋊D11—82no—
162C22⋊D11—82no—
163C22⋊D11—84no—
164C22⋊D11—84no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—82no—
175C2×Dic11—82no—
176C2×Dic11—82no—
177D44—82no—
178C8×C11—82no—
179C2×#121—111no—
180C2×#120—221no—
181C22×C22⋊C4C2×D1111yescharacteristic
182#407—21no—
183#397—111no—
184#397—111no—
185#394—221no—
186#394—221no—
187#392—111no—
188#392—111no—
189#386—221no—
190#380—111no—
191#379—221no—
192#342—112no—
193#342—221no—
194#323—21no—
195#323C2×D1112yes—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—22no—
205C22×C11—42no—
206C22×C11—42no—
207C22×C11—42no—
208C22×C11—42no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—84no—
217C22×C11—84no—
218C22×C11C2×#9911yescharacteristic
219C22×C11#41811yescharacteristic
220C22×C11#42111yescharacteristic
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C4×C11—41no—
229C4×C11—41no—
230C4×C11—41no—
231C4×C11—41no—
232Dic11—81no—
233Dic11—81no—
234Dic11—81no—
235Dic11—162no—
236C25D4411yescharacteristic
237C22×D4—111no—
238C22×D4—221no—
239C22×D4—221no—
240C22×D4—221no—
241C23×C4C4×D1111yescharacteristic
242C23×C4C22⋊D1111yescharacteristic
243C2×M16—41no—
244#121—441no—
245#121—441no—
246#120—444no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—221no—
249C2×C22⋊C4—41no—
250C2×C22⋊C4—41no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—221no—
254C2×C22⋊C4—221no—
255C2×C22⋊C4—222no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—441no—
259C2×C22⋊C4—441no—
260C2×C22⋊C4C4×D1111yescharacteristic
261C2×C22⋊C4D4411yescharacteristic
262C2×C22⋊C4C22⋊D1111yescharacteristic
263C2×C22⋊C4C22×D1111yescharacteristic
264C22⋊C8—22no—
265C22⋊C8—41no—
266#95—111no—
267#95—111no—
268#95—221no—
269#95—221no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—42no—
273C2×C11—41no—
274C2×C11—41no—
275C2×C11—81no—
276C2×C11#151011yescharacteristic
277C2×C11#212111yescharacteristic
278C2×C11#212711yescharacteristic
279D11—161no—
280C24—21no—
281C24—21no—
282C24—22no—
283C24—41no—
284C24—81no—
285C24—81no—
286C24—221no—
287C24(C2×D11)⋊C411yescharacteristic
288C24(C2×D11)⋊C411yescharacteristic
289C24C2×D4411yescharacteristic
290C2×D4—441no—
291C2×D4—442no—
292C2×D4—442no—
293C2×D4—442no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—442no—
297C2×D4—881no—
298C2×D4—881no—
299C2×D4—881no—
300C2×D4—881no—
301C2×D4—881no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—81no—
307C22×C4—81no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—221no—
311C22×C4—442no—
312C22×C4(C2×D11)⋊C411yescharacteristic
313C22×C4(C2×D11)⋊C411yescharacteristic
314C22×C4C2×C4×D1111yescharacteristic
315C22×C4C2×C22⋊D1111yescharacteristic
316M16—82no—
317C2×C8—42no—
318C4⋊C4—441no—
319C4⋊C4—881no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—442no—
325C22⋊C4—442no—
326C22⋊C4—442no—
327C22⋊C4—442no—
328C22⋊C4—442no—
329C22⋊C4—442no—
330C22⋊C4—881no—
331C22⋊C4—881no—
332C22⋊C4—882no—
333C22⋊C4—882no—
334C11#1179911yescharacteristic, complemented, Sylow
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—41no—
343C23—41no—
344C23—42no—
345C23—42no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—42no—
351C23—42no—
352C23—81no—
353C23—81no—
354C23—84no—
355C23—84no—
356C23—441no—
357C23—441no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23#6687011yescharacteristic
364C23#6687011yescharacteristic
365C23#6696112yes—
366C23C2×(C2×D11)⋊C411yescharacteristic
367D4—882no—
368D4—882no—
369D4—882no—
370D4—884no—
371D4—884no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—882no—
394C2×C4—882no—
395C2×C4—882no—
396C8—82no—
397C22—21no—
398C22—21no—
399C22—22no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—42no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—81no—
416C22—81no—
417C22—84no—
418C22—84no—
419C22—881no—
420C22—881no—
421C22—881no—
422C22—881no—
423C22—881no—
424C22—881no—
425C22—881no—
426C22C2×#6687011yescharacteristic
427C22#1062274411yescharacteristic
428C22#1062275211yescharacteristic
429C4—41no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—881no—
434C4—881no—
435C4—881no—
436C4—1762no—
437C2—21no—
438C2—21no—
439C2—42no—
440C2—41no—
441C2—41no—
442C2—81no—
443C2—1761no—
444C2#1306714611yescharacteristic
445C2#1307026311yescharacteristic
446C2#1307028311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1462C2
socleC22×C11C2×#99
prime radical#13074350C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1462D11
hypocenterC11#11799
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
2. #13068690C2semidirect
3. #13066617C2semidirect
4. #13066614C2semidirect
5. C11×#1462C2semidirect
8. C2×#66983C4semidirect
12. #10622825C4semidirect
15. #10622573C4semidirect
17. #10622566C4semidirect
114. #1462D11semidirect
334. C11#11799semidirect

Maximal subgroups

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

subgroupindex
#130743502
#130686902
#130666172
#130666142
C11×#14622
#1179911