Finite Group Databasebeta

← #14663287

Subgroups — #14663287

Order 2816.

700 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 83 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#13071943C211yesmaximal, characteristic
2#13066943C211yesmaximal, characteristic, complemented
3#13066563C212yesmaximal, complemented
4#13066543C212yesmaximal, complemented
5C2×C11×#323C211yesmaximal, characteristic, complemented
6C23×C22⋊D11C411yescharacteristic
7C22×C11×C22⋊C4C2211yescharacteristic
8C2×#66982—21no—
9C2×C11×C22⋊C8—21no—
10#10622860C411yescharacteristic
11#10622826—21no—
12#10622820—21no—
13#10622572—21no—
14#10622572—21no—
15#10622568C411yescharacteristic
16#10622568C2211yescharacteristic
17#10622559C411yescharacteristic
18#10622559C2211yescharacteristic
19C11×#323—21no—
20C11×#323C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C25×C11C2×C411yescharacteristic
24C24×D11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C22×C22⋊D11—21no—
28C22×C22⋊D11—21no—
29C22×C22⋊D11—44no—
30C22×C22⋊D11—41no—
31C22×C22⋊D11—41no—
32C23×Dic11C2×C411yescharacteristic
33C22×C8×C11—41no—
34C2×C11×C22⋊C4—41no—
35C2×C11×C22⋊C4—41no—
36C2×C11×C22⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C11×C22⋊C4C2311yescharacteristic
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11C2×C411yescharacteristic
43C2×C22⋊Dic11C2×C411yescharacteristic
44#66982—44no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×#4318—41no—
52C11×C22⋊C8—22no—
53C11×C22⋊C8—41no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58#11541—111nomaximal, Sylow
59C24×C11—21no—
60C24×C11—21no—
61C24×C11—22no—
62C24×C11—41no—
63C24×C11—42no—
64C24×C11—81no—
65C24×C11C22⋊C411yescharacteristic
66C24×C11C22⋊C411yescharacteristic
67C24×C11C22×C411yescharacteristic
68C23×D11—21no—
69C23×D11—22no—
70C23×D11—42no—
71C23×D11—41no—
72C23×D11—41no—
73C23×D11—81no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—42no—
79C22×C4×C11—81no—
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C2×C22⋊D11—24no—
85C2×C22⋊D11—42no—
86C2×C22⋊D11—42no—
87C2×C22⋊D11—42no—
88C2×C22⋊D11—42no—
89C2×C22⋊D11—44no—
90C2×C22⋊D11—44no—
91C2×C22⋊D11—44no—
92C2×C22⋊D11—44no—
93C2×C22⋊D11—41no—
94C2×C22⋊D11—41no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—41no—
99C22×Dic11—42no—
100C2×C8×C11—42no—
101C2×C8×C11—82no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C22⋊Dic11—22no—
107C22⋊Dic11—41no—
108C22⋊Dic11—42no—
109C22⋊Dic11—81no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—81no—
113(C2×D11)⋊C4—81no—
114Dic11⋊C4—42no—
115Dic11⋊C4—42no—
116#4318—82no—
117C2×C11⋊C8—42no—
118#2405—111no—
119#1462—111no—
120C2×#323D1111yescharacteristic, complemented
121#1326—112no—
122#1316—112no—
123C23×C11—22no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—41no—
132C23×C11—42no—
133C23×C11—42no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—42no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—42no—
140C23×C11—81no—
141C23×C11—81no—
142C23×C11—84no—
143C23×C11—84no—
144C23×C11#9911yescharacteristic
145C23×C11#9911yescharacteristic
146C23×C11C2×C22⋊C411yescharacteristic
147C23×C11#13112yes—
148C22×D11—22no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—41no—
152C22×D11—42no—
153C22×D11—41no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—42no—
157C22×D11—84no—
158C22×D11—84no—
159C22×D11—82no—
160C22×D11—82no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C22⋊D11—44no—
174C22⋊D11—48no—
175C22⋊D11—44no—
176C2×Dic11—22no—
177C2×Dic11—41no—
178C2×Dic11—42no—
179C2×Dic11—41no—
180C2×Dic11—42no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C8×C11—82no—
188C11⋊C8—82no—
189C23×D4—111no—
190C2×#123—221no—
191C22×C22⋊C4C2×D1111yescharacteristic
192#407—221no—
193C2×C22⋊C8—21no—
194#394—221no—
195#394—221no—
196#386—221no—
197#385—111no—
198#385—111no—
199#379—111no—
200#379—111no—
201#379—111no—
202#323—21no—
203#323—112no—
204#323—221no—
205#323C2×D1112yes—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—22no—
213C22×C11—21no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—84no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11—84no—
227C22×C11AΣL(1,𝔽16)12yes—
228C22×C11#40811yescharacteristic
229C22×C11C2×#9911yescharacteristic
230C22×C11#41311yescharacteristic
231C2×D11—42no—
232C2×D11—42no—
233C2×D11—42no—
234C2×D11—81no—
235C2×D11—81no—
236C2×D11—84no—
237C2×D11—81no—
238C2×D11—81no—
239C2×D11—84no—
240C4×C11—41no—
241C4×C11—41no—
242C4×C11—41no—
243C4×C11—41no—
244Dic11—42no—
245Dic11—81no—
246Dic11—81no—
247C25—111no—
248C25C4×D1111yescharacteristic
249C22×D4—221no—
250C22×D4—221no—
251C22×D4—444no—
252C22×D4—441no—
253C22×D4—441no—
254C23×C4—111no—
255C23×C4D4411yescharacteristic
256C23×C4C22⋊D1111yescharacteristic
257C2×M16—441no—
258C22×C8—41no—
259#123—444no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C22⋊C4—41no—
263C2×C22⋊C4—41no—
264C2×C22⋊C4—111no—
265C2×C22⋊C4—111no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—221no—
271C2×C22⋊C4—221no—
272C2×C22⋊C4C4×D1111yescharacteristic
273C2×C22⋊C4D4411yescharacteristic
274C2×C22⋊C4C22⋊D1111yescharacteristic
275C2×C22⋊C4C22×D1111yescharacteristic
276C22⋊C8—22no—
277C22⋊C8—41no—
278C22⋊C8—222no—
279C22⋊C8—441no—
280#95—221no—
281#95—221no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—22no—
285C2×C11—42no—
286C2×C11—41no—
287C2×C11—81no—
288C2×C11#146811yescharacteristic
289C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
290C2×C11#212111yescharacteristic
291D11—82no—
292C24—21no—
293C24—21no—
294C24—22no—
295C24—41no—
296C24—42no—
297C24—81no—
298C24—221no—
299C24—222no—
300C24—441no—
301C24—441no—
302C24—442no—
303C24—881no—
304C24(C2×D11)⋊C411yescharacteristic
305C24(C2×D11)⋊C411yescharacteristic
306C24C2×C4×D1111yescharacteristic
307C2×D4—224no—
308C2×D4—442no—
309C2×D4—442no—
310C2×D4—442no—
311C2×D4—442no—
312C2×D4—444no—
313C2×D4—444no—
314C2×D4—444no—
315C2×D4—441no—
316C2×D4—441no—
317C2×D4—444no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—42no—
323C22×C4—81no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—221no—
327C22×C4—442no—
328C22×C4—441no—
329C22×C4(C2×D11)⋊C411yescharacteristic
330C22×C4(C2×D11)⋊C411yescharacteristic
331C22×C4C2×D4411yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333M16—882no—
334C2×C8—42no—
335C2×C8—82no—
336C2×C8—442no—
337C4⋊C4—442no—
338C4⋊C4—442no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—222no—
344C22⋊C4—442no—
345C22⋊C4—442no—
346C22⋊C4—442no—
347C22⋊C4—441no—
348C22⋊C4—881no—
349C22⋊C4—881no—
350C22⋊C4—881no—
351C11#1154111yescharacteristic, complemented, Sylow
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—22no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—41no—
361C23—42no—
362C23—42no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23—81no—
370C23—81no—
371C23—84no—
372C23—84no—
373C23—222no—
374C23—441no—
375C23—441no—
376C23—441no—
377C23—442no—
378C23—442no—
379C23—441no—
380C23—441no—
381C23—441no—
382C23—882no—
383C23—884no—
384C23—884no—
385C23—882no—
386C23#6687011yescharacteristic
387C23#6687011yescharacteristic
388C23#6695412yes—
389C23C2×(C2×D11)⋊C411yescharacteristic
390D4—444no—
391D4—448no—
392D4—444no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—222no—
406C2×C4—441no—
407C2×C4—442no—
408C2×C4—441no—
409C2×C4—442no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—441no—
416C8—82no—
417C8—882no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—22no—
425C22—21no—
426C22—42no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—84no—
436C22—81no—
437C22—81no—
438C22—84no—
439C22—442no—
440C22—442no—
441C22—442no—
442C22—881no—
443C22—881no—
444C22—884no—
445C22—884no—
446C22—881no—
447C22—881no—
448C22#1062210912yes—
449C22C2×#6687011yescharacteristic
450C22#1062272311yescharacteristic
451C22#1062274511yescharacteristic
452C4—41no—
453C4—41no—
454C4—41no—
455C4—41no—
456C4—442no—
457C4—881no—
458C4—881no—
459C2—21no—
460C2—21no—
461C2—22no—
462C2—41no—
463C2—42no—
464C2—81no—
465C2—882no—
466C2#1306696211yescharacteristic
467C2C2×#1062210911yescharacteristic
468C2#1307026311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC2×C11×#323C2
socleC22×C11C2×#99
prime radicalC23×C22⋊D11C4
cosocleC2×C11×C22⋊C4C23
hypercenterC2×#323D11
hypocenterC11#11541
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. #13066943C2semidirect
3. #13066563C2semidirect
4. #13066543C2semidirect
5. C2×C11×#323C2semidirect
120. C2×#323D11semidirect
351. C11#11541semidirect

Maximal subgroups

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

subgroupindex
#130719432
#130669432
#130665632
#130665432
C2×C11×#3232
#1154111