Finite Group Databasebeta

← #14647147

Subgroups — #14647147

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622825C211yesmaximal, characteristic
2#13066839C211yesmaximal, characteristic
3#13066496C214yesmaximal, complemented
4C11×#1779C211yesmaximal, characteristic
5C24×C4×C11C2211yescharacteristic
6C22×C22⋊Dic11—21no—
7C22×C22⋊Dic11—21no—
8C22×C4⋊Dic11C411yescharacteristic, complemented
9C22×C4⋊Dic11C411yescharacteristic, complemented
10C2×C11×C22⋊C8—21no—
11C2×C11×C22⋊C8—21no—
12C2×C11×C22⋊C8C2212yes—
13#10622825—21no—
14#10622825—21no—
15#10622825C412yescomplemented
16#10622825C2212yes—
17C2×C11⋊#95—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2212yes—
20C25×C11D411yescharacteristic
21C23×C4×C11—24no—
22C23×C4×C11—42no—
23C23×C4×C11—42no—
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—21no—
31C23×Dic11—21no—
32C23×Dic11—22no—
33C22×C8×C11—22no—
34C2×C22⋊Dic11—24no—
35C2×C22⋊Dic11—22no—
36C2×C22⋊Dic11—22no—
37C2×C22⋊Dic11—42no—
38C2×C22⋊Dic11—42no—
39C2×C22⋊Dic11—42no—
40C2×C22⋊Dic11—42no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—42no—
44C2×C4⋊Dic11—42no—
45C2×C4⋊Dic11C2×C412yes—
46C2×C4⋊Dic11C2×C412yes—
47C11×C22⋊C8—24no—
48C11×C22⋊C8—42no—
49C11×C22⋊C8—42no—
50C11⋊#95—22no—
51C11⋊#95—22no—
52C11⋊#95—24no—
53C11⋊#95—42no—
54#8712—111nomaximal, Sylow
55C24×C11—22no—
56C24×C11—22no—
57C24×C11—22no—
58C24×C11—22no—
59C24×C11—41no—
60C24×C11—41no—
61C24×C11C22⋊C411yescharacteristic
62C24×C11C22⋊C411yescharacteristic
63C24×C11D812yes—
64C24×C11SD1612yes—
65C24×C11C2×D411yescharacteristic
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—416no—
84C22×C4×C11C22⋊C411yescharacteristic
85C22×C4×C11C22⋊C411yescharacteristic
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4114yes—
89C22×Dic11—24no—
90C22×Dic11—22no—
91C22×Dic11—22no—
92C22×Dic11—42no—
93C22×Dic11—42no—
94C22×Dic11—42no—
95C22×Dic11—42no—
96C22×Dic11—42no—
97C22×Dic11—42no—
98C22×Dic11—42no—
99C22×Dic11—42no—
100C22×Dic11—42no—
101C22×Dic11—42no—
102C22×Dic11—42no—
103C22×Dic11—42no—
104C2×C8×C11—42no—
105C2×C8×C11—42no—
106C2×C8×C11—42no—
107C22⋊Dic11—48no—
108C22⋊Dic11—44no—
109C22⋊Dic11—42no—
110C22⋊Dic11—42no—
111C4⋊Dic11—42no—
112C4⋊Dic11—42no—
113C4⋊Dic11—42no—
114C4⋊Dic11—42no—
115C2×#380—111no—
116#1779D1111yescharacteristic
117C22⋊#95—111no—
118#1294—114no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—24no—
128C23×C11—24no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—24no—
136C23×C11—24no—
137C23×C11—42no—
138C23×C11—42no—
139C23×C11—44no—
140C23×C11—44no—
141C23×C11—44no—
142C23×C11—44no—
143C23×C11#9912yes—
144C23×C11#10212yes—
145C23×C11#10212yes—
146C23×C11#10412yes—
147C23×C11C2×C22⋊C411yescharacteristic
148C23×C11#12312yes—
149C23×C11C2×D811yescharacteristic
150C23×C11C2×SD1611yescharacteristic
151C23×C11#13712yes—
152C2×C4×C11—28no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—44no—
163C2×C4×C11—44no—
164C2×C4×C11—44no—
165C2×C4×C11—44no—
166C2×C4×C11—44no—
167C2×C4×C11#9912yes—
168C2×C4×C11#11712yes—
169C2×C4×C11#12312yes—
170C2×Dic11—44no—
171C2×Dic11—44no—
172C2×Dic11—44no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—82no—
180C2×Dic11—82no—
181C2×Dic11—82no—
182C2×Dic11—84no—
183C2×Dic11—84no—
184C2×Dic11—82no—
185C8×C11—82no—
186C24×C4C2×D1111yescharacteristic
187C22×C4⋊C4—111no—
188C22×C4⋊C4—111no—
189C22×C22⋊C4—221no—
190C22×C22⋊C4—221no—
191C2×C22⋊C8—21no—
192C2×C22⋊C8—21no—
193C2×C22⋊C8C2×D1112yes—
194#380—112no—
195#380—112no—
196#380—221no—
197#380—221no—
198C2×#95—112no—
199C2×#95—221no—
200C2×#95—221no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—48no—
219C22×C11—48no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11#32714yes—
225C22×C11#38111yescharacteristic
226C22×C11C2×#9911yescharacteristic
227C22×C11C2×#9911yescharacteristic
228C22×C11C2×#10211yescharacteristic
229C22×C11#41911yescharacteristic
230C22×C11C2×#10411yescharacteristic
231C22×C11#42111yescharacteristic
232C22×C11#48012yes—
233C22×C11#48312yes—
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—41no—
238Dic11—84no—
239Dic11—82no—
240Dic11—82no—
241C25D4411yescharacteristic
242C23×C4—24no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—221no—
246C23×C4—221no—
247C23×C4—222no—
248C23×C4C4×D1111yescharacteristic
249C23×C4C4×D1111yescharacteristic
250C23×C4D4411yescharacteristic
251C23×C4C22⋊D1111yescharacteristic
252C23×C4C22⋊D1111yescharacteristic
253C23×C4C22×D1111yescharacteristic
254C22×C8—22no—
255C2×C4⋊C4—112no—
256C2×C4⋊C4—112no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—442no—
260C2×C4⋊C4—442no—
261C2×C22⋊C4—224no—
262C2×C22⋊C4—222no—
263C2×C22⋊C4—222no—
264C2×C22⋊C4—442no—
265C2×C22⋊C4—442no—
266C2×C22⋊C4—442no—
267C2×C22⋊C4—442no—
268C22⋊C8—24no—
269C22⋊C8—42no—
270C22⋊C8—42no—
271#95—222no—
272#95—222no—
273#95—224no—
274#95—442no—
275C2×C11—22no—
276C2×C11—24no—
277C2×C11—22no—
278C2×C11—42no—
279C2×C11C2×#32711yescharacteristic
280C2×C11#150811yescharacteristic
281C2×C11#151111yescharacteristic
282C2×C11#151911yescharacteristic
283C2×C11#181911yescharacteristic
284C2×C11#182311yescharacteristic
285C2×C11#182611yescharacteristic
286C24—22no—
287C24—22no—
288C24—22no—
289C24—22no—
290C24—41no—
291C24—41no—
292C24#431412yes—
293C24D8812yes—
294C24(C2×D11)⋊C411yescharacteristic
295C24(C2×D11)⋊C411yescharacteristic
296C24C2×D4411yescharacteristic
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—416no—
315C22×C4—224no—
316C22×C4—222no—
317C22×C4—222no—
318C22×C4—442no—
319C22×C4—442no—
320C22×C4—442no—
321C22×C4—442no—
322C22×C4—442no—
323C22×C4—442no—
324C22×C4—442no—
325C22×C4—442no—
326C22×C4—442no—
327C22×C4—442no—
328C22×C4—442no—
329C22×C4—442no—
330C22×C4(C2×D11)⋊C411yescharacteristic
331C22×C4(C2×D11)⋊C411yescharacteristic
332C22×C4C2×C4×D1111yescharacteristic
333C22×C4#434114yes—
334C22×C4C2×C22⋊D1111yescharacteristic
335C2×C8—42no—
336C2×C8—42no—
337C2×C8—42no—
338C4⋊C4—442no—
339C4⋊C4—442no—
340C4⋊C4—442no—
341C4⋊C4—442no—
342C22⋊C4—448no—
343C22⋊C4—444no—
344C22⋊C4—442no—
345C22⋊C4—442no—
346C11#871211yescharacteristic, complemented, Sylow
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—24no—
362C23—24no—
363C23—24no—
364C23—24no—
365C23—42no—
366C23—42no—
367C23—44no—
368C23—44no—
369C23—44no—
370C23—44no—
371C23#6687012yes—
372C23#6688512yes—
373C23#6688512yes—
374C23#6688912yes—
375C23#6693912yes—
376C23C2×#431411yescharacteristic
377C23C2×D8811yescharacteristic
378C23#6696212yes—
379C23C2×(C2×D11)⋊C411yescharacteristic
380C2×C4—28no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—444no—
396C2×C4—444no—
397C2×C4—444no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—882no—
405C2×C4—882no—
406C2×C4—882no—
407C2×C4—884no—
408C2×C4—882no—
409C2×C4—884no—
410C2×C4#6687012yes—
411C2×C4#6693012yes—
412C2×C4#6698812yes—
413C8—82no—
414C22—21no—
415C22—21no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—21no—
427C22—21no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—48no—
432C22—48no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22#1062210814yes—
438C22#1062233412yes—
439C22#1062234912yes—
440C22#1062255611yescharacteristic
441C22C2×#6687011yescharacteristic
442C22C2×#6687011yescharacteristic
443C22C2×#6688511yescharacteristic
444C22#1062273311yescharacteristic
445C22C2×#6688911yescharacteristic
446C22#1062275211yescharacteristic
447C4—22no—
448C4—22no—
449C4—22no—
450C4—41no—
451C4—884no—
452C4—882no—
453C4—882no—
454C2—22no—
455C2—22no—
456C2—24no—
457C2—42no—
458C2C2×#1062210811yescharacteristic
459C2#1306713711yescharacteristic
460C2#1306715011yescharacteristic
461C2#1306718511yescharacteristic
462C2#1306868811yescharacteristic
463C2#1306870311yescharacteristic
464C2#1306871311yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1779C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11D4
cosocleC23×C4×C11C23
hypercenter#1779D11
hypocenterC11#8712
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. #13066496C2semidirect
8. C22×C4⋊Dic11C4semidirect
9. C22×C4⋊Dic11C4semidirect
15. #10622825C4semidirect
346. C11#8712semidirect

Maximal subgroups

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

subgroupindex
C2×#106228252
#130668392
#130664962
C11×#17792
#871211