Finite Group Databasebeta

← #14644123

Subgroups — #14644123

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C211yesmaximal, characteristic
2C2×#10622820C211yesmaximal, characteristic
3#13066522C214yesmaximal, complemented
4C11×#2280C211yesmaximal, characteristic
5C24×C4×C11C2211yescharacteristic
6C2×C11×#117—21no—
7C22×#4318—21no—
8C22×#4318C412yescomplemented
9C11×#381—21no—
10C11×#380—21no—
11C11×#380C2212yes—
12C11×#379C412yes—
13C4×C11×C22⋊C4—21no—
14C4×C11×C22⋊C4C412yes—
15#10622820—21no—
16#10622820—21no—
17#10622820—21no—
18#10622820—21no—
19#10622820C412yescomplemented
20#10622820C412yescomplemented
21#10622820C2212yes—
22#10622820C2212yes—
23C2×C22⋊(C11⋊C8)—21no—
24C2×C22⋊(C11⋊C8)—21no—
25C2×C22⋊(C11⋊C8)—21no—
26C2×C22⋊(C11⋊C8)C412yescomplemented
27C25×C11C2×C411yescharacteristic
28C23×C4×C11—44no—
29C23×C4×C11C2×C411yescharacteristic
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11Q811yescharacteristic
41C23×C4×C11Q811yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C11×#117—44no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4C2×C414yes—
48C2×C42×C11—22no—
49C2×#4318—22no—
50C2×#4318—22no—
51C2×#4318—22no—
52C2×#4318—44no—
53C2×#4318—44no—
54C2×#4318C2×C414yes—
55C22×C11⋊C8—22no—
56C22×C11⋊C8—22no—
57C11×#95—22no—
58C11×#95—22no—
59C22⋊(C11⋊C8)—22no—
60C22⋊(C11⋊C8)—22no—
61C22⋊(C11⋊C8)—22no—
62C22⋊(C11⋊C8)—22no—
63C22⋊(C11⋊C8)—22no—
64C22⋊(C11⋊C8)—22no—
65C22⋊(C11⋊C8)—22no—
66C22⋊(C11⋊C8)C2×C414yes—
67#8108—111nomaximal, Sylow
68C24×C11—42no—
69C24×C11—42no—
70C24×C11—42no—
71C24×C11C4211yescharacteristic
72C24×C11C4211yescharacteristic
73C24×C11C22⋊C411yescharacteristic
74C24×C11C22⋊C411yescharacteristic
75C24×C11C4⋊C411yescharacteristic
76C24×C11C4⋊C411yescharacteristic
77C24×C11C22×C411yescharacteristic
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—42no—
83C22×C4×C11—42no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11C4211yescharacteristic
94C22×C4×C11C4211yescharacteristic
95C22×C4×C11C22⋊C411yescharacteristic
96C22×C4×C11C22⋊C411yescharacteristic
97C22×C4×C11C22⋊C411yescharacteristic
98C22×C4×C11C22⋊C411yescharacteristic
99C22×C4×C11C22⋊C411yescharacteristic
100C22×C4×C11C22⋊C411yescharacteristic
101C22×C4×C11C22⋊C411yescharacteristic
102C22×C4×C11C22⋊C411yescharacteristic
103C22×C4×C11C22⋊C411yescharacteristic
104C22×C4×C11C22⋊C411yescharacteristic
105C22×C4×C11C4⋊C411yescharacteristic
106C22×C4×C11C4⋊C411yescharacteristic
107C22×C4×C11C4⋊C411yescharacteristic
108C22×C4×C11C4⋊C411yescharacteristic
109C22×C4×C11C4⋊C411yescharacteristic
110C22×C4×C11C4⋊C411yescharacteristic
111C22×C4×C11C4⋊C411yescharacteristic
112C22×C4×C11C4⋊C411yescharacteristic
113C22×C4×C11C4⋊C411yescharacteristic
114C22×C4×C11C4⋊C411yescharacteristic
115C22×C4×C11C22×C411yescharacteristic
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×Q811yescharacteristic
121C11×C4⋊C4—44no—
122C11×C22⋊C4—44no—
123C11×C22⋊C4—44no—
124C11×C22⋊C4—44no—
125C42×C11—44no—
126#4318—44no—
127#4318—44no—
128#4318—44no—
129#4318—44no—
130C2×C11⋊C8—24no—
131C2×C11⋊C8—24no—
132C2×C11⋊C8—44no—
133C2×C11⋊C8—44no—
134C2×#407—111no—
135C2×#407—111no—
136#2280D1111yescharacteristic
137#1305—114no—
138C23×C11—22no—
139C23×C11—22no—
140C23×C11—22no—
141C23×C11—22no—
142C23×C11—22no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—416no—
160C23×C11#9511yescharacteristic
161C23×C11#9511yescharacteristic
162C23×C11#9511yescharacteristic
163C23×C11#9511yescharacteristic
164C23×C11C2×C4211yescharacteristic
165C23×C11C2×C22⋊C411yescharacteristic
166C23×C11C2×C4⋊C411yescharacteristic
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—44no—
195C2×C4×C11—44no—
196C2×C4×C11—44no—
197C2×C4×C11#9511yescharacteristic
198C2×C4×C11#9511yescharacteristic
199C2×C4×C11#9511yescharacteristic
200C2×C4×C11#9511yescharacteristic
201C2×C4×C11#9914yes—
202C2×C4×C11C2×C22⋊C411yescharacteristic
203C2×C4×C11C2×C22⋊C411yescharacteristic
204C2×C4×C11C2×C4⋊C411yescharacteristic
205C2×C4×C11C2×C4⋊C411yescharacteristic
206C11⋊C8—44no—
207C11⋊C8—44no—
208C24×C4C2×D1111yescharacteristic
209C22×M16—112no—
210C22×M16—221no—
211C2×#117—21no—
212#407—112no—
213#407—112no—
214#407—112no—
215#407—112no—
216#407—221no—
217#407—221no—
218#407—221no—
219#407—221no—
220C2×C22⋊C8—112no—
221C2×C22⋊C8—221no—
222C2×C22⋊C8—221no—
223C2×C22⋊C8—221no—
224#381—21no—
225#380—21no—
226#380C2×D1112yes—
227#379Dic1112yes—
228C4×C22⋊C4—21no—
229C4×C22⋊C4Dic1112yes—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—44no—
249C22×C11—44no—
250C22×C11—44no—
251C22×C11—44no—
252C22×C11—44no—
253C22×C11—44no—
254C22×C11—44no—
255C22×C11#34212yes—
256C22×C11#34412yes—
257C22×C11C2×#9511yescharacteristic
258C22×C11#41312yes—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—84no—
266C4×C11#34212yes—
267C4×C11C2×#9912yes—
268C25C2×Dic1111yescharacteristic
269C23×C4—44no—
270C23×C4Dic2211yescharacteristic
271C23×C4Dic2211yescharacteristic
272C23×C4C4×D1111yescharacteristic
273C23×C4C4×D1111yescharacteristic
274C23×C4C4×D1111yescharacteristic
275C23×C4C4×D1111yescharacteristic
276C23×C4D4411yescharacteristic
277C23×C4D4411yescharacteristic
278C23×C4C2×Dic1111yescharacteristic
279C23×C4C22⋊D1111yescharacteristic
280C23×C4C22⋊D1111yescharacteristic
281C23×C4C22⋊D1111yescharacteristic
282C23×C4C22⋊D1111yescharacteristic
283C23×C4C22×D1111yescharacteristic
284C2×M16—114no—
285C2×M16—222no—
286C2×M16—222no—
287C2×M16—222no—
288C2×M16—444no—
289C2×M16—444no—
290C22×C8—222no—
291C22×C8—222no—
292#117—44no—
293C2×C4⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4C2×Dic1114yes—
297C2×C42—22no—
298C22⋊C8—114no—
299C22⋊C8—222no—
300C22⋊C8—222no—
301C22⋊C8—222no—
302C22⋊C8—222no—
303C22⋊C8—222no—
304C22⋊C8—222no—
305C22⋊C8—222no—
306#95—22no—
307#95—22no—
308C2×C11—22no—
309C2×C11—22no—
310C2×C11—22no—
311C2×C11—41no—
312C2×C11—41no—
313C2×C11—41no—
314C2×C11—41no—
315C2×C11C2×#34211yescharacteristic
316C2×C11#174211yescharacteristic
317C2×C11C2×#34411yescharacteristic
318C24—42no—
319C24—42no—
320C24—42no—
321C24C4×Dic1111yescharacteristic
322C24C4×Dic1111yescharacteristic
323C24C4⋊Dic1111yescharacteristic
324C24C4⋊Dic1111yescharacteristic
325C24C22⋊Dic1111yescharacteristic
326C24C22⋊Dic1111yescharacteristic
327C24C22×Dic1111yescharacteristic
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4C4×Dic1111yescharacteristic
344C22×C4C4×Dic1111yescharacteristic
345C22×C4Dic11⋊C411yescharacteristic
346C22×C4Dic11⋊C411yescharacteristic
347C22×C4Dic11⋊C411yescharacteristic
348C22×C4Dic11⋊C411yescharacteristic
349C22×C4Dic11⋊C411yescharacteristic
350C22×C4Dic11⋊C411yescharacteristic
351C22×C4Dic11⋊C411yescharacteristic
352C22×C4Dic11⋊C411yescharacteristic
353C22×C4C4⋊Dic1111yescharacteristic
354C22×C4C4⋊Dic1111yescharacteristic
355C22×C4(C2×D11)⋊C411yescharacteristic
356C22×C4(C2×D11)⋊C411yescharacteristic
357C22×C4(C2×D11)⋊C411yescharacteristic
358C22×C4(C2×D11)⋊C411yescharacteristic
359C22×C4(C2×D11)⋊C411yescharacteristic
360C22×C4(C2×D11)⋊C411yescharacteristic
361C22×C4(C2×D11)⋊C411yescharacteristic
362C22×C4(C2×D11)⋊C411yescharacteristic
363C22×C4C22⋊Dic1111yescharacteristic
364C22×C4C22⋊Dic1111yescharacteristic
365C22×C4C2×Dic2211yescharacteristic
366C22×C4C2×C4×D1111yescharacteristic
367C22×C4C2×C4×D1111yescharacteristic
368C22×C4C2×D4411yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371M16—444no—
372M16—444no—
373M16—444no—
374M16—444no—
375C2×C8—224no—
376C2×C8—224no—
377C2×C8—444no—
378C2×C8—444no—
379C4⋊C4—44no—
380C22⋊C4—44no—
381C22⋊C4—44no—
382C22⋊C4—44no—
383C42—44no—
384C11#810811yescharacteristic, complemented, Sylow
385C23—22no—
386C23—22no—
387C23—22no—
388C23—22no—
389C23—22no—
390C23—22no—
391C23—22no—
392C23—22no—
393C23—22no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—416no—
407C23C11⋊#9511yescharacteristic
408C23C11⋊#9511yescharacteristic
409C23C11⋊#9511yescharacteristic
410C23C11⋊#9511yescharacteristic
411C23C2×C4×Dic1111yescharacteristic
412C23C2×C4⋊Dic1111yescharacteristic
413C23C2×C22⋊Dic1111yescharacteristic
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—44no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4#6687014yes—
445C2×C4C11⋊#9511yescharacteristic
446C2×C4C11⋊#9511yescharacteristic
447C2×C4C11⋊#9511yescharacteristic
448C2×C4C11⋊#9511yescharacteristic
449C2×C4C2×Dic11⋊C411yescharacteristic
450C2×C4C2×Dic11⋊C411yescharacteristic
451C2×C4C2×(C2×D11)⋊C411yescharacteristic
452C2×C4C2×(C2×D11)⋊C411yescharacteristic
453C8—444no—
454C8—444no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—44no—
474C22—44no—
475C22—44no—
476C22—44no—
477C22—44no—
478C22—44no—
479C22—44no—
480C22#1062216512yes—
481C22#1062217112yes—
482C22C2×C11⋊#9511yescharacteristic
483C22#1062285012yes—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—84no—
491C4#1062216512yes—
492C4C2×#6687012yes—
493C2—22no—
494C2—22no—
495C2—22no—
496C2—41no—
497C2—41no—
498C2—41no—
499C2—41no—
500C2C2×#1062216511yescharacteristic
501C2#1306835511yescharacteristic
502C2C2×#1062217111yescharacteristic
subgroupG/H
centerC22C2×C11⋊#95
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#2280C2
socleC22×C11C2×#95
prime radicalC25×C11C2×C4
cosocleC23×C4×C11C23
hypercenter#2280D11
hypocenterC11#8108
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
3. #13066522C2semidirect
8. C22×#4318C4semidirect
19. #10622820C4semidirect
20. #10622820C4semidirect
26. C2×C22⋊(C11⋊C8)C4semidirect
384. C11#8108semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130665222
C11×#22802
#810811