Finite Group Databasebeta

← #14643446

Subgroups — #14643446

Order 2816.

1058 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C211yesmaximal, characteristic
2C2×#10622820C211yesmaximal, characteristic
3#13066464C214yesmaximal, complemented
4C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
5C24×C4×C11C2211yescharacteristic
6C22×C11×C22⋊C4C412yes—
7C22×C42×C11—21no—
8C22×#4318—21no—
9C22×#4318C412yescomplemented
10C4×C11×C22⋊C4—21no—
11C4×C11×C22⋊C4—21no—
12C4×C11×C22⋊C4C412yes—
13C4×C11×C22⋊C4C2212yes—
14C2×C11×#95—21no—
15#10622820—21no—
16#10622820—21no—
17#10622820—21no—
18#10622820—21no—
19#10622820—21no—
20#10622820—21no—
21#10622820C412yescomplemented
22#10622820C412yescomplemented
23C2×C22⋊(C11⋊C8)—21no—
24C2×C22⋊(C11⋊C8)C412yescomplemented
25C2×C22⋊(C11⋊C8)C2212yes—
26C2×C22⋊(C11⋊C8)C2212yes—
27C25×C11C2×C411yescharacteristic
28C23×C4×C11—22no—
29C23×C4×C11—44no—
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11Q811yescharacteristic
42C23×C4×C11Q811yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—28no—
46C2×C11×C22⋊C4C2×C414yes—
47C2×C42×C11—22no—
48C2×C42×C11—22no—
49C2×C42×C11—44no—
50C2×#4318—22no—
51C2×#4318—22no—
52C2×#4318—22no—
53C2×#4318—22no—
54C2×#4318—44no—
55C2×#4318—44no—
56C22×C11⋊C8—22no—
57C22×C11⋊C8C2×C414yescomplemented
58C11×#95—22no—
59C11×#95—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)—22no—
67C22⋊(C11⋊C8)C2×C414yescomplemented
68#7929—111nomaximal, Sylow
69C24×C11—24no—
70C24×C11—42no—
71C24×C11—42no—
72C24×C11C4211yescharacteristic
73C24×C11C4211yescharacteristic
74C24×C11C22⋊C411yescharacteristic
75C24×C11C22⋊C411yescharacteristic
76C24×C11C4⋊C411yescharacteristic
77C24×C11C4⋊C411yescharacteristic
78C24×C11C22×C411yescharacteristic
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—28no—
83C22×C4×C11—24no—
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×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—44no—
96C22×C4×C11—44no—
97C22×C4×C11C4211yescharacteristic
98C22×C4×C11C4211yescharacteristic
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×C11C22⋊C411yescharacteristic
106C22×C4×C11C22⋊C411yescharacteristic
107C22×C4×C11C22⋊C411yescharacteristic
108C22×C4×C11C22⋊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×C11C4⋊C411yescharacteristic
116C22×C4×C11C4⋊C411yescharacteristic
117C22×C4×C11C4⋊C411yescharacteristic
118C22×C4×C11C4⋊C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×Q811yescharacteristic
125C11×C22⋊C4—28no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4M1618yescomplemented
128C42×C11—44no—
129C42×C11—44no—
130#4318—44no—
131#4318—44no—
132#4318—44no—
133#4318—44no—
134C2×C11⋊C8—24no—
135C2×C11⋊C8—24no—
136C2×C11⋊C8—44no—
137C2×C11⋊C8—44no—
138C2×#407—111no—
139C2×#407—111no—
140C2×C4×C22⋊C4D1111yescharacteristic
141#1282—114no—
142C23×C11—22no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11—22no—
153C23×C11—22no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—416no—
163C23×C11#9511yescharacteristic
164C23×C11#9511yescharacteristic
165C23×C11#9511yescharacteristic
166C23×C11#9511yescharacteristic
167C23×C11C2×C4211yescharacteristic
168C23×C11C2×C22⋊C411yescharacteristic
169C23×C11C2×C4⋊C411yescharacteristic
170C23×C11C2×M1614yes—
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—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—28no—
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—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—44no—
200C2×C4×C11—416no—
201C2×C4×C11—44no—
202C2×C4×C11#9511yescharacteristic
203C2×C4×C11#9511yescharacteristic
204C2×C4×C11#9511yescharacteristic
205C2×C4×C11#9511yescharacteristic
206C2×C4×C11#9914yes—
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C2×C22⋊C411yescharacteristic
209C2×C4×C11C2×C4⋊C411yescharacteristic
210C2×C4×C11C2×C4⋊C411yescharacteristic
211C11⋊C8—44no—
212C11⋊C8—44no—
213C24×C4C2×D1111yescharacteristic
214C22×M16—112no—
215C22×M16—221no—
216C22×C22⋊C4Dic1112yes—
217C22×C42—21no—
218#407—112no—
219#407—112no—
220#407—221no—
221#407—221no—
222#407—221no—
223#407—221no—
224#407—221no—
225#407—221no—
226C2×C22⋊C8—112no—
227C2×C22⋊C8—112no—
228C2×C22⋊C8—112no—
229C2×C22⋊C8—221no—
230C4×C22⋊C4—21no—
231C4×C22⋊C4—21no—
232C4×C22⋊C4Dic1112yes—
233C4×C22⋊C4C2×D1112yes—
234C2×#95—21no—
235C22×C11—28no—
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—21no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—44no—
253C22×C11—44no—
254C22×C11—44no—
255C22×C11—44no—
256C22×C11—44no—
257C22×C11—44no—
258C22×C11#34212yes—
259C22×C11#34412yes—
260C22×C11C2×#9511yescharacteristic
261C22×C11C4×M1612yes—
262C22×C11#40712yes—
263C22×C11#42312yes—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—48no—
271C4×C11#34212yes—
272C4×C11C2×#9912yes—
273C25C2×Dic1111yescharacteristic
274C23×C4—22no—
275C23×C4—44no—
276C23×C4Dic2211yescharacteristic
277C23×C4Dic2211yescharacteristic
278C23×C4C4×D1111yescharacteristic
279C23×C4C4×D1111yescharacteristic
280C23×C4C4×D1111yescharacteristic
281C23×C4C4×D1111yescharacteristic
282C23×C4D4411yescharacteristic
283C23×C4D4411yescharacteristic
284C23×C4C2×Dic1111yescharacteristic
285C23×C4C22⋊D1111yescharacteristic
286C23×C4C22⋊D1111yescharacteristic
287C23×C4C22⋊D1111yescharacteristic
288C23×C4C22⋊D1111yescharacteristic
289C23×C4C22×D1111yescharacteristic
290C2×M16—222no—
291C2×M16—222no—
292C2×M16—222no—
293C2×M16—222no—
294C2×M16—444no—
295C2×M16—444no—
296C22×C8—114no—
297C22×C8—222no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—28no—
300C2×C22⋊C4C2×Dic1114yes—
301C2×C42—22no—
302C2×C42—22no—
303C2×C42—44no—
304C22⋊C8—114no—
305C22⋊C8—222no—
306C22⋊C8—222no—
307C22⋊C8—222no—
308C22⋊C8—222no—
309C22⋊C8—222no—
310C22⋊C8—222no—
311C22⋊C8—222no—
312#95—22no—
313#95—22no—
314C2×C11—22no—
315C2×C11—22no—
316C2×C11—22no—
317C2×C11—22no—
318C2×C11—22no—
319C2×C11—41no—
320C2×C11—41no—
321C2×C11#172811yescharacteristic
322C2×C11C2×#34211yescharacteristic
323C2×C11C2×#34411yescharacteristic
324C24—24no—
325C24—42no—
326C24—42no—
327C24C4×Dic1111yescharacteristic
328C24C4×Dic1111yescharacteristic
329C24C4⋊Dic1111yescharacteristic
330C24C4⋊Dic1111yescharacteristic
331C24C22⋊Dic1111yescharacteristic
332C24C22⋊Dic1111yescharacteristic
333C24C22×Dic1111yescharacteristic
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—28no—
338C22×C4—24no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—44no—
351C22×C4—44no—
352C22×C4C4×Dic1111yescharacteristic
353C22×C4C4×Dic1111yescharacteristic
354C22×C4Dic11⋊C411yescharacteristic
355C22×C4Dic11⋊C411yescharacteristic
356C22×C4Dic11⋊C411yescharacteristic
357C22×C4Dic11⋊C411yescharacteristic
358C22×C4Dic11⋊C411yescharacteristic
359C22×C4Dic11⋊C411yescharacteristic
360C22×C4Dic11⋊C411yescharacteristic
361C22×C4Dic11⋊C411yescharacteristic
362C22×C4C4⋊Dic1111yescharacteristic
363C22×C4C4⋊Dic1111yescharacteristic
364C22×C4(C2×D11)⋊C411yescharacteristic
365C22×C4(C2×D11)⋊C411yescharacteristic
366C22×C4(C2×D11)⋊C411yescharacteristic
367C22×C4(C2×D11)⋊C411yescharacteristic
368C22×C4(C2×D11)⋊C411yescharacteristic
369C22×C4(C2×D11)⋊C411yescharacteristic
370C22×C4(C2×D11)⋊C411yescharacteristic
371C22×C4(C2×D11)⋊C411yescharacteristic
372C22×C4C22⋊Dic1111yescharacteristic
373C22×C4C22⋊Dic1111yescharacteristic
374C22×C4C2×Dic2211yescharacteristic
375C22×C4C2×C4×D1111yescharacteristic
376C22×C4C2×C4×D1111yescharacteristic
377C22×C4C2×D4411yescharacteristic
378C22×C4C2×C22⋊D1111yescharacteristic
379C22×C4C2×C22⋊D1111yescharacteristic
380M16—444no—
381M16—444no—
382M16—444no—
383M16—444no—
384C2×C8—224no—
385C2×C8—224no—
386C2×C8—444no—
387C2×C8—444no—
388C22⋊C4—28no—
389C22⋊C4—24no—
390C22⋊C4#431818yescomplemented
391C42—44no—
392C42—44no—
393C11#792911yescharacteristic, complemented, Sylow
394C23—22no—
395C23—22no—
396C23—22no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—416no—
415C23C11⋊#9511yescharacteristic
416C23C11⋊#9511yescharacteristic
417C23C11⋊#9511yescharacteristic
418C23C11⋊#9511yescharacteristic
419C23C2×#431814yes—
420C23C2×C4×Dic1111yescharacteristic
421C23C2×C4⋊Dic1111yescharacteristic
422C23C2×C22⋊Dic1111yescharacteristic
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—28no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—44no—
452C2×C4—416no—
453C2×C4—44no—
454C2×C4#6687014yes—
455C2×C4C11⋊#9511yescharacteristic
456C2×C4C11⋊#9511yescharacteristic
457C2×C4C11⋊#9511yescharacteristic
458C2×C4C11⋊#9511yescharacteristic
459C2×C4C2×Dic11⋊C411yescharacteristic
460C2×C4C2×Dic11⋊C411yescharacteristic
461C2×C4C2×(C2×D11)⋊C411yescharacteristic
462C2×C4C2×(C2×D11)⋊C411yescharacteristic
463C8—444no—
464C8—444no—
465C22—28no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—44no—
483C22—44no—
484C22—44no—
485C22—44no—
486C22—44no—
487C22—44no—
488C22#1062216512yes—
489C22#1062217112yes—
490C22C4×#431812yes—
491C22#1062253712yes—
492C22#1062282012yes—
493C22C2×C11⋊#9511yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—48no—
501C4#1062216512yes—
502C4C2×#6687012yes—
503C2—22no—
504C2—22no—
505C2—22no—
506C2—22no—
507C2—22no—
508C2—41no—
509C2—41no—
510C2#1306831011yescharacteristic
511C2C2×#1062216511yescharacteristic
512C2C2×#1062217111yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D11)⋊C4
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C4×C11×C22⋊C4C2
socleC22×C11C2×#95
prime radicalC25×C11C2×C4
cosocleC23×C4×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#7929
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #13066464C2semidirect
9. C22×#4318C4semidirect
21. #10622820C4semidirect
22. #10622820C4semidirect
24. C2×C22⋊(C11⋊C8)C4semidirect
57. C22×C11⋊C8C2×C4semidirect
67. C22⋊(C11⋊C8)C2×C4semidirect
127. C11×C22⋊C4M16semidirect
390. C22⋊C4#4318semidirect
393. C11#7929semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130664642
C2×C4×C11×C22⋊C42
#792911