Finite Group Databasebeta

← #14643748

Subgroups — #14643748

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C211yesmaximal, characteristic
2C2×#10622820C211yesmaximal, characteristic
3#13066492C214yesmaximal, complemented
4C2×C11×#407C211yesmaximal, characteristic
5C24×C4×C11C2211yescharacteristic
6C22×C11×M16—21no—
7C22×#4318—21no—
8C22×#4318C412yes—
9C11×#407—21no—
10C11×#407—21no—
11C11×#407C412yes—
12C11×#407C2212yes—
13C2×C11×C22⋊C8—21no—
14C2×C11×C22⋊C8C412yes—
15#10622820—21no—
16#10622820—21no—
17#10622820—21no—
18#10622820—21no—
19#10622820—21no—
20#10622820—21no—
21#10622820C412yes—
22#10622820C2212yes—
23C2×C22⋊(C11⋊C8)—21no—
24C2×C22⋊(C11⋊C8)C412yes—
25C2×C22⋊(C11⋊C8)C412yes—
26C2×C22⋊(C11⋊C8)C2212yes—
27C25×C11Q811yescharacteristic
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×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×C11C2311yescharacteristic
43C2×C11×M16—22no—
44C2×C11×M16—22no—
45C2×C11×M16—44no—
46C22×C8×C11—22no—
47C2×#4318—22no—
48C2×#4318—22no—
49C2×#4318—22no—
50C2×#4318—22no—
51C2×#4318—44no—
52C2×#4318—44no—
53C22×C11⋊C8—22no—
54C22×C11⋊C8C2×C414yes—
55C11×C22⋊C8—22no—
56C11×C22⋊C8—22no—
57C11×C22⋊C8—22no—
58C11×C22⋊C8C2×C414yes—
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#8009—111nomaximal, Sylow
68C24×C11—42no—
69C24×C11—42no—
70C24×C11—42no—
71C24×C11C4⋊C411yescharacteristic
72C24×C11C4⋊C411yescharacteristic
73C24×C11C4⋊C411yescharacteristic
74C24×C11C4⋊C411yescharacteristic
75C24×C11C4⋊C411yescharacteristic
76C24×C11C4⋊C411yescharacteristic
77C24×C11C2×Q811yescharacteristic
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—42no—
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×C11C4211yescharacteristic
93C22×C4×C11C4211yescharacteristic
94C22×C4×C11C4211yescharacteristic
95C22×C4×C11C4211yescharacteristic
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×C11C22⋊C411yescharacteristic
106C22×C4×C11C22⋊C411yescharacteristic
107C22×C4×C11C22⋊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×C11C22×C411yescharacteristic
115C22×C4×C11C22×C411yescharacteristic
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C11×M16—44no—
121C11×M16—44no—
122C2×C8×C11—24no—
123C2×C8×C11—44no—
124#4318—44no—
125#4318—44no—
126#4318—44no—
127#4318—44no—
128C2×C11⋊C8—24no—
129C2×C11⋊C8—24no—
130C2×C11⋊C8—44no—
131C2×C11⋊C8—44no—
132C2×#407—111no—
133C2×#407—111no—
134C2×#407D1111yescharacteristic
135#1293—114no—
136C23×C11—22no—
137C23×C11—22no—
138C23×C11—22no—
139C23×C11—22no—
140C23×C11—22no—
141C23×C11—22no—
142C23×C11—22no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—41no—
146C23×C11—41no—
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—416no—
158C23×C11#9511yescharacteristic
159C23×C11#9511yescharacteristic
160C23×C11#9511yescharacteristic
161C23×C11#9511yescharacteristic
162C23×C11C2×C4⋊C411yescharacteristic
163C23×C11C2×C4⋊C411yescharacteristic
164C23×C11C2×C4⋊C411yescharacteristic
165C2×C4×C11—22no—
166C2×C4×C11—22no—
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—41no—
181C2×C4×C11—41no—
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#9511yescharacteristic
193C2×C4×C11#9511yescharacteristic
194C2×C4×C11#9511yescharacteristic
195C2×C4×C11#9511yescharacteristic
196C2×C4×C11#9914yes—
197C2×C4×C11C2×C4211yescharacteristic
198C2×C4×C11C2×C22⋊C411yescharacteristic
199C2×C4×C11C2×C22⋊C411yescharacteristic
200C2×C4×C11C2×C22⋊C411yescharacteristic
201C8×C11—44no—
202C11⋊C8—44no—
203C11⋊C8—44no—
204C24×C4C2×D1111yescharacteristic
205C22×M16—21no—
206C22×M16—112no—
207C22×M16—221no—
208#407—21no—
209#407—21no—
210#407—112no—
211#407—112no—
212#407—221no—
213#407—221no—
214#407—221no—
215#407—221no—
216#407—221no—
217#407—221no—
218#407Dic1112yes—
219#407C2×D1112yes—
220C2×C22⋊C8—21no—
221C2×C22⋊C8—112no—
222C2×C22⋊C8—112no—
223C2×C22⋊C8—112no—
224C2×C22⋊C8—221no—
225C2×C22⋊C8Dic1112yes—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
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—44no—
245C22×C11—44no—
246C22×C11—44no—
247C22×C11—44no—
248C22×C11—44no—
249C22×C11—44no—
250C22×C11—44no—
251C22×C11#33812yes—
252C22×C11#34212yes—
253C22×C11C2×#9511yescharacteristic
254C22×C11#43012yes—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11#34212yes—
262C4×C11C2×#9912yes—
263C25Dic2211yescharacteristic
264C23×C4—44no—
265C23×C4Dic2211yescharacteristic
266C23×C4C4×D1111yescharacteristic
267C23×C4C4×D1111yescharacteristic
268C23×C4C4×D1111yescharacteristic
269C23×C4C4×D1111yescharacteristic
270C23×C4D4411yescharacteristic
271C23×C4D4411yescharacteristic
272C23×C4C2×Dic1111yescharacteristic
273C23×C4C2×Dic1111yescharacteristic
274C23×C4C22⋊D1111yescharacteristic
275C23×C4C22⋊D1111yescharacteristic
276C23×C4C22⋊D1111yescharacteristic
277C23×C4C22⋊D1111yescharacteristic
278C23×C4C22×D1111yescharacteristic
279C2×M16—22no—
280C2×M16—22no—
281C2×M16—44no—
282C2×M16—222no—
283C2×M16—222no—
284C2×M16—222no—
285C2×M16—222no—
286C2×M16—444no—
287C2×M16—444no—
288C22×C8—22no—
289C22×C8—114no—
290C22×C8—222no—
291C22⋊C8—22no—
292C22⋊C8—22no—
293C22⋊C8—22no—
294C22⋊C8—114no—
295C22⋊C8—222no—
296C22⋊C8—222no—
297C22⋊C8—222no—
298C22⋊C8—222no—
299C22⋊C8—222no—
300C22⋊C8—222no—
301C22⋊C8—222no—
302C22⋊C8C2×Dic1114yes—
303C2×C11—22no—
304C2×C11—22no—
305C2×C11—22no—
306C2×C11—41no—
307C2×C11—41no—
308C2×C11—41no—
309C2×C11—41no—
310C2×C11C2×#33811yescharacteristic
311C2×C11#173811yescharacteristic
312C2×C11C2×#34211yescharacteristic
313C24—42no—
314C24—42no—
315C24—42no—
316C24Dic11⋊C411yescharacteristic
317C24Dic11⋊C411yescharacteristic
318C24Dic11⋊C411yescharacteristic
319C24Dic11⋊C411yescharacteristic
320C24C4⋊Dic1111yescharacteristic
321C24C4⋊Dic1111yescharacteristic
322C24C2×Dic2211yescharacteristic
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4C4×Dic1111yescharacteristic
338C22×C4C4×Dic1111yescharacteristic
339C22×C4C4×Dic1111yescharacteristic
340C22×C4C4×Dic1111yescharacteristic
341C22×C4Dic11⋊C411yescharacteristic
342C22×C4Dic11⋊C411yescharacteristic
343C22×C4Dic11⋊C411yescharacteristic
344C22×C4Dic11⋊C411yescharacteristic
345C22×C4C4⋊Dic1111yescharacteristic
346C22×C4C4⋊Dic1111yescharacteristic
347C22×C4(C2×D11)⋊C411yescharacteristic
348C22×C4(C2×D11)⋊C411yescharacteristic
349C22×C4(C2×D11)⋊C411yescharacteristic
350C22×C4(C2×D11)⋊C411yescharacteristic
351C22×C4(C2×D11)⋊C411yescharacteristic
352C22×C4(C2×D11)⋊C411yescharacteristic
353C22×C4(C2×D11)⋊C411yescharacteristic
354C22×C4(C2×D11)⋊C411yescharacteristic
355C22×C4C22⋊Dic1111yescharacteristic
356C22×C4C22⋊Dic1111yescharacteristic
357C22×C4C22⋊Dic1111yescharacteristic
358C22×C4C22⋊Dic1111yescharacteristic
359C22×C4C2×C4×D1111yescharacteristic
360C22×C4C2×C4×D1111yescharacteristic
361C22×C4C2×D4411yescharacteristic
362C22×C4C22×Dic1111yescharacteristic
363C22×C4C2×C22⋊D1111yescharacteristic
364C22×C4C2×C22⋊D1111yescharacteristic
365M16—44no—
366M16—44no—
367M16—444no—
368M16—444no—
369M16—444no—
370M16—444no—
371C2×C8—24no—
372C2×C8—44no—
373C2×C8—224no—
374C2×C8—224no—
375C2×C8—444no—
376C2×C8—444no—
377C11#800911yescharacteristic, complemented, Sylow
378C23—22no—
379C23—22no—
380C23—22no—
381C23—22no—
382C23—22no—
383C23—22no—
384C23—22no—
385C23—22no—
386C23—22no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—416no—
400C23C11⋊#9511yescharacteristic
401C23C11⋊#9511yescharacteristic
402C23C11⋊#9511yescharacteristic
403C23C11⋊#9511yescharacteristic
404C23C2×Dic11⋊C411yescharacteristic
405C23C2×Dic11⋊C411yescharacteristic
406C23C2×C4⋊Dic1111yescharacteristic
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
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—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4#6687014yes—
435C2×C4C11⋊#9511yescharacteristic
436C2×C4C11⋊#9511yescharacteristic
437C2×C4C11⋊#9511yescharacteristic
438C2×C4C11⋊#9511yescharacteristic
439C2×C4C2×C4×Dic1111yescharacteristic
440C2×C4C2×(C2×D11)⋊C411yescharacteristic
441C2×C4C2×(C2×D11)⋊C411yescharacteristic
442C2×C4C2×C22⋊Dic1111yescharacteristic
443C8—44no—
444C8—444no—
445C8—444no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—44no—
465C22—44no—
466C22—44no—
467C22—44no—
468C22—44no—
469C22—44no—
470C22—44no—
471C22#1062216512yes—
472C22C11⋊#33812yes—
473C22#1062273712yes—
474C22C2×C11⋊#9511yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4#1062216512yes—
482C4C2×#6687012yes—
483C2—22no—
484C2—22no—
485C2—22no—
486C2—41no—
487C2—41no—
488C2—41no—
489C2—41no—
490C2C2×C11⋊#33811yescharacteristic
491C2#1306834211yescharacteristic
492C2C2×#1062216511yescharacteristic
subgroupG/H
centerC22C2×C11⋊#95
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#407C2
socleC22×C11C2×#95
prime radicalC25×C11Q8
cosocleC23×C4×C11C23
hypercenterC2×#407D11
hypocenterC11#8009
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
3. #13066492C2semidirect
377. C11#8009semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130664922
C2×C11×#4072
#800911