Finite Group Databasebeta

← #14644118

Subgroups — #14644118

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C211yesmaximal, characteristic
2C2×#10622825C211yesmaximal, characteristic
3#13066521C214yesmaximal, complemented
4C2×C11×#407C211yesmaximal, characteristic
5C24×C4×C11C2211yescharacteristic
6C22×C11×M16C412yescomplemented
7C22×C22⋊Dic11C412yes—
8C22×C4⋊Dic11—21no—
9C22×#4318—21no—
10C11×#407—21no—
11C11×#407—21no—
12C11×#407C412yescomplemented
13C11×#407C2212yes—
14C2×C11×C22⋊C8—21no—
15C2×C11×C22⋊C8—21no—
16#10622825—21no—
17#10622825—21no—
18#10622825C412yes—
19#10622825C2212yes—
20C2×C11⋊#95—21no—
21#10622820—21no—
22#10622820—21no—
23#10622820C412yescomplemented
24#10622820C2212yes—
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
43C23×Dic11—22no—
44C2×C11×M16—22no—
45C2×C11×M16—44no—
46C2×C11×M16C2×C414yescomplemented
47C22×C8×C11—22no—
48C2×C22⋊Dic11—22no—
49C2×C22⋊Dic11—44no—
50C2×C22⋊Dic11C2×C414yes—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—44no—
54C2×#4318—22no—
55C2×#4318—22no—
56C2×#4318—44no—
57C22×C11⋊C8—22no—
58C11×C22⋊C8—22no—
59C11×C22⋊C8—22no—
60C11×C22⋊C8—22no—
61C11×C22⋊C8—22no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C22⋊(C11⋊C8)—22no—
65C22⋊(C11⋊C8)—22no—
66C22⋊(C11⋊C8)—22no—
67C22⋊(C11⋊C8)C2×C414yescomplemented
68#8107—111nomaximal, Sylow
69C24×C11—22no—
70C24×C11—22no—
71C24×C11—42no—
72C24×C11—42no—
73C24×C11C4211yescharacteristic
74C24×C11C4211yescharacteristic
75C24×C11C22⋊C411yescharacteristic
76C24×C11C22⋊C411yescharacteristic
77C24×C11C4⋊C411yescharacteristic
78C24×C11C4⋊C411yescharacteristic
79C24×C11C22×C411yescharacteristic
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—24no—
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×C11—42no—
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×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×C11C4⋊C411yescharacteristic
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×Q811yescharacteristic
122C22×Dic11—24no—
123C22×Dic11—44no—
124C22×Dic11—44no—
125C22×Dic11—44no—
126C11×M16—44no—
127C11×M16—44no—
128C2×C8×C11—24no—
129C2×C8×C11—44no—
130C22⋊Dic11—44no—
131C22⋊Dic11—44no—
132C4⋊Dic11—44no—
133C4⋊Dic11—44no—
134#4318—44no—
135#4318—44no—
136C2×C11⋊C8—24no—
137C2×C11⋊C8—44no—
138C2×#407—111no—
139C2×#407D1111yescharacteristic
140C2×#380—111no—
141#1305—114no—
142C23×C11—22no—
143C23×C11—22no—
144C23×C11—21no—
145C23×C11—21no—
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—21no—
155C23×C11—21no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—48no—
165C23×C11—48no—
166C23×C11#9511yescharacteristic
167C23×C11#9511yescharacteristic
168C23×C11#9511yescharacteristic
169C23×C11#9511yescharacteristic
170C23×C11#10012yes—
171C23×C11#10112yes—
172C23×C11C2×C4211yescharacteristic
173C23×C11C2×C22⋊C411yescharacteristic
174C23×C11C2×C4⋊C411yescharacteristic
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—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
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—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
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
211C2×Dic11—44no—
212C2×Dic11—44no—
213C2×Dic11—44no—
214C2×Dic11—88no—
215C8×C11—44no—
216C11⋊C8—44no—
217C24×C4C2×D1111yescharacteristic
218C22×M16—221no—
219C22×M16Dic1112yescomplemented
220C22×C4⋊C4—221no—
221C22×C22⋊C4—112no—
222#407—21no—
223#407—21no—
224#407—112no—
225#407—112no—
226#407—221no—
227#407—221no—
228#407Dic1112yescomplemented
229#407C2×D1112yes—
230C2×C22⋊C8—21no—
231C2×C22⋊C8—21no—
232C2×C22⋊C8—112no—
233C2×C22⋊C8—221no—
234#380—112no—
235#380—112no—
236#380—221no—
237#380—221no—
238C2×#95—221no—
239C22×C11—24no—
240C22×C11—24no—
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—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—44no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11—44no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11#34212yes—
266C22×C11#34312yes—
267C22×C11#34312yes—
268C22×C11#34412yes—
269C22×C11C2×#9511yescharacteristic
270C22×C11C2×#10011yescharacteristic
271C22×C11C2×#10111yescharacteristic
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11#34212yes—
279C4×C11C2×#9912yes—
280Dic11—84no—
281C25C4×D1111yescharacteristic
282C23×C4—44no—
283C23×C4—222no—
284C23×C4Dic2211yescharacteristic
285C23×C4Dic2211yescharacteristic
286C23×C4C4×D1111yescharacteristic
287C23×C4C4×D1111yescharacteristic
288C23×C4C4×D1111yescharacteristic
289C23×C4D4411yescharacteristic
290C23×C4D4411yescharacteristic
291C23×C4C2×Dic1111yescharacteristic
292C23×C4C2×Dic1111yescharacteristic
293C23×C4C22⋊D1111yescharacteristic
294C23×C4C22⋊D1111yescharacteristic
295C23×C4C22⋊D1111yescharacteristic
296C23×C4C22⋊D1111yescharacteristic
297C23×C4C22×D1111yescharacteristic
298C2×M16—22no—
299C2×M16—44no—
300C2×M16—222no—
301C2×M16—222no—
302C2×M16—444no—
303C2×M16C2×Dic1114yescomplemented
304C22×C8—22no—
305C22×C8—222no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—444no—
309C2×C22⋊C4—114no—
310C2×C22⋊C4—222no—
311C2×C22⋊C4—444no—
312C22⋊C8—22no—
313C22⋊C8—22no—
314C22⋊C8—22no—
315C22⋊C8—22no—
316C22⋊C8—114no—
317C22⋊C8—222no—
318C22⋊C8—222no—
319C22⋊C8—222no—
320#95—222no—
321#95—222no—
322C2×C11—21no—
323C2×C11—22no—
324C2×C11—22no—
325C2×C11—21no—
326C2×C11—22no—
327C2×C11—22no—
328C2×C11—41no—
329C2×C11—41no—
330C2×C11C2×#34211yescharacteristic
331C2×C11C2×#34311yescharacteristic
332C2×C11C2×#34411yescharacteristic
333C24—22no—
334C24—22no—
335C24—42no—
336C24—42no—
337C24C4×Dic1111yescharacteristic
338C24C4×Dic1111yescharacteristic
339C24Dic11⋊C411yescharacteristic
340C24Dic11⋊C411yescharacteristic
341C24(C2×D11)⋊C411yescharacteristic
342C24(C2×D11)⋊C411yescharacteristic
343C24C2×C4×D1111yescharacteristic
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—224no—
359C22×C4—444no—
360C22×C4—444no—
361C22×C4—444no—
362C22×C4C4×Dic1111yescharacteristic
363C22×C4C4×Dic1111yescharacteristic
364C22×C4Dic11⋊C411yescharacteristic
365C22×C4Dic11⋊C411yescharacteristic
366C22×C4Dic11⋊C411yescharacteristic
367C22×C4Dic11⋊C411yescharacteristic
368C22×C4Dic11⋊C411yescharacteristic
369C22×C4Dic11⋊C411yescharacteristic
370C22×C4C4⋊Dic1111yescharacteristic
371C22×C4C4⋊Dic1111yescharacteristic
372C22×C4C4⋊Dic1111yescharacteristic
373C22×C4C4⋊Dic1111yescharacteristic
374C22×C4(C2×D11)⋊C411yescharacteristic
375C22×C4(C2×D11)⋊C411yescharacteristic
376C22×C4(C2×D11)⋊C411yescharacteristic
377C22×C4(C2×D11)⋊C411yescharacteristic
378C22×C4(C2×D11)⋊C411yescharacteristic
379C22×C4(C2×D11)⋊C411yescharacteristic
380C22×C4C22⋊Dic1111yescharacteristic
381C22×C4C22⋊Dic1111yescharacteristic
382C22×C4C22⋊Dic1111yescharacteristic
383C22×C4C22⋊Dic1111yescharacteristic
384C22×C4C2×Dic2211yescharacteristic
385C22×C4C2×C4×D1111yescharacteristic
386C22×C4C2×D4411yescharacteristic
387C22×C4C22×Dic1111yescharacteristic
388C22×C4C2×C22⋊D1111yescharacteristic
389C22×C4C2×C22⋊D1111yescharacteristic
390M16—44no—
391M16—44no—
392M16—444no—
393M16—444no—
394C2×C8—24no—
395C2×C8—44no—
396C2×C8—224no—
397C2×C8—444no—
398C4⋊C4—444no—
399C4⋊C4—444no—
400C22⋊C4—444no—
401C22⋊C4—444no—
402C11#810711yescharacteristic, complemented, Sylow
403C23—21no—
404C23—21no—
405C23—22no—
406C23—22no—
407C23—21no—
408C23—21no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—22no—
414C23—22no—
415C23—22no—
416C23—22no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—48no—
426C23—48no—
427C23#6688712yes—
428C23#6688812yes—
429C23C11⋊#9511yescharacteristic
430C23C11⋊#9511yescharacteristic
431C23C11⋊#9511yescharacteristic
432C23C11⋊#9511yescharacteristic
433C23C2×C4×Dic1111yescharacteristic
434C23C2×Dic11⋊C411yescharacteristic
435C23C2×(C2×D11)⋊C411yescharacteristic
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—444no—
464C2×C4—444no—
465C2×C4—444no—
466C2×C4—888no—
467C2×C4C11⋊#9511yescharacteristic
468C2×C4C11⋊#9511yescharacteristic
469C2×C4C11⋊#9511yescharacteristic
470C2×C4C11⋊#9511yescharacteristic
471C2×C4#6689814yes—
472C2×C4C2×Dic11⋊C411yescharacteristic
473C2×C4C2×C4⋊Dic1111yescharacteristic
474C2×C4C2×(C2×D11)⋊C411yescharacteristic
475C2×C4C2×C22⋊Dic1111yescharacteristic
476C8—44no—
477C8—444no—
478C22—24no—
479C22—24no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—42no—
497C22—42no—
498C22—44no—
499C22—44no—
500C22—44no—
501C22—44no—
502C22—42no—
503C22—42no—
504C22#1062216412yes—
505C22#1062219212yes—
506C22#1062219212yes—
507C22#1062219712yes—
508C22C2×#6688711yescharacteristic
509C22C2×#6688811yescharacteristic
510C22C2×C11⋊#9511yescharacteristic
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—884no—
518C4#1062216412yes—
519C4C2×#6689812yes—
520C2—21no—
521C2—21no—
522C2—22no—
523C2—22no—
524C2—22no—
525C2—22no—
526C2—41no—
527C2—41no—
528C2C2×#1062216411yescharacteristic
529C2C2×#1062219211yescharacteristic
530C2C2×#1062219711yescharacteristic
subgroupG/H
centerC22C2×C11⋊#95
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#407C2
socleC22×C11C2×#95
prime radicalC25×C11C2×C4
cosocleC23×C4×C11C23
hypercenterC2×#407D11
hypocenterC11#8107
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
3. #13066521C2semidirect
6. C22×C11×M16C4semidirect
12. C11×#407C4semidirect
23. #10622820C4semidirect
26. C2×C22⋊(C11⋊C8)C4semidirect
46. C2×C11×M16C2×C4semidirect
67. C22⋊(C11⋊C8)C2×C4semidirect
219. C22×M16Dic11semidirect
228. #407Dic11semidirect
303. C2×M16C2×Dic11semidirect
402. C11#8107semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
C2×#106228252
#130665212
C2×C11×#4072
#810711