Finite Group Databasebeta

← #14651774

Subgroups — #14651774

Order 2816.

626 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077655C211yesmaximal, characteristic, complemented
2#13073506C211yesmaximal, characteristic
3#13066952C211yesmaximal, characteristic, complemented
4#13066943C211yesmaximal, characteristic, complemented
5#13066523C211yesmaximal, characteristic, complemented
6#13066521C211yesmaximal, characteristic, complemented
7C11×#1462C211yesmaximal, characteristic, complemented
8C22×C11×C22⋊C4C2211yescharacteristic
9C2×#67006C411yescharacteristic
10C2×#66982C411yescharacteristic
11C2×C4×C22⋊D11C2211yescharacteristic
12C11×#407C2211yescharacteristic
13C11×#407C2211yescharacteristic
14#10622860C411yescharacteristic
15#10622825C2211yescharacteristic
16#10622824C411yescharacteristic
17#10622820C2211yescharacteristic
18#10622820C2211yescharacteristic
19#10622741—22no—
20#10622574—21no—
21#10622569—21no—
22#10622561—21no—
23#10622557—21no—
24#10622342—22no—
25#10622339—21no—
26#10622331—21no—
27C11×#323—22no—
28#10622163—22no—
29#10622107—21no—
30#10622106—21no—
31C25×C11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C22×C22⋊D11C2×C411yescharacteristic
36C22×C4×D11D411yescharacteristic
37C2×C11×M16—21no—
38C2×C11×M16—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45#67006—42no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11C2×C411yescharacteristic
50C2×C22⋊Dic11C2×C411yescharacteristic
51C2×C22⋊Dic11C2×C411yescharacteristic
52#66982—42no—
53C4×C22⋊D11—21no—
54C4×C22⋊D11—21no—
55C4×C22⋊D11—21no—
56C4×C22⋊D11—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4D411yescharacteristic
59C2×C4⋊Dic11—21no—
60C2×Dic11⋊C4—21no—
61C2×Dic11⋊C4D411yescharacteristic
62C2×C4×Dic11D411yescharacteristic
63C2×#4318—21no—
64C2×#4318—21no—
65C2×#4313—22no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C11×C22⋊C8D412yescomplemented
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)D412yescomplemented
77(C2×D11)⋊C8—22no—
78Dic11⋊C8—22no—
79C8×Dic11—22no—
80#9516—111nomaximal, Sylow
81C24×C11—21no—
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—42no—
85C24×C11—41no—
86C24×C11—41no—
87C24×C11—81no—
88C24×C11C22×C411yescharacteristic
89C23×D11C22⋊C411yescharacteristic
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—81no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C2×C22⋊D11—22no—
103C2×C22⋊D11—21no—
104C2×C22⋊D11—21no—
105C2×C22⋊D11—41no—
106C2×C22⋊D11—42no—
107C2×C22⋊D11—42no—
108C2×C22⋊D11—81no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11C22⋊C411yescharacteristic
112C22×Dic11C22⋊C411yescharacteristic
113C22×Dic11C22⋊C411yescharacteristic
114C2×C4×D11—21no—
115C2×C4×D11—21no—
116C2×C4×D11—81no—
117C11×M16—81no—
118C11×M16—81no—
119C2×C8×C11—22no—
120C2×C8×C11—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C22⋊Dic11—21no—
126C22⋊Dic11—21no—
127C22⋊Dic11—41no—
128C22⋊Dic11—41no—
129C22⋊Dic11—42no—
130C22⋊Dic11—42no—
131C22⋊Dic11—81no—
132(C2×D11)⋊C4—21no—
133(C2×D11)⋊C4—21no—
134(C2×D11)⋊C4—42no—
135C4⋊Dic11—81no—
136Dic11⋊C4—21no—
137Dic11⋊C4—21no—
138Dic11⋊C4—42no—
139C4×Dic11—21no—
140C4×Dic11—21no—
141#4318—81no—
142#4318—81no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—41no—
145#4313—82no—
146#2975—111no—
147#2534—111no—
148#1465—111no—
149#1462—111no—
150#1462D1111yescharacteristic, complemented
151#1305—111no—
152#1305—111no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—81no—
169C23×C11—81no—
170C23×C11—81no—
171C23×C11—81no—
172C23×C11—84no—
173C23×C11—84no—
174C23×C11C2×C22⋊C411yescharacteristic
175C23×C11C4×D411yescharacteristic
176C23×C11C4×D411yescharacteristic
177C22×D11—21no—
178C22×D11—21no—
179C22×D11—21no—
180C22×D11—41no—
181C22×D11—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—81no—
192C2×C4×C11—81no—
193C2×C4×C11#12011yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12311yescharacteristic
197C22⋊D11—42no—
198C22⋊D11—42no—
199C22⋊D11—84no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11#10012yes—
213C4×D11—42no—
214C4×D11—81no—
215C8×C11—42no—
216C8×C11—81no—
217C11⋊C8—42no—
218C11⋊C8—81no—
219C2×#123—111no—
220C2×#120—111no—
221C2×C4×D4—111no—
222C22×C22⋊C4C2×D1111yescharacteristic
223#436—222no—
224#436—222no—
225#431—221no—
226#407—111no—
227#407—111no—
228#407—221no—
229#407C2×D1111yescharacteristic
230#407C2×D1111yescharacteristic
231#396—221no—
232#394—221no—
233#388—221no—
234#386—221no—
235#381—111no—
236#380—111no—
237#379—111no—
238#324—221no—
239#323—22no—
240#323—221no—
241#323—222no—
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—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11—82no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11—82no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11#38611yescharacteristic
264C22×C11C2×#10011yescharacteristic
265C22×C11#41311yescharacteristic
266C2×D11—42no—
267C2×D11—41no—
268C2×D11—41no—
269C2×D11—41no—
270C2×D11—81no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—81no—
276Dic11—22no—
277Dic11—41no—
278Dic11—41no—
279Dic11—81no—
280Dic11—81no—
281C25C4×D1111yescharacteristic
282C22×D4—111no—
283C22×D4—221no—
284C23×C4—111no—
285C23×C4C4×D1111yescharacteristic
286C23×C4C22×D1111yescharacteristic
287C2×M16—21no—
288C2×M16—21no—
289C2×M16—222no—
290C2×M16—221no—
291C2×M16—221no—
292#123—442no—
293#120—442no—
294C4×D4—221no—
295C4×D4—221no—
296C4×D4—221no—
297C4×D4—221no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4—221no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—111no—
308C2×C22⋊C4—111no—
309C2×C22⋊C4—111no—
310C2×C22⋊C4—111no—
311C2×C22⋊C4—221no—
312C2×C22⋊C4—221no—
313C2×C22⋊C4—221no—
314C2×C22⋊C4—221no—
315C2×C42—111no—
316C4⋊C8—222no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8—112no—
321C22⋊C8—222no—
322C22⋊C8—221no—
323C22⋊C8—221no—
324C22⋊C8—221no—
325C22⋊C8C22⋊D1112yescomplemented
326C4×C8—222no—
327#95—221no—
328#95—221no—
329#95—221no—
330C2×C11—21no—
331C2×C11—21no—
332C2×C11—41no—
333C2×C11—41no—
334C2×C11—82no—
335C2×C11#189111yescharacteristic
336C2×C11#190011yescharacteristic
337C2×C11#191311yescharacteristic
338D11—81no—
339C24—21no—
340C24—21no—
341C24—21no—
342C24—42no—
343C24—41no—
344C24—41no—
345C24—81no—
346C24—111no—
347C24C2×C4×D1111yescharacteristic
348C2×D4—222no—
349C2×D4—221no—
350C2×D4—221no—
351C2×D4—441no—
352C2×D4—442no—
353C2×D4—442no—
354C2×D4—881no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—81no—
361C22×C4—111no—
362C22×C4—111no—
363C22×C4—111no—
364C22×C4—221no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—881no—
369C22×C4#433911yescharacteristic
370C22×C4D4×D1111yescharacteristic
371C22×C4D4×D1111yescharacteristic
372C22×C4D4×D1111yescharacteristic
373C22×C4#434111yescharacteristic
374C22×C4C2×C22⋊D1111yescharacteristic
375M16—81no—
376M16—81no—
377M16—882no—
378M16—881no—
379M16—881no—
380C2×C8—22no—
381C2×C8—41no—
382C2×C8—222no—
383C2×C8—441no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—442no—
387C4⋊C4—881no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—221no—
393C22⋊C4—221no—
394C22⋊C4—221no—
395C22⋊C4—221no—
396C22⋊C4—442no—
397C22⋊C4—442no—
398C22⋊C4—442no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—881no—
402C42—221no—
403C42—221no—
404C11#951611yescharacteristic, complemented, Sylow
405C23—21no—
406C23—21no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—81no—
421C23—81no—
422C23—81no—
423C23—81no—
424C23—84no—
425C23—84no—
426C23—221no—
427C23—221no—
428C23—221no—
429C23—441no—
430C23—441no—
431C23C22⋊C4×D1111yescharacteristic
432C23(C22⋊D11)⋊C411yescharacteristic
433C23C4×C22⋊D1111yescharacteristic
434D4—442no—
435D4—442no—
436D4—884no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—112no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—442no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—881no—
463C2×C4#6693611yescharacteristic
464C2×C4#6693711yescharacteristic
465C2×C4#6699011yescharacteristic
466C2×C4#6699111yescharacteristic
467C8—42no—
468C8—81no—
469C8—442no—
470C8—881no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—81no—
485C22—81no—
486C22—82no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—81no—
491C22—81no—
492C22—442no—
493C22—441no—
494C22—441no—
495C22—441no—
496C22—881no—
497C22D11×#10011yescharacteristic
498C22#1062235811yescharacteristic
499C22#1062256911yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—81no—
505C4—222no—
506C4—441no—
507C4—441no—
508C4—881no—
509C4—881no—
510C2—21no—
511C2—21no—
512C2—41no—
513C2—41no—
514C2—82no—
515C2—881no—
516C2#1306903111yescharacteristic
517C2#1306907611yescharacteristic
518C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1462C2
socleC22×C11#386
prime radicalC2×#67006C4
cosocleC23×C4×C11C23
hypercenter#1462D11
hypocenterC11#9516
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
1. #13077655C2semidirect
3. #13066952C2semidirect
4. #13066943C2semidirect
5. #13066523C2semidirect
6. #13066521C2semidirect
7. C11×#1462C2semidirect
69. C11×C22⋊C8D4semidirect
76. C22⋊(C11⋊C8)D4semidirect
150. #1462D11semidirect
325. C22⋊C8C22⋊D11semidirect
404. C11#9516semidirect

Maximal subgroups

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

subgroupindex
#130776552
#130735062
#130669522
#130669432
#130665232
#130665212
C11×#14622
#951611