Finite Group Databasebeta

← #14649750

Subgroups — #14649750

Order 2816.

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

normal subgroups only

This group has 580 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#13074503C211yesmaximal, characteristic
3C4×#66870C211yesmaximal, characteristic, complemented
4#13067133C211yesmaximal, characteristic, complemented
5#13067131C211yesmaximal, characteristic, complemented
6#13066468C211yesmaximal, characteristic, complemented
7C11×#1284C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C2×C4×C22⋊D11C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C11×#381C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13C4×C22⋊Dic11C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622741—22no—
16#10622574—21no—
17#10622573—21no—
18C2×#66870—21no—
19#10622342—22no—
20#10622339—21no—
21#10622331—21no—
22#10622290C411yescharacteristic, complemented
23#10622285C411yescharacteristic, complemented
24#10622284C411yescharacteristic, complemented
25#10622283—21no—
26#10622278—21no—
27#10622272C411yescharacteristic, complemented
28#10622165—21no—
29#10622108—22no—
30#10622089—22no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—21no—
33C22×C22⋊D11D411yescharacteristic
34C22×D44—21no—
35C22×D44C2×C411yescharacteristic
36C22×C4×D11D411yescharacteristic
37C2×C11×M16—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11D411yescharacteristic
43#66983—21no—
44#66983—21no—
45#66983—21no—
46#66983—21no—
47C4×C22⋊D11—21no—
48C4×C22⋊D11—21no—
49C4×C22⋊D11—21no—
50C4×C22⋊D11—21no—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4C2×C411yescharacteristic
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11C2×C411yescharacteristic
59C2×Dic11⋊C4C2×C411yescharacteristic
60C2×C4×Dic11—21no—
61C2×C4×Dic11D411yescharacteristic
62C2×#4318—21no—
63C2×#4313—22no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8D412yescomplemented
66C11×#95—21no—
67C11×#95—21no—
68C11×#95C2×C411yescharacteristic
69C11×#95C2×C411yescharacteristic
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)D412yescomplemented
75(C2×D11)⋊C8—22no—
76Dic11⋊C8—22no—
77C8×Dic11—22no—
78#66870—24no—
79#9186—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11—21no—
82C23×D11C22⋊C411yescharacteristic
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11—81no—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C2×C22⋊D11—22no—
94C2×C22⋊D11—21no—
95C2×C22⋊D11—21no—
96C2×C22⋊D11—41no—
97C2×C22⋊D11—41no—
98C2×C22⋊D11—41no—
99C2×C22⋊D11—81no—
100C2×C22⋊D11—81no—
101C22×Dic11—21no—
102C22×Dic11—41no—
103C22×Dic11C22⋊C411yescharacteristic
104C22×Dic11C22⋊C411yescharacteristic
105C22×Dic11C22⋊C411yescharacteristic
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—42no—
109C2×D44—81no—
110C2×D44—81no—
111C2×D44—81no—
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—81no—
115C11×M16—81no—
116C2×C8×C11—22no—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—81no—
120C42×C11—81no—
121C22⋊Dic11—22no—
122C22⋊Dic11—21no—
123C22⋊Dic11—21no—
124C22⋊Dic11—41no—
125(C2×D11)⋊C4—21no—
126(C2×D11)⋊C4—21no—
127(C2×D11)⋊C4—42no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—81no—
131(C2×D11)⋊C4—81no—
132(C2×D11)⋊C4—81no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135C4⋊Dic11—81no—
136Dic11⋊C4—21no—
137Dic11⋊C4—21no—
138C4×Dic11—21no—
139C4×Dic11—21no—
140C4×Dic11—81no—
141#4318—81no—
142C2×C11⋊C8—22no—
143#4313—82no—
144#2975—111no—
145#2635—111no—
146C4×#99—111no—
147#1507—111no—
148#1507—111no—
149#1284—111no—
150#1284D1111yescharacteristic, complemented
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11C2×C22⋊C411yescharacteristic
156C23×C11#12111yescharacteristic
157C23×C11#12111yescharacteristic
158C22×D11—21no—
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—81no—
184C2×C4×C11—81no—
185C2×C4×C11C4×D411yescharacteristic
186C2×C4×C11C4×D411yescharacteristic
187C2×C4×C11#12011yescharacteristic
188C2×C4×C11#12311yescharacteristic
189C22⋊D11—42no—
190C22⋊D11—42no—
191C22⋊D11—82no—
192C22⋊D11—82no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11—81no—
204C2×Dic11—81no—
205C2×Dic11#10412yes—
206D44—81no—
207D44—81no—
208D44—84no—
209C4×D11—42no—
210C4×D11—81no—
211C8×C11—42no—
212C11⋊C8—42no—
213C2×#121—111no—
214C2×C4×D4—111no—
215#436—222no—
216#436—222no—
217#431—221no—
218C2×#99—221no—
219#407—111no—
220#407—221no—
221#407C2×D1111yescharacteristic
222#400—111no—
223#399—111no—
224#394—111no—
225#394—221no—
226#392—111no—
227#392—221no—
228#388—221no—
229#386—221no—
230#381C2×D1111yescharacteristic
231C4×C22⋊C4—111no—
232C4×C22⋊C4C2×D1111yescharacteristic
233#342—221no—
234#327—222no—
235#327—222no—
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—81no—
245C22×C11—81no—
246C22×C11#38611yescharacteristic
247C22×C11C2×#10411yescharacteristic
248C22×C11#42111yescharacteristic
249C2×D11—42no—
250C2×D11—41no—
251C2×D11—41no—
252C2×D11—41no—
253C2×D11—81no—
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C2×D11—81no—
260C2×D11—81no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—81no—
266C4×C11—81no—
267C4×C11—82no—
268Dic11—22no—
269Dic11—41no—
270Dic11—41no—
271Dic11—82no—
272Dic11—81no—
273C22×D4—111no—
274C22×D4—111no—
275C22×D4—221no—
276C22×D4—221no—
277C23×C4—111no—
278C23×C4C22×D1111yescharacteristic
279C2×M16—21no—
280C2×M16—222no—
281C2×M16—221no—
282#121—221no—
283#121—221no—
284#121—221no—
285#121—221no—
286C4×D4—221no—
287C4×D4—221no—
288C4×D4—221no—
289C4×D4—221no—
290C2×C4⋊C4—111no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—221no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—111no—
296C2×C22⋊C4—111no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4—221no—
303C2×C42—21no—
304C2×C42—111no—
305C2×C42—221no—
306C4⋊C8—222no—
307#99—224no—
308C22⋊C8—21no—
309C22⋊C8—112no—
310C22⋊C8—222no—
311C22⋊C8—221no—
312C22⋊C8D4412yescomplemented
313C4×C8—222no—
314#95—21no—
315#95—21no—
316#95—221no—
317#95—221no—
318#95—221no—
319#95C4×D1111yescharacteristic
320#95C4×D1111yescharacteristic
321C2×C11—21no—
322C2×C11—21no—
323C2×C11—41no—
324C2×C11—41no—
325C2×C11#187111yescharacteristic
326C2×C11#191011yescharacteristic
327C2×C11#191311yescharacteristic
328D11—81no—
329D11—161no—
330C24—111no—
331C24—221no—
332C24D4×D1111yescharacteristic
333C2×D4—222no—
334C2×D4—221no—
335C2×D4—221no—
336C2×D4—221no—
337C2×D4—221no—
338C2×D4—442no—
339C2×D4—441no—
340C2×D4—441no—
341C2×D4—441no—
342C2×D4—881no—
343C2×D4—881no—
344C2×D4—881no—
345C2×D4—881no—
346C2×D4—881no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—41no—
350C22×C4—81no—
351C22×C4—111no—
352C22×C4—111no—
353C22×C4—111no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—441no—
358C22×C4—881no—
359C22×C4C2×C4×D1111yescharacteristic
360C22×C4C2×D4411yescharacteristic
361C22×C4#433911yescharacteristic
362C22×C4D4×D1111yescharacteristic
363C22×C4D4×D1111yescharacteristic
364C22×C4#434311yescharacteristic
365M16—81no—
366M16—882no—
367M16—881no—
368C2×C8—22no—
369C2×C8—222no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—881no—
375C22⋊C4—22no—
376C22⋊C4—41no—
377C22⋊C4—81no—
378C22⋊C4—221no—
379C22⋊C4—221no—
380C22⋊C4—221no—
381C22⋊C4—221no—
382C22⋊C4—222no—
383C22⋊C4—442no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—881no—
388C22⋊C4—881no—
389C22⋊C4—881no—
390C42—81no—
391C42—221no—
392C42—221no—
393C42—881no—
394C11#918611yescharacteristic, complemented, Sylow
395C23—21no—
396C23—21no—
397C23—41no—
398C23—41no—
399C23—221no—
400C23—221no—
401C23—221no—
402C23—441no—
403C23—441no—
404C23—441no—
405C23—441no—
406C23—441no—
407C23—441no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23C22⋊C4×D1111yescharacteristic
412C23#6693711yescharacteristic
413C23#6694811yescharacteristic
414D4—442no—
415D4—442no—
416D4—881no—
417D4—881no—
418D4—884no—
419D4—882no—
420D4—882no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—112no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—442no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—442no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—881no—
449C2×C4—881no—
450C2×C4—881no—
451C2×C4C4×D4411yescharacteristic
452C2×C4#6693511yescharacteristic
453C2×C4#6694611yescharacteristic
454C2×C4#6694711yescharacteristic
455C8—42no—
456C8—442no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—81no—
466C22—81no—
467C22—442no—
468C22—441no—
469C22—441no—
470C22—441no—
471C22—881no—
472C22—881no—
473C22—881no—
474C22—881no—
475C22—881no—
476C22—881no—
477C22—881no—
478C22—881no—
479C22#1062227811yescharacteristic
480C22D11×#10411yescharacteristic
481C22#1062243411yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—81no—
487C4—81no—
488C4—82no—
489C4—222no—
490C4—441no—
491C4—441no—
492C4—882no—
493C4—881no—
494C2—21no—
495C2—21no—
496C2—41no—
497C2—41no—
498C2—881no—
499C2—1761no—
500C2#1306891711yescharacteristic
501C2#1306914211yescharacteristic
502C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1284C2
socleC22×C11#386
prime radical#13074503C2
cosocleC23×C4×C11C23
hypercenter#1284D11
hypocenterC11#9186
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
1. #13077655C2semidirect
3. C4×#66870C2semidirect
4. #13067133C2semidirect
5. #13067131C2semidirect
6. #13066468C2semidirect
7. C11×#1284C2semidirect
22. #10622290C4semidirect
23. #10622285C4semidirect
24. #10622284C4semidirect
27. #10622272C4semidirect
65. C11×C22⋊C8D4semidirect
74. C22⋊(C11⋊C8)D4semidirect
150. #1284D11semidirect
312. C22⋊C8D44semidirect
394. C11#9186semidirect

Maximal subgroups

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

subgroupindex
#130776552
#130745032
C4×#668702
#130671332
#130671312
#130664682
C11×#12842
#918611