Finite Group Databasebeta

← #14650258

Subgroups — #14650258

Order 2816.

504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 93 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#13079381C211yesmaximal, characteristic
2#13077670C211yesmaximal, characteristic, complemented
3#13067121C211yesmaximal, characteristic, complemented
4C2×#10622175C211yesmaximal, characteristic, complemented
5#13066503C211yesmaximal, characteristic, complemented
6#13066458C211yesmaximal, characteristic, complemented
7C11×#1471C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9#10623322C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12#10622831C411yescharacteristic, complemented
13#10622830C411yescharacteristic, complemented
14C2×C11⋊#95C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622724—21no—
18C8×C22⋊D11—21no—
19#10622654—21no—
20#10622651—21no—
21#10622650—21no—
22#10622648—21no—
23#10622583C411yescharacteristic, complemented
24#10622581C411yescharacteristic, complemented
25#10622343—21no—
26#10622340—21no—
27(C22⋊D11)⋊C8—21no—
28#10622333—21no—
29C11×#323—21no—
30C11×#323—21no—
31#10622175—21no—
32#10622175—21no—
33#10622108—21no—
34#10622105—21no—
35C22×D4×C11—21no—
36C22×D4×C11C2×C411yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×Dic11—21no—
39C2×#4339D411yescharacteristic
40C2×C11×M16—21no—
41C22×C8×C11—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C11×#121—21no—
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4—21no—
48#67006—21no—
49C2×#4324—21no—
50C2×#4323—21no—
51#66983C2×C411yescharacteristic
52#66983D411yescharacteristic
53#66982—21no—
54C4×C22⋊D11—21no—
55C4×C22⋊D11—21no—
56#66979D411yescharacteristic
57#66977C2×C411yescharacteristic
58#66977D411yescharacteristic
59C22×C11⋊C8—21no—
60C22×C11⋊C8—21no—
61C2×#4313—21no—
62C2×C8×D11—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8D411yescharacteristic
67C11×C22⋊C8D411yescharacteristic
68#66896—21no—
69#66896—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)C2×C411yescharacteristic
75C22⋊(C11⋊C8)C2×C411yescharacteristic
76C22⋊(C11⋊C8)D411yescharacteristic
77C22⋊(C11⋊C8)D411yescharacteristic
78(C2×D11)⋊C8—21no—
79(C2×D11)⋊C8—21no—
80#66879—21no—
81Dic11⋊C8—21no—
82Dic11⋊C8—21no—
83C8×Dic11—21no—
84#66874—21no—
85#66873—21no—
86#66872—21no—
87#66871—21no—
88#9264—111nomaximal, Sylow
89C24×C11—21no—
90C24×C11#4111yescharacteristic
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—81no—
96C2×D4×C11—81no—
97C2×D4×C11—81no—
98C22×C4×C11—21no—
99C22×C4×C11—81no—
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C2×C22⋊D11—21no—
107C2×C22⋊D11—21no—
108C2×C22⋊D11—21no—
109C22×Dic11—22no—
110C22×Dic11—41no—
111C22×Dic11—41no—
112C22×Dic11—81no—
113C22×Dic11—81no—
114#4339—81no—
115C2×D44C22⋊C411yescharacteristic
116C2×C4×D11—21no—
117C2×Dic22C22⋊C411yescharacteristic
118C11×M16—81no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—41no—
122C2×C8×C11—81no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C22⋊Dic11—21no—
128C22⋊Dic11—21no—
129C22⋊Dic11—21no—
130#4324—81no—
131#4323—81no—
132(C2×D11)⋊C4—21no—
133(C2×D11)⋊C4—21no—
134C4⋊Dic11C22⋊C411yescharacteristic
135C4⋊Dic11C22⋊C411yescharacteristic
136Dic11⋊C4—21no—
137Dic11⋊C4—21no—
138C4×Dic11—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—81no—
144C2×C11⋊C8—81no—
145#4313—81no—
146C8×D11—81no—
147#3188—111no—
148#2977—111no—
149#1504—111no—
150C2×#327—111no—
151#1471D1111yescharacteristic, complemented
152#1298—111no—
153#1280—111no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—21no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—81no—
163C23×C11—81no—
164C23×C11C4×D411yescharacteristic
165C23×C11#12111yescharacteristic
166C23×C11#12311yescharacteristic
167C22×D11—21no—
168D4×C11—41no—
169D4×C11—41no—
170D4×C11—81no—
171D4×C11—82no—
172D4×C11—81no—
173D4×C11—81no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—81no—
182C2×C4×C11C2×C22⋊C411yescharacteristic
183C2×C4×C11C4×D411yescharacteristic
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C22⋊D11—41no—
187C22⋊D11—41no—
188C22⋊D11—41no—
189C22⋊D11—41no—
190C22⋊D11—81no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—42no—
195C2×Dic11—81no—
196C2×Dic11—82no—
197C2×Dic11—81no—
198C2×Dic11—82no—
199D44—41no—
200C4×D11—41no—
201C4×D11—41no—
202Dic22—41no—
203C8×C11—41no—
204C8×C11—41no—
205C8×C11—81no—
206C11⋊C8—41no—
207C11⋊C8—41no—
208C11⋊C8—41no—
209C11⋊C8—41no—
210#525—111no—
211C2×#121C2×D1111yescharacteristic
212#484—111no—
213#482—221no—
214#481—111no—
215#466—221no—
216#465—221no—
217#450—111no—
218#449—221no—
219#447—111no—
220#435—221no—
221#435—221no—
222C8×D4—221no—
223C8×D4—221no—
224#433—221no—
225#408—221no—
226#407C2×D1111yescharacteristic
227C2×C22⋊C8—111no—
228C2×C22⋊C8—111no—
229C2×C22⋊C8C2×D1111yescharacteristic
230C2×#95—111no—
231#328—221no—
232#327—221no—
233#327—221no—
234#327—221no—
235#323—21no—
236#323—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—41no—
245C22×C11—41no—
246C22×C11—41no—
247C22×C11—41no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—161no—
252C22×C11—161no—
253C22×C11#38611yescharacteristic
254C22×C11#44311yescharacteristic
255C22×C11#44411yescharacteristic
256C22×C11#47111yescharacteristic
257C22×C11#47211yescharacteristic
258C2×D11—41no—
259C2×D11—41no—
260C2×D11—41no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—81no—
266Dic11—41no—
267Dic11—41no—
268Dic11—41no—
269Dic11—82no—
270C2×#41—111no—
271C22×D4—21no—
272C22×D4C4×D1111yescharacteristic
273C23×C4—221no—
274C23×C4C22×D1111yescharacteristic
275C2×SD16—221no—
276C2×D8—221no—
277C2×M16—21no—
278C2×M16—221no—
279C22×C8—21no—
280C22×C8—221no—
281C22×C8—221no—
282C22×C8—221no—
283#123—221no—
284C22⋊Q8—111no—
285C22⋊Q8—111no—
286#121—21no—
287#121—21no—
288#121—21no—
289#121—21no—
290#121—111no—
291#121—111no—
292#120—221no—
293C4×D4—221no—
294C4×D4—221no—
295#117—111no—
296C2×C4⋊C4C4×D1111yescharacteristic
297C2×C22⋊C4—21no—
298#107—221no—
299#106—221no—
300C4⋊C8—221no—
301C4⋊C8—221no—
302#103—221no—
303#102—221no—
304#102—221no—
305#102—221no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8—111no—
310C22⋊C8—111no—
311C22⋊C8—111no—
312C22⋊C8—111no—
313C22⋊C8—221no—
314C22⋊C8—221no—
315C22⋊C8—221no—
316C22⋊C8—221no—
317C22⋊C8C22⋊D1111yescharacteristic
318C22⋊C8C22⋊D1111yescharacteristic
319#97—221no—
320C4×C8—221no—
321#95—221no—
322#95—221no—
323C2×C11—21no—
324C2×C11—21no—
325C2×C11—21no—
326C2×C11—21no—
327C2×C11—41no—
328C2×C11—161no—
329C2×C11#187611yescharacteristic
330C2×C11#190711yescharacteristic
331C2×C11#191311yescharacteristic
332D11—81no—
333C24—21no—
334C24#433911yescharacteristic
335#41—881no—
336C2×Q8—111no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—81no—
342C2×D4—81no—
343C2×D4—81no—
344C2×D4—111no—
345C2×D4—221no—
346C2×D4—221no—
347C2×D4—221no—
348C22×C4—21no—
349C22×C4—81no—
350C22×C4—221no—
351C22×C4—222no—
352C22×C4—441no—
353C22×C4—441no—
354C22×C4—881no—
355C22×C4—881no—
356C22×C4C2×C4×D1111yescharacteristic
357C22×C4D4×D1111yescharacteristic
358C22×C4D4×D1111yescharacteristic
359C22×C4D4×D1111yescharacteristic
360C22×C4#434111yescharacteristic
361C22×C4C2×C22⋊D1111yescharacteristic
362SD16—881no—
363D8—881no—
364M16—81no—
365M16—881no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—41no—
369C2×C8—81no—
370C2×C8—221no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—881no—
375C2×C8—881no—
376C2×C8—881no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—111no—
380C4⋊C4—111no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—221no—
386C22⋊C4—221no—
387C22⋊C4—221no—
388C22⋊C4—221no—
389C22⋊C4—221no—
390C42—221no—
391C11#926411yescharacteristic, complemented, Sylow
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—81no—
401C23—81no—
402C23—221no—
403C23#6693611yescharacteristic
404C23#6693711yescharacteristic
405C23C4×C22⋊D1111yescharacteristic
406Q8—441no—
407D4—41no—
408D4—41no—
409D4—81no—
410D4—82no—
411D4—81no—
412D4—81no—
413D4—441no—
414D4—441no—
415D4—441no—
416D4—441no—
417D4—441no—
418D4—881no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—81no—
427C2×C4—221no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—442no—
433C2×C4—881no—
434C2×C4—882no—
435C2×C4—881no—
436C2×C4—882no—
437C2×C4C22⋊C4×D1111yescharacteristic
438C2×C4(C22⋊D11)⋊C411yescharacteristic
439C2×C4#6699011yescharacteristic
440C2×C4#6699111yescharacteristic
441C8—41no—
442C8—41no—
443C8—81no—
444C8—441no—
445C8—441no—
446C8—441no—
447C8—441no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—161no—
463C22—161no—
464C22—441no—
465C22—441no—
466C22—441no—
467C22#1062236111yescharacteristic
468C22#1062236211yescharacteristic
469C22#1062256911yescharacteristic
470C22#1062275711yescharacteristic
471C22#1062275811yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—81no—
477C4—441no—
478C4—441no—
479C4—441no—
480C4—882no—
481C2—21no—
482C2—21no—
483C2—21no—
484C2—21no—
485C2—41no—
486C2—161no—
487C2—881no—
488C2#1306894611yescharacteristic
489C2#1306912111yescharacteristic
490C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1471C2
socleC22×C11#386
prime radical#13079381C2
cosocleC23×C4×C11C23
hypercenter#1471D11
hypocenterC11#9264
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1471

Complements

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

NH ≅ G/Ntype
2. #13077670C2semidirect
3. #13067121C2semidirect
4. C2×#10622175C2semidirect
5. #13066503C2semidirect
6. #13066458C2semidirect
7. C11×#1471C2semidirect
12. #10622831C4semidirect
13. #10622830C4semidirect
23. #10622583C4semidirect
24. #10622581C4semidirect
151. #1471D11semidirect
391. C11#9264semidirect

Maximal subgroups

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

subgroupindex
#130793812
#130776702
#130671212
C2×#106221752
#130665032
#130664582
C11×#14712
#926411