Finite Group Databasebeta

← #14654207

Subgroups — #14654207

Order 2816.

812 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079364C211yesmaximal, characteristic
2C2×#10622840C211yesmaximal, characteristic, complemented
3#13069452C211yesmaximal, characteristic, complemented
4#13068551C211yesmaximal, characteristic, complemented
5#13067184C211yesmaximal, characteristic, complemented
6#13066464C211yesmaximal, characteristic, complemented
7C11×#2436C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic
9C2×C11×#124—21no—
10C2×C11×#121C2211yescharacteristic
11C22×#4325—21no—
12C2×#66983C2211yescharacteristic
13C11×#393—22no—
14C11×#391—21no—
15C11×#386—22no—
16C4×C11×C22⋊C4C2211yescharacteristic
17#10622840—22no—
18#10622840—22no—
19C2×#66899—21no—
20C2×#66899—22no—
21#10622830—21no—
22#10622825C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25#10622651—22no—
26#10622649—21no—
27#10622646—21no—
28#10622580—21no—
29C2×#66870—22no—
30#10622175—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C22×Q8×C11—21no—
35C22×Q8×C11—21no—
36C22×Q8×C11—44no—
37C22×Q8×C11D412yes—
38C22×D4×C11—21no—
39C22×D4×C11D411yescharacteristic
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11—21no—
43C22×D44D411yescharacteristic
44C11×#124—44no—
45C11×#121—21no—
46C11×#121—21no—
47C11×#121—21no—
48C11×#121—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C22⋊C4—24no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4D412yes—
53C2×C42×C11—21no—
54C2×C22⋊Dic11—21no—
55C2×#4325—24no—
56C2×#4325—44no—
57C2×#4323—22no—
58#66983—21no—
59#66983—21no—
60#66983—21no—
61#66983—21no—
62C2×(C2×D11)⋊C4—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11D411yescharacteristic
65C22×C11⋊C8—21no—
66C22×C11⋊C8D412yes—
67C11×#95—24no—
68C11×#95—21no—
69#66899—24no—
70#66899—44no—
71#66896—22no—
72C11⋊#95—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)D412yes—
77#66873—22no—
78#66871—22no—
79#66870—44no—
80#9948—111nomaximal, Sylow
81C24×C11—21no—
82C24×C11C2×D411yescharacteristic
83C23×D11—21no—
84C2×Q8×C11—24no—
85C2×Q8×C11—24no—
86C2×Q8×C11—24no—
87C2×Q8×C11—22no—
88C2×Q8×C11—22no—
89C2×Q8×C11—44no—
90C2×Q8×C11—42no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C2×Q8×C11—44no—
94C2×Q8×C11—44no—
95C2×Q8×C11—41no—
96C2×Q8×C11—41no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—42no—
103C2×D4×C11—42no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—42no—
108C22×C4×C11—44no—
109C22×C4×C11—41no—
110C22×C4×C11—41no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119C2×C22⋊D11—42no—
120C2×C22⋊D11—42no—
121C22×Dic11—21no—
122C22×Dic11—41no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—42no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C22⋊C4—22no—
129C11×C22⋊C4—22no—
130C11×C22⋊C4—48no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C42×C11—42no—
134C22⋊Dic11—42no—
135#4325—48no—
136#4323—82no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—42no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—42no—
145C2×C11⋊C8—42no—
146#3186—111no—
147C2×#448—111no—
148#2436D1111yescharacteristic, complemented
149#1964—111no—
150#1787—111no—
151#1519—111no—
152#1282—111no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11—41no—
158C23×C11—42no—
159C23×C11#12011yescharacteristic
160C23×C11#12111yescharacteristic
161C23×C11#12711yescharacteristic
162C23×C11#13512yes—
163C23×C11AGL(1,ℤ/8)12yes—
164C22×D11—41no—
165C22×D11—42no—
166C22×D11—81no—
167C22×D11—81no—
168Q8×C11—24no—
169Q8×C11—24no—
170Q8×C11—42no—
171Q8×C11—44no—
172Q8×C11—42no—
173Q8×C11—44no—
174D4×C11—42no—
175D4×C11—81no—
176D4×C11—82no—
177D4×C11—81no—
178D4×C11—81no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—24no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—44no—
188C2×C4×C11—44no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C22⋊D11—82no—
200C22⋊D11—81no—
201C22⋊D11—81no—
202C2×Dic11—41no—
203C2×Dic11—42no—
204C2×Dic11—81no—
205C2×Dic11—81no—
206C2×Dic11—81no—
207D44—42no—
208D44—42no—
209C11⋊C8—42no—
210C11⋊C8—42no—
211C23×Q8C2×D1111yescharacteristic
212C22×SD16—221no—
213C2×#124—21no—
214C2×#121—111no—
215C2×#121C2×D1111yescharacteristic
216#480—221no—
217#480—221no—
218#466—222no—
219#448—222no—
220#448—222no—
221#447—221no—
222#447—221no—
223C2×#103—221no—
224C2×#103—222no—
225C2×#99—222no—
226C2×C22⋊C8—111no—
227C2×C22⋊C8—111no—
228#393—22no—
229#391—21no—
230#386—22no—
231#380—111no—
232C4×C22⋊C4C2×D1111yescharacteristic
233#327—222no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—84no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11#39211yescharacteristic
247C22×C11#44912yes—
248C22×C11#46312yes—
249C22×C11#49511yescharacteristic
250C22×C11#49611yescharacteristic
251C2×D11—81no—
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—162no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—44no—
259C4×C11—82no—
260C4×C11—81no—
261C4×C11B(4,𝔽2)12yes—
262Dic11—81no—
263Dic11—161no—
264C22×Q8—21no—
265C22×Q8—21no—
266C22×Q8—21no—
267C22×Q8—21no—
268C22×Q8—21no—
269C22×Q8—44no—
270C22×Q8C22⋊D1112yes—
271C22×D4—21no—
272C22×D4—111no—
273C22×D4—221no—
274C22×D4C22⋊D1111yescharacteristic
275C23×C4—21no—
276C23×C4C22×D1111yescharacteristic
277C2×SD16—224no—
278C2×SD16—444no—
279C2×D8—222no—
280C22×C8—112no—
281C22×C8—221no—
282#124—44no—
283#121—21no—
284#121—21no—
285#121—21no—
286#121—21no—
287#121—221no—
288#121—221no—
289#121—221no—
290#121—221no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4C22⋊D1111yescharacteristic
294C2×C22⋊C4—24no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4C22⋊D1112yes—
299C2×C42—21no—
300#107—222no—
301#103—224no—
302#103—444no—
303#102—222no—
304#102—222no—
305#99—444no—
306C22⋊C8—112no—
307C22⋊C8—221no—
308C22⋊C8—221no—
309C22⋊C8—221no—
310#95—24no—
311#95—21no—
312#95—221no—
313C2×C11—21no—
314C2×C11—22no—
315C2×C11—22no—
316C2×C11—21no—
317C2×C11—161no—
318C2×C11#200911yescharacteristic
319C2×C11#201211yescharacteristic
320C2×C11#202111yescharacteristic
321D11—161no—
322C24—21no—
323C24—221no—
324C24C2×C22⋊D1111yescharacteristic
325C2×Q8—24no—
326C2×Q8—24no—
327C2×Q8—24no—
328C2×Q8—22no—
329C2×Q8—22no—
330C2×Q8—44no—
331C2×Q8—42no—
332C2×Q8—42no—
333C2×Q8—42no—
334C2×Q8—44no—
335C2×Q8—44no—
336C2×Q8—41no—
337C2×Q8—41no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—42no—
344C2×D4—42no—
345C2×D4—221no—
346C2×D4—221no—
347C2×D4—442no—
348C2×D4—441no—
349C2×D4—442no—
350C2×D4—442no—
351C2×D4—441no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—42no—
356C22×C4—44no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—221no—
360C22×C4—441no—
361C22×C4D4×D1111yescharacteristic
362C22×C4D4×D1111yescharacteristic
363C22×C4D4×D1111yescharacteristic
364C22×C4#434111yescharacteristic
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367SD16—448no—
368D8—882no—
369C2×C8—222no—
370C2×C8—222no—
371C2×C8—442no—
372C2×C8—442no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—442no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—48no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—442no—
386C42—42no—
387C11#994811yescharacteristic, complemented, Sylow
388C23—41no—
389C23—41no—
390C23—42no—
391C23—42no—
392C23—41no—
393C23—42no—
394C23—441no—
395C23—442no—
396C23—881no—
397C23—881no—
398C23#6699111yescharacteristic
399C23#6699311yescharacteristic
400C23#6700212yes—
401C23#6700312yes—
402C23#6700611yescharacteristic
403Q8—24no—
404Q8—24no—
405Q8—42no—
406Q8—44no—
407Q8—42no—
408Q8—44no—
409D4—42no—
410D4—81no—
411D4—82no—
412D4—81no—
413D4—81no—
414D4—442no—
415D4—442no—
416D4—882no—
417D4—881no—
418D4—881no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—24no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—441no—
436C2×C4—442no—
437C2×C4—881no—
438C2×C4—881no—
439C2×C4—881no—
440C2×C4#6699011yescharacteristic
441C2×C4#6699011yescharacteristic
442C2×C4#6699211yescharacteristic
443C2×C4#6699211yescharacteristic
444C8—442no—
445C8—442no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—881no—
459C22—881no—
460C22—881no—
461C22—1762no—
462C22#1062267012yes—
463C22#1062267111yescharacteristic
464C22#1062267211yescharacteristic
465C22#1062283611yescharacteristic
466C22#1062285112yes—
467C4—21no—
468C4—21no—
469C4—21no—
470C4—44no—
471C4—82no—
472C4—81no—
473C4—881no—
474C4—1761no—
475C4#1062264512yes—
476C2—22no—
477C2—21no—
478C2—22no—
479C2—21no—
480C2—161no—
481C2—1761no—
482C2#1306967611yescharacteristic
483C2#1306969311yescharacteristic
484C2#1306973911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2436C2
socleC22×C11#392
prime radical#13079364C2
hypercenter#2436D11
hypocenterC11#9948
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2436

Complements

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

NH ≅ G/Ntype
2. C2×#10622840C2semidirect
3. #13069452C2semidirect
4. #13068551C2semidirect
5. #13067184C2semidirect
6. #13066464C2semidirect
7. C11×#2436C2semidirect
148. #2436D11semidirect
387. C11#9948semidirect

Maximal subgroups

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

subgroupindex
#130793642
C2×#106228402
#130694522
#130685512
#130671842
#130664642
C11×#24362
#994811