Finite Group Databasebeta

← #14671297

Subgroups — #14671297

Order 2816.

782 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 782 conjugacy classes of subgroups — too many to draw. Only its 107 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#13072231C211yesmaximal, characteristic
2C2×#10622112C212yesmaximal, complemented
3#13068534C211yesmaximal, characteristic, complemented
4#13066740C212yesmaximal, complemented
5C2×C11×#410C211yesmaximal, characteristic, complemented
6C22×C11×#41C2211yescharacteristic
7C2×C11×#117—21no—
8C2×#67000C411yescharacteristic, complemented
9C2×#66993C2211yescharacteristic
10C2×#66983C411yescharacteristic, complemented
11C11×#410—24no—
12C2×C11×#99—21no—
13C2×C11×#99C2212yes—
14#10622843C411yescharacteristic, complemented
15#10622836—21no—
16#10622836—21no—
17#10622834C2211yescharacteristic
18C2×#66898—21no—
19C2×#66898C2212yes—
20#10622826—21no—
21#10622826—21no—
22#10622824—21no—
23C4×C22⋊Dic11C411yescharacteristic, complemented
24#10622112—24no—
25C2×C11×#41—22no—
26C2×C11×#41—22no—
27C2×C11×#41—41no—
28C2×C11×#41—41no—
29C2×C11×#41—42no—
30C22×Q8×C11C2×C411yescharacteristic
31C22×D4×C11D411yescharacteristic
32C22×D4×C11D411yescharacteristic
33C22×D4×C11C2311yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C22×C22⋊D11—21no—
38C22×C22⋊D11—21no—
39C22×C22⋊D11—21no—
40C22×D44C2×C411yescharacteristic
41C11×#117—24no—
42C11×#117—42no—
43C2×C11×C4⋊C4—41no—
44C2×C11×C22⋊C4—22no—
45C2×C42×C11—41no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—22no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—21no—
50#67000—42no—
51#66993—22no—
52#66993—22no—
53#66983—41no—
54#66983—41no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×C4⋊Dic11C2×C411yescharacteristic
59C2×C4×Dic11C2×C411yescharacteristic
60C2×C4×Dic11C2×C411yescharacteristic
61C11×#99—24no—
62C11×#99—22no—
63C11×#99D414yescomplemented
64#66898—22no—
65#66898—22no—
66#66898—42no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—41no—
71C11⋊#95—41no—
72#13089—111nomaximal, Sylow
73C24×C11C22⋊C411yescharacteristic
74C24×C11C2×D411yescharacteristic
75C24×C11C2×D411yescharacteristic
76C23×D11—21no—
77C11×#41—44no—
78C11×#41—44no—
79C11×#41—44no—
80C11×#41—44no—
81C2×Q8×C11—22no—
82C2×Q8×C11—22no—
83C2×Q8×C11—41no—
84C2×D4×C11—21no—
85C2×D4×C11—22no—
86C2×D4×C11—21no—
87C2×D4×C11—22no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11C2×D412yes—
94C2×D4×C11#4112yes—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—42no—
109C22×C4×C11C22⋊C411yescharacteristic
110C22×C4×C11C22⋊C411yescharacteristic
111C22×C4×C11C22⋊C411yescharacteristic
112C22×C4×C11C22×C411yescharacteristic
113C2×C22⋊D11—42no—
114C2×C22⋊D11—42no—
115C2×C22⋊D11—42no—
116C2×C22⋊D11—41no—
117C2×C22⋊D11—42no—
118C2×C22⋊D11—41no—
119C2×C22⋊D11—81no—
120C2×C22⋊D11—81no—
121C2×C22⋊D11—81no—
122C2×C22⋊D11—81no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—42no—
127C2×D44—22no—
128C2×D44—41no—
129C2×D44—41no—
130C11×C4⋊C4—44no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—42no—
133C42×C11—44no—
134C22⋊Dic11—42no—
135C22⋊Dic11—42no—
136C22⋊Dic11—42no—
137C22⋊Dic11—81no—
138C22⋊Dic11—81no—
139(C2×D11)⋊C4—42no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—42no—
143C4⋊Dic11—41no—
144C4×Dic11—22no—
145C4×Dic11—41no—
146C2×#410D1111yescharacteristic, complemented
147#2431—111no—
148C2×#353—112no—
149#1782—111no—
150#1393—112no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—21no—
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—41no—
163C23×C11—41no—
164C23×C11C2×C22⋊C411yescharacteristic
165C23×C11#12011yescharacteristic
166C23×C11#12112yes—
167C23×C11#12311yescharacteristic
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175Q8×C11—44no—
176D4×C11—42no—
177D4×C11—42no—
178D4×C11—44no—
179D4×C11—42no—
180D4×C11—42no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—44no—
199C2×C4×C11—82no—
200C2×C4×C11—82no—
201C2×C4×C11#9911yescharacteristic
202C2×C4×C11#9911yescharacteristic
203C2×C4×C11#9912yes—
204C2×C4×C11C4×D412yes—
205C22⋊D11—82no—
206C22⋊D11—84no—
207C22⋊D11—82no—
208C22⋊D11—84no—
209C2×Dic11—22no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—82no—
219C2×Dic11—82no—
220C2×Dic11—82no—
221D44—82no—
222C22×#41C2×D1111yescharacteristic
223C2×#127—111no—
224C2×#124—111no—
225C2×#121—111no—
226C2×#117—21no—
227#410—24no—
228C2×#99—21no—
229C2×#99—112no—
230C2×#99—221no—
231C2×#99C2×D1112yes—
232#392—221no—
233#392—221no—
234#391—111no—
235#390—111no—
236#386—221no—
237#386—221no—
238#381—221no—
239C4×C22⋊C4—111no—
240#353—224no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—22no—
246C22×C11—41no—
247C22×C11—42no—
248C22×C11—41no—
249C22×C11—41no—
250C22×C11—41no—
251C22×C11—41no—
252C22×C11—41no—
253C22×C11—41no—
254C22×C11—41no—
255C22×C11—41no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11#38611yescharacteristic
261C22×C11C2×#9911yescharacteristic
262C22×C11C2×#9911yescharacteristic
263C2×D11—81no—
264C2×D11—81no—
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C2×D11—81no—
269C2×D11—81no—
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—22no—
273C4×C11—22no—
274C4×C11—41no—
275C4×C11—84no—
276Dic11—42no—
277Dic11—81no—
278Dic11—81no—
279Dic11—162no—
280C2×#41—22no—
281C2×#41—22no—
282C2×#41—41no—
283C2×#41—41no—
284C2×#41—42no—
285C22×Q8C4×D1111yescharacteristic
286C22×D4—111no—
287C22×D4—221no—
288C22×D4—221no—
289C22×D4—221no—
290C22×D4D4411yescharacteristic
291C22×D4C22⋊D1111yescharacteristic
292C22×D4C22×D1111yescharacteristic
293C23×C4C4×D1111yescharacteristic
294C23×C4D4411yescharacteristic
295C23×C4C22⋊D1111yescharacteristic
296#127—222no—
297#127—222no—
298#124—442no—
299#121—441no—
300#121—441no—
301#117—24no—
302#117—42no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—111no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—221no—
307C2×C22⋊C4—221no—
308C2×C22⋊C4—221no—
309C2×C22⋊C4—221no—
310C2×C22⋊C4—222no—
311C2×C22⋊C4—221no—
312C2×C22⋊C4—221no—
313C2×C42—41no—
314C2×C42—111no—
315C2×C42—111no—
316#99—24no—
317#99—22no—
318#99—222no—
319#99—222no—
320#99—442no—
321#99C22⋊D1114yescomplemented
322#95—221no—
323#95—221no—
324#95—221no—
325#95—441no—
326#95—441no—
327C2×C11—21no—
328C2×C11—21no—
329C2×C11—42no—
330C2×C11—41no—
331C2×C11—41no—
332C2×C11—81no—
333C2×C11#189811yescharacteristic
334C2×C11#212611yescharacteristic
335C2×C11#212811yescharacteristic
336D11—161no—
337C24—221no—
338C24(C2×D11)⋊C411yescharacteristic
339C24C2×D4411yescharacteristic
340C24C2×C22⋊D1111yescharacteristic
341#41—44no—
342#41—44no—
343#41—44no—
344#41—44no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—41no—
348C2×D4—21no—
349C2×D4—22no—
350C2×D4—21no—
351C2×D4—22no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—222no—
358C2×D4—441no—
359C2×D4—441no—
360C2×D4—442no—
361C2×D4—442no—
362C2×D4—442no—
363C2×D4—441no—
364C2×D4—442no—
365C2×D4—441no—
366C2×D4—881no—
367C2×D4—881no—
368C2×D4—881no—
369C2×D4—881no—
370C2×D4#433912yes—
371C2×D4C2×C22⋊D1112yes—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—42no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—442no—
390C22×C4(C2×D11)⋊C411yescharacteristic
391C22×C4(C2×D11)⋊C411yescharacteristic
392C22×C4(C2×D11)⋊C411yescharacteristic
393C22×C4C2×C4×D1111yescharacteristic
394C4⋊C4—44no—
395C4⋊C4—441no—
396C22⋊C4—24no—
397C22⋊C4—42no—
398C22⋊C4—442no—
399C22⋊C4—442no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C22⋊C4—442no—
403C22⋊C4—442no—
404C22⋊C4—442no—
405C22⋊C4—881no—
406C22⋊C4—881no—
407C42—44no—
408C42—222no—
409C42—441no—
410C11#1308911yescharacteristic, complemented, Sylow
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—441no—
425C23—441no—
426C23—441no—
427C23—441no—
428C23—441no—
429C23—441no—
430C23—441no—
431C23C2×(C2×D11)⋊C411yescharacteristic
432C23#6698211yescharacteristic
433C23#6698312yes—
434C23#6700611yescharacteristic
435Q8—44no—
436D4—42no—
437D4—42no—
438D4—44no—
439D4—42no—
440D4—42no—
441D4—882no—
442D4—882no—
443D4—884no—
444D4—882no—
445D4—884no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—44no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—222no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—882no—
476C2×C4—882no—
477C2×C4—882no—
478C2×C4#6687012yes—
479C2×C4#6687011yescharacteristic
480C2×C4#6687011yescharacteristic
481C2×C4C4×C22⋊D1112yes—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—22no—
487C22—41no—
488C22—42no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22—881no—
505C22—881no—
506C22—881no—
507C22—881no—
508C22C2×#6687011yescharacteristic
509C22C2×#6687011yescharacteristic
510C22#1062282611yescharacteristic
511C4—21no—
512C4—21no—
513C4—22no—
514C4—22no—
515C4—41no—
516C4—84no—
517C4—442no—
518C4—881no—
519C4—881no—
520C4—1762no—
521C2—21no—
522C2—21no—
523C2—41no—
524C2—42no—
525C2—41no—
526C2—81no—
527C2—1761no—
528C2#1306906911yescharacteristic
529C2#1307027911yescharacteristic
530C2#1307028711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC2×C11×#410C2
socleC22×C11C2×#99
prime radical#13072231C2
cosocleC22×D4×C11C23
hypercenterC2×#410D11
hypocenterC11#13089
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#10622112C2semidirect
3. #13068534C2semidirect
4. #13066740C2semidirect
5. C2×C11×#410C2semidirect
8. C2×#67000C4semidirect
10. C2×#66983C4semidirect
14. #10622843C4semidirect
23. C4×C22⋊Dic11C4semidirect
63. C11×#99D4semidirect
146. C2×#410D11semidirect
321. #99C22⋊D11semidirect
410. C11#13089semidirect

Maximal subgroups

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

subgroupindex
#130722312
C2×#106221122
#130685342
#130667402
C2×C11×#4102
#1308911