Finite Group Databasebeta

← #14649748

Subgroups — #14649748

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#13074501C211yesmaximal, characteristic
3C4×#66870C211yesmaximal, characteristic, complemented
4#13067132C211yesmaximal, characteristic, complemented
5#13066470C211yesmaximal, characteristic, complemented
6#13066469C211yesmaximal, characteristic, complemented
7C11×#1507C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C2×C4×C22⋊D11C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C4×C11×C22⋊C4C2211yescharacteristic
12#10622836—21no—
13#10622836C411yescharacteristic, complemented
14#10622835—21no—
15#10622835C411yescharacteristic, complemented
16#10622824C2211yescharacteristic
17C4×C22⋊Dic11C2211yescharacteristic
18#10622820C2211yescharacteristic
19#10622741—22no—
20#10622605C411yescharacteristic, complemented
21#10622595C411yescharacteristic, complemented
22#10622569—21no—
23C2×#66870—21no—
24#10622557—21no—
25#10622342—22no—
26#10622339—21no—
27#10622331—21no—
28C11×#327—22no—
29#10622175—22no—
30#10622165—21no—
31C22×D4×C11—21no—
32C22×D4×C11C2×C411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C22×C22⋊D11D411yescharacteristic
36C22×C4×D11D411yescharacteristic
37C2×C11×M16—21no—
38C11×#121—21no—
39C11×#121—21no—
40C11×#121—21no—
41C11×#121—21no—
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C42×C11—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—21no—
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11D411yescharacteristic
52C4×C22⋊D11—21no—
53C4×C22⋊D11—21no—
54C4×C22⋊D11—21no—
55C4×C22⋊D11—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4C2×C411yescharacteristic
58C2×Dic11⋊C4—21no—
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⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95C2×C411yescharacteristic
72C11⋊#95C2×C411yescharacteristic
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×C11—21no—
81C24×C11C2×D411yescharacteristic
82C23×D11C22⋊C411yescharacteristic
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—81no—
88C2×D4×C11—81no—
89C2×D4×C11—81no—
90C22×C4×C11—21no—
91C22×C4×C11—41no—
92C22×C4×C11—81no—
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C2×C22⋊D11—22no—
100C2×C22⋊D11—21no—
101C2×C22⋊D11—21no—
102C2×C22⋊D11—41no—
103C2×C22⋊D11—42no—
104C2×C22⋊D11—81no—
105C2×C22⋊D11—81no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—41no—
109C22×Dic11C22⋊C411yescharacteristic
110C22×Dic11C22⋊C411yescharacteristic
111C22×Dic11C22⋊C411yescharacteristic
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—81no—
115C11×M16—81no—
116C2×C8×C11—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C22⋊C4—22no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C42×C11—81no—
124C22⋊Dic11—22no—
125C22⋊Dic11—21no—
126C22⋊Dic11—21no—
127C22⋊Dic11—41no—
128C22⋊Dic11—42no—
129C22⋊Dic11—81no—
130C22⋊Dic11—81no—
131C22⋊Dic11—81no—
132(C2×D11)⋊C4—21no—
133(C2×D11)⋊C4—21no—
134(C2×D11)⋊C4—81no—
135Dic11⋊C4—21no—
136Dic11⋊C4—21no—
137Dic11⋊C4—81no—
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#1507D1111yescharacteristic, complemented
149#1284—111no—
150#1284—111no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11C2×C22⋊C411yescharacteristic
163C23×C11#12111yescharacteristic
164C23×C11#12111yescharacteristic
165C22×D11—21no—
166C22×D11—21no—
167C22×D11—21no—
168C22×D11—41no—
169C22×D11—41no—
170D4×C11—81no—
171D4×C11—81no—
172D4×C11—82no—
173D4×C11—82no—
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—41no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—81no—
185C2×C4×C11—81no—
186C2×C4×C11C4×D411yescharacteristic
187C2×C4×C11C4×D411yescharacteristic
188C2×C4×C11#12011yescharacteristic
189C2×C4×C11#12311yescharacteristic
190C22⋊D11—42no—
191C22⋊D11—42no—
192C22⋊D11—84no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—81no—
207C2×Dic11—81no—
208C2×Dic11#10412yes—
209C4×D11—42no—
210C4×D11—81no—
211C8×C11—42no—
212C11⋊C8—42no—
213C2×#121C2×D1111yescharacteristic
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#381—111no—
231C4×C22⋊C4—111no—
232C4×C22⋊C4C2×D1111yescharacteristic
233#342—221no—
234#327—22no—
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—81no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11—81no—
253C22×C11#38611yescharacteristic
254C22×C11C2×#10411yescharacteristic
255C22×C11#42111yescharacteristic
256C2×D11—42no—
257C2×D11—41no—
258C2×D11—41no—
259C2×D11—41no—
260C2×D11—81no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—82no—
266C4×C11—81no—
267Dic11—22no—
268Dic11—41no—
269Dic11—41no—
270Dic11—81no—
271Dic11—81no—
272Dic11—82no—
273C22×D4—21no—
274C22×D4—111no—
275C22×D4—221no—
276C22×D4C4×D1111yescharacteristic
277C23×C4—111no—
278C23×C4C22×D1111yescharacteristic
279C2×M16—21no—
280C2×M16—222no—
281C2×M16—221no—
282#121—21no—
283#121—21no—
284#121—21no—
285#121—21no—
286C4×D4—221no—
287C4×D4—221no—
288C4×D4—221no—
289C4×D4—221no—
290C2×C4⋊C4—111no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4C4×D1111yescharacteristic
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⋊C8C22⋊D1112yescomplemented
313C4×C8—222no—
314#95—21no—
315#95—111no—
316#95—111no—
317#95—221no—
318#95—221no—
319#95—221no—
320#95—221no—
321C2×C11—21no—
322C2×C11—21no—
323C2×C11—41no—
324C2×C11—41no—
325C2×C11—161no—
326C2×C11#187111yescharacteristic
327C2×C11#191011yescharacteristic
328C2×C11#191311yescharacteristic
329D11—81no—
330C24—21no—
331C24—111no—
332C24D4×D1111yescharacteristic
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—81no—
338C2×D4—81no—
339C2×D4—81no—
340C2×D4—222no—
341C2×D4—221no—
342C2×D4—221no—
343C2×D4—441no—
344C2×D4—442no—
345C2×D4—881no—
346C2×D4—881no—
347C22×C4—21no—
348C22×C4—41no—
349C22×C4—81no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—111no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—441no—
358C22×C4—881no—
359C22×C4C2×C4×D1111yescharacteristic
360C22×C4#433911yescharacteristic
361C22×C4D4×D1111yescharacteristic
362C22×C4D4×D1111yescharacteristic
363C22×C4#434111yescharacteristic
364C22×C4C2×C22⋊D1111yescharacteristic
365M16—81no—
366M16—882no—
367M16—881no—
368C2×C8—22no—
369C2×C8—222no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—881no—
375C22⋊C4—22no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—221no—
380C22⋊C4—221no—
381C22⋊C4—221no—
382C22⋊C4—221no—
383C22⋊C4—222no—
384C22⋊C4—442no—
385C22⋊C4—441no—
386C22⋊C4—881no—
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—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—221no—
407C23—221no—
408C23—221no—
409C23—441no—
410C23—441no—
411C23C22⋊C4×D1111yescharacteristic
412C23#6693711yescharacteristic
413C23#6699111yescharacteristic
414D4—81no—
415D4—81no—
416D4—82no—
417D4—82no—
418D4—442no—
419D4—442no—
420D4—884no—
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—81no—
432C2×C4—81no—
433C2×C4—112no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—442no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—442no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—881no—
449C2×C4—881no—
450C2×C4—881no—
451C2×C4(C22⋊D11)⋊C411yescharacteristic
452C2×C4#6693611yescharacteristic
453C2×C4C4×C22⋊D1111yescharacteristic
454C2×C4#6699011yescharacteristic
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—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—442no—
475C22—441no—
476C22—441no—
477C22—441no—
478C22—881no—
479C22D11×#10411yescharacteristic
480C22#1062243411yescharacteristic
481C22#1062256911yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—82no—
487C4—81no—
488C4—222no—
489C4—441no—
490C4—441no—
491C4—881no—
492C4—881no—
493C4—882no—
494C2—21no—
495C2—21no—
496C2—41no—
497C2—41no—
498C2—161no—
499C2—881no—
500C2#1306891511yescharacteristic
501C2#1306914011yescharacteristic
502C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1507C2
socleC22×C11#386
prime radical#13074501C2
cosocleC23×C4×C11C23
hypercenter#1507D11
hypocenterC11#9186
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
1. #13077655C2semidirect
3. C4×#66870C2semidirect
4. #13067132C2semidirect
5. #13066470C2semidirect
6. #13066469C2semidirect
7. C11×#1507C2semidirect
13. #10622836C4semidirect
15. #10622835C4semidirect
20. #10622605C4semidirect
21. #10622595C4semidirect
65. C11×C22⋊C8D4semidirect
74. C22⋊(C11⋊C8)D4semidirect
148. #1507D11semidirect
312. C22⋊C8C22⋊D11semidirect
394. C11#9186semidirect

Maximal subgroups

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

subgroupindex
#130776552
#130745012
C4×#668702
#130671322
#130664702
#130664692
C11×#15072
#918611