Finite Group Databasebeta

← #14658166

Subgroups — #14658166

Order 2816.

532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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#13079374C211yesmaximal, characteristic
2#13069601C211yesmaximal, characteristic, complemented
3#13069452C211yesmaximal, characteristic
4#13069044C211yesmaximal, characteristic
5#13069039C211yesmaximal, characteristic, complemented
6#13066484C211yesmaximal, characteristic, complemented
7C11×#1850C211yesmaximal, characteristic, complemented
8C23×C8×C11C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C2×#66977C2211yescharacteristic
11C2×C11×C4⋊C8—21no—
12C2×C11×C22⋊C8C2211yescharacteristic
13C4×C11×C22⋊C4C2211yescharacteristic
14#10622825C2211yescharacteristic
15#10622825C2211yescharacteristic
16#10622727—21no—
17#10622727—21no—
18C2×#66885—21no—
19C2×#66880—21no—
20C2×#66870—21no—
21C2×#66870—21no—
22#10622351—21no—
23#10622348—21no—
24#10622344—21no—
25#10622334—21no—
26C11×#336—21no—
27#10622189—21no—
28#10622189—21no—
29#10622165—21no—
30#10622165—21no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—21no—
33C22×D44D411yescharacteristic
34C22×Dic22D411yescharacteristic
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C22×C8×C11—42no—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11D411yescharacteristic
41C2×C11×C22⋊C4D411yescharacteristic
42C2×C11×C22⋊C4D411yescharacteristic
43C2×C42×C11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—21no—
47#66983—21no—
48#66983—21no—
49#66983—21no—
50#66983—21no—
51C2×(C2×D11)⋊C4—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11D411yescharacteristic
55C2×C4⋊Dic11D411yescharacteristic
56#66977—21no—
57#66977—21no—
58#66977—21no—
59#66977—21no—
60C2×Dic11⋊C4—21no—
61C2×#4314—21no—
62C2×#4314—21no—
63C11×C4⋊C8—42no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8—21no—
66C11×#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69#66885—21no—
70#66885—21no—
71#66885—42no—
72#66881—21no—
73#66881—21no—
74#66880—21no—
75#66880—21no—
76#66880—42no—
77#66870—42no—
78#66870—42no—
79#10565—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C2×C22⋊D11—41no—
93C2×C22⋊D11—41no—
94C2×C22⋊D11—41no—
95C2×C22⋊D11—41no—
96C2×C22⋊D11—41no—
97C2×C22⋊D11—41no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—41no—
106C2×D44—41no—
107C2×Dic22—21no—
108C2×Dic22—21no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C2×C8×C11—41no—
120C2×C8×C11—41no—
121C2×C8×C11—41no—
122C11×C22⋊C4—21no—
123C11×C22⋊C4—21no—
124C11×C22⋊C4—21no—
125C11×C22⋊C4SD1612yescomplemented
126C42×C11—41no—
127C42×C11—41no—
128C22⋊Dic11—41no—
129C22⋊Dic11—41no—
130C22⋊Dic11—41no—
131C22⋊Dic11—41no—
132C22⋊Dic11—41no—
133C22⋊Dic11—41no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—41no—
141C4⋊Dic11—41no—
142C4⋊Dic11—41no—
143C4⋊Dic11—41no—
144Dic11⋊C4—41no—
145Dic11⋊C4—41no—
146#4314—81no—
147#4314—81no—
148#3187—111no—
149#1996—111no—
150#1964—111no—
151#1893—111no—
152#1892—111no—
153#1850D1111yescharacteristic, complemented
154#1289—111no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11#12111yescharacteristic
158C23×C11#12111yescharacteristic
159C23×C11#12111yescharacteristic
160C23×C11C2×SD1611yescharacteristic
161C23×C11#13511yescharacteristic
162C23×C11AGL(1,ℤ/8)11yescharacteristic
163C23×C11#13711yescharacteristic
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—81no—
168C22×D11—81no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—22no—
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—41no—
183C2×C4×C11—41no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12311yescharacteristic
186C2×C4×C11#12311yescharacteristic
187C2×C4×C11#12411yescharacteristic
188C22⋊D11—81no—
189C22⋊D11—81no—
190C22⋊D11—81no—
191C22⋊D11—81no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—81no—
198C2×Dic11—81no—
199C2×Dic11—81no—
200C2×Dic11—81no—
201C2×Dic11—81no—
202C2×Dic11—81no—
203C2×Dic11—81no—
204C2×Dic11—81no—
205D44—42no—
206D44—41no—
207D44—41no—
208Dic22—42no—
209Dic22—41no—
210Dic22—41no—
211C8×C11—41no—
212C8×C11—42no—
213C8×C11—41no—
214C23×C8C2×D1111yescharacteristic
215C2×C22⋊Q8—111no—
216C2×#121—111no—
217#483—221no—
218#481—221no—
219#465—221no—
220#465—221no—
221#450—221no—
222#448—221no—
223C2×C4⋊C8—21no—
224C2×#103—221no—
225C2×#102—221no—
226C2×#99—221no—
227C2×#99—221no—
228C2×C22⋊C8C2×D1111yescharacteristic
229#380—111no—
230#380—111no—
231C4×C22⋊C4C2×D1111yescharacteristic
232#342—221no—
233#342—221no—
234#340—221no—
235#340—221no—
236#336—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—41no—
246C22×C11—41no—
247C22×C11#39411yescharacteristic
248C22×C11#46011yescharacteristic
249C22×C11#46111yescharacteristic
250C22×C11#46311yescharacteristic
251C22×C11#46411yescharacteristic
252C22×C11#46511yescharacteristic
253C22×C11#46811yescharacteristic
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—161no—
258C2×D11—161no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—42no—
263C4×C11—81no—
264C4×C11B(4,𝔽2)11yescharacteristic
265C4×C11#45811yescharacteristic
266Dic11—81no—
267Dic11—81no—
268Dic11—81no—
269Dic11—161no—
270Dic11—161no—
271C22×Q8—111no—
272C22×D4—111no—
273C22×D4—221no—
274C23×C4C22×D1111yescharacteristic
275C2×SD16—221no—
276C2×SD16—221no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—42no—
281C22×C8C22⋊D1111yescharacteristic
282C22×C8C22⋊D1111yescharacteristic
283C22⋊Q8—221no—
284C22⋊Q8—221no—
285C22⋊Q8—221no—
286C22⋊Q8—221no—
287#121—221no—
288#121—221no—
289#121—221no—
290#121—221no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—221no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4D4411yescharacteristic
301C2×C22⋊C4D4411yescharacteristic
302C2×C42—21no—
303#106—221no—
304#106—221no—
305C4⋊C8—42no—
306#103—221no—
307#103—221no—
308#103—442no—
309#102—221no—
310#102—221no—
311#102—442no—
312#99—442no—
313#99—442no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316#95—21no—
317#95—221no—
318#95—221no—
319C2×C11—21no—
320C2×C11—21no—
321C2×C11—21no—
322C2×C11—21no—
323C2×C11—21no—
324C2×C11—21no—
325C2×C11#204411yescharacteristic
326C2×C11#205311yescharacteristic
327C2×C11#205511yescharacteristic
328D11—161no—
329C24—221no—
330C24C2×D4411yescharacteristic
331C2×Q8—221no—
332C2×Q8—221no—
333C2×Q8—441no—
334C2×Q8—441no—
335C2×D4—221no—
336C2×D4—221no—
337C2×D4—441no—
338C2×D4—441no—
339C2×D4—441no—
340C2×D4—441no—
341C2×D4—441no—
342C2×D4—441no—
343C2×D4—441no—
344C2×D4—441no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—441no—
353C22×C4—441no—
354C22×C4#433911yescharacteristic
355C22×C4D4×D1111yescharacteristic
356C22×C4D4×D1111yescharacteristic
357C22×C4#434311yescharacteristic
358C22×C4#434311yescharacteristic
359C22×C4C2×C22⋊D1111yescharacteristic
360SD16—881no—
361SD16—881no—
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—41no—
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—41no—
371C2×C8—41no—
372C2×C8—41no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C22⋊C4—21no—
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4#431412yescomplemented
395C42—41no—
396C42—41no—
397C11#1056511yescharacteristic, complemented, Sylow
398C23—41no—
399C23—41no—
400C23—441no—
401C23—441no—
402C23—441no—
403C23—881no—
404C23—881no—
405C23#6694811yescharacteristic
406C23#6694811yescharacteristic
407C23C2×#431411yescharacteristic
408C23#6695711yescharacteristic
409C23#6696111yescharacteristic
410C23#6696211yescharacteristic
411C23#6698311yescharacteristic
412Q8—442no—
413Q8—441no—
414Q8—441no—
415D4—442no—
416D4—441no—
417D4—441no—
418D4—881no—
419D4—881no—
420D4—881no—
421D4—881no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—881no—
443C2×C4—881no—
444C2×C4—881no—
445C2×C4—881no—
446C2×C4—881no—
447C2×C4—881no—
448C2×C4—881no—
449C2×C4—881no—
450C2×C4#6694711yescharacteristic
451C2×C4#6694711yescharacteristic
452C2×C4#6699011yescharacteristic
453C2×C4#6700011yescharacteristic
454C8—42no—
455C8—41no—
456C8—41no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—881no—
468C22—881no—
469C22—881no—
470C22—1761no—
471C22—1761no—
472C22#1062245411yescharacteristic
473C22#1062245711yescharacteristic
474C22#1062245811yescharacteristic
475C22#1062246111yescharacteristic
476C22#1062260411yescharacteristic
477C22#1062272711yescharacteristic
478C22#1062274711yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—881no—
485C4—881no—
486C4—881no—
487C4—1761no—
488C4—1761no—
489C4#1062264511yescharacteristic
490C4#1062266611yescharacteristic
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—1761no—
498C2#1306986711yescharacteristic
499C2#1306992211yescharacteristic
500C2#1306993411yescharacteristic
subgroupG/H
centerC22#10622604
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1850C2
socleC22×C11#394
prime radicalC2×#66983C22
hypercenter#1850D11
hypocenterC11#10565
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
2. #13069601C2semidirect
5. #13069039C2semidirect
6. #13066484C2semidirect
7. C11×#1850C2semidirect
125. C11×C22⋊C4SD16semidirect
153. #1850D11semidirect
394. C22⋊C4#4314semidirect
397. C11#10565semidirect

Maximal subgroups

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

subgroupindex
#130793742
#130696012
#130694522
#130690442
#130690392
#130664842
C11×#18502
#1056511