Finite Group Databasebeta

← #14650331

Subgroups — #14650331

Order 2816.

606 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 109 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#13071666C211yesmaximal, characteristic
3#13069601C211yesmaximal, characteristic, complemented
4#13067185C211yesmaximal, characteristic
5C2×#10622105C211yesmaximal, characteristic, complemented
6#13066496C211yesmaximal, characteristic, complemented
7C11×#1282C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C2×(C22⋊D11)⋊C4—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C4×C11×C22⋊C4C2211yescharacteristic
14#10622825C2211yescharacteristic
15C2×C11⋊#95C2211yescharacteristic
16#10622727—22no—
17#10622571—21no—
18#10622553—21no—
19C4×(C2×D11)⋊C4—21no—
20#10622351C412yescomplemented
21#10622348C412yescomplemented
22#10622344—21no—
23#10622334—21no—
24#10622278—21no—
25#10622266—21no—
26#10622165—21no—
27#10622165—21no—
28#10622108—22no—
29#10622105—21no—
30#10622105—21no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—21no—
33C23×Dic11—21no—
34C22×D44D411yescharacteristic
35C22×C4×D11—21no—
36C22×Dic22C2×C411yescharacteristic, complemented
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C11×C22⋊C4D411yescharacteristic
41C2×C42×C11—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44#66983—21no—
45#66983—21no—
46#66983C2×C412yes—
47#66983D412yes—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11C2×C411yescharacteristic, complemented
54C2×C4⋊Dic11D411yescharacteristic
55#66977—21no—
56#66977—21no—
57#66977—21no—
58#66977—21no—
59C2×Dic11⋊C4—21no—
60C2×Dic11⋊C4—21no—
61C2×C4×Dic11—21no—
62C2×#4314—22no—
63(C22⋊D11)⋊C4—42no—
64(C22⋊D11)⋊C4—42no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8C2×C412yescomplemented
69C11×#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—21no—
74C11⋊#95D411yescharacteristic
75C11⋊#95D411yescharacteristic
76#66885—22no—
77#66881—22no—
78#66880—22no—
79#9275—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—81no—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C2×C22⋊D11—22no—
92C2×C22⋊D11—22no—
93C2×C22⋊D11—41no—
94C2×C22⋊D11—41no—
95C2×C22⋊D11—41no—
96C2×C22⋊D11—41no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—42no—
103C22×Dic11—41no—
104C22×Dic11—41no—
105C22×Dic11—41no—
106C22×Dic11—81no—
107C2×D44—21no—
108C2×D44—81no—
109C2×D44C22⋊C412yes—
110C2×C4×D11—42no—
111C2×C4×D11—42no—
112C2×C4×D11—81no—
113C2×Dic22—21no—
114C2×Dic22—21no—
115C2×Dic22—81no—
116C2×C8×C11—22no—
117C2×C8×C11—41no—
118C2×C8×C11—81no—
119C2×C8×C11—81no—
120C11×C22⋊C4—21no—
121C11×C22⋊C4—21no—
122C11×C22⋊C4—21no—
123C11×C22⋊C4SD1612yescomplemented
124C42×C11—81no—
125C22⋊Dic11—41no—
126C22⋊Dic11—41no—
127C22⋊Dic11—41no—
128C22⋊Dic11—41no—
129(C2×D11)⋊C4—22no—
130(C2×D11)⋊C4—22no—
131(C2×D11)⋊C4—42no—
132(C2×D11)⋊C4—42no—
133(C2×D11)⋊C4—81no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—81no—
138C4⋊Dic11C22⋊C412yes—
139Dic11⋊C4—42no—
140Dic11⋊C4—41no—
141Dic11⋊C4—41no—
142C4×Dic11—42no—
143#4314—82no—
144#3187—111no—
145#2364—111no—
146#1996—111no—
147#1519—111no—
148C2×#328—111no—
149#1294—111no—
150#1282D1111yescharacteristic, complemented
151C23×C11—41no—
152C23×C11—41no—
153C23×C11C4×D411yescharacteristic
154C23×C11#12011yescharacteristic
155C23×C11#12111yescharacteristic
156C23×C11C2×SD1611yescharacteristic
157C23×C11#13511yescharacteristic
158C23×C11AGL(1,ℤ/8)11yescharacteristic
159C23×C11#13711yescharacteristic
160C22×D11—22no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C2×C4×C11—22no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11C2×C22⋊C411yescharacteristic
180C2×C4×C11C4×D411yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12311yescharacteristic
183C22⋊D11—42no—
184C22⋊D11—42no—
185C22⋊D11—42no—
186C22⋊D11—42no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—82no—
199C2×Dic11—82no—
200C2×Dic11—81no—
201C2×Dic11—81no—
202C2×Dic11—81no—
203C2×Dic11—81no—
204C2×Dic11—81no—
205D44—42no—
206D44—81no—
207C4×D11—84no—
208Dic22—42no—
209Dic22—81no—
210C8×C11—42no—
211C8×C11—81no—
212C2×C22⋊Q8—111no—
213C2×#121—111no—
214C2×C4×D4—221no—
215#483—221no—
216#481—112no—
217#465—222no—
218#450—221no—
219#448—112no—
220C2×C22⋊C8C2×D1111yescharacteristic
221C2×C22⋊C8C2×D1111yescharacteristic
222#388—221no—
223#387—221no—
224#386—221no—
225#386—221no—
226#380—111no—
227C4×C22⋊C4—221no—
228C4×C22⋊C4C2×D1111yescharacteristic
229C2×#95—111no—
230#342—221no—
231#342—221no—
232#328—221no—
233#328—221no—
234#327—222no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11#38611yescharacteristic
246C22×C11C4×SD1611yescharacteristic
247C22×C11#44011yescharacteristic
248C22×C11#45011yescharacteristic
249C22×C11#45211yescharacteristic
250C22×C11#46111yescharacteristic
251C22×C11#46311yescharacteristic
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—42no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—42no—
264C4×C11—81no—
265Dic11—42no—
266Dic11—42no—
267Dic11—81no—
268Dic11—81no—
269Dic11—81no—
270Dic11—161no—
271C22×Q8—111no—
272C22×D4—111no—
273C22×D4—221no—
274C23×C4—221no—
275C23×C4—221no—
276C23×C4C22×D1111yescharacteristic
277C2×SD16—222no—
278C22×C8—21no—
279C22×C8—21no—
280C22⋊Q8—221no—
281C22⋊Q8—221no—
282C22⋊Q8—221no—
283C22⋊Q8—221no—
284#121—112no—
285#121—112no—
286#121—221no—
287#121—221no—
288C4×D4—442no—
289C4×D4—442no—
290C2×C4⋊C4—111no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—221no—
295C2×C22⋊C4—221no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4D4411yescharacteristic
302C2×C22⋊C4D4411yescharacteristic
303C2×C42—21no—
304C2×C42—221no—
305#106—222no—
306#103—222no—
307#102—222no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311C22⋊C8C4×D1112yescomplemented
312#95—21no—
313#95—111no—
314#95—111no—
315#95—221no—
316#95—221no—
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#187711yescharacteristic
326C2×C11#190611yescharacteristic
327C2×C11#191311yescharacteristic
328D11—82no—
329C24—221no—
330C24C2×D4411yescharacteristic
331C2×Q8—221no—
332C2×Q8—221no—
333C2×Q8—881no—
334C2×D4—112no—
335C2×D4—222no—
336C2×D4—222no—
337C2×D4—221no—
338C2×D4—441no—
339C2×D4—441no—
340C2×D4—441no—
341C2×D4—441no—
342C2×D4—881no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—81no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—442no—
352C22×C4—442no—
353C22×C4—442no—
354C22×C4—441no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4—881no—
358C22×C4—881no—
359C22×C4C2×C4×D1111yescharacteristic
360C22×C4#433911yescharacteristic
361C22×C4D4×D1111yescharacteristic
362C22×C4D4×D1111yescharacteristic
363C22×C4D4×D1111yescharacteristic
364C22×C4#434311yescharacteristic
365SD16—882no—
366C2×C8—22no—
367C2×C8—41no—
368C2×C8—81no—
369C2×C8—81no—
370C4⋊C4—112no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—442no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—881no—
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—222no—
382C22⋊C4—222no—
383C22⋊C4—442no—
384C22⋊C4—442no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—881no—
390C22⋊C4#431412yescomplemented
391C42—81no—
392C42—442no—
393C11#927511yescharacteristic, complemented, Sylow
394C23—41no—
395C23—41no—
396C23—222no—
397C23—441no—
398C23—441no—
399C23—441no—
400C23—441no—
401C23—441no—
402C23—441no—
403C23C4×D4411yescharacteristic
404C23#6693511yescharacteristic
405C23#6694811yescharacteristic
406C23C2×#431411yescharacteristic
407C23#6695711yescharacteristic
408C23#6696111yescharacteristic
409C23#6696211yescharacteristic
410Q8—442no—
411Q8—881no—
412D4—442no—
413D4—442no—
414D4—442no—
415D4—442no—
416D4—442no—
417D4—881no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—884no—
442C2×C4—882no—
443C2×C4—882no—
444C2×C4—881no—
445C2×C4—881no—
446C2×C4—881no—
447C2×C4—881no—
448C2×C4—881no—
449C2×C4C22⋊C4×D1111yescharacteristic
450C2×C4#6693711yescharacteristic
451C2×C4#6694611yescharacteristic
452C2×C4#6694711yescharacteristic
453C8—42no—
454C8—81no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—442no—
466C22—442no—
467C22—442no—
468C22—881no—
469C22—881no—
470C22—881no—
471C22—881no—
472C22#1062227811yescharacteristic
473C22C4×#431411yescharacteristic
474C22#1062232311yescharacteristic
475C22#1062234411yescharacteristic
476C22#1062234611yescharacteristic
477C22#1062245411yescharacteristic
478C22#1062245711yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—81no—
485C4—442no—
486C4—442no—
487C4—881no—
488C4—881no—
489C4—881no—
490C4—1761no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—882no—
498C2#1306894911yescharacteristic
499C2#1306911811yescharacteristic
500C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1282C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1282D11
hypocenterC11#9275
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
3. #13069601C2semidirect
5. C2×#10622105C2semidirect
6. #13066496C2semidirect
7. C11×#1282C2semidirect
20. #10622351C4semidirect
21. #10622348C4semidirect
36. C22×Dic22C2×C4semidirect
53. C2×C4⋊Dic11C2×C4semidirect
68. C11×C22⋊C8C2×C4semidirect
123. C11×C22⋊C4SD16semidirect
150. #1282D11semidirect
311. C22⋊C8C4×D11semidirect
390. C22⋊C4#4314semidirect
393. C11#9275semidirect

Maximal subgroups

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

subgroupindex
#130793742
#130716662
#130696012
#130671852
C2×#106221052
#130664962
C11×#12822
#927511