Finite Group Databasebeta

← #14650330

Subgroups — #14650330

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079373C211yesmaximal, characteristic
2#13071668C211yesmaximal, characteristic
3#13069600C211yesmaximal, characteristic, complemented
4C2×#10622105C211yesmaximal, characteristic, complemented
5#13066494C211yesmaximal, characteristic, complemented
6#13066463C211yesmaximal, characteristic, complemented
7C11×#1519C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×D4×Dic11—21no—
10C2×#66977C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13#10622833—21no—
14#10622833—21no—
15#10622831—21no—
16C4×C22⋊Dic11C2211yescharacteristic
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19#10622654—22no—
20#10622653C412yescomplemented
21#10622647C412yescomplemented
22#10622594—21no—
23#10622584—21no—
24#10622564—21no—
25C22⋊C4×Dic11—21no—
26C11×#327—22no—
27#10622165—21no—
28#10622165—21no—
29#10622105—21no—
30#10622105—21no—
31C22×D4×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C23×Dic11—21no—
35C23×Dic11—21no—
36C22×Dic22C2×C411yescharacteristic, complemented
37C22×C8×C11—21no—
38C11×#121—21no—
39C11×#121—21no—
40C11×#121C2×C412yes—
41C11×#121D412yes—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—21no—
50C2×C22⋊Dic11D411yescharacteristic
51C2×C22⋊Dic11D411yescharacteristic
52D4×Dic11—42no—
53D4×Dic11—42no—
54C2×#4324—22no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11C2×C411yescharacteristic, complemented
57#66977—21no—
58#66977—21no—
59#66977—21no—
60#66977—21no—
61C2×Dic11⋊C4—21no—
62C2×C4×Dic11—21no—
63C2×C4×Dic11—21no—
64C22×C11⋊C8—21no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8—21no—
67C11×#95—21no—
68#66896—22no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95D411yescharacteristic
74C11⋊#95D411yescharacteristic
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)C2×C412yescomplemented
77#66874—22no—
78#66872—22no—
79#9275—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11C2×D411yescharacteristic
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11—21no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—81no—
90C2×D4×C11C22⋊C412yes—
91C22×C4×C11—21no—
92C22×C4×C11—41no—
93C22×C4×C11—81no—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—42no—
107C22×Dic11—42no—
108C22×Dic11—42no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C22×Dic11—81no—
112C22×Dic11—81no—
113C2×Dic22—21no—
114C2×Dic22—21no—
115C2×Dic22—81no—
116C2×C8×C11—41no—
117C2×C8×C11—81no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—81no—
120C11×C4⋊C4C22⋊C412yes—
121C11×C22⋊C4—22no—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C22⋊Dic11—21no—
126C22⋊Dic11—21no—
127C22⋊Dic11—21no—
128C22⋊Dic11—42no—
129C22⋊Dic11—42no—
130C22⋊Dic11—41no—
131C22⋊Dic11—41no—
132C22⋊Dic11—81no—
133C22⋊Dic11SD1612yescomplemented
134#4324—82no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—42no—
138Dic11⋊C4—41no—
139Dic11⋊C4—41no—
140C4×Dic11—42no—
141C4×Dic11—81no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—81no—
144#3187—111no—
145#2364—111no—
146#1996—111no—
147#1519D1111yescharacteristic
148C2×#328—111no—
149#1294—111no—
150#1282—111no—
151C23×C11—22no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11C4×D411yescharacteristic
161C23×C11#12011yescharacteristic
162C23×C11#12111yescharacteristic
163C23×C11C2×SD1611yescharacteristic
164C23×C11#13511yescharacteristic
165C23×C11AGL(1,ℤ/8)11yescharacteristic
166C23×C11#13711yescharacteristic
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—42no—
170D4×C11—42no—
171D4×C11—42no—
172D4×C11—81no—
173C2×C4×C11—22no—
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—81no—
183C2×C4×C11—81no—
184C2×C4×C11—81no—
185C2×C4×C11C2×C22⋊C411yescharacteristic
186C2×C4×C11C4×D411yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12311yescharacteristic
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—84no—
204C2×Dic11—82no—
205C2×Dic11—82no—
206C2×Dic11—81no—
207C2×Dic11—81no—
208Dic22—42no—
209Dic22—81no—
210C8×C11—81no—
211C11⋊C8—42no—
212C2×C22⋊Q8—111no—
213C2×#121C2×D1111yescharacteristic
214C2×C4×D4—221no—
215#483—221no—
216#481—112no—
217#465—222no—
218#450—221no—
219#448—112no—
220C2×C22⋊C8—111no—
221C2×C22⋊C8C2×D1111yescharacteristic
222#388—221no—
223#387—221no—
224#386—221no—
225#386—221no—
226#380C2×D1111yescharacteristic
227C4×C22⋊C4—111no—
228C4×C22⋊C4—221no—
229C2×#95—111no—
230#342—221no—
231#342—221no—
232#328—221no—
233#328—221no—
234#327—22no—
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—42no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11#38611yescharacteristic
253C22×C11C4×SD1611yescharacteristic
254C22×C11#44011yescharacteristic
255C22×C11#45011yescharacteristic
256C22×C11#45211yescharacteristic
257C22×C11#46111yescharacteristic
258C22×C11#46311yescharacteristic
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—42no—
264C4×C11—161no—
265Dic11—42no—
266Dic11—42no—
267Dic11—81no—
268Dic11—81no—
269Dic11—81no—
270Dic11—81no—
271C22×Q8—111no—
272C22×D4—21no—
273C22×D4D4411yescharacteristic
274C23×C4—221no—
275C23×C4—221no—
276C23×C4C22×D1111yescharacteristic
277C2×SD16—222no—
278C22×C8—21no—
279C22×C8—221no—
280C22⋊Q8—221no—
281C22⋊Q8—221no—
282C22⋊Q8—221no—
283C22⋊Q8—221no—
284#121—21no—
285#121—21no—
286#121C4×D1112yes—
287#121C22⋊D1112yes—
288C4×D4—442no—
289C4×D4—442no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4D4411yescharacteristic
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—111no—
298C2×C22⋊C4—111no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4—221no—
303C2×C42—221no—
304C2×C42—221no—
305#106—222no—
306#103—222no—
307#102—222no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310C22⋊C8—112no—
311C22⋊C8—221no—
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—82no—
326C2×C11#187711yescharacteristic
327C2×C11#190611yescharacteristic
328C2×C11#191311yescharacteristic
329C24—21no—
330C24D4×D1111yescharacteristic
331C2×Q8—221no—
332C2×Q8—221no—
333C2×Q8—881no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—21no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—81no—
342C2×D4(C2×D11)⋊C412yes—
343C22×C4—21no—
344C22×C4—41no—
345C22×C4—81no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—442no—
353C22×C4—442no—
354C22×C4—442no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4—881no—
358C22×C4—881no—
359C22×C4C2×C4×D1111yescharacteristic
360C22×C4C2×D4411yescharacteristic
361C22×C4D4×D1111yescharacteristic
362C22×C4#434111yescharacteristic
363C22×C4#434111yescharacteristic
364C22×C4C2×C22⋊D1111yescharacteristic
365SD16—882no—
366C2×C8—41no—
367C2×C8—81no—
368C2×C8—222no—
369C2×C8—881no—
370C4⋊C4—21no—
371C4⋊C4—81no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—442no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4(C2×D11)⋊C412yes—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—112no—
383C22⋊C4—221no—
384C22⋊C4—221no—
385C22⋊C4—221no—
386C22⋊C4—442no—
387C22⋊C4—442no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—881no—
391C42—442no—
392C42—881no—
393C11#927511yescharacteristic, complemented, Sylow
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23(C22⋊D11)⋊C411yescharacteristic
404C23#6693511yescharacteristic
405C23#6696411yescharacteristic
406C23#6696511yescharacteristic
407C23SD16×D1111yescharacteristic
408C23#6696811yescharacteristic
409C23#6699211yescharacteristic
410Q8—442no—
411Q8—881no—
412D4—42no—
413D4—42no—
414D4—42no—
415D4—42no—
416D4—42no—
417D4—81no—
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—81no—
428C2×C4—81no—
429C2×C4—81no—
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—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—884no—
445C2×C4—882no—
446C2×C4—882no—
447C2×C4—881no—
448C2×C4—881no—
449C2×C4(C22⋊D11)⋊C411yescharacteristic
450C2×C4#6693911yescharacteristic
451C2×C4C2×(C2×D11)⋊C411yescharacteristic
452C2×C4#6699211yescharacteristic
453C8—81no—
454C8—442no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22#1062237011yescharacteristic
473C22#1062237111yescharacteristic
474C22#1062238911yescharacteristic
475C22#1062239611yescharacteristic
476C22#1062257111yescharacteristic
477C22#1062276611yescharacteristic
478C22#1062277511yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—161no—
485C4—442no—
486C4—442no—
487C4—881no—
488C4—881no—
489C4—881no—
490C4—881no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—82no—
498C2#1306894811yescharacteristic
499C2#1306911511yescharacteristic
500C2#1306915611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1519C2
socleC22×C11#386
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#1519D11
hypocenterC11#9275
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
3. #13069600C2semidirect
4. C2×#10622105C2semidirect
5. #13066494C2semidirect
6. #13066463C2semidirect
20. #10622653C4semidirect
21. #10622647C4semidirect
36. C22×Dic22C2×C4semidirect
56. C2×C4⋊Dic11C2×C4semidirect
76. C22⋊(C11⋊C8)C2×C4semidirect
133. C22⋊Dic11SD16semidirect
393. C11#9275semidirect

Maximal subgroups

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

subgroupindex
#130793732
#130716682
#130696002
C2×#106221052
#130664942
#130664632
C11×#15192
#927511