Finite Group Databasebeta

← #14803632

Subgroups — #14803632

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622694C211yesmaximal, characteristic, complemented
2C2×#10622696C211yesmaximal, characteristic
3#13073565C211yesmaximal, characteristic
4#13070024C212yesmaximal, complemented
5#13069931C212yesmaximal
6#13069568C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13068971C212yesmaximal
9#13068621C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic
11C11×#2365C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C22×#4325C2212yes—
15C2×#66950—21no—
16C2×#66950—21no—
17C2×C4×D44C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C11×#391C2212yes—
20C11×#389—21no—
21C11×#387—22no—
22C4×C11×C4⋊C4—21no—
23C4×C11×C4⋊C4C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66899C2212yes—
26C2×#66899C2212yes—
27C2×#66899C2212yes—
28#10622696—24no—
29#10622694—24no—
30C2×#66873C2211yescharacteristic
31C2×#66873C2211yescharacteristic
32#10622552C2212yes—
33#10622548C2212yes—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2212yes—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622290—22no—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42#10622162C2212yes—
43C22×Q8×C11C2312yes—
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22—21no—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8D414yes—
49C4×Q8×C11—24no—
50C4×Q8×C11—42no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C42×C11—21no—
59C2×C42×C11—22no—
60C2×C42×C11C2312yes—
61C2×C42×C11C2311yescharacteristic
62C2×#4325—24no—
63C2×#4325—24no—
64C2×#4325—42no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2312yes—
76#66950—44no—
77#66950—44no—
78C4×D44—22no—
79C4×D44—22no—
80#66922—22no—
81#66922—22no—
82C11×#95—22no—
83C11×#95—21no—
84C11×#95—22no—
85C11×#95D412yes—
86#66899—24no—
87#66899—24no—
88#66899—24no—
89#66873—22no—
90#66873—22no—
91C4⋊(C11⋊C8)—22no—
92C4⋊(C11⋊C8)—42no—
93C4×C11⋊C8—22no—
94#25320—111nomaximal, Sylow
95C23×D11—21no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11C2×D414yes—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—22no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44#4112yes—
118C2×C4×D11—42no—
119C2×C4×D11—42no—
120C2×C4×D11—42no—
121C2×Dic22—42no—
122C2×Dic22—42no—
123C2×Dic22—42no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—44no—
131C11×C4⋊C4SD1614yescomplemented
132C11×C4⋊C4#4112yes—
133C42×C11—22no—
134C42×C11—22no—
135C42×C11—44no—
136C42×C11—42no—
137C42×C11C2×D412yes—
138C42×C11#4112yes—
139#4325—48no—
140(C2×D11)⋊C4—44no—
141(C2×D11)⋊C4—42no—
142(C2×D11)⋊C4—44no—
143C4⋊Dic11—22no—
144C4⋊Dic11—21no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—44no—
148C4⋊Dic11—42no—
149C4⋊Dic11—44no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—21no—
159C2×#487—111no—
160C2×#461—111no—
161#2542—111no—
162#2365D1111yescharacteristic, complemented
163#2072—112no—
164#2055—112no—
165#1988—111no—
166#1939—111no—
167#1880—112no—
168#1803—112no—
169C4×#102—111no—
170C23×C11C22×D411yescharacteristic
171C22×D11—22no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178Q8×C11—24no—
179Q8×C11—24no—
180Q8×C11—42no—
181Q8×C11—42no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—24no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11#12112yes—
199C2×C4×C11#12112yes—
200C2×C4×C11C2×SD1614yes—
201C2×C4×C11C2×SD1612yes—
202C2×C4×C11AGL(1,ℤ/8)12yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11H(5,𝔽2)11yescharacteristic
208C2×C4×C112−1+411yescharacteristic
209C2×Dic11—42no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—42no—
213C2×Dic11—41no—
214C2×Dic11—42no—
215D44—22no—
216D44—22no—
217D44—41no—
218D44—41no—
219C4×D11—84no—
220Dic22—84no—
221C11⋊C8—41no—
222C11⋊C8—42no—
223C11⋊C8—41no—
224C22×SD16—112no—
225C2×C4⋊Q8—111no—
226C2×C4⋊Q8C2×D1111yescharacteristic
227C2×C22⋊Q8—221no—
228C2×C22⋊Q8—221no—
229C2×C4×Q8C2×D1112yes—
230C2×C4×D4—111no—
231#487—224no—
232#461—224no—
233C2×C4⋊C8—111no—
234C2×C4⋊C8—112no—
235C2×#103—112no—
236C2×#103—112no—
237C2×#103—112no—
238C2×#102—111no—
239C2×#102—111no—
240C2×C4×C8—111no—
241#399—222no—
242#391C2×D1112yes—
243#390—112no—
244#389—21no—
245#387—22no—
246#384—112no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4C2×D1111yescharacteristic
249C4×C4⋊C4C2×D1111yescharacteristic
250#340—112no—
251#340—111no—
252#340—112no—
253#340—111no—
254#336—112no—
255C22×C11C2×#12111yescharacteristic
256C22×C11#54611yescharacteristic
257C22×C11#54811yescharacteristic
258C22×C11C22×SD1611yescharacteristic
259C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C11#57811yescharacteristic
261C22×C11#57811yescharacteristic
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C2×D11—81no—
269C4×C11—24no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—44no—
274C4×C11—81no—
275C4×C11#46014yes—
276C4×C11#52911yescharacteristic
277C4×C11#54211yescharacteristic
278C4×C11#54611yescharacteristic
279C4×C11#54711yescharacteristic
280Dic11—82no—
281Dic11—81no—
282C22×Q8—221no—
283C22×Q8C22×D1112yes—
284C22×D4—111no—
285C23×C4—221no—
286C2×SD16—224no—
287C2×SD16—224no—
288C2×SD16—442no—
289C22×C8—112no—
290C22×C8—111no—
291C22×C8—111no—
292C4⋊Q8—22no—
293C4⋊Q8—222no—
294C4⋊Q8—222no—
295C4⋊Q8D4414yes—
296C22⋊Q8—444no—
297C22⋊Q8—444no—
298C4×Q8—24no—
299C4×Q8—42no—
300C4×D4—222no—
301C4×D4—222no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4C22⋊D1111yescharacteristic
311C2×C4⋊C4C22⋊D1111yescharacteristic
312C2×C4⋊C4C22×D1111yescharacteristic
313C2×C4⋊C4C22×D1111yescharacteristic
314C2×C22⋊C4—221no—
315C2×C22⋊C4—222no—
316C2×C22⋊C4—222no—
317C2×C42—22no—
318C2×C42—21no—
319C2×C42C22×D1112yes—
320C2×C42C22×D1111yescharacteristic
321C4⋊C8—222no—
322C4⋊C8—442no—
323#103—224no—
324#103—224no—
325#103—224no—
326#102—222no—
327#102—222no—
328C4×C8—222no—
329#95—22no—
330#95—21no—
331#95—22no—
332#95C22⋊D1112yes—
333C2×C11#242711yescharacteristic
334C2×C11C2×#46011yescharacteristic
335C2×C11#304411yescharacteristic
336C2×C11#329811yescharacteristic
337C2×C11#333011yescharacteristic
338C2×C11#335911yescharacteristic
339C2×C11#336711yescharacteristic
340D11—82no—
341C24—221no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—442no—
348C2×Q8—442no—
349C2×Q8—442no—
350C2×Q8C2×D4414yes—
351C2×D4—112no—
352C2×D4—221no—
353C2×D4—221no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—221no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—222no—
361C22×C4—221no—
362C22×C4—442no—
363C22×C4—442no—
364C22×C4—442no—
365C22×C4C2×C22⋊D1112yes—
366C22×C4C2×C22⋊D1111yescharacteristic
367C22×C4C2×C22⋊D1112yes—
368C22×C4C2×C22⋊D1111yescharacteristic
369C22×C4C23×D1111yescharacteristic
370SD16—448no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8—222no—
374C2×C8—221no—
375C2×C8—221no—
376C2×C8—222no—
377C2×C8—221no—
378C2×C8—222no—
379C2×C8—221no—
380C4⋊C4—24no—
381C4⋊C4—24no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—44no—
387C4⋊C4—221no—
388C4⋊C4—222no—
389C4⋊C4—221no—
390C4⋊C4—222no—
391C4⋊C4—444no—
392C4⋊C4—442no—
393C4⋊C4—444no—
394C4⋊C4#432514yescomplemented
395C4⋊C4#434112yes—
396C22⋊C4—444no—
397C22⋊C4—442no—
398C22⋊C4—444no—
399C42—22no—
400C42—22no—
401C42—44no—
402C42—42no—
403C42C2×D4412yes—
404C42#433912yes—
405C11#2532011yescharacteristic, complemented, Sylow
406C23—222no—
407C23—441no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23—441no—
413C23C22×C22⋊D1111yescharacteristic
414Q8—24no—
415Q8—24no—
416Q8—42no—
417Q8—42no—
418Q8—884no—
419D4—222no—
420D4—222no—
421D4—441no—
422D4—441no—
423C2×C4—22no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—441no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—441no—
443C2×C4—442no—
444C2×C4—441no—
445C2×C4—884no—
446C2×C4#6698312yes—
447C2×C4#6698312yes—
448C2×C4C2×#432514yes—
449C2×C4C2×#432512yes—
450C2×C4#6700212yes—
451C2×C4C22×D4411yescharacteristic
452C2×C4C2×#433911yescharacteristic
453C2×C4C2×#434111yescharacteristic
454C2×C4#6703711yescharacteristic
455C2×C4#41×D1111yescharacteristic
456C2×C4#6704311yescharacteristic
457C8—442no—
458C8—441no—
459C8—441no—
460C22—442no—
461C22—442no—
462C22—442no—
463C22—881no—
464C22—881no—
465C22—881no—
466C22—881no—
467C22C2×#6698311yescharacteristic
468C22#1062333711yescharacteristic
469C22C22×#432511yescharacteristic
470C22C2×#6700211yescharacteristic
471C22#1062336211yescharacteristic
472C22#1062336911yescharacteristic
473C22#1062336911yescharacteristic
474C4—22no—
475C4—24no—
476C4—44no—
477C4—42no—
478C4—42no—
479C4—81no—
480C4—881no—
481C4—882no—
482C4#1062264014yes—
483C4#1062308511yescharacteristic
484C4#1062308611yescharacteristic
485C4#1062308811yescharacteristic
486C4#1062309211yescharacteristic
487C2—882no—
488C2#1307218711yescharacteristic
489C2C2×#1062264011yescharacteristic
490C2#1307814611yescharacteristic
491C2#1308048111yescharacteristic
492C2#1308092111yescharacteristic
493C2#1308125411yescharacteristic
494C2#1308133011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2365C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2365D11
hypocenterC11#25320
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
1. C2×#10622694C2semidirect
4. #13070024C2semidirect
6. #13069568C2semidirect
7. #13069335C2semidirect
9. #13068621C2semidirect
11. C11×#2365C2semidirect
131. C11×C4⋊C4SD16semidirect
162. #2365D11semidirect
394. C4⋊C4#4325semidirect
405. C11#25320semidirect

Maximal subgroups

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

subgroupindex
C2×#106226942
C2×#106226962
#130735652
#130700242
#130699312
#130695682
#130693352
#130689712
#130686212
C4×#668732
C11×#23652
#2532011