Finite Group Databasebeta

← #14796415

Subgroups — #14796415

Order 2816.

894 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
1C2×#10622464C211yesmaximal, characteristic, complemented
2C2×C4×#4314C211yesmaximal, characteristic
3#13073565C211yesmaximal, characteristic
4C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
5#13070094C212yesmaximal, complemented
6#13069989C212yesmaximal
7#13069577C211yesmaximal, characteristic, complemented
8#13068970C212yesmaximal
9#13068622C212yesmaximal, complemented
10#13068617C211yesmaximal, characteristic
11C11×#1939C211yesmaximal, characteristic, complemented
12C22×#4314C2211yescharacteristic
13C2×#66950—21no—
14C2×#66950—21no—
15C2×C4×D44C2211yescharacteristic
16C2×#66922C2211yescharacteristic
17C2×C4×Dic22C2212yes—
18C2×C4×Dic22C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2212yes—
25C2×#66881C2211yescharacteristic
26C2×#66881C2212yes—
27C2×#66880C2211yescharacteristic
28C2×#66880C2212yes—
29#10622589—21no—
30C4⋊C4×Dic11—21no—
31#10622552C2212yes—
32#10622548C2211yescharacteristic
33#10622548C2212yes—
34#10622541C2212yes—
35#10622464—24no—
36C4×#4314—24no—
37#10622290—22no—
38#10622260—22no—
39C11×#336C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622189C2212yes—
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×Dic22—21no—
46C22×Dic22C2311yescharacteristic
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C42×C11C2312yes—
53C2×C42×C11C2311yescharacteristic
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2312yes—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—21no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11—21no—
70C2×C4×Dic11—22no—
71C2×#4314—22no—
72C2×#4314—22no—
73C2×#4314Q814yescomplemented
74#66950—44no—
75#66950—44no—
76C4×D44—22no—
77C4×D44—22no—
78#66922—22no—
79#66922—22no—
80C4×Dic22—22no—
81C4×Dic22—24no—
82C4×Dic22—42no—
83C4×Dic22D414yes—
84C11×C4⋊C8—22no—
85C11×C4⋊C8—42no—
86C4×C8×C11—22no—
87C11×#95D412yes—
88C11⋊#95—22no—
89#66885—22no—
90#66885—42no—
91#66881—24no—
92#66881—22no—
93#66880—24no—
94#66880—22no—
95#24813—111nomaximal, Sylow
96C23×D11—21no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—22no—
105C22×Dic11—21no—
106C22×Dic11—22no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44C2×Q812yes—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C2×C4×D11—42no—
116C2×Dic22—21no—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—42no—
120C2×Dic22—42no—
121C2×Dic22—42no—
122C2×Dic22C2×D412yes—
123C2×Dic22C2×Q812yes—
124C2×Dic22#4112yes—
125C2×C8×C11—21no—
126C2×C8×C11—22no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C2×C8×C11—21no—
131C2×C8×C11—22no—
132C2×C8×C11—21no—
133C2×C8×C11C2×Q812yes—
134C11×C4⋊C4—22no—
135C11×C4⋊C4SD1614yescomplemented
136C42×C11—22no—
137C42×C11—22no—
138C42×C11C2×D412yes—
139C42×C11#4112yes—
140(C2×D11)⋊C4—44no—
141(C2×D11)⋊C4—42no—
142(C2×D11)⋊C4—44no—
143C4⋊Dic11—22no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—21no—
149C4⋊Dic11—22no—
150C4⋊Dic11—44no—
151C4⋊Dic11—42no—
152C4⋊Dic11—44no—
153C4⋊Dic11—42no—
154C4⋊Dic11—81no—
155C4⋊Dic11C2×D412yes—
156Dic11⋊C4—24no—
157Dic11⋊C4—44no—
158Dic11⋊C4—82no—
159C4×Dic11—24no—
160C4×Dic11—44no—
161#4314—28no—
162C2×#475—111no—
163C2×C4×SD16—111no—
164#2542—111no—
165Q8×C4⋊C4—111no—
166#2084—112no—
167#2065—112no—
168#1990—111no—
169#1939D1111yescharacteristic, complemented
170#1880—112no—
171#1803—112no—
172#1802—111no—
173C23×C11C22×D411yescharacteristic
174C22×D11—22no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181C2×C4×C11—22no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11#12112yes—
189C2×C4×C11#12112yes—
190C2×C4×C11C2×SD1614yes—
191C2×C4×C11C2×SD1612yes—
192C2×C4×C11AGL(1,ℤ/8)12yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×Q811yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11H(5,𝔽2)11yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—42no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—41no—
209C2×Dic11—42no—
210C2×Dic11—41no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214D44—22no—
215D44—22no—
216D44—41no—
217D44—41no—
218C4×D11—84no—
219Dic22—22no—
220Dic22—22no—
221Dic22—22no—
222Dic22—84no—
223Dic22C22⋊Q814yescomplemented
224C8×C11—22no—
225C8×C11—42no—
226C8×C11—41no—
227C22×SD16—111no—
228C2×C4⋊Q8—111no—
229C2×C22⋊Q8—221no—
230C2×C22⋊Q8—221no—
231C2×C4×Q8—111no—
232C2×C4×Q8—112no—
233C2×C4×D4—111no—
234#475—224no—
235C4×SD16—224no—
236C2×#106—112no—
237C2×#106—111no—
238C2×C4⋊C8C2×D1111yescharacteristic
239C2×C4⋊C8C2×D1112yes—
240C2×#103—112no—
241C2×#103—111no—
242C2×#102—111no—
243C2×#102—112no—
244C2×C4×C8C2×D1111yescharacteristic
245#399—222no—
246#390—112no—
247#389—112no—
248#389—222no—
249#384—111no—
250#384—112no—
251#384—221no—
252C4×C4⋊C4—221no—
253C4×C4⋊C4C2×D1111yescharacteristic
254#340—112no—
255#340—112no—
256#340—112no—
257#336C2×D1112yes—
258C22×C11C2×#12111yescharacteristic
259C22×C11#54611yescharacteristic
260C22×C11D4×Q811yescharacteristic
261C22×C11C22×SD1611yescharacteristic
262C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C11#57711yescharacteristic
264C22×C11#57811yescharacteristic
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—81no—
272C4×C11—24no—
273C4×C11—22no—
274C4×C11—42no—
275C4×C11#46014yes—
276C4×C11C2×C22⋊Q811yescharacteristic
277C4×C11#53711yescharacteristic
278C4×C11#55211yescharacteristic
279C4×C11#55411yescharacteristic
280Dic11—24no—
281Dic11—42no—
282Dic11—82no—
283Dic11—82no—
284Dic11—81no—
285C22×Q8—111no—
286C22×Q8—221no—
287C22×D4—111no—
288C23×C4—221no—
289C2×SD16—114no—
290C2×SD16—222no—
291C2×SD16—222no—
292C22×C8C22×D1112yes—
293C22×C8C22×D1111yescharacteristic
294C22×C8C22×D1111yescharacteristic
295C4⋊Q8—222no—
296C4⋊Q8—222no—
297C22⋊Q8—444no—
298C22⋊Q8—444no—
299C4×Q8—114no—
300C4×Q8—224no—
301C4×Q8—222no—
302C4×Q8—442no—
303C4×D4—222no—
304C4×D4—222no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—112no—
308C2×C4⋊C4—112no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4D4411yescharacteristic
318C2×C4⋊C4D4411yescharacteristic
319C2×C22⋊C4—221no—
320C2×C22⋊C4—222no—
321C2×C22⋊C4—222no—
322C2×C42—221no—
323C2×C42—222no—
324C2×C42C22×D1112yes—
325C2×C42C22×D1111yescharacteristic
326#106—222no—
327#106—224no—
328C4⋊C8—22no—
329C4⋊C8—42no—
330#103—222no—
331#103—224no—
332#102—222no—
333#102—442no—
334C4×C8—22no—
335#95—222no—
336#95D4412yes—
337C2×C11#241711yescharacteristic
338C2×C11C2×#46011yescharacteristic
339C2×C11#304611yescharacteristic
340C2×C11#329811yescharacteristic
341C2×C11#333211yescharacteristic
342C2×C11Q8×SD1611yescharacteristic
343C2×C11#338611yescharacteristic
344D11—82no—
345C24—221no—
346C2×Q8—112no—
347C2×Q8—112no—
348C2×Q8—112no—
349C2×Q8—221no—
350C2×Q8—221no—
351C2×Q8—221no—
352C2×Q8—442no—
353C2×Q8—442no—
354C2×Q8—442no—
355C2×D4—112no—
356C2×D4—221no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—221no—
360C2×D4—221no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—221no—
366C22×C4—442no—
367C22×C4—442no—
368C22×C4—442no—
369C22×C4C2×D4412yes—
370C22×C4C2×D4411yescharacteristic
371C22×C4C2×D4412yes—
372C22×C4C2×D4411yescharacteristic
373C22×C4C23×D1111yescharacteristic
374SD16—228no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—21no—
381C2×C8—22no—
382C2×C8—21no—
383C2×C8Q8×D1112yes—
384C4⋊C4—22no—
385C4⋊C4—112no—
386C4⋊C4—224no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4—221no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4—444no—
395C4⋊C4—444no—
396C4⋊C4—442no—
397C4⋊C4—444no—
398C4⋊C4—442no—
399C4⋊C4—882no—
400C4⋊C4—881no—
401C4⋊C4#431414yescomplemented
402C22⋊C4—444no—
403C22⋊C4—442no—
404C22⋊C4—444no—
405C42—22no—
406C42—22no—
407C42—224no—
408C42—444no—
409C42D4×D1112yes—
410C42#434312yes—
411C11#2481311yescharacteristic, complemented, Sylow
412C23—222no—
413C23—441no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23—441no—
418C23—441no—
419C23C22×D4411yescharacteristic
420Q8—114no—
421Q8—222no—
422Q8—222no—
423Q8—222no—
424Q8—884no—
425D4—222no—
426D4—222no—
427D4—441no—
428D4—441no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—442no—
443C2×C4—441no—
444C2×C4—442no—
445C2×C4—441no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—441no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—884no—
452C2×C4#6694812yes—
453C2×C4#6694812yes—
454C2×C4C2×#431414yes—
455C2×C4C2×#431412yes—
456C2×C4#6696112yes—
457C2×C4C2×D4×D1111yescharacteristic
458C2×C4#6703711yescharacteristic
459C2×C4C2×Q8×D1111yescharacteristic
460C2×C4C2×#434311yescharacteristic
461C2×C4#41×D1111yescharacteristic
462C2×C4#6704311yescharacteristic
463C8—22no—
464C8—41no—
465C8—42no—
466C22—442no—
467C22—442no—
468C22—442no—
469C22—881no—
470C22—881no—
471C22—881no—
472C22—881no—
473C22C2×#6694811yescharacteristic
474C22#1062308511yescharacteristic
475C22Q8×D4411yescharacteristic
476C22C22×#431411yescharacteristic
477C22C2×#6696111yescharacteristic
478C22#1062328211yescharacteristic
479C22#1062328411yescharacteristic
480C4—22no—
481C4—24no—
482C4—42no—
483C4—224no—
484C4—442no—
485C4—881no—
486C4—882no—
487C4—882no—
488C4#1062246114yes—
489C4#1062313911yescharacteristic
490C4D11×C22⋊Q811yescharacteristic
491C4#1062322511yescharacteristic
492C4#1062326111yescharacteristic
493C2—882no—
494C2#1307206511yescharacteristic
495C2C2×#1062246111yescharacteristic
496C2#1307816811yescharacteristic
497C2#1308048211yescharacteristic
498C2#1308094411yescharacteristic
499C2Q8×#431411yescharacteristic
500C2#1308153911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1939D11
hypocenterC11#24813
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. C2×#10622464C2semidirect
4. C4⋊C4×Dic22C2semidirect
5. #13070094C2semidirect
7. #13069577C2semidirect
9. #13068622C2semidirect
11. C11×#1939C2semidirect
73. C2×#4314Q8semidirect
135. C11×C4⋊C4SD16semidirect
169. #1939D11semidirect
223. Dic22C22⋊Q8semidirect
401. C4⋊C4#4314semidirect
411. C11#24813semidirect

Maximal subgroups

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

subgroupindex
C2×#106224642
C2×C4×#43142
#130735652
C4⋊C4×Dic222
#130700942
#130699892
#130695772
#130689702
#130686222
#130686172
C11×#19392
#2481311