Finite Group Databasebeta

← #14803279

Subgroups — #14803279

Order 2816.

850 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622454C211yesmaximal, characteristic
2#13073828C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic
4#13069996C212yesmaximal, complemented
5#13069934C212yesmaximal
6#13069470C212yesmaximal
7#13069418C211yesmaximal, characteristic, complemented
8#13069380C211yesmaximal, characteristic, complemented
9#13069292C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic
11C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999—21no—
14C22×#4314C2212yes—
15C2×C4×D44C2211yescharacteristic
16C2×#66922C2211yescharacteristic
17C8×Q8×C11—24no—
18C2×C11×C4⋊C8C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C2×C4×C8×C11C2212yes—
22#10622843—21no—
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66881C2212yes—
26C2×#66880C2212yes—
27C2×#66880C2212yes—
28C2×#66880C2212yes—
29#10622607—22no—
30#10622600—21no—
31#10622599—22no—
32#10622590—21no—
33#10622552C2212yes—
34#10622548C2211yescharacteristic
35C4×C4⋊Dic11C2211yescharacteristic
36#10622542C2212yes—
37#10622542C2212yes—
38#10622541C2212yes—
39#10622454—24no—
40#10622189C2212yes—
41#10622189C2211yescharacteristic
42#10622189C2211yescharacteristic
43C22×Q8×C11D411yescharacteristic
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22C2312yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2312yes—
49C22×C8×C11C2311yescharacteristic
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4D412yes—
54C2×C42×C11C2312yes—
55C2×C42×C11C2311yescharacteristic
56#66999—44no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2312yes—
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11—21no—
70C2×#4314—24no—
71C2×#4314—24no—
72C2×#4314—42no—
73C4×D44—22no—
74C4×D44—22no—
75#66922—22no—
76#66922—22no—
77C11×C4⋊C8—24no—
78C11×C4⋊C8D414yes—
79C4×C8×C11—24no—
80C4×C8×C11—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—21no—
87#66885—22no—
88#66885—22no—
89#66881—42no—
90#66880—24no—
91#66880—24no—
92#66880—42no—
93#25293—111nomaximal, Sylow
94C23×D11—21no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11SD1614yescomplemented
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—22no—
106C22×Dic11—21no—
107C22×Dic11—22no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44#4112yes—
114C2×C4×D11—42no—
115C2×C4×D11—42no—
116C2×C4×D11—42no—
117C2×Dic22—22no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22—22no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11C2×D414yes—
131C2×C8×C11#4112yes—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—22no—
134C42×C11—22no—
135C42×C11—22no—
136C42×C11C2×D412yes—
137C42×C11#4112yes—
138(C2×D11)⋊C4—42no—
139(C2×D11)⋊C4—44no—
140(C2×D11)⋊C4—82no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—42no—
150C4⋊Dic11—42no—
151C4⋊Dic11—42no—
152C4⋊Dic11—81no—
153Dic11⋊C4—44no—
154C4×Dic11—42no—
155#4314—48no—
156C2×#461—111no—
157C2×C8×Q8D1111yescharacteristic, complemented
158#2568—111no—
159#2538—111no—
160#2066—112no—
161#2055—112no—
162#1968—112no—
163#1956—111no—
164#1948—111no—
165#1933—112no—
166C4×#102—111no—
167C23×C11C22×D411yescharacteristic
168C22×D11—22no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175Q8×C11—28no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11#12112yes—
184C2×C4×C11#12112yes—
185C2×C4×C11C2×SD1614yes—
186C2×C4×C11C2×SD1612yes—
187C2×C4×C11#13512yes—
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11H(5,𝔽2)11yescharacteristic
193C2×C4×C112−1+411yescharacteristic
194C2×Dic11—41no—
195C2×Dic11—42no—
196C2×Dic11—41no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—42no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—42no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209D44—22no—
210D44—22no—
211D44—41no—
212D44—41no—
213C4×D11—84no—
214Dic22—42no—
215Dic22—42no—
216Dic22—42no—
217Dic22—42no—
218C8×C11—24no—
219C8×C11—22no—
220C8×C11—41no—
221C22×SD16—112no—
222C2×C4⋊Q8—111no—
223C2×C22⋊Q8—221no—
224C2×C4×Q8C2×D1111yescharacteristic
225C2×C4×D4—111no—
226#461—224no—
227C8×Q8—24no—
228C2×#106—112no—
229C2×C4⋊C8C2×D1112yes—
230C2×C4⋊C8C2×D1111yescharacteristic
231C2×#103—112no—
232C2×#103—112no—
233C2×#103—112no—
234C2×#102—111no—
235C2×#102—111no—
236C2×C4×C8C2×D1112yes—
237C2×C4×C8C2×D1111yescharacteristic
238#400—222no—
239#396—222no—
240#391—112no—
241#391—112no—
242#391—221no—
243#390—112no—
244#389—112no—
245#384—111no—
246#382—221no—
247#380—221no—
248C4×C4⋊C4—111no—
249#340—112no—
250#340—111no—
251#340—111no—
252C22×C11C2×#12111yescharacteristic
253C22×C11#54811yescharacteristic
254C22×C11#55011yescharacteristic
255C22×C11C22×SD1611yescharacteristic
256C22×C11C2×#13511yescharacteristic
257C22×C11#57711yescharacteristic
258C22×C11#57811yescharacteristic
259C2×D11—42no—
260C2×D11—42no—
261C2×D11—42no—
262C2×D11—81no—
263C2×D11—81no—
264C2×D11—81no—
265C2×D11—81no—
266C4×C11—24no—
267C4×C11—22no—
268C4×C11—42no—
269C4×C11#46514yes—
270C4×C11#52911yescharacteristic
271C4×C11#54211yescharacteristic
272C4×C11#54611yescharacteristic
273C4×C11#54811yescharacteristic
274Dic11—81no—
275Dic11—82no—
276Dic11—81no—
277Dic11—82no—
278Dic11—81no—
279C22×Q8—112no—
280C22×Q8D4411yescharacteristic
281C22×D4—111no—
282C23×C4—221no—
283C2×SD16—224no—
284C2×SD16—224no—
285C2×SD16—442no—
286C22×C8C22×D1111yescharacteristic
287C22×C8C22×D1111yescharacteristic
288C22×C8C22×D1112yes—
289C4⋊Q8—222no—
290C4⋊Q8—222no—
291C22⋊Q8—444no—
292C4×Q8—22no—
293C4×Q8—22no—
294C4×D4—222no—
295C4×D4—222no—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4D4411yescharacteristic
306C2×C4⋊C4D4412yes—
307C2×C22⋊C4—221no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4—222no—
310C2×C42—221no—
311C2×C42C22×D1112yes—
312C2×C42C22×D1111yescharacteristic
313#106—442no—
314C4⋊C8—24no—
315C4⋊C8C22⋊D1114yes—
316#103—224no—
317#103—224no—
318#103—442no—
319#102—222no—
320#102—222no—
321C4×C8—24no—
322C4×C8—22no—
323#95—221no—
324#95—222no—
325#95—222no—
326#95—222no—
327#95—222no—
328#95—222no—
329C2×C11#242611yescharacteristic
330C2×C11C2×#46511yescharacteristic
331C2×C11#306311yescharacteristic
332C2×C11#335911yescharacteristic
333C2×C11#336011yescharacteristic
334C2×C11#339211yescharacteristic
335C2×C11#339311yescharacteristic
336D11—82no—
337C24—221no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—222no—
341C2×Q8—222no—
342C2×Q8—222no—
343C2×Q8—222no—
344C2×Q8—222no—
345C2×Q8—222no—
346C2×Q8#431414yescomplemented
347C2×D4—112no—
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—221no—
351C2×D4—221no—
352C2×D4—221no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—222no—
356C22×C4—221no—
357C22×C4—222no—
358C22×C4—442no—
359C22×C4—442no—
360C22×C4—442no—
361C22×C4C2×D4412yes—
362C22×C4C2×D4412yes—
363C22×C4C2×D4411yescharacteristic
364C22×C4C2×D4411yescharacteristic
365C22×C4C23×D1111yescharacteristic
366SD16—448no—
367C2×C8—21no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8#434312yes—
375C2×C8C2×C22⋊D1114yes—
376C4⋊C4—24no—
377C4⋊C4—22no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—222no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—222no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—444no—
387C4⋊C4—442no—
388C4⋊C4—442no—
389C4⋊C4—442no—
390C4⋊C4—881no—
391C22⋊C4—444no—
392C22⋊C4—442no—
393C22⋊C4—882no—
394C42—22no—
395C42—22no—
396C42—442no—
397C42#433912yes—
398C42C2×C22⋊D1112yes—
399C11#2529311yescharacteristic, complemented, Sylow
400C23—222no—
401C23—441no—
402C23—441no—
403C23—441no—
404C23—441no—
405C23—441no—
406C23—441no—
407C23C22×D4411yescharacteristic
408Q8—28no—
409Q8—442no—
410Q8—442no—
411Q8—442no—
412Q8—442no—
413D4—222no—
414D4—222no—
415D4—441no—
416D4—441no—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—442no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—442no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—442no—
434C2×C4—441no—
435C2×C4—442no—
436C2×C4—441no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—884no—
440C2×C4C2×#431414yes—
441C2×C4C2×#431412yes—
442C2×C4#6695712yes—
443C2×C4#6698312yes—
444C2×C4#6698312yes—
445C2×C4C2×#433911yescharacteristic
446C2×C4C2×#434311yescharacteristic
447C2×C4#6704011yescharacteristic
448C2×C4#41×D1111yescharacteristic
449C2×C4#6704211yescharacteristic
450C2×C4C22×C22⋊D1111yescharacteristic
451C8—22no—
452C8—24no—
453C8—41no—
454C22—442no—
455C22—442no—
456C22—442no—
457C22—881no—
458C22—881no—
459C22—881no—
460C22—881no—
461C22#1062310711yescharacteristic
462C22#1062310811yescharacteristic
463C22C22×#431411yescharacteristic
464C22C2×#6695711yescharacteristic
465C22#1062328211yescharacteristic
466C22#1062328411yescharacteristic
467C22C2×#6698311yescharacteristic
468C4—22no—
469C4—24no—
470C4—42no—
471C4—881no—
472C4—882no—
473C4—881no—
474C4—881no—
475C4—882no—
476C4#1062272714yes—
477C4#1062311111yescharacteristic
478C4#1062311311yescharacteristic
479C4#1062334811yescharacteristic
480C4#1062336011yescharacteristic
481C2—882no—
482C2#1307217611yescharacteristic
483C2C2×#1062272711yescharacteristic
484C2#1307830711yescharacteristic
485C2#1308125911yescharacteristic
486C2#1308126711yescharacteristic
487C2#1308159811yescharacteristic
488C2#1308160511yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C8×Q8×C11C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×C8×Q8D11
hypocenterC11#25293
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. #13073828C2semidirect
4. #13069996C2semidirect
7. #13069418C2semidirect
8. #13069380C2semidirect
9. #13069292C2semidirect
11. C2×C8×Q8×C11C2semidirect
97. C2×Q8×C11SD16semidirect
157. C2×C8×Q8D11semidirect
346. C2×Q8#4314semidirect
399. C11#25293semidirect

Maximal subgroups

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

subgroupindex
C2×#106224542
#130738282
#130735342
#130699962
#130699342
#130694702
#130694182
#130693802
#130692922
C4×#668852
C2×C8×Q8×C112
#2529311