Finite Group Databasebeta

← #14803287

Subgroups — #14803287

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×#10622632C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13073828C211yesmaximal, characteristic, complemented
4#13069994C212yesmaximal, complemented
5#13069933C212yesmaximal
6#13069469C212yesmaximal
7#13069417C211yesmaximal, characteristic, complemented
8#13069377C211yesmaximal, characteristic, complemented
9#13069291C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic
11C11×#2538C211yesmaximal, characteristic
12C2×C11×C22⋊Q8—21no—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C22×#4324C2212yes—
16C2×#66922C2211yescharacteristic
17C11×#396—22no—
18C11×#390C2212yes—
19C11×#389C2212yes—
20C11×#384C2211yescharacteristic
21C11×#380—21no—
22#10622843—21no—
23C2×#66896C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25Q8×C11⋊C8—24no—
26#10622632—24no—
27#10622599—22no—
28#10622590—21no—
29C2×#66874C2212yes—
30C2×#66874C2212yes—
31C2×#66874C2212yes—
32C2×#66872C2212yes—
33C4×C4⋊Dic11C2211yescharacteristic
34#10622542C2212yes—
35#10622542C2212yes—
36C2×C4⋊(C11⋊C8)C2212yes—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39C2×C4×C11⋊C8C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11D411yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×Dic22C2312yes—
47C11×C22⋊Q8—44no—
48C4×Q8×C11—22no—
49C4×Q8×C11—22no—
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D412yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11C2312yes—
63C2×C42×C11C2311yescharacteristic
64C2×#4324—24no—
65C2×#4324—24no—
66C2×#4324—42no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4×Dic11—21no—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2312yes—
74C22×C11⋊C8C2311yescharacteristic
75#66922—22no—
76#66922—22no—
77C11×#95—22no—
78#66896—22no—
79#66896—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—21no—
85#66874—24no—
86#66874—24no—
87#66874—42no—
88#66872—42no—
89C4⋊(C11⋊C8)—24no—
90C4⋊(C11⋊C8)D414yes—
91C4×C11⋊C8—22no—
92C4×C11⋊C8—24no—
93#25293—111nomaximal, Sylow
94C24×C11—21no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11SD1614yescomplemented
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11#4112yes—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—22no—
117C2×Dic22—22no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22—22no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—44no—
131C11×C4⋊C4—81no—
132C11×C22⋊C4—42no—
133C11×C22⋊C4—44no—
134C11×C22⋊C4—82no—
135C42×C11—22no—
136C42×C11—22no—
137C42×C11C2×D412yes—
138C42×C11#4112yes—
139#4324—48no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—42no—
145C4⋊Dic11—42no—
146C4×Dic11—42no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8C2×D414yes—
155C2×C11⋊C8#4112yes—
156C2×#461—111no—
157C2×C8×Q8—111no—
158#2568—111no—
159#2538D1111yescharacteristic
160#2066—112no—
161#2055—112no—
162#1968—112no—
163#1956—111no—
164#1948—111no—
165#1933—112no—
166C4×#102—111no—
167C23×C11—22no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11C22×D411yescharacteristic
175Q8×C11—28no—
176D4×C11—22no—
177D4×C11—22no—
178D4×C11—41no—
179D4×C11—41no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—84no—
194C2×C4×C11#12112yes—
195C2×C4×C11#12112yes—
196C2×C4×C11C2×SD1614yes—
197C2×C4×C11C2×SD1612yes—
198C2×C4×C11#13512yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11H(5,𝔽2)11yescharacteristic
204C2×C4×C112−1+411yescharacteristic
205C2×Dic11—42no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—41no—
209C2×Dic11—42no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214Dic22—42no—
215Dic22—42no—
216Dic22—42no—
217Dic22—42no—
218C11⋊C8—24no—
219C11⋊C8—22no—
220C11⋊C8—41no—
221C22×SD16—112no—
222C2×C4⋊Q8—111no—
223C2×C22⋊Q8—21no—
224C2×C4×Q8C2×D1111yescharacteristic
225C2×C4×D4C2×D1111yescharacteristic
226#461—224no—
227C8×Q8—224no—
228C2×#106—112no—
229C2×C4⋊C8—111no—
230C2×C4⋊C8—112no—
231C2×#103—112no—
232C2×#103—112no—
233C2×#103—112no—
234C2×#102—111no—
235C2×#102—111no—
236C2×C4×C8—112no—
237C2×C4×C8—111no—
238#400—222no—
239#396—22no—
240#391—112no—
241#391—112no—
242#391—221no—
243#390C2×D1112yes—
244#389C2×D1112yes—
245#384C2×D1111yescharacteristic
246#382—221no—
247#380—21no—
248C4×C4⋊C4—111no—
249#340—112no—
250#340—111no—
251#340—111no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11C2×#12111yescharacteristic
260C22×C11#54811yescharacteristic
261C22×C11#55011yescharacteristic
262C22×C11C22×SD1611yescharacteristic
263C22×C11C2×#13511yescharacteristic
264C22×C11#57711yescharacteristic
265C22×C11#57811yescharacteristic
266C4×C11—24no—
267C4×C11—22no—
268C4×C11—42no—
269C4×C11—82no—
270C4×C11—81no—
271C4×C11#46514yes—
272C4×C11#52911yescharacteristic
273C4×C11#54211yescharacteristic
274C4×C11#54611yescharacteristic
275C4×C11#54811yescharacteristic
276Dic11—81no—
277Dic11—81no—
278Dic11—82no—
279C22×Q8—112no—
280C22×Q8C22⋊D1111yescharacteristic
281C22×D4C22×D1111yescharacteristic
282C23×C4—21no—
283C2×SD16—224no—
284C2×SD16—224no—
285C2×SD16—442no—
286C22×C8—112no—
287C22×C8—111no—
288C22×C8—111no—
289C4⋊Q8—222no—
290C4⋊Q8—222no—
291C22⋊Q8—44no—
292C4×Q8—22no—
293C4×Q8—22no—
294C4×D4—22no—
295C4×D4—22no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4C22⋊D1111yescharacteristic
304C2×C4⋊C4C22⋊D1112yes—
305C2×C4⋊C4C22×D1111yescharacteristic
306C2×C4⋊C4C22×D1112yes—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C42—221no—
311C2×C42C22×D1112yes—
312C2×C42C22×D1111yescharacteristic
313#106—442no—
314C4⋊C8—114no—
315C4⋊C8—224no—
316#103—224no—
317#103—224no—
318#103—442no—
319#102—222no—
320#102—222no—
321C4×C8—224no—
322C4×C8—222no—
323#95—22no—
324#95—221no—
325#95—222no—
326#95—222no—
327#95—222no—
328#95—222no—
329C2×C11—82no—
330C2×C11#242611yescharacteristic
331C2×C11C2×#46511yescharacteristic
332C2×C11#306311yescharacteristic
333C2×C11#335911yescharacteristic
334C2×C11#336011yescharacteristic
335C2×C11#339211yescharacteristic
336C2×C11#339311yescharacteristic
337C24—21no—
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#432414yescomplemented
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4#434312yes—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—222no—
361C22×C4C2×C22⋊D1112yes—
362C22×C4C2×C22⋊D1112yes—
363C22×C4C2×C22⋊D1111yescharacteristic
364C22×C4C2×C22⋊D1111yescharacteristic
365C22×C4C23×D1111yescharacteristic
366SD16—448no—
367C2×C8—114no—
368C2×C8—112no—
369C2×C8—221no—
370C2×C8—222no—
371C2×C8—221no—
372C2×C8—222no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—221no—
376C4⋊C4—24no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—42no—
383C4⋊C4—44no—
384C4⋊C4—81no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—442no—
390C4⋊C4—442no—
391C22⋊C4—44no—
392C22⋊C4—42no—
393C22⋊C4—82no—
394C42—22no—
395C42—22no—
396C42—442no—
397C42D4×D1112yes—
398C42#434112yes—
399C11#2529311yescharacteristic, complemented, Sylow
400C23—22no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23C22×C22⋊D1111yescharacteristic
408Q8—28no—
409Q8—442no—
410Q8—442no—
411Q8—442no—
412Q8—442no—
413D4—22no—
414D4—22no—
415D4—41no—
416D4—41no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—84no—
431C2×C4—442no—
432C2×C4—441no—
433C2×C4—442no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—442no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4C2×#432414yes—
441C2×C4C2×#432412yes—
442C2×C4#6699212yes—
443C2×C4#6699212yes—
444C2×C4#6700312yes—
445C2×C4C2×D4×D1111yescharacteristic
446C2×C4C2×#434111yescharacteristic
447C2×C4C2×#434311yescharacteristic
448C2×C4#6704011yescharacteristic
449C2×C4#41×D1111yescharacteristic
450C2×C4#6704211yescharacteristic
451C8—224no—
452C8—222no—
453C8—441no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22C22×#432411yescharacteristic
462C22C2×#6699211yescharacteristic
463C22#1062334811yescharacteristic
464C22C2×#6700311yescharacteristic
465C22#1062336511yescharacteristic
466C22#1062336711yescharacteristic
467C22#1062336911yescharacteristic
468C4—22no—
469C4—24no—
470C4—42no—
471C4—81no—
472C4—82no—
473C4—881no—
474C4—882no—
475C4—881no—
476C4#1062265414yes—
477C4#1062315511yescharacteristic
478C4#1062316111yescharacteristic
479C4#1062316411yescharacteristic
480C4#1062317411yescharacteristic
481C2—82no—
482C2#1307218411yescharacteristic
483C2C2×#1062265411yescharacteristic
484C2#1307830911yescharacteristic
485C2#1308125811yescharacteristic
486C2#1308126511yescharacteristic
487C2#1308159711yescharacteristic
488C2#1308160011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2538C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2538D11
hypocenterC11#25293
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
3. #13073828C2semidirect
4. #13069994C2semidirect
7. #13069417C2semidirect
8. #13069377C2semidirect
9. #13069291C2semidirect
97. C2×Q8×C11SD16semidirect
346. C2×Q8#4324semidirect
399. C11#25293semidirect

Maximal subgroups

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

subgroupindex
C2×#106226322
C2×Q8×C11⋊C82
#130738282
#130699942
#130699332
#130694692
#130694172
#130693772
#130692912
C4×#668962
C11×#25382
#2529311