Finite Group Databasebeta

← #14803629

Subgroups — #14803629

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622694C211yesmaximal, characteristic, complemented
2#13073789C211yesmaximal, characteristic
3#13071676C211yesmaximal, characteristic, complemented
4#13070037C212yesmaximal, complemented
5#13069929C212yesmaximal
6#13069563C211yesmaximal, characteristic, complemented
7#13069332C211yesmaximal, characteristic, complemented
8#13068973C212yesmaximal
9#13068629C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic
11C2×C11×#461C211yesmaximal, characteristic
12C22×C11×SD16C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×Q8×Dic11C2212yes—
16C2×#66922C2211yescharacteristic
17C11×#461—24no—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103C2212yes—
20#10622843C2212yes—
21C2×#66899C2212yes—
22C2×#66899C2212yes—
23#10622834C2212yes—
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26#10622825—21no—
27#10622825—21no—
28C2×Dic11⋊C8C2212yes—
29#10622694—24no—
30#10622598—21no—
31#10622594—22no—
32#10622590C2212yes—
33C4⋊C4×Dic11—21no—
34#10622560—22no—
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622189C2212yes—
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11C2312yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×Dic22—21no—
47C2×C11×SD16—24no—
48C2×C11×SD16—24no—
49C2×C11×SD16—42no—
50C22×C8×C11C2312yes—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8D414yes—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62Q8×Dic11—24no—
63Q8×Dic11—42no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4×Dic11—21no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11C2312yes—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76#66922—22no—
77#66922—22no—
78C11×C4⋊C8—22no—
79C11×#103—24no—
80#66899—24no—
81#66899—24no—
82#66896—22no—
83#66896—22no—
84C11⋊#95—21no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95D412yes—
90Dic11⋊C8—42no—
91C4×C11⋊C8—22no—
92#25319—111nomaximal, Sylow
93C24×C11—21no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11C2×D414yes—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11#4112yes—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—22no—
117C22×Dic11C2×D412yes—
118C22×Dic11C2×D412yes—
119C2×Dic22—42no—
120C2×Dic22—81no—
121C2×Dic22—81no—
122C11×SD16—48no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C22⋊C4—42no—
131C42×C11C2×D412yes—
132C42×C11#4112yes—
133C22⋊Dic11—82no—
134C22⋊Dic11—82no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—21no—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—44no—
143C4⋊Dic11—42no—
144C4⋊Dic11#4112yes—
145C4×Dic11—22no—
146C4×Dic11—22no—
147C4×Dic11—44no—
148C4×Dic11—42no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×#487—111no—
156C2×#461D1111yescharacteristic
157#2563—111no—
158#2365—111no—
159#2074—112no—
160#2055—112no—
161#1987—111no—
162#1939—111no—
163#1880—112no—
164#1805—112no—
165C4×#102—111no—
166C23×C11—22no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11C22×D411yescharacteristic
174Q8×C11—24no—
175Q8×C11—24no—
176Q8×C11—42no—
177Q8×C11—42no—
178D4×C11—22no—
179D4×C11—22no—
180D4×C11—41no—
181D4×C11—41no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—24no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—84no—
191C2×C4×C11#12112yes—
192C2×C4×C11#12112yes—
193C2×C4×C11#13512yes—
194C2×C4×C11#13712yes—
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11H(5,𝔽2)11yescharacteristic
200C2×C4×C112−1+411yescharacteristic
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216Dic22—84no—
217C8×C11—42no—
218C11⋊C8—41no—
219C11⋊C8—41no—
220C22×SD16C2×D1112yes—
221C2×C4⋊Q8—111no—
222C2×C4⋊Q8C2×D1111yescharacteristic
223C2×C4×Q8—112no—
224C2×C4×D4C2×D1111yescharacteristic
225#487—224no—
226#461—24no—
227C2×C4⋊C8—112no—
228C2×C4⋊C8C2×D1111yescharacteristic
229C2×#103—112no—
230C2×#103—112no—
231C2×#103C2×D1112yes—
232C2×#102—111no—
233C2×#102—111no—
234C2×C4×C8—111no—
235#393—222no—
236#391—112no—
237#390—112no—
238#389—221no—
239#387—222no—
240#382—112no—
241#380—221no—
242#380—221no—
243C4×C4⋊C4—111no—
244C4×C4⋊C4—111no—
245C4×C4⋊C4—221no—
246#340—112no—
247#340—112no—
248#340—111no—
249#340—111no—
250#336—112no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—81no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11C2×#12111yescharacteristic
259C22×C11#54611yescharacteristic
260C22×C11#54811yescharacteristic
261C22×C11C2×#13511yescharacteristic
262C22×C11C2×#13711yescharacteristic
263C22×C11#57711yescharacteristic
264C22×C11#57711yescharacteristic
265C4×C11—22no—
266C4×C11—44no—
267C4×C11—81no—
268C4×C11#46414yes—
269C4×C11#52911yescharacteristic
270C4×C11#54211yescharacteristic
271C4×C11#54611yescharacteristic
272C4×C11#54711yescharacteristic
273Dic11—42no—
274Dic11—42no—
275Dic11—42no—
276Dic11—81no—
277Dic11—82no—
278C22×Q8—221no—
279C22×Q8C22×D1112yes—
280C22×D4C22×D1111yescharacteristic
281C23×C4—21no—
282C2×SD16—24no—
283C2×SD16—24no—
284C2×SD16—42no—
285C22×C8—111no—
286C22×C8—111no—
287C22×C8C22×D1112yes—
288C4⋊Q8—22no—
289C4⋊Q8—222no—
290C4⋊Q8—222no—
291C4⋊Q8C22⋊D1114yes—
292C4×Q8—224no—
293C4×Q8—442no—
294C4×D4—22no—
295C4×D4—22no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4C22×D1111yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—222no—
309C2×C42—112no—
310C2×C42—222no—
311C2×C42—221no—
312C2×C42C22×D1111yescharacteristic
313C4⋊C8—22no—
314C4⋊C8—442no—
315#103—24no—
316#103—224no—
317#103—224no—
318#102—222no—
319#102—222no—
320C4×C8—222no—
321#95—112no—
322#95—222no—
323#95—222no—
324#95—222no—
325#95—222no—
326#95—221no—
327C2×C11—82no—
328C2×C11#242711yescharacteristic
329C2×C11C2×#46411yescharacteristic
330C2×C11#304311yescharacteristic
331C2×C11#330311yescharacteristic
332C2×C11#332911yescharacteristic
333C2×C11#336011yescharacteristic
334C2×C11#337211yescharacteristic
335C24—21no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—442no—
342C2×Q8—881no—
343C2×Q8—881no—
344C2×Q8C2×C22⋊D1114yes—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4#434112yes—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—112no—
357C22×C4—112no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—222no—
361C22×C4D4×D1111yescharacteristic
362C22×C4D4×D1111yescharacteristic
363C22×C4C23×D1111yescharacteristic
364SD16—48no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—221no—
369C2×C8—221no—
370C2×C8—221no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8—221no—
374C4⋊C4—24no—
375C4⋊C4—24no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—112no—
379C4⋊C4—222no—
380C4⋊C4—222no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—222no—
384C4⋊C4—221no—
385C4⋊C4—222no—
386C4⋊C4—444no—
387C4⋊C4—442no—
388C22⋊C4—42no—
389C22⋊C4—882no—
390C22⋊C4—882no—
391C42—222no—
392C42—222no—
393C42—444no—
394C42—442no—
395C42#434112yes—
396C42C2×C22⋊D1112yes—
397C11#2531911yescharacteristic, complemented, Sylow
398C23—22no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23C2×D4×D1111yescharacteristic
406Q8—24no—
407Q8—24no—
408Q8—42no—
409Q8—42no—
410Q8—884no—
411D4—22no—
412D4—22no—
413D4—41no—
414D4—41no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—24no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—84no—
424C2×C4—222no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—441no—
437C2×C4—442no—
438C2×C4—441no—
439C2×C4#6696812yes—
440C2×C4#6696912yes—
441C2×C4#6699212yes—
442C2×C4#6699212yes—
443C2×C4C2×#434111yescharacteristic
444C2×C4C2×#434111yescharacteristic
445C2×C4#6703711yescharacteristic
446C2×C4#41×D1111yescharacteristic
447C2×C4#6704311yescharacteristic
448C2×C4C22×C22⋊D1111yescharacteristic
449C8—42no—
450C8—441no—
451C8—441no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22#1062312911yescharacteristic
460C22#1062314311yescharacteristic
461C22C2×#6696811yescharacteristic
462C22C2×#6696911yescharacteristic
463C22#1062330911yescharacteristic
464C22#1062330911yescharacteristic
465C22C2×#6699211yescharacteristic
466C4—22no—
467C4—44no—
468C4—81no—
469C4—442no—
470C4—442no—
471C4—442no—
472C4—882no—
473C4—881no—
474C4#1062277914yes—
475C4#1062313111yescharacteristic
476C4#1062313411yescharacteristic
477C4#1062333711yescharacteristic
478C4#1062335511yescharacteristic
479C2—82no—
480C2#1307219511yescharacteristic
481C2C2×#1062277911yescharacteristic
482C2#1307813911yescharacteristic
483C2#1308054711yescharacteristic
484C2#1308091311yescharacteristic
485C2#1308126911yescharacteristic
486C2#1308140111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#461D11
hypocenterC11#25319
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10622694C2semidirect
3. #13071676C2semidirect
4. #13070037C2semidirect
6. #13069563C2semidirect
7. #13069332C2semidirect
9. #13068629C2semidirect
397. C11#25319semidirect

Maximal subgroups

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

subgroupindex
C2×#106226942
#130737892
#130716762
#130700372
#130699292
#130695632
#130693322
#130689732
#130686292
C4×#668962
C2×C11×#4612
#2531911