Finite Group Databasebeta

← #14803920

Subgroups — #14803920

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622707C211yesmaximal, characteristic, complemented
2C2×D4×C11⋊C8C211yesmaximal, characteristic
3#13073538C211yesmaximal, characteristic
4#13070052C212yesmaximal, complemented
5#13069812C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069379C211yesmaximal, characteristic, complemented
8#13069037C212yesmaximal, complemented
9#13068639C212yesmaximal, complemented
10C4×#66874C211yesmaximal, characteristic, complemented
11C11×#2547C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#124—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66977C2212yes—
16C23×C11⋊C8C2212yes—
17C2×C4×Dic22C2211yescharacteristic
18C11×#397—22no—
19C11×#391—21no—
20C11×#380C2212yes—
21C11×#380C2212yes—
22C4×C11×C4⋊C4C2211yescharacteristic
23#10622834—21no—
24#10622825C2212yes—
25C2×C22⋊(C11⋊C8)C2212yes—
26#10622707—24no—
27D4×C11⋊C8—24no—
28#10622586—21no—
29C2×#66874C2212yes—
30C2×#66874C2211yescharacteristic
31C2×#66874C2211yescharacteristic
32C2×#66872C2212yes—
33C2×#66872C2212yes—
34#10622561—22no—
35#10622548C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×D4×C11D411yescharacteristic
45C23×C4×C11C2312yes—
46C22×Dic22C2311yescharacteristic
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C11×#124—44no—
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4D412yes—
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2312yes—
68#66977—24no—
69#66977—42no—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—21no—
73C22×C11⋊C8—24no—
74C22×C11⋊C8—24no—
75C22×C11⋊C8—42no—
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2312yes—
78C22×C11⋊C8C2311yescharacteristic
79C4×Dic22—22no—
80C4×Dic22—22no—
81C11×#95—21no—
82C11×#95—22no—
83C11×#95—22no—
84C11⋊#95—22no—
85C22⋊(C11⋊C8)—24no—
86#66874—22no—
87#66874—24no—
88#66874—22no—
89#66872—24no—
90#66872—42no—
91C4⋊(C11⋊C8)D414yes—
92C4×C11⋊C8—22no—
93#25341—111nomaximal, Sylow
94C24×C11C2×D412yes—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11SD1614yes—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—22no—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22—21no—
121C2×Dic22—21no—
122C2×Dic22#4112yes—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—42no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—44no—
133C11×C22⋊C4—44no—
134C42×C11—42no—
135C42×C11C2×D412yes—
136C42×C11#4112yes—
137C22⋊Dic11—44no—
138C22⋊Dic11—82no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—42no—
144C4⋊Dic11—81no—
145Dic11⋊C4—44no—
146Dic11⋊C4—42no—
147C4×Dic11—42no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—48no—
156C2×C11⋊C8C2×D414yes—
157C2×C11⋊C8#4112yes—
158C2×#475—111no—
159C2×C8×D4—111no—
160#2547D1111yescharacteristic
161#2538—111no—
162#2077—112no—
163#2035—112no—
164#1990—111no—
165#1948—111no—
166#1892—112no—
167#1807—112no—
168C4×#103—111no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11C2×SD1614yes—
176C23×C11C22×D411yescharacteristic
177Q8×C11—84no—
178D4×C11—28no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11#12112yes—
198C2×C4×C11#12112yes—
199C2×C4×C11C2×SD1612yes—
200C2×C4×C11#13512yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×Dic11—22no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216Dic22—22no—
217Dic22—22no—
218Dic22—41no—
219Dic22—41no—
220C11⋊C8—22no—
221C11⋊C8—24no—
222C11⋊C8—41no—
223C23×C8—112no—
224C2×C4⋊Q8C2×D1111yescharacteristic
225C2×#124—21no—
226C2×C22⋊Q8—112no—
227C2×C4×Q8—111no—
228C2×C4×D4C2×D1111yescharacteristic
229#475—224no—
230C8×D4—224no—
231C2×#106—112no—
232C2×#106—112no—
233C2×C4⋊C8—111no—
234C2×#103—112no—
235C2×#103—111no—
236C2×#103—111no—
237C2×C22⋊C8—112no—
238C2×C4×C8—111no—
239#397—22no—
240#396—222no—
241#391—21no—
242#390—221no—
243#389—221no—
244#384—111no—
245#380—112no—
246#380C2×D1112yes—
247#380C2×D1112yes—
248C4×C4⋊C4C2×D1111yescharacteristic
249#340—111no—
250#340—112no—
251#340—111no—
252#340—112no—
253#340—112no—
254C22×C11—24no—
255C22×C11—24no—
256C22×C11—24no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11C2×#12111yescharacteristic
262C22×C11#54611yescharacteristic
263C22×C11#54711yescharacteristic
264C22×C11C22×SD1611yescharacteristic
265C22×C11C2×#13511yescharacteristic
266C22×C11#57711yescharacteristic
267C22×C11#57811yescharacteristic
268C4×C11—22no—
269C4×C11—42no—
270C4×C11—81no—
271C4×C11—81no—
272C4×C11—82no—
273C4×C11#46514yes—
274C4×C11#52911yescharacteristic
275C4×C11#54211yescharacteristic
276C4×C11#54611yescharacteristic
277C4×C11#54811yescharacteristic
278Dic11—42no—
279Dic11—82no—
280Dic11—81no—
281C22×Q8—21no—
282C22×Q8—111no—
283C22×D4C22⋊D1111yescharacteristic
284C23×C4C22×D1112yes—
285C22×C8—111no—
286C22×C8—112no—
287C22×C8—111no—
288C22×C8—224no—
289C22×C8—224no—
290C22×C8—442no—
291C4⋊Q8—22no—
292C4⋊Q8—22no—
293#124—44no—
294C22⋊Q8—224no—
295C22⋊Q8—442no—
296C4×Q8—222no—
297C4×Q8—222no—
298C4×D4—22no—
299C4×D4—22no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4C22⋊D1111yescharacteristic
308C2×C4⋊C4C22×D1112yes—
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4C22⋊D1112yes—
316C2×C42—21no—
317C2×C42—221no—
318C2×C42C22×D1111yescharacteristic
319#106—224no—
320#106—442no—
321C4⋊C8—114no—
322#103—222no—
323#103—224no—
324#103—222no—
325C22⋊C8—224no—
326C4×C8—222no—
327#95—21no—
328#95—22no—
329#95—22no—
330#95—222no—
331C2×C11—44no—
332C2×C11#242711yescharacteristic
333C2×C11C2×#46511yescharacteristic
334C2×C11#306311yescharacteristic
335C2×C11#329811yescharacteristic
336C2×C11#330411yescharacteristic
337C2×C11#333511yescharacteristic
338C2×C11#334211yescharacteristic
339C24C2×C22⋊D1112yes—
340C2×Q8—42no—
341C2×Q8—42no—
342C2×Q8—42no—
343C2×Q8—112no—
344C2×Q8—221no—
345C2×Q8—221no—
346C2×Q8—221no—
347C2×Q8—221no—
348C2×Q8—221no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4#432414yes—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—222no—
364C22×C4C2×C22⋊D1112yes—
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367C22×C4C23×D1111yescharacteristic
368C2×C8—114no—
369C2×C8—112no—
370C2×C8—221no—
371C2×C8—222no—
372C2×C8—222no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—221no—
376C2×C8—221no—
377C2×C8—448no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—42no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—222no—
389C4⋊C4—222no—
390C4⋊C4—444no—
391C4⋊C4—442no—
392C4⋊C4—442no—
393C4⋊C4—881no—
394C22⋊C4—24no—
395C22⋊C4—44no—
396C22⋊C4—44no—
397C22⋊C4—444no—
398C22⋊C4—882no—
399C42—42no—
400C42—442no—
401C42D4×D1112yes—
402C42#434112yes—
403C11#2534111yescharacteristic, complemented, Sylow
404C23—22no—
405C23—22no—
406C23—22no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23C2×#432414yes—
411C23C22×C22⋊D1111yescharacteristic
412Q8—84no—
413Q8—222no—
414Q8—222no—
415Q8—441no—
416Q8—441no—
417D4—28no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—222no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—441no—
443C2×C4—442no—
444C2×C4—441no—
445C2×C4C2×#432412yes—
446C2×C4#6699212yes—
447C2×C4#6699212yes—
448C2×C4#6700312yes—
449C2×C4C2×D4×D1111yescharacteristic
450C2×C4C2×#434111yescharacteristic
451C2×C4#41×D1111yescharacteristic
452C2×C4#41×D1111yescharacteristic
453C2×C4#6704211yescharacteristic
454C2×C4#6704311yescharacteristic
455C8—222no—
456C8—224no—
457C8—441no—
458C22—24no—
459C22—24no—
460C22—24no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22C22×#432411yescharacteristic
466C22C2×#6699211yescharacteristic
467C22C2×#6700311yescharacteristic
468C22#1062335511yescharacteristic
469C22#1062336011yescharacteristic
470C22#1062336811yescharacteristic
471C22#1062336911yescharacteristic
472C4—22no—
473C4—42no—
474C4—81no—
475C4—81no—
476C4—82no—
477C4—442no—
478C4—881no—
479C4—882no—
480C4#1062265414yes—
481C4#1062320711yescharacteristic
482C4#1062320811yescharacteristic
483C4#1062321111yescharacteristic
484C4#1062321311yescharacteristic
485C2—44no—
486C2#1307219611yescharacteristic
487C2C2×#1062265411yescharacteristic
488C2#1307830311yescharacteristic
489C2#1308047511yescharacteristic
490C2#1308054911yescharacteristic
491C2#1308097311yescharacteristic
492C2#1308104211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2547C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2547D11
hypocenterC11#25341
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2547

Complements

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

NH ≅ G/Ntype
1. C2×#10622707C2semidirect
4. #13070052C2semidirect
5. #13069812C2semidirect
6. #13069578C2semidirect
7. #13069379C2semidirect
8. #13069037C2semidirect
9. #13068639C2semidirect
10. C4×#66874C2semidirect
403. C11#25341semidirect

Maximal subgroups

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

subgroupindex
C2×#106227072
C2×D4×C11⋊C82
#130735382
#130700522
#130698122
#130695782
#130693792
#130690372
#130686392
C4×#668742
C11×#25472
#2534111