Finite Group Databasebeta

← #14719992

Subgroups — #14719992

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623096C211yesmaximal, characteristic
2#13077276C212yesmaximal, complemented
3#13066984C214yesmaximal, complemented
4#13066977C212yesmaximal, complemented
5#13066955C212yesmaximal, complemented
6#13066935C212yesmaximal, complemented
7#13066934C211yesmaximal, characteristic, complemented
8C11×#1465C211yesmaximal, characteristic, complemented
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66992C412yes—
11C2×#66983C411yescharacteristic
12C2×#66983C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4⋊Dic11C411yescharacteristic
15#10623096—22no—
16#10623096—22no—
17#10623096—24no—
18C2×#66951C2212yes—
19C2×#66936C412yes—
20C2×(C22⋊D11)⋊C4C2212yes—
21C2×C4×D44C411yescharacteristic
22C2×#66923C411yescharacteristic
23C11×#407C2212yes—
24C2×C22⋊(C11⋊C8)C2212yes—
25#10622735—22no—
26#10622732—22no—
27#10622333—24no—
28#10622332C2214yes—
29#10622331C2214yes—
30C11×#324C2212yes—
31C11×#323C2212yes—
32#10622166C2212yes—
33#10622163C2211yescharacteristic
34#10622163C2211yescharacteristic
35#10622106C2214yes—
36#10622106C2214yes—
37C22×D4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11C2×C412yes—
41C22×C22⋊D11C2×C412yes—
42C23×Dic11C2×C412yes—
43C22×D44C2×C411yescharacteristic
44C22×C4×D11C2×C412yes—
45C2×C11×M16—22no—
46C4×D4×C11—22no—
47C4×D4×C11—22no—
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C22⋊C4C2×C411yescharacteristic
50C2×C11×C22⋊C4C2311yescharacteristic
51C2×C42×C11C2×C411yescharacteristic
52C2×C22⋊Dic11C2×C412yes—
53#66992—24no—
54#66992—24no—
55#66983—22no—
56#66983—22no—
57#66983—22no—
58#66983—22no—
59C2×(C2×D11)⋊C4C2×C412yes—
60C2×(C2×D11)⋊C4C2×C412yes—
61C2×(C2×D11)⋊C4C2312yes—
62#66979D412yes—
63#66979D412yes—
64#66979D414yes—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11C2×C411yescharacteristic
69C2×C4⋊Dic11C2×C412yes—
70C2×C4⋊Dic11C2×C411yescharacteristic
71C2×C4⋊Dic11C2×C411yescharacteristic
72C2×Dic11⋊C4C2×C412yes—
73C2×Dic11⋊C4C2×C412yes—
74C2×C4×Dic11C2312yes—
75C22×C11⋊C8—22no—
76#66951—24no—
77#66951—24no—
78#66936—24no—
79#66936—24no—
80(C22⋊D11)⋊C4—24no—
81(C22⋊D11)⋊C4—24no—
82C4×D44—22no—
83C4×D44—21no—
84C4×D44—21no—
85#66923—22no—
86#66923—22no—
87C11×C22⋊C8—22no—
88C11×C22⋊C8C2314yes—
89C22⋊(C11⋊C8)—22no—
90C22⋊(C11⋊C8)C2312yes—
91C22⋊(C11⋊C8)C2312yes—
92#66879—24no—
93Dic11⋊C8—24no—
94Dic11⋊C8—24no—
95C8×Dic11—24no—
96#17415—111nomaximal, Sylow
97C24×C11C22×C411yescharacteristic
98C24×C11C22×C411yescharacteristic
99C23×D11C22×C412yes—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—41no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C22×C411yescharacteristic
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2411yescharacteristic
114C2×C22⋊D11—24no—
115C2×C22⋊D11—24no—
116C2×C22⋊D11—24no—
117C2×C22⋊D11—42no—
118C2×C22⋊D11—82no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—82no—
122C22×Dic11C22×C412yes—
123C22×Dic11C22×C412yes—
124C22×Dic11C22×C412yes—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—42no—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—82no—
131C11×M16—44no—
132C2×C8×C11—24no—
133C11×C4⋊C4—22no—
134C11×C22⋊C4—22no—
135C11×C22⋊C4—22no—
136C42×C11—21no—
137C42×C11—21no—
138C22⋊Dic11C22⋊C414yes—
139C22⋊Dic11C22⋊C414yes—
140(C2×D11)⋊C4—22no—
141(C2×D11)⋊C4—22no—
142(C2×D11)⋊C4—24no—
143(C2×D11)⋊C4—24no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11C22⋊C412yes—
149C4⋊Dic11C22⋊C412yes—
150C4⋊Dic11C22⋊C412yes—
151C4⋊Dic11C22⋊C411yescharacteristic
152C4⋊Dic11C22⋊C411yescharacteristic
153Dic11⋊C4—24no—
154Dic11⋊C4—24no—
155C4×Dic11C2×D414yes—
156C4×Dic11C2×D414yes—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—44no—
160C2×#553—111no—
161#2924—112no—
162#1473—114no—
163#1471—112no—
164#1466—112no—
165#1465D1111yescharacteristic, complemented
166#1460—112no—
167#1459—111no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11C2×C22⋊C412yes—
177C23×C11#13112yes—
178C23×C11C23×C411yescharacteristic
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—42no—
183C22×D11—42no—
184D4×C11—44no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11C2×C22⋊C411yescharacteristic
199C2×C4×C11C2×C22⋊C411yescharacteristic
200C2×C4×C11C22×D412yes—
201C22⋊D11—48no—
202C22⋊D11—84no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—82no—
209C2×Dic11—82no—
210C2×Dic11C2×C22⋊C414yes—
211C2×Dic11C2×C22⋊C412yes—
212C2×Dic11C2×C22⋊C412yes—
213D44—42no—
214D44—42no—
215C4×D11—82no—
216C4×D11—82no—
217C8×C11—44no—
218C11⋊C8—42no—
219C11⋊C8—42no—
220#553—222no—
221#553—222no—
222#553—224no—
223C2×#126—112no—
224C2×#125—111no—
225C2×#123—112no—
226C2×#121—112no—
227C2×#121—111no—
228C2×#121—111no—
229C2×C4×D4—112no—
230C2×C4×D4—111no—
231C2×C4×D4C2×D1111yescharacteristic
232C2×#117—111no—
233C22×C4⋊C4—111no—
234#433—224no—
235#432—114no—
236#431—114no—
237#424—222no—
238#407C2×D1112yes—
239C2×C22⋊C8—112no—
240#405—222no—
241#324—112no—
242#324C2×D1112yes—
243#323—111no—
244#323—111no—
245#323—114no—
246#323—114no—
247#323C2×D1112yes—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—41no—
257C22×C11—41no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11C22×C22⋊C411yescharacteristic
261C22×C11C2×#13111yescharacteristic
262C22×C11#56811yescharacteristic
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—82no—
267C2×D11—82no—
268C4×C11—21no—
269C4×C11—22no—
270C4×C11—41no—
271C4×C11—41no—
272C4×C11—41no—
273C4×C11#41012yes—
274Dic11—24no—
275Dic11—22no—
276Dic11—22no—
277Dic11—42no—
278C22×D4—112no—
279C22×D4—112no—
280C22×D4—111no—
281C22×D4C4×D1111yescharacteristic
282C23×C4—112no—
283C23×C4—112no—
284C23×C4C4×D1111yescharacteristic
285C23×C4C22×D1111yescharacteristic
286C2×M16—22no—
287C22×C8—222no—
288#126—224no—
289#126—224no—
290#125—222no—
291#125—222no—
292#123—224no—
293#123—224no—
294#121—224no—
295#121—224no—
296#121—222no—
297#121—222no—
298#121—222no—
299#121—222no—
300C4×D4—22no—
301C4×D4—22no—
302C4×D4—222no—
303C4×D4—221no—
304C4×D4—221no—
305C4×D4—224no—
306C4×D4—224no—
307#117—112no—
308#117—112no—
309#117—114no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—111no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—112no—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4C22×D1111yescharacteristic
320C2×C22⋊C4—112no—
321C2×C22⋊C4—112no—
322C2×C22⋊C4—112no—
323C2×C22⋊C4—112no—
324C2×C22⋊C4C4×D1111yescharacteristic
325C2×C22⋊C4C22×D1111yescharacteristic
326C2×C42—112no—
327C2×C42C4×D1111yescharacteristic
328C4⋊C8—224no—
329C4⋊C8—224no—
330C22⋊C8—22no—
331C22⋊C8—112no—
332C22⋊C8—112no—
333C22⋊C8—222no—
334C22⋊C8C22×D1114yes—
335#97—224no—
336C4×C8—224no—
337C2×C11—21no—
338C2×C11—21no—
339C2×C11—42no—
340C2×C11—42no—
341C2×C11#288011yescharacteristic
342C2×C11C2×#41011yescharacteristic
343C2×C11#288811yescharacteristic
344D11—82no—
345C24—112no—
346C24C2×C4×D1111yescharacteristic
347C24C2×C4×D1111yescharacteristic
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—41no—
351C2×D4—224no—
352C2×D4—224no—
353C2×D4—224no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—442no—
357C2×D4—442no—
358C2×D4—882no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—112no—
364C22×C4—112no—
365C22×C4—112no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—882no—
371C22×C4—882no—
372C22×C4C2×C4×D1111yescharacteristic
373C22×C4C2×C4×D1111yescharacteristic
374C22×C4C2×C4×D1111yescharacteristic
375C22×C4C2×C4×D1111yescharacteristic
376C22×C4D4×D1112yes—
377C22×C4D4×D1112yes—
378C22×C4C23×D1111yescharacteristic
379M16—44no—
380C2×C8—24no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—444no—
384C4⋊C4—22no—
385C4⋊C4—112no—
386C4⋊C4—111no—
387C4⋊C4—111no—
388C4⋊C4—112no—
389C4⋊C4—112no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—224no—
393C4⋊C4—224no—
394C4⋊C4—221no—
395C4⋊C4—221no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—114no—
399C22⋊C4—114no—
400C22⋊C4—222no—
401C22⋊C4—222no—
402C22⋊C4—224no—
403C22⋊C4—224no—
404C42—21no—
405C42—21no—
406C42—114no—
407C42—114no—
408C11#1741511yescharacteristic, complemented, Sylow
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—222no—
418C23—222no—
419C23—222no—
420C23—442no—
421C23—442no—
422C23C22⋊C4×D1112yes—
423C23#6696012yes—
424C23C22×C4×D1111yescharacteristic
425D4—44no—
426D4—442no—
427D4—448no—
428D4—442no—
429D4—884no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—114no—
444C2×C4—112no—
445C2×C4—112no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—882no—
452C2×C4—882no—
453C2×C4—882no—
454C2×C4—882no—
455C2×C4C22⋊C4×D1111yescharacteristic
456C2×C4C22⋊C4×D1111yescharacteristic
457C2×C4C2×D4×D1112yes—
458C8—44no—
459C8—442no—
460C8—442no—
461C22—21no—
462C22—21no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—42no—
468C22—42no—
469C22—41no—
470C22—41no—
471C22—81no—
472C22—81no—
473C22—442no—
474C22—442no—
475C22—442no—
476C22—882no—
477C22—882no—
478C22C2×C22⋊C4×D1111yescharacteristic
479C22C2×#6696011yescharacteristic
480C22#1062327611yescharacteristic
481C4—22no—
482C4—21no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—224no—
487C4—222no—
488C4—222no—
489C4—442no—
490C4#1062235312yes—
491C2—21no—
492C2—21no—
493C2—42no—
494C2—42no—
495C2—882no—
496C2#1307706611yescharacteristic
497C2C2×#1062235311yescharacteristic
498C2#1307709311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1465C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623096C2
cosocleC22×C4×C11C24
hypercenter#1465D11
hypocenterC11#17415
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #13077276C2semidirect
3. #13066984C2semidirect
4. #13066977C2semidirect
5. #13066955C2semidirect
6. #13066935C2semidirect
7. #13066934C2semidirect
8. C11×#1465C2semidirect
165. #1465D11semidirect
408. C11#17415semidirect

Maximal subgroups

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

subgroupindex
C2×#106230962
#130772762
#130669842
#130669772
#130669552
#130669352
#130669342
C11×#14652
#1741511