Finite Group Databasebeta

← #14719828

Subgroups — #14719828

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623092C211yesmaximal, characteristic
2#13077699C211yesmaximal, characteristic, complemented
3#13077696C211yesmaximal, characteristic, complemented
4#13066982C214yesmaximal, complemented
5#13066966C214yesmaximal, complemented
6#13066937C211yesmaximal, characteristic, complemented
7#13066928C211yesmaximal, characteristic, complemented
8#13066928C211yesmaximal, characteristic, complemented
9C11×#1460C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66991C411yescharacteristic
12C2×#66989C411yescharacteristic
13C2×#66982C412yes—
14C2×#66977C412yes—
15#10623092—22no—
16#10623092—22no—
17#10623092—22no—
18#10623092—22no—
19C2×#66950C411yescharacteristic
20C2×#66941C411yescharacteristic
21C2×#66938C2212yes—
22C2×#66932C2212yes—
23C2×#66925C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C11×#431C2211yescharacteristic
26C11×#431C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622444—22no—
30#10622443—22no—
31#10622332C2214yes—
32#10622331C2214yes—
33#10622292—22no—
34C8×Dic22—22no—
35C11×#323C2214yes—
36#10622163C2214yes—
37#10622107C2212yes—
38#10622107C2212yes—
39#10622106C2212yes—
40#10622106C2212yes—
41C22×D4×C11C2×C411yescharacteristic
42C23×C4×C11C2×C412yes—
43C22×C22⋊D11C2×C412yes—
44C22×C4×D11C2×C411yescharacteristic
45C22×Dic22C2×C411yescharacteristic
46C22×Dic22C2×C412yes—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C2×C11×C4⋊C4C2×C411yescharacteristic
52C2×C11×C22⋊C4C2312yes—
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11C2×C412yes—
55C2×C22⋊Dic11C2×C412yes—
56C2×C22⋊Dic11C2×C412yes—
57#66991—22no—
58#66991—22no—
59#66989—22no—
60#66989—22no—
61#66982—24no—
62#66982—24no—
63C2×(C2×D11)⋊C4C2×C411yescharacteristic
64C2×(C2×D11)⋊C4C2×C412yes—
65C2×(C2×D11)⋊C4C2311yescharacteristic
66C2×C4⋊Dic11C2×C412yes—
67C2×C4⋊Dic11C2×C411yescharacteristic
68#66977—24no—
69#66977—24no—
70C2×Dic11⋊C4C2×C411yescharacteristic
71C2×Dic11⋊C4C2×C412yes—
72C2×Dic11⋊C4C2×C412yes—
73C2×Dic11⋊C4C2311yescharacteristic
74C2×C4×Dic11C2×C411yescharacteristic
75C2×C4×Dic11C2312yes—
76#66950—22no—
77#66950—22no—
78#66941—22no—
79#66941—22no—
80#66938—24no—
81#66938—24no—
82#66932—24no—
83#66932—24no—
84#66925—21no—
85#66925—21no—
86#66925—21no—
87#66925—21no—
88C4×Dic22D412yes—
89C4×Dic22D412yes—
90C4×Dic22D412yes—
91C4×Dic22D412yes—
92C11×C4⋊C8—21no—
93C11×C4⋊C8—21no—
94C11×C22⋊C8C2312yes—
95C11×C22⋊C8C2312yes—
96C4×C8×C11—21no—
97C4×C8×C11—21no—
98C22⋊(C11⋊C8)C2312yes—
99C22⋊(C11⋊C8)C2312yes—
100#66879—24no—
101Dic11⋊C8—24no—
102Dic11⋊C8—24no—
103C8×Dic11—24no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4×C11⋊C8—21no—
107C4×C11⋊C8—21no—
108#17390—111nomaximal, Sylow
109C24×C11C22×C412yes—
110C23×D11C22×C411yescharacteristic
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—82no—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C2×C22⋊D11—24no—
123C2×C22⋊D11—82no—
124C22×Dic11C22×C411yescharacteristic
125C22×Dic11C22×C412yes—
126C22×Dic11C22×C411yescharacteristic
127C22×Dic11C22×C411yescharacteristic
128C22×Dic11C22×C412yes—
129C2×C4×D11—21no—
130C2×C4×D11—21no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×Dic22—24no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22—82no—
137C2×Dic22C22⋊C412yes—
138C2×Dic22C22⋊C412yes—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C42×C11C2×D411yescharacteristic
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C22⋊Dic11—24no—
150C22⋊Dic11—24no—
151C22⋊Dic11—24no—
152(C2×D11)⋊C4—24no—
153(C2×D11)⋊C4—21no—
154(C2×D11)⋊C4—21no—
155(C2×D11)⋊C4—21no—
156(C2×D11)⋊C4—21no—
157C4⋊Dic11—24no—
158C4⋊Dic11C22⋊C412yes—
159C4⋊Dic11C22⋊C412yes—
160Dic11⋊C4—24no—
161Dic11⋊C4—21no—
162Dic11⋊C4—21no—
163Dic11⋊C4—21no—
164Dic11⋊C4—21no—
165Dic11⋊C4C22⋊C414yes—
166Dic11⋊C4C22⋊C414yes—
167C4×Dic11—21no—
168C4×Dic11—21no—
169C4×Dic11C2×D414yes—
170C4×Dic11C2×D414yes—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×#542—111no—
174#2983—111no—
175#2982—111no—
176#1473—114no—
177#1469—114no—
178#1460—111no—
179#1460D1111yescharacteristic, complemented
180#1458—111no—
181#1458—111no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11C23×C411yescharacteristic
188C22×D11—21no—
189C22×D11—21no—
190C22×D11—21no—
191C22×D11—41no—
192C22×D11—41no—
193D4×C11—42no—
194D4×C11—42no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—82no—
200C2×C4×C11—82no—
201C2×C4×C11C2×C22⋊C411yescharacteristic
202C2×C4×C11C2×C22⋊C411yescharacteristic
203C2×C4×C11C2×C22⋊C411yescharacteristic
204C2×C4×C11C2×C22⋊C411yescharacteristic
205C2×C4×C11#13112yes—
206C2×C4×C11#13112yes—
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C22⋊D11—84no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11C2×C22⋊C414yes—
221C2×Dic11C2×C22⋊C414yes—
222C4×D11—42no—
223C4×D11—42no—
224Dic22—24no—
225Dic22—24no—
226Dic22—84no—
227C8×C11—42no—
228C8×C11—42no—
229C11⋊C8—42no—
230C11⋊C8—42no—
231#542—222no—
232#542—222no—
233#542—222no—
234#542—222no—
235C2×C4⋊Q8—111no—
236C2×#126—112no—
237C2×#124—111no—
238C2×#124—112no—
239C2×#123—112no—
240C2×C22⋊Q8—112no—
241C2×C22⋊Q8—111no—
242C2×#121—111no—
243C2×C4×Q8—111no—
244C2×C4×D4C2×D1111yescharacteristic
245C2×#117—111no—
246#446—222no—
247#446—222no—
248C8×Q8—222no—
249C8×Q8—222no—
250#432—114no—
251#431—111no—
252#431—111no—
253#431—114no—
254#431C2×D1111yescharacteristic
255#431C2×D1111yescharacteristic
256#324—112no—
257#324—112no—
258#323—114no—
259#323—112no—
260#323—112no—
261#323C2×D1114yes—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11C2×#13111yescharacteristic
271C22×C11C2×#13111yescharacteristic
272C2×D11—41no—
273C2×D11—41no—
274C2×D11—41no—
275C2×D11—81no—
276C2×D11—81no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—42no—
282C4×C11#40812yes—
283C4×C11#40812yes—
284Dic11—24no—
285Dic11—24no—
286Dic11—41no—
287Dic11—41no—
288Dic11—41no—
289C22×Q8—111no—
290C22×Q8—112no—
291C22×D4—112no—
292C22×D4C4×D1111yescharacteristic
293C23×C4—111no—
294C23×C4C4×D1112yes—
295C4⋊Q8—222no—
296C4⋊Q8—222no—
297#126—224no—
298#126—224no—
299#124—224no—
300#124—224no—
301#124—222no—
302#124—222no—
303#123—224no—
304#123—224no—
305C22⋊Q8—222no—
306C22⋊Q8—222no—
307C22⋊Q8—224no—
308C22⋊Q8—224no—
309#121—222no—
310#121—222no—
311C4×Q8—112no—
312C4×Q8—112no—
313C4×Q8—112no—
314C4×Q8—112no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—21no—
319#117—221no—
320#117—221no—
321#117—221no—
322#117—221no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—112no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4C4×D1111yescharacteristic
330C2×C22⋊C4—112no—
331C2×C22⋊C4—112no—
332C2×C22⋊C4—112no—
333C2×C22⋊C4—111no—
334C2×C22⋊C4—112no—
335C2×C22⋊C4—111no—
336C2×C22⋊C4C22×D1112yes—
337C2×C42—112no—
338C2×C42—111no—
339C2×C42C22×D1111yescharacteristic
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8—224no—
343C4⋊C8—224no—
344C4⋊C8—221no—
345C4⋊C8—221no—
346C22⋊C8—112no—
347C22⋊C8—112no—
348C22⋊C8C22×D1112yes—
349C22⋊C8C22×D1112yes—
350#97—224no—
351C4×C8—21no—
352C4×C8—21no—
353C4×C8—224no—
354C4×C8—221no—
355C4×C8—221no—
356C2×C11—21no—
357C2×C11—21no—
358C2×C11—82no—
359C2×C11C2×#40811yescharacteristic
360C2×C11#288411yescharacteristic
361C2×C11#288811yescharacteristic
362D11—81no—
363C24—111no—
364C24C2×C4×D1112yes—
365C2×Q8—112no—
366C2×Q8—112no—
367C2×Q8—224no—
368C2×Q8—222no—
369C2×Q8—222no—
370C2×Q8—882no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—224no—
376C2×D4—882no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—82no—
380C22×C4—112no—
381C22×C4—112no—
382C22×C4—111no—
383C22×C4—111no—
384C22×C4—111no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4C2×C4×D1112yes—
390C22×C4C2×C4×D1111yescharacteristic
391C22×C4C2×C4×D1111yescharacteristic
392C22×C4C23×D1111yescharacteristic
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—222no—
396C2×C8—222no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—112no—
400C4⋊C4—112no—
401C4⋊C4—114no—
402C4⋊C4—114no—
403C4⋊C4—224no—
404C4⋊C4—224no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—224no—
412C22⋊C4—224no—
413C22⋊C4—224no—
414C22⋊C4—224no—
415C22⋊C4—221no—
416C22⋊C4—221no—
417C22⋊C4—221no—
418C22⋊C4—221no—
419C42—114no—
420C42—114no—
421C42—221no—
422C42—221no—
423C42D4×D1111yescharacteristic
424C42D4×D1111yescharacteristic
425C42D4×D1111yescharacteristic
426C42D4×D1111yescharacteristic
427C11#1739011yescharacteristic, complemented, Sylow
428C23—22no—
429C23—22no—
430C23—22no—
431C23—42no—
432C23—42no—
433C23—221no—
434C23—221no—
435C23—221no—
436C23—441no—
437C23—441no—
438C23C22×C4×D1111yescharacteristic
439Q8—224no—
440Q8—224no—
441Q8—884no—
442D4—42no—
443D4—42no—
444D4—884no—
445C2×C4—22no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—82no—
450C2×C4—82no—
451C2×C4—114no—
452C2×C4—114no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4C22⋊C4×D1111yescharacteristic
466C2×C4C22⋊C4×D1111yescharacteristic
467C2×C4C22⋊C4×D1111yescharacteristic
468C2×C4C22⋊C4×D1111yescharacteristic
469C2×C4#6695412yes—
470C2×C4#6696012yes—
471C2×C4C2×D4×D1111yescharacteristic
472C2×C4C2×D4×D1111yescharacteristic
473C8—42no—
474C8—42no—
475C8—442no—
476C8—442no—
477C22—21no—
478C22—21no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—82no—
483C22—82no—
484C22—441no—
485C22—441no—
486C22—441no—
487C22—881no—
488C22—881no—
489C22C2×C22⋊C4×D1111yescharacteristic
490C22C2×#6695411yescharacteristic
491C22C2×#6696011yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—224no—
498C4—224no—
499C4—441no—
500C4—441no—
501C4—441no—
502C4#1062234012yes—
503C4#1062234012yes—
504C2—21no—
505C2—21no—
506C2—82no—
507C2—881no—
508C2C2×#1062234011yescharacteristic
509C2#1307707811yescharacteristic
510C2#1307709211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1460C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66991C4
cosocleC22×C4×C11C24
hypercenter#1460D11
hypocenterC11#17390
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #13077699C2semidirect
3. #13077696C2semidirect
4. #13066982C2semidirect
5. #13066966C2semidirect
6. #13066937C2semidirect
7. #13066928C2semidirect
8. #13066928C2semidirect
9. C11×#1460C2semidirect
179. #1460D11semidirect
427. C11#17390semidirect

Maximal subgroups

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

subgroupindex
C2×#106230922
#130776992
#130776962
#130669822
#130669662
#130669372
#130669282
C11×#14602
#1739011