Finite Group Databasebeta

← #14722279

Subgroups — #14722279

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077727C211yesmaximal, characteristic, complemented
2#13077282C211yesmaximal, characteristic, complemented
3#13067321C212yesmaximal, complemented
4#13067316C212yesmaximal, complemented
5#13067301C211yesmaximal, characteristic, complemented
6#13067293C211yesmaximal, characteristic, complemented
7#13067281C212yesmaximal, complemented
8#13067265C211yesmaximal, characteristic, complemented
9#13067265C212yesmaximal, complemented
10C2×#10622185C211yesmaximal, characteristic, complemented
11C11×#3511C211yesmaximal, characteristic
12C11×#556—21no—
13C11×#555C412yes—
14C11×#554C412yes—
15C11×#553C414yes—
16C11×#548—22no—
17C11×#547—21no—
18C11×#542—22no—
19C11×#537—21no—
20C11×#533C2212yes—
21C11×#532C2211yescharacteristic
22C11×#532C2212yes—
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#520—21no—
25C4×C11×#41C2211yescharacteristic
26#10622847—21no—
27Q8×C11⋊C8—21no—
28D4×C11⋊C8—21no—
29D4×C11⋊C8—22no—
30#10622613—22no—
31#10622610—21no—
32#10622539C2212yes—
33#10622538C2212yes—
34#10622538C2211yescharacteristic
35#10622538C2212yes—
36#10622537C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2212yes—
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622185C2211yescharacteristic
41#10622185C2212yes—
42#10622185C2212yes—
43#10622185C2211yescharacteristic
44#10622185C2212yes—
45#10622185C2212yes—
46#10622185C2212yes—
47#10622182C2211yescharacteristic
48#10622182C2212yes—
49#10622182C2211yescharacteristic
50C2×C11×#41—21no—
51C2×C11×#41—22no—
52C2×C11×#41D411yescharacteristic
53C22×Q8×C11—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8C2×C412yes—
57C11×C4⋊Q8C2312yes—
58C11×C4⋊Q8C2311yescharacteristic
59C11×#127C2311yescharacteristic
60C11×#126—24no—
61C11×#125C2×C414yes—
62C11×#124—24no—
63C11×#124—21no—
64C11×#124—22no—
65C11×#123—24no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—24no—
70C11×#121—22no—
71C11×#121—24no—
72C11×#121—22no—
73C11×#121—21no—
74C11×#121C2×C412yes—
75C11×#121C2×C414yes—
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C4×Q8×C11C2×C411yescharacteristic
79C4×Q8×C11D411yescharacteristic
80C4×D4×C11—24no—
81C4×D4×C11—22no—
82C4×D4×C11—21no—
83C4×D4×C11C2×C414yes—
84C4×D4×C11C2×C412yes—
85C4×D4×C11C2×C412yes—
86C4×D4×C11C2×C411yescharacteristic
87C4×D4×C11D411yescharacteristic
88C4×D4×C11D412yes—
89C11×#117—22no—
90C11×#117C2×C414yes—
91C11×#117D411yescharacteristic
92C11×#117D412yes—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4C2×C412yes—
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2312yes—
98C2×#4318—21no—
99C22×C11⋊C8—21no—
100C22×C11⋊C8—21no—
101C22×C11⋊C8—22no—
102C22⋊(C11⋊C8)—22no—
103C22⋊(C11⋊C8)—21no—
104C22⋊(C11⋊C8)—22no—
105C22⋊(C11⋊C8)—22no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)—22no—
109C4⋊(C11⋊C8)—21no—
110C4⋊(C11⋊C8)C2311yescharacteristic
111C4⋊(C11⋊C8)C2312yes—
112C4⋊(C11⋊C8)C2311yescharacteristic
113C4⋊(C11⋊C8)C2311yescharacteristic
114C4⋊(C11⋊C8)C2312yes—
115C4⋊(C11⋊C8)C2311yescharacteristic
116#66867—22no—
117C4×C11⋊C8—22no—
118C4×C11⋊C8—21no—
119C4×C11⋊C8—22no—
120#17727—111nomaximal, Sylow
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—42no—
124C11×#41—42no—
125C11×#41—82no—
126C11×#41—82no—
127C2×Q8×C11—22no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—81no—
131C2×Q8×C11—81no—
132C2×Q8×C11C22⋊C411yescharacteristic
133C2×D4×C11—22no—
134C2×D4×C11—24no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11C22⋊C412yes—
138C2×D4×C11C22⋊C411yescharacteristic
139C2×D4×C11C22×C412yes—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C11×C4⋊C4—22no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4C22⋊C411yescharacteristic
156C11×C4⋊C4C22⋊C411yescharacteristic
157C11×C4⋊C4C22⋊C412yes—
158C11×C4⋊C4C22⋊C412yes—
159C11×C4⋊C4C22×C414yes—
160C11×C4⋊C4C22×C412yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4C22⋊C412yes—
167C11×C22⋊C4C22⋊C412yes—
168C11×C22⋊C4C22⋊C412yes—
169C42×C11—24no—
170C42×C11C22×C412yes—
171C42×C11C22×C411yescharacteristic
172C42×C11C2×D412yes—
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D412yes—
175C42×C11C2×D411yescharacteristic
176C42×C11C2411yescharacteristic
177#4318—42no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—42no—
185C2×C11⋊C8—81no—
186C2×C11⋊C8—82no—
187#3511D1111yescharacteristic
188#2988—111no—
189#2925—111no—
190#1553—112no—
191#1552—112no—
192#1549—111no—
193#1547—111no—
194#1544—112no—
195#1540—111no—
196#1540—112no—
197C2×#332—111no—
198C23×C11—22no—
199C23×C11C2×C22⋊C412yes—
200C23×C11C2×C22⋊C411yescharacteristic
201Q8×C11—22no—
202Q8×C11—41no—
203Q8×C11—41no—
204Q8×C11—42no—
205Q8×C11—42no—
206Q8×C11—82no—
207D4×C11—24no—
208D4×C11—22no—
209D4×C11—42no—
210D4×C11—44no—
211D4×C11—41no—
212D4×C11—41no—
213D4×C11—41no—
214D4×C11—41no—
215D4×C11—84no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—44no—
227C2×C4×C11—84no—
228C2×C4×C11—82no—
229C2×C4×C11C2×C22⋊C412yes—
230C2×C4×C11C2×C22⋊C411yescharacteristic
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11C2×C22⋊C412yes—
233C2×C4×C11C2×C22⋊C411yescharacteristic
234C2×C4×C11C2×C22⋊C411yescharacteristic
235C2×C4×C11#13512yes—
236C2×C4×C11#13512yes—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C11⋊C8—41no—
241C11⋊C8—41no—
242C11⋊C8—42no—
243C11⋊C8—42no—
244C11⋊C8—41no—
245C11⋊C8—41no—
246#556—21no—
247#555Dic1112yes—
248#554Dic1112yes—
249#553Dic1114yes—
250#548—22no—
251#547—21no—
252#542—22no—
253#537—21no—
254#533C2×D1112yes—
255#532C2×D1111yescharacteristic
256#532C2×D1112yes—
257C2×C4⋊Q8C2×D1111yescharacteristic
258#520—21no—
259C4×#41C2×D1111yescharacteristic
260C8×Q8—221no—
261C8×D4—221no—
262C8×D4—222no—
263#433—222no—
264#432—112no—
265#431—112no—
266#431—111no—
267#431—112no—
268#423—111no—
269C2×C4⋊C8—111no—
270C2×C4⋊C8—111no—
271C2×C4⋊C8—112no—
272#408—221no—
273#405—221no—
274#332—112no—
275#332—112no—
276#332—111no—
277#332—112no—
278#332—111no—
279#332—112no—
280#332—112no—
281#331—111no—
282#331—112no—
283#331—111no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11#41612yes—
293C22×C11C22×C22⋊C411yescharacteristic
294C4×C11—21no—
295C4×C11—22no—
296C4×C11—21no—
297C4×C11—22no—
298C4×C11—22no—
299C4×C11—21no—
300C4×C11—42no—
301C4×C11—44no—
302C4×C11#41612yes—
303C4×C11C2×#13511yescharacteristic
304C4×C11C2×#13511yescharacteristic
305C4×C11#57611yescharacteristic
306C4×C11#57711yescharacteristic
307C2×#41—21no—
308C2×#41—22no—
309C2×#41C22⋊D1111yescharacteristic
310C22×Q8—21no—
311C2×M16—221no—
312C22×C8—221no—
313C22×C8—221no—
314C22×C8—222no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8C2×Dic1112yes—
318C4⋊Q8C22×D1112yes—
319C4⋊Q8C22×D1111yescharacteristic
320#127C22×D1111yescharacteristic
321#126—24no—
322#125C2×Dic1114yes—
323#124—24no—
324#124—21no—
325#124—22no—
326#123—24no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—24no—
331#121—22no—
332#121—24no—
333#121—22no—
334#121—21no—
335#121C2×Dic1112yes—
336#121C2×Dic1114yes—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8C2×Dic1111yescharacteristic
340C4×Q8C22⋊D1111yescharacteristic
341C4×D4—24no—
342C4×D4—22no—
343C4×D4—21no—
344C4×D4C2×Dic1114yes—
345C4×D4C2×Dic1112yes—
346C4×D4C2×Dic1112yes—
347C4×D4C2×Dic1111yescharacteristic
348C4×D4C22⋊D1111yescharacteristic
349C4×D4C22⋊D1112yes—
350#117—22no—
351#117C2×Dic1114yes—
352#117C22⋊D1111yescharacteristic
353#117C22⋊D1112yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4C2×Dic1112yes—
357C2×C42C22×D1111yescharacteristic
358C2×C42C22×D1112yes—
359C4⋊C8—111no—
360C4⋊C8—112no—
361C4⋊C8—111no—
362C4⋊C8—111no—
363C4⋊C8—112no—
364C4⋊C8—111no—
365C4⋊C8—221no—
366C4⋊C8—221no—
367C4⋊C8—222no—
368C4⋊C8—221no—
369C22⋊C8—222no—
370C22⋊C8—222no—
371C22⋊C8—221no—
372C22⋊C8—222no—
373#97—222no—
374C4×C8—222no—
375C4×C8—221no—
376C4×C8—222no—
377C2×C11—22no—
378C2×C11—42no—
379C2×C11—82no—
380C2×C11#288911yescharacteristic
381C2×C11C2×#41611yescharacteristic
382C2×C11#289711yescharacteristic
383#41—22no—
384#41—22no—
385#41—42no—
386#41—42no—
387#41—82no—
388#41—82no—
389C2×Q8—22no—
390C2×Q8—21no—
391C2×Q8—22no—
392C2×Q8—81no—
393C2×Q8—81no—
394C2×Q8C22⋊Dic1111yescharacteristic
395C2×D4—22no—
396C2×D4—24no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4C22⋊Dic1112yes—
400C2×D4C22⋊Dic1111yescharacteristic
401C2×D4C22×Dic1112yes—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4C22×Dic1111yescharacteristic
406C22×C4C22×Dic1112yes—
407C22×C4C2×C22⋊D1112yes—
408C22×C4C2×C22⋊D1111yescharacteristic
409C22×C4C2×C22⋊D1112yes—
410C22×C4C2×C22⋊D1111yescharacteristic
411M16—442no—
412C2×C8—221no—
413C2×C8—221no—
414C2×C8—222no—
415C2×C8—221no—
416C2×C8—222no—
417C2×C8—221no—
418C2×C8—442no—
419C2×C8—881no—
420C2×C8—882no—
421C4⋊C4—22no—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4C22⋊Dic1111yescharacteristic
428C4⋊C4C22⋊Dic1111yescharacteristic
429C4⋊C4C22⋊Dic1112yes—
430C4⋊C4C22⋊Dic1112yes—
431C4⋊C4C22×Dic1114yes—
432C4⋊C4C22×Dic1112yes—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—22no—
436C22⋊C4—24no—
437C22⋊C4—22no—
438C22⋊C4C22⋊Dic1112yes—
439C22⋊C4C22⋊Dic1112yes—
440C22⋊C4C22⋊Dic1112yes—
441C42—24no—
442C42C22×Dic1112yes—
443C42C22×Dic1111yescharacteristic
444C42C2×C22⋊D1112yes—
445C42C2×C22⋊D1111yescharacteristic
446C42C2×C22⋊D1112yes—
447C42C2×C22⋊D1111yescharacteristic
448C42C23×D1111yescharacteristic
449C11#1772711yescharacteristic, complemented, Sylow
450C23—22no—
451C23C2×C22⋊Dic1112yes—
452C23C2×C22⋊Dic1111yescharacteristic
453Q8—22no—
454Q8—41no—
455Q8—41no—
456Q8—42no—
457Q8—42no—
458Q8—82no—
459D4—24no—
460D4—22no—
461D4—42no—
462D4—44no—
463D4—41no—
464D4—41no—
465D4—41no—
466D4—41no—
467D4—84no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—44no—
479C2×C4—84no—
480C2×C4—82no—
481C2×C4#6700312yes—
482C2×C4#6700312yes—
483C2×C4C2×C22⋊Dic1112yes—
484C2×C4C2×C22⋊Dic1111yescharacteristic
485C2×C4C2×C22⋊Dic1112yes—
486C2×C4C2×C22⋊Dic1112yes—
487C2×C4C2×C22⋊Dic1111yescharacteristic
488C2×C4C2×C22⋊Dic1111yescharacteristic
489C2×C4C23×Dic1111yescharacteristic
490C2×C4C22×C22⋊D1111yescharacteristic
491C2×C4C22×C22⋊D1111yescharacteristic
492C8—441no—
493C8—441no—
494C8—442no—
495C8—442no—
496C8—441no—
497C8—441no—
498C22—21no—
499C22—21no—
500C22—22no—
501C22—22no—
502C22—22no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22#1062284612yes—
507C22C22×C22⋊Dic1111yescharacteristic
508C4—21no—
509C4—22no—
510C4—21no—
511C4—22no—
512C4—22no—
513C4—21no—
514C4—42no—
515C4—44no—
516C4#1062284612yes—
517C4C2×#6700311yescharacteristic
518C4C2×#6700311yescharacteristic
519C4#1062336611yescharacteristic
520C4#1062336711yescharacteristic
521C2—22no—
522C2—42no—
523C2—82no—
524C2#1307709911yescharacteristic
525C2C2×#1062284611yescharacteristic
526C2#1307714211yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3511C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3511D11
hypocenterC11#17727
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13077727C2semidirect
2. #13077282C2semidirect
3. #13067321C2semidirect
4. #13067316C2semidirect
5. #13067301C2semidirect
6. #13067293C2semidirect
7. #13067281C2semidirect
8. #13067265C2semidirect
9. #13067265C2semidirect
10. C2×#10622185C2semidirect
449. C11#17727semidirect

Maximal subgroups

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

subgroupindex
#130777272
#130772822
#130673212
#130673162
#130673012
#130672932
#130672812
#130672652
C2×#106221852
C11×#35112
#1772711