Finite Group Databasebeta

← #14719947

Subgroups — #14719947

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623227C211yesmaximal, characteristic
2#13077700C211yesmaximal, characteristic, complemented
3#13077699C211yesmaximal, characteristic, complemented
4#13066986C211yesmaximal, characteristic
5#13066984C212yesmaximal
6#13066983C211yesmaximal, characteristic
7#13066972C211yesmaximal, characteristic, complemented
8#13066970C212yesmaximal, complemented
9#13066958C212yesmaximal, complemented
10#13066949C212yesmaximal
11C11×#1470C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13#10623227—22no—
14#10623227—22no—
15#10623227—22no—
16#10623227—22no—
17C2×#66951C411yescharacteristic
18C2×#66951C411yescharacteristic
19C2×#66951C2211yescharacteristic
20C2×#66949C411yescharacteristic
21C2×#66949C411yescharacteristic
22C2×#66945C2211yescharacteristic
23C2×#66943C411yescharacteristic
24C2×#66942C411yescharacteristic
25C2×#66942C411yescharacteristic
26C2×#66942C2211yescharacteristic
27C2×#66941C411yescharacteristic
28C2×#66940C2211yescharacteristic
29C2×#66929C2211yescharacteristic
30C2×C4×Dic22C2211yescharacteristic
31C11×#432C2211yescharacteristic
32C11×#431C2211yescharacteristic
33#10622539C2211yescharacteristic
34#10622538C2211yescharacteristic
35#10622444—22no—
36#10622441—22no—
37#10622332C2212yes—
38#10622332C2212yes—
39#10622332C2212yes—
40#10622331C2212yes—
41#10622314—22no—
42#10622292—22no—
43C11×#324C2212yes—
44C11×#324C2212yes—
45#10622166C2212yes—
46#10622166C2212yes—
47#10622107C2212yes—
48#10622107C2212yes—
49#10622106C2212yes—
50#10622106C2212yes—
51C22×C4×D11C2×C411yescharacteristic
52C22×Dic22C2×C411yescharacteristic
53C22×Dic22C2×C411yescharacteristic
54C11×#125—21no—
55C11×#125—21no—
56C11×#125—21no—
57C11×#125—21no—
58C2×C11×C4⋊C4C2×C411yescharacteristic
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×(C2×D11)⋊C4C2×C411yescharacteristic
66C2×(C2×D11)⋊C4C2×C411yescharacteristic
67C2×(C2×D11)⋊C4C2×C411yescharacteristic
68C2×(C2×D11)⋊C4C2×C411yescharacteristic
69C2×(C2×D11)⋊C4C2×C411yescharacteristic
70C2×(C2×D11)⋊C4C2311yescharacteristic
71C2×C4⋊Dic11C2×C411yescharacteristic
72C2×C4⋊Dic11C2×C411yescharacteristic
73C2×C4⋊Dic11C2×C411yescharacteristic
74C2×C4⋊Dic11C2×C411yescharacteristic
75C2×Dic11⋊C4C2×C411yescharacteristic
76C2×Dic11⋊C4C2×C411yescharacteristic
77C2×Dic11⋊C4C2×C411yescharacteristic
78C2×Dic11⋊C4C2×C411yescharacteristic
79C2×Dic11⋊C4C2×C411yescharacteristic
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2311yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90#66951—22no—
91#66951—22no—
92#66951—22no—
93#66951—22no—
94#66951—22no—
95#66951—22no—
96#66949—22no—
97#66949—22no—
98#66949—22no—
99#66949—22no—
100#66945—22no—
101#66945—22no—
102#66943—22no—
103#66943—22no—
104#66942—22no—
105#66942—22no—
106#66942—22no—
107#66942—22no—
108#66942—22no—
109#66942—22no—
110#66941—22no—
111#66941—22no—
112#66940—22no—
113#66940—22no—
114#66929—21no—
115#66929—21no—
116#66929—21no—
117#66929—21no—
118C4×Dic22D412yes—
119C4×Dic22D412yes—
120C4×Dic22D412yes—
121C4×Dic22D412yes—
122C11×C4⋊C8—21no—
123C11×C4⋊C8—21no—
124C11×C22⋊C8C2312yes—
125C11×C22⋊C8C2312yes—
126C11×#97—21no—
127C4×C8×C11—21no—
128C22⋊(C11⋊C8)C2312yes—
129C22⋊(C11⋊C8)C2312yes—
130#66879—22no—
131#66879—22no—
132#66879—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135Dic11⋊C8—22no—
136Dic11⋊C8—22no—
137C8×Dic11—22no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)—21no—
140#66867—21no—
141C4×C11⋊C8—21no—
142#17410—111nomaximal, Sylow
143C23×D11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11C22×C411yescharacteristic
152C22×Dic11C22×C411yescharacteristic
153C22×Dic11C22×C411yescharacteristic
154C22×Dic11C22×C411yescharacteristic
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158C2×C4×D11—22no—
159C2×C4×D11—42no—
160C2×Dic22—22no—
161C2×Dic22—42no—
162C2×Dic22—42no—
163C2×Dic22C22⋊C412yes—
164C2×Dic22C22⋊C412yes—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183(C2×D11)⋊C4—22no—
184(C2×D11)⋊C4—22no—
185(C2×D11)⋊C4—22no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192C4⋊Dic11—22no—
193C4⋊Dic11—22no—
194C4⋊Dic11—22no—
195C4⋊Dic11C22⋊C412yes—
196C4⋊Dic11C22⋊C412yes—
197Dic11⋊C4—22no—
198Dic11⋊C4—22no—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—21no—
203Dic11⋊C4—21no—
204Dic11⋊C4—21no—
205Dic11⋊C4—21no—
206Dic11⋊C4—21no—
207Dic11⋊C4—21no—
208Dic11⋊C4C22⋊C412yes—
209Dic11⋊C4C22⋊C412yes—
210Dic11⋊C4C22⋊C412yes—
211Dic11⋊C4C22⋊C412yes—
212C4×Dic11—22no—
213C4×Dic11—22no—
214C4×Dic11—22no—
215C4×Dic11C2×D412yes—
216C4×Dic11C2×D412yes—
217C4×Dic11C2×D412yes—
218C4×Dic11C2×D412yes—
219C2×C11⋊C8—22no—
220C2×C11⋊C8—22no—
221C2×#541—111no—
222#2983—111no—
223#2983—111no—
224#1473—111no—
225#1473—111no—
226#1473—112no—
227#1470—112no—
228#1470—111no—
229#1470D1111yescharacteristic, complemented
230#1467—112no—
231#1464—112no—
232C23×C11C23×C411yescharacteristic
233C22×D11—21no—
234C22×D11—22no—
235C22×D11—41no—
236C22×D11—41no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11C2×C22⋊C411yescharacteristic
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—22no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11C2×C22⋊C412yes—
265C2×Dic11C2×C22⋊C412yes—
266C2×Dic11C2×C22⋊C412yes—
267C2×Dic11C2×C22⋊C412yes—
268C4×D11—44no—
269Dic22—42no—
270Dic22—42no—
271Dic22—44no—
272C8×C11—42no—
273C8×C11—42no—
274C11⋊C8—42no—
275C11⋊C8—42no—
276#541—222no—
277#541—222no—
278#541—222no—
279#541—222no—
280C2×C4⋊Q8—111no—
281C2×#126—111no—
282C2×#126—111no—
283C2×#126—111no—
284C2×#126—111no—
285C2×#125—111no—
286C2×#125—111no—
287C2×#125—111no—
288C2×#125—111no—
289C2×#125C2×D1111yescharacteristic
290C2×C22⋊Q8—111no—
291C2×C22⋊Q8—111no—
292C2×C4×Q8—111no—
293C2×C4×Q8—111no—
294C2×#117—111no—
295#446—222no—
296#446—222no—
297#446—222no—
298#446—222no—
299#432—111no—
300#432—112no—
301#432—112no—
302#432—112no—
303#432C2×D1111yescharacteristic
304#431—111no—
305#431—112no—
306#431C2×D1111yescharacteristic
307#324—112no—
308#324—112no—
309#324—112no—
310#324—112no—
311#324C2×D1112yes—
312#324C2×D1112yes—
313#323—112no—
314#323—112no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11C22×C22⋊C411yescharacteristic
318C22×C11#56812yes—
319C2×D11—41no—
320C2×D11—41no—
321C2×D11—41no—
322C2×D11—82no—
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333Dic11—22no—
334Dic11—22no—
335Dic11—22no—
336Dic11—22no—
337Dic11—41no—
338Dic11—41no—
339Dic11—41no—
340C22×Q8—111no—
341C22×Q8—111no—
342C23×C4—111no—
343C4⋊Q8—222no—
344C4⋊Q8—222no—
345#126—222no—
346#126—222no—
347#126—222no—
348#126—222no—
349#126—222no—
350#126—222no—
351#126—221no—
352#126—221no—
353#126—221no—
354#126—221no—
355#125—21no—
356#125—21no—
357#125—21no—
358#125—21no—
359#125—222no—
360#125—222no—
361#125—222no—
362#125—222no—
363#125—222no—
364#125—222no—
365#125—222no—
366#125—222no—
367C22⋊Q8—222no—
368C22⋊Q8—222no—
369C22⋊Q8—222no—
370C22⋊Q8—222no—
371C4×Q8—112no—
372C4×Q8—112no—
373C4×Q8—112no—
374C4×Q8—112no—
375C4×Q8—222no—
376C4×Q8—222no—
377#117—222no—
378#117—222no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4C4×D1111yescharacteristic
394C2×C4⋊C4C4×D1111yescharacteristic
395C2×C4⋊C4C4×D1111yescharacteristic
396C2×C4⋊C4C4×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C22⋊C4—111no—
400C2×C22⋊C4—111no—
401C2×C22⋊C4—111no—
402C2×C22⋊C4—111no—
403C2×C22⋊C4—111no—
404C2×C22⋊C4—111no—
405C2×C42—111no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42—111no—
409C2×C42—111no—
410C2×C42C22×D1111yescharacteristic
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8—222no—
414C4⋊C8—222no—
415C4⋊C8—222no—
416C4⋊C8—222no—
417C4⋊C8—221no—
418C4⋊C8—221no—
419C22⋊C8—112no—
420C22⋊C8—112no—
421C22⋊C8C22×D1112yes—
422C22⋊C8C22×D1112yes—
423#97—21no—
424#97—222no—
425#97—222no—
426#97—222no—
427#97—221no—
428C4×C8—21no—
429C4×C8—222no—
430C4×C8—221no—
431C2×C11—22no—
432C2×C11#287911yescharacteristic
433C2×C11#288411yescharacteristic
434C2×C11#288911yescharacteristic
435D11—81no—
436C24—111no—
437C2×Q8—112no—
438C2×Q8—112no—
439C2×Q8—222no—
440C2×Q8—442no—
441C2×Q8—442no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—222no—
450C22×C4—442no—
451C22×C4C2×C4×D1111yescharacteristic
452C22×C4C2×C4×D1111yescharacteristic
453C22×C4C2×C4×D1111yescharacteristic
454C22×C4C2×C4×D1111yescharacteristic
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4C23×D1111yescharacteristic
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—222no—
461C2×C8—222no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—112no—
475C4⋊C4—112no—
476C4⋊C4—112no—
477C4⋊C4—112no—
478C4⋊C4—112no—
479C4⋊C4—112no—
480C4⋊C4—222no—
481C4⋊C4—222no—
482C4⋊C4—222no—
483C4⋊C4—222no—
484C4⋊C4—222no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C22⋊C4—222no—
495C22⋊C4—222no—
496C22⋊C4—222no—
497C22⋊C4—221no—
498C22⋊C4—221no—
499C22⋊C4—221no—
500C22⋊C4—221no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C42—112no—
504C42—112no—
505C42—112no—
506C42—112no—
507C42—222no—
508C42—222no—
509C42—222no—
510C42D4×D1111yescharacteristic
511C42D4×D1111yescharacteristic
512C42D4×D1111yescharacteristic
513C42D4×D1111yescharacteristic
514C11#1741011yescharacteristic, complemented, Sylow
515C23—221no—
516C23—222no—
517C23—441no—
518C23—441no—
519C23C22×C4×D1111yescharacteristic
520Q8—442no—
521Q8—442no—
522Q8—444no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—112no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—222no—
544C2×C4—444no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4C22⋊C4×D1111yescharacteristic
550C2×C4C22⋊C4×D1111yescharacteristic
551C2×C4C22⋊C4×D1111yescharacteristic
552C2×C4C22⋊C4×D1111yescharacteristic
553C2×C4C2×D4×D1111yescharacteristic
554C2×C4C2×D4×D1111yescharacteristic
555C8—42no—
556C8—42no—
557C8—442no—
558C8—442no—
559C22—21no—
560C22—21no—
561C22—441no—
562C22—441no—
563C22—441no—
564C22—882no—
565C22C2×C22⋊C4×D1111yescharacteristic
566C22#1062328112yes—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—222no—
578C4—222no—
579C4—222no—
580C4—222no—
581C4—441no—
582C4—441no—
583C4—441no—
584C2—22no—
585C2—881no—
586C2#1307705811yescharacteristic
587C2#1307707811yescharacteristic
588C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1470C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1470D11
hypocenterC11#17410
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1470

Complements

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

NH ≅ G/Ntype
2. #13077700C2semidirect
3. #13077699C2semidirect
7. #13066972C2semidirect
8. #13066970C2semidirect
9. #13066958C2semidirect
11. C11×#1470C2semidirect
229. #1470D11semidirect
514. C11#17410semidirect

Maximal subgroups

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

subgroupindex
C2×#106232272
#130777002
#130776992
#130669862
#130669842
#130669832
#130669722
#130669702
#130669582
#130669492
C11×#14702
#1741011