Finite Group Databasebeta

← #14719974

Subgroups — #14719974

Order 2816.

944 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623060C211yesmaximal, characteristic
2#13077274C211yesmaximal, characteristic, complemented
3#13066981C211yesmaximal, characteristic, complemented
4#13066979C211yesmaximal, characteristic, complemented
5#13066973C212yesmaximal, complemented
6#13066971C212yesmaximal, complemented
7#13066952C211yesmaximal, characteristic
8#13066948C212yesmaximal, complemented
9#13066932C211yesmaximal, characteristic
10#13066928C212yesmaximal, complemented
11C11×#2924C211yesmaximal, characteristic, complemented
12C2×C11×#117C2211yescharacteristic
13C2×C4×C22⋊D11C2211yescharacteristic
14C2×#66977C2211yescharacteristic
15#10623060—21no—
16#10623060—21no—
17#10623060—22no—
18#10623060—21no—
19#10623060—21no—
20#10623060—22no—
21C2×#66950C411yescharacteristic
22C2×C4⋊C4×D11C411yescharacteristic
23C2×#66943C411yescharacteristic
24C2×#66940C411yescharacteristic
25C2×#66936C412yes—
26C2×#66932C412yes—
27C2×#66925C2212yes—
28C2×#66923C2212yes—
29C11×#433—22no—
30C11×#432C2212yes—
31C11×#431C2212yes—
32C11×#424—21no—
33C11×#407C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C11×#405—21no—
36#10622820C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38#10622613—22no—
39#10622612—21no—
40#10622610—21no—
41#10622539C2212yes—
42#10622538C2212yes—
43#10622107C2212yes—
44#10622107C2212yes—
45#10622107C2211yescharacteristic
46#10622107C2211yescharacteristic
47#10622107C2212yes—
48#10622107C2212yes—
49#10622107C2212yes—
50#10622106C2211yescharacteristic
51#10622106C2212yes—
52#10622106C2211yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11C2×C411yescharacteristic
55C22×C4×D11C2×C412yes—
56C22×C4×D11C2×C411yescharacteristic
57C22×Dic22C2×C411yescharacteristic
58C2×C11×M16—21no—
59C22×C8×C11—21no—
60C11×#117D411yescharacteristic
61C11×#117D411yescharacteristic
62C11×#117D412yes—
63C11×#117D411yescharacteristic
64C11×#117D411yescharacteristic
65C11×#117D412yes—
66C2×C11×C4⋊C4C2×C411yescharacteristic
67C2×C11×C4⋊C4C2×C411yescharacteristic
68C2×C11×C22⋊C4C2×C412yes—
69C2×C42×C11C2312yes—
70C2×C22⋊Dic11C2×C411yescharacteristic
71C2×C22⋊Dic11C2×C412yes—
72C4×C22⋊D11—21no—
73C4×C22⋊D11—21no—
74C4×C22⋊D11—21no—
75C4×C22⋊D11—21no—
76C2×(C2×D11)⋊C4C2×C412yes—
77C2×(C2×D11)⋊C4C2311yescharacteristic
78C2×C4⋊Dic11C2×C412yes—
79C2×C4⋊Dic11C2×C412yes—
80C2×C4⋊Dic11C2×C411yescharacteristic
81#66977—21no—
82#66977—21no—
83#66977—21no—
84#66977—21no—
85C2×Dic11⋊C4C2×C412yes—
86C2×Dic11⋊C4C2×C412yes—
87C2×Dic11⋊C4C2×C412yes—
88C2×Dic11⋊C4C2311yescharacteristic
89C2×Dic11⋊C4C2312yes—
90C2×C4×Dic11C2×C412yes—
91C2×C4×Dic11C2×C411yescharacteristic
92C2×#4318—21no—
93C22×C11⋊C8—21no—
94#66950—22no—
95#66950—21no—
96#66950—21no—
97C4⋊C4×D11—22no—
98C4⋊C4×D11—21no—
99C4⋊C4×D11—21no—
100#66943—22no—
101#66943—21no—
102#66943—21no—
103#66940—22no—
104#66940—21no—
105#66940—21no—
106#66936—22no—
107#66936—22no—
108#66936—22no—
109#66936—22no—
110#66932—22no—
111#66932—22no—
112#66932—22no—
113#66932—22no—
114#66925—22no—
115#66925—22no—
116#66925—22no—
117#66925—22no—
118#66923—22no—
119#66923—22no—
120#66923—22no—
121#66923—22no—
122C11×C4⋊C8—22no—
123C11×C4⋊C8—22no—
124C11×C22⋊C8—21no—
125C11×C22⋊C8—21no—
126C11×C22⋊C8C2311yescharacteristic
127C11×C22⋊C8C2311yescharacteristic
128C11×C22⋊C8C2312yes—
129C11×#97—22no—
130C4×C8×C11—22no—
131C22⋊(C11⋊C8)—21no—
132C22⋊(C11⋊C8)—21no—
133C22⋊(C11⋊C8)C2311yescharacteristic
134C22⋊(C11⋊C8)C2312yes—
135C22⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)—22no—
137C4⋊(C11⋊C8)—22no—
138#66867—22no—
139C4×C11⋊C8—22no—
140#17413—111nomaximal, Sylow
141C24×C11C22×C411yescharacteristic
142C23×D11C22×C411yescharacteristic
143C22×C4×C11—42no—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—21no—
153C2×C22⋊D11—21no—
154C2×C22⋊D11—22no—
155C2×C22⋊D11—41no—
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C412yes—
158C22×Dic11C22×C411yescharacteristic
159C22×Dic11C22×C412yes—
160C22×Dic11C22×C411yescharacteristic
161C2×C4×D11—24no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—42no—
171C11×M16—42no—
172C2×C8×C11—21no—
173C2×C8×C11—22no—
174C2×C8×C11—21no—
175C2×C8×C11—42no—
176C11×C4⋊C4C22⋊C412yes—
177C11×C4⋊C4C22⋊C411yescharacteristic
178C11×C4⋊C4C22⋊C411yescharacteristic
179C11×C4⋊C4C22⋊C412yes—
180C11×C4⋊C4C22⋊C411yescharacteristic
181C11×C4⋊C4C22⋊C411yescharacteristic
182C11×C22⋊C4C22⋊C412yes—
183C11×C22⋊C4C22⋊C412yes—
184C11×C22⋊C4C22⋊C412yes—
185C11×C22⋊C4C22⋊C412yes—
186C42×C11C2×D412yes—
187C42×C11C2×D412yes—
188C42×C11C2×D412yes—
189C42×C11C2×D412yes—
190C22⋊Dic11—21no—
191C22⋊Dic11—21no—
192C22⋊Dic11—22no—
193C22⋊Dic11—22no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—21no—
197(C2×D11)⋊C4—21no—
198C4⋊Dic11—22no—
199C4⋊Dic11—22no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—21no—
211Dic11⋊C4—21no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214C4×Dic11—22no—
215C4×Dic11—22no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218#4318—42no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—22no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—42no—
223C2×#552—111no—
224#2924—111no—
225#2924D1111yescharacteristic, complemented
226#1472—111no—
227#1472—111no—
228#1470—112no—
229#1470—112no—
230#1465—111no—
231#1464—112no—
232#1459—111no—
233#1458—112no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11C2×C22⋊C411yescharacteristic
239C23×C11C2×C22⋊C411yescharacteristic
240C23×C11C23×C411yescharacteristic
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11#13112yes—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11C2×C22⋊C412yes—
256C2×C4×C11C2×C22⋊C412yes—
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C2×C22⋊C412yes—
259C2×C4×C11C2×C22⋊C412yes—
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C22⋊D11—42no—
264C22⋊D11—42no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—21no—
270C2×Dic11—22no—
271C2×Dic11—21no—
272C2×Dic11—22no—
273C2×Dic11—21no—
274C2×Dic11—42no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C4×D11—44no—
278C4×D11—44no—
279C4×D11—42no—
280C4×D11—42no—
281Dic22—42no—
282Dic22—42no—
283C8×C11—41no—
284C8×C11—41no—
285C8×C11—42no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288C11⋊C8—42no—
289#552—221no—
290#552—221no—
291#552—222no—
292#552—221no—
293#552—221no—
294#552—222no—
295C2×#126—112no—
296C2×#125—111no—
297C2×#125—112no—
298C2×#123—112no—
299C2×C22⋊Q8—111no—
300C2×C22⋊Q8—111no—
301C2×C4×Q8—111no—
302C2×C4×D4—111no—
303C2×#117—112no—
304C2×#117C2×D1111yescharacteristic
305C22×C4⋊C4—111no—
306#433—22no—
307#433—222no—
308#432—112no—
309#432C2×D1112yes—
310#431—112no—
311#431C2×D1112yes—
312#424—21no—
313#424—221no—
314#407—111no—
315#407C2×D1111yescharacteristic
316C2×C22⋊C8—111no—
317C2×C22⋊C8C2×D1111yescharacteristic
318#405—21no—
319#405—221no—
320#324—112no—
321#324—112no—
322#324—111no—
323#324—111no—
324#324—112no—
325#324—112no—
326#324—112no—
327#323—111no—
328#323—112no—
329#323—111no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11C22×C22⋊C411yescharacteristic
341C22×C11C2×#13111yescharacteristic
342C22×C11#56811yescharacteristic
343C2×D11—22no—
344C2×D11—42no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—42no—
348C4×C11—22no—
349C4×C11—22no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—22no—
354C4×C11—22no—
355C4×C11#41012yes—
356Dic11—42no—
357Dic11—41no—
358Dic11—42no—
359Dic11—41no—
360Dic11—41no—
361C22×Q8—111no—
362C22×D4—111no—
363C23×C4—112no—
364C23×C4—111no—
365C23×C4C22×D1111yescharacteristic
366C2×M16—21no—
367C2×M16—221no—
368C22×C8—21no—
369C22×C8—221no—
370#126—222no—
371#126—222no—
372#126—222no—
373#126—222no—
374#125—222no—
375#125—221no—
376#125—221no—
377#125—222no—
378#125—222no—
379#125—222no—
380#125—222no—
381#123—222no—
382#123—222no—
383#123—222no—
384#123—222no—
385C22⋊Q8—221no—
386C22⋊Q8—221no—
387C22⋊Q8—221no—
388C22⋊Q8—221no—
389C22⋊Q8—222no—
390C22⋊Q8—221no—
391C22⋊Q8—221no—
392C4×Q8—222no—
393C4×Q8—221no—
394C4×Q8—221no—
395C4×D4—221no—
396C4×D4—221no—
397C4×D4—221no—
398C4×D4—221no—
399#117—222no—
400#117—222no—
401#117—222no—
402#117—222no—
403#117D4411yescharacteristic
404#117D4411yescharacteristic
405#117D4412yes—
406#117C22⋊D1111yescharacteristic
407#117C22⋊D1111yescharacteristic
408#117C22⋊D1112yes—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—112no—
411C2×C4⋊C4—112no—
412C2×C4⋊C4—112no—
413C2×C4⋊C4—112no—
414C2×C4⋊C4—112no—
415C2×C4⋊C4—112no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—222no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4C4×D1111yescharacteristic
421C2×C4⋊C4C4×D1111yescharacteristic
422C2×C22⋊C4—111no—
423C2×C22⋊C4—112no—
424C2×C22⋊C4—112no—
425C2×C22⋊C4—111no—
426C2×C22⋊C4C4×D1112yes—
427C2×C42—112no—
428C2×C42—111no—
429C2×C42C22×D1112yes—
430C4⋊C8—22no—
431C4⋊C8—22no—
432C4⋊C8—222no—
433C4⋊C8—222no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—111no—
437C22⋊C8—111no—
438C22⋊C8—112no—
439C22⋊C8—221no—
440C22⋊C8—221no—
441C22⋊C8C22×D1111yescharacteristic
442C22⋊C8C22×D1111yescharacteristic
443C22⋊C8C22×D1112yes—
444#97—22no—
445#97—222no—
446C4×C8—22no—
447C4×C8—222no—
448C2×C11—21no—
449C2×C11—21no—
450C2×C11—41no—
451C2×C11—41no—
452C2×C11#288011yescharacteristic
453C2×C11C2×#41011yescharacteristic
454C2×C11#288911yescharacteristic
455D11—42no—
456C24—111no—
457C24C2×C4×D1111yescharacteristic
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—442no—
461C2×D4—222no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—441no—
465C22×C4—42no—
466C22×C4—111no—
467C22×C4—112no—
468C22×C4—111no—
469C22×C4—112no—
470C22×C4—111no—
471C22×C4—224no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4C2×C4×D1112yes—
479C22×C4C2×C4×D1111yescharacteristic
480C22×C4C2×C4×D1112yes—
481C22×C4C2×D4411yescharacteristic
482C22×C4C2×D4411yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C23×D1111yescharacteristic
486M16—42no—
487M16—442no—
488C2×C8—21no—
489C2×C8—22no—
490C2×C8—21no—
491C2×C8—42no—
492C2×C8—221no—
493C2×C8—222no—
494C2×C8—221no—
495C2×C8—442no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—222no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—221no—
510C4⋊C4—222no—
511C4⋊C4—221no—
512C4⋊C4(C2×D11)⋊C412yes—
513C4⋊C4(C2×D11)⋊C411yescharacteristic
514C4⋊C4(C2×D11)⋊C411yescharacteristic
515C4⋊C4(C2×D11)⋊C412yes—
516C4⋊C4(C2×D11)⋊C411yescharacteristic
517C4⋊C4(C2×D11)⋊C411yescharacteristic
518C22⋊C4—221no—
519C22⋊C4—221no—
520C22⋊C4—222no—
521C22⋊C4—222no—
522C22⋊C4—222no—
523C22⋊C4—222no—
524C22⋊C4—221no—
525C22⋊C4—221no—
526C22⋊C4(C2×D11)⋊C412yes—
527C22⋊C4(C2×D11)⋊C412yes—
528C22⋊C4(C2×D11)⋊C412yes—
529C22⋊C4(C2×D11)⋊C412yes—
530C42—222no—
531C42—222no—
532C42—221no—
533C42—221no—
534C42C2×D4412yes—
535C42C2×D4412yes—
536C42C2×C22⋊D1112yes—
537C42C2×C22⋊D1112yes—
538C11#1741311yescharacteristic, complemented, Sylow
539C23—21no—
540C23—21no—
541C23—41no—
542C23—41no—
543C23—112no—
544C23—221no—
545C23—221no—
546C23—441no—
547C23—441no—
548C23C2×(C2×D11)⋊C411yescharacteristic
549C23C2×(C2×D11)⋊C411yescharacteristic
550C23C22×C4×D1111yescharacteristic
551Q8—442no—
552Q8—442no—
553D4—442no—
554D4—442no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—222no—
565C2×C4—221no—
566C2×C4—222no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—222no—
570C2×C4—221no—
571C2×C4—222no—
572C2×C4—221no—
573C2×C4—444no—
574C2×C4—444no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—441no—
578C2×C4—442no—
579C2×C4—441no—
580C2×C4C2×(C2×D11)⋊C412yes—
581C2×C4C2×(C2×D11)⋊C412yes—
582C2×C4C2×(C2×D11)⋊C411yescharacteristic
583C2×C4C2×(C2×D11)⋊C412yes—
584C2×C4C2×(C2×D11)⋊C412yes—
585C2×C4C2×(C2×D11)⋊C411yescharacteristic
586C2×C4C22×D4411yescharacteristic
587C2×C4C22×C22⋊D1111yescharacteristic
588C8—41no—
589C8—41no—
590C8—42no—
591C8—441no—
592C8—441no—
593C8—442no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—81no—
603C22—81no—
604C22—222no—
605C22—442no—
606C22—442no—
607C22—441no—
608C22—441no—
609C22D11×#13111yescharacteristic
610C22#1062328111yescharacteristic
611C22C22×(C2×D11)⋊C411yescharacteristic
612C4—22no—
613C4—22no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—22no—
618C4—22no—
619C4—442no—
620C4—441no—
621C4—441no—
622C4—442no—
623C4—441no—
624C4#1062261912yes—
625C2—21no—
626C2—21no—
627C2—41no—
628C2—41no—
629C2—442no—
630C2#1307706311yescharacteristic
631C2C2×#1062261911yescharacteristic
632C2#1307709811yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2924C2
socleC22×C11C22×C22⋊C4
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#2924D11
hypocenterC11#17413
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #13077274C2semidirect
3. #13066981C2semidirect
4. #13066979C2semidirect
5. #13066973C2semidirect
6. #13066971C2semidirect
8. #13066948C2semidirect
10. #13066928C2semidirect
11. C11×#2924C2semidirect
225. #2924D11semidirect
538. C11#17413semidirect

Maximal subgroups

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

subgroupindex
C2×#106230602
#130772742
#130669812
#130669792
#130669732
#130669712
#130669522
#130669482
#130669322
#130669282
C11×#29242
#1741311