Finite Group Databasebeta

← #14719944

Subgroups — #14719944

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623241C211yesmaximal, characteristic
2#13077700C211yesmaximal, characteristic, complemented
3#13077699C211yesmaximal, characteristic, complemented
4#13066985C211yesmaximal, characteristic, complemented
5#13066984C212yesmaximal, complemented
6#13066969C211yesmaximal, characteristic, complemented
7#13066967C211yesmaximal, characteristic, complemented
8#13066966C212yesmaximal, complemented
9#13066955C212yesmaximal, complemented
10#13066949C212yesmaximal, complemented
11C11×#1473C211yesmaximal, characteristic, complemented
12C2×C11×#126C2211yescharacteristic
13#10623241—22no—
14#10623241—22no—
15#10623241—22no—
16#10623241—22no—
17C2×#66951C2211yescharacteristic
18C2×#66950C411yescharacteristic
19C2×#66949C411yescharacteristic
20C2×#66947C411yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×#66941C411yescharacteristic
23C2×#66939C411yescharacteristic
24C2×#66938C411yescharacteristic
25C2×#66938C2211yescharacteristic
26C2×#66937C411yescharacteristic
27C2×(C22⋊D11)⋊C4C2211yescharacteristic
28C2×#66931C411yescharacteristic
29C2×#66928C2211yescharacteristic
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×#323C2212yes—
45#10622166C2212yes—
46#10622163C2212yes—
47#10622106C2212yes—
48#10622106C2212yes—
49#10622106C2212yes—
50#10622106C2212yes—
51C22×C22⋊D11C2×C411yescharacteristic
52C22×C22⋊D11C2×C411yescharacteristic
53C23×Dic11C2×C411yescharacteristic
54C22×D44C2×C411yescharacteristic
55C22×C4×D11C2×C411yescharacteristic
56C22×C4×D11C2×C411yescharacteristic
57C22×Dic22C2×C411yescharacteristic
58C22×Dic22C2×C411yescharacteristic
59C22×Dic22C2×C411yescharacteristic
60C11×#126—21no—
61C11×#126—21no—
62C11×#126—21no—
63C11×#126—21no—
64C2×C11×C4⋊C4C2×C411yescharacteristic
65C2×C11×C4⋊C4C2×C411yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4C2×C411yescharacteristic
68C2×C11×C22⋊C4C2×C411yescharacteristic
69C2×C11×C22⋊C4C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11C2×C411yescharacteristic
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78C2×(C2×D11)⋊C4C2311yescharacteristic
79C2×(C2×D11)⋊C4C2311yescharacteristic
80C2×C4⋊Dic11C2×C411yescharacteristic
81C2×C4⋊Dic11C2×C411yescharacteristic
82C2×C4⋊Dic11C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90#66951—22no—
91#66951—22no—
92#66950—22no—
93#66950—22no—
94#66949—22no—
95#66949—22no—
96#66947—22no—
97#66947—22no—
98#66945—22no—
99#66945—22no—
100#66941—22no—
101#66941—22no—
102#66939—22no—
103#66939—22no—
104#66938—22no—
105#66938—22no—
106#66938—22no—
107#66938—22no—
108#66937—22no—
109#66937—22no—
110(C22⋊D11)⋊C4—22no—
111(C22⋊D11)⋊C4—22no—
112#66931—22no—
113#66931—22no—
114#66928—21no—
115#66928—21no—
116#66928—21no—
117#66928—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#17409—111nomaximal, Sylow
143C24×C11C22×C411yescharacteristic
144C23×D11C22×C411yescharacteristic
145C23×D11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—22no—
153C2×C22⋊D11—22no—
154C2×C22⋊D11—42no—
155C2×C22⋊D11—81no—
156C22×Dic11—22no—
157C22×Dic11—81no—
158C22×Dic11C22×C411yescharacteristic
159C22×Dic11C22×C411yescharacteristic
160C22×Dic11C22×C411yescharacteristic
161C22×Dic11C22×C411yescharacteristic
162C22×Dic11C22×C411yescharacteristic
163C22×Dic11C22×C411yescharacteristic
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—81no—
167C2×C4×D11—22no—
168C2×C4×D11—22no—
169C2×C4×D11—42no—
170C2×C4×D11—81no—
171C2×Dic22—22no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—42no—
175C2×Dic22—81no—
176C2×Dic22—81no—
177C2×Dic22C22⋊C412yes—
178C2×Dic22C22⋊C412yes—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C22⋊Dic11—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—21no—
203(C2×D11)⋊C4—21no—
204(C2×D11)⋊C4—21no—
205(C2×D11)⋊C4—21no—
206(C2×D11)⋊C4—21no—
207(C2×D11)⋊C4—21no—
208(C2×D11)⋊C4—21no—
209(C2×D11)⋊C4—21no—
210C4⋊Dic11—22no—
211C4⋊Dic11—22no—
212C4⋊Dic11C22⋊C412yes—
213C4⋊Dic11C22⋊C412yes—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4C22⋊C412yes—
217Dic11⋊C4C22⋊C412yes—
218Dic11⋊C4C22⋊C412yes—
219Dic11⋊C4C22⋊C412yes—
220C4×Dic11—22no—
221C4×Dic11C2×D412yes—
222C4×Dic11C2×D412yes—
223C4×Dic11C2×D412yes—
224C4×Dic11C2×D412yes—
225C2×C11⋊C8—22no—
226C2×C11⋊C8—22no—
227C2×#542—111no—
228#2983—111no—
229#2983—111no—
230#1473—112no—
231#1473—111no—
232#1473D1111yescharacteristic, complemented
233#1469—111no—
234#1469—111no—
235#1469—112no—
236#1466—112no—
237#1464—112no—
238C23×C11—21no—
239C23×C11—22no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11C23×C411yescharacteristic
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C22⋊D11—44no—
267C22⋊D11—82no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—82no—
277C2×Dic11C2×C22⋊C412yes—
278C2×Dic11C2×C22⋊C412yes—
279C2×Dic11C2×C22⋊C412yes—
280C2×Dic11C2×C22⋊C412yes—
281D44—81no—
282D44—81no—
283C4×D11—44no—
284C4×D11—82no—
285Dic22—42no—
286Dic22—42no—
287Dic22—82no—
288Dic22—81no—
289Dic22—81no—
290C8×C11—42no—
291C8×C11—42no—
292C11⋊C8—42no—
293C11⋊C8—42no—
294#542—222no—
295#542—222no—
296#542—222no—
297#542—222no—
298C2×C4⋊Q8—111no—
299C2×#126—111no—
300C2×#126C2×D1111yescharacteristic
301C2×#124—111no—
302C2×#124—111no—
303C2×#124—111no—
304C2×#123—111no—
305C2×#123—111no—
306C2×C22⋊Q8—111no—
307C2×C22⋊Q8—111no—
308C2×C22⋊Q8—111no—
309C2×#121—111no—
310C2×C4×Q8—111no—
311C2×C4×D4—111no—
312C2×#117—111no—
313#446—222no—
314#446—222no—
315#446—222no—
316#446—222no—
317#432—111no—
318#432—112no—
319#432—112no—
320#432—112no—
321#432C2×D1111yescharacteristic
322#431—111no—
323#431—112no—
324#431C2×D1111yescharacteristic
325#324—112no—
326#324C2×D1112yes—
327#323—112no—
328#323—112no—
329#323—112no—
330#323—112no—
331#323—112no—
332#323C2×D1112yes—
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—82no—
339C22×C11C22×C22⋊C411yescharacteristic
340C22×C11#56812yes—
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—82no—
348C2×D11—82no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—41no—
358Dic11—22no—
359Dic11—22no—
360Dic11—22no—
361Dic11—22no—
362Dic11—41no—
363Dic11—41no—
364C22×Q8—111no—
365C22×Q8—111no—
366C22×Q8—111no—
367C22×D4—111no—
368C22×D4—111no—
369C22×D4—111no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—111no—
373C4⋊Q8—222no—
374C4⋊Q8—222no—
375#126—21no—
376#126—21no—
377#126—21no—
378#126—21no—
379#126—222no—
380#126—222no—
381#124—222no—
382#124—222no—
383#124—222no—
384#124—222no—
385#124—221no—
386#124—221no—
387#124—221no—
388#124—221no—
389#123—222no—
390#123—222no—
391#123—222no—
392#123—222no—
393C22⋊Q8—222no—
394C22⋊Q8—222no—
395C22⋊Q8—222no—
396C22⋊Q8—222no—
397C22⋊Q8—222no—
398C22⋊Q8—222no—
399#121—222no—
400#121—222no—
401C4×Q8—112no—
402C4×Q8—112no—
403C4×Q8—112no—
404C4×Q8—112no—
405C4×D4—222no—
406C4×D4—222no—
407#117—222no—
408#117—222no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4C4×D1111yescharacteristic
417C2×C4⋊C4C4×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C22⋊C4—111no—
420C2×C22⋊C4—111no—
421C2×C22⋊C4—111no—
422C2×C22⋊C4—111no—
423C2×C22⋊C4—111no—
424C2×C22⋊C4—111no—
425C2×C22⋊C4—111no—
426C2×C22⋊C4—111no—
427C2×C22⋊C4—111no—
428C2×C22⋊C4C4×D1111yescharacteristic
429C2×C22⋊C4C4×D1111yescharacteristic
430C2×C22⋊C4C22×D1111yescharacteristic
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42C22×D1111yescharacteristic
435C4⋊C8—21no—
436C4⋊C8—21no—
437C4⋊C8—222no—
438C4⋊C8—222no—
439C4⋊C8—222no—
440C4⋊C8—222no—
441C4⋊C8—221no—
442C4⋊C8—221no—
443C22⋊C8—112no—
444C22⋊C8—112no—
445C22⋊C8C22×D1112yes—
446C22⋊C8C22×D1112yes—
447#97—21no—
448#97—222no—
449#97—222no—
450#97—222no—
451#97—221no—
452C4×C8—21no—
453C4×C8—222no—
454C4×C8—221no—
455C2×C11—22no—
456C2×C11—81no—
457C2×C11#287911yescharacteristic
458C2×C11#288411yescharacteristic
459C2×C11#288811yescharacteristic
460D11—81no—
461D11—81no—
462C24—111no—
463C24—111no—
464C24C2×C4×D1111yescharacteristic
465C2×Q8—112no—
466C2×Q8—112no—
467C2×Q8—222no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—442no—
471C2×Q8—881no—
472C2×Q8—881no—
473C2×D4—222no—
474C2×D4—222no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—442no—
478C2×D4—881no—
479C2×D4—881no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—442no—
490C22×C4—881no—
491C22×C4—881no—
492C22×C4C2×C4×D1111yescharacteristic
493C22×C4C2×C4×D1111yescharacteristic
494C22×C4C2×C4×D1111yescharacteristic
495C22×C4C2×C4×D1111yescharacteristic
496C22×C4C2×C4×D1111yescharacteristic
497C22×C4C23×D1111yescharacteristic
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—222no—
501C2×C8—222no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—112no—
509C4⋊C4—112no—
510C4⋊C4—112no—
511C4⋊C4—112no—
512C4⋊C4—112no—
513C4⋊C4—112no—
514C4⋊C4—222no—
515C4⋊C4—222no—
516C4⋊C4—222no—
517C4⋊C4—222no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—222no—
525C22⋊C4—222no—
526C22⋊C4—222no—
527C22⋊C4—222no—
528C22⋊C4—222no—
529C22⋊C4—221no—
530C22⋊C4—221no—
531C22⋊C4—221no—
532C22⋊C4—221no—
533C22⋊C4—221no—
534C22⋊C4—221no—
535C22⋊C4—221no—
536C22⋊C4—221no—
537C42—112no—
538C42—112no—
539C42—112no—
540C42—112no—
541C42—222no—
542C42D4×D1111yescharacteristic
543C42D4×D1111yescharacteristic
544C42D4×D1111yescharacteristic
545C42D4×D1111yescharacteristic
546C11#1740911yescharacteristic, complemented, Sylow
547C23—21no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—221no—
552C23—221no—
553C23—222no—
554C23—222no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23C22×C4×D1111yescharacteristic
560Q8—442no—
561Q8—442no—
562Q8—881no—
563Q8—881no—
564Q8—882no—
565D4—444no—
566D4—881no—
567D4—881no—
568D4—882no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—112no—
579C2×C4—112no—
580C2×C4—112no—
581C2×C4—112no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—444no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—882no—
592C2×C4—882no—
593C2×C4C22⋊C4×D1111yescharacteristic
594C2×C4C22⋊C4×D1111yescharacteristic
595C2×C4C22⋊C4×D1111yescharacteristic
596C2×C4C22⋊C4×D1111yescharacteristic
597C2×C4C2×D4×D1111yescharacteristic
598C2×C4C2×D4×D1111yescharacteristic
599C8—42no—
600C8—42no—
601C8—442no—
602C8—442no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—82no—
609C22—441no—
610C22—441no—
611C22—441no—
612C22—441no—
613C22—441no—
614C22—441no—
615C22—882no—
616C22—882no—
617C22C2×C22⋊C4×D1111yescharacteristic
618C22#1062328112yes—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—222no—
629C4—222no—
630C4—222no—
631C4—222no—
632C4—441no—
633C4—441no—
634C2—22no—
635C2—81no—
636C2—881no—
637C2—881no—
638C2#1307705811yescharacteristic
639C2#1307707811yescharacteristic
640C2#1307709311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1473C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66937C4
cosocleC22×C4×C11C24
hypercenter#1473D11
hypocenterC11#17409
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #13077700C2semidirect
3. #13077699C2semidirect
4. #13066985C2semidirect
5. #13066984C2semidirect
6. #13066969C2semidirect
7. #13066967C2semidirect
8. #13066966C2semidirect
9. #13066955C2semidirect
10. #13066949C2semidirect
11. C11×#1473C2semidirect
232. #1473D11semidirect
546. C11#17409semidirect

Maximal subgroups

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

subgroupindex
C2×#106232412
#130777002
#130776992
#130669852
#130669842
#130669692
#130669672
#130669662
#130669552
#130669492
C11×#14732
#1740911