Finite Group Databasebeta

← #14771574

Subgroups — #14771574

Order 2816.

744 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071020C211yesmaximal, characteristic
2#13069333C211yesmaximal, characteristic, complemented
3#13069331C211yesmaximal, characteristic, complemented
4#13069182C211yesmaximal, characteristic, complemented
5#13069181C211yesmaximal, characteristic, complemented
6#13069172C211yesmaximal, characteristic, complemented
7#13068599C211yesmaximal, characteristic
8#13068597C211yesmaximal, characteristic
9#13068595C211yesmaximal, characteristic
10#13068482C211yesmaximal, characteristic, complemented
11C8×Dic11⋊C4C211yesmaximal, characteristic, complemented
12#13068383C211yesmaximal, characteristic
13#13068381C211yesmaximal, characteristic
14#13068373C211yesmaximal, characteristic
15C11×#1916C211yesmaximal, characteristic, complemented
16C2×#66925C2211yescharacteristic
17C2×#66925C2211yescharacteristic
18C2×C42×D11C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C8C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622600C411yescharacteristic
35#10622600C411yescharacteristic
36#10622589C411yescharacteristic
37#10622589C411yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39C4×Dic11⋊C4C2211yescharacteristic
40C4×Dic11⋊C4C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43#10622280C411yescharacteristic
44#10622280C411yescharacteristic
45#10622263C411yescharacteristic
46#10622263C411yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×C4×D11C2×C411yescharacteristic
60C22×C4×D11C2×C411yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4C2×C411yescharacteristic
67C2×C11×C4⋊C4C2×C411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4C2×C411yescharacteristic
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×C4⋊Dic11C2×C411yescharacteristic
76C2×C4⋊Dic11C2×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⋊C4C2×C411yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66925—41no—
95#66925—41no—
96#66925—41no—
97#66925—41no—
98C42×D11—22no—
99C42×D11—22no—
100C11×C4⋊C8—41no—
101C4×C8×C11—41no—
102C11×#95C2×C411yescharacteristic
103C11×#95C2×C411yescharacteristic
104C11⋊#95C2×C411yescharacteristic
105C11⋊#95C2×C411yescharacteristic
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110(C2×D11)⋊C8—22no—
111(C2×D11)⋊C8—22no—
112(C2×D11)⋊C8—22no—
113(C2×D11)⋊C8Q814yes—
114#66879—41no—
115Dic11⋊C8—22no—
116Dic11⋊C8—22no—
117Dic11⋊C8—41no—
118Dic11⋊C8—41no—
119C8×Dic11—22no—
120C8×Dic11—22no—
121C8×Dic11—41no—
122C4⋊(C11⋊C8)—41no—
123#66867—41no—
124#22626—111nomaximal, Sylow
125C23×D11C22×C411yescharacteristic
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11C22×C411yescharacteristic
134C22×Dic11C22×C411yescharacteristic
135C22×Dic11C22×C411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C411yescharacteristic
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—41no—
150C2×C4×D11C2×Q812yes—
151C2×C4×D11#4112yes—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C2×Q812yes—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—41no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172(C2×D11)⋊C4—41no—
173(C2×D11)⋊C4—41no—
174(C2×D11)⋊C4—41no—
175(C2×D11)⋊C4—41no—
176C4⋊Dic11—22no—
177C4⋊Dic11—41no—
178Dic11⋊C4—22no—
179Dic11⋊C4—22no—
180Dic11⋊C4—22no—
181Dic11⋊C4—22no—
182Dic11⋊C4—41no—
183Dic11⋊C4—41no—
184Dic11⋊C4—41no—
185Dic11⋊C4—41no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11#4112yes—
193C4×Dic11#4112yes—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C2×Q812yes—
206#2285—111no—
207#1939—111no—
208#1939—111no—
209#1917—111no—
210#1917—111no—
211#1916—111no—
212#1916D1111yescharacteristic, complemented
213#1798—111no—
214#1798—111no—
215#1797—111no—
216#1770—111no—
217C8×C4⋊C4—111no—
218#1750—111no—
219#1750—111no—
220C4×C22⋊C8—111no—
221C23×C11C23×C411yescharacteristic
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—21no—
228C22×D11C4×Q812yes—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11#13112yes—
247C2×C4×C11C22×Q811yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11#11712yes—
270C2×Dic11#11712yes—
271C2×Dic11C4×Q812yes—
272C2×Dic11#13112yes—
273C2×Dic11#13112yes—
274C4×D11—22no—
275C4×D11—22no—
276C4×D11—22no—
277C4×D11—22no—
278C4×D11—44no—
279C4×D11—44no—
280C8×C11—22no—
281C8×C11—41no—
282C8×C11—41no—
283C8×C11—41no—
284C11⋊C8—22no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288C2×#117—111no—
289C2×#117—111no—
290C22×C42—111no—
291C2×C4⋊C8—111no—
292C2×C4⋊C8—111no—
293C2×C4⋊C8—111no—
294C2×C4⋊C8—111no—
295C2×C4⋊C8—111no—
296C2×C4⋊C8C2×D1111yescharacteristic
297C2×C22⋊C8—111no—
298C2×C22⋊C8—111no—
299C2×C22⋊C8—111no—
300C2×C22⋊C8—111no—
301C2×#97—111no—
302C2×#97—111no—
303C2×C4×C8—111no—
304C2×C4×C8—111no—
305C2×C4×C8—111no—
306C2×C4×C8C2×D1111yescharacteristic
307#384—111no—
308#384—111no—
309#382—111no—
310#382—111no—
311#380—111no—
312#380—111no—
313#380—111no—
314#380—111no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—111no—
318C4×C4⋊C4C2×D1111yescharacteristic
319#336—111no—
320#336—111no—
321#336—111no—
322#336—111no—
323#336—111no—
324#336—111no—
325#336—111no—
326#336—111no—
327#336C2×D1111yescharacteristic
328#336C2×D1111yescharacteristic
329#336C2×D1111yescharacteristic
330#336C2×D1111yescharacteristic
331C22×C11C2×#11711yescharacteristic
332C22×C11C2×C4×Q811yescharacteristic
333C22×C11#51811yescharacteristic
334C22×C11C2×#13111yescharacteristic
335C22×C11C2×#13111yescharacteristic
336C22×C11C2×#13111yescharacteristic
337C22×C11#56811yescharacteristic
338C2×D11—22no—
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C4×C11—22no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11#55311yescharacteristic
352C4×C11#55311yescharacteristic
353C4×C11#55411yescharacteristic
354C4×C11#55411yescharacteristic
355Dic11—22no—
356Dic11—22no—
357Dic11—41no—
358Dic11—41no—
359Dic11—41no—
360Dic11—41no—
361Dic11#43314yes—
362C23×C4—111no—
363C23×C4—111no—
364C23×C4—111no—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373#117—441no—
374#117—441no—
375#117—441no—
376#117—441no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
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⋊C4C4×D1111yescharacteristic
388C2×C4⋊C4C4×D1111yescharacteristic
389C2×C22⋊C4—111no—
390C2×C22⋊C4—111no—
391C2×C22⋊C4—111no—
392C2×C22⋊C4—111no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—222no—
399C2×C42—222no—
400C2×C42C22×D1111yescharacteristic
401C2×C42C22×D1111yescharacteristic
402C2×C42C22×D1111yescharacteristic
403C4⋊C8—41no—
404C4⋊C8—222no—
405C4⋊C8—222no—
406C4⋊C8—441no—
407C4⋊C8—441no—
408C4⋊C8—441no—
409C22⋊C8—114no—
410C22⋊C8—222no—
411C22⋊C8—222no—
412C22⋊C8—222no—
413#97—441no—
414#97—441no—
415C4×C8—41no—
416C4×C8—222no—
417C4×C8—222no—
418C4×C8—441no—
419#95—111no—
420#95—111no—
421#95—111no—
422#95—111no—
423#95—111no—
424#95—111no—
425#95C4×D1111yescharacteristic
426#95C4×D1111yescharacteristic
427C2×C11#234511yescharacteristic
428C2×C11C2×#43311yescharacteristic
429C2×C11#292411yescharacteristic
430C2×C11#296011yescharacteristic
431C2×C11#296211yescharacteristic
432C2×C11#297911yescharacteristic
433C2×C11#298111yescharacteristic
434D11—42no—
435C24—111no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—112no—
440C22×C4—112no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—222no—
454C22×C4—441no—
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4C2×C4×D1111yescharacteristic
458C22×C4C2×C4×D1111yescharacteristic
459C22×C4C2×C4×D1111yescharacteristic
460C22×C4C2×C4×D1111yescharacteristic
461C22×C4C23×D1111yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—112no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8Q8×D1112yes—
486C4⋊C4—22no—
487C4⋊C4—41no—
488C4⋊C4—222no—
489C4⋊C4—222no—
490C4⋊C4—222no—
491C4⋊C4—222no—
492C4⋊C4—222no—
493C4⋊C4—441no—
494C4⋊C4—441no—
495C4⋊C4—441no—
496C4⋊C4—441no—
497C4⋊C4—441no—
498C22⋊C4—441no—
499C22⋊C4—441no—
500C22⋊C4—441no—
501C22⋊C4—441no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—112no—
509C42—112no—
510C42—222no—
511C42—222no—
512C42—221no—
513C42—221no—
514C42—221no—
515C42—221no—
516C11#2262611yescharacteristic, complemented, Sylow
517C23—112no—
518C23—221no—
519C23—221no—
520C23—221no—
521C23—221no—
522C23—221no—
523C23—221no—
524C23C22×C4×D1111yescharacteristic
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—112no—
543C2×C4—112no—
544C2×C4—112no—
545C2×C4—112no—
546C2×C4—112no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—444no—
568C2×C4—444no—
569C2×C4#6695412yes—
570C2×C4#6703711yescharacteristic
571C2×C4C2×Q8×D1111yescharacteristic
572C2×C4#41×D1111yescharacteristic
573C2×C4#41×D1111yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C2×C4#6704211yescharacteristic
576C8—22no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—222no—
581C8—441no—
582C8—441no—
583C8—441no—
584C22—222no—
585C22—222no—
586C22—222no—
587C22—441no—
588C22—441no—
589C22—441no—
590C22—441no—
591C22D11×#11711yescharacteristic
592C22#1062307611yescharacteristic
593C22C4×Q8×D1111yescharacteristic
594C22C2×#6695411yescharacteristic
595C22#1062327611yescharacteristic
596C22D11×#13111yescharacteristic
597C22D11×#13111yescharacteristic
598C4—22no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—114no—
605C4—222no—
606C4—222no—
607C4—441no—
608C4—441no—
609C4—441no—
610C4—441no—
611C4#1062316711yescharacteristic
612C4#1062319211yescharacteristic
613C4#1062322111yescharacteristic
614C4#1062324011yescharacteristic
615C2—442no—
616C2#1307149011yescharacteristic
617C2D11×#43311yescharacteristic
618C2#1307726911yescharacteristic
619C2#1307754511yescharacteristic
620C2#1307756111yescharacteristic
621C2#1307767911yescharacteristic
622C2#1307768811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1916C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1916D11
hypocenterC11#22626
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
2. #13069333C2semidirect
3. #13069331C2semidirect
4. #13069182C2semidirect
5. #13069181C2semidirect
6. #13069172C2semidirect
10. #13068482C2semidirect
11. C8×Dic11⋊C4C2semidirect
15. C11×#1916C2semidirect
212. #1916D11semidirect
516. C11#22626semidirect

Maximal subgroups

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

subgroupindex
#130710202
#130693332
#130693312
#130691822
#130691812
#130691722
#130685992
#130685972
#130685952
#130684822
C8×Dic11⋊C42
#130683832
#130683812
#130683732
C11×#19162
#2262611