Finite Group Databasebeta

← #14765787

Subgroups — #14765787

Order 2816.

786 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622314C211yesmaximal, characteristic, complemented
2C2×#10622332C211yesmaximal, characteristic
3C4×#66931C211yesmaximal, characteristic
4#13069554C211yesmaximal, characteristic, complemented
5#13069337C211yesmaximal, characteristic, complemented
6#13069336C211yesmaximal, characteristic, complemented
7#13069333C211yesmaximal, characteristic, complemented
8#13069231C211yesmaximal, characteristic
9#13069219C211yesmaximal, characteristic
10#13069219C211yesmaximal, characteristic
11#13069180C211yesmaximal, characteristic, complemented
12#13069174C211yesmaximal, characteristic, complemented
13#13068594C211yesmaximal, characteristic
14#13068489C211yesmaximal, characteristic, complemented
15C11×#1924C211yesmaximal, characteristic
16C22×C4×Dic11C2211yescharacteristic
17C2×#66931C411yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C4×C11×C22⋊C4C2211yescharacteristic
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622563C411yescharacteristic
38#10622559C411yescharacteristic
39#10622555C411yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×Dic11⋊C4C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622332—24no—
46#10622314—24no—
47#10622268C411yescharacteristic
48#10622267C411yescharacteristic
49#10622260C411yescharacteristic
50#10622259C411yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2×C411yescharacteristic
63C23×Dic11C2×C411yescharacteristic
64C22×Dic22C2×C411yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C22⋊C4C2×C411yescharacteristic
70C2×C11×C22⋊C4C2×C411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11C2×C411yescharacteristic
74C2×C22⋊Dic11C2×C411yescharacteristic
75C2×C4⋊Dic11C2×C411yescharacteristic
76C2×C4⋊Dic11C2×C411yescharacteristic
77C2×C4⋊Dic11C2×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×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96#66931—24no—
97C4×Dic22—22no—
98C4×Dic22—22no—
99C11×C4⋊C8—41no—
100C11×C22⋊C8—22no—
101C11×C22⋊C8—41no—
102C11×#97—22no—
103C11×#95C2×C411yescharacteristic
104C11×#95C2×C411yescharacteristic
105C11⋊#95C2×C411yescharacteristic
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110C11⋊#95C2×C411yescharacteristic
111C11⋊#95C2×C411yescharacteristic
112C11⋊#95C2×C411yescharacteristic
113C22⋊(C11⋊C8)—22no—
114C22⋊(C11⋊C8)—41no—
115#66879—22no—
116#66879D414yes—
117Dic11⋊C8—22no—
118Dic11⋊C8—22no—
119Dic11⋊C8—22no—
120Dic11⋊C8—22no—
121Dic11⋊C8—22no—
122Dic11⋊C8—41no—
123C8×Dic11—22no—
124C8×Dic11—41no—
125C4⋊(C11⋊C8)—22no—
126#66867—41no—
127#22108—111nomaximal, Sylow
128C24×C11C22×C411yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—41no—
146C22×Dic11—41no—
147C22×Dic11C22×C411yescharacteristic
148C22×Dic11C22×C411yescharacteristic
149C22×Dic11C22×C411yescharacteristic
150C22×Dic11C22×C411yescharacteristic
151C22×Dic11C22×C411yescharacteristic
152C22×Dic11C22×C411yescharacteristic
153C22×Dic11C22×C411yescharacteristic
154C22×Dic11C22×C411yescharacteristic
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—41no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11C2×D412yes—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—41no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C22⋊Dic11—41no—
177C22⋊Dic11M1614yes—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181Dic11⋊C4—22no—
182Dic11⋊C4—22no—
183Dic11⋊C4—22no—
184Dic11⋊C4—22no—
185Dic11⋊C4—22no—
186Dic11⋊C4—41no—
187C4×Dic11—22no—
188C4×Dic11—22no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11C2×D412yes—
196C4×Dic11#4112yes—
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⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8C2×D412yes—
209C2×#446—111no—
210C2×#432—111no—
211C4×C22⋊Q8—111no—
212#1985—111no—
213#1940—111no—
214#1940—111no—
215#1939—111no—
216#1924—111no—
217#1924D1111yescharacteristic
218#1923—111no—
219#1923—111no—
220#1917—111no—
221#1916—111no—
222#1797—111no—
223#1771—111no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11C2×M1612yes—
231C23×C11C23×C411yescharacteristic
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—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×C4×C112−1+411yescharacteristic
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—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—44no—
277C2×Dic11—44no—
278C2×Dic11C4×D412yes—
279C2×Dic11C4×D412yes—
280C2×Dic11C2×M1612yes—
281C2×Dic11C2×M1612yes—
282C2×Dic11#13112yes—
283Dic22—44no—
284C8×C11—22no—
285C8×C11—41no—
286C8×C11—41no—
287C8×C11—41no—
288C11⋊C8—22no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C2×C22⋊Q8—111no—
293C2×C4×Q8—111no—
294C22×C42—111no—
295#446—224no—
296#432—224no—
297C2×C4⋊C8—111no—
298C2×C4⋊C8—111no—
299C2×C4⋊C8—111no—
300C2×C4⋊C8—111no—
301C2×C4⋊C8—111no—
302C2×C4⋊C8—111no—
303C2×C4⋊C8—111no—
304C2×C4⋊C8C2×D1111yescharacteristic
305C2×C22⋊C8—111no—
306C2×C22⋊C8—111no—
307C2×C22⋊C8C2×D1111yescharacteristic
308C2×C22⋊C8C2×D1111yescharacteristic
309C2×#97—111no—
310C2×#97—111no—
311C2×#97—111no—
312C2×#97C2×D1111yescharacteristic
313C2×C4×C8—111no—
314C2×C4×C8—111no—
315#391—111no—
316#389—111no—
317#387—111no—
318#387—111no—
319#385—111no—
320#385—111no—
321#380—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—111no—
325C4×C22⋊C4—111no—
326C4×C22⋊C4C2×D1111yescharacteristic
327#336—111no—
328#336—111no—
329#336—111no—
330#336—111no—
331#336—111no—
332#336—111no—
333#336—111no—
334#336—111no—
335#336C2×D1111yescharacteristic
336#336C2×D1111yescharacteristic
337C22×C11—22no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11C2×C4×D411yescharacteristic
345C22×C11#51911yescharacteristic
346C22×C11#52011yescharacteristic
347C22×C11C22×M1611yescharacteristic
348C22×C11C2×#13111yescharacteristic
349C22×C11#56811yescharacteristic
350C22×C11#56811yescharacteristic
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11#53611yescharacteristic
357C4×C11#53711yescharacteristic
358C4×C11#54111yescharacteristic
359C4×C11#54211yescharacteristic
360Dic11—22no—
361Dic11—22no—
362Dic11—22no—
363Dic11—22no—
364Dic11—22no—
365Dic11—41no—
366Dic11—41no—
367Dic11—41no—
368C22×Q8—111no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4C22×D1111yescharacteristic
372C22×C8—111no—
373C22×C8—111no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380C22⋊Q8—224no—
381C4×Q8—222no—
382C4×Q8—222no—
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×C22⋊C4—111no—
393C2×C22⋊C4—111no—
394C2×C22⋊C4C4×D1111yescharacteristic
395C2×C22⋊C4C4×D1111yescharacteristic
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—111no—
402C2×C42—222no—
403C2×C42—222no—
404C2×C42C22×D1111yescharacteristic
405C2×C42C22×D1111yescharacteristic
406C4⋊C8—41no—
407C4⋊C8—222no—
408C4⋊C8—222no—
409C4⋊C8—222no—
410C4⋊C8—222no—
411C4⋊C8—222no—
412C4⋊C8—222no—
413C4⋊C8—441no—
414C22⋊C8—22no—
415C22⋊C8—41no—
416C22⋊C8—222no—
417C22⋊C8—441no—
418#97—22no—
419#97—114no—
420#97—222no—
421#97—441no—
422C4×C8—222no—
423C4×C8—441no—
424#95—111no—
425#95—111no—
426#95—111no—
427#95—111no—
428#95—111no—
429#95—111no—
430#95—111no—
431#95—111no—
432#95C4×D1111yescharacteristic
433#95C4×D1111yescharacteristic
434C2×C11—42no—
435C2×C11#232311yescharacteristic
436C2×C11#293311yescharacteristic
437C2×C11D4×M1611yescharacteristic
438C2×C11#298311yescharacteristic
439C2×C11#298511yescharacteristic
440C2×C11#299011yescharacteristic
441C2×C11#299511yescharacteristic
442C24C2×C4×D1111yescharacteristic
443C2×Q8—222no—
444C2×Q8—222no—
445C2×Q8—441no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—441no—
465C22×C4—441no—
466C22×C4C2×C4×D1111yescharacteristic
467C22×C4C2×C4×D1111yescharacteristic
468C22×C4C2×C4×D1111yescharacteristic
469C22×C4C2×C4×D1111yescharacteristic
470C22×C4C2×C4×D1111yescharacteristic
471C22×C4C23×D1111yescharacteristic
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—112no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8D4×D1112yes—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—441no—
505C22⋊C4—22no—
506C22⋊C4—41no—
507C22⋊C4—114no—
508C22⋊C4—441no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—112no—
514C42—112no—
515C42—222no—
516C42—222no—
517C42—221no—
518C42—221no—
519C42—221no—
520C42—221no—
521C42—221no—
522C42—221no—
523C11#2210811yescharacteristic, complemented, Sylow
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23M16×D1112yes—
531C23C22×C4×D1111yescharacteristic
532Q8—444no—
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—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—112no—
555C2×C4—112no—
556C2×C4—112no—
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—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—444no—
577C2×C4—444no—
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4#6703711yescharacteristic
580C2×C4#41×D1111yescharacteristic
581C2×C4#6704311yescharacteristic
582C2×C4#6704311yescharacteristic
583C2×C4#6704311yescharacteristic
584C8—22no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—222no—
589C8—441no—
590C8—441no—
591C8—441no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22#1062304711yescharacteristic
600C22C4×D4×D1111yescharacteristic
601C22#1062307711yescharacteristic
602C22C2×M16×D1111yescharacteristic
603C22#1062327611yescharacteristic
604C22D11×#13111yescharacteristic
605C22#1062328111yescharacteristic
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—222no—
612C4—222no—
613C4—222no—
614C4—222no—
615C4—222no—
616C4—441no—
617C4—441no—
618C4—441no—
619C4#1062313911yescharacteristic
620C4#1062317911yescharacteristic
621C4#1062320011yescharacteristic
622C4#1062323211yescharacteristic
623C2—42no—
624C2#1307129511yescharacteristic
625C2#1307734511yescharacteristic
626C2#1307734911yescharacteristic
627C2#1307770011yescharacteristic
628C2#1307770811yescharacteristic
629C2#1307773611yescharacteristic
630C2#1307778711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1924C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1924D11
hypocenterC11#22108
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#10622314C2semidirect
4. #13069554C2semidirect
5. #13069337C2semidirect
6. #13069336C2semidirect
7. #13069333C2semidirect
11. #13069180C2semidirect
12. #13069174C2semidirect
14. #13068489C2semidirect
523. C11#22108semidirect

Maximal subgroups

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

subgroupindex
C2×#106223142
C2×#106223322
C4×#669312
#130695542
#130693372
#130693362
#130693332
#130692312
#130692192
#130691802
#130691742
#130685942
#130684892
C11×#19242
#2210811