Finite Group Databasebeta

← #14765789

Subgroups — #14765789

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×#10622448C211yesmaximal, characteristic
3C4×#66949C211yesmaximal, characteristic
4#13069554C211yesmaximal, characteristic, complemented
5#13069338C211yesmaximal, characteristic, complemented
6#13069338C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13069230C211yesmaximal, characteristic
9#13069229C211yesmaximal, characteristic
10#13069223C211yesmaximal, characteristic
11#13069220C211yesmaximal, characteristic
12#13069170C211yesmaximal, characteristic, complemented
13#13068595C211yesmaximal, characteristic
14#13068487C211yesmaximal, characteristic, complemented
15C11×#1917C211yesmaximal, characteristic, complemented
16C2×#66949C411yescharacteristic
17C2×C42×D11C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C8C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622602C411yescharacteristic
35#10622594C411yescharacteristic
36#10622585C411yescharacteristic
37C4×(C2×D11)⋊C4C2211yescharacteristic
38C4×(C2×D11)⋊C4C2211yescharacteristic
39C4×Dic11⋊C4C2211yescharacteristic
40C4×Dic11⋊C4C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622448—24no—
46#10622314—24no—
47#10622281C411yescharacteristic
48#10622280C411yescharacteristic
49#10622265C411yescharacteristic
50#10622259C411yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×C4×D11C2×C411yescharacteristic
62C22×C4×D11C2×C411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×Dic22C2×C411yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78C2×C4⋊Dic11C2×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#66949—24no—
95C42×D11—22no—
96C42×D11—22no—
97C4×Dic22—22no—
98C4×Dic22—22no—
99C11×C4⋊C8—22no—
100C11×#97—22no—
101C11×#95C2×C411yescharacteristic
102C11×#95C2×C411yescharacteristic
103C11⋊#95C2×C411yescharacteristic
104C11⋊#95C2×C411yescharacteristic
105C11⋊#95C2×C411yescharacteristic
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110C11⋊#95C2×C411yescharacteristic
111(C2×D11)⋊C8—22no—
112(C2×D11)⋊C8—22no—
113(C2×D11)⋊C8—41no—
114(C2×D11)⋊C8—41no—
115#66879—22no—
116#66879—41no—
117#66879D414yes—
118Dic11⋊C8—22no—
119Dic11⋊C8—22no—
120Dic11⋊C8—22no—
121Dic11⋊C8—41no—
122C8×Dic11—22no—
123C4⋊(C11⋊C8)—22no—
124C4⋊(C11⋊C8)—22no—
125C4⋊(C11⋊C8)—41no—
126C4×C11⋊C8—41no—
127#22108—111nomaximal, Sylow
128C23×D11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C411yescharacteristic
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C22×Dic11C22×C411yescharacteristic
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—41no—
154C2×C4×D11—41no—
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×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4M1614yes—
182C4⋊Dic11—22no—
183Dic11⋊C4—22no—
184Dic11⋊C4—22no—
185Dic11⋊C4—22no—
186Dic11⋊C4—22no—
187Dic11⋊C4—22no—
188Dic11⋊C4—41no—
189C4×Dic11—22no—
190C4×Dic11—22no—
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#1924—111no—
218#1923—111no—
219#1923—111no—
220#1917D1111yescharacteristic, complemented
221#1916—111no—
222#1797—111no—
223#1771—111no—
224C23×C11C23×C411yescharacteristic
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11C2×M1612yes—
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—21no—
248C2×C4×C11C2×M1612yes—
249C2×C4×C11#13112yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C112−1+411yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×C4×C112−1+411yescharacteristic
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—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11C4×D412yes—
275C2×Dic11C4×D412yes—
276C2×Dic11C2×M1612yes—
277C4×D11—44no—
278C4×D11—44no—
279C4×D11—41no—
280C4×D11—41no—
281C4×D11—41no—
282C4×D11—41no—
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⋊C8—111no—
308C2×C22⋊C8—111no—
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⋊C4C2×D1111yescharacteristic
325C4×C22⋊C4—111no—
326C4×C22⋊C4—111no—
327#336—111no—
328#336—111no—
329#336—111no—
330#336—111no—
331#336—111no—
332#336—111no—
333#336C2×D1111yescharacteristic
334#336C2×D1111yescharacteristic
335#336C2×D1111yescharacteristic
336#336C2×D1111yescharacteristic
337C22×C11C2×C4×D411yescharacteristic
338C22×C11#51911yescharacteristic
339C22×C11#52011yescharacteristic
340C22×C11C22×M1611yescharacteristic
341C22×C11C2×#13111yescharacteristic
342C22×C11#56811yescharacteristic
343C22×C11#56811yescharacteristic
344C2×D11—22no—
345C2×D11—22no—
346C2×D11—22no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11#53611yescharacteristic
358C4×C11#53711yescharacteristic
359C4×C11#54111yescharacteristic
360C4×C11#54211yescharacteristic
361Dic11—22no—
362Dic11—22no—
363Dic11—22no—
364Dic11—41no—
365Dic11—41no—
366Dic11—41no—
367Dic11—41no—
368C22×Q8—111no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—111no—
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⋊C4C4×D1111yescharacteristic
391C2×C4⋊C4C4×D1111yescharacteristic
392C2×C22⋊C4—111no—
393C2×C22⋊C4—111no—
394C2×C22⋊C4—111no—
395C2×C22⋊C4—111no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—222no—
402C2×C42—222no—
403C2×C42C22×D1111yescharacteristic
404C2×C42C22×D1111yescharacteristic
405C2×C42C22×D1111yescharacteristic
406C4⋊C8—22no—
407C4⋊C8—222no—
408C4⋊C8—222no—
409C4⋊C8—222no—
410C4⋊C8—222no—
411C4⋊C8—222no—
412C4⋊C8—441no—
413C4⋊C8—441no—
414C22⋊C8—222no—
415C22⋊C8—222no—
416C22⋊C8—441no—
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#232311yescharacteristic
435C2×C11#293311yescharacteristic
436C2×C11D4×M1611yescharacteristic
437C2×C11#298311yescharacteristic
438C2×C11#298511yescharacteristic
439C2×C11#299011yescharacteristic
440C2×C11#299511yescharacteristic
441D11—42no—
442C24—111no—
443C2×Q8—222no—
444C2×Q8—222no—
445C2×Q8—441no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—441no—
464C22×C4—441no—
465C22×C4C2×C4×D1111yescharacteristic
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—22no—
497C4⋊C4—22no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—441no—
505C22⋊C4—114no—
506C22⋊C4—222no—
507C22⋊C4—441no—
508C22⋊C4—441no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—112no—
516C42—112no—
517C42—222no—
518C42—222no—
519C42—221no—
520C42—221no—
521C42—221no—
522C42—221no—
523C11#2210811yescharacteristic, complemented, Sylow
524C23—112no—
525C23—221no—
526C23—221no—
527C23—221no—
528C23—221no—
529C23—221no—
530C23—221no—
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—21no—
549C2×C4—112no—
550C2×C4—112no—
551C2×C4—112no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
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—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—444no—
571C2×C4—444no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4M16×D1112yes—
577C2×C4#6696012yes—
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4#6704011yescharacteristic
580C2×C4#41×D1111yescharacteristic
581C2×C4#6704211yescharacteristic
582C2×C4#6704311yescharacteristic
583C2×C4#6704311yescharacteristic
584C8—22no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—222no—
589C8—441no—
590C8—441no—
591C8—441no—
592C22—222no—
593C22—222no—
594C22—222no—
595C22—441no—
596C22—441no—
597C22—441no—
598C22—441no—
599C22#1062305411yescharacteristic
600C22C4×D4×D1111yescharacteristic
601C22#1062310311yescharacteristic
602C22C2×M16×D1111yescharacteristic
603C22C2×#6696011yescharacteristic
604C22#1062328111yescharacteristic
605C22#1062328111yescharacteristic
606C4—22no—
607C4—22no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—222no—
613C4—222no—
614C4—222no—
615C4—441no—
616C4—441no—
617C4—441no—
618C4—441no—
619C4#1062316011yescharacteristic
620C4#1062317911yescharacteristic
621C4#1062322711yescharacteristic
622C4#1062324111yescharacteristic
623C2—442no—
624C2#1307129711yescharacteristic
625C2#1307734211yescharacteristic
626C2#1307735211yescharacteristic
627C2#1307769811yescharacteristic
628C2#1307771211yescharacteristic
629C2#1307774311yescharacteristic
630C2#1307778111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1917C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1917D11
hypocenterC11#22108
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
1. C2×#10622314C2semidirect
4. #13069554C2semidirect
5. #13069338C2semidirect
6. #13069338C2semidirect
7. #13069335C2semidirect
12. #13069170C2semidirect
14. #13068487C2semidirect
15. C11×#1917C2semidirect
220. #1917D11semidirect
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×#106224482
C4×#669492
#130695542
#130693382
#130693352
#130692302
#130692292
#130692232
#130692202
#130691702
#130685952
#130684872
C11×#19172
#2210811