Finite Group Databasebeta

← #14780315

Subgroups — #14780315

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071903C211yesmaximal, characteristic
2#13069555C211yesmaximal, characteristic, complemented
3#13069554C211yesmaximal, characteristic, complemented
4#13069232C211yesmaximal, characteristic, complemented
5#13069231C211yesmaximal, characteristic, complemented
6#13069230C211yesmaximal, characteristic, complemented
7#13069227C211yesmaximal, characteristic, complemented
8#13068910C211yesmaximal, characteristic
9#13068908C211yesmaximal, characteristic
10#13068797C211yesmaximal, characteristic, complemented
11#13068797C211yesmaximal, characteristic, complemented
12#13068794C211yesmaximal, characteristic, complemented
13#13068735C211yesmaximal, characteristic, complemented
14#13068734C211yesmaximal, characteristic, complemented
15C11×#1850C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C22×#4313C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C4×C11×C22⋊C4C2211yescharacteristic
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34#10622574C411yescharacteristic
35#10622572C411yescharacteristic
36#10622565C411yescharacteristic
37#10622560C411yescharacteristic
38C4×(C2×D11)⋊C4C2211yescharacteristic
39C4×(C2×D11)⋊C4C2211yescharacteristic
40#10622545C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43#10622288C411yescharacteristic
44#10622286C411yescharacteristic
45#10622273C411yescharacteristic
46#10622271C411yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11C2×C411yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×Dic22C2×C411yescharacteristic
63C22×C8×C11—41no—
64C22×C8×C11—41no—
65C22×C8×C11—41no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C22⋊C4C2×C411yescharacteristic
71C2×C11×C22⋊C4C2×C411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11C2×C411yescharacteristic
75C2×C22⋊Dic11C2×C411yescharacteristic
76C2×C22⋊Dic11C2×C411yescharacteristic
77C4×C22⋊D11—41no—
78C4×C22⋊D11—41no—
79C2×(C2×D11)⋊C4C2×C411yescharacteristic
80C2×(C2×D11)⋊C4C2×C411yescharacteristic
81C2×(C2×D11)⋊C4C2×C411yescharacteristic
82C2×(C2×D11)⋊C4C2×C411yescharacteristic
83C2×(C2×D11)⋊C4C2×C411yescharacteristic
84C2×C4⋊Dic11C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×Dic11⋊C4C2×C411yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C2×#4313—41no—
96C2×#4313—41no—
97C2×#4313—41no—
98C4×Dic22—41no—
99C4×Dic22—41no—
100C11×C4⋊C8—41no—
101C11×C4⋊C8—41no—
102C11×C22⋊C8—41no—
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
113C11⋊#95C2×C411yescharacteristic
114C11⋊#95C2×C411yescharacteristic
115C22⋊(C11⋊C8)—41no—
116C22⋊(C11⋊C8)—41no—
117(C2×D11)⋊C8—41no—
118(C2×D11)⋊C8—41no—
119(C2×D11)⋊C8—41no—
120#66879—41no—
121Dic11⋊C8—41no—
122Dic11⋊C8—41no—
123Dic11⋊C8—41no—
124C4⋊(C11⋊C8)—41no—
125#66867—41no—
126#23354—111nomaximal, Sylow
127C24×C11C22×C411yescharacteristic
128C23×D11C22×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
141C2×C22⋊D11—22no—
142C2×C22⋊D11—41no—
143C2×C22⋊D11—41no—
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C22×Dic11C22×C411yescharacteristic
148C22×Dic11C22×C411yescharacteristic
149C22×Dic11C22×C411yescharacteristic
150C22×Dic11C22×C411yescharacteristic
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×Dic22—41no—
158C2×Dic22—41no—
159C2×Dic22—41no—
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×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—44no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—41no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C22⋊Dic11—22no—
180C22⋊Dic11—41no—
181C22⋊Dic11—41no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—41no—
187C4⋊Dic11—41no—
188Dic11⋊C4—41no—
189Dic11⋊C4—41no—
190Dic11⋊C4—41no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—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⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209#4313—44no—
210#2398—111no—
211#1985—111no—
212#1985—111no—
213#1924—111no—
214#1924—111no—
215#1924—111no—
216#1924—111no—
217#1870—111no—
218#1869—111no—
219#1851—111no—
220#1851—111no—
221#1850—111no—
222#1850D1111yescharacteristic, complemented
223#1832—111no—
224#1832—111no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11#13112yes—
232C23×C11C23×C411yescharacteristic
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—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×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C22⋊D11—44no—
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—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C4×D11—41no—
288C4×D11—41no—
289C4×D11—41no—
290C4×D11—41no—
291Dic22—44no—
292C8×C11—41no—
293C8×C11—41no—
294C8×C11—41no—
295C8×C11—41no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C22×M16—111no—
301C23×C8C2×D1111yescharacteristic
302C2×C4×Q8—111no—
303C2×C4×D4—111no—
304C2×C4⋊C8—111no—
305C2×C4⋊C8—111no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8C2×D1111yescharacteristic
309C2×C4⋊C8C2×D1111yescharacteristic
310C2×C22⋊C8—111no—
311C2×C22⋊C8—111no—
312C2×C22⋊C8—111no—
313C2×C22⋊C8—111no—
314C2×C22⋊C8—111no—
315C2×C22⋊C8C2×D1111yescharacteristic
316C2×#97—111no—
317C2×#97—111no—
318#400—111no—
319#400—111no—
320#397—111no—
321#397—111no—
322#394—111no—
323#394—111no—
324#393—111no—
325#393—111no—
326C4×C22⋊C4—111no—
327C4×C22⋊C4—111no—
328C4×C22⋊C4—111no—
329C4×C22⋊C4C2×D1111yescharacteristic
330#376—111no—
331#336—111no—
332#336—111no—
333#336—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337#336—111no—
338#336—111no—
339#336—111no—
340#336—111no—
341#336C2×D1111yescharacteristic
342#336C2×D1111yescharacteristic
343C22×C11—22no—
344C22×C11—22no—
345C22×C11—22no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11#51811yescharacteristic
351C22×C11#52011yescharacteristic
352C22×C11#52011yescharacteristic
353C22×C11C2×#13111yescharacteristic
354C22×C11#56811yescharacteristic
355C22×C11#56811yescharacteristic
356C22×C11#56811yescharacteristic
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11H(3,𝔽4)11yescharacteristic
370C4×C11#56211yescharacteristic
371C4×C11#56211yescharacteristic
372C4×C11#56311yescharacteristic
373Dic11—41no—
374Dic11—41no—
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378Dic11—41no—
379Dic11—41no—
380C22×Q8—111no—
381C22×D4—111no—
382C23×C4—111no—
383C23×C4C22×D1111yescharacteristic
384C2×M16—441no—
385C2×M16—441no—
386C2×M16—441no—
387C22×C8—41no—
388C22×C8—41no—
389C22×C8—41no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8C22×D1111yescharacteristic
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398C4×Q8—441no—
399C4×Q8—441no—
400C4×D4—441no—
401C4×D4—441no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C22⋊C4—111no—
407C2×C22⋊C4—111no—
408C2×C22⋊C4—111no—
409C2×C22⋊C4—111no—
410C2×C22⋊C4—111no—
411C2×C22⋊C4—111no—
412C2×C22⋊C4—111no—
413C2×C22⋊C4—111no—
414C2×C22⋊C4C4×D1111yescharacteristic
415C2×C22⋊C4C4×D1111yescharacteristic
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42C22×D1111yescharacteristic
420C2×C42C22×D1111yescharacteristic
421C4⋊C8—41no—
422C4⋊C8—41no—
423C4⋊C8—441no—
424C4⋊C8—441no—
425C4⋊C8—441no—
426C4⋊C8—441no—
427C22⋊C8—41no—
428C22⋊C8—441no—
429C22⋊C8—441no—
430C22⋊C8—441no—
431C22⋊C8—441no—
432C22⋊C8—441no—
433#97—441no—
434#97—441no—
435#95—111no—
436#95—111no—
437#95—111no—
438#95—111no—
439#95—111no—
440#95—111no—
441#95—111no—
442#95—111no—
443#95—111no—
444#95—111no—
445#95C4×D1111yescharacteristic
446#95C4×D1111yescharacteristic
447C2×C11—42no—
448C2×C11#237911yescharacteristic
449C2×C11#297611yescharacteristic
450C2×C11#297811yescharacteristic
451C2×C11#299211yescharacteristic
452C2×C11#299211yescharacteristic
453C2×C11#299511yescharacteristic
454C2×C11#299511yescharacteristic
455D11—81no—
456C24—111no—
457C24C2×C4×D1111yescharacteristic
458C2×Q8—441no—
459C2×Q8—441no—
460C2×Q8—441no—
461C2×D4—222no—
462C2×D4—441no—
463C2×D4—441no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4C2×C4×D1111yescharacteristic
484C22×C4C2×C4×D1111yescharacteristic
485C22×C4C2×C4×D1111yescharacteristic
486C22×C4C2×C4×D1111yescharacteristic
487C22×C4C2×C4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489M16—444no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—44no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C4⋊C4—441no—
516C4⋊C4—441no—
517C4⋊C4—441no—
518C4⋊C4—441no—
519C22⋊C4—22no—
520C22⋊C4—41no—
521C22⋊C4—222no—
522C22⋊C4—441no—
523C22⋊C4—441no—
524C22⋊C4—441no—
525C22⋊C4—441no—
526C22⋊C4—441no—
527C22⋊C4—441no—
528C22⋊C4—441no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—221no—
534C42—221no—
535C42—221no—
536C42—221no—
537C42—221no—
538C42—221no—
539C11#2335411yescharacteristic, complemented, Sylow
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—221no—
547C23—221no—
548C23—221no—
549C23—221no—
550C23—221no—
551C23—221no—
552C23—221no—
553C23#6695412yes—
554C23C22×C4×D1111yescharacteristic
555Q8—444no—
556D4—444no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4#6703711yescharacteristic
602C2×C4#6703711yescharacteristic
603C2×C4#6703711yescharacteristic
604C2×C4#6704011yescharacteristic
605C2×C4#6704211yescharacteristic
606C2×C4#6704311yescharacteristic
607C8—41no—
608C8—41no—
609C8—41no—
610C8—41no—
611C8—441no—
612C8—441no—
613C8—441no—
614C8—441no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—441no—
623C22—441no—
624C22—441no—
625C22—441no—
626C22—441no—
627C22—441no—
628C22—441no—
629C22#1062303511yescharacteristic
630C22#1062307611yescharacteristic
631C22#1062307711yescharacteristic
632C22C2×#6695411yescharacteristic
633C22#1062327611yescharacteristic
634C22#1062328111yescharacteristic
635C22#1062328111yescharacteristic
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—441no—
642C4—441no—
643C4—441no—
644C4—441no—
645C4—441no—
646C4—441no—
647C4—441no—
648C4#1062312511yescharacteristic
649C4#1062317711yescharacteristic
650C4#1062317811yescharacteristic
651C4#1062319811yescharacteristic
652C2—42no—
653C2—881no—
654C2#1307178911yescharacteristic
655C2#1307765811yescharacteristic
656C2#1307767511yescharacteristic
657C2#1307774911yescharacteristic
658C2#1307775211yescharacteristic
659C2#1307778211yescharacteristic
660C2#1307778411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1850C2
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1850D11
hypocenterC11#23354
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
2. #13069555C2semidirect
3. #13069554C2semidirect
4. #13069232C2semidirect
5. #13069231C2semidirect
6. #13069230C2semidirect
7. #13069227C2semidirect
10. #13068797C2semidirect
11. #13068797C2semidirect
12. #13068794C2semidirect
13. #13068735C2semidirect
14. #13068734C2semidirect
15. C11×#1850C2semidirect
222. #1850D11semidirect
539. C11#23354semidirect

Maximal subgroups

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

subgroupindex
#130719032
#130695552
#130695542
#130692322
#130692312
#130692302
#130692272
#130689102
#130689082
#130687972
#130687942
#130687352
#130687342
C11×#18502
#2335411