Finite Group Databasebeta

← #14780229

Subgroups — #14780229

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071892C211yesmaximal, characteristic
2#13069554C211yesmaximal, characteristic, complemented
3#13069551C211yesmaximal, characteristic, complemented
4#13069338C211yesmaximal, characteristic, complemented
5#13069229C211yesmaximal, characteristic
6#13069228C211yesmaximal, characteristic
7#13069228C211yesmaximal, characteristic
8#13069220C211yesmaximal, characteristic
9#13069180C211yesmaximal, characteristic, complemented
10#13069177C211yesmaximal, characteristic, complemented
11#13069177C211yesmaximal, characteristic, complemented
12#13069175C211yesmaximal, characteristic, complemented
13#13068686C211yesmaximal, characteristic
14#13068597C211yesmaximal, characteristic
15C11×#1940C211yesmaximal, characteristic, complemented
16C2×#66925C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622607C411yescharacteristic
32#10622605C411yescharacteristic
33#10622593C411yescharacteristic
34#10622592C411yescharacteristic
35C4×(C2×D11)⋊C4C2211yescharacteristic
36C4×(C2×D11)⋊C4C2211yescharacteristic
37C4×Dic11⋊C4C2211yescharacteristic
38C4×Dic11⋊C4C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622289C411yescharacteristic
42#10622286C411yescharacteristic
43#10622271C411yescharacteristic
44#10622270C411yescharacteristic
45C11×#336C2211yescharacteristic
46C11×#336C2211yescharacteristic
47#10622188C2211yescharacteristic
48#10622188C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C22×Dic22C2×C411yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4C2×C411yescharacteristic
66C2×C11×C4⋊C4C2×C411yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×(C2×D11)⋊C4C2×C411yescharacteristic
71C2×(C2×D11)⋊C4C2×C411yescharacteristic
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×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×Dic11C2311yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92#66925—41no—
93#66925—41no—
94C4×Dic22—41no—
95C4×Dic22—41no—
96C11×C4⋊C8—41no—
97C11×C4⋊C8—41no—
98C11×C4⋊C8—41no—
99C11×#97—41no—
100C11×#95C2×C411yescharacteristic
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
110(C2×D11)⋊C8—41no—
111(C2×D11)⋊C8—41no—
112(C2×D11)⋊C8—41no—
113(C2×D11)⋊C8—41no—
114#66879—41no—
115#66879—41no—
116Dic11⋊C8—41no—
117Dic11⋊C8—41no—
118C4⋊(C11⋊C8)—41no—
119C4×C11⋊C8—41no—
120#23345—111nomaximal, Sylow
121C23×D11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11C22×C411yescharacteristic
130C22×Dic11C22×C411yescharacteristic
131C22×Dic11C22×C411yescharacteristic
132C22×Dic11C22×C411yescharacteristic
133C22×Dic11C22×C411yescharacteristic
134C22×Dic11C22×C411yescharacteristic
135C22×Dic11C22×C411yescharacteristic
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×Dic22—22no—
143C2×Dic22—41no—
144C2×Dic22—41no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—41no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165(C2×D11)⋊C4—22no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170(C2×D11)⋊C4—41no—
171C4⋊Dic11—41no—
172Dic11⋊C4—41no—
173Dic11⋊C4—41no—
174Dic11⋊C4—41no—
175Dic11⋊C4—41no—
176Dic11⋊C4—41no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179Dic11⋊C4—41no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198#2396—111no—
199#1985—111no—
200#1984—111no—
201#1940—111no—
202#1940D1111yescharacteristic, complemented
203#1924—111no—
204#1924—111no—
205#1924—111no—
206#1923—111no—
207#1917—111no—
208#1917—111no—
209#1917—111no—
210#1916—111no—
211#1818—111no—
212#1798—111no—
213C23×C11C23×C411yescharacteristic
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11—21no—
218C22×D11—21no—
219C22×D11—21no—
220C22×D11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
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#13112yes—
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
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—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—41no—
270Dic22—44no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C2×C4×Q8—111no—
280C2×#117—111no—
281C2×C4⋊C8—111no—
282C2×C4⋊C8—111no—
283C2×C4⋊C8—111no—
284C2×C4⋊C8C2×D1111yescharacteristic
285C2×C4⋊C8C2×D1111yescharacteristic
286C2×C4⋊C8C2×D1111yescharacteristic
287C2×C22⋊C8—111no—
288C2×C22⋊C8—111no—
289C2×C22⋊C8—111no—
290C2×C22⋊C8—111no—
291C2×#97—111no—
292C2×#97—111no—
293C2×#97C2×D1111yescharacteristic
294C2×C4×C8—111no—
295#400—111no—
296#399—111no—
297#398—111no—
298#398—111no—
299#396—111no—
300#396—111no—
301#395—111no—
302#393—111no—
303C4×C4⋊C4—111no—
304C4×C4⋊C4—111no—
305C4×C4⋊C4C2×D1111yescharacteristic
306C4×C22⋊C4—111no—
307C4×C22⋊C4—111no—
308#336—111no—
309#336—111no—
310#336—111no—
311#336—111no—
312#336—111no—
313#336—111no—
314#336—111no—
315#336—111no—
316#336—111no—
317#336—111no—
318#336—111no—
319#336—111no—
320#336C2×D1111yescharacteristic
321#336C2×D1111yescharacteristic
322C22×C11#51811yescharacteristic
323C22×C11#51911yescharacteristic
324C22×C11#52011yescharacteristic
325C22×C11C2×#13111yescharacteristic
326C22×C11#56811yescharacteristic
327C22×C11#56811yescharacteristic
328C22×C11#56811yescharacteristic
329C2×D11—41no—
330C2×D11—41no—
331C2×D11—41no—
332C2×D11—41no—
333C2×D11—41no—
334C2×D11—41no—
335C2×D11—41no—
336C4×C11—22no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11#56211yescharacteristic
343C4×C11#56211yescharacteristic
344C4×C11#56311yescharacteristic
345C4×C11#56311yescharacteristic
346Dic11—41no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350Dic11—41no—
351Dic11—41no—
352Dic11—41no—
353C22×Q8—111no—
354C23×C4—111no—
355C22×C8—111no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8C22×D1111yescharacteristic
360C22×C8C22×D1111yescharacteristic
361C22×C8C22×D1111yescharacteristic
362C22×C8C22×D1111yescharacteristic
363C4×Q8—441no—
364C4×Q8—441no—
365#117—441no—
366#117—441no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4C4×D1111yescharacteristic
377C2×C4⋊C4C4×D1111yescharacteristic
378C2×C22⋊C4—111no—
379C2×C22⋊C4—111no—
380C2×C22⋊C4—111no—
381C2×C22⋊C4—111no—
382C2×C22⋊C4—111no—
383C2×C22⋊C4—111no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—111no—
387C2×C42C22×D1111yescharacteristic
388C2×C42C22×D1111yescharacteristic
389C2×C42C22×D1111yescharacteristic
390C4⋊C8—41no—
391C4⋊C8—41no—
392C4⋊C8—41no—
393C4⋊C8—441no—
394C4⋊C8—441no—
395C4⋊C8—441no—
396C22⋊C8—441no—
397C22⋊C8—441no—
398C22⋊C8—441no—
399C22⋊C8—441no—
400#97—41no—
401#97—441no—
402#97—441no—
403C4×C8—441no—
404#95—111no—
405#95—111no—
406#95—111no—
407#95—111no—
408#95—111no—
409#95—111no—
410#95—111no—
411#95—111no—
412#95C4×D1111yescharacteristic
413#95C4×D1111yescharacteristic
414C2×C11#237811yescharacteristic
415C2×C11#297611yescharacteristic
416C2×C11#298011yescharacteristic
417C2×C11#298511yescharacteristic
418C2×C11#298711yescharacteristic
419C2×C11#299311yescharacteristic
420C2×C11#299511yescharacteristic
421D11—81no—
422C24—111no—
423C2×Q8—222no—
424C2×Q8—441no—
425C2×Q8—441no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4C2×C4×D1111yescharacteristic
440C22×C4C2×C4×D1111yescharacteristic
441C22×C4C2×C4×D1111yescharacteristic
442C22×C4C2×C4×D1111yescharacteristic
443C22×C4C2×C4×D1111yescharacteristic
444C22×C4C2×C4×D1111yescharacteristic
445C22×C4C23×D1111yescharacteristic
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C4⋊C4—22no—
471C4⋊C4—41no—
472C4⋊C4—441no—
473C4⋊C4—441no—
474C4⋊C4—441no—
475C4⋊C4—441no—
476C4⋊C4—441no—
477C4⋊C4—441no—
478C4⋊C4—441no—
479C4⋊C4—441no—
480C4⋊C4—441no—
481C22⋊C4—222no—
482C22⋊C4—441no—
483C22⋊C4—441no—
484C22⋊C4—441no—
485C22⋊C4—441no—
486C22⋊C4—441no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—221no—
494C42—221no—
495C42—221no—
496C42—221no—
497C42—221no—
498C42—221no—
499C11#2334511yescharacteristic, complemented, Sylow
500C23—221no—
501C23—221no—
502C23—221no—
503C23—221no—
504C23—221no—
505C23—221no—
506C23—221no—
507C23C22×C4×D1111yescharacteristic
508Q8—444no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4#6696012yes—
552C2×C4#6703711yescharacteristic
553C2×C4#6703711yescharacteristic
554C2×C4#6704011yescharacteristic
555C2×C4#6704011yescharacteristic
556C2×C4#6704211yescharacteristic
557C2×C4#6704311yescharacteristic
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—441no—
563C8—441no—
564C8—441no—
565C8—441no—
566C22—441no—
567C22—441no—
568C22—441no—
569C22—441no—
570C22—441no—
571C22—441no—
572C22—441no—
573C22#1062303511yescharacteristic
574C22#1062307611yescharacteristic
575C22#1062310311yescharacteristic
576C22C2×#6696011yescharacteristic
577C22#1062327611yescharacteristic
578C22#1062328111yescharacteristic
579C22#1062328111yescharacteristic
580C4—22no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—441no—
587C4—441no—
588C4—441no—
589C4—441no—
590C4—441no—
591C4—441no—
592C4—441no—
593C4#1062315211yescharacteristic
594C4#1062317811yescharacteristic
595C4#1062323011yescharacteristic
596C4#1062326611yescharacteristic
597C2—881no—
598C2#1307177811yescharacteristic
599C2#1307766511yescharacteristic
600C2#1307768411yescharacteristic
601C2#1307771211yescharacteristic
602C2#1307771911yescharacteristic
603C2#1307776111yescharacteristic
604C2#1307778411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1940C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1940D11
hypocenterC11#23345
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
2. #13069554C2semidirect
3. #13069551C2semidirect
4. #13069338C2semidirect
9. #13069180C2semidirect
10. #13069177C2semidirect
11. #13069177C2semidirect
12. #13069175C2semidirect
15. C11×#1940C2semidirect
202. #1940D11semidirect
499. C11#23345semidirect

Maximal subgroups

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

subgroupindex
#130718922
#130695542
#130695512
#130693382
#130692292
#130692282
#130692202
#130691802
#130691772
#130691752
#130686862
#130685972
C11×#19402
#2334511