Finite Group Databasebeta

← #14780550

Subgroups — #14780550

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071917C211yesmaximal, characteristic
2#13069336C211yesmaximal, characteristic, complemented
3#13069332C211yesmaximal, characteristic, complemented
4#13069229C211yesmaximal, characteristic
5#13069228C211yesmaximal, characteristic
6#13069220C211yesmaximal, characteristic
7#13069181C211yesmaximal, characteristic, complemented
8#13069180C211yesmaximal, characteristic, complemented
9#13069175C211yesmaximal, characteristic, complemented
10#13068800C211yesmaximal, characteristic
11#13068797C211yesmaximal, characteristic
12#13068797C211yesmaximal, characteristic
13#13068769C211yesmaximal, characteristic, complemented
14#13068760C211yesmaximal, characteristic, complemented
15C11×#1940C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C8C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×#66879C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622607C411yescharacteristic
32#10622606C411yescharacteristic
33#10622599C411yescharacteristic
34#10622595C411yescharacteristic
35C4×(C2×D11)⋊C4C2211yescharacteristic
36C4×(C2×D11)⋊C4C2211yescharacteristic
37C4×(C2×D11)⋊C4C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39#10622545C2211yescharacteristic
40C4×Dic11⋊C4C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622288C411yescharacteristic
44#10622287C411yescharacteristic
45C11⋊#401C411yescharacteristic
46#10622273C411yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4C2×C411yescharacteristic
65C2×C11×C4⋊C4C2×C411yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×(C2×D11)⋊C4C2×C411yescharacteristic
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×C4⋊Dic11C2×C411yescharacteristic
76C2×C4⋊Dic11C2×C411yescharacteristic
77C2×Dic11⋊C4C2×C411yescharacteristic
78C2×Dic11⋊C4C2×C411yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C2×#4313—41no—
87C2×#4313—41no—
88C2×#4313—41no—
89C11×C4⋊C8—41no—
90C11×C4⋊C8—41no—
91C11×C4⋊C8—41no—
92C11×#97—41no—
93C11×#95C2×C411yescharacteristic
94C11×#95C2×C411yescharacteristic
95C11⋊#95C2×C411yescharacteristic
96C11⋊#95C2×C411yescharacteristic
97C11⋊#95C2×C411yescharacteristic
98C11⋊#95C2×C411yescharacteristic
99C11⋊#95C2×C411yescharacteristic
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
109(C2×D11)⋊C8—41no—
110(C2×D11)⋊C8—41no—
111(C2×D11)⋊C8—41no—
112#66879—41no—
113Dic11⋊C8—41no—
114Dic11⋊C8—41no—
115Dic11⋊C8—41no—
116Dic11⋊C8—41no—
117Dic11⋊C8—41no—
118C4⋊(C11⋊C8)—41no—
119C4×C11⋊C8—41no—
120#23382—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×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
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—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—41no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162(C2×D11)⋊C4—22no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168C4⋊Dic11—22no—
169C4⋊Dic11—41no—
170Dic11⋊C4—41no—
171Dic11⋊C4—41no—
172C4×Dic11—21no—
173C4×Dic11—21no—
174C4×Dic11—21no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190#4313—44no—
191#2401—111no—
192#1940—111no—
193#1940D1111yescharacteristic, complemented
194#1939—111no—
195#1924—111no—
196#1924—111no—
197#1923—111no—
198#1917—111no—
199#1917—111no—
200#1916—111no—
201#1851—111no—
202#1851—111no—
203#1851—111no—
204#1843—111no—
205#1840—111no—
206C23×C11C23×C411yescharacteristic
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—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#13112yes—
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C2×C4×C112−1+411yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
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—
259C4×D11—41no—
260C4×D11—41no—
261C4×D11—41no—
262C4×D11—41no—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C22×M16—111no—
272C2×C4⋊C8—111no—
273C2×C4⋊C8—111no—
274C2×C4⋊C8—111no—
275C2×C4⋊C8—111no—
276C2×C4⋊C8—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8C2×D1111yescharacteristic
279C2×C4⋊C8C2×D1111yescharacteristic
280C2×C4⋊C8C2×D1111yescharacteristic
281C2×C22⋊C8—111no—
282C2×C22⋊C8—111no—
283C2×C22⋊C8—111no—
284C2×#97—111no—
285C2×#97C2×D1111yescharacteristic
286C2×C4×C8—111no—
287#401—111no—
288#400—111no—
289#400—111no—
290#400—111no—
291#397—111no—
292#397—111no—
293#397—111no—
294#396—111no—
295C4×C4⋊C4—111no—
296C4×C4⋊C4—111no—
297C4×C4⋊C4C2×D1111yescharacteristic
298C4×C22⋊C4—111no—
299C4×C22⋊C4—111no—
300C4×C22⋊C4—111no—
301#376—111no—
302#336—111no—
303#336—111no—
304#336—111no—
305#336—111no—
306#336—111no—
307#336—111no—
308#336—111no—
309#336—111no—
310#336—111no—
311#336—111no—
312#336C2×D1111yescharacteristic
313#336C2×D1111yescharacteristic
314C22×C11#52011yescharacteristic
315C22×C11#52011yescharacteristic
316C22×C11#52011yescharacteristic
317C22×C11C2×#13111yescharacteristic
318C22×C11#56811yescharacteristic
319C22×C11#56811yescharacteristic
320C22×C11#56811yescharacteristic
321C2×D11—41no—
322C2×D11—41no—
323C2×D11—41no—
324C2×D11—41no—
325C2×D11—41no—
326C2×D11—41no—
327C2×D11—41no—
328C4×C11—22no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11#56011yescharacteristic
335C4×C11#56311yescharacteristic
336C4×C11#56311yescharacteristic
337C4×C11#56311yescharacteristic
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344Dic11—41no—
345C23×C4—111no—
346C2×M16—441no—
347C2×M16—441no—
348C2×M16—441no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8C22×D1111yescharacteristic
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4C4×D1111yescharacteristic
362C2×C4⋊C4C4×D1111yescharacteristic
363C2×C22⋊C4—111no—
364C2×C22⋊C4—111no—
365C2×C22⋊C4—111no—
366C2×C22⋊C4—111no—
367C2×C22⋊C4—111no—
368C2×C22⋊C4—111no—
369C2×C42—111no—
370C2×C42—111no—
371C2×C42—111no—
372C2×C42C22×D1111yescharacteristic
373C2×C42C22×D1111yescharacteristic
374C2×C42C22×D1111yescharacteristic
375C4⋊C8—41no—
376C4⋊C8—41no—
377C4⋊C8—41no—
378C4⋊C8—441no—
379C4⋊C8—441no—
380C4⋊C8—441no—
381C4⋊C8—441no—
382C4⋊C8—441no—
383C4⋊C8—441no—
384C22⋊C8—441no—
385C22⋊C8—441no—
386C22⋊C8—441no—
387#97—41no—
388#97—441no—
389C4×C8—441no—
390#95—111no—
391#95—111no—
392#95—111no—
393#95—111no—
394#95—111no—
395#95—111no—
396#95—111no—
397#95—111no—
398#95—111no—
399#95—111no—
400#95—111no—
401#95—111no—
402#95—111no—
403#95—111no—
404#95C4×D1111yescharacteristic
405#95C4×D1111yescharacteristic
406C2×C11#238311yescharacteristic
407C2×C11#299211yescharacteristic
408C2×C11#299311yescharacteristic
409C2×C11#299311yescharacteristic
410C2×C11#299511yescharacteristic
411C2×C11#299511yescharacteristic
412C2×C11#299511yescharacteristic
413D11—81no—
414C24—111no—
415C22×C4—111no—
416C22×C4—111no—
417C22×C4—111no—
418C22×C4—111no—
419C22×C4—111no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4C2×C4×D1111yescharacteristic
429C22×C4C2×C4×D1111yescharacteristic
430C22×C4C2×C4×D1111yescharacteristic
431C22×C4C2×C4×D1111yescharacteristic
432C22×C4C2×C4×D1111yescharacteristic
433C22×C4C2×C4×D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435M16—444no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C4⋊C4—22no—
461C4⋊C4—41no—
462C4⋊C4—222no—
463C4⋊C4—441no—
464C4⋊C4—441no—
465C4⋊C4—441no—
466C22⋊C4—222no—
467C22⋊C4—441no—
468C22⋊C4—441no—
469C22⋊C4—441no—
470C22⋊C4—441no—
471C22⋊C4—441no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—221no—
479C42—221no—
480C42—221no—
481C42—221no—
482C42—221no—
483C42—221no—
484C11#2338211yescharacteristic, complemented, Sylow
485C23—221no—
486C23—221no—
487C23—221no—
488C23—221no—
489C23—221no—
490C23—221no—
491C23—221no—
492C23C22×C4×D1111yescharacteristic
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4#6696012yes—
536C2×C4#6703711yescharacteristic
537C2×C4#6703711yescharacteristic
538C2×C4#6704011yescharacteristic
539C2×C4#6704011yescharacteristic
540C2×C4#6704211yescharacteristic
541C2×C4#6704311yescharacteristic
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—441no—
547C8—441no—
548C8—441no—
549C8—441no—
550C22—441no—
551C22—441no—
552C22—441no—
553C22—441no—
554C22—441no—
555C22—441no—
556C22—441no—
557C22#1062303511yescharacteristic
558C22#1062307711yescharacteristic
559C22#1062310511yescharacteristic
560C22C2×#6696011yescharacteristic
561C22#1062327611yescharacteristic
562C22#1062328111yescharacteristic
563C22#1062328111yescharacteristic
564C4—22no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—441no—
571C4—441no—
572C4—441no—
573C4—441no—
574C4—441no—
575C4—441no—
576C4—441no—
577C4#1062315111yescharacteristic
578C4#1062317711yescharacteristic
579C4#1062323011yescharacteristic
580C4#1062326611yescharacteristic
581C2—881no—
582C2#1307180711yescharacteristic
583C2#1307775611yescharacteristic
584C2#1307776111yescharacteristic
585C2#1307776811yescharacteristic
586C2#1307778211yescharacteristic
587C2#1307778411yescharacteristic
588C2#1307778511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1940C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1940D11
hypocenterC11#23382
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
2. #13069336C2semidirect
3. #13069332C2semidirect
7. #13069181C2semidirect
8. #13069180C2semidirect
9. #13069175C2semidirect
13. #13068769C2semidirect
14. #13068760C2semidirect
15. C11×#1940C2semidirect
193. #1940D11semidirect
484. C11#23382semidirect

Maximal subgroups

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

subgroupindex
#130719172
#130693362
#130693322
#130692292
#130692282
#130692202
#130691812
#130691802
#130691752
#130688002
#130687972
#130687692
#130687602
C11×#19402
#2338211