Finite Group Databasebeta

← #14827009

Subgroups — #14827009

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073213C211yesmaximal, characteristic
2#13070164C211yesmaximal, characteristic, complemented
3#13069931C211yesmaximal, characteristic
4#13069859C211yesmaximal, characteristic, complemented
5#13069699C211yesmaximal, characteristic
6#13069473C211yesmaximal, characteristic
7#13069254C211yesmaximal, characteristic, complemented
8#13069236C211yesmaximal, characteristic
9#13069201C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068971C211yesmaximal, characteristic
12#13068971C211yesmaximal, characteristic
13#13068631C211yesmaximal, characteristic, complemented
14C4×#66899C211yesmaximal, characteristic, complemented
15C11×#2365C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C11×#391C2211yescharacteristic
22C11×#391C2211yescharacteristic
23C11×#389—21no—
24C11×#387—21no—
25C11×#387—21no—
26C4×C11×C4⋊C4—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35#10622606—21no—
36#10622603—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622552C2211yescharacteristic
42#10622552C2211yescharacteristic
43#10622552C2211yescharacteristic
44#10622549C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622288—21no—
50#10622282—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D44C2311yescharacteristic
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—41no—
67C4×Q8×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×#4325—22no—
83C2×#4325—22no—
84C2×#4325—22no—
85C2×#4325—41no—
86C2×#4325—41no—
87C2×#4325—41no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110#66899—22no—
111#66899—22no—
112#66899—22no—
113#66899—41no—
114#66899—41no—
115#66899—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66873—22no—
121#66873—41no—
122#66872—22no—
123#66871—41no—
124C4⋊(C11⋊C8)—41no—
125C4×C11⋊C8—41no—
126#27069—111nomaximal, Sylow
127C23×D11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11#4112yes—
139C2×Q8×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4#4112yes—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—42no—
177C42×C11—42no—
178C42×C11—42no—
179#4325—44no—
180#4325—44no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—42no—
183(C2×D11)⋊C4—81no—
184(C2×D11)⋊C4—81no—
185(C2×D11)⋊C4—81no—
186(C2×D11)⋊C4—81no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193Dic11⋊C4—81no—
194C4×Dic11—81no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—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#4112yes—
207#2513—111no—
208#2365D1111yescharacteristic, complemented
209#2097—111no—
210#2055—111no—
211#2043—111no—
212#2013—111no—
213#1968—111no—
214#1928—111no—
215#1925—111no—
216#1920—111no—
217#1916—111no—
218#1880—111no—
219#1880—111no—
220#1805—111no—
221C4×#103—111no—
222C23×C11C22×D411yescharacteristic
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—41no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
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—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11#13512yes—
267C2×C4×C11#13712yes—
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283D44—41no—
284D44—41no—
285D44—41no—
286D44—41no—
287C11⋊C8—22no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C22×SD16—111no—
292C22×SD16—111no—
293C2×C4⋊Q8C2×D1111yescharacteristic
294C2×C4×Q8C2×D1111yescharacteristic
295C2×C4×Q8C2×D1111yescharacteristic
296C2×#107—111no—
297C2×#106—111no—
298C2×C4⋊C8—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#102—111no—
306C2×#102—111no—
307C2×C4×C8—111no—
308#397—221no—
309#397—221no—
310#391C2×D1111yescharacteristic
311#391C2×D1111yescharacteristic
312#390—111no—
313#390—111no—
314#390—111no—
315#389—21no—
316#389—111no—
317#388—221no—
318#388—221no—
319#387—21no—
320#387—21no—
321#382—111no—
322C4×C4⋊C4—21no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4C2×D1111yescharacteristic
325C4×C4⋊C4C2×D1111yescharacteristic
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#336—111no—
331#336—111no—
332#336—111no—
333#336—111no—
334C22×C11#52511yescharacteristic
335C22×C11#54611yescharacteristic
336C22×C11#55011yescharacteristic
337C22×C11C2×#13511yescharacteristic
338C22×C11C2×#13711yescharacteristic
339C22×C11#57711yescharacteristic
340C22×C11#57711yescharacteristic
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C4×C11—22no—
349C4×C11—22no—
350C4×C11—41no—
351C4×C11—42no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—41no—
357C4×C11—81no—
358C4×C11#52911yescharacteristic
359C4×C11#53811yescharacteristic
360C4×C11#55111yescharacteristic
361C4×C11#55311yescharacteristic
362Dic11—81no—
363Dic11—81no—
364Dic11—81no—
365C22×Q8C22×D1111yescharacteristic
366C22×Q8C22×D1111yescharacteristic
367C22×D4—111no—
368C2×SD16—222no—
369C2×SD16—222no—
370C2×SD16—222no—
371C2×SD16—441no—
372C2×SD16—441no—
373C2×SD16—441no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8—111no—
377C22×C8—111no—
378C4⋊Q8—22no—
379C4⋊Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—41no—
383C4×Q8—41no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4C22⋊D1111yescharacteristic
393C2×C4⋊C4C22⋊D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—221no—
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1111yescharacteristic
408C2×C42C22×D1111yescharacteristic
409#107—441no—
410#106—222no—
411C4⋊C8—441no—
412#103—222no—
413#103—222no—
414#103—222no—
415#103—441no—
416#103—441no—
417#103—441no—
418#102—222no—
419#102—441no—
420C4×C8—441no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95C22⋊D1111yescharacteristic
431#95C22⋊D1111yescharacteristic
432C2×C11#246711yescharacteristic
433C2×C11#310811yescharacteristic
434C2×C11#312611yescharacteristic
435C2×C11#330311yescharacteristic
436C2×C11#332011yescharacteristic
437C2×C11#339411yescharacteristic
438C2×C11#340011yescharacteristic
439D11—161no—
440C24—221no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8#433912yes—
452C2×Q8#433912yes—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C23×D1111yescharacteristic
473SD16—444no—
474SD16—444no—
475C2×C8—112no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C4⋊C4—24no—
488C4⋊C4—24no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—881no—
503C4⋊C4#434112yes—
504C22⋊C4—442no—
505C22⋊C4—442no—
506C22⋊C4—881no—
507C22⋊C4—881no—
508C22⋊C4—881no—
509C22⋊C4—881no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—42no—
517C42—42no—
518C42—42no—
519C42—881no—
520C11#2706911yescharacteristic, complemented, Sylow
521C23—441no—
522C23—441no—
523C23—441no—
524C23—441no—
525C23—441no—
526C23—441no—
527C23—441no—
528C23C22×C22⋊D1111yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8—22no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537D4—441no—
538D4—441no—
539D4—441no—
540D4—441no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4#6699512yes—
579C2×C4#6700312yes—
580C2×C4C2×#433911yescharacteristic
581C2×C4C2×#433911yescharacteristic
582C2×C4C2×#434111yescharacteristic
583C2×C4#6703711yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#6704211yescharacteristic
586C8—222no—
587C8—441no—
588C8—441no—
589C8—441no—
590C22—881no—
591C22—881no—
592C22—881no—
593C22—881no—
594C22—881no—
595C22—881no—
596C22—881no—
597C22#1062332211yescharacteristic
598C22#1062333711yescharacteristic
599C22C2×#6699511yescharacteristic
600C22C2×#6700311yescharacteristic
601C22#1062336511yescharacteristic
602C22#1062336811yescharacteristic
603C22#1062336811yescharacteristic
604C4—22no—
605C4—22no—
606C4—42no—
607C4—42no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—42no—
613C4—81no—
614C4—881no—
615C4—881no—
616C4—881no—
617C4#1062306911yescharacteristic
618C4#1062308711yescharacteristic
619C4#1062309111yescharacteristic
620C4#1062309611yescharacteristic
621C2—1761no—
622C2#1307266111yescharacteristic
623C2#1307869611yescharacteristic
624C2#1307890711yescharacteristic
625C2#1308054411yescharacteristic
626C2#1308078711yescharacteristic
627C2#1308161211yescharacteristic
628C2#1308166511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2365C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2365D11
hypocenterC11#27069
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
2. #13070164C2semidirect
4. #13069859C2semidirect
7. #13069254C2semidirect
9. #13069201C2semidirect
10. #13069175C2semidirect
13. #13068631C2semidirect
14. C4×#66899C2semidirect
15. C11×#2365C2semidirect
208. #2365D11semidirect
520. C11#27069semidirect

Maximal subgroups

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

subgroupindex
#130732132
#130701642
#130699312
#130698592
#130696992
#130694732
#130692542
#130692362
#130692012
#130691752
#130689712
#130686312
C4×#668992
C11×#23652
#2706911