Finite Group Databasebeta

← #14764208

Subgroups — #14764208

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077253C211yesmaximal, characteristic
2#13077252C211yesmaximal, characteristic
3C2×#10622452C211yesmaximal, characteristic
4#13069392C211yesmaximal, characteristic, complemented
5#13069391C211yesmaximal, characteristic, complemented
6#13069390C211yesmaximal, characteristic, complemented
7#13069390C211yesmaximal, characteristic, complemented
8#13069389C211yesmaximal, characteristic, complemented
9#13069388C211yesmaximal, characteristic, complemented
10#13069388C211yesmaximal, characteristic, complemented
11#13068657C211yesmaximal, characteristic
12#13068655C211yesmaximal, characteristic
13#13068653C211yesmaximal, characteristic
14#13068651C211yesmaximal, characteristic
15C11×#1950C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66925C2211yescharacteristic
19C2×C11×#108C2211yescharacteristic
20C2×C11×#108C2211yescharacteristic
21C11×#423C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C4×C11×M16C2211yescharacteristic
24#10622739C2211yescharacteristic
25#10622739C2211yescharacteristic
26#10622739C2211yescharacteristic
27#10622739C2211yescharacteristic
28C2×#66886C2211yescharacteristic
29C2×#66886C2211yescharacteristic
30C2×#66886C2211yescharacteristic
31C2×#66886C2211yescharacteristic
32#10622731C2211yescharacteristic
33#10622731C2211yescharacteristic
34M16×Dic11C2211yescharacteristic
35M16×Dic11C2211yescharacteristic
36C2×#66883C2211yescharacteristic
37C2×#66883C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622537C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622453—21no—
44#10622453—21no—
45#10622453—21no—
46#10622453—21no—
47#10622452C412yes—
48#10622452C412yes—
49#10622452C412yes—
50#10622452C412yes—
51#10622322—21no—
52#10622322—21no—
53#10622303—21no—
54#10622303—21no—
55C11×#341C2211yescharacteristic
56C11×#341C2211yescharacteristic
57#10622196C2211yescharacteristic
58#10622196C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622196C2211yescharacteristic
61#10622190C2211yescharacteristic
62#10622190C2211yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C2×C11×M16C2311yescharacteristic
65C2×C11×M16C2311yescharacteristic
66C2×C11×M16C2311yescharacteristic
67C2×C11×M16C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4Q811yescharacteristic
72C2×(C2×D11)⋊C4Q811yescharacteristic
73C2×Dic11⋊C4Q811yescharacteristic
74C2×Dic11⋊C4Q811yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C2×#4318C2311yescharacteristic
77C2×#4318C2311yescharacteristic
78C2×#4318C2311yescharacteristic
79C2×#4318C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C2×#4313—41no—
83C2×#4313—41no—
84C2×#4313C2×C412yes—
85C2×#4313C2×C412yes—
86C2×C8×D11—41no—
87C2×C8×D11—41no—
88C2×C8×D11C2×C412yes—
89C2×C8×D11C2×C412yes—
90#66925C2×C411yescharacteristic
91#66925C2×C411yescharacteristic
92#66925C2×C411yescharacteristic
93#66925C2×C411yescharacteristic
94#66925D411yescharacteristic
95#66925D411yescharacteristic
96#66925D411yescharacteristic
97#66925D411yescharacteristic
98C11×#108—41no—
99C11×#108—41no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2×C412yes—
103C11×C4⋊C8C2×C412yes—
104C11×#97—21no—
105C4×C8×C11—21no—
106#66886—41no—
107#66886—41no—
108#66886—41no—
109#66886—41no—
110(C2×D11)⋊C8—21no—
111(C2×D11)⋊C8—21no—
112(C2×D11)⋊C8—21no—
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118#66883—41no—
119#66883—41no—
120#66879—21no—
121#66879—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8C2×C412yes—
127Dic11⋊C8C2×C412yes—
128Dic11⋊C8C2×C412yes—
129Dic11⋊C8C2×C412yes—
130C8×Dic11—21no—
131C8×Dic11—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)C2×C412yes—
135C4⋊(C11⋊C8)C2×C412yes—
136#66867—21no—
137C4×C11⋊C8—21no—
138#21971—111nomaximal, Sylow
139C23×D11C2×Q811yescharacteristic
140C22×C4×C11C2×Q811yescharacteristic
141C22×C4×C11C2×Q811yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11C2×Q811yescharacteristic
144C22×Dic11C2×Q811yescharacteristic
145C22×Dic11C2×Q811yescharacteristic
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11C22×C411yescharacteristic
151C2×C4×D11C22×C411yescharacteristic
152C2×C4×D11C2×D411yescharacteristic
153C2×C4×D11C2×D411yescharacteristic
154C11×M16—21no—
155C11×M16—21no—
156C11×M16—21no—
157C11×M16—21no—
158C11×M16—21no—
159C11×M16—21no—
160C11×M16—21no—
161C11×M16—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×C11C22×C412yes—
171C2×C8×C11C22×C412yes—
172C42×C11C22×C411yescharacteristic
173C42×C11C22×C411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11C2×D411yescharacteristic
176(C2×D11)⋊C4C4⋊C411yescharacteristic
177(C2×D11)⋊C4C4⋊C411yescharacteristic
178(C2×D11)⋊C4C4⋊C411yescharacteristic
179(C2×D11)⋊C4C4⋊C411yescharacteristic
180(C2×D11)⋊C4C4⋊C411yescharacteristic
181(C2×D11)⋊C4C4⋊C411yescharacteristic
182(C2×D11)⋊C4C4⋊C411yescharacteristic
183(C2×D11)⋊C4C4⋊C411yescharacteristic
184Dic11⋊C4C4⋊C411yescharacteristic
185Dic11⋊C4C4⋊C411yescharacteristic
186Dic11⋊C4C4⋊C411yescharacteristic
187Dic11⋊C4C4⋊C411yescharacteristic
188Dic11⋊C4C4⋊C411yescharacteristic
189Dic11⋊C4C4⋊C411yescharacteristic
190Dic11⋊C4C4⋊C411yescharacteristic
191Dic11⋊C4C4⋊C411yescharacteristic
192C4×Dic11C22×C411yescharacteristic
193C4×Dic11C22×C411yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C4×Dic11C2×D411yescharacteristic
196#4318—21no—
197#4318—21no—
198#4318—21no—
199#4318—21no—
200#4318—21no—
201#4318—21no—
202#4318—21no—
203#4318—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C22×C412yes—
213C2×C11⋊C8C22×C412yes—
214#4313—42no—
215#4313—42no—
216C8×D11—42no—
217C8×D11—42no—
218#2921—111no—
219#2921—111no—
220C2×#424—111no—
221#1950—111no—
222#1950—111no—
223#1950—111no—
224#1950—111no—
225#1950—111no—
226#1950—111no—
227#1950—111no—
228#1950D1111yescharacteristic, complemented
229#1811—111no—
230#1811—111no—
231#1810—111no—
232#1810—111no—
233C23×C11C22×Q811yescharacteristic
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11C2×C4⋊C411yescharacteristic
239C22×D11C2×C4⋊C411yescharacteristic
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11C2×C4⋊C411yescharacteristic
243C2×C4×C11C2×C4⋊C411yescharacteristic
244C2×C4×C11C2×C4⋊C411yescharacteristic
245C2×C4×C11C2×C4⋊C411yescharacteristic
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11C2×C4⋊C411yescharacteristic
257C2×Dic11C2×C4⋊C411yescharacteristic
258C2×Dic11C2×C4⋊C411yescharacteristic
259C2×Dic11C2×C4⋊C411yescharacteristic
260C2×Dic11C2×C4⋊C411yescharacteristic
261C2×Dic11C2×C4⋊C411yescharacteristic
262C4×D11—21no—
263C4×D11—21no—
264C4×D11—21no—
265C4×D11—21no—
266C4×D11—21no—
267C4×D11—21no—
268C4×D11—21no—
269C4×D11—21no—
270C8×C11—22no—
271C8×C11—22no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—41no—
276C11⋊C8—22no—
277C11⋊C8—22no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C22×M16—111no—
283C23×C8—111no—
284C2×#117—111no—
285#433—221no—
286#433—221no—
287#433—221no—
288#433—221no—
289#433—221no—
290#433—221no—
291#433—221no—
292#433—221no—
293C2×#108—111no—
294C2×#108—111no—
295C2×#108—111no—
296C2×#108—111no—
297C2×#108—111no—
298C2×#108—111no—
299C2×#108C2×D1111yescharacteristic
300C2×#108C2×D1111yescharacteristic
301#424—112no—
302#424—112no—
303#424—112no—
304#424—112no—
305#423—111no—
306#423—111no—
307#423—111no—
308#423C2×D1111yescharacteristic
309C2×C4⋊C8—111no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8C2×D1111yescharacteristic
313#407—111no—
314#407—111no—
315#407—111no—
316#407—111no—
317C4×M16—111no—
318C4×M16—111no—
319C4×M16—111no—
320C4×M16C2×D1111yescharacteristic
321#341—111no—
322#341—111no—
323#341—111no—
324#341—111no—
325#341—111no—
326#341—111no—
327#341C2×D1111yescharacteristic
328#341C2×D1111yescharacteristic
329C22×C11—21no—
330C22×C11—21no—
331C22×C11C22×C4⋊C411yescharacteristic
332C22×C11#54411yescharacteristic
333C22×C11#54411yescharacteristic
334C2×D11—21no—
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—21no—
338C2×D11—21no—
339C2×D11—21no—
340C2×D11—42no—
341C2×D11—42no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11#51811yescharacteristic
347C4×C11#51911yescharacteristic
348C4×C11#53711yescharacteristic
349C4×C11#53711yescharacteristic
350Dic11—21no—
351Dic11—21no—
352Dic11—21no—
353Dic11—21no—
354Dic11—21no—
355Dic11—21no—
356C23×C4—111no—
357C2×M16—112no—
358C2×M16—112no—
359C2×M16—111no—
360C2×M16—111no—
361C2×M16—111no—
362C2×M16—111no—
363C2×M16—441no—
364C2×M16—441no—
365C2×M16C22×D1111yescharacteristic
366C2×M16C22×D1111yescharacteristic
367C2×M16C22×D1111yescharacteristic
368C2×M16C22×D1111yescharacteristic
369C22×C8—111no—
370C22×C8—111no—
371C22×C8—112no—
372C22×C8—112no—
373C22×C8—441no—
374C22×C8—441no—
375C22×C8C22×D1111yescharacteristic
376C22×C8C22×D1111yescharacteristic
377#117—111no—
378#117—111no—
379#117—111no—
380#117—111no—
381#117—111no—
382#117—111no—
383#117—111no—
384#117—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C22⋊C4—111no—
388C2×C22⋊C4—111no—
389C2×C42—111no—
390C2×C42C22×D1111yescharacteristic
391#108—41no—
392#108—41no—
393#108—441no—
394#108—441no—
395#108—441no—
396#108—441no—
397#108—441no—
398#108—441no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—112no—
402C4⋊C8—112no—
403C4⋊C8—112no—
404C4⋊C8—112no—
405C4⋊C8—112no—
406C4⋊C8—112no—
407C4⋊C8—221no—
408C4⋊C8—221no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8—221no—
412C4⋊C8—221no—
413C4⋊C8C4×D1112yes—
414C4⋊C8C4×D1112yes—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423#97—21no—
424#97—221no—
425#97—221no—
426#97—221no—
427C4×C8—21no—
428C4×C8—221no—
429C4×C8—221no—
430C4×C8—221no—
431C2×C11—21no—
432C2×C11—21no—
433C2×C11#231611yescharacteristic
434C2×C11#291611yescharacteristic
435C2×C11#291611yescharacteristic
436D11—41no—
437D11—41no—
438C24—111no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4Q8×D1111yescharacteristic
451C22×C4Q8×D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453M16—21no—
454M16—21no—
455M16—21no—
456M16—21no—
457M16—21no—
458M16—21no—
459M16—21no—
460M16—21no—
461M16—221no—
462M16—221no—
463M16—221no—
464M16—221no—
465M16—221no—
466M16—221no—
467M16—221no—
468M16—221no—
469M16—442no—
470M16—442no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—112no—
480C2×C8—112no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—442no—
490C2×C8—442no—
491C2×C8C2×C4×D1112yes—
492C2×C8C2×C4×D1112yes—
493C4⋊C4—111no—
494C4⋊C4—111no—
495C4⋊C4—111no—
496C4⋊C4—111no—
497C4⋊C4—111no—
498C4⋊C4—111no—
499C4⋊C4—111no—
500C4⋊C4—111no—
501C22⋊C4—111no—
502C22⋊C4—111no—
503C22⋊C4—111no—
504C22⋊C4—111no—
505C22⋊C4—111no—
506C22⋊C4—111no—
507C22⋊C4—111no—
508C22⋊C4—111no—
509C42—111no—
510C42—111no—
511C42—111no—
512C42—111no—
513C42C2×C4×D1111yescharacteristic
514C42C2×C4×D1111yescharacteristic
515C42D4×D1111yescharacteristic
516C42D4×D1111yescharacteristic
517C11#2197111yescharacteristic, complemented, Sylow
518C23—111no—
519C23—111no—
520C23—221no—
521C23—221no—
522C23—441no—
523C23—441no—
524C23C2×Q8×D1111yescharacteristic
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—111no—
528C2×C4—111no—
529C2×C4—111no—
530C2×C4—111no—
531C2×C4—111no—
532C2×C4—111no—
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—441no—
544C2×C4—441no—
545C2×C4C4⋊C4×D1111yescharacteristic
546C2×C4C4⋊C4×D1111yescharacteristic
547C2×C4C4⋊C4×D1111yescharacteristic
548C2×C4C4⋊C4×D1111yescharacteristic
549C2×C4C22×C4×D1111yescharacteristic
550C2×C4C2×D4×D1111yescharacteristic
551C2×C4#6703711yescharacteristic
552C2×C4#6704011yescharacteristic
553C2×C4#6704211yescharacteristic
554C2×C4#6704311yescharacteristic
555C8—22no—
556C8—22no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—222no—
562C8—222no—
563C8—441no—
564C8—441no—
565C8—441no—
566C8—441no—
567C22—21no—
568C22—21no—
569C22—221no—
570C22—221no—
571C22—221no—
572C22—221no—
573C22—221no—
574C22—221no—
575C22—442no—
576C22—442no—
577C22C2×C4⋊C4×D1111yescharacteristic
578C22#1062322011yescharacteristic
579C22#1062326011yescharacteristic
580C4—21no—
581C4—21no—
582C4—21no—
583C4—21no—
584C4—221no—
585C4—221no—
586C4—221no—
587C4—221no—
588C4—221no—
589C4—221no—
590C4#1062307611yescharacteristic
591C4#1062310311yescharacteristic
592C4#1062313911yescharacteristic
593C4#1062316011yescharacteristic
594C2—21no—
595C2—21no—
596C2—441no—
597C2—441no—
598C2#1307123111yescharacteristic
599C2#1307722411yescharacteristic
600C2#1307722611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1950C2
socleC22×C11C22×C4⋊C4
prime radicalC23×D11C2×Q8
cosocleC22×C4×C11C24
hypercenter#1950D11
hypocenterC11#21971
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
4. #13069392C2semidirect
5. #13069391C2semidirect
6. #13069390C2semidirect
7. #13069390C2semidirect
8. #13069389C2semidirect
9. #13069388C2semidirect
10. #13069388C2semidirect
15. C11×#1950C2semidirect
228. #1950D11semidirect
517. C11#21971semidirect

Maximal subgroups

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

subgroupindex
#130772532
#130772522
C2×#106224522
#130693922
#130693912
#130693902
#130693892
#130693882
#130686572
#130686552
#130686532
#130686512
C11×#19502
#2197111