Finite Group Databasebeta

← #14771506

Subgroups — #14771506

Order 2816.

782 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622577C211yesmaximal, characteristic
2#13071499C211yesmaximal, characteristic
3#13069351C211yesmaximal, characteristic, complemented
4#13069346C211yesmaximal, characteristic, complemented
5#13069208C211yesmaximal, characteristic, complemented
6#13069198C211yesmaximal, characteristic, complemented
7#13069191C211yesmaximal, characteristic, complemented
8#13069187C211yesmaximal, characteristic, complemented
9#13068708C211yesmaximal, characteristic
10#13068702C211yesmaximal, characteristic
11#13068647C211yesmaximal, characteristic
12#13068514C211yesmaximal, characteristic, complemented
13C4×#66872C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic
15C11×#2345C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C11×#389C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C11×#387—21no—
22C11×#387—21no—
23C11×#380—21no—
24C11×#380C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C22⋊C4—21no—
28C4×C11×C22⋊C4C2211yescharacteristic
29#10622825C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31#10622577C418yescomplemented
32C2×#66872C2211yescharacteristic
33C2×#66872C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66871C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38#10622557—21no—
39#10622557—21no—
40C4×C4⋊Dic11C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45C2×C4×C11⋊C8C2211yescharacteristic
46#10622263—21no—
47#10622261—21no—
48#10622167C2211yescharacteristic
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2×C414yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80#66979—22no—
81#66979C2×C414yes—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318C2×C414yes—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95D411yescharacteristic
104C11×#95D411yescharacteristic
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C22⋊(C11⋊C8)—22no—
111#66872—22no—
112#66872C2×C414yes—
113#66872C2×C414yes—
114#66871—22no—
115#66871C2×C414yes—
116#66871C2×C414yes—
117#66867—22no—
118C4×C11⋊C8—22no—
119#22621—111nomaximal, Sylow
120C24×C11C2×D411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—24no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—81no—
131C22×C4×C11—81no—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11#4112yes—
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—81no—
152C11×C4⋊C4—81no—
153C11×C4⋊C4C22×C412yes—
154C11×C4⋊C4C22×C412yes—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—41no—
157C11×C22⋊C4—42no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—81no—
163C42×C11—81no—
164C22⋊Dic11—24no—
165C22⋊Dic11—81no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11C22×C412yes—
173C4⋊Dic11C22×C412yes—
174Dic11⋊C4—81no—
175Dic11⋊C4—81no—
176C4×Dic11—24no—
177C4×Dic11—42no—
178C4×Dic11—42no—
179#4318—28no—
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⋊C8C22×C412yes—
189C2×C11⋊C8C22×C412yes—
190C2×C11⋊C8#4112yes—
191C2×C11⋊C8#4112yes—
192C2×#428—111no—
193#2346—111no—
194#2345D1111yescharacteristic
195#1943—111no—
196#1942—111no—
197#1921—111no—
198#1920—111no—
199#1919—111no—
200#1918—111no—
201#1825—111no—
202#1823—111no—
203#1809—111no—
204#1776—111no—
205C4×#106—111no—
206#1753—111no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11C4×D412yes—
214C23×C11C22×D411yescharacteristic
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
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—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—84no—
245C2×C4×C11C4×D412yes—
246C2×C4×C11#13712yes—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C11⋊C8—22no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8#11714yes—
269C22×M16—111no—
270C2×#117—111no—
271C22×C4⋊C4C2×D1111yescharacteristic
272#428—118no—
273C2×#107—111no—
274C2×#107—111no—
275C2×#107—111no—
276C2×#106—111no—
277C2×#106—111no—
278C2×#106—111no—
279C2×C22⋊C8—111no—
280C2×#97—111no—
281C2×C4×C8—111no—
282#389—111no—
283#389—111no—
284#389C2×D1111yescharacteristic
285#389C2×D1111yescharacteristic
286#388—221no—
287#388—221no—
288#387—21no—
289#387—21no—
290#382—221no—
291#380—21no—
292#380—111no—
293#380C2×D1111yescharacteristic
294C4×C4⋊C4—111no—
295C4×C4⋊C4—111no—
296C4×C4⋊C4C2×D1111yescharacteristic
297C4×C4⋊C4C2×D1111yescharacteristic
298C4×C22⋊C4—21no—
299C4×C22⋊C4C2×D1111yescharacteristic
300#376—221no—
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#336—111no—
312#336—111no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11C2×C4×D411yescharacteristic
321C22×C11#54711yescharacteristic
322C22×C11#54711yescharacteristic
323C22×C11C2×#13711yescharacteristic
324C22×C11#57511yescharacteristic
325C22×C11#57611yescharacteristic
326C22×C11#57711yescharacteristic
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—42no—
333C4×C11—42no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11C2×#11711yescharacteristic
337C4×C11#51911yescharacteristic
338C4×C11#55211yescharacteristic
339C4×C11#55211yescharacteristic
340Dic11—42no—
341Dic11—42no—
342Dic11—81no—
343Dic11—81no—
344C23×C4—21no—
345C23×C4C22×D1111yescharacteristic
346C2×M16—114no—
347C2×M16—222no—
348C2×M16—222no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—111no—
353#117—114no—
354#117—222no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4C4×D1114yes—
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4C22⋊D1111yescharacteristic
374C2×C22⋊C4C22⋊D1111yescharacteristic
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—221no—
378C2×C42—221no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381C2×C42C22×D1111yescharacteristic
382#107—114no—
383#107—114no—
384#107—222no—
385#106—114no—
386#106—114no—
387#106—222no—
388C22⋊C8—222no—
389#97—222no—
390C4×C8—222no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95C22⋊D1111yescharacteristic
402#95C22⋊D1111yescharacteristic
403C2×C11—42no—
404C2×C11#234411yescharacteristic
405C2×C11C4×#13711yescharacteristic
406C2×C11#294611yescharacteristic
407C2×C11#334411yescharacteristic
408C2×C11#334711yescharacteristic
409C2×C11#335111yescharacteristic
410C2×C11#335711yescharacteristic
411C24C2×C22⋊D1111yescharacteristic
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—24no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4C2×C4×D1112yes—
428C22×C4#433912yes—
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435M16—228no—
436C2×C8—112no—
437C2×C8—112no—
438C2×C8—112no—
439C2×C8—112no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C4⋊C4—24no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—81no—
456C4⋊C4—81no—
457C4⋊C4—112no—
458C4⋊C4—112no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—881no—
466C4⋊C4—881no—
467C4⋊C4C2×C4×D1112yes—
468C4⋊C4C2×C4×D1112yes—
469C22⋊C4—22no—
470C22⋊C4—41no—
471C22⋊C4—42no—
472C22⋊C4—224no—
473C22⋊C4—881no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—81no—
479C42—81no—
480C42—224no—
481C42—442no—
482C42—442no—
483C11#2262111yescharacteristic, complemented, Sylow
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23C4×C22⋊D1112yes—
491C23C22×C22⋊D1111yescharacteristic
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
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—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—84no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4C4×C22⋊D1112yes—
535C2×C4#6699512yes—
536C2×C4C22×C4×D1111yescharacteristic
537C2×C4C2×#433911yescharacteristic
538C2×C4#41×D1111yescharacteristic
539C2×C4#41×D1111yescharacteristic
540C2×C4#6704311yescharacteristic
541C2×C4#6704311yescharacteristic
542C8—114no—
543C8—222no—
544C8—441no—
545C8—441no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22C2×C4×C22⋊D1111yescharacteristic
554C22C2×#6699511yescharacteristic
555C22#1062335311yescharacteristic
556C22#1062335511yescharacteristic
557C22#1062335511yescharacteristic
558C22#1062336611yescharacteristic
559C22#1062336711yescharacteristic
560C4—22no—
561C4—22no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—42no—
566C4—42no—
567C4—81no—
568C4—81no—
569C4—442no—
570C4—442no—
571C4—881no—
572C4—881no—
573C4#1062304711yescharacteristic
574C4D11×#11711yescharacteristic
575C4#1062306211yescharacteristic
576C4#1062306211yescharacteristic
577C2—42no—
578C2#1307148611yescharacteristic
579C2C4×#6699511yescharacteristic
580C2#1307744811yescharacteristic
581C2#1308106511yescharacteristic
582C2#1308111011yescharacteristic
583C2#1308117011yescharacteristic
584C2#1308124211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2345C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2345D11
hypocenterC11#22621
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2345

Complements

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

NH ≅ G/Ntype
3. #13069351C2semidirect
4. #13069346C2semidirect
5. #13069208C2semidirect
6. #13069198C2semidirect
7. #13069191C2semidirect
8. #13069187C2semidirect
12. #13068514C2semidirect
13. C4×#66872C2semidirect
31. #10622577C4semidirect
483. C11#22621semidirect

Maximal subgroups

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

subgroupindex
C2×#106225772
#130714992
#130693512
#130693462
#130692082
#130691982
#130691912
#130691872
#130687082
#130687022
#130686472
#130685142
C4×#668722
#130684002
C11×#23452
#2262111