Finite Group Databasebeta

← #14652893

Subgroups — #14652893

Order 2816.

716 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076964C211yesmaximal, characteristic
2#13068594C211yesmaximal, characteristic
3C2×#10622105C211yesmaximal, characteristic
4C2×#10622176C211yesmaximal, characteristic
5C2×#10622090C211yesmaximal, characteristic
6#95×Dic11C211yesmaximal, characteristic
7C2×C11×#328C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×#66997C411yescharacteristic, complemented
10C2×#66977C2211yescharacteristic
11C22×C4×Dic11—21no—
12C22×C4×Dic11C2211yescharacteristic
13C2×C11×C22⋊C8C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15#10622843C411yescharacteristic, complemented
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×Dic11⋊C8—21no—
20#10622589C411yescharacteristic, complemented
21#10622587C411yescharacteristic, complemented
22#10622585—21no—
23#10622585—21no—
24#10622555—21no—
25#10622555—21no—
26C11×#328—22no—
27#10622188—21no—
28#10622176—22no—
29#10622105—22no—
30#10622090—22no—
31C22×Q8×C11C2×C411yescharacteristic
32C23×C4×C11—21no—
33C23×C4×C11C2311yescharacteristic
34C23×Dic11—21no—
35C23×Dic11D411yescharacteristic
36C23×Dic11D411yescharacteristic
37C22×Dic22C2×C411yescharacteristic
38C22×C8×C11—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C22⋊Dic11—21no—
47#66997—42no—
48C2×C4⋊Dic11C2×C411yescharacteristic
49#66977—21no—
50#66977—21no—
51#66977—21no—
52#66977—21no—
53C2×Dic11⋊C4—21no—
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—21no—
58C2×C4×Dic11—24no—
59C2×C4×Dic11—42no—
60C2×C4×Dic11—42no—
61C2×C4×Dic11—42no—
62C2×C4×Dic11C2×C411yescharacteristic
63C2×C4×Dic11C2×C411yescharacteristic
64C2×C4×Dic11D411yescharacteristic
65C2×C4×Dic11D411yescharacteristic
66C22×C11⋊C8—21no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C11×#95—21no—
70C11×#95D412yes—
71C11⋊#95—24no—
72C11⋊#95—21no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C11⋊#95—21no—
77C11⋊#95D412yes—
78C22⋊(C11⋊C8)—21no—
79C22⋊(C11⋊C8)—21no—
80Dic11⋊C8—42no—
81#9711—111nomaximal, Sylow
82C24×C11C2×D411yescharacteristic
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11C22⋊C411yescharacteristic
120C22×Dic11C22⋊C411yescharacteristic
121C22×Dic11C22⋊C411yescharacteristic
122C22×Dic11C22⋊C411yescharacteristic
123C22×Dic11SD1612yes—
124C22×Dic11Q1612yes—
125C2×Dic22—21no—
126C2×Dic22—21no—
127C2×Dic22—41no—
128C2×Dic22—41no—
129C2×C8×C11—41no—
130C2×C8×C11—41no—
131C2×C8×C11—41no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142Dic11⋊C4—42no—
143Dic11⋊C4—42no—
144Dic11⋊C4—42no—
145Dic11⋊C4—42no—
146Dic11⋊C4—41no—
147Dic11⋊C4—41no—
148C4×Dic11—22no—
149C4×Dic11—22no—
150C4×Dic11—41no—
151C4×Dic11—41no—
152C4×Dic11—48no—
153C2×C11⋊C8—41no—
154C2×C11⋊C8—41no—
155C2×C11⋊C8—41no—
156#2857—111no—
157#1797—111no—
158C2×#328—111no—
159C2×#328—111no—
160C2×#328—111no—
161C2×#328D1111yescharacteristic
162C4×#95—111no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11C2×C22⋊C411yescharacteristic
168C23×C11#12111yescharacteristic
169C23×C11#12111yescharacteristic
170C23×C11C2×SD1611yescharacteristic
171C23×C11C2×Q1611yescharacteristic
172C23×C11#13711yescharacteristic
173C23×C11#13711yescharacteristic
174Q8×C11—81no—
175Q8×C11—81no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—24no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11C4×D411yescharacteristic
198C2×C4×C11C4×D411yescharacteristic
199C2×C4×C11#12411yescharacteristic
200C2×C4×C11#12711yescharacteristic
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11#9912yes—
226C2×Dic11#10312yes—
227C2×Dic11#10312yes—
228C2×Dic11#10412yes—
229C2×Dic11#10412yes—
230Dic22—81no—
231Dic22—81no—
232C8×C11—81no—
233C11⋊C8—81no—
234C2×C4⋊Q8—111no—
235C2×C22⋊Q8—111no—
236C2×C22⋊Q8C2×D1111yescharacteristic
237C22×C42—111no—
238C22×C42—221no—
239C2×C4⋊C8—221no—
240C2×C22⋊C8—111no—
241C2×C22⋊C8C2×D1111yescharacteristic
242#391—111no—
243#391—111no—
244#389—221no—
245#389—221no—
246#384—111no—
247#380—221no—
248#380—221no—
249C2×#95—111no—
250C2×#95—221no—
251C2×#95C2×D1111yescharacteristic
252#336—221no—
253#328—22no—
254#328—222no—
255#328—222no—
256#328—222no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11#39011yescharacteristic
270C22×C11C2×#9911yescharacteristic
271C22×C11#41011yescharacteristic
272C22×C11C2×#10311yescharacteristic
273C22×C11#41911yescharacteristic
274C22×C11C2×#10411yescharacteristic
275C22×C11C2×#10411yescharacteristic
276C22×C11#46111yescharacteristic
277C22×C11#46111yescharacteristic
278C22×C11#46211yescharacteristic
279C22×C11#46211yescharacteristic
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—44no—
285C4×C11—81no—
286C4×C11—81no—
287Dic11—22no—
288Dic11—22no—
289Dic11—44no—
290Dic11—41no—
291Dic11—81no—
292Dic11—81no—
293Dic11#32814yescomplemented
294C22×Q8—111no—
295C22×Q8C4×D1111yescharacteristic
296C23×C4—21no—
297C23×C4—111no—
298C23×C4—111no—
299C23×C4—221no—
300C23×C4C22×D1111yescharacteristic
301C22×C8—21no—
302C22×C8—221no—
303C4⋊Q8—442no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—221no—
309C22⋊Q8—221no—
310C22⋊Q8—221no—
311C22⋊Q8—221no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4C4×D1111yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—221no—
322C2×C42—111no—
323C2×C42—111no—
324C2×C42—111no—
325C2×C42—111no—
326C2×C42—224no—
327C2×C42—442no—
328C2×C42—442no—
329C2×C42—442no—
330C4⋊C8—442no—
331C22⋊C8—21no—
332C22⋊C8—21no—
333C22⋊C8—221no—
334C22⋊C8—221no—
335#95—21no—
336#95—112no—
337#95—221no—
338#95—221no—
339#95—221no—
340#95—221no—
341#95—224no—
342#95—221no—
343#95C22⋊D1112yes—
344C2×C11—21no—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11—21no—
348C2×C11C2×#32811yescharacteristic
349C2×C11#150311yescharacteristic
350C2×C11#150611yescharacteristic
351C2×C11#150811yescharacteristic
352C2×C11#196211yescharacteristic
353C2×C11#196411yescharacteristic
354C2×C11#198111yescharacteristic
355C24D4×D1111yescharacteristic
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—41no—
359C2×Q8—41no—
360C2×Q8—221no—
361C2×Q8—221no—
362C2×Q8—441no—
363C2×Q8—441no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—111no—
376C22×C4—111no—
377C22×C4—111no—
378C22×C4—112no—
379C22×C4—112no—
380C22×C4—111no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—221no—
390C22×C4—221no—
391C22×C4—441no—
392C22×C4—441no—
393C22×C4—441no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4C2×C4×D1111yescharacteristic
397C22×C4#433911yescharacteristic
398C22×C4D4×D1111yescharacteristic
399C22×C4D4×D1111yescharacteristic
400C22×C4#434111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402C2×C8—41no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—441no—
406C2×C8—441no—
407C2×C8—441no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—442no—
415C4⋊C4—442no—
416C4⋊C4—442no—
417C4⋊C4—442no—
418C4⋊C4—441no—
419C4⋊C4—441no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—441no—
423C22⋊C4—441no—
424C42—222no—
425C42—222no—
426C42—441no—
427C42—441no—
428C42—448no—
429C11#971111yescharacteristic, complemented, Sylow
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23C22⋊C4×D1111yescharacteristic
435C23#6693711yescharacteristic
436C23SD16×D1111yescharacteristic
437C23#6696811yescharacteristic
438C23Q16×D1111yescharacteristic
439C23#6697111yescharacteristic
440C23#6699211yescharacteristic
441Q8—81no—
442Q8—81no—
443Q8—881no—
444Q8—881no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—112no—
467C2×C4—112no—
468C2×C4—112no—
469C2×C4—112no—
470C2×C4—112no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—224no—
478C2×C4—221no—
479C2×C4—221no—
480C2×C4—221no—
481C2×C4—442no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4—441no—
495C2×C4(C22⋊D11)⋊C411yescharacteristic
496C2×C4#6693811yescharacteristic
497C2×C4C4×C22⋊D1111yescharacteristic
498C2×C4#6699311yescharacteristic
499C8—81no—
500C8—881no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22#1062235311yescharacteristic
514C22D11×#9911yescharacteristic
515C22#1062240611yescharacteristic
516C22D11×#10311yescharacteristic
517C22#1062241511yescharacteristic
518C22#1062243111yescharacteristic
519C22D11×#10411yescharacteristic
520C22D11×#10411yescharacteristic
521C22#1062257011yescharacteristic
522C22#1062277511yescharacteristic
523C22#1062279511yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—44no—
529C4—81no—
530C4—81no—
531C4—114no—
532C4—222no—
533C4—222no—
534C4—444no—
535C4—441no—
536C4—881no—
537C4—881no—
538C2—21no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2D11×#32811yescharacteristic
543C2#1306711311yescharacteristic
544C2#1306712611yescharacteristic
545C2#1306713411yescharacteristic
546C2#1306944211yescharacteristic
547C2#1306945011yescharacteristic
548C2#1306953711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#328C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#328D11
hypocenterC11#9711
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
9. C2×#66997C4semidirect
15. #10622843C4semidirect
20. #10622589C4semidirect
21. #10622587C4semidirect
293. Dic11#328semidirect
429. C11#9711semidirect

Maximal subgroups

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

subgroupindex
#130769642
#130685942
C2×#106221052
C2×#106221762
C2×#106220902
#95×Dic112
C2×C11×#3282
#971111