Finite Group Databasebeta

← #14682898

Subgroups — #14682898

Order 2816.

1310 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622843C211yesmaximal, characteristic
2C2×#10622843C211yesmaximal, characteristic
3#13066875C212yesmaximal
4#13066872C212yesmaximal
5#13066868C212yesmaximal
6#13066849C212yesmaximal
7#13066847C212yesmaximal
8#13066842C212yesmaximal
9C2×C11×#391C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×Dic11⋊C4C2212yes—
16C22×C4×Dic11C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C11×#391—24no—
19C2×C11×#95C2212yes—
20C2×C11×#95C2212yes—
21#10622843—24no—
22#10622843C418yescomplemented
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C22×Q8×C11—41no—
35C22×Q8×C11—41no—
36C22×Q8×C11—41no—
37C22×Q8×C11—41no—
38C22×Q8×C11C2×C414yes—
39C22×Q8×C11D414yes—
40C22×Q8×C11Q814yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—41no—
52C2×C11×C4⋊C4—41no—
53C2×C42×C11—22no—
54C2×C42×C11—41no—
55C2×C42×C11—41no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—41no—
58C2×C4⋊Dic11—41no—
59C2×C4⋊Dic11—41no—
60C2×C4⋊Dic11—41no—
61C2×C4⋊Dic11C2×C414yes—
62C2×Dic11⋊C4—24no—
63C2×Dic11⋊C4—24no—
64C2×Dic11⋊C4—42no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11—41no—
67C2×C4×Dic11—41no—
68C2×C4×Dic11—41no—
69C2×C4×Dic11—41no—
70C2×C4×Dic11C2×C414yes—
71C11×#95—24no—
72C11×#95—24no—
73C11⋊#95—24no—
74C11⋊#95—24no—
75C11⋊#95—24no—
76C11⋊#95—24no—
77C11⋊#95—24no—
78C11⋊#95—24no—
79C11⋊#95—42no—
80C11⋊#95—42no—
81C11⋊#95—42no—
82C11⋊#95C2×C418yes—
83C11⋊#95C2×C418yes—
84#14501—111nomaximal, Sylow
85C24×C11C2411yescharacteristic
86C2×Q8×C11—44no—
87C2×Q8×C11—44no—
88C2×Q8×C11—44no—
89C2×Q8×C11—44no—
90C2×Q8×C11—44no—
91C2×Q8×C11—44no—
92C2×Q8×C11C4⋊C4116yescomplemented
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×Q812yes—
125C22×C4×C11C2×Q812yes—
126C22×C4×C11C2×Q812yes—
127C22×C4×C11#4114yes—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11C22×C414yes—
154C22×Dic11C22×C414yes—
155C22×Dic11#4114yes—
156C11×C4⋊C4—44no—
157C42×C11—44no—
158C4⋊Dic11—44no—
159C4⋊Dic11—44no—
160Dic11⋊C4—48no—
161C4×Dic11—44no—
162C4×Dic11—44no—
163C2×#391—111no—
164C2×#391—111no—
165C2×#391D1111yescharacteristic
166#1442—112no—
167#1442—112no—
168#1441—112no—
169#1436—112no—
170#1436—112no—
171#1434—112no—
172C23×C11C23×C411yescharacteristic
173C23×C11C22×D411yescharacteristic
174C23×C11C22×Q811yescharacteristic
175C23×C11C2×#4112yes—
176C23×C11C2×#4112yes—
177C23×C11H(5,𝔽2)11yescharacteristic
178C23×C11H(5,𝔽2)11yescharacteristic
179C23×C11H(5,𝔽2)11yescharacteristic
180C23×C11H(5,𝔽2)11yescharacteristic
181C23×C112−1+412yes—
182C23×C112−1+412yes—
183Q8×C11—416no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11C2×C4⋊C414yes—
217C2×C4×C11C2×C4⋊C414yes—
218C2×C4×C11C2×C4⋊C414yes—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C23×Q8C2×D1111yescharacteristic
248C22×C4⋊C4—111no—
249C22×C4⋊C4—112no—
250C22×C4⋊C4—111no—
251C22×C4⋊C4C2×D1111yescharacteristic
252C22×C42—111no—
253C22×C42—111no—
254C22×C42C2×D1111yescharacteristic
255#391—24no—
256#391—118no—
257#391—224no—
258C2×#95—112no—
259C2×#95—112no—
260C2×#95—112no—
261C2×#95—112no—
262C2×#95—112no—
263C2×#95—112no—
264C2×#95—112no—
265C2×#95—112no—
266C2×#95—112no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95C2×D1112yes—
270C2×#95C2×D1112yes—
271C22×C11C22×C4⋊C411yescharacteristic
272C22×C11C4×#4112yes—
273C22×C11#51811yescharacteristic
274C22×C11#51811yescharacteristic
275C22×C11#51912yes—
276C22×C11#53411yescharacteristic
277C22×C11#53411yescharacteristic
278C22×C11#53912yes—
279C22×C11#53912yes—
280C22×C11#54212yes—
281C22×C11#54212yes—
282C22×C11#54311yescharacteristic
283C22×C11#54311yescharacteristic
284C22×C11#54812yes—
285C22×C11#54812yes—
286C22×C11#55112yes—
287C22×C11#55511yescharacteristic
288C22×C11#55511yescharacteristic
289C22×C11#55712yes—
290C22×C11#55712yes—
291C22×C11#56311yescharacteristic
292C22×C11#56312yes—
293C22×C11#56311yescharacteristic
294C4×C11—24no—
295C4×C11—24no—
296C4×C11—24no—
297C4×C11—44no—
298C4×C11—82no—
299Dic11—44no—
300Dic11—44no—
301Dic11—44no—
302Dic11—82no—
303C22×Q8—41no—
304C22×Q8—41no—
305C22×Q8—41no—
306C22×Q8—41no—
307C22×Q8Dic2214yes—
308C22×Q8C4×D1114yes—
309C22×Q8C22⋊D1114yes—
310C23×C4—112no—
311C23×C4—112no—
312C23×C4—112no—
313C23×C4—112no—
314C23×C4C22×D1112yes—
315C23×C4C22×D1112yes—
316C23×C4C22×D1111yescharacteristic
317C23×C4C22×D1111yescharacteristic
318C23×C4C22×D1111yescharacteristic
319C2×C4⋊C4—22no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—114no—
323C2×C4⋊C4—224no—
324C2×C4⋊C4—224no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—442no—
327C2×C4⋊C4—441no—
328C2×C4⋊C4—441no—
329C2×C4⋊C4—441no—
330C2×C4⋊C4—441no—
331C2×C42—22no—
332C2×C42—41no—
333C2×C42—41no—
334C2×C42—114no—
335C2×C42—222no—
336C2×C42—441no—
337C2×C42—441no—
338C2×C42—441no—
339C2×C42—441no—
340#95—24no—
341#95—24no—
342#95—118no—
343#95—118no—
344#95—224no—
345#95—224no—
346#95—224no—
347#95—224no—
348#95—224no—
349#95—224no—
350#95—442no—
351#95—442no—
352#95—442no—
353C2×C11#231511yescharacteristic
354C2×C11#233212yes—
355C2×C11#235112yes—
356C2×C11#237211yescharacteristic
357C2×C11#238111yescharacteristic
358C2×C11#272812yes—
359C2×C11#273111yescharacteristic
360C2×C11#273111yescharacteristic
361C2×C11#279912yes—
362C2×C11#280911yescharacteristic
363C2×C11#280911yescharacteristic
364C24C23×D1111yescharacteristic
365C2×Q8—44no—
366C2×Q8—44no—
367C2×Q8—44no—
368C2×Q8—44no—
369C2×Q8—44no—
370C2×Q8—44no—
371C2×Q8Dic11⋊C4116yescomplemented
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—114no—
398C22×C4—114no—
399C22×C4—114no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4C2×Dic2212yes—
426C22×C4C2×Dic2212yes—
427C22×C4C2×Dic2212yes—
428C22×C4C2×C4×D1112yes—
429C22×C4C2×C4×D1112yes—
430C22×C4C2×C4×D1112yes—
431C22×C4#434314yes—
432C22×C4C2×C22⋊D1112yes—
433C22×C4C2×C22⋊D1112yes—
434C22×C4C2×C22⋊D1112yes—
435C4⋊C4—44no—
436C4⋊C4—444no—
437C4⋊C4—448no—
438C4⋊C4—444no—
439C42—44no—
440C42—444no—
441C42—444no—
442C11#1450111yescharacteristic, complemented, Sylow
443C23C22×Dic2211yescharacteristic
444C23C22×C4×D1111yescharacteristic
445C23#6703711yescharacteristic
446C23#6703711yescharacteristic
447C23#6703711yescharacteristic
448C23#6703711yescharacteristic
449C23C2×#434312yes—
450C23#6704012yes—
451C23#41×D1112yes—
452C23#6704312yes—
453C23C22×C22⋊D1111yescharacteristic
454Q8—416no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—224no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4C2×Dic11⋊C414yes—
516C2×C4C2×Dic11⋊C414yes—
517C2×C4C2×Dic11⋊C414yes—
518C22#1062301411yescharacteristic
519C22#1062301411yescharacteristic
520C22#1062301711yescharacteristic
521C22#1062301711yescharacteristic
522C22#1062310012yes—
523C22#1062310112yes—
524C22#1062310312yes—
525C22C4×#434312yes—
526C22#1062316812yes—
527C22#1062316912yes—
528C22#1062317612yes—
529C22#1062317712yes—
530C22#1062320012yes—
531C22#1062320111yescharacteristic
532C22#1062320311yescharacteristic
533C22#1062326412yes—
534C22#1062326511yescharacteristic
535C22#1062326611yescharacteristic
536C22C22×Dic11⋊C411yescharacteristic
537C22#1062333511yescharacteristic
538C22#1062333511yescharacteristic
539C22#1062334812yes—
540C22#1062336212yes—
541C4—24no—
542C4—24no—
543C4—24no—
544C4—44no—
545C4—82no—
546C4—444no—
547C4—444no—
548C4—444no—
549C4—882no—
550C2#1307122811yescharacteristic
551C2#1307137112yes—
552C2#1307153412yes—
553C2#1307172711yescharacteristic
554C2#1307179511yescharacteristic
555C2#1307558312yes—
556C2#1307562211yescharacteristic
557C2#1307562411yescharacteristic
558C2#1307650212yes—
559C2#1307660211yescharacteristic
560C2#1307660411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#391C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#391D11
hypocenterC11#14501
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
22. #10622843C4semidirect
92. C2×Q8×C11C4⋊C4semidirect
371. C2×Q8Dic11⋊C4semidirect
442. C11#14501semidirect

Maximal subgroups

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

subgroupindex
C2×#106228432
#130668752
#130668722
#130668682
#130668492
#130668472
#130668422
C2×C11×#3912
#1450111