Finite Group Databasebeta

← #14684187

Subgroups — #14684187

Order 2816.

1182 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622596C211yesmaximal, characteristic
2#13066884C211yesmaximal, characteristic
3#13066868C212yesmaximal
4#13066867C212yesmaximal
5#13066851C212yesmaximal
6#13066849C212yesmaximal
7#13066847C212yesmaximal
8Dic11⋊#95C212yesmaximal
9C11×#1436C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×Dic11⋊C4C2212yes—
14C22×Dic11⋊C4C2212yes—
15C22×Dic11⋊C4C2212yes—
16C22×C4×Dic11C2212yes—
17C2×C11×#95C2212yes—
18C2×C11×#95C2212yes—
19C2×C11×#95C2211yescharacteristic
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31#10622596C418yescomplemented
32C23×C4×C11C2311yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C2×C11×C4⋊C4—41no—
42C2×C11×C4⋊C4—41no—
43C2×C11×C4⋊C4C2×C414yes—
44C2×C42×C11—41no—
45C2×C42×C11—42no—
46C2×C4⋊Dic11—41no—
47C2×C4⋊Dic11—41no—
48C2×C4⋊Dic11C2×C414yes—
49C2×Dic11⋊C4—24no—
50C2×Dic11⋊C4—42no—
51C2×Dic11⋊C4—42no—
52C2×Dic11⋊C4—42no—
53C2×Dic11⋊C4—42no—
54C2×Dic11⋊C4—42no—
55C2×Dic11⋊C4—42no—
56C2×Dic11⋊C4C2×C418yes—
57C2×Dic11⋊C4Q818yes—
58C2×C4×Dic11—24no—
59C2×C4×Dic11—42no—
60C2×C4×Dic11—42no—
61C11×#95—24no—
62C11×#95—42no—
63C11×#95—41no—
64C11⋊#95—24no—
65C11⋊#95—24no—
66C11⋊#95—24no—
67C11⋊#95—41no—
68C11⋊#95—42no—
69C11⋊#95—42no—
70C11⋊#95—42no—
71C11⋊#95—42no—
72C11⋊#95—41no—
73C11⋊#95C2×C418yes—
74C11⋊#95C2×C414yes—
75#14600—111nomaximal, Sylow
76C24×C11C2411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C2×Q814yes—
105C22×C4×C11#4114yes—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11C22×C414yes—
130C22×Dic11C22×C414yes—
131C22×Dic11C2×Q814yes—
132C22×Dic11C2×Q814yes—
133C22×Dic11#4114yes—
134C11×C4⋊C4—44no—
135C42×C11—44no—
136C4⋊Dic11—44no—
137Dic11⋊C4—48no—
138Dic11⋊C4—48no—
139Dic11⋊C4—48no—
140C4×Dic11—48no—
141C2×#398—111no—
142#1445—111no—
143#1441—112no—
144#1441—112no—
145#1436—112no—
146#1436—112no—
147#1436—112no—
148#1436D1111yescharacteristic
149C4⋊#95—112no—
150C23×C11C23×C411yescharacteristic
151C23×C11C22×Q812yes—
152C23×C11C2×#4112yes—
153C23×C11C2×#4112yes—
154C23×C11H(5,𝔽2)11yescharacteristic
155C23×C11H(5,𝔽2)11yescharacteristic
156C23×C11H(5,𝔽2)12yes—
157C23×C11H(5,𝔽2)12yes—
158C23×C112−1+412yes—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×Dic11—24no—
189C2×Dic11—24no—
190C2×Dic11—24no—
191C2×Dic11—24no—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11C4×Q818yes—
216C22×C4⋊C4—112no—
217C22×C4⋊C4—112no—
218C22×C4⋊C4—111no—
219C22×C4⋊C4—112no—
220C22×C4⋊C4C2×D1111yescharacteristic
221C22×C42—112no—
222C22×C42C2×D1111yescharacteristic
223#398—118no—
224C2×#95—111no—
225C2×#95—112no—
226C2×#95—112no—
227C2×#95—112no—
228C2×#95—112no—
229C2×#95—111no—
230C2×#95—112no—
231C2×#95—112no—
232C2×#95—112no—
233C2×#95—112no—
234C2×#95—111no—
235C2×#95C2×D1112yes—
236C2×#95C2×D1111yescharacteristic
237C2×#95C2×D1112yes—
238C22×C11C2×C4×Q812yes—
239C22×C11C4×#4111yescharacteristic
240C22×C11#51811yescharacteristic
241C22×C11#51811yescharacteristic
242C22×C11#52012yes—
243C22×C11#53812yes—
244C22×C11#53812yes—
245C22×C11#53912yes—
246C22×C11#54012yes—
247C22×C11#54312yes—
248C22×C11#54412yes—
249C22×C11#55212yes—
250C22×C11#55312yes—
251C22×C11#55412yes—
252C22×C11#55412yes—
253C22×C11#55511yescharacteristic
254C22×C11#55712yes—
255C22×C11Q8211yescharacteristic
256C22×C11#56011yescharacteristic
257C22×C11#56212yes—
258C22×C11#56311yescharacteristic
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—44no—
263C4×C11—44no—
264Dic11—28no—
265Dic11—44no—
266Dic11—44no—
267Dic11—82no—
268C23×C4—112no—
269C23×C4—112no—
270C23×C4—112no—
271C23×C4—112no—
272C23×C4C22×D1111yescharacteristic
273C23×C4C22×D1111yescharacteristic
274C23×C4C22×D1111yescharacteristic
275C23×C4C22×D1112yes—
276C23×C4C22×D1112yes—
277C2×C4⋊C4—41no—
278C2×C4⋊C4—41no—
279C2×C4⋊C4—118no—
280C2×C4⋊C4—114no—
281C2×C4⋊C4—118no—
282C2×C4⋊C4—224no—
283C2×C4⋊C4—442no—
284C2×C4⋊C4—442no—
285C2×C4⋊C4—442no—
286C2×C4⋊C4—442no—
287C2×C4⋊C4—442no—
288C2×C4⋊C4—442no—
289C2×C4⋊C4—441no—
290C2×C4⋊C4—441no—
291C2×C4⋊C4C4×D1114yes—
292C2×C42—42no—
293C2×C42—41no—
294C2×C42—224no—
295C2×C42—442no—
296C2×C42—442no—
297#95—24no—
298#95—42no—
299#95—41no—
300#95—114no—
301#95—118no—
302#95—224no—
303#95—224no—
304#95—224no—
305#95—442no—
306#95—442no—
307#95—442no—
308#95—441no—
309#95—441no—
310#95—442no—
311C2×C11#232912yes—
312C2×C11#233311yescharacteristic
313C2×C11#236911yescharacteristic
314C2×C11#237012yes—
315C2×C11#237611yescharacteristic
316C2×C11#278012yes—
317C2×C11#278112yes—
318C2×C11#279112yes—
319C2×C11#280612yes—
320C24C23×D1111yescharacteristic
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—114no—
346C22×C4—114no—
347C22×C4—114no—
348C22×C4—114no—
349C22×C4—114no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4C2×C4×D1112yes—
374C22×C4C2×C4×D1112yes—
375C22×C4C2×C4×D1112yes—
376C22×C4#433914yes—
377C22×C4Q8×D1114yes—
378C4⋊C4—44no—
379C4⋊C4—448no—
380C4⋊C4—448no—
381C4⋊C4—444no—
382C4⋊C4—448no—
383C42—44no—
384C42—448no—
385C11#1460011yescharacteristic, complemented, Sylow
386C23C22×C4×D1111yescharacteristic
387C23C2×#433912yes—
388C23#6703711yescharacteristic
389C23#6703711yescharacteristic
390C23#6703712yes—
391C23C2×Q8×D1112yes—
392C23#41×D1112yes—
393C23#6704212yes—
394C23#6704312yes—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—118no—
425C2×C4—224no—
426C2×C4—224no—
427C2×C4—224no—
428C2×C4—224no—
429C2×C4—224no—
430C2×C4—224no—
431C2×C4—224no—
432C2×C4—224no—
433C2×C4—224no—
434C2×C4—224no—
435C2×C4—224no—
436C2×C4—224no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C22C4×#433911yescharacteristic
453C22#1062301711yescharacteristic
454C22#1062304212yes—
455C22#1062305211yescharacteristic
456C22#1062306212yes—
457C22#1062307112yes—
458C22#1062307712yes—
459C22#1062309112yes—
460C22#1062309312yes—
461C22#1062309812yes—
462C22C4×Q8×D1112yes—
463C22#1062312611yescharacteristic
464C22#1062315212yes—
465C22#1062316512yes—
466C22#1062316712yes—
467C22#1062318211yescharacteristic
468C22#1062318812yes—
469C22#1062320111yescharacteristic
470C22#1062322012yes—
471C22#1062323812yes—
472C22#1062325311yescharacteristic
473C4—42no—
474C4—44no—
475C4—44no—
476C4—42no—
477C4—42no—
478C4—228no—
479C4—444no—
480C4—444no—
481C4—882no—
482C2#1307134512yes—
483C2#1307138111yescharacteristic
484C2#1307170411yescharacteristic
485C2#1307171312yes—
486C2#1307175911yescharacteristic
487C2#1307625912yes—
488C2#1307627412yes—
489C2#1307640212yes—
490C2#1307657312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11#14600
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
31. #10622596C4semidirect
385. C11#14600semidirect

Maximal subgroups

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

subgroupindex
C2×#106225962
#130668842
#130668682
#130668672
#130668512
#130668492
#130668472
Dic11⋊#952
C11×#14362
#1460011