Finite Group Databasebeta

← #14682753

Subgroups — #14682753

Order 2816.

1166 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622843C211yesmaximal, characteristic
2#13066887C211yesmaximal, characteristic
3#13066877C212yesmaximal
4#13066876C212yesmaximal
5#13066850C212yesmaximal
6#13066842C212yesmaximal
7#13066842C212yesmaximal
8#13066840C212yesmaximal
9C11×#1446C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C4⋊Dic11C2211yescharacteristic
12C22×C4×Dic11C2212yes—
13C22×C4×Dic11C2211yescharacteristic
14C2×C11×#95C2212yes—
15C2×C11×#95C2211yescharacteristic
16C2×C11×#95C2212yes—
17C2×C11×#95C2211yescharacteristic
18#10622843C418yescomplemented
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C22×Q8×C11—24no—
33C22×Q8×C11—42no—
34C22×Q8×C11—41no—
35C22×Q8×C11—41no—
36C22×Q8×C11C2×C414yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C2×C4⋊Dic11—41no—
47C2×C4⋊Dic11—41no—
48C2×C4⋊Dic11C2×C414yes—
49C2×C4×Dic11—24no—
50C2×C4×Dic11—24no—
51C2×C4×Dic11—42no—
52C2×C4×Dic11—42no—
53C2×C4×Dic11C2×C414yes—
54C11×#95—24no—
55C11×#95—42no—
56C11×#95—41no—
57C11×#95—41no—
58C11⋊#95—24no—
59C11⋊#95—24no—
60C11⋊#95—24no—
61C11⋊#95—24no—
62C11⋊#95—24no—
63C11⋊#95—42no—
64C11⋊#95—42no—
65C11⋊#95—41no—
66C11⋊#95—42no—
67C11⋊#95—42no—
68C11⋊#95—41no—
69C11⋊#95C2×C418yes—
70C11⋊#95C2×C418yes—
71#14489—111nomaximal, Sylow
72C24×C11C2411yescharacteristic
73C2×Q8×C11—28no—
74C2×Q8×C11—44no—
75C2×Q8×C11—44no—
76C2×Q8×C11—48no—
77C2×Q8×C11—48no—
78C22×C4×C11—22no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C22×C412yes—
105C22×C4×C11#4114yes—
106C22×C4×C11#4114yes—
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×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11C22×C414yes—
133C22×Dic11C22×C414yes—
134C22×Dic11#4114yes—
135C4⋊Dic11—44no—
136C4×Dic11—44no—
137C4×Dic11—48no—
138C2×#391—111no—
139#1446—111no—
140#1446D1111yescharacteristic
141#1443—112no—
142#1443—112no—
143#1436—112no—
144#1434—112no—
145#1434—112no—
146#1434—112no—
147C23×C11C23×C411yescharacteristic
148C23×C11C2×#4112yes—
149C23×C11C2×#4112yes—
150C23×C11C2×#4112yes—
151C23×C11H(5,𝔽2)12yes—
152C23×C11H(5,𝔽2)11yescharacteristic
153C23×C11H(5,𝔽2)11yescharacteristic
154C23×C112−1+412yes—
155C23×C112−1+412yes—
156Q8×C11—416no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
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—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11#11714yes—
186C2×Dic11—24no—
187C2×Dic11—24no—
188C2×Dic11—24no—
189C2×Dic11—24no—
190C2×Dic11—24no—
191C2×Dic11—24no—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
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—
214C23×Q8C2×D1111yescharacteristic
215C22×C4⋊C4—111no—
216C22×C42—111no—
217C22×C42—112no—
218#391—118no—
219C2×#95—112no—
220C2×#95—112no—
221C2×#95—112no—
222C2×#95—112no—
223C2×#95—112no—
224C2×#95—112no—
225C2×#95—112no—
226C2×#95—112no—
227C2×#95—111no—
228C2×#95—112no—
229C2×#95—112no—
230C2×#95—112no—
231C2×#95—111no—
232C2×#95C2×D1112yes—
233C2×#95C2×D1111yescharacteristic
234C2×#95C2×D1112yes—
235C2×#95C2×D1111yescharacteristic
236C22×C11C2×#11711yescharacteristic
237C22×C11C4×#4112yes—
238C22×C11#51811yescharacteristic
239C22×C11#51811yescharacteristic
240C22×C11#51912yes—
241C22×C11#53812yes—
242C22×C11#53812yes—
243C22×C11#53912yes—
244C22×C11#53912yes—
245C22×C11#54212yes—
246C22×C11#54212yes—
247C22×C11#55112yes—
248C22×C11#55212yes—
249C22×C11#55212yes—
250C22×C11#55511yescharacteristic
251C22×C11#55511yescharacteristic
252C22×C11#55612yes—
253C22×C11#55612yes—
254C22×C11#56311yescharacteristic
255C22×C11#56312yes—
256C22×C11#56311yescharacteristic
257C4×C11—24no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—44no—
261C4×C11—82no—
262Dic11—44no—
263Dic11—44no—
264Dic11—44no—
265Dic11—82no—
266C22×Q8—24no—
267C22×Q8—42no—
268C22×Q8—41no—
269C22×Q8—41no—
270C22×Q8C4×D1114yes—
271C23×C4—112no—
272C23×C4—112no—
273C23×C4—112no—
274C23×C4—112no—
275C23×C4C22×D1112yes—
276C23×C4C22×D1111yescharacteristic
277C23×C4C22×D1111yescharacteristic
278C23×C4C22×D1112yes—
279C23×C4C22×D1111yescharacteristic
280C2×C4⋊C4—114no—
281C2×C4⋊C4—441no—
282C2×C4⋊C4—441no—
283C2×C42—114no—
284C2×C42—224no—
285C2×C42—224no—
286C2×C42—442no—
287C2×C42—442no—
288#95—24no—
289#95—42no—
290#95—41no—
291#95—41no—
292#95—118no—
293#95—118no—
294#95—224no—
295#95—224no—
296#95—224no—
297#95—224no—
298#95—224no—
299#95—442no—
300#95—442no—
301#95—441no—
302#95—441no—
303#95—442no—
304#95—442no—
305C2×C11#231211yescharacteristic
306C2×C11#233212yes—
307C2×C11#235612yes—
308C2×C11#237211yescharacteristic
309C2×C11#238111yescharacteristic
310C2×C11#274512yes—
311C2×C11#274512yes—
312C2×C11#277512yes—
313C2×C11#277512yes—
314C24C23×D1111yescharacteristic
315C2×Q8—28no—
316C2×Q8—44no—
317C2×Q8—44no—
318C2×Q8—48no—
319C2×Q8—48no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—22no—
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—114no—
345C22×C4—114no—
346C22×C4—114no—
347C22×C4—222no—
348C22×C4—222no—
349C22×C4—222no—
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×C4C2×C4×D1112yes—
373C22×C4C2×C4×D1112yes—
374C22×C4C2×C4×D1112yes—
375C22×C4#434114yes—
376C22×C4#434314yes—
377C4⋊C4—444no—
378C42—444no—
379C42—448no—
380C11#1448911yescharacteristic, complemented, Sylow
381C23C22×C4×D1111yescharacteristic
382C23C2×#434112yes—
383C23#6703712yes—
384C23#6703711yescharacteristic
385C23#6703711yescharacteristic
386C23C2×#434312yes—
387C23#6704012yes—
388C23#41×D1112yes—
389C23#6704312yes—
390Q8—416no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—224no—
420C2×C4—224no—
421C2×C4—224no—
422C2×C4—224no—
423C2×C4—224no—
424C2×C4—224no—
425C2×C4—224no—
426C2×C4—224no—
427C2×C4—224no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
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#6693014yes—
448C22C2×#6693011yescharacteristic
449C22#1062301711yescharacteristic
450C22#1062301711yescharacteristic
451C22#1062310312yes—
452C22C4×#434312yes—
453C22#1062312412yes—
454C22#1062312412yes—
455C22#1062316812yes—
456C22#1062316912yes—
457C22#1062317012yes—
458C22#1062317312yes—
459C22#1062317612yes—
460C22#1062317712yes—
461C22#1062320012yes—
462C22#1062320111yescharacteristic
463C22#1062320212yes—
464C22#1062320311yescharacteristic
465C22#1062326312yes—
466C22#1062326412yes—
467C22#1062326511yescharacteristic
468C22#1062326611yescharacteristic
469C4—24no—
470C4—44no—
471C4—42no—
472C4—42no—
473C4—82no—
474C4—444no—
475C4—444no—
476C4—444no—
477C4—882no—
478C2#1307121211yescharacteristic
479C2#1307137112yes—
480C2#1307158012yes—
481C2#1307172711yescharacteristic
482C2#1307179511yescharacteristic
483C2#1307578412yes—
484C2#1307579112yes—
485C2#1307619412yes—
486C2#1307619512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1446C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1446D11
hypocenterC11#14489
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
18. #10622843C4semidirect
380. C11#14489semidirect

Maximal subgroups

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

subgroupindex
C2×#106228432
#130668872
#130668772
#130668762
#130668502
#130668422
#130668402
C11×#14462
#1448911