Finite Group Databasebeta

← #14682532

Subgroups — #14682532

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622541C211yesmaximal, characteristic
2#13066883C212yesmaximal
3#13066882C212yesmaximal
4#13066875C212yesmaximal
5#13066850C212yesmaximal
6#13066848C212yesmaximal
7#13066847C212yesmaximal
8#13066843C211yesmaximal, characteristic
9C11×C4⋊#95C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2212yes—
11C22×C42×C11C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×Dic11⋊C4C2212yes—
15C22×C4×Dic11C2212yes—
16C2×C11×#95C2212yes—
17C2×C11×#95C2211yescharacteristic
18C2×C11×#95C2211yescharacteristic
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2211yescharacteristic
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31#10622541C418yescomplemented
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C2×C11×C4⋊C4—24no—
42C2×C11×C4⋊C4—24no—
43C2×C11×C4⋊C4—42no—
44C2×C42×C11—42no—
45C2×C42×C11C2×C414yes—
46C2×C4⋊Dic11—22no—
47C2×C4⋊Dic11—22no—
48C2×C4⋊Dic11—42no—
49C2×C4⋊Dic11C2×C414yes—
50C2×C4⋊Dic11C2×C414yes—
51C2×Dic11⋊C4—42no—
52C2×Dic11⋊C4—42no—
53C2×Dic11⋊C4C2×C418yes—
54C2×C4×Dic11—42no—
55C2×C4×Dic11—42no—
56C2×C4×Dic11—42no—
57C11×#95—24no—
58C11×#95—41no—
59C11×#95—41no—
60C11⋊#95—24no—
61C11⋊#95—24no—
62C11⋊#95—22no—
63C11⋊#95—24no—
64C11⋊#95—42no—
65C11⋊#95—42no—
66C11⋊#95—42no—
67C11⋊#95—42no—
68C11⋊#95—42no—
69C11⋊#95—42no—
70C11⋊#95C2×C418yes—
71C11⋊#95Q814yes—
72#14470—111nomaximal, Sylow
73C24×C11C2411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11C22×C412yes—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C22×C412yes—
98C22×C4×C11C2×Q812yes—
99C22×C4×C11#4114yes—
100C22×C4×C11#4112yes—
101C22×C4×C11#4112yes—
102C22×C4×C11#4112yes—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—22no—
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×Dic11C22×C414yes—
129C22×Dic11C22×C414yes—
130C22×Dic11C2×Q814yes—
131C11×C4⋊C4—48no—
132C42×C11—44no—
133C4⋊Dic11—28no—
134C4⋊Dic11—44no—
135Dic11⋊C4—48no—
136C4×Dic11—48no—
137C2×#389—111no—
138#1445—112no—
139#1445—112no—
140#1442—112no—
141#1436—112no—
142#1436—112no—
143#1436—112no—
144C4⋊#95D1111yescharacteristic
145#1434—111no—
146C23×C11C23×C411yescharacteristic
147C23×C11C22×Q811yescharacteristic
148C23×C11C2×#4112yes—
149C23×C11C2×#4111yescharacteristic
150C23×C11C2×#4111yescharacteristic
151C23×C11C2×#4111yescharacteristic
152C23×C11H(5,𝔽2)12yes—
153C23×C11H(5,𝔽2)11yescharacteristic
154C23×C11H(5,𝔽2)12yes—
155C23×C112−1+411yescharacteristic
156C23×C112−1+412yes—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
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#11714yes—
185C2×C4×C11C4×Q814yes—
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—
214C22×C4⋊C4—111no—
215C22×C4⋊C4—112no—
216C22×C4⋊C4—111no—
217C22×C4⋊C4C2×D1112yes—
218C22×C42—112no—
219C22×C42C2×D1111yescharacteristic
220#389—118no—
221C2×#95—111no—
222C2×#95—112no—
223C2×#95—112no—
224C2×#95—111no—
225C2×#95—112no—
226C2×#95—112no—
227C2×#95—112no—
228C2×#95—112no—
229C2×#95—112no—
230C2×#95—112no—
231C2×#95—112no—
232C2×#95—112no—
233C2×#95C2×D1112yes—
234C2×#95C2×D1111yescharacteristic
235C2×#95C2×D1111yescharacteristic
236C22×C11C2×#11711yescharacteristic
237C22×C11C2×C4×Q811yescharacteristic
238C22×C11C4×#4111yescharacteristic
239C22×C11#51811yescharacteristic
240C22×C11#51811yescharacteristic
241C22×C11#51911yescharacteristic
242C22×C11#52011yescharacteristic
243C22×C11#53912yes—
244C22×C11#53912yes—
245C22×C11#53912yes—
246C22×C11#54112yes—
247C22×C11#54212yes—
248C22×C11#54412yes—
249C22×C11#55112yes—
250C22×C11#55312yes—
251C22×C11#55411yescharacteristic
252C22×C11#55412yes—
253C22×C11#55611yescharacteristic
254C22×C11#55711yescharacteristic
255C22×C11#55911yescharacteristic
256C22×C11#55912yes—
257C22×C11#56012yes—
258C22×C11#56212yes—
259C4×C11—24no—
260C4×C11—24no—
261C4×C11—42no—
262C4×C11—44no—
263C4×C11—82no—
264Dic11—44no—
265Dic11—44no—
266Dic11—44no—
267Dic11—82no—
268C23×C4—112no—
269C23×C4—112no—
270C23×C4—112no—
271C23×C4—112no—
272C23×C4C22×D1112yes—
273C23×C4C22×D1111yescharacteristic
274C23×C4C22×D1112yes—
275C23×C4C22×D1111yescharacteristic
276C23×C4C22×D1111yescharacteristic
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—114no—
281C2×C4⋊C4—118no—
282C2×C4⋊C4—114no—
283C2×C4⋊C4—222no—
284C2×C4⋊C4—222no—
285C2×C4⋊C4—442no—
286C2×C4⋊C4—442no—
287C2×C4⋊C4—442no—
288C2×C42—42no—
289C2×C42—442no—
290C2×C42—442no—
291C2×C42—442no—
292C2×C42C4×D1114yes—
293#95—24no—
294#95—41no—
295#95—41no—
296#95—118no—
297#95—114no—
298#95—224no—
299#95—224no—
300#95—222no—
301#95—224no—
302#95—442no—
303#95—442no—
304#95—442no—
305#95—442no—
306#95—442no—
307#95—442no—
308C2×C11#231311yescharacteristic
309C2×C11#233111yescharacteristic
310C2×C11#233611yescharacteristic
311C2×C11#235511yescharacteristic
312C2×C11#235711yescharacteristic
313C2×C11#236811yescharacteristic
314C2×C11#237711yescharacteristic
315C2×C11#279612yes—
316C2×C11#279812yes—
317C2×C11#280212yes—
318C2×C11#280712yes—
319C24C23×D1111yescharacteristic
320C22×C4—22no—
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—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—114no—
342C22×C4—114no—
343C22×C4—114no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—222no—
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×C4C2×C4×D1112yes—
370C22×C4C2×C4×D1112yes—
371C22×C4C2×C4×D1112yes—
372C22×C4#433914yes—
373C22×C4#434112yes—
374C22×C4#434112yes—
375C22×C4Q8×D1112yes—
376C22×C4#434312yes—
377C4⋊C4—48no—
378C4⋊C4—228no—
379C4⋊C4—448no—
380C4⋊C4—444no—
381C42—44no—
382C42—448no—
383C11#1447011yescharacteristic, complemented, Sylow
384C23C22×C4×D1111yescharacteristic
385C23C2×#433912yes—
386C23C2×#434111yescharacteristic
387C23C2×#434111yescharacteristic
388C23#6703711yescharacteristic
389C23#6703712yes—
390C23C2×Q8×D1111yescharacteristic
391C23C2×#434311yescharacteristic
392C23#6704011yescharacteristic
393C23#6704212yes—
394C23#6704312yes—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—24no—
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—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—224no—
423C2×C4—224no—
424C2×C4—224no—
425C2×C4—224no—
426C2×C4—224no—
427C2×C4—224no—
428C2×C4—224no—
429C2×C4—224no—
430C2×C4—224no—
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—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4#6694014yes—
451C2×C4#6694514yes—
452C22C4×#433911yescharacteristic
453C22#1062301711yescharacteristic
454C22#1062302612yes—
455C22C2×#6694011yescharacteristic
456C22C2×#6694511yescharacteristic
457C22#1062303511yescharacteristic
458C22#1062304212yes—
459C22#1062304711yescharacteristic
460C22#1062305211yescharacteristic
461C22#1062309512yes—
462C22#1062309612yes—
463C22#1062311412yes—
464C22#1062311612yes—
465C22#1062313312yes—
466C22#1062315112yes—
467C22#1062317612yes—
468C22#1062317812yes—
469C22#1062321312yes—
470C22#1062322012yes—
471C22#1062324411yescharacteristic
472C22#1062325211yescharacteristic
473C22#1062326111yescharacteristic
474C22#1062326311yescharacteristic
475C4—24no—
476C4—24no—
477C4—42no—
478C4—44no—
479C4—82no—
480C4—444no—
481C4—444no—
482C4—444no—
483C4—882no—
484C2#1307121811yescharacteristic
485C2#1307136211yescharacteristic
486C2#1307142011yescharacteristic
487C2#1307157511yescharacteristic
488C2#1307158711yescharacteristic
489C2#1307169611yescharacteristic
490C2#1307177011yescharacteristic
491C2#1307645212yes—
492C2#1307648812yes—
493C2#1307653412yes—
494C2#1307658512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, prime radical, cosocleC24×C11C24
hypercenterC4⋊#95D11
hypocenterC11#14470
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
31. #10622541C4semidirect
383. C11#14470semidirect

Maximal subgroups

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

subgroupindex
C2×#106225412
#130668832
#130668822
#130668752
#130668502
#130668482
#130668472
#130668432
C11×C4⋊#952
#1447011