Finite Group Databasebeta

← D53⋊#1821 #28319165

Subgroups — D53⋊#1821 #28319165

Order 13568.

1734 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
1D53⋊#407C212yesmaximal
2#20290615C214yesmaximal, complemented
3#20290614C214yesmaximal, complemented
4#20290418C214yesmaximal, complemented
5C22×C4⋊C4×D53C211yesmaximal, characteristic
6C2×D53⋊M16C2214yes—
7#16811595C2214yes—
8#16811594—22no—
9#16811594—22no—
10#16811593C2214yes—
11D53⋊(C22⋊C8)—22no—
12D53⋊(C22⋊C8)—22no—
13#16811503C22116yescomplemented
14C23×C4×D53C412yes—
15C23×C4×D53C2211yescharacteristic
16C22×C4⋊Dic53C411yescharacteristic
17C22×#11719919C2212yes—
18C2×C4⋊C4×D53—22no—
19C2×C4⋊C4×D53—22no—
20C2×C4⋊C4×D53—22no—
21C2×C4⋊C4×D53—22no—
22C2×C4⋊C4×D53C412yes—
23C2×C4⋊C4×D53C412yes—
24C2×C4⋊C4×D53C2212yes—
25C2×C4⋊C4×D53C2212yes—
26C22×C4⋊C4×C53C411yescharacteristic
27C2×#11719936—24no—
28D53⋊M16—216no—
29C2×#11719940C2318yes—
30C2×D53⋊C8—24no—
31#13133274—24no—
32#13133274—24no—
33C22⋊#88324—24no—
34C22⋊#88324—24no—
35C24×D53C2×C411yescharacteristic
36C23×Dic53C2×C412yes—
37C23×Dic53C2311yescharacteristic
38C22×C4×D53—28no—
39C22×C4×D53—22no—
40C22×C4×D53—22no—
41C22×C4×D53—22no—
42C22×C4×D53—22no—
43C22×C4×D53—48no—
44C22×C4×D53C2×C411yescharacteristic
45C22×C4×D53C2×C411yescharacteristic
46C22×C4×D53C2×C414yes—
47C22×C4×D53C2×C414yes—
48C22×C4×D53D412yes—
49C22×C4×D53D412yes—
50C22×C4×D53D412yes—
51C22×C4×D53D412yes—
52C22×C4×D53C2311yescharacteristic
53C22×C4×D53C2311yescharacteristic
54C2×C4⋊Dic53—22no—
55C2×C4⋊Dic53—22no—
56C2×C4⋊Dic53C2×C412yes—
57C2×C4⋊Dic53C2×C412yes—
58C2×#11719919—24no—
59C2×#11719919—24no—
60C2×#11719919C2×C414yes—
61C2×#11719919C2314yes—
62C4⋊C4×D53—24no—
63C4⋊C4×D53—24no—
64C4⋊C4×D53—24no—
65C4⋊C4×D53—24no—
66C4⋊C4×D53—24no—
67C4⋊C4×D53—24no—
68C4⋊C4×D53—24no—
69C4⋊C4×D53—24no—
70C23×C4×C53C2×C411yescharacteristic
71C23×C4×C53C2×C412yes—
72C2×C4⋊C4×C53—22no—
73C2×C4⋊C4×C53—22no—
74C2×C4⋊C4×C53C2×C412yes—
75C2×C4⋊C4×C53C2×C412yes—
76C24×C53C22×C411yescharacteristic
77C23×D53—24no—
78C23×D53—24no—
79C23×D53—24no—
80C23×D53C22⋊C411yescharacteristic
81C23×D53C22⋊C411yescharacteristic
82C23×D53C22⋊C411yescharacteristic
83C23×D53C22⋊C411yescharacteristic
84C23×D53C22×C411yescharacteristic
85C23×D53C22×C411yescharacteristic
86C22×C4×C53—24no—
87C22×C4×C53—22no—
88C22×C4×C53—22no—
89C22×C4×C53—44no—
90C22×C4×C53C22⋊C412yes—
91C22×C4×C53C22⋊C412yes—
92C22×C4×C53C22×C411yescharacteristic
93C22×C4×C53C22×C414yes—
94C22×C4×C53C22×C411yescharacteristic
95C22×Dic53—24no—
96C22×Dic53—22no—
97C22×Dic53—22no—
98C22×Dic53—44no—
99C22×Dic53C22×C411yescharacteristic
100C22×Dic53C22×C414yes—
101C22×Dic53C2×D412yes—
102C22×Dic53C2×D412yes—
103C22×Dic53C2411yescharacteristic
104C2×C4×D53—24no—
105C2×C4×D53—24no—
106C2×C4×D53—24no—
107C2×C4×D53—28no—
108C2×C4×D53—28no—
109C2×C4×D53—28no—
110C2×C4×D53—28no—
111C2×C4×D53—24no—
112C2×C4×D53—24no—
113C2×C4×D53—24no—
114C2×C4×D53—24no—
115C2×C4×D53—48no—
116C2×C4×D53—48no—
117C2×C4×D53—48no—
118C2×C4×D53—48no—
119C2×C4×D53—48no—
120C2×C4×D53—48no—
121C2×C4×D53C22⋊C412yes—
122C2×C4×D53C22⋊C412yes—
123C2×C4×D53C22⋊C412yes—
124C2×C4×D53C22⋊C412yes—
125C2×C4×D53C2×D412yes—
126C2×C4×D53C2×D412yes—
127C2×C4×D53C2×D412yes—
128C2×C4×D53C2×D412yes—
129C2×C4×D53#4118yes—
130#11719940—216no—
131C2×#88324—28no—
132#11719936—48no—
133D53⋊C8—48no—
134C4⋊C4×C53—24no—
135C4⋊C4×C53—24no—
136C4⋊Dic53—24no—
137C4⋊Dic53—24no—
138#11719919—28no—
139#11719919—28no—
140C23×C53—22no—
141C23×C53—22no—
142C23×C53—22no—
143C23×C53C2×C22⋊C411yescharacteristic
144C23×C53C2×C22⋊C411yescharacteristic
145C23×C53C23×C411yescharacteristic
146C22×D53—232no—
147C22×D53—22no—
148C22×D53—22no—
149C22×D53—22no—
150C22×D53—22no—
151C22×D53—22no—
152C22×D53—22no—
153C22×D53—22no—
154C22×D53—22no—
155C22×D53—22no—
156C22×D53—22no—
157C22×D53—22no—
158C22×D53—22no—
159C22×D53—22no—
160C22×D53—22no—
161C22×D53—22no—
162C22×D53#10014yes—
163C22×D53#10114yes—
164C22×D53C2×C22⋊C411yescharacteristic
165C22×D53C2×C22⋊C411yescharacteristic
166C22×D53C2×C22⋊C411yescharacteristic
167C22×D53C2×C22⋊C411yescharacteristic
168C22×D53#11714yes—
169C2×C4×C53—22no—
170C2×C4×C53—24no—
171C2×C4×C53—24no—
172C2×C4×C53—24no—
173C2×C4×C53—44no—
174C2×C4×C53—44no—
175C2×C4×C53—44no—
176C2×C4×C53C2×C22⋊C412yes—
177C2×C4×C53C2×C22⋊C412yes—
178C2×C4×C53#11714yes—
179C2×Dic53—22no—
180C2×Dic53—24no—
181C2×Dic53—24no—
182C2×Dic53—24no—
183C2×Dic53—44no—
184C2×Dic53—44no—
185C2×Dic53—44no—
186C2×Dic53C2×C22⋊C412yes—
187C2×Dic53C22×D412yes—
188C2×Dic53C2×#4114yes—
189C4×D53—24no—
190C4×D53—24no—
191C4×D53—24no—
192C4×D53—24no—
193C4×D53—24no—
194C4×D53—24no—
195C4×D53—48no—
196C4×D53—48no—
197C4×D53—48no—
198C4×D53—48no—
199C4×D53#12318yes—
200C4×D53#12318yes—
201#88324—48no—
202C2×#1821—531nomaximal, Sylow
203C22×C53—28no—
204C22×C53—21no—
205C22×C53—21no—
206C22×C53—21no—
207C22×C53—21no—
208C22×C53—21no—
209C22×C53—21no—
210C22×C53C2×#10012yes—
211C22×C53C2×#10112yes—
212C22×C53C22×C22⋊C411yescharacteristic
213C22×C53C2×#11712yes—
214C2×D53—28no—
215C2×D53—28no—
216C2×D53—28no—
217C2×D53—21no—
218C2×D53—21no—
219C2×D53—21no—
220C2×D53—21no—
221C2×D53—21no—
222C2×D53—21no—
223C2×D53—28no—
224C2×D53—28no—
225C2×D53—28no—
226C2×D53#38112yes—
227C2×D53#38112yes—
228C2×D53C2×#10012yes—
229C2×D53C2×#10012yes—
230C2×D53C2×#10112yes—
231C2×D53C2×#10112yes—
232C4×C53—22no—
233C4×C53—44no—
234C4×C53#38114yes—
235Dic53—22no—
236Dic53—44no—
237Dic53C2×#12314yes—
238C23×C4⋊C4—531no—
239C2×#407—532no—
240#1821—534no—
241#1821—534no—
242C2×#343—534no—
243C2×C53—22no—
244C2×C53—22no—
245C2×C53—22no—
246C2×C53C2×#38111yescharacteristic
247C2×C53C22×#10011yescharacteristic
248C2×C53C22×#10111yescharacteristic
249D53—22no—
250D53—22no—
251D53—22no—
252D53#182114yescomplemented
253C24×C4—531no—
254C24×C4—532no—
255C22×M16—534no—
256C22×C4⋊C4—532no—
257C22×C4⋊C4—531no—
258C22×C4⋊C4—532no—
259C22×C4⋊C4—532no—
260C22×C4⋊C4—532no—
261C22×C4⋊C4—532no—
262C22×C4⋊C4—1062no—
263C22×C4⋊C4—1062no—
264C22×C4⋊C4—1062no—
265C22×C4⋊C4—1062no—
266C22×C4⋊C4#615711yescharacteristic
267#407—534no—
268#407—534no—
269#407—1062no—
270#407—1062no—
271C2×C22⋊C8—1062no—
272C2×C22⋊C8—1062no—
273#343—5316no—
274C53C2×#182111yescharacteristic, complemented, Sylow
275C25—531no—
276C23×C4—531no—
277C23×C4—531no—
278C23×C4—532no—
279C23×C4—532no—
280C23×C4—532no—
281C23×C4—532no—
282C23×C4—531no—
283C23×C4—531no—
284C23×C4—531no—
285C23×C4—532no—
286C23×C4—534no—
287C23×C4—534no—
288C23×C4—1068no—
289C23×C4—1062no—
290C23×C4—1062no—
291C23×C4—1062no—
292C23×C4—1062no—
293C23×C4—2128no—
294C23×C4C2×#615712yes—
295C23×C4C2×#615711yescharacteristic
296C2×M16—538no—
297C2×M16—1064no—
298C2×M16—10616no—
299C22×C8—1064no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—534no—
303C2×C4⋊C4—534no—
304C2×C4⋊C4—532no—
305C2×C4⋊C4—532no—
306C2×C4⋊C4—1064no—
307C2×C4⋊C4—1064no—
308C2×C4⋊C4—1064no—
309C2×C4⋊C4—1064no—
310C2×C4⋊C4—1064no—
311C2×C4⋊C4—1064no—
312C2×C4⋊C4—1064no—
313C2×C4⋊C4—1064no—
314C2×C4⋊C4—1064no—
315C2×C4⋊C4—1064no—
316C2×C4⋊C4—1062no—
317C2×C4⋊C4—1062no—
318C2×C4⋊C4C2×#615712yes—
319C2×C4⋊C4C2×#615712yes—
320C22⋊C8—1064no—
321C22⋊C8—1064no—
322C22⋊C8—1064no—
323C22⋊C8—1064no—
324C24—531no—
325C24—531no—
326C24—531no—
327C24—531no—
328C24—531no—
329C24—531no—
330C24—1064no—
331C24—1064no—
332C24—1064no—
333C24C22×#615711yescharacteristic
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—44no—
338C22×C4—531no—
339C22×C4—532no—
340C22×C4—532no—
341C22×C4—538no—
342C22×C4—532no—
343C22×C4—532no—
344C22×C4—531no—
345C22×C4—532no—
346C22×C4—532no—
347C22×C4—532no—
348C22×C4—532no—
349C22×C4—532no—
350C22×C4—532no—
351C22×C4—534no—
352C22×C4—1064no—
353C22×C4—1068no—
354C22×C4—1068no—
355C22×C4—1068no—
356C22×C4—1068no—
357C22×C4—1064no—
358C22×C4—1064no—
359C22×C4—1064no—
360C22×C4—1064no—
361C22×C4—1064no—
362C22×C4—1064no—
363C22×C4—1064no—
364C22×C4—1062no—
365C22×C4—1062no—
366C22×C4—2128no—
367C22×C4—2128no—
368C22×C4—2128no—
369C22×C4—2128no—
370C22×C4—2128no—
371C22×C4—2128no—
372C22×C4—2124no—
373C22×C4C22⋊#615712yes—
374C22×C4C22⋊#615712yes—
375C22×C4C22×#615711yescharacteristic
376C22×C4C22×#615714yes—
377C22×C4C22×#615711yescharacteristic
378M16—10616no—
379M16—2128no—
380C2×C8—1068no—
381C2×C8—2128no—
382C4⋊C4—24no—
383C4⋊C4—24no—
384C4⋊C4—1068no—
385C4⋊C4—1068no—
386C4⋊C4—1064no—
387C4⋊C4—1064no—
388C23—22no—
389C23—22no—
390C23—22no—
391C23—531no—
392C23—534no—
393C23—534no—
394C23—531no—
395C23—531no—
396C23—531no—
397C23—534no—
398C23—1062no—
399C23—1062no—
400C23—1062no—
401C23—1062no—
402C23—1062no—
403C23—1062no—
404C23—1062no—
405C23—1062no—
406C23—1062no—
407C23—1062no—
408C23—1062no—
409C23—1062no—
410C23—10632no—
411C23—1062no—
412C23—1062no—
413C23—1062no—
414C23C2×C22⋊#615711yescharacteristic
415C23C2×C22⋊#615711yescharacteristic
416C23C23×#615711yescharacteristic
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—44no—
424C2×C4—532no—
425C2×C4—534no—
426C2×C4—538no—
427C2×C4—538no—
428C2×C4—532no—
429C2×C4—1064no—
430C2×C4—1064no—
431C2×C4—1064no—
432C2×C4—1064no—
433C2×C4—1064no—
434C2×C4—1064no—
435C2×C4—1062no—
436C2×C4—1064no—
437C2×C4—1064no—
438C2×C4—1064no—
439C2×C4—2128no—
440C2×C4—2128no—
441C2×C4—2128no—
442C2×C4—2128no—
443C2×C4—2124no—
444C2×C4—2124no—
445C2×C4—2124no—
446C2×C4C2×C22⋊#615712yes—
447C2×C4C2×C22⋊#615712yes—
448C2×C4#1313329614yes—
449C8—2128no—
450C22—28no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—532no—
458C22—532no—
459C22—532no—
460C22—532no—
461C22—532no—
462C22—532no—
463C22—1068no—
464C22—1068no—
465C22—1068no—
466C22—1068no—
467C22—1068no—
468C22—1068no—
469C22—1061no—
470C22—1061no—
471C22—1061no—
472C22—1061no—
473C22—1061no—
474C22—1061no—
475C22D53⋊#10012yes—
476C22D53⋊#10112yes—
477C22C22×C22⋊#615711yescharacteristic
478C22C2×#1313329612yes—
479C4—22no—
480C4—44no—
481C4—534no—
482C4—1062no—
483C4—2124no—
484C4#1681156614yes—
485C2—22no—
486C2—22no—
487C2—22no—
488C2—534no—
489C2—1062no—
490C2—1062no—
491C2—1062no—
492C2C2×#1681156611yescharacteristic
493C2C2×D53⋊#10011yescharacteristic
494C2C2×D53⋊#10111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6157
commutatorC23×C53C23×C4
FrattiniC23C23×#6157
FittingC22×C4⋊C4×C53C4
socleC22×C53C22×C22⋊C4
prime radicalC24×D53C2×C4
cosocleC22×Dic53C24
hypercenterC22×C4⋊C4#6157
hypocenterC53C2×#1821
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #20290615C2semidirect
3. #20290614C2semidirect
4. #20290418C2semidirect
13. #16811503C22semidirect
252. D53#1821semidirect
274. C53C2×#1821semidirect

Maximal subgroups

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

subgroupindex
D53⋊#4072
#202906152
#202906142
#202904182
C22×C4⋊C4×D532
C2×#182153