Finite Group Databasebeta

← #14913914

Subgroups — #14913914

Order 2816.

2542 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623053C211yesmaximal, characteristic
2#13071569C214yesmaximal, complemented
3#13071561C214yesmaximal, complemented
4#13071539C218yesmaximal, complemented
5#13071221C214yesmaximal, complemented
6#13071209C211yesmaximal, characteristic
7#13071204C211yesmaximal, characteristic
8#13071020C214yesmaximal, complemented
9#13071019C211yesmaximal, characteristic, complemented
10C2×#10622589C211yesmaximal, characteristic, complemented
11#13070972C211yesmaximal, characteristic, complemented
12C11×#2274C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2214yes—
20C22×C4×Dic11C2211yescharacteristic
21#10623053C4116yescomplemented
22C2×#66946C2212yes—
23C2×#66940C2212yes—
24C2×(C22⋊D11)⋊C4C2214yes—
25C2×#66925C2218yes—
26C2×#66925C2212yes—
27C2×C42×D11C2212yes—
28C4×C11×C4⋊C4C2214yes—
29C4×C11×C4⋊C4C2214yes—
30C4×C11×C22⋊C4C2214yes—
31#10622826C2214yes—
32#10622601C2212yes—
33#10622600C2214yes—
34#10622600C2214yes—
35#10622590C2212yes—
36#10622589C2212yes—
37#10622589C2212yes—
38#10622589C2214yes—
39#10622589C2212yes—
40C4⋊C4×Dic11C2214yes—
41#10622587C2212yes—
42#10622571C2214yes—
43#10622555C2214yes—
44C22⋊C4×Dic11C2214yes—
45#10622553C2218yes—
46#10622552C2212yes—
47C4×C4⋊Dic11C2214yes—
48#10622546C2218yes—
49C4×Dic11⋊C4C2214yes—
50C4×Dic11⋊C4C2218yes—
51#10622542C2212yes—
52#10622282C2218yes—
53#10622280C2218yes—
54#10622265C2218yes—
55#10622263C2218yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11C2312yes—
59C23×Dic11C2312yes—
60C23×Dic11C2312yes—
61C2×#4339—24no—
62C2×#4339—24no—
63C2×#4339C2×C418yes—
64C22×D44C2311yescharacteristic
65C22×C4×D11C2314yes—
66C22×C4×D11C2312yes—
67C22×Dic22C2311yescharacteristic
68C11×#117—24no—
69C11×#117C2×C418yes—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C22⋊C4C2312yes—
76C2×C11×C22⋊C4C2312yes—
77C2×C42×C11C2312yes—
78C2×C42×C11C2318yes—
79C2×C42×C11C2312yes—
80C2×C22⋊Dic11C2312yes—
81C2×(C2×D11)⋊C4C2318yes—
82C2×(C2×D11)⋊C4C2318yes—
83C2×(C2×D11)⋊C4C2314yes—
84#66979—24no—
85C2×C4⋊Dic11—24no—
86C2×C4⋊Dic11C2312yes—
87C2×C4⋊Dic11C2312yes—
88C2×C4⋊Dic11C2312yes—
89C2×Dic11⋊C4—48no—
90C2×Dic11⋊C4C2314yes—
91C2×Dic11⋊C4C2318yes—
92C2×Dic11⋊C4C2314yes—
93C2×Dic11⋊C4C2318yes—
94C2×Dic11⋊C4C2314yes—
95C2×C4×Dic11C2×C418yes—
96C2×C4×Dic11C2312yes—
97C2×C4×Dic11C2318yes—
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2314yes—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2312yes—
102#66946C2×C4116yescomplemented
103#66940C2×C4116yescomplemented
104(C22⋊D11)⋊C4C2×C4132yes—
105#66925—416no—
106#66925C2×C4116yescomplemented
107C42×D11C2×C4116yescomplemented
108C11×#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C11⋊#95C2314yes—
113C11⋊#95C2314yes—
114#34188—111nomaximal, Sylow
115C24×C11C2411yescharacteristic
116C23×D11C2412yes—
117C22×C4×C11—24no—
118C22×C4×C11—44no—
119C22×C4×C11C22×C414yes—
120C22×C4×C11#4114yes—
121C22×C4×C11#4114yes—
122C22×C4×C11C2414yes—
123C22×C4×C11C2414yes—
124C22×C4×C11C2414yes—
125C22×C4×C11C2411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C2×C22⋊D11—24no—
128C2×C22⋊D11—24no—
129C2×C22⋊D11C22×C418yes—
130C22×Dic11—24no—
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—44no—
134C22×Dic11C22×C418yes—
135C22×Dic11C2414yes—
136C22×Dic11C2414yes—
137C22×Dic11C2412yes—
138C22×Dic11C2412yes—
139C22×Dic11C2412yes—
140#4339—232no—
141C2×D44—22no—
142C2×D44—22no—
143C2×D44C22×C414yes—
144C2×C4×D11—28no—
145C2×C4×D11—28no—
146C2×C4×D11—24no—
147C2×C4×D11—24no—
148C2×C4×D11C22×C418yes—
149C2×C4×D11C22×C4116yes—
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×Dic22C22×C414yes—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4C22×C418yes—
157C11×C22⋊C4—24no—
158C11×C22⋊C4C22×C418yes—
159C42×C11—24no—
160C42×C11—48no—
161C42×C11C22×C418yes—
162C22⋊Dic11—24no—
163(C2×D11)⋊C4—48no—
164(C2×D11)⋊C4—48no—
165(C2×D11)⋊C4C22×C4116yes—
166C4⋊Dic11—24no—
167C4⋊Dic11—24no—
168C4⋊Dic11—24no—
169Dic11⋊C4—28no—
170Dic11⋊C4—216no—
171Dic11⋊C4—28no—
172Dic11⋊C4—48no—
173Dic11⋊C4C22×C4116yes—
174C4×Dic11—24no—
175C4×Dic11—48no—
176C4×Dic11C22×C414yes—
177C4×Dic11C22×C4116yes—
178C4×Dic11C22×C414yes—
179C4×Dic11C22×C418yes—
180C2×C4×#41—111no—
181#2355—114no—
182#2354—114no—
183#2352—118no—
184#2314—114no—
185#2311—111no—
186#2311—111no—
187#2285—114no—
188#2285—111no—
189C2×#384—111no—
190#2274—111no—
191#2274D1111yescharacteristic, complemented
192C23×C11—22no—
193C23×C11—22no—
194C23×C11C23×C412yes—
195C23×C11C2×#4112yes—
196C23×C11C2×#4112yes—
197C23×C11C2511yescharacteristic
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—24no—
201C22×D11—24no—
202C22×D11C23×C414yes—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—28no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—84no—
211C2×C4×C11#117116yescomplemented
212C2×C4×C11C23×C418yes—
213C2×C4×C11C23×C412yes—
214C2×C4×C11C23×C412yes—
215C2×C4×C11C2×#4112yes—
216C2×C4×C11C2×#4112yes—
217C2×C4×C11C2×#4112yes—
218C2×C4×C11C2×#4112yes—
219C22⋊D11—216no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—216no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—28no—
229C2×Dic11—24no—
230C2×Dic11—84no—
231C2×Dic11C23×C414yes—
232C2×Dic11C23×C414yes—
233C2×Dic11C23×C414yes—
234C2×Dic11H(5,𝔽2)14yes—
235C2×Dic112−1+414yes—
236D44—28no—
237C4×D11—216no—
238C4×D11—232no—
239Dic22—28no—
240C22×#41—111no—
241C4×#41—1116no—
242C2×C4×Q8—112no—
243C2×C4×D4—112no—
244C2×C4×D4—114no—
245C2×#117—111no—
246C2×#117—112no—
247C2×#117—118no—
248C2×#117C2×D1111yescharacteristic
249C2×#117C2×D1111yescharacteristic
250C22×C4⋊C4—111no—
251C22×C4⋊C4—114no—
252C22×C4⋊C4C2×D1111yescharacteristic
253C22×C42—111no—
254C22×C42—112no—
255#391—112no—
256#391—112no—
257#390—112no—
258#390—112no—
259#388—118no—
260#388—118no—
261#387—118no—
262#387—118no—
263#386—114no—
264#386—114no—
265#384—112no—
266#384—114no—
267#384—112no—
268#384—112no—
269#382—112no—
270#382—118no—
271#380—114no—
272#380—114no—
273#380—114no—
274#380—118no—
275C4×C4⋊C4—114no—
276C4×C4⋊C4—114no—
277C4×C4⋊C4—118no—
278C4×C4⋊C4—114no—
279C4×C4⋊C4C2×D1114yes—
280C4×C4⋊C4C2×D1114yes—
281C4×C22⋊C4—114no—
282C4×C22⋊C4C2×D1114yes—
283C22×C11—24no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—24no—
287C22×C11C2×#11714yes—
288C22×C11C24×C411yescharacteristic
289C22×C11C22×#4111yescharacteristic
290C22×C11C22×#4111yescharacteristic
291C22×C11C2×H(5,𝔽2)12yes—
292C22×C11C2×2−1+412yes—
293C2×D11—24no—
294C2×D11—28no—
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—44no—
298C4×C11—28no—
299C4×C11—44no—
300C4×C11—44no—
301C4×C11C2×#11714yes—
302C4×C11C2×#11714yes—
303Dic11—24no—
304Dic11—24no—
305Dic11—44no—
306Dic11—44no—
307Dic11#52018yes—
308C2×#41—118no—
309C2×#41—224no—
310C2×#41—224no—
311C22×Q8—111no—
312C22×D4—112no—
313C22×D4—111no—
314C23×C4—112no—
315C23×C4—114no—
316C23×C4—112no—
317C23×C4—112no—
318C23×C4C22×D1112yes—
319C23×C4C22×D1111yescharacteristic
320C4×Q8—1116no—
321C4×D4—1116no—
322C4×D4—1132no—
323#117—24no—
324#117—1116no—
325#117—224no—
326#117—4416no—
327#117C4×D1118yes—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—118no—
331C2×C4⋊C4—112no—
332C2×C4⋊C4—112no—
333C2×C4⋊C4—114no—
334C2×C4⋊C4—112no—
335C2×C4⋊C4—114no—
336C2×C4⋊C4—118no—
337C2×C4⋊C4—224no—
338C2×C4⋊C4—448no—
339C2×C4⋊C4C22×D1112yes—
340C2×C4⋊C4C22×D1112yes—
341C2×C4⋊C4C22×D1112yes—
342C2×C4⋊C4C22×D1112yes—
343C2×C22⋊C4—114no—
344C2×C22⋊C4—112no—
345C2×C22⋊C4—118no—
346C2×C22⋊C4—118no—
347C2×C22⋊C4C22×D1112yes—
348C2×C22⋊C4C22×D1112yes—
349C2×C42—118no—
350C2×C42—111no—
351C2×C42—114no—
352C2×C42—112no—
353C2×C42—111no—
354C2×C42—1116no—
355C2×C42—112no—
356C2×C42—118no—
357C2×C42C22×D1112yes—
358C2×C42C22×D1118yes—
359C2×C42C22×D1112yes—
360#95—118no—
361#95—118no—
362#95—118no—
363#95—114no—
364#95—114no—
365#95C22×D1118yes—
366C2×C11—24no—
367C2×C11C22×#11711yescharacteristic
368C2×C11C2×#52012yes—
369C2×C11#350811yescharacteristic
370C2×C11#350911yescharacteristic
371C2×C11#351112yes—
372D11—44no—
373C24—112no—
374C24C23×D1111yescharacteristic
375#41—2232no—
376C2×Q8—114no—
377C2×Q8—222no—
378C2×Q8—222no—
379C2×D4—118no—
380C2×D4—114no—
381C2×D4—224no—
382C2×D4—224no—
383C2×D4—222no—
384C2×D4—222no—
385C22×C4—24no—
386C22×C4—44no—
387C22×C4—112no—
388C22×C4—118no—
389C22×C4—112no—
390C22×C4—112no—
391C22×C4—118no—
392C22×C4—1116no—
393C22×C4—114no—
394C22×C4—114no—
395C22×C4—228no—
396C22×C4—228no—
397C22×C4—224no—
398C22×C4—224no—
399C22×C4—224no—
400C22×C4—224no—
401C22×C4—224no—
402C22×C4—444no—
403C22×C4C2×C4×D1114yes—
404C22×C4#433914yes—
405C22×C4#433914yes—
406C22×C4C23×D1114yes—
407C22×C4C23×D1114yes—
408C22×C4C23×D1114yes—
409C22×C4C23×D1111yescharacteristic
410C22×C4C23×D1111yescharacteristic
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—1116no—
415C4⋊C4—2216no—
416C4⋊C4—228no—
417C4⋊C4—228no—
418C4⋊C4—224no—
419C4⋊C4—224no—
420C4⋊C4—224no—
421C4⋊C4—448no—
422C4⋊C4C2×C4×D1118yes—
423C22⋊C4—24no—
424C22⋊C4—1116no—
425C22⋊C4—224no—
426C22⋊C4—448no—
427C22⋊C4—448no—
428C22⋊C4C2×C4×D1118yes—
429C42—24no—
430C42—48no—
431C42—114no—
432C42—114no—
433C42—118no—
434C42—1116no—
435C42—224no—
436C42—448no—
437C42C2×C4×D1118yes—
438C11#3418811yescharacteristic, complemented, Sylow
439C23—22no—
440C23—22no—
441C23—114no—
442C23—222no—
443C23—222no—
444C23—224no—
445C23—224no—
446C23C22×C4×D1112yes—
447C23C2×#433912yes—
448C23C2×#433912yes—
449C23C24×D1111yescharacteristic
450Q8—228no—
451D4—2216no—
452D4—228no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—28no—
459C2×C4—24no—
460C2×C4—84no—
461C2×C4—114no—
462C2×C4—114no—
463C2×C4—114no—
464C2×C4—114no—
465C2×C4—114no—
466C2×C4—2232no—
467C2×C4—2216no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—2216no—
473C2×C4—224no—
474C2×C4—224no—
475C2×C4—224no—
476C2×C4—228no—
477C2×C4—224no—
478C2×C4—884no—
479C2×C4#66925116yescomplemented
480C2×C4C22×C4×D1118yes—
481C2×C4C22×C4×D1112yes—
482C2×C4C22×C4×D1112yes—
483C2×C4C2×#433912yes—
484C2×C4C2×#433912yes—
485C2×C4C2×#433912yes—
486C2×C4C2×#433912yes—
487C22—22no—
488C22—22no—
489C22—24no—
490C22—24no—
491C22—224no—
492C22—228no—
493C22—442no—
494C22—442no—
495C22—444no—
496C22C2×#6692514yes—
497C22C23×C4×D1111yescharacteristic
498C22C22×#433911yescharacteristic
499C22C22×#433911yescharacteristic
500C22D11×H(5,𝔽2)12yes—
501C22D11×2−1+412yes—
502C4—28no—
503C4—44no—
504C4—44no—
505C4—118no—
506C4—224no—
507C4—224no—
508C4—444no—
509C4—444no—
510C4C2×#6692514yes—
511C4C2×#6692514yes—
512C2—24no—
513C2—444no—
514C2C22×#6692511yescharacteristic
515C2D11×#52012yes—
516C2#1308248711yescharacteristic
517C2#1308249711yescharacteristic
518C2#1308251912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2274C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenter#2274D11
hypocenterC11#34188
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. #13071569C2semidirect
3. #13071561C2semidirect
4. #13071539C2semidirect
5. #13071221C2semidirect
8. #13071020C2semidirect
9. #13071019C2semidirect
10. C2×#10622589C2semidirect
11. #13070972C2semidirect
12. C11×#2274C2semidirect
21. #10623053C4semidirect
102. #66946C2×C4semidirect
103. #66940C2×C4semidirect
106. #66925C2×C4semidirect
107. C42×D11C2×C4semidirect
191. #2274D11semidirect
211. C2×C4×C11#117semidirect
438. C11#34188semidirect
479. C2×C4#66925semidirect

Maximal subgroups

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

subgroupindex
C2×#106230532
#130715692
#130715612
#130715392
#130712212
#130712092
#130712042
#130710202
#130710192
C2×#106225892
#130709722
C11×#22742
#3418811