Finite Group Databasebeta

← #14781184

Subgroups — #14781184

Order 2816.

1506 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic, complemented
2#13071191C211yesmaximal, characteristic
3#13071191C212yesmaximal
4#13069784C214yesmaximal, complemented
5#13069781C214yesmaximal, complemented
6C2×#10622165C212yesmaximal, complemented
7C2×C11×#342C211yesmaximal, characteristic, complemented
8C23×C22⋊D11C2211yescharacteristic
9C22×C11×C22⋊C4C2212yes—
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C22⋊Dic11C2211yescharacteristic
12C22×C22⋊Dic11C2212yes—
13C2×#66977—22no—
14#10623014—22no—
15#10623014—24no—
16#10623014C2214yes—
17C2×#66931—24no—
18#10622826—22no—
19#10622826—24no—
20#10622571—24no—
21#10622571—22no—
22#10622568C2212yes—
23#10622568C2214yes—
24#10622556C2212yes—
25#10622556C2214yes—
26C11×#342C2214yes—
27#10622165C2218yes—
28C25×C11C2311yescharacteristic
29C24×D11C2311yescharacteristic
30C23×C4×C11—22no—
31C23×C4×C11D412yes—
32C22×C22⋊D11—21no—
33C22×C22⋊D11—22no—
34C22×C22⋊D11—21no—
35C22×C22⋊D11—22no—
36C22×C22⋊D11—24no—
37C22×C22⋊D11—22no—
38C22×C22⋊D11Q814yescomplemented
39C23×Dic11—21no—
40C23×Dic11D414yes—
41C23×Dic11C2311yescharacteristic
42C22×Dic22—22no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—24no—
46C2×C11×C22⋊C4—24no—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4D412yes—
49C2×C11×C22⋊C4C2314yes—
50C2×C11×C22⋊C4C2312yes—
51C2×C22⋊Dic11—22no—
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—24no—
56C2×C22⋊Dic11—21no—
57C2×C22⋊Dic11D414yes—
58C2×C22⋊Dic11C2312yes—
59C2×C22⋊Dic11C2314yes—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—28no—
62C2×C4⋊Dic11—22no—
63#66977—28no—
64#66977—28no—
65C2×Dic11⋊C4—24no—
66#66931—216no—
67#66931—216no—
68C11⋊#95—24no—
69C11⋊#95—28no—
70#23468—111nomaximal, Sylow
71C24×C11—82no—
72C24×C11C2×D411yescharacteristic
73C24×C11C2×D411yescharacteristic
74C24×C11C2×D412yes—
75C24×C11C2×D412yes—
76C24×C11C2×Q812yes—
77C24×C11#4114yes—
78C24×C11#4112yes—
79C24×C11C2411yescharacteristic
80C23×D11—21no—
81C23×D11—22no—
82C23×D11—22no—
83C23×D11—21no—
84C23×D11—82no—
85C23×D11C2×Q812yescomplemented
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—24no—
89C22×C4×C11—44no—
90C22×C4×C11—82no—
91C22×C4×C11—84no—
92C22×C4×C11C2×D414yes—
93C2×C22⋊D11—28no—
94C2×C22⋊D11—28no—
95C2×C22⋊D11—24no—
96C2×C22⋊D11—24no—
97C2×C22⋊D11—41no—
98C2×C22⋊D11—42no—
99C2×C22⋊D11—41no—
100C2×C22⋊D11—42no—
101C2×C22⋊D11—42no—
102C2×C22⋊D11—44no—
103C2×C22⋊D11—44no—
104C22×Dic11—24no—
105C22×Dic11—24no—
106C22×Dic11—21no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—21no—
111C22×Dic11—42no—
112C22×Dic11—84no—
113C22×Dic11—82no—
114C22×Dic11C2×D418yes—
115C22×Dic11C2×Q812yescomplemented
116C2×Dic22—28no—
117C2×Dic22—84no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—44no—
123C22⋊Dic11—24no—
124C22⋊Dic11—24no—
125C22⋊Dic11—24no—
126C22⋊Dic11—24no—
127C22⋊Dic11—24no—
128C22⋊Dic11—42no—
129(C2×D11)⋊C4—84no—
130(C2×D11)⋊C4—88no—
131C4⋊Dic11—28no—
132Dic11⋊C4—216no—
133C2×#543—111no—
134#2308—112no—
135#2308—111no—
136#2030—114no—
137#2029—114no—
138C2×#342—112no—
139C2×#342D1111yescharacteristic, complemented
140C23×C11—42no—
141C23×C11—44no—
142C23×C11—42no—
143C23×C11—44no—
144C23×C11—42no—
145C23×C11—82no—
146C23×C11—84no—
147C23×C11—82no—
148C23×C11#12011yescharacteristic
149C23×C11#12012yes—
150C23×C11#12011yescharacteristic
151C23×C11C22⋊Q814yes—
152C23×C11C22⋊Q814yes—
153C23×C11C22⋊Q812yes—
154C23×C11C22⋊Q812yes—
155C23×C11#12412yes—
156C23×C11#12412yes—
157C23×C11#12414yes—
158C23×C11#12414yes—
159C23×C11C22×D411yescharacteristic
160C23×C11C22×D412yes—
161C23×C11C22×Q811yescharacteristic
162C23×C11C2×#4112yes—
163C23×C11C2×#4111yescharacteristic
164C22×D11—24no—
165C22×D11—22no—
166C22×D11—44no—
167C22×D11—48no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—42no—
171C22×D11—82no—
172C22×D11—84no—
173C22×D11—82no—
174C2×C4×C11—24no—
175C2×C4×C11—44no—
176C2×C4×C11—44no—
177C2×C4×C11—48no—
178C2×C4×C11—44no—
179C2×C4×C11—82no—
180C2×C4×C11—88no—
181C22⋊D11—44no—
182C22⋊D11—48no—
183C22⋊D11—44no—
184C2×Dic11—28no—
185C2×Dic11—24no—
186C2×Dic11—22no—
187C2×Dic11—48no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—42no—
191C2×Dic11—48no—
192C2×Dic11—44no—
193C2×Dic11—42no—
194C2×Dic11—84no—
195C2×Dic11—84no—
196Dic22—88no—
197C23×D4—111no—
198#543—114no—
199#543—224no—
200#543—222no—
201C2×C22⋊Q8—224no—
202C2×C22⋊Q8—222no—
203C22×C22⋊C4—112no—
204C22×C22⋊C4—111no—
205C22×C22⋊C4C2×D1112yes—
206C22×C22⋊C4C2×D1111yescharacteristic
207#386—224no—
208#386—224no—
209#386—222no—
210#386—222no—
211#381—114no—
212#381—112no—
213#379—114no—
214#379—112no—
215#342—118no—
216#342C2×D1114yes—
217C22×C11—22no—
218C22×C11—24no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—24no—
222C22×C11—44no—
223C22×C11—41no—
224C22×C11—42no—
225C22×C11—41no—
226C22×C11—44no—
227C22×C11—44no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—44no—
232C22×C11—42no—
233C22×C11#39312yes—
234C22×C11#39314yes—
235C22×C11#39312yes—
236C22×C11C2×#12011yescharacteristic
237C22×C11C2×C22⋊Q812yes—
238C22×C11C2×C22⋊Q811yescharacteristic
239C22×C11C2×#12411yescharacteristic
240C22×C11C2×#12412yes—
241C2×D11—48no—
242C2×D11—44no—
243C2×D11—42no—
244C2×D11—82no—
245C2×D11—84no—
246C2×D11—82no—
247C4×C11—44no—
248C4×C11—84no—
249Dic11—42no—
250Dic11—48no—
251Dic11—82no—
252C25—111no—
253C25C22×D1111yescharacteristic
254C22×Q8—222no—
255C22×D4—114no—
256C22×D4—221no—
257C22×D4—221no—
258C22×D4—224no—
259C22×D4—222no—
260C22×D4—222no—
261C22×D4—222no—
262C23×C4—22no—
263C23×C4—111no—
264C23×C4—114no—
265C23×C4—221no—
266C23×C4D4412yes—
267C22⋊Q8—2216no—
268C22⋊Q8—2216no—
269C22⋊Q8—228no—
270C22⋊Q8—228no—
271C2×C4⋊C4—224no—
272C2×C4⋊C4—222no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—24no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—114no—
279C2×C22⋊C4—114no—
280C2×C22⋊C4—112no—
281C2×C22⋊C4—222no—
282C2×C22⋊C4—222no—
283C2×C22⋊C4—222no—
284C2×C22⋊C4—222no—
285C2×C22⋊C4—224no—
286C2×C22⋊C4—221no—
287C2×C22⋊C4—228no—
288C2×C22⋊C4—224no—
289C2×C22⋊C4D4412yes—
290C2×C22⋊C4C22×D1114yes—
291C2×C22⋊C4C22×D1112yes—
292#95—228no—
293#95—224no—
294C2×C11—21no—
295C2×C11—22no—
296C2×C11—22no—
297C2×C11—21no—
298C2×C11—22no—
299C2×C11—22no—
300C2×C11—24no—
301C2×C11C2×#39311yescharacteristic
302C2×C11#302612yes—
303D11—82no—
304C24—82no—
305C24—112no—
306C24—221no—
307C24—222no—
308C24—222no—
309C24—221no—
310C24—882no—
311C24C2×D4411yescharacteristic
312C24C2×D4411yescharacteristic
313C24#433914yes—
314C24D4×D1112yes—
315C24D4×D1112yes—
316C24#434112yes—
317C24Q8×D1112yes—
318C24C23×D1111yescharacteristic
319C2×Q8—228no—
320C2×Q8—884no—
321C2×D4—228no—
322C2×D4—228no—
323C2×D4—224no—
324C2×D4—224no—
325C2×D4—442no—
326C2×D4—442no—
327C2×D4—442no—
328C2×D4—441no—
329C2×D4—441no—
330C2×D4—444no—
331C2×D4—444no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—24no—
335C22×C4—44no—
336C22×C4—82no—
337C22×C4—84no—
338C22×C4—112no—
339C22×C4—118no—
340C22×C4—224no—
341C22×C4—221no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—221no—
345C22×C4—224no—
346C22×C4—222no—
347C22×C4—442no—
348C22×C4—884no—
349C22×C4—882no—
350C22×C4C2×D4414yes—
351C4⋊C4—2216no—
352C4⋊C4—228no—
353C22⋊C4—24no—
354C22⋊C4—24no—
355C22⋊C4—24no—
356C22⋊C4—24no—
357C22⋊C4—44no—
358C22⋊C4—224no—
359C22⋊C4—224no—
360C22⋊C4—224no—
361C22⋊C4—224no—
362C22⋊C4—224no—
363C22⋊C4—442no—
364C22⋊C4—884no—
365C22⋊C4—888no—
366C11#2346811yescharacteristic, complemented, Sylow
367C23—42no—
368C23—44no—
369C23—42no—
370C23—44no—
371C23—42no—
372C23—84no—
373C23—82no—
374C23—82no—
375C23—224no—
376C23—222no—
377C23—444no—
378C23—448no—
379C23—441no—
380C23—441no—
381C23—442no—
382C23—882no—
383C23—884no—
384C23—882no—
385C23#6692812yes—
386C23#6692812yes—
387C23#6693512yes—
388C23#6693511yescharacteristic
389C23#6693511yescharacteristic
390C23#6693814yes—
391C23#6693814yes—
392C23#6694914yes—
393C23#6694914yes—
394C23#6695012yes—
395C23#6695012yes—
396C23C22×D4411yescharacteristic
397C23C2×#433912yes—
398C23C2×D4×D1112yes—
399C23C2×#434111yescharacteristic
400C23C2×Q8×D1111yescharacteristic
401Q8—888no—
402D4—444no—
403D4—444no—
404D4—448no—
405C2×C4—24no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—48no—
409C2×C4—44no—
410C2×C4—82no—
411C2×C4—88no—
412C2×C4—228no—
413C2×C4—224no—
414C2×C4—222no—
415C2×C4—448no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—442no—
419C2×C4—448no—
420C2×C4—444no—
421C2×C4—442no—
422C2×C4—884no—
423C2×C4—884no—
424C22—22no—
425C22—22no—
426C22—24no—
427C22—22no—
428C22—24no—
429C22—44no—
430C22—42no—
431C22—42no—
432C22—41no—
433C22—41no—
434C22—42no—
435C22—44no—
436C22—44no—
437C22—44no—
438C22—42no—
439C22—42no—
440C22—448no—
441C22—444no—
442C22—442no—
443C22—884no—
444C22—882no—
445C22—882no—
446C22#1062228612yes—
447C22#1062228612yes—
448C22#1062228614yes—
449C22C2×#6692811yescharacteristic
450C22C2×#6693511yescharacteristic
451C22C2×#6693812yes—
452C22C2×#6694912yes—
453C22C2×#6695011yescharacteristic
454C4—44no—
455C4—84no—
456C4—442no—
457C4—448no—
458C4—882no—
459C2—22no—
460C2—21no—
461C2—22no—
462C2—21no—
463C2—22no—
464C2—22no—
465C2—24no—
466C2—882no—
467C2C2×#1062228611yescharacteristic
468C2#1307801512yes—
subgroupG/H
centerC22C2×#66935
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC2×C11×#342C2
socleC22×C11C2×#120
prime radicalC23×C22⋊D11C22
hypercenterC2×#342D11
hypocenterC11#23468
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
4. #13069784C2semidirect
5. #13069781C2semidirect
6. C2×#10622165C2semidirect
7. C2×C11×#342C2semidirect
38. C22×C22⋊D11Q8semidirect
85. C23×D11C2×Q8semidirect
115. C22×Dic11C2×Q8semidirect
139. C2×#342D11semidirect
366. C11#23468semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
#130711912
#130697842
#130697812
C2×#106221652
C2×C11×#3422
#2346811