Finite Group Databasebeta

← #14783693

Subgroups — #14783693

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071097C211yesmaximal, characteristic
2D11×#384C211yesmaximal, characteristic
3#13070182C212yesmaximal, complemented
4#13070181C212yesmaximal, complemented
5#13070175C211yesmaximal, characteristic, complemented
6#13070174C211yesmaximal, characteristic, complemented
7#13070173C211yesmaximal, characteristic, complemented
8#13068334C212yesmaximal
9#13068334C212yesmaximal
10#13068308C211yesmaximal, characteristic
11C11×#2099C211yesmaximal, characteristic, complemented
12C22×#4313C2212yes—
13C2×#66945C2211yescharacteristic
14C2×#66945C2211yescharacteristic
15C2×C4⋊C4×D11—21no—
16C2×C4⋊C4×D11—21no—
17C2×C4⋊C4×D11C2212yes—
18C2×C42×D11C2211yescharacteristic
19C11×#389C2211yescharacteristic
20C11×#384C2211yescharacteristic
21#10622602—21no—
22#10622598C2211yescharacteristic
23#10622589—21no—
24#10622589—21no—
25#10622589C2212yes—
26C4⋊C4×Dic11—21no—
27#10622586C2211yescharacteristic
28#10622548C2211yescharacteristic
29#10622541C2211yescharacteristic
30#10622281—21no—
31#10622262—21no—
32C11×#340C2212yes—
33C11×#340C2212yes—
34C11×#336C2211yescharacteristic
35#10622189C2212yes—
36#10622189C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2211yescharacteristic
43C22×C4×D11—22no—
44C22×C4×D11D411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11C2311yescharacteristic
47C22×C8×C11C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×C4×Dic11—21no—
69C2×C4×Dic11—21no—
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11D411yescharacteristic
72C2×C4×Dic11C2311yescharacteristic
73C22×C11⋊C8C2312yes—
74C2×#4313—24no—
75C2×#4313—24no—
76C2×#4313—24no—
77#66945—22no—
78#66945—24no—
79#66945Q814yes—
80C4⋊C4×D11—28no—
81C4⋊C4×D11—44no—
82C4⋊C4×D11—44no—
83C42×D11—24no—
84C11×#95—21no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—21no—
88#23745—111nomaximal, Sylow
89C23×D11C2×D411yescharacteristic
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2411yescharacteristic
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—22no—
99C22×Dic11C2×D411yescharacteristic
100C22×Dic11C2×D411yescharacteristic
101C22×Dic11C2×D411yescharacteristic
102C2×C4×D11—22no—
103C2×C4×D11—22no—
104C2×C4×D11—22no—
105C2×C4×D11—22no—
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—44no—
109C2×C4×D11—44no—
110C2×C4×D11—44no—
111C2×C4×D11C2×Q812yes—
112C2×C4×D11#4112yes—
113C2×C4×D11#4114yes—
114C2×C4×D11#4114yes—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—42no—
122C11×C4⋊C4—42no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4C2×Q812yes—
125C42×C11—22no—
126(C2×D11)⋊C4—24no—
127(C2×D11)⋊C4—42no—
128C4⋊Dic11—21no—
129C4⋊Dic11—24no—
130C4⋊Dic11—22no—
131C4⋊Dic11—42no—
132C4⋊Dic11—42no—
133C4⋊Dic11—42no—
134C4⋊Dic11C2×Q812yes—
135Dic11⋊C4—44no—
136Dic11⋊C4—44no—
137Dic11⋊C4—44no—
138Dic11⋊C4—42no—
139Dic11⋊C4—42no—
140C4×Dic11—24no—
141C4×Dic11—22no—
142C4×Dic11—22no—
143C4×Dic11—22no—
144C4×Dic11—42no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148#4313—48no—
149#2296—111no—
150C2×#384—111no—
151#2100—112no—
152#2100—112no—
153#2099—111no—
154#2099—111no—
155#2099—111no—
156#2099D1111yescharacteristic, complemented
157#1736—112no—
158#1736—112no—
159#1728—111no—
160C23×C11C22×D411yescharacteristic
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11C22⋊Q812yes—
166C22×D11#12312yes—
167C22×D11#12412yes—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11AGL(1,ℤ/8)12yes—
182C2×C4×C11AGL(1,ℤ/8)12yes—
183C2×C4×C11C22×Q811yescharacteristic
184C2×C4×C11C2×#4112yes—
185C2×C4×C11C2×#4112yes—
186C2×C4×C11C2×#4111yescharacteristic
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—22no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11C22⋊Q812yes—
201C2×Dic11#12312yes—
202C2×Dic11#12412yes—
203C2×Dic11#13712yes—
204C2×Dic11#13712yes—
205C4×D11—28no—
206C4×D11—28no—
207C4×D11—88no—
208C4×D11#12518yes—
209C4×D11#12618yes—
210C8×C11—42no—
211C11⋊C8—42no—
212C22×M16—112no—
213C2×#117—111no—
214C2×#117—111no—
215C22×C4⋊C4—112no—
216C22×C4⋊C4—221no—
217C22×C4⋊C4—221no—
218C22×C42—111no—
219#389—111no—
220#389—111no—
221#389—111no—
222#389C2×D1111yescharacteristic
223#385—221no—
224#385—221no—
225#384—112no—
226#384—111no—
227#384—221no—
228#384—221no—
229#384C2×D1111yescharacteristic
230C4×C4⋊C4—221no—
231C4×C4⋊C4—221no—
232#340—112no—
233#340—112no—
234#340—112no—
235#340—112no—
236#340—112no—
237#340—112no—
238#340C2×D1112yes—
239#340C2×D1112yes—
240#336—112no—
241#336—111no—
242#336C2×D1111yescharacteristic
243C22×C11C2×C22⋊Q811yescharacteristic
244C22×C11C2×#12311yescharacteristic
245C22×C11C2×#12411yescharacteristic
246C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
247C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
248C22×C11C2×#13711yescharacteristic
249C22×C11C2×#13711yescharacteristic
250C2×D11—22no—
251C2×D11—22no—
252C2×D11—22no—
253C2×D11—22no—
254C2×D11—22no—
255C2×D11—22no—
256C2×D11#40014yes—
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—42no—
260C4×C11—81no—
261C4×C11—82no—
262C4×C11C2×#12512yes—
263C4×C11C2×#12612yes—
264Dic11—22no—
265Dic11—22no—
266Dic11—42no—
267Dic11—81no—
268Dic11—82no—
269Dic11#40014yes—
270C23×C4—111no—
271C23×C4—111no—
272C23×C4—111no—
273C23×C4—222no—
274C2×M16—224no—
275C2×M16—224no—
276C2×M16—224no—
277C22×C8—112no—
278C22×C8C22×D1112yes—
279#117—114no—
280#117—222no—
281#117—224no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—228no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4—444no—
298C2×C4⋊C4—444no—
299C2×C4⋊C4C22×D1112yes—
300C2×C4⋊C4C22×D1111yescharacteristic
301C2×C4⋊C4C22×D1111yescharacteristic
302C2×C22⋊C4—221no—
303C2×C22⋊C4—221no—
304C2×C42—111no—
305C2×C42—111no—
306C2×C42—111no—
307C2×C42—224no—
308C2×C42—221no—
309C2×C42—221no—
310C2×C42C22×D1111yescharacteristic
311#95—21no—
312#95—221no—
313#95—221no—
314#95—221no—
315C2×C11C2×#40011yescharacteristic
316C2×C11#307911yescharacteristic
317C2×C11#307911yescharacteristic
318C2×C11#309211yescharacteristic
319C2×C11#309211yescharacteristic
320C2×C11#313811yescharacteristic
321C2×C11#313911yescharacteristic
322D11—24no—
323C24—111no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—111no—
328C22×C4—112no—
329C22×C4—114no—
330C22×C4—114no—
331C22×C4—112no—
332C22×C4—111no—
333C22×C4—111no—
334C22×C4—222no—
335C22×C4—222no—
336C22×C4—222no—
337C22×C4—222no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—221no—
341C22×C4—221no—
342C22×C4—222no—
343C22×C4—444no—
344C22×C4—444no—
345C22×C4—444no—
346C22×C4D4×D1111yescharacteristic
347C22×C4D4×D1111yescharacteristic
348C22×C4C23×D1111yescharacteristic
349M16—448no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—222no—
354C2×C8—222no—
355C2×C8—222no—
356C4⋊C4—21no—
357C4⋊C4—24no—
358C4⋊C4—22no—
359C4⋊C4—42no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—112no—
363C4⋊C4—221no—
364C4⋊C4—224no—
365C4⋊C4—222no—
366C4⋊C4—444no—
367C4⋊C4—442no—
368C4⋊C4—442no—
369C4⋊C4—444no—
370C4⋊C4—444no—
371C4⋊C4—442no—
372C4⋊C4—442no—
373C4⋊C4—442no—
374C4⋊C4Q8×D1112yes—
375C22⋊C4—224no—
376C22⋊C4—442no—
377C42—22no—
378C42—222no—
379C42—222no—
380C42—224no—
381C42—222no—
382C42—442no—
383C11#2374511yescharacteristic, complemented, Sylow
384C23—112no—
385C23—112no—
386C23—112no—
387C23—221no—
388C23—221no—
389C23—221no—
390C23—221no—
391C23C2×D4×D1111yescharacteristic
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—112no—
406C2×C4—112no—
407C2×C4—112no—
408C2×C4—118no—
409C2×C4—118no—
410C2×C4—112no—
411C2×C4—112no—
412C2×C4—228no—
413C2×C4—228no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—222no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—442no—
427C2×C4—888no—
428C2×C4#6696412yes—
429C2×C4#6696712yes—
430C2×C4C2×Q8×D1111yescharacteristic
431C2×C4#41×D1111yescharacteristic
432C2×C4#41×D1112yes—
433C2×C4#41×D1112yes—
434C8—42no—
435C8—442no—
436C22—114no—
437C22—222no—
438C22—222no—
439C22—222no—
440C22—222no—
441C22—222no—
442C22—222no—
443C22D11×C22⋊Q811yescharacteristic
444C22D11×#12311yescharacteristic
445C22D11×#12411yescharacteristic
446C22C2×#6696411yescharacteristic
447C22C2×#6696711yescharacteristic
448C22D11×#13711yescharacteristic
449C22D11×#13711yescharacteristic
450C4—22no—
451C4—22no—
452C4—42no—
453C4—81no—
454C4—82no—
455C4—114no—
456C4—222no—
457C4—222no—
458C4—442no—
459C4—881no—
460C4—882no—
461C4D11×#12512yes—
462C4D11×#12612yes—
463C2—224no—
464C2D11×#40011yescharacteristic
465C2#1307842411yescharacteristic
466C2#1307842611yescharacteristic
467C2#1307853511yescharacteristic
468C2#1307854011yescharacteristic
469C2#1307898711yescharacteristic
470C2#1307899511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2099C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2099D11
hypocenterC11#23745
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
3. #13070182C2semidirect
4. #13070181C2semidirect
5. #13070175C2semidirect
6. #13070174C2semidirect
7. #13070173C2semidirect
11. C11×#2099C2semidirect
156. #2099D11semidirect
383. C11#23745semidirect

Maximal subgroups

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

subgroupindex
#130710972
D11×#3842
#130701822
#130701812
#130701752
#130701742
#130701732
#130683342
#130683082
C11×#20992
#2374511