Finite Group Databasebeta

← #14810808

Subgroups — #14810808

Order 2816.

1082 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#13073102C212yesmaximal, complemented
2#13072924C211yesmaximal, characteristic
3#13069782C214yesmaximal, complemented
4#13069602C212yesmaximal, complemented
5#13069029C214yesmaximal
6C4×#66898C211yesmaximal, characteristic
7C11×#3501C211yesmaximal, characteristic
8C11×#554—22no—
9C11×#554—24no—
10D4×Q8×C11—22no—
11C11×#544—21no—
12C11×#543—21no—
13C11×#543C2212yes—
14C11×#533—21no—
15C2×C11×C22⋊Q8—21no—
16C2×C11×C22⋊Q8C2212yes—
17C11×#518C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66988C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21#10622843—22no—
22C2×#66898C2212yes—
23#10622825—21no—
24#10622825C2211yescharacteristic
25C4×C22⋊Dic11C2212yes—
26#10622599—24no—
27#10622596—21no—
28#10622590—22no—
29#10622566—21no—
30#10622556C2212yes—
31#10622556C2218yes—
32#10622541—21no—
33#10622164C2218yes—
34#10622164C2212yes—
35C22×Q8×C11—21no—
36C22×Q8×C11D412yes—
37C22×D4×C11C2311yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2312yes—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—24no—
44C11×#125—22no—
45C11×#125—24no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—24no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—24no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11—24no—
63C4×D4×C11—24no—
64C11×#117—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D414yes—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C11×C22⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4C2314yes—
74C2×C42×C11D411yescharacteristic
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11C2314yes—
77C2×C22⋊Dic11C2312yes—
78#66988—28no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×Dic11⋊C4—22no—
85C2×C4×Dic11—22no—
86#66898—24no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95—28no—
90C11⋊#95—28no—
91C11⋊#95—21no—
92C11⋊#95—22no—
93#25948—111nomaximal, Sylow
94C24×C11C2×D411yescharacteristic
95C24×C11C2411yescharacteristic
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—44no—
101C2×Q8×C11—82no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11#4114yes—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D414yes—
116C22×C4×C11C2×D414yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D412yes—
120C22×Dic11—24no—
121C22×Dic11—24no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—24no—
125C22×Dic11—24no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—24no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—22no—
142C42×C11—24no—
143C42×C11—21no—
144C42×C11—21no—
145C22⋊Dic11—24no—
146C22⋊Dic11—24no—
147C22⋊Dic11—24no—
148C22⋊Dic11—44no—
149C4⋊Dic11—42no—
150C4⋊Dic11—41no—
151C4⋊Dic11—42no—
152C4⋊Dic11—41no—
153Dic11⋊C4—44no—
154C4×Dic11—44no—
155#3501D1111yescharacteristic
156#2503—112no—
157#2486—111no—
158#2030—114no—
159#1996—112no—
160#1890—114no—
161C4×#99—111no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11#12412yes—
169C23×C11C22×D411yescharacteristic
170C23×C11C22×D412yes—
171C23×C11C2×#4112yes—
172C23×C112−1+412yes—
173Q8×C11—44no—
174Q8×C11—82no—
175Q8×C11—82no—
176Q8×C11—82no—
177D4×C11—28no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—24no—
181C2×C4×C11—22no—
182C2×C4×C11—21no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—21no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—44no—
191C2×C4×C11—41no—
192C2×C4×C11—44no—
193C2×C4×C11—81no—
194C2×C4×C11—82no—
195C2×C4×C11—82no—
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11#12012yes—
198C2×C4×C11#12011yescharacteristic
199C2×C4×C11#12412yes—
200C2×Dic11—44no—
201C2×Dic11—42no—
202C2×Dic11—44no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—44no—
209C2×Dic11—48no—
210#554—22no—
211#554—24no—
212D4×Q8—22no—
213#544—21no—
214#543—21no—
215#543C2×D1112yes—
216#533—21no—
217C2×#123—112no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8C2×D1112yes—
220#518C2×D1112yes—
221C2×C4×D4C2×D1111yescharacteristic
222C22×C4⋊C4—111no—
223C2×#99—112no—
224#400—224no—
225#398—221no—
226#397—221no—
227#391—222no—
228#389—221no—
229#382—222no—
230#381—118no—
231#381—112no—
232#380—111no—
233#380—221no—
234C4×C22⋊C4—112no—
235#342—118no—
236#342—112no—
237C22×C11—22no—
238C22×C11—21no—
239C22×C11—22no—
240C22×C11—21no—
241C22×C11—22no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—41no—
246C22×C11—41no—
247C22×C11—81no—
248C22×C11C2×#12011yescharacteristic
249C22×C11C2×#12411yescharacteristic
250C22×C11#53611yescharacteristic
251C22×C11#54814yes—
252C4×C11—22no—
253C4×C11—21no—
254C4×C11—22no—
255C4×C11—41no—
256C4×C11—44no—
257C4×C11—44no—
258C4×C11—41no—
259C4×C11#45812yes—
260Dic11—82no—
261Dic11—84no—
262Dic11—82no—
263C22×Q8—21no—
264C22×Q8C22⋊D1112yes—
265C22×D4C22×D1111yescharacteristic
266C23×C4—112no—
267C23×C4C22⋊D1111yescharacteristic
268C23×C4C22×D1111yescharacteristic
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8—24no—
272#125—22no—
273#125—24no—
274#123—228no—
275C22⋊Q8—22no—
276C22⋊Q8—22no—
277C22⋊Q8—24no—
278C22⋊Q8—24no—
279C22⋊Q8—22no—
280C22⋊Q8—22no—
281C22⋊Q8—22no—
282C22⋊Q8—22no—
283C22⋊Q8—22no—
284C22⋊Q8—22no—
285C22⋊Q8—24no—
286C22⋊Q8—24no—
287C4×Q8—22no—
288C4×Q8—22no—
289C4×D4—22no—
290C4×D4—22no—
291C4×D4—24no—
292C4×D4—24no—
293#117—22no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—221no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4—222no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4C22⋊D1111yescharacteristic
303C2×C4⋊C4C22⋊D1112yes—
304C2×C4⋊C4C22⋊D1114yes—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—112no—
307C2×C22⋊C4—114no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4C22⋊D1111yescharacteristic
310C2×C22⋊C4C22×D1111yescharacteristic
311C2×C22⋊C4C22×D1114yes—
312C2×C42—222no—
313C2×C42C22⋊D1111yescharacteristic
314#99—224no—
315#95—222no—
316#95—221no—
317#95—222no—
318#95—228no—
319#95—222no—
320#95—228no—
321C2×C11—21no—
322C2×C11—24no—
323C2×C11—21no—
324C2×C11—42no—
325C2×C11#243611yescharacteristic
326C2×C11C2×#45811yescharacteristic
327C2×C11#302811yescharacteristic
328C24C2×C22⋊D1111yescharacteristic
329C24C23×D1111yescharacteristic
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—44no—
335C2×Q8—82no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4#434314yes—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—224no—
346C22×C4—224no—
347C22×C4—224no—
348C22×C4—224no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4C2×C22⋊D1111yescharacteristic
352C22×C4C2×C22⋊D1112yes—
353C22×C4C2×C22⋊D1111yescharacteristic
354C22×C4C2×C22⋊D1111yescharacteristic
355C22×C4C2×C22⋊D1114yes—
356C22×C4C2×C22⋊D1114yes—
357C22×C4C2×C22⋊D1111yescharacteristic
358C22×C4C2×C22⋊D1111yescharacteristic
359C22×C4C2×C22⋊D1112yes—
360C4⋊C4—22no—
361C4⋊C4—24no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—24no—
365C4⋊C4—22no—
366C4⋊C4—24no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—24no—
371C4⋊C4—442no—
372C4⋊C4—444no—
373C4⋊C4—441no—
374C4⋊C4—442no—
375C4⋊C4—441no—
376C22⋊C4—24no—
377C22⋊C4—24no—
378C22⋊C4—22no—
379C22⋊C4—24no—
380C22⋊C4—22no—
381C22⋊C4—224no—
382C22⋊C4—224no—
383C22⋊C4—224no—
384C22⋊C4—444no—
385C42—24no—
386C42—21no—
387C42—21no—
388C42—444no—
389C11#2594811yescharacteristic, complemented, Sylow
390C23—21no—
391C23—21no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23#6700012yes—
397C23C2×#434312yes—
398C23#6704012yes—
399C23C22×C22⋊D1111yescharacteristic
400C23C22×C22⋊D1112yes—
401Q8—44no—
402Q8—82no—
403Q8—82no—
404Q8—82no—
405D4—28no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—21no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—44no—
419C2×C4—41no—
420C2×C4—44no—
421C2×C4—81no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—444no—
425C2×C4—442no—
426C2×C4—444no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—444no—
432C2×C4—448no—
433C2×C4—442no—
434C2×C4#6700012yes—
435C2×C4#6700611yescharacteristic
436C2×C4#6700612yes—
437C2×C4#6700611yescharacteristic
438C22—22no—
439C22—21no—
440C22—22no—
441C22—21no—
442C22—22no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—41no—
447C22—41no—
448C22—81no—
449C22C2×#6700011yescharacteristic
450C22#1062334711yescharacteristic
451C22#1062334814yes—
452C22C2×#6700611yescharacteristic
453C4—22no—
454C4—21no—
455C4—22no—
456C4—44no—
457C4—41no—
458C4—41no—
459C4—44no—
460C4—882no—
461C4—884no—
462C4—882no—
463C4#1062285612yes—
464C2—21no—
465C2—24no—
466C2—21no—
467C2—42no—
468C2#1307227011yescharacteristic
469C2C2×#1062285611yescharacteristic
470C2#1307802211yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radicalC22×D4×C11C23
hypercenter#3501D11
hypocenterC11#25948
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13073102C2semidirect
3. #13069782C2semidirect
4. #13069602C2semidirect
389. C11#25948semidirect

Maximal subgroups

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

subgroupindex
#130731022
#130729242
#130697822
#130696022
#130690292
C4×#668982
C11×#35012
#2594811