Finite Group Databasebeta

← #14726770

Subgroups — #14726770

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082419C211yesmaximal, characteristic
2C2×#10622583C212yesmaximal, complemented
3#13067657C214yesmaximal, complemented
4#13067640C214yesmaximal, complemented
5#13067187C212yesmaximal, complemented
6#13066934C211yesmaximal, characteristic
7C11×#2487C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10#10623329—21no—
11C2×#66977—21no—
12C2×#66977C2212yes—
13#10623074—22no—
14#10623070—24no—
15D4×Dic22—22no—
16#10623031C2212yes—
17#10623014—21no—
18#10623014C2212yes—
19#10623001—21no—
20C11×#400C2212yes—
21C11×#399C2212yes—
22C11×#389—21no—
23C11×#386—21no—
24C11×#385—21no—
25C11×#380—21no—
26C11×#380C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2212yes—
28#10622583—24no—
29#10622583C2218yes—
30C2×#66874—22no—
31C2×#66871—22no—
32#10622166C2212yes—
33#10622163C2212yes—
34#10622090C2218yes—
35C22×D4×C11D411yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×Dic22—21no—
40C22×Dic22D412yes—
41C4×D4×C11—22no—
42C4×D4×C11—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4D411yescharacteristic
53C2×C11×C22⋊C4C2311yescharacteristic
54C2×C42×C11D411yescharacteristic
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—22no—
57D4×Dic11—24no—
58D4×Dic11—24no—
59#66979—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11D412yes—
62#66977—22no—
63#66977—22no—
64#66977—22no—
65#66977—22no—
66#66977—22no—
67#66977—22no—
68#66977D414yes—
69#66977C2314yes—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C22×C11⋊C8—22no—
73#66943—24no—
74#66941—24no—
75#66931—24no—
76#66931—24no—
77#66931—24no—
78#66931—24no—
79#66923—22no—
80#66922—21no—
81#66922—21no—
82C4×Dic22—22no—
83C4×Dic22—22no—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95C2312yes—
87C22⋊(C11⋊C8)—22no—
88C22⋊(C11⋊C8)C2314yes—
89#66874—28no—
90#66871—28no—
91#18205—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C24×C11C2×D411yescharacteristic
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11Q1614yes—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—82no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C2×Dic22—22no—
117C2×Dic22—22no—
118C2×Dic22—22no—
119C2×Dic22—44no—
120C2×Dic22—82no—
121C2×Dic22C2×D414yes—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—82no—
128C11×C22⋊C4—22no—
129C11×C22⋊C4—22no—
130C11×C22⋊C4—42no—
131C11×C22⋊C4—82no—
132C42×C11—21no—
133C42×C11—21no—
134C22⋊Dic11—24no—
135C22⋊Dic11—24no—
136C22⋊Dic11—24no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11C2×D414yes—
143Dic11⋊C4—24no—
144Dic11⋊C4—24no—
145Dic11⋊C4—24no—
146Dic11⋊C4—24no—
147C4×Dic11—24no—
148C2×C11⋊C8—24no—
149C2×C11⋊C8—44no—
150#3501—111no—
151C2×#484—112no—
152#2487D1111yescharacteristic
153#1617—114no—
154#1614—114no—
155#1520—112no—
156#1459—111no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11#12012yes—
164C23×C11C2×Q1612yes—
165C23×C11C2×Q1612yes—
166C23×C11#13712yes—
167C23×C11C22×D411yescharacteristic
168D4×C11—28no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—24no—
172C2×C4×C11—22no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—81no—
187C2×C4×C11—84no—
188C2×C4×C11#12011yescharacteristic
189C2×C4×C11#12011yescharacteristic
190C2×C4×C11C2×Q1612yes—
191C2×C4×C11C22×D412yes—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—82no—
195C2×Dic11—82no—
196C2×Dic11—82no—
197C2×Dic11—82no—
198Dic22—44no—
199Dic22—44no—
200Dic22—82no—
201Dic22—82no—
202C11⋊C8—44no—
203#554—222no—
204#554—224no—
205D4×Q8—222no—
206#544—112no—
207#543—112no—
208#543—221no—
209#533—221no—
210C2×C22⋊Q8—112no—
211C2×C22⋊Q8—221no—
212#518—221no—
213C2×C4×D4C2×D1111yescharacteristic
214C22×C4⋊C4C2×D1111yescharacteristic
215#484—118no—
216#484—224no—
217C2×#107—222no—
218C2×#103—222no—
219C2×C22⋊C8—112no—
220#400C2×D1112yes—
221#399C2×D1112yes—
222#389—21no—
223#386—21no—
224#385—21no—
225#380—21no—
226#380C2×D1111yescharacteristic
227#328—118no—
228#324—112no—
229#323—112no—
230C22×C11—21no—
231C22×C11—22no—
232C22×C11—21no—
233C22×C11—22no—
234C22×C11—22no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—81no—
241C22×C11#45114yes—
242C22×C11C2×#12011yescharacteristic
243C22×C11C22×Q1611yescharacteristic
244C22×C11C2×#13711yescharacteristic
245C4×C11—22no—
246C4×C11—21no—
247C4×C11—22no—
248C4×C11—41no—
249C4×C11—41no—
250C4×C11—82no—
251C4×C11—82no—
252C4×C11#45812yes—
253Dic11—44no—
254Dic11—44no—
255C22×Q8—112no—
256C22×Q8—221no—
257C22×D4C22⋊D1111yescharacteristic
258C23×C4—21no—
259C23×C4C22⋊D1111yescharacteristic
260C23×C4C22×D1111yescharacteristic
261C22×C8—222no—
262C4⋊Q8—221no—
263C4⋊Q8—221no—
264C4⋊Q8—224no—
265#125—222no—
266#125—224no—
267C22⋊Q8—114no—
268C22⋊Q8—114no—
269C22⋊Q8—224no—
270C22⋊Q8—224no—
271C22⋊Q8—224no—
272C22⋊Q8—224no—
273C22⋊Q8—222no—
274C22⋊Q8—222no—
275C22⋊Q8—222no—
276C22⋊Q8—222no—
277C22⋊Q8—222no—
278C22⋊Q8—222no—
279C4×Q8—222no—
280C4×Q8—222no—
281C4×D4—22no—
282C4×D4—22no—
283C4×D4—224no—
284C4×D4—224no—
285#117—222no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—112no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4C22×D1112yes—
296C2×C4⋊C4C22×D1111yescharacteristic
297C2×C22⋊C4—21no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—222no—
301C2×C22⋊C4C22⋊D1111yescharacteristic
302C2×C22⋊C4C22×D1111yescharacteristic
303C2×C42C22⋊D1111yescharacteristic
304#107—228no—
305#103—228no—
306C22⋊C8—114no—
307C22⋊C8—222no—
308#95—22no—
309#95—22no—
310#95C22×D1112yes—
311C2×C11—21no—
312C2×C11—21no—
313C2×C11—24no—
314C2×C11—42no—
315C2×C11C2×#45111yescharacteristic
316C2×C11#302111yescharacteristic
317C2×C11C2×#45811yescharacteristic
318C24C2×C22⋊D1111yescharacteristic
319C24C2×C22⋊D1111yescharacteristic
320C2×Q8—114no—
321C2×Q8—222no—
322C2×Q8—222no—
323C2×Q8—222no—
324C2×Q8—444no—
325C2×Q8—882no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4#432614yes—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—82no—
337C22×C4—222no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—222no—
341C22×C4D4×D1112yes—
342C22×C4D4×D1112yes—
343C22×C4C2×C22⋊D1111yescharacteristic
344C22×C4C2×C22⋊D1111yescharacteristic
345C22×C4C2×C22⋊D1111yescharacteristic
346C22×C4C2×C22⋊D1111yescharacteristic
347C22×C4C23×D1111yescharacteristic
348C2×C8—224no—
349C2×C8—444no—
350C4⋊C4—22no—
351C4⋊C4—24no—
352C4⋊C4—42no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—82no—
356C4⋊C4—114no—
357C4⋊C4—222no—
358C4⋊C4—224no—
359C4⋊C4—222no—
360C4⋊C4—222no—
361C4⋊C4—224no—
362C4⋊C4—222no—
363C4⋊C4—222no—
364C4⋊C4—224no—
365C4⋊C4—224no—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C22⋊C4—42no—
369C22⋊C4—82no—
370C22⋊C4—224no—
371C22⋊C4—224no—
372C22⋊C4—224no—
373C42—21no—
374C42—21no—
375C42—224no—
376C11#1820511yescharacteristic, complemented, Sylow
377C23—21no—
378C23—21no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23#6699012yes—
384C23C2×#432612yes—
385C23C2×#432612yes—
386C23#6700412yes—
387C23C22×C22⋊D1111yescharacteristic
388Q8—444no—
389Q8—444no—
390Q8—882no—
391Q8—882no—
392D4—28no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—81no—
411C2×C4—84no—
412C2×C4—224no—
413C2×C4—224no—
414C2×C4—882no—
415C2×C4—882no—
416C2×C4—882no—
417C2×C4—882no—
418C2×C4#6699011yescharacteristic
419C2×C4#6699011yescharacteristic
420C2×C4C2×#432612yes—
421C2×C4C2×D4×D1112yes—
422C8—444no—
423C22—21no—
424C22—22no—
425C22—21no—
426C22—22no—
427C22—22no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—41no—
432C22—41no—
433C22—81no—
434C22#1062266314yes—
435C22C2×#6699011yescharacteristic
436C22C22×#432611yescharacteristic
437C22C2×#6700411yescharacteristic
438C4—22no—
439C4—22no—
440C4—21no—
441C4—41no—
442C4—41no—
443C4—82no—
444C4—82no—
445C4—444no—
446C4—444no—
447C4#1062266612yes—
448C2—21no—
449C2—21no—
450C2—24no—
451C2—42no—
452C2C2×#1062266311yescharacteristic
453C2#1307798711yescharacteristic
454C2C2×#1062266611yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2487C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenter#2487D11
hypocenterC11#18205
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2487

Complements

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

NH ≅ G/Ntype
2. C2×#10622583C2semidirect
3. #13067657C2semidirect
4. #13067640C2semidirect
5. #13067187C2semidirect
376. C11#18205semidirect

Maximal subgroups

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

subgroupindex
#130824192
C2×#106225832
#130676572
#130676402
#130671872
#130669342
C11×#24872
#1820511