Finite Group Databasebeta

← #14783685

Subgroups — #14783685

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071097C211yesmaximal, characteristic
2#13071021C211yesmaximal, characteristic
3#13070187C212yesmaximal, complemented
4#13070186C212yesmaximal, complemented
5#13070180C211yesmaximal, characteristic, complemented
6#13070179C211yesmaximal, characteristic, complemented
7#13070173C211yesmaximal, characteristic, complemented
8#13068331C212yesmaximal
9#13068331C212yesmaximal
10D11×#336C211yesmaximal, characteristic
11C11×#2099C211yesmaximal, characteristic, complemented
12C22×C8×D11C2212yes—
13C2×#66945C2212yes—
14C2×#66945C2211yescharacteristic
15C2×#66945C2211yescharacteristic
16C2×C42×D11C2211yescharacteristic
17C11×#389C2211yescharacteristic
18C11×#384C2211yescharacteristic
19#10622602—21no—
20#10622600—21no—
21#10622600—21no—
22#10622598C2211yescharacteristic
23#10622590C2212yes—
24C4⋊C4×Dic11—21no—
25C4⋊C4×Dic11—21no—
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×D11D411yescharacteristic
44C22×C4×D11D411yescharacteristic
45C22×C4×D11C2311yescharacteristic
46C22×C8×C11C2312yes—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C22×C11⋊C8C2312yes—
72C2×C8×D11—24no—
73C2×C8×D11—24no—
74C2×C8×D11—24no—
75#66945—22no—
76#66945—24no—
77#66945—28no—
78#66945Q814yes—
79C42×D11—24no—
80C11×#95—21no—
81C11⋊#95—21no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#23744—111nomaximal, Sylow
87C23×D11C2×D411yescharacteristic
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2411yescharacteristic
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—22no—
97C22×Dic11C2×D411yescharacteristic
98C22×Dic11C2×D411yescharacteristic
99C22×Dic11C2×D411yescharacteristic
100C2×C4×D11—22no—
101C2×C4×D11—22no—
102C2×C4×D11—22no—
103C2×C4×D11—22no—
104C2×C4×D11—41no—
105C2×C4×D11—41no—
106C2×C4×D11C2×Q812yes—
107C2×C4×D11#4112yes—
108C2×C4×D11#4114yes—
109C2×C4×D11#4114yes—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4—42no—
119C11×C4⋊C4C2×Q812yes—
120C42×C11—22no—
121(C2×D11)⋊C4—24no—
122(C2×D11)⋊C4—42no—
123(C2×D11)⋊C4—44no—
124C4⋊Dic11—21no—
125C4⋊Dic11—22no—
126C4⋊Dic11—24no—
127C4⋊Dic11—42no—
128C4⋊Dic11—42no—
129C4⋊Dic11—42no—
130C4⋊Dic11C2×Q812yes—
131Dic11⋊C4—42no—
132Dic11⋊C4—42no—
133C4×Dic11—24no—
134C4×Dic11—22no—
135C4×Dic11—22no—
136C4×Dic11—22no—
137C4×Dic11—42no—
138C4×Dic11—44no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C8×D11—48no—
143#2296—111no—
144#2285—111no—
145#2101—112no—
146#2101—112no—
147#2100—111no—
148#2100—111no—
149#2099—111no—
150#2099D1111yescharacteristic, complemented
151#1735—112no—
152#1735—112no—
153C2×#336—111no—
154C23×C11C22×D411yescharacteristic
155C22×D11—21no—
156C22×D11—21no—
157C22×D11—21no—
158C22×D11—21no—
159C22×D11C22⋊Q812yes—
160C22×D11#12312yes—
161C22×D11#12412yes—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11#13512yes—
176C2×C4×C11#13512yes—
177C2×C4×C11C22×Q811yescharacteristic
178C2×C4×C11C2×#4112yes—
179C2×C4×C11C2×#4112yes—
180C2×C4×C11C2×#4111yescharacteristic
181C2×Dic11—22no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—42no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11C22⋊Q812yes—
197C2×Dic11#12312yes—
198C2×Dic11#12412yes—
199C4×D11—44no—
200C4×D11—44no—
201C4×D11#12518yes—
202C4×D11#12618yes—
203C8×C11—42no—
204C11⋊C8—42no—
205C23×C8—112no—
206C2×#117—111no—
207C2×#117—112no—
208C2×#117—111no—
209C22×C42—111no—
210#389—111no—
211#389—111no—
212#389—111no—
213#389C2×D1111yescharacteristic
214#385—221no—
215#385—221no—
216#384—111no—
217#384C2×D1111yescharacteristic
218#382—112no—
219#380—221no—
220#380—221no—
221C4×C4⋊C4—221no—
222C4×C4⋊C4—221no—
223C4×C4⋊C4—221no—
224C4×C4⋊C4—221no—
225#340—112no—
226#340—112no—
227#340—112no—
228#340—112no—
229#340—112no—
230#340—112no—
231#340C2×D1112yes—
232#340C2×D1112yes—
233#336—112no—
234#336—111no—
235#336C2×D1111yescharacteristic
236C22×C11C2×C22⋊Q811yescharacteristic
237C22×C11C2×#12311yescharacteristic
238C22×C11C2×#12411yescharacteristic
239C22×C11C2×#13511yescharacteristic
240C22×C11C2×#13511yescharacteristic
241C22×C11#57511yescharacteristic
242C22×C11#57511yescharacteristic
243C2×D11—22no—
244C2×D11—22no—
245C2×D11—22no—
246C2×D11—22no—
247C2×D11—22no—
248C2×D11—22no—
249C2×D11#40014yes—
250C4×C11—22no—
251C4×C11—22no—
252C4×C11—42no—
253C4×C11—81no—
254C4×C11—82no—
255C4×C11C2×#12512yes—
256C4×C11C2×#12612yes—
257Dic11—42no—
258Dic11—41no—
259Dic11—41no—
260Dic11—81no—
261Dic11—82no—
262Dic11#40014yes—
263C23×C4—111no—
264C23×C4—111no—
265C23×C4—111no—
266C22×C8—112no—
267C22×C8—224no—
268C22×C8—224no—
269C22×C8—224no—
270C22×C8C22×D1112yes—
271#117—114no—
272#117—222no—
273#117—224no—
274#117—228no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—111no—
279C2×C4⋊C4—112no—
280C2×C4⋊C4—111no—
281C2×C4⋊C4—221no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4—221no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4C22×D1112yes—
287C2×C4⋊C4C22×D1111yescharacteristic
288C2×C4⋊C4C22×D1111yescharacteristic
289C2×C22⋊C4—221no—
290C2×C22⋊C4—222no—
291C2×C22⋊C4—221no—
292C2×C42—111no—
293C2×C42—111no—
294C2×C42—111no—
295C2×C42—224no—
296C2×C42—221no—
297C2×C42—221no—
298C2×C42—222no—
299C2×C42C22×D1111yescharacteristic
300#95—21no—
301#95—222no—
302#95—222no—
303#95—221no—
304#95—221no—
305#95—221no—
306C2×C11C2×#40011yescharacteristic
307C2×C11#307611yescharacteristic
308C2×C11#307611yescharacteristic
309C2×C11#309111yescharacteristic
310C2×C11#309111yescharacteristic
311C2×C11#313111yescharacteristic
312C2×C11#313511yescharacteristic
313D11—24no—
314C24—111no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—111no—
319C22×C4—112no—
320C22×C4—114no—
321C22×C4—114no—
322C22×C4—112no—
323C22×C4—111no—
324C22×C4—111no—
325C22×C4—222no—
326C22×C4—222no—
327C22×C4—221no—
328C22×C4—222no—
329C22×C4—222no—
330C22×C4—221no—
331C22×C4—222no—
332C22×C4—441no—
333C22×C4—441no—
334C22×C4D4×D1111yescharacteristic
335C22×C4D4×D1111yescharacteristic
336C22×C4C23×D1111yescharacteristic
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—222no—
341C2×C8—222no—
342C2×C8—222no—
343C2×C8—448no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—24no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—112no—
351C4⋊C4—221no—
352C4⋊C4—222no—
353C4⋊C4—224no—
354C4⋊C4—442no—
355C4⋊C4—442no—
356C4⋊C4—442no—
357C4⋊C4—442no—
358C4⋊C4—442no—
359C4⋊C4Q8×D1112yes—
360C22⋊C4—224no—
361C22⋊C4—442no—
362C22⋊C4—444no—
363C42—22no—
364C42—222no—
365C42—222no—
366C42—224no—
367C42—222no—
368C42—442no—
369C42—444no—
370C11#2374411yescharacteristic, complemented, Sylow
371C23—112no—
372C23—112no—
373C23—112no—
374C23—221no—
375C23—221no—
376C23—221no—
377C23—221no—
378C23C2×D4×D1111yescharacteristic
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—112no—
393C2×C4—112no—
394C2×C4—112no—
395C2×C4—118no—
396C2×C4—118no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—221no—
401C2×C4—222no—
402C2×C4—221no—
403C2×C4—221no—
404C2×C4—444no—
405C2×C4—444no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—441no—
413C2×C4—442no—
414C2×C4#6696512yes—
415C2×C4#6696912yes—
416C2×C4C2×Q8×D1111yescharacteristic
417C2×C4#41×D1111yescharacteristic
418C2×C4#41×D1112yes—
419C2×C4#41×D1112yes—
420C8—42no—
421C8—442no—
422C22—114no—
423C22—222no—
424C22—222no—
425C22—222no—
426C22—222no—
427C22—222no—
428C22—222no—
429C22D11×C22⋊Q811yescharacteristic
430C22D11×#12311yescharacteristic
431C22D11×#12411yescharacteristic
432C22C2×#6696511yescharacteristic
433C22C2×#6696911yescharacteristic
434C22#1062330811yescharacteristic
435C22#1062330811yescharacteristic
436C4—22no—
437C4—22no—
438C4—42no—
439C4—82no—
440C4—81no—
441C4—114no—
442C4—441no—
443C4—442no—
444C4—441no—
445C4—881no—
446C4—882no—
447C4D11×#12512yes—
448C4D11×#12612yes—
449C2—224no—
450C2D11×#40011yescharacteristic
451C2#1307839711yescharacteristic
452C2#1307839911yescharacteristic
453C2#1307852411yescharacteristic
454C2#1307853011yescharacteristic
455C2#1307893511yescharacteristic
456C2#1307896311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2099C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2099D11
hypocenterC11#23744
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. #13070187C2semidirect
4. #13070186C2semidirect
5. #13070180C2semidirect
6. #13070179C2semidirect
7. #13070173C2semidirect
11. C11×#2099C2semidirect
150. #2099D11semidirect
370. C11#23744semidirect

Maximal subgroups

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

subgroupindex
#130710972
#130710212
#130701872
#130701862
#130701802
#130701792
#130701732
#130683312
D11×#3362
C11×#20992
#2374411