Finite Group Databasebeta

← #14808163

Subgroups — #14808163

Order 2816.

960 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623228C211yesmaximal, characteristic
2C2×#10622682C211yesmaximal, characteristic, complemented
3#13074447C211yesmaximal, characteristic
4#13069821C212yesmaximal
5#13069814C212yesmaximal
6#13069586C211yesmaximal, characteristic, complemented
7#13069418C211yesmaximal, characteristic, complemented
8#13068881C212yesmaximal, complemented
9#13068867C212yesmaximal, complemented
10#13068383C211yesmaximal, characteristic
11C2×C11×#499C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13C2×C11×#125C2211yescharacteristic
14#10623228—24no—
15#10623228—24no—
16C2×#66951—22no—
17C2×#66950C2212yes—
18C2×#66943—22no—
19C2×#66940C2212yes—
20C2×#66925C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C11×#499—24no—
23C2×C11×#107C2212yes—
24C2×C11×#106C2212yes—
25C2×C4×C8×C11C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×#66880C2212yes—
29C2×#66880C2212yes—
30#10622682—24no—
31#10622607—22no—
32#10622600C2212yes—
33#10622597—22no—
34#10622586C2212yes—
35C2×#66874C2212yes—
36C2×#66874C2212yes—
37#10622548C2211yescharacteristic
38C2×#66867C2211yescharacteristic
39#10622188C2211yescharacteristic
40#10622188C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2212yes—
43C22×C4×D11C2311yescharacteristic
44C22×Dic22C2312yes—
45C22×C8×C11C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C11×#125—22no—
48C11×#125—22no—
49C11×#125—22no—
50C11×#125D414yes—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C42×C11C2311yescharacteristic
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4D412yes—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11C2312yes—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4D412yes—
66C2×C4×Dic11—22no—
67C2×C4×Dic11C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69C22×C11⋊C8C2311yescharacteristic
70#66951—216no—
71#66950—24no—
72#66950—24no—
73#66943—216no—
74#66940—24no—
75#66940—24no—
76#66925—22no—
77#66925—22no—
78#66922—22no—
79#66922D414yes—
80C11×#107—24no—
81C11×#106—24no—
82C4×C8×C11—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85(C2×D11)⋊C8—22no—
86(C2×D11)⋊C8—22no—
87#66880—24no—
88#66880—24no—
89#66874—24no—
90#66874—24no—
91#66867—22no—
92#25683—111nomaximal, Sylow
93C23×D11C2×D411yescharacteristic
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—22no—
99C22×Dic11—22no—
100C22×Dic11C2×D411yescharacteristic
101C22×Dic11C2×D412yes—
102C2×C4×D11—21no—
103C2×C4×D11—21no—
104C2×C4×D11—21no—
105C2×C4×D11—21no—
106C2×C4×D11—21no—
107C2×C4×D11—21no—
108C2×Dic22—22no—
109C2×Dic22—22no—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C2×Dic22C2×D414yes—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11#4112yes—
119C2×C8×C11#4112yes—
120C11×C4⋊C4—28no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—44no—
125C11×C4⋊C4C2×D414yes—
126C42×C11C2×D412yes—
127C42×C11C2×D412yes—
128(C2×D11)⋊C4—28no—
129(C2×D11)⋊C4—24no—
130(C2×D11)⋊C4—82no—
131C4⋊Dic11—28no—
132C4⋊Dic11—28no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11—82no—
136Dic11⋊C4—28no—
137Dic11⋊C4—24no—
138Dic11⋊C4—82no—
139C4×Dic11—28no—
140C4×Dic11—21no—
141C4×Dic11—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×#541—111no—
149C2×#499D1111yescharacteristic, complemented
150C2×#491—111no—
151#2629—111no—
152#2036—112no—
153#2035—112no—
154#1992—111no—
155#1956—111no—
156#1865—112no—
157#1863—112no—
158#1750—111no—
159C23×C11C22×D411yescharacteristic
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—22no—
164C22×D11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11#12014yes—
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C2×#4111yescharacteristic
177C2×C4×C11C2×#4111yescharacteristic
178C2×C4×C112−1+411yescharacteristic
179C2×C4×C112−1+411yescharacteristic
180C2×Dic11—22no—
181C2×Dic11—24no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C4×D11—41no—
193C4×D11—41no—
194C4×D11—41no—
195C4×D11—41no—
196Dic22—24no—
197Dic22—24no—
198Dic22—42no—
199Dic22—42no—
200C8×C11—22no—
201C8×C11—22no—
202C11⋊C8—41no—
203C11⋊C8—41no—
204#541—224no—
205#541—224no—
206C2×C4⋊Q8—111no—
207C2×#126—222no—
208C2×#125—222no—
209C2×#125C2×D1111yescharacteristic
210C2×#125C2×D1111yescharacteristic
211C2×C22⋊Q8—112no—
212C2×C4×Q8—112no—
213C2×#117—111no—
214#499—24no—
215#491—224no—
216C2×#107C2×D1112yes—
217C2×#106C2×D1112yes—
218C2×#103—112no—
219C2×#103—112no—
220C2×#103—112no—
221C2×#103—112no—
222C2×C22⋊C8—111no—
223C2×C22⋊C8—111no—
224C2×#97—111no—
225C2×C4×C8C2×D1111yescharacteristic
226#398—222no—
227#396—222no—
228#389—112no—
229#384—111no—
230#380—112no—
231#340—112no—
232#340—112no—
233#336—111no—
234#336—111no—
235C22×C11C2×#12011yescharacteristic
236C22×C11#53211yescharacteristic
237C22×C11#53611yescharacteristic
238C22×C11#57712yes—
239C22×C11#57812yes—
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—41no—
243C2×D11—42no—
244C2×D11—42no—
245C4×C11—24no—
246C4×C11—44no—
247C4×C11—82no—
248C4×C11#54711yescharacteristic
249C4×C11#54711yescharacteristic
250C4×C11#54811yescharacteristic
251C4×C11#54811yescharacteristic
252Dic11—44no—
253Dic11—41no—
254Dic11—42no—
255Dic11—82no—
256C22×Q8—112no—
257C23×C4—111no—
258C22×C8—111no—
259C22×C8—111no—
260C22×C8C22×D1111yescharacteristic
261C22×C8C22×D1111yescharacteristic
262C4⋊Q8—114no—
263C4⋊Q8—222no—
264#126—2216no—
265#125—22no—
266#125—22no—
267#125—22no—
268#125—2216no—
269#125C22⋊D1114yes—
270C22⋊Q8—224no—
271C22⋊Q8—224no—
272C4×Q8—224no—
273C4×Q8—224no—
274#117—222no—
275#117—222no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—112no—
279C2×C4⋊C4—112no—
280C2×C4⋊C4—222no—
281C2×C4⋊C4—222no—
282C2×C4⋊C4—222no—
283C2×C4⋊C4—222no—
284C2×C4⋊C4—222no—
285C2×C4⋊C4C22×D1112yes—
286C2×C4⋊C4C22×D1112yes—
287C2×C22⋊C4—112no—
288C2×C22⋊C4—222no—
289C2×C22⋊C4—222no—
290C2×C42—111no—
291C2×C42—222no—
292C2×C42C22×D1111yescharacteristic
293#107—24no—
294#106—24no—
295#103—224no—
296#103—224no—
297#103—224no—
298#103—224no—
299C22⋊C8—222no—
300C22⋊C8—222no—
301#97—222no—
302C4×C8—22no—
303#95—222no—
304#95—222no—
305C2×C11#243211yescharacteristic
306C2×C11#301312yes—
307C2×C11#317411yescharacteristic
308C2×C11#317711yescharacteristic
309C2×C11#324212yes—
310D11—81no—
311C24—111no—
312C2×Q8—114no—
313C2×Q8—222no—
314C2×Q8—222no—
315C2×Q8—222no—
316C2×Q8—222no—
317C2×Q8—222no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—111no—
321C22×C4—112no—
322C22×C4—222no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—221no—
329C22×C4—222no—
330C22×C4D4×D1112yes—
331C22×C4C23×D1111yescharacteristic
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—221no—
337C2×C8—221no—
338C2×C8—221no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—221no—
342C2×C8#434312yes—
343C2×C8#434312yes—
344C4⋊C4—28no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—44no—
349C4⋊C4—228no—
350C4⋊C4—228no—
351C4⋊C4—224no—
352C4⋊C4—228no—
353C4⋊C4—222no—
354C4⋊C4—222no—
355C4⋊C4—882no—
356C4⋊C4—882no—
357C4⋊C4C2×C22⋊D1114yes—
358C22⋊C4—228no—
359C22⋊C4—224no—
360C22⋊C4—882no—
361C42—228no—
362C42—221no—
363C42—221no—
364C42D4×D1112yes—
365C42C2×C22⋊D1112yes—
366C11#2568311yescharacteristic, complemented, Sylow
367C23—221no—
368C23—221no—
369C23—222no—
370C23—222no—
371C23—221no—
372C23C2×D4×D1111yescharacteristic
373Q8—224no—
374Q8—224no—
375Q8—442no—
376Q8—442no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—24no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—224no—
391C2×C4—221no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4#6699014yes—
402C2×C4C2×D4×D1111yescharacteristic
403C2×C4C2×#434311yescharacteristic
404C2×C4C2×#434311yescharacteristic
405C2×C4#6704011yescharacteristic
406C2×C4#6704011yescharacteristic
407C2×C4C22×C22⋊D1111yescharacteristic
408C8—22no—
409C8—22no—
410C8—441no—
411C8—441no—
412C22—442no—
413C22—441no—
414C22—442no—
415C22—441no—
416C22—441no—
417C22#1062325511yescharacteristic
418C22#1062325611yescharacteristic
419C22#1062330112yes—
420C22#1062330212yes—
421C22C2×#6699011yescharacteristic
422C4—24no—
423C4—44no—
424C4—82no—
425C4—441no—
426C4—444no—
427C4—442no—
428C4—882no—
429C4#1062325711yescharacteristic
430C4#1062325711yescharacteristic
431C4#1062334811yescharacteristic
432C4#1062334811yescharacteristic
433C2—881no—
434C2#1307224111yescharacteristic
435C2#1307792712yes—
436C2#1307924611yescharacteristic
437C2#1307927611yescharacteristic
438C2#1307988712yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#499C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#499D11
hypocenterC11#25683
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#499

Complements

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

NH ≅ G/Ntype
2. C2×#10622682C2semidirect
6. #13069586C2semidirect
7. #13069418C2semidirect
8. #13068881C2semidirect
9. #13068867C2semidirect
11. C2×C11×#499C2semidirect
149. C2×#499D11semidirect
366. C11#25683semidirect

Maximal subgroups

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

subgroupindex
C2×#106232282
C2×#106226822
#130744472
#130698212
#130698142
#130695862
#130694182
#130688812
#130688672
#130683832
C2×C11×#4992
#2568311