Finite Group Databasebeta

← #14782837

Subgroups — #14782837

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#107C211yesmaximal, characteristic
2C2×#10622452C211yesmaximal, characteristic
3#13071238C212yesmaximal
4#13070113C212yesmaximal, complemented
5#13070112C212yesmaximal, complemented
6#13070106C211yesmaximal, characteristic, complemented
7#13070105C211yesmaximal, characteristic, complemented
8#13070104C211yesmaximal, characteristic, complemented
9#13068334C212yesmaximal
10#13068331C211yesmaximal, characteristic
11C11×#2086C211yesmaximal, characteristic, complemented
12C22×#4313C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14C2×#66945C2212yes—
15C2×C4⋊C4×D11C2212yes—
16C2×#66925C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C11×#389C2212yes—
20C2×#66882C2211yescharacteristic
21C2×Dic11⋊C8C2211yescharacteristic
22C2×Dic11⋊C8C2211yescharacteristic
23#10622602—22no—
24#10622598C2212yes—
25#10622589—22no—
26#10622586C2212yes—
27C2×#66871C2212yes—
28#10622541C2212yes—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30D11×#107—24no—
31#10622452—24no—
32#10622281—22no—
33#10622263—22no—
34C11×#340C2211yescharacteristic
35C11×#340C2212yes—
36#10622189C2211yescharacteristic
37#10622189C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41C22×C4×D11—22no—
42C22×C4×D11C2311yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4C2312yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C42×C11C2311yescharacteristic
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4D411yescharacteristic
51C2×(C2×D11)⋊C4D411yescharacteristic
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11C2312yes—
54C2×C4⋊Dic11C2312yes—
55C2×Dic11⋊C4—22no—
56C2×Dic11⋊C4—22no—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4D411yescharacteristic
59C2×Dic11⋊C4D411yescharacteristic
60C2×C4×Dic11—22no—
61C2×C4×Dic11C2311yescharacteristic
62C22×C11⋊C8C2311yescharacteristic
63C22×C11⋊C8C2311yescharacteristic
64C2×#4313—22no—
65C2×#4313—24no—
66C2×C8×D11—24no—
67C2×C8×D11D414yes—
68#66945—24no—
69#66945Q818yes—
70C4⋊C4×D11—24no—
71C4⋊C4×D11—24no—
72#66925—22no—
73#66925—22no—
74C11×#107—22no—
75C11×C4⋊C8—22no—
76C11×#95—22no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80#66882—22no—
81Dic11⋊C8—22no—
82Dic11⋊C8—22no—
83#66871—24no—
84C4⋊(C11⋊C8)—22no—
85#23667—111nomaximal, Sylow
86C23×D11C2×D411yescharacteristic
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2411yescharacteristic
92C22×Dic11—22no—
93C22×Dic11—22no—
94C22×Dic11C2×D411yescharacteristic
95C22×Dic11C2×D411yescharacteristic
96C22×Dic11C2×D411yescharacteristic
97C2×C4×D11—44no—
98C2×C4×D11—82no—
99C2×C4×D11—82no—
100C2×C4×D11C2×D412yes—
101C2×C4×D11C2×Q814yes—
102C2×C4×D11#4112yes—
103C2×C4×D11#4114yes—
104C2×C8×C11—21no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11C2×D412yes—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—82no—
112C11×C4⋊C4C2×Q814yes—
113C42×C11—21no—
114C42×C11—21no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—22no—
117(C2×D11)⋊C4—28no—
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11—82no—
122C4⋊Dic11C2×Q814yes—
123Dic11⋊C4—22no—
124Dic11⋊C4—22no—
125Dic11⋊C4—44no—
126Dic11⋊C4—82no—
127Dic11⋊C4—82no—
128C4×Dic11—28no—
129C4×Dic11—21no—
130C4×Dic11—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8C2×D412yes—
135#4313—44no—
136C8×D11—28no—
137C22×#107—111no—
138C2×#424—111no—
139#2317—112no—
140#2087—112no—
141#2087—112no—
142#2086—111no—
143#2086—111no—
144#2086—111no—
145#2086D1111yescharacteristic, complemented
146#1736—112no—
147#1735—111no—
148C23×C11C22×D411yescharacteristic
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—22no—
152C22×D11#12112yes—
153C22×D11C22⋊Q814yes—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—24no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—22no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C22×Q812yes—
167C2×C4×C11C2×#4112yes—
168C2×C4×C11C2×#4111yescharacteristic
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—24no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—22no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11#12112yes—
181C2×Dic11C22⋊Q814yes—
182C4×D11—88no—
183C4×D11#12314yes—
184C4×D11#12518yes—
185C4×D11C4⋊Q814yes—
186C8×C11—22no—
187C8×C11—41no—
188C11⋊C8—22no—
189C11⋊C8—41no—
190C22×M16—111no—
191C23×C8—111no—
192C2×#117—111no—
193C2×#117—112no—
194C22×C4⋊C4—112no—
195C2×#107—111no—
196C2×#107—112no—
197C2×#107—224no—
198C2×#107C2×D1111yescharacteristic
199#424—224no—
200C2×C4⋊C8—111no—
201C2×C4⋊C8—111no—
202C2×C4⋊C8—111no—
203C2×C4⋊C8C2×D1111yescharacteristic
204#389—112no—
205#389—112no—
206#389—112no—
207#389C2×D1112yes—
208#385—222no—
209#385—222no—
210#384—222no—
211#382—222no—
212#340—111no—
213#340—112no—
214#340—112no—
215#340—112no—
216#340—112no—
217#340C2×D1111yescharacteristic
218#340C2×D1112yes—
219C22×C11C2×#12111yescharacteristic
220C22×C11C2×C22⋊Q812yes—
221C22×C11#57611yescharacteristic
222C22×C11#57611yescharacteristic
223C22×C11#57812yes—
224C2×D11—24no—
225C2×D11—24no—
226C2×D11—22no—
227C2×D11—22no—
228C2×D11#39814yes—
229C4×C11—44no—
230C4×C11—41no—
231C4×C11—41no—
232C4×C11—82no—
233C4×C11C2×#12311yescharacteristic
234C4×C11C2×#12512yes—
235C4×C11C2×C4⋊Q811yescharacteristic
236Dic11—44no—
237Dic11—41no—
238Dic11—41no—
239Dic11—82no—
240Dic11#39814yes—
241C23×C4—111no—
242C23×C4—222no—
243C2×M16—224no—
244C2×M16—222no—
245C22×C8—111no—
246C22×C8—114no—
247C22×C8—111no—
248C22×C8—224no—
249C22×C8C22×D1111yescharacteristic
250C22×C8C22×D1111yescharacteristic
251#117—118no—
252#117—222no—
253#117—222no—
254#117—224no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—112no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—112no—
260C2×C4⋊C4—224no—
261C2×C4⋊C4—224no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4—222no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4C22×D1112yes—
267C2×C4⋊C4C22×D1112yes—
268C2×C22⋊C4—111no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—222no—
271C2×C42—111no—
272C2×C42—222no—
273C2×C42C22×D1111yescharacteristic
274#107—22no—
275#107—224no—
276#107—222no—
277C4⋊C8—22no—
278C4⋊C8—222no—
279C4⋊C8—222no—
280C4⋊C8—222no—
281#95—22no—
282#95—222no—
283#95—222no—
284#95—222no—
285C2×C11C2×#39811yescharacteristic
286C2×C11#305811yescharacteristic
287C2×C11#305911yescharacteristic
288C2×C11#308312yes—
289C2×C11#308312yes—
290D11—24no—
291C24—111no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—111no—
295C22×C4—112no—
296C22×C4—114no—
297C22×C4—112no—
298C22×C4—114no—
299C22×C4—111no—
300C22×C4—111no—
301C22×C4—222no—
302C22×C4—222no—
303C22×C4—444no—
304C22×C4—882no—
305C22×C4—882no—
306C22×C4D4×D1111yescharacteristic
307C22×C4D4×D1111yescharacteristic
308C22×C4C23×D1111yescharacteristic
309M16—444no—
310C2×C8—22no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—112no—
314C2×C8—228no—
315C2×C8—222no—
316C2×C8—221no—
317C2×C8—222no—
318C2×C8D4×D1112yes—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—82no—
323C4⋊C4—114no—
324C4⋊C4—222no—
325C4⋊C4—222no—
326C4⋊C4—222no—
327C4⋊C4—222no—
328C4⋊C4—222no—
329C4⋊C4—444no—
330C4⋊C4—882no—
331C4⋊C4—882no—
332C4⋊C4—882no—
333C4⋊C4Q8×D1114yes—
334C22⋊C4—222no—
335C22⋊C4—222no—
336C22⋊C4—228no—
337C42—21no—
338C42—21no—
339C42—228no—
340C42—221no—
341C42—221no—
342C11#2366711yescharacteristic, complemented, Sylow
343C23—112no—
344C23—114no—
345C23—221no—
346C23—221no—
347C23—222no—
348C23C2×D4×D1111yescharacteristic
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—24no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—112no—
361C2×C4—114no—
362C2×C4—114no—
363C2×C4—114no—
364C2×C4—118no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—222no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—224no—
371C2×C4—442no—
372C2×C4—442no—
373C2×C4—442no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4—888no—
377C2×C4C2×D4×D1111yescharacteristic
378C2×C4C2×Q8×D1112yes—
379C2×C4#41×D1112yes—
380C2×C4#41×D1111yescharacteristic
381C8—22no—
382C8—41no—
383C8—222no—
384C8—441no—
385C22—114no—
386C22—224no—
387C22—224no—
388C22—222no—
389C22—222no—
390C22D11×#12111yescharacteristic
391C22D11×C22⋊Q812yes—
392C22#1062328811yescharacteristic
393C22#1062330011yescharacteristic
394C22#1062331012yes—
395C4—44no—
396C4—41no—
397C4—41no—
398C4—82no—
399C4—114no—
400C4—444no—
401C4—441no—
402C4—441no—
403C4—882no—
404C4D11×#12311yescharacteristic
405C4D11×#12512yes—
406C4D11×C4⋊Q811yescharacteristic
407C2—224no—
408C2D11×#39811yescharacteristic
409C2#1307825911yescharacteristic
410C2#1307826911yescharacteristic
411C2#1307846212yes—
412C2#1307847012yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2086C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2086D11
hypocenterC11#23667
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2086

Complements

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

NH ≅ G/Ntype
4. #13070113C2semidirect
5. #13070112C2semidirect
6. #13070106C2semidirect
7. #13070105C2semidirect
8. #13070104C2semidirect
11. C11×#2086C2semidirect
145. #2086D11semidirect
342. C11#23667semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1072
C2×#106224522
#130712382
#130701132
#130701122
#130701062
#130701052
#130701042
#130683342
#130683312
C11×#20862
#2366711