Finite Group Databasebeta

← #14642244

Subgroups — #14642244

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076967C211yesmaximal, characteristic
2#13068373C211yesmaximal, characteristic
3#13068308C211yesmaximal, characteristic
4#13066440C211yesmaximal, characteristic, complemented
5#13066439C211yesmaximal, characteristic, complemented
6#13066438C211yesmaximal, characteristic, complemented
7C11×#1271C211yesmaximal, characteristic, complemented
8C22×#4313—21no—
9C2×#66949—21no—
10C2×#66941C411yescharacteristic
11C2×C42×D11C2211yescharacteristic
12C11×#389C2211yescharacteristic
13C2×(C2×D11)⋊C8—21no—
14C2×C8×Dic11—21no—
15#10622600C411yescharacteristic
16#10622600C411yescharacteristic
17#10622589C411yescharacteristic
18#10622585—21no—
19#10622541C2211yescharacteristic
20#10622280—21no—
21#10622259—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×Dic22—21no—
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C22×C11⋊C8—21no—
49C22×C11⋊C8—21no—
50C2×#4313—24no—
51C2×#4313—42no—
52C2×#4313—42no—
53#66949—42no—
54#66949—42no—
55#66941—42no—
56C42×D11—42no—
57C11×#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61(C2×D11)⋊C8—24no—
62C8×Dic11—42no—
63#7685—111nomaximal, Sylow
64C23×D11C22⋊C411yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C2×C4×D11—22no—
76C2×C4×D11—22no—
77C2×C4×D11—22no—
78C2×C4×D11—22no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×C4×D11D812yes—
86C2×C4×D11SD1612yes—
87C2×Dic22—42no—
88C2×Dic22—42no—
89C2×Dic22—42no—
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C42×C11—41no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—41no—
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109Dic11⋊C4—42no—
110Dic11⋊C4—41no—
111Dic11⋊C4—41no—
112C4×Dic11—22no—
113C4×Dic11—22no—
114C4×Dic11—41no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121#4313—48no—
122#2857—111no—
123C4×C22⋊C8—111no—
124#1728—111no—
125#1271—111no—
126#1271—111no—
127#1271—111no—
128#1271D1111yescharacteristic, complemented
129C23×C11C2×C22⋊C411yescharacteristic
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11#10212yes—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11#13111yescharacteristic
150C2×C4×C11#13111yescharacteristic
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C2×SD1611yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C2×C4×C11#13711yescharacteristic
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11#9912yes—
166C2×Dic11#10112yes—
167C2×Dic11#10212yes—
168C2×Dic11#10412yes—
169C2×Dic11#10412yes—
170C4×D11—24no—
171C4×D11—24no—
172C4×D11—42no—
173C4×D11—42no—
174C4×D11—42no—
175C4×D11—42no—
176Dic22—84no—
177C8×C11—42no—
178C8×C11—42no—
179C11⋊C8—42no—
180C11⋊C8—42no—
181C22×M16—221no—
182C2×C4⋊Q8—111no—
183C2×C22⋊Q8—221no—
184C22×C42—111no—
185C2×C22⋊C8—221no—
186C2×C4×C8—221no—
187#391—221no—
188#389—111no—
189#389—221no—
190#389C2×D1111yescharacteristic
191#384—111no—
192#380—111no—
193#380—111no—
194#380—221no—
195#336—111no—
196#336—111no—
197#336—221no—
198#336C2×D1111yescharacteristic
199#336C2×D1111yescharacteristic
200C22×C11#40811yescharacteristic
201C22×C11C2×#9911yescharacteristic
202C22×C11C2×#10111yescharacteristic
203C22×C11C2×#10211yescharacteristic
204C22×C11#41911yescharacteristic
205C22×C11C2×#10411yescharacteristic
206C22×C11C2×#10411yescharacteristic
207C2×D11—22no—
208C2×D11—22no—
209C2×D11—22no—
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—41no—
213C2×D11—41no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—81no—
221C4×C11—81no—
222Dic11—22no—
223Dic11—22no—
224Dic11—81no—
225Dic11—81no—
226Dic11#32714yes—
227C22×Q8—221no—
228C23×C4—111no—
229C23×C4—111no—
230C23×C4—111no—
231C2×M16—224no—
232C2×M16—442no—
233C2×M16—442no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—221no—
237C22×C8—221no—
238C4⋊Q8—442no—
239C22⋊Q8—442no—
240C22⋊Q8—442no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4C4×D1111yescharacteristic
249C2×C4⋊C4C4×D1111yescharacteristic
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C42—111no—
253C2×C42—111no—
254C2×C42—111no—
255C2×C42—442no—
256C2×C42C22×D1111yescharacteristic
257C22⋊C8—224no—
258C4×C8—442no—
259#95—21no—
260#95—221no—
261#95—221no—
262#95—221no—
263C2×C11#147211yescharacteristic
264C2×C11#148511yescharacteristic
265C2×C11#149211yescharacteristic
266C2×C11C2×#32711yescharacteristic
267C2×C11#150811yescharacteristic
268C2×C11#152611yescharacteristic
269C2×C11#154611yescharacteristic
270D11—42no—
271C24—111no—
272C2×Q8—442no—
273C2×Q8—442no—
274C2×Q8—442no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—111no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—112no—
281C22×C4—112no—
282C22×C4—222no—
283C22×C4—222no—
284C22×C4—222no—
285C22×C4—222no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4C2×C4×D1111yescharacteristic
295C22×C4D4×D1111yescharacteristic
296C22×C4D4×D1111yescharacteristic
297M16—448no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—222no—
305C2×C8—222no—
306C2×C8—441no—
307C2×C8—441no—
308C2×C8—441no—
309C2×C8—441no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4—441no—
318C4⋊C4—442no—
319C4⋊C4—442no—
320C4⋊C4—442no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C22⋊C4—442no—
324C22⋊C4—442no—
325C42—41no—
326C42—222no—
327C42—222no—
328C42—441no—
329C11#768511yescharacteristic, complemented, Sylow
330C23—112no—
331C23—221no—
332C23—221no—
333C23—221no—
334C23—221no—
335C23—221no—
336C23—221no—
337C23C22⋊C4×D1111yescharacteristic
338Q8—884no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—112no—
352C2×C4—112no—
353C2×C4—112no—
354C2×C4—112no—
355C2×C4—112no—
356C2×C4—224no—
357C2×C4—224no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—221no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4#6695411yescharacteristic
373C2×C4#6696011yescharacteristic
374C2×C4D8×D1111yescharacteristic
375C2×C4SD16×D1111yescharacteristic
376C2×C4#6696811yescharacteristic
377C2×C4#6697111yescharacteristic
378C8—42no—
379C8—42no—
380C8—442no—
381C8—442no—
382C22—222no—
383C22—222no—
384C22—222no—
385C22—441no—
386C22—441no—
387C22—441no—
388C22—441no—
389C22#1062234011yescharacteristic
390C22D11×#9911yescharacteristic
391C22D11×#10111yescharacteristic
392C22D11×#10211yescharacteristic
393C22#1062241511yescharacteristic
394C22D11×#10411yescharacteristic
395C22D11×#10411yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—81no—
403C4—81no—
404C4—114no—
405C4—222no—
406C4—222no—
407C4—881no—
408C4—881no—
409C2—442no—
410C2#1306697811yescharacteristic
411C2#1306703511yescharacteristic
412C2#1306706511yescharacteristic
413C2D11×#32711yescharacteristic
414C2#1306713411yescharacteristic
415C2#1306720911yescharacteristic
416C2#1306728611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1271C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1271D11
hypocenterC11#7685
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #13066440C2semidirect
5. #13066439C2semidirect
6. #13066438C2semidirect
7. C11×#1271C2semidirect
128. #1271D11semidirect
329. C11#7685semidirect

Maximal subgroups

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

subgroupindex
#130769672
#130683732
#130683082
#130664402
#130664392
#130664382
C11×#12712
#768511