Finite Group Databasebeta

← #14642253

Subgroups — #14642253

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076965C211yesmaximal, characteristic
2#13068373C211yesmaximal, characteristic
3#13068308C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic, complemented
5#13066441C211yesmaximal, characteristic, complemented
6#13066441C211yesmaximal, characteristic, complemented
7C11×#1272C211yesmaximal, characteristic, complemented
8C2×#66999C411yescharacteristic
9C2×#66997C411yescharacteristic
10C22×#4313—21no—
11C2×#66950C411yescharacteristic
12C2×C42×D11C2211yescharacteristic
13C11×#391C2211yescharacteristic
14C2×(C2×D11)⋊C8—21no—
15C2×C8×Dic11—21no—
16#10622589C411yescharacteristic
17#10622542C2211yescharacteristic
18#10622280—21no—
19#10622280—21no—
20#10622260—21no—
21#10622260—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11C2×C411yescharacteristic
28C22×C4×D11C2×C411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×Dic22C2×C411yescharacteristic
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36#66999—42no—
37#66997—42no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C22×C11⋊C8—21no—
51C22×C11⋊C8—21no—
52C2×#4313—24no—
53C2×#4313—42no—
54C2×#4313—42no—
55#66950—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#7687—111nomaximal, Sylow
64C23×D11C22⋊C411yescharacteristic
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11C22⋊C411yescharacteristic
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C2×C4×D11—22no—
80C2×C4×D11—22no—
81C2×C4×D11—22no—
82C2×C4×D11—22no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×C4×D11SD1612yes—
90C2×C4×D11Q1612yes—
91C2×Dic22—21no—
92C2×Dic22—21no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C11×C4⋊C4—41no—
102C42×C11—41no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—42no—
105C4⋊Dic11—41no—
106C4⋊Dic11—42no—
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109Dic11⋊C4—42no—
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
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#1272—111no—
126#1272—111no—
127#1272—111no—
128#1272D1111yescharacteristic, 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#10312yes—
137Q8×C11—81no—
138Q8×C11—81no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11#13111yescharacteristic
152C2×C4×C11#13111yescharacteristic
153C2×C4×C11C2×SD1611yescharacteristic
154C2×C4×C11C2×Q1611yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11#9912yes—
168C2×Dic11#10012yes—
169C2×Dic11#10312yes—
170C2×Dic11#10412yes—
171C2×Dic11#10412yes—
172C4×D11—24no—
173C4×D11—24no—
174C4×D11—42no—
175C4×D11—42no—
176C4×D11—42no—
177C4×D11—42no—
178Dic22—81no—
179Dic22—81no—
180C8×C11—42no—
181C8×C11—42no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C22×M16—221no—
185C2×C4⋊Q8—111no—
186C2×C22⋊Q8—111no—
187C2×C22⋊Q8—111no—
188C22×C42—111no—
189C2×C22⋊C8—221no—
190C2×C4×C8—221no—
191#391—111no—
192#391C2×D1111yescharacteristic
193#389—221no—
194#389—221no—
195#384—111no—
196#380—221no—
197#380—221no—
198#336—111no—
199#336—111no—
200#336—221no—
201#336C2×D1111yescharacteristic
202#336C2×D1111yescharacteristic
203C22×C11#40811yescharacteristic
204C22×C11C2×#9911yescharacteristic
205C22×C11C2×#10011yescharacteristic
206C22×C11C2×#10311yescharacteristic
207C22×C11#41911yescharacteristic
208C22×C11C2×#10411yescharacteristic
209C22×C11C2×#10411yescharacteristic
210C2×D11—22no—
211C2×D11—22no—
212C2×D11—22no—
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—41no—
216C2×D11—41no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—81no—
224C4×C11—81no—
225Dic11—22no—
226Dic11—22no—
227Dic11—81no—
228Dic11—81no—
229Dic11#32814yes—
230C22×Q8—111no—
231C22×Q8C4×D1111yescharacteristic
232C23×C4—111no—
233C23×C4—111no—
234C23×C4—111no—
235C2×M16—224no—
236C2×M16—442no—
237C2×M16—442no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—221no—
241C22×C8—221no—
242C4⋊Q8—442no—
243C22⋊Q8—442no—
244C22⋊Q8—442no—
245C2×C4⋊C4—111no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4C4×D1111yescharacteristic
253C2×C22⋊C4—221no—
254C2×C22⋊C4—221no—
255C2×C42—111no—
256C2×C42—111no—
257C2×C42—111no—
258C2×C42—442no—
259C2×C42C22×D1111yescharacteristic
260C22⋊C8—224no—
261C4×C8—442no—
262#95—21no—
263#95—21no—
264#95—221no—
265#95—221no—
266C2×C11#147111yescharacteristic
267C2×C11#148511yescharacteristic
268C2×C11#149311yescharacteristic
269C2×C11C2×#32811yescharacteristic
270C2×C11#150811yescharacteristic
271C2×C11#152511yescharacteristic
272C2×C11#154811yescharacteristic
273D11—42no—
274C24—111no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—221no—
280C2×Q8—221no—
281C2×Q8—441no—
282C2×Q8—441no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—112no—
289C22×C4—112no—
290C22×C4—222no—
291C22×C4—222no—
292C22×C4—222no—
293C22×C4—222no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—221no—
298C22×C4—221no—
299C22×C4—221no—
300C22×C4—441no—
301C22×C4—441no—
302C22×C4C2×C4×D1111yescharacteristic
303C22×C4D4×D1111yescharacteristic
304C22×C4D4×D1111yescharacteristic
305M16—448no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—222no—
313C2×C8—222no—
314C2×C8—441no—
315C2×C8—441no—
316C2×C8—441no—
317C2×C8—441no—
318C4⋊C4—41no—
319C4⋊C4—441no—
320C4⋊C4—442no—
321C4⋊C4—442no—
322C4⋊C4—442no—
323C4⋊C4—442no—
324C4⋊C4—442no—
325C4⋊C4—442no—
326C22⋊C4—442no—
327C22⋊C4—442no—
328C42—41no—
329C42—222no—
330C42—222no—
331C42—441no—
332C11#768711yescharacteristic, complemented, Sylow
333C23—112no—
334C23—221no—
335C23—221no—
336C23—221no—
337C23—221no—
338C23—221no—
339C23—221no—
340C23C22⋊C4×D1111yescharacteristic
341Q8—81no—
342Q8—81no—
343Q8—881no—
344Q8—881no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—112no—
358C2×C4—112no—
359C2×C4—112no—
360C2×C4—112no—
361C2×C4—112no—
362C2×C4—224no—
363C2×C4—224no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4#6695411yescharacteristic
379C2×C4#6696011yescharacteristic
380C2×C4SD16×D1111yescharacteristic
381C2×C4#6696811yescharacteristic
382C2×C4Q16×D1111yescharacteristic
383C2×C4#6697111yescharacteristic
384C8—42no—
385C8—42no—
386C8—442no—
387C8—442no—
388C22—222no—
389C22—222no—
390C22—222no—
391C22—441no—
392C22—441no—
393C22—441no—
394C22—441no—
395C22#1062234011yescharacteristic
396C22D11×#9911yescharacteristic
397C22D11×#10011yescharacteristic
398C22D11×#10311yescharacteristic
399C22#1062241511yescharacteristic
400C22D11×#10411yescharacteristic
401C22D11×#10411yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—114no—
411C4—222no—
412C4—222no—
413C4—881no—
414C4—881no—
415C2—442no—
416C2#1306697411yescharacteristic
417C2#1306703511yescharacteristic
418C2#1306706911yescharacteristic
419C2D11×#32811yescharacteristic
420C2#1306713411yescharacteristic
421C2#1306720611yescharacteristic
422C2#1306729511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1272D11
hypocenterC11#7687
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #13066442C2semidirect
5. #13066441C2semidirect
6. #13066441C2semidirect
7. C11×#1272C2semidirect
128. #1272D11semidirect
332. C11#7687semidirect

Maximal subgroups

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

subgroupindex
#130769652
#130683732
#130683082
#130664422
#130664412
C11×#12722
#768711