Finite Group Databasebeta

← #14654524

Subgroups — #14654524

Order 2816.

554 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078647C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic
3#13067175C211yesmaximal, characteristic
4#13067045C211yesmaximal, characteristic, complemented
5#13067011C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#2581C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66995—21no—
11#10623008C2211yescharacteristic
12C11×#400—21no—
13C11×#395—21no—
14C11×#391—21no—
15C11×#389—21no—
16C11×#387—22no—
17C11×#382C2211yescharacteristic
18#10622840—21no—
19#10622644—21no—
20#10622641—22no—
21#10622640—21no—
22#10622640—21no—
23C4×#4325—22no—
24#10622633—21no—
25#10622581—21no—
26#10622579—21no—
27#10622538C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622537C2211yescharacteristic
30Q8⋊(C11⋊C8)—22no—
31Q8⋊(C11⋊C8)—22no—
32#10622089—22no—
33C22×Q8×C11D411yescharacteristic
34C22×Q8×C11D411yescharacteristic
35C2×#4339—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C42×C11—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4326—22no—
54#66995—42no—
55#66995—42no—
56C2×#4325—22no—
57C2×#4325—22no—
58#66983—21no—
59#66983—21no—
60C2×#4318—21no—
61#66928—21no—
62#66927D411yescharacteristic
63C4×D44—21no—
64C4×D44—21no—
65#66922D411yescharacteristic
66C11×#95—22no—
67C11×#95—22no—
68C11×#95—22no—
69C11×#95—21no—
70C11×#95D412yes—
71#66899—22no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74#66874—22no—
75#66873—22no—
76#66873—22no—
77#66872—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yes—
82C4×C11⋊C8—21no—
83C4×C11⋊C8D412yes—
84#9999—111nomaximal, Sylow
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—42no—
93C2×Q8×C11SD1612yescomplemented
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—41no—
103#4339—41no—
104#4339—41no—
105#4339—41no—
106#4339—41no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×C4×D11—41no—
111C2×Dic22—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—44no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C42×C11—41no—
124C42×C11—41no—
125C42×C11—41no—
126C42×C11—41no—
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131#4326—44no—
132#4325—44no—
133#4325—44no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138#4318—41no—
139#4318—41no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—41no—
143#3103—111no—
144#3037—111no—
145#2581D1111yescharacteristic, complemented
146#1517—111no—
147#1487—111no—
148#1479—111no—
149#1286—111no—
150C23×C11#12011yescharacteristic
151C22×D11—41no—
152Q8×C11—22no—
153Q8×C11—22no—
154Q8×C11—22no—
155Q8×C11—22no—
156Q8×C11—41no—
157Q8×C11—41no—
158Q8×C11—41no—
159Q8×C11—41no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12011yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12711yescharacteristic
181C2×C4×C11C2×SD1611yescharacteristic
182C2×C4×C11#13511yescharacteristic
183C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C11#13711yescharacteristic
185C22⋊D11—81no—
186C22⋊D11—81no—
187C2×Dic11—41no—
188D44—42no—
189D44—41no—
190D44—41no—
191D44—81no—
192C4×D11—81no—
193C4×D11—81no—
194Dic22—41no—
195Dic22—41no—
196C11⋊C8—42no—
197C11⋊C8—42no—
198C11⋊C8—81no—
199C2×#137—221no—
200#532—111no—
201C2×C4×Q8C2×D1111yescharacteristic
202C2×C4×Q8C2×D1111yescharacteristic
203#481—221no—
204#475—221no—
205#464—222no—
206#462—221no—
207#460—221no—
208#460—221no—
209#448—221no—
210C4×SD16—222no—
211#431—111no—
212#431—111no—
213#423—111no—
214#417—221no—
215#400—21no—
216#395—21no—
217#391—21no—
218#389—21no—
219#387—22no—
220#382C2×D1111yescharacteristic
221#327—222no—
222Q8⋊C8—222no—
223Q8⋊C8—222no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11#39211yescharacteristic
227C22×C11#44811yescharacteristic
228C22×C11#44911yescharacteristic
229C2×D11—81no—
230C2×D11—81no—
231C2×D11—81no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—42no—
237C4×C11—42no—
238C4×C11—82no—
239C4×C11—81no—
240C4×C11—81no—
241C4×C11#45011yescharacteristic
242C4×C11#45211yescharacteristic
243C4×C11#46511yescharacteristic
244C4×C11#46811yescharacteristic
245Dic11—81no—
246C2×#41—221no—
247C22×Q8C22⋊D1111yescharacteristic
248C22×Q8C22⋊D1111yescharacteristic
249#137—442no—
250#137—442no—
251C2×Q16—222no—
252C2×SD16—222no—
253C2×SD16—222no—
254C2×M16—221no—
255C4⋊Q8—111no—
256#127—111no—
257#124—221no—
258#121—221no—
259#121—221no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×Q8—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×Q8—21no—
267C4×Q8—21no—
268C4×D4—221no—
269C4×D4—221no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4C22⋊D1111yescharacteristic
275C2×C4⋊C4C22⋊D1111yescharacteristic
276C2×C42—21no—
277C2×C42—21no—
278C2×C42C22×D1111yescharacteristic
279#106—222no—
280C4⋊C8—112no—
281C4⋊C8—221no—
282C4⋊C8—221no—
283C4⋊C8—221no—
284#103—222no—
285#103—222no—
286#102—222no—
287#102—222no—
288C22⋊C8—221no—
289C22⋊C8—221no—
290C4×C8—112no—
291C4×C8—221no—
292#95—22no—
293#95—22no—
294#95—22no—
295#95—21no—
296#95C22⋊D1112yes—
297C2×C11—21no—
298C2×C11—21no—
299C2×C11#200011yescharacteristic
300C2×C11#200911yescharacteristic
301C2×C11#201011yescharacteristic
302D11—161no—
303#41—441no—
304#41—441no—
305#41—441no—
306#41—441no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—42no—
315C2×Q8—221no—
316C2×Q8#432512yescomplemented
317C2×D4—221no—
318C2×D4—221no—
319C2×D4—221no—
320C2×D4—441no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—441no—
327C22×C4C2×C22⋊D1111yescharacteristic
328C22×C4C2×C22⋊D1111yescharacteristic
329C22×C4C2×C22⋊D1111yescharacteristic
330Q16—444no—
331SD16—444no—
332SD16—444no—
333M16—441no—
334M16—441no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8—441no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—44no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C42—41no—
354C42—41no—
355C42—41no—
356C42—41no—
357C42D4×D1111yescharacteristic
358C42D4×D1111yescharacteristic
359C42D4×D1111yescharacteristic
360C42#434111yescharacteristic
361C11#999911yescharacteristic, complemented, Sylow
362C23—441no—
363C23#6700611yescharacteristic
364Q8—22no—
365Q8—22no—
366Q8—22no—
367Q8—22no—
368Q8—41no—
369Q8—41no—
370Q8—41no—
371Q8—41no—
372Q8—441no—
373Q8—441no—
374D4—442no—
375D4—441no—
376D4—441no—
377D4—881no—
378D4—881no—
379D4—881no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—441no—
396C2×C4—881no—
397C2×C4—881no—
398C2×C4#6699011yescharacteristic
399C2×C4#6699011yescharacteristic
400C2×C4#6699111yescharacteristic
401C2×C4#6699211yescharacteristic
402C2×C4#6699211yescharacteristic
403C2×C4#6699311yescharacteristic
404C2×C4C2×#432511yescharacteristic
405C2×C4#6699511yescharacteristic
406C2×C4#6700211yescharacteristic
407C2×C4#6700311yescharacteristic
408C8—442no—
409C8—442no—
410C8—881no—
411C22—21no—
412C22—21no—
413C22—881no—
414C22—881no—
415C22—881no—
416C22#1062283611yescharacteristic
417C22#1062284011yescharacteristic
418C22#1062285111yescharacteristic
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—42no—
425C4—82no—
426C4—81no—
427C4—81no—
428C4—881no—
429C4#1062265911yescharacteristic
430C4#1062266011yescharacteristic
431C4#1062266111yescharacteristic
432C4#1062266211yescharacteristic
433C2—21no—
434C2—21no—
435C2—1761no—
436C2#1306961711yescharacteristic
437C2#1306967611yescharacteristic
438C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2581C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#2581D11
hypocenterC11#9999
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2581

Complements

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

NH ≅ G/Ntype
4. #13067045C2semidirect
5. #13067011C2semidirect
6. #13066474C2semidirect
7. C11×#2581C2semidirect
93. C2×Q8×C11SD16semidirect
145. #2581D11semidirect
316. C2×Q8#4325semidirect
361. C11#9999semidirect

Maximal subgroups

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

subgroupindex
#130786472
#130780882
#130671752
#130670452
#130670112
#130664742
C11×#25812
#999911