Finite Group Databasebeta

← #14666386

Subgroups — #14666386

Order 2816.

508 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 59 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#13069747C211yesmaximal, characteristic, complemented
2#13067567C211yesmaximal, characteristic, complemented
3#13067533C211yesmaximal, characteristic
4#13066637C211yesmaximal, characteristic, complemented
5#13066613C211yesmaximal, characteristic, complemented
6#13066546C211yesmaximal, characteristic, complemented
7C11×#2760C211yesmaximal, characteristic, complemented
8C2×#66982—21no—
9#10623024C2211yescharacteristic
10C11×#401—21no—
11C11×#393—21no—
12C11×#393C2211yescharacteristic
13C11×#392C2211yescharacteristic
14C11×#386—21no—
15C11×#386—21no—
16C11×#386—21no—
17C11×#381—21no—
18C11×#381C2211yescharacteristic
19#10622840—21no—
20#10622830—21no—
21C2×#66870—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11—21no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11D411yescharacteristic
32C22×C22⋊D11—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C11×C22⋊C4C2311yescharacteristic
40C2×C22⋊Dic11—21no—
41C2×#4325—41no—
42C2×#4323—41no—
43#66983—21no—
44#66983—21no—
45#66982—42no—
46#66982—42no—
47C2×(C2×D11)⋊C4—41no—
48C2×Dic11⋊C4—41no—
49#66939—41no—
50#66935—41no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95D411yescharacteristic
59C11×#95D411yescharacteristic
60#66899—41no—
61#66896—41no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)—21no—
64#66870—42no—
65#12187—111nomaximal, Sylow
66C24×C11—21no—
67C24×C11C2×D411yescharacteristic
68C23×D11—21no—
69C2×Q8×C11—41no—
70C2×Q8×C11—81no—
71C2×D4×C11—41no—
72C2×D4×C11—42no—
73C2×D4×C11—42no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—81no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—42no—
87C22×C4×C11—81no—
88C22×C4×C11—81no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C2×C22⋊D11—41no—
92C2×C22⋊D11—41no—
93C2×C22⋊D11—41no—
94C2×C22⋊D11—41no—
95C2×C22⋊D11—41no—
96C2×C22⋊D11—41no—
97C22×Dic11—21no—
98C22×Dic11—41no—
99C2×D44—21no—
100C2×D44—21no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—81no—
104C11×C22⋊C4—81no—
105C11×C22⋊C4—81no—
106C11×C22⋊C4—81no—
107C11×C22⋊C4—81no—
108C22⋊Dic11—22no—
109C22⋊Dic11—41no—
110#4325—82no—
111#4323—82no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—44no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117Dic11⋊C4—44no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120#2760D1111yescharacteristic, complemented
121#2022—111no—
122#1601—111no—
123#1595—111no—
124#1351—111no—
125#1343—111no—
126#1317—111no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—22no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11#12011yescharacteristic
139C23×C11#13511yescharacteristic
140C23×C11AGL(1,ℤ/8)11yescharacteristic
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—81no—
145C22×D11—81no—
146Q8×C11—42no—
147Q8×C11—81no—
148D4×C11—42no—
149D4×C11—81no—
150D4×C11—82no—
151D4×C11—82no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
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—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—84no—
173C2×C4×C11—81no—
174C22⋊D11—81no—
175C22⋊D11—81no—
176C22⋊D11—81no—
177C22⋊D11—81no—
178C2×Dic11—41no—
179C2×Dic11—42no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—81no—
183C2×Dic11—81no—
184D44—81no—
185D44—81no—
186C11⋊C8—81no—
187C11⋊C8—81no—
188#534—111no—
189C2×#123—221no—
190#448—221no—
191#447—221no—
192C2×#99—221no—
193#401—21no—
194#393—21no—
195#393C2×D1111yescharacteristic
196#392C2×D1111yescharacteristic
197#386—21no—
198#386—21no—
199#386—21no—
200#381—21no—
201#381C2×D1111yescharacteristic
202#342—111no—
203#327—221no—
204#327—221no—
205#323—111no—
206#323—111no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—42no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11#44911yescharacteristic
224C22×C11#45311yescharacteristic
225C22×C11B(4,𝔽2)11yescharacteristic
226C2×D11—82no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—161no—
231C4×C11—41no—
232C4×C11—41no—
233C4×C11—81no—
234C4×C11—81no—
235C4×C11—81no—
236C4×C11—81no—
237C4×C11—81no—
238Dic11—82no—
239Dic11—81no—
240C22×Q8C22⋊D1111yescharacteristic
241C22×D4—21no—
242C22×D4—221no—
243C22×D4C22⋊D1111yescharacteristic
244C23×C4—21no—
245C23×C4C22⋊D1111yescharacteristic
246C2×SD16—441no—
247C2×D8—441no—
248#123—441no—
249#123—442no—
250#123—442no—
251#121—221no—
252#121—221no—
253#120—441no—
254C2×C4⋊C4—441no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—441no—
262C2×C22⋊C4C22⋊D1111yescharacteristic
263C2×C22⋊C4C22×D1111yescharacteristic
264#103—441no—
265#102—441no—
266#99—442no—
267C22⋊C8—221no—
268C22⋊C8—221no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—21no—
273#95—21no—
274#95—21no—
275#95—21no—
276#95C22⋊D1111yescharacteristic
277#95C22⋊D1111yescharacteristic
278C2×C11—21no—
279C2×C11—21no—
280C2×C11—41no—
281C2×C11—41no—
282C2×C11—82no—
283C2×C11#160011yescharacteristic
284C2×C11#219711yescharacteristic
285C2×C11#220011yescharacteristic
286D11—161no—
287C24—21no—
288C24—221no—
289C24C2×C22⋊D1111yescharacteristic
290C2×Q8—41no—
291C2×Q8—81no—
292C2×D4—41no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—81no—
298C2×D4—221no—
299C2×D4—221no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—441no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—42no—
316C22×C4—81no—
317C22×C4—81no—
318C22×C4—221no—
319C22×C4—441no—
320C22×C4C2×C22⋊D1111yescharacteristic
321C22×C4C2×C22⋊D1111yescharacteristic
322SD16—882no—
323D8—882no—
324C2×C8—441no—
325C2×C8—441no—
326C4⋊C4—221no—
327C4⋊C4—221no—
328C4⋊C4—444no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C22⋊C4—81no—
334C22⋊C4—81no—
335C22⋊C4—81no—
336C22⋊C4—222no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C22⋊C4—444no—
340C22⋊C4—441no—
341C11#1218711yescharacteristic, complemented, Sylow
342C23—21no—
343C23—21no—
344C23—22no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23—881no—
357C23—881no—
358C23#6700211yescharacteristic
359C23#6700311yescharacteristic
360C23#6700611yescharacteristic
361Q8—42no—
362Q8—81no—
363D4—42no—
364D4—81no—
365D4—82no—
366D4—82no—
367D4—881no—
368D4—881no—
369D4—881no—
370D4—881no—
371D4—881no—
372D4—881no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—84no—
394C2×C4—81no—
395C2×C4—442no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—881no—
400C2×C4—881no—
401C8—881no—
402C8—881no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—41no—
408C22—41no—
409C22—42no—
410C22—42no—
411C22—41no—
412C22—41no—
413C22—42no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—882no—
420C22—881no—
421C22—881no—
422C22—881no—
423C22—1761no—
424C22#1062285111yescharacteristic
425C22#1062285411yescharacteristic
426C22#1062285711yescharacteristic
427C4—41no—
428C4—41no—
429C4—81no—
430C4—81no—
431C4—81no—
432C4—81no—
433C4—81no—
434C4—882no—
435C4—881no—
436C2—21no—
437C2—21no—
438C2—41no—
439C2—41no—
440C2—82no—
441C2—1761no—
442C2#1306756211yescharacteristic
443C2#1307060611yescharacteristic
444C2#1307062311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2760C2
socleC22×C11B(4,𝔽2)
prime radical#13067533C2
hypercenter#2760D11
hypocenterC11#12187
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2760

Complements

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

NH ≅ G/Ntype
1. #13069747C2semidirect
2. #13067567C2semidirect
4. #13066637C2semidirect
5. #13066613C2semidirect
6. #13066546C2semidirect
7. C11×#2760C2semidirect
120. #2760D11semidirect
341. C11#12187semidirect

Maximal subgroups

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

subgroupindex
#130697472
#130675672
#130675332
#130666372
#130666132
#130665462
C11×#27602
#1218711