Finite Group Databasebeta

← #14642959

Subgroups — #14642959

Order 2816.

478 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 81 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#13075641C211yesmaximal, characteristic
2#13070158C211yesmaximal, characteristic, complemented
3#13070021C211yesmaximal, characteristic, complemented
4#13070019C211yesmaximal, characteristic, complemented
5#13066441C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic, complemented
7C11×#1270C211yesmaximal, characteristic, complemented
8C2×#66938—21no—
9C11×#390C2211yescharacteristic
10#10622836—21no—
11C2×#66896—21no—
12C2×#66885—21no—
13C2×#66881—21no—
14C2×#66880—21no—
15#10622603—21no—
16#10622574—21no—
17#10622573—21no—
18#10622564—21no—
19#10622552C2211yescharacteristic
20#10622548C2211yescharacteristic
21#10622542C2211yescharacteristic
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622189—21no—
25#10622167—21no—
26#10622162C2211yescharacteristic
27C22×D4×C11D411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11—21no—
30C22×D44D411yescharacteristic
31C22×Dic22D411yescharacteristic
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11D411yescharacteristic
48C2×C4⋊Dic11D411yescharacteristic
49C2×C4×Dic11—21no—
50C22×C11⋊C8—21no—
51#66938—42no—
52#66938—42no—
53#66896—42no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57#66885—42no—
58#66881—42no—
59#66880—42no—
60#7810—111nomaximal, Sylow
61C24×C11—21no—
62C23×D11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C22×C4×C11—21no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C2×C22⋊D11—42no—
72C2×C22⋊D11—81no—
73C2×C22⋊D11—81no—
74C2×C22⋊D11—81no—
75C2×C22⋊D11—81no—
76C2×C22⋊D11—81no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—41no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—41no—
84C2×D44—41no—
85C2×Dic22—21no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×Dic22SD1612yes—
89C2×C8×C11—22no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C42×C11—41no—
101C22⋊Dic11—42no—
102C22⋊Dic11—81no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—81no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4×Dic11—42no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121#2733—111no—
122#2096—111no—
123#2071—111no—
124#2071—111no—
125#1272—111no—
126#1270—111no—
127#1270D1111yescharacteristic, complemented
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11#12011yescharacteristic
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143D4×C11—42no—
144D4×C11—81no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11C2×SD1611yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
160C22⋊D11—84no—
161C22⋊D11—84no—
162C2×Dic11—22no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—81no—
172C2×Dic11—81no—
173C2×Dic11—81no—
174D44—42no—
175D44—81no—
176Dic22—42no—
177Dic22—81no—
178C8×C11—42no—
179C8×C11—81no—
180C11⋊C8—81no—
181C2×#124—221no—
182C2×#106—221no—
183C2×#103—221no—
184C2×#102—221no—
185C2×#102—221no—
186#394—221no—
187#392—221no—
188#392—221no—
189#391—111no—
190#390—111no—
191#390C2×D1111yescharacteristic
192#388—221no—
193#388—221no—
194#384—111no—
195#340—221no—
196#340—221no—
197#336—111no—
198#336C2×D1111yescharacteristic
199#336C2×D1111yescharacteristic
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11#44911yescharacteristic
208C22×C11#44911yescharacteristic
209C22×C11#45011yescharacteristic
210C22×C11#45311yescharacteristic
211C22×C11#45511yescharacteristic
212C22×C11#45511yescharacteristic
213C22×C11#45811yescharacteristic
214C2×D11—81no—
215C2×D11—81no—
216C2×D11—81no—
217C2×D11—81no—
218C2×D11—81no—
219C2×D11—81no—
220C2×D11—81no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—81no—
228Dic11—42no—
229Dic11—81no—
230Dic11—81no—
231Dic11—161no—
232C22×Q8—111no—
233C22×D4—111no—
234C22×D4—221no—
235C22×D4—221no—
236C22×D4D4411yescharacteristic
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—221no—
240#124—442no—
241#124—442no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4D4411yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—221no—
254C2×C22⋊C4—221no—
255C2×C22⋊C4—221no—
256C2×C42—221no—
257C2×C42C22×D1111yescharacteristic
258#106—442no—
259#103—442no—
260#102—442no—
261#102—442no—
262#95—221no—
263#95—221no—
264#95—221no—
265C2×C11—161no—
266C2×C11#161211yescharacteristic
267C2×C11#161211yescharacteristic
268C2×C11#161311yescharacteristic
269C2×C11#162411yescharacteristic
270C2×C11#164211yescharacteristic
271C2×C11#164211yescharacteristic
272C2×C11#165911yescharacteristic
273D11—161no—
274C24—21no—
275C24—221no—
276C2×Q8—112no—
277C2×Q8—221no—
278C2×Q8—441no—
279C2×Q8—441no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—441no—
287C2×D4—441no—
288C2×D4—442no—
289C2×D4—881no—
290C2×D4—881no—
291C2×D4—881no—
292C2×D4—881no—
293C2×D4—881no—
294C22×C4—21no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—221no—
298C22×C4—441no—
299C22×C4C2×D4411yescharacteristic
300C22×C4D4×D1111yescharacteristic
301C22×C4D4×D1111yescharacteristic
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—441no—
309C2×C8—441no—
310C2×C8—441no—
311C4⋊C4—41no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C4⋊C4—441no—
315C4⋊C4—441no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C4⋊C4—441no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—442no—
325C22⋊C4—442no—
326C22⋊C4—441no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C22⋊C4—441no—
330C22⋊C4—881no—
331C22⋊C4—881no—
332C42—41no—
333C42—442no—
334C11#781011yescharacteristic, complemented, Sylow
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—441no—
343C23—441no—
344C23—441no—
345C23—441no—
346C23—441no—
347C23—441no—
348C23—441no—
349C23#6693511yescharacteristic
350Q8—442no—
351Q8—881no—
352D4—42no—
353D4—81no—
354D4—442no—
355D4—881no—
356D4—884no—
357D4—884no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—222no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—881no—
377C2×C4—881no—
378C2×C4—881no—
379C2×C4#6695711yescharacteristic
380C2×C4#6696111yescharacteristic
381C2×C4#6696411yescharacteristic
382C2×C4#6696411yescharacteristic
383C2×C4SD16×D1111yescharacteristic
384C2×C4#6696911yescharacteristic
385C8—42no—
386C8—81no—
387C8—881no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—881no—
396C22—881no—
397C22—881no—
398C22—881no—
399C22—881no—
400C22—881no—
401C22—881no—
402C22#1062234711yescharacteristic
403C22#1062235511yescharacteristic
404C22#1062235911yescharacteristic
405C22#1062238911yescharacteristic
406C22#1062239411yescharacteristic
407C22#1062243511yescharacteristic
408C22#1062243811yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—81no—
416C4—442no—
417C4—881no—
418C4—881no—
419C4—1761no—
420C2—161no—
421C2—1761no—
422C2#1306763111yescharacteristic
423C2#1306763211yescharacteristic
424C2#1306763711yescharacteristic
425C2#1306770111yescharacteristic
426C2#1306781711yescharacteristic
427C2#1306781811yescharacteristic
428C2#1306792411yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1270C2
socleC23×C11#120
prime radical#13075641C2
hypercenter#1270D11
hypocenterC11#7810
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13070158C2semidirect
3. #13070021C2semidirect
4. #13070019C2semidirect
5. #13066441C2semidirect
6. #13066436C2semidirect
7. C11×#1270C2semidirect
127. #1270D11semidirect
334. C11#7810semidirect

Maximal subgroups

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

subgroupindex
#130756412
#130701582
#130700212
#130700192
#130664412
#130664362
C11×#12702
#781011