Finite Group Databasebeta

← #14652818

Subgroups — #14652818

Order 2816.

882 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077010C211yesmaximal, characteristic
2#13068767C211yesmaximal, characteristic, complemented
3C4⋊C8×Dic11C211yesmaximal, characteristic, complemented
4C2×#10622182C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic, complemented
6C2×#10622123C211yesmaximal, characteristic, complemented
7C2×C11×#331C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C2×#66993—21no—
10C2×#66993—21no—
11C2×#66993—22no—
12C2×#66993C414yes—
13C2×#66927C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×Dic11⋊C8—22no—
17C2×C8×Dic11—21no—
18C42×Dic11C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C11×#331—22no—
22#10622188—21no—
23#10622182—22no—
24#10622123—22no—
25#10622123—22no—
26C22×D4×C11—21no—
27C22×D4×C11—21no—
28C22×D4×C11C2×C412yes—
29C22×C22⋊D11—24no—
30C22×C22⋊D11—24no—
31C22×D44—21no—
32C22×D44—21no—
33C22×D44C2×C412yes—
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C2×C42×C11C2311yescharacteristic
41#66993—42no—
42#66993—42no—
43#66993—48no—
44#66993—42no—
45#66993—44no—
46#66993—42no—
47#66993—44no—
48C2×C4×Dic11C2×C412yes—
49C2×C4×Dic11D411yescharacteristic
50C2×C4×Dic11D411yescharacteristic
51C2×C4×Dic11D412yes—
52C22×C11⋊C8—21no—
53C22×C11⋊C8—21no—
54#66927—21no—
55#66927—21no—
56#66927—21no—
57#66927—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8D412yescomplemented
62Dic11⋊C8—44no—
63C8×Dic11—42no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)D412yescomplemented
68#9695—111nomaximal, Sylow
69C24×C11—22no—
70C23×D11—22no—
71C2×D4×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—44no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—42no—
80C2×D4×C11—41no—
81C2×D4×C11—42no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C2×C22⋊D11—48no—
88C2×C22⋊D11—48no—
89C2×C22⋊D11—48no—
90C2×C22⋊D11—48no—
91C2×C22⋊D11—48no—
92C2×C22⋊D11—48no—
93C22×Dic11C22⋊C412yes—
94C22×Dic11C22⋊C412yes—
95C2×D44—22no—
96C2×D44—22no—
97C2×D44—44no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—42no—
104C2×D44—41no—
105C2×D44—42no—
106C2×D44—41no—
107C2×D44—41no—
108C2×C8×C11—22no—
109C2×C8×C11—41no—
110C2×C8×C11—41no—
111C2×C8×C11—42no—
112C2×C8×C11—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11#4111yescharacteristic
117C4×Dic11—24no—
118C4×Dic11—21no—
119C4×Dic11—21no—
120C4×Dic11D812yes—
121C4×Dic11D814yes—
122C4×Dic11SD1612yes—
123C4×Dic11SD1614yes—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—42no—
128C2×C11⋊C8—41no—
129#2867—111no—
130#1842—111no—
131C4×C4⋊C8—111no—
132C2×#331—111no—
133C2×#331—111no—
134C2×#331—111no—
135C2×#331D1111yescharacteristic, complemented
136C23×C11—42no—
137C23×C11—44no—
138C23×C11—42no—
139C23×C11—44no—
140C23×C11—42no—
141C23×C11C2×C22⋊C411yescharacteristic
142C22×D11—42no—
143C22×D11—44no—
144C22×D11—42no—
145C22×D11—44no—
146C22×D11—42no—
147D4×C11—82no—
148D4×C11—82no—
149D4×C11—81no—
150D4×C11—81no—
151D4×C11—81no—
152D4×C11—81no—
153D4×C11—82no—
154D4×C11—81no—
155D4×C11—81no—
156C2×C4×C11—22no—
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11C4×D411yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12411yescharacteristic
162C2×C4×C11#12711yescharacteristic
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C2×D812yes—
165C2×C4×C11C2×SD1611yescharacteristic
166C2×C4×C11C2×SD1612yes—
167C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
169C22⋊D11—816no—
170C22⋊D11—816no—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11#10014yes—
174C2×Dic11#10214yes—
175C2×Dic11#10214yes—
176C2×Dic11#10214yes—
177D44—82no—
178D44—82no—
179D44—81no—
180D44—81no—
181D44—81no—
182D44—81no—
183D44—82no—
184D44—81no—
185D44—81no—
186C8×C11—42no—
187C8×C11—81no—
188C11⋊C8—42no—
189C11⋊C8—81no—
190C2×#127—114no—
191C2×#127—111no—
192C2×#127—221no—
193C2×#127—222no—
194C2×#127—221no—
195C2×#127C2×D1111yescharacteristic
196C2×C4⋊C8—111no—
197C2×C4⋊C8—111no—
198C2×C4⋊C8—222no—
199C2×C4⋊C8C2×D1111yescharacteristic
200C2×C4⋊C8C2×D1111yescharacteristic
201C2×C4×C8—221no—
202C43—111no—
203#336—221no—
204#331—22no—
205#331—222no—
206#331—222no—
207#331—222no—
208C22×C11—84no—
209C22×C11—84no—
210C22×C11—82no—
211C22×C11—82no—
212C22×C11—82no—
213C22×C11#39011yescharacteristic
214C22×C11C2×#10012yes—
215C22×C11C2×#10211yescharacteristic
216C22×C11C2×#10212yes—
217C22×C11#41811yescharacteristic
218C2×D11—84no—
219C2×D11—84no—
220C2×D11—82no—
221C2×D11—82no—
222C2×D11—82no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11#45911yescharacteristic
226C4×C11#45911yescharacteristic
227C4×C11#46011yescharacteristic
228C4×C11#46011yescharacteristic
229C4×C11#48612yes—
230C4×C11#49211yescharacteristic
231C4×C11#49311yescharacteristic
232Dic11—24no—
233Dic11#33118yescomplemented
234C22×D4—21no—
235C22×D4—21no—
236C22×D4—112no—
237C22×D4—224no—
238C22×D4—224no—
239C22×D4—221no—
240C22×D4—221no—
241C22×D4C4×D1112yes—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—221no—
245C22×C8—221no—
246#127—21no—
247#127—21no—
248#127—21no—
249#127—21no—
250#127—221no—
251#127—221no—
252#127—221no—
253#127—221no—
254#127—442no—
255#127—444no—
256#127—442no—
257#127—444no—
258#127—448no—
259#127—442no—
260#127—442no—
261C2×C42—111no—
262C2×C42—112no—
263C2×C42—112no—
264C2×C42—111no—
265C2×C42C22×D1111yescharacteristic
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—112no—
270C4⋊C8—221no—
271C4⋊C8—221no—
272C4⋊C8—221no—
273C4⋊C8—444no—
274C4⋊C8C22⋊D1112yescomplemented
275C4×C8—442no—
276C2×C11—162no—
277C2×C11C2×#33112yes—
278C2×C11#154512yes—
279C2×C11#195711yescharacteristic
280C2×C11#196511yescharacteristic
281C2×C11#198211yescharacteristic
282D11—162no—
283C24—22no—
284C24—222no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—44no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—42no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—42no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—222no—
299C2×D4—222no—
300C2×D4—444no—
301C2×D4—448no—
302C2×D4—448no—
303C2×D4—448no—
304C2×D4—448no—
305C2×D4—448no—
306C2×D4—448no—
307C2×D4—441no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—442no—
311C2×D4—441no—
312C2×D4—441no—
313C2×D4—442no—
314C2×D4—441no—
315C2×D4—441no—
316C2×D4—441no—
317C22×C4—112no—
318C22×C4—112no—
319C22×C4C2×C4×D1111yescharacteristic
320C22×C4D4×D1111yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C2×C8—22no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—42no—
326C2×C8—41no—
327C2×C8—222no—
328C2×C8—441no—
329C2×C8—441no—
330C2×C8—442no—
331C2×C8—441no—
332C42—112no—
333C42—114no—
334C42—112no—
335C42—114no—
336C42—224no—
337C42—221no—
338C42—221no—
339C42#433911yescharacteristic
340C42D4×D1111yescharacteristic
341C42#434111yescharacteristic
342C42C2×C22⋊D1111yescharacteristic
343C11#969511yescharacteristic, complemented, Sylow
344C23—42no—
345C23—44no—
346C23—44no—
347C23—42no—
348C23—42no—
349C23—442no—
350C23—444no—
351C23—444no—
352C23—442no—
353C23—442no—
354C23C22⋊C4×D1111yescharacteristic
355D4—82no—
356D4—82no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—82no—
362D4—81no—
363D4—81no—
364D4—882no—
365D4—882no—
366D4—8816no—
367D4—8816no—
368D4—881no—
369D4—881no—
370D4—881no—
371D4—881no—
372D4—882no—
373D4—881no—
374D4—881no—
375C2×C4—22no—
376C2×C4—114no—
377C2×C4—114no—
378C2×C4—114no—
379C2×C4—114no—
380C2×C4—222no—
381C2×C4—222no—
382C2×C4(C22⋊D11)⋊C411yescharacteristic
383C2×C4#6693711yescharacteristic
384C2×C4#6693811yescharacteristic
385C2×C4D8×D1111yescharacteristic
386C2×C4D8×D1112yes—
387C2×C4#6696411yescharacteristic
388C2×C4SD16×D1111yescharacteristic
389C2×C4SD16×D1112yes—
390C2×C4#6696711yescharacteristic
391C2×C4C4×C22⋊D1111yescharacteristic
392C2×C4#6699211yescharacteristic
393C2×C4#6699311yescharacteristic
394C8—42no—
395C8—81no—
396C8—442no—
397C8—881no—
398C22—84no—
399C22—82no—
400C22—82no—
401C22—82no—
402C22—84no—
403C22—884no—
404C22—882no—
405C22—882no—
406C22—882no—
407C22—884no—
408C22D11×#10012yes—
409C22D11×#10212yes—
410C22D11×#10211yescharacteristic
411C22#1062238311yescharacteristic
412C22#1062257011yescharacteristic
413C4—21no—
414C4—21no—
415C4—118no—
416C4—224no—
417C4#1062237312yes—
418C4#1062237511yescharacteristic
419C4#1062239911yescharacteristic
420C4#1062276311yescharacteristic
421C4#1062276411yescharacteristic
422C4#1062277611yescharacteristic
423C4#1062278811yescharacteristic
424C2—162no—
425C2—1762no—
426C2D11×#33112yes—
427C2#1306728212yes—
428C2#1306942011yescharacteristic
429C2#1306945411yescharacteristic
430C2#1306954111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#331C2
socleC23×C11C2×C22⋊C4
prime radical#13077010C2
cosocleC2×C42×C11C23
hypercenterC2×#331D11
hypocenterC11#9695
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #13068767C2semidirect
3. C4⋊C8×Dic11C2semidirect
4. C2×#10622182C2semidirect
5. C2×#10622123C2semidirect
6. C2×#10622123C2semidirect
7. C2×C11×#331C2semidirect
61. C11×C4⋊C8D4semidirect
67. C4⋊(C11⋊C8)D4semidirect
135. C2×#331D11semidirect
233. Dic11#331semidirect
274. C4⋊C8C22⋊D11semidirect
343. C11#9695semidirect

Maximal subgroups

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

subgroupindex
#130770102
#130687672
C4⋊C8×Dic112
C2×#106221822
C2×#106221232
C2×C11×#3312
#969511