Finite Group Databasebeta

← #14649663

Subgroups — #14649663

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078092C211yesmaximal, characteristic
2#13077185C211yesmaximal, characteristic, complemented
3C2×#10622182C211yesmaximal, characteristic, complemented
4#13067004C211yesmaximal, characteristic, complemented
5#13066512C211yesmaximal, characteristic, complemented
6#13066490C211yesmaximal, characteristic, complemented
7C11×#1545C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C2×#66985—21no—
10C2×#66960—21no—
11C4×#4339C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#423C2211yescharacteristic
14#10622828—21no—
15#10622732—21no—
16#10622688—21no—
17#10622688C412yes—
18#10622685—21no—
19#10622685C412yes—
20#10622537C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23#10622452—22no—
24#10622450—21no—
25D11×C4⋊C8—21no—
26C11×#331—22no—
27#10622182—21no—
28#10622182—21no—
29#10622097—21no—
30#10622094—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C2×#4339D411yescharacteristic
35C2×C11×M16—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127C2×C412yes—
40C2×C42×C11C2311yescharacteristic
41C2×#4324—22no—
42#66985—42no—
43#66985—42no—
44C2×#4323—22no—
45C4×C22⋊D11—21no—
46C4×C22⋊D11—21no—
47#66979D411yescharacteristic
48C2×#4318—21no—
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51#66960—42no—
52#66960—42no—
53C2×#4313—22no—
54C2×C8×D11—22no—
55C4×D44C2×C411yescharacteristic
56C4×D44D411yescharacteristic
57#66925—21no—
58C42×D11—21no—
59C4×Dic22C2×C411yescharacteristic
60C4×Dic22D411yescharacteristic
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×C22⋊C8—21no—
65C4×C8×C11—21no—
66#66896—22no—
67#66896—22no—
68Dic11⋊C8—22no—
69Dic11⋊C8—22no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)C2×C412yes—
75C4⋊(C11⋊C8)D411yescharacteristic
76C4⋊(C11⋊C8)D411yescharacteristic
77#9173—111nomaximal, Sylow
78C24×C11—41no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—81no—
90C2×D4×C11—81no—
91C2×D4×C11—82no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C2×C22⋊D11—21no—
96#4339—21no—
97#4339—21no—
98#4339D812yes—
99#4339SD1612yes—
100C2×D44C22⋊C411yescharacteristic
101C2×C4×D11—21no—
102C2×C4×D11—21no—
103C2×C4×D11—21no—
104C2×Dic22C22⋊C411yescharacteristic
105C11×M16—41no—
106C11×M16—41no—
107C2×C8×C11—22no—
108C2×C8×C11—41no—
109C42×C11C22×C411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C22⋊Dic11—21no—
114#4324—44no—
115#4323—44no—
116(C2×D11)⋊C4—21no—
117(C2×D11)⋊C4—21no—
118C4⋊Dic11C22⋊C411yescharacteristic
119C4⋊Dic11C22⋊C411yescharacteristic
120Dic11⋊C4—21no—
121Dic11⋊C4—21no—
122C4×Dic11—21no—
123C4×Dic11—21no—
124C4×Dic11—21no—
125#4318—41no—
126#4318—41no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—81no—
134#4313—44no—
135C8×D11—44no—
136#3038—111no—
137#2906—111no—
138#1545D1111yescharacteristic, complemented
139C2×#331—111no—
140#1477—111no—
141#1301—111no—
142#1292—111no—
143C23×C11—42no—
144C23×C11—82no—
145C23×C11—82no—
146C23×C11—81no—
147C23×C11—81no—
148C23×C11#12311yescharacteristic
149C22×D11—21no—
150D4×C11—42no—
151D4×C11—42no—
152D4×C11—82no—
153D4×C11—82no—
154D4×C11—82no—
155D4×C11—81no—
156D4×C11—81no—
157D4×C11—81no—
158D4×C11—81no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—41no—
162C2×C4×C11C2×C22⋊C411yescharacteristic
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C2×SD1611yescharacteristic
170C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C11#13711yescharacteristic
172C22⋊D11—22no—
173C22⋊D11—22no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177D44—21no—
178D44#10212yes—
179C4×D11—22no—
180C4×D11—22no—
181C4×D11—41no—
182C4×D11—41no—
183C4×D11—81no—
184Dic22—21no—
185Dic22#10212yes—
186C8×C11—42no—
187C8×C11—81no—
188C11⋊C8—42no—
189C11⋊C8—41no—
190C11⋊C8—41no—
191C11⋊C8—81no—
192C2×AGL(1,ℤ/8)—221no—
193C2×#131—221no—
194C2×#127C2×D1111yescharacteristic
195C4×#41—111no—
196#460—112no—
197#460—221no—
198#459—112no—
199#459—221no—
200#431C2×D1111yescharacteristic
201#424—221no—
202#424—222no—
203#423—111no—
204#423—221no—
205#423C2×D1111yescharacteristic
206C2×C4⋊C8—111no—
207C2×C4⋊C8—111no—
208C2×C4⋊C8—221no—
209#418—221no—
210#331—22no—
211#331—221no—
212#331—221no—
213Q8⋊C8—221no—
214D4⋊C8—221no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—82no—
218C22×C11—82no—
219C22×C11—82no—
220C22×C11—162no—
221C22×C11—162no—
222C22×C11#38611yescharacteristic
223C22×C11#48011yescharacteristic
224C22×C11#48111yescharacteristic
225C2×D11—22no—
226C2×D11—41no—
227C2×D11—41no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11C2×#10211yescharacteristic
232C4×C11#41711yescharacteristic
233C4×C11#44711yescharacteristic
234C4×C11#44811yescharacteristic
235C4×C11#47111yescharacteristic
236C4×C11#47211yescharacteristic
237Dic11—22no—
238Dic11—41no—
239Dic11—41no—
240C2×#41—111no—
241C22×D4—21no—
242C22×D4—21no—
243C22×D4—21no—
244AGL(1,ℤ/8)—442no—
245AGL(1,ℤ/8)—442no—
246C2×SD16—222no—
247C2×D8—222no—
248#131—442no—
249#131—442no—
250C2×M16—21no—
251C2×M16—222no—
252C2×M16—221no—
253C22×C8—222no—
254C22×C8—221no—
255C22×C8—221no—
256#127—21no—
257#127—21no—
258#127—21no—
259#127C4×D1112yes—
260C4×Q8—111no—
261C4×Q8—111no—
262C4×D4—111no—
263C4×D4—111no—
264C4×D4—221no—
265C4×D4—221no—
266#117—111no—
267#117—221no—
268C2×C42—221no—
269C2×C42C22×D1111yescharacteristic
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—112no—
273C4⋊C8—111no—
274C4⋊C8—111no—
275C4⋊C8—222no—
276C4⋊C8—222no—
277C4⋊C8—221no—
278C4⋊C8—221no—
279C4⋊C8—221no—
280C4⋊C8—221no—
281C4⋊C8C22⋊D1112yes—
282#102—222no—
283#102—222no—
284C22⋊C8—21no—
285C4×C8—21no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—162no—
289C2×C11#187411yescharacteristic
290C2×C11#190311yescharacteristic
291C2×C11#190711yescharacteristic
292D11—42no—
293C24—41no—
294#41—112no—
295#41—112no—
296#41—221no—
297#41—221no—
298C2×Q8—111no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—81no—
310C2×D4—81no—
311C2×D4—82no—
312C2×D4—111no—
313C2×D4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4#433911yescharacteristic
318C22×C4D4×D1111yescharacteristic
319C22×C4#434111yescharacteristic
320SD16—444no—
321D8—444no—
322M16—41no—
323M16—41no—
324M16—444no—
325M16—441no—
326M16—441no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—222no—
330C2×C8—221no—
331C2×C8—221no—
332C2×C8—444no—
333C2×C8—441no—
334C2×C8—441no—
335C2×C8—441no—
336C2×C8—881no—
337C4⋊C4—111no—
338C4⋊C4—111no—
339C4⋊C4—221no—
340C4⋊C4—221no—
341C22⋊C4—221no—
342C22⋊C4—221no—
343C22⋊C4—221no—
344C42—221no—
345C42—221no—
346C42—221no—
347C42C2×C4×D1111yescharacteristic
348C42D4×D1111yescharacteristic
349C42D4×D1111yescharacteristic
350C42C2×C22⋊D1111yescharacteristic
351C11#917311yescharacteristic, complemented, Sylow
352C23—42no—
353C23—82no—
354C23—82no—
355C23—81no—
356C23—81no—
357C23—221no—
358C23#6693611yescharacteristic
359Q8—112no—
360Q8—221no—
361D4—42no—
362D4—42no—
363D4—82no—
364D4—82no—
365D4—82no—
366D4—81no—
367D4—81no—
368D4—81no—
369D4—81no—
370D4—112no—
371D4—222no—
372D4—222no—
373D4—221no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—221no—
378C2×C4—222no—
379C2×C4—222no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—881no—
385C2×C4C22⋊C4×D1111yescharacteristic
386C2×C4(C22⋊D11)⋊C411yescharacteristic
387C2×C4#6693711yescharacteristic
388C2×C4D8×D1111yescharacteristic
389C2×C4#6696411yescharacteristic
390C2×C4SD16×D1111yescharacteristic
391C2×C4#6696811yescharacteristic
392C2×C4C4×C22⋊D1111yescharacteristic
393C2×C4#6699011yescharacteristic
394C2×C4#6699111yescharacteristic
395C8—42no—
396C8—81no—
397C8—441no—
398C8—441no—
399C8—442no—
400C8—881no—
401C22—21no—
402C22—21no—
403C22—82no—
404C22—82no—
405C22—82no—
406C22—162no—
407C22—162no—
408C22—222no—
409C22—441no—
410C22—441no—
411C22#1062238711yescharacteristic
412C22#1062239011yescharacteristic
413C22#1062256911yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—222no—
418C4—441no—
419C4—441no—
420C4#1062236111yescharacteristic
421C4#1062236211yescharacteristic
422C4D11×#10211yescharacteristic
423C4#1062238411yescharacteristic
424C4#1062276911yescharacteristic
425C4#1062278311yescharacteristic
426C2—21no—
427C2—21no—
428C2—162no—
429C2—442no—
430C2#1306893011yescharacteristic
431C2#1306909311yescharacteristic
432C2#1306912111yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1545C2
socleC22×C11#386
prime radical#13078092C2
cosocleC2×C42×C11C23
hypercenter#1545D11
hypocenterC11#9173
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
2. #13077185C2semidirect
3. C2×#10622182C2semidirect
4. #13067004C2semidirect
5. #13066512C2semidirect
6. #13066490C2semidirect
7. C11×#1545C2semidirect
138. #1545D11semidirect
351. C11#9173semidirect

Maximal subgroups

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

subgroupindex
#130780922
#130771852
C2×#106221822
#130670042
#130665122
#130664902
C11×#15452
#917311