Finite Group Databasebeta

← #14653149

Subgroups — #14653149

Order 2816.

502 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079042C211yesmaximal, characteristic
2#13068778C211yesmaximal, characteristic, complemented
3#13067177C211yesmaximal, characteristic, complemented
4#13067176C211yesmaximal, characteristic, complemented
5#13067175C211yesmaximal, characteristic, complemented
6#13066900C211yesmaximal, characteristic, complemented
7C11×#1517C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×#67003—21no—
10C2×#67003—21no—
11#10623008C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#382C2211yescharacteristic
14#10622705C411yescharacteristic, complemented
15#10622698C411yescharacteristic, complemented
16#10622689C411yescharacteristic, complemented
17#10622686C411yescharacteristic, complemented
18#10622672—21no—
19#10622672—21no—
20C2×#66872—21no—
21C2×#66871—21no—
22#10622549C2211yescharacteristic
23#10622538C2211yescharacteristic
24C2×C4×C11⋊C8C2211yescharacteristic
25C11×#327—22no—
26#10622175—22no—
27#10622108—22no—
28#10622092—21no—
29C8×C11⋊C8—21no—
30#10622089—22no—
31C2×C11×#41—21no—
32C2×#4339—21no—
33C11×C4⋊Q8C2×C411yescharacteristic
34C11×#127C2×C411yescharacteristic
35C11×#124—21no—
36C11×#121—21no—
37C11×#121—21no—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42#67003—42no—
43#67003—42no—
44#67003—42no—
45#67003—42no—
46C2×#4326—21no—
47C2×#4326—21no—
48C2×#4325—21no—
49C2×#4325—21no—
50C2×#4324—21no—
51C2×#4324—21no—
52C2×#4323—21no—
53C2×#4323—21no—
54#66983—21no—
55#66983—21no—
56C2×C4⋊Dic11—21no—
57C22×C11⋊C8D411yescharacteristic
58C22×C11⋊C8D411yescharacteristic
59#66928—21no—
60#66927C2×C411yescharacteristic
61C4×D44—21no—
62C4×D44—21no—
63#66922C2×C411yescharacteristic
64C11×C4⋊C8—21no—
65C11×C22⋊C8D412yes—
66C4×C8×C11—21no—
67C11×#95—21no—
68C11×#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C22⋊(C11⋊C8)D412yes—
72#66872—42no—
73#66871—42no—
74C4⋊(C11⋊C8)—21no—
75C4×C11⋊C8—21no—
76C4×C11⋊C8C2×C411yescharacteristic
77C4×C11⋊C8C2×C411yescharacteristic
78C4×C11⋊C8D411yescharacteristic
79C4×C11⋊C8D411yescharacteristic
80#9756—111nomaximal, Sylow
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C2×Q8×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C2×C22⋊D11—41no—
96C22×Dic11—41no—
97#4339—41no—
98#4339—41no—
99#4339—41no—
100#4339—41no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×C4×D11—41no—
105C2×Dic22—21no—
106C2×C8×C11—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11C22×C411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11#4111yescharacteristic
117#4326—42no—
118#4326—42no—
119#4325—42no—
120#4325—42no—
121#4324—42no—
122#4324—42no—
123#4323—42no—
124#4323—42no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129C4⋊Dic11—41no—
130C4⋊Dic11—41no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8C22⋊C411yescharacteristic
133C2×C11⋊C8C22⋊C411yescharacteristic
134C2×C11⋊C8C22⋊C411yescharacteristic
135C2×C11⋊C8C22⋊C411yescharacteristic
136C2×C11⋊C8D812yes—
137C2×C11⋊C8D812yes—
138C2×C11⋊C8SD1612yes—
139C2×C11⋊C8SD1612yes—
140#3147—111no—
141#1846—111no—
142#1517—111no—
143#1517—111no—
144#1517—111no—
145#1517D1111yescharacteristic, complemented
146#1450—111no—
147C23×C11—41no—
148C23×C11#12711yescharacteristic
149C22×D11—41no—
150Q8×C11—41no—
151Q8×C11—41no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—81no—
155D4×C11—81no—
156D4×C11—81no—
157D4×C11—81no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11C2×C22⋊C411yescharacteristic
167C2×C4×C11C4×D411yescharacteristic
168C2×C4×C11C4×D411yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12411yescharacteristic
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×SD1611yescharacteristic
175C2×C4×C11C2×SD1611yescharacteristic
176C22⋊D11—81no—
177C22⋊D11—81no—
178C2×Dic11—41no—
179C2×Dic11—81no—
180C2×Dic11—81no—
181C2×Dic11—81no—
182D44—41no—
183D44—41no—
184D44—81no—
185D44—81no—
186C4×D11—81no—
187C4×D11—81no—
188Dic22—41no—
189Dic22—41no—
190C8×C11—42no—
191C11⋊C8—42no—
192C11⋊C8#10212yes—
193C11⋊C8#10212yes—
194C11⋊C8#10212yes—
195C11⋊C8#10212yes—
196C2×#135—221no—
197C2×#135—221no—
198#532—111no—
199#532C2×D1111yescharacteristic
200#495—221no—
201#495—221no—
202#494—111no—
203#493—111no—
204#492—111no—
205#492—111no—
206#431—111no—
207#431C2×D1111yescharacteristic
208C2×#107—221no—
209C2×#106—221no—
210C2×C4×C8—111no—
211#382—111no—
212#382C2×D1111yescharacteristic
213#327—22no—
214#327—222no—
215#327—222no—
216#327—222no—
217#322—221no—
218C82—221no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11#39011yescharacteristic
225C22×C11#49211yescharacteristic
226C22×C11#49311yescharacteristic
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—81no—
235C4×C11—161no—
236C4×C11C2×#10211yescharacteristic
237C4×C11C2×#10211yescharacteristic
238C4×C11#48611yescharacteristic
239C4×C11#48611yescharacteristic
240Dic11—81no—
241Dic11—161no—
242C2×#41—21no—
243C2×#41—221no—
244#135—442no—
245#135—442no—
246#135—442no—
247#135—442no—
248C2×Q16—221no—
249C2×Q16—221no—
250C2×SD16—221no—
251C2×SD16—221no—
252C2×SD16—221no—
253C2×SD16—221no—
254C2×D8—221no—
255C2×D8—221no—
256C22×C8—111no—
257C22×C8—111no—
258C4⋊Q8—111no—
259C4⋊Q8C4×D1111yescharacteristic
260#127—111no—
261#127C4×D1111yescharacteristic
262#124—21no—
263#124—221no—
264#121—21no—
265#121—21no—
266#121—221no—
267#121—221no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—221no—
271C4×D4—221no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—221no—
274C2×C42C22×D1111yescharacteristic
275#107—442no—
276#106—442no—
277C4⋊C8—21no—
278C4⋊C8—221no—
279C22⋊C8—112no—
280C22⋊C8C22⋊D1112yes—
281C4×C8—21no—
282C4×C8—111no—
283C4×C8—111no—
284C4×C8—111no—
285C4×C8—111no—
286C4×C8—221no—
287#95—21no—
288#95—21no—
289#95—221no—
290#95—221no—
291C2×C11—21no—
292C2×C11—21no—
293C2×C11—161no—
294C2×C11#195711yescharacteristic
295C2×C11#197611yescharacteristic
296C2×C11#197611yescharacteristic
297D11—161no—
298#41—41no—
299#41—41no—
300#41—41no—
301#41—41no—
302#41—441no—
303#41—441no—
304#41—441no—
305#41—441no—
306C2×Q8—21no—
307C2×Q8—221no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—41no—
312C2×D4—221no—
313C2×D4—221no—
314C2×D4—221no—
315C2×D4—441no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—441no—
319C22×C4—441no—
320C22×C4D4×D1111yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C22×C4C2×C22⋊D1111yescharacteristic
323Q16—442no—
324Q16—442no—
325SD16—442no—
326SD16—442no—
327SD16—442no—
328SD16—442no—
329D8—442no—
330D8—442no—
331C2×C8—22no—
332C2×C8—111no—
333C2×C8—111no—
334C2×C8—111no—
335C2×C8—111no—
336C2×C8—112no—
337C2×C8—112no—
338C2×C8—112no—
339C2×C8—112no—
340C2×C8—222no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4—441no—
348C4⋊C4—441no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C42C2×C4×D1111yescharacteristic
354C42#433911yescharacteristic
355C42D4×D1111yescharacteristic
356C42#434111yescharacteristic
357C11#975611yescharacteristic, complemented, Sylow
358C23—41no—
359C23—441no—
360C23#6699311yescharacteristic
361Q8—41no—
362Q8—41no—
363Q8—441no—
364Q8—441no—
365D4—41no—
366D4—41no—
367D4—81no—
368D4—81no—
369D4—81no—
370D4—81no—
371D4—441no—
372D4—441no—
373D4—881no—
374D4—881no—
375D4—881no—
376D4—881no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—441no—
386C2×C4—881no—
387C2×C4—881no—
388C2×C4—881no—
389C2×C4—881no—
390C2×C4—881no—
391C2×C4C22⋊C4×D1111yescharacteristic
392C2×C4(C22⋊D11)⋊C411yescharacteristic
393C2×C4#6693711yescharacteristic
394C2×C4#6693811yescharacteristic
395C2×C4D8×D1111yescharacteristic
396C2×C4D8×D1111yescharacteristic
397C2×C4SD16×D1111yescharacteristic
398C2×C4SD16×D1111yescharacteristic
399C2×C4C4×C22⋊D1111yescharacteristic
400C2×C4#6699211yescharacteristic
401C8—42no—
402C8—112no—
403C8—112no—
404C8—112no—
405C8—112no—
406C8—442no—
407C22—21no—
408C22—21no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—881no—
413C22—881no—
414C22—881no—
415C22#1062257011yescharacteristic
416C22#1062276411yescharacteristic
417C22#1062278811yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—81no—
423C4—161no—
424C4—881no—
425C4—1761no—
426C4#1062237311yescharacteristic
427C4#1062237311yescharacteristic
428C4D11×#10211yescharacteristic
429C4D11×#10211yescharacteristic
430C2—21no—
431C2—21no—
432C2—161no—
433C2—1761no—
434C2#1306942011yescharacteristic
435C2#1306951111yescharacteristic
436C2#1306951311yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1517C2
socleC22×C11#390
prime radical#13079042C2
cosocleC2×C42×C11C23
hypercenter#1517D11
hypocenterC11#9756
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #13068778C2semidirect
3. #13067177C2semidirect
4. #13067176C2semidirect
5. #13067175C2semidirect
6. #13066900C2semidirect
7. C11×#1517C2semidirect
14. #10622705C4semidirect
15. #10622698C4semidirect
16. #10622689C4semidirect
17. #10622686C4semidirect
145. #1517D11semidirect
357. C11#9756semidirect

Maximal subgroups

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

subgroupindex
#130790422
#130687782
#130671772
#130671762
#130671752
#130669002
C11×#15172
#975611