Finite Group Databasebeta

← #14648481

Subgroups — #14648481

Order 2816.

516 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 99 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#13078670C211yesmaximal, characteristic
2#13077737C211yesmaximal, characteristic, complemented
3#13069445C211yesmaximal, characteristic, complemented
4C4×#66889C211yesmaximal, characteristic, complemented
5#13066506C211yesmaximal, characteristic, complemented
6#13066448C211yesmaximal, characteristic, complemented
7C11×#1484C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C4×#4339C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C2×#66901—22no—
13C2×#66889—21no—
14#10622704C411yescharacteristic, complemented
15#10622697C411yescharacteristic, complemented
16#10622688C411yescharacteristic, complemented
17#10622685C411yescharacteristic, complemented
18#10622650—21no—
19#10622648—21no—
20C4×#4324—21no—
21C4×#4323—21no—
22C42×Dic11C2211yescharacteristic
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25#10622448—21no—
26D11×C4⋊C8—21no—
27#10622341—22no—
28C8×D44—21no—
29#10622292—21no—
30C11×D4⋊C8—21no—
31C11×D4⋊C8—21no—
32#10622193—21no—
33C2×C11×#41—21no—
34C2×#4339D411yescharacteristic
35C2×C11×M16—21no—
36C11×C4⋊Q8C2×C411yescharacteristic
37C11×#127C2×C411yescharacteristic
38C11×#124—21no—
39C11×#121—21no—
40C11×#121—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C2×C42×C11C2311yescharacteristic
44C2×#4324—21no—
45C2×#4323—21no—
46C4×C22⋊D11—21no—
47C4×C22⋊D11—21no—
48#66979D411yescharacteristic
49C2×C4×Dic11—21no—
50C2×C4×Dic11—21no—
51C2×C4×Dic11—21no—
52C2×#4318D412yes—
53C2×C8×D11—22no—
54C4×D44C2×C411yescharacteristic
55C4×D44D411yescharacteristic
56#66925—21no—
57C42×D11—21no—
58C4×Dic22C2×C411yescharacteristic
59C4×Dic22D411yescharacteristic
60C11×C4⋊C8D411yescharacteristic
61C11×C4⋊C8D411yescharacteristic
62C11×C22⋊C8—21no—
63C11×#97—21no—
64C4×C8×C11—21no—
65C4×C8×C11—21no—
66#66901—44no—
67#66896—21no—
68#66896—21no—
69C22⋊(C11⋊C8)—21no—
70#66889—24no—
71(C2×D11)⋊C8—22no—
72#66879—22no—
73Dic11⋊C8—22no—
74#66874—21no—
75#66873—21no—
76#66872—21no—
77#66871—21no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)C2×C411yescharacteristic
81C4⋊(C11⋊C8)C2×C411yescharacteristic
82C4×C11⋊C8—21no—
83#8969—111nomaximal, Sylow
84C11×#41—42no—
85C11×#41—42no—
86C2×Q8×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C2×C22⋊D11—21no—
96C22×Dic11—41no—
97#4339—22no—
98#4339—41no—
99C2×D44C22⋊C411yescharacteristic
100C2×C4×D11—21no—
101C2×C4×D11—21no—
102C2×C4×D11—21no—
103C2×Dic22C22⋊C411yescharacteristic
104C11×M16—22no—
105C11×M16—41no—
106C2×C8×C11—21no—
107C2×C8×C11—21no—
108C2×C8×C11—41no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11C22×C411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C22⋊Dic11—21no—
118#4324—42no—
119#4323—42no—
120(C2×D11)⋊C4—21no—
121(C2×D11)⋊C4—21no—
122C4⋊Dic11C22⋊C411yescharacteristic
123C4⋊Dic11C22⋊C411yescharacteristic
124Dic11⋊C4—21no—
125Dic11⋊C4—21no—
126C4×Dic11—22no—
127C4×Dic11—22no—
128C4×Dic11—22no—
129C4×Dic11—21no—
130C4×Dic11—21no—
131C4×Dic11—21no—
132C4×Dic11—41no—
133C4×Dic11—41no—
134C4×Dic11—41no—
135#4318—42no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—22no—
139C8×D11—82no—
140#3106—111no—
141#2990—111no—
142#1962—111no—
143C4×#104—111no—
144#1484D1111yescharacteristic, complemented
145#1299—111no—
146#1276—111no—
147C23×C11—41no—
148C23×C11#12111yescharacteristic
149C22×D11—21no—
150Q8×C11—42no—
151D4×C11—42no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—41no—
155D4×C11—41no—
156D4×C11—82no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—41no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11C2×C22⋊C411yescharacteristic
167C2×C4×C11C4×D411yescharacteristic
168C2×C4×C11C4×D411yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12311yescharacteristic
172C22⋊D11—42no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179D44—21no—
180D44#10412yescomplemented
181C4×D11—42no—
182C4×D11—41no—
183C4×D11—41no—
184C4×D11—41no—
185C4×D11—41no—
186Dic22—21no—
187Dic22—21no—
188C8×C11—42no—
189C8×C11—41no—
190C8×C11—41no—
191C11⋊C8—41no—
192C11⋊C8—41no—
193C11⋊C8—42no—
194#532C2×D1111yescharacteristic
195C4×#41—111no—
196#482—221no—
197#477—111no—
198#476—111no—
199#460—111no—
200#459—111no—
201#449—221no—
202#446—221no—
203C4×SD16—221no—
204C4×D8—221no—
205#435—222no—
206C8×D4—221no—
207#432—221no—
208#431—111no—
209#431C2×D1111yescharacteristic
210#423—111no—
211C2×C4⋊C8—221no—
212C2×#104—221no—
213C2×#104—222no—
214C4×M16C2×D1111yescharacteristic
215C43—111no—
216#339—221no—
217D4⋊C8—21no—
218D4⋊C8—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11#38611yescharacteristic
226C2×D11—22no—
227C2×D11—41no—
228C2×D11—41no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—81no—
233C4×C11C2×#10411yescharacteristic
234C4×C11#42111yescharacteristic
235C4×C11#44311yescharacteristic
236C4×C11#44411yescharacteristic
237C4×C11#45311yescharacteristic
238C4×C11#45411yescharacteristic
239Dic11—44no—
240Dic11—41no—
241Dic11—41no—
242Dic11—41no—
243C2×#41—21no—
244C2×#41—111no—
245C2×SD16—221no—
246C2×D8—221no—
247C2×M16—21no—
248C2×M16—112no—
249C22×C8—222no—
250C4⋊Q8C4×D1111yescharacteristic
251#127C4×D1111yescharacteristic
252#124—21no—
253#121—21no—
254#121—21no—
255C4×Q8—111no—
256C4×Q8—111no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—111no—
260C4×D4—111no—
261C4×D4—221no—
262C4×D4—221no—
263#117—111no—
264#117—221no—
265C2×C42—221no—
266C2×C42—221no—
267C2×C42—221no—
268C2×C42—221no—
269C2×C42C22×D1111yescharacteristic
270#107—221no—
271#106—221no—
272C4⋊C8—111no—
273C4⋊C8—111no—
274C4⋊C8—222no—
275C4⋊C8—221no—
276C4⋊C8—221no—
277C4⋊C8C22⋊D1111yescharacteristic
278C4⋊C8C22⋊D1111yescharacteristic
279#104—224no—
280#104—444no—
281#103—221no—
282#102—221no—
283#102—221no—
284#102—221no—
285C22⋊C8—21no—
286C22⋊C8—222no—
287C22⋊C8—221no—
288#97—21no—
289#97—222no—
290C4×C8—21no—
291C4×C8—21no—
292C4×C8—221no—
293C2×C11—41no—
294C2×C11—161no—
295C2×C11#187111yescharacteristic
296C2×C11#187611yescharacteristic
297C2×C11#188311yescharacteristic
298D11—42no—
299#41—42no—
300#41—42no—
301#41—222no—
302#41—441no—
303C2×Q8—21no—
304C2×Q8—111no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—41no—
309C2×D4—111no—
310C2×D4—221no—
311C22×C4—41no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—441no—
316C22×C4#433911yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4D4×D1111yescharacteristic
319SD16—442no—
320D8—442no—
321M16—22no—
322M16—41no—
323M16—442no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—41no—
327C2×C8—221no—
328C2×C8—221no—
329C2×C8—222no—
330C2×C8—882no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—111no—
334C4⋊C4—111no—
335C4⋊C4—221no—
336C4⋊C4—221no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—221no—
340C22⋊C4—221no—
341C22⋊C4—221no—
342C42—222no—
343C42—222no—
344C42—222no—
345C42—221no—
346C42—221no—
347C42—221no—
348C42—441no—
349C42—441no—
350C42—441no—
351C42C2×C4×D1111yescharacteristic
352C42D4×D1111yescharacteristic
353C42#434111yescharacteristic
354C42C2×C22⋊D1111yescharacteristic
355C11#896911yescharacteristic, complemented, Sylow
356C23—41no—
357C23—221no—
358C23#6693711yescharacteristic
359Q8—42no—
360Q8—221no—
361Q8—221no—
362D4—42no—
363D4—41no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—82no—
368D4—112no—
369D4—221no—
370D4—442no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—442no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4C22⋊C4×D1111yescharacteristic
392C2×C4(C22⋊D11)⋊C411yescharacteristic
393C2×C4#6693611yescharacteristic
394C2×C4C4×C22⋊D1111yescharacteristic
395C2×C4#6699011yescharacteristic
396C2×C4#6699111yescharacteristic
397C8—42no—
398C8—41no—
399C8—41no—
400C8—442no—
401C8—441no—
402C8—441no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—222no—
410C22—441no—
411C22—441no—
412C22#1062256911yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—81no—
417C4—444no—
418C4—441no—
419C4—441no—
420C4—441no—
421C4D11×#10411yescharacteristic
422C4#1062243411yescharacteristic
423C4#1062275711yescharacteristic
424C4#1062275811yescharacteristic
425C4#1062281111yescharacteristic
426C4#1062281411yescharacteristic
427C2—41no—
428C2—161no—
429C2—442no—
430C2#1306891511yescharacteristic
431C2#1306894611yescharacteristic
432C2#1306898911yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1484C2
socleC22×C11#386
prime radical#13078670C2
cosocleC2×C42×C11C23
hypercenter#1484D11
hypocenterC11#8969
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1484

Complements

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

NH ≅ G/Ntype
2. #13077737C2semidirect
3. #13069445C2semidirect
4. C4×#66889C2semidirect
5. #13066506C2semidirect
6. #13066448C2semidirect
7. C11×#1484C2semidirect
14. #10622704C4semidirect
15. #10622697C4semidirect
16. #10622688C4semidirect
17. #10622685C4semidirect
144. #1484D11semidirect
180. D44#104semidirect
355. C11#8969semidirect

Maximal subgroups

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

subgroupindex
#130786702
#130777372
#130694452
C4×#668892
#130665062
#130664482
C11×#14842
#896911