Finite Group Databasebeta

← #14648711

Subgroups — #14648711

Order 2816.

578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C2×#10622328C211yesmaximal, characteristic
2#13071787C211yesmaximal, characteristic
3#13069589C211yesmaximal, characteristic, complemented
4#13069588C211yesmaximal, characteristic, complemented
5C2×#10622102C211yesmaximal, characteristic
6#13066498C211yesmaximal, characteristic, complemented
7C11×#1295C211yesmaximal, characteristic, complemented
8C22×Dic44—21no—
9C22×#4314—21no—
10C2×#66928C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C2×C11×#97C2211yescharacteristic
13C2×C11×#97C2211yescharacteristic
14C11×#382C2211yescharacteristic
15#10622603—21no—
16#10622602—21no—
17#10622549C2211yescharacteristic
18C2×#66867C2211yescharacteristic
19#10622328—22no—
20#10622328C414yescomplemented
21#10622283—21no—
22#10622281—21no—
23#10622278—21no—
24#10622259—21no—
25#10622189—21no—
26#10622189—21no—
27#10622167—21no—
28#10622167—21no—
29#10622102—22no—
30C22×D44D411yescharacteristic
31C22×C4×D11—21no—
32C22×Dic22—21no—
33C22×Dic22D411yescharacteristic
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—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⋊Dic11D411yescharacteristic
47C2×C4⋊Dic11D411yescharacteristic
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50C22×C11⋊C8—21no—
51C2×Dic44—24no—
52C2×Dic44—42no—
53C2×Dic44—42no—
54C2×#4314—24no—
55C2×#4314—42no—
56C2×#4314—42no—
57#66928—21no—
58#66928—21no—
59#66928C2×C412yes—
60#66928D412yes—
61#66922—21no—
62#66922—21no—
63#66922—21no—
64#66922C2×C412yescomplemented
65C11×#97—21no—
66C11×#97—21no—
67C11×#97—21no—
68C11×#97C2×C412yescomplemented
69C11×#95—21no—
70C11×#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75#66867—21no—
76#66867—21no—
77#9003—111nomaximal, Sylow
78C23×D11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—41no—
88C2×D44—21no—
89C2×D44—41no—
90C2×D44—41no—
91C2×D44C22⋊C412yes—
92C2×C4×D11—81no—
93C2×C4×D11—81no—
94C2×C4×D11—81no—
95C2×Dic22—22no—
96C2×Dic22—21no—
97C2×Dic22—41no—
98C2×Dic22—41no—
99C2×Dic22—41no—
100C2×Dic22—41no—
101C2×Dic22—41no—
102C2×Dic22—41no—
103C2×Dic22—41no—
104C2×Dic22C22⋊C412yes—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—41no—
110C2×C8×C11—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C42×C11C22×C411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11#4111yescharacteristic
117(C2×D11)⋊C4—22no—
118(C2×D11)⋊C4—22no—
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—81no—
122(C2×D11)⋊C4—81no—
123(C2×D11)⋊C4—81no—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130Dic11⋊C4—81no—
131C4×Dic11—81no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135Dic44—48no—
136#4314—48no—
137C2×#497—111no—
138#2379—111no—
139#1993—111no—
140#1993—111no—
141C2×#329—111no—
142#1295—111no—
143#1295D1111yescharacteristic, complemented
144C23×C11#12011yescharacteristic
145C22×D11—22no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—41no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11C2×C22⋊C411yescharacteristic
165C2×C4×C11C4×D411yescharacteristic
166C2×C4×C11C4×D411yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12311yescharacteristic
170C2×Dic11—22no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—42no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—81no—
181C2×Dic11—81no—
182D44—42no—
183D44—81no—
184C4×D11—84no—
185Dic22—42no—
186Dic22—42no—
187Dic22—42no—
188Dic22—81no—
189Dic22—81no—
190Dic22—81no—
191C8×C11—24no—
192C8×C11—42no—
193C11⋊C8—42no—
194C22×Q16—221no—
195C22×SD16—221no—
196C2×C4⋊Q8—111no—
197C2×#124—111no—
198#497—114no—
199#497—222no—
200C2×#97—111no—
201C2×#97C2×D1111yescharacteristic
202C2×#97C2×D1111yescharacteristic
203#391—221no—
204#388—221no—
205#388—221no—
206#386—221no—
207#385—221no—
208#385—221no—
209#382—111no—
210#382C2×D1111yescharacteristic
211#340—221no—
212#340—221no—
213#340—221no—
214#340—221no—
215#329—222no—
216C22×C11#38611yescharacteristic
217C22×C11#45311yescharacteristic
218C22×C11#45311yescharacteristic
219C22×C11#45511yescharacteristic
220C22×C11#45511yescharacteristic
221C22×C11#45611yescharacteristic
222C22×C11#45611yescharacteristic
223C2×D11—42no—
224C2×D11—42no—
225C2×D11—42no—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—81no—
237C4×C11—81no—
238Dic11—42no—
239Dic11—82no—
240Dic11—81no—
241Dic11—81no—
242C22×Q8—111no—
243C22×Q8—221no—
244C22×D4—111no—
245C23×C4—221no—
246C2×Q16—224no—
247C2×Q16—442no—
248C2×Q16—442no—
249C2×SD16—224no—
250C2×SD16—442no—
251C2×SD16—442no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—221no—
255C4⋊Q8—112no—
256C4⋊Q8—221no—
257C4⋊Q8—221no—
258C4⋊Q8—221no—
259#124—112no—
260#124—112no—
261#124—221no—
262#124—221no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4D4411yescharacteristic
269C2×C4⋊C4D4411yescharacteristic
270C2×C22⋊C4—221no—
271C2×C22⋊C4—221no—
272C2×C22⋊C4—221no—
273C2×C22⋊C4—221no—
274C2×C22⋊C4—221no—
275C2×C42—221no—
276C2×C42C22×D1111yescharacteristic
277#97—21no—
278#97—21no—
279#97—21no—
280#97—221no—
281#97—221no—
282#97C4×D1112yescomplemented
283#95—21no—
284#95—21no—
285#95—221no—
286#95—221no—
287#95—221no—
288#95—221no—
289C2×C11#165911yescharacteristic
290C2×C11#166011yescharacteristic
291C2×C11#166111yescharacteristic
292C2×C11#166111yescharacteristic
293C2×C11#188211yescharacteristic
294C2×C11#188211yescharacteristic
295C2×C11#188711yescharacteristic
296D11—82no—
297C24—221no—
298C2×Q8—112no—
299C2×Q8—221no—
300C2×Q8—222no—
301C2×Q8—441no—
302C2×Q8—441no—
303C2×Q8—441no—
304C2×Q8—441no—
305C2×Q8—441no—
306C2×Q8—441no—
307C2×Q8—441no—
308C2×D4—112no—
309C2×D4—221no—
310C2×D4—441no—
311C2×D4—441no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—441no—
318C22×C4—881no—
319C22×C4—881no—
320C22×C4—881no—
321C22×C4C2×D4411yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C22×C4D4×D1111yescharacteristic
324Q16—448no—
325SD16—448no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—222no—
333C2×C8—441no—
334C2×C8—441no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—222no—
338C4⋊C4—222no—
339C4⋊C4—441no—
340C4⋊C4—441no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C4⋊C4—881no—
344C22⋊C4—222no—
345C22⋊C4—222no—
346C22⋊C4—222no—
347C22⋊C4—222no—
348C22⋊C4—881no—
349C22⋊C4—881no—
350C22⋊C4—881no—
351C42—881no—
352C42C2×C4×D1111yescharacteristic
353C42#433911yescharacteristic
354C42D4×D1111yescharacteristic
355C42#434311yescharacteristic
356C11#900311yescharacteristic, complemented, Sylow
357C23—222no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23—441no—
364C23#6693511yescharacteristic
365Q8—442no—
366Q8—442no—
367Q8—442no—
368Q8—881no—
369Q8—881no—
370Q8—881no—
371D4—442no—
372D4—881no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—222no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—442no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—884no—
396C2×C4—881no—
397C2×C4—881no—
398C2×C4C4×D4411yescharacteristic
399C2×C4C22⋊C4×D1111yescharacteristic
400C2×C4#6693711yescharacteristic
401C2×C4#6694611yescharacteristic
402C2×C4#6694711yescharacteristic
403C2×C4#6694811yescharacteristic
404C8—24no—
405C8—42no—
406C8—442no—
407C22—442no—
408C22—442no—
409C22—442no—
410C22—881no—
411C22—881no—
412C22—881no—
413C22—881no—
414C22#1062227811yescharacteristic
415C22#1062235911yescharacteristic
416C22#1062236511yescharacteristic
417C22#1062243511yescharacteristic
418C22#1062243511yescharacteristic
419C22#1062243811yescharacteristic
420C22#1062243911yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—81no—
428C4—81no—
429C4—442no—
430C4—881no—
431C4—881no—
432C4—882no—
433C2—882no—
434C2#1306792411yescharacteristic
435C2#1306792911yescharacteristic
436C2#1306793511yescharacteristic
437C2#1306793611yescharacteristic
438C2#1306898411yescharacteristic
439C2#1306898611yescharacteristic
440C2#1306901311yescharacteristic
subgroupG/H
centerC23#66935
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socleC23×C11#120
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1295D11
hypocenterC11#9003
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
3. #13069589C2semidirect
4. #13069588C2semidirect
6. #13066498C2semidirect
7. C11×#1295C2semidirect
20. #10622328C4semidirect
64. #66922C2×C4semidirect
68. C11×#97C2×C4semidirect
143. #1295D11semidirect
282. #97C4×D11semidirect
356. C11#9003semidirect

Maximal subgroups

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

subgroupindex
C2×#106223282
#130717872
#130695892
#130695882
C2×#106221022
#130664982
C11×#12952
#900311