Finite Group Databasebeta

← #14656187

Subgroups — #14656187

Order 2816.

740 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 103 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#13078409C211yesmaximal, characteristic, complemented
2#13073563C211yesmaximal, characteristic
3#13067284C211yesmaximal, characteristic, complemented
4#13067115C211yesmaximal, characteristic, complemented
5#13067006C211yesmaximal, characteristic, complemented
6#13066518C211yesmaximal, characteristic, complemented
7C11×#3208C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×#66993—21no—
11C2×#66991—22no—
12C2×C4×D44C2211yescharacteristic
13C11×#492—21no—
14C11×#486—21no—
15C11×#460—22no—
16C11×#450—22no—
17C11×#431C2211yescharacteristic
18#10622836—22no—
19#10622834—21no—
20#10622700—21no—
21#10622697—21no—
22#10622679—22no—
23#10622614—21no—
24#10622608—21no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622182—22no—
29#10622176—22no—
30#10622121—22no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D412yes—
34C22×C22⋊D11—24no—
35C22×D44D411yescharacteristic
36C22×C4×D11—21no—
37C2×C11×SD16—24no—
38C11×C4⋊Q8D411yescharacteristic, complemented
39C11×C4⋊Q8D411yescharacteristic, complemented
40C11×#127—21no—
41C11×#127—21no—
42C11×#127—21no—
43C11×#127—21no—
44C11×#125—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C11×#117—21no—
50C2×C42×C11C2311yescharacteristic
51C2×C22⋊Dic11—24no—
52#66993—42no—
53#66993—42no—
54#66991—48no—
55C2×(C2×D11)⋊C4—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11D411yescharacteristic
58C2×C4×Dic11—21no—
59C2×#4318—21no—
60C4×D44—21no—
61C4×D44—21no—
62C4×D44—21no—
63C4×D44—21no—
64C11×C4⋊C8D412yescomplemented
65C11×#102—24no—
66C11×C22⋊C8—21no—
67C4×C8×C11—21no—
68C11⋊#95D412yes—
69C22⋊(C11⋊C8)—21no—
70#66873—22no—
71#66873—22no—
72#66872—22no—
73#66871—22no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yescomplemented
77C4×C11⋊C8—21no—
78#10246—111nomaximal, Sylow
79C24×C11—22no—
80C23×D11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×D4×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—44no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—82no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C2×C22⋊D11—48no—
99C2×C22⋊D11—48no—
100C2×C22⋊D11—84no—
101C22×Dic11—22no—
102C22×Dic11—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44SD1612yescomplemented
109C2×C4×D11—44no—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C11×SD16—84no—
113C2×C8×C11—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11—41no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126C22⋊Dic11—48no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129C4⋊Dic11—24no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C4×Dic11—41no—
133C4×Dic11—41no—
134#4318—41no—
135#4318—41no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—41no—
138#3208D1111yescharacteristic, complemented
139#3077—111no—
140#2541—111no—
141#1545—111no—
142#1503—111no—
143#1478—111no—
144#1303—111no—
145C23×C11—44no—
146C23×C11—44no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11#12011yescharacteristic
151C22×D11—22no—
152C22×D11—42no—
153C22×D11—42no—
154C22×D11—41no—
155C22×D11—41no—
156Q8×C11—42no—
157Q8×C11—81no—
158D4×C11—44no—
159D4×C11—82no—
160D4×C11—82no—
161D4×C11—82no—
162D4×C11—81no—
163D4×C11—81no—
164D4×C11—81no—
165D4×C11—81no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12711yescharacteristic
176C2×C4×C11C2×SD1611yescharacteristic
177C2×C4×C11#13511yescharacteristic
178C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C11#13711yescharacteristic
180C22⋊D11—816no—
181C2×Dic11—24no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—41no—
186D44—22no—
187D44—22no—
188D44—41no—
189D44—41no—
190C4×D11—82no—
191C4×D11—82no—
192C8×C11—42no—
193C11⋊C8—42no—
194C11⋊C8—81no—
195#533C2×D1111yescharacteristic
196C2×#127—221no—
197C2×#127C2×D1111yescharacteristic
198C2×#121—222no—
199C2×C4×D4—111no—
200#492—21no—
201#486—21no—
202#478—222no—
203#476—221no—
204#474—221no—
205#460—22no—
206#450—22no—
207#431—111no—
208#431C2×D1111yescharacteristic
209#428—221no—
210#423—111no—
211#418—221no—
212#392—222no—
213#390—221no—
214C4×C4⋊C4—111no—
215#331—222no—
216#328—222no—
217D4⋊C8—222no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—84no—
221C22×C11—84no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11—82no—
225C22×C11#39211yescharacteristic
226C22×C11#45011yescharacteristic
227C22×C11#45211yescharacteristic
228C2×D11—44no—
229C2×D11—42no—
230C2×D11—82no—
231C2×D11—81no—
232C2×D11—81no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—81no—
237C4×C11—81no—
238C4×C11#44811yescharacteristic
239C4×C11#44911yescharacteristic
240C4×C11#45312yes—
241C4×C11#46511yescharacteristic
242C4×C11#46811yescharacteristic
243Dic11—44no—
244Dic11—81no—
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—111no—
248C22×D4—224no—
249C22×D4C22⋊D1112yes—
250C23×C4—221no—
251C2×SD16—24no—
252C2×M16—221no—
253C4⋊Q8C22⋊D1111yescharacteristic, complemented
254C4⋊Q8C22⋊D1111yescharacteristic, complemented
255#127—21no—
256#127—21no—
257#127—21no—
258#127—21no—
259#127—442no—
260#127—442no—
261#125—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264#121—448no—
265C4×Q8—21no—
266C4×Q8—21no—
267C4×D4—221no—
268C4×D4—221no—
269C4×D4—221no—
270C4×D4—221no—
271#117—21no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4—221no—
274C2×C22⋊C4—224no—
275C2×C22⋊C4—221no—
276C2×C42—221no—
277C2×C42C22×D1111yescharacteristic
278#107—222no—
279#106—222no—
280C4⋊C8—112no—
281C4⋊C8—221no—
282C4⋊C8—221no—
283C4⋊C8C22⋊D1112yescomplemented
284#102—24no—
285#102—222no—
286#102—222no—
287C22⋊C8—21no—
288C22⋊C8—221no—
289C4×C8—21no—
290C4×C8—221no—
291#95—112no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—162no—
295C2×C11#200011yescharacteristic
296C2×C11#200211yescharacteristic
297C2×C11#200811yescharacteristic
298D11—82no—
299C24—22no—
300C24—221no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—44no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—82no—
315C2×D4—112no—
316C2×D4—221no—
317C2×D4—221no—
318C2×D4—221no—
319C2×D4—221no—
320C2×D4—221no—
321C2×D4—448no—
322C2×D4—448no—
323C2×D4—884no—
324C22×C4—222no—
325C22×C4—221no—
326C22×C4—444no—
327C22×C4—441no—
328C22×C4—441no—
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332SD16—84no—
333M16—441no—
334M16—441no—
335C2×C8—22no—
336C2×C8—222no—
337C2×C8—441no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—224no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C22⋊C4—41no—
348C22⋊C4—448no—
349C22⋊C4—441no—
350C22⋊C4—441no—
351C42—41no—
352C42—441no—
353C42—441no—
354C42D4×D1111yescharacteristic
355C42#434111yescharacteristic
356C42C2×C22⋊D1111yescharacteristic
357C42C2×C22⋊D1111yescharacteristic
358C11#1024611yescharacteristic, complemented, Sylow
359C23—44no—
360C23—44no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—222no—
365C23—442no—
366C23—442no—
367C23—441no—
368C23—441no—
369C23#6699011yescharacteristic
370Q8—42no—
371Q8—81no—
372D4—44no—
373D4—82no—
374D4—82no—
375D4—82no—
376D4—81no—
377D4—81no—
378D4—81no—
379D4—81no—
380D4—222no—
381D4—222no—
382D4—441no—
383D4—441no—
384D4—8816no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—224no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—441no—
394C2×C4—882no—
395C2×C4—882no—
396C2×C4SD16×D1111yescharacteristic
397C2×C4#6696711yescharacteristic
398C2×C4#6696811yescharacteristic
399C2×C4#6696911yescharacteristic
400C2×C4#6699011yescharacteristic
401C2×C4#6699111yescharacteristic
402C2×C4#6699211yescharacteristic
403C2×C4#6699211yescharacteristic
404C2×C4#6699311yescharacteristic
405C2×C4#6700611yescharacteristic
406C8—42no—
407C8—442no—
408C8—881no—
409C22—21no—
410C22—21no—
411C22—84no—
412C22—84no—
413C22—82no—
414C22—82no—
415C22—82no—
416C22—444no—
417C22—442no—
418C22—882no—
419C22—881no—
420C22—881no—
421C22#1062278211yescharacteristic
422C22#1062278611yescharacteristic
423C22#1062283611yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—81no—
428C4—81no—
429C4—444no—
430C4—881no—
431C4#1062278311yescharacteristic
432C4#1062278411yescharacteristic
433C4#1062278511yescharacteristic
434C4#1062278711yescharacteristic
435C4#1062285412yes—
436C2—21no—
437C2—21no—
438C2—162no—
439C2—882no—
440C2#1306961611yescharacteristic
441C2#1306962911yescharacteristic
442C2#1306966711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3208C2
socleC22×C11#392
prime radical#13073563C2
hypercenter#3208D11
hypocenterC11#10246
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
1. #13078409C2semidirect
3. #13067284C2semidirect
4. #13067115C2semidirect
5. #13067006C2semidirect
6. #13066518C2semidirect
7. C11×#3208C2semidirect
38. C11×C4⋊Q8D4semidirect
39. C11×C4⋊Q8D4semidirect
64. C11×C4⋊C8D4semidirect
76. C4⋊(C11⋊C8)D4semidirect
108. C2×D44SD16semidirect
138. #3208D11semidirect
253. C4⋊Q8C22⋊D11semidirect
254. C4⋊Q8C22⋊D11semidirect
283. C4⋊C8C22⋊D11semidirect
358. C11#10246semidirect

Maximal subgroups

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

subgroupindex
#130784092
#130735632
#130672842
#130671152
#130670062
#130665182
C11×#32082
#1024611