Finite Group Databasebeta

← #14656144

Subgroups — #14656144

Order 2816.

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

normal subgroups only

This group has 658 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
1#13079538C211yesmaximal, characteristic, complemented
2#13073569C211yesmaximal, characteristic, complemented
3#13067298C211yesmaximal, characteristic, complemented
4#13067111C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic, complemented
6#13066517C211yesmaximal, characteristic, complemented
7C11×#3036C211yesmaximal, characteristic
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66977—22no—
12C2×#66922C2211yescharacteristic
13C11×#463—22no—
14C11×#461—21no—
15C11×#459—21no—
16C11×#423C2211yescharacteristic
17C11×#417—21no—
18#10622834—21no—
19#10622706—21no—
20#10622689—21no—
21#10622653—22no—
22#10622632—22no—
23#10622589—21no—
24#10622562—22no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622175—22no—
29D4⋊(C11⋊C8)—22no—
30#10622119—22no—
31C2×C11×#41—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C22×Dic22D412yes—
35C11×AGL(1,ℤ/8)—42no—
36C11×AGL(1,ℤ/8)—42no—
37C2×C11×SD16—22no—
38C2×C11×D8—22no—
39C2×C11×M16—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×#127D411yescharacteristic
42C11×#124—21no—
43C11×#121—21no—
44C11×#121—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11—24no—
55C2×#4324—24no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59#66977—48no—
60C2×Dic11⋊C4—24no—
61C2×C4×Dic11—21no—
62#66922—21no—
63#66922—21no—
64#66922—21no—
65#66922—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×#103—22no—
69C11×#102—22no—
70C11⋊#95D412yes—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73#66874—24no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4×C11⋊C8—21no—
77C4×C11⋊C8—21no—
78#10240—111nomaximal, Sylow
79C24×C11—21no—
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C2×Q8×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—41no—
94C2×D4×C11SD1612yescomplemented
95C22×C4×C11—21no—
96C22×C4×C11—44no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×Dic11—22no—
104C22×Dic11—22no—
105C2×Dic22—22no—
106C2×Dic22—22no—
107C2×Dic22—44no—
108C11×SD16—44no—
109C11×D8—44no—
110C11×M16—41no—
111C11×M16—41no—
112C2×C8×C11—22no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125C22⋊Dic11—48no—
126#4324—84no—
127C4⋊Dic11—24no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130C4⋊Dic11—41no—
131C4⋊Dic11—41no—
132Dic11⋊C4—48no—
133C4×Dic11—41no—
134C4×Dic11—41no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—41no—
137#3206—111no—
138#3036D1111yescharacteristic
139#2542—111no—
140#1548—111no—
141#1502—111no—
142#1478—111no—
143#1303—111no—
144C23×C11—22no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11#12011yescharacteristic
151Q8×C11—41no—
152Q8×C11—41no—
153D4×C11—22no—
154D4×C11—22no—
155D4×C11—41no—
156D4×C11—41no—
157D4×C11—41no—
158D4×C11—42no—
159D4×C11—41no—
160D4×C11—81no—
161D4×C11—81no—
162D4×C11—81no—
163C2×C4×C11—22no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—82no—
169C2×C4×C11—82no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12711yescharacteristic
178C2×C4×C11C2×SD1611yescharacteristic
179C2×C4×C11#13511yescharacteristic
180C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C11#13711yescharacteristic
182C2×Dic11—24no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—44no—
186C2×Dic11—42no—
187Dic22—44no—
188Dic22—82no—
189C8×C11—42no—
190C11⋊C8—42no—
191C11⋊C8—81no—
192C2×AGL(1,ℤ/8)—21no—
193#532C2×D1111yescharacteristic
194C2×C4⋊Q8—111no—
195C2×C22⋊Q8—222no—
196C2×C4×D4C2×D1111yescharacteristic
197#492—221no—
198#487—221no—
199#463—22no—
200#461—21no—
201#461—222no—
202#459—21no—
203#448—222no—
204#431—111no—
205#431—111no—
206#423C2×D1111yescharacteristic
207#417—21no—
208#399—222no—
209#390—221no—
210#384—221no—
211C4×C4⋊C4—111no—
212#333—222no—
213#327—222no—
214D4⋊C8—222no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—44no—
218C22×C11—42no—
219C22×C11—82no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11#39211yescharacteristic
226C22×C11#44811yescharacteristic
227C22×C11#44911yescharacteristic
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—81no—
232C4×C11—81no—
233C4×C11#45011yescharacteristic
234C4×C11#45211yescharacteristic
235C4×C11#45312yes—
236C4×C11#46511yescharacteristic
237C4×C11#46811yescharacteristic
238Dic11—44no—
239Dic11—82no—
240C2×#41—21no—
241C22×Q8—112no—
242C22×D4C22⋊D1111yescharacteristic
243C23×C4—21no—
244AGL(1,ℤ/8)—42no—
245AGL(1,ℤ/8)—42no—
246C2×SD16—22no—
247C2×SD16—224no—
248C2×D8—22no—
249C2×M16—21no—
250C4⋊Q8—221no—
251C4⋊Q8—221no—
252C4⋊Q8—221no—
253C4⋊Q8—221no—
254C4⋊Q8C22⋊D1111yescharacteristic
255#127C22⋊D1111yescharacteristic
256#124—21no—
257C22⋊Q8—448no—
258#121—21no—
259#121—21no—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—224no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4C22⋊D1111yescharacteristic
271C2×C22⋊C4—21no—
272C2×C22⋊C4—224no—
273C2×C42—221no—
274C2×C42C22×D1111yescharacteristic
275C4⋊C8—21no—
276C4⋊C8—112no—
277C4⋊C8—221no—
278C4⋊C8C22⋊D1112yes—
279#103—22no—
280#103—224no—
281#102—22no—
282C22⋊C8—221no—
283C22⋊C8—221no—
284C4×C8—221no—
285C4×C8—221no—
286#95—112no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—82no—
290C2×C11—161no—
291C2×C11#200011yescharacteristic
292C2×C11#200211yescharacteristic
293C2×C11#200911yescharacteristic
294C24—21no—
295#41—41no—
296#41—41no—
297#41—41no—
298#41—41no—
299C2×Q8—21no—
300C2×Q8—222no—
301C2×Q8—222no—
302C2×Q8—444no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—41no—
312C2×D4#432412yescomplemented
313C22×C4—21no—
314C22×C4—44no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—222no—
319C22×C4—222no—
320C22×C4D4×D1111yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C22×C4C2×C22⋊D1111yescharacteristic
323SD16—44no—
324SD16—884no—
325D8—44no—
326M16—41no—
327M16—41no—
328C2×C8—22no—
329C2×C8—222no—
330C2×C8—441no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—224no—
336C4⋊C4—448no—
337C4⋊C4—441no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C4⋊C4—441no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—448no—
346C42—441no—
347C42—441no—
348C42D4×D1111yescharacteristic
349C42#434111yescharacteristic
350C42C2×C22⋊D1111yescharacteristic
351C42C2×C22⋊D1111yescharacteristic
352C11#1024011yescharacteristic, complemented, Sylow
353C23—22no—
354C23—42no—
355C23—42no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23#6699011yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—444no—
363Q8—882no—
364D4—22no—
365D4—22no—
366D4—42no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—41no—
371D4—81no—
372D4—81no—
373D4—81no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—224no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4—444no—
387C2×C4—442no—
388C2×C4#6698511yescharacteristic
389C2×C4C2×#432411yescharacteristic
390C2×C4#6699011yescharacteristic
391C2×C4#6699111yescharacteristic
392C2×C4#6699211yescharacteristic
393C2×C4#6699211yescharacteristic
394C2×C4#6699311yescharacteristic
395C2×C4#6700311yescharacteristic
396C2×C4#6700411yescharacteristic
397C2×C4#6700611yescharacteristic
398C8—42no—
399C8—442no—
400C8—881no—
401C22—21no—
402C22—21no—
403C22—44no—
404C22—42no—
405C22—82no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22#1062265011yescharacteristic
412C22#1062265311yescharacteristic
413C22#1062283611yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—81no—
418C4—81no—
419C4—444no—
420C4—882no—
421C4#1062265411yescharacteristic
422C4#1062265511yescharacteristic
423C4#1062281112yes—
424C4#1062283111yescharacteristic
425C4#1062285211yescharacteristic
426C2—21no—
427C2—21no—
428C2—82no—
429C2—161no—
430C2#1306961911yescharacteristic
431C2#1306962811yescharacteristic
432C2#1306967311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3036C2
socleC22×C11#392
hypercenter#3036D11
hypocenterC11#10240
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13079538C2semidirect
2. #13073569C2semidirect
3. #13067298C2semidirect
4. #13067111C2semidirect
5. #13067007C2semidirect
6. #13066517C2semidirect
94. C2×D4×C11SD16semidirect
312. C2×D4#4324semidirect
352. C11#10240semidirect

Maximal subgroups

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

subgroupindex
#130795382
#130735692
#130672982
#130671112
#130670072
#130665172
C11×#30362
#1024011