Finite Group Databasebeta

← #14656147

Subgroups — #14656147

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#13079541C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic
3#13067297C211yesmaximal, characteristic, complemented
4#13067110C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#2542C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C22⋊Q8—22no—
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66985—21no—
12#10623008C2211yescharacteristic
13C11×#399—22no—
14C11×#390—21no—
15C11×#384—21no—
16C4×C11×C4⋊C4C2211yescharacteristic
17#10622840—22no—
18#10622698—21no—
19#10622696—22no—
20#10622694—21no—
21#10622632—21no—
22#10622629—22no—
23#10622628—21no—
24#10622579—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622184—22no—
29D4⋊(C11⋊C8)—22no—
30#10622089—22no—
31C22×Q8×C11D412yes—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C2×#4339—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C22⋊Q8—48no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—24no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—24no—
50C2×C11×C22⋊C4—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4325—24no—
54C2×#4324—22no—
55#66985—42no—
56#66985—42no—
57C2×#4323—22no—
58#66983—21no—
59#66983—21no—
60C2×#4318—21no—
61#66928—21no—
62#66927D411yescharacteristic
63C4×D44—21no—
64C4×D44—21no—
65#66922D411yescharacteristic
66C11×#95D412yes—
67#66899—24no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66874—22no—
71#66873—22no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75C4⋊(C11⋊C8)D412yes—
76C4×C11⋊C8—21no—
77C4×C11⋊C8—21no—
78#10240—111nomaximal, Sylow
79C24×C11—21no—
80C2×Q8×C11—22no—
81C2×Q8×C11—22no—
82C2×Q8×C11—44no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11SD1612yescomplemented
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—44no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C2×C22⋊D11—41no—
99#4339—41no—
100#4339—41no—
101#4339—41no—
102#4339—41no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—21no—
106C2×C4×D11—41no—
107C2×Dic22—21no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—48no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—48no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11—41no—
120C42×C11—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125#4325—84no—
126#4324—44no—
127#4323—44no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132#4318—41no—
133#4318—41no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—41no—
137#3206—111no—
138#3036—111no—
139#2542D1111yescharacteristic, complemented
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#12011yescharacteristic
150C22×D11—41no—
151Q8×C11—44no—
152Q8×C11—82no—
153D4×C11—22no—
154D4×C11—22no—
155D4×C11—41no—
156D4×C11—41no—
157C2×C4×C11—22no—
158C2×C4×C11—24no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—44no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—82no—
167C2×C4×C11—82no—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12711yescharacteristic
174C2×C4×C11C2×SD1611yescharacteristic
175C2×C4×C11#13511yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C11#13711yescharacteristic
178C22⋊D11—81no—
179C22⋊D11—81no—
180C2×Dic11—41no—
181D44—41no—
182D44—41no—
183D44—42no—
184D44—81no—
185C4×D11—81no—
186C4×D11—81no—
187Dic22—41no—
188Dic22—41no—
189C11⋊C8—42no—
190C11⋊C8—42no—
191C11⋊C8—81no—
192C2×AGL(1,ℤ/8)—221no—
193#532—111no—
194C2×C4⋊Q8C2×D1111yescharacteristic
195C2×C22⋊Q8—22no—
196C2×C4×D4C2×D1111yescharacteristic
197#492—221no—
198#487—221no—
199#463—222no—
200#461—222no—
201#461—221no—
202#459—221no—
203#448—222no—
204#431—111no—
205#431—111no—
206#423—111no—
207#417—221no—
208#399—22no—
209#390—21no—
210#384—21no—
211C4×C4⋊C4C2×D1111yescharacteristic
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#39211yescharacteristic
223C22×C11#44811yescharacteristic
224C22×C11#44911yescharacteristic
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—44no—
232C4×C11—81no—
233C4×C11—82no—
234C4×C11#45011yescharacteristic
235C4×C11#45211yescharacteristic
236C4×C11#45312yes—
237C4×C11#46511yescharacteristic
238C4×C11#46811yescharacteristic
239Dic11—81no—
240C2×#41—221no—
241C22×Q8C22⋊D1112yes—
242C22×D4C22⋊D1111yescharacteristic
243C23×C4—21no—
244AGL(1,ℤ/8)—442no—
245AGL(1,ℤ/8)—442no—
246C2×SD16—222no—
247C2×SD16—224no—
248C2×D8—222no—
249C2×M16—221no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—111no—
255#127—111no—
256#124—221no—
257C22⋊Q8—48no—
258#121—221no—
259#121—221no—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—221no—
265C4×D4—221no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4C22⋊D1111yescharacteristic
271C2×C22⋊C4—24no—
272C2×C22⋊C4—21no—
273C2×C42—21no—
274C2×C42C22×D1111yescharacteristic
275C4⋊C8—112no—
276C4⋊C8—112no—
277C4⋊C8—221no—
278C4⋊C8—221no—
279#103—222no—
280#103—224no—
281#102—222no—
282C22⋊C8—221no—
283C22⋊C8—221no—
284C4×C8—221no—
285C4×C8—221no—
286#95C22⋊D1112yes—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—82no—
290C2×C11#200011yescharacteristic
291C2×C11#200211yescharacteristic
292C2×C11#200911yescharacteristic
293D11—161no—
294C24—21no—
295#41—441no—
296#41—441no—
297#41—441no—
298#41—441no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—44no—
302C2×Q8—221no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—221no—
311C2×D4—441no—
312C2×D4#432512yescomplemented
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—44no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—441no—
320C22×C4C2×C22⋊D1111yescharacteristic
321C22×C4C2×C22⋊D1111yescharacteristic
322C22×C4C2×C22⋊D1111yescharacteristic
323SD16—444no—
324SD16—884no—
325D8—444no—
326M16—441no—
327M16—441no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—441no—
331C4⋊C4—24no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—48no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—221no—
340C4⋊C4—221no—
341C22⋊C4—48no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C42—41no—
347C42—41no—
348C42D4×D1111yescharacteristic
349C42D4×D1111yescharacteristic
350C42D4×D1111yescharacteristic
351C42#434111yescharacteristic
352C11#1024011yescharacteristic, complemented, Sylow
353C23—22no—
354C23—42no—
355C23—42no—
356C23—41no—
357C23—41no—
358C23—441no—
359C23#6700611yescharacteristic
360Q8—44no—
361Q8—82no—
362Q8—441no—
363Q8—441no—
364D4—22no—
365D4—22no—
366D4—41no—
367D4—41no—
368D4—441no—
369D4—441no—
370D4—442no—
371D4—881no—
372D4—881no—
373D4—881no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—44no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4—441no—
386C2×C4—881no—
387C2×C4—881no—
388C2×C4#6699011yescharacteristic
389C2×C4#6699011yescharacteristic
390C2×C4#6699111yescharacteristic
391C2×C4#6699211yescharacteristic
392C2×C4#6699211yescharacteristic
393C2×C4#6699311yescharacteristic
394C2×C4C2×#432511yescharacteristic
395C2×C4#6699511yescharacteristic
396C2×C4#6700211yescharacteristic
397C2×C4#6700311yescharacteristic
398C8—442no—
399C8—442no—
400C8—881no—
401C22—21no—
402C22—21no—
403C22—44no—
404C22—42no—
405C22—82no—
406C22—81no—
407C22—81no—
408C22—881no—
409C22—881no—
410C22—881no—
411C22#1062283611yescharacteristic
412C22#1062284011yescharacteristic
413C22#1062285111yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—44no—
418C4—81no—
419C4—82no—
420C4—881no—
421C4#1062265911yescharacteristic
422C4#1062266011yescharacteristic
423C4#1062266111yescharacteristic
424C4#1062266211yescharacteristic
425C4#1062269012yes—
426C2—21no—
427C2—21no—
428C2—82no—
429C2—1761no—
430C2#1306961711yescharacteristic
431C2#1306963111yescharacteristic
432C2#1306967611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2542C2
socleC22×C11#392
prime radical#13078080C2
hypercenter#2542D11
hypocenterC11#10240
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2542

Complements

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

NH ≅ G/Ntype
1. #13079541C2semidirect
3. #13067297C2semidirect
4. #13067110C2semidirect
5. #13067007C2semidirect
6. #13066519C2semidirect
7. C11×#2542C2semidirect
88. C2×D4×C11SD16semidirect
139. #2542D11semidirect
312. C2×D4#4325semidirect
352. C11#10240semidirect

Maximal subgroups

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

subgroupindex
#130795412
#130780802
#130672972
#130671102
#130670072
#130665192
C11×#25422
#1024011