Finite Group Databasebeta

← #14656145

Subgroups — #14656145

Order 2816.

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

normal subgroups only

This group has 658 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#13078076C211yesmaximal, characteristic
2#13073570C211yesmaximal, characteristic, complemented
3#13067297C211yesmaximal, characteristic, complemented
4#13067111C211yesmaximal, characteristic, complemented
5#13067006C211yesmaximal, characteristic, complemented
6#13066518C211yesmaximal, characteristic, complemented
7C11×#3206C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#67002—21no—
11C2×#66999—22no—
12C2×C4×D44C2211yescharacteristic
13C11×#492—21no—
14C11×#487—21no—
15C11×#461—22no—
16C11×#448—22no—
17C11×#431C2211yescharacteristic
18#10622845—21no—
19#10622696—21no—
20#10622685—21no—
21#10622670—22no—
22#10622605—22no—
23#10622601—21no—
24#10622589—21no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622184—22no—
29#10622175—22no—
30#10622121—22no—
31C2×C11×#41—21no—
32C22×Q8×C11D412yes—
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C2×C11×SD16—24no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×#127D411yescharacteristic
42C11×#124—21no—
43C11×#121—21no—
44C11×#121—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C42×C11C2311yescharacteristic
50#67002—42no—
51#67002—42no—
52#66999—48no—
53C2×#4325—22no—
54C2×#4323—22no—
55C2×(C2×D11)⋊C4—24no—
56C2×(C2×D11)⋊C4—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11D411yescharacteristic
59C2×Dic11⋊C4—24no—
60C2×C4×Dic11—21no—
61C2×#4318—21no—
62C4×D44—21no—
63C4×D44—21no—
64C4×D44—21no—
65C4×D44—21no—
66C11×C4⋊C8D412yes—
67C11×#103—24no—
68C11×C22⋊C8—21no—
69C4×C8×C11—21no—
70#66899—22no—
71#66896—22no—
72C11⋊#95D412yes—
73C22⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77C4×C11⋊C8—21no—
78#10240—111nomaximal, Sylow
79C23×D11—21no—
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C2×Q8×C11—21no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—44no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—41no—
92C22×C4×C11—22no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×Dic11—22no—
98C22×Dic11—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44SD1612yescomplemented
105C2×C4×D11—44no—
106C2×C4×D11—41no—
107C2×C4×D11—41no—
108C11×SD16—84no—
109C2×C8×C11—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122#4325—44no—
123#4323—44no—
124(C2×D11)⋊C4—48no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—24no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130Dic11⋊C4—48no—
131C4×Dic11—41no—
132C4×Dic11—41no—
133#4318—41no—
134#4318—41no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—41no—
137#3206D1111yescharacteristic, complemented
138#3036—111no—
139#2542—111no—
140#1548—111no—
141#1502—111no—
142#1478—111no—
143#1303—111no—
144C23×C11—41no—
145C23×C11#12011yescharacteristic
146C22×D11—22no—
147C22×D11—42no—
148C22×D11—42no—
149C22×D11—41no—
150C22×D11—41no—
151Q8×C11—41no—
152Q8×C11—41no—
153Q8×C11—44no—
154Q8×C11—82no—
155D4×C11—41no—
156D4×C11—41no—
157D4×C11—42no—
158D4×C11—81no—
159D4×C11—81no—
160D4×C11—81no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—44no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
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
178C2×Dic11—24no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—41no—
183D44—22no—
184D44—22no—
185D44—41no—
186D44—41no—
187C4×D11—82no—
188C4×D11—82no—
189C8×C11—42no—
190C11⋊C8—42no—
191C11⋊C8—81no—
192C2×AGL(1,ℤ/8)—221no—
193#532C2×D1111yescharacteristic
194C2×C4⋊Q8C2×D1111yescharacteristic
195C2×C22⋊Q8—222no—
196C2×C4×D4—111no—
197#492—21no—
198#487—21no—
199#463—222no—
200#461—22no—
201#461—221no—
202#459—221no—
203#448—22no—
204#431—111no—
205#431C2×D1111yescharacteristic
206#423—111no—
207#417—221no—
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—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11#39211yescharacteristic
221C22×C11#44811yescharacteristic
222C22×C11#44911yescharacteristic
223C2×D11—44no—
224C2×D11—42no—
225C2×D11—82no—
226C2×D11—81no—
227C2×D11—81no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—81no—
232C4×C11—82no—
233C4×C11#45011yescharacteristic
234C4×C11#45211yescharacteristic
235C4×C11#45312yes—
236C4×C11#46511yescharacteristic
237C4×C11#46811yescharacteristic
238Dic11—44no—
239Dic11—81no—
240C2×#41—21no—
241C22×Q8C22⋊D1112yes—
242C22×D4—111no—
243C23×C4—221no—
244AGL(1,ℤ/8)—442no—
245AGL(1,ℤ/8)—442no—
246C2×SD16—24no—
247C2×SD16—222no—
248C2×D8—222no—
249C2×M16—221no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
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—221no—
263C4×D4—221no—
264C4×D4—221no—
265C4×D4—221no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—224no—
271C2×C22⋊C4—224no—
272C2×C22⋊C4—221no—
273C2×C42—221no—
274C2×C42C22×D1111yescharacteristic
275C4⋊C8—112no—
276C4⋊C8—221no—
277C4⋊C8—221no—
278C4⋊C8C22⋊D1112yes—
279#103—24no—
280#103—222no—
281#102—222no—
282C22⋊C8—21no—
283C22⋊C8—221no—
284C4×C8—21no—
285C4×C8—221no—
286#95—112no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—161no—
290C2×C11#200011yescharacteristic
291C2×C11#200211yescharacteristic
292C2×C11#200911yescharacteristic
293D11—82no—
294C24—221no—
295#41—41no—
296#41—41no—
297#41—41no—
298#41—41no—
299C2×Q8—21no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—44no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—112no—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—221no—
311C2×D4—221no—
312C2×D4—221no—
313C22×C4—22no—
314C22×C4—41no—
315C22×C4—222no—
316C22×C4—221no—
317C22×C4—444no—
318C22×C4—441no—
319C22×C4—441no—
320C22×C4D4×D1111yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C22×C4C2×C22⋊D1111yescharacteristic
323SD16—84no—
324SD16—444no—
325D8—444no—
326M16—441no—
327M16—441no—
328C2×C8—22no—
329C2×C8—222no—
330C2×C8—441no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—224no—
338C4⋊C4—221no—
339C4⋊C4—221no—
340C4⋊C4—448no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—448no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C42—441no—
347C42—441no—
348C42D4×D1111yescharacteristic
349C42#434111yescharacteristic
350C42C2×C22⋊D1111yescharacteristic
351C42C2×C22⋊D1111yescharacteristic
352C11#1024011yescharacteristic, complemented, Sylow
353C23—41no—
354C23—222no—
355C23—442no—
356C23—442no—
357C23—441no—
358C23—441no—
359C23#6699011yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—44no—
363Q8—82no—
364D4—41no—
365D4—41no—
366D4—42no—
367D4—81no—
368D4—81no—
369D4—81no—
370D4—222no—
371D4—222no—
372D4—441no—
373D4—441no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—44no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—224no—
382C2×C4—442no—
383C2×C4—442no—
384C2×C4—442no—
385C2×C4—441no—
386C2×C4—882no—
387C2×C4—882no—
388C2×C4SD16×D1111yescharacteristic
389C2×C4#6696711yescharacteristic
390C2×C4#6696811yescharacteristic
391C2×C4#6696911yescharacteristic
392C2×C4#6699011yescharacteristic
393C2×C4#6699111yescharacteristic
394C2×C4#6699211yescharacteristic
395C2×C4#6699211yescharacteristic
396C2×C4#6699311yescharacteristic
397C2×C4#6700611yescharacteristic
398C8—42no—
399C8—442no—
400C8—881no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—444no—
407C22—442no—
408C22—882no—
409C22—881no—
410C22—881no—
411C22#1062278311yescharacteristic
412C22#1062278511yescharacteristic
413C22#1062283611yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—81no—
418C4—82no—
419C4—444no—
420C4—881no—
421C4#1062278211yescharacteristic
422C4#1062278411yescharacteristic
423C4#1062278611yescharacteristic
424C4#1062278711yescharacteristic
425C4#1062285412yes—
426C2—21no—
427C2—21no—
428C2—161no—
429C2—882no—
430C2#1306961611yescharacteristic
431C2#1306962911yescharacteristic
432C2#1306967411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3206C2
socleC22×C11#392
prime radical#13078076C2
hypercenter#3206D11
hypocenterC11#10240
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
2. #13073570C2semidirect
3. #13067297C2semidirect
4. #13067111C2semidirect
5. #13067006C2semidirect
6. #13066518C2semidirect
7. C11×#3206C2semidirect
104. C2×D44SD16semidirect
137. #3206D11semidirect
352. C11#10240semidirect

Maximal subgroups

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

subgroupindex
#130780762
#130735702
#130672972
#130671112
#130670062
#130665182
C11×#32062
#1024011