Finite Group Databasebeta

← #14655812

Subgroups — #14655812

Order 2816.

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

normal subgroups only

This group has 550 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
1C2×#10622700C211yesmaximal, characteristic, complemented
2#13078076C211yesmaximal, characteristic
3#13067297C211yesmaximal, characteristic, complemented
4#13067015C211yesmaximal, characteristic, complemented
5#13066936C211yesmaximal, characteristic, complemented
6#13066512C211yesmaximal, characteristic, complemented
7C11×#3227C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#67002—21no—
11C2×C4×D44C2211yescharacteristic
12C11×#498—21no—
13C11×#486—21no—
14C11×#481—22no—
15C11×#476—22no—
16C11×#431C2211yescharacteristic
17#10622845—21no—
18#10622700—22no—
19#10622700—22no—
20#10622696—21no—
21#10622685—21no—
22#10622670—22no—
23C2×#66873—21no—
24C2×#66871—21no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28#10622184—22no—
29D4⋊(C11⋊C8)—22no—
30#10622106—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D412yes—
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49#67002—42no—
50#67002—42no—
51C2×#4325—22no—
52C2×#4323—22no—
53C2×(C2×D11)⋊C4—21no—
54C2×C4⋊Dic11D411yescharacteristic
55C2×#4318—21no—
56C22×C11⋊C8—21no—
57C4×D44—21no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44—21no—
61C11×#106—24no—
62C11×C4⋊C8—21no—
63C11×#102—24no—
64C11×C22⋊C8D412yes—
65C4×C8×C11—21no—
66#66899—22no—
67#66896—22no—
68C22⋊(C11⋊C8)—21no—
69#66873—24no—
70#66871—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75C4⋊(C11⋊C8)D412yes—
76C4×C11⋊C8—21no—
77#10188—111nomaximal, Sylow
78C23×D11—21no—
79C11×#41—41no—
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C2×Q8×C11—21no—
84C2×Q8×C11—22no—
85C2×Q8×C11—41no—
86C2×Q8×C11—82no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C22×Dic11—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44SD1612yes—
103C2×C4×D11—41no—
104C2×C4×D11—41no—
105C2×C4×D11—82no—
106C2×C8×C11—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119#4325—44no—
120#4323—44no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125#4318—41no—
126#4318—41no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132#3227D1111yescharacteristic, complemented
133C2×#474—111no—
134#3036—111no—
135#1548—111no—
136#1480—111no—
137#1460—111no—
138#1301—111no—
139C23×C11—41no—
140C23×C11#12111yescharacteristic
141C22×D11—22no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—81no—
145C22×D11—81no—
146Q8×C11—41no—
147Q8×C11—41no—
148Q8×C11—82no—
149Q8×C11—82no—
150D4×C11—42no—
151D4×C11—41no—
152D4×C11—41no—
153D4×C11—42no—
154D4×C11—81no—
155D4×C11—81no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—82no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12711yescharacteristic
169C2×C4×C11C2×SD1611yescharacteristic
170C2×C4×C11#13511yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C11#13711yescharacteristic
173C2×Dic11—41no—
174C2×Dic11—81no—
175D44—22no—
176D44—22no—
177D44—41no—
178D44—41no—
179C4×D11—82no—
180C4×D11—82no—
181C8×C11—42no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C11⋊C8—81no—
185C2×AGL(1,ℤ/8)—221no—
186#532C2×D1111yescharacteristic
187C2×C4⋊Q8C2×D1111yescharacteristic
188C2×C4×D4—111no—
189#498—21no—
190#486—21no—
191#481—22no—
192#476—22no—
193#474—222no—
194#474—222no—
195#463—222no—
196#461—221no—
197#459—221no—
198#431—111no—
199#431C2×D1111yescharacteristic
200C2×#107—221no—
201#423—111no—
202C2×C4⋊C8—111no—
203#417—221no—
204C2×#102—221no—
205#333—222no—
206D4⋊C8—222no—
207#323—222no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11#39211yescharacteristic
214C22×C11#46511yescharacteristic
215C22×C11#46811yescharacteristic
216C2×D11—42no—
217C2×D11—82no—
218C2×D11—81no—
219C2×D11—81no—
220C2×D11—82no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—81no—
225C4×C11—82no—
226C4×C11#44811yescharacteristic
227C4×C11#44911yescharacteristic
228C4×C11#45011yescharacteristic
229C4×C11#45211yescharacteristic
230C4×C11#47212yes—
231Dic11—81no—
232C2×#41—21no—
233C22×Q8—21no—
234C22×D4—111no—
235C23×C4—221no—
236AGL(1,ℤ/8)—442no—
237AGL(1,ℤ/8)—442no—
238C2×SD16—222no—
239C2×D8—222no—
240C2×M16—221no—
241C22×C8—221no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8C22⋊D1112yes—
246C4⋊Q8C22⋊D1111yescharacteristic
247#127C22⋊D1111yescharacteristic
248#124—21no—
249#121—21no—
250#121—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—221no—
254C4×D4—221no—
255C4×D4—221no—
256C4×D4—221no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—111no—
260C2×C22⋊C4—221no—
261C2×C42C22×D1111yescharacteristic
262#107—224no—
263#106—24no—
264C4⋊C8—21no—
265C4⋊C8—112no—
266C4⋊C8—112no—
267C4⋊C8—221no—
268C4⋊C8—221no—
269C4⋊C8—221no—
270#103—222no—
271#102—24no—
272#102—224no—
273#102—222no—
274C22⋊C8—221no—
275C22⋊C8C22⋊D1112yes—
276C4×C8—21no—
277C4×C8—221no—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11—161no—
281C2×C11#200011yescharacteristic
282C2×C11#200911yescharacteristic
283C2×C11#201811yescharacteristic
284D11—82no—
285C24—221no—
286#41—41no—
287#41—41no—
288#41—41no—
289#41—41no—
290C2×Q8—21no—
291C2×Q8—22no—
292C2×Q8—41no—
293C2×Q8—82no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—112no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—221no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—221no—
307C22×C4—441no—
308C22×C4—441no—
309C22×C4—882no—
310C22×C4D4×D1111yescharacteristic
311C22×C4#434111yescharacteristic
312C22×C4C2×C22⋊D1111yescharacteristic
313SD16—444no—
314D8—444no—
315M16—441no—
316M16—441no—
317C2×C8—22no—
318C2×C8—222no—
319C2×C8—222no—
320C2×C8—441no—
321C2×C8—441no—
322C2×C8—441no—
323C4⋊C4—22no—
324C4⋊C4—21no—
325C4⋊C4—22no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—221no—
330C4⋊C4—221no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C42D4×D1111yescharacteristic
336C42D4×D1111yescharacteristic
337C42C2×C22⋊D1111yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C11#1018811yescharacteristic, complemented, Sylow
340C23—41no—
341C23—222no—
342C23—441no—
343C23—441no—
344C23—881no—
345C23—881no—
346C23#6699111yescharacteristic
347Q8—41no—
348Q8—41no—
349Q8—82no—
350Q8—82no—
351D4—42no—
352D4—41no—
353D4—41no—
354D4—42no—
355D4—81no—
356D4—81no—
357D4—222no—
358D4—222no—
359D4—441no—
360D4—441no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—441no—
369C2×C4—882no—
370C2×C4—882no—
371C2×C4—881no—
372C2×C4SD16×D1111yescharacteristic
373C2×C4#6696711yescharacteristic
374C2×C4#6696811yescharacteristic
375C2×C4#6696911yescharacteristic
376C2×C4#6699011yescharacteristic
377C2×C4#6699011yescharacteristic
378C2×C4#6699211yescharacteristic
379C2×C4#6699211yescharacteristic
380C2×C4#6699311yescharacteristic
381C2×C4#6700611yescharacteristic
382C8—42no—
383C8—442no—
384C8—442no—
385C8—881no—
386C22—21no—
387C22—21no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—442no—
392C22—882no—
393C22—882no—
394C22—881no—
395C22—881no—
396C22#1062278411yescharacteristic
397C22#1062278711yescharacteristic
398C22#1062283611yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—81no—
403C4—82no—
404C4—881no—
405C4#1062278211yescharacteristic
406C4#1062278311yescharacteristic
407C4#1062278511yescharacteristic
408C4#1062278611yescharacteristic
409C4#1062281212yes—
410C2—21no—
411C2—21no—
412C2—161no—
413C2—882no—
414C2#1306961611yescharacteristic
415C2#1306967611yescharacteristic
416C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3227C2
socleC22×C11#392
prime radical#13078076C2
hypercenter#3227D11
hypocenterC11#10188
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
1. C2×#10622700C2semidirect
3. #13067297C2semidirect
4. #13067015C2semidirect
5. #13066936C2semidirect
6. #13066512C2semidirect
7. C11×#3227C2semidirect
132. #3227D11semidirect
339. C11#10188semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
#130780762
#130672972
#130670152
#130669362
#130665122
C11×#32272
#1018811