Finite Group Databasebeta

← #14664660

Subgroups — #14664660

Order 2816.

506 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 71 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#13073770C211yesmaximal, characteristic
2#13068689C211yesmaximal, characteristic
3D11×#323C211yesmaximal, characteristic
4#13066637C211yesmaximal, characteristic, complemented
5#13066617C211yesmaximal, characteristic, complemented
6#13066615C211yesmaximal, characteristic, complemented
7C11×#1351C211yesmaximal, characteristic, complemented
8C2×#66999C411yescharacteristic, complemented
9C2×C22⋊C4×D11C2211yescharacteristic
10C11×#393C2211yescharacteristic
11#10622844C411yescharacteristic, complemented
12#10622568—21no—
13#10622568—21no—
14#10622566C2211yescharacteristic
15#10622557—21no—
16D11×C22⋊C8—21no—
17#10622287C411yescharacteristic, complemented
18#10622282—21no—
19#10622279C411yescharacteristic, complemented
20#10622277—21no—
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C24×D11D411yescharacteristic
28C22×Q8×C11C2×C411yescharacteristic
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4C2311yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11D411yescharacteristic
37#66999—41no—
38#66999—41no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—41no—
44C2×(C2×D11)⋊C4—41no—
45C2×(C2×D11)⋊C4C2×C411yescharacteristic
46C2×(C2×D11)⋊C4D411yescharacteristic
47C2×C4⋊Dic11C2×C411yescharacteristic
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50C2×C8×D11—41no—
51C22⋊C4×D11—41no—
52C22⋊C4×D11—41no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95C2×C411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61(C2×D11)⋊C8—41no—
62#11845—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C23×D11—21no—
65C23×D11—21no—
66C23×D11—21no—
67C23×D11—21no—
68C23×D11—41no—
69C23×D11—42no—
70C23×D11—81no—
71C23×D11C22⋊C411yescharacteristic
72C23×D11C22⋊C411yescharacteristic
73C2×Q8×C11—41no—
74C2×Q8×C11—81no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—41no—
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—42no—
90C2×C4×D11—81no—
91C2×C8×C11—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—81no—
96C22⋊Dic11—41no—
97C22⋊Dic11—41no—
98C22⋊Dic11—41no—
99C22⋊Dic11—41no—
100C22⋊Dic11—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—81no—
108(C2×D11)⋊C4—82no—
109(C2×D11)⋊C4—82no—
110C4⋊Dic11—41no—
111Dic11⋊C4—42no—
112C4×Dic11—81no—
113C2×C11⋊C8—41no—
114C8×D11—82no—
115#2561—111no—
116#1819—111no—
117C2×#323—111no—
118#1351—111no—
119#1351D1111yescharacteristic, complemented
120#1344—111no—
121#1344—111no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11C2×C22⋊C411yescharacteristic
127C23×C11#13511yescharacteristic
128C23×C11#13511yescharacteristic
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—22no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—42no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—42no—
144C22×D11—81no—
145C22×D11—81no—
146C22×D11—84no—
147C22×D11—82no—
148C22×D11—82no—
149C22×D11#9911yescharacteristic
150C22×D11#9911yescharacteristic
151Q8×C11—82no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—81no—
176C2×Dic11—81no—
177C2×Dic11—81no—
178C4×D11—42no—
179C4×D11—81no—
180C4×D11—81no—
181C4×D11—81no—
182C8×C11—81no—
183C11⋊C8—81no—
184C2×C22⋊Q8—111no—
185C22×C22⋊C4—111no—
186C2×C22⋊C8—221no—
187#397—111no—
188#397—111no—
189#393—111no—
190#393C2×D1111yescharacteristic
191#388—221no—
192#388—221no—
193#381—221no—
194#379—221no—
195#379—221no—
196C4×C22⋊C4—111no—
197#342—111no—
198#342—221no—
199#342C2×D1111yescharacteristic
200#323—111no—
201#323—221no—
202#323C2×D1111yescharacteristic
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—81no—
212C22×C11C2×#9911yescharacteristic
213C22×C11#41611yescharacteristic
214C22×C11#42111yescharacteristic
215C2×D11—21no—
216C2×D11—21no—
217C2×D11—21no—
218C2×D11—21no—
219C2×D11—21no—
220C2×D11—42no—
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—41no—
224C2×D11—41no—
225C2×D11—41no—
226C2×D11—82no—
227C2×D11—82no—
228C2×D11—82no—
229C2×D11—82no—
230C2×D11—81no—
231C2×D11#35412yes—
232C4×C11—41no—
233C4×C11—41no—
234C4×C11—81no—
235C4×C11—81no—
236C4×C11—161no—
237Dic11—41no—
238Dic11—41no—
239Dic11—81no—
240Dic11—81no—
241Dic11—161no—
242C25—111no—
243C22×Q8C4×D1111yescharacteristic
244C23×C4—111no—
245C23×C4—111no—
246C22×C8—441no—
247C22⋊Q8—441no—
248C22⋊Q8—441no—
249C2×C4⋊C4—111no—
250C2×C4⋊C4—221no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—111no—
254C2×C22⋊C4—111no—
255C2×C22⋊C4—111no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—441no—
263C2×C22⋊C4—441no—
264C2×C22⋊C4—441no—
265C2×C22⋊C4—441no—
266C2×C22⋊C4C22×D1111yescharacteristic
267C2×C42—221no—
268C22⋊C8—21no—
269C22⋊C8—221no—
270C22⋊C8—441no—
271#95—21no—
272#95—111no—
273#95—221no—
274#95—221no—
275#95—221no—
276#95C4×D1111yescharacteristic
277C2×C11—21no—
278C2×C11—21no—
279C2×C11—41no—
280C2×C11—41no—
281C2×C11#151611yescharacteristic
282C2×C11#212111yescharacteristic
283C2×C11C2×#35411yescharacteristic
284D11—22no—
285D11—41no—
286D11—81no—
287C24—111no—
288C24—111no—
289C24—221no—
290C24—221no—
291C24—221no—
292C24—221no—
293C24—441no—
294C24—442no—
295C24—881no—
296C24D4×D1111yescharacteristic
297C2×Q8—41no—
298C2×Q8—81no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—41no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—442no—
311C22×C4—441no—
312C22×C4—881no—
313C22×C4C2×C4×D1111yescharacteristic
314C22×C4D4×D1111yescharacteristic
315C2×C8—41no—
316C2×C8—441no—
317C2×C8—882no—
318C4⋊C4—441no—
319C4⋊C4—442no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—81no—
324C22⋊C4—441no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C22⋊C4—441no—
328C22⋊C4—442no—
329C22⋊C4—442no—
330C22⋊C4—441no—
331C22⋊C4—441no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C22⋊C4—881no—
336C22⋊C4—882no—
337C22⋊C4—882no—
338C42—881no—
339C11#1184511yescharacteristic, complemented, Sylow
340C23—21no—
341C23—21no—
342C23—41no—
343C23—41no—
344C23—111no—
345C23—111no—
346C23—222no—
347C23—221no—
348C23—221no—
349C23—221no—
350C23—221no—
351C23—221no—
352C23—441no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23—441no—
357C23—441no—
358C23—441no—
359C23—442no—
360C23—442no—
361C23—881no—
362C23—881no—
363C23—882no—
364C23—882no—
365C23—884no—
366C23C22⋊C4×D1111yescharacteristic
367C23#6696911yescharacteristic
368C23#6697211yescharacteristic
369Q8—82no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—442no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—881no—
395C2×C4—881no—
396C2×C4—881no—
397C2×C4—881no—
398C2×C4—881no—
399C2×C4—881no—
400C8—81no—
401C8—881no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—81no—
411C22—112no—
412C22—221no—
413C22—221no—
414C22—221no—
415C22—221no—
416C22—221no—
417C22—442no—
418C22—442no—
419C22—442no—
420C22—441no—
421C22—441no—
422C22—441no—
423C22—881no—
424C22—882no—
425C22—882no—
426C22—882no—
427C22—882no—
428C22D11×#9911yescharacteristic
429C22#1062241711yescharacteristic
430C22#1062243411yescharacteristic
431C4—41no—
432C4—41no—
433C4—81no—
434C4—81no—
435C4—161no—
436C4—441no—
437C4—441no—
438C4—881no—
439C4—881no—
440C4—1761no—
441C2—21no—
442C2—21no—
443C2—41no—
444C2—41no—
445C2—222no—
446C2—441no—
447C2—881no—
448C2#1306717111yescharacteristic
449C2#1307025911yescharacteristic
450C2D11×#35411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1351C2
socleC22×C11C2×#99
prime radicalC24×D11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1351D11
hypocenterC11#11845
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
4. #13066637C2semidirect
5. #13066617C2semidirect
6. #13066615C2semidirect
7. C11×#1351C2semidirect
8. C2×#66999C4semidirect
11. #10622844C4semidirect
17. #10622287C4semidirect
19. #10622279C4semidirect
119. #1351D11semidirect
339. C11#11845semidirect

Maximal subgroups

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

subgroupindex
#130737702
#130686892
D11×#3232
#130666372
#130666172
#130666152
C11×#13512
#1184511