Finite Group Databasebeta

← #14664638

Subgroups — #14664638

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#13072885C211yesmaximal, characteristic
2#13068689C211yesmaximal, characteristic
3D11×#323C211yesmaximal, characteristic
4#13066641C211yesmaximal, characteristic, complemented
5#13066639C211yesmaximal, characteristic, complemented
6#13066616C211yesmaximal, characteristic, complemented
7C11×#1344C211yesmaximal, characteristic, complemented
8C2×#66945C411yescharacteristic, complemented
9C2×C22⋊C4×D11C2211yescharacteristic
10C11×#397C2211yescharacteristic
11#10622606C411yescharacteristic, complemented
12#10622568—21no—
13#10622568—21no—
14#10622564—21no—
15#10622562C2211yescharacteristic
16D11×C22⋊C8—21no—
17#10622290C411yescharacteristic, complemented
18#10622282—21no—
19#10622281—21no—
20#10622277C411yescharacteristic, complemented
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C24×D11D411yescharacteristic
28C22×C4×D11C2×C411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C2×C11×C4⋊C4C2×C411yescharacteristic
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
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—41no—
42C2×(C2×D11)⋊C4—41no—
43C2×(C2×D11)⋊C4C2×C411yescharacteristic
44C2×(C2×D11)⋊C4D411yescharacteristic
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—21no—
49C2×C8×D11—41no—
50#66945—41no—
51#66945—41no—
52C22⋊C4×D11—41no—
53C22⋊C4×D11—41no—
54C11×C22⋊C8—21no—
55C11×#95—21no—
56C11×#95C2×C411yescharacteristic
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95C2×C411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61(C2×D11)⋊C8—41no—
62#11841—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
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—41no—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—41no—
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—42no—
88C2×C4×D11—81no—
89C2×C8×C11—41no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C22⋊Dic11—41no—
97C22⋊Dic11—41no—
98C22⋊Dic11—41no—
99C22⋊Dic11—81no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—81no—
107(C2×D11)⋊C4—82no—
108(C2×D11)⋊C4—82no—
109C4⋊Dic11—41no—
110C4⋊Dic11—81no—
111Dic11⋊C4—81no—
112C4×Dic11—42no—
113C2×C11⋊C8—41no—
114C8×D11—82no—
115#2482—111no—
116#1819—111no—
117C2×#323—111no—
118#1352—111no—
119#1352—111no—
120#1344—111no—
121#1344D1111yescharacteristic, complemented
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
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—41no—
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—81no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—81no—
175C2×Dic11—81no—
176C2×Dic11—81no—
177C4×D11—42no—
178C4×D11—42no—
179C4×D11—42no—
180C4×D11—81no—
181C8×C11—81no—
182C11⋊C8—81no—
183C2×#117—111no—
184C22×C22⋊C4—111no—
185C2×C22⋊C8—221no—
186#399—111no—
187#399—111no—
188#397—111no—
189#397C2×D1111yescharacteristic
190#388—221no—
191#388—221no—
192#385—221no—
193#381—111no—
194#379—221no—
195#379—221no—
196#342—111no—
197#342—221no—
198#342C2×D1111yescharacteristic
199#323—111no—
200#323—221no—
201#323C2×D1111yescharacteristic
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—81no—
211C22×C11C2×#9911yescharacteristic
212C22×C11#41611yescharacteristic
213C22×C11#42111yescharacteristic
214C2×D11—21no—
215C2×D11—21no—
216C2×D11—21no—
217C2×D11—21no—
218C2×D11—21no—
219C2×D11—42no—
220C2×D11—42no—
221C2×D11—42no—
222C2×D11—41no—
223C2×D11—41no—
224C2×D11—41no—
225C2×D11—82no—
226C2×D11—82no—
227C2×D11—82no—
228C2×D11—82no—
229C2×D11—81no—
230C2×D11#35212yes—
231C4×C11—41no—
232C4×C11—41no—
233C4×C11—81no—
234C4×C11—81no—
235C4×C11—161no—
236Dic11—41no—
237Dic11—41no—
238Dic11—81no—
239Dic11—81no—
240Dic11—161no—
241C25—111no—
242C23×C4—111no—
243C23×C4—111no—
244C22×C8—441no—
245#117—441no—
246#117—441no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4C4×D1111yescharacteristic
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#95C4×D1111yescharacteristic
276C2×C11—21no—
277C2×C11—21no—
278C2×C11—41no—
279C2×C11—41no—
280C2×C11#151611yescharacteristic
281C2×C11C2×#35211yescharacteristic
282C2×C11#212711yescharacteristic
283D11—22no—
284D11—41no—
285D11—81no—
286C24—111no—
287C24—111no—
288C24—221no—
289C24—221no—
290C24—221no—
291C24—221no—
292C24—441no—
293C24—442no—
294C24—881no—
295C24D4×D1111yescharacteristic
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—111no—
300C22×C4—111no—
301C22×C4—221no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—442no—
308C22×C4—441no—
309C22×C4—881no—
310C22×C4C2×C4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312C2×C8—41no—
313C2×C8—441no—
314C2×C8—882no—
315C4⋊C4—41no—
316C4⋊C4—441no—
317C4⋊C4—881no—
318C4⋊C4—881no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
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—881no—
334C22⋊C4—882no—
335C22⋊C4—882no—
336C22⋊C4—881no—
337C42—442no—
338C11#1184111yescharacteristic, complemented, Sylow
339C23—21no—
340C23—21no—
341C23—41no—
342C23—41no—
343C23—111no—
344C23—111no—
345C23—222no—
346C23—221no—
347C23—221no—
348C23—221no—
349C23—221no—
350C23—221no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23—441no—
357C23—441no—
358C23—442no—
359C23—442no—
360C23—881no—
361C23—881no—
362C23—882no—
363C23—882no—
364C23—884no—
365C23C22⋊C4×D1111yescharacteristic
366C23#6696511yescharacteristic
367C23#6696911yescharacteristic
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—442no—
384C2×C4—442no—
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—
398C8—81no—
399C8—881no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—81no—
409C22—112no—
410C22—221no—
411C22—221no—
412C22—221no—
413C22—221no—
414C22—221no—
415C22—442no—
416C22—442no—
417C22—442no—
418C22—441no—
419C22—441no—
420C22—441no—
421C22—881no—
422C22—882no—
423C22—882no—
424C22—882no—
425C22—882no—
426C22D11×#9911yescharacteristic
427C22#1062238511yescharacteristic
428C22#1062243411yescharacteristic
429C4—41no—
430C4—41no—
431C4—81no—
432C4—81no—
433C4—161no—
434C4—441no—
435C4—441no—
436C4—881no—
437C4—881no—
438C4—1761no—
439C2—21no—
440C2—21no—
441C2—41no—
442C2—41no—
443C2—222no—
444C2—441no—
445C2—881no—
446C2#1306716911yescharacteristic
447C2D11×#35211yescharacteristic
448C2#1307028411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1344C2
socleC22×C11C2×#99
prime radicalC24×D11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1344D11
hypocenterC11#11841
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
4. #13066641C2semidirect
5. #13066639C2semidirect
6. #13066616C2semidirect
7. C11×#1344C2semidirect
8. C2×#66945C4semidirect
11. #10622606C4semidirect
17. #10622290C4semidirect
20. #10622277C4semidirect
121. #1344D11semidirect
338. C11#11841semidirect

Maximal subgroups

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

subgroupindex
#130728852
#130686892
D11×#3232
#130666412
#130666392
#130666162
C11×#13442
#1184111