Finite Group Databasebeta

← #14664483

Subgroups — #14664483

Order 2816.

616 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 73 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
1D11×#399C211yesmaximal, characteristic
2#13068689C211yesmaximal, characteristic
3#13066941C211yesmaximal, characteristic
4#13066641C211yesmaximal, characteristic, complemented
5#13066640C211yesmaximal, characteristic, complemented
6#13066639C211yesmaximal, characteristic, complemented
7C11×#1352C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D11—21no—
9C2×C4⋊C4×D11C411yescharacteristic, complemented
10C2×C22⋊C4×D11—21no—
11C2×C22⋊C4×D11C2211yescharacteristic
12C11×#399C2211yescharacteristic
13#10622605—21no—
14#10622605C411yescharacteristic, complemented
15#10622568—21no—
16#10622562—21no—
17#10622562C2211yescharacteristic
18#10622339—21no—
19#10622290C411yescharacteristic, complemented
20D11×#95C411yescharacteristic, complemented
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C24×D11D411yescharacteristic
28C22×C4×D11—21no—
29C22×C4×D11—21no—
30C22×C4×D11C2×C411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11D411yescharacteristic
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—41no—
43C2×(C2×D11)⋊C4—41no—
44C2×(C2×D11)⋊C4C2×C411yescharacteristic
45C2×(C2×D11)⋊C4D411yescharacteristic
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11C2×C411yescharacteristic
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×#4313—41no—
52C4⋊C4×D11—41no—
53C4⋊C4×D11—41no—
54C4⋊C4×D11—44no—
55C22⋊C4×D11—41no—
56C22⋊C4×D11—41no—
57C22⋊C4×D11—44no—
58C11×C22⋊C8—21no—
59C11×#95C2×C411yescharacteristic
60C11⋊#95—21no—
61C11⋊#95C2×C411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—41no—
64#11809—111nomaximal, Sylow
65C24×C11C2×D411yescharacteristic
66C23×D11—21no—
67C23×D11—21no—
68C23×D11—21no—
69C23×D11—21no—
70C23×D11—41no—
71C23×D11—42no—
72C23×D11—42no—
73C23×D11C22⋊C411yescharacteristic
74C23×D11C22⋊C411yescharacteristic
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—24no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—42no—
91C2×C4×D11—42no—
92C2×C4×D11—42no—
93C2×C4×D11—42no—
94C2×C4×D11—42no—
95C2×C4×D11—42no—
96C2×C4×D11—41no—
97C2×C4×D11—41no—
98C2×C8×C11—41no—
99C11×C4⋊C4—42no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C22⋊Dic11—41no—
106C22⋊Dic11—41no—
107C22⋊Dic11—42no—
108C22⋊Dic11—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—82no—
114(C2×D11)⋊C4—82no—
115C4⋊Dic11—41no—
116C4⋊Dic11—42no—
117Dic11⋊C4—42no—
118Dic11⋊C4—42no—
119Dic11⋊C4—42no—
120C2×C11⋊C8—41no—
121#4313—82no—
122C2×#399—111no—
123#1819—111no—
124#1462—111no—
125#1352—111no—
126#1352—111no—
127#1352—111no—
128#1352D1111yescharacteristic, complemented
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11C2×C22⋊C411yescharacteristic
134C23×C11#13711yescharacteristic
135C23×C11#13711yescharacteristic
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—22no—
139C22×D11—22no—
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—44no—
148C22×D11—44no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—42no—
152C22×D11—42no—
153C22×D11—81no—
154C22×D11—81no—
155C22×D11—84no—
156C22×D11#9911yescharacteristic
157C22×D11#9911yescharacteristic
158C2×C4×C11—22no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×Dic11—22no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—81no—
182C2×Dic11—81no—
183C2×Dic11—81no—
184C4×D11—48no—
185C4×D11—42no—
186C4×D11—42no—
187C4×D11—42no—
188C4×D11—81no—
189C4×D11—82no—
190C4×D11—82no—
191C8×C11—81no—
192C11⋊C8—81no—
193C22×C4⋊C4—111no—
194C22×C4⋊C4—221no—
195C22×C22⋊C4—111no—
196C22×C22⋊C4—221no—
197#407—221no—
198#399—111no—
199#399—111no—
200#399—111no—
201#399—221no—
202#399—221no—
203#399C2×D1111yescharacteristic
204#379—221no—
205C2×#95—111no—
206#342—111no—
207#342—221no—
208#342C2×D1111yescharacteristic
209#323—111no—
210#323—221no—
211#323C2×D1111yescharacteristic
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—81no—
221C22×C11C2×#9911yescharacteristic
222C22×C11#41911yescharacteristic
223C22×C11#42111yescharacteristic
224C2×D11—24no—
225C2×D11—24no—
226C2×D11—21no—
227C2×D11—21no—
228C2×D11—21no—
229C2×D11—21no—
230C2×D11—42no—
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C2×D11—82no—
235C2×D11—82no—
236C2×D11—82no—
237C2×D11—82no—
238C2×D11—81no—
239C2×D11#35212yes—
240C2×D11#35312yes—
241C4×C11—42no—
242C4×C11—41no—
243C4×C11—41no—
244C4×C11—81no—
245C4×C11—161no—
246Dic11—42no—
247Dic11—41no—
248Dic11—41no—
249Dic11—81no—
250Dic11—161no—
251C25—111no—
252C23×C4—111no—
253C23×C4—111no—
254C23×C4—221no—
255C23×C4—221no—
256C2×M16—441no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—441no—
264C2×C4⋊C4—441no—
265C2×C4⋊C4—444no—
266C2×C4⋊C4C4×D1111yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—111no—
272C2×C22⋊C4—221no—
273C2×C22⋊C4—221no—
274C2×C22⋊C4—221no—
275C2×C22⋊C4—221no—
276C2×C22⋊C4—441no—
277C2×C22⋊C4—441no—
278C2×C22⋊C4—444no—
279C2×C22⋊C4—441no—
280C2×C22⋊C4—441no—
281C2×C22⋊C4C22×D1111yescharacteristic
282C22⋊C8—21no—
283C22⋊C8—221no—
284C22⋊C8—441no—
285#95—111no—
286#95—221no—
287#95C4×D1111yescharacteristic
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—41no—
291C2×C11—41no—
292C2×C11#151111yescharacteristic
293C2×C11C2×#35211yescharacteristic
294C2×C11C2×#35311yescharacteristic
295D11—22no—
296D11—22no—
297D11—81no—
298C24—111no—
299C24—111no—
300C24—221no—
301C24—221no—
302C24—221no—
303C24—221no—
304C24—441no—
305C24—442no—
306C24—442no—
307C24D4×D1111yescharacteristic
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—41no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—224no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—442no—
321C22×C4—442no—
322C22×C4—442no—
323C22×C4—442no—
324C22×C4—441no—
325C22×C4—441no—
326C22×C4—442no—
327C22×C4—442no—
328C22×C4—441no—
329C22×C4C2×C4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331M16—882no—
332C2×C8—41no—
333C2×C8—441no—
334C4⋊C4—41no—
335C4⋊C4—42no—
336C4⋊C4—441no—
337C4⋊C4—442no—
338C4⋊C4—442no—
339C4⋊C4—442no—
340C4⋊C4—442no—
341C22⋊C4—41no—
342C22⋊C4—42no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—442no—
348C22⋊C4—442no—
349C22⋊C4—441no—
350C22⋊C4—442no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C22⋊C4—882no—
354C22⋊C4—882no—
355C11#1180911yescharacteristic, complemented, Sylow
356C23—21no—
357C23—21no—
358C23—41no—
359C23—41no—
360C23—111no—
361C23—111no—
362C23—222no—
363C23—222no—
364C23—221no—
365C23—221no—
366C23—221no—
367C23—221no—
368C23—221no—
369C23—441no—
370C23—441no—
371C23—441no—
372C23—441no—
373C23—441no—
374C23—441no—
375C23—442no—
376C23—442no—
377C23—444no—
378C23—444no—
379C23—881no—
380C23—881no—
381C23—884no—
382C23C22⋊C4×D1111yescharacteristic
383C23#6696811yescharacteristic
384C23#6697111yescharacteristic
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—222no—
399C2×C4—221no—
400C2×C4—221no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—448no—
404C2×C4—442no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—881no—
413C2×C4—882no—
414C2×C4—882no—
415C2×C4—881no—
416C2×C4—881no—
417C2×C4—881no—
418C8—81no—
419C8—881no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—81no—
429C22—112no—
430C22—112no—
431C22—224no—
432C22—224no—
433C22—221no—
434C22—221no—
435C22—221no—
436C22—221no—
437C22—442no—
438C22—441no—
439C22—441no—
440C22—441no—
441C22—881no—
442C22—882no—
443C22—882no—
444C22—882no—
445C22—882no—
446C22D11×#9911yescharacteristic
447C22#1062241511yescharacteristic
448C22#1062243411yescharacteristic
449C4—42no—
450C4—41no—
451C4—41no—
452C4—81no—
453C4—161no—
454C4—442no—
455C4—441no—
456C4—441no—
457C4—881no—
458C4—1761no—
459C2—21no—
460C2—21no—
461C2—41no—
462C2—41no—
463C2—222no—
464C2—222no—
465C2—881no—
466C2#1306714711yescharacteristic
467C2D11×#35211yescharacteristic
468C2D11×#35311yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1352C2
socleC22×C11C2×#99
prime radicalC24×D11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1352D11
hypocenterC11#11809
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
4. #13066641C2semidirect
5. #13066640C2semidirect
6. #13066639C2semidirect
7. C11×#1352C2semidirect
9. C2×C4⋊C4×D11C4semidirect
14. #10622605C4semidirect
19. #10622290C4semidirect
20. D11×#95C4semidirect
128. #1352D11semidirect
355. C11#11809semidirect

Maximal subgroups

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

subgroupindex
D11×#3992
#130686892
#130669412
#130666412
#130666402
#130666392
C11×#13522
#1180911