Finite Group Databasebeta

← #14664628

Subgroups — #14664628

Order 2816.

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

normal subgroups only

This group has 698 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#13071930C211yesmaximal, characteristic
2#13068689C211yesmaximal, characteristic, complemented
3D11×#323C211yesmaximal, characteristic, complemented
4#13066638C211yesmaximal, characteristic, complemented
5#13066636C211yesmaximal, characteristic, complemented
6#13066613C211yesmaximal, characteristic, complemented
7C11×#1343C211yesmaximal, characteristic, complemented
8C22×#4341C411yescharacteristic, complemented
9C2×#66990—21no—
10C2×C22⋊C4×D11C2211yescharacteristic
11C11×#392C2211yescharacteristic
12#10622836C411yescharacteristic, complemented
13#10622833—21no—
14#10622571—21no—
15#10622569—21no—
16#10622568—21no—
17#10622560C2211yescharacteristic
18D11×C22⋊C8—21no—
19#10622286C411yescharacteristic, complemented
20#10622277C411yescharacteristic, complemented
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C24×D11D411yescharacteristic
28C22×D4×C11—21no—
29C22×D4×C11C2×C411yescharacteristic
30C22×C22⋊D11—21no—
31C22×C22⋊D11—21no—
32C23×Dic11—21no—
33C2×#4341—41no—
34C2×#4341—41no—
35C2×#4341—44no—
36C22×C4×D11C2×C411yescharacteristic
37C22×C4×D11D411yescharacteristic
38C22×Dic22C2×C411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4C2311yescharacteristic
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11D411yescharacteristic
46#66990—44no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—41no—
50C2×(C2×D11)⋊C4—41no—
51C2×(C2×D11)⋊C4C2×C411yescharacteristic
52C2×(C2×D11)⋊C4D411yescharacteristic
53C2×C8×D11—41no—
54C22⋊C4×D11—41no—
55C22⋊C4×D11—41no—
56C11×C22⋊C8—21no—
57C11×#95C2×C411yescharacteristic
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95C2×C411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—41no—
64#11839—111nomaximal, Sylow
65C24×C11—21no—
66C24×C11C2×D411yescharacteristic
67C23×D11—21no—
68C23×D11—21no—
69C23×D11—21no—
70C23×D11—21no—
71C23×D11—41no—
72C23×D11—42no—
73C23×D11—81no—
74C23×D11C22⋊C411yescharacteristic
75C23×D11C22⋊C411yescharacteristic
76C2×D4×C11—41no—
77C2×D4×C11—42no—
78C2×D4×C11—42no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—81no—
82C22×C4×C11—21no—
83C22×C4×C11—41no—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C2×C22⋊D11—24no—
87C2×C22⋊D11—42no—
88C2×C22⋊D11—42no—
89C2×C22⋊D11—42no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11—81no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—42no—
96C22×Dic11—41no—
97C22×Dic11—42no—
98C22×Dic11—42no—
99C22×Dic11C22⋊C411yescharacteristic
100C22×Dic11C22⋊C411yescharacteristic
101#4341—44no—
102#4341—44no—
103#4341—44no—
104#4341—44no—
105C2×C4×D11—21no—
106C2×C4×D11—21no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—42no—
110C2×C4×D11—81no—
111C2×Dic22—41no—
112C2×Dic22—42no—
113C2×C8×C11—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—81no—
118C22⋊Dic11—41no—
119C22⋊Dic11—41no—
120C22⋊Dic11—42no—
121C22⋊Dic11—41no—
122C22⋊Dic11—81no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—82no—
128(C2×D11)⋊C4—82no—
129C2×C11⋊C8—41no—
130C8×D11—82no—
131#2404—111no—
132#1819—111no—
133C2×#323—111no—
134#1351—111no—
135#1351—111no—
136#1343—111no—
137#1343D1111yescharacteristic, complemented
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11C2×C22⋊C411yescharacteristic
150C23×C11#13511yescharacteristic
151C23×C11#13511yescharacteristic
152C22×D11—21no—
153C22×D11—21no—
154C22×D11—22no—
155C22×D11—21no—
156C22×D11—21no—
157C22×D11—21no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—42no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—42no—
167C22×D11—81no—
168C22×D11—81no—
169C22×D11—84no—
170C22×D11—82no—
171C22×D11—82no—
172C22×D11#9911yescharacteristic
173C22×D11#9911yescharacteristic
174D4×C11—42no—
175D4×C11—42no—
176D4×C11—82no—
177D4×C11—82no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C22⋊D11—44no—
189C22⋊D11—44no—
190C22⋊D11—84no—
191C2×Dic11—22no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—41no—
195C2×Dic11—48no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—81no—
203C2×Dic11—81no—
204C2×Dic11—81no—
205C4×D11—42no—
206C4×D11—42no—
207C4×D11—42no—
208C4×D11—81no—
209Dic22—42no—
210Dic22—42no—
211C8×C11—81no—
212C11⋊C8—81no—
213C22×#41—111no—
214C2×#120—221no—
215C22×C22⋊C4—111no—
216C2×C22⋊C8—221no—
217#393—111no—
218#393—111no—
219#392—111no—
220#392C2×D1111yescharacteristic
221#386—221no—
222#386—221no—
223#386—221no—
224#381—111no—
225#379—221no—
226#342—111no—
227#342—221no—
228#342C2×D1111yescharacteristic
229#323—111no—
230#323—221no—
231#323C2×D1111yescharacteristic
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—42no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11—81no—
248C22×C11C2×#9911yescharacteristic
249C22×C11#41611yescharacteristic
250C22×C11#42111yescharacteristic
251C2×D11—21no—
252C2×D11—21no—
253C2×D11—21no—
254C2×D11—21no—
255C2×D11—21no—
256C2×D11—42no—
257C2×D11—42no—
258C2×D11—42no—
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—82no—
263C2×D11—82no—
264C2×D11—82no—
265C2×D11—82no—
266C2×D11—81no—
267C2×D11AΣL(1,𝔽16)12yes—
268C4×C11—41no—
269C4×C11—41no—
270C4×C11—81no—
271C4×C11—161no—
272Dic11—42no—
273Dic11—41no—
274Dic11—41no—
275Dic11—81no—
276Dic11—161no—
277C25—111no—
278C2×#41—441no—
279C2×#41—441no—
280C2×#41—444no—
281C22×Q8—111no—
282C22×D4—21no—
283C22×D4—221no—
284C22×D4—221no—
285C22×D4C4×D1111yescharacteristic
286C23×C4—111no—
287C23×C4—111no—
288C23×C4—221no—
289C22×C8—441no—
290#120—444no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—111no—
294C2×C22⋊C4—111no—
295C2×C22⋊C4—111no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—441no—
302C2×C22⋊C4—441no—
303C2×C22⋊C4—441no—
304C2×C22⋊C4—441no—
305C2×C22⋊C4C22×D1111yescharacteristic
306C22⋊C8—21no—
307C22⋊C8—221no—
308C22⋊C8—441no—
309#95—111no—
310#95—221no—
311#95—221no—
312#95—221no—
313#95C4×D1111yescharacteristic
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—41no—
317C2×C11—41no—
318C2×C11—82no—
319C2×C11#151611yescharacteristic
320C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
321C2×C11#212711yescharacteristic
322D11—22no—
323D11—41no—
324D11—81no—
325C24—21no—
326C24—111no—
327C24—111no—
328C24—221no—
329C24—221no—
330C24—221no—
331C24—221no—
332C24—441no—
333C24—442no—
334C24—881no—
335C24D4×D1111yescharacteristic
336#41—444no—
337#41—444no—
338#41—444no—
339#41—444no—
340C2×Q8—441no—
341C2×Q8—442no—
342C2×D4—41no—
343C2×D4—42no—
344C2×D4—42no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—81no—
348C2×D4—224no—
349C2×D4—441no—
350C2×D4—441no—
351C2×D4—442no—
352C2×D4—442no—
353C2×D4—442no—
354C2×D4—881no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4—111no—
358C22×C4—111no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4—442no—
366C22×C4—442no—
367C22×C4—442no—
368C22×C4—442no—
369C22×C4—441no—
370C22×C4—881no—
371C22×C4C2×C4×D1111yescharacteristic
372C22×C4D4×D1111yescharacteristic
373C2×C8—41no—
374C2×C8—441no—
375C2×C8—882no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—81no—
380C22⋊C4—441no—
381C22⋊C4—441no—
382C22⋊C4—442no—
383C22⋊C4—442no—
384C22⋊C4—441no—
385C22⋊C4—442no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—882no—
389C22⋊C4—882no—
390C22⋊C4—881no—
391C11#1183911yescharacteristic, complemented, Sylow
392C23—21no—
393C23—21no—
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—111no—
404C23—111no—
405C23—222no—
406C23—221no—
407C23—221no—
408C23—221no—
409C23—221no—
410C23—221no—
411C23—441no—
412C23—441no—
413C23—441no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23—441no—
418C23—442no—
419C23—442no—
420C23—881no—
421C23—881no—
422C23—882no—
423C23—882no—
424C23—884no—
425C23C22⋊C4×D1111yescharacteristic
426C23#6696511yescharacteristic
427C23#6696911yescharacteristic
428Q8—442no—
429Q8—442no—
430D4—42no—
431D4—42no—
432D4—82no—
433D4—82no—
434D4—444no—
435D4—444no—
436D4—884no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—222no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—441no—
454C2×C4—448no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—881no—
462C2×C4—881no—
463C2×C4—881no—
464C2×C4—881no—
465C8—81no—
466C8—881no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—41no—
472C22—41no—
473C22—42no—
474C22—42no—
475C22—41no—
476C22—41no—
477C22—42no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22—112no—
484C22—221no—
485C22—221no—
486C22—221no—
487C22—221no—
488C22—221no—
489C22—442no—
490C22—442no—
491C22—442no—
492C22—441no—
493C22—441no—
494C22—441no—
495C22—881no—
496C22—882no—
497C22—882no—
498C22—882no—
499C22—882no—
500C22D11×#9911yescharacteristic
501C22#1062238511yescharacteristic
502C22#1062243411yescharacteristic
503C4—41no—
504C4—41no—
505C4—81no—
506C4—161no—
507C4—441no—
508C4—442no—
509C4—441no—
510C4—881no—
511C4—1761no—
512C2—21no—
513C2—21no—
514C2—41no—
515C2—41no—
516C2—82no—
517C2—222no—
518C2—441no—
519C2—881no—
520C2#1306716911yescharacteristic
521C2D11×AΣL(1,𝔽16)11yescharacteristic
522C2#1307028211yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1343C2
socleC22×C11C2×#99
prime radical#13071930C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1343D11
hypocenterC11#11839
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. #13068689C2semidirect
3. D11×#323C2semidirect
4. #13066638C2semidirect
5. #13066636C2semidirect
6. #13066613C2semidirect
7. C11×#1343C2semidirect
8. C22×#4341C4semidirect
12. #10622836C4semidirect
19. #10622286C4semidirect
20. #10622277C4semidirect
137. #1343D11semidirect
391. C11#11839semidirect

Maximal subgroups

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

subgroupindex
#130719302
#130686892
D11×#3232
#130666382
#130666362
#130666132
C11×#13432
#1183911