Finite Group Databasebeta

← #14664648

Subgroups — #14664648

Order 2816.

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

normal subgroups only

This group has 620 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#13073541C211yesmaximal, characteristic
2#13068689C211yesmaximal, characteristic, complemented
3D11×#323C211yesmaximal, characteristic, complemented
4#13066641C211yesmaximal, characteristic, complemented
5#13066639C211yesmaximal, characteristic, complemented
6#13066613C211yesmaximal, characteristic, complemented
7C11×#1343C211yesmaximal, characteristic, complemented
8C2×#66991C411yescharacteristic, complemented
9C2×#66990—21no—
10C2×#66936—21no—
11C2×C22⋊C4×D11C2211yescharacteristic
12C11×#392C2211yescharacteristic
13#10622836C411yescharacteristic, complemented
14#10622834—21no—
15#10622570—21no—
16#10622568—21no—
17#10622562C2211yescharacteristic
18D11×C22⋊C8—21no—
19#10622290C411yescharacteristic, complemented
20#10622279C411yescharacteristic, 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—
32C22×C4×D11C2×C411yescharacteristic
33C22×C4×D11D411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11D411yescharacteristic
42#66991—41no—
43#66991—41no—
44#66990—44no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—41no—
48C2×(C2×D11)⋊C4—41no—
49C2×(C2×D11)⋊C4C2×C411yescharacteristic
50C2×(C2×D11)⋊C4D411yescharacteristic
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11C2×C411yescharacteristic
53C2×Dic11⋊C4—21no—
54C2×C4×Dic11—21no—
55C2×C8×D11—41no—
56#66936—44no—
57C22⋊C4×D11—41no—
58C22⋊C4×D11—41no—
59C11×C22⋊C8—21no—
60C11×#95C2×C411yescharacteristic
61C11⋊#95C2×C411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—41no—
64#11843—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—42no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—81no—
81C2×D4×C11—81no—
82C22×C4×C11—21no—
83C22×C4×C11—41no—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C2×C22⋊D11—42no—
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—41no—
96C22×Dic11C22⋊C411yescharacteristic
97C22×Dic11C22⋊C411yescharacteristic
98C2×C4×D11—21no—
99C2×C4×D11—21no—
100C2×C4×D11—21no—
101C2×C4×D11—21no—
102C2×C4×D11—42no—
103C2×C4×D11—81no—
104C2×C8×C11—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C22⋊Dic11—41no—
110C22⋊Dic11—41no—
111C22⋊Dic11—42no—
112C22⋊Dic11—42no—
113C22⋊Dic11—42no—
114C22⋊Dic11—41no—
115(C2×D11)⋊C4—24no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—42no—
119(C2×D11)⋊C4—82no—
120(C2×D11)⋊C4—82no—
121C4⋊Dic11—41no—
122C4⋊Dic11—42no—
123Dic11⋊C4—42no—
124C4×Dic11—81no—
125C2×C11⋊C8—41no—
126C8×D11—82no—
127#2539—111no—
128#1819—111no—
129C2×#323—111no—
130#1352—111no—
131#1352—111no—
132#1343—111no—
133#1343D1111yescharacteristic, complemented
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11C2×C22⋊C411yescharacteristic
146C23×C11#13511yescharacteristic
147C23×C11#13511yescharacteristic
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—22no—
151C22×D11—21no—
152C22×D11—21no—
153C22×D11—21no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—42no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—42no—
163C22×D11—81no—
164C22×D11—81no—
165C22×D11—84no—
166C22×D11—82no—
167C22×D11—82no—
168C22×D11#9911yescharacteristic
169C22×D11#9911yescharacteristic
170D4×C11—82no—
171D4×C11—82no—
172D4×C11—82no—
173C2×C4×C11—22no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C22⋊D11—84no—
184C22⋊D11—82no—
185C22⋊D11—82no—
186C2×Dic11—22no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—81no—
197C2×Dic11—81no—
198C2×Dic11—81no—
199C4×D11—42no—
200C4×D11—81no—
201C4×D11—81no—
202C4×D11—81no—
203C8×C11—81no—
204C11⋊C8—81no—
205C2×#123—221no—
206C2×#121—111no—
207C2×#120—221no—
208C22×C22⋊C4—111no—
209C2×C22⋊C8—221no—
210#399—111no—
211#399—111no—
212#392—111no—
213#392C2×D1111yescharacteristic
214#390—221no—
215#390—221no—
216#379—221no—
217C4×C22⋊C4—111no—
218#342—111no—
219#342—221no—
220#342C2×D1111yescharacteristic
221#323—111no—
222#323—221no—
223#323C2×D1111yescharacteristic
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11C2×#9911yescharacteristic
241C22×C11#41611yescharacteristic
242C22×C11#42111yescharacteristic
243C2×D11—21no—
244C2×D11—21no—
245C2×D11—21no—
246C2×D11—21no—
247C2×D11—21no—
248C2×D11—42no—
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—41no—
252C2×D11—41no—
253C2×D11—41no—
254C2×D11—82no—
255C2×D11—82no—
256C2×D11—82no—
257C2×D11—82no—
258C2×D11—81no—
259C2×D11#35312yes—
260C4×C11—42no—
261C4×C11—41no—
262C4×C11—41no—
263C4×C11—161no—
264Dic11—42no—
265Dic11—41no—
266Dic11—41no—
267Dic11—81no—
268Dic11—161no—
269C25—111no—
270C22×D4—21no—
271C22×D4—221no—
272C22×D4—221no—
273C22×D4C4×D1111yescharacteristic
274C23×C4—111no—
275C23×C4—111no—
276C22×C8—441no—
277#123—444no—
278#121—441no—
279#121—441no—
280#120—444no—
281C2×C4⋊C4—111no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4—221no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—111no—
287C2×C22⋊C4—111no—
288C2×C22⋊C4—111no—
289C2×C22⋊C4—221no—
290C2×C22⋊C4—221no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—221no—
293C2×C22⋊C4—221no—
294C2×C22⋊C4—221no—
295C2×C22⋊C4—441no—
296C2×C22⋊C4—441no—
297C2×C22⋊C4—441no—
298C2×C22⋊C4—441no—
299C2×C22⋊C4C22×D1111yescharacteristic
300C2×C42—221no—
301C22⋊C8—21no—
302C22⋊C8—221no—
303C22⋊C8—441no—
304#95—111no—
305#95C4×D1111yescharacteristic
306C2×C11—21no—
307C2×C11—21no—
308C2×C11—41no—
309C2×C11—41no—
310C2×C11—161no—
311C2×C11#151611yescharacteristic
312C2×C11#212111yescharacteristic
313C2×C11C2×#35311yescharacteristic
314D11—22no—
315D11—41no—
316D11—81no—
317C24—21no—
318C24—111no—
319C24—111no—
320C24—221no—
321C24—221no—
322C24—221no—
323C24—221no—
324C24—441no—
325C24—442no—
326C24—881no—
327C24D4×D1111yescharacteristic
328C2×D4—41no—
329C2×D4—42no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—81no—
333C2×D4—81no—
334C2×D4—442no—
335C2×D4—441no—
336C2×D4—441no—
337C2×D4—442no—
338C2×D4—442no—
339C2×D4—442no—
340C2×D4—881no—
341C22×C4—21no—
342C22×C4—41no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—442no—
352C22×C4—441no—
353C22×C4—881no—
354C22×C4C2×C4×D1111yescharacteristic
355C22×C4D4×D1111yescharacteristic
356C2×C8—41no—
357C2×C8—441no—
358C2×C8—882no—
359C4⋊C4—441no—
360C4⋊C4—442no—
361C4⋊C4—442no—
362C22⋊C4—41no—
363C22⋊C4—42no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—224no—
367C22⋊C4—441no—
368C22⋊C4—441no—
369C22⋊C4—442no—
370C22⋊C4—441no—
371C22⋊C4—442no—
372C22⋊C4—442no—
373C22⋊C4—442no—
374C22⋊C4—441no—
375C22⋊C4—441no—
376C22⋊C4—882no—
377C22⋊C4—882no—
378C42—881no—
379C11#1184311yescharacteristic, complemented, Sylow
380C23—21no—
381C23—21no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—111no—
392C23—111no—
393C23—222no—
394C23—221no—
395C23—221no—
396C23—221no—
397C23—221no—
398C23—221no—
399C23—441no—
400C23—441no—
401C23—441no—
402C23—441no—
403C23—441no—
404C23—441no—
405C23—441no—
406C23—442no—
407C23—442no—
408C23—881no—
409C23—881no—
410C23—882no—
411C23—882no—
412C23—884no—
413C23C22⋊C4×D1111yescharacteristic
414C23#6696511yescharacteristic
415C23#6696911yescharacteristic
416D4—82no—
417D4—82no—
418D4—82no—
419D4—884no—
420D4—882no—
421D4—882no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—222no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—442no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—881no—
444C2×C4—881no—
445C2×C4—881no—
446C2×C4—881no—
447C2×C4—881no—
448C2×C4—881no—
449C8—81no—
450C8—881no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—112no—
468C22—221no—
469C22—221no—
470C22—221no—
471C22—221no—
472C22—221no—
473C22—442no—
474C22—442no—
475C22—442no—
476C22—441no—
477C22—441no—
478C22—441no—
479C22—881no—
480C22—882no—
481C22—882no—
482C22—882no—
483C22—882no—
484C22D11×#9911yescharacteristic
485C22#1062238511yescharacteristic
486C22#1062243411yescharacteristic
487C4—42no—
488C4—41no—
489C4—41no—
490C4—161no—
491C4—442no—
492C4—441no—
493C4—441no—
494C4—881no—
495C4—1761no—
496C2—21no—
497C2—21no—
498C2—41no—
499C2—41no—
500C2—161no—
501C2—222no—
502C2—441no—
503C2—881no—
504C2#1306716911yescharacteristic
505C2#1307025911yescharacteristic
506C2D11×#35311yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1343C2
socleC22×C11C2×#99
prime radical#13073541C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1343D11
hypocenterC11#11843
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. #13066641C2semidirect
5. #13066639C2semidirect
6. #13066613C2semidirect
7. C11×#1343C2semidirect
8. C2×#66991C4semidirect
13. #10622836C4semidirect
19. #10622290C4semidirect
20. #10622279C4semidirect
133. #1343D11semidirect
379. C11#11843semidirect

Maximal subgroups

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

subgroupindex
#130735412
#130686892
D11×#3232
#130666412
#130666392
#130666132
C11×#13432
#1184311