Finite Group Databasebeta

← #14664246

Subgroups — #14664246

Order 2816.

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

normal subgroups only

This group has 700 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
1#13073541C211yesmaximal, characteristic
2D11×#342C211yesmaximal, characteristic, complemented
3#13066941C211yesmaximal, 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×D11—21no—
12C2×C22⋊C4×D11C2211yescharacteristic
13C11×#392C2211yescharacteristic
14#10622836C411yescharacteristic, complemented
15#10622834—21no—
16#10622570—21no—
17#10622562C2211yescharacteristic
18#10622339—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, complemented
30C22×C22⋊D11—21no—
31C22×C22⋊D11—21no—
32C22×C4×D11—41no—
33C22×C4×D11C2×C411yescharacteristic
34C22×C4×D11D411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4C2311yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11D411yescharacteristic
43#66991—41no—
44#66991—41no—
45#66990—44no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—41no—
49C2×(C2×D11)⋊C4C2×C411yescharacteristic
50C2×(C2×D11)⋊C4D411yescharacteristic
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11C2×C411yescharacteristic, complemented
53C2×Dic11⋊C4—21no—
54C2×C4×Dic11—21no—
55C2×#4313—41no—
56#66936—44no—
57C22⋊C4×D11—24no—
58C22⋊C4×D11—41no—
59C22⋊C4×D11—41no—
60C22⋊C4×D11—42no—
61C11×C22⋊C8—21no—
62C11×#95C2×C411yescharacteristic, complemented
63C11⋊#95C2×C411yescharacteristic, complemented
64C22⋊(C11⋊C8)—21no—
65(C2×D11)⋊C8—41no—
66#11757—111nomaximal, Sylow
67C24×C11—21no—
68C24×C11C2×D411yescharacteristic
69C23×D11—21no—
70C23×D11—21no—
71C23×D11—21no—
72C23×D11—21no—
73C23×D11—22no—
74C23×D11—42no—
75C23×D11—81no—
76C23×D11C22⋊C411yescharacteristic
77C23×D11C22⋊C411yescharacteristic
78C2×D4×C11—42no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—81no—
83C2×D4×C11—81no—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C2×C22⋊D11—42no—
89C2×C22⋊D11—42no—
90C2×C22⋊D11—42no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11—41no—
93C2×C22⋊D11—42no—
94C2×C22⋊D11—81no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—41no—
98C22×Dic11C22⋊C411yescharacteristic
99C22×Dic11C22⋊C411yescharacteristic
100C2×C4×D11—21no—
101C2×C4×D11—21no—
102C2×C4×D11—21no—
103C2×C4×D11—21no—
104C2×C4×D11—42no—
105C2×C4×D11—44no—
106C2×C4×D11—81no—
107C2×C4×D11—82no—
108C2×C4×D11—82no—
109C2×C8×C11—41no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—41no—
114C22⋊Dic11—22no—
115C22⋊Dic11—41no—
116C22⋊Dic11—42no—
117C22⋊Dic11—42no—
118C22⋊Dic11—42no—
119C22⋊Dic11—41no—
120(C2×D11)⋊C4—24no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—42no—
124(C2×D11)⋊C4—44no—
125C4⋊Dic11—41no—
126C4⋊Dic11—42no—
127Dic11⋊C4—42no—
128C4×Dic11—81no—
129C2×C11⋊C8—41no—
130#4313—82no—
131#2539—111no—
132C2×#342—111no—
133#1462—111no—
134#1352—111no—
135#1352—111no—
136#1343—111no—
137#1343D1111yescharacteristic, complemented
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—41no—
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×C11AGL(1,ℤ/8)11yescharacteristic
151C23×C11#13711yescharacteristic
152C22×D11—22no—
153C22×D11—22no—
154C22×D11—21no—
155C22×D11—21no—
156C22×D11—21no—
157C22×D11—22no—
158C22×D11—22no—
159C22×D11—21no—
160C22×D11—22no—
161C22×D11—41no—
162C22×D11—42no—
163C22×D11—42no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—81no—
167C22×D11—81no—
168C22×D11—84no—
169C22×D11—82no—
170C22×D11—82no—
171C22×D11#9911yescharacteristic
172C22×D11#9911yescharacteristic
173C22×D11#10412yes—
174D4×C11—82no—
175D4×C11—82no—
176D4×C11—82no—
177C2×C4×C11—22no—
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—42no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C22⋊D11—84no—
188C22⋊D11—82no—
189C22⋊D11—82no—
190C2×Dic11—22no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—81no—
202C2×Dic11—81no—
203C4×D11—42no—
204C4×D11—81no—
205C4×D11—81no—
206C4×D11—81no—
207C4×D11—88no—
208C8×C11—81no—
209C11⋊C8—81no—
210C2×#123—221no—
211C2×#121—111no—
212C2×#120—221no—
213C22×C22⋊C4—111no—
214C22×C22⋊C4—221no—
215#407—221no—
216#399—111no—
217#399—111no—
218#392—111no—
219#392C2×D1111yescharacteristic
220#390—221no—
221#390—221no—
222C4×C22⋊C4—111no—
223#342—111no—
224#342—221no—
225#342C2×D1111yescharacteristic
226#323—111no—
227#323—221no—
228#323C2×D1111yescharacteristic
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11C2×#9911yescharacteristic
246C22×C11#41711yescharacteristic
247C22×C11C2×#10411yescharacteristic
248C2×D11—21no—
249C2×D11—21no—
250C2×D11—21no—
251C2×D11—21no—
252C2×D11—21no—
253C2×D11—22no—
254C2×D11—42no—
255C2×D11—42no—
256C2×D11—44no—
257C2×D11—44no—
258C2×D11—41no—
259C2×D11—41no—
260C2×D11—42no—
261C2×D11—81no—
262C2×D11—82no—
263C2×D11—82no—
264C2×D11#35312yes—
265C4×C11—42no—
266C4×C11—41no—
267C4×C11—41no—
268C4×C11—82no—
269Dic11—42no—
270Dic11—41no—
271Dic11—41no—
272Dic11—82no—
273Dic11—81no—
274C25—111no—
275C22×D4—21no—
276C22×D4—221no—
277C22×D4—221no—
278C22×D4C4×D1111yescharacteristic, complemented
279C23×C4—111no—
280C23×C4—111no—
281C23×C4—441no—
282C2×M16—441no—
283#123—444no—
284#121—441no—
285#121—441no—
286#120—444no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—221no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—111no—
293C2×C22⋊C4—111no—
294C2×C22⋊C4—111no—
295C2×C22⋊C4—224no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4—441no—
303C2×C22⋊C4—441no—
304C2×C22⋊C4—442no—
305C2×C22⋊C4—441no—
306C2×C22⋊C4C22×D1111yescharacteristic
307C2×C42—221no—
308C22⋊C8—21no—
309C22⋊C8—221no—
310C22⋊C8—441no—
311#95—111no—
312#95C4×D1111yescharacteristic, complemented
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—41no—
316C2×C11—41no—
317C2×C11—161no—
318C2×C11#150411yescharacteristic
319C2×C11#212111yescharacteristic
320C2×C11C2×#35311yescharacteristic
321D11—22no—
322D11—41no—
323D11—42no—
324C24—21no—
325C24—111no—
326C24—111no—
327C24—221no—
328C24—222no—
329C24—221no—
330C24—221no—
331C24—221no—
332C24—442no—
333C24—881no—
334C24D4×D1111yescharacteristic
335C2×D4—41no—
336C2×D4—42no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—81no—
340C2×D4—81no—
341C2×D4—442no—
342C2×D4—441no—
343C2×D4—441no—
344C2×D4—442no—
345C2×D4—442no—
346C2×D4—442no—
347C2×D4—881no—
348C22×C4—21no—
349C22×C4—41no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—442no—
359C22×C4—444no—
360C22×C4—441no—
361C22×C4—881no—
362C22×C4—882no—
363C22×C4—882no—
364C22×C4C2×C4×D1111yescharacteristic
365C22×C4D4×D1111yescharacteristic
366M16—882no—
367C2×C8—41no—
368C2×C8—441no—
369C4⋊C4—441no—
370C4⋊C4—442no—
371C4⋊C4—442no—
372C22⋊C4—22no—
373C22⋊C4—41no—
374C22⋊C4—42no—
375C22⋊C4—41no—
376C22⋊C4—224no—
377C22⋊C4—222no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C22⋊C4—442no—
381C22⋊C4—444no—
382C22⋊C4—441no—
383C22⋊C4—442no—
384C22⋊C4—442no—
385C22⋊C4—442no—
386C22⋊C4—441no—
387C42—881no—
388C11#1175711yescharacteristic, complemented, Sylow
389C23—21no—
390C23—21no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—111no—
401C23—111no—
402C23—112no—
403C23—222no—
404C23—222no—
405C23—222no—
406C23—222no—
407C23—222no—
408C23—221no—
409C23—221no—
410C23—221no—
411C23—221no—
412C23—441no—
413C23—441no—
414C23—441no—
415C23—442no—
416C23—442no—
417C23—881no—
418C23—881no—
419C23—882no—
420C23—882no—
421C23—884no—
422C23C22⋊C4×D1111yescharacteristic
423C23#6696411yescharacteristic
424C23#6696811yescharacteristic
425D4—82no—
426D4—82no—
427D4—82no—
428D4—884no—
429D4—882no—
430D4—882no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—222no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—442no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—442no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—881no—
454C2×C4—881no—
455C2×C4—881no—
456C2×C4—888no—
457C2×C4—881no—
458C2×C4—881no—
459C8—81no—
460C8—881no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—112no—
478C22—221no—
479C22—221no—
480C22—221no—
481C22—222no—
482C22—221no—
483C22—221no—
484C22—442no—
485C22—442no—
486C22—442no—
487C22—444no—
488C22—444no—
489C22—441no—
490C22—441no—
491C22—881no—
492C22—882no—
493C22—882no—
494C22D11×#9911yescharacteristic
495C22#1062238411yescharacteristic
496C22D11×#10411yescharacteristic
497C4—42no—
498C4—41no—
499C4—41no—
500C4—82no—
501C4—442no—
502C4—441no—
503C4—441no—
504C4—882no—
505C4—881no—
506C2—21no—
507C2—21no—
508C2—41no—
509C2—41no—
510C2—161no—
511C2—222no—
512C2—441no—
513C2—442no—
514C2#1306711711yescharacteristic
515C2#1307025911yescharacteristic
516C2D11×#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#11757
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. D11×#342C2semidirect
3. #13066941C2semidirect
4. #13066641C2semidirect
5. #13066639C2semidirect
6. #13066613C2semidirect
7. C11×#1343C2semidirect
8. C2×#66991C4semidirect
14. #10622836C4semidirect
19. #10622290C4semidirect
20. #10622279C4semidirect
29. C22×D4×C11C2×C4semidirect
52. C2×C4⋊Dic11C2×C4semidirect
62. C11×#95C2×C4semidirect
63. C11⋊#95C2×C4semidirect
137. #1343D11semidirect
278. C22×D4C4×D11semidirect
312. #95C4×D11semidirect
388. C11#11757semidirect

Maximal subgroups

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

subgroupindex
#130735412
D11×#3422
#130669412
#130666412
#130666392
#130666132
C11×#13432
#1175711