Finite Group Databasebeta

← #14650980

Subgroups — #14650980

Order 2816.

774 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 774 conjugacy classes of subgroups — too many to draw. Only its 97 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#13077866C211yesmaximal, characteristic
2#13071456C211yesmaximal, characteristic, complemented
3#13069453C211yesmaximal, characteristic, complemented
4#13068559C211yesmaximal, characteristic, complemented
5#13066523C211yesmaximal, characteristic, complemented
6#13066502C211yesmaximal, characteristic, complemented
7C11×#1507C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C2×C11×#121C2211yescharacteristic
10C2×#66985C412yescomplemented
11C2×C4×Dic22—21no—
12C11×#407C2211yescharacteristic
13C4×C11×C22⋊C4C2211yescharacteristic
14C2×#66898—22no—
15#10622825C2211yescharacteristic
16C4×C22⋊Dic11C2211yescharacteristic
17#10622820C2211yescharacteristic
18C2×#66889—22no—
19#10622653—21no—
20#10622650—22no—
21#10622649—21no—
22#10622579C412yescomplemented
23#10622570—22no—
24#10622552—21no—
25#10622280—21no—
26#10622279—21no—
27C11×#327—21no—
28C11×#327—21no—
29C22×D4×C11—21no—
30C22×D4×C11C2×C411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—21no—
33C2×#4339—21no—
34C2×#4339—21no—
35C2×#4339—44no—
36C2×#4339C2×C412yes—
37C2×#4339D412yes—
38C22×D44D411yescharacteristic
39C22×C4×D11—21no—
40C22×Dic22D411yescharacteristic
41C2×C11×M16—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C11×#121—21no—
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C42×C11—21no—
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11D412yes—
52C2×#4324—22no—
53#66985—44no—
54C2×#4323—22no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11—21no—
58C2×Dic11⋊C4—22no—
59C2×C4×Dic11—22no—
60C2×C4×Dic11—21no—
61C2×#4318C2×C412yes—
62C4×Dic22—44no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×#95D411yescharacteristic
66C11×#95D411yescharacteristic
67#66898—44no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72#66889—44no—
73#66874—22no—
74#66873—22no—
75#9368—111nomaximal, Sylow
76C24×C11—21no—
77C24×C11C2×D411yescharacteristic
78C23×D11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—42no—
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C2×C22⋊D11—22no—
97C2×C22⋊D11—22no—
98C2×C22⋊D11—44no—
99C22×Dic11—21no—
100C22×Dic11—22no—
101C22×Dic11—41no—
102#4339—24no—
103#4339—24no—
104#4339—42no—
105#4339—42no—
106#4339—44no—
107#4339—44no—
108C2×D44—21no—
109C2×D44—42no—
110C2×D44C22⋊C412yes—
111C2×C4×D11—22no—
112C2×C4×D11—22no—
113C2×C4×D11—44no—
114C2×Dic22—24no—
115C2×Dic22—21no—
116C2×Dic22C22⋊C412yes—
117C11×M16—42no—
118C2×C8×C11—41no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C22⋊C4—42no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C42×C11—42no—
125C22⋊Dic11—22no—
126C22⋊Dic11—42no—
127C22⋊Dic11—41no—
128#4324—44no—
129#4323—44no—
130(C2×D11)⋊C4—44no—
131(C2×D11)⋊C4—82no—
132C4⋊Dic11—42no—
133Dic11⋊C4—44no—
134C4×Dic11—42no—
135C4×Dic11—44no—
136#4318—42no—
137C2×C11⋊C8—22no—
138#3006—111no—
139#2341—111no—
140#1964—111no—
141#1789—111no—
142#1507D1111yescharacteristic, complemented
143#1305—111no—
144#1297—111no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—42no—
150C23×C11—41no—
151C23×C11—81no—
152C23×C11—81no—
153C23×C11C4×D411yescharacteristic
154C23×C11#12011yescharacteristic
155C23×C11#12111yescharacteristic
156C22×D11—22no—
157C22×D11—42no—
158C22×D11—42no—
159C22×D11—41no—
160C22×D11—41no—
161D4×C11—42no—
162D4×C11—81no—
163D4×C11—82no—
164D4×C11—81no—
165D4×C11—81no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11C2×C22⋊C411yescharacteristic
181C2×C4×C11C4×D411yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12311yescharacteristic
184C22⋊D11—44no—
185C22⋊D11—44no—
186C2×Dic11—24no—
187C2×Dic11—22no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—81no—
193C2×Dic11—81no—
194D44—22no—
195D44—22no—
196D44—42no—
197C4×D11—44no—
198C4×D11—44no—
199Dic22—24no—
200Dic22—22no—
201Dic22#9914yescomplemented
202C8×C11—81no—
203C11⋊C8—42no—
204C22×#41—111no—
205C2×AGL(1,ℤ/8)—112no—
206C2×#121C2×D1111yescharacteristic
207C2×C4×Q8—221no—
208#449—222no—
209#448—221no—
210#447—221no—
211C2×#104—222no—
212#417—112no—
213C2×#99—222no—
214#407—111no—
215#407C2×D1111yescharacteristic
216#390—221no—
217#390—222no—
218#380—111no—
219#380—221no—
220C4×C22⋊C4—111no—
221C4×C22⋊C4—221no—
222C4×C22⋊C4C2×D1111yescharacteristic
223#327—21no—
224#327—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—162no—
239C22×C11#38611yescharacteristic
240C22×C11#45311yescharacteristic
241C22×C11#45411yescharacteristic
242C2×D11—42no—
243C2×D11—42no—
244C2×D11—42no—
245C2×D11—82no—
246C2×D11—82no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—42no—
251C4×C11—81no—
252C4×C11—81no—
253C4×C11C2×#9912yes—
254Dic11—24no—
255Dic11—82no—
256Dic11—82no—
257C2×#41—112no—
258C2×#41—112no—
259C2×#41—221no—
260C2×#41—221no—
261C2×#41—444no—
262C22×Q8—111no—
263C22×D4—21no—
264C22×D4—111no—
265C22×D4—221no—
266C22×D4C4×D1111yescharacteristic
267C23×C4—221no—
268C23×C4C22×D1111yescharacteristic
269AGL(1,ℤ/8)—444no—
270C2×SD16—222no—
271C2×D8—222no—
272C2×M16—21no—
273C2×M16—112no—
274#121—21no—
275#121—21no—
276#121—21no—
277#121—21no—
278C4×Q8—444no—
279C2×C4⋊C4—222no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4C4×D1111yescharacteristic
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—112no—
285C2×C22⋊C4—221no—
286C2×C22⋊C4—222no—
287C2×C22⋊C4—222no—
288C2×C42—21no—
289C2×C42—222no—
290C2×C42—221no—
291#104—444no—
292#103—222no—
293#102—222no—
294#99—444no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—221no—
298C22⋊C8—221no—
299#95—221no—
300#95—221no—
301#95C22⋊D1111yescharacteristic
302#95C22⋊D1111yescharacteristic
303C2×C11—21no—
304C2×C11—21no—
305C2×C11—41no—
306C2×C11—41no—
307C2×C11—161no—
308C2×C11#188311yescharacteristic
309C2×C11#189811yescharacteristic
310C2×C11#190611yescharacteristic
311D11—82no—
312C24—21no—
313C24—221no—
314C24D4×D1111yescharacteristic
315#41—224no—
316#41—224no—
317#41—442no—
318#41—442no—
319#41—444no—
320#41—444no—
321C2×Q8—112no—
322C2×Q8—224no—
323C2×Q8—221no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—42no—
327C2×D4—42no—
328C2×D4—42no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—112no—
332C2×D4—222no—
333C2×D4—222no—
334C2×D4—221no—
335C2×D4—442no—
336C2×D4—444no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—42no—
341C22×C4—221no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4—444no—
346C22×C4—441no—
347C22×C4C2×C4×D1111yescharacteristic
348C22×C4#433911yescharacteristic
349C22×C4D4×D1111yescharacteristic
350C22×C4D4×D1111yescharacteristic
351C22×C4#434111yescharacteristic
352C22×C4C2×C22⋊D1111yescharacteristic
353SD16—444no—
354D8—444no—
355M16—42no—
356M16—442no—
357C2×C8—41no—
358C2×C8—222no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—442no—
362C4⋊C4—444no—
363C22⋊C4—42no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—222no—
367C22⋊C4—444no—
368C22⋊C4—441no—
369C22⋊C4—442no—
370C22⋊C4—882no—
371C42—42no—
372C42—442no—
373C42—444no—
374C11#936811yescharacteristic, complemented, Sylow
375C23—21no—
376C23—21no—
377C23—41no—
378C23—41no—
379C23—42no—
380C23—41no—
381C23—81no—
382C23—81no—
383C23—222no—
384C23—442no—
385C23—442no—
386C23—441no—
387C23—441no—
388C23(C22⋊D11)⋊C411yescharacteristic
389C23#6693711yescharacteristic
390C23#6699011yescharacteristic
391Q8—114no—
392Q8—224no—
393Q8—222no—
394D4—42no—
395D4—81no—
396D4—82no—
397D4—81no—
398D4—81no—
399D4—222no—
400D4—222no—
401D4—442no—
402D4—444no—
403D4—444no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—224no—
419C2×C4—222no—
420C2×C4—444no—
421C2×C4—444no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—881no—
427C2×C4—881no—
428C2×C4C22⋊C4×D1111yescharacteristic
429C2×C4#6693611yescharacteristic
430C2×C4C4×C22⋊D1111yescharacteristic
431C2×C4#6699111yescharacteristic
432C8—81no—
433C8—442no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22—162no—
448C22—442no—
449C22—442no—
450C22—442no—
451C22—882no—
452C22—882no—
453C22#1062256911yescharacteristic
454C22#1062281111yescharacteristic
455C22#1062281411yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—42no—
460C4—81no—
461C4—81no—
462C4—224no—
463C4—882no—
464C4—882no—
465C4D11×#9912yes—
466C2—21no—
467C2—21no—
468C2—41no—
469C2—41no—
470C2—161no—
471C2—882no—
472C2#1306898911yescharacteristic
473C2#1306906611yescharacteristic
474C2#1306912011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1507C2
socleC22×C11#386
prime radical#13077866C2
cosocleC23×C4×C11C23
hypercenter#1507D11
hypocenterC11#9368
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #13071456C2semidirect
3. #13069453C2semidirect
4. #13068559C2semidirect
5. #13066523C2semidirect
6. #13066502C2semidirect
7. C11×#1507C2semidirect
10. C2×#66985C4semidirect
22. #10622579C4semidirect
142. #1507D11semidirect
201. Dic22#99semidirect
374. C11#9368semidirect

Maximal subgroups

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

subgroupindex
#130778662
#130714562
#130694532
#130685592
#130665232
#130665022
C11×#15072
#936811