Finite Group Databasebeta

← #14650811

Subgroups — #14650811

Order 2816.

576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079413C211yesmaximal, characteristic
2#13071770C211yesmaximal, characteristic, complemented
3#13067145C211yesmaximal, characteristic, complemented
4#13067131C211yesmaximal, characteristic, complemented
5#13066522C211yesmaximal, characteristic, complemented
6#13066469C211yesmaximal, characteristic, complemented
7C11×#1964C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C2×C11×#99—21no—
11C2×C11×#99—21no—
12C11×#380C2211yescharacteristic
13C4×C11×C22⋊C4C2211yescharacteristic
14#10622830C412yescomplemented
15#10622824C2211yescharacteristic
16#10622820C2211yescharacteristic
17#10622820C2211yescharacteristic
18#10622652—22no—
19#10622649—21no—
20#10622647—21no—
21#10622603—21no—
22#10622602—21no—
23#10622581C412yescomplemented
24#10622570—21no—
25#10622569—21no—
26#10622278—21no—
27#10622266—21no—
28#10622175—21no—
29#10622175—21no—
30#10622089—22no—
31C22×D4×C11—21no—
32C22×D4×C11C2×C411yescharacteristic, complemented
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C22×D44D411yescharacteristic
36C22×C4×D11—21no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#121—21no—
40C11×#121—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4D411yescharacteristic
46C2×C11×C22⋊C4D411yescharacteristic
47C2×C42×C11—21no—
48C2×C22⋊Dic11—21no—
49C2×#4323—22no—
50#66983—21no—
51#66983—21no—
52#66983C2×C412yes—
53#66983D412yes—
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×C4⋊Dic11D411yescharacteristic
59C2×Dic11⋊C4—21no—
60C2×C4×Dic11—21no—
61C2×#4318—21no—
62C2×#4318—21no—
63C11×#99—42no—
64C11×#99—42no—
65C11×#95—21no—
66C11×#95—21no—
67#66896—22no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95D411yescharacteristic
72C11⋊#95D411yescharacteristic
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)C2×C412yescomplemented
77#66873—22no—
78#66872—22no—
79#9343—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11C2×D411yescharacteristic
82C23×D11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—81no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11—81no—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C2×C22⋊D11—22no—
104C2×C22⋊D11—22no—
105C2×C22⋊D11—81no—
106C2×C22⋊D11—81no—
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—21no—
110C2×D44—21no—
111C2×D44—81no—
112C2×D44C22⋊C412yes—
113C2×C4×D11—81no—
114C2×C4×D11—81no—
115C2×C4×D11—81no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—81no—
119C11×C22⋊C4—22no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C42×C11—81no—
126C22⋊Dic11—81no—
127#4323—82no—
128(C2×D11)⋊C4—22no—
129(C2×D11)⋊C4—22no—
130(C2×D11)⋊C4—81no—
131(C2×D11)⋊C4—81no—
132(C2×D11)⋊C4—81no—
133C4⋊Dic11—21no—
134C4⋊Dic11C22⋊C412yes—
135Dic11⋊C4—81no—
136C4×Dic11—81no—
137#4318—81no—
138#4318—81no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—41no—
141#3192—111no—
142#2377—111no—
143#1964D1111yescharacteristic, complemented
144#1510—111no—
145#1507—111no—
146#1305—111no—
147#1284—111no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—81no—
156C23×C11—81no—
157C23×C11C4×D411yescharacteristic
158C23×C11#12011yescharacteristic
159C23×C11#12111yescharacteristic
160C22×D11—22no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167D4×C11—42no—
168D4×C11—81no—
169D4×C11—81no—
170D4×C11—81no—
171D4×C11—81no—
172D4×C11—81no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—81no—
190C2×C4×C11—81no—
191C2×C4×C11C2×C22⋊C411yescharacteristic
192C2×C4×C11C4×D411yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12311yescharacteristic
195C22⋊D11—82no—
196C22⋊D11—82no—
197C2×Dic11—22no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206D44—42no—
207D44—81no—
208C4×D11—84no—
209C11⋊C8—42no—
210C11⋊C8—81no—
211C2×#121—111no—
212C2×#121C2×D1111yescharacteristic
213#481—112no—
214#481—221no—
215#469—222no—
216#447—112no—
217#447—221no—
218C2×#99—21no—
219C2×#99—21no—
220#407—111no—
221#407—111no—
222#390—221no—
223#388—221no—
224#387—221no—
225#386—221no—
226#386—221no—
227#385—221no—
228#381—111no—
229#380C2×D1111yescharacteristic
230C4×C22⋊C4C2×D1111yescharacteristic
231#327—222no—
232#327—221no—
233#327—221no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11—161no—
248C22×C11—161no—
249C22×C11#38611yescharacteristic
250C22×C11#45311yescharacteristic
251C22×C11#45411yescharacteristic
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—42no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—81no—
264C4×C11—81no—
265C4×C11—82no—
266C4×C11—81no—
267Dic11—42no—
268Dic11—81no—
269Dic11—81no—
270C22×D4—21no—
271C22×D4—111no—
272C22×D4—221no—
273C22×D4C4×D1111yescharacteristic, complemented
274C23×C4—221no—
275C23×C4C22×D1111yescharacteristic
276C2×D8—222no—
277C2×M16—221no—
278C2×M16—221no—
279#121—21no—
280#121—21no—
281#121—21no—
282#121—21no—
283#121—112no—
284#121—112no—
285#121—221no—
286#121—221no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4C4×D1111yescharacteristic, complemented
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—221no—
294C2×C22⋊C4—221no—
295C2×C22⋊C4—221no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4C22⋊D1111yescharacteristic
299C2×C22⋊C4C22⋊D1111yescharacteristic
300C2×C42—21no—
301C2×C42—221no—
302#106—222no—
303#102—222no—
304#102—222no—
305#99—42no—
306#99—42no—
307C22⋊C8—112no—
308C22⋊C8—221no—
309C22⋊C8—221no—
310C22⋊C8—221no—
311#95—21no—
312#95—21no—
313#95—111no—
314#95—111no—
315#95—221no—
316#95—221no—
317#95—221no—
318C2×C11—21no—
319C2×C11—21no—
320C2×C11—41no—
321C2×C11—41no—
322C2×C11—161no—
323C2×C11#188311yescharacteristic
324C2×C11#190411yescharacteristic
325C2×C11#191311yescharacteristic
326D11—82no—
327C24—21no—
328C24—221no—
329C24C2×C22⋊D1111yescharacteristic
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—81no—
339C2×D4—112no—
340C2×D4—222no—
341C2×D4—222no—
342C2×D4—221no—
343C2×D4—881no—
344C2×D4—881no—
345C2×D4—881no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—41no—
350C22×C4—81no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—881no—
355C22×C4—881no—
356C22×C4—881no—
357C22×C4C2×C4×D1111yescharacteristic
358C22×C4#433911yescharacteristic
359C22×C4D4×D1111yescharacteristic
360C22×C4D4×D1111yescharacteristic
361C22×C4D4×D1111yescharacteristic
362C22×C4#434111yescharacteristic
363D8—882no—
364M16—881no—
365M16—881no—
366C2×C8—222no—
367C2×C8—441no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—81no—
371C4⋊C4—112no—
372C4⋊C4—221no—
373C4⋊C4—881no—
374C22⋊C4—22no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—222no—
381C22⋊C4—222no—
382C22⋊C4—881no—
383C22⋊C4—881no—
384C22⋊C4—881no—
385C22⋊C4—881no—
386C42—81no—
387C42—881no—
388C11#934311yescharacteristic, complemented, Sylow
389C23—21no—
390C23—21no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—81no—
397C23—81no—
398C23—222no—
399C23—441no—
400C23—441no—
401C23—441no—
402C23—441no—
403C23—441no—
404C23—441no—
405C23C4×C22⋊D1111yescharacteristic
406C23#6699011yescharacteristic
407C23#6699111yescharacteristic
408D4—42no—
409D4—81no—
410D4—81no—
411D4—81no—
412D4—81no—
413D4—81no—
414D4—442no—
415D4—881no—
416D4—882no—
417D4—882no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—222no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—884no—
446C2×C4C22⋊C4×D1111yescharacteristic
447C2×C4(C22⋊D11)⋊C411yescharacteristic
448C2×C4#6693611yescharacteristic
449C2×C4#6693711yescharacteristic
450C8—442no—
451C8—881no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—161no—
466C22—161no—
467C22—442no—
468C22—442no—
469C22—442no—
470C22—881no—
471C22—881no—
472C22—881no—
473C22—881no—
474C22#1062256911yescharacteristic
475C22#1062267511yescharacteristic
476C22#1062269011yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—81no—
482C4—81no—
483C4—82no—
484C4—81no—
485C4—442no—
486C4—881no—
487C4—881no—
488C2—21no—
489C2—21no—
490C2—41no—
491C2—41no—
492C2—161no—
493C2—882no—
494C2#1306899511yescharacteristic
495C2#1306910611yescharacteristic
496C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1964C2
socleC22×C11#386
prime radical#13079413C2
cosocleC23×C4×C11C23
hypercenter#1964D11
hypocenterC11#9343
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #13071770C2semidirect
3. #13067145C2semidirect
4. #13067131C2semidirect
5. #13066522C2semidirect
6. #13066469C2semidirect
7. C11×#1964C2semidirect
14. #10622830C4semidirect
23. #10622581C4semidirect
32. C22×D4×C11C2×C4semidirect
42. C2×C11×C4⋊C4C2×C4semidirect
76. C22⋊(C11⋊C8)C2×C4semidirect
143. #1964D11semidirect
273. C22×D4C4×D11semidirect
290. C2×C4⋊C4C4×D11semidirect
388. C11#9343semidirect

Maximal subgroups

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

subgroupindex
#130794132
#130717702
#130671452
#130671312
#130665222
#130664692
C11×#19642
#934311