Finite Group Databasebeta

← #14663221

Subgroups — #14663221

Order 2816.

738 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 99 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#13066957C211yesmaximal, characteristic, complemented
2#13066954C211yesmaximal, characteristic, complemented
3#13066564C212yesmaximal, complemented
4#13066544C212yesmaximal, complemented
5C4×C11×#120C211yesmaximal, characteristic
6C24×C4×C11C411yescharacteristic
7C2×C11×#120C411yescharacteristic
8C2×C4×D4×C11—21no—
9C2×C4×D4×C11C2211yescharacteristic
10C11×#386—21no—
11C11×#386C411yescharacteristic
12C11×#385—21no—
13C11×#385C2211yescharacteristic
14C11×#379C2211yescharacteristic
15C4×C11×C22⋊C4—21no—
16C4×C11×C22⋊C4C411yescharacteristic
17#10622820—21no—
18#10622539—21no—
19#10622166—21no—
20#10622163—21no—
21#10622163C2212yes—
22#10622163C2212yes—
23C25×C11C2×C411yescharacteristic
24C22×D4×C11—21no—
25C22×D4×C11C2×C411yescharacteristic
26C23×C4×C11—21no—
27C23×C4×C11—21no—
28C23×C4×C11—44no—
29C23×C4×C11—41no—
30C23×C4×C11—41no—
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C11×#120—22no—
35C11×#120—22no—
36C4×D4×C11—41no—
37C4×D4×C11—41no—
38C4×D4×C11—44no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4C2×C411yescharacteristic
46C2×C11×C22⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4D411yescharacteristic
48C2×C11×C22⋊C4C2311yescharacteristic
49C2×C42×C11—21no—
50C2×C42×C11D411yescharacteristic
51C2×#4318—41no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C22⋊(C11⋊C8)—22no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58C4⋊(C11⋊C8)—41no—
59#66867—41no—
60#11525—111nomaximal, Sylow
61C24×C11—21no—
62C24×C11—21no—
63C24×C11—42no—
64C24×C11—41no—
65C24×C11—42no—
66C24×C11—41no—
67C24×C11C22⋊C411yescharacteristic
68C24×C11M1612yescomplemented
69C24×C11C22×C411yescharacteristic
70C2×D4×C11—24no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—42no—
76C2×D4×C11—42no—
77C22×C4×C11—24no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11—44no—
93C22×C4×C11—44no—
94C22×C4×C11—44no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—44no—
99C22×C4×C11C22⋊C411yescharacteristic
100C22×C4×C11C22⋊C411yescharacteristic
101C22×C4×C11C22⋊C411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C11×C4⋊C4—41no—
105C11×C4⋊C4—42no—
106C11×C22⋊C4—24no—
107C11×C22⋊C4—21no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4M1612yescomplemented
115C42×C11—21no—
116C42×C11—21no—
117C42×C11—42no—
118#4318—82no—
119C2×C11⋊C8—42no—
120C2×C11⋊C8—42no—
121C4×#120D1111yescharacteristic
122#1466—111no—
123#1465—111no—
124#1326—112no—
125#1316—112no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—22no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—41no—
135C23×C11—44no—
136C23×C11—42no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—44no—
141C23×C11—42no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—48no—
148C23×C11—42no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11C2×C22⋊C411yescharacteristic
152C23×C11C2×M1611yescharacteristic
153C23×C11C2×M1611yescharacteristic
154D4×C11—48no—
155D4×C11—42no—
156D4×C11—42no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—21no—
160C2×C4×C11—22no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—44no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—48no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—44no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—81no—
185C2×C4×C11#9911yescharacteristic
186C2×C4×C11#9911yescharacteristic
187C11⋊C8—82no—
188C11⋊C8—82no—
189C24×C4Dic1111yescharacteristic
190C2×#120Dic1111yescharacteristic
191C2×C4×D4—21no—
192C2×C4×D4C2×D1111yescharacteristic
193#432—221no—
194#407—221no—
195#386—21no—
196#386Dic1111yescharacteristic
197#385—21no—
198#385C2×D1111yescharacteristic
199#379C2×D1111yescharacteristic
200C4×C22⋊C4—21no—
201C4×C22⋊C4Dic1111yescharacteristic
202#324—221no—
203#323—112no—
204#323—112no—
205#323—221no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—24no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—44no—
219C22×C11—44no—
220C22×C11—44no—
221C22×C11—44no—
222C22×C11—42no—
223C22×C11—41no—
224C22×C11—42no—
225C22×C11—41no—
226C22×C11—42no—
227C22×C11—41no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—81no—
231C22×C11#40711yescharacteristic
232C22×C11C2×#9911yescharacteristic
233C22×C11#41311yescharacteristic
234C4×C11—21no—
235C4×C11—42no—
236C4×C11—42no—
237C4×C11—41no—
238C4×C11—41no—
239C4×C11—41no—
240C4×C11—41no—
241C4×C11—81no—
242C4×C11AΣL(1,𝔽16)12yes—
243C25C2×Dic1111yescharacteristic
244C22×D4—21no—
245C22×D4C2×Dic1111yescharacteristic
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—44no—
249C23×C4—41no—
250C23×C4—41no—
251C23×C4C2×Dic1111yescharacteristic
252C23×C4C2×Dic1111yescharacteristic
253C23×C4C22⋊D1111yescharacteristic
254C2×M16—441no—
255#120—22no—
256#120—22no—
257C4×D4—41no—
258C4×D4—41no—
259C4×D4—44no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4C22⋊D1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4C2×Dic1111yescharacteristic
267C2×C22⋊C4C2×Dic1111yescharacteristic
268C2×C22⋊C4C22⋊D1111yescharacteristic
269C2×C22⋊C4C22×D1111yescharacteristic
270C2×C42—21no—
271C2×C42C22⋊D1111yescharacteristic
272C4⋊C8—441no—
273C22⋊C8—222no—
274C22⋊C8—222no—
275C22⋊C8—441no—
276#97—441no—
277#95—21no—
278#95—21no—
279#95—21no—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11—44no—
283C2×C11—41no—
284C2×C11—41no—
285C2×C11—81no—
286C2×C11#146511yescharacteristic
287C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
288C2×C11#212011yescharacteristic
289C24—21no—
290C24—21no—
291C24—42no—
292C24—41no—
293C24—42no—
294C24—41no—
295C24#431812yescomplemented
296C24C22⋊Dic1111yescharacteristic
297C24C22×Dic1111yescharacteristic
298C2×D4—24no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—42no—
304C2×D4—42no—
305C22×C4—24no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—44no—
321C22×C4—44no—
322C22×C4—44no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—44no—
327C22×C4C22⋊Dic1111yescharacteristic
328C22×C4C22⋊Dic1111yescharacteristic
329C22×C4C22⋊Dic1111yescharacteristic
330C22×C4C2×C22⋊D1111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332M16—882no—
333C2×C8—442no—
334C2×C8—442no—
335C4⋊C4—41no—
336C4⋊C4—42no—
337C22⋊C4—24no—
338C22⋊C4—21no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—42no—
344C22⋊C4—41no—
345C22⋊C4#431812yescomplemented
346C42—21no—
347C42—21no—
348C42—42no—
349C11#1152511yescharacteristic, complemented, Sylow
350C23—22no—
351C23—22no—
352C23—22no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—41no—
359C23—44no—
360C23—42no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—44no—
365C23—42no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23—48no—
372C23—42no—
373C23—41no—
374C23—41no—
375C23C2×#431811yescharacteristic
376C23C2×#431811yescharacteristic
377C23C2×C22⋊Dic1111yescharacteristic
378D4—48no—
379D4—42no—
380D4—42no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—44no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—48no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—44no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—81no—
409C2×C4#6689811yescharacteristic
410C2×C4#6689811yescharacteristic
411C8—882no—
412C8—882no—
413C22—21no—
414C22—21no—
415C22—24no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—44no—
426C22—44no—
427C22—44no—
428C22—44no—
429C22—42no—
430C22—41no—
431C22—42no—
432C22—41no—
433C22—42no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—81no—
438C22#1062282011yescharacteristic
439C22C2×#6689811yescharacteristic
440C22#1062285011yescharacteristic
441C4—21no—
442C4—42no—
443C4—41no—
444C4—42no—
445C4—41no—
446C4—41no—
447C4—41no—
448C4—81no—
449C4#1062217412yes—
450C2—21no—
451C2—21no—
452C2—44no—
453C2—41no—
454C2—41no—
455C2—81no—
456C2#1306695411yescharacteristic
457C2C2×#1062217411yescharacteristic
458C2#1307025711yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC4×C11×#120C2
socleC22×C11C2×#99
prime radicalC2×C11×#120C4
cosocleC2×C11×C22⋊C4C23
hypercenterC4×#120D11
hypocenterC11#11525
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. #13066957C2semidirect
2. #13066954C2semidirect
3. #13066564C2semidirect
4. #13066544C2semidirect
68. C24×C11M16semidirect
114. C11×C22⋊C4M16semidirect
295. C24#4318semidirect
345. C22⋊C4#4318semidirect
349. C11#11525semidirect

Maximal subgroups

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

subgroupindex
#130669572
#130669542
#130665642
#130665442
C4×C11×#1202
#1152511