Finite Group Databasebeta

← #14664337

Subgroups — #14664337

Order 2816.

532 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 83 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#13073572C211yesmaximal, characteristic
2#13066957C211yesmaximal, characteristic, complemented
3#13066615C212yesmaximal, complemented
4#13066612C212yesmaximal, complemented
5C4×C11×#99C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66992—21no—
8C2×#66983C411yescharacteristic, complemented
9C2×C11×#99—21no—
10C4×C11×C22⋊C4—21no—
11#10622826—21no—
12C2×C11⋊#95C411yescharacteristic, complemented
13#10622604C411yescharacteristic, complemented
14#10622596C411yescharacteristic, complemented
15#10622573C2211yescharacteristic
16#10622571—21no—
17#10622566C2211yescharacteristic
18#10622553—21no—
19#10622539—21no—
20C11×#342C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C23×Dic11—21no—
29C22×D44C2×C411yescharacteristic
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C11×C22⋊C4C2311yescharacteristic
36C2×C42×C11—41no—
37C2×C42×C11D411yescharacteristic
38C2×C22⋊Dic11—21no—
39#66992—44no—
40#66983—41no—
41#66983—41no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×Dic11⋊C4—21no—
48C11×#99—24no—
49C11×#95—41no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55C22⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—41no—
57#66867—41no—
58#11775—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C24×C11C2×D411yescharacteristic
61C23×D11—21no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—41no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—42no—
70C22×C4×C11—81no—
71C22×C4×C11—81no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—42no—
81C2×C22⋊D11—42no—
82C2×C22⋊D11—81no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—42no—
87C22×Dic11—42no—
88C22×Dic11—81no—
89C2×D44—41no—
90C2×D44—81no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—24no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—42no—
96C42×C11—21no—
97C42×C11—21no—
98C42×C11—82no—
99C22⋊Dic11—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—81no—
105C4⋊Dic11—41no—
106Dic11⋊C4—42no—
107C2×C11⋊C8—42no—
108#2543—111no—
109C4×#99D1111yescharacteristic, complemented
110#1466—111no—
111#1344—112no—
112#1343—112no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11#10412yes—
122C23×C11C2×C22⋊C411yescharacteristic
123C23×C11AGL(1,ℤ/8)12yes—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131D4×C11—44no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—44no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11—82no—
148C2×C4×C11—82no—
149C2×C4×C11#9911yescharacteristic
150C2×C4×C11#9911yescharacteristic
151C22⋊D11—84no—
152C22⋊D11—84no—
153C2×Dic11—22no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—84no—
163D44—82no—
164C11⋊C8—82no—
165C2×#121—111no—
166C2×#121—221no—
167C2×C4×D4C2×D1111yescharacteristic
168#432—221no—
169C2×#99—21no—
170#398—111no—
171#397—111no—
172#394—111no—
173#392—111no—
174#388—221no—
175#386—221no—
176#386—221no—
177C4×C22⋊C4—21no—
178C2×#95—111no—
179#342C2×D1112yes—
180#323—112no—
181#323—221no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—42no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—81no—
194C22×C11C2×#9911yescharacteristic
195C22×C11#41811yescharacteristic
196C22×C11C2×#10411yescharacteristic
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—84no—
211Dic11—42no—
212Dic11—81no—
213Dic11—81no—
214C22×D4—111no—
215C22×D4—221no—
216C22×D4—221no—
217C22×D4C22⋊D1111yescharacteristic
218C23×C4—221no—
219C23×C4C4×D1111yescharacteristic
220C23×C4C22⋊D1111yescharacteristic
221#121—444no—
222#121—441no—
223#121—441no—
224C4×D4—41no—
225C4×D4—41no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4C4×D1111yescharacteristic
229C2×C22⋊C4—22no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4D4411yescharacteristic
236C2×C22⋊C4C22×D1111yescharacteristic
237C2×C42—41no—
238C2×C42D4411yescharacteristic
239C4⋊C8—441no—
240#99—24no—
241C22⋊C8—222no—
242#97—441no—
243#95—41no—
244#95—111no—
245#95—111no—
246#95—221no—
247#95—221no—
248#95—221no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11—42no—
252C2×C11—42no—
253C2×C11#150711yescharacteristic
254C2×C11#212111yescharacteristic
255C2×C11#212611yescharacteristic
256D11—161no—
257C24—221no—
258C24(C2×D11)⋊C411yescharacteristic
259C24C2×C22⋊D1111yescharacteristic
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—41no—
263C2×D4—441no—
264C2×D4—442no—
265C2×D4—442no—
266C2×D4—442no—
267C2×D4—442no—
268C2×D4—442no—
269C2×D4—881no—
270C2×D4—881no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—42no—
276C22×C4—81no—
277C22×C4—81no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—442no—
282C22×C4—442no—
283C22×C4—881no—
284C22×C4(C2×D11)⋊C411yescharacteristic
285C22×C4(C2×D11)⋊C411yescharacteristic
286C22×C4(C2×D11)⋊C411yescharacteristic
287C22×C4C2×C4×D1111yescharacteristic
288C22×C4C2×D4411yescharacteristic
289C2×C8—442no—
290C4⋊C4—41no—
291C4⋊C4—441no—
292C4⋊C4—442no—
293C22⋊C4—24no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—42no—
297C22⋊C4—442no—
298C22⋊C4—442no—
299C22⋊C4—442no—
300C22⋊C4—441no—
301C22⋊C4—441no—
302C22⋊C4—881no—
303C42—21no—
304C42—21no—
305C42—82no—
306C11#1177511yescharacteristic, complemented, Sylow
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—441no—
316C23—441no—
317C23—441no—
318C23—441no—
319C23—441no—
320C23—441no—
321C23—441no—
322C23#6686912yes—
323C23C2×(C2×D11)⋊C411yescharacteristic
324C23#6700212yes—
325D4—44no—
326D4—882no—
327D4—884no—
328D4—884no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—44no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4—222no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—884no—
356C2×C4#6687011yescharacteristic
357C2×C4#6687011yescharacteristic
358C8—882no—
359C22—21no—
360C22—21no—
361C22—22no—
362C22—22no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—81no—
371C22—881no—
372C22—881no—
373C22—881no—
374C22—881no—
375C22—881no—
376C22—881no—
377C22—881no—
378C22C2×#6686911yescharacteristic
379C22C2×#6687011yescharacteristic
380C22#1062261411yescharacteristic
381C4—21no—
382C4—21no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—84no—
388C4—442no—
389C4—881no—
390C4—881no—
391C2—21no—
392C2—21no—
393C2—42no—
394C2—42no—
395C2—1761no—
396C2#1306713111yescharacteristic
397C2#1307026011yescharacteristic
398C2#1307027911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC4×C11×#99C2
socleC22×C11C2×#99
prime radical#13073572C2
cosocleC2×C11×C22⋊C4C23
hypercenterC4×#99D11
hypocenterC11#11775
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #13066957C2semidirect
3. #13066615C2semidirect
4. #13066612C2semidirect
5. C4×C11×#99C2semidirect
8. C2×#66983C4semidirect
12. C2×C11⋊#95C4semidirect
13. #10622604C4semidirect
14. #10622596C4semidirect
109. C4×#99D11semidirect
306. C11#11775semidirect

Maximal subgroups

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

subgroupindex
#130735722
#130669572
#130666152
#130666122
C4×C11×#992
#1177511