Finite Group Databasebeta

← #14664120

Subgroups — #14664120

Order 2816.

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

normal subgroups only

This group has 500 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#13074468C211yesmaximal, characteristic
2#13066934C211yesmaximal, characteristic, complemented
3#13066636C212yesmaximal, complemented
4#13066612C212yesmaximal, complemented
5C4×C11×#99C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66928C411yescharacteristic, complemented
8C2×C11×#99—21no—
9C4×C11×C22⋊C4—21no—
10#10622836—21no—
11#10622826—21no—
12#10622826—21no—
13C2×C22⋊(C11⋊C8)—21no—
14#10622606—21no—
15#10622573C411yescharacteristic, complemented
16#10622573C2211yescharacteristic
17#10622560C411yescharacteristic, complemented
18#10622560C2211yescharacteristic
19#10622550C411yescharacteristic, complemented
20C11×#342C2212yes—
21#10622166—21no—
22#10622163C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C22×D44C2×C411yescharacteristic
29C22×Dic22C2×C411yescharacteristic
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4C2311yescharacteristic
36C2×C42×C11—41no—
37C2×C42×C11C2×C411yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C22×C11⋊C8—41no—
45#66928—41no—
46#66928—41no—
47C11×#99—24no—
48C11×#95—41no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55C22⋊(C11⋊C8)—22no—
56C22⋊(C11⋊C8)—41no—
57#11730—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C2×D411yescharacteristic
60C23×D11—21no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—41no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—42no—
69C22×C4×C11—81no—
70C22×C4×C11—81no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C2×C22⋊D11—42no—
77C2×C22⋊D11—42no—
78C2×C22⋊D11—81no—
79C2×C22⋊D11—81no—
80C2×C22⋊D11—81no—
81C2×C22⋊D11—81no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×D44—41no—
86C2×D44—81no—
87C2×Dic22—41no—
88C2×Dic22—81no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—24no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—42no—
94C42×C11—21no—
95C42×C11—21no—
96C42×C11—82no—
97C22⋊Dic11—81no—
98C22⋊Dic11—81no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—81no—
103(C2×D11)⋊C4—81no—
104C2×C11⋊C8—42no—
105C2×C11⋊C8—82no—
106#2631—111no—
107C4×#99D1111yescharacteristic, complemented
108#1459—111no—
109#1351—112no—
110#1343—112no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11#10412yes—
120C23×C11C2×C22⋊C411yescharacteristic
121C23×C11#13512yes—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129D4×C11—44no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—44no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—82no—
146C2×C4×C11—82no—
147C2×C4×C11#9911yescharacteristic
148C2×C4×C11#9911yescharacteristic
149C22⋊D11—84no—
150C22⋊D11—84no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160D44—82no—
161Dic22—82no—
162C11⋊C8—82no—
163C2×#124—111no—
164C2×C4×D4C2×D1111yescharacteristic
165C2×#99—21no—
166C2×C22⋊C8—221no—
167#397—221no—
168#393—111no—
169#393—111no—
170#392—111no—
171#392—111no—
172#392—221no—
173#386—221no—
174#386—221no—
175#383—111no—
176C4×C22⋊C4—21no—
177#342C2×D1112yes—
178#324—221no—
179#323—112no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—22no—
183C22×C11—22no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11C2×#9911yescharacteristic
193C22×C11#41611yescharacteristic
194C22×C11C2×#10411yescharacteristic
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—84no—
209Dic11—81no—
210Dic11—81no—
211Dic11—81no—
212C22×Q8—111no—
213C22×D4—111no—
214C22×D4—221no—
215C22×D4—221no—
216C22×D4C22⋊D1111yescharacteristic
217C23×C4D4411yescharacteristic
218C23×C4C22⋊D1111yescharacteristic
219C22×C8—441no—
220#124—441no—
221#124—441no—
222C4×D4—41no—
223C4×D4—41no—
224C2×C4⋊C4D4411yescharacteristic
225C2×C22⋊C4—22no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4C4×D1111yescharacteristic
233C2×C22⋊C4C22×D1111yescharacteristic
234C2×C42—41no—
235C2×C42C4×D1111yescharacteristic
236#99—24no—
237C22⋊C8—222no—
238C22⋊C8—441no—
239#95—41no—
240#95—111no—
241#95—111no—
242#95—221no—
243#95—221no—
244#95—221no—
245#95—221no—
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—42no—
249C2×C11—42no—
250C2×C11#150111yescharacteristic
251C2×C11#212211yescharacteristic
252C2×C11#212711yescharacteristic
253D11—161no—
254C24—221no—
255C24(C2×D11)⋊C411yescharacteristic
256C24C2×C22⋊D1111yescharacteristic
257C2×Q8—441no—
258C2×Q8—881no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—41no—
262C2×D4—441no—
263C2×D4—442no—
264C2×D4—442no—
265C2×D4—881no—
266C2×D4—881no—
267C2×D4—881no—
268C2×D4—881no—
269C2×D4—881no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—42no—
275C22×C4—81no—
276C22×C4—81no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4(C2×D11)⋊C411yescharacteristic
281C22×C4(C2×D11)⋊C411yescharacteristic
282C22×C4(C2×D11)⋊C411yescharacteristic
283C22×C4C2×C4×D1111yescharacteristic
284C22×C4C2×D4411yescharacteristic
285C2×C8—442no—
286C2×C8—882no—
287C4⋊C4—41no—
288C22⋊C4—24no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—42no—
292C22⋊C4—442no—
293C22⋊C4—441no—
294C22⋊C4—441no—
295C22⋊C4—881no—
296C22⋊C4—881no—
297C22⋊C4—881no—
298C22⋊C4—881no—
299C42—21no—
300C42—21no—
301C42—82no—
302C11#1173011yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—441no—
312C23—441no—
313C23—441no—
314C23—441no—
315C23—441no—
316C23—441no—
317C23—441no—
318C23#6686912yes—
319C23C2×(C2×D11)⋊C411yescharacteristic
320C23#6700312yes—
321Q8—882no—
322D4—44no—
323D4—882no—
324D4—884no—
325D4—884no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—44no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4#6687011yescharacteristic
353C2×C4#6687011yescharacteristic
354C8—882no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—22no—
359C22—42no—
360C22—42no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22—81no—
367C22—881no—
368C22—881no—
369C22—881no—
370C22—881no—
371C22—881no—
372C22—881no—
373C22—881no—
374C22C2×#6686911yescharacteristic
375C22C2×#6687011yescharacteristic
376C22#1062261511yescharacteristic
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—84no—
384C4—881no—
385C4—881no—
386C4—881no—
387C2—21no—
388C2—21no—
389C2—42no—
390C2—42no—
391C2—1761no—
392C2#1306710511yescharacteristic
393C2#1307026511yescharacteristic
394C2#1307028311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC4×C11×#99C2
socleC22×C11C2×#99
prime radical#13074468C2
cosocleC2×C11×C22⋊C4C23
hypercenterC4×#99D11
hypocenterC11#11730
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. #13066934C2semidirect
3. #13066636C2semidirect
4. #13066612C2semidirect
5. C4×C11×#99C2semidirect
7. C2×#66928C4semidirect
15. #10622573C4semidirect
17. #10622560C4semidirect
19. #10622550C4semidirect
107. C4×#99D11semidirect
302. C11#11730semidirect

Maximal subgroups

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

subgroupindex
#130744682
#130669342
#130666362
#130666122
C4×C11×#992
#1173011