Finite Group Databasebeta

← #14664379

Subgroups — #14664379

Order 2816.

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

normal subgroups only

This group has 460 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#13073970C211yesmaximal, characteristic
2C4×#66898C211yesmaximal, characteristic
3#13066641C212yesmaximal, complemented
4#13066638C212yesmaximal, complemented
5C11×#1465C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×C4×Dic22C411yescharacteristic, complemented
8C11×#407—21no—
9#10622834—21no—
10C2×#66898—21no—
11#10622823—21no—
12#10622823—21no—
13C4×C22⋊Dic11—21no—
14#10622586—21no—
15#10622562C411yescharacteristic, complemented
16#10622562C2211yescharacteristic
17#10622560C411yescharacteristic, complemented
18#10622560C2211yescharacteristic
19#10622549C411yescharacteristic, complemented
20C11×#324—21no—
21C11×#323C2212yes—
22#10622164C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C2×C11×M16—41no—
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C22⋊Dic11—22no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11—41no—
46C4×Dic22—41no—
47C4×Dic22—41no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8—41no—
50#66898—24no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—41no—
55C11⋊#95C2×C411yescharacteristic
56C11⋊#95C2×C411yescharacteristic
57#11784—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C2×D411yescharacteristic
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—41no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—81no—
68C22×C4×C11—81no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—42no—
79C2×Dic22—41no—
80C2×Dic22—42no—
81C11×M16—82no—
82C2×C8×C11—42no—
83C11×C4⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C42×C11—21no—
87C42×C11—21no—
88C22⋊Dic11—24no—
89C22⋊Dic11—42no—
90C22⋊Dic11—42no—
91C22⋊Dic11—42no—
92C22⋊Dic11—81no—
93C22⋊Dic11—81no—
94C4⋊Dic11—41no—
95C4⋊Dic11—42no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—81no—
99Dic11⋊C4—81no—
100C4×Dic11—42no—
101C4×Dic11—82no—
102#2580—111no—
103C4×#99—111no—
104#1465D1111yescharacteristic
105#1352—112no—
106#1351—112no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11C2×C22⋊C411yescharacteristic
117C23×C11#13712yes—
118D4×C11—44no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11#9911yescharacteristic
133C2×C4×C11#9911yescharacteristic
134C2×C4×C11#10412yes—
135C2×Dic11—22no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—44no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—82no—
149C2×Dic11—82no—
150Dic22—42no—
151Dic22—42no—
152C8×C11—82no—
153C2×C4×Q8—111no—
154C2×C4×D4C2×D1111yescharacteristic
155C2×#99—221no—
156#407—21no—
157#399—111no—
158#399—111no—
159#393—111no—
160#393—111no—
161#390—221no—
162#389—221no—
163#385—221no—
164#385—221no—
165#382—111no—
166C4×C22⋊C4—221no—
167#342—112no—
168#324—21no—
169#323C2×D1112yes—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—22no—
173C22×C11—42no—
174C22×C11—42no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11C2×#9911yescharacteristic
183C22×C11#41911yescharacteristic
184C22×C11C2×#10411yescharacteristic
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—22no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191Dic11—42no—
192Dic11—81no—
193Dic11—81no—
194Dic11—84no—
195Dic11—81no—
196C22×Q8—111no—
197C22×D4D4411yescharacteristic
198C23×C4D4411yescharacteristic
199C23×C4C22⋊D1111yescharacteristic
200C2×M16—41no—
201C4×Q8—441no—
202C4×Q8—441no—
203C4×D4—41no—
204C4×D4—41no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4C22⋊D1111yescharacteristic
211C2×C22⋊C4—222no—
212C2×C22⋊C4—221no—
213C2×C22⋊C4—221no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4—221no—
216C2×C22⋊C4C4×D1111yescharacteristic
217C2×C22⋊C4C22×D1111yescharacteristic
218C2×C42—221no—
219C2×C42—441no—
220C2×C42C4×D1111yescharacteristic
221#99—224no—
222C22⋊C8—22no—
223C22⋊C8—41no—
224#95—111no—
225#95—111no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95—441no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—42no—
233C2×C11—81no—
234C2×C11#150811yescharacteristic
235C2×C11#212011yescharacteristic
236C2×C11#212711yescharacteristic
237C24(C2×D11)⋊C411yescharacteristic
238C24C2×D4411yescharacteristic
239C2×Q8—441no—
240C2×Q8—442no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—442no—
255C22×C4(C2×D11)⋊C411yescharacteristic
256C22×C4(C2×D11)⋊C411yescharacteristic
257C22×C4(C2×D11)⋊C411yescharacteristic
258C22×C4C2×C4×D1111yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260M16—82no—
261C2×C8—42no—
262C4⋊C4—41no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—442no—
267C4⋊C4—881no—
268C4⋊C4—881no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—224no—
272C22⋊C4—442no—
273C22⋊C4—442no—
274C22⋊C4—442no—
275C22⋊C4—881no—
276C22⋊C4—881no—
277C42—21no—
278C42—21no—
279C42—442no—
280C42—882no—
281C11#1178411yescharacteristic, complemented, Sylow
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23#6696212yes—
292C23C2×(C2×D11)⋊C411yescharacteristic
293Q8—442no—
294Q8—442no—
295D4—44no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—222no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—444no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—882no—
323C2×C4—882no—
324C2×C4#6687011yescharacteristic
325C2×C4#6687011yescharacteristic
326C2×C4#6688912yes—
327C8—82no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—81no—
339C22—81no—
340C22C2×#6687011yescharacteristic
341C22#1062273311yescharacteristic
342C22C2×#6688911yescharacteristic
343C4—22no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—442no—
350C4—881no—
351C4—881no—
352C4—884no—
353C4—881no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—81no—
358C2#1306713711yescharacteristic
359C2#1307025811yescharacteristic
360C2#1307028311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1465C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1465D11
hypocenterC11#11784
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #13066641C2semidirect
4. #13066638C2semidirect
7. C2×C4×Dic22C4semidirect
15. #10622562C4semidirect
17. #10622560C4semidirect
19. #10622549C4semidirect
281. C11#11784semidirect

Maximal subgroups

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

subgroupindex
#130739702
C4×#668982
#130666412
#130666382
C11×#14652
#1178411