Finite Group Databasebeta

← #14663227

Subgroups — #14663227

Order 2816.

470 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C4×#66988C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066563C212yesmaximal, complemented
4#13066545C212yesmaximal, complemented
5C11×#1466C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66988C411yescharacteristic
8C22×C4×Dic11C411yescharacteristic
9C11×#432—21no—
10#10622833C411yescharacteristic
11C4×C22⋊Dic11—21no—
12C4×C22⋊Dic11C411yescharacteristic
13#10622820—21no—
14#10622591—21no—
15#10622559C2211yescharacteristic
16#10622557—21no—
17#10622556C2211yescharacteristic
18C4×Dic11⋊C4—21no—
19C11×#323—21no—
20C11×#323C2212yes—
21#10622166—21no—
22#10622163C2212yes—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×Dic11C2×C411yescharacteristic
27C23×Dic11C2×C411yescharacteristic
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11C2×C411yescharacteristic
37C2×C22⋊Dic11C2×C411yescharacteristic
38#66988—22no—
39#66988—22no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11—41no—
46C2×C4×Dic11—41no—
47C2×#4318—41no—
48C11×C4⋊C8—41no—
49C11×C22⋊C8—22no—
50C11×#97—41no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58#11526—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C24×C11C22×C411yescharacteristic
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—41no—
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—42no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—41no—
82C22×Dic11—41no—
83C22×Dic11—41no—
84C22×Dic11—42no—
85C22×Dic11M1612yescomplemented
86C2×C8×C11—42no—
87C11×C4⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C42×C11—21no—
91C42×C11—21no—
92C22⋊Dic11—24no—
93C22⋊Dic11—21no—
94C22⋊Dic11—41no—
95C22⋊Dic11—42no—
96C22⋊Dic11M1612yescomplemented
97Dic11⋊C4—24no—
98Dic11⋊C4—42no—
99C4×Dic11—42no—
100C4×Dic11—42no—
101C4×Dic11—41no—
102C4×Dic11—41no—
103#4318—82no—
104C2×C11⋊C8—42no—
105C4×#123—111no—
106#1466D1111yescharacteristic
107#1465—111no—
108#1326—112no—
109#1317—112no—
110C23×C11—21no—
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×C11C2×C22⋊C411yescharacteristic
120C23×C11C2×M1611yescharacteristic
121C23×C11C2×M1611yescharacteristic
122D4×C11—42no—
123D4×C11—42no—
124C2×C4×C11—22no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—81no—
138C2×C4×C11#9911yescharacteristic
139C2×C4×C11#9911yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—22no—
142C2×Dic11—22no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C8×C11—82no—
157C11⋊C8—82no—
158C2×#123—111no—
159C2×C4×D4C2×D1111yescharacteristic
160C22×C42—111no—
161#432—21no—
162#407—221no—
163#388—221no—
164#387—221no—
165#386—111no—
166#385—111no—
167#381—111no—
168C4×C4⋊C4—221no—
169C4×C22⋊C4—111no—
170C4×C22⋊C4—221no—
171#324—221no—
172#323—21no—
173#323—112no—
174#323C2×D1112yes—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—42no—
182C22×C11—42no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—81no—
189C22×C11#40711yescharacteristic
190C22×C11C2×#9911yescharacteristic
191C22×C11#41311yescharacteristic
192C4×C11—21no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11#35212yes—
198Dic11—42no—
199Dic11—42no—
200Dic11—42no—
201Dic11—81no—
202C22×D4C4×D1111yescharacteristic
203C23×C4—111no—
204C23×C4—111no—
205C23×C4C4×D1111yescharacteristic
206C23×C4D4411yescharacteristic
207C2×M16—441no—
208#123—222no—
209#123—222no—
210C4×D4—41no—
211C4×D4—41no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4D4411yescharacteristic
215C2×C22⋊C4—111no—
216C2×C22⋊C4—111no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4C22⋊D1111yescharacteristic
220C2×C22⋊C4C22×D1111yescharacteristic
221C2×C42—221no—
222C2×C42—221no—
223C2×C42—221no—
224C2×C42—441no—
225C2×C42—441no—
226C2×C42C22⋊D1111yescharacteristic
227C4⋊C8—41no—
228C22⋊C8—22no—
229C22⋊C8—222no—
230C22⋊C8—441no—
231#97—41no—
232#95—221no—
233#95—221no—
234#95—221no—
235#95—221no—
236#95—221no—
237C2×C11—21no—
238C2×C11—21no—
239C2×C11—41no—
240C2×C11—41no—
241C2×C11—81no—
242C2×C11#146511yescharacteristic
243C2×C11C2×#35211yescharacteristic
244C2×C11#212011yescharacteristic
245C24(C2×D11)⋊C411yescharacteristic
246C24C2×C4×D1111yescharacteristic
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—41no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—112no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—442no—
264C22×C4—441no—
265C22×C4—441no—
266C22×C4—441no—
267C22×C4(C2×D11)⋊C411yescharacteristic
268C22×C4(C2×D11)⋊C411yescharacteristic
269C22×C4(C2×D11)⋊C411yescharacteristic
270C22×C4C2×D4411yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272M16—882no—
273C2×C8—42no—
274C2×C8—442no—
275C4⋊C4—41no—
276C4⋊C4—224no—
277C4⋊C4—442no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—112no—
281C22⋊C4—224no—
282C22⋊C4—221no—
283C22⋊C4—442no—
284C22⋊C4—441no—
285C42—21no—
286C42—21no—
287C42—442no—
288C42—442no—
289C42—441no—
290C42—441no—
291C11#1152611yescharacteristic, complemented, Sylow
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23M16×D1111yescharacteristic
302C23M16×D1111yescharacteristic
303C23C2×(C2×D11)⋊C411yescharacteristic
304D4—42no—
305D4—42no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—222no—
321C2×C4—222no—
322C2×C4—222no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4#6687011yescharacteristic
337C2×C4#6687011yescharacteristic
338C8—82no—
339C8—882no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—42no—
347C22—42no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—81no—
354C22C2×#6687011yescharacteristic
355C22#1062273911yescharacteristic
356C22#1062274511yescharacteristic
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—442no—
363C4—442no—
364C4—442no—
365C4—881no—
366C4#1062211412yes—
367C2—21no—
368C2—21no—
369C2—41no—
370C2—41no—
371C2—81no—
372C2#1306695211yescharacteristic
373C2C2×#1062211411yescharacteristic
374C2#1307025511yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1466C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1466D11
hypocenterC11#11526
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #13066563C2semidirect
4. #13066545C2semidirect
85. C22×Dic11M16semidirect
96. C22⋊Dic11M16semidirect
291. C11#11526semidirect

Maximal subgroups

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

subgroupindex
C4×#669882
#130669542
#130665632
#130665452
C11×#14662
#1152611