Finite Group Databasebeta

← #14651437

Subgroups — #14651437

Order 2816.

486 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 103 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#13073592C211yesmaximal, characteristic
2#13067239C212yesmaximal
3#13066960C211yesmaximal, characteristic, complemented
4#13066471C212yesmaximal, complemented
5C11×#2983C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#67000C411yescharacteristic
8C2×#66997C411yescharacteristic
9C2×#66928C2211yescharacteristic
10C11×#446—24no—
11C11×#432—21no—
12C11×#432C2212yes—
13C11×#431—21no—
14#10622607—21no—
15#10622607—21no—
16#10622601C411yescharacteristic
17#10622587C411yescharacteristic
18#10622553—21no—
19#10622553—21no—
20C4×C4⋊Dic11C2211yescharacteristic
21#10622539C2212yes—
22#10622166—21no—
23#10622166—21no—
24#10622102—24no—
25C22×Q8×C11C2×C411yescharacteristic
26C22×D44C2×C411yescharacteristic
27C22×Dic22C2×C411yescharacteristic
28C4×Q8×C11—22no—
29C4×Q8×C11—22no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36#67000—42no—
37#66997—42no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×C4⋊Dic11—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11C2×C411yescharacteristic
49#66928—22no—
50#66928—22no—
51C11×C4⋊C8—22no—
52C11×C4⋊C8—22no—
53C11×C4⋊C8—22no—
54C11×C22⋊C8—22no—
55C11×#97—22no—
56C11×#97D414yes—
57C4×C8×C11—22no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C22⋊(C11⋊C8)—22no—
62C4⋊(C11⋊C8)—22no—
63#66867—22no—
64#9448—111nomaximal, Sylow
65C23×D11—21no—
66C2×Q8×C11—22no—
67C2×Q8×C11—22no—
68C2×Q8×C11—41no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
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—
79C2×D44—22no—
80C2×D44—41no—
81C2×D44—41no—
82C2×Dic22—22no—
83C2×Dic22—41no—
84C2×Dic22—41no—
85C2×C8×C11—24no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—22no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—21no—
93C42×C11C2×D412yes—
94C42×C11#4112yes—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—41no—
102C4⋊Dic11—42no—
103Dic11⋊C4—42no—
104Dic11⋊C4—42no—
105C4×Dic11—41no—
106C4×Dic11—41no—
107C2×C11⋊C8—42no—
108#2983D1111yescharacteristic, complemented
109#2545—111no—
110#1533—112no—
111#1467—111no—
112#1285—112no—
113C23×C11C2×C22⋊C411yescharacteristic
114C22×D11—41no—
115C22×D11—41no—
116C22×D11—41no—
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121Q8×C11—44no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
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—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11#10012yes—
136C2×C4×C11C4×D412yes—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12112yes—
139C2×C4×C11#12311yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149D44—82no—
150Dic22—82no—
151C8×C11—44no—
152C11⋊C8—82no—
153C2×C4⋊Q8—111no—
154C2×#124—111no—
155C2×#124—111no—
156C2×C4×Q8C2×D1111yescharacteristic
157#446—24no—
158#432—21no—
159#432—112no—
160#432C2×D1112yes—
161#431—21no—
162#396—221no—
163#396—221no—
164#391—111no—
165#390—111no—
166#388—221no—
167#388—221no—
168C4×C4⋊C4—111no—
169#329—224no—
170#324—221no—
171#324—221no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11#38611yescharacteristic
175C22×C11C2×#10011yescharacteristic
176C22×C11#41311yescharacteristic
177C2×D11—81no—
178C2×D11—81no—
179C2×D11—81no—
180C2×D11—81no—
181C2×D11—81no—
182C2×D11—81no—
183C2×D11—81no—
184C4×C11—22no—
185C4×C11—22no—
186C4×C11—22no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192Dic11—42no—
193Dic11—81no—
194Dic11—81no—
195C22×Q8—111no—
196C22×Q8C4×D1111yescharacteristic
197C22×D4—111no—
198C4⋊Q8—442no—
199#124—222no—
200#124—222no—
201#124—442no—
202C4×Q8—22no—
203C4×Q8—22no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4C4×D1111yescharacteristic
208C2×C4⋊C4D4411yescharacteristic
209C2×C4⋊C4D4411yescharacteristic
210C2×C22⋊C4—221no—
211C2×C22⋊C4—221no—
212C2×C22⋊C4—221no—
213C2×C22⋊C4—221no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4—221no—
216C2×C42—111no—
217C2×C42—111no—
218C2×C42C22⋊D1111yescharacteristic
219C2×C42C22⋊D1111yescharacteristic
220C2×C42C22×D1111yescharacteristic
221C4⋊C8—22no—
222C4⋊C8—22no—
223C4⋊C8—22no—
224C4⋊C8—222no—
225C22⋊C8—22no—
226C22⋊C8—222no—
227#97—22no—
228#97—222no—
229#97C22⋊D1114yes—
230C4×C8—22no—
231#95—221no—
232#95—221no—
233#95—221no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11#188411yescharacteristic
237C2×C11#190011yescharacteristic
238C2×C11#191211yescharacteristic
239D11—161no—
240C24—221no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—222no—
245C2×Q8—441no—
246C2×Q8—441no—
247C2×D4—222no—
248C2×D4—441no—
249C2×D4—441no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4(C2×D11)⋊C411yescharacteristic
254C22×C4(C2×D11)⋊C411yescharacteristic
255C22×C4(C2×D11)⋊C411yescharacteristic
256C22×C4(C2×D11)⋊C411yescharacteristic
257C22×C4C2×C4×D1111yescharacteristic
258C22×C4C2×D4411yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260C2×C8—24no—
261C2×C8—442no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—442no—
266C4⋊C4—442no—
267C4⋊C4—442no—
268C22⋊C4—442no—
269C22⋊C4—442no—
270C22⋊C4—442no—
271C22⋊C4—442no—
272C22⋊C4—441no—
273C22⋊C4—442no—
274C22⋊C4—441no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—441no—
280C42—441no—
281C42#433912yes—
282C42C2×C22⋊D1112yes—
283C11#944811yescharacteristic, complemented, Sylow
284C23—441no—
285C23—441no—
286C23—441no—
287C23—441no—
288C23—441no—
289C23—441no—
290C23—441no—
291C23C2×(C2×D11)⋊C411yescharacteristic
292Q8—44no—
293Q8—882no—
294D4—882no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—222no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4#6688712yes—
318C2×C4C4×C22⋊D1112yes—
319C2×C4#6698211yescharacteristic
320C2×C4#6698312yes—
321C2×C4#6700611yescharacteristic
322C8—44no—
323C8—882no—
324C22—21no—
325C22—21no—
326C22—881no—
327C22—881no—
328C22—881no—
329C22—881no—
330C22—881no—
331C22—881no—
332C22—881no—
333C22C2×#6688711yescharacteristic
334C22#1062274511yescharacteristic
335C22#1062282611yescharacteristic
336C4—22no—
337C4—22no—
338C4—21no—
339C4—21no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—442no—
345C4—881no—
346C4—881no—
347C2—21no—
348C2—21no—
349C2—1761no—
350C2#1306899911yescharacteristic
351C2#1306907911yescharacteristic
352C2#1306915311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2983C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#2983D11
hypocenterC11#9448
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
3. #13066960C2semidirect
4. #13066471C2semidirect
5. C11×#2983C2semidirect
108. #2983D11semidirect
283. C11#9448semidirect

Maximal subgroups

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

subgroupindex
#130735922
#130672392
#130669602
#130664712
C11×#29832
#944811