Finite Group Databasebeta

← #14651785

Subgroups — #14651785

Order 2816.

518 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 99 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#13077657C211yesmaximal, characteristic
2#13073959C211yesmaximal, characteristic
3#13066945C212yesmaximal, complemented
4#13066521C212yesmaximal, complemented
5C11×#1465C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C22×Dic11⋊C4C2211yescharacteristic
8C11×#407C2212yes—
9#10622833C411yescharacteristic
10#10622833C411yescharacteristic
11#10622825C2211yescharacteristic
12#10622823—21no—
13#10622820—21no—
14#10622820C2212yes—
15#10622625—24no—
16#10622597—21no—
17#10622561—21no—
18#10622559C411yescharacteristic
19#10622559C411yescharacteristic
20#10622546—21no—
21#10622538—21no—
22C11×#324—21no—
23C11×#323—21no—
24#10622107—24no—
25C22×D4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C23×Dic11C2×C411yescharacteristic
29C23×Dic11C2×C411yescharacteristic
30C2×C11×M16—22no—
31C4×D4×C11—22no—
32C4×D4×C11—22no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C22⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11C2×C411yescharacteristic
40C2×C22⋊Dic11C2×C411yescharacteristic
41C2×C4⋊Dic11—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—22no—
46C2×Dic11⋊C4—22no—
47C2×Dic11⋊C4—21no—
48C2×#4318—22no—
49C2×#4318—22no—
50C11×C22⋊C8—22no—
51C11×C22⋊C8—22no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C22⋊(C11⋊C8)—22no—
58C22⋊(C11⋊C8)—22no—
59C22⋊(C11⋊C8)D414yes—
60C4⋊(C11⋊C8)—22no—
61C4×C11⋊C8—22no—
62#9518—111nomaximal, Sylow
63C24×C11C22⋊C411yescharacteristic
64C24×C11C22×C411yescharacteristic
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—41no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—81no—
71C22×C4×C11—81no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C2×D412yes—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4112yes—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—22no—
84C22×Dic11—22no—
85C22×Dic11—42no—
86C22×Dic11—81no—
87C11×M16—82no—
88C2×C8×C11—42no—
89C11×C4⋊C4—22no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—22no—
92C42×C11—21no—
93C42×C11—21no—
94C22⋊Dic11—41no—
95C22⋊Dic11—41no—
96C22⋊Dic11—42no—
97C22⋊Dic11—81no—
98C4⋊Dic11—81no—
99Dic11⋊C4—42no—
100Dic11⋊C4—41no—
101Dic11⋊C4—42no—
102Dic11⋊C4—41no—
103Dic11⋊C4—81no—
104#4318—82no—
105#4318—82no—
106C2×C11⋊C8—24no—
107#2975—111no—
108#2579—111no—
109#1465D1111yescharacteristic
110#1463—112no—
111#1305—112no—
112C23×C11—21no—
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×C11C2×C22⋊C411yescharacteristic
122C23×C11C4×D412yes—
123D4×C11—44no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—81no—
136C2×C4×C11#10112yes—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12112yes—
139C2×C4×C11#12311yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—24no—
142C2×Dic11—41no—
143C2×Dic11—42no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—82no—
155C8×C11—82no—
156C11⋊C8—44no—
157C2×C4×D4C2×D1111yescharacteristic
158C22×C4⋊C4—111no—
159#436—224no—
160#431—221no—
161#407—112no—
162#407—221no—
163#407C2×D1112yes—
164#398—221no—
165#396—221no—
166#387—221no—
167#386—111no—
168#386—111no—
169#385—111no—
170#385—111no—
171#385—221no—
172#380—111no—
173#324—21no—
174#324—224no—
175#323—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—42no—
182C22×C11—42no—
183C22×C11—42no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—81no—
188C22×C11#38611yescharacteristic
189C22×C11C2×#10111yescharacteristic
190C22×C11#41311yescharacteristic
191C4×C11—22no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—22no—
195C4×C11—41no—
196C4×C11—41no—
197Dic11—42no—
198Dic11—81no—
199Dic11—81no—
200Dic11—81no—
201C22×D4C4×D1111yescharacteristic
202C23×C4—111no—
203C23×C4—111no—
204C23×C4D4411yescharacteristic
205C23×C4C22×D1111yescharacteristic
206C2×M16—22no—
207C2×M16—222no—
208C2×M16—222no—
209C4×D4—22no—
210C4×D4—22no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—222no—
214C2×C4⋊C4—222no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4C22⋊D1111yescharacteristic
219C2×C22⋊C4—111no—
220C2×C22⋊C4—111no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4—221no—
223C2×C22⋊C4C4×D1111yescharacteristic
224C2×C22⋊C4C22⋊D1111yescharacteristic
225C2×C42D4411yescharacteristic
226C4⋊C8—222no—
227C22⋊C8—22no—
228C22⋊C8—22no—
229C22⋊C8—114no—
230C22⋊C8—222no—
231C22⋊C8—222no—
232C4×C8—222no—
233#95—221no—
234#95—221no—
235#95—221no—
236#95—221no—
237#95—221no—
238C2×C11—21no—
239C2×C11—21no—
240C2×C11—42no—
241C2×C11—81no—
242C2×C11#189111yescharacteristic
243C2×C11#190111yescharacteristic
244C2×C11#191311yescharacteristic
245C24(C2×D11)⋊C411yescharacteristic
246C24C2×C4×D1111yescharacteristic
247C2×D4—22no—
248C2×D4—22no—
249C2×D4—41no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—81no—
253C22×C4—81no—
254C22×C4—222no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—222no—
260C22×C4—442no—
261C22×C4—881no—
262C22×C4(C2×D11)⋊C411yescharacteristic
263C22×C4(C2×D11)⋊C411yescharacteristic
264C22×C4(C2×D11)⋊C411yescharacteristic
265C22×C4C2×D4411yescharacteristic
266C22×C4D4×D1112yes—
267C22×C4#434112yes—
268C22×C4C2×C22⋊D1111yescharacteristic
269M16—82no—
270M16—882no—
271M16—882no—
272C2×C8—42no—
273C2×C8—224no—
274C4⋊C4—22no—
275C4⋊C4—442no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—442no—
279C4⋊C4—881no—
280C4⋊C4—881no—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C22⋊C4—442no—
284C22⋊C4—441no—
285C22⋊C4—441no—
286C22⋊C4—881no—
287C42—21no—
288C42—21no—
289C11#951811yescharacteristic, complemented, Sylow
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23(C22⋊D11)⋊C412yes—
300C23C2×(C2×D11)⋊C411yescharacteristic
301D4—44no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—222no—
315C2×C4—224no—
316C2×C4—441no—
317C2×C4—442no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—882no—
329C2×C4#6688812yes—
330C2×C4#6693511yescharacteristic
331C2×C4#6693911yescharacteristic
332C2×C4#6699212yes—
333C8—82no—
334C8—444no—
335C22—21no—
336C22—21no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22#1062257111yescharacteristic
348C22#1062274511yescharacteristic
349C22C2×#6688811yescharacteristic
350C4—22no—
351C4—22no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—442no—
357C4—881no—
358C4—881no—
359C4—881no—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—81no—
364C2#1306903211yescharacteristic
365C2#1306908211yescharacteristic
366C2#1306915611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1465C2
socleC22×C11#386
prime radicalC22×D4×C11C2×C4
cosocleC23×C4×C11C23
hypercenter#1465D11
hypocenterC11#9518
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #13066945C2semidirect
4. #13066521C2semidirect
289. C11#9518semidirect

Maximal subgroups

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

subgroupindex
#130776572
#130739592
#130669452
#130665212
C11×#14652
#951811