Finite Group Databasebeta

← #14648842

Subgroups — #14648842

Order 2816.

534 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 107 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#13071900C211yesmaximal, characteristic
2C4×#66897C211yesmaximal, characteristic
3#13067062C212yesmaximal, complemented
4#13066508C212yesmaximal, complemented
5C11×#2973C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×C4×Dic22C2211yescharacteristic
8C11×#435—24no—
9C11×#432C2212yes—
10C11×#407—21no—
11C2×C11×C22⋊C8—21no—
12#10622835—21no—
13C2×#66897—21no—
14C4×C22⋊Dic11—21no—
15C4×C22⋊Dic11—21no—
16#10622595—21no—
17#10622566C411yescharacteristic
18#10622566C411yescharacteristic
19#10622560C411yescharacteristic
20#10622560C411yescharacteristic
21#10622545C2211yescharacteristic
22C4×#4318C2212yes—
23#10622168—21no—
24#10622122—24no—
25C22×D4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C2×C11×M16—22no—
30C22×C8×C11—22no—
31C4×D4×C11—22no—
32C4×D4×C11—22no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C22⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11—21no—
45C2×#4318—22no—
46C4×Dic22—22no—
47C4×Dic22—22no—
48C11×C4⋊C8D414yes—
49C11×C22⋊C8—22no—
50C11×C22⋊C8—22no—
51C11×C22⋊C8—22no—
52C11×#97—22no—
53#66897—24no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95C2×C411yescharacteristic
60C11⋊#95C2×C411yescharacteristic
61#66867—22no—
62C4×C11⋊C8—22no—
63#9029—111nomaximal, Sylow
64C24×C11C22⋊C411yescharacteristic
65C24×C11C22⋊C411yescharacteristic
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—41no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C2×Dic22—22no—
85C2×Dic22—42no—
86C11×M16—82no—
87C2×C8×C11—24no—
88C2×C8×C11—82no—
89C11×C4⋊C4—22no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—22no—
92C42×C11C2×D412yes—
93C42×C11#4112yes—
94C22⋊Dic11—42no—
95C22⋊Dic11—42no—
96C22⋊Dic11—42no—
97C22⋊Dic11—42no—
98C4⋊Dic11—22no—
99Dic11⋊C4—42no—
100C4×Dic11—42no—
101C4×Dic11—41no—
102C4×Dic11—41no—
103#4318—24no—
104#4318—42no—
105C2×C11⋊C8—42no—
106#2973D1111yescharacteristic
107#2398—111no—
108C4×#100—111no—
109#1491—112no—
110#1300—112no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11#10412yes—
121C23×C11C2×C22⋊C411yescharacteristic
122D4×C11—44no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—22no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11C4×D412yes—
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12112yes—
138C2×C4×C11#12311yescharacteristic
139C2×Dic11—22no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151Dic22—24no—
152Dic22—42no—
153C8×C11—44no—
154C11⋊C8—44no—
155C2×C4×Q8—111no—
156C2×C4×D4C2×D1111yescharacteristic
157#435—24no—
158#432C2×D1112yes—
159C2×#100—221no—
160#407—21no—
161C2×C22⋊C8—21no—
162C4×M16—112no—
163#400—221no—
164#397—111no—
165#397—111no—
166#394—221no—
167#393—111no—
168#393—111no—
169C4×C22⋊C4—221no—
170C4×C22⋊C4—221no—
171#376—111no—
172#343—221no—
173Q8⋊C8—224no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—22no—
177C22×C11—42no—
178C22×C11—42no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11#38611yescharacteristic
187C22×C11C2×#10411yescharacteristic
188C22×C11#42111yescharacteristic
189C4×C11—22no—
190C4×C11—21no—
191C4×C11—22no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11#45512yes—
195Dic11—42no—
196Dic11—81no—
197Dic11—81no—
198Dic11—81no—
199C22×Q8—111no—
200C22×D4D4411yescharacteristic
201C23×C4C22⋊D1111yescharacteristic
202C23×C4C22⋊D1111yescharacteristic
203C2×M16—22no—
204C2×M16—222no—
205C22×C8—22no—
206C4×Q8—222no—
207C4×Q8—222no—
208C4×D4—22no—
209C4×D4—22no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4D4411yescharacteristic
213C2×C22⋊C4—221no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4—221no—
216C2×C22⋊C4—221no—
217C2×C22⋊C4C4×D1111yescharacteristic
218C2×C22⋊C4C4×D1111yescharacteristic
219C2×C42—221no—
220C2×C42—221no—
221C2×C42C22×D1111yescharacteristic
222C4⋊C8C22⋊D1114yes—
223#100—224no—
224C22⋊C8—22no—
225C22⋊C8—22no—
226C22⋊C8—22no—
227#97—22no—
228#97—222no—
229C4×C8—222no—
230#95—111no—
231#95—111no—
232#95—221no—
233#95—221no—
234#95—221no—
235#95—221no—
236#95—221no—
237C2×C11—21no—
238C2×C11—21no—
239C2×C11—42no—
240C2×C11—81no—
241C2×C11#187111yescharacteristic
242C2×C11#188511yescharacteristic
243C2×C11#189111yescharacteristic
244C24(C2×D11)⋊C411yescharacteristic
245C24(C2×D11)⋊C411yescharacteristic
246C2×Q8—222no—
247C2×Q8—442no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4(C2×D11)⋊C411yescharacteristic
262C22×C4(C2×D11)⋊C411yescharacteristic
263C22×C4C2×C4×D1111yescharacteristic
264C22×C4C2×D4411yescharacteristic
265C22×C4C2×C22⋊D1111yescharacteristic
266M16—82no—
267M16—224no—
268M16—442no—
269C2×C8—24no—
270C2×C8—82no—
271C2×C8—442no—
272C4⋊C4—22no—
273C4⋊C4—222no—
274C4⋊C4—442no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—442no—
278C22⋊C4—442no—
279C22⋊C4—442no—
280C22⋊C4—442no—
281C42—442no—
282C42—441no—
283C42—441no—
284C42#433912yes—
285C42C2×C22⋊D1112yes—
286C11#902911yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23#6688912yes—
297C23C2×(C2×D11)⋊C411yescharacteristic
298Q8—224no—
299Q8—442no—
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—222no—
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—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4C4×C22⋊D1112yes—
326C2×C4#6698211yescharacteristic
327C2×C4#6698312yes—
328C2×C4#6700611yescharacteristic
329C8—44no—
330C8—444no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—81no—
343C22C2×#6688911yescharacteristic
344C22#1062275211yescharacteristic
345C22#1062282611yescharacteristic
346C4—22no—
347C4—21no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—442no—
352C4—881no—
353C4—881no—
354C4—881no—
355C4#1062285512yes—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—81no—
360C2#1306891811yescharacteristic
361C2#1306900411yescharacteristic
362C2#1306903411yescharacteristic
subgroupG/H
centerC2×C4#67006
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2973C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#2973D11
hypocenterC11#9029
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
3. #13067062C2semidirect
4. #13066508C2semidirect
286. C11#9029semidirect

Maximal subgroups

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

subgroupindex
#130719002
C4×#668972
#130670622
#130665082
C11×#29732
#902911