Finite Group Databasebeta

← #14663263

Subgroups — #14663263

Order 2816.

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

normal subgroups only

This group has 440 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#13071328C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066561C212yesmaximal, complemented
4#13066549C212yesmaximal, complemented
5C11×#1465C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66989C411yescharacteristic
8C2×C4×Dic22C411yescharacteristic
9C11×#407—21no—
10#10622834C411yescharacteristic
11#10622823—21no—
12#10622823—21no—
13#10622820—21no—
14#10622589C2211yescharacteristic
15#10622587C2211yescharacteristic
16#10622557—21no—
17#10622557—21no—
18#10622545C411yescharacteristic
19C11×#324C2212yes—
20C11×#323—21no—
21#10622166C2212yes—
22#10622163—21no—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C2×C11×M16—41no—
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38#66989—22no—
39#66989—22no—
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11C2×C411yescharacteristic
47C2×#4318—41no—
48C4×Dic22—41no—
49C4×Dic22—41no—
50C11×C22⋊C8—22no—
51C11×C22⋊C8—41no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58#11535—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—81no—
70C22×C4×C11—81no—
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—
80C2×Dic22—21no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C2×Dic22M1612yescomplemented
84C11×M16—82no—
85C2×C8×C11—42no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C42×C11—21no—
90C42×C11—21no—
91C22⋊Dic11—24no—
92C22⋊Dic11—24no—
93C22⋊Dic11—81no—
94C22⋊Dic11—81no—
95C4⋊Dic11—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—81no—
99Dic11⋊C4—81no—
100C4×Dic11—21no—
101C4×Dic11—41no—
102C4×Dic11—42no—
103C4×Dic11M1612yescomplemented
104#4318—82no—
105C2×C11⋊C8—42no—
106#2326—111no—
107#1465—111no—
108#1465D1111yescharacteristic
109#1325—112no—
110#1319—112no—
111C23×C11—21no—
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
122D4×C11—42no—
123D4×C11—42no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11#9911yescharacteristic
138C2×C4×C11#9911yescharacteristic
139C2×C4×C11C2×M1611yescharacteristic
140C2×C4×C11C2×M1611yescharacteristic
141C2×Dic11—22no—
142C2×Dic11—22no—
143C2×Dic11—41no—
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—
153Dic22—42no—
154Dic22—42no—
155C8×C11—82no—
156C11⋊C8—82no—
157C2×#124—111no—
158C2×C4×Q8—111no—
159C2×C4×D4C2×D1111yescharacteristic
160#407—21no—
161#407—221no—
162#391—111no—
163#390—111no—
164#388—221no—
165#388—221no—
166#385—221no—
167#385—221no—
168#384—111no—
169#376—111no—
170#324—112no—
171#324C2×D1112yes—
172#323—21no—
173#323—221no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—42no—
177C22×C11—42no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11#40711yescharacteristic
187C22×C11C2×#9911yescharacteristic
188C22×C11#41311yescharacteristic
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196Dic11—42no—
197Dic11—42no—
198Dic11—81no—
199Dic11—81no—
200C22×Q8—111no—
201C22×D4C4×D1111yescharacteristic
202C23×C4D4411yescharacteristic
203C23×C4C22⋊D1111yescharacteristic
204C2×M16—41no—
205C2×M16—441no—
206#124—222no—
207#124—222no—
208C4×Q8—441no—
209C4×Q8—441no—
210C4×D4—41no—
211C4×D4—41no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4C22×D1111yescharacteristic
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4—221no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4D4411yescharacteristic
222C2×C22⋊C4C22⋊D1111yescharacteristic
223C2×C42—111no—
224C2×C42—111no—
225C2×C42—221no—
226C2×C42C4×D1111yescharacteristic
227C22⋊C8—22no—
228C22⋊C8—41no—
229C22⋊C8—222no—
230C22⋊C8—441no—
231#95—221no—
232#95—221no—
233#95—221no—
234#95—221no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—81no—
238C2×C11—81no—
239C2×C11#146511yescharacteristic
240C2×C11#212711yescharacteristic
241C2×C11#213511yescharacteristic
242C24(C2×D11)⋊C411yescharacteristic
243C24(C2×D11)⋊C411yescharacteristic
244C2×Q8—112no—
245C2×Q8—221no—
246C2×Q8—441no—
247C2×Q8—441no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—41no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4(C2×D11)⋊C411yescharacteristic
263C22×C4(C2×D11)⋊C411yescharacteristic
264C22×C4C2×C4×D1111yescharacteristic
265C22×C4C2×D4411yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267M16—82no—
268M16—882no—
269C2×C8—42no—
270C2×C8—442no—
271C4⋊C4—41no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—881no—
276C4⋊C4—881no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—224no—
280C22⋊C4—224no—
281C22⋊C4—881no—
282C22⋊C4—881no—
283C42—21no—
284C42—21no—
285C42—112no—
286C42—221no—
287C42—441no—
288C42—442no—
289C11#1153511yescharacteristic, complemented, Sylow
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23C2×(C2×D11)⋊C411yescharacteristic
301Q8—442no—
302Q8—442no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—222no—
319C2×C4—222no—
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—441no—
329C2×C4—441no—
330C2×C4#6687011yescharacteristic
331C2×C4#6687011yescharacteristic
332C2×C4M16×D1111yescharacteristic
333C2×C4M16×D1111yescharacteristic
334C8—82no—
335C8—882no—
336C22—21no—
337C22—21no—
338C22—42no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—81no—
348C22C2×#6687011yescharacteristic
349C22#1062273911yescharacteristic
350C22#1062274511yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—442no—
359C4—442no—
360C4—881no—
361C4—881no—
362C2—21no—
363C2—21no—
364C2—81no—
365C2—81no—
366C2#1306695211yescharacteristic
367C2#1307028311yescharacteristic
368C2#1307031011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1465C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1465D11
hypocenterC11#11535
LCSG ▷ C22×C4×C11 ▷ C22×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. #13066561C2semidirect
4. #13066549C2semidirect
83. C2×Dic22M16semidirect
103. C4×Dic11M16semidirect
289. C11#11535semidirect

Maximal subgroups

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

subgroupindex
#130713282
#130669542
#130665612
#130665492
C11×#14652
#1153511