Finite Group Databasebeta

← #14664678

Subgroups — #14664678

Order 2816.

376 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 69 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#13074196C211yesmaximal, characteristic
2#13068698C211yesmaximal, characteristic
3#13066929C211yesmaximal, characteristic
4#13066647C211yesmaximal, characteristic, complemented
5#13066645C211yesmaximal, characteristic, complemented
6#13066622C211yesmaximal, characteristic, complemented
7C11×#1346C211yesmaximal, characteristic, complemented
8C2×#66945C2211yescharacteristic
9C2×#66940C411yescharacteristic
10C11×#398C2211yescharacteristic
11#10622739—21no—
12#10622606C411yescharacteristic
13#10622602—21no—
14#10622594—21no—
15#10622592C2211yescharacteristic
16#10622331—21no—
17#10622286C411yescharacteristic
18#10622282—21no—
19#10622265—21no—
20#10622264C411yescharacteristic
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×C4×D11D411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C2×C11×M16—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4C2×C411yescharacteristic
36C2×(C2×D11)⋊C4D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×C4×Dic11—21no—
41C2×C4×Dic11C2×C411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43C2×#4318—21no—
44#66945—41no—
45#66945—41no—
46#66940—41no—
47#66940—41no—
48C11×C22⋊C8—21no—
49C11×#95—21no—
50C11×#95C2×C411yescharacteristic
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C22⋊(C11⋊C8)—21no—
58(C2×D11)⋊C8—41no—
59(C2×D11)⋊C8—41no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#11849—111nomaximal, Sylow
63C23×D11C22⋊C411yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—41no—
79C2×Dic22—41no—
80C2×Dic22—42no—
81C11×M16—41no—
82C11×M16—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—42no—
92(C2×D11)⋊C4—42no—
93C4⋊Dic11—41no—
94Dic11⋊C4—42no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—42no—
102#4318—41no—
103#4318—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106#2599—111no—
107#1822—111no—
108#1458—111no—
109#1354—111no—
110#1354—111no—
111#1346—111no—
112#1346D1111yescharacteristic, complemented
113C23×C11C2×C22⋊C411yescharacteristic
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—41no—
118C22×D11—41no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11#13511yescharacteristic
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—22no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11#9911yescharacteristic
146C2×Dic11#9911yescharacteristic
147C4×D11—41no—
148C4×D11—41no—
149C4×D11—41no—
150C4×D11—41no—
151Dic22—42no—
152Dic22—42no—
153C8×C11—81no—
154C8×C11—81no—
155C11⋊C8—81no—
156C11⋊C8—81no—
157C2×C4×Q8—111no—
158C2×#117—111no—
159#431—221no—
160#407—221no—
161#398C2×D1111yescharacteristic
162#397—111no—
163#395—111no—
164#393—111no—
165#388—221no—
166#387—221no—
167#387—221no—
168#385—221no—
169#383—111no—
170#343—111no—
171#343—221no—
172#343C2×D1111yescharacteristic
173#324—111no—
174#324C2×D1111yescharacteristic
175#323—221no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11C2×#9911yescharacteristic
179C22×C11#41611yescharacteristic
180C22×C11#42111yescharacteristic
181C2×D11—42no—
182C2×D11—41no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—81no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—81no—
191C4×C11—81no—
192Dic11—21no—
193Dic11—21no—
194Dic11—42no—
195Dic11—41no—
196Dic11—41no—
197Dic11—81no—
198C22×Q8—111no—
199C23×C4—111no—
200C2×M16—21no—
201C2×M16—221no—
202C4×Q8—441no—
203C4×Q8—441no—
204#117—441no—
205#117—441no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4C4×D1111yescharacteristic
211C2×C4⋊C4C22×D1111yescharacteristic
212C2×C22⋊C4—111no—
213C2×C22⋊C4—111no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4—221no—
216C2×C42—111no—
217C2×C42—111no—
218C2×C42—221no—
219C4⋊C8—441no—
220C22⋊C8—21no—
221C22⋊C8—221no—
222C22⋊C8—441no—
223C22⋊C8—441no—
224C4×C8—441no—
225#95—21no—
226#95—111no—
227#95—221no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95C4×D1111yescharacteristic
233C2×C11—21no—
234C2×C11—21no—
235C2×C11#151611yescharacteristic
236C2×C11#212011yescharacteristic
237C2×C11#213511yescharacteristic
238D11—81no—
239C24—111no—
240C2×Q8—441no—
241C2×Q8—442no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—441no—
254C22×C4C2×C4×D1111yescharacteristic
255C22×C4D4×D1111yescharacteristic
256C22×C4D4×D1111yescharacteristic
257M16—41no—
258M16—41no—
259M16—441no—
260M16—441no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—441no—
264C2×C8—441no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—442no—
273C22⋊C4—441no—
274C22⋊C4—441no—
275C22⋊C4—442no—
276C22⋊C4—442no—
277C42—221no—
278C42—221no—
279C42—221no—
280C42—221no—
281C42—442no—
282C11#1184911yescharacteristic, complemented, Sylow
283C23—221no—
284C23—221no—
285C23—221no—
286C23—441no—
287C23—441no—
288C23C22⋊C4×D1111yescharacteristic
289Q8—442no—
290Q8—442no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—222no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4#6696511yescharacteristic
322C2×C4#6696911yescharacteristic
323C8—81no—
324C8—81no—
325C8—881no—
326C8—881no—
327C22—21no—
328C22—21no—
329C22—442no—
330C22—441no—
331C22—441no—
332C22—441no—
333C22—881no—
334C22D11×#9911yescharacteristic
335C22#1062238511yescharacteristic
336C22#1062243411yescharacteristic
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—221no—
344C4—221no—
345C4—442no—
346C4—441no—
347C4—441no—
348C4—881no—
349C2—21no—
350C2—21no—
351C2—881no—
352C2#1306716911yescharacteristic
353C2#1307025611yescharacteristic
354C2#1307030911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1346C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1346D11
hypocenterC11#11849
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
4. #13066647C2semidirect
5. #13066645C2semidirect
6. #13066622C2semidirect
7. C11×#1346C2semidirect
112. #1346D11semidirect
282. C11#11849semidirect

Maximal subgroups

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

subgroupindex
#130741962
#130686982
#130669292
#130666472
#130666452
#130666222
C11×#13462
#1184911