Finite Group Databasebeta

← #14652791

Subgroups — #14652791

Order 2816.

482 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 119 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#13076988C211yesmaximal, characteristic
2#13068469C211yesmaximal, characteristic, complemented
3C2×#10622103C212yesmaximal, complemented
4C2×#10622102C212yesmaximal
5C11×#1745C211yesmaximal, characteristic, complemented
6C2×#66928C2211yescharacteristic
7C2×#66923C2211yescharacteristic
8C2×C11×#97C2212yes—
9C43×C11C2211yescharacteristic
10#10622553—21no—
11#10622553—21no—
12#10622553—21no—
13#10622553—21no—
14#10622552C411yescharacteristic
15#10622552C411yescharacteristic
16#10622542C411yescharacteristic
17#10622542C411yescharacteristic
18C2×C4⋊(C11⋊C8)—21no—
19C2×#66867C2212yes—
20C11×#336—21no—
21C11×#336—21no—
22#10622162—21no—
23#10622103—24no—
24#10622102—24no—
25C22×D44C2×C411yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C22×C8×C11—22no—
28C2×C42×C11C2×C411yescharacteristic
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C22×C11⋊C8—22no—
46#66928—22no—
47#66928—22no—
48#66923—22no—
49#66923—22no—
50C11×#97—22no—
51C11×#97D414yes—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C4⋊(C11⋊C8)—24no—
57#66867—22no—
58#66867—22no—
59#9688—111nomaximal, Sylow
60C23×D11—21no—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C2×D44—22no—
72C2×D44—41no—
73C2×D44—41no—
74C2×Dic22—22no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×C8×C11—24no—
78C2×C8×C11—42no—
79C2×C8×C11—42no—
80C42×C11—22no—
81C42×C11—41no—
82C42×C11—41no—
83C42×C11—41no—
84C42×C11—41no—
85C42×C11—41no—
86C42×C11C2×D412yes—
87C42×C11#4112yes—
88(C2×D11)⋊C4—42no—
89(C2×D11)⋊C4—42no—
90(C2×D11)⋊C4—42no—
91(C2×D11)⋊C4—42no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95C4⋊Dic11—22no—
96C4⋊Dic11—22no—
97Dic11⋊C4—42no—
98Dic11⋊C4—41no—
99Dic11⋊C4—41no—
100C2×C11⋊C8—24no—
101C2×C11⋊C8—42no—
102C2×C11⋊C8—42no—
103#2861—111no—
104#1767—111no—
105#1745D1111yescharacteristic, complemented
106C2×#330—112no—
107C2×#329—112no—
108C23×C11C2×C22⋊C411yescharacteristic
109C22×D11—41no—
110C22×D11—41no—
111C22×D11—41no—
112C22×D11—41no—
113C22×D11—41no—
114C22×D11—41no—
115C22×D11—41no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
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—21no—
132C2×C4×C11—21no—
133C2×C4×C11#10412yes—
134C2×C4×C11C4×D412yes—
135C2×C4×C11#12112yes—
136C2×C4×C11#12411yescharacteristic
137C2×C4×C11#12711yescharacteristic
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147D44—82no—
148Dic22—82no—
149C8×C11—44no—
150C11⋊C8—44no—
151C2×#125—111no—
152C2×#124—111no—
153C2×C4⋊C8—221no—
154C2×#97—112no—
155C2×#97C2×D1112yes—
156#391—111no—
157#391—111no—
158#390—111no—
159#390—111no—
160#388—221no—
161#388—221no—
162#388—221no—
163#388—221no—
164C43C2×D1111yescharacteristic
165#336—21no—
166#336—21no—
167#336—221no—
168#330—224no—
169#329—224no—
170C22×C11#39011yescharacteristic
171C22×C11#41311yescharacteristic
172C22×C11#41311yescharacteristic
173C22×C11C2×#10411yescharacteristic
174C22×C11#42111yescharacteristic
175C22×C11#42111yescharacteristic
176C22×C11#42111yescharacteristic
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—21no—
187C4×C11—21no—
188C4×C11—22no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192Dic11—81no—
193Dic11—81no—
194Dic11—81no—
195C22×Q8—111no—
196C22×D4—111no—
197C22×C8—22no—
198C22×C8—222no—
199#125—222no—
200#125—222no—
201#124—222no—
202#124—222no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C22⋊C4—221no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210C2×C22⋊C4—221no—
211C2×C22⋊C4—221no—
212C2×C22⋊C4—221no—
213C2×C42C4×D1111yescharacteristic
214C2×C42C4×D1111yescharacteristic
215C2×C42D4411yescharacteristic
216C2×C42D4411yescharacteristic
217C2×C42C22⋊D1111yescharacteristic
218C2×C42C22⋊D1111yescharacteristic
219C2×C42C22×D1111yescharacteristic
220C4⋊C8—224no—
221#97—22no—
222#97—222no—
223#97—222no—
224#97D4414yes—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229C2×C11#152911yescharacteristic
230C2×C11#153211yescharacteristic
231C2×C11#153511yescharacteristic
232C2×C11#153511yescharacteristic
233C2×C11#196311yescharacteristic
234C2×C11#196711yescharacteristic
235C2×C11#198011yescharacteristic
236D11—161no—
237C24—221no—
238C2×Q8—222no—
239C2×Q8—441no—
240C2×Q8—441no—
241C2×D4—222no—
242C2×D4—441no—
243C2×D4—441no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4(C2×D11)⋊C411yescharacteristic
248C22×C4(C2×D11)⋊C411yescharacteristic
249C22×C4(C2×D11)⋊C411yescharacteristic
250C22×C4(C2×D11)⋊C411yescharacteristic
251C22×C4C2×C4×D1111yescharacteristic
252C22×C4C2×D4411yescharacteristic
253C22×C4C2×C22⋊D1111yescharacteristic
254C2×C8—24no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—224no—
258C2×C8—442no—
259C2×C8—442no—
260C4⋊C4—222no—
261C4⋊C4—222no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—442no—
265C22⋊C4—442no—
266C22⋊C4—442no—
267C22⋊C4—442no—
268C22⋊C4—442no—
269C22⋊C4—441no—
270C22⋊C4—441no—
271C22⋊C4—442no—
272C42—22no—
273C42—41no—
274C42—41no—
275C42—41no—
276C42—41no—
277C42—41no—
278C42C2×D4412yes—
279C42#433912yes—
280C11#968811yescharacteristic, complemented, Sylow
281C23—441no—
282C23—441no—
283C23—441no—
284C23—441no—
285C23—441no—
286C23—441no—
287C23—441no—
288C23C2×(C2×D11)⋊C411yescharacteristic
289Q8—882no—
290D4—882no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
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—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—441no—
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#6688912yes—
318C2×C4C4×D4412yes—
319C2×C4#6692711yescharacteristic
320C2×C4#6692811yescharacteristic
321C2×C4#6698312yes—
322C8—44no—
323C8—444no—
324C22—881no—
325C22—881no—
326C22—881no—
327C22—881no—
328C22—881no—
329C22—881no—
330C22—881no—
331C22#1062255211yescharacteristic
332C22#1062261811yescharacteristic
333C22#1062261811yescharacteristic
334C22#1062274511yescharacteristic
335C22#1062274511yescharacteristic
336C22C2×#6688911yescharacteristic
337C22#1062275211yescharacteristic
338C4—22no—
339C4—22no—
340C4—21no—
341C4—21no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—881no—
347C4—881no—
348C4—881no—
349C2—1761no—
350C2#1306722411yescharacteristic
351C2#1306723711yescharacteristic
352C2#1306724511yescharacteristic
353C2#1306724811yescharacteristic
354C2#1306944811yescharacteristic
355C2#1306946511yescharacteristic
356C2#1306953511yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1745C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1745D11
hypocenterC11#9688
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1745

Complements

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

NH ≅ G/Ntype
2. #13068469C2semidirect
3. C2×#10622103C2semidirect
5. C11×#1745C2semidirect
105. #1745D11semidirect
280. C11#9688semidirect

Maximal subgroups

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

subgroupindex
#130769882
#130684692
C2×#106221032
C2×#106221022
C11×#17452
#968811