Finite Group Databasebeta

← #14649826

Subgroups — #14649826

Order 2816.

612 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 115 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#13074421C211yesmaximal, characteristic
2#13067187C212yesmaximal, complemented
3C2×#10622163C211yesmaximal, characteristic
4#13066483C212yesmaximal, complemented
5C11×#2312C211yesmaximal, characteristic
6C22×C11×C22⋊C4C2211yescharacteristic
7C2×#66977C2211yescharacteristic
8C11×#388—24no—
9C11×#380C2212yes—
10C11×#379—21no—
11C4×C11×C22⋊C4—21no—
12#10622860—21no—
13#10622825C2211yescharacteristic
14#10622823—21no—
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622562C412yescomplemented
17#10622561—22no—
18#10622560C412yescomplemented
19#10622163—22no—
20#10622090—24no—
21C25×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C2×C11×C4⋊C4—22no—
26C2×C11×C22⋊C4—22no—
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4C2×C412yes—
32C2×C11×C22⋊C4D412yes—
33C2×C42×C11—22no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—22no—
37C2×C22⋊Dic11—22no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40#66977—22no—
41#66977—22no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—22no—
44C22×C11⋊C8—22no—
45C11×#95—22no—
46C11×#95D414yes—
47C11⋊#95—22no—
48C11⋊#95C2×C412yes—
49C22⋊(C11⋊C8)—22no—
50C22⋊(C11⋊C8)—22no—
51#9201—111nomaximal, Sylow
52C24×C11—21no—
53C24×C11—21no—
54C24×C11—22no—
55C24×C11—22no—
56C24×C11—81no—
57C24×C11—81no—
58C24×C11C22⋊C412yes—
59C24×C11C2×D411yescharacteristic
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—24no—
63C22×C4×C11—81no—
64C22×C4×C11—81no—
65C22×C4×C11C22⋊C412yes—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D412yes—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4112yes—
70C22×Dic11—21no—
71C22×Dic11—22no—
72C22×Dic11—21no—
73C2×Dic22—22no—
74C2×Dic22—81no—
75C11×C4⋊C4—82no—
76C11×C22⋊C4—24no—
77C11×C22⋊C4—24no—
78C11×C22⋊C4—42no—
79C11×C22⋊C4—42no—
80C11×C22⋊C4—82no—
81C11×C22⋊C4—82no—
82C42×C11—82no—
83C22⋊Dic11—41no—
84C22⋊Dic11—41no—
85C22⋊Dic11—42no—
86C22⋊Dic11—82no—
87C22⋊Dic11—82no—
88C4⋊Dic11—22no—
89C4⋊Dic11—81no—
90Dic11⋊C4—42no—
91Dic11⋊C4—82no—
92C2×C11⋊C8—42no—
93C2×C11⋊C8—82no—
94#2626—111no—
95#2312D1111yescharacteristic
96#1520—112no—
97C2×#323—111no—
98#1289—112no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11—22no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11—42no—
105C23×C11—42no—
106C23×C11—42no—
107C23×C11—42no—
108C23×C11—42no—
109C23×C11—42no—
110C23×C11—81no—
111C23×C11—81no—
112C23×C11—84no—
113C23×C11—84no—
114C23×C11C2×C22⋊C411yescharacteristic
115C23×C11#12011yescharacteristic
116C23×C11#12311yescharacteristic
117C23×C11#13512yes—
118C23×C11#13712yes—
119C2×C4×C11—22no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—44no—
127C2×C4×C11—44no—
128C2×C4×C11—44no—
129C2×C4×C11—81no—
130C2×C4×C11C4×D412yes—
131C2×C4×C11#12112yes—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—42no—
139Dic22—82no—
140C11⋊C8—82no—
141C2×C22⋊Q8—111no—
142C22×C22⋊C4C2×D1111yescharacteristic
143C2×C22⋊C8—112no—
144#399—112no—
145#396—222no—
146#393—112no—
147#388—24no—
148#385—221no—
149#380—111no—
150#380C2×D1112yes—
151#379—21no—
152#379—221no—
153C4×C22⋊C4—21no—
154#328—224no—
155#323—222no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—42no—
163C22×C11—42no—
164C22×C11—44no—
165C22×C11—42no—
166C22×C11—42no—
167C22×C11—42no—
168C22×C11—82no—
169C22×C11—84no—
170C22×C11—84no—
171C22×C11#38611yescharacteristic
172C22×C11#41611yescharacteristic
173C22×C11#41911yescharacteristic
174C22×C11#45212yes—
175C22×C11#48512yes—
176C4×C11—22no—
177C4×C11—22no—
178C4×C11—42no—
179C4×C11—84no—
180Dic11—82no—
181Dic11—81no—
182Dic11—81no—
183C25C22⋊D1111yescharacteristic
184C22×Q8—111no—
185C23×C4C22⋊D1111yescharacteristic
186C23×C4C22×D1111yescharacteristic
187C22×C8—222no—
188C22⋊Q8—222no—
189C22⋊Q8—222no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—111no—
192C2×C4⋊C4—221no—
193C2×C4⋊C4—222no—
194C2×C4⋊C4—221no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—221no—
201C2×C22⋊C4—221no—
202C2×C22⋊C4—222no—
203C2×C22⋊C4—222no—
204C2×C22⋊C4C4×D1112yes—
205C2×C22⋊C4D4412yes—
206C2×C42—22no—
207C22⋊C8—222no—
208C22⋊C8—222no—
209#95—22no—
210#95—112no—
211#95—222no—
212#95C22⋊D1114yes—
213C2×C11—21no—
214C2×C11—22no—
215C2×C11—21no—
216C2×C11—22no—
217C2×C11—82no—
218C2×C11#187311yescharacteristic
219C2×C11#191111yescharacteristic
220C2×C11#191311yescharacteristic
221C24—21no—
222C24—21no—
223C24—22no—
224C24—22no—
225C24—81no—
226C24—81no—
227C24(C2×D11)⋊C412yes—
228C24C2×C22⋊D1111yescharacteristic
229C2×Q8—222no—
230C2×Q8—881no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—24no—
234C22×C4—81no—
235C22×C4—81no—
236C22×C4—222no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4(C2×D11)⋊C412yes—
240C22×C4C2×C4×D1111yescharacteristic
241C22×C4C2×D4411yescharacteristic
242C22×C4#433912yes—
243C22×C4C2×C22⋊D1112yes—
244C2×C8—442no—
245C2×C8—882no—
246C4⋊C4—82no—
247C4⋊C4—222no—
248C4⋊C4—442no—
249C4⋊C4—882no—
250C4⋊C4—881no—
251C22⋊C4—24no—
252C22⋊C4—24no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—82no—
256C22⋊C4—82no—
257C22⋊C4—441no—
258C22⋊C4—442no—
259C22⋊C4—441no—
260C22⋊C4—882no—
261C22⋊C4—882no—
262C42—82no—
263C11#920111yescharacteristic, complemented, Sylow
264C23—22no—
265C23—22no—
266C23—22no—
267C23—41no—
268C23—41no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—42no—
273C23—42no—
274C23—42no—
275C23—81no—
276C23—81no—
277C23—84no—
278C23—84no—
279C23C2×(C2×D11)⋊C411yescharacteristic
280C23#6698211yescharacteristic
281C23#6700312yes—
282C23#6700412yes—
283C23#6700611yescharacteristic
284Q8—882no—
285C2×C4—22no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—81no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—442no—
303C2×C4C4×C22⋊D1112yes—
304C2×C4#6698312yes—
305C8—882no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—42no—
313C22—42no—
314C22—44no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—82no—
319C22—84no—
320C22—84no—
321C22#1062260912yes—
322C22#1062261511yescharacteristic
323C22#1062261711yescharacteristic
324C22#1062282611yescharacteristic
325C22#1062285212yes—
326C4—22no—
327C4—22no—
328C4—42no—
329C4—84no—
330C4—882no—
331C4—881no—
332C4—881no—
333C2—22no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—82no—
338C2#1306892811yescharacteristic
339C2#1306914811yescharacteristic
340C2#1306915811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2312C2
socleC22×C11#386
prime radicalC25×C11D4
cosocleC23×C4×C11C23
hypercenter#2312D11
hypocenterC11#9201
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2312

Complements

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

NH ≅ G/Ntype
2. #13067187C2semidirect
4. #13066483C2semidirect
16. #10622562C4semidirect
18. #10622560C4semidirect
263. C11#9201semidirect

Maximal subgroups

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

subgroupindex
#130744212
#130671872
C2×#106221632
#130664832
C11×#23122
#920111