Finite Group Databasebeta

← #14651560

Subgroups — #14651560

Order 2816.

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

normal subgroups only

This group has 556 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#13077645C211yesmaximal, characteristic
2#13072933C211yesmaximal, characteristic
3#13068704C212yesmaximal, complemented
4#13066483C212yesmaximal, complemented
5C11×#1799C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C22×C4⋊Dic11C2211yescharacteristic
8C2×C11×#99—21no—
9C11×#380C2212yes—
10#10622833—21no—
11#10622825—21no—
12#10622825C2211yescharacteristic
13#10622820—21no—
14C2×C22⋊(C11⋊C8)C2212yes—
15#10622624—24no—
16#10622599C412yescomplemented
17#10622562C412yescomplemented
18#10622559—21no—
19#10622541—21no—
20#10622539—21no—
21C11×#342—21no—
22#10622167—24no—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11—21no—
27C4×D4×C11—22no—
28C4×D4×C11—22no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—22no—
37C2×C4⋊Dic11—22no—
38C2×C4⋊Dic11—22no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11C2×C412yes—
42C2×Dic11⋊C4—22no—
43C2×#4318—22no—
44C22×C11⋊C8D414yes—
45C11×#99—42no—
46C11×#95—22no—
47C11⋊#95—22no—
48C11⋊#95—22no—
49C11⋊#95C2×C412yes—
50C22⋊(C11⋊C8)—22no—
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—22no—
54#66867—22no—
55#9473—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C24×C11C2×D411yescharacteristic
58C2×D4×C11—22no—
59C2×D4×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D412yes—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4112yes—
74C22×Dic11—22no—
75C22×Dic11—22no—
76C22×Dic11—42no—
77C22×Dic11—82no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—44no—
80C11×C22⋊C4—22no—
81C11×C22⋊C4—22no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—42no—
84C42×C11—21no—
85C42×C11—21no—
86C22⋊Dic11—41no—
87C22⋊Dic11—41no—
88C22⋊Dic11—82no—
89C4⋊Dic11—24no—
90C4⋊Dic11—42no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93Dic11⋊C4—82no—
94#4318—82no—
95C2×C11⋊C8—24no—
96C2×C11⋊C8—44no—
97#2973—111no—
98#2487—111no—
99#1824—112no—
100#1799D1111yescharacteristic
101#1289—112no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11C2×C22⋊C411yescharacteristic
110C23×C11#12112yes—
111C23×C11AGL(1,ℤ/8)11yescharacteristic
112C23×C11#13711yescharacteristic
113C23×C11#13712yes—
114D4×C11—42no—
115D4×C11—42no—
116C2×C4×C11—24no—
117C2×C4×C11—22no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—81no—
129C2×C4×C11—82no—
130C2×C4×C11—82no—
131C2×C4×C11—82no—
132C2×C4×C11C4×D412yes—
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12311yescharacteristic
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—84no—
142C11⋊C8—44no—
143C2×C4×D4C2×D1111yescharacteristic
144C22×C4⋊C4—111no—
145#435—224no—
146#432—221no—
147C2×#99—21no—
148#407—221no—
149C2×C22⋊C8—112no—
150#400—112no—
151#399—112no—
152#389—221no—
153#386—221no—
154#385—221no—
155#380—111no—
156#380—221no—
157#380C2×D1112yes—
158#342—21no—
159#340—224no—
160C22×C11—21no—
161C22×C11—22no—
162C22×C11—21no—
163C22×C11—22no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—42no—
167C22×C11—42no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—81no—
172C22×C11#38611yescharacteristic
173C22×C11#41711yescharacteristic
174C22×C11#41911yescharacteristic
175C22×C11#46812yes—
176C22×C11#47012yes—
177C4×C11—21no—
178C4×C11—22no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—162no—
183C4×C11#45812yes—
184Dic11—82no—
185Dic11—82no—
186C22×D4C22⋊D1111yescharacteristic
187C23×C4—221no—
188C23×C4D4411yescharacteristic
189C23×C4C22×D1111yescharacteristic
190C2×M16—222no—
191C22×C8—114no—
192C4×D4—22no—
193C4×D4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—112no—
196C2×C4⋊C4—222no—
197C2×C4⋊C4—222no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—222no—
201C2×C4⋊C4C4×D1111yescharacteristic
202C2×C22⋊C4—22no—
203C2×C22⋊C4—221no—
204C2×C22⋊C4—222no—
205C2×C22⋊C4C4×D1111yescharacteristic
206C2×C22⋊C4C22⋊D1111yescharacteristic
207C2×C42D4411yescharacteristic
208C4⋊C8—222no—
209#99—42no—
210C22⋊C8—222no—
211C22⋊C8—222no—
212C22⋊C8—222no—
213#97—222no—
214#95—22no—
215#95—112no—
216#95—222no—
217#95—222no—
218C2×C11—21no—
219C2×C11—22no—
220C2×C11—21no—
221C2×C11—22no—
222C2×C11—81no—
223C2×C11#189011yescharacteristic
224C2×C11#189411yescharacteristic
225C2×C11#191011yescharacteristic
226C24(C2×D11)⋊C411yescharacteristic
227C24C2×C22⋊D1111yescharacteristic
228C2×D4—21no—
229C2×D4—22no—
230C2×D4—21no—
231C2×D4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—222no—
238C22×C4—222no—
239C22×C4—442no—
240C22×C4—882no—
241C22×C4(C2×D11)⋊C411yescharacteristic
242C22×C4(C2×D11)⋊C411yescharacteristic
243C22×C4(C2×D11)⋊C411yescharacteristic
244C22×C4C2×C4×D1111yescharacteristic
245C22×C4C2×D4411yescharacteristic
246C22×C4D4×D1112yes—
247C22×C4#434112yes—
248M16—882no—
249C2×C8—224no—
250C2×C8—444no—
251C4⋊C4—22no—
252C4⋊C4—44no—
253C4⋊C4—224no—
254C4⋊C4—442no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—882no—
258C22⋊C4—22no—
259C22⋊C4—22no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—441no—
263C22⋊C4—441no—
264C22⋊C4—882no—
265C42—21no—
266C42—21no—
267C11#947311yescharacteristic, complemented, Sylow
268C23—21no—
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23C2×(C2×D11)⋊C411yescharacteristic
276C23#6698511yescharacteristic
277C23#6699212yes—
278C23#6699511yescharacteristic
279C23#6700412yes—
280D4—42no—
281D4—42no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—81no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—82no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4—884no—
305C2×C4(C22⋊D11)⋊C412yes—
306C2×C4#6693511yescharacteristic
307C2×C4#6693911yescharacteristic
308C8—444no—
309C22—21no—
310C22—22no—
311C22—21no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—42no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22#1062257111yescharacteristic
322C22#1062257911yescharacteristic
323C22#1062261711yescharacteristic
324C22#1062265512yes—
325C22#1062266512yes—
326C4—21no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—162no—
332C4—882no—
333C4—882no—
334C4#1062235512yes—
335C2—22no—
336C2—21no—
337C2—21no—
338C2—22no—
339C2—81no—
340C2#1306902711yescharacteristic
341C2#1306904711yescharacteristic
342C2#1306914111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1799C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC23×C4×C11C23
hypercenter#1799D11
hypocenterC11#9473
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #13068704C2semidirect
4. #13066483C2semidirect
16. #10622599C4semidirect
17. #10622562C4semidirect
267. C11#9473semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130729332
#130687042
#130664832
C11×#17992
#947311