Finite Group Databasebeta

← #14649533

Subgroups — #14649533

Order 2816.

630 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 147 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#13076955C211yesmaximal, characteristic
2#13068684C211yesmaximal, characteristic
3C2×#10622090C212yesmaximal
4#13066495C212yesmaximal
5C2×C11×#382C211yesmaximal, characteristic
6C22×C11×C4⋊C4—21no—
7C22×C42×C11C2211yescharacteristic
8C2×#66977C2211yescharacteristic
9C11×#382—24no—
10C2×C11×#95—21no—
11C2×C11×#95C2212yes—
12#10622825C2211yescharacteristic
13#10622824—21no—
14#10622823—21no—
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622546—22no—
17#10622542C412yescomplemented
18#10622541C412yescomplemented
19#10622162—22no—
20#10622090—24no—
21C23×C4×C11—22no—
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C22×Dic22C2×C411yescharacteristic
26C2×C11×C4⋊C4—24no—
27C2×C11×C4⋊C4—42no—
28C2×C11×C4⋊C4—42no—
29C2×C42×C11—22no—
30C2×C42×C11—22no—
31C2×C42×C11C2×C412yes—
32C2×C42×C11D412yes—
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×C4⋊Dic11C2×C412yes—
37#66977—22no—
38#66977—22no—
39C2×Dic11⋊C4—22no—
40C2×Dic11⋊C4—21no—
41C22×C11⋊C8—22no—
42C11×#95—24no—
43C11×#95—22no—
44C11×#95D414yes—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95—21no—
49C22⋊(C11⋊C8)—22no—
50C22⋊(C11⋊C8)—22no—
51#9152—111nomaximal, Sylow
52C24×C11C2×D411yescharacteristic
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—24no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11—44no—
63C22×C4×C11—44no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11C22⋊C412yes—
67C22×C4×C11C22⋊C412yes—
68C22×C4×C11SD1612yes—
69C22×C4×C11Q1612yes—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D412yes—
73C22×C4×C11#4112yes—
74C22×Dic11—22no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C2×Dic22—22no—
78C2×Dic22—42no—
79C11×C4⋊C4—48no—
80C42×C11—24no—
81C42×C11—24no—
82C22⋊Dic11—41no—
83C22⋊Dic11—41no—
84C22⋊Dic11—41no—
85C22⋊Dic11—41no—
86C4⋊Dic11—22no—
87C4⋊Dic11—42no—
88Dic11⋊C4—44no—
89Dic11⋊C4—42no—
90C2×C11⋊C8—44no—
91C2×C11⋊C8—42no—
92#2855—111no—
93C2×#382D1111yescharacteristic
94#1817—111no—
95C2×#328—112no—
96#1294—112no—
97C23×C11—22no—
98C23×C11—22no—
99C23×C11C2×C22⋊C411yescharacteristic
100C23×C11#12011yescharacteristic
101C23×C11#12311yescharacteristic
102C23×C11C2×SD1611yescharacteristic
103C23×C11C2×Q1611yescharacteristic
104C23×C11AGL(1,ℤ/8)11yescharacteristic
105C23×C11#13711yescharacteristic
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—44no—
122C2×C4×C11—44no—
123C2×C4×C11—44no—
124C2×C4×C11—84no—
125C2×C4×C11—84no—
126C2×C4×C11#10314yes—
127C2×C4×C11C4×D412yes—
128C2×C4×C11#12112yes—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136Dic22—82no—
137C11⋊C8—82no—
138C2×C22⋊Q8—111no—
139C22×C4⋊C4—21no—
140C22×C42C2×D1111yescharacteristic
141C2×C22⋊C8—112no—
142#391—112no—
143#389—112no—
144#387—222no—
145#385—221no—
146#382—24no—
147#381—221no—
148#380—111no—
149C2×#95—21no—
150C2×#95C2×D1112yes—
151#336—222no—
152#328—224no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11#38611yescharacteristic
162C22×C11#41012yes—
163C22×C11C2×#10311yescharacteristic
164C22×C11#41711yescharacteristic
165C22×C11#42112yes—
166C22×C11#45011yescharacteristic
167C22×C11#45111yescharacteristic
168C22×C11#48311yescharacteristic
169C22×C11#48411yescharacteristic
170C4×C11—24no—
171C4×C11—22no—
172C4×C11—22no—
173C4×C11—42no—
174C4×C11—84no—
175Dic11—81no—
176Dic11—81no—
177Dic11—82no—
178C22×Q8—111no—
179C23×C4—22no—
180C23×C4C22⋊D1111yescharacteristic
181C23×C4C22⋊D1111yescharacteristic
182C23×C4C22×D1111yescharacteristic
183C22×C8—222no—
184C22⋊Q8—222no—
185C22⋊Q8—222no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—42no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—112no—
191C2×C4⋊C4—222no—
192C2×C4⋊C4—221no—
193C2×C22⋊C4—221no—
194C2×C22⋊C4—221no—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42C4×D1112yes—
198C2×C42D4412yes—
199C22⋊C8—222no—
200C22⋊C8—222no—
201#95—24no—
202#95—22no—
203#95—222no—
204#95—222no—
205#95—222no—
206#95—221no—
207#95C22⋊D1114yes—
208C2×C11—21no—
209C2×C11—21no—
210C2×C11—21no—
211C2×C11—21no—
212C2×C11#151212yes—
213C2×C11#151812yes—
214C2×C11#187211yescharacteristic
215C2×C11#189711yescharacteristic
216C2×C11#189911yescharacteristic
217C24C2×C22⋊D1111yescharacteristic
218C2×Q8—222no—
219C2×Q8—442no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—24no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—44no—
230C22×C4—44no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—222no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4(C2×D11)⋊C412yes—
237C22×C4(C2×D11)⋊C412yes—
238C22×C4#432412yes—
239C22×C4#432612yes—
240C22×C4C2×C4×D1111yescharacteristic
241C22×C4C2×D4411yescharacteristic
242C22×C4#433912yes—
243C22×C4C2×C22⋊D1112yes—
244C2×C8—444no—
245C2×C8—442no—
246C4⋊C4—48no—
247C4⋊C4—222no—
248C4⋊C4—442no—
249C4⋊C4—444no—
250C4⋊C4—442no—
251C22⋊C4—441no—
252C22⋊C4—441no—
253C22⋊C4—441no—
254C22⋊C4—441no—
255C42—24no—
256C42—24no—
257C11#915211yescharacteristic, complemented, Sylow
258C23—22no—
259C23—22no—
260C23C2×(C2×D11)⋊C411yescharacteristic
261C23#6698211yescharacteristic
262C23#6698511yescharacteristic
263C23C2×#432411yescharacteristic
264C23#6699511yescharacteristic
265C23C2×#432611yescharacteristic
266C23#6700611yescharacteristic
267Q8—882no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—84no—
287C2×C4—84no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4—442no—
295C2×C4#6687414yes—
296C2×C4C4×C22⋊D1112yes—
297C2×C4#6698312yes—
298C8—882no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22#1062257911yescharacteristic
308C22C2×#6687411yescharacteristic
309C22#1062258311yescharacteristic
310C22#1062258411yescharacteristic
311C22#1062261812yes—
312C22#1062261912yes—
313C22#1062282611yescharacteristic
314C22#1062283111yescharacteristic
315C22#1062284111yescharacteristic
316C4—22no—
317C4—22no—
318C4—24no—
319C4—42no—
320C4—84no—
321C4—881no—
322C4—881no—
323C4—882no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2#1306715212yes—
329C2#1306717912yes—
330C2#1306892311yescharacteristic
331C2#1306906411yescharacteristic
332C2#1306907411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#382C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#382D11
hypocenterC11#9152
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
17. #10622542C4semidirect
18. #10622541C4semidirect
257. C11#9152semidirect

Maximal subgroups

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

subgroupindex
#130769552
#130686842
C2×#106220902
#130664952
C2×C11×#3822
#915211