Finite Group Databasebeta

← #14648970

Subgroups — #14648970

Order 2816.

476 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 107 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#13078624C211yesmaximal, characteristic
2#13077553C211yesmaximal, characteristic, complemented
3#13069415C211yesmaximal, characteristic
4#13067271C211yesmaximal, characteristic, complemented
5#13066511C211yesmaximal, characteristic, complemented
6#13066460C211yesmaximal, characteristic, complemented
7C11×#1486C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622831C412yes—
13C2×C22⋊(C11⋊C8)—21no—
14C2×C22⋊(C11⋊C8)—21no—
15#10622735—21no—
16#10622732—21no—
17#10622632—21no—
18C4×#4324—22no—
19#10622621—21no—
20#10622584C412yes—
21#10622538C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×#66867C2211yescharacteristic
24#10622441—22no—
25#10622441—22no—
26C11×D4⋊C8—22no—
27#10622120—21no—
28#10622119—21no—
29C22×D4×C11C2×C411yescharacteristic
30C23×C4×C11—21no—
31C2×C11×M16—21no—
32C4×D4×C11—21no—
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C42×C11C2311yescharacteristic
39C2×#4324—22no—
40#66979—21no—
41#66977—21no—
42#66977C2×C412yes—
43C22×C11⋊C8—21no—
44C22×C11⋊C8D411yescharacteristic
45C22×C11⋊C8D411yescharacteristic
46#66923—21no—
47#66922D411yescharacteristic
48#66922D411yescharacteristic
49C4×Dic22—21no—
50C4×Dic22D412yes—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8D412yes—
54C11×C22⋊C8—21no—
55C4×C8×C11—21no—
56#66896—22no—
57C22⋊(C11⋊C8)—42no—
58C22⋊(C11⋊C8)—42no—
59C22⋊(C11⋊C8)C2×C412yes—
60#66879—22no—
61Dic11⋊C8—24no—
62C8×Dic11—22no—
63#66874—22no—
64#66872—22no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68#66867—21no—
69#66867—21no—
70C4×C11⋊C8—21no—
71#9050—111nomaximal, Sylow
72C24×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—42no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C2×Dic22—21no—
87C2×Dic22C22⋊C412yes—
88C11×M16—41no—
89C11×M16—41no—
90C2×C8×C11—22no—
91C2×C8×C11—41no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C22⋊Dic11—22no—
101#4324—44no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11C22⋊C412yes—
106Dic11⋊C4—22no—
107Dic11⋊C4—22no—
108C4×Dic11—22no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8—21no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8SD1612yescomplemented
119#3101—111no—
120#2961—111no—
121#1955—111no—
122#1542—111no—
123#1486D1111yescharacteristic
124#1301—111no—
125#1281—111no—
126C23×C11—22no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11C4×D411yescharacteristic
134D4×C11—22no—
135D4×C11—22no—
136D4×C11—41no—
137D4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11C2×C22⋊C411yescharacteristic
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C2×C4×C11C2×SD1611yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×Dic11—22no—
158C2×Dic11—22no—
159Dic22—42no—
160Dic22—81no—
161C8×C11—42no—
162C8×C11—81no—
163C11⋊C8—22no—
164C11⋊C8—42no—
165C11⋊C8—41no—
166C11⋊C8—81no—
167#533—111no—
168C2×C4×D4C2×D1111yescharacteristic
169#483—112no—
170#476—221no—
171#461—221no—
172#450—112no—
173#446—222no—
174#446—222no—
175C4×SD16—222no—
176#431—111no—
177#431C2×D1111yescharacteristic
178#424—221no—
179#423C2×D1111yescharacteristic
180C2×C4⋊C8—111no—
181C2×C22⋊C8—221no—
182C2×C22⋊C8—221no—
183#405—221no—
184C2×#97—111no—
185#333—221no—
186#332—221no—
187D4⋊C8—22no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—42no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#38611yescharacteristic
198C22×C11C4×SD1611yescharacteristic
199C22×C11#44011yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11#44811yescharacteristic
206C4×C11#44911yescharacteristic
207C4×C11#46011yescharacteristic
208C4×C11#46411yescharacteristic
209Dic11—42no—
210Dic11—42no—
211C22×D4C4×D1111yescharacteristic
212C23×C4—21no—
213C2×SD16—222no—
214C2×M16—21no—
215C22×C8—111no—
216C22×C8—111no—
217C22×C8—221no—
218C4⋊Q8—111no—
219C4⋊Q8—111no—
220#125—221no—
221C22⋊Q8—112no—
222C22⋊Q8—221no—
223C4×Q8—112no—
224C4×Q8—221no—
225C4×D4—21no—
226C4×D4—21no—
227C4×D4—21no—
228C4×D4—21no—
229#117—221no—
230C2×C4⋊C4C4×D1111yescharacteristic
231C2×C22⋊C4—21no—
232C2×C42C22×D1111yescharacteristic
233#106—222no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—224no—
237C4⋊C8—221no—
238C4⋊C8—221no—
239C4⋊C8—221no—
240C4⋊C8C22⋊D1112yes—
241#103—222no—
242#102—222no—
243C22⋊C8—21no—
244C22⋊C8—112no—
245C22⋊C8—442no—
246C22⋊C8—442no—
247#97—222no—
248#97—221no—
249#97—221no—
250C4×C8—21no—
251C4×C8—222no—
252C4×C8—221no—
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—82no—
256C2×C11#188011yescharacteristic
257C2×C11#188111yescharacteristic
258C2×C11#189111yescharacteristic
259C24—21no—
260C2×Q8—112no—
261C2×Q8—221no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—42no—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4C2×C4×D1111yescharacteristic
273C22×C4D4×D1111yescharacteristic
274C22×C4#434111yescharacteristic
275SD16—444no—
276M16—41no—
277M16—41no—
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—112no—
281C2×C8—221no—
282C2×C8—221no—
283C2×C8—222no—
284C2×C8—221no—
285C2×C8—221no—
286C2×C8—221no—
287C2×C8—441no—
288C2×C8—441no—
289C2×C8—441no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—112no—
293C4⋊C4—222no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—222no—
297C4⋊C4—221no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—222no—
301C42—222no—
302C42#433911yescharacteristic
303C42D4×D1111yescharacteristic
304C42D4×D1111yescharacteristic
305C42C2×C22⋊D1111yescharacteristic
306C11#905011yescharacteristic, complemented, Sylow
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23(C22⋊D11)⋊C411yescharacteristic
315Q8—442no—
316Q8—881no—
317D4—22no—
318D4—22no—
319D4—41no—
320D4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—222no—
331C2×C4—222no—
332C2×C4C22⋊C4×D1111yescharacteristic
333C2×C4#6693611yescharacteristic
334C2×C4#6693711yescharacteristic
335C2×C4#6696411yescharacteristic
336C2×C4#6696511yescharacteristic
337C2×C4SD16×D1111yescharacteristic
338C2×C4#6696811yescharacteristic
339C2×C4C4×C22⋊D1111yescharacteristic
340C2×C4#6699011yescharacteristic
341C2×C4#6699111yescharacteristic
342C8—42no—
343C8—81no—
344C8—222no—
345C8—442no—
346C8—441no—
347C8—881no—
348C22—21no—
349C22—21no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22#1062237011yescharacteristic
358C22#1062237111yescharacteristic
359C22#1062256911yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—442no—
366C4—442no—
367C4#1062237511yescharacteristic
368C4#1062238011yescharacteristic
369C4#1062277111yescharacteristic
370C4#1062278311yescharacteristic
371C2—21no—
372C2—21no—
373C2—82no—
374C2#1306896811yescharacteristic
375C2#1306897511yescharacteristic
376C2#1306903111yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1486C2
socleC22×C11#386
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#1486D11
hypocenterC11#9050
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #13077553C2semidirect
4. #13067271C2semidirect
5. #13066511C2semidirect
6. #13066460C2semidirect
118. C2×C11⋊C8SD16semidirect
306. C11#9050semidirect

Maximal subgroups

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

subgroupindex
#130786242
#130775532
#130694152
#130672712
#130665112
#130664602
C11×#14862
#905011