Finite Group Databasebeta

← #14650524

Subgroups — #14650524

Order 2816.

480 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079741C211yesmaximal, characteristic
2#13071364C211yesmaximal, characteristic, complemented
3#13067302C211yesmaximal, characteristic, complemented
4#13067176C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic, complemented
6#13066445C211yesmaximal, characteristic, complemented
7C11×#1963C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C11×#104—21no—
12C2×C11×#104—21no—
13C11×#376C2211yescharacteristic
14#10622692C412yescomplemented
15#10622683C412yescomplemented
16#10622647—22no—
17#10622621—22no—
18#10622549C2211yescharacteristic
19C4×C4⋊Dic11—21no—
20#10622541—21no—
21#10622538C2211yescharacteristic
22#10622538C2211yescharacteristic
23#10622267—22no—
24#10622259—22no—
25#10622175—22no—
26#10622124—22no—
27C2×C11×#41—21no—
28C22×Dic22—21no—
29C2×C11×M16—21no—
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×#127C2×C411yescharacteristic
32C11×#124—21no—
33C11×#121—21no—
34C11×#121—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11C2311yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D412yes—
43C2×Dic11⋊C4—22no—
44C2×C4×Dic11—22no—
45#66922—21no—
46#66922—21no—
47#66922C2×C412yes—
48#66922D412yes—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×#104—42no—
52C11×#104—42no—
53C11×#95—21no—
54C11×#95—21no—
55#66896—24no—
56C11⋊#95—22no—
57C11⋊#95—22no—
58C11⋊#95—21no—
59C11⋊#95D412yes—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66872—24no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4×C11⋊C8—21no—
66C4×C11⋊C8C2×C412yes—
67#9302—111nomaximal, Sylow
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C11×#41—41no—
72C2×Q8×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—41no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—22no—
84C22×Dic11—22no—
85C2×Dic22—22no—
86C2×Dic22—22no—
87C2×Dic22—82no—
88C11×M16—41no—
89C11×M16—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11—21no—
96C42×C11—21no—
97C42×C11—21no—
98C42×C11SD1612yes—
99C42×C11C22×C411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4⋊Dic11C22⋊C414yes—
109Dic11⋊C4—82no—
110C4×Dic11—82no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—41no—
113#3227—111no—
114#2331—111no—
115#1963D1111yescharacteristic
116#1549—111no—
117#1517—111no—
118#1286—111no—
119#1274—111no—
120C23×C11—41no—
121C23×C11#12011yescharacteristic
122Q8×C11—41no—
123Q8×C11—41no—
124D4×C11—42no—
125D4×C11—41no—
126D4×C11—41no—
127D4×C11—81no—
128D4×C11—81no—
129D4×C11—81no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11C2×C22⋊C411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12311yescharacteristic
147C2×C4×C11C2×SD1611yescharacteristic
148C2×C4×C11#13511yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C2×Dic11—24no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157Dic22—82no—
158Dic22—82no—
159C8×C11—81no—
160C11⋊C8—42no—
161C11⋊C8—81no—
162#532C2×D1111yescharacteristic
163C2×C4⋊Q8—111no—
164#498—112no—
165#486—112no—
166#481—222no—
167#476—222no—
168#431—111no—
169#431—111no—
170#423C2×D1111yescharacteristic
171C2×#104—21no—
172C2×#104—21no—
173#391—222no—
174#389—221no—
175#387—222no—
176#382—111no—
177C4×C4⋊C4—221no—
178#376C2×D1111yescharacteristic
179#332—222no—
180#327—222no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11#38611yescharacteristic
187C22×C11#44811yescharacteristic
188C22×C11#44911yescharacteristic
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—42no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11C4×SD1611yescharacteristic
197C4×C11#44011yescharacteristic
198C4×C11#46011yescharacteristic
199C4×C11#46411yescharacteristic
200Dic11—44no—
201Dic11—82no—
202C2×#41—21no—
203C22×Q8—221no—
204C2×M16—21no—
205C4⋊Q8—112no—
206C4⋊Q8—112no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8C4×D1111yescharacteristic
210#127C4×D1111yescharacteristic
211#124—21no—
212#121—21no—
213#121—21no—
214C4×D4—21no—
215C4×D4—21no—
216C2×C4⋊C4—112no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—222no—
220C2×C42—222no—
221C2×C42C22⋊D1111yescharacteristic
222C2×C42C22⋊D1111yescharacteristic
223C2×C42C22×D1111yescharacteristic
224#106—224no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—221no—
228C4⋊C8—221no—
229#104—42no—
230#104—42no—
231#102—224no—
232C22⋊C8—221no—
233C22⋊C8—221no—
234C4×C8—112no—
235C4×C8—221no—
236#95—21no—
237#95—21no—
238#95—112no—
239#95—222no—
240#95—222no—
241#95—221no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11—161no—
245C2×C11#188011yescharacteristic
246C2×C11#190411yescharacteristic
247C2×C11#191211yescharacteristic
248#41—41no—
249#41—41no—
250#41—41no—
251#41—41no—
252C2×Q8—21no—
253C2×Q8—222no—
254C2×Q8—222no—
255C2×Q8—882no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—222no—
264C22×C4—222no—
265C22×C4D4×D1111yescharacteristic
266C22×C4D4×D1111yescharacteristic
267C22×C4C2×C22⋊D1111yescharacteristic
268M16—41no—
269M16—41no—
270C2×C8—41no—
271C2×C8—222no—
272C2×C8—441no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—114no—
276C4⋊C4—222no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—882no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C42—21no—
285C42—21no—
286C42—21no—
287C42—882no—
288C42#432412yes—
289C42C2×C4×D1111yescharacteristic
290C42#433911yescharacteristic
291C42D4×D1111yescharacteristic
292C42#434111yescharacteristic
293C11#930211yescharacteristic, complemented, Sylow
294C23—41no—
295C23#6699011yescharacteristic
296Q8—41no—
297Q8—41no—
298Q8—882no—
299Q8—882no—
300D4—42no—
301D4—41no—
302D4—41no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—224no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4C22⋊C4×D1111yescharacteristic
324C2×C4(C22⋊D11)⋊C411yescharacteristic
325C2×C4#6693611yescharacteristic
326C2×C4#6693711yescharacteristic
327C2×C4C4×C22⋊D1111yescharacteristic
328C2×C4#6698511yescharacteristic
329C2×C4C2×#432411yescharacteristic
330C2×C4#6699111yescharacteristic
331C2×C4#6700311yescharacteristic
332C2×C4#6700411yescharacteristic
333C8—81no—
334C8—442no—
335C8—881no—
336C22—21no—
337C22—21no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22#1062256911yescharacteristic
342C22#1062265011yescharacteristic
343C22#1062265311yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—81no—
350C4—81no—
351C4—444no—
352C4—882no—
353C4C4×#432411yescharacteristic
354C4#1062263111yescharacteristic
355C4#1062266711yescharacteristic
356C4#1062268811yescharacteristic
357C2—21no—
358C2—21no—
359C2—161no—
360C2#1306897411yescharacteristic
361C2#1306910011yescharacteristic
362C2#1306915011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1963C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1963D11
hypocenterC11#9302
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
2. #13071364C2semidirect
3. #13067302C2semidirect
5. #13066476C2semidirect
6. #13066445C2semidirect
14. #10622692C4semidirect
15. #10622683C4semidirect
293. C11#9302semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130713642
#130673022
#130671762
#130664762
#130664452
C11×#19632
#930211