Finite Group Databasebeta

← #14650511

Subgroups — #14650511

Order 2816.

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

normal subgroups only

This group has 492 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#13079538C211yesmaximal, characteristic
2#13071362C211yesmaximal, characteristic, complemented
3#13069449C211yesmaximal, characteristic
4#13067296C211yesmaximal, characteristic, complemented
5#13066474C211yesmaximal, characteristic, complemented
6#13066444C211yesmaximal, characteristic, complemented
7C11×#1517C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#382C2211yescharacteristic
12C2×#66901—21no—
13C2×#66901—21no—
14#10622706C412yescomplemented
15#10622689C412yescomplemented
16#10622653—22no—
17#10622632—22no—
18C4⋊C4×Dic11—21no—
19#10622586—21no—
20#10622545C2211yescharacteristic
21#10622538C2211yescharacteristic
22#10622537C2211yescharacteristic
23#10622266—22no—
24#10622259—22no—
25C11×#327—22no—
26#10622119—22no—
27C2×C11×#41—21no—
28C22×Dic22D412yes—
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×#127C2×C411yescharacteristic
31C11×#124—21no—
32C11×#121—21no—
33C11×#121—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×#4324—24no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×Dic11⋊C4—22no—
42C2×C4×Dic11—22no—
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C2×#4318—21no—
46#66922—21no—
47#66922—21no—
48#66922C2×C412yes—
49#66922D412yes—
50C11×C4⋊C8—21no—
51C11×C22⋊C8—21no—
52C4×C8×C11—21no—
53C11×#95—21no—
54C11×#95D412yes—
55#66901—42no—
56#66901—42no—
57C11⋊#95—22no—
58C11⋊#95—22no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C22⋊(C11⋊C8)—21no—
62#66874—24no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8C2×C412yes—
67#9301—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—22no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—21no—
83C22×Dic11—22no—
84C22×Dic11—21no—
85C2×Dic22—22no—
86C2×Dic22—82no—
87C2×Dic22C22⋊C414yes—
88C2×C8×C11—41no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11C22×C411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11#4111yescharacteristic
98C42×C11#4111yescharacteristic
99#4324—84no—
100C4⋊Dic11—22no—
101C4⋊Dic11—22no—
102C4⋊Dic11—22no—
103C4⋊Dic11—22no—
104Dic11⋊C4—82no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—82no—
109C4×Dic11SD1612yescomplemented
110#4318—41no—
111#4318—41no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—41no—
114#3206—111no—
115#2331—111no—
116#1963—111no—
117#1548—111no—
118#1517D1111yescharacteristic
119#1286—111no—
120#1274—111no—
121C23×C11—41no—
122C23×C11#12011yescharacteristic
123Q8×C11—41no—
124Q8×C11—41no—
125D4×C11—42no—
126D4×C11—41no—
127D4×C11—41no—
128D4×C11—81no—
129D4×C11—81no—
130D4×C11—81no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11C2×C22⋊C411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C2×C4×C11C2×SD1611yescharacteristic
146C2×C4×C11#13511yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C2×Dic11—24no—
150C2×Dic11—22no—
151C2×Dic11—41no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158Dic22—44no—
159Dic22—82no—
160C8×C11—81no—
161C11⋊C8—42no—
162C11⋊C8—81no—
163#532C2×D1111yescharacteristic
164C2×C4⋊Q8—111no—
165#492—112no—
166#487—112no—
167#461—222no—
168#448—222no—
169#431—111no—
170#431C2×D1111yescharacteristic
171#423—111no—
172C2×#104—221no—
173C2×#104—221no—
174#391—222no—
175#389—221no—
176#387—222no—
177#382C2×D1111yescharacteristic
178C4×C4⋊C4—221no—
179#376—111no—
180#333—222no—
181#327—22no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11#38611yescharacteristic
188C22×C11#44811yescharacteristic
189C22×C11#44911yescharacteristic
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—82no—
195C4×C11—81no—
196C4×C11C4×SD1611yescharacteristic
197C4×C11#44011yescharacteristic
198C4×C11#46011yescharacteristic
199C4×C11#46411yescharacteristic
200Dic11—42no—
201Dic11—44no—
202Dic11—81no—
203C2×#41—21no—
204C22×Q8—112no—
205C2×SD16—224no—
206C2×M16—221no—
207C4⋊Q8—112no—
208C4⋊Q8—112no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211C4⋊Q8C4×D1111yescharacteristic
212#127C4×D1111yescharacteristic
213#124—21no—
214#121—21no—
215#121—21no—
216C4×D4—21no—
217C4×D4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—222no—
222C2×C42—111no—
223C2×C42—111no—
224C2×C42—222no—
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—221no—
228C4⋊C8—221no—
229C4⋊C8—221no—
230#104—442no—
231#104—442no—
232#103—224no—
233C22⋊C8—21no—
234C22⋊C8—221no—
235C4×C8—21no—
236C4×C8—112no—
237#95—21no—
238#95—222no—
239#95—222no—
240#95—221no—
241#95—221no—
242#95C22⋊D1112yes—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11—161no—
246C2×C11#188011yescharacteristic
247C2×C11#190511yescharacteristic
248C2×C11#191111yescharacteristic
249#41—41no—
250#41—41no—
251#41—41no—
252#41—41no—
253C2×Q8—21no—
254C2×Q8—114no—
255C2×Q8—222no—
256C2×Q8—882no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4—221no—
264C22×C4—222no—
265C22×C4—221no—
266C22×C4D4×D1111yescharacteristic
267C22×C4D4×D1111yescharacteristic
268C22×C4C2×C22⋊D1111yescharacteristic
269SD16—884no—
270M16—441no—
271M16—441no—
272C2×C8—41no—
273C2×C8—222no—
274C2×C8—441no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—222no—
280C4⋊C4—222no—
281C4⋊C4—222no—
282C4⋊C4—222no—
283C4⋊C4—882no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C42—112no—
287C42—221no—
288C42—221no—
289C42—221no—
290C42—882no—
291C42C2×C4×D1111yescharacteristic
292C42#433911yescharacteristic
293C42D4×D1111yescharacteristic
294C42#434111yescharacteristic
295C11#930111yescharacteristic, complemented, Sylow
296C23—41no—
297C23#6699011yescharacteristic
298Q8—41no—
299Q8—41no—
300Q8—444no—
301Q8—882no—
302D4—42no—
303D4—41no—
304D4—41no—
305D4—81no—
306D4—81no—
307D4—81no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—222no—
317C2×C4—224no—
318C2×C4—441no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4C22⋊C4×D1111yescharacteristic
326C2×C4(C22⋊D11)⋊C411yescharacteristic
327C2×C4#6693611yescharacteristic
328C2×C4#6693711yescharacteristic
329C2×C4#6696411yescharacteristic
330C2×C4#6696511yescharacteristic
331C2×C4SD16×D1111yescharacteristic
332C2×C4#6696811yescharacteristic
333C2×C4C4×C22⋊D1111yescharacteristic
334C2×C4#6699111yescharacteristic
335C8—81no—
336C8—442no—
337C8—881no—
338C22—21no—
339C22—21no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22#1062256911yescharacteristic
344C22#1062277111yescharacteristic
345C22#1062278311yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—82no—
351C4—81no—
352C4—442no—
353C4—444no—
354C4—881no—
355C4#1062237011yescharacteristic
356C4#1062237111yescharacteristic
357C4#1062237511yescharacteristic
358C4#1062238011yescharacteristic
359C2—21no—
360C2—21no—
361C2—161no—
362C2#1306896811yescharacteristic
363C2#1306911311yescharacteristic
364C2#1306914511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1517C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1517D11
hypocenterC11#9301
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #13071362C2semidirect
4. #13067296C2semidirect
5. #13066474C2semidirect
6. #13066444C2semidirect
14. #10622706C4semidirect
15. #10622689C4semidirect
109. C4×Dic11SD16semidirect
295. C11#9301semidirect

Maximal subgroups

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

subgroupindex
#130795382
#130713622
#130694492
#130672962
#130664742
#130664442
C11×#15172
#930111