Finite Group Databasebeta

← #13082627

Subgroups — #13082627

Order 1408.

1010 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#519C211yesmaximal, characteristic, complemented
2#10623348C211yesmaximal, characteristic, complemented
3Q8×C22⋊D11C211yesmaximal, characteristic, complemented
4#10623115C213yesmaximal, complemented
5#10623113C213yesmaximal, complemented
6#10623109C213yesmaximal, complemented
7#10623107C211yesmaximal, characteristic, complemented
8C4×#4343C211yesmaximal, characteristic, complemented
9#10623103C211yesmaximal, characteristic, complemented
10#10623099C213yesmaximal, complemented
11Q8×Dic22C211yesmaximal, characteristic, complemented
12#10623065C213yesmaximal, complemented
13#10623064C213yesmaximal, complemented
14#10623063C213yesmaximal, complemented
15#10623059C213yesmaximal, complemented
16C22×Q8×C11C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×Q8×D11C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20C4×Q8×C11C2213yes—
21C4×Q8×C11C2211yescharacteristic
22C4×Q8×C11C2213yes—
23C11×#117C2213yes—
24C11×#117C2213yes—
25#67000C2213yes—
26#66999C2213yes—
27#66999C2213yes—
28Q8×Dic11C2211yescharacteristic
29Q8×Dic11C2211yescharacteristic
30#66997C2213yes—
31#66983C2213yes—
32C4×C22⋊D11C2213yes—
33C4×C22⋊D11C2213yes—
34#66977C2213yes—
35#66951C2213yes—
36#66951C2216yes—
37#66950C2213yes—
38#66949C2213yes—
39#66949C2216yes—
40#66948C2213yes—
41#66947C2213yes—
42#66946C2213yes—
43#66945C2213yes—
44#66945C2213yes—
45#66942C2213yes—
46#66941C2213yes—
47#66941C2213yes—
48#66940C2213yes—
49#66938C2211yescharacteristic
50#66938C2216yes—
51#66937C2213yes—
52#66936C2213yes—
53#66932C2213yes—
54#66929C2216yes—
55#66928C2216yes—
56#66928C2213yes—
57C4×D44C2213yes—
58C4×D44C2213yes—
59#66925C2213yes—
60#66925C2216yes—
61C42×D11C2213yes—
62#66922C2213yes—
63C4×Dic22C2213yes—
64C4×Dic22C2216yes—
65C4×Dic22C2213yes—
66C2×Q8×C11—24no—
67C2×Q8×C11C2313yes—
68C2×Q8×C11C2311yescharacteristic
69C22×C4×C11C2313yes—
70C2×C22⋊D11C2311yescharacteristic
71C2×C22⋊D11C2313yes—
72#4343—24no—
73Q8×D11—24no—
74C2×D44C2313yes—
75C2×D44C2313yes—
76C2×C4×D11C2313yes—
77C2×C4×D11C2313yes—
78C2×C4×D11C2313yes—
79C2×C4×D11C2313yes—
80C2×Dic22C2311yescharacteristic
81C2×Dic22C2313yes—
82C2×Dic22C2316yes—
83C11×C4⋊C4C2313yes—
84C11×C4⋊C4C2313yes—
85C11×C4⋊C4C2313yes—
86C11×C4⋊C4C2313yes—
87C11×C22⋊C4C2313yes—
88C11×C22⋊C4C2311yescharacteristic
89C42×C11C2313yes—
90C42×C11C2313yes—
91C42×C11C2316yes—
92C22⋊Dic11C2311yescharacteristic
93C22⋊Dic11C2313yes—
94(C2×D11)⋊C4C2311yescharacteristic
95(C2×D11)⋊C4C2313yes—
96(C2×D11)⋊C4C2316yes—
97(C2×D11)⋊C4C2316yes—
98(C2×D11)⋊C4C2311yescharacteristic
99(C2×D11)⋊C4C2313yes—
100(C2×D11)⋊C4C2316yes—
101(C2×D11)⋊C4C2313yes—
102(C2×D11)⋊C4C2313yes—
103C4⋊Dic11C2313yes—
104C4⋊Dic11C2313yes—
105C4⋊Dic11C2313yes—
106C4⋊Dic11C2313yes—
107Dic11⋊C4C2313yes—
108Dic11⋊C4C2313yes—
109Dic11⋊C4C2313yes—
110Dic11⋊C4C2313yes—
111Dic11⋊C4C2316yes—
112Dic11⋊C4C2313yes—
113Dic11⋊C4C2313yes—
114C4×Dic11C2313yes—
115C4×Dic11C2316yes—
116C4×Dic11C2313yes—
117C4×Dic11C2313yes—
118C4×Dic11C2311yescharacteristic
119#3518—111nomaximal, Sylow
120C23×C11C2411yescharacteristic
121C22×D11C2411yescharacteristic
122C22×D11C2413yes—
123Q8×C11—26no—
124Q8×C11#4114yes—
125C2×C4×C11—26no—
126C2×C4×C11C2413yes—
127C2×C4×C11C2411yescharacteristic
128C2×C4×C11C2413yes—
129C2×C4×C11C2413yes—
130C2×C4×C11C2411yescharacteristic
131C2×C4×C11C2413yes—
132C22⋊D11—22no—
133C22⋊D11—43no—
134C2×Dic11C2411yescharacteristic
135C2×Dic11C2411yescharacteristic
136C2×Dic11C2413yes—
137C2×Dic11C2413yes—
138C2×Dic11C2413yes—
139C2×Dic11C2411yescharacteristic
140D44—26no—
141D44—43no—
142C4×D11—26no—
143C4×D11—26no—
144C4×D11—26no—
145C4×D11—43no—
146Dic22—26no—
147Dic22—22no—
148Dic22—46no—
149Q82—111no—
150#556—113no—
151#556—113no—
152#556—113no—
153#555—113no—
154D4×Q8—111no—
155#548—111no—
156#548—111no—
157#542—113no—
158#542—113no—
159#533—113no—
160#529—113no—
161#519—111no—
162#519D1111yescharacteristic, complemented
163C4×#41—111no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11C2511yescharacteristic
168C2×D11—21no—
169C2×D11—23no—
170C2×D11—23no—
171C2×D11—21no—
172C2×D11—23no—
173C2×D11—21no—
174C4×C11—23no—
175C4×C11—21no—
176C4×C11—23no—
177C4×C11—23no—
178C4×C11—21no—
179C4×C11C2×#4116yes—
180Dic11—23no—
181Dic11—21no—
182Dic11—21no—
183Dic11—23no—
184Dic11—23no—
185Dic112−1+412yes—
186C2×#41—111no—
187C22×Q8—111no—
188C22×Q8C2×D1111yescharacteristic
189C4⋊Q8—113no—
190C4⋊Q8—113no—
191C4⋊Q8—113no—
192C4⋊Q8—113no—
193#126—113no—
194#126—116no—
195#126—113no—
196#126—116no—
197#125—113no—
198#124—113no—
199#124—111no—
200#124—116no—
201#124—113no—
202#124—116no—
203#123—113no—
204#123—113no—
205C22⋊Q8—113no—
206C22⋊Q8—113no—
207C22⋊Q8—113no—
208C22⋊Q8—113no—
209C22⋊Q8—116no—
210C22⋊Q8—113no—
211#121—113no—
212#121—113no—
213#121—113no—
214C4×Q8—111no—
215C4×Q8—111no—
216C4×Q8—113no—
217C4×Q8—113no—
218C4×Q8—113no—
219C4×Q8—116no—
220C4×Q8C2×D1111yescharacteristic
221C4×Q8C2×D1113yes—
222C4×Q8C2×D1111yescharacteristic
223C4×Q8C2×D1113yes—
224C4×D4—113no—
225C4×D4—113no—
226C4×D4—113no—
227C4×D4—113no—
228C4×D4—113no—
229#117—113no—
230#117—113no—
231#117—113no—
232#117—116no—
233#117C2×D1113yes—
234#117C2×D1113yes—
235C2×C42—113no—
236C2×C11—41no—
237C2×C11C22×#4111yescharacteristic
238C2×C11C2×2−1+411yescharacteristic
239C2×C11#58511yescharacteristic
240D11—41no—
241D11—43no—
242#41—224no—
243C2×Q8—24no—
244C2×Q8—111no—
245C2×Q8—113no—
246C2×Q8—116no—
247C2×Q8—224no—
248C2×Q8C22×D1113yes—
249C2×Q8C22×D1111yescharacteristic
250C2×D4—111no—
251C2×D4—113no—
252C2×D4—113no—
253C2×D4—113no—
254C22×C4—113no—
255C22×C4—113no—
256C22×C4—113no—
257C22×C4—113no—
258C22×C4C22×D1113yes—
259C4⋊C4—113no—
260C4⋊C4—113no—
261C4⋊C4—113no—
262C4⋊C4—113no—
263C4⋊C4—113no—
264C4⋊C4—113no—
265C4⋊C4—113no—
266C4⋊C4—113no—
267C4⋊C4—116no—
268C4⋊C4—113no—
269C4⋊C4—113no—
270C4⋊C4C22×D1113yes—
271C4⋊C4C22×D1113yes—
272C4⋊C4C22×D1113yes—
273C4⋊C4C22×D1113yes—
274C22⋊C4—111no—
275C22⋊C4—113no—
276C22⋊C4—113no—
277C22⋊C4—111no—
278C22⋊C4—116no—
279C22⋊C4—116no—
280C22⋊C4—116no—
281C22⋊C4—111no—
282C22⋊C4—113no—
283C22⋊C4—113no—
284C22⋊C4—113no—
285C22⋊C4C22×D1113yes—
286C22⋊C4C22×D1111yescharacteristic
287C42—111no—
288C42—113no—
289C42—113no—
290C42—116no—
291C42—113no—
292C42C22×D1113yes—
293C42C22×D1116yes—
294C42C22×D1113yes—
295C11#351811yescharacteristic, complemented, Sylow
296C23—111no—
297C23—113no—
298C23C23×D1111yescharacteristic
299Q8—26no—
300Q8—222no—
301Q8—226no—
302Q8—446no—
303Q8#433914yes—
304D4—222no—
305D4—226no—
306D4—443no—
307D4—443no—
308C2×C4—26no—
309C2×C4—111no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—113no—
313C2×C4—113no—
314C2×C4—113no—
315C2×C4—226no—
316C2×C4—226no—
317C2×C4—226no—
318C2×C4—443no—
319C2×C4C23×D1113yes—
320C2×C4C23×D1111yescharacteristic
321C2×C4C23×D1111yescharacteristic
322C2×C4C23×D1113yes—
323C2×C4C23×D1113yes—
324C2×C4C23×D1113yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—221no—
329C22—223no—
330C22—223no—
331C22—221no—
332C22—223no—
333C22—221no—
334C22C24×D1111yescharacteristic
335C4—23no—
336C4—23no—
337C4—21no—
338C4—21no—
339C4—23no—
340C4—112no—
341C4—221no—
342C4—223no—
343C4—221no—
344C4—223no—
345C4—223no—
346C4C2×#433916yes—
347C2—41no—
348C2—441no—
349C2—443no—
350C2C22×#433911yescharacteristic
351C2D11×2−1+411yescharacteristic
352C2#1062345711yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#519C2
hypercenter#519D11
hypocenterC11#3518
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #519

Complements

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

NH ≅ G/Ntype
1. C11×#519C2semidirect
2. #10623348C2semidirect
3. Q8×C22⋊D11C2semidirect
4. #10623115C2semidirect
5. #10623113C2semidirect
6. #10623109C2semidirect
7. #10623107C2semidirect
8. C4×#4343C2semidirect
9. #10623103C2semidirect
10. #10623099C2semidirect
11. Q8×Dic22C2semidirect
12. #10623065C2semidirect
13. #10623064C2semidirect
14. #10623063C2semidirect
15. #10623059C2semidirect
162. #519D11semidirect
295. C11#3518semidirect

Maximal subgroups

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

subgroupindex
C11×#5192
#106233482
Q8×C22⋊D112
#106231152
#106231132
#106231092
#106231072
C4×#43432
#106231032
#106230992
Q8×Dic222
#106230652
#106230642
#106230632
#106230592
#351811