Finite Group Databasebeta

← #14739088

Subgroups — #14739088

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079568C211yesmaximal, characteristic
2#13078647C211yesmaximal, characteristic
3#13077697C211yesmaximal, characteristic, complemented
4#13068062C212yesmaximal, complemented
5#13068048C212yesmaximal, complemented
6#13067984C212yesmaximal, complemented
7#13067966C212yesmaximal, complemented
8#13067397C211yesmaximal, characteristic, complemented
9#13067322C211yesmaximal, characteristic
10#13067281C211yesmaximal, characteristic, complemented
11C11×#3113C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#483—21no—
16C11×#475C2212yes—
17C11×#462C2212yes—
18C11×#451—21no—
19C11×#441—22no—
20C11×#432C2211yescharacteristic
21#10622840—21no—
22#10622706C2211yescharacteristic
23#10622705C2211yescharacteristic
24#10622701C2211yescharacteristic
25#10622698C2211yescharacteristic
26#10622660—22no—
27#10622641—22no—
28#10622640C2212yes—
29C4×#4325—22no—
30Q8×C11⋊C8—22no—
31Q8×C11⋊C8C2212yes—
32Q8×C11⋊C8C2212yes—
33#10622633C2212yes—
34#10622581—21no—
35#10622538—22no—
36#10622538C2211yescharacteristic
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622185C2212yes—
40#10622185C2212yes—
41#10622124C2212yes—
42#10622123C2212yes—
43#10622118C2212yes—
44#10622117C2212yes—
45C22×Q8×C11D411yescharacteristic
46C2×#4339—21no—
47C2×C11×Q16—22no—
48C11×C4⋊Q8C2311yescharacteristic
49C11×C4⋊Q8C2311yescharacteristic
50C11×#125—21no—
51C11×C22⋊Q8—21no—
52C11×C22⋊Q8—21no—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11D412yes—
58C4×Q8×C11C2312yes—
59C11×#117—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C2×#4326—22no—
65C2×#4325—22no—
66C2×#4325—22no—
67#66983—21no—
68#66983—21no—
69#66928—21no—
70#66927C2311yescharacteristic
71C4×D44—21no—
72C4×D44—21no—
73#66922C2311yescharacteristic
74C11×#106—22no—
75C11×C4⋊C8C2312yes—
76C11×#103—22no—
77C11×#103—22no—
78C11×C22⋊C8—21no—
79C11×#97—21no—
80#66899—22no—
81C22⋊(C11⋊C8)—21no—
82C22⋊(C11⋊C8)—21no—
83C22⋊(C11⋊C8)D412yes—
84#66874—22no—
85#66873—22no—
86#66873—22no—
87#66872—22no—
88C4⋊(C11⋊C8)—22no—
89C4⋊(C11⋊C8)—22no—
90C4⋊(C11⋊C8)D412yes—
91C4⋊(C11⋊C8)C2312yes—
92C4⋊(C11⋊C8)C2312yes—
93C4×C11⋊C8—21no—
94C4×C11⋊C8—21no—
95C4×C11⋊C8—22no—
96C4×C11⋊C8—22no—
97C4×C11⋊C8C2311yescharacteristic
98C4×C11⋊C8C2311yescharacteristic
99#19400—111nomaximal, Sylow
100C2×Q8×C11—24no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11C2×D412yes—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C2×C22⋊D11—41no—
111#4339—82no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×C4×D11—41no—
116C2×Dic22—21no—
117C11×Q16—44no—
118C2×C8×C11—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4C2×D412yes—
129C11×C22⋊C4—41no—
130C42×C11—22no—
131C42×C11—22no—
132C42×C11—41no—
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11#4111yescharacteristic
136C42×C11C2411yescharacteristic
137#4326—82no—
138#4325—44no—
139#4325—82no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8C2×D412yes—
147C2×C11⋊C8C2×D412yes—
148#3210—111no—
149#3113D1111yescharacteristic, complemented
150#3103—111no—
151#2982—111no—
152#1682—112no—
153#1680—112no—
154#1670—112no—
155#1666—112no—
156#1572—111no—
157#1553—111no—
158#1544—111no—
159C23×C11#12111yescharacteristic
160C22×D11—41no—
161Q8×C11—24no—
162Q8×C11—22no—
163Q8×C11—42no—
164Q8×C11—42no—
165Q8×C11#13514yes—
166C2×C4×C11—24no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—81no—
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C22⋊D11—82no—
182C2×Dic11—41no—
183D44—42no—
184D44—42no—
185D44—81no—
186C4×D11—82no—
187Dic22—42no—
188C8×C11—42no—
189C11⋊C8—22no—
190C11⋊C8—22no—
191C11⋊C8—42no—
192C11⋊C8—42no—
193#533C2×D1111yescharacteristic
194#532—111no—
195C2×C4×Q8C2×D1111yescharacteristic
196#494—111no—
197#492—111no—
198#487—111no—
199#486—111no—
200#483—21no—
201#481—221no—
202#475—112no—
203#475C2×D1112yes—
204#464—222no—
205#462C2×D1112yes—
206#460—112no—
207#452—222no—
208#451—21no—
209#448—221no—
210C8×Q8—112no—
211C8×Q8—112no—
212C8×Q8—222no—
213#441—22no—
214C4×SD16—222no—
215#432C2×D1111yescharacteristic
216#431—111no—
217#431—111no—
218#431—111no—
219#431—222no—
220#335—112no—
221#334—112no—
222#332—112no—
223#332—112no—
224#332—112no—
225#331—112no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11C2×#12111yescharacteristic
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—81no—
233C4×C11—21no—
234C4×C11—24no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—42no—
239C4×C11—81no—
240C4×C11—81no—
241C4×C11C2×#13512yes—
242C4×C11#57712yes—
243Dic11—81no—
244C2×#41—221no—
245C22×Q8C22⋊D1111yescharacteristic
246C2×Q16—22no—
247C2×Q16—222no—
248C2×SD16—222no—
249C2×SD16—222no—
250C4⋊Q8—111no—
251C4⋊Q8C22×D1111yescharacteristic
252C4⋊Q8C22×D1111yescharacteristic
253#127—111no—
254#125—21no—
255#124—221no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258#121—221no—
259#121—221no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×Q8—21no—
264C4×Q8C22⋊D1112yes—
265C4×Q8C22×D1112yes—
266C4×D4—221no—
267C4×D4—221no—
268#117—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4C22⋊D1111yescharacteristic
271C2×C42—21no—
272C2×C42C22×D1111yescharacteristic
273#106—22no—
274#106—222no—
275C4⋊C8—112no—
276C4⋊C8—112no—
277C4⋊C8—112no—
278C4⋊C8—222no—
279C4⋊C8—222no—
280C4⋊C8C22×D1112yes—
281#103—22no—
282#103—22no—
283#103—222no—
284#103—222no—
285#102—222no—
286#102—222no—
287C22⋊C8—21no—
288C22⋊C8—112no—
289C22⋊C8—221no—
290C22⋊C8—221no—
291#97—21no—
292C4×C8—111no—
293C4×C8—111no—
294C4×C8—222no—
295C4×C8—222no—
296C4×C8—221no—
297C4×C8—221no—
298C2×C11—41no—
299C2×C11#304311yescharacteristic
300C2×C11#305011yescharacteristic
301C2×C11#306911yescharacteristic
302D11—161no—
303#41—882no—
304C2×Q8—24no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—221no—
309C2×Q8C2×C22⋊D1112yes—
310C2×D4—221no—
311C2×D4—221no—
312C2×D4—221no—
313C2×D4—441no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—441no—
317C22×C4D4×D1111yescharacteristic
318C22×C4#434111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320Q16—44no—
321Q16—882no—
322SD16—444no—
323SD16—882no—
324C2×C8—22no—
325C2×C8—112no—
326C2×C8—112no—
327C2×C8—222no—
328C2×C8—222no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—221no—
339C4⋊C4—221no—
340C4⋊C4C2×C22⋊D1112yes—
341C22⋊C4—41no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C42—22no—
345C42—22no—
346C42—41no—
347C42D4×D1111yescharacteristic
348C42#434111yescharacteristic
349C42C2×C22⋊D1111yescharacteristic
350C42C23×D1111yescharacteristic
351C11#1940011yescharacteristic, complemented, Sylow
352C23—441no—
353C23#6699211yescharacteristic
354Q8—24no—
355Q8—22no—
356Q8—42no—
357Q8—42no—
358Q8—442no—
359Q8#6700314yes—
360D4—442no—
361D4—442no—
362D4—881no—
363D4—882no—
364C2×C4—24no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—81no—
373C2×C4—441no—
374C2×C4—882no—
375C2×C4#6699211yescharacteristic
376C2×C4#6699211yescharacteristic
377C2×C4#6699211yescharacteristic
378C2×C4C2×D4×D1111yescharacteristic
379C2×C4C2×#434111yescharacteristic
380C2×C4C22×C22⋊D1111yescharacteristic
381C8—42no—
382C8—222no—
383C8—222no—
384C8—442no—
385C8—442no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—881no—
390C22—881no—
391C22—881no—
392C22C2×#6699211yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—24no—
397C4—21no—
398C4—42no—
399C4—81no—
400C4—81no—
401C4—881no—
402C4#1062330912yes—
403C4C2×#6700312yes—
404C2—41no—
405C2—1761no—
406C2#1307813911yescharacteristic
407C2#1307819411yescharacteristic
408C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3113C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3113D11
hypocenterC11#19400
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

Complements

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

NH ≅ G/Ntype
3. #13077697C2semidirect
4. #13068062C2semidirect
5. #13068048C2semidirect
6. #13067984C2semidirect
7. #13067966C2semidirect
8. #13067397C2semidirect
10. #13067281C2semidirect
11. C11×#3113C2semidirect
149. #3113D11semidirect
351. C11#19400semidirect

Maximal subgroups

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

subgroupindex
#130795682
#130786472
#130776972
#130680622
#130680482
#130679842
#130679662
#130673972
#130673222
#130672812
C11×#31132
#1940011