Finite Group Databasebeta

← #14719930

Subgroups — #14719930

Order 2816.

948 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623065C211yesmaximal, characteristic
2#13077644C212yesmaximal, complemented
3#13066978C214yesmaximal, complemented
4#13066961C214yesmaximal, complemented
5#13066959C212yesmaximal, complemented
6#13066950C211yesmaximal, characteristic, complemented
7C11×#1464C211yesmaximal, characteristic, complemented
8C2×C11×#117C2211yescharacteristic
9C2×#66983C411yescharacteristic
10C2×#66977C411yescharacteristic
11#10623065—24no—
12#10623065—24no—
13C2×#66951C412yes—
14C2×#66949C2212yes—
15C2×#66938C412yes—
16C2×#66936C2212yes—
17C2×#66928C411yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×#66922C411yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C11×#432C2212yes—
22#10622539C2212yes—
23#10622449—24no—
24#10622339C2214yes—
25D11×C22⋊C8C2214yes—
26#10622319—24no—
27C11×#324C2212yes—
28C11×#323C2212yes—
29#10622166C2212yes—
30#10622163C2212yes—
31#10622107C2218yes—
32C23×C4×C11C2×C411yescharacteristic
33C22×C22⋊D11C2×C412yes—
34C22×D44C2×C411yescharacteristic
35C22×C4×D11C2312yes—
36C22×Dic22C2×C411yescharacteristic
37C22×Dic22C2×C412yes—
38C11×#117—22no—
39C11×#117—22no—
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C4⋊C4C2311yescharacteristic
42C2×C11×C22⋊C4C2×C411yescharacteristic
43C2×C11×C22⋊C4C2311yescharacteristic
44C2×C42×C11C2×C411yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C2×C22⋊Dic11C2×C412yes—
47#66983—22no—
48#66983—22no—
49C2×(C2×D11)⋊C4C2×C412yes—
50C2×(C2×D11)⋊C4C2×C412yes—
51C2×(C2×D11)⋊C4C2×C412yes—
52C2×(C2×D11)⋊C4C2×C412yes—
53C2×C4⋊Dic11C2×C411yescharacteristic
54C2×C4⋊Dic11C2×C412yes—
55C2×C4⋊Dic11C2×C411yescharacteristic
56#66977—22no—
57#66977—22no—
58C2×Dic11⋊C4C2×C412yes—
59C2×Dic11⋊C4C2312yes—
60C2×C4×Dic11C2×C412yes—
61C2×#4313—24no—
62C2×C8×D11—24no—
63#66951—28no—
64#66949—24no—
65#66949—24no—
66#66938—28no—
67#66936—24no—
68#66936—24no—
69#66928—22no—
70#66928—22no—
71C4×D44D414yes—
72C4×D44D414yes—
73#66922—22no—
74#66922—22no—
75C4×Dic22—22no—
76C4×Dic22—22no—
77C11×C4⋊C8—22no—
78C11×C22⋊C8C2314yes—
79C11×#97—22no—
80C22⋊(C11⋊C8)C2314yes—
81(C2×D11)⋊C8—24no—
82(C2×D11)⋊C8—24no—
83C4⋊(C11⋊C8)—22no—
84#66867—22no—
85#17407—111nomaximal, Sylow
86C24×C11C22×C411yescharacteristic
87C23×D11C22×C412yes—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—42no—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2411yescharacteristic
97C2×C22⋊D11—24no—
98C2×C22⋊D11—82no—
99C22×Dic11C22×C412yes—
100C22×Dic11C22×C412yes—
101C22×Dic11C22×C412yes—
102C2×D44—42no—
103C2×D44C22⋊C412yes—
104C2×D44C22⋊C412yes—
105C2×C4×D11—82no—
106C2×C4×D11C2×D414yes—
107C2×C4×D11C2×D414yes—
108C2×Dic22—24no—
109C2×Dic22—21no—
110C2×Dic22—21no—
111C2×Dic22—42no—
112C2×Dic22—82no—
113C2×C8×C11—24no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C22⋊C4—22no—
117C11×C22⋊C4—22no—
118C42×C11—21no—
119C42×C11—21no—
120C42×C11C2×D412yes—
121C42×C11C2×D412yes—
122C22⋊Dic11—24no—
123(C2×D11)⋊C4—24no—
124(C2×D11)⋊C4—24no—
125(C2×D11)⋊C4—24no—
126(C2×D11)⋊C4C22⋊C418yes—
127C4⋊Dic11—24no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11C22⋊C412yes—
131C4⋊Dic11C22⋊C412yes—
132Dic11⋊C4—24no—
133Dic11⋊C4—22no—
134Dic11⋊C4—22no—
135C4×Dic11—24no—
136C2×C11⋊C8—24no—
137#4313—84no—
138C8×D11—84no—
139C2×#542—111no—
140#2973—112no—
141#1472—114no—
142#1468—114no—
143#1467—112no—
144#1464—111no—
145#1464D1111yescharacteristic, complemented
146C23×C11—21no—
147C23×C11—22no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11C23×C411yescharacteristic
151C22×D11—24no—
152C22×D11—42no—
153C22×D11—42no—
154C22×D11C2×C22⋊C414yes—
155C2×C4×C11—22no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11C2×C22⋊C412yes—
167C2×C4×C11C2×C22⋊C411yescharacteristic
168C2×C4×C11C2×C22⋊C411yescharacteristic
169C2×C4×C11C22×D412yes—
170C22⋊D11—84no—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—24no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11C2×C22⋊C414yes—
177D44—42no—
178D44—42no—
179C4×D11—44no—
180C4×D11—44no—
181Dic22—42no—
182Dic22—42no—
183Dic22—84no—
184C8×C11—44no—
185C11⋊C8—44no—
186#542—224no—
187#542—224no—
188C2×C4⋊Q8—111no—
189C2×#126—112no—
190C2×#124—112no—
191C2×#124—111no—
192C2×#123—112no—
193C2×C22⋊Q8—111no—
194C2×C22⋊Q8—112no—
195C2×#121—111no—
196C2×C4×Q8—111no—
197C2×C4×D4—111no—
198C2×#117C2×D1111yescharacteristic
199#435—224no—
200#435—224no—
201#432—112no—
202#432C2×D1112yes—
203#407—114no—
204C2×C22⋊C8—114no—
205#324—112no—
206#324—118no—
207#324C2×D1112yes—
208#323—112no—
209#323C2×D1112yes—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—82no—
216C22×C11C22×C22⋊C411yescharacteristic
217C22×C11#56812yes—
218C2×D11—24no—
219C2×D11—24no—
220C2×D11—24no—
221C2×D11—84no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—22no—
225C4×C11—22no—
226C4×C11—41no—
227C4×C11—41no—
228C4×C11—41no—
229Dic11—24no—
230Dic11—42no—
231Dic11—42no—
232C22×Q8—111no—
233C22×Q8—112no—
234C22×D4—112no—
235C22×D4—111no—
236C23×C4—112no—
237C23×C4C4×D1111yescharacteristic
238C2×M16—224no—
239C22×C8—224no—
240C4⋊Q8—222no—
241C4⋊Q8—222no—
242#126—228no—
243#124—222no—
244#124—222no—
245#124—228no—
246#123—224no—
247#123—224no—
248C22⋊Q8—224no—
249C22⋊Q8—224no—
250C22⋊Q8—222no—
251C22⋊Q8—222no—
252#121—222no—
253#121—222no—
254C4×Q8—222no—
255C4×Q8—222no—
256C4×D4—114no—
257C4×D4—114no—
258#117—22no—
259#117—22no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—112no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—112no—
265C2×C4⋊C4C4×D1111yescharacteristic
266C2×C4⋊C4C22×D1111yescharacteristic
267C2×C22⋊C4—112no—
268C2×C22⋊C4—112no—
269C2×C22⋊C4—112no—
270C2×C22⋊C4—112no—
271C2×C22⋊C4—112no—
272C2×C22⋊C4C4×D1111yescharacteristic
273C2×C22⋊C4C22×D1111yescharacteristic
274C2×C42—112no—
275C2×C42C4×D1111yescharacteristic
276C2×C42C22×D1111yescharacteristic
277C4⋊C8—22no—
278C4⋊C8—222no—
279C22⋊C8—114no—
280C22⋊C8—224no—
281C22⋊C8—224no—
282C22⋊C8C22×D1114yes—
283#97—22no—
284#97—222no—
285C2×C11—22no—
286C2×C11—81no—
287C2×C11#287911yescharacteristic
288C2×C11#288311yescharacteristic
289C2×C11#288911yescharacteristic
290D11—44no—
291C24—112no—
292C24C2×C4×D1111yescharacteristic
293C2×Q8—224no—
294C2×Q8—221no—
295C2×Q8—221no—
296C2×Q8—442no—
297C2×Q8—882no—
298C2×D4—112no—
299C2×D4—112no—
300C2×D4—224no—
301C2×D4—442no—
302C2×D4—882no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—42no—
306C22×C4—112no—
307C22×C4—114no—
308C22×C4—114no—
309C22×C4—112no—
310C22×C4—112no—
311C22×C4—882no—
312C22×C4C2×C4×D1111yescharacteristic
313C22×C4C2×C4×D1111yescharacteristic
314C22×C4C2×C4×D1111yescharacteristic
315C22×C4C2×C4×D1111yescharacteristic
316C22×C4C2×C4×D1111yescharacteristic
317C22×C4C23×D1111yescharacteristic
318M16—884no—
319C2×C8—24no—
320C2×C8—224no—
321C2×C8—884no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—112no—
325C4⋊C4—112no—
326C4⋊C4—224no—
327C4⋊C4—224no—
328C4⋊C4—221no—
329C4⋊C4—221no—
330C4⋊C4—222no—
331C4⋊C4—222no—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—118no—
335C22⋊C4—224no—
336C22⋊C4—224no—
337C22⋊C4—224no—
338C22⋊C4—224no—
339C42—21no—
340C42—21no—
341C42—224no—
342C42D4×D1112yes—
343C42D4×D1112yes—
344C11#1740711yescharacteristic, complemented, Sylow
345C23—21no—
346C23—22no—
347C23—41no—
348C23—41no—
349C23—114no—
350C23—224no—
351C23—442no—
352C23—442no—
353C23C22×C4×D1111yescharacteristic
354Q8—442no—
355Q8—442no—
356Q8—884no—
357D4—442no—
358D4—442no—
359D4—884no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—114no—
372C2×C4—222no—
373C2×C4—222no—
374C2×C4—224no—
375C2×C4—444no—
376C2×C4—444no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4C22⋊C4×D1111yescharacteristic
380C2×C4C22⋊C4×D1111yescharacteristic
381C2×C4C22⋊C4×D1112yes—
382C2×C4C2×D4×D1112yes—
383C8—44no—
384C8—444no—
385C22—21no—
386C22—21no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—82no—
391C22—224no—
392C22—224no—
393C22—224no—
394C22—884no—
395C22C2×C22⋊C4×D1111yescharacteristic
396C22#1062327612yes—
397C4—21no—
398C4—21no—
399C4—22no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—224no—
405C4—442no—
406C4—442no—
407C2—22no—
408C2—81no—
409C2—444no—
410C2#1307705911yescharacteristic
411C2#1307707511yescharacteristic
412C2#1307709711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1464C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenter#1464D11
hypocenterC11#17407
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #13077644C2semidirect
3. #13066978C2semidirect
4. #13066961C2semidirect
5. #13066959C2semidirect
6. #13066950C2semidirect
7. C11×#1464C2semidirect
145. #1464D11semidirect
344. C11#17407semidirect

Maximal subgroups

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

subgroupindex
C2×#106230652
#130776442
#130669782
#130669612
#130669592
#130669502
C11×#14642
#1740711