Finite Group Databasebeta

← #14739096

Subgroups — #14739096

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079551C211yesmaximal, characteristic
2#13078738C211yesmaximal, characteristic, complemented
3#13078647C211yesmaximal, characteristic, complemented
4#13068074C212yesmaximal, complemented
5#13068032C212yesmaximal, complemented
6#13067976C212yesmaximal, complemented
7#13067964C212yesmaximal, complemented
8#13067396C211yesmaximal, characteristic, complemented
9#13067319C211yesmaximal, characteristic, complemented
10#13067276C211yesmaximal, characteristic, complemented
11C11×#2982C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13#10623008C2211yescharacteristic
14#10623008C2211yescharacteristic
15C8×Q8×C11—22no—
16C8×Q8×C11C2212yes—
17C8×Q8×C11C2212yes—
18C11×#431—22no—
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21#10622840—21no—
22#10622840—21no—
23#10622640C2212yes—
24#10622640C2212yes—
25#10622639—22no—
26C4×#4325—22no—
27#10622634C2212yes—
28#10622633C2212yes—
29#10622581—21no—
30#10622580—21no—
31#10622539C2211yescharacteristic
32#10622538C2211yescharacteristic
33#10622457—22no—
34#10622347—22no—
35#10622308C2211yescharacteristic
36#10622307C2211yescharacteristic
37#10622306C2211yescharacteristic
38#10622294C2211yescharacteristic
39#10622123C2212yes—
40#10622123C2212yes—
41#10622120C2212yes—
42#10622119C2212yes—
43#10622096C2212yes—
44#10622095C2212yes—
45C22×Q8×C11D411yescharacteristic
46C2×#4339—21no—
47C2×#4339—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11D412yes—
51C4×Q8×C11C2312yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56C2×#4325—22no—
57C2×#4325—22no—
58#66983—21no—
59#66983—21no—
60#66983—21no—
61#66983—21no—
62C2×D88—22no—
63C2×#4314—22no—
64#66928—21no—
65#66928—21no—
66#66927C2311yescharacteristic
67#66927C2311yescharacteristic
68C4×D44—21no—
69C4×D44—21no—
70C4×D44—21no—
71C4×D44—21no—
72#66922C2311yescharacteristic
73#66922C2311yescharacteristic
74C11×C4⋊C8—22no—
75C11×C4⋊C8—22no—
76C11×C4⋊C8D412yes—
77C11×C4⋊C8C2312yes—
78C11×C22⋊C8—21no—
79C11×C22⋊C8D412yes—
80C4×C8×C11—22no—
81C4×C8×C11—22no—
82C4×C8×C11—21no—
83C4×C8×C11C2311yescharacteristic
84C4×C8×C11C2311yescharacteristic
85#66899—22no—
86#66899—22no—
87C22⋊(C11⋊C8)—21no—
88C22⋊(C11⋊C8)—21no—
89#66885—22no—
90#66880—22no—
91#66873—22no—
92#66873—22no—
93#66872—22no—
94#66871—22no—
95C4⋊(C11⋊C8)C2312yes—
96C4⋊(C11⋊C8)C2312yes—
97#66867—21no—
98C4×C11⋊C8—21no—
99#19401—111nomaximal, Sylow
100C2×Q8×C11—24no—
101C2×Q8×C11—21no—
102C2×Q8×C11C2×D412yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C2×C22⋊D11—41no—
109C2×C22⋊D11—41no—
110#4339—82no—
111#4339—82no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×C4×D11—41no—
119C2×C4×D11—41no—
120C2×Dic22—21no—
121C2×Dic22—21no—
122C2×C8×C11—22no—
123C2×C8×C11C2×D412yes—
124C2×C8×C11C2×D412yes—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4C2×D412yes—
129C42×C11—22no—
130C42×C11—22no—
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134C42×C11C2411yescharacteristic
135#4325—44no—
136#4325—44no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147D88—82no—
148#4314—82no—
149#3207—111no—
150#3112—111no—
151#3103—111no—
152#2982D1111yescharacteristic, complemented
153#1684—112no—
154#1678—112no—
155#1668—112no—
156#1666—112no—
157#1572—111no—
158#1553—111no—
159#1543—111no—
160C23×C11#12111yescharacteristic
161C22×D11—41no—
162C22×D11—41no—
163Q8×C11—24no—
164Q8×C11—22no—
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—81no—
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C22⋊D11—82no—
180C22⋊D11—82no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183D44—42no—
184D44—42no—
185D44—42no—
186D44—42no—
187D44—81no—
188D44—81no—
189C4×D11—82no—
190C4×D11—82no—
191Dic22—42no—
192Dic22—81no—
193C8×C11—22no—
194C8×C11—22no—
195C8×C11—42no—
196C11⋊C8—42no—
197C11⋊C8—42no—
198#532—111no—
199#532—111no—
200C2×C4×Q8C2×D1111yescharacteristic
201#493—111no—
202#492—111no—
203#487—111no—
204#486—111no—
205#481—221no—
206#480—221no—
207#477—112no—
208#475—112no—
209#463—222no—
210#460—112no—
211#460—112no—
212#449—222no—
213#448—221no—
214#448—221no—
215C8×Q8—22no—
216C8×Q8C2×D1112yes—
217C8×Q8C2×D1112yes—
218#440—222no—
219C4×SD16—222no—
220#432—111no—
221#431—22no—
222#431—111no—
223#431C2×D1111yescharacteristic
224#431C2×D1111yescharacteristic
225#335—112no—
226#334—112no—
227#333—112no—
228#332—112no—
229#331—112no—
230#331—112no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11C2×#12111yescharacteristic
235C2×D11—81no—
236C2×D11—81no—
237C2×D11—81no—
238C2×D11—81no—
239C2×D11—81no—
240C2×D11—81no—
241C4×C11—21no—
242C4×C11—24no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—42no—
247C4×C11C2×#13512yes—
248C4×C11#57712yes—
249Dic11—81no—
250Dic11—81no—
251C2×#41—221no—
252C2×#41—221no—
253C22×Q8D4411yescharacteristic
254C2×SD16—222no—
255C2×SD16—222no—
256C2×SD16—222no—
257C2×D8—222no—
258C4⋊Q8—111no—
259C4⋊Q8—111no—
260#127—111no—
261#127—111no—
262#124—221no—
263#124—221no—
264#121—221no—
265#121—221no—
266#121—221no—
267#121—221no—
268C4×Q8—21no—
269C4×Q8—21no—
270C4×Q8D4412yes—
271C4×Q8C22×D1112yes—
272C4×D4—221no—
273C4×D4—221no—
274C4×D4—221no—
275C4×D4—221no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4D4411yescharacteristic
278C2×C42—21no—
279C2×C42C22×D1111yescharacteristic
280#107—222no—
281#106—222no—
282C4⋊C8—22no—
283C4⋊C8—22no—
284C4⋊C8—112no—
285C4⋊C8—112no—
286C4⋊C8C22⋊D1112yes—
287C4⋊C8C22×D1112yes—
288#103—222no—
289#103—222no—
290#103—222no—
291#102—222no—
292#102—222no—
293#102—222no—
294C22⋊C8—21no—
295C22⋊C8—221no—
296C22⋊C8—221no—
297C22⋊C8C22⋊D1112yes—
298#97—221no—
299C4×C8—22no—
300C4×C8—22no—
301C4×C8—21no—
302C4×C8—221no—
303C4×C8C22×D1111yescharacteristic
304C4×C8C22×D1111yescharacteristic
305C2×C11—41no—
306C2×C11#304311yescharacteristic
307C2×C11#305011yescharacteristic
308C2×C11#306811yescharacteristic
309D11—161no—
310D11—161no—
311#41—882no—
312#41—882no—
313C2×Q8—24no—
314C2×Q8—21no—
315C2×Q8—221no—
316C2×Q8—221no—
317C2×Q8C2×D4412yes—
318C2×D4—221no—
319C2×D4—221no—
320C2×D4—221no—
321C2×D4—221no—
322C2×D4—221no—
323C2×D4—221no—
324C2×D4—441no—
325C2×D4—441no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—441no—
329C22×C4—441no—
330C22×C4C2×D4411yescharacteristic
331C22×C4#433911yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—444no—
334SD16—444no—
335SD16—882no—
336D8—882no—
337C2×C8—22no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8C2×C22⋊D1112yes—
341C2×C8C2×C22⋊D1112yes—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—22no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C4⋊C4C2×D4412yes—
350C22⋊C4—441no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C22⋊C4—441no—
354C42—22no—
355C42—22no—
356C42C2×D4411yescharacteristic
357C42#433911yescharacteristic
358C42C2×C22⋊D1111yescharacteristic
359C42C23×D1111yescharacteristic
360C11#1940111yescharacteristic, complemented, Sylow
361C23—441no—
362C23—441no—
363C23#6698311yescharacteristic
364Q8—24no—
365Q8—22no—
366Q8—442no—
367Q8—881no—
368Q8#6695714yes—
369D4—442no—
370D4—442no—
371D4—442no—
372D4—442no—
373D4—881no—
374D4—881no—
375D4—882no—
376D4—882no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—882no—
387C2×C4—882no—
388C2×C4#6698311yescharacteristic
389C2×C4#6698311yescharacteristic
390C2×C4#6698311yescharacteristic
391C2×C4C22×D4411yescharacteristic
392C2×C4C2×#433911yescharacteristic
393C2×C4C22×C22⋊D1111yescharacteristic
394C8—22no—
395C8—22no—
396C8—42no—
397C8—442no—
398C8—442no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—881no—
403C22—881no—
404C22—881no—
405C22—881no—
406C22—881no—
407C22—881no—
408C22C2×#6698311yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—24no—
413C4—21no—
414C4—42no—
415C4—881no—
416C4—881no—
417C4C2×#6695712yes—
418C4#1062336812yes—
419C2—41no—
420C2—1761no—
421C2—1761no—
422C2#1307813711yescharacteristic
423C2#1307819711yescharacteristic
424C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2982C2
socleC22×C11C2×#121
prime radical#13079551C2
hypercenter#2982D11
hypocenterC11#19401
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #13078738C2semidirect
3. #13078647C2semidirect
4. #13068074C2semidirect
5. #13068032C2semidirect
6. #13067976C2semidirect
7. #13067964C2semidirect
8. #13067396C2semidirect
9. #13067319C2semidirect
10. #13067276C2semidirect
11. C11×#2982C2semidirect
152. #2982D11semidirect
360. C11#19401semidirect

Maximal subgroups

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

subgroupindex
#130795512
#130787382
#130786472
#130680742
#130680322
#130679762
#130679642
#130673962
#130673192
#130672762
C11×#29822
#1940111