Finite Group Databasebeta

← #14739143

Subgroups — #14739143

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079754C211yesmaximal, characteristic
2#13078738C211yesmaximal, characteristic
3#13078655C211yesmaximal, characteristic, complemented
4#13068060C212yesmaximal, complemented
5#13068032C212yesmaximal, complemented
6#13068020C212yesmaximal, complemented
7#13067998C212yesmaximal, complemented
8#13067396C211yesmaximal, characteristic, complemented
9#13067324C211yesmaximal, characteristic, complemented
10#13067276C211yesmaximal, characteristic
11C11×#2982C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13#10623008C2211yescharacteristic
14#10623001C2211yescharacteristic
15C8×Q8×C11—22no—
16C8×Q8×C11C2212yes—
17C8×Q8×C11C2212yes—
18C11×#431—22no—
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21#10622841—21no—
22#10622840—21no—
23#10622644C2212yes—
24C4×#4326—22no—
25#10622640C2212yes—
26#10622639—22no—
27#10622634C2212yes—
28#10622634C2212yes—
29#10622583—21no—
30#10622580—21no—
31#10622539C2211yescharacteristic
32#10622538C2211yescharacteristic
33#10622460—22no—
34#10622350—22no—
35#10622307C2211yescharacteristic
36#10622307C2211yescharacteristic
37#10622295C2211yescharacteristic
38#10622293C2211yescharacteristic
39#10622124C2212yes—
40#10622123C2212yes—
41#10622119C2212yes—
42#10622119C2212yes—
43#10622096C2212yes—
44#10622095C2212yes—
45C22×Q8×C11D411yescharacteristic
46C2×#4339—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11D412yes—
50C4×Q8×C11C2312yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55C2×#4326—22no—
56C2×#4325—22no—
57#66983—21no—
58#66983—21no—
59#66979—21no—
60#66977—21no—
61#66977—21no—
62#66928—21no—
63#66927C2311yescharacteristic
64C4×D44—21no—
65C4×D44—21no—
66#66923—21no—
67#66922C2311yescharacteristic
68#66922C2311yescharacteristic
69#66922C2311yescharacteristic
70C4×Dic22—21no—
71C4×Dic22—21no—
72C11×C4⋊C8—22no—
73C11×C4⋊C8—22no—
74C11×C4⋊C8D412yes—
75C11×C4⋊C8C2312yes—
76C11×C22⋊C8—21no—
77C11×C22⋊C8D412yes—
78C4×C8×C11—22no—
79C4×C8×C11—22no—
80C4×C8×C11—21no—
81C4×C8×C11C2311yescharacteristic
82C4×C8×C11C2311yescharacteristic
83#66899—22no—
84#66899—22no—
85C22⋊(C11⋊C8)—21no—
86C22⋊(C11⋊C8)—21no—
87#66885—22no—
88#66885—22no—
89#66882—22no—
90#66881—22no—
91#66874—22no—
92#66873—22no—
93#66871—22no—
94#66871—22no—
95C4⋊(C11⋊C8)C2312yes—
96C4⋊(C11⋊C8)C2312yes—
97#66867—21no—
98C4×C11⋊C8—21no—
99#19406—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—
109#4339—82no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×C4×D11—41no—
114C2×Dic22—21no—
115C2×Dic22—21no—
116C2×Dic22—21no—
117C2×C8×C11—22no—
118C2×C8×C11C2×D412yes—
119C2×C8×C11C2×D412yes—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4C2×D412yes—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129C42×C11C2411yescharacteristic
130C22⋊Dic11—41no—
131#4326—44no—
132#4325—44no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141Dic11⋊C4—41no—
142Dic11⋊C4—41no—
143C4×Dic11—41no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146#3228—111no—
147#3112—111no—
148#3104—111no—
149#2982D1111yescharacteristic, complemented
150#1682—112no—
151#1678—112no—
152#1676—112no—
153#1672—112no—
154#1572—111no—
155#1554—111no—
156#1543—111no—
157C23×C11#12111yescharacteristic
158C22×D11—41no—
159Q8×C11—24no—
160Q8×C11—22no—
161Q8×C11#13514yes—
162C2×C4×C11—24no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—81no—
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C22⋊D11—82no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179D44—42no—
180D44—42no—
181D44—81no—
182C4×D11—82no—
183Dic22—42no—
184Dic22—81no—
185Dic22—81no—
186C8×C11—22no—
187C8×C11—22no—
188C8×C11—42no—
189C11⋊C8—42no—
190C11⋊C8—42no—
191#533—111no—
192#532—111no—
193C2×C4×Q8C2×D1111yescharacteristic
194#500—111no—
195#498—111no—
196#486—111no—
197#486—111no—
198#484—221no—
199#482—222no—
200#480—221no—
201#478—222no—
202#477—112no—
203#477—112no—
204#462—112no—
205#460—112no—
206#451—221no—
207#448—221no—
208C8×Q8—22no—
209C8×Q8C2×D1112yes—
210C8×Q8C2×D1112yes—
211#440—222no—
212C4×Q16—222no—
213#432—111no—
214#431—22no—
215#431—111no—
216#431C2×D1111yescharacteristic
217#431C2×D1111yescharacteristic
218#335—112no—
219#334—112no—
220#333—112no—
221#333—112no—
222#332—112no—
223#331—112no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11C2×#12111yescharacteristic
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—81no—
231C4×C11—21no—
232C4×C11—24no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—42no—
237C4×C11C2×#13512yes—
238C4×C11#57812yes—
239Dic11—81no—
240Dic11—81no—
241Dic11—81no—
242C2×#41—221no—
243C22×Q8D4411yescharacteristic
244C2×Q16—222no—
245C2×SD16—222no—
246C4⋊Q8—111no—
247C4⋊Q8—111no—
248C4⋊Q8—111no—
249#127—111no—
250#125—221no—
251#124—221no—
252C22⋊Q8—221no—
253C22⋊Q8—221no—
254#121—221no—
255#121—221no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—221no—
259C4×Q8—221no—
260C4×Q8D4412yes—
261C4×Q8C22×D1112yes—
262C4×D4—221no—
263C4×D4—221no—
264#117—221no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4D4411yescharacteristic
267C2×C42—21no—
268C2×C42C22×D1111yescharacteristic
269#107—222no—
270#107—222no—
271#107—222no—
272#106—222no—
273C4⋊C8—22no—
274C4⋊C8—22no—
275C4⋊C8—112no—
276C4⋊C8—112no—
277C4⋊C8C22⋊D1112yes—
278C4⋊C8C22×D1112yes—
279#103—222no—
280#103—222no—
281#103—222no—
282#102—222no—
283#102—222no—
284#102—222no—
285C22⋊C8—21no—
286C22⋊C8—221no—
287C22⋊C8—221no—
288C22⋊C8C22⋊D1112yes—
289#97—221no—
290C4×C8—22no—
291C4×C8—22no—
292C4×C8—21no—
293C4×C8—221no—
294C4×C8C22×D1111yescharacteristic
295C4×C8C22×D1111yescharacteristic
296C2×C11—41no—
297C2×C11#304411yescharacteristic
298C2×C11#305011yescharacteristic
299C2×C11#306811yescharacteristic
300D11—161no—
301#41—882no—
302C2×Q8—24no—
303C2×Q8—21no—
304C2×Q8—221no—
305C2×Q8—221no—
306C2×Q8—221no—
307C2×Q8C2×D4412yes—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—221no—
311C2×D4—441no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—441no—
315C22×C4C2×D4411yescharacteristic
316C22×C4#433911yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318Q16—444no—
319SD16—444no—
320C2×C8—22no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8C2×C22⋊D1112yes—
324C2×C8C2×C22⋊D1112yes—
325C4⋊C4—22no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—221no—
329C4⋊C4—221no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—441no—
335C4⋊C4—441no—
336C4⋊C4C2×D4412yes—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C22⋊C4—441no—
340C42—22no—
341C42—22no—
342C42—441no—
343C42C2×D4411yescharacteristic
344C42#433911yescharacteristic
345C42C2×C22⋊D1111yescharacteristic
346C42C23×D1111yescharacteristic
347C11#1940611yescharacteristic, complemented, Sylow
348C23—441no—
349C23#6698311yescharacteristic
350Q8—24no—
351Q8—22no—
352Q8—442no—
353Q8—881no—
354Q8—881no—
355Q8#6695714yes—
356D4—442no—
357D4—442no—
358D4—881no—
359D4—882no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—882no—
371C2×C4#6698311yescharacteristic
372C2×C4#6698311yescharacteristic
373C2×C4#6698311yescharacteristic
374C2×C4C22×D4411yescharacteristic
375C2×C4C2×#433911yescharacteristic
376C2×C4C22×C22⋊D1111yescharacteristic
377C8—22no—
378C8—22no—
379C8—42no—
380C8—442no—
381C8—442no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—881no—
386C22—881no—
387C22—881no—
388C22C2×#6698311yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—24no—
393C4—21no—
394C4—42no—
395C4—881no—
396C4—881no—
397C4—881no—
398C4C2×#6695712yes—
399C4#1062336912yes—
400C2—41no—
401C2—1761no—
402C2#1307814611yescharacteristic
403C2#1307819711yescharacteristic
404C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2982C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#2982D11
hypocenterC11#19406
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
3. #13078655C2semidirect
4. #13068060C2semidirect
5. #13068032C2semidirect
6. #13068020C2semidirect
7. #13067998C2semidirect
8. #13067396C2semidirect
9. #13067324C2semidirect
11. C11×#2982C2semidirect
149. #2982D11semidirect
347. C11#19406semidirect

Maximal subgroups

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

subgroupindex
#130797542
#130787382
#130786552
#130680602
#130680322
#130680202
#130679982
#130673962
#130673242
#130672762
C11×#29822
#1940611