Finite Group Databasebeta

← #14739099

Subgroups — #14739099

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#13079545C211yesmaximal, characteristic
2#13078647C211yesmaximal, characteristic, complemented
3#13077697C211yesmaximal, characteristic, complemented
4#13068076C212yesmaximal, complemented
5#13068034C212yesmaximal, complemented
6#13067974C212yesmaximal, complemented
7#13067962C212yesmaximal, complemented
8#13067397C211yesmaximal, characteristic, complemented
9#13067322C211yesmaximal, characteristic, complemented
10#13067278C211yesmaximal, characteristic, complemented
11C11×#3112C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#480—21no—
16C11×#477C2212yes—
17C11×#460C2212yes—
18C11×#448—21no—
19C11×#440—22no—
20C11×#432C2211yescharacteristic
21#10622840—21no—
22#10622706C2211yescharacteristic
23#10622701C2211yescharacteristic
24#10622689C2211yescharacteristic
25#10622686C2211yescharacteristic
26#10622650—22no—
27#10622640C2212yes—
28C4×#4325—22no—
29Q8×C11⋊C8—22no—
30Q8×C11⋊C8C2212yes—
31Q8×C11⋊C8C2212yes—
32#10622633C2212yes—
33#10622629—22no—
34#10622581—21no—
35#10622538—22no—
36#10622538C2211yescharacteristic
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622184C2212yes—
40#10622182C2212yes—
41#10622124C2212yes—
42#10622123C2212yes—
43#10622118C2212yes—
44#10622117C2212yes—
45C2×C11×#41—21no—
46C22×Q8×C11D411yescharacteristic
47C2×#4339—21no—
48C2×C11×SD16—22no—
49C11×C4⋊Q8C2311yescharacteristic
50C11×#127C2311yescharacteristic
51C11×#124—21no—
52C11×#121—21no—
53C11×#121—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11D412yes—
57C4×Q8×C11C2312yes—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C2×#4325—22no—
65C2×#4324—22no—
66C2×#4323—22no—
67#66983—21no—
68#66983—21no—
69#66928—21no—
70#66927C2311yescharacteristic
71C4×D44—21no—
72C4×D44—21no—
73#66922C2311yescharacteristic
74C11×#107—22no—
75C11×C4⋊C8C2312yes—
76C11×#103—22no—
77C11×#102—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#19401—111nomaximal, Sylow
100C11×#41—82no—
101C2×Q8×C11—24no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11C2×D412yes—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—41no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—41no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C2×C22⋊D11—41no—
116#4339—82no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×C4×D11—41no—
121C2×Dic22—21no—
122C11×SD16—44no—
123C2×C8×C11—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4C2×D412yes—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C42×C11—22no—
133C42×C11—22no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138#4325—44no—
139#4324—82no—
140#4323—82no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8C2×D412yes—
148C2×C11⋊C8C2×D412yes—
149#3207—111no—
150#3112D1111yescharacteristic, complemented
151#3103—111no—
152#2982—111no—
153#1684—112no—
154#1678—112no—
155#1668—112no—
156#1666—112no—
157#1572—111no—
158#1553—111no—
159#1543—111no—
160C23×C11—41no—
161C23×C11#12111yescharacteristic
162C22×D11—41no—
163Q8×C11—24no—
164Q8×C11—22no—
165Q8×C11—81no—
166Q8×C11#13514yes—
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—81no—
170D4×C11—82no—
171C2×C4×C11—24no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—82no—
179C2×C4×C11—81no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C22⋊D11—82no—
187C2×Dic11—41no—
188D44—42no—
189D44—42no—
190D44—81no—
191C4×D11—82no—
192Dic22—42no—
193C8×C11—42no—
194C11⋊C8—22no—
195C11⋊C8—22no—
196C11⋊C8—42no—
197C11⋊C8—42no—
198#532—111no—
199#532C2×D1111yescharacteristic
200C2×C4×Q8C2×D1111yescharacteristic
201#493—111no—
202#492—111no—
203#487—111no—
204#486—111no—
205#481—221no—
206#480—21no—
207#477C2×D1112yes—
208#475—112no—
209#463—222no—
210#460—112no—
211#460C2×D1112yes—
212#449—222no—
213#448—21no—
214#448—221no—
215C8×Q8—112no—
216C8×Q8—112no—
217C8×Q8—222no—
218#440—22no—
219C4×SD16—222no—
220#432C2×D1111yescharacteristic
221#431—111no—
222#431—111no—
223#431—111no—
224#431—222no—
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×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11C2×#12111yescharacteristic
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×C11—81no—
248C4×C11C2×#13512yes—
249C4×C11#57712yes—
250Dic11—81no—
251C2×#41—21no—
252C2×#41—221no—
253C22×Q8C22⋊D1111yescharacteristic
254C2×SD16—22no—
255C2×SD16—222no—
256C2×SD16—222no—
257C2×D8—222no—
258C4⋊Q8—111no—
259C4⋊Q8C22×D1111yescharacteristic
260#127—111no—
261#127C22×D1111yescharacteristic
262#124—21no—
263#124—221no—
264#121—21no—
265#121—21no—
266#121—221no—
267#121—221no—
268C4×Q8—21no—
269C4×Q8—21no—
270C4×Q8C22⋊D1112yes—
271C4×Q8C22×D1112yes—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4—221no—
275C4×D4—221no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4C22⋊D1111yescharacteristic
278C2×C42—21no—
279C2×C42C22×D1111yescharacteristic
280#107—22no—
281#106—222no—
282C4⋊C8—112no—
283C4⋊C8—112no—
284C4⋊C8—112no—
285C4⋊C8—222no—
286C4⋊C8—222no—
287C4⋊C8C22×D1112yes—
288#103—22no—
289#103—222no—
290#103—222no—
291#102—22no—
292#102—222no—
293#102—222no—
294C22⋊C8—21no—
295C22⋊C8—112no—
296C22⋊C8—221no—
297C22⋊C8—221no—
298#97—21no—
299C4×C8—111no—
300C4×C8—111no—
301C4×C8—222no—
302C4×C8—222no—
303C4×C8—221no—
304C4×C8—221no—
305C2×C11—41no—
306C2×C11—161no—
307C2×C11#304311yescharacteristic
308C2×C11#305011yescharacteristic
309C2×C11#306811yescharacteristic
310D11—161no—
311#41—82no—
312#41—882no—
313C2×Q8—24no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—221no—
317C2×Q8C2×C22⋊D1112yes—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—41no—
322C2×D4—221no—
323C2×D4—221no—
324C2×D4—221no—
325C2×D4—441no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—441no—
330C22×C4D4×D1111yescharacteristic
331C22×C4#434111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—44no—
334SD16—444no—
335SD16—882no—
336D8—882no—
337C2×C8—22no—
338C2×C8—112no—
339C2×C8—112no—
340C2×C8—222no—
341C2×C8—222no—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—22no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C4⋊C4C2×C22⋊D1112yes—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—441no—
353C22⋊C4—441no—
354C42—22no—
355C42—22no—
356C42D4×D1111yescharacteristic
357C42#434111yescharacteristic
358C42C2×C22⋊D1111yescharacteristic
359C42C23×D1111yescharacteristic
360C11#1940111yescharacteristic, complemented, Sylow
361C23—41no—
362C23—441no—
363C23#6699211yescharacteristic
364Q8—24no—
365Q8—22no—
366Q8—81no—
367Q8—442no—
368Q8#6700314yes—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—82no—
373D4—442no—
374D4—442no—
375D4—881no—
376D4—882no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—82no—
385C2×C4—81no—
386C2×C4—441no—
387C2×C4—882no—
388C2×C4#6699211yescharacteristic
389C2×C4#6699211yescharacteristic
390C2×C4#6699211yescharacteristic
391C2×C4C2×D4×D1111yescharacteristic
392C2×C4C2×#434111yescharacteristic
393C2×C4C22×C22⋊D1111yescharacteristic
394C8—42no—
395C8—222no—
396C8—222no—
397C8—442no—
398C8—442no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—881no—
406C22—881no—
407C22—881no—
408C22C2×#6699211yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—24no—
413C4—21no—
414C4—42no—
415C4—81no—
416C4—881no—
417C4#1062330912yes—
418C4C2×#6700312yes—
419C2—41no—
420C2—161no—
421C2—1761no—
422C2#1307813911yescharacteristic
423C2#1307819411yescharacteristic
424C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3112C2
socleC22×C11C2×#121
prime radical#13079545C2
hypercenter#3112D11
hypocenterC11#19401
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3112

Complements

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

NH ≅ G/Ntype
2. #13078647C2semidirect
3. #13077697C2semidirect
4. #13068076C2semidirect
5. #13068034C2semidirect
6. #13067974C2semidirect
7. #13067962C2semidirect
8. #13067397C2semidirect
9. #13067322C2semidirect
10. #13067278C2semidirect
11. C11×#3112C2semidirect
150. #3112D11semidirect
360. C11#19401semidirect

Maximal subgroups

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

subgroupindex
#130795452
#130786472
#130776972
#130680762
#130680342
#130679742
#130679622
#130673972
#130673222
#130672782
C11×#31122
#1940111