Finite Group Databasebeta

← #14739063

Subgroups — #14739063

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078084C211yesmaximal, characteristic, complemented
2C2×#10622688C211yesmaximal, characteristic, complemented
3#13077696C211yesmaximal, characteristic, complemented
4#13068057C214yesmaximal, complemented
5#13067973C214yesmaximal, complemented
6#13067391C211yesmaximal, characteristic, complemented
7#13067284C211yesmaximal, characteristic, complemented
8#13067265C211yesmaximal, characteristic, complemented
9C11×#3205C211yesmaximal, characteristic
10C11×#532C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×#67004—21no—
13C22×#4324—21no—
14C2×C4×Dic22C2211yescharacteristic
15C11×#493C2212yes—
16C11×#486C2212yes—
17C11×#459—22no—
18C11×#447—22no—
19C11×#431C2211yescharacteristic
20#10622845—21no—
21C2×#66896—21no—
22#10622703C2212yescomplemented
23#10622688—22no—
24#10622688C2214yes—
25#10622688C2212yescomplemented
26#10622667—22no—
27#10622538C2211yescharacteristic
28#10622537C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30#10622443—22no—
31#10622331—22no—
32C8×Dic22C2214yescomplemented
33#10622185C2212yescomplemented
34#10622182C2214yes—
35#10622182C2212yescomplemented
36#10622096C2214yescomplemented
37C2×C11×#41—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×Dic22D411yescharacteristic
42C2×C11×D8—24no—
43C11×C4⋊Q8C2311yescharacteristic
44C11×#127—21no—
45C11×#127—21no—
46C11×#127—21no—
47C11×#127C2311yescharacteristic
48C11×#127C2312yes—
49C11×#124—21no—
50C11×#121—21no—
51C11×#121—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C2×C42×C11C2311yescharacteristic
55#67004—44no—
56C2×#4326—22no—
57C2×#4324—24no—
58C2×#4324—22no—
59C2×#4324—44no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×Dic11⋊C4—21no—
62C2×C4×Dic11—21no—
63C2×#4318—21no—
64C22×C11⋊C8—21no—
65C4×Dic22—21no—
66C4×Dic22—21no—
67C4×Dic22D412yes—
68C4×Dic22C2312yes—
69C11×C4⋊C8D412yes—
70C11×#102—24no—
71C11×C22⋊C8D412yes—
72C4×C8×C11C2312yes—
73#66899—22no—
74#66896—24no—
75#66896—22no—
76C22⋊(C11⋊C8)—21no—
77Dic11⋊C8—24no—
78C8×Dic11—24no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)C2312yes—
82C4⋊(C11⋊C8)C2312yes—
83C4⋊(C11⋊C8)C2312yes—
84C4×C11⋊C8—21no—
85#19398—111nomaximal, Sylow
86C24×C11—41no—
87C11×#41—42no—
88C11×#41—42no—
89C2×Q8×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—22no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—42no—
101C2×D4×C11—42no—
102C2×D4×C11—82no—
103C2×D4×C11—82no—
104C22×C4×C11—41no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×Dic11—21no—
109C22×Dic11—21no—
110C2×Dic22—21no—
111C2×Dic22—22no—
112C2×Dic22D814yescomplemented
113C2×Dic22C2×D412yes—
114C11×D8—84no—
115C2×C8×C11C2×D414yes—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123C42×C11C2411yescharacteristic
124#4326—44no—
125#4324—48no—
126#4324—44no—
127C4⋊Dic11—21no—
128C4⋊Dic11C2×D412yes—
129Dic11⋊C4—22no—
130Dic11⋊C4—22no—
131C4×Dic11—22no—
132C4×Dic11—22no—
133#4318—42no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—42no—
138#3205D1111yescharacteristic
139#3037—111no—
140C2×#460—111no—
141#2982—111no—
142#1682—114no—
143#1668—114no—
144#1571—111no—
145#1545—111no—
146#1540—111no—
147C23×C11—41no—
148C23×C11—42no—
149C23×C11—82no—
150C23×C11—82no—
151C23×C11—82no—
152C23×C11#12111yescharacteristic
153Q8×C11—41no—
154Q8×C11—41no—
155D4×C11—42no—
156D4×C11—41no—
157D4×C11—42no—
158D4×C11—41no—
159D4×C11—42no—
160D4×C11—44no—
161D4×C11—81no—
162D4×C11—82no—
163D4×C11—82no—
164D4×C11—82no—
165D4×C11—82no—
166D4×C11—82no—
167C2×C4×C11—22no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—82no—
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11C2×D812yes—
175C2×C4×C11#13512yes—
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C2×Dic11—22no—
180C2×Dic11—24no—
181C2×Dic11—22no—
182C2×Dic11—81no—
183Dic22—22no—
184Dic22—24no—
185Dic22C2×D814yes—
186C8×C11—24no—
187C11⋊C8—42no—
188C11⋊C8—42no—
189C11⋊C8—42no—
190C2×#137—221no—
191C22×SD16—221no—
192#532C2×D1111yescharacteristic
193C2×#127C2×D1111yescharacteristic
194C2×C4×Q8—111no—
195#493C2×D1112yes—
196#486C2×D1112yes—
197#464—222no—
198#462—112no—
199#460—112no—
200#460—114no—
201#460—222no—
202#459—22no—
203#447—22no—
204C8×Q8—114no—
205C8×Q8—222no—
206#431—111no—
207#431—222no—
208#431C2×D1111yescharacteristic
209#423—111no—
210C2×C4⋊C8—111no—
211#417—221no—
212C2×#102—221no—
213#335—114no—
214#332—112no—
215#331—112no—
216#331—114no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—82no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11—81no—
225C22×C11—164no—
226C22×C11#46612yes—
227C22×C11C2×#12111yescharacteristic
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—81no—
232C4×C11#46612yes—
233C4×C11C22×D811yescharacteristic
234C4×C11C2×#13511yescharacteristic
235C4×C11#57712yes—
236Dic11—24no—
237Dic11—42no—
238C2×#41—21no—
239C22×Q8—111no—
240C22×D4—21no—
241C22×D4—21no—
242C22×D4—21no—
243#137—444no—
244C2×Q16—222no—
245C2×SD16—224no—
246C2×SD16—222no—
247C2×SD16—444no—
248C2×D8—24no—
249C2×M16—221no—
250C22×C8—221no—
251C4⋊Q8C22×D1111yescharacteristic
252#127—21no—
253#127—21no—
254#127—21no—
255#127C22×D1112yes—
256#127C22×D1111yescharacteristic
257#124—21no—
258#121—21no—
259#121—21no—
260C4×Q8—112no—
261C4×Q8—112no—
262C4×Q8—221no—
263C4×Q8—221no—
264C4×D4—21no—
265C4×D4—21no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—221no—
268C2×C42—221no—
269C2×C42C22×D1111yescharacteristic
270C4⋊C8—112no—
271C4⋊C8—112no—
272C4⋊C8—112no—
273C4⋊C8—224no—
274C4⋊C8—221no—
275C4⋊C8—221no—
276C4⋊C8C22⋊D1112yes—
277#103—222no—
278#102—24no—
279#102—224no—
280#102—222no—
281C22⋊C8—221no—
282C22⋊C8C22⋊D1112yes—
283C4×C8—224no—
284C4×C8—221no—
285C4×C8C22×D1112yes—
286C2×C11—22no—
287C2×C11—161no—
288C2×C11—162no—
289C2×C11#304311yescharacteristic
290C2×C11C2×#46611yescharacteristic
291C2×C11#306811yescharacteristic
292C24—41no—
293#41—42no—
294#41—42no—
295C2×Q8—21no—
296C2×Q8—114no—
297C2×Q8—112no—
298C2×Q8—222no—
299C2×Q8—221no—
300C2×D4—21no—
301C2×D4—22no—
302C2×D4—21no—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—42no—
308C2×D4—42no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—82no—
313C2×D4—82no—
314C22×C4—41no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4D4×D1111yescharacteristic
318C22×C4#434111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320Q16—444no—
321SD16—448no—
322SD16—444no—
323D8—84no—
324M16—442no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8—222no—
328C2×C8—442no—
329C2×C8C2×C22⋊D1114yes—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—112no—
333C4⋊C4—221no—
334C4⋊C4—222no—
335C4⋊C4—222no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C42—222no—
339C42—222no—
340C42D4×D1111yescharacteristic
341C42#434111yescharacteristic
342C42C2×C22⋊D1111yescharacteristic
343C42C23×D1111yescharacteristic
344C11#1939811yescharacteristic, complemented, Sylow
345C23—41no—
346C23—42no—
347C23—82no—
348C23—82no—
349C23—82no—
350C23#6699111yescharacteristic
351Q8—41no—
352Q8—41no—
353Q8—114no—
354Q8—224no—
355Q8—222no—
356D4—42no—
357D4—41no—
358D4—42no—
359D4—41no—
360D4—42no—
361D4—44no—
362D4—81no—
363D4—82no—
364D4—82no—
365D4—82no—
366D4—82no—
367D4—82no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—82no—
372C2×C4—224no—
373C2×C4—222no—
374C2×C4—222no—
375C2×C4—881no—
376C2×C4D8×D1112yes—
377C2×C4#6696512yes—
378C2×C4#6699111yescharacteristic
379C2×C4#6699111yescharacteristic
380C2×C4#6699111yescharacteristic
381C2×C4C2×D4×D1111yescharacteristic
382C2×C4C2×#434111yescharacteristic
383C2×C4C22×C22⋊D1111yescharacteristic
384C8—24no—
385C8—442no—
386C8—442no—
387C8—442no—
388C22—21no—
389C22—21no—
390C22—82no—
391C22—81no—
392C22—82no—
393C22—81no—
394C22—81no—
395C22—82no—
396C22—164no—
397C22#1062277012yes—
398C22C2×#6699111yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—81no—
403C4—224no—
404C4—442no—
405C4#1062277012yes—
406C4C2×D8×D1111yescharacteristic
407C4C2×#6696511yescharacteristic
408C4#1062336712yes—
409C2—22no—
410C2—162no—
411C2—161no—
412C2#1307813311yescharacteristic
413C2C2×#1062277011yescharacteristic
414C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3205C2
socleC22×C11C2×#121
hypercenter#3205D11
hypocenterC11#19398
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3205

Complements

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

NH ≅ G/Ntype
1. #13078084C2semidirect
2. C2×#10622688C2semidirect
3. #13077696C2semidirect
4. #13068057C2semidirect
5. #13067973C2semidirect
6. #13067391C2semidirect
7. #13067284C2semidirect
8. #13067265C2semidirect
22. #10622703C22semidirect
25. #10622688C22semidirect
32. C8×Dic22C22semidirect
33. #10622185C22semidirect
35. #10622182C22semidirect
36. #10622096C22semidirect
112. C2×Dic22D8semidirect
344. C11#19398semidirect

Maximal subgroups

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

subgroupindex
#130780842
C2×#106226882
#130776962
#130680572
#130679732
#130673912
#130672842
#130672652
C11×#32052
#1939811