Finite Group Databasebeta

← #14736972

Subgroups — #14736972

Order 2816.

710 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
1#13079762C211yesmaximal, characteristic, complemented
2#13079559C211yesmaximal, characteristic
3C2×#10622306C211yesmaximal, characteristic
4#13077550C211yesmaximal, characteristic, complemented
5#13068089C214yesmaximal, complemented
6#13067965C214yesmaximal, complemented
7#13067287C211yesmaximal, characteristic, complemented
8#13067283C211yesmaximal, characteristic
9C11×#1564C211yesmaximal, characteristic, complemented
10C22×#4314—21no—
11C22×#4314—21no—
12C2×#66927C2211yescharacteristic
13#10623001C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C11×#431C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18#10622715—21no—
19#10622714—21no—
20#10622537C2211yescharacteristic
21#10622464C2214yescomplemented
22#10622461C2214yes—
23#10622344—22no—
24#10622334—22no—
25#10622307—21no—
26#10622306—21no—
27#10622306—21no—
28#10622306—21no—
29#10622306C2212yes—
30#10622306C2212yes—
31#10622294—21no—
32#10622293—21no—
33#10622292—21no—
34#10622292C2212yescomplemented
35C8×Dic22—21no—
36C8×Dic22C2212yescomplemented
37C11×#335C2212yescomplemented
38C11×#334C2212yescomplemented
39#10622124C2214yescomplemented
40#10622123C2214yes—
41C22×D44—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×Dic22—21no—
45C22×C8×C11D411yescharacteristic
46C22×C8×C11D411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48#66979—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51#66977—21no—
52#66977D412yes—
53C2×#4318—21no—
54C2×#4314—22no—
55C2×#4314—22no—
56C2×#4314—22no—
57C2×#4314—22no—
58C2×#4314—24no—
59C2×#4314—44no—
60C2×#4314—44no—
61#66927—21no—
62#66927—21no—
63#66927—21no—
64#66927C2312yes—
65#66923—21no—
66#66922—21no—
67#66922—21no—
68#66922—21no—
69#66922D411yescharacteristic
70#66922D411yescharacteristic
71#66922C2312yes—
72C4×Dic22—21no—
73C4×Dic22C2312yes—
74C11×C4⋊C8C2312yes—
75C11×C4⋊C8C2312yes—
76C11×C22⋊C8—21no—
77C11×C22⋊C8—21no—
78C4×C8×C11—21no—
79C4×C8×C11—21no—
80C4×C8×C11D411yescharacteristic
81C4×C8×C11D411yescharacteristic
82C4×C8×C11C2311yescharacteristic
83C4×C8×C11C2311yescharacteristic
84#66885—24no—
85#66881—24no—
86#66880—24no—
87#66879—22no—
88Dic11⋊C8—22no—
89Dic11⋊C8—22no—
90C8×Dic11—22no—
91C4⋊(C11⋊C8)—21no—
92C4⋊(C11⋊C8)C2312yes—
93#19202—111nomaximal, Sylow
94C23×D11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×Dic11—41no—
99C2×D44—22no—
100C2×D44—22no—
101C2×D44—22no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—42no—
106C2×D44—42no—
107C2×D44—82no—
108C2×D44—82no—
109C2×Dic22—21no—
110C2×Dic22—22no—
111C2×Dic22—41no—
112C2×Dic22—42no—
113C2×Dic22—42no—
114C2×Dic22C2×D412yes—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11SD1614yescomplemented
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126C42×C11C2411yescharacteristic
127C22⋊Dic11—22no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11—41no—
134C4⋊Dic11—41no—
135C4⋊Dic11C2×D412yes—
136Dic11⋊C4—22no—
137Dic11⋊C4—22no—
138C4×Dic11—22no—
139#4318—42no—
140C2×C11⋊C8—22no—
141#4314—44no—
142#4314—44no—
143#4314—44no—
144#4314—44no—
145#4314—84no—
146#3229—111no—
147#3208—111no—
148C2×#492—111no—
149#2960—111no—
150#1686—114no—
151#1666—114no—
152#1564D1111yescharacteristic, complemented
153#1546—111no—
154#1545—111no—
155C23×C11#12111yescharacteristic
156C22×D11—42no—
157C22×D11—82no—
158C22×D11—82no—
159C22×D11—82no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11C2×SD1612yes—
166C2×C4×C11AGL(1,ℤ/8)12yes—
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—42no—
173C2×Dic11—82no—
174D44—42no—
175D44—42no—
176D44—44no—
177D44—82no—
178D44—82no—
179D44—82no—
180D44—82no—
181Dic22—24no—
182Dic22—42no—
183Dic22—42no—
184Dic22—42no—
185Dic22—82no—
186C8×C11—21no—
187C8×C11—21no—
188C8×C11—42no—
189C8×C11—42no—
190C8×C11C2×SD1612yes—
191C8×C11C2×SD1612yes—
192C11⋊C8—42no—
193C22×SD16—221no—
194C22×SD16—221no—
195#533—111no—
196C2×C4⋊Q8—111no—
197C2×#127—111no—
198#498—221no—
199#492—112no—
200#492—112no—
201#492—221no—
202#492—221no—
203#492—221no—
204#487—221no—
205#486—221no—
206#483—222no—
207#475—114no—
208#460—114no—
209#450—222no—
210#446—112no—
211#446—221no—
212C8×Q8—112no—
213C8×Q8—221no—
214#431C2×D1111yescharacteristic
215#431C2×D1111yescharacteristic
216#424—221no—
217#423—111no—
218#405—221no—
219C2×C4×C8C2×D1111yescharacteristic
220#335C2×D1112yescomplemented
221#334C2×D1112yescomplemented
222#332—114no—
223#331—114no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11#46012yes—
227C22×C11C2×#12111yescharacteristic
228C2×D11—82no—
229C2×D11—82no—
230C2×D11—82no—
231C2×D11—164no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11#46012yes—
235C4×C11#47112yes—
236C4×C11C22×SD1611yescharacteristic
237C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
238C4×C11#57712yes—
239Dic11—42no—
240Dic11—42no—
241Dic11—82no—
242C22×Q8—221no—
243C22×D4—221no—
244C22×D4—221no—
245C22×D4—221no—
246C2×SD16—224no—
247C2×SD16—222no—
248C2×SD16—222no—
249C2×SD16—222no—
250C2×SD16—222no—
251C2×SD16—444no—
252C2×SD16—444no—
253C2×M16—221no—
254C22×C8D4411yescharacteristic
255C22×C8D4411yescharacteristic
256C4⋊Q8—111no—
257C4⋊Q8—111no—
258C4⋊Q8—112no—
259C4⋊Q8—221no—
260C4⋊Q8—221no—
261C4⋊Q8—221no—
262#127—112no—
263#127—221no—
264#127—221no—
265#127—221no—
266#125—221no—
267C22⋊Q8—112no—
268C22⋊Q8—221no—
269C4×Q8—112no—
270C4×Q8—221no—
271#117—221no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C42C22×D1111yescharacteristic
275#106—224no—
276C4⋊C8—112no—
277C4⋊C8—222no—
278C4⋊C8—222no—
279C4⋊C8—221no—
280C4⋊C8C22×D1112yes—
281C4⋊C8C22×D1112yes—
282#103—224no—
283#102—224no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286#97—222no—
287C4×C8—21no—
288C4×C8—21no—
289C4×C8—222no—
290C4×C8D4411yescharacteristic
291C4×C8D4411yescharacteristic
292C4×C8C22×D1111yescharacteristic
293C4×C8C22×D1111yescharacteristic
294C2×C11—22no—
295C2×C11C2×#46011yescharacteristic
296C2×C11#305711yescharacteristic
297C2×C11C2×#47111yescharacteristic
298D11—162no—
299C24—441no—
300C2×Q8—112no—
301C2×Q8—221no—
302C2×Q8—222no—
303C2×Q8—441no—
304C2×Q8—442no—
305C2×Q8—442no—
306C2×D4—222no—
307C2×D4—222no—
308C2×D4—222no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—442no—
313C2×D4—442no—
314C2×D4—882no—
315C2×D4—882no—
316C22×C4—441no—
317C22×C4C2×D4411yescharacteristic
318C22×C4D4×D1111yescharacteristic
319C22×C4#434311yescharacteristic
320SD16—444no—
321SD16—444no—
322SD16—444no—
323SD16—444no—
324SD16—884no—
325M16—442no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—222no—
330C2×C8#431414yescomplemented
331C2×C8C2×D4411yescharacteristic
332C2×C8C2×D4411yescharacteristic
333C2×C8C2×D4411yescharacteristic
334C2×C8C2×D4411yescharacteristic
335C4⋊C4—112no—
336C4⋊C4—221no—
337C4⋊C4—221no—
338C4⋊C4—222no—
339C4⋊C4—221no—
340C4⋊C4—222no—
341C4⋊C4—222no—
342C4⋊C4—222no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C22⋊C4—222no—
346C42—222no—
347C42C2×D4411yescharacteristic
348C42D4×D1111yescharacteristic
349C42#434311yescharacteristic
350C42C23×D1111yescharacteristic
351C11#1920211yescharacteristic, complemented, Sylow
352C23—442no—
353C23—882no—
354C23—882no—
355C23—882no—
356C23#6694811yescharacteristic
357Q8—224no—
358Q8—442no—
359Q8—442no—
360Q8—442no—
361Q8—882no—
362D4—442no—
363D4—442no—
364D4—444no—
365D4—882no—
366D4—882no—
367D4—882no—
368D4—882no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4—442no—
374C2×C4—882no—
375C2×C4#6694811yescharacteristic
376C2×C4#6694811yescharacteristic
377C2×C4#6694811yescharacteristic
378C2×C4C2×#431412yes—
379C2×C4#6696112yes—
380C2×C4C22×D4411yescharacteristic
381C2×C4C2×D4×D1111yescharacteristic
382C2×C4C2×#434311yescharacteristic
383C8—21no—
384C8—21no—
385C8—42no—
386C8—42no—
387C8—442no—
388C8C2×#431412yes—
389C8C2×#431412yes—
390C22—21no—
391C22—21no—
392C22—882no—
393C22—882no—
394C22—882no—
395C22—1764no—
396C22#1062246112yes—
397C22C2×#6694811yescharacteristic
398C4—21no—
399C4—21no—
400C4—442no—
401C4—442no—
402C4—882no—
403C4#1062246112yes—
404C4#1062251112yes—
405C4C22×#431411yescharacteristic
406C4C2×#6696111yescharacteristic
407C4#1062330112yes—
408C2—22no—
409C2—1762no—
410C2C2×#1062246111yescharacteristic
411C2#1307825611yescharacteristic
412C2C2×#1062251111yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1564C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#1564D11
hypocenterC11#19202
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
1. #13079762C2semidirect
4. #13077550C2semidirect
5. #13068089C2semidirect
6. #13067965C2semidirect
7. #13067287C2semidirect
9. C11×#1564C2semidirect
21. #10622464C22semidirect
34. #10622292C22semidirect
36. C8×Dic22C22semidirect
37. C11×#335C22semidirect
38. C11×#334C22semidirect
39. #10622124C22semidirect
118. C2×C8×C11SD16semidirect
152. #1564D11semidirect
220. #335C2×D11semidirect
221. #334C2×D11semidirect
330. C2×C8#4314semidirect
351. C11#19202semidirect

Maximal subgroups

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

subgroupindex
#130797622
#130795592
C2×#106223062
#130775502
#130680892
#130679652
#130672872
#130672832
C11×#15642
#1920211