Finite Group Databasebeta

← #14736971

Subgroups — #14736971

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#13079757C211yesmaximal, characteristic, complemented
2#13079554C211yesmaximal, characteristic
3C2×#10622306C211yesmaximal, characteristic
4#13068088C214yesmaximal, complemented
5#13067964C214yesmaximal, complemented
6#13067364C211yesmaximal, characteristic, complemented
7#13067289C211yesmaximal, characteristic, complemented
8#13067285C211yesmaximal, characteristic
9C11×#2960C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C22×#4314—21no—
12C22×#4314—21no—
13C2×#66927C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#446—21no—
16C11×#446C2212yescomplemented
17C8×Q8×C11—21no—
18C8×Q8×C11C2212yescomplemented
19C11×#424—21no—
20C11×#423C2211yescharacteristic
21C11×#405—21no—
22C2×C4×C8×C11C2211yescharacteristic
23#10622701—21no—
24#10622698—21no—
25#10622694—21no—
26#10622692—21no—
27#10622659—22no—
28#10622656—22no—
29#10622640C2214yes—
30#10622633C2214yescomplemented
31#10622538C2211yescharacteristic
32#10622538C2211yescharacteristic
33#10622306—21no—
34#10622306—21no—
35#10622306C2212yes—
36#10622306C2212yes—
37#10622123C2214yes—
38#10622120C2214yescomplemented
39#10622096C2212yescomplemented
40#10622095C2212yescomplemented
41C22×D44—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×Dic22—21no—
45C2×C11×M16—21no—
46C22×C8×C11D411yescharacteristic
47C22×C8×C11D411yescharacteristic
48C11×C4⋊Q8D411yescharacteristic
49C11×C4⋊Q8D411yescharacteristic
50C11×#125—21no—
51C11×C22⋊Q8—21no—
52C11×C22⋊Q8D412yes—
53C4×Q8×C11—21no—
54C4×Q8×C11C2312yes—
55C11×#117—21no—
56C2×C42×C11C2311yescharacteristic
57C2×#4325—24no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×#4314—22no—
61C2×#4314—22no—
62C2×#4314—22no—
63C2×#4314—22no—
64C2×#4314—44no—
65C2×#4314—44no—
66#66927—21no—
67#66927—21no—
68#66927—21no—
69#66927C2312yes—
70#66922—21no—
71#66922—21no—
72#66922—21no—
73#66922C2312yes—
74C11×C4⋊C8—22no—
75C11×C4⋊C8—22no—
76C11×C4⋊C8—21no—
77C11×C4⋊C8C2312yes—
78C11×#97—22no—
79C4×C8×C11—22no—
80C4×C8×C11D411yescharacteristic
81C4×C8×C11D411yescharacteristic
82C4×C8×C11C2311yescharacteristic
83C4×C8×C11C2311yescharacteristic
84#66899—24no—
85C22⋊(C11⋊C8)—21no—
86C22⋊(C11⋊C8)—21no—
87#66873—24no—
88#66872—24no—
89C4⋊(C11⋊C8)C2312yes—
90C4⋊(C11⋊C8)C2312yes—
91C4×C11⋊C8—21no—
92C4×C11⋊C8—21no—
93#19202—111nomaximal, Sylow
94C23×D11—41no—
95C2×Q8×C11—21no—
96C2×Q8×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C22×Dic11—41no—
101C2×D44—22no—
102C2×D44—22no—
103C2×D44—22no—
104C2×D44—41no—
105C2×D44—41no—
106C2×D44—41no—
107C2×D44—42no—
108C2×D44—42no—
109C2×D44—82no—
110C2×D44—82no—
111C2×Dic22—22no—
112C2×Dic22—41no—
113C2×Dic22—42no—
114C2×Dic22—42no—
115C11×M16—42no—
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
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4C2×D412yes—
129C11×C22⋊C4—22no—
130C42×C11—22no—
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134C42×C11C2411yescharacteristic
135#4325—84no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—41no—
139C4⋊Dic11—41no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142#4314—44no—
143#4314—44no—
144#4314—44no—
145#4314—44no—
146#3229—111no—
147#3208—111no—
148C2×#492—111no—
149#2960D1111yescharacteristic, complemented
150#1686—114no—
151#1666—114no—
152#1564—111no—
153#1546—111no—
154#1545—111no—
155C23×C11#12111yescharacteristic
156C22×D11—42no—
157C22×D11—82no—
158C22×D11—82no—
159C22×D11—82no—
160Q8×C11—24no—
161Q8×C11—42no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11C2×SD1612yes—
170C2×C4×C11AGL(1,ℤ/8)12yes—
171C2×C4×C11C22×D411yescharacteristic
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C2×#4111yescharacteristic
174C2×Dic11—42no—
175C2×Dic11—82no—
176D44—42no—
177D44—42no—
178D44—44no—
179D44—82no—
180D44—82no—
181D44—82no—
182D44—82no—
183Dic22—42no—
184Dic22—42no—
185Dic22—82no—
186C8×C11—21no—
187C8×C11—21no—
188C8×C11—42no—
189C8×C11C2×SD1612yes—
190C8×C11C2×SD1612yes—
191C11⋊C8—42no—
192C11⋊C8—42no—
193C22×SD16—221no—
194C22×SD16—221no—
195#533C2×D1111yescharacteristic
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—21no—
211#446C2×D1112yescomplemented
212C8×Q8—21no—
213C8×Q8C2×D1112yescomplemented
214#431—111no—
215#431—111no—
216#424—21no—
217#423C2×D1111yescharacteristic
218#405—21no—
219C2×C4×C8C2×D1111yescharacteristic
220#335—112no—
221#334—112no—
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—42no—
235C4×C11—42no—
236C4×C11#46012yes—
237C4×C11#47112yes—
238C4×C11C22×SD1611yescharacteristic
239C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
240C4×C11#57712yes—
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—21no—
254C22×C8C22⋊D1111yescharacteristic
255C22×C8C22⋊D1111yescharacteristic
256C4⋊Q8—112no—
257C4⋊Q8—221no—
258C4⋊Q8—221no—
259C4⋊Q8—221no—
260C4⋊Q8D4411yescharacteristic
261C4⋊Q8D4411yescharacteristic
262#127—112no—
263#127—221no—
264#127—221no—
265#127—221no—
266#125—21no—
267C22⋊Q8—21no—
268C22⋊Q8D4412yes—
269C4×Q8—21no—
270C4×Q8C22×D1112yes—
271#117—21no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C42C22×D1111yescharacteristic
275#106—224no—
276C4⋊C8—22no—
277C4⋊C8—22no—
278C4⋊C8—21no—
279C4⋊C8—112no—
280C4⋊C8—112no—
281C4⋊C8C22×D1112yes—
282#103—224no—
283#102—224no—
284C22⋊C8—221no—
285C22⋊C8—221no—
286#97—22no—
287C4×C8—22no—
288C4×C8—221no—
289C4×C8—221no—
290C4×C8C22⋊D1111yescharacteristic
291C4×C8C22⋊D1111yescharacteristic
292C4×C8C22×D1111yescharacteristic
293C4×C8C22×D1111yescharacteristic
294C2×C11—22no—
295C2×C11C2×#46011yescharacteristic
296C2×C11#305711yescharacteristic
297C2×C11C2×#47111yescharacteristic
298D11—162no—
299C24—441no—
300C2×Q8—21no—
301C2×Q8—222no—
302C2×Q8—441no—
303C2×Q8—442no—
304C2×Q8—442no—
305C2×Q8C2×D4412yes—
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×C4#433911yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320SD16—444no—
321SD16—444no—
322SD16—444no—
323SD16—444no—
324SD16—884no—
325M16—42no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8#432514yescomplemented
331C2×C8C2×C22⋊D1111yescharacteristic
332C2×C8C2×C22⋊D1111yescharacteristic
333C2×C8C2×C22⋊D1111yescharacteristic
334C2×C8C2×C22⋊D1111yescharacteristic
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—222no—
341C4⋊C4—222no—
342C4⋊C4—441no—
343C4⋊C4—441no—
344C4⋊C4C2×D4412yes—
345C22⋊C4—22no—
346C42—22no—
347C42C2×D4411yescharacteristic
348C42#433911yescharacteristic
349C42C2×C22⋊D1111yescharacteristic
350C42C23×D1111yescharacteristic
351C11#1920211yescharacteristic, complemented, Sylow
352C23—442no—
353C23—882no—
354C23—882no—
355C23—882no—
356C23#6698311yescharacteristic
357Q8—24no—
358Q8—42no—
359Q8—442no—
360Q8—442no—
361Q8—882no—
362D4—444no—
363D4—442no—
364D4—442no—
365D4—882no—
366D4—882no—
367D4—882no—
368D4—882no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—442no—
374C2×C4—882no—
375C2×C4#6698311yescharacteristic
376C2×C4#6698311yescharacteristic
377C2×C4#6698311yescharacteristic
378C2×C4C2×#432512yes—
379C2×C4#6700212yes—
380C2×C4C22×D4411yescharacteristic
381C2×C4C2×#433911yescharacteristic
382C2×C4C22×C22⋊D1111yescharacteristic
383C8—21no—
384C8—21no—
385C8—42no—
386C8—442no—
387C8—442no—
388C8C2×#432512yes—
389C8C2×#432512yes—
390C22—21no—
391C22—21no—
392C22—882no—
393C22—882no—
394C22—882no—
395C22—1764no—
396C22#1062264012yes—
397C22C2×#6698311yescharacteristic
398C4—21no—
399C4—21no—
400C4—42no—
401C4—42no—
402C4—882no—
403C4#1062264012yes—
404C4#1062275412yes—
405C4#1062328212yes—
406C4C22×#432511yescharacteristic
407C4C2×#6700211yescharacteristic
408C2—22no—
409C2—1762no—
410C2C2×#1062264011yescharacteristic
411C2#1307825511yescharacteristic
412C2C2×#1062275411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2960C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#2960D11
hypocenterC11#19202
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2960

Complements

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

NH ≅ G/Ntype
1. #13079757C2semidirect
4. #13068088C2semidirect
5. #13067964C2semidirect
6. #13067364C2semidirect
7. #13067289C2semidirect
9. C11×#2960C2semidirect
16. C11×#446C22semidirect
18. C8×Q8×C11C22semidirect
30. #10622633C22semidirect
38. #10622120C22semidirect
39. #10622096C22semidirect
40. #10622095C22semidirect
118. C2×C8×C11SD16semidirect
149. #2960D11semidirect
211. #446C2×D11semidirect
213. C8×Q8C2×D11semidirect
330. C2×C8#4325semidirect
351. C11#19202semidirect

Maximal subgroups

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

subgroupindex
#130797572
#130795542
C2×#106223062
#130680882
#130679642
#130673642
#130672892
#130672852
C11×#29602
#1920211