Finite Group Databasebeta

← #14736973

Subgroups — #14736973

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#13079554C211yesmaximal, characteristic
2C2×#10622698C211yesmaximal, characteristic
3#13077551C211yesmaximal, characteristic, complemented
4#13068090C214yesmaximal, complemented
5#13067966C214yesmaximal, complemented
6#13067362C211yesmaximal, characteristic, complemented
7#13067288C211yesmaximal, characteristic, complemented
8#13067283C211yesmaximal, characteristic
9C11×#3229C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C22×#4325—21no—
13C22×#4325—21no—
14C2×#66927C2211yescharacteristic
15C11×#498—21no—
16C11×#487—21no—
17C11×#483—22no—
18C11×#475C2214yescomplemented
19C11×#431C2211yescharacteristic
20#10622701—21no—
21#10622698—21no—
22#10622698—21no—
23#10622698—21no—
24#10622698C2212yes—
25#10622698C2212yes—
26#10622659—22no—
27#10622640C2214yes—
28#10622637—21no—
29#10622637C2212yescomplemented
30Q8×C11⋊C8—21no—
31Q8×C11⋊C8C2212yescomplemented
32#10622612—21no—
33#10622610—21no—
34#10622538C2211yescharacteristic
35#10622537C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622185C2214yescomplemented
38#10622123C2214yes—
39#10622118C2212yescomplemented
40#10622117C2212yescomplemented
41C22×Q8×C11—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×D44—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8D411yescharacteristic
49C11×C4⋊Q8D411yescharacteristic
50C11×C4⋊Q8C2312yes—
51C11×#125—21no—
52C11×C22⋊Q8—21no—
53C11×C22⋊Q8D412yes—
54C4×Q8×C11—21no—
55C4×Q8×C11C2312yes—
56C11×#117—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60C2×#4325—24no—
61C2×#4325—22no—
62C2×#4325—22no—
63C2×#4325—22no—
64C2×#4325—22no—
65C2×#4325—44no—
66C2×#4325—44no—
67C2×#4318—21no—
68C22×C11⋊C8D411yescharacteristic
69C22×C11⋊C8D411yescharacteristic
70#66927—21no—
71#66927—21no—
72#66927—21no—
73#66927C2312yes—
74C11×#106—24no—
75C11×C4⋊C8C2312yes—
76C11×#103—24no—
77C11×C22⋊C8—21no—
78C4×C8×C11—21no—
79C22⋊(C11⋊C8)—21no—
80#66873—24no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)—22no—
83C4⋊(C11⋊C8)—22no—
84C4⋊(C11⋊C8)C2312yes—
85C4⋊(C11⋊C8)C2312yes—
86#66867—22no—
87C4×C11⋊C8—21no—
88C4×C11⋊C8—22no—
89C4×C11⋊C8D411yescharacteristic
90C4×C11⋊C8D411yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92C4×C11⋊C8C2311yescharacteristic
93#19202—111nomaximal, Sylow
94C23×D11—41no—
95C2×Q8×C11—21no—
96C2×Q8×C11—22no—
97C2×Q8×C11—41no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×Q8×C11C2×D412yes—
101C22×C4×C11—41no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C2×D44—22no—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44—41no—
109C2×D44—41no—
110C2×D44—41no—
111C2×D44—42no—
112C2×D44—42no—
113C2×D44—82no—
114C2×D44—82no—
115C2×C8×C11—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4C2×D412yes—
126C11×C22⋊C4—22no—
127C42×C11—22no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131C42×C11C2411yescharacteristic
132#4325—44no—
133#4325—44no—
134#4325—44no—
135#4325—44no—
136#4325—84no—
137#4318—42no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8SD1614yescomplemented
142C2×C11⋊C8C2×D411yescharacteristic
143C2×C11⋊C8C2×D411yescharacteristic
144C2×C11⋊C8C2×D411yescharacteristic
145C2×C11⋊C8C2×D411yescharacteristic
146#3229D1111yescharacteristic, complemented
147#3208—111no—
148C2×#492—111no—
149#2960—111no—
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—
162Q8×C11—42no—
163Q8×C11—42no—
164Q8×C11—82no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—42no—
170C2×C4×C11—82no—
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11C2×SD1612yes—
175C2×C4×C11AGL(1,ℤ/8)12yes—
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179D44—42no—
180D44—42no—
181D44—44no—
182D44—82no—
183D44—82no—
184D44—82no—
185D44—82no—
186C8×C11—42no—
187C11⋊C8—21no—
188C11⋊C8—21no—
189C11⋊C8—42no—
190C11⋊C8—42no—
191C11⋊C8C2×SD1612yes—
192C11⋊C8C2×SD1612yes—
193C22×SD16—221no—
194C22×SD16—221no—
195#533C2×D1111yescharacteristic
196C2×C4⋊Q8C2×D1111yescharacteristic
197C2×#127—111no—
198#498—21no—
199#492—112no—
200#492—112no—
201#492—221no—
202#492—221no—
203#492—221no—
204#487—21no—
205#486—221no—
206#483—22no—
207#475C2×D1114yescomplemented
208#460—114no—
209#450—222no—
210#446—112no—
211#446—221no—
212C8×Q8—112no—
213C8×Q8—221no—
214#431—111no—
215#431C2×D1111yescharacteristic
216#424—221no—
217#423—111no—
218#405—221no—
219C2×C4×C8—111no—
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—82no—
237C4×C11#46012yes—
238C4×C11#47112yes—
239C4×C11C22×SD1611yescharacteristic
240C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
241C4×C11#57712yes—
242C22×Q8—21no—
243C22×D4—221no—
244C22×D4—221no—
245C22×D4—221no—
246C2×SD16—222no—
247C2×SD16—222no—
248C2×SD16—222no—
249C2×SD16—222no—
250C2×SD16—224no—
251C2×SD16—444no—
252C2×SD16—444no—
253C2×M16—221no—
254C22×C8—111no—
255C22×C8—111no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8C22⋊D1111yescharacteristic
260C4⋊Q8C22⋊D1111yescharacteristic
261C4⋊Q8C22×D1112yes—
262#127—112no—
263#127—221no—
264#127—221no—
265#127—221no—
266#125—21no—
267C22⋊Q8—21no—
268C22⋊Q8C22⋊D1112yes—
269C4×Q8—21no—
270C4×Q8C22×D1112yes—
271#117—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C42C22×D1111yescharacteristic
275#106—24no—
276C4⋊C8—112no—
277C4⋊C8—112no—
278C4⋊C8—222no—
279C4⋊C8—222no—
280C4⋊C8—221no—
281C4⋊C8C22×D1112yes—
282#103—24no—
283#102—224no—
284C22⋊C8—21no—
285C22⋊C8—221no—
286#97—222no—
287C4×C8—21no—
288C4×C8—111no—
289C4×C8—111no—
290C4×C8—111no—
291C4×C8—111no—
292C4×C8—222no—
293C4×C8—221no—
294C2×C11—22no—
295C2×C11C2×#46011yescharacteristic
296C2×C11#305711yescharacteristic
297C2×C11C2×#47111yescharacteristic
298D11—162no—
299C24—441no—
300C2×Q8—21no—
301C2×Q8—22no—
302C2×Q8—41no—
303C2×Q8—42no—
304C2×Q8—42no—
305C2×Q8C2×C22⋊D1112yes—
306C2×D4—222no—
307C2×D4—222no—
308C2×D4—222no—
309C2×D4—442no—
310C2×D4—442no—
311C2×D4—441no—
312C2×D4—441no—
313C2×D4—441no—
314C2×D4—882no—
315C2×D4—882no—
316C22×C4—41no—
317C22×C4D4×D1111yescharacteristic
318C22×C4#434111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320SD16—444no—
321SD16—444no—
322SD16—444no—
323SD16—444no—
324SD16—884no—
325M16—442no—
326C2×C8—22no—
327C2×C8—114no—
328C2×C8—111no—
329C2×C8—111no—
330C2×C8—111no—
331C2×C8—111no—
332C2×C8—222no—
333C2×C8—222no—
334C2×C8—222no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4C2×C22⋊D1112yes—
345C22⋊C4—22no—
346C42—22no—
347C42D4×D1111yescharacteristic
348C42#434111yescharacteristic
349C42C2×C22⋊D1111yescharacteristic
350C42C23×D1111yescharacteristic
351C11#1920211yescharacteristic, complemented, Sylow
352C23—442no—
353C23—882no—
354C23—882no—
355C23—882no—
356C23#6699211yescharacteristic
357Q8—24no—
358Q8—42no—
359Q8—42no—
360Q8—42no—
361Q8—82no—
362D4—442no—
363D4—442no—
364D4—444no—
365D4—882no—
366D4—882no—
367D4—882no—
368D4—882no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—42no—
374C2×C4—82no—
375C2×C4SD16×D1112yes—
376C2×C4#6696712yes—
377C2×C4#6699211yescharacteristic
378C2×C4#6699211yescharacteristic
379C2×C4#6699211yescharacteristic
380C2×C4C2×D4×D1111yescharacteristic
381C2×C4C2×#434111yescharacteristic
382C2×C4C22×C22⋊D1111yescharacteristic
383C8—42no—
384C8—112no—
385C8—112no—
386C8—221no—
387C8—221no—
388C8—442no—
389C8—442no—
390C22—21no—
391C22—21no—
392C22—882no—
393C22—882no—
394C22—882no—
395C22—1764no—
396C22#1062277612yes—
397C22C2×#6699211yescharacteristic
398C4—21no—
399C4—21no—
400C4—42no—
401C4—42no—
402C4—82no—
403C4#1062277612yes—
404C4#1062281612yes—
405C4C2×SD16×D1111yescharacteristic
406C4C2×#6696711yescharacteristic
407C4#1062336812yes—
408C2—22no—
409C2—1762no—
410C2C2×#1062277611yescharacteristic
411C2#1307825711yescharacteristic
412C2C2×#1062281611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3229C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#3229D11
hypocenterC11#19202
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
3. #13077551C2semidirect
4. #13068090C2semidirect
5. #13067966C2semidirect
6. #13067362C2semidirect
7. #13067288C2semidirect
9. C11×#3229C2semidirect
18. C11×#475C22semidirect
29. #10622637C22semidirect
31. Q8×C11⋊C8C22semidirect
37. #10622185C22semidirect
39. #10622118C22semidirect
40. #10622117C22semidirect
141. C2×C11⋊C8SD16semidirect
146. #3229D11semidirect
207. #475C2×D11semidirect
351. C11#19202semidirect

Maximal subgroups

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

subgroupindex
#130795542
C2×#106226982
#130775512
#130680902
#130679662
#130673622
#130672882
#130672832
C11×#32292
#1920211