Finite Group Databasebeta

← #14737723

Subgroups — #14737723

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078425C211yesmaximal, characteristic, complemented
2#13078092C211yesmaximal, characteristic
3C8×#4339C211yesmaximal, characteristic, complemented
4#13068029C214yesmaximal, complemented
5#13068022C214yesmaximal, complemented
6#13067372C211yesmaximal, characteristic, complemented
7#13067297C211yesmaximal, characteristic, complemented
8#13067284C211yesmaximal, characteristic, complemented
9C2×C11×#486C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×#66985—21no—
13C4×#4339C2211yescharacteristic
14C11×#486—21no—
15C11×#486—21no—
16C11×#486C2214yes—
17C2×C11×#102—22no—
18C2×C4×C8×C11C2211yescharacteristic
19#10622828—21no—
20C8×C22⋊D11—22no—
21#10622707—21no—
22#10622704C2212yescomplemented
23#10622700—21no—
24#10622697C2212yescomplemented
25#10622688—21no—
26#10622688C2212yes—
27#10622685—21no—
28#10622685C2212yes—
29#10622579—21no—
30#10622577—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622537C2211yescharacteristic
34C8×D44C2212yescomplemented
35#10622298—21no—
36C4×C8×D11—21no—
37C8×Dic22C2212yescomplemented
38#10622184C2214yescomplemented
39#10622182C2214yes—
40#10622095C2214yescomplemented
41C22×Q8×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C2×#4339D411yescharacteristic
46C22×C8×C11D412yes—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8C2312yes—
51C11×#127—21no—
52C11×#127—21no—
53C11×#127—21no—
54C11×#127C2312yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58C2×#4324—22no—
59#66985—44no—
60C2×#4323—22no—
61C4×C22⋊D11—21no—
62C4×C22⋊D11—21no—
63#66979D411yescharacteristic
64C2×#4318—21no—
65C2×#4318—21no—
66C2×C8×D11—22no—
67C4×D44D411yescharacteristic
68C4×D44C2311yescharacteristic
69#66925—21no—
70C42×D11—21no—
71C4×Dic22D411yescharacteristic
72C4×Dic22C2311yescharacteristic
73C11×#102—24no—
74C11×#102—24no—
75C4×C8×C11D411yescharacteristic
76C4×C8×C11D411yescharacteristic
77C4×C8×C11C2312yes—
78#66896—22no—
79#66896—22no—
80C22⋊(C11⋊C8)—21no—
81(C2×D11)⋊C8—22no—
82Dic11⋊C8—22no—
83C8×Dic11—22no—
84#66874—22no—
85#66873—22no—
86#66872—22no—
87#66871—22no—
88C4⋊(C11⋊C8)—21no—
89C4⋊(C11⋊C8)—21no—
90C4⋊(C11⋊C8)C2312yes—
91C4⋊(C11⋊C8)C2312yes—
92C4⋊(C11⋊C8)C2312yes—
93C4×C11⋊C8—21no—
94#19274—111nomaximal, Sylow
95C24×C11—41no—
96C2×Q8×C11—22no—
97C2×Q8×C11—41no—
98C2×Q8×C11—82no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—44no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C2×D4×C11—41no—
106C2×D4×C11—42no—
107C2×D4×C11—42no—
108C2×D4×C11—82no—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×C22⋊D11—21no—
114#4339—22no—
115#4339SD1614yes—
116C2×D44C2×D411yescharacteristic
117C2×C4×D11—21no—
118C2×C4×D11—21no—
119C2×C4×D11—21no—
120C2×Dic22C2×D411yescharacteristic
121C2×C8×C11—42no—
122C2×C8×C11C2×D412yes—
123C2×C8×C11C2×D412yes—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131C42×C11C2411yescharacteristic
132C22⋊Dic11—21no—
133#4324—44no—
134#4323—44no—
135(C2×D11)⋊C4—21no—
136(C2×D11)⋊C4—21no—
137C4⋊Dic11C2×D411yescharacteristic
138C4⋊Dic11C2×D411yescharacteristic
139Dic11⋊C4—21no—
140Dic11⋊C4—21no—
141C4×Dic11—21no—
142C4×Dic11—21no—
143C4×Dic11—21no—
144#4318—42no—
145#4318—42no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C8×D11—44no—
150C2×#486D1111yescharacteristic, complemented
151#3079—111no—
152#3038—111no—
153C8×#41—111no—
154#1678—114no—
155#1677—114no—
156#1566—111no—
157#1548—111no—
158#1545—111no—
159C23×C11—42no—
160C23×C11—82no—
161C23×C11—82no—
162C23×C11—82no—
163C23×C11#12111yescharacteristic
164C22×D11—21no—
165Q8×C11—82no—
166Q8×C11—82no—
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—44no—
170D4×C11—82no—
171D4×C11—82no—
172D4×C11—82no—
173D4×C11—82no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—42no—
177C2×C4×C11—82no—
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11C2×SD1612yes—
182C2×C4×C11#13512yes—
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C22⋊D11—24no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190D44—21no—
191D44C2×SD1612yes—
192C4×D11—24no—
193C4×D11—42no—
194C4×D11—42no—
195Dic22—21no—
196Dic22C2×SD1612yes—
197C8×C11—22no—
198C8×C11—22no—
199C11⋊C8—42no—
200C11⋊C8—42no—
201C11⋊C8—42no—
202C2×AGL(1,ℤ/8)—221no—
203C2×C4⋊Q8C2×D1111yescharacteristic
204C2×#127C2×D1111yescharacteristic
205C4×#41—111no—
206#486—21no—
207#486—21no—
208#486C2×D1114yes—
209#477—112no—
210#476—112no—
211#475—221no—
212#474—221no—
213#460—112no—
214#460—221no—
215#459—112no—
216#459—221no—
217C8×Q8—112no—
218C8×D4—112no—
219C8×D4—222no—
220#431—111no—
221#431—221no—
222#428—221no—
223#423—111no—
224#423—111no—
225#418—221no—
226#417—221no—
227C2×#102—22no—
228C2×C4×C8—221no—
229C2×C4×C8C2×D1111yescharacteristic
230#334—114no—
231#333—114no—
232#331—114no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—82no—
236C22×C11—82no—
237C22×C11—82no—
238C22×C11—164no—
239C22×C11#46512yes—
240C22×C11C2×#12111yescharacteristic
241C2×D11—22no—
242C2×D11—41no—
243C2×D11—41no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—82no—
247C4×C11#46512yes—
248C4×C11#47212yes—
249C4×C11C22×SD1611yescharacteristic
250C4×C11C2×#13511yescharacteristic
251C4×C11#57512yes—
252Dic11—22no—
253Dic11—41no—
254Dic11—41no—
255C2×#41—111no—
256C22×Q8—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—21no—
260AGL(1,ℤ/8)—444no—
261C2×SD16—222no—
262C2×D8—222no—
263C2×M16—221no—
264C2×M16—221no—
265C22×C8—222no—
266C22×C8C22⋊D1112yes—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8C22×D1112yes—
271#127—21no—
272#127—21no—
273#127—21no—
274#127C22×D1112yes—
275C4×Q8—111no—
276C4×Q8—111no—
277C4×D4—111no—
278C4×D4—111no—
279C4×D4—221no—
280C4×D4—221no—
281#117—111no—
282#117—221no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C42—221no—
286C2×C42C22×D1111yescharacteristic
287#107—222no—
288#106—222no—
289C4⋊C8—112no—
290C4⋊C8—112no—
291C4⋊C8—112no—
292C4⋊C8—222no—
293C4⋊C8—221no—
294C4⋊C8—221no—
295#103—222no—
296#102—24no—
297#102—24no—
298#102—222no—
299#102—222no—
300#102—222no—
301C22⋊C8—221no—
302C22⋊C8—222no—
303C4×C8—222no—
304C4×C8—221no—
305C4×C8C22⋊D1111yescharacteristic
306C4×C8C22⋊D1111yescharacteristic
307C4×C8C22×D1112yes—
308C2×C11—22no—
309C2×C11—162no—
310C2×C11#304011yescharacteristic
311C2×C11C2×#46511yescharacteristic
312C2×C11C2×#47211yescharacteristic
313D11—42no—
314C24—41no—
315#41—114no—
316#41—222no—
317C2×Q8—22no—
318C2×Q8—41no—
319C2×Q8—82no—
320C2×Q8—111no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—44no—
325C2×D4—42no—
326C2×D4—42no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—82no—
331C2×D4—111no—
332C2×D4—221no—
333C22×C4—41no—
334C22×C4—221no—
335C22×C4—221no—
336C22×C4—221no—
337C22×C4D4×D1111yescharacteristic
338C22×C4#434111yescharacteristic
339C22×C4C2×C22⋊D1111yescharacteristic
340SD16—444no—
341D8—444no—
342M16—442no—
343M16—442no—
344C2×C8—42no—
345C2×C8—222no—
346C2×C8—222no—
347C2×C8—222no—
348C2×C8—444no—
349C2×C8C2×C22⋊D1112yes—
350C2×C8C2×C22⋊D1112yes—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—111no—
356C4⋊C4—111no—
357C4⋊C4—221no—
358C4⋊C4—221no—
359C22⋊C4—221no—
360C22⋊C4—221no—
361C22⋊C4—221no—
362C42—221no—
363C42—221no—
364C42—221no—
365C42D4×D1111yescharacteristic
366C42#434111yescharacteristic
367C42C2×C22⋊D1111yescharacteristic
368C42C23×D1111yescharacteristic
369C11#1927411yescharacteristic, complemented, Sylow
370C23—42no—
371C23—82no—
372C23—82no—
373C23—82no—
374C23—221no—
375C23#6699111yescharacteristic
376Q8—82no—
377Q8—82no—
378Q8—112no—
379Q8—221no—
380D4—42no—
381D4—42no—
382D4—44no—
383D4—82no—
384D4—82no—
385D4—82no—
386D4—82no—
387D4—112no—
388D4—224no—
389D4—221no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—42no—
393C2×C4—82no—
394C2×C4—221no—
395C2×C4—224no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4SD16×D1112yes—
401C2×C4#6696912yes—
402C2×C4#6699111yescharacteristic
403C2×C4#6699111yescharacteristic
404C2×C4#6699111yescharacteristic
405C2×C4C2×D4×D1111yescharacteristic
406C2×C4C2×#434111yescharacteristic
407C2×C4C22×C22⋊D1111yescharacteristic
408C8—22no—
409C8—22no—
410C8—442no—
411C8—442no—
412C8—442no—
413C22—21no—
414C22—21no—
415C22—82no—
416C22—82no—
417C22—82no—
418C22—164no—
419C22—222no—
420C22—441no—
421C22—441no—
422C22#1062278412yes—
423C22C2×#6699111yescharacteristic
424C4—21no—
425C4—21no—
426C4—82no—
427C4—222no—
428C4—441no—
429C4—441no—
430C4#1062277312yes—
431C4#1062278412yes—
432C4C2×SD16×D1111yescharacteristic
433C4C2×#6696911yescharacteristic
434C4#1062335312yes—
435C2—22no—
436C2—162no—
437C2—442no—
438C2#1307810611yescharacteristic
439C2C2×#1062278411yescharacteristic
440C2C2×#1062277311yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#486C2
socleC22×C11C2×#121
prime radical#13078092C2
hypercenterC2×#486D11
hypocenterC11#19274
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. #13078425C2semidirect
3. C8×#4339C2semidirect
4. #13068029C2semidirect
5. #13068022C2semidirect
6. #13067372C2semidirect
7. #13067297C2semidirect
8. #13067284C2semidirect
9. C2×C11×#486C2semidirect
22. #10622704C22semidirect
24. #10622697C22semidirect
34. C8×D44C22semidirect
37. C8×Dic22C22semidirect
38. #10622184C22semidirect
40. #10622095C22semidirect
150. C2×#486D11semidirect
369. C11#19274semidirect

Maximal subgroups

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

subgroupindex
#130784252
#130780922
C8×#43392
#130680292
#130680222
#130673722
#130672972
#130672842
C2×C11×#4862
#1927411