Finite Group Databasebeta

← #14737729

Subgroups — #14737729

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
1C2×#10622701C211yesmaximal, characteristic, complemented
2#13078096C211yesmaximal, characteristic
3#41×C11⋊C8C211yesmaximal, characteristic, complemented
4#13068034C214yesmaximal, complemented
5#13068027C214yesmaximal, complemented
6#13067371C211yesmaximal, characteristic, complemented
7#13067297C211yesmaximal, characteristic, complemented
8#13067285C211yesmaximal, characteristic, complemented
9C11×#3079C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C4×C11×#41C2211yescharacteristic
12C2×#67002—21no—
13C2×#66927C2211yescharacteristic
14C11×#477C2212yescomplemented
15C11×#476C2212yescomplemented
16C11×#475—21no—
17C11×#474—21no—
18C11×#428—21no—
19C11×#423C2211yescharacteristic
20C11×#417—21no—
21#10622701—21no—
22#10622701—21no—
23#10622701C2214yes—
24#10622640—21no—
25#10622640C2212yes—
26Q8×C11⋊C8C2212yescomplemented
27#10622628—21no—
28#10622628C2212yes—
29D4×C11⋊C8—22no—
30D4×C11⋊C8C2212yescomplemented
31#10622614—21no—
32C2×#66873—22no—
33#10622538—21no—
34#10622538C2211yescharacteristic
35#10622537C2211yescharacteristic
36C2×C4×C11⋊C8—21no—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622184C2214yescomplemented
39#10622123C2214yes—
40#10622118C2214yescomplemented
41C2×C11×#41D411yescharacteristic
42C22×Q8×C11—21no—
43C22×D44—21no—
44C22×D44—21no—
45C22×D44—21no—
46C2×C11×M16—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8C2312yes—
51C4×Q8×C11D411yescharacteristic
52C4×Q8×C11C2311yescharacteristic
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11D411yescharacteristic
56C4×D4×C11C2311yescharacteristic
57C11×#117—21no—
58C11×#117D411yescharacteristic
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63#67002—44no—
64C2×#4325—22no—
65C2×#4323—22no—
66C2×#4318—21no—
67C22×C11⋊C8—22no—
68C22×C11⋊C8D412yes—
69#66927—21no—
70#66927—21no—
71#66927—21no—
72#66927C2312yes—
73C11×#107—22no—
74C11×#106—22no—
75C11×C4⋊C8—21no—
76C11×C4⋊C8C2312yes—
77C11×#103—22no—
78C11×#102—22no—
79C22⋊(C11⋊C8)—21no—
80C22⋊(C11⋊C8)—22no—
81#66873—22no—
82#66873—22no—
83#66873—24no—
84#66873—24no—
85C4⋊(C11⋊C8)—21no—
86C4⋊(C11⋊C8)—22no—
87C4⋊(C11⋊C8)C2312yes—
88C4⋊(C11⋊C8)C2312yes—
89C4×C11⋊C8—21no—
90C4×C11⋊C8—22no—
91C4×C11⋊C8D411yescharacteristic
92C4×C11⋊C8D411yescharacteristic
93C4×C11⋊C8C2312yes—
94#19274—111nomaximal, Sylow
95C23×D11—41no—
96C11×#41—22no—
97C11×#41SD1614yes—
98C2×Q8×C11—22no—
99C2×Q8×C11—41no—
100C2×Q8×C11—82no—
101C2×Q8×C11C2×D411yescharacteristic
102C2×D4×C11—21no—
103C2×D4×C11C2×D411yescharacteristic
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—41no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—44no—
115C2×D44—41no—
116C2×D44—41no—
117C2×D44—41no—
118C2×D44—42no—
119C2×D44—42no—
120C2×D44—82no—
121C11×M16—42no—
122C2×C8×C11—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4C2×D411yescharacteristic
130C11×C4⋊C4C2×D411yescharacteristic
131C11×C22⋊C4—21no—
132C11×C22⋊C4—21no—
133C11×C22⋊C4—21no—
134C42×C11—21no—
135C42×C11—21no—
136C42×C11—21no—
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11#4111yescharacteristic
140C42×C11C2411yescharacteristic
141#4325—44no—
142#4323—44no—
143#4318—42no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—42no—
147C2×C11⋊C8—44no—
148C2×C11⋊C8C2×D412yes—
149C2×C11⋊C8C2×D412yes—
150C2×#486—111no—
151#3079D1111yescharacteristic, complemented
152#3038—111no—
153C8×#41—111no—
154#1678—114no—
155#1677—114no—
156#1566—111no—
157#1548—111no—
158#1545—111no—
159C23×C11—21no—
160C23×C11#12111yescharacteristic
161C22×D11—42no—
162C22×D11—82no—
163C22×D11—82no—
164C22×D11—82no—
165Q8×C11—21no—
166Q8×C11—82no—
167Q8×C11—82no—
168Q8×C11C2×SD1612yes—
169D4×C11—24no—
170D4×C11—21no—
171D4×C11C2×SD1612yes—
172C2×C4×C11—21no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—82no—
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11C2×SD1612yes—
186C2×C4×C11#13512yes—
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190D44—42no—
191D44—42no—
192D44—44no—
193D44—82no—
194D44—82no—
195D44—82no—
196D44—82no—
197C8×C11—42no—
198C11⋊C8—22no—
199C11⋊C8—22no—
200C11⋊C8—42no—
201C11⋊C8—42no—
202C2×AGL(1,ℤ/8)—221no—
203C2×C4⋊Q8C2×D1111yescharacteristic
204C2×#127—111no—
205C4×#41C2×D1111yescharacteristic
206#486—114no—
207#486—221no—
208#486—221no—
209#477C2×D1112yescomplemented
210#476C2×D1112yescomplemented
211#475—21no—
212#474—21no—
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—21no—
223#423—111no—
224#423C2×D1111yescharacteristic
225#418—221no—
226#417—21no—
227C2×#102—222no—
228C2×C4×C8—111no—
229C2×C4×C8—221no—
230#334—114no—
231#333—114no—
232#331—114no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—22no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11#46512yes—
239C22×C11C2×#12111yescharacteristic
240C2×D11—82no—
241C2×D11—82no—
242C2×D11—82no—
243C2×D11—164no—
244C4×C11—21no—
245C4×C11—22no—
246C4×C11—21no—
247C4×C11—41no—
248C4×C11—41no—
249C4×C11—82no—
250C4×C11#46512yes—
251C4×C11#47212yes—
252C4×C11C22×SD1611yescharacteristic
253C4×C11C2×#13511yescharacteristic
254C4×C11#57512yes—
255C2×#41C22⋊D1111yescharacteristic
256C22×Q8—21no—
257C22×D4—221no—
258C22×D4—221no—
259C22×D4—221no—
260AGL(1,ℤ/8)—444no—
261C2×SD16—222no—
262C2×D8—222no—
263C2×M16—21no—
264C2×M16—221no—
265C22×C8—112no—
266C22×C8—222no—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8C22×D1112yes—
271#127—112no—
272#127—221no—
273#127—221no—
274#127—221no—
275C4×Q8C22⋊D1111yescharacteristic
276C4×Q8C22×D1111yescharacteristic
277C4×D4—21no—
278C4×D4—21no—
279C4×D4C22⋊D1111yescharacteristic
280C4×D4C22×D1111yescharacteristic
281#117—21no—
282#117C22⋊D1111yescharacteristic
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C42—21no—
286C2×C42C22×D1111yescharacteristic
287#107—22no—
288#106—22no—
289C4⋊C8—21no—
290C4⋊C8—112no—
291C4⋊C8—112no—
292C4⋊C8—222no—
293C4⋊C8—221no—
294C4⋊C8C22×D1112yes—
295#103—22no—
296#102—22no—
297#102—224no—
298#102—224no—
299#102—222no—
300#102—222no—
301C22⋊C8—222no—
302C22⋊C8—221no—
303C4×C8—111no—
304C4×C8—111no—
305C4×C8—112no—
306C4×C8—222no—
307C4×C8—221no—
308C2×C11—22no—
309C2×C11—42no—
310C2×C11#304011yescharacteristic
311C2×C11C2×#46511yescharacteristic
312C2×C11C2×#47211yescharacteristic
313D11—162no—
314C24—441no—
315#41—22no—
316#41#432514yes—
317C2×Q8—22no—
318C2×Q8—41no—
319C2×Q8—82no—
320C2×Q8C2×C22⋊D1111yescharacteristic
321C2×D4—21no—
322C2×D4—222no—
323C2×D4—222no—
324C2×D4—222no—
325C2×D4—444no—
326C2×D4—441no—
327C2×D4—441no—
328C2×D4—441no—
329C2×D4—442no—
330C2×D4—442no—
331C2×D4—882no—
332C2×D4C2×C22⋊D1111yescharacteristic
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—41no—
337C22×C4D4×D1111yescharacteristic
338C22×C4#434111yescharacteristic
339C22×C4C2×C22⋊D1111yescharacteristic
340SD16—444no—
341D8—444no—
342M16—42no—
343M16—442no—
344C2×C8—22no—
345C2×C8—112no—
346C2×C8—112no—
347C2×C8—222no—
348C2×C8—222no—
349C2×C8—442no—
350C2×C8—444no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4C2×C22⋊D1111yescharacteristic
358C4⋊C4C2×C22⋊D1111yescharacteristic
359C22⋊C4—21no—
360C22⋊C4—21no—
361C22⋊C4—21no—
362C42—21no—
363C42—21no—
364C42—21no—
365C42D4×D1111yescharacteristic
366C42#434111yescharacteristic
367C42C2×C22⋊D1111yescharacteristic
368C42C23×D1111yescharacteristic
369C11#1927411yescharacteristic, complemented, Sylow
370C23—21no—
371C23—442no—
372C23—882no—
373C23—882no—
374C23—882no—
375C23#6699211yescharacteristic
376Q8—21no—
377Q8—82no—
378Q8—82no—
379Q8C2×#432512yes—
380D4—24no—
381D4—21no—
382D4—444no—
383D4—442no—
384D4—442no—
385D4—882no—
386D4—882no—
387D4—882no—
388D4—882no—
389D4C2×#432512yes—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—82no—
400C2×C4#6699211yescharacteristic
401C2×C4#6699211yescharacteristic
402C2×C4#6699211yescharacteristic
403C2×C4C2×#432512yes—
404C2×C4#6700312yes—
405C2×C4C2×D4×D1111yescharacteristic
406C2×C4C2×#434111yescharacteristic
407C2×C4C22×C22⋊D1111yescharacteristic
408C8—42no—
409C8—222no—
410C8—222no—
411C8—442no—
412C8—442no—
413C22—21no—
414C22—21no—
415C22—22no—
416C22—41no—
417C22—41no—
418C22—882no—
419C22—882no—
420C22—882no—
421C22—1764no—
422C22#1062266112yes—
423C22C2×#6699211yescharacteristic
424C4—21no—
425C4—21no—
426C4—22no—
427C4—41no—
428C4—41no—
429C4—82no—
430C4#1062266112yes—
431C4#1062281212yes—
432C4#1062330812yes—
433C4C22×#432511yescharacteristic
434C4C2×#6700311yescharacteristic
435C2—22no—
436C2—42no—
437C2—1762no—
438C2#1307811211yescharacteristic
439C2C2×#1062266111yescharacteristic
440C2C2×#1062281211yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3079C2
socleC22×C11C2×#121
prime radical#13078096C2
hypercenter#3079D11
hypocenterC11#19274
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. C2×#10622701C2semidirect
3. #41×C11⋊C8C2semidirect
4. #13068034C2semidirect
5. #13068027C2semidirect
6. #13067371C2semidirect
7. #13067297C2semidirect
8. #13067285C2semidirect
9. C11×#3079C2semidirect
14. C11×#477C22semidirect
15. C11×#476C22semidirect
26. Q8×C11⋊C8C22semidirect
30. D4×C11⋊C8C22semidirect
38. #10622184C22semidirect
40. #10622118C22semidirect
151. #3079D11semidirect
209. #477C2×D11semidirect
210. #476C2×D11semidirect
369. C11#19274semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
#130780962
#41×C11⋊C82
#130680342
#130680272
#130673712
#130672972
#130672852
C11×#30792
#1927411