Finite Group Databasebeta

← #14722972

Subgroups — #14722972

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077248C211yesmaximal, characteristic
2#13077244C211yesmaximal, characteristic
3#13077244C211yesmaximal, characteristic
4#13067407C211yesmaximal, characteristic, complemented
5#13067405C211yesmaximal, characteristic, complemented
6#13067404C211yesmaximal, characteristic, complemented
7#13067395C212yesmaximal, complemented
8#13067393C212yesmaximal, complemented
9#13067382C212yesmaximal, complemented
10#13067380C212yesmaximal, complemented
11C11×#1574C211yesmaximal, characteristic, complemented
12C2×C42×D11C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16#10622739—21no—
17M16×Dic11—21no—
18#10622538C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21#10622450C412yes—
22#10622450C2211yescharacteristic
23#10622450C2211yescharacteristic
24#10622448—21no—
25#10622448C412yes—
26#10622448C2212yes—
27#10622448C2211yescharacteristic
28#10622448C2211yescharacteristic
29#10622446—21no—
30#10622446C2212yes—
31#10622339—21no—
32#10622339C412yes—
33#10622332—21no—
34#10622332C412yes—
35C4×#4313—21no—
36C4×#4313C2212yes—
37#10622298—21no—
38#10622298C2212yes—
39C11×#335C2212yescomplemented
40C11×#334C2212yescomplemented
41#10622118C2212yescomplemented
42#10622118C2212yescomplemented
43#10622117C2212yescomplemented
44#10622117C2212yescomplemented
45#10622096C2212yescomplemented
46#10622095C2212yescomplemented
47C22×C4×D11C2×C411yescharacteristic
48C22×C4×D11D411yescharacteristic
49C22×C4×D11Q811yescharacteristic
50C2×C11×M16—21no—
51C2×C42×C11C2311yescharacteristic
52C2×C4×Dic11C2×C411yescharacteristic
53C2×C4×Dic11D411yescharacteristic
54C2×C4×Dic11Q811yescharacteristic
55C2×#4318—21no—
56C2×#4313—21no—
57C2×#4313—21no—
58C2×#4313C2×C414yes—
59C42×D11C2×C411yescharacteristic
60C42×D11C2×C411yescharacteristic
61C42×D11D411yescharacteristic
62C42×D11D411yescharacteristic
63C42×D11Q811yescharacteristic
64C42×D11Q811yescharacteristic
65C42×D11C2311yescharacteristic
66C42×D11C2311yescharacteristic
67C11×C4⋊C8—21no—
68C11×C4⋊C8C2×C412yes—
69C11×C4⋊C8C2311yescharacteristic
70C11×C4⋊C8C2312yes—
71C11×C4⋊C8C2311yescharacteristic
72C11×C22⋊C8—21no—
73C11×C22⋊C8C2×C412yes—
74C4×C8×C11—21no—
75C4×C8×C11C2312yes—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)C2×C412yes—
78(C2×D11)⋊C8—22no—
79(C2×D11)⋊C8—22no—
80(C2×D11)⋊C8—21no—
81(C2×D11)⋊C8—21no—
82(C2×D11)⋊C8C2×C414yes—
83#66879—22no—
84#66879—21no—
85#66879—21no—
86#66879C2×C414yes—
87Dic11⋊C8—21no—
88Dic11⋊C8—21no—
89Dic11⋊C8C2×C414yes—
90C8×Dic11—22no—
91C4⋊(C11⋊C8)—21no—
92C4⋊(C11⋊C8)C2×C412yes—
93C4⋊(C11⋊C8)C2312yes—
94C4⋊(C11⋊C8)C2311yescharacteristic
95C4⋊(C11⋊C8)C2311yescharacteristic
96C4×C11⋊C8—21no—
97C4×C11⋊C8C2312yes—
98#17823—111nomaximal, Sylow
99C23×D11C4⋊C411yescharacteristic
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×Q811yescharacteristic
103C22×Dic11C4⋊C411yescharacteristic
104C22×Dic11C4⋊C411yescharacteristic
105C22×Dic11C4⋊C411yescharacteristic
106C2×C4×D11—42no—
107C2×C4×D11—41no—
108C2×C4×D11—41no—
109C2×C4×D11—42no—
110C2×C4×D11C4⋊C411yescharacteristic
111C2×C4×D11C4⋊C411yescharacteristic
112C2×C4×D11C4⋊C411yescharacteristic
113C2×C4×D11C4⋊C411yescharacteristic
114C2×C4×D11C4⋊C411yescharacteristic
115C2×C4×D11C4⋊C411yescharacteristic
116C2×C4×D11C22×C411yescharacteristic
117C2×C4×D11C22×C411yescharacteristic
118C2×C4×D11C2×D411yescharacteristic
119C2×C4×D11C2×D411yescharacteristic
120C2×C4×D11C2×Q811yescharacteristic
121C2×C4×D11C2×Q811yescharacteristic
122C11×M16—42no—
123C2×C8×C11—22no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11C22×C414yes—
127C42×C11C22×C411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11C2×Q811yescharacteristic
130C42×C11C2411yescharacteristic
131C4×Dic11C4⋊C411yescharacteristic
132C4×Dic11C4⋊C411yescharacteristic
133C4×Dic11C4⋊C411yescharacteristic
134C4×Dic11C4⋊C411yescharacteristic
135C4×Dic11C4⋊C411yescharacteristic
136C4×Dic11C4⋊C411yescharacteristic
137C4×Dic11C22×C411yescharacteristic
138C4×Dic11C22×C411yescharacteristic
139C4×Dic11C2×D411yescharacteristic
140C4×Dic11C2×D411yescharacteristic
141C4×Dic11C2×Q811yescharacteristic
142C4×Dic11C2×Q811yescharacteristic
143#4318—42no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8C22×C414yes—
148#4313—44no—
149#4313—42no—
150#4313—42no—
151#2920—111no—
152#2920—111no—
153#2920—111no—
154#1574—111no—
155#1574—111no—
156#1574—111no—
157#1574D1111yescharacteristic, complemented
158#1572—112no—
159#1572—112no—
160#1569—112no—
161#1569—112no—
162C23×C11C2×C4⋊C411yescharacteristic
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11C2×C4⋊C411yescharacteristic
167C22×D11C2×C4⋊C411yescharacteristic
168C2×C4×C11—22no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—22no—
172C2×C4×C11C2×C4⋊C411yescharacteristic
173C2×C4×C11C2×C4⋊C411yescharacteristic
174C2×C4×C11C2×C4⋊C411yescharacteristic
175C2×C4×C11C23×C411yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×Q811yescharacteristic
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11C2×C4⋊C411yescharacteristic
182C2×Dic11C2×C4⋊C411yescharacteristic
183C2×Dic11C2×C4⋊C411yescharacteristic
184C2×Dic11C2×C4⋊C411yescharacteristic
185C2×Dic11C2×C4⋊C411yescharacteristic
186C2×Dic11C2×C4⋊C411yescharacteristic
187C4×D11—22no—
188C4×D11—22no—
189C4×D11—21no—
190C4×D11—21no—
191C4×D11—21no—
192C4×D11—21no—
193C4×D11—22no—
194C4×D11—22no—
195C4×D11—41no—
196C4×D11—41no—
197C4×D11—41no—
198C4×D11—41no—
199C4×D11—41no—
200C4×D11—41no—
201C8×C11—24no—
202C8×C11—41no—
203C8×C11—41no—
204C8×C11—42no—
205C11⋊C8—24no—
206C11⋊C8—41no—
207C11⋊C8—41no—
208C11⋊C8—42no—
209C22×C42—111no—
210#432—112no—
211#432—112no—
212#432—112no—
213#432—111no—
214#432—111no—
215#432—221no—
216#432—221no—
217#431—111no—
218#431—112no—
219#431—111no—
220#431—112no—
221#431—221no—
222#431—221no—
223#431C2×D1111yescharacteristic
224#431C2×D1111yescharacteristic
225#423—112no—
226#423—111no—
227#423—111no—
228#423—111no—
229#423C2×D1111yescharacteristic
230#407—112no—
231#407—221no—
232#407—221no—
233C4×M16—112no—
234C4×M16—221no—
235C4×M16—221no—
236#335—112no—
237#335—112no—
238#335—112no—
239#335C2×D1112yescomplemented
240#334—112no—
241#334—112no—
242#334—112no—
243#334C2×D1112yescomplemented
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11C22×C4⋊C411yescharacteristic
248C2×D11—21no—
249C2×D11—21no—
250C2×D11—21no—
251C2×D11—21no—
252C2×D11—21no—
253C2×D11—21no—
254C2×D11—44no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11#43012yes—
259C4×C11#56812yes—
260C4×C11#57511yescharacteristic
261C4×C11#57511yescharacteristic
262Dic11—21no—
263Dic11—21no—
264Dic11—21no—
265Dic11—21no—
266Dic11—21no—
267Dic11—21no—
268C23×C4—111no—
269C23×C4—111no—
270C23×C4—111no—
271C2×M16—21no—
272C2×M16—114no—
273C2×M16—221no—
274C2×M16—221no—
275C2×M16—221no—
276C2×C42—111no—
277C2×C42—111no—
278C2×C42—111no—
279C2×C42—111no—
280C2×C42—111no—
281C2×C42—111no—
282C2×C42—111no—
283C2×C42—111no—
284C2×C42—111no—
285C2×C42—111no—
286C2×C42—111no—
287C2×C42C22×D1111yescharacteristic
288C4⋊C8—21no—
289C4⋊C8—114no—
290C4⋊C8—112no—
291C4⋊C8—112no—
292C4⋊C8—111no—
293C4⋊C8—111no—
294C4⋊C8—221no—
295C4⋊C8—221no—
296C4⋊C8—221no—
297C4⋊C8C4×D1112yes—
298C4⋊C8C22×D1111yescharacteristic
299C4⋊C8C22×D1112yes—
300C4⋊C8C22×D1111yescharacteristic
301C22⋊C8—21no—
302C22⋊C8—112no—
303C22⋊C8—114no—
304C22⋊C8—222no—
305C22⋊C8—221no—
306C22⋊C8—221no—
307C22⋊C8—222no—
308C22⋊C8—221no—
309C22⋊C8C4×D1112yes—
310#97—114no—
311#97—221no—
312#97—221no—
313#97—222no—
314C4×C8—21no—
315C4×C8—112no—
316C4×C8—222no—
317C4×C8—221no—
318C4×C8C22×D1112yes—
319C2×C11—41no—
320C2×C11#290511yescharacteristic
321C2×C11#291111yescharacteristic
322C2×C11C2×#43011yescharacteristic
323D11—41no—
324D11—41no—
325C24—111no—
326C22×C4—111no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—111no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—111no—
334C22×C4—111no—
335C22×C4—111no—
336C22×C4—111no—
337C22×C4—111no—
338C22×C4—111no—
339C22×C4—111no—
340C22×C4—111no—
341C22×C4—442no—
342C22×C4—442no—
343C22×C4—441no—
344C22×C4—441no—
345C22×C4C2×C4×D1111yescharacteristic
346C22×C4D4×D1111yescharacteristic
347C22×C4Q8×D1111yescharacteristic
348M16—42no—
349M16—444no—
350M16—442no—
351M16—442no—
352M16—442no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—22no—
356C2×C8—114no—
357C2×C8—221no—
358C2×C8—222no—
359C2×C8—221no—
360C2×C8C2×C4×D1114yes—
361C42—111no—
362C42—111no—
363C42—111no—
364C42—111no—
365C42—111no—
366C42—111no—
367C42—111no—
368C42—111no—
369C42—111no—
370C42—111no—
371C42—111no—
372C42—111no—
373C42C2×C4×D1111yescharacteristic
374C42D4×D1111yescharacteristic
375C42Q8×D1111yescharacteristic
376C42C23×D1111yescharacteristic
377C11#1782311yescharacteristic, complemented, Sylow
378C23—111no—
379C23—111no—
380C23—441no—
381C23—441no—
382C23—441no—
383C23C4⋊C4×D1111yescharacteristic
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—111no—
389C2×C4—111no—
390C2×C4—111no—
391C2×C4—111no—
392C2×C4—111no—
393C2×C4—111no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—221no—
401C2×C4—221no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4C4⋊C4×D1111yescharacteristic
412C2×C4C4⋊C4×D1111yescharacteristic
413C2×C4C4⋊C4×D1111yescharacteristic
414C2×C4C22×C4×D1111yescharacteristic
415C2×C4C2×D4×D1111yescharacteristic
416C2×C4C2×Q8×D1111yescharacteristic
417C8—24no—
418C8—42no—
419C8—41no—
420C8—41no—
421C8—224no—
422C8—441no—
423C8—441no—
424C8—442no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—221no—
429C22—221no—
430C22—221no—
431C22—221no—
432C22—221no—
433C22—221no—
434C22—444no—
435C22C2×C4⋊C4×D1111yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—221no—
440C4—221no—
441C4—221no—
442C4—221no—
443C4—221no—
444C4—221no—
445C4#1062250612yes—
446C4#1062328112yes—
447C4#1062330411yescharacteristic
448C4#1062330811yescharacteristic
449C2—41no—
450C2—441no—
451C2—441no—
452C2#1307717711yescharacteristic
453C2#1307720311yescharacteristic
454C2C2×#1062250611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1574C2
socleC22×C11C22×C4⋊C4
prime radicalC23×D11C4⋊C4
cosocleC42×C11C24
hypercenter#1574D11
hypocenterC11#17823
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
4. #13067407C2semidirect
5. #13067405C2semidirect
6. #13067404C2semidirect
7. #13067395C2semidirect
8. #13067393C2semidirect
9. #13067382C2semidirect
10. #13067380C2semidirect
11. C11×#1574C2semidirect
39. C11×#335C22semidirect
40. C11×#334C22semidirect
41. #10622118C22semidirect
42. #10622118C22semidirect
43. #10622117C22semidirect
44. #10622117C22semidirect
45. #10622096C22semidirect
46. #10622095C22semidirect
157. #1574D11semidirect
239. #335C2×D11semidirect
243. #334C2×D11semidirect
377. C11#17823semidirect

Maximal subgroups

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

subgroupindex
#130772482
#130772442
#130674072
#130674052
#130674042
#130673952
#130673932
#130673822
#130673802
C11×#15742
#1782311