Finite Group Databasebeta

← #14759016

Subgroups — #14759016

Order 2816.

1186 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×C4×#4313C211yesmaximal, characteristic
3#13071021C211yesmaximal, characteristic
4#13069578C211yesmaximal, characteristic, complemented
5#13069418C211yesmaximal, characteristic, complemented
6#13069417C211yesmaximal, characteristic, complemented
7#13069048C214yesmaximal
8#13068445C214yesmaximal, complemented
9C11×#1990C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—21no—
12C2×Q8×Dic11—21no—
13C22×#4313C2212yes—
14#10623259—24no—
15#10623259C418yescomplemented
16C2×#66950C2212yes—
17C2×#66945—21no—
18C2×#66945—21no—
19C2×#66943—21no—
20C2×#66940C2212yes—
21C2×C42×D11C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C11×#384C2211yescharacteristic
25C2×#66880C2214yes—
26C2×#66879C2212yes—
27#10622600—21no—
28#10622600C2212yes—
29#10622590—21no—
30C4⋊C4×Dic11—21no—
31C4⋊C4×Dic11C2212yes—
32C2×#66874C2214yes—
33#10622548C2211yescharacteristic
34C2×C4×C11⋊C8C2211yescharacteristic
35C4×#4313—24no—
36C11×#340C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C22×C4×D11D411yescharacteristic
40C22×C4×D11D411yescharacteristic
41C22×C4×D11C2311yescharacteristic
42C22×Dic22C2312yes—
43C22×C8×C11C2312yes—
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8C2×C414yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C42×C11C2311yescharacteristic
52#66999—28no—
53Q8×Dic11—28no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—22no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11C2312yes—
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11C2311yescharacteristic
68C22×C11⋊C8C2312yes—
69C2×#4313—24no—
70C2×#4313—24no—
71C2×#4313—24no—
72#66950—24no—
73#66950C2×C418yes—
74#66945—28no—
75#66945—44no—
76#66943—28no—
77#66940—24no—
78#66940C2×C418yes—
79C42×D11C2×C414yes—
80C42×D11D414yes—
81#66922—22no—
82#66922C2×C414yes—
83C4×C8×C11—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#66880—28no—
87#66879—24no—
88#66874—28no—
89C4×C11⋊C8—22no—
90#21409—111nomaximal, Sylow
91C23×D11C2×D411yescharacteristic
92C2×Q8×C11—24no—
93C2×Q8×C11—42no—
94C2×Q8×C11—42no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—22no—
101C22×Dic11—22no—
102C22×Dic11C2×D411yescharacteristic
103C22×Dic11C2×D411yescharacteristic
104C22×Dic11C2×D411yescharacteristic
105C2×C4×D11—22no—
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11C22⋊C414yes—
112C2×C4×D11C22⋊C414yes—
113C2×C4×D11C22×C412yes—
114C2×C4×D11C2×D412yes—
115C2×Dic22—22no—
116C2×Dic22—24no—
117C2×Dic22—24no—
118C2×Dic22C22×C414yes—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11#4114yes—
122C11×C4⋊C4—24no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—42no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4C22×C414yes—
128C42×C11C22×C412yes—
129C42×C11C2×D412yes—
130(C2×D11)⋊C4—28no—
131(C2×D11)⋊C4—44no—
132C4⋊Dic11—28no—
133C4⋊Dic11—24no—
134C4⋊Dic11—24no—
135C4⋊Dic11—24no—
136C4⋊Dic11—42no—
137C4⋊Dic11—42no—
138Dic11⋊C4—28no—
139C4×Dic11—28no—
140C4×Dic11—44no—
141C4×Dic11C22⋊C414yes—
142C4×Dic11C22⋊C414yes—
143C4×Dic11C22×C412yes—
144C4×Dic11C2×D412yes—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8#4114yes—
148#4313—216no—
149C2×#533—111no—
150C2×C4×M16—111no—
151#2285—111no—
152#1990—111no—
153#1990D1111yescharacteristic, complemented
154#1956—111no—
155#1956—111no—
156#1894—114no—
157#1763—114no—
158C23×C11C22×D411yescharacteristic
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11C2×C22⋊C412yes—
166Q8×C11—48no—
167C2×C4×C11—24no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11C2×C22⋊C412yes—
174C2×C4×C11C2×C22⋊C412yes—
175C2×C4×C11AGL(1,ℤ/8)12yes—
176C2×C4×C11#13712yes—
177C2×C4×C11#13712yes—
178C2×C4×C11#13712yes—
179C2×C4×C11C23×C411yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C2×#4112yes—
182C2×C4×C11C2×#4112yes—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—24no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11C2×C22⋊C412yes—
196C2×Dic11C2×C22⋊C412yes—
197C2×Dic11C2×C22⋊C412yes—
198C4×D11—24no—
199C4×D11—24no—
200C4×D11—28no—
201C4×D11—28no—
202Dic22—28no—
203Dic22—44no—
204C8×C11—24no—
205C11⋊C8—24no—
206C22×M16—112no—
207#533—118no—
208#533—224no—
209C2×C4⋊Q8—111no—
210C2×C4⋊Q8C2×D1111yescharacteristic
211C2×#125—221no—
212C2×C22⋊Q8—112no—
213C2×C22⋊Q8—221no—
214C2×C4×Q8—112no—
215C2×C4×Q8—221no—
216C2×#117—221no—
217C2×#117—221no—
218C22×C42—111no—
219C2×#103—114no—
220C2×#103—114no—
221C4×M16—224no—
222C2×#97—112no—
223C2×C4×C8—111no—
224C2×C4×C8C2×D1111yescharacteristic
225#384—111no—
226#384C2×D1111yescharacteristic
227#382—221no—
228#380—112no—
229#380—221no—
230C4×C4⋊C4—112no—
231C4×C4⋊C4—221no—
232#340—114no—
233#340C2×D1114yes—
234C22×C11C22×C22⋊C411yescharacteristic
235C22×C11#53211yescharacteristic
236C22×C11#53211yescharacteristic
237C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
238C22×C11C2×#13711yescharacteristic
239C22×C11C2×#13711yescharacteristic
240C22×C11C2×#13711yescharacteristic
241C2×D11—22no—
242C2×D11—22no—
243C2×D11—22no—
244C2×D11—41no—
245C2×D11—41no—
246C2×D11—41no—
247C2×D11—41no—
248C4×C11—44no—
249C4×C11—82no—
250C4×C11#41714yes—
251C4×C11#41914yes—
252C4×C11C4×#4112yes—
253C4×C11#52512yes—
254Dic11—22no—
255Dic11—22no—
256Dic11—22no—
257Dic11—44no—
258Dic11—82no—
259C22×Q8—21no—
260C22×Q8—112no—
261C23×C4—111no—
262C23×C4—111no—
263C23×C4—111no—
264C2×M16—224no—
265C2×M16—224no—
266C2×M16—224no—
267C22×C8—112no—
268C22×C8C22×D1112yes—
269C4⋊Q8—22no—
270C4⋊Q8—114no—
271C4⋊Q8—222no—
272C4⋊Q8C4×D1114yes—
273#125—228no—
274C22⋊Q8—118no—
275C22⋊Q8—224no—
276C22⋊Q8—228no—
277C4×Q8—118no—
278C4×Q8—224no—
279C4×Q8—228no—
280#117—228no—
281#117—444no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—112no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4C22×D1112yes—
293C2×C4⋊C4C22×D1112yes—
294C2×C22⋊C4—222no—
295C2×C22⋊C4—222no—
296C2×C42—111no—
297C2×C42—111no—
298C2×C42—111no—
299C2×C42—114no—
300C2×C42—114no—
301C2×C42—222no—
302C2×C42—222no—
303C2×C42C22×D1111yescharacteristic
304#103—228no—
305#103—228no—
306#97—224no—
307C4×C8—22no—
308C4×C8—222no—
309#95—222no—
310#95—222no—
311C2×C11#229711yescharacteristic
312C2×C11C2×#41911yescharacteristic
313C2×C11C2×#41711yescharacteristic
314C2×C11#318211yescharacteristic
315C2×C11#318211yescharacteristic
316C2×C11#318511yescharacteristic
317C2×C11#318511yescharacteristic
318D11—42no—
319C24—111no—
320C2×Q8—24no—
321C2×Q8—42no—
322C2×Q8—42no—
323C2×Q8—114no—
324C2×Q8—222no—
325C2×Q8—224no—
326C2×Q8—224no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—111no—
330C22×C4—111no—
331C22×C4—111no—
332C22×C4—114no—
333C22×C4—114no—
334C22×C4—112no—
335C22×C4—112no—
336C22×C4—222no—
337C22×C4—222no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4D4×D1111yescharacteristic
345C22×C4D4×D1111yescharacteristic
346C22×C4C23×D1111yescharacteristic
347M16—2216no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—114no—
351C2×C8—222no—
352C2×C8—222no—
353C2×C8#434314yes—
354C4⋊C4—24no—
355C4⋊C4—22no—
356C4⋊C4—24no—
357C4⋊C4—42no—
358C4⋊C4—42no—
359C4⋊C4—228no—
360C4⋊C4—228no—
361C4⋊C4—224no—
362C4⋊C4—224no—
363C4⋊C4—224no—
364C4⋊C4—442no—
365C4⋊C4—442no—
366C4⋊C4C2×C4×D1114yes—
367C22⋊C4—228no—
368C22⋊C4—444no—
369C42—114no—
370C42—114no—
371C42—112no—
372C42—112no—
373C42—228no—
374C42—444no—
375C42C2×C4×D1112yes—
376C42D4×D1112yes—
377C11#2140911yescharacteristic, complemented, Sylow
378C23—112no—
379C23—221no—
380C23—221no—
381C23—221no—
382C23—221no—
383C23—221no—
384C23—221no—
385C23C2×D4×D1111yescharacteristic
386Q8—48no—
387Q8—228no—
388Q8—444no—
389C2×C4—24no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—112no—
396C2×C4—112no—
397C2×C4—112no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—221no—
401C2×C4—221no—
402C2×C4—221no—
403C2×C4—221no—
404C2×C4—224no—
405C2×C4—228no—
406C2×C4—224no—
407C2×C4—228no—
408C2×C4—224no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4C22⋊C4×D1112yes—
415C2×C4C22⋊C4×D1112yes—
416C2×C4#6696412yes—
417C2×C4#6696812yes—
418C2×C4#6696812yes—
419C2×C4#6697112yes—
420C2×C4C22×C4×D1111yescharacteristic
421C2×C4C2×D4×D1111yescharacteristic
422C2×C4C2×#434312yes—
423C2×C4#41×D1112yes—
424C8—24no—
425C8—224no—
426C22—222no—
427C22—222no—
428C22—222no—
429C22—441no—
430C22—441no—
431C22—441no—
432C22—441no—
433C22C2×C22⋊C4×D1111yescharacteristic
434C22#1062319911yescharacteristic
435C22#1062325611yescharacteristic
436C22C2×#6696411yescharacteristic
437C22C2×#6696811yescharacteristic
438C22C2×#6696811yescharacteristic
439C22C2×#6697111yescharacteristic
440C4—44no—
441C4—82no—
442C4—222no—
443C4—222no—
444C4—222no—
445C4—444no—
446C4—882no—
447C4#1062238414yes—
448C4#1062241514yes—
449C4C4×#434312yes—
450C4#1062315812yes—
451C2—442no—
452C2#1307110511yescharacteristic
453C2C2×#1062241511yescharacteristic
454C2C2×#1062238411yescharacteristic
455C2#1307933311yescharacteristic
456C2#1307933611yescharacteristic
457C2#1307936011yescharacteristic
458C2#1307936211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1990D11
hypocenterC11#21409
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. #13069578C2semidirect
5. #13069418C2semidirect
6. #13069417C2semidirect
8. #13068445C2semidirect
9. C11×#1990C2semidirect
15. #10623259C4semidirect
153. #1990D11semidirect
377. C11#21409semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×C4×#43132
#130710212
#130695782
#130694182
#130694172
#130690482
#130684452
C11×#19902
#2140911