Finite Group Databasebeta

← #14756195

Subgroups — #14756195

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622577C211yesmaximal, characteristic
2C2×#10622838C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic
4C4×#66979C211yesmaximal, characteristic
5#13069254C214yesmaximal, complemented
6#13069247C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic
8#13068310C211yesmaximal, characteristic
9C2×C11×#391C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C11×#391—21no—
18C11×#391—21no—
19C11×#391C2214yes—
20C2×C11×#95—22no—
21#10622838—24no—
22#10622838C418yescomplemented
23C2×#66899C2212yes—
24C2×#66899C2212yes—
25C2×#66899C2214yes—
26C4×C22⋊Dic11—22no—
27#10622577—24no—
28C2×#66872C2212yes—
29C2×#66871C2212yes—
30C4×C4⋊Dic11C2212yes—
31C4×C4⋊Dic11C2212yes—
32#10622545—21no—
33C42×Dic11—21no—
34#10622167C2214yes—
35#10622162C2214yes—
36C22×Q8×C11—21no—
37C22×Q8×C11—22no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11C2×C414yes—
43C22×Q8×C11C2312yes—
44C23×C4×C11—21no—
45C23×C4×C11—21no—
46C23×C4×C11D412yes—
47C23×C4×C11C2311yescharacteristic
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2312yes—
52C2×C42×C11—22no—
53C2×C42×C11—22no—
54C2×C42×C11D411yescharacteristic
55C2×C42×C11D411yescharacteristic
56C2×C42×C11C2312yes—
57C2×C22⋊Dic11—21no—
58C2×C22⋊Dic11—21no—
59#66979—22no—
60#66979—22no—
61#66979C2×C414yes—
62#66979D414yes—
63C2×C4⋊Dic11C2312yes—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4×Dic11—21no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11—22no—
70C2×#4318—22no—
71C2×#4318—22no—
72C2×#4318—22no—
73C2×#4318—22no—
74C2×#4318—22no—
75C2×#4318C2×C414yes—
76C22×C11⋊C8C2312yes—
77C22×C11⋊C8C2312yes—
78C11×#95—24no—
79C11×#95—24no—
80#66899—24no—
81#66899—24no—
82#66899C2×C4116yescomplemented
83C11⋊#95—22no—
84C11⋊#95—22no—
85#66872—24no—
86#66871—24no—
87#21061—111nomaximal, Sylow
88C24×C11C2×D411yescharacteristic
89C2×Q8×C11—24no—
90C2×Q8×C11—22no—
91C2×Q8×C11—28no—
92C2×Q8×C11—28no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×Q8×C11—44no—
100C2×Q8×C11—44no—
101C2×Q8×C11C22×C414yes—
102C22×C4×C11—24no—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—22no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—44no—
111C22×C4×C11—42no—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11#4112yes—
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×C4×C11#4112yes—
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—22no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—42no—
128C42×C11—22no—
129C42×C11—22no—
130C42×C11—22no—
131C42×C11—22no—
132C22⋊Dic11—24no—
133C22⋊Dic11—24no—
134C4⋊Dic11—22no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11C22×C414yes—
138C4⋊Dic11C2×D412yes—
139C4⋊Dic11C2×D412yes—
140C4×Dic11—24no—
141C4×Dic11—24no—
142C4×Dic11—44no—
143C4×Dic11—44no—
144#4318—28no—
145#4318—44no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8C22×C414yes—
152C2×#428—111no—
153C2×#419—111no—
154C2×#419—111no—
155C2×#391D1111yescharacteristic
156C4×#117—111no—
157#1928—114no—
158#1927—114no—
159#1736—111no—
160#1728—111no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11C4×D412yes—
164C23×C11#12112yes—
165C23×C11#12312yes—
166C23×C11C22×D411yescharacteristic
167Q8×C11—24no—
168Q8×C11—24no—
169Q8×C11—42no—
170Q8×C11—42no—
171Q8×C11—48no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—48no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—48no—
182C2×C4×C11—42no—
183C2×C4×C11—44no—
184C2×C4×C11—84no—
185C2×C4×C11#11714yes—
186C2×C4×C11C4×D414yes—
187C2×C4×C11C4×D412yes—
188C2×C4×C11#12112yes—
189C2×C4×C11#12312yes—
190C2×C4×C11#12414yes—
191C2×C4×C11#12614yes—
192C2×C4×C11#13714yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×Dic11—24no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C11⋊C8—24no—
207C11⋊C8—42no—
208C23×Q8C2×D1111yescharacteristic
209C22×M16—111no—
210C22×M16—111no—
211C2×#117—111no—
212C2×#117—111no—
213C22×C4⋊C4C2×D1111yescharacteristic
214C22×C42C2×D1111yescharacteristic
215#428—224no—
216C2×#107—112no—
217C2×#106—112no—
218#419—118no—
219#419—224no—
220C2×#103—114no—
221C2×#103—112no—
222C2×#103—112no—
223#391—21no—
224#391—21no—
225#391C2×D1114yes—
226C4×C4⋊C4—112no—
227C4×C4⋊C4—112no—
228C4×C22⋊C4—222no—
229#376—221no—
230C2×#95—22no—
231C43—221no—
232#340—114no—
233#336—114no—
234C22×C11—24no—
235C22×C11—24no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11#38814yes—
239C22×C11C2×C4×D411yescharacteristic
240C22×C11C2×#12111yescharacteristic
241C22×C11C2×#12311yescharacteristic
242C22×C11C2×#13712yes—
243C22×C11#57512yes—
244C4×C11—24no—
245C4×C11—42no—
246C4×C11—44no—
247C4×C11—82no—
248C4×C11#38814yes—
249C4×C11C2×#11711yescharacteristic
250C4×C11C2×C4×D411yescharacteristic
251C4×C11C2×#12411yescharacteristic
252C4×C11C2×#12611yescharacteristic
253Dic11—44no—
254Dic11—42no—
255Dic11—42no—
256C22×Q8—22no—
257C22×Q8—21no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8C4×D1114yes—
263C22×Q8C22×D1112yes—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4C22⋊D1112yes—
267C23×C4C22×D1111yescharacteristic
268C2×M16—114no—
269C2×M16—222no—
270C2×M16—222no—
271C2×M16—222no—
272C2×M16—222no—
273C2×M16—222no—
274C22×C8—112no—
275C22×C8—112no—
276#117—114no—
277#117—114no—
278#117—222no—
279#117—222no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—112no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4C22×D1112yes—
287C2×C22⋊C4—221no—
288C2×C22⋊C4—221no—
289C2×C42—22no—
290C2×C42—22no—
291C2×C42—221no—
292C2×C42—221no—
293C2×C42—222no—
294C2×C42—222no—
295C2×C42C22⋊D1111yescharacteristic
296C2×C42C22⋊D1111yescharacteristic
297C2×C42C22×D1112yes—
298#107—224no—
299#106—224no—
300#103—1116no—
301#103—224no—
302#103—224no—
303#95—24no—
304#95—24no—
305#95—222no—
306#95—222no—
307C2×C11—24no—
308C2×C11C2×#38811yescharacteristic
309C2×C11C4×#13712yes—
310C2×C11#303911yescharacteristic
311C2×C11#304011yescharacteristic
312C2×C11#309512yes—
313C24C2×C22⋊D1111yescharacteristic
314C2×Q8—24no—
315C2×Q8—22no—
316C2×Q8—28no—
317C2×Q8—28no—
318C2×Q8—22no—
319C2×Q8—22no—
320C2×Q8—22no—
321C2×Q8—22no—
322C2×Q8—44no—
323C2×Q8—44no—
324C2×Q8—42no—
325C2×Q8—42no—
326C2×Q8C2×C4×D1114yes—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—44no—
336C22×C4—42no—
337C22×C4—222no—
338C22×C4—221no—
339C22×C4—221no—
340C22×C4C2×C4×D1112yes—
341C22×C4#433912yes—
342C22×C4D4×D1112yes—
343C22×C4#434112yes—
344C22×C4#434112yes—
345C22×C4#434112yes—
346C22×C4C2×C22⋊D1112yes—
347C22×C4C2×C22⋊D1112yes—
348C22×C4C2×C22⋊D1111yescharacteristic
349C22×C4C23×D1111yescharacteristic
350M16—228no—
351M16—444no—
352C2×C8—114no—
353C2×C8—222no—
354C2×C8—222no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8—222no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—42no—
361C4⋊C4—114no—
362C4⋊C4—112no—
363C4⋊C4—112no—
364C4⋊C4—222no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C22⋊C4—224no—
368C22⋊C4—224no—
369C42—22no—
370C42—22no—
371C42—22no—
372C42—22no—
373C42—224no—
374C42—224no—
375C42—444no—
376C42—444no—
377C11#2106111yescharacteristic, complemented, Sylow
378C23—22no—
379C23—22no—
380C23C4×C22⋊D1112yes—
381C23#6698812yes—
382C23#6699112yes—
383C23C22×C22⋊D1111yescharacteristic
384Q8—24no—
385Q8—24no—
386Q8—42no—
387Q8—42no—
388Q8—48no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—24no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—48no—
396C2×C4—48no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—44no—
401C2×C4—84no—
402C2×C4—224no—
403C2×C4—222no—
404C2×C4—222no—
405C2×C4—442no—
406C2×C4—442no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4#6693014yes—
410C2×C4#6693214yes—
411C2×C4(C22⋊D11)⋊C414yes—
412C2×C4#6693814yes—
413C2×C4C4×C22⋊D1112yes—
414C2×C4#6698812yes—
415C2×C4#6699112yes—
416C2×C4#6699514yes—
417C2×C4C22×C4×D1111yescharacteristic
418C2×C4C2×#433911yescharacteristic
419C2×C4C2×D4×D1111yescharacteristic
420C2×C4C2×#434111yescharacteristic
421C2×C4C2×#434111yescharacteristic
422C2×C4C2×#434111yescharacteristic
423C8—224no—
424C8—442no—
425C22—24no—
426C22—22no—
427C22—22no—
428C22—24no—
429C22#1062255714yes—
430C22C2×C4×C22⋊D1111yescharacteristic
431C22C2×#6698811yescharacteristic
432C22C2×#6699111yescharacteristic
433C22C2×#6699512yes—
434C22#1062335312yes—
435C4—24no—
436C4—42no—
437C4—44no—
438C4—82no—
439C4—442no—
440C4—442no—
441C4—444no—
442C4#1062255714yes—
443C4C2×#6693011yescharacteristic
444C4C2×#6693211yescharacteristic
445C4C2×(C22⋊D11)⋊C411yescharacteristic
446C4C2×#6693811yescharacteristic
447C2—24no—
448C2C2×#1062255711yescharacteristic
449C2C4×#6699512yes—
450C2#1307809911yescharacteristic
451C2#1307810611yescharacteristic
452C2#1307856012yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#391C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#391D11
hypocenterC11#21061
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
5. #13069254C2semidirect
6. #13069247C2semidirect
22. #10622838C4semidirect
82. #66899C2×C4semidirect
377. C11#21061semidirect

Maximal subgroups

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

subgroupindex
C2×#106225772
C2×#106228382
C4×#669792
#130692542
#130692472
#130683352
#130683102
C2×C11×#3912
#2106111