Finite Group Databasebeta

← #14758288

Subgroups — #14758288

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×D11×C4⋊C8C211yesmaximal, characteristic
3C4×#66945C211yesmaximal, characteristic
4#13069572C214yesmaximal, complemented
5#13069569C211yesmaximal, characteristic, complemented
6#13069564C211yesmaximal, characteristic, complemented
7#13069563C211yesmaximal, characteristic, complemented
8#13068331C214yesmaximal
9C11×#1988C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—21no—
12C2×Q8×Dic11—21no—
13C22×C8×D11C2212yes—
14#10623259—24no—
15#10623259C418yescomplemented
16C2×#66950—21no—
17C2×#66945C2212yes—
18C2×#66945C2212yes—
19C2×#66943C2212yes—
20C2×#66940—21no—
21C2×C42×D11C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×Dic11⋊C8C2212yes—
26C4⋊C4×Dic11C2212yes—
27C4×(C2×D11)⋊C4—21no—
28C4×C4⋊Dic11C2211yescharacteristic
29C42×Dic11—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31D11×C4⋊C8—24no—
32#10622279—21no—
33#10622261—21no—
34C11×#340C2214yes—
35#10622189C2214yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C22×C4×D11D411yescharacteristic
40C22×C4×D11D411yescharacteristic
41C22×C4×D11C2311yescharacteristic
42C22×Dic22—21no—
43C22×C8×C11C2312yes—
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8C2×C414yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51#66999—28no—
52Q8×Dic11—28no—
53C2×(C2×D11)⋊C4—22no—
54C2×(C2×D11)⋊C4—22no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11C2312yes—
58C2×C4⋊Dic11C2312yes—
59C2×Dic11⋊C4—22no—
60C2×C4×Dic11—22no—
61C2×C4×Dic11—22no—
62C2×C4×Dic11—21no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11D411yescharacteristic
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11C2311yescharacteristic
67C22×C11⋊C8C2312yes—
68C2×C8×D11—24no—
69C2×C8×D11—28no—
70#66950—28no—
71#66945—24no—
72#66945—24no—
73#66945C2×C418yes—
74#66945Q818yescomplemented
75#66943—24no—
76#66943C2×C418yes—
77#66940—28no—
78C42×D11C2×C414yes—
79C42×D11D414yes—
80#66922—22no—
81#66922C2×C414yes—
82C11×C4⋊C8—22no—
83C11×#95—21no—
84C11⋊#95—21no—
85C11⋊#95—22no—
86Dic11⋊C8—24no—
87C4⋊(C11⋊C8)—22no—
88#21311—111nomaximal, Sylow
89C23×D11C2×D411yescharacteristic
90C2×Q8×C11—24no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—22no—
99C22×Dic11—22no—
100C22×Dic11C2×D411yescharacteristic
101C22×Dic11C2×D411yescharacteristic
102C22×Dic11C2×D411yescharacteristic
103C2×C4×D11—22no—
104C2×C4×D11—22no—
105C2×C4×D11—42no—
106C2×C4×D11C22⋊C414yes—
107C2×C4×D11C22⋊C414yes—
108C2×C4×D11C22×C412yes—
109C2×C4×D11C2×D412yes—
110C2×C4×D11C2×Q814yes—
111C2×C4×D11#4114yes—
112C2×Dic22—24no—
113C2×Dic22—44no—
114C2×C8×C11—22no—
115C2×C8×C11—24no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4C22×C414yes—
120C11×C4⋊C4C2×Q814yes—
121C42×C11—42no—
122C42×C11C22×C412yes—
123C42×C11C2×D412yes—
124(C2×D11)⋊C4—28no—
125(C2×D11)⋊C4—28no—
126C4⋊Dic11—28no—
127C4⋊Dic11—24no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11C22×C414yes—
131C4⋊Dic11C2×Q814yes—
132Dic11⋊C4—28no—
133C4×Dic11—28no—
134C4×Dic11—28no—
135C4×Dic11—44no—
136C4×Dic11—42no—
137C4×Dic11C22⋊C414yes—
138C4×Dic11C22⋊C414yes—
139C4×Dic11C22×C412yes—
140C4×Dic11C2×D412yes—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—24no—
143C8×D11—48no—
144C2×#533—111no—
145C22×C4⋊C8—111no—
146C4×#117—111no—
147#1989—114no—
148#1988—111no—
149#1988D1111yescharacteristic, complemented
150#1987—111no—
151#1987—111no—
152#1735—114no—
153C23×C11C22×D411yescharacteristic
154C22×D11—21no—
155C22×D11—21no—
156C22×D11—22no—
157C22×D11C2×C22⋊C412yes—
158C22×D11C22⋊Q814yes—
159Q8×C11—48no—
160C2×C4×C11—22no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11C2×C22⋊C412yes—
168C2×C4×C11C2×C22⋊C412yes—
169C2×C4×C11#13512yes—
170C2×C4×C11#13512yes—
171C2×C4×C11C23×C411yescharacteristic
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C22×Q812yes—
174C2×C4×C11C2×#4112yes—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—22no—
178C2×Dic11—24no—
179C2×Dic11—24no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—44no—
183C2×Dic11C2×C22⋊C412yes—
184C2×Dic11C2×C22⋊C412yes—
185C2×Dic11C2×C22⋊C412yes—
186C2×Dic11C22⋊Q814yes—
187C4×D11—28no—
188C4×D11—44no—
189C4×D11C4×Q818yes—
190C4×D11#12414yes—
191C4×D11C4⋊Q814yes—
192Dic22—48no—
193C8×C11—42no—
194C11⋊C8—42no—
195C23×C8—112no—
196#533—118no—
197#533—224no—
198C2×C4⋊Q8—111no—
199C2×C4⋊Q8C2×D1111yescharacteristic
200C2×#125—112no—
201C2×C22⋊Q8—221no—
202C2×C22⋊Q8—221no—
203C2×C4×Q8—221no—
204C2×C4×Q8—221no—
205C2×#117—112no—
206C2×#117—112no—
207C22×C42—111no—
208C2×C4⋊C8—112no—
209C2×C4⋊C8—111no—
210C2×C4⋊C8—224no—
211C2×C4⋊C8C2×D1111yescharacteristic
212C4×C4⋊C4—112no—
213C4×C4⋊C4—111no—
214C4×C4⋊C4C2×D1111yescharacteristic
215C4×C22⋊C4—221no—
216C4×C22⋊C4—221no—
217#376—221no—
218C43—221no—
219#340—114no—
220#340—114no—
221#340—114no—
222#340C2×D1114yes—
223C22×C11C22×C22⋊C411yescharacteristic
224C22×C11C2×C22⋊Q812yes—
225C22×C11C2×#13511yescharacteristic
226C22×C11C2×#13511yescharacteristic
227C22×C11#57512yes—
228C2×D11—24no—
229C2×D11—24no—
230C2×D11—22no—
231C2×D11—22no—
232C2×D11#39114yes—
233C4×C11—22no—
234C4×C11—44no—
235C4×C11—44no—
236C4×C11#41614yes—
237C4×C11C2×C4×Q812yes—
238C4×C11C2×#12411yescharacteristic
239C4×C11C2×C4⋊Q811yescharacteristic
240Dic11—22no—
241Dic11—22no—
242Dic11—44no—
243Dic11—44no—
244Dic11#39114yes—
245C22×Q8—21no—
246C22×Q8—221no—
247C23×C4—111no—
248C23×C4—111no—
249C23×C4—111no—
250C22×C8—112no—
251C22×C8—228no—
252C22×C8—224no—
253C22×C8C22×D1112yes—
254C4⋊Q8—22no—
255C4⋊Q8—114no—
256C4⋊Q8—222no—
257C4⋊Q8C4×D1114yes—
258#125—118no—
259#125—224no—
260C22⋊Q8—228no—
261C22⋊Q8—228no—
262C4×Q8—228no—
263C4×Q8—228no—
264#117—118no—
265#117—118no—
266#117—224no—
267#117—224no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—112no—
270C2×C4⋊C4—112no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4—222no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4C22×D1112yes—
275C2×C4⋊C4C22×D1112yes—
276C2×C22⋊C4—222no—
277C2×C22⋊C4—222no—
278C2×C42—21no—
279C2×C42—111no—
280C2×C42—111no—
281C2×C42—111no—
282C2×C42—114no—
283C2×C42—114no—
284C2×C42—222no—
285C2×C42—222no—
286C2×C42—222no—
287C2×C42—221no—
288C2×C42C22×D1111yescharacteristic
289C4⋊C8—22no—
290C4⋊C8—224no—
291C4⋊C8—222no—
292#95—21no—
293#95—222no—
294#95—221no—
295C2×C11C2×#39111yescharacteristic
296C2×C11C2×#41611yescharacteristic
297C2×C11#289611yescharacteristic
298C2×C11#307612yes—
299C2×C11#307612yes—
300D11—24no—
301C24—111no—
302C2×Q8—24no—
303C2×Q8—42no—
304C2×Q8—42no—
305C2×Q8—224no—
306C2×Q8—444no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—111no—
310C22×C4—112no—
311C22×C4—112no—
312C22×C4—114no—
313C22×C4—114no—
314C22×C4—111no—
315C22×C4—111no—
316C22×C4—114no—
317C22×C4—114no—
318C22×C4—222no—
319C22×C4—222no—
320C22×C4—222no—
321C22×C4—222no—
322C22×C4—442no—
323C22×C4D4×D1111yescharacteristic
324C22×C4D4×D1111yescharacteristic
325C22×C4C23×D1111yescharacteristic
326C2×C8—22no—
327C2×C8—24no—
328C2×C8—222no—
329C2×C8—224no—
330C2×C8—448no—
331C4⋊C4—24no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—114no—
335C4⋊C4—114no—
336C4⋊C4—228no—
337C4⋊C4—228no—
338C4⋊C4—224no—
339C4⋊C4—222no—
340C4⋊C4—222no—
341C4⋊C4C2×C4×D1114yes—
342C4⋊C4Q8×D1114yes—
343C22⋊C4—228no—
344C22⋊C4—228no—
345C42—42no—
346C42—114no—
347C42—114no—
348C42—112no—
349C42—112no—
350C42—228no—
351C42—228no—
352C42—444no—
353C42—442no—
354C42C2×C4×D1112yes—
355C42D4×D1112yes—
356C11#2131111yescharacteristic, complemented, Sylow
357C23—112no—
358C23—114no—
359C23—221no—
360C23—221no—
361C23—222no—
362C23C2×D4×D1111yescharacteristic
363Q8—48no—
364Q8—448no—
365C2×C4—22no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—112no—
373C2×C4—114no—
374C2×C4—114no—
375C2×C4—118no—
376C2×C4—114no—
377C2×C4—112no—
378C2×C4—112no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—222no—
382C2×C4—228no—
383C2×C4—224no—
384C2×C4—224no—
385C2×C4—444no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—444no—
389C2×C4C22⋊C4×D1112yes—
390C2×C4C22⋊C4×D1112yes—
391C2×C4#6696512yes—
392C2×C4#6696912yes—
393C2×C4C22×C4×D1111yescharacteristic
394C2×C4C2×D4×D1111yescharacteristic
395C2×C4C2×Q8×D1112yes—
396C2×C4#41×D1112yes—
397C8—42no—
398C8—442no—
399C22—114no—
400C22—222no—
401C22—224no—
402C22—224no—
403C22—222no—
404C22C2×C22⋊C4×D1111yescharacteristic
405C22D11×C22⋊Q812yes—
406C22C2×#6696511yescharacteristic
407C22C2×#6696911yescharacteristic
408C22#1062330812yes—
409C4—22no—
410C4—44no—
411C4—44no—
412C4—114no—
413C4—222no—
414C4—222no—
415C4—444no—
416C4—444no—
417C4#1062238514yes—
418C4C4×Q8×D1112yes—
419C4D11×#12411yescharacteristic
420C4D11×C4⋊Q811yescharacteristic
421C2—224no—
422C2D11×#39111yescharacteristic
423C2C2×#1062238511yescharacteristic
424C2#1307713411yescharacteristic
425C2#1307839712yes—
426C2#1307839912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1988C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1988D11
hypocenterC11#21311
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
4. #13069572C2semidirect
5. #13069569C2semidirect
6. #13069564C2semidirect
7. #13069563C2semidirect
9. C11×#1988C2semidirect
15. #10623259C4semidirect
74. #66945Q8semidirect
149. #1988D11semidirect
356. C11#21311semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×D11×C4⋊C82
C4×#669452
#130695722
#130695692
#130695642
#130695632
#130683312
C11×#19882
#2131111