Finite Group Databasebeta

← #14668744

Subgroups — #14668744

Order 2816.

1026 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#99C212yesmaximal
2#13071195C211yesmaximal, characteristic
3#13066741C211yesmaximal, characteristic, complemented
4#13066740C212yesmaximal, complemented
5C11×#1393C211yesmaximal, characteristic, complemented
6C22×D4×D11C2211yescharacteristic
7C2×#66945C411yescharacteristic, complemented
8C2×C22⋊C4×D11—22no—
9C2×#66925C411yescharacteristic, complemented
10C2×C11×#99C2212yes—
11C11×#390C2211yescharacteristic
12#10622834C2211yescharacteristic
13C2×#66898C2212yes—
14#10622601C411yescharacteristic, complemented
15#10622570—22no—
16#10622568—22no—
17C2×#66870—22no—
18#10622552C411yescharacteristic, complemented
19D11×#99—24no—
20D11×#99C418yescomplemented
21C24×D11D412yes—
22C22×D4×C11C2311yescharacteristic
23C22×C22⋊D11D412yes—
24C2×D4×D11—42no—
25C2×D4×D11—42no—
26C2×D4×D11C2×C414yes—
27C2×D4×D11D412yes—
28C2×D4×D11Q812yes—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11—42no—
31C22×C4×D11C2×C411yescharacteristic
32C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4—22no—
35C2×C42×C11C2×C411yescharacteristic, complemented
36C2×C22⋊Dic11—22no—
37C2×C22⋊Dic11—22no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—22no—
41C2×(C2×D11)⋊C4—22no—
42C2×(C2×D11)⋊C4—42no—
43C2×C4⋊Dic11C2×C411yescharacteristic, complemented
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C2×C4×Dic11C2×C411yescharacteristic, complemented
47#66945—42no—
48C22⋊C4×D11—28no—
49C22⋊C4×D11—44no—
50#66925—42no—
51C11×#99—22no—
52C11×#99C2×C414yescomplemented
53#66898—22no—
54#66898C2×C414yescomplemented
55#66870—28no—
56#12582—111nomaximal, Sylow
57C24×C11C2×D412yes—
58C23×D11—22no—
59C23×D11—24no—
60C23×D11—22no—
61C23×D11—82no—
62C23×D11—82no—
63C23×D11C22⋊C412yes—
64C23×D11C22⋊C414yes—
65C23×D11C22⋊C411yescharacteristic
66C23×D11C4⋊C414yes—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11C22×C412yes—
70C2×D4×C11C2×D411yescharacteristic
71C2×D4×C11C2×Q811yescharacteristic
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—42no—
75C22×C4×C11C22×C411yescharacteristic
76C2×C22⋊D11—42no—
77C2×C22⋊D11—42no—
78C2×C22⋊D11C22⋊C414yes—
79C2×C22⋊D11C4⋊C414yes—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—42no—
83C22×Dic11C22⋊C411yescharacteristic
84D4×D11—44no—
85D4×D11—44no—
86D4×D11—44no—
87D4×D11—44no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44C4212yes—
91C2×D44C4⋊C412yes—
92C2×C4×D11—22no—
93C2×C4×D11—22no—
94C2×C4×D11—48no—
95C2×C4×D11—84no—
96C2×C4×D11—84no—
97C2×C4×D11C4212yes—
98C2×C4×D11C4⋊C412yes—
99C11×C4⋊C4—41no—
100C11×C22⋊C4—24no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—82no—
103C42×C11—41no—
104C22⋊Dic11—24no—
105C22⋊Dic11—42no—
106C22⋊Dic11—82no—
107(C2×D11)⋊C4—48no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—82no—
111(C2×D11)⋊C4—82no—
112C4⋊Dic11—41no—
113Dic11⋊C4—42no—
114C4×Dic11—41no—
115C4×Dic11—42no—
116C22×#99—112no—
117#2309—111no—
118#1393—112no—
119#1393—111no—
120#1393D1111yescharacteristic, complemented
121C23×C11—22no—
122C23×C11—22no—
123C23×C11—42no—
124C23×C11—42no—
125C23×C11C2×C22⋊C412yes—
126C23×C11C2×C22⋊C411yescharacteristic
127C23×C11C2×C4⋊C412yes—
128C22×D11—22no—
129C22×D11—22no—
130C22×D11—24no—
131C22×D11—24no—
132C22×D11—24no—
133C22×D11—24no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—44no—
137C22×D11—44no—
138C22×D11—42no—
139C22×D11—42no—
140C22×D11—82no—
141C22×D11—82no—
142C22×D11—84no—
143C22×D11—84no—
144C22×D11—88no—
145C22×D11#9514yes—
146C22×D11#9512yes—
147C22×D11#9912yes—
148C22×D11#9912yes—
149D4×C11—42no—
150D4×C11—41no—
151D4×C11—41no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—44no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—82no—
161C2×C4×C11—82no—
162C2×C4×C11C2×C4211yescharacteristic
163C2×C4×C11C2×C4⋊C411yescharacteristic
164C22⋊D11—44no—
165C22⋊D11—44no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—44no—
169C2×Dic11—41no—
170C2×Dic11—42no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—82no—
175C2×Dic11—82no—
176C2×Dic11#9512yes—
177D44—42no—
178D44—42no—
179C4×D11—24no—
180C4×D11—24no—
181C4×D11—816no—
182C23×D4—111no—
183C2×#117—111no—
184C2×#117—111no—
185C22×C22⋊C4—222no—
186C2×#99—112no—
187C2×#99—118no—
188C2×#99—224no—
189C2×#99—222no—
190C2×#99C2×D1112yes—
191#390—111no—
192#390—111no—
193#390—111no—
194#390—222no—
195#390C2×D1111yescharacteristic
196#379—222no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11—42no—
204C22×C11—42no—
205C22×C11—82no—
206C22×C11C2×#9511yescharacteristic
207C22×C11C2×#9911yescharacteristic
208C22×C11C2×#9911yescharacteristic
209C2×D11—22no—
210C2×D11—22no—
211C2×D11—24no—
212C2×D11—42no—
213C2×D11—42no—
214C2×D11—48no—
215C2×D11—48no—
216C2×D11—42no—
217C2×D11—42no—
218C2×D11—44no—
219C2×D11—84no—
220C2×D11—84no—
221C2×D11—82no—
222C2×D11#34214yes—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—81no—
226C4×C11—84no—
227C4×C11—81no—
228Dic11—22no—
229Dic11—81no—
230Dic11—84no—
231Dic11—81no—
232C25—112no—
233C22×D4—112no—
234C22×D4—114no—
235C22×D4—112no—
236C22×D4—112no—
237C22×D4—111no—
238C22×D4—442no—
239C22×D4—442no—
240C22×D4C22×D1111yescharacteristic
241C23×C4—111no—
242C23×C4—442no—
243#117—442no—
244#117—442no—
245C2×C4⋊C4—111no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4C4×D1111yescharacteristic, complemented
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—228no—
251C2×C22⋊C4—222no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—221no—
254C2×C22⋊C4—222no—
255C2×C22⋊C4—222no—
256C2×C22⋊C4—222no—
257C2×C22⋊C4—444no—
258C2×C22⋊C4—442no—
259C2×C42—111no—
260C2×C42—221no—
261C2×C42C4×D1111yescharacteristic, complemented
262#99—22no—
263#99—114no—
264#99—228no—
265#99—222no—
266#99C4×D1114yescomplemented
267C2×C11—21no—
268C2×C11—21no—
269C2×C11—42no—
270C2×C11—42no—
271C2×C11C2×#34211yescharacteristic
272C2×C11#212711yescharacteristic
273C2×C11#212711yescharacteristic
274D11—24no—
275D11—44no—
276C24—111no—
277C24—112no—
278C24—114no—
279C24—114no—
280C24—222no—
281C24—222no—
282C24—224no—
283C24—882no—
284C24—882no—
285C24D4×D1112yes—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—114no—
289C2×D4—114no—
290C2×D4—112no—
291C2×D4—112no—
292C2×D4—441no—
293C2×D4—441no—
294C2×D4—444no—
295C2×D4—444no—
296C2×D4—444no—
297C2×D4—444no—
298C2×D4—442no—
299C2×D4—442no—
300C2×D4C2×C4×D1112yes—
301C2×D4D4×D1111yescharacteristic
302C2×D4Q8×D1111yescharacteristic
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—42no—
306C22×C4—111no—
307C22×C4—112no—
308C22×C4—112no—
309C22×C4—222no—
310C22×C4—222no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—448no—
314C22×C4—442no—
315C22×C4—884no—
316C22×C4—884no—
317C22×C4C2×C4×D1111yescharacteristic
318C4⋊C4—41no—
319C4⋊C4—441no—
320C4⋊C4—442no—
321C22⋊C4—24no—
322C22⋊C4—42no—
323C22⋊C4—82no—
324C22⋊C4—224no—
325C22⋊C4—442no—
326C22⋊C4—442no—
327C22⋊C4—448no—
328C22⋊C4—442no—
329C22⋊C4—882no—
330C22⋊C4—882no—
331C22⋊C4—882no—
332C42—41no—
333C42—441no—
334C42—442no—
335C11#1258211yescharacteristic, complemented, Sylow
336C23—22no—
337C23—22no—
338C23—42no—
339C23—42no—
340C23—112no—
341C23—112no—
342C23—112no—
343C23—114no—
344C23—224no—
345C23—224no—
346C23—224no—
347C23—224no—
348C23—222no—
349C23—222no—
350C23—441no—
351C23—441no—
352C23—442no—
353C23—442no—
354C23—444no—
355C23—444no—
356C23—882no—
357C23—882no—
358C23—884no—
359C23—884no—
360C23—888no—
361C23C22⋊C4×D1112yes—
362C23C22⋊C4×D1111yescharacteristic
363C23C4⋊C4×D1112yes—
364D4—42no—
365D4—41no—
366D4—41no—
367D4—442no—
368D4—442no—
369D4—444no—
370D4—444no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—44no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4—112no—
382C2×C4—224no—
383C2×C4—224no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—444no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—442no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—8816no—
393C2×C4—882no—
394C2×C4—882no—
395C2×C4C42×D1111yescharacteristic
396C2×C4C4⋊C4×D1111yescharacteristic
397C22—21no—
398C22—21no—
399C22—22no—
400C22—22no—
401C22—42no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—82no—
406C22—114no—
407C22—222no—
408C22—222no—
409C22—224no—
410C22—442no—
411C22—442no—
412C22—444no—
413C22—448no—
414C22—448no—
415C22—442no—
416C22—442no—
417C22—882no—
418C22—884no—
419C22—884no—
420C22D11×#9511yescharacteristic
421C22D11×#9911yescharacteristic
422C22D11×#9911yescharacteristic
423C4—21no—
424C4—21no—
425C4—81no—
426C4—84no—
427C4—81no—
428C4—222no—
429C4—881no—
430C4—884no—
431C4—881no—
432C2—21no—
433C2—21no—
434C2—42no—
435C2—42no—
436C2—224no—
437C2—444no—
438C2D11×#34211yescharacteristic
439C2#1307028211yescharacteristic
440C2#1307028411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC2×C4×C11C2×C42
FrattiniC22×D4C22×D11
FittingC11×#1393C2
socleC22×C11C2×#99
prime radicalC22×D4×D11C22
cosocleC22×D4×C11C23
hypercenter#1393D11
hypocenterC11#12582
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
3. #13066741C2semidirect
4. #13066740C2semidirect
5. C11×#1393C2semidirect
7. C2×#66945C4semidirect
9. C2×#66925C4semidirect
14. #10622601C4semidirect
18. #10622552C4semidirect
20. D11×#99C4semidirect
32. C2×C11×C4⋊C4C2×C4semidirect
35. C2×C42×C11C2×C4semidirect
43. C2×C4⋊Dic11C2×C4semidirect
46. C2×C4×Dic11C2×C4semidirect
52. C11×#99C2×C4semidirect
54. #66898C2×C4semidirect
120. #1393D11semidirect
247. C2×C4⋊C4C4×D11semidirect
261. C2×C42C4×D11semidirect
266. #99C4×D11semidirect
335. C11#12582semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#992
#130711952
#130667412
#130667402
C11×#13932
#1258211