Finite Group Databasebeta

← #14770950

Subgroups — #14770950

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622726C211yesmaximal, characteristic
2#13071499C211yesmaximal, characteristic, complemented
3#13071456C211yesmaximal, characteristic
4#13069299C212yesmaximal, complemented
5#13069237C212yesmaximal, complemented
6#13068873C212yesmaximal, complemented
7#13068712C211yesmaximal, characteristic, complemented
8#13068645C211yesmaximal, characteristic, complemented
9#13068557C211yesmaximal, characteristic
10C4×#66880C212yesmaximal, complemented
11C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×C4×Dic22C2212yes—
16C2×C11×C22⋊C8C2211yescharacteristic
17C2×C4×C8×C11C2212yes—
18C4×C11×C22⋊C4C2211yescharacteristic
19#10622825C2211yescharacteristic
20#10622825C2211yescharacteristic
21#10622726C418yescomplemented
22C2×#66885C2212yes—
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66882C2212yes—
26C2×#66880C2212yes—
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29#10622570—22no—
30#10622557—22no—
31#10622552C2212yes—
32C4×C4⋊Dic11C2212yes—
33#10622541C2212yes—
34#10622280—21no—
35#10622279—21no—
36#10622263—21no—
37#10622261—21no—
38C11×#336C2212yes—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—21no—
44C2×#4339—22no—
45C2×#4339—24no—
46C2×#4339—42no—
47C2×#4339C2×C414yes—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×Dic22C2311yescharacteristic
51C22×C8×C11—42no—
52C22×C8×C11C2×C414yes—
53C22×C8×C11C2312yes—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C2×C11×C22⋊C4D412yes—
57C2×C42×C11C2312yes—
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11—21no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63#66979—22no—
64#66979C2×C414yes—
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11—21no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—22no—
74C4×Dic22—24no—
75C4×Dic22—42no—
76C11×C22⋊C8—22no—
77C4×C8×C11—42no—
78C11×#95D411yescharacteristic
79C11×#95D411yescharacteristic
80C11⋊#95—21no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—21no—
84#66885—42no—
85#66885C2×C414yes—
86#66885C2×C414yes—
87#66882—42no—
88#66880—24no—
89#66880C2×C414yes—
90#66880C2×C414yes—
91#22573—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C23×D11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11#4112yes—
101C22×C4×C11C2411yescharacteristic
102C2×C22⋊D11—24no—
103C2×C22⋊D11—44no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109#4339—28no—
110#4339—44no—
111#4339—48no—
112C2×D44—21no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44C22×C412yes—
116C2×C4×D11—24no—
117C2×C4×D11—44no—
118C2×Dic22—21no—
119C2×Dic22—22no—
120C2×Dic22C22×C412yes—
121C2×Dic22#4114yes—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—44no—
128C2×C8×C11C22×C412yes—
129C2×C8×C11C22×C412yes—
130C11×C22⋊C4—24no—
131C42×C11—22no—
132C42×C11—22no—
133C22⋊Dic11—24no—
134C22⋊Dic11—81no—
135C22⋊Dic11—81no—
136(C2×D11)⋊C4—44no—
137(C2×D11)⋊C4—82no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11C22×C412yes—
145C4⋊Dic11C22×C412yes—
146Dic11⋊C4—44no—
147Dic11⋊C4—82no—
148C4×Dic11—24no—
149C4×Dic11—44no—
150C4×Dic11—44no—
151C2×#416—111no—
152#2346—111no—
153#2341—111no—
154#1934—112no—
155#1925—112no—
156#1863—112no—
157#1825—111no—
158#1808—111no—
159#1788—111no—
160C4×#103—112no—
161C8×C22⋊C4D1111yescharacteristic, complemented
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11C4×D412yes—
167C23×C11C22×D411yescharacteristic
168C22×D11—22no—
169C22×D11—42no—
170C22×D11—42no—
171C22×D11—41no—
172C22×D11—41no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11C4×D412yes—
183C2×C4×C11#13514yes—
184C2×C4×C11C23×C411yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4112yes—
187C2×C4×C11H(5,𝔽2)12yes—
188C22⋊D11—48no—
189C2×Dic11—22no—
190C2×Dic11—24no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—42no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202D44—22no—
203D44—22no—
204D44—42no—
205C4×D11—48no—
206Dic22—22no—
207Dic22—24no—
208Dic22#11714yes—
209C8×C11—22no—
210C8×C11—22no—
211C8×C11—42no—
212C22×#41—111no—
213C23×C8C2×D1111yescharacteristic
214C2×C4×Q8—112no—
215C2×#117—111no—
216C2×#107—112no—
217#416—118no—
218C2×#103—111no—
219C2×#103—111no—
220C2×#103—112no—
221C2×#102—111no—
222C2×#102—111no—
223C2×#102—112no—
224C2×C22⋊C8C2×D1111yescharacteristic
225C2×C4×C8C2×D1112yes—
226#390—112no—
227#390—222no—
228#389—112no—
229#388—222no—
230#382—221no—
231#380—111no—
232#380—111no—
233#380—221no—
234C4×C4⋊C4—112no—
235C4×C22⋊C4—221no—
236C4×C22⋊C4C2×D1111yescharacteristic
237#376—221no—
238#340—112no—
239#340—112no—
240#340—112no—
241#336C2×D1112yes—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11C2×C4×D411yescharacteristic
248C22×C11#54612yes—
249C22×C11C2×#13512yes—
250C22×C11#57611yescharacteristic
251C22×C11#57811yescharacteristic
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—42no—
255C2×D11—82no—
256C2×D11—82no—
257C4×C11—22no—
258C4×C11—24no—
259C4×C11—42no—
260C4×C11C2×#11711yescharacteristic
261C4×C11#51811yescharacteristic
262C4×C11#55112yes—
263Dic11—24no—
264Dic11—42no—
265Dic11—42no—
266Dic11—82no—
267Dic11—82no—
268C2×#41—114no—
269C2×#41—224no—
270C2×#41—222no—
271C2×#41—442no—
272C22×Q8—111no—
273C22×D4—111no—
274C22×D4—221no—
275C23×C4—221no—
276C23×C4C22×D1111yescharacteristic
277C22×C8—42no—
278C22×C8C4×D1114yes—
279C22×C8C22×D1112yes—
280C22×C8C22×D1111yescharacteristic
281C22×C8C22×D1111yescharacteristic
282C4×Q8—224no—
283C4×Q8—442no—
284#117—114no—
285#117—222no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—112no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C22⋊C4—221no—
293C2×C22⋊C4—222no—
294C2×C22⋊C4—221no—
295C2×C22⋊C4—221no—
296C2×C22⋊C4—222no—
297C2×C22⋊C4D4412yes—
298C2×C42—221no—
299C2×C42—222no—
300C2×C42—222no—
301C2×C42C22×D1112yes—
302#107—442no—
303#103—114no—
304#103—114no—
305#103—224no—
306#102—114no—
307#102—114no—
308#102—442no—
309C22⋊C8—22no—
310C4×C8—42no—
311#95—221no—
312#95—222no—
313#95—221no—
314#95—222no—
315#95D4411yescharacteristic
316#95D4411yescharacteristic
317C2×C11—42no—
318C2×C11#234211yescharacteristic
319C2×C11C4×#13511yescharacteristic
320C2×C11#295111yescharacteristic
321C2×C11#330012yes—
322C2×C11#330512yes—
323D11—82no—
324C24—221no—
325C24C2×D4411yescharacteristic
326#41—228no—
327#41—444no—
328#41—448no—
329C2×Q8—112no—
330C2×Q8—114no—
331C2×Q8—221no—
332C2×Q8—222no—
333C2×D4—112no—
334C2×D4—224no—
335C2×D4—221no—
336C2×D4—222no—
337C2×D4—222no—
338C2×D4—444no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—224no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—444no—
348C22×C4C2×C4×D1112yes—
349C22×C4C2×D4412yes—
350C22×C4C2×D4411yescharacteristic
351C22×C4C2×D4412yes—
352C22×C4#433912yes—
353C22×C4C23×D1111yescharacteristic
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—44no—
360C2×C8C2×C4×D1112yes—
361C2×C8C2×C4×D1112yes—
362C4⋊C4—112no—
363C4⋊C4—112no—
364C4⋊C4—221no—
365C4⋊C4—221no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—222no—
369C4⋊C4—222no—
370C4⋊C4—444no—
371C4⋊C4—882no—
372C22⋊C4—24no—
373C22⋊C4—224no—
374C22⋊C4—444no—
375C22⋊C4—882no—
376C22⋊C4—881no—
377C22⋊C4—881no—
378C42—22no—
379C42—22no—
380C42—224no—
381C42—444no—
382C42—444no—
383C11#2257311yescharacteristic, complemented, Sylow
384C23—22no—
385C23—21no—
386C23—21no—
387C23—22no—
388C23—222no—
389C23—442no—
390C23—441no—
391C23—441no—
392C23—442no—
393C23C4×D4412yes—
394C23C22×D4411yescharacteristic
395Q8—114no—
396Q8—222no—
397Q8—224no—
398D4—222no—
399D4—222no—
400D4—448no—
401D4—442no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—222no—
412C2×C4—224no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—448no—
416C2×C4—442no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4C4×D4412yes—
426C2×C4#6695714yes—
427C2×C4C22×C4×D1111yescharacteristic
428C2×C4C2×#433911yescharacteristic
429C2×C4#6703712yes—
430C2×C4#41×D1112yes—
431C8—22no—
432C8—22no—
433C8—42no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—42no—
438C22—42no—
439C22—442no—
440C22—442no—
441C22—442no—
442C22—882no—
443C22—882no—
444C22C2×C4×D4411yescharacteristic
445C22#1062308512yes—
446C22C2×#6695712yes—
447C22#1062328311yescharacteristic
448C22#1062328411yescharacteristic
449C4—22no—
450C4—24no—
451C4—42no—
452C4—224no—
453C4—442no—
454C4—442no—
455C4—882no—
456C4—882no—
457C4#1062301711yescharacteristic
458C4D11×#11711yescharacteristic
459C4#1062308712yes—
460C2—42no—
461C2—882no—
462C2#1307146811yescharacteristic
463C2C4×#6695711yescharacteristic
464C2#1307749311yescharacteristic
465C2#1308050512yes—
466C2#1308056712yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC8×C22⋊C4D11
hypocenterC11#22573
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071499C2semidirect
4. #13069299C2semidirect
5. #13069237C2semidirect
6. #13068873C2semidirect
7. #13068712C2semidirect
8. #13068645C2semidirect
10. C4×#66880C2semidirect
11. C8×C11×C22⋊C4C2semidirect
21. #10622726C4semidirect
161. C8×C22⋊C4D11semidirect
383. C11#22573semidirect

Maximal subgroups

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

subgroupindex
C2×#106227262
#130714992
#130714562
#130692992
#130692372
#130688732
#130687122
#130686452
#130685572
C4×#668802
C8×C11×C22⋊C42
#2257311