Finite Group Databasebeta

← #14775583

Subgroups — #14775583

Order 2816.

898 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×#10622621C211yesmaximal, characteristic
2#13071705C211yesmaximal, characteristic, complemented
3#13069576C211yesmaximal, characteristic, complemented
4#13069377C211yesmaximal, characteristic, complemented
5#13069341C212yesmaximal, complemented
6#13069191C212yesmaximal, complemented
7#13068877C212yesmaximal
8C4⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
9C4×#66896C211yesmaximal, characteristic
10C4×#66896C212yesmaximal
11D4×C11×C4⋊C4C211yesmaximal, characteristic
12C2×C4×D4×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C22×C11×C4⋊C4—21no—
15C2×#66922C2211yescharacteristic
16C11×#389C2212yes—
17C11×#385—22no—
18C11×#384C2211yescharacteristic
19C11×#380—21no—
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×#66896C2211yescharacteristic
22C2×#66896C2212yes—
23C2×#66896C2211yescharacteristic
24#10622621C418yescomplemented
25C4⋊C4×Dic11—21no—
26#10622586—21no—
27C2×#66872C2212yes—
28C2×#66872C2212yes—
29C4×C4⋊Dic11C2211yescharacteristic
30C4×C4⋊Dic11C2212yes—
31#10622541C2212yes—
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34C2×C4×C11⋊C8C2212yes—
35#10622259—22no—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622162C2212yes—
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—21no—
44C23×C4×C11—22no—
45C22×Dic22—21no—
46C4×D4×C11—24no—
47C4×D4×C11—22no—
48C4×D4×C11—42no—
49C4×D4×C11C2×C414yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—44no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—22no—
60C2×C42×C11C2312yes—
61C2×C42×C11C2311yescharacteristic
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—22no—
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2312yes—
71C22×C11⋊C8C2311yescharacteristic
72#66922—22no—
73#66922C2×C414yescomplemented
74C11×#95—22no—
75C11×#95D412yes—
76#66896—22no—
77#66896C2×C418yes—
78#66896Q814yescomplemented
79C11⋊#95—21no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82#66872—42no—
83#66872C2×C418yescomplemented
84C4⋊(C11⋊C8)C2×C414yescomplemented
85C4×C11⋊C8—22no—
86C4×C11⋊C8—42no—
87#22963—111nomaximal, Sylow
88C24×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11C22×C412yes—
93C2×D4×C11C2×Q812yes—
94C2×D4×C11#4112yes—
95C22×C4×C11—21no—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—44no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11—44no—
102C22×C4×C11—82no—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—21no—
109C22×Dic11—22no—
110C22×Dic11—21no—
111C2×Dic22—24no—
112C2×Dic22—81no—
113C2×Dic22—81no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—44no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4—81no—
121C11×C4⋊C4SD1614yes—
122C11×C4⋊C4C22×C412yes—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—44no—
125C42×C11—22no—
126C42×C11—22no—
127C42×C11C22×C412yes—
128C42×C11#4112yes—
129C4⋊Dic11—24no—
130C4⋊Dic11—22no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11C22×C414yes—
135C4⋊Dic11C2×Q812yes—
136Dic11⋊C4—82no—
137C4×Dic11—42no—
138C4×Dic11—82no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8C22×C414yes—
147C2×C11⋊C8C2×Q812yes—
148C2×#476—111no—
149#2369—111no—
150D4×C4⋊C4D1111yescharacteristic
151#1990—111no—
152#1948—111no—
153#1941—112no—
154#1919—112no—
155#1864—112no—
156C8×C4⋊C4—111no—
157C4×#102—112no—
158C4×#102—111no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11C22×D411yescharacteristic
167D4×C11—22no—
168D4×C11—22no—
169D4×C11—22no—
170D4×C11C4×Q814yes—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—48no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—88no—
186C2×C4×C11C4×D412yes—
187C2×C4×C11C4×D412yes—
188C2×C4×C11C2×SD1614yes—
189C2×C4×C11C2×SD1612yes—
190C2×C4×C11#13512yes—
191C2×C4×C11C23×C411yescharacteristic
192C2×C4×C11C22×Q811yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11H(5,𝔽2)11yescharacteristic
196C2×C4×C112−1+411yescharacteristic
197C2×Dic11—24no—
198C2×Dic11—22no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206Dic22—84no—
207C11⋊C8—24no—
208C11⋊C8—22no—
209C11⋊C8—41no—
210C2×C4⋊Q8—111no—
211C2×C4×D4C2×D1112yes—
212C2×C4×D4C2×D1111yescharacteristic
213C22×C4⋊C4—21no—
214#476—118no—
215C2×#106—112no—
216C2×#106—112no—
217C2×C4⋊C8—111no—
218C2×#102—112no—
219C2×#102—111no—
220C2×#102—111no—
221C2×C4×C8—111no—
222C2×C4×C8—112no—
223#391—222no—
224#389—112no—
225#389—221no—
226#389C2×D1112yes—
227#385—22no—
228#384C2×D1111yescharacteristic
229#380—21no—
230C4×C4⋊C4—112no—
231C4×C4⋊C4—111no—
232C4×C4⋊C4—221no—
233C4×C4⋊C4C2×D1111yescharacteristic
234#340—112no—
235#340—111no—
236#340—112no—
237#340—111no—
238#340—112no—
239#336—112no—
240C22×C11—24no—
241C22×C11—42no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11C2×C4×D411yescharacteristic
248C22×C11#54611yescharacteristic
249C22×C11D4×Q811yescharacteristic
250C22×C11C22×SD1611yescharacteristic
251C22×C11C2×#13511yescharacteristic
252C22×C11#57611yescharacteristic
253C22×C11#57711yescharacteristic
254C4×C11—22no—
255C4×C11—24no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—82no—
259C4×C11C4×SD1614yes—
260C4×C11C2×C4×Q811yescharacteristic
261C4×C11#52011yescharacteristic
262C4×C11#55211yescharacteristic
263C4×C11#55411yescharacteristic
264Dic11—42no—
265Dic11—44no—
266Dic11—81no—
267C22×Q8—221no—
268C22×D4C22×D1111yescharacteristic
269C23×C4—21no—
270C23×C4—22no—
271C22×C8—112no—
272C22×C8—111no—
273C22×C8—111no—
274C4⋊Q8—114no—
275C4⋊Q8—222no—
276C4×D4—24no—
277C4×D4—22no—
278C4×D4—42no—
279C4×D4C4×D1114yes—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4C22⋊D1111yescharacteristic
290C2×C4⋊C4C22⋊D1111yescharacteristic
291C2×C4⋊C4C22×D1112yes—
292C2×C4⋊C4C22×D1111yescharacteristic
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C42—221no—
296C2×C42—222no—
297C2×C42C22×D1112yes—
298C2×C42C22×D1111yescharacteristic
299#106—118no—
300#106—442no—
301C4⋊C8—114no—
302#102—118no—
303#102—114no—
304#102—222no—
305C4×C8—222no—
306C4×C8—442no—
307#95—22no—
308#95—222no—
309#95—221no—
310#95—222no—
311#95C22⋊D1112yes—
312C2×C11—44no—
313C2×C11#236011yescharacteristic
314C2×C11C2×C4×SD1611yescharacteristic
315C2×C11#294611yescharacteristic
316C2×C11#329511yescharacteristic
317C2×C11#330311yescharacteristic
318C2×C11Q8×SD1611yescharacteristic
319C2×C11#338011yescharacteristic
320C24—21no—
321C2×Q8—224no—
322C2×Q8—881no—
323C2×Q8—881no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4C2×C4×D1112yes—
328C2×D4#434112yes—
329C2×D4Q8×D1112yes—
330C22×C4—21no—
331C22×C4—24no—
332C22×C4—22no—
333C22×C4—44no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—44no—
337C22×C4—82no—
338C22×C4—221no—
339C22×C4—222no—
340C22×C4—221no—
341C22×C4C2×C22⋊D1112yes—
342C22×C4C2×C22⋊D1111yescharacteristic
343C22×C4C2×C22⋊D1112yes—
344C22×C4C2×C22⋊D1111yescharacteristic
345C22×C4C23×D1111yescharacteristic
346C2×C8—114no—
347C2×C8—112no—
348C2×C8—221no—
349C2×C8—221no—
350C2×C8—222no—
351C2×C8—222no—
352C2×C8—221no—
353C2×C8—221no—
354C2×C8—221no—
355C4⋊C4—22no—
356C4⋊C4—21no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—44no—
360C4⋊C4—42no—
361C4⋊C4—81no—
362C4⋊C4—114no—
363C4⋊C4—112no—
364C4⋊C4—224no—
365C4⋊C4—222no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—882no—
370C4⋊C4#432414yes—
371C4⋊C4C2×C4×D1112yes—
372C22⋊C4—24no—
373C22⋊C4—44no—
374C42—22no—
375C42—22no—
376C42—442no—
377C42—882no—
378C42C2×C4×D1112yes—
379C42#433912yes—
380C11#2296311yescharacteristic, complemented, Sylow
381C23—22no—
382C23—22no—
383C23—22no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23C22×C22⋊D1111yescharacteristic
389Q8—884no—
390D4—22no—
391D4—22no—
392D4—22no—
393D4#6694014yes—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—48no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—88no—
409C2×C4—224no—
410C2×C4—222no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4C4×C22⋊D1112yes—
419C2×C4C4×C22⋊D1112yes—
420C2×C4C2×#432414yes—
421C2×C4C2×#432412yes—
422C2×C4#6700312yes—
423C2×C4C22×C4×D1111yescharacteristic
424C2×C4C2×#433911yescharacteristic
425C2×C4C2×#434111yescharacteristic
426C2×C4#6703711yescharacteristic
427C2×C4C2×Q8×D1111yescharacteristic
428C2×C4#6704011yescharacteristic
429C8—224no—
430C8—222no—
431C8—441no—
432C22—24no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22C2×C4×C22⋊D1111yescharacteristic
440C22C22×#432411yescharacteristic
441C22#1062333711yescharacteristic
442C22Q8×C22⋊D1111yescharacteristic
443C22C2×#6700311yescharacteristic
444C22#1062336611yescharacteristic
445C22#1062336811yescharacteristic
446C4—24no—
447C4—22no—
448C4—42no—
449C4—42no—
450C4—82no—
451C4—442no—
452C4—444no—
453C4—881no—
454C4C4×#432414yes—
455C4C2×#6694011yescharacteristic
456C4#1062303511yescharacteristic
457C4#1062304211yescharacteristic
458C4#1062304411yescharacteristic
459C2—44no—
460C2#1307162111yescharacteristic
461C2C2×C4×#432411yescharacteristic
462C2#1307744411yescharacteristic
463C2#1308044011yescharacteristic
464C2#1308054411yescharacteristic
465C2Q8×#432411yescharacteristic
466C2#1308147911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterD4×C4⋊C4D11
hypocenterC11#22963
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071705C2semidirect
3. #13069576C2semidirect
4. #13069377C2semidirect
5. #13069341C2semidirect
6. #13069191C2semidirect
8. C4⋊C4×C11⋊C8C2semidirect
24. #10622621C4semidirect
73. #66922C2×C4semidirect
78. #66896Q8semidirect
83. #66872C2×C4semidirect
84. C4⋊(C11⋊C8)C2×C4semidirect
380. C11#22963semidirect

Maximal subgroups

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

subgroupindex
C2×#106226212
#130717052
#130695762
#130693772
#130693412
#130691912
#130688772
C4⋊C4×C11⋊C82
C4×#668962
D4×C11×C4⋊C42
#2296311