Finite Group Databasebeta

← #14773538

Subgroups — #14773538

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4323C211yesmaximal, characteristic
2#13071591C211yesmaximal, characteristic, complemented
3#13071589C211yesmaximal, characteristic, complemented
4#13069479C212yesmaximal
5#13069246C212yesmaximal, complemented
6#13069241C212yesmaximal, complemented
7#13068778C211yesmaximal, characteristic, complemented
8#13068627C211yesmaximal, characteristic, complemented
9#13068508C212yesmaximal, complemented
10#13068481C211yesmaximal, characteristic, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4323C2211yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#102C2212yes—
17C11×#382C2211yescharacteristic
18#10622834C2212yes—
19C2×#66896C2211yescharacteristic
20#10622824—21no—
21C4×C22⋊Dic11—21no—
22C2×#66885C2212yes—
23C2×C8×Dic11C2212yes—
24C4×#4323C418yescomplemented
25#10622601C2212yes—
26C4⋊C4×Dic11C2212yes—
27C4⋊C4×Dic11C2212yes—
28C2×#66873C2211yescharacteristic
29C2×#66872C2212yes—
30C2×#66871C2212yes—
31C2×#66871C2211yescharacteristic
32#10622564—22no—
33#10622549C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622283—22no—
37#10622279—21no—
38#10622277—21no—
39C11×#340C2212yes—
40#10622189C2212yes—
41#10622188C2212yes—
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—21no—
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×C8×C11C2312yes—
47C4×D4×C11—22no—
48C4×D4×C11C2×C414yes—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×#4323—22no—
56C2×#4323—22no—
57C2×#4323C2×C414yes—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11D412yes—
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4×Dic11—22no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11C2312yes—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69C4×D44—22no—
70C4×D44C2×C414yes—
71C11×C4⋊C8—22no—
72C11×#102—42no—
73C11×#95—21no—
74C11×#95—21no—
75#66896C2×C414yes—
76C11⋊#95—21no—
77C11⋊#95—21no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95D411yescharacteristic
81C11⋊#95D411yescharacteristic
82#66885—42no—
83C8×Dic11—24no—
84#66873C2×C414yes—
85#66872—42no—
86#66871—24no—
87#66871C2×C414yes—
88C4×C11⋊C8C2×C414yes—
89#22810—111nomaximal, Sylow
90C24×C11—21no—
91C23×D11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11C22×C412yes—
98C22×C4×C11—21no—
99C22×C4×C11—24no—
100C22×C4×C11—22no—
101C22×C4×C11—82no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—21no—
106C22×Dic11—22no—
107C22×Dic11C2×D412yes—
108C22×Dic11C2×D412yes—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44C22×C412yes—
115C2×C4×D11—24no—
116C2×C4×D11—82no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4C22×C412yes—
124C11×C22⋊C4—24no—
125C42×C11C22×C412yes—
126C42×C11#4112yes—
127C22⋊Dic11—44no—
128C22⋊Dic11—82no—
129#4323—28no—
130(C2×D11)⋊C4—24no—
131(C2×D11)⋊C4—44no—
132(C2×D11)⋊C4—82no—
133C4⋊Dic11—24no—
134C4⋊Dic11—21no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11C22×C412yes—
138C4×Dic11—22no—
139C4×Dic11—22no—
140C4×Dic11—82no—
141C4×Dic11—82no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8C22×C412yes—
145C2×C11⋊C8C22×C412yes—
146C2×C11⋊C8#4112yes—
147C2×C11⋊C8#4112yes—
148C2×C4×D8—111no—
149#2357—111no—
150#2357—111no—
151#1970—112no—
152#1926—112no—
153#1926—112no—
154#1846—111no—
155#1804—111no—
156#1804D1111yescharacteristic, complemented
157C4×#107—112no—
158C8×C4⋊C4—111no—
159C23×C11—22no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11C22×D411yescharacteristic
165C22×D11—22no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—42no—
169C22×D11—42no—
170D4×C11—22no—
171D4×C11—22no—
172D4×C11—41no—
173D4×C11—41no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—84no—
182C2×C4×C11C4×D412yes—
183C2×C4×C11C4×D412yes—
184C2×C4×C11C23×C411yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C11H(5,𝔽2)11yescharacteristic
189C2×C4×C112−1+411yescharacteristic
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11#13514yes—
201D44—22no—
202D44—22no—
203D44—41no—
204D44—41no—
205C4×D11—84no—
206C8×C11—42no—
207C11⋊C8—22no—
208C11⋊C8#11714yes—
209C22×D8—111no—
210C2×C4×D4—111no—
211C2×C4×D4C2×D1111yescharacteristic
212C4×D8—118no—
213C2×#107—111no—
214C2×#107—112no—
215C2×#106—112no—
216C2×C4⋊C8C2×D1111yescharacteristic
217C2×#102—111no—
218C2×#102—111no—
219C2×#102—112no—
220C2×#102C2×D1112yes—
221C2×C4×C8—111no—
222C2×C4×C8—112no—
223#390—112no—
224#390—112no—
225#388—222no—
226#388—222no—
227#382—111no—
228#382C2×D1111yescharacteristic
229#381—221no—
230#381—221no—
231C4×C4⋊C4—111no—
232C4×C4⋊C4—112no—
233C4×C4⋊C4—112no—
234C4×C22⋊C4—221no—
235C4×C22⋊C4—221no—
236#340—112no—
237#340C2×D1112yes—
238#336—112no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—82no—
243C22×C11—82no—
244C22×C11C2×C4×D411yescharacteristic
245C22×C11#54711yescharacteristic
246C22×C11#55011yescharacteristic
247C22×C11C2×#13512yes—
248C22×C11#57612yes—
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—82no—
253C2×D11—82no—
254C4×C11—22no—
255C4×C11—22no—
256C4×C11—42no—
257C4×C11—82no—
258C4×C11C2×#11711yescharacteristic
259C4×C11#52011yescharacteristic
260C4×C11#55511yescharacteristic
261C4×C11#55611yescharacteristic
262Dic11—24no—
263Dic11—42no—
264Dic11—42no—
265Dic11—82no—
266C22×D4—111no—
267C22×D4C22×D1111yescharacteristic
268C23×C4—21no—
269C23×C4—221no—
270C2×D8—114no—
271C2×D8—222no—
272C2×D8—222no—
273C22×C8—111no—
274C22×C8—111no—
275C22×C8C22×D1112yes—
276C4×D4—22no—
277C4×D4—114no—
278C4×D4—222no—
279C4×D4C4×D1114yes—
280C2×C4⋊C4—111no—
281C2×C4⋊C4—112no—
282C2×C4⋊C4—112no—
283C2×C4⋊C4C22×D1112yes—
284C2×C4⋊C4C22×D1111yescharacteristic
285C2×C22⋊C4—21no—
286C2×C22⋊C4—221no—
287C2×C22⋊C4—222no—
288C2×C22⋊C4—222no—
289C2×C22⋊C4—222no—
290C2×C22⋊C4—222no—
291C2×C42—112no—
292C2×C42—222no—
293C2×C42—222no—
294C2×C42C22×D1111yescharacteristic
295#107—114no—
296#107—224no—
297#106—442no—
298C4⋊C8—22no—
299#102—42no—
300#102—114no—
301#102—114no—
302#102—442no—
303C4×C8—114no—
304C4×C8—224no—
305#95—21no—
306#95—21no—
307#95—111no—
308#95—111no—
309#95—222no—
310#95—222no—
311#95—221no—
312#95—221no—
313C2×C11—82no—
314C2×C11#235411yescharacteristic
315C2×C11C4×#13511yescharacteristic
316C2×C11#294811yescharacteristic
317C2×C11#333912yes—
318C2×C11#339612yes—
319D11—82no—
320C24—21no—
321C24—221no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—112no—
328C2×D4—221no—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C2×D4—221no—
333C2×D4C2×C4×D1112yes—
334C22×C4—21no—
335C22×C4—24no—
336C22×C4—22no—
337C22×C4—82no—
338C22×C4—112no—
339C22×C4—112no—
340C22×C4—221no—
341C22×C4—224no—
342C22×C4—222no—
343C22×C4—882no—
344C22×C4D4×D1111yescharacteristic
345C22×C4D4×D1111yescharacteristic
346C22×C4C23×D1111yescharacteristic
347D8—228no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—112no—
352C2×C8—112no—
353C2×C8—112no—
354C2×C8—112no—
355C2×C8—221no—
356C2×C8—221no—
357C4⋊C4—21no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—112no—
361C4⋊C4—224no—
362C4⋊C4—221no—
363C4⋊C4—222no—
364C4⋊C4—222no—
365C4⋊C4C2×C4×D1112yes—
366C22⋊C4—24no—
367C22⋊C4—224no—
368C22⋊C4—444no—
369C22⋊C4—444no—
370C22⋊C4—882no—
371C22⋊C4—882no—
372C42—222no—
373C42—222no—
374C42—882no—
375C42—882no—
376C42C2×C4×D1112yes—
377C42#434112yes—
378C11#2281011yescharacteristic, complemented, Sylow
379C23—22no—
380C23—42no—
381C23—42no—
382C23—41no—
383C23—41no—
384C23—222no—
385C23—442no—
386C23—442no—
387C23—441no—
388C23—441no—
389C23C2×D4×D1111yescharacteristic
390D4—22no—
391D4—22no—
392D4—41no—
393D4—41no—
394D4—222no—
395D4—222no—
396D4—441no—
397D4—441no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—84no—
406C2×C4—114no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—884no—
418C2×C4(C22⋊D11)⋊C412yes—
419C2×C4(C22⋊D11)⋊C412yes—
420C2×C4C22×C4×D1111yescharacteristic
421C2×C4C2×#434111yescharacteristic
422C2×C4#6703711yescharacteristic
423C2×C4#6704011yescharacteristic
424C2×C4#41×D1111yescharacteristic
425C2×C4#41×D1111yescharacteristic
426C8—42no—
427C8—114no—
428C8—222no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—82no—
433C22—82no—
434C22—442no—
435C22—442no—
436C22—442no—
437C22—882no—
438C22—882no—
439C22C2×(C22⋊D11)⋊C411yescharacteristic
440C22#1062313011yescharacteristic
441C22#1062316211yescharacteristic
442C22D11×#13512yes—
443C22#1062330512yes—
444C4—22no—
445C4—22no—
446C4—42no—
447C4—82no—
448C4—224no—
449C4—442no—
450C4—442no—
451C4—882no—
452C4#1062303511yescharacteristic
453C4D11×#11711yescharacteristic
454C4#1062314711yescharacteristic
455C4#1062317211yescharacteristic
456C2—82no—
457C2—882no—
458C2#1307156011yescharacteristic
459C2#1307738411yescharacteristic
460C2#1307746411yescharacteristic
461C2#1308101512yes—
462C2#1308162312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1804C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenter#1804D11
hypocenterC11#22810
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. #13071591C2semidirect
3. #13071589C2semidirect
5. #13069246C2semidirect
6. #13069241C2semidirect
7. #13068778C2semidirect
8. #13068627C2semidirect
9. #13068508C2semidirect
10. #13068481C2semidirect
11. C11×#1804C2semidirect
24. C4×#4323C4semidirect
156. #1804D11semidirect
378. C11#22810semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43232
#130715912
#130715892
#130694792
#130692462
#130692412
#130687782
#130686272
#130685082
#130684812
C11×#18042
#2281011