Finite Group Databasebeta

← #14756774

Subgroups — #14756774

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4325C211yesmaximal, characteristic
2#13071077C211yesmaximal, characteristic
3C4×Q8×Dic11C211yesmaximal, characteristic, complemented
4#13069234C212yesmaximal
5#13069199C212yesmaximal, complemented
6#13068969C212yesmaximal
7#13068868C212yesmaximal, complemented
8C4×#66871C211yesmaximal, characteristic, complemented
9C4×#66885C211yesmaximal, characteristic
10#13068361C211yesmaximal, characteristic, complemented
11C4×C11×#103C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×Q8×Dic11C2212yes—
14C22×#4325C2211yescharacteristic
15C2×C4×D44C2211yescharacteristic
16C2×#66925—21no—
17C2×C11×#103C2212yes—
18C2×C4×C8×C11C2211yescharacteristic
19C4×C11×C4⋊C4C2211yescharacteristic
20C2×#66899C2211yescharacteristic
21C2×#66885C2212yes—
22C4×#4325C418yescomplemented
23#10622601C2212yes—
24C4⋊C4×Dic11—22no—
25C4⋊C4×Dic11C2212yes—
26#10622586C2212yes—
27C2×#66873C2211yescharacteristic
28C2×#66872C2211yescharacteristic
29C2×#66871C2212yes—
30C4×(C2×D11)⋊C4—21no—
31C4×C4⋊Dic11—21no—
32C4×C4⋊Dic11C2211yescharacteristic
33C42×Dic11—21no—
34C42×Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622282—22no—
37C11×#340C2212yes—
38#10622189C2212yes—
39#10622188C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×C8×C11C2312yes—
46C4×Q8×C11—22no—
47C4×Q8×C11C2×C414yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C42×C11—21no—
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54Q8×Dic11—24no—
55Q8×Dic11—24no—
56C2×#4325—24no—
57C2×#4325C2×C414yes—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2312yes—
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11D412yes—
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11C2312yes—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C4×D44—22no—
75C4×D44C2×C414yes—
76#66925—44no—
77C11×#103—24no—
78C4×C8×C11—22no—
79C11×#95—21no—
80#66899C2×C414yes—
81C11⋊#95—21no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84#66885—24no—
85#66873C2×C414yes—
86#66872C2×C414yes—
87#66871—24no—
88C4×C11⋊C8C2×C414yes—
89#21120—111nomaximal, Sylow
90C23×D11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—21no—
93C2×Q8×C11C22×C412yes—
94C2×Q8×C11#4114yes—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—22no—
102C22×Dic11—21no—
103C22×Dic11C2×D412yes—
104C22×Dic11C2×D412yes—
105C2×D44—21no—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44C22×C412yes—
109C2×C4×D11—24no—
110C2×C4×D11—42no—
111C2×C4×D11—42no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4C22×C412yes—
120C42×C11—24no—
121C42×C11—42no—
122C42×C11C22×C412yes—
123C42×C11#4112yes—
124#4325—28no—
125(C2×D11)⋊C4—24no—
126(C2×D11)⋊C4—44no—
127(C2×D11)⋊C4—44no—
128C4⋊Dic11—28no—
129C4⋊Dic11—21no—
130C4⋊Dic11—22no—
131C4⋊Dic11C22×C412yes—
132C4⋊Dic11#4114yes—
133Dic11⋊C4—44no—
134C4×Dic11—28no—
135C4×Dic11—24no—
136C4×Dic11—22no—
137C4×Dic11—22no—
138C4×Dic11—22no—
139C4×Dic11—22no—
140C4×Dic11—44no—
141C4×Dic11—42no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8C22×C412yes—
145C2×C11⋊C8C22×C412yes—
146C2×C4×SD16—111no—
147#2293—111no—
148C42×Q8—111no—
149#1925—112no—
150#1920—112no—
151#1880—112no—
152#1863—112no—
153C4×#107—111no—
154C4×#103D1111yescharacteristic, complemented
155C4×#102—111no—
156#1744—111no—
157C23×C11C22×D411yescharacteristic
158C22×D11—22no—
159C22×D11—42no—
160C22×D11—42no—
161C22×D11—41no—
162C22×D11—41no—
163Q8×C11—22no—
164Q8×C11—24no—
165Q8×C11#11714yescomplemented
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11C4×D412yes—
175C2×C4×C11C4×D412yes—
176C2×C4×C11AGL(1,ℤ/8)12yes—
177C2×C4×C11#13712yes—
178C2×C4×C11C23×C411yescharacteristic
179C2×C4×C11C2×#4112yes—
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4112yes—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—24no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11#13514yes—
194D44—22no—
195D44—22no—
196D44—42no—
197C4×D11—48no—
198C8×C11—42no—
199C11⋊C8—22no—
200C11⋊C8—22no—
201C22×SD16—111no—
202C2×C4×Q8—112no—
203C2×C4×Q8C2×D1111yescharacteristic
204C2×C4×D4—111no—
205C2×#117—221no—
206C4×SD16—118no—
207C2×#107—112no—
208C2×#106—111no—
209C2×#103—111no—
210C2×#103C2×D1112yes—
211C2×#102—111no—
212C2×#102—112no—
213C2×C4×C8—111no—
214C2×C4×C8C2×D1111yescharacteristic
215#390—112no—
216#389—112no—
217#388—222no—
218C4×C4⋊C4—112no—
219C4×C4⋊C4—111no—
220C4×C4⋊C4—221no—
221C4×C4⋊C4—222no—
222C4×C4⋊C4C2×D1111yescharacteristic
223C4×C22⋊C4—221no—
224C43—111no—
225C43—221no—
226#340—112no—
227#340—112no—
228#340C2×D1112yes—
229#336—112no—
230#336—112no—
231C22×C11C2×C4×D411yescharacteristic
232C22×C11#52512yes—
233C22×C11C2×#13512yes—
234C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
235C22×C11C2×#13711yescharacteristic
236C2×D11—42no—
237C2×D11—42no—
238C2×D11—42no—
239C2×D11—82no—
240C2×D11—82no—
241C4×C11—22no—
242C4×C11—24no—
243C4×C11—42no—
244C4×C11—82no—
245C4×C11#44014yes—
246C4×C11C2×#11711yescharacteristic
247C4×C11C4×#4111yescharacteristic
248C4×C11#52912yes—
249Dic11—24no—
250Dic11—42no—
251Dic11—44no—
252Dic11—42no—
253C22×Q8C22×D1111yescharacteristic
254C22×D4—111no—
255C23×C4—221no—
256C2×SD16—114no—
257C2×SD16—224no—
258C22×C8—111no—
259C22×C8—111no—
260C22×C8C22×D1112yes—
261C4×Q8—22no—
262C4×Q8—224no—
263C4×Q8—224no—
264C4×Q8C4×D1114yes—
265C4×D4—114no—
266C4×D4—222no—
267#117—444no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—111no—
270C2×C4⋊C4—112no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4—222no—
273C2×C4⋊C4C22×D1112yes—
274C2×C4⋊C4C22×D1111yescharacteristic
275C2×C22⋊C4—221no—
276C2×C22⋊C4—222no—
277C2×C22⋊C4—222no—
278C2×C42—21no—
279C2×C42—21no—
280C2×C42—112no—
281C2×C42—111no—
282C2×C42—111no—
283C2×C42—112no—
284C2×C42—222no—
285C2×C42—222no—
286C2×C42—221no—
287C2×C42C22×D1111yescharacteristic
288#107—224no—
289#106—114no—
290#103—24no—
291#103—114no—
292#102—114no—
293#102—224no—
294C4×C8—22no—
295C4×C8—114no—
296#95—21no—
297#95—222no—
298#95—222no—
299#95—221no—
300C2×C11#229011yescharacteristic
301C2×C11C4×#13511yescharacteristic
302C2×C11C2×#44011yescharacteristic
303C2×C11#310612yes—
304C2×C11#310812yes—
305D11—82no—
306C24—221no—
307C2×Q8—21no—
308C2×Q8—22no—
309C2×Q8C2×C4×D1112yes—
310C2×Q8#433914yes—
311C2×D4—112no—
312C2×D4—222no—
313C2×D4—221no—
314C2×D4—222no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—112no—
319C22×C4—112no—
320C22×C4—222no—
321C22×C4—221no—
322C22×C4—224no—
323C22×C4—442no—
324C22×C4—442no—
325C22×C4D4×D1111yescharacteristic
326C22×C4D4×D1111yescharacteristic
327C22×C4C23×D1111yescharacteristic
328SD16—228no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—112no—
333C2×C8—112no—
334C2×C8—222no—
335C2×C8—222no—
336C4⋊C4—24no—
337C4⋊C4—21no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—112no—
341C4⋊C4—114no—
342C4⋊C4—228no—
343C4⋊C4—222no—
344C4⋊C4—221no—
345C4⋊C4—444no—
346C4⋊C4C2×C4×D1112yes—
347C22⋊C4—224no—
348C22⋊C4—444no—
349C22⋊C4—444no—
350C42—24no—
351C42—42no—
352C42—224no—
353C42—228no—
354C42—222no—
355C42—222no—
356C42—222no—
357C42—222no—
358C42—444no—
359C42—442no—
360C42C2×C4×D1112yes—
361C42#434112yes—
362C11#2112011yescharacteristic, complemented, Sylow
363C23—222no—
364C23—441no—
365C23—441no—
366C23—442no—
367C23—442no—
368C23C2×D4×D1111yescharacteristic
369Q8—22no—
370Q8—24no—
371Q8#6692514yescomplemented
372D4—222no—
373D4—222no—
374D4—442no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—114no—
384C2×C4—222no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—224no—
390C2×C4—222no—
391C2×C4—442no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—442no—
395C2×C4—448no—
396C2×C4(C22⋊D11)⋊C412yes—
397C2×C4(C22⋊D11)⋊C412yes—
398C2×C4#6696712yes—
399C2×C4#6697112yes—
400C2×C4C22×C4×D1111yescharacteristic
401C2×C4C2×#433912yes—
402C2×C4C2×#434111yescharacteristic
403C2×C4#41×D1112yes—
404C8—42no—
405C8—222no—
406C8—222no—
407C22—442no—
408C22—442no—
409C22—442no—
410C22—882no—
411C22—882no—
412C22C2×(C22⋊D11)⋊C411yescharacteristic
413C22#1062307812yes—
414C22C2×#6696711yescharacteristic
415C22C2×#6697111yescharacteristic
416C22D11×#13512yes—
417C4—22no—
418C4—24no—
419C4—42no—
420C4—82no—
421C4—224no—
422C4—442no—
423C4—444no—
424C4—442no—
425C4#1062243014yes—
426C4C2×#6692511yescharacteristic
427C4#1062305311yescharacteristic
428C4#1062306912yes—
429C2—882no—
430C2#1307105511yescharacteristic
431C2#1307738411yescharacteristic
432C2C2×#1062243011yescharacteristic
433C2#1307867412yes—
434C2#1307870012yes—
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#103C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenterC4×#103D11
hypocenterC11#21120
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
3. C4×Q8×Dic11C2semidirect
5. #13069199C2semidirect
7. #13068868C2semidirect
8. C4×#66871C2semidirect
10. #13068361C2semidirect
11. C4×C11×#103C2semidirect
22. C4×#4325C4semidirect
154. C4×#103D11semidirect
165. Q8×C11#117semidirect
362. C11#21120semidirect
371. Q8#66925semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43252
#130710772
C4×Q8×Dic112
#130692342
#130691992
#130689692
#130688682
C4×#668712
C4×#668852
#130683612
C4×C11×#1032
#2112011