Finite Group Databasebeta

← #14756706

Subgroups — #14756706

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4325C211yesmaximal, characteristic
2C42×D44C211yesmaximal, characteristic
3#13069254C212yesmaximal, complemented
4#13069191C212yesmaximal, complemented
5#13068953C212yesmaximal
6#13068862C212yesmaximal
7C4×#66871C211yesmaximal, characteristic, complemented
8C4×#66899C211yesmaximal, characteristic, complemented
9C4×#66873C211yesmaximal, characteristic
10#13068362C211yesmaximal, characteristic, complemented
11C11×#2295C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C22×#4325C2211yescharacteristic
14C2×C4×D44C2212yes—
15C2×C4×D44C2211yescharacteristic
16C2×C42×D11—21no—
17C11×#391C2212yes—
18C11×#389C2212yes—
19C11×#387—22no—
20C4×C11×C4⋊C4—21no—
21C4×C11×C4⋊C4C2211yescharacteristic
22C11×#376—21no—
23C43×C11C2211yescharacteristic
24C2×#66899C2212yes—
25C2×#66899C2211yescharacteristic
26C4×#4325C418yescomplemented
27C2×#66873C2212yes—
28C2×#66873C2211yescharacteristic
29C2×#66872C2211yescharacteristic
30C2×#66871C2212yes—
31C4×(C2×D11)⋊C4—21no—
32C4×(C2×D11)⋊C4—22no—
33C4×C4⋊Dic11C2212yes—
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622162C2212yes—
41#10622162C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D44C2311yescharacteristic
44C22×C4×D11—22no—
45C22×C4×D11—21no—
46C4×Q8×C11—22no—
47C4×Q8×C11C2×C414yescomplemented
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4C2312yes—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C42×C11—21no—
53C2×C42×C11—21no—
54C2×C42×C11D411yescharacteristic
55C2×C42×C11D411yescharacteristic
56C2×C42×C11D412yes—
57C2×C42×C11C2312yes—
58C2×C42×C11C2311yescharacteristic
59C2×#4325—24no—
60C2×#4325C2×C414yes—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—21no—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×C4×Dic11—22no—
66C2×C4×Dic11—21no—
67C22×C11⋊C8C2312yes—
68C22×C11⋊C8C2311yescharacteristic
69C22×C11⋊C8C2311yescharacteristic
70C4×D44—24no—
71C4×D44—22no—
72C4×D44—24no—
73C4×D44C2×C414yes—
74C42×D11—44no—
75C11×#95—22no—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—21no—
79#66899—24no—
80#66899C2×C414yescomplemented
81C11⋊#95—22no—
82C11⋊#95—21no—
83#66873—24no—
84#66873C2×C414yes—
85#66872C2×C414yescomplemented
86#66871—24no—
87C4×C11⋊C8—22no—
88C4×C11⋊C8C2×C414yescomplemented
89#21114—111nomaximal, Sylow
90C23×D11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11C22×C412yes—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—21no—
104C22×Dic11—22no—
105C2×D44—21no—
106C2×D44—22no—
107C2×D44C22×C412yes—
108C2×D44#4114yes—
109C2×C4×D11—28no—
110C2×C4×D11—24no—
111C2×C4×D11—44no—
112C2×C4×D11—44no—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—44no—
120C11×C4⋊C4C22×C412yes—
121C42×C11—24no—
122C42×C11—24no—
123C42×C11—22no—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11—22no—
127C42×C11—42no—
128C42×C11C22×C412yes—
129C42×C11#4112yes—
130#4325—28no—
131(C2×D11)⋊C4—28no—
132(C2×D11)⋊C4—24no—
133C4⋊Dic11—21no—
134C4⋊Dic11—22no—
135C4⋊Dic11C22×C412yes—
136C4⋊Dic11#4114yes—
137C4×Dic11—44no—
138C4×Dic11—42no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8C22×C412yes—
145C2×C11⋊C8C22×C412yes—
146C2×C4×SD16—111no—
147#2295D1111yescharacteristic, complemented
148C42×D4—111no—
149#1928—112no—
150#1919—112no—
151#1877—112no—
152#1862—112no—
153C4×#107—111no—
154C4×#103—111no—
155C4×#102—111no—
156#1744—111no—
157C23×C11C22×D411yescharacteristic
158C22×D11—22no—
159C22×D11—24no—
160C22×D11—42no—
161C22×D11—41no—
162C22×D11—41no—
163Q8×C11—22no—
164Q8×C11—22no—
165Q8×C11—42no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11C4×D412yes—
180C2×C4×C11C4×D412yes—
181C2×C4×C11#13514yes—
182C2×C4×C11AGL(1,ℤ/8)12yes—
183C2×C4×C11#13712yes—
184C2×C4×C11C23×C411yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4112yes—
187C2×C4×C11C2×#4112yes—
188C2×Dic11—22no—
189C2×Dic11—24no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194D44—22no—
195D44—24no—
196D44#11714yes—
197C4×D11—416no—
198C4×D11—48no—
199C11⋊C8—22no—
200C11⋊C8—22no—
201C11⋊C8—42no—
202C22×SD16—111no—
203C2×C4×Q8C2×D1111yescharacteristic
204C2×C4×D4—111no—
205C2×C4×D4—112no—
206C22×C42—221no—
207C4×SD16—118no—
208C2×#107—112no—
209C2×#106—111no—
210C2×#103—111no—
211C2×#103—112no—
212C2×#102—111no—
213C2×#102—112no—
214C2×C4×C8—111no—
215C2×C4×C8—111no—
216#391C2×D1112yes—
217#389C2×D1112yes—
218#387—22no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4—112no—
221C4×C4⋊C4—111no—
222C4×C4⋊C4C2×D1111yescharacteristic
223C4×C22⋊C4—222no—
224C4×C22⋊C4—221no—
225#376—21no—
226C43C2×D1111yescharacteristic
227#340—112no—
228#340—112no—
229#340—112no—
230#336—112no—
231#336—112no—
232C22×C11C2×C4×D411yescharacteristic
233C22×C11#52512yes—
234C22×C11C2×#13512yes—
235C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
236C22×C11C2×#13711yescharacteristic
237C2×D11—24no—
238C2×D11—44no—
239C2×D11—44no—
240C2×D11—42no—
241C2×D11—42no—
242C4×C11—24no—
243C4×C11—22no—
244C4×C11—42no—
245C4×C11—42no—
246C4×C11—42no—
247C4×C11—82no—
248C4×C11#44014yes—
249C4×C11C2×#11711yescharacteristic
250C4×C11C4×#4111yescharacteristic
251C4×C11#52912yes—
252Dic11—44no—
253Dic11—42no—
254C22×Q8C22×D1111yescharacteristic
255C22×D4—111no—
256C23×C4—222no—
257C23×C4—221no—
258C2×SD16—114no—
259C2×SD16—224no—
260C22×C8—111no—
261C22×C8—111no—
262C22×C8—112no—
263C4×Q8—22no—
264C4×Q8C4×D1114yescomplemented
265C4×D4—114no—
266C4×D4—224no—
267C4×D4—224no—
268C4×D4—222no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—111no—
272C2×C4⋊C4—112no—
273C2×C4⋊C4C22×D1112yes—
274C2×C4⋊C4C22×D1111yescharacteristic
275C2×C22⋊C4—222no—
276C2×C22⋊C4—221no—
277C2×C42—21no—
278C2×C42—21no—
279C2×C42—222no—
280C2×C42—221no—
281C2×C42—444no—
282C2×C42C22⋊D1112yes—
283C2×C42C22⋊D1111yescharacteristic
284C2×C42C22⋊D1111yescharacteristic
285C2×C42C22×D1112yes—
286C2×C42C22×D1111yescharacteristic
287#107—224no—
288#106—114no—
289#103—114no—
290#103—224no—
291#102—114no—
292#102—224no—
293C4×C8—114no—
294C4×C8—222no—
295#95—22no—
296#95—22no—
297#95—22no—
298#95—21no—
299#95—222no—
300#95—221no—
301C2×C11#229011yescharacteristic
302C2×C11C4×#13511yescharacteristic
303C2×C11C2×#44011yescharacteristic
304C2×C11#310512yes—
305C2×C11#310712yes—
306D11—44no—
307C24—221no—
308C2×Q8—21no—
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8C2×C4×D1112yes—
312C2×D4—112no—
313C2×D4—114no—
314C2×D4—221no—
315C2×D4—222no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—228no—
320C22×C4—221no—
321C22×C4—222no—
322C22×C4—224no—
323C22×C4—444no—
324C22×C4—442no—
325C22×C4—442no—
326C22×C4—444no—
327C22×C4C2×C22⋊D1112yes—
328C22×C4C2×C22⋊D1111yescharacteristic
329C22×C4C2×C22⋊D1112yes—
330C22×C4C2×C22⋊D1111yescharacteristic
331C22×C4C23×D1111yescharacteristic
332SD16—228no—
333C2×C8—112no—
334C2×C8—112no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8—222no—
338C2×C8—222no—
339C2×C8—222no—
340C4⋊C4—24no—
341C4⋊C4—21no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—44no—
345C4⋊C4—112no—
346C4⋊C4—114no—
347C4⋊C4—221no—
348C4⋊C4—222no—
349C4⋊C4C2×C4×D1112yes—
350C22⋊C4—228no—
351C22⋊C4—224no—
352C42—24no—
353C42—22no—
354C42—22no—
355C42—24no—
356C42—22no—
357C42—22no—
358C42—42no—
359C42—444no—
360C42—442no—
361C42C2×C4×D1112yes—
362C42#433912yes—
363C11#2111411yescharacteristic, complemented, Sylow
364C23—222no—
365C23—224no—
366C23—441no—
367C23—441no—
368C23—442no—
369C23C22×C22⋊D1111yescharacteristic
370Q8—22no—
371Q8—22no—
372Q8—42no—
373D4—114no—
374D4—222no—
375D4—224no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—222no—
390C2×C4—224no—
391C2×C4—4416no—
392C2×C4—441no—
393C2×C4—442no—
394C2×C4—441no—
395C2×C4—442no—
396C2×C4—448no—
397C2×C4C4×C22⋊D1112yes—
398C2×C4C4×C22⋊D1112yes—
399C2×C4#6699512yes—
400C2×C4#6700212yes—
401C2×C4#6700314yes—
402C2×C4C22×C4×D1111yescharacteristic
403C2×C4C2×#433911yescharacteristic
404C2×C4#41×D1112yes—
405C2×C4#41×D1112yes—
406C8—222no—
407C8—222no—
408C8—442no—
409C22—224no—
410C22—444no—
411C22—442no—
412C22—442no—
413C22—444no—
414C22C2×C4×C22⋊D1111yescharacteristic
415C22C2×#6699511yescharacteristic
416C22C2×#6700211yescharacteristic
417C22C2×#6700312yes—
418C22#1062335912yes—
419C4—24no—
420C4—22no—
421C4—42no—
422C4—42no—
423C4—42no—
424C4—82no—
425C4—444no—
426C4—442no—
427C4#1062263914yes—
428C4D11×#11711yescharacteristic
429C4#1062305311yescharacteristic
430C4#1062305912yes—
431C2—444no—
432C2#1307105311yescharacteristic
433C2C4×#6700311yescharacteristic
434C2C2×#1062263911yescharacteristic
435C2#1307865912yes—
436C2#1307868112yes—
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2295C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#2295D11
hypocenterC11#21114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C43 ◁ #2295

Complements

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

NH ≅ G/Ntype
3. #13069254C2semidirect
4. #13069191C2semidirect
7. C4×#66871C2semidirect
8. C4×#66899C2semidirect
10. #13068362C2semidirect
11. C11×#2295C2semidirect
26. C4×#4325C4semidirect
47. C4×Q8×C11C2×C4semidirect
80. #66899C2×C4semidirect
85. #66872C2×C4semidirect
88. C4×C11⋊C8C2×C4semidirect
147. #2295D11semidirect
264. C4×Q8C4×D11semidirect
363. C11#21114semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43252
C42×D442
#130692542
#130691912
#130689532
#130688622
C4×#668712
C4×#668992
C4×#668732
#130683622
C11×#22952
#2111411