Finite Group Databasebeta

← #14756927

Subgroups — #14756927

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4325C211yesmaximal, characteristic
2#13071254C211yesmaximal, characteristic
3#13070981C211yesmaximal, characteristic, complemented
4#13069241C212yesmaximal
5#13069199C212yesmaximal, complemented
6#13068969C212yesmaximal
7#13068882C212yesmaximal, complemented
8C4×#66872C211yesmaximal, characteristic, complemented
9#13068442C211yesmaximal, characteristic
10#13068369C211yesmaximal, characteristic, complemented
11C11×#1763C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×Q8×Dic11C2212yes—
14C22×#4325C2211yescharacteristic
15C2×C4×D44C2211yescharacteristic
16C2×C11×#103C2212yes—
17C2×C11×#97C2211yescharacteristic
18C4×C11×C4⋊C4C2211yescharacteristic
19C2×#66899C2211yescharacteristic
20C2×#66885C2212yes—
21C4×#4325C418yescomplemented
22#10622601C2212yes—
23C4⋊C4×Dic11—22no—
24C4⋊C4×Dic11C2212yes—
25#10622586C2212yes—
26C2×#66873C2211yescharacteristic
27C2×#66872C2212yes—
28C2×#66872C2211yescharacteristic
29#10622553—22no—
30C4×C4⋊Dic11—21no—
31C4×C4⋊Dic11C2211yescharacteristic
32#10622545—21no—
33#10622545C2211yescharacteristic
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622280—21no—
36#10622277—21no—
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×Dic11C2312yes—
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2311yescharacteristic
71C4×D44—22no—
72C4×D44C2×C414yes—
73C11×#103—24no—
74C11×#97—22no—
75C11×#95—21no—
76#66899C2×C414yes—
77C11⋊#95—21no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95D411yescharacteristic
81C11⋊#95D411yescharacteristic
82C11⋊#95D412yes—
83#66885—24no—
84#66873C2×C414yes—
85#66872—24no—
86#66872C2×C414yes—
87C4×C11⋊C8C2×C414yes—
88#21131—111nomaximal, Sylow
89C23×D11—21no—
90C2×Q8×C11—22no—
91C2×Q8×C11—21no—
92C2×Q8×C11C22×C412yes—
93C2×Q8×C11#4114yes—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—22no—
101C22×Dic11—21no—
102C22×Dic11C2×D412yes—
103C22×Dic11C2×D412yes—
104C2×D44—21no—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44C22×C412yes—
108C2×C4×D11—24no—
109C2×C4×D11—82no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4C22×C412yes—
118C42×C11—24no—
119C42×C11—81no—
120C42×C11C22×C412yes—
121C42×C11#4112yes—
122#4325—28no—
123(C2×D11)⋊C4—24no—
124(C2×D11)⋊C4—82no—
125(C2×D11)⋊C4—82no—
126C4⋊Dic11—28no—
127C4⋊Dic11—21no—
128C4⋊Dic11—22no—
129C4⋊Dic11C22×C412yes—
130C4⋊Dic11#4114yes—
131Dic11⋊C4—82no—
132C4×Dic11—28no—
133C4×Dic11—22no—
134C4×Dic11—22no—
135C4×Dic11—81no—
136C4×Dic11—82no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8C22×C412yes—
140C2×C11⋊C8C22×C412yes—
141C2×C4×SD16—111no—
142#2319—111no—
143#2276—111no—
144#1926—112no—
145#1920—112no—
146#1880—112no—
147#1865—112no—
148C4×#106—111no—
149#1763D1111yescharacteristic, complemented
150#1762—111no—
151#1746—111no—
152C23×C11C22×D411yescharacteristic
153C22×D11—22no—
154C22×D11—42no—
155C22×D11—41no—
156C22×D11—42no—
157C22×D11—41no—
158Q8×C11—22no—
159Q8×C11—24no—
160Q8×C11#11714yes—
161C2×C4×C11—22no—
162C2×C4×C11—24no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11C4×D412yes—
173C2×C4×C11C4×D412yes—
174C2×C4×C11C23×C411yescharacteristic
175C2×C4×C11C2×#4112yes—
176C2×C4×C11C2×#4111yescharacteristic
177C2×C4×C11C2×#4112yes—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—24no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189D44—22no—
190D44—22no—
191D44—42no—
192C4×D11—84no—
193C8×C11—42no—
194C11⋊C8—22no—
195C11⋊C8—22no—
196C22×SD16—111no—
197C2×C4×Q8—112no—
198C2×C4×Q8C2×D1111yescharacteristic
199C2×C4×D4—111no—
200C4×SD16—118no—
201C2×#106—111no—
202C2×#106—112no—
203C2×#103—111no—
204C2×#103C2×D1112yes—
205C2×#102—111no—
206C2×#102—112no—
207C2×#97C2×D1111yescharacteristic
208C2×C4×C8—111no—
209#390—112no—
210#389—112no—
211#388—222no—
212#381—221no—
213#380—221no—
214C4×C4⋊C4—112no—
215C4×C4⋊C4—111no—
216C4×C4⋊C4—221no—
217C4×C4⋊C4—222no—
218C4×C4⋊C4C2×D1111yescharacteristic
219#376—111no—
220#376—221no—
221#340—112no—
222#340—112no—
223#340C2×D1112yes—
224#336—112no—
225#336—112no—
226C22×C11C2×C4×D411yescharacteristic
227C22×C11#52512yes—
228C22×C11#57711yescharacteristic
229C22×C11#57711yescharacteristic
230C22×C11#57712yes—
231C2×D11—42no—
232C2×D11—42no—
233C2×D11—42no—
234C2×D11—82no—
235C2×D11—82no—
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—24no—
239C4×C11—42no—
240C4×C11—82no—
241C4×C11C2×#11711yescharacteristic
242C4×C11C4×#4111yescharacteristic
243C4×C11#52912yes—
244Dic11—42no—
245Dic11—44no—
246Dic11—42no—
247Dic11—42no—
248C22×Q8C22×D1111yescharacteristic
249C22×D4—111no—
250C23×C4—221no—
251C2×SD16—114no—
252C2×SD16—224no—
253C22×C8—111no—
254C22×C8—111no—
255C22×C8C22×D1112yes—
256C4×Q8—22no—
257C4×Q8—224no—
258C4×Q8—224no—
259C4×Q8C4×D1114yes—
260C4×D4—114no—
261C4×D4—222no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—112no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4C22×D1112yes—
268C2×C4⋊C4C22×D1111yescharacteristic
269C2×C22⋊C4—221no—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—222no—
272C2×C42—21no—
273C2×C42—21no—
274C2×C42—112no—
275C2×C42—222no—
276C2×C42—222no—
277C2×C42—221no—
278C2×C42C22×D1111yescharacteristic
279#106—114no—
280#106—224no—
281#103—24no—
282#103—114no—
283#102—114no—
284#102—224no—
285#97—22no—
286C4×C8—114no—
287#95—21no—
288#95—111no—
289#95—111no—
290#95—112no—
291#95—222no—
292#95—222no—
293#95—221no—
294C2×C11#229011yescharacteristic
295C2×C11#294911yescharacteristic
296C2×C11#295211yescharacteristic
297C2×C11#312512yes—
298C2×C11#312612yes—
299D11—82no—
300C24—221no—
301C2×Q8—21no—
302C2×Q8—22no—
303C2×Q8C2×C4×D1112yes—
304C2×Q8#433914yes—
305C2×D4—112no—
306C2×D4—222no—
307C2×D4—221no—
308C2×D4—222no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—112no—
313C22×C4—112no—
314C22×C4—222no—
315C22×C4—221no—
316C22×C4—224no—
317C22×C4—882no—
318C22×C4D4×D1111yescharacteristic
319C22×C4D4×D1111yescharacteristic
320C22×C4C23×D1111yescharacteristic
321SD16—228no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—112no—
326C2×C8—112no—
327C2×C8—222no—
328C2×C8—222no—
329C4⋊C4—24no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—112no—
334C4⋊C4—114no—
335C4⋊C4—228no—
336C4⋊C4—222no—
337C4⋊C4—221no—
338C4⋊C4—882no—
339C4⋊C4C2×C4×D1112yes—
340C22⋊C4—224no—
341C22⋊C4—882no—
342C22⋊C4—882no—
343C42—24no—
344C42—81no—
345C42—228no—
346C42—222no—
347C42—222no—
348C42—881no—
349C42—882no—
350C42C2×C4×D1112yes—
351C42#434112yes—
352C11#2113111yescharacteristic, complemented, Sylow
353C23—222no—
354C23—441no—
355C23—442no—
356C23—441no—
357C23—442no—
358C23C2×D4×D1111yescharacteristic
359Q8—22no—
360Q8—24no—
361Q8#6692514yes—
362D4—222no—
363D4—222no—
364D4—442no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4—222no—
379C2×C4—222no—
380C2×C4—222no—
381C2×C4—222no—
382C2×C4—224no—
383C2×C4—222no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—884no—
388C2×C4(C22⋊D11)⋊C412yes—
389C2×C4(C22⋊D11)⋊C412yes—
390C2×C4C22×C4×D1111yescharacteristic
391C2×C4C2×#433912yes—
392C2×C4C2×#434111yescharacteristic
393C2×C4#41×D1112yes—
394C8—42no—
395C8—222no—
396C8—222no—
397C22—442no—
398C22—442no—
399C22—442no—
400C22—882no—
401C22—882no—
402C22C2×(C22⋊D11)⋊C411yescharacteristic
403C22#1062307812yes—
404C22#1062330611yescharacteristic
405C22#1062330911yescharacteristic
406C22#1062330912yes—
407C4—24no—
408C4—22no—
409C4—22no—
410C4—42no—
411C4—82no—
412C4—442no—
413C4—444no—
414C4—442no—
415C4—442no—
416C4C2×#6692511yescharacteristic
417C4#1062305311yescharacteristic
418C4#1062306912yes—
419C2—882no—
420C2#1307105511yescharacteristic
421C2#1307747111yescharacteristic
422C2#1307749511yescharacteristic
423C2#1307889112yes—
424C2#1307890612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1763C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1763D11
hypocenterC11#21131
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
3. #13070981C2semidirect
5. #13069199C2semidirect
7. #13068882C2semidirect
8. C4×#66872C2semidirect
10. #13068369C2semidirect
11. C11×#1763C2semidirect
21. C4×#4325C4semidirect
149. #1763D11semidirect
352. C11#21131semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43252
#130712542
#130709812
#130692412
#130691992
#130689692
#130688822
C4×#668722
#130684422
#130683692
C11×#17632
#2113111