Finite Group Databasebeta

← #14756925

Subgroups — #14756925

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×#4324C211yesmaximal, characteristic
2#13070979C211yesmaximal, characteristic, complemented
3#13069240C212yesmaximal
4#13069198C212yesmaximal, complemented
5#13068974C212yesmaximal
6#13068883C212yesmaximal, complemented
7C4×#66872C211yesmaximal, characteristic, complemented
8#13068449C211yesmaximal, characteristic, complemented
9#13068441C211yesmaximal, characteristic
10#13068368C211yesmaximal, characteristic, complemented
11C11×#2319C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4324C2211yescharacteristic
14C2×C4×Dic22C2212yes—
15C2×C4×Dic22C2211yescharacteristic
16C11×#390C2212yes—
17C11×#389C2212yes—
18C11×#388—22no—
19C11×#381—21no—
20C11×#380—21no—
21C4×C11×C4⋊C4C2211yescharacteristic
22C11×#376C2211yescharacteristic
23C2×#66896C2212yes—
24C2×#66896C2211yescharacteristic
25C4×#4324C418yescomplemented
26C2×#66874C2212yes—
27C2×#66874C2211yescharacteristic
28C2×#66872C2212yes—
29C2×#66872C2211yescharacteristic
30C4×C4⋊Dic11C2212yes—
31C4×C4⋊Dic11C2211yescharacteristic
32C2×#66867C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622262—21no—
35#10622262—22no—
36#10622261—21no—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622162C2212yes—
41#10622162C2212yes—
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—21no—
44C22×Dic22C2311yescharacteristic
45C4×D4×C11—22no—
46C4×D4×C11C2×C414yes—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C42×C11—21no—
54C2×C42×C11C2312yes—
55C2×C42×C11C2311yescharacteristic
56C2×#4324—24no—
57C2×#4324C2×C414yes—
58C2×C4⋊Dic11C2311yescharacteristic
59C2×C4⋊Dic11C2312yes—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—21no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11—21no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11—21no—
66C22×C11⋊C8C2312yes—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69C4×Dic22—24no—
70C4×Dic22—22no—
71C4×Dic22—24no—
72C4×Dic22C2×C414yes—
73C11×#95—21no—
74C11×#95—22no—
75C11×#95D411yescharacteristic
76C11×#95D411yescharacteristic
77C11×#95D412yes—
78#66896—24no—
79#66896C2×C414yes—
80C11⋊#95—22no—
81C11⋊#95—21no—
82#66874—24no—
83#66874C2×C414yes—
84#66872—24no—
85#66872C2×C414yes—
86#66867—22no—
87C4×C11⋊C8C2×C414yes—
88#21131—111nomaximal, Sylow
89C24×C11—21no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—21no—
93C2×D4×C11C22×C412yes—
94C22×C4×C11—21no—
95C22×C4×C11—24no—
96C22×C4×C11—22no—
97C22×C4×C11—82no—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—22no—
106C2×Dic22—21no—
107C2×Dic22—22no—
108C2×Dic22C22×C412yes—
109C2×Dic22#4114yes—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—82no—
114C11×C4⋊C4C22×C412yes—
115C11×C22⋊C4—24no—
116C11×C22⋊C4—82no—
117C11×C22⋊C4—82no—
118C42×C11—22no—
119C42×C11—22no—
120C42×C11—81no—
121C42×C11C22×C412yes—
122C42×C11#4112yes—
123#4324—28no—
124C4⋊Dic11—21no—
125C4⋊Dic11—22no—
126C4⋊Dic11C22×C412yes—
127C4⋊Dic11#4114yes—
128Dic11⋊C4—28no—
129Dic11⋊C4—24no—
130C4×Dic11—28no—
131C4×Dic11—24no—
132C4×Dic11—81no—
133C4×Dic11—82no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8C22×C412yes—
140C2×C11⋊C8C22×C412yes—
141C2×C4×SD16—111no—
142#2319D1111yescharacteristic
143#2276—111no—
144#1926—112no—
145#1920—112no—
146#1880—112no—
147#1865—112no—
148C4×#106—111no—
149#1763—111no—
150#1762—111no—
151#1746—111no—
152C23×C11—22no—
153C23×C11—42no—
154C23×C11—41no—
155C23×C11—42no—
156C23×C11—41no—
157C23×C11C22×D411yescharacteristic
158D4×C11—22no—
159D4×C11—22no—
160D4×C11—42no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—84no—
176C2×C4×C11C4×D412yes—
177C2×C4×C11C4×D412yes—
178C2×C4×C11C23×C411yescharacteristic
179C2×C4×C11C2×#4111yescharacteristic
180C2×C4×C11C2×#4112yes—
181C2×C4×C11C2×#4112yes—
182C2×Dic11—22no—
183C2×Dic11—24no—
184C2×Dic11—22no—
185C2×Dic11—24no—
186C2×Dic11—42no—
187C2×Dic11—41no—
188C2×Dic11—42no—
189C2×Dic11—41no—
190Dic22—22no—
191Dic22—24no—
192Dic22#11714yes—
193C11⋊C8—22no—
194C11⋊C8—22no—
195C11⋊C8—42no—
196C22×SD16—111no—
197C2×C4×Q8—111no—
198C2×C4×Q8—112no—
199C2×C4×D4C2×D1111yescharacteristic
200C4×SD16—118no—
201C2×#106—111no—
202C2×#106—112no—
203C2×#103—111no—
204C2×#103—112no—
205C2×#102—111no—
206C2×#102—112no—
207C2×#97—111no—
208C2×C4×C8—111no—
209#390C2×D1112yes—
210#389C2×D1112yes—
211#388—22no—
212#381—21no—
213#380—21no—
214C4×C4⋊C4—112no—
215C4×C4⋊C4—111no—
216C4×C4⋊C4—221no—
217C4×C4⋊C4—222no—
218C4×C4⋊C4C2×D1111yescharacteristic
219#376—221no—
220#376C2×D1111yescharacteristic
221#340—112no—
222#340—112no—
223#340—112no—
224#336—112no—
225#336—112no—
226C22×C11—42no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—82no—
230C22×C11—82no—
231C22×C11C2×C4×D411yescharacteristic
232C22×C11#52512yes—
233C22×C11#57712yes—
234C22×C11#57711yescharacteristic
235C22×C11#57711yescharacteristic
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—42no—
239C4×C11—42no—
240C4×C11—42no—
241C4×C11—82no—
242C4×C11C2×#11711yescharacteristic
243C4×C11C4×#4111yescharacteristic
244C4×C11#52912yes—
245Dic11—24no—
246Dic11—44no—
247Dic11—42no—
248C22×Q8—111no—
249C22×D4C22×D1111yescharacteristic
250C23×C4—21no—
251C2×SD16—114no—
252C2×SD16—224no—
253C22×C8—111no—
254C22×C8—111no—
255C22×C8—112no—
256C4×Q8—114no—
257C4×Q8—224no—
258C4×Q8—224no—
259C4×Q8—222no—
260C4×D4—22no—
261C4×D4C4×D1114yes—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—112no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4C22×D1112yes—
268C2×C4⋊C4C22×D1111yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C42—21no—
273C2×C42—222no—
274C2×C42—221no—
275C2×C42—222no—
276C2×C42—221no—
277C2×C42C22×D1112yes—
278C2×C42C22×D1111yescharacteristic
279#106—114no—
280#106—224no—
281#103—114no—
282#103—224no—
283#102—114no—
284#102—224no—
285#97—222no—
286C4×C8—114no—
287#95—21no—
288#95—22no—
289#95—222no—
290#95—221no—
291#95C22⋊D1111yescharacteristic
292#95C22⋊D1111yescharacteristic
293#95C22⋊D1112yes—
294C2×C11—82no—
295C2×C11#229011yescharacteristic
296C2×C11#294911yescharacteristic
297C2×C11#295211yescharacteristic
298C2×C11#312512yes—
299C2×C11#312612yes—
300C24—21no—
301C2×Q8—112no—
302C2×Q8—114no—
303C2×Q8—221no—
304C2×Q8—222no—
305C2×D4—21no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4C2×C4×D1112yes—
309C22×C4—21no—
310C22×C4—24no—
311C22×C4—22no—
312C22×C4—82no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—222no—
316C22×C4C2×C22⋊D1112yes—
317C22×C4C2×C22⋊D1112yes—
318C22×C4C2×C22⋊D1111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320C22×C4C23×D1111yescharacteristic
321SD16—228no—
322C2×C8—112no—
323C2×C8—112no—
324C2×C8—222no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8—222no—
328C2×C8—222no—
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—82no—
333C4⋊C4—112no—
334C4⋊C4—114no—
335C4⋊C4—228no—
336C4⋊C4—224no—
337C4⋊C4—221no—
338C4⋊C4—222no—
339C4⋊C4C2×C4×D1112yes—
340C22⋊C4—24no—
341C22⋊C4—82no—
342C22⋊C4—82no—
343C42—22no—
344C42—22no—
345C42—81no—
346C42—228no—
347C42—224no—
348C42—881no—
349C42—882no—
350C42C2×C4×D1112yes—
351C42#433912yes—
352C11#2113111yescharacteristic, complemented, Sylow
353C23—22no—
354C23—42no—
355C23—41no—
356C23—42no—
357C23—41no—
358C23C22×C22⋊D1111yescharacteristic
359Q8—114no—
360Q8—222no—
361Q8—224no—
362D4—22no—
363D4—22no—
364D4—42no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—84no—
380C2×C4—222no—
381C2×C4—224no—
382C2×C4—222no—
383C2×C4—224no—
384C2×C4—442no—
385C2×C4—441no—
386C2×C4—442no—
387C2×C4—441no—
388C2×C4C4×C22⋊D1112yes—
389C2×C4C4×C22⋊D1112yes—
390C2×C4C22×C4×D1111yescharacteristic
391C2×C4C2×#433911yescharacteristic
392C2×C4#41×D1112yes—
393C2×C4#41×D1112yes—
394C8—222no—
395C8—222no—
396C8—442no—
397C22—42no—
398C22—42no—
399C22—42no—
400C22—82no—
401C22—82no—
402C22C2×C4×C22⋊D1111yescharacteristic
403C22#1062335912yes—
404C22#1062336712yes—
405C22#1062336711yescharacteristic
406C22#1062336811yescharacteristic
407C4—22no—
408C4—22no—
409C4—42no—
410C4—42no—
411C4—42no—
412C4—82no—
413C4—224no—
414C4—444no—
415C4—442no—
416C4D11×#11711yescharacteristic
417C4#1062305311yescharacteristic
418C4#1062305912yes—
419C2—82no—
420C2#1307105311yescharacteristic
421C2#1307747311yescharacteristic
422C2#1307749711yescharacteristic
423C2#1307888712yes—
424C2#1307890212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2319C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#2319D11
hypocenterC11#21131
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #13070979C2semidirect
4. #13069198C2semidirect
6. #13068883C2semidirect
7. C4×#66872C2semidirect
8. #13068449C2semidirect
10. #13068368C2semidirect
25. C4×#4324C4semidirect
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×#43242
#130709792
#130692402
#130691982
#130689742
#130688832
C4×#668722
#130684492
#130684412
#130683682
C11×#23192
#2113111