Finite Group Databasebeta

← #14756953

Subgroups — #14756953

Order 2816.

890 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4324C211yesmaximal, characteristic
2#13071268C211yesmaximal, characteristic, complemented
3#13069250C212yesmaximal, complemented
4#13069194C212yesmaximal, complemented
5#13068950C212yesmaximal
6#13068877C212yesmaximal
7C4×#66872C211yesmaximal, characteristic, complemented
8#13068449C211yesmaximal, characteristic, complemented
9#13068441C211yesmaximal, characteristic
10#13068368C211yesmaximal, characteristic, complemented
11C11×#2275C211yesmaximal, characteristic
12C2×C4×D4×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4324C2211yescharacteristic
15C2×C4×Dic22C2211yescharacteristic
16C4×C11×C4⋊C4C2212yes—
17C4×C11×C4⋊C4C2211yescharacteristic
18C4×C11×C22⋊C4—21no—
19C4×C11×C22⋊C4—22no—
20C11×#376C2211yescharacteristic
21C2×C11×#95—21no—
22C2×#66896C2212yes—
23C2×#66896C2211yescharacteristic
24C4×#4324C418yescomplemented
25C2×#66874C2212yes—
26C2×#66874C2211yescharacteristic
27C2×#66872C2212yes—
28C2×#66872C2211yescharacteristic
29C4×C4⋊Dic11C2211yescharacteristic
30#10622542C2212yes—
31#10622541C2212yes—
32C2×#66867C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622265—22no—
35#10622264—21no—
36#10622263—21no—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622162C2212yes—
41#10622162C2212yes—
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—22no—
44C23×C4×C11—21no—
45C22×Dic22C2311yescharacteristic
46C4×D4×C11—24no—
47C4×D4×C11—24no—
48C4×D4×C11—22no—
49C4×D4×C11C2×C414yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—21no—
54C2×C42×C11—22no—
55C2×C42×C11—21no—
56C2×C42×C11C2312yes—
57C2×C42×C11C2311yescharacteristic
58C2×#4324—24no—
59C2×#4324C2×C414yes—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×Dic11⋊C4—21no—
63C2×Dic11⋊C4—22no—
64C2×C4×Dic11—21no—
65C2×C4×Dic11—21no—
66C22×C11⋊C8C2312yes—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69C4×Dic22—22no—
70C4×Dic22C2×C414yescomplemented
71C11×#95—22no—
72C11×#95—21no—
73C11×#95D411yescharacteristic
74C11×#95D411yescharacteristic
75C11×#95D412yes—
76#66896—24no—
77#66896C2×C414yes—
78C11⋊#95—21no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82#66874—24no—
83#66874C2×C414yescomplemented
84#66872—24no—
85#66872C2×C414yescomplemented
86#66867—22no—
87C4×C11⋊C8C2×C414yescomplemented
88#21133—111nomaximal, Sylow
89C24×C11—21no—
90C2×D4×C11—22no—
91C2×D4×C11—21no—
92C2×D4×C11C22×C412yes—
93C2×D4×C11#4114yes—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—28no—
97C22×C4×C11—24no—
98C22×C4×C11—82no—
99C22×C4×C11—82no—
100C22×C4×C11—82no—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—22no—
109C2×Dic22—22no—
110C2×Dic22—22no—
111C2×Dic22—21no—
112C2×Dic22C22×C412yes—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4C22×C412yes—
116C11×C4⋊C4#4114yes—
117C11×C22⋊C4—28no—
118C11×C22⋊C4—24no—
119C42×C11—22no—
120C42×C11—22no—
121C42×C11—81no—
122C42×C11—82no—
123C42×C11C22×C412yes—
124C42×C11#4112yes—
125#4324—28no—
126C4⋊Dic11—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11C22×C412yes—
130Dic11⋊C4—24no—
131Dic11⋊C4—82no—
132C4×Dic11—24no—
133C4×Dic11—81no—
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#2320—111no—
143#2275D1111yescharacteristic
144#1927—112no—
145#1919—112no—
146#1877—112no—
147#1864—112no—
148C4×#106—111no—
149#1763—111no—
150#1762—111no—
151#1746—111no—
152C23×C11—22no—
153C23×C11—24no—
154C23×C11—41no—
155C23×C11—42no—
156C23×C11—41no—
157C23×C11C22×D411yescharacteristic
158D4×C11—22no—
159D4×C11—24no—
160D4×C11#11714yes—
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—24no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—84no—
176C2×C4×C11—88no—
177C2×C4×C11C4×D412yes—
178C2×C4×C11C4×D412yes—
179C2×C4×C11C23×C411yescharacteristic
180C2×C4×C11C2×#4112yes—
181C2×C4×C11C2×#4112yes—
182C2×C4×C11C2×#4111yescharacteristic
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—42no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191Dic22—22no—
192Dic22—22no—
193Dic22—42no—
194C11⋊C8—22no—
195C11⋊C8—22no—
196C11⋊C8—42no—
197C22×SD16—111no—
198C2×C4×Q8—111no—
199C2×C4×D4C2×D1112yes—
200C2×C4×D4C2×D1111yescharacteristic
201C4×SD16—118no—
202C2×#106—111no—
203C2×#106—112no—
204C2×#103—111no—
205C2×#103—112no—
206C2×#102—111no—
207C2×#102—112no—
208C2×#97—111no—
209C2×C4×C8—111no—
210#391—112no—
211#389—112no—
212#387—222no—
213#383—221no—
214#382—221no—
215C4×C4⋊C4—111no—
216C4×C4⋊C4C2×D1112yes—
217C4×C4⋊C4C2×D1111yescharacteristic
218C4×C22⋊C4—21no—
219C4×C22⋊C4—22no—
220#376C2×D1111yescharacteristic
221C2×#95—21no—
222#340—112no—
223#340—112no—
224#340—112no—
225#336—112no—
226#336—112no—
227C22×C11—24no—
228C22×C11—44no—
229C22×C11—44no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11C2×C4×D411yescharacteristic
233C22×C11#52512yes—
234C22×C11#57711yescharacteristic
235C22×C11#57712yes—
236C22×C11#57711yescharacteristic
237C4×C11—22no—
238C4×C11—22no—
239C4×C11—42no—
240C4×C11—44no—
241C4×C11—42no—
242C4×C11—42no—
243C4×C11C2×#11711yescharacteristic
244C4×C11C4×#4111yescharacteristic
245C4×C11#52912yes—
246Dic11—42no—
247Dic11—42no—
248Dic11—82no—
249C22×Q8—111no—
250C22×D4C22×D1111yescharacteristic
251C23×C4—22no—
252C23×C4—21no—
253C2×SD16—114no—
254C2×SD16—224no—
255C22×C8—111no—
256C22×C8—111no—
257C22×C8—112no—
258C4×Q8—114no—
259C4×Q8—222no—
260C4×D4—24no—
261C4×D4—24no—
262C4×D4—22no—
263C4×D4C4×D1114yes—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—112no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—222no—
268C2×C4⋊C4C22×D1111yescharacteristic
269C2×C4⋊C4C22×D1112yes—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—21no—
272C2×C42—22no—
273C2×C42—21no—
274C2×C42—221no—
275C2×C42—221no—
276C2×C42C22×D1112yes—
277C2×C42C22×D1111yescharacteristic
278#106—114no—
279#106—224no—
280#103—114no—
281#103—224no—
282#102—114no—
283#102—224no—
284#97—222no—
285C4×C8—114no—
286#95—22no—
287#95—21no—
288#95—221no—
289#95—222no—
290#95—222no—
291#95—222no—
292#95C22⋊D1111yescharacteristic
293#95C22⋊D1111yescharacteristic
294#95C22⋊D1112yes—
295C2×C11—44no—
296C2×C11#229011yescharacteristic
297C2×C11#294911yescharacteristic
298C2×C11#295211yescharacteristic
299C2×C11#312312yes—
300C2×C11#312512yes—
301C24—21no—
302C2×Q8—112no—
303C2×Q8—221no—
304C2×Q8—222no—
305C2×Q8—222no—
306C2×D4—22no—
307C2×D4—21no—
308C2×D4C2×C4×D1112yes—
309C2×D4#433914yes—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—28no—
313C22×C4—24no—
314C22×C4—82no—
315C22×C4—82no—
316C22×C4—82no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—222no—
320C22×C4C2×C22⋊D1112yes—
321C22×C4C2×C22⋊D1112yes—
322C22×C4C2×C22⋊D1111yescharacteristic
323C22×C4C2×C22⋊D1111yescharacteristic
324C22×C4C23×D1111yescharacteristic
325SD16—228no—
326C2×C8—112no—
327C2×C8—112no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—222no—
331C2×C8—222no—
332C2×C8—222no—
333C4⋊C4—21no—
334C4⋊C4—22no—
335C4⋊C4—112no—
336C4⋊C4—224no—
337C4⋊C4—221no—
338C4⋊C4—222no—
339C4⋊C4—222no—
340C4⋊C4—882no—
341C4⋊C4C2×C4×D1112yes—
342C4⋊C4#433914yes—
343C22⋊C4—28no—
344C22⋊C4—24no—
345C42—22no—
346C42—22no—
347C42—81no—
348C42—82no—
349C42—224no—
350C42—881no—
351C42C2×C4×D1112yes—
352C42#433912yes—
353C11#2113311yescharacteristic, complemented, Sylow
354C23—22no—
355C23—24no—
356C23—41no—
357C23—42no—
358C23—41no—
359C23C22×C22⋊D1111yescharacteristic
360Q8—222no—
361Q8—222no—
362Q8—442no—
363D4—22no—
364D4—24no—
365D4#6692514yes—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—84no—
381C2×C4—88no—
382C2×C4—222no—
383C2×C4—222no—
384C2×C4—442no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4C4×C22⋊D1112yes—
391C2×C4C4×C22⋊D1112yes—
392C2×C4C22×C4×D1111yescharacteristic
393C2×C4C2×#433912yes—
394C2×C4C2×#433912yes—
395C2×C4C2×#433911yescharacteristic
396C8—222no—
397C8—222no—
398C8—442no—
399C22—24no—
400C22—44no—
401C22—44no—
402C22—42no—
403C22—42no—
404C22C2×C4×C22⋊D1111yescharacteristic
405C22#1062332212yes—
406C22#1062336711yescharacteristic
407C22#1062336712yes—
408C22#1062336811yescharacteristic
409C4—22no—
410C4—22no—
411C4—42no—
412C4—44no—
413C4—42no—
414C4—42no—
415C4—442no—
416C4—442no—
417C4—882no—
418C4C2×#6692511yescharacteristic
419C4C4×#433911yescharacteristic
420C4#1062301012yes—
421C2—44no—
422C2#1307105911yescharacteristic
423C2#1307747311yescharacteristic
424C2#1307749711yescharacteristic
425C2#1307886812yes—
426C2#1307889312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2275C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#2275D11
hypocenterC11#21133
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2275

Complements

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

NH ≅ G/Ntype
2. #13071268C2semidirect
3. #13069250C2semidirect
4. #13069194C2semidirect
7. C4×#66872C2semidirect
8. #13068449C2semidirect
10. #13068368C2semidirect
24. C4×#4324C4semidirect
70. C4×Dic22C2×C4semidirect
83. #66874C2×C4semidirect
85. #66872C2×C4semidirect
87. C4×C11⋊C8C2×C4semidirect
353. C11#21133semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43242
#130712682
#130692502
#130691942
#130689502
#130688772
C4×#668722
#130684492
#130684412
#130683682
C11×#22752
#2113311