Finite Group Databasebeta

← #14760377

Subgroups — #14760377

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622797C211yesmaximal, characteristic, complemented
2C2×#10622714C211yesmaximal, characteristic
3#13071300C212yesmaximal
4#13069488C211yesmaximal, characteristic, complemented
5#13069355C211yesmaximal, characteristic, complemented
6#13069294C212yesmaximal, complemented
7#13069050C212yesmaximal
8#13068641C211yesmaximal, characteristic
9#13068515C211yesmaximal, characteristic, complemented
10#103×Dic11C212yesmaximal, complemented
11C2×C11×#467C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×C22⋊Q8C2212yes—
15C2×Q8×Dic11C2212yes—
16C2×#66979C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18C11×#467C418yescomplemented
19C2×C11×#107C2211yescharacteristic
20C2×C11×#103C2212yes—
21#10622843C2212yes—
22C2×#66899C2212yes—
23C2×#66899C2212yes—
24#10622825C2212yes—
25#10622797—24no—
26C2×#66881C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28#10622714—24no—
29C2×#66879C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622598—22no—
34#10622598C2212yes—
35#10622594—22no—
36C4⋊C4×Dic11C2212yes—
37#10622564—22no—
38#10622564—22no—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×Q8×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C2×C11×Q16—22no—
45C2×C11×Q16—22no—
46C2×C11×Q16C2×C414yes—
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C22×C8×C11C2×C414yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8C2×C418yes—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C22⋊C4—22no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11D412yes—
59Q8×Dic11—24no—
60Q8×Dic11—24no—
61#66979—22no—
62#66979—22no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11D412yes—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2312yes—
68C2×C4×Dic11—22no—
69C2×C4×Dic11—22no—
70C2×C4×Dic11C2311yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C2×#4318—22no—
73C2×#4318—22no—
74C2×#4318—22no—
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2311yescharacteristic
77C11×#107C2×C414yes—
78C11×#103C2×C418yes—
79#66899—24no—
80#66899—24no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#66881—22no—
87#66881—22no—
88#66879—22no—
89#66879D414yes—
90C8×Dic11—22no—
91C8×Dic11—22no—
92#21530—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11C22×C414yes—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4112yes—
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11C2×D412yes—
113C22×Dic11C2×D412yes—
114C11×Q16—28no—
115C2×C8×C11—28no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11C22×C412yes—
119C2×C8×C11C22×C412yes—
120C2×C8×C11C2×D412yes—
121C2×C8×C11#4112yes—
122C11×C4⋊C4—28no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4C22×C414yes—
125C11×C22⋊C4—28no—
126C22⋊Dic11—24no—
127C22⋊Dic11—82no—
128C4⋊Dic11—24no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11—44no—
134C4⋊Dic11—82no—
135C4×Dic11—21no—
136C4×Dic11—21no—
137C4×Dic11—44no—
138C4×Dic11—82no—
139C4×Dic11C2×D412yes—
140C4×Dic11#4112yes—
141#4318—28no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8C2×D412yes—
147C2×C11⋊C8#4112yes—
148C2×#467D1111yescharacteristic
149C2×#441—111no—
150C2×#405—111no—
151#2323—112no—
152#1971—111no—
153#1943—111no—
154#1933—112no—
155#1894—112no—
156#1807—111no—
157#1776—111no—
158C4×#103—112no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11C4×D412yes—
164C23×C11C22×D411yescharacteristic
165Q8×C11—24no—
166Q8×C11—24no—
167Q8×C11—42no—
168Q8×C11—42no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11C4×D412yes—
182C2×C4×C11C23×C411yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11#12114yes—
200C8×C11—22no—
201C8×C11C4×D414yes—
202C11⋊C8—22no—
203C11⋊C8—22no—
204C22×Q16C2×D1111yescharacteristic
205C22×M16—111no—
206C23×C8C2×D1111yescharacteristic
207C2×C22⋊Q8C2×D1112yes—
208C2×C4×Q8—112no—
209C2×#117—111no—
210#467Dic1118yescomplemented
211#441—224no—
212C2×#107C2×D1111yescharacteristic
213C2×#106—111no—
214C2×#106—111no—
215C2×#103—112no—
216C2×#103—112no—
217C2×#103C2×D1112yes—
218#405—224no—
219C2×#97—111no—
220C2×#97—111no—
221C2×C4×C8—111no—
222C2×C4×C8—111no—
223#391—112no—
224#389—112no—
225#389—222no—
226#388—222no—
227#388—222no—
228#387—222no—
229#380—112no—
230C4×C4⋊C4—112no—
231#340—112no—
232#340—112no—
233#340—112no—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—42no—
238C22×C11—42no—
239C22×C11C2×C4×D411yescharacteristic
240C22×C11C2×#12111yescharacteristic
241C22×C11#53211yescharacteristic
242C22×C11#57712yes—
243C22×C11#57812yes—
244C4×C11—22no—
245C4×C11—44no—
246C4×C11—44no—
247C4×C11C2×C4×D411yescharacteristic
248C4×C11C4×#4111yescharacteristic
249C4×C11#52511yescharacteristic
250C4×C11#52911yescharacteristic
251Dic11—24no—
252Dic11—42no—
253Dic11—82no—
254Dic11—82no—
255C22×Q8C22×D1112yes—
256C23×C4C22×D1111yescharacteristic
257C2×Q16—22no—
258C2×Q16—22no—
259C2×Q16C2×Dic1114yes—
260C2×M16—222no—
261C2×M16—222no—
262C2×M16—222no—
263C22×C8—22no—
264C22×C8—22no—
265C22×C8—111no—
266C22×C8—111no—
267C22×C8C2×Dic1114yes—
268C22×C8C22×D1111yescharacteristic
269C22×C8C22×D1111yescharacteristic
270C22⋊Q8—24no—
271C22⋊Q8C2×Dic1118yes—
272C4×Q8—224no—
273C4×Q8—224no—
274#117—222no—
275#117—222no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—112no—
278C2×C4⋊C4—112no—
279C2×C4⋊C4—112no—
280C2×C4⋊C4—222no—
281C2×C4⋊C4—222no—
282C2×C4⋊C4C22×D1112yes—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—112no—
285C2×C22⋊C4—222no—
286C2×C42—111no—
287C2×C42—111no—
288C2×C42—222no—
289C2×C42—222no—
290#107C2×Dic1114yes—
291#106—222no—
292#106—222no—
293#103—224no—
294#103—224no—
295#103C2×Dic1118yes—
296#97—114no—
297#97—222no—
298C4×C8—222no—
299C4×C8—222no—
300#95—222no—
301#95—222no—
302#95—222no—
303#95—222no—
304#95—222no—
305C2×C11—42no—
306C2×C11C4×#12111yescharacteristic
307C2×C11#295011yescharacteristic
308C2×C11#295211yescharacteristic
309C2×C11#306312yes—
310C2×C11#317812yes—
311C24D4×D1111yescharacteristic
312C2×Q8—22no—
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8—22no—
316C2×Q8—22no—
317C2×Q8C22×Dic1114yes—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—112no—
325C22×C4—112no—
326C22×C4—222no—
327C22×C4—222no—
328C22×C4D4×D1111yescharacteristic
329C22×C4#434112yes—
330C22×C4C22×Dic1112yes—
331C22×C4C23×D1111yescharacteristic
332Q16—28no—
333M16—228no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—28no—
337C2×C8—112no—
338C2×C8—112no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—221no—
342C2×C8—221no—
343C2×C8D4×D1112yes—
344C2×C8#434112yes—
345C2×C8C22×Dic1112yes—
346C2×C8C22×Dic1112yes—
347C4⋊C4—28no—
348C4⋊C4—22no—
349C4⋊C4—224no—
350C4⋊C4—222no—
351C4⋊C4—222no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C4⋊C4—444no—
355C4⋊C4—882no—
356C4⋊C4C22×Dic1114yes—
357C22⋊C4—28no—
358C22⋊C4—224no—
359C22⋊C4—882no—
360C42—112no—
361C42—112no—
362C42—221no—
363C42—221no—
364C42—444no—
365C42—882no—
366C11#2153011yescharacteristic, complemented, Sylow
367C23—22no—
368C23—22no—
369C23—21no—
370C23—21no—
371C23D4×Dic1112yes—
372C23C2×D4×D1111yescharacteristic
373Q8—24no—
374Q8—24no—
375Q8—42no—
376Q8—42no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—114no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4D4×Dic1112yes—
402C2×C4C2×D4×D1111yescharacteristic
403C2×C4C2×#434111yescharacteristic
404C2×C4C2×#434111yescharacteristic
405C2×C4#41×D1111yescharacteristic
406C2×C4#41×D1111yescharacteristic
407C2×C4C23×Dic1111yescharacteristic
408C8—22no—
409C8—222no—
410C8—222no—
411C8D4×Dic1114yes—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—42no—
416C22—42no—
417C22#1062312711yescharacteristic
418C22D11×#12111yescharacteristic
419C22#1062329712yes—
420C22#1062330112yes—
421C22C2×D4×Dic1111yescharacteristic
422C4—22no—
423C4—44no—
424C4—44no—
425C4—224no—
426C4—442no—
427C4—882no—
428C4—882no—
429C4#1062313111yescharacteristic
430C4#1062313711yescharacteristic
431C4C2×D4×Dic1111yescharacteristic
432C4#41×Dic1111yescharacteristic
433C2—42no—
434C2#121×Dic1111yescharacteristic
435C2#1307748411yescharacteristic
436C2#1307750011yescharacteristic
437C2#1307830612yes—
438C2#1307928712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#467C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#467D11
hypocenterC11#21530
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#10622797C2semidirect
4. #13069488C2semidirect
5. #13069355C2semidirect
6. #13069294C2semidirect
9. #13068515C2semidirect
10. #103×Dic11C2semidirect
18. C11×#467C4semidirect
210. #467Dic11semidirect
366. C11#21530semidirect

Maximal subgroups

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

subgroupindex
C2×#106227972
C2×#106227142
#130713002
#130694882
#130693552
#130692942
#130690502
#130686412
#130685152
#103×Dic112
C2×C11×#4672
#2153011