Finite Group Databasebeta

← #14760379

Subgroups — #14760379

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×#10622801C211yesmaximal, characteristic
2C2×#10622797C211yesmaximal, characteristic, complemented
3C2×#10622321C211yesmaximal, characteristic
4#13071301C212yesmaximal
5#13069354C211yesmaximal, characteristic, complemented
6#13069295C212yesmaximal, complemented
7#13069046C212yesmaximal
8#13068638C211yesmaximal, characteristic
9#13068516C211yesmaximal, characteristic, complemented
10#103×Dic11C212yesmaximal, complemented
11C11×#1971C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×#66999C2212yes—
14C2×Q8×Dic11C2212yes—
15C22×#4313C2211yescharacteristic
16C22×C8×D11C2211yescharacteristic
17C2×#66925C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#103C2212yes—
20C2×C11×#97C2211yescharacteristic
21C11×#391C2212yes—
22C2×#66899C2212yes—
23C2×#66899C2212yes—
24#10622801C418yescomplemented
25#10622797—24no—
26C2×#66882C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622600C2212yes—
31C4⋊C4×Dic11C2212yes—
32#10622541C2212yes—
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622321—24no—
35#10622283—22no—
36#10622282—22no—
37#10622265—22no—
38#10622260—22no—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×Q8×C11C2312yes—
43C22×C4×D11C2311yescharacteristic
44C2×C11×Q16—22no—
45C2×C11×Q16—22no—
46C2×C11×Q16C2×C414yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11C2311yescharacteristic
51#66999—24no—
52#66999C2×C418yes—
53Q8×Dic11—24no—
54Q8×Dic11—24no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4D412yes—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2312yes—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4D412yes—
64C2×C4×Dic11—22no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11C2311yescharacteristic
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69C2×#4313—22no—
70C2×#4313—22no—
71C2×#4313—22no—
72C2×C8×D11—22no—
73C2×C8×D11—22no—
74C2×C8×D11C2×C414yes—
75#66925—22no—
76#66925—22no—
77C11×#106—22no—
78C11×#103—24no—
79C11×#97—22no—
80C11×#95—22no—
81C11×#95—22no—
82#66899—24no—
83#66899C2×C418yes—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#66882C2×C414yes—
88#66881—22no—
89#66879D414yes—
90C8×Dic11—22no—
91C4×C11⋊C8—22no—
92#21530—111nomaximal, Sylow
93C23×D11C2×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—22no—
101C22×C4×C11—22no—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11C2×D411yescharacteristic
107C22×Dic11C2×D412yes—
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×C4×D11—21no—
111C2×C4×D11—21no—
112C2×C4×D11C22×C412yes—
113C2×C4×D11#4112yes—
114C11×Q16—28no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11C22×C412yes—
118C2×C8×C11C2×D412yes—
119C2×C8×C11#4112yes—
120C2×C8×C11#4112yes—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C42×C11—21no—
124C42×C11—21no—
125(C2×D11)⋊C4—24no—
126(C2×D11)⋊C4—28no—
127(C2×D11)⋊C4—82no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—44no—
132C4⋊Dic11C22×C414yes—
133Dic11⋊C4—28no—
134Dic11⋊C4—24no—
135Dic11⋊C4—82no—
136C4×Dic11—44no—
137C4×Dic11—82no—
138C4×Dic11C2×D412yes—
139C4×Dic11#4112yes—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8C22×C412yes—
145C2×C11⋊C8C2×D412yes—
146#4313—28no—
147C8×D11—28no—
148C2×#467—111no—
149C2×#441—111no—
150C2×#405—111no—
151#2323—112no—
152#1971D1111yescharacteristic, complemented
153#1943—111no—
154#1933—112no—
155#1894—112no—
156#1807—111no—
157#1776—111no—
158C4×#103—112no—
159C23×C11C22×D411yescharacteristic
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—22no—
163C22×D11—22no—
164C22×D11C4×D412yes—
165Q8×C11—24no—
166Q8×C11—24no—
167Q8×C11—42no—
168Q8×C11—42no—
169C2×C4×C11—24no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11C23×C411yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—24no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11C4×D412yes—
195C2×Dic11#12114yes—
196C4×D11—22no—
197C4×D11—22no—
198C4×D11—22no—
199C4×D11—22no—
200C8×C11—22no—
201C8×C11C4×D414yes—
202C11⋊C8—22no—
203C11⋊C8—22no—
204C22×Q16C2×D1111yescharacteristic
205C22×M16—111no—
206C23×C8—111no—
207C2×C22⋊Q8—112no—
208C2×C4×Q8—112no—
209C2×#117—111no—
210#467—118no—
211#441—224no—
212C2×#107—111no—
213C2×#106—111no—
214C2×#106C2×D1111yescharacteristic
215C2×#103—112no—
216C2×#103—112no—
217C2×#103C2×D1112yes—
218#405—224no—
219C2×#97—111no—
220C2×#97C2×D1111yescharacteristic
221C2×C4×C8—111no—
222C2×C4×C8—111no—
223#391C2×D1112yes—
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×C11C2×C4×D411yescharacteristic
235C22×C11C2×#12111yescharacteristic
236C22×C11#53211yescharacteristic
237C22×C11#57712yes—
238C22×C11#57812yes—
239C2×D11—22no—
240C2×D11—22no—
241C2×D11—22no—
242C2×D11—42no—
243C2×D11—42no—
244C4×C11—42no—
245C4×C11—44no—
246C4×C11—82no—
247C4×C11C2×C4×D411yescharacteristic
248C4×C11C4×#4111yescharacteristic
249C4×C11#52511yescharacteristic
250C4×C11#52911yescharacteristic
251Dic11—24no—
252Dic11—22no—
253Dic11—44no—
254Dic11—82no—
255C22×Q8C22×D1112yes—
256C23×C4—111no—
257C2×Q16—22no—
258C2×Q16—22no—
259C2×Q16C4×D1114yes—
260C2×M16—222no—
261C2×M16—222no—
262C2×M16—222no—
263C22×C8—111no—
264C22×C8—111no—
265C22×C8—114no—
266C22×C8—222no—
267C22×C8—222no—
268C22×C8C22×D1111yescharacteristic
269C22×C8C22×D1111yescharacteristic
270C22⋊Q8—118no—
271C22⋊Q8—224no—
272C4×Q8—224no—
273C4×Q8—224no—
274#117—222no—
275#117—222no—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—112no—
278C2×C4⋊C4—112no—
279C2×C4⋊C4—222no—
280C2×C4⋊C4—222no—
281C2×C4⋊C4—222no—
282C2×C4⋊C4C22×D1112yes—
283C2×C22⋊C4—112no—
284C2×C22⋊C4—222no—
285C2×C22⋊C4—222no—
286C2×C42—111no—
287C2×C42—222no—
288C2×C42—222no—
289C2×C42C22×D1111yescharacteristic
290#107—114no—
291#106—22no—
292#106—222no—
293#103—24no—
294#103—118no—
295#103—224no—
296#97—22no—
297#97—114no—
298C4×C8—222no—
299C4×C8—222no—
300#95—22no—
301#95—22no—
302#95—222no—
303#95—222no—
304#95—222no—
305C2×C11C4×#12111yescharacteristic
306C2×C11#295011yescharacteristic
307C2×C11#295211yescharacteristic
308C2×C11#306312yes—
309C2×C11#317812yes—
310D11—42no—
311C24—111no—
312C2×Q8—22no—
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8—22no—
316C2×Q8—22no—
317C2×Q8C2×C4×D1114yes—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—111no—
321C22×C4—112no—
322C22×C4—112no—
323C22×C4—112no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—222no—
329C22×C4—222no—
330C22×C4D4×D1112yes—
331C22×C4C23×D1111yescharacteristic
332Q16—28no—
333M16—228no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—112no—
337C2×C8—112no—
338C2×C8—221no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—221no—
342C2×C8—228no—
343C2×C8C2×C4×D1112yes—
344C2×C8D4×D1112yes—
345C2×C8#434112yes—
346C2×C8#434112yes—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—114no—
350C4⋊C4—224no—
351C4⋊C4—228no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C4⋊C4—222no—
355C4⋊C4—444no—
356C4⋊C4—882no—
357C22⋊C4—224no—
358C22⋊C4—228no—
359C22⋊C4—882no—
360C42—21no—
361C42—21no—
362C42—112no—
363C42—112no—
364C42—444no—
365C42—882no—
366C11#2153011yescharacteristic, complemented, Sylow
367C23—112no—
368C23—221no—
369C23—222no—
370C23—222no—
371C23—221no—
372C23C2×D4×D1111yescharacteristic
373Q8—24no—
374Q8—24no—
375Q8—42no—
376Q8—42no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—24no—
380C2×C4—22no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—112no—
387C2×C4—114no—
388C2×C4—221no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—221no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—224no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4C22×C4×D1111yescharacteristic
403C2×C4C2×D4×D1111yescharacteristic
404C2×C4C2×#434111yescharacteristic
405C2×C4C2×#434111yescharacteristic
406C2×C4#41×D1111yescharacteristic
407C2×C4#41×D1111yescharacteristic
408C8—22no—
409C8—222no—
410C8—222no—
411C8(C22⋊D11)⋊C414yes—
412C22—222no—
413C22—222no—
414C22—222no—
415C22—442no—
416C22—442no—
417C22C4×D4×D1111yescharacteristic
418C22D11×#12111yescharacteristic
419C22#1062324711yescharacteristic
420C22#1062330912yes—
421C22#1062331012yes—
422C4—44no—
423C4—42no—
424C4—82no—
425C4—222no—
426C4—224no—
427C4—444no—
428C4—882no—
429C4C2×(C22⋊D11)⋊C411yescharacteristic
430C4C4×#434111yescharacteristic
431C4#1062313711yescharacteristic
432C4#1062321111yescharacteristic
433C2—442no—
434C2#1307113211yescharacteristic
435C2#1307748111yescharacteristic
436C2#1307749611yescharacteristic
437C2#1307830412yes—
438C2#1307928112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1971C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1971D11
hypocenterC11#21530
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1971

Complements

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

NH ≅ G/Ntype
2. C2×#10622797C2semidirect
5. #13069354C2semidirect
6. #13069295C2semidirect
9. #13068516C2semidirect
10. #103×Dic11C2semidirect
11. C11×#1971C2semidirect
24. #10622801C4semidirect
152. #1971D11semidirect
366. C11#21530semidirect

Maximal subgroups

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

subgroupindex
C2×#106228012
C2×#106227972
C2×#106223212
#130713012
#130693542
#130692952
#130690462
#130686382
#130685162
#103×Dic112
C11×#19712
#2153011