Finite Group Databasebeta

← #14756009

Subgroups — #14756009

Order 2816.

898 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622611C211yesmaximal, characteristic
2#13071236C211yesmaximal, characteristic
3#13069208C212yesmaximal, complemented
4#13069201C212yesmaximal, complemented
5#13069194C212yesmaximal, complemented
6#13069187C212yesmaximal, complemented
7#13068337C211yesmaximal, characteristic
8#13068335C211yesmaximal, characteristic
9C2×#10622167C211yesmaximal, characteristic
10#13068313C211yesmaximal, characteristic
11C11×#2274C211yesmaximal, characteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C4×C11×C4⋊C4—21no—
20C4×C11×C4⋊C4—21no—
21C4×C11×C4⋊C4C2212yes—
22C4×C11×C4⋊C4C2212yes—
23C4×C11×C22⋊C4—22no—
24#10622611C418yescomplemented
25#10622590—21no—
26#10622589—21no—
27C2×#66872C2211yescharacteristic
28C2×#66872C2211yescharacteristic
29C2×#66871C2211yescharacteristic
30C2×#66871C2211yescharacteristic
31#10622559—22no—
32#10622541C2212yes—
33#10622541C2212yes—
34#10622167C2212yes—
35#10622167C2212yes—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622162C2212yes—
41#10622162C2212yes—
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—21no—
45C11×#117—22no—
46C11×#117—22no—
47C11×#117—22no—
48C11×#117C2×C414yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4Q814yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4D412yes—
59C2×C42×C11—21no—
60C2×C42×C11—22no—
61C2×C42×C11—22no—
62C2×C42×C11C2312yes—
63C2×C22⋊Dic11—21no—
64#66979—22no—
65#66979C2×C414yes—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×C4×Dic11—21no—
75C2×#4318—22no—
76C2×#4318—22no—
77C2×#4318—22no—
78C22×C11⋊C8—22no—
79C22×C11⋊C8—22no—
80C22×C11⋊C8C2×C414yes—
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84C11×#95—22no—
85C11×#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66872C2×C414yescomplemented
89#66872C2×C414yescomplemented
90#66871C2×C414yescomplemented
91#66871C2×C414yescomplemented
92#21039—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—24no—
98C22×C4×C11—81no—
99C22×C4×C11—81no—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×Q812yes—
105C22×C4×C11#4112yes—
106C22×C4×C11#4112yes—
107C22×C4×C11#4112yes—
108C22×C4×C11#4112yes—
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11—42no—
114C22×Dic11—81no—
115C22×Dic11—81no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4C22×C412yes—
123C11×C4⋊C4C22×C412yes—
124C11×C4⋊C4C2×Q814yes—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—24no—
127C42×C11—24no—
128C42×C11—22no—
129C42×C11—22no—
130C42×C11—82no—
131C42×C11—82no—
132C22⋊Dic11—24no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11—42no—
138C4⋊Dic11C22×C412yes—
139C4⋊Dic11C22×C412yes—
140Dic11⋊C4—82no—
141Dic11⋊C4—82no—
142C4×Dic11—24no—
143#4318—44no—
144C2×C11⋊C8—28no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8C22×C412yes—
153C2×C11⋊C8C22×C412yes—
154C2×#427—111no—
155#2317—111no—
156#2274D1111yescharacteristic
157#1921—112no—
158#1920—112no—
159#1919—112no—
160#1918—112no—
161#1736—111no—
162#1736—111no—
163C2×#340—111no—
164#1729—111no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11C4×D412yes—
170C23×C11C22⋊Q812yes—
171C23×C11#12312yes—
172C23×C11C22×D411yescharacteristic
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—84no—
189C2×C4×C11#11714yes—
190C2×C4×C11C4×D412yes—
191C2×C4×C11C4×Q814yes—
192C2×C4×C11C22⋊Q812yes—
193C2×C4×C11#12312yes—
194C2×C4×C11#12514yes—
195C2×C4×C11#12614yes—
196C2×C4×C11C23×C411yescharacteristic
197C2×C4×C11C22×Q811yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—84no—
212C11⋊C8—22no—
213C11⋊C8—22no—
214C11⋊C8—42no—
215C22×M16—111no—
216C23×C8—111no—
217C2×#117—111no—
218C2×#117C2×D1111yescharacteristic
219C2×#117C2×D1111yescharacteristic
220C22×C4⋊C4—111no—
221C22×C4⋊C4C2×D1111yescharacteristic
222#427—118no—
223C2×#107—111no—
224C2×#107—111no—
225C2×#106—111no—
226C2×#106—111no—
227#389—112no—
228#389—112no—
229#385—222no—
230#384—221no—
231#382—221no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4C2×D1112yes—
235C4×C4⋊C4C2×D1112yes—
236C4×C22⋊C4—22no—
237#340—112no—
238#340—112no—
239#340—112no—
240#340—112no—
241#340—112no—
242#340—112no—
243#336—112no—
244#336—112no—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11#38714yes—
252C22×C11C2×C4×D411yescharacteristic
253C22×C11C2×C22⋊Q811yescharacteristic
254C22×C11C2×#12311yescharacteristic
255C22×C11#57611yescharacteristic
256C22×C11#57711yescharacteristic
257C22×C11#57711yescharacteristic
258C22×C11#57811yescharacteristic
259C4×C11—44no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11#38714yes—
265C4×C11C2×#11711yescharacteristic
266C4×C11C2×C4×Q811yescharacteristic
267C4×C11C2×#12511yescharacteristic
268C4×C11C2×#12611yescharacteristic
269Dic11—42no—
270Dic11—42no—
271Dic11—82no—
272C23×C4—21no—
273C23×C4—221no—
274C23×C4C22×D1111yescharacteristic
275C2×M16—222no—
276C2×M16—222no—
277C2×M16—222no—
278C22×C8—114no—
279C22×C8—111no—
280C22×C8—111no—
281C22×C8—112no—
282C22×C8—222no—
283C22×C8—222no—
284#117—22no—
285#117—22no—
286#117—22no—
287#117—114no—
288#117—222no—
289#117C4×D1114yes—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—112no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—221no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4Dic2214yes—
301C2×C4⋊C4C22⋊D1111yescharacteristic
302C2×C4⋊C4C22⋊D1111yescharacteristic
303C2×C4⋊C4C22×D1112yes—
304C2×C4⋊C4C22×D1111yescharacteristic
305C2×C4⋊C4C22×D1111yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—221no—
308C2×C22⋊C4C22⋊D1112yes—
309C2×C42—21no—
310C2×C42—22no—
311C2×C42—22no—
312C2×C42—221no—
313C2×C42C22×D1112yes—
314#107—114no—
315#107—114no—
316#106—114no—
317#106—114no—
318#95—22no—
319#95—22no—
320#95—222no—
321#95—222no—
322C2×C11—24no—
323C2×C11C2×#38711yescharacteristic
324C2×C11#295111yescharacteristic
325C2×C11#295211yescharacteristic
326C2×C11#308111yescharacteristic
327C2×C11#308211yescharacteristic
328C2×C11#309611yescharacteristic
329C2×C11#309711yescharacteristic
330C24C2×C22⋊D1111yescharacteristic
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—24no—
335C22×C4—81no—
336C22×C4—81no—
337C22×C4—221no—
338C22×C4—221no—
339C22×C4—222no—
340C22×C4—442no—
341C22×C4—881no—
342C22×C4—881no—
343C22×C4C2×Dic2212yes—
344C22×C4C2×C4×D1112yes—
345C22×C4#433912yes—
346C22×C4#433912yes—
347C22×C4#433912yes—
348C22×C4#433912yes—
349C22×C4C2×C22⋊D1112yes—
350C22×C4C2×C22⋊D1112yes—
351C22×C4C2×C22⋊D1111yescharacteristic
352C22×C4C23×D1111yescharacteristic
353M16—444no—
354C2×C8—112no—
355C2×C8—112no—
356C2×C8—228no—
357C2×C8—221no—
358C2×C8—221no—
359C2×C8—221no—
360C2×C8—221no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—222no—
364C4⋊C4—24no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—112no—
371C4⋊C4—112no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—222no—
375C4⋊C4—222no—
376C4⋊C4—442no—
377C4⋊C4—882no—
378C4⋊C4—882no—
379C4⋊C4C2×Dic2214yes—
380C4⋊C4C2×C4×D1112yes—
381C4⋊C4C2×C4×D1112yes—
382C22⋊C4—24no—
383C22⋊C4—24no—
384C22⋊C4—224no—
385C42—24no—
386C42—22no—
387C42—22no—
388C42—82no—
389C42—82no—
390C42—224no—
391C11#2103911yescharacteristic, complemented, Sylow
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23#6697712yes—
397C23C4×C22⋊D1112yes—
398C23#6698212yes—
399C23C22×C22⋊D1111yescharacteristic
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—84no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—884no—
426C2×C4C4×Dic2214yes—
427C2×C4#6692314yes—
428C2×C4#6692514yes—
429C2×C4#6692914yes—
430C2×C4#6697712yes—
431C2×C4C4×C22⋊D1112yes—
432C2×C4#6698212yes—
433C2×C4C22×Dic2211yescharacteristic
434C2×C4C22×C4×D1111yescharacteristic
435C2×C4C2×#433911yescharacteristic
436C2×C4C2×#433911yescharacteristic
437C2×C4C2×#433911yescharacteristic
438C2×C4C2×#433911yescharacteristic
439C8—222no—
440C8—222no—
441C8—442no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22#1062254614yes—
449C22C2×#6697711yescharacteristic
450C22C2×C4×C22⋊D1111yescharacteristic
451C22C2×#6698211yescharacteristic
452C22#1062336611yescharacteristic
453C22#1062336711yescharacteristic
454C22#1062336811yescharacteristic
455C22#1062336911yescharacteristic
456C4—42no—
457C4—42no—
458C4—44no—
459C4—42no—
460C4—42no—
461C4—442no—
462C4—442no—
463C4—882no—
464C4#1062254614yes—
465C4C2×C4×Dic2211yescharacteristic
466C4C2×#6692311yescharacteristic
467C4C2×#6692511yescharacteristic
468C4C2×#6692911yescharacteristic
469C2—24no—
470C2C2×#1062254611yescharacteristic
471C2#1307748911yescharacteristic
472C2#1307749711yescharacteristic
473C2#1307844711yescharacteristic
474C2#1307845811yescharacteristic
475C2#1307857411yescharacteristic
476C2#1307858511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2274C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2274D11
hypocenterC11#21039
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2274

Complements

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

NH ≅ G/Ntype
3. #13069208C2semidirect
4. #13069201C2semidirect
5. #13069194C2semidirect
6. #13069187C2semidirect
24. #10622611C4semidirect
88. #66872C2×C4semidirect
89. #66872C2×C4semidirect
90. #66871C2×C4semidirect
91. #66871C2×C4semidirect
391. C11#21039semidirect

Maximal subgroups

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

subgroupindex
C2×#106226112
#130712362
#130692082
#130692012
#130691942
#130691872
#130683372
#130683352
C2×#106221672
#130683132
C11×#22742
#2103911