Finite Group Databasebeta

← #14809930

Subgroups — #14809930

Order 2816.

1094 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073997C212yesmaximal, complemented
2#13073959C211yesmaximal, characteristic
3#13069968C212yesmaximal, complemented
4#13069968C212yesmaximal, complemented
5#13069602C212yesmaximal, complemented
6#13068897C212yesmaximal
7#13068897C212yesmaximal
8C4×#66898C211yesmaximal, characteristic
9C11×#3501C211yesmaximal, characteristic
10C11×#554—24no—
11C11×#554—22no—
12D4×Q8×C11—22no—
13C11×#544—21no—
14C11×#543—21no—
15C11×#543C2212yes—
16C11×#533—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2212yes—
19C11×#518C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22#10622842—22no—
23#10622833C2211yescharacteristic
24#10622833C2211yescharacteristic
25C2×#66898C2212yes—
26#10622825C2211yescharacteristic
27#10622823—21no—
28C4×C22⋊Dic11C2212yes—
29#10622597—21no—
30#10622593—22no—
31#10622585—24no—
32#10622561—21no—
33#10622559C2211yescharacteristic
34#10622559C2211yescharacteristic
35#10622559C2214yes—
36#10622559C2214yes—
37#10622546—21no—
38#10622164C2214yes—
39#10622164C2214yes—
40#10622164C2212yes—
41C22×Q8×C11—21no—
42C22×Q8×C11D412yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—24no—
51C11×#125—22no—
52C11×#125—24no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—24no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—24no—
70C4×D4×C11—24no—
71C11×#117—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4D414yes—
75C2×C11×C4⋊C4D412yes—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4C2314yes—
81C2×C42×C11D411yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11C2311yescharacteristic
85C2×C22⋊Dic11C2311yescharacteristic
86C2×C22⋊Dic11C2314yes—
87C2×C4⋊Dic11—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—24no—
96C2×C4×Dic11—22no—
97#66898Q818yescomplemented
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105C11⋊#95—22no—
106#25854—111nomaximal, Sylow
107C24×C11C2×D411yescharacteristic
108C24×C11C2411yescharacteristic
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—82no—
114C2×Q8×C11—82no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11C2×Q814yes—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—81no—
123C22×C4×C11—81no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D414yes—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×Dic11—24no—
134C22×Dic11—22no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C22×Dic11—21no—
140C22×Dic11—42no—
141C22×Dic11—81no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—24no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—22no—
158C42×C11—24no—
159C42×C11—21no—
160C42×C11—21no—
161C22⋊Dic11—24no—
162C22⋊Dic11—22no—
163C22⋊Dic11—22no—
164C22⋊Dic11—42no—
165C22⋊Dic11—81no—
166C22⋊Dic11C2×Q818yescomplemented
167C4⋊Dic11—81no—
168Dic11⋊C4—48no—
169Dic11⋊C4—42no—
170Dic11⋊C4—41no—
171Dic11⋊C4—41no—
172Dic11⋊C4—42no—
173Dic11⋊C4—81no—
174Dic11⋊C4—84no—
175C4×Dic11—82no—
176#3501D1111yescharacteristic
177#2583—112no—
178#2579—111no—
179#2062—112no—
180#2062—112no—
181#1996—112no—
182#1867—112no—
183#1867—112no—
184C4×#99—111no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11C4⋊Q812yes—
192C23×C11C22×D411yescharacteristic
193C23×C11C22×D412yes—
194C23×C11C22×Q812yes—
195C23×C112−1+412yes—
196Q8×C11—44no—
197Q8×C11—82no—
198Q8×C11—82no—
199Q8×C11—82no—
200D4×C11—28no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—21no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—44no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—44no—
216C2×C4×C11—81no—
217C2×C4×C11—82no—
218C2×C4×C11—82no—
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11#12012yes—
222C2×C4×C11C4⋊Q812yes—
223C2×Dic11—24no—
224C2×Dic11—22no—
225C2×Dic11—28no—
226C2×Dic11—44no—
227C2×Dic11—44no—
228C2×Dic11—42no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—44no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241#554—24no—
242#554—22no—
243D4×Q8—22no—
244#544—21no—
245#543—21no—
246#543C2×D1112yes—
247#533—21no—
248C2×C22⋊Q8—21no—
249C2×C22⋊Q8C2×D1112yes—
250#518C2×D1112yes—
251C2×C4×D4C2×D1111yescharacteristic
252C22×C4⋊C4—111no—
253C2×#99—112no—
254#398—221no—
255#398—222no—
256#396—221no—
257#395—222no—
258#389—224no—
259#387—221no—
260#386—111no—
261#386—111no—
262#385—111no—
263#385—111no—
264#385—114no—
265#385—114no—
266#385—221no—
267#380—111no—
268C4×C22⋊C4—112no—
269#342—112no—
270#342—114no—
271#342—114no—
272C22×C11—22no—
273C22×C11—21no—
274C22×C11—22no—
275C22×C11—21no—
276C22×C11—22no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—41no—
281C22×C11—41no—
282C22×C11—81no—
283C22×C11C2×#12011yescharacteristic
284C22×C11C2×C4⋊Q811yescharacteristic
285C22×C11#53611yescharacteristic
286C22×C11D4×Q814yes—
287C4×C11—22no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—22no—
291C4×C11—44no—
292C4×C11—41no—
293C4×C11—41no—
294C4×C11—44no—
295Dic11—48no—
296Dic11—42no—
297Dic11—81no—
298Dic11—81no—
299Dic11—81no—
300C22×Q8—21no—
301C22×Q8C22⋊D1112yes—
302C22×D4C22×D1111yescharacteristic
303C23×C4—111no—
304C23×C4—111no—
305C23×C4C22⋊D1111yescharacteristic
306C23×C4C22×D1111yescharacteristic
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—24no—
310#125—22no—
311#125—24no—
312C22⋊Q8—22no—
313C22⋊Q8—22no—
314C22⋊Q8—24no—
315C22⋊Q8—24no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—24no—
323C22⋊Q8—24no—
324C4×Q8—22no—
325C4×Q8—22no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—24no—
329C4×D4—24no—
330#117—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—224no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—224no—
342C2×C4⋊C4C22⋊D1111yescharacteristic
343C2×C4⋊C4C22⋊D1114yes—
344C2×C4⋊C4C22⋊D1112yes—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—114no—
347C2×C22⋊C4—111no—
348C2×C22⋊C4—111no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4C22⋊D1111yescharacteristic
352C2×C22⋊C4C22×D1111yescharacteristic
353C2×C22⋊C4C22×D1114yes—
354C2×C42—222no—
355C2×C42C22⋊D1111yescharacteristic
356#99—118no—
357#95—222no—
358#95—221no—
359#95—221no—
360#95—221no—
361#95—224no—
362#95—224no—
363#95—221no—
364#95—221no—
365C2×C11—24no—
366C2×C11—21no—
367C2×C11—21no—
368C2×C11—42no—
369C2×C11#243411yescharacteristic
370C2×C11#302511yescharacteristic
371C2×C11#302611yescharacteristic
372C24C2×C22⋊D1111yescharacteristic
373C24C23×D1111yescharacteristic
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—82no—
379C2×Q8—82no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4Q8×D1114yes—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—81no—
388C22×C4—81no—
389C22×C4—224no—
390C22×C4—221no—
391C22×C4—222no—
392C22×C4—221no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4—222no—
396C22×C4—442no—
397C22×C4—881no—
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C2×C22⋊D1111yescharacteristic
400C22×C4C2×C22⋊D1114yes—
401C22×C4C2×C22⋊D1114yes—
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C2×C22⋊D1111yescharacteristic
404C22×C4C2×C22⋊D1112yes—
405C22×C4C2×C22⋊D1112yes—
406C22×C4C2×C22⋊D1111yescharacteristic
407C4⋊C4—22no—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—24no—
412C4⋊C4—22no—
413C4⋊C4—24no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—24no—
418C4⋊C4—442no—
419C4⋊C4—448no—
420C4⋊C4—441no—
421C4⋊C4—441no—
422C4⋊C4—442no—
423C4⋊C4—881no—
424C4⋊C4—884no—
425C4⋊C4—881no—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—22no—
429C22⋊C4—24no—
430C22⋊C4—22no—
431C22⋊C4—118no—
432C22⋊C4—224no—
433C22⋊C4—222no—
434C22⋊C4—222no—
435C22⋊C4—442no—
436C22⋊C4—881no—
437C42—24no—
438C42—21no—
439C42—21no—
440C42—882no—
441C11#2585411yescharacteristic, complemented, Sylow
442C23—21no—
443C23—21no—
444C23—41no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23#6699712yes—
449C23C2×Q8×D1112yes—
450C23#6704012yes—
451C23C22×C22⋊D1111yescharacteristic
452C23C22×C22⋊D1112yes—
453Q8—44no—
454Q8—82no—
455Q8—82no—
456Q8—82no—
457D4—28no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—21no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—44no—
473C2×C4—81no—
474C2×C4—82no—
475C2×C4—82no—
476C2×C4—222no—
477C2×C4—224no—
478C2×C4—228no—
479C2×C4—444no—
480C2×C4—444no—
481C2×C4—442no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—441no—
488C2×C4—441no—
489C2×C4—444no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4#6699712yes—
495C2×C4#6700611yescharacteristic
496C2×C4#6700611yescharacteristic
497C2×C4#6700612yes—
498C22—22no—
499C22—21no—
500C22—22no—
501C22—21no—
502C22—22no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—81no—
509C22C2×#6699711yescharacteristic
510C22Q8×C22⋊D1114yes—
511C22#1062334711yescharacteristic
512C22C2×#6700611yescharacteristic
513C4—22no—
514C4—21no—
515C4—21no—
516C4—22no—
517C4—44no—
518C4—41no—
519C4—41no—
520C4—44no—
521C4—448no—
522C4—442no—
523C4—881no—
524C4—881no—
525C4—881no—
526C2—24no—
527C2—21no—
528C2—21no—
529C2—42no—
530C2#1307225611yescharacteristic
531C2#1307800811yescharacteristic
532C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radicalC22×D4×C11C23
hypercenter#3501D11
hypocenterC11#25854
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13073997C2semidirect
3. #13069968C2semidirect
4. #13069968C2semidirect
5. #13069602C2semidirect
97. #66898Q8semidirect
166. C22⋊Dic11C2×Q8semidirect
441. C11#25854semidirect

Maximal subgroups

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

subgroupindex
#130739972
#130739592
#130699682
#130696022
#130688972
C4×#668982
C11×#35012
#2585411