Finite Group Databasebeta

← #14722237

Subgroups — #14722237

Order 2816.

964 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082428C211yesmaximal, characteristic
2#13077725C211yesmaximal, characteristic
3#13077185C211yesmaximal, characteristic
4#13067303C212yesmaximal, complemented
5#13067302C211yesmaximal, characteristic, complemented
6#13067299C212yesmaximal, complemented
7#13067273C211yesmaximal, characteristic, complemented
8#13067270C212yesmaximal, complemented
9C2×#10622120C211yesmaximal, characteristic, complemented
10D11×#332C212yesmaximal, complemented
11C11×#1550C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×#66960—21no—
14#10623259C2212yes—
15D11×C4⋊Q8C2212yes—
16#10623220—22no—
17#10623166C414yes—
18#10623163—22no—
19#10623110C412yes—
20Q8×D44—21no—
21#10623098—21no—
22Q8×Dic22C412yes—
23#10623054—21no—
24#10623050—21no—
25C4×#4339C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C11×#423C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29#10622732—21no—
30C8×C22⋊D11—22no—
31#10622538C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622452—22no—
34#10622450C2212yes—
35#10622447—21no—
36#10622446C2212yes—
37D11×C4⋊C8C2212yes—
38D11×C4⋊C8C2212yes—
39#10622443—21no—
40C11×#333C2212yes—
41C11×#332C2212yes—
42#10622185C2211yescharacteristic
43#10622185C2211yescharacteristic
44#10622184C2211yescharacteristic
45#10622184C2211yescharacteristic
46#10622124C2212yes—
47#10622124C2212yes—
48#10622120C2212yes—
49#10622120C2212yes—
50C2×Q8×D11—22no—
51C2×#4339D411yescharacteristic
52C22×Dic22—21no—
53C2×C11×M16—21no—
54C22×C8×C11—21no—
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×#125—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8C2×C412yes—
60C4×Q8×C11—21no—
61C4×Q8×C11C2×C412yes—
62C11×#117—21no—
63C2×C42×C11C2311yescharacteristic
64#66999C2×C414yes—
65Q8×Dic11C2×C414yes—
66#66997—22no—
67C4×C22⋊D11C2×C412yes—
68C4×C22⋊D11D412yes—
69#66979D411yescharacteristic
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11C2×C412yes—
72C22×C11⋊C8—21no—
73#66960—44no—
74C2×#4313—22no—
75C2×C8×D11—22no—
76C2×C8×D11—22no—
77#66950—22no—
78#66950—24no—
79#66949—24no—
80#66945—22no—
81C4⋊C4×D11—22no—
82C4⋊C4×D11C2×C414yes—
83#66943—22no—
84#66942—24no—
85#66941—24no—
86#66941—22no—
87#66941C2×C414yes—
88#66940—22no—
89(C22⋊D11)⋊C4—24no—
90#66931—24no—
91C4×D44—22no—
92C4×D44C2×C411yescharacteristic
93C4×D44D411yescharacteristic
94#66925D412yes—
95C42×D11C2312yes—
96#66923—22no—
97#66922—21no—
98#66922—21no—
99#66922—22no—
100#66922C2×C412yes—
101#66922C2312yes—
102C4×Dic22—22no—
103C4×Dic22C2×C411yescharacteristic
104C4×Dic22D411yescharacteristic
105C11×C4⋊C8—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8C2312yes—
108C11×C4⋊C8C2312yes—
109C22⋊(C11⋊C8)—21no—
110(C2×D11)⋊C8—22no—
111Dic11⋊C8—22no—
112Dic11⋊C8—22no—
113Dic11⋊C8—22no—
114C8×Dic11—22no—
115C4⋊(C11⋊C8)—21no—
116C4⋊(C11⋊C8)C2311yescharacteristic
117C4⋊(C11⋊C8)C2311yescharacteristic
118C4⋊(C11⋊C8)C2311yescharacteristic
119C4⋊(C11⋊C8)C2311yescharacteristic
120C4×C11⋊C8—21no—
121#17723—111nomaximal, Sylow
122C2×Q8×C11—21no—
123C2×Q8×C11C22×C412yes—
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C2×C22⋊D11C22⋊C412yes—
128C22×Dic11—22no—
129Q8×D11—82no—
130Q8×D11—82no—
131#4339SD1614yes—
132#4339Q1614yes—
133C2×D44C22⋊C411yescharacteristic
134C2×C4×D11—24no—
135C2×C4×D11C22×C412yes—
136C2×C4×D11C2×D412yes—
137C2×C4×D11C2×D412yes—
138C2×Dic22—24no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—81no—
142C2×Dic22—81no—
143C2×Dic22C22⋊C411yescharacteristic
144C11×M16—42no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—81no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4C22×C412yes—
154C11×C22⋊C4—22no—
155C42×C11—22no—
156C42×C11C22×C411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2411yescharacteristic
160C22⋊Dic11C22⋊C412yes—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4C22⋊C412yes—
163(C2×D11)⋊C4C22⋊C412yes—
164C4⋊Dic11—24no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11C22⋊C411yescharacteristic
169C4⋊Dic11C22⋊C411yescharacteristic
170C4⋊Dic11C22×C414yes—
171Dic11⋊C4—24no—
172Dic11⋊C4—24no—
173Dic11⋊C4—24no—
174Dic11⋊C4C22⋊C412yes—
175Dic11⋊C4C22⋊C412yes—
176C4×Dic11—24no—
177C4×Dic11C22×C412yes—
178C4×Dic11C2×D412yes—
179C4×Dic11C2×D412yes—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—42no—
185#4313—44no—
186C8×D11—44no—
187C8×D11—82no—
188#3503—111no—
189#2988—111no—
190#2906—111no—
191#1550—112no—
192#1550D1111yescharacteristic, complemented
193#1549—111no—
194#1549—112no—
195#1542—112no—
196#1542—111no—
197C2×#332—111no—
198C2×#332—112no—
199C23×C11C2×C22⋊C411yescharacteristic
200C22×D11C2×C22⋊C412yes—
201Q8×C11—42no—
202Q8×C11—41no—
203Q8×C11—41no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—41no—
209C2×C4×C11C2×C22⋊C411yescharacteristic
210C2×C4×C11C2×C22⋊C411yescharacteristic
211C2×C4×C11C2×C22⋊C411yescharacteristic
212C2×C4×C11C2×SD1612yes—
213C2×C4×C11C2×Q1612yes—
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C22⋊D11#10318yes—
218C2×Dic11—24no—
219C2×Dic11—82no—
220C2×Dic11C2×C22⋊C412yes—
221C2×Dic11C2×C22⋊C412yes—
222C2×Dic11C2×C22⋊C412yes—
223D44#10314yes—
224C4×D11—22no—
225C4×D11—22no—
226C4×D11—42no—
227C4×D11—84no—
228C4×D11C2×SD1614yes—
229C4×D11C2×Q1614yes—
230Dic22—42no—
231Dic22—42no—
232Dic22—84no—
233Dic22—82no—
234Dic22#10314yes—
235C8×C11—42no—
236C8×C11—42no—
237C11⋊C8—41no—
238C11⋊C8—41no—
239C11⋊C8—41no—
240C11⋊C8—41no—
241C2×#131—221no—
242Q82—112no—
243#557—221no—
244#554—114no—
245#554—112no—
246D4×Q8—221no—
247D4×Q8—222no—
248#544—221no—
249#544—222no—
250#533—112no—
251#533C2×D1111yescharacteristic
252C2×C4⋊Q8—112no—
253C2×C4⋊Q8—111no—
254#520—221no—
255C4×#41—111no—
256C8×Q8—221no—
257C8×D4—221no—
258C8×D4—222no—
259#431—111no—
260#431—112no—
261#424—222no—
262#424—221no—
263#423—112no—
264#423C2×D1111yescharacteristic
265C2×C4⋊C8—111no—
266C2×C4⋊C8—112no—
267C2×C4⋊C8—112no—
268C2×C4⋊C8C2×D1111yescharacteristic
269#333—111no—
270#333—111no—
271#333C2×D1112yes—
272#332—111no—
273#332—111no—
274#332—112no—
275#332—112no—
276#332—112no—
277#332—112no—
278#332C2×D1112yes—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11C2×#10312yes—
282C22×C11C22×C22⋊C411yescharacteristic
283C2×D11—22no—
284C2×D11—22no—
285C2×D11C2×#10314yes—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11C2×#10312yes—
292C4×C11C22×SD1611yescharacteristic
293C4×C11C22×Q1611yescharacteristic
294C4×C11#57611yescharacteristic
295C4×C11#57711yescharacteristic
296Dic11—22no—
297Dic11—22no—
298Dic11—44no—
299Dic11C2×#10314yes—
300C2×#41—111no—
301C22×Q8—222no—
302C22×Q8—221no—
303#131—444no—
304C2×M16—21no—
305C2×M16—222no—
306C22×C8—21no—
307C22×C8—222no—
308C22×C8—222no—
309C22×C8—221no—
310C4⋊Q8—114no—
311C4⋊Q8—112no—
312C4⋊Q8—112no—
313C4⋊Q8—222no—
314C4⋊Q8—222no—
315C4⋊Q8—222no—
316C4⋊Q8—224no—
317C4⋊Q8—221no—
318C4⋊Q8—221no—
319C4⋊Q8C22×D1111yescharacteristic
320C4⋊Q8C22×D1111yescharacteristic
321#125—21no—
322#125—222no—
323#125—222no—
324#125—224no—
325C22⋊Q8—21no—
326C22⋊Q8—114no—
327C22⋊Q8—224no—
328C22⋊Q8—224no—
329C22⋊Q8—224no—
330C22⋊Q8—222no—
331C22⋊Q8C4×D1112yes—
332C4×Q8—21no—
333C4×Q8—111no—
334C4×Q8—111no—
335C4×Q8—114no—
336C4×Q8—222no—
337C4×Q8—222no—
338C4×Q8C4×D1112yes—
339C4×D4—112no—
340C4×D4—112no—
341C4×D4—111no—
342C4×D4—111no—
343C4×D4—222no—
344C4×D4—224no—
345#117—21no—
346#117—111no—
347#117—112no—
348#117—222no—
349C2×C4⋊C4—112no—
350C2×C4⋊C4—114no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—221no—
353C2×C42—112no—
354C2×C42C22×D1111yescharacteristic
355C4⋊C8—21no—
356C4⋊C8—21no—
357C4⋊C8—111no—
358C4⋊C8—111no—
359C4⋊C8—111no—
360C4⋊C8—111no—
361C4⋊C8—222no—
362C4⋊C8—222no—
363C4⋊C8—222no—
364C4⋊C8—221no—
365C4⋊C8C22×D1112yes—
366C4⋊C8C22×D1112yes—
367C22⋊C8—222no—
368C22⋊C8—221no—
369C4×C8—222no—
370C4×C8—221no—
371C2×C11—22no—
372C2×C11#288911yescharacteristic
373C2×C11C22×#10311yescharacteristic
374C2×C11#289711yescharacteristic
375D11—24no—
376#41—114no—
377#41—114no—
378C2×Q8—21no—
379C2×Q8—111no—
380C2×Q8—224no—
381C2×Q8—222no—
382C2×Q8—222no—
383C2×Q8—881no—
384C2×Q8—881no—
385C2×Q8—882no—
386C2×Q8—882no—
387C2×Q8C2×C4×D1112yes—
388C2×D4—112no—
389C2×D4—111no—
390C22×C4—112no—
391C22×C4—112no—
392C22×C4—112no—
393C22×C4—224no—
394C22×C4—222no—
395C22×C4C2×C4×D1111yescharacteristic
396C22×C4D4×D1111yescharacteristic
397C22×C4D4×D1111yescharacteristic
398M16—42no—
399M16—444no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—81no—
403C2×C8—221no—
404C2×C8—221no—
405C2×C8—221no—
406C2×C8—221no—
407C2×C8—444no—
408C2×C8—442no—
409C2×C8—882no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—112no—
416C4⋊C4—111no—
417C4⋊C4—112no—
418C4⋊C4—111no—
419C4⋊C4—114no—
420C4⋊C4—224no—
421C4⋊C4—224no—
422C4⋊C4—224no—
423C4⋊C4—224no—
424C4⋊C4—222no—
425C4⋊C4—222no—
426C4⋊C4—222no—
427C4⋊C4C2×C4×D1112yes—
428C22⋊C4—22no—
429C22⋊C4—112no—
430C22⋊C4—112no—
431C22⋊C4—112no—
432C22⋊C4—224no—
433C42—22no—
434C42—112no—
435C42—112no—
436C42—112no—
437C42—224no—
438C42C2×C4×D1111yescharacteristic
439C42D4×D1111yescharacteristic
440C42D4×D1111yescharacteristic
441C42C23×D1111yescharacteristic
442C11#1772311yescharacteristic, complemented, Sylow
443C23—112no—
444C23C22⋊C4×D1111yescharacteristic
445Q8—42no—
446Q8—41no—
447Q8—41no—
448Q8—114no—
449Q8—442no—
450Q8—442no—
451Q8—882no—
452Q8—884no—
453D4—118no—
454D4—114no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—112no—
461C2×C4—114no—
462C2×C4—114no—
463C2×C4—112no—
464C2×C4—112no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—224no—
468C2×C4—442no—
469C2×C4—884no—
470C2×C4—882no—
471C2×C4C22⋊C4×D1111yescharacteristic
472C2×C4C22⋊C4×D1111yescharacteristic
473C2×C4C22⋊C4×D1111yescharacteristic
474C2×C4SD16×D1112yes—
475C2×C4Q16×D1112yes—
476C2×C4C22×C4×D1111yescharacteristic
477C2×C4C2×D4×D1111yescharacteristic
478C2×C4C2×D4×D1111yescharacteristic
479C8—42no—
480C8—42no—
481C8—441no—
482C8—441no—
483C8—441no—
484C8—441no—
485C22—21no—
486C22—21no—
487C22—114no—
488C22—222no—
489C22—222no—
490C22D11×#10312yes—
491C22C2×C22⋊C4×D1111yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—42no—
496C4—42no—
497C4—114no—
498C4—222no—
499C4—222no—
500C4—444no—
501C4D11×#10312yes—
502C4C2×SD16×D1111yescharacteristic
503C4C2×Q16×D1111yescharacteristic
504C4#1062330511yescharacteristic
505C4#1062330911yescharacteristic
506C2—22no—
507C2—224no—
508C2#1307709711yescharacteristic
509C2C2×D11×#10311yescharacteristic
510C2#1307714011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1550C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#4339D4
cosocleC42×C11C24
hypercenter#1550D11
hypocenterC11#17723
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
4. #13067303C2semidirect
5. #13067302C2semidirect
6. #13067299C2semidirect
7. #13067273C2semidirect
8. #13067270C2semidirect
9. C2×#10622120C2semidirect
10. D11×#332C2semidirect
11. C11×#1550C2semidirect
192. #1550D11semidirect
442. C11#17723semidirect

Maximal subgroups

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

subgroupindex
#130824282
#130777252
#130771852
#130673032
#130673022
#130672992
#130672732
#130672702
C2×#106221202
D11×#3322
C11×#15502
#1772311