Finite Group Databasebeta

← #14722238

Subgroups — #14722238

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#13082432C211yesmaximal, characteristic
2#13077724C211yesmaximal, characteristic
3#13077185C211yesmaximal, characteristic
4#13067307C211yesmaximal, characteristic, complemented
5#13067305C212yesmaximal, complemented
6#13067299C212yesmaximal, complemented
7#13067272C212yesmaximal, complemented
8#13067271C211yesmaximal, characteristic, complemented
9C2×#10622185C211yesmaximal, characteristic, complemented
10D11×#332C212yesmaximal, complemented
11C11×#1549C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13Q8×C22⋊D11—22no—
14C2×#66960—21no—
15#10623261C412yes—
16#10623260—22no—
17#10623259C2212yes—
18#10623258—21no—
19D11×C4⋊Q8C2212yes—
20#10623253C412yes—
21#10623252—21no—
22#10623042C414yes—
23#10623035—21no—
24#10623031—21no—
25C4×#4339C2211yescharacteristic
26#10623001C2211yescharacteristic
27C11×#431C2211yescharacteristic
28C11×#423C2211yescharacteristic
29#10622732—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622452—22no—
33#10622450C2212yes—
34#10622446C2212yes—
35D11×C4⋊C8C2212yes—
36D11×C4⋊C8C2212yes—
37(C22⋊D11)⋊C8—22no—
38C8×D44—21no—
39C8×Dic22—21no—
40C11×#332C2212yes—
41C11×#332C2212yes—
42#10622185C2212yes—
43#10622185C2212yes—
44#10622124C2212yes—
45#10622120C2211yescharacteristic
46#10622120C2211yescharacteristic
47#10622119C2211yescharacteristic
48#10622119C2211yescharacteristic
49#10622119C2212yes—
50C22×Q8×C11—21no—
51C2×Q8×D11—22no—
52C2×#4339D411yescharacteristic
53C2×C11×M16—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8C2×C412yes—
57C11×C4⋊Q8C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2×C412yes—
60C2×C42×C11C2311yescharacteristic
61#66999—22no—
62#66999—24no—
63Q8×Dic11—22no—
64#66997—24no—
65#66997—22no—
66C4×C22⋊D11—24no—
67C4×C22⋊D11C2×C412yes—
68C4×C22⋊D11D412yes—
69#66979—21no—
70#66979D411yescharacteristic
71#66977—21no—
72#66977—24no—
73#66977C2×C412yes—
74C22×C11⋊C8—21no—
75C22×C11⋊C8—21no—
76#66960—44no—
77C2×#4313—22no—
78C2×C8×D11—22no—
79C2×C8×D11—22no—
80#66950C2×C414yes—
81#66949—24no—
82#66946—22no—
83#66945—22no—
84C4⋊C4×D11—22no—
85C4⋊C4×D11C2×C414yes—
86#66943—22no—
87#66943—22no—
88#66942—24no—
89#66941—22no—
90#66941—22no—
91#66941C2×C414yes—
92#66940—22no—
93#66940C2×C414yes—
94C4×D44C2×C411yescharacteristic
95C4×D44D411yescharacteristic
96#66925D412yes—
97C42×D11C2312yes—
98#66923—21no—
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101C4×Dic22—21no—
102C4×Dic22C2×C412yes—
103C4×Dic22C2×C411yescharacteristic
104C4×Dic22D411yescharacteristic
105C11×C4⋊C8—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2312yes—
109C11×C22⋊C8—21no—
110C4×C8×C11—21no—
111(C2×D11)⋊C8—22no—
112Dic11⋊C8—22no—
113Dic11⋊C8—22no—
114Dic11⋊C8—22no—
115C8×Dic11—22no—
116C4⋊(C11⋊C8)—21no—
117C4⋊(C11⋊C8)—21no—
118C4⋊(C11⋊C8)C2311yescharacteristic
119C4⋊(C11⋊C8)C2311yescharacteristic
120C4⋊(C11⋊C8)C2312yes—
121#17723—111nomaximal, Sylow
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—81no—
125C2×Q8×C11—81no—
126C22×C4×C11—22no—
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C2×C22⋊D11C22⋊C412yes—
131Q8×D11—82no—
132Q8×D11—82no—
133#4339SD1614yes—
134#4339Q1614yes—
135C2×D44C22⋊C411yescharacteristic
136C2×C4×D11—24no—
137C2×C4×D11C22×C412yes—
138C2×C4×D11C2×D412yes—
139C2×C4×D11C2×D412yes—
140C2×Dic22—24no—
141C2×Dic22—21no—
142C2×Dic22C22⋊C411yescharacteristic
143C2×Dic22C22×C412yes—
144C11×M16—42no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4C22×C414yes—
152C42×C11C22×C411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2411yescharacteristic
156C22⋊Dic11—22no—
157C22⋊Dic11C22⋊C412yes—
158(C2×D11)⋊C4—24no—
159(C2×D11)⋊C4C22⋊C412yes—
160(C2×D11)⋊C4C22⋊C412yes—
161C4⋊Dic11—24no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11C22⋊C411yescharacteristic
166C4⋊Dic11C22⋊C411yescharacteristic
167C4⋊Dic11C22×C412yes—
168Dic11⋊C4—24no—
169Dic11⋊C4—24no—
170Dic11⋊C4—24no—
171Dic11⋊C4—22no—
172Dic11⋊C4—22no—
173Dic11⋊C4C22⋊C412yes—
174Dic11⋊C4C22⋊C412yes—
175C4×Dic11—24no—
176C4×Dic11—22no—
177C4×Dic11C22×C412yes—
178C4×Dic11C2×D412yes—
179C4×Dic11C2×D412yes—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—42no—
184C2×C11⋊C8—81no—
185#4313—44no—
186C8×D11—44no—
187C8×D11—82no—
188#3503—111no—
189#2988—111no—
190#2906—111no—
191#1550—111no—
192#1550—112no—
193#1549—112no—
194#1549D1111yescharacteristic, complemented
195#1542—111no—
196#1542—112no—
197C2×#332—112no—
198C2×#332—111no—
199C23×C11C2×C22⋊C411yescharacteristic
200C22×D11C2×C22⋊C412yes—
201Q8×C11—42no—
202Q8×C11—42no—
203Q8×C11—82no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—24no—
207C2×C4×C11—41no—
208C2×C4×C11—82no—
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—22no—
219C2×Dic11—22no—
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—41no—
231Dic22—41no—
232Dic22—42no—
233Dic22—84no—
234Dic22#10314yes—
235C8×C11—42no—
236C8×C11—41no—
237C8×C11—41no—
238C11⋊C8—41no—
239C11⋊C8—41no—
240C11⋊C8—42no—
241C2×#131—221no—
242Q82—112no—
243#557—221no—
244#554—112no—
245#554—114no—
246D4×Q8—221no—
247D4×Q8—222no—
248#544—221no—
249#544—222no—
250#533—112no—
251#533—111no—
252C2×C4⋊Q8—112no—
253C2×C4⋊Q8C2×D1111yescharacteristic
254#520—221no—
255C4×#41—111no—
256C8×Q8—221no—
257C8×D4—221no—
258C8×D4—222no—
259#431—112no—
260#431C2×D1111yescharacteristic
261#424—222no—
262#424—221no—
263#423—112no—
264#423C2×D1111yescharacteristic
265C2×C4⋊C8—111no—
266C2×C4⋊C8—111no—
267C2×C4⋊C8—112no—
268C2×C4⋊C8—112no—
269#333—111no—
270#333—112no—
271#333—111no—
272#332—112no—
273#332—112no—
274#332—111no—
275#332—112no—
276#332—111no—
277#332C2×D1112yes—
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—44no—
290C4×C11C2×#10312yes—
291C4×C11C22×SD1611yescharacteristic
292C4×C11C22×Q1611yescharacteristic
293C4×C11#57611yescharacteristic
294C4×C11#57711yescharacteristic
295Dic11—22no—
296Dic11—22no—
297Dic11—42no—
298Dic11—42no—
299Dic11C2×#10314yes—
300C2×#41—111no—
301C22×Q8—21no—
302C22×Q8—222no—
303#131—444no—
304C2×M16—21no—
305C2×M16—222no—
306C22×C8—222no—
307C22×C8—222no—
308C22×C8—221no—
309C22×C8—221no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8—114no—
313C4⋊Q8—111no—
314C4⋊Q8—111no—
315C4⋊Q8—222no—
316C4⋊Q8—222no—
317C4⋊Q8—222no—
318C4⋊Q8—224no—
319C4⋊Q8C4×D1112yes—
320C4⋊Q8C22×D1112yes—
321#125—222no—
322#125—224no—
323#125—222no—
324#125—221no—
325C22⋊Q8—112no—
326C22⋊Q8—114no—
327C22⋊Q8—224no—
328C22⋊Q8—224no—
329C22⋊Q8—224no—
330C22⋊Q8—222no—
331C22⋊Q8—221no—
332C4×Q8—111no—
333C4×Q8—111no—
334C4×Q8—114no—
335C4×Q8—112no—
336C4×Q8—222no—
337C4×Q8—222no—
338C4×Q8—221no—
339C4×D4—112no—
340C4×D4—112no—
341C4×D4—111no—
342C4×D4—111no—
343C4×D4—222no—
344C4×D4—224no—
345#117—111no—
346#117—112no—
347#117—222no—
348#117—221no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—114no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4C4×D1112yes—
353C2×C42—112no—
354C2×C42C22×D1111yescharacteristic
355C4⋊C8—21no—
356C4⋊C8—111no—
357C4⋊C8—112no—
358C4⋊C8—111no—
359C4⋊C8—222no—
360C4⋊C8—222no—
361C4⋊C8—222no—
362C4⋊C8—221no—
363C4⋊C8—221no—
364C4⋊C8C22×D1111yescharacteristic
365C4⋊C8C22×D1112yes—
366C4⋊C8C22×D1111yescharacteristic
367C22⋊C8—21no—
368C22⋊C8—222no—
369C4×C8—21no—
370C4×C8—222no—
371C2×C11—22no—
372C2×C11#288911yescharacteristic
373C2×C11C22×#10311yescharacteristic
374C2×C11#289711yescharacteristic
375D11—24no—
376#41—114no—
377#41—114no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—81no—
381C2×Q8—81no—
382C2×Q8—111no—
383C2×Q8—112no—
384C2×Q8—224no—
385C2×Q8—221no—
386C2×Q8—882no—
387C2×Q8—882no—
388C2×D4—112no—
389C2×D4—111no—
390C22×C4—22no—
391C22×C4—112no—
392C22×C4—112no—
393C22×C4—112no—
394C22×C4—224no—
395C22×C4C2×C4×D1111yescharacteristic
396C22×C4D4×D1111yescharacteristic
397C22×C4D4×D1111yescharacteristic
398M16—42no—
399M16—444no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—22no—
403C2×C8—222no—
404C2×C8—221no—
405C2×C8—221no—
406C2×C8—444no—
407C2×C8—442no—
408C2×C8—882no—
409C2×C8—881no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—112no—
414C4⋊C4—111no—
415C4⋊C4—112no—
416C4⋊C4—111no—
417C4⋊C4—112no—
418C4⋊C4—224no—
419C4⋊C4—224no—
420C4⋊C4—224no—
421C4⋊C4—224no—
422C4⋊C4—222no—
423C4⋊C4—222no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4C2×C4×D1114yes—
428C22⋊C4—112no—
429C22⋊C4—112no—
430C22⋊C4—112no—
431C22⋊C4—224no—
432C22⋊C4—222no—
433C42—112no—
434C42—112no—
435C42—112no—
436C42—224no—
437C42—222no—
438C42C2×C4×D1111yescharacteristic
439C42D4×D1111yescharacteristic
440C42D4×D1111yescharacteristic
441C42C23×D1111yescharacteristic
442C11#1772311yescharacteristic, complemented, Sylow
443C23—112no—
444C23C22⋊C4×D1111yescharacteristic
445Q8—42no—
446Q8—42no—
447Q8—82no—
448Q8—114no—
449Q8—442no—
450Q8—441no—
451Q8—441no—
452Q8—884no—
453D4—118no—
454D4—114no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—24no—
458C2×C4—41no—
459C2×C4—82no—
460C2×C4—112no—
461C2×C4—114no—
462C2×C4—114no—
463C2×C4—112no—
464C2×C4—112no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—442no—
470C2×C4—884no—
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—41no—
481C8—41no—
482C8—441no—
483C8—441no—
484C8—442no—
485C22—21no—
486C22—21no—
487C22—114no—
488C22—222no—
489C22—222no—
490C22D11×#10312yes—
491C22C2×C22⋊C4×D1111yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—44no—
496C4—114no—
497C4—222no—
498C4—222no—
499C4—442no—
500C4—442no—
501C4D11×#10312yes—
502C4C2×SD16×D1111yescharacteristic
503C4C2×Q16×D1111yescharacteristic
504C4#1062330511yescharacteristic
505C4#1062330611yescharacteristic
506C2—22no—
507C2—224no—
508C2#1307709611yescharacteristic
509C2C2×D11×#10311yescharacteristic
510C2#1307714111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1549C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#4339D4
cosocleC42×C11C24
hypercenter#1549D11
hypocenterC11#17723
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
4. #13067307C2semidirect
5. #13067305C2semidirect
6. #13067299C2semidirect
7. #13067272C2semidirect
8. #13067271C2semidirect
9. C2×#10622185C2semidirect
10. D11×#332C2semidirect
11. C11×#1549C2semidirect
194. #1549D11semidirect
442. C11#17723semidirect

Maximal subgroups

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

subgroupindex
#130824322
#130777242
#130771852
#130673072
#130673052
#130672992
#130672722
#130672712
C2×#106221852
D11×#3322
C11×#15492
#1772311