Finite Group Databasebeta

← #14722688

Subgroups — #14722688

Order 2816.

900 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082432C211yesmaximal, characteristic
2#13077746C211yesmaximal, characteristic
3#13077745C211yesmaximal, characteristic
4#13067353C211yesmaximal, characteristic, complemented
5#13067352C212yesmaximal, complemented
6#13067299C212yesmaximal, complemented
7#13067288C211yesmaximal, characteristic, complemented
8#13067286C212yesmaximal, complemented
9#13067280C211yesmaximal, characteristic, complemented
10#13067279C212yesmaximal, complemented
11C11×#1549C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13Q8×C22⋊D11—22no—
14#10623261—21no—
15#10623260C414yes—
16#10623259C2212yes—
17#10623258—21no—
18D11×C4⋊Q8C2212yes—
19#10623253—21no—
20#10623252—21no—
21#10623042—22no—
22#10623035C412yes—
23#10623031C412yes—
24C4×#4339C2211yescharacteristic
25#10623001C2211yescharacteristic
26C11×#431C2211yescharacteristic
27C11×#423C2211yescharacteristic
28#10622741—22no—
29#10622538C2211yescharacteristic
30#10622537C2211yescharacteristic
31#10622451—21no—
32#10622450C2212yes—
33#10622450C2212yes—
34#10622446C2212yes—
35#10622446C2212yes—
36#10622443—21no—
37#10622342—22no—
38#10622301—21no—
39C8×Dic22—21no—
40C11×#332C2212yes—
41C11×#332C2212yes—
42#10622185C2212yes—
43#10622185C2212yes—
44#10622124C2211yescharacteristic
45#10622124C2211yescharacteristic
46#10622124C2212yes—
47#10622120C2212yes—
48#10622120C2211yescharacteristic
49#10622120C2211yescharacteristic
50C22×Q8×C11—21no—
51C2×Q8×D11—22no—
52C2×#4339C2×C411yescharacteristic
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⋊D11D412yes—
68C4×C22⋊D11D412yes—
69#66979C2×C412yes—
70#66979C2×C411yescharacteristic
71#66977—21no—
72#66977—21no—
73#66977—24no—
74C2×#4318—21no—
75C2×#4313—22no—
76C2×#4313—22no—
77#66950—22no—
78#66949—24no—
79#66946—22no—
80#66945C2×C414yes—
81C4⋊C4×D11—22no—
82C4⋊C4×D11C2×C414yes—
83#66943—22no—
84#66943C2×C414yes—
85#66942—24no—
86#66941—22no—
87#66941—22no—
88#66941C2×C414yes—
89#66940—22no—
90#66940—22no—
91C4×D44D411yescharacteristic
92C4×D44D411yescharacteristic
93#66925C2×C412yes—
94C42×D11C2312yes—
95#66923C2×C412yes—
96#66922C2311yescharacteristic
97#66922C2311yescharacteristic
98C4×Dic22—21no—
99C4×Dic22—21no—
100C4×Dic22D411yescharacteristic
101C4×Dic22D411yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2312yes—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C22⋊C8—21no—
107C4×C8×C11—21no—
108C22⋊(C11⋊C8)—21no—
109(C2×D11)⋊C8—22no—
110(C2×D11)⋊C8—22no—
111Dic11⋊C8—22no—
112Dic11⋊C8—22no—
113C8×Dic11—22no—
114C8×Dic11—22no—
115C4⋊(C11⋊C8)—21no—
116C4⋊(C11⋊C8)C2312yes—
117C4⋊(C11⋊C8)C2311yescharacteristic
118C4⋊(C11⋊C8)C2311yescharacteristic
119C4×C11⋊C8—21no—
120#17777—111nomaximal, Sylow
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—81no—
124C2×Q8×C11—81no—
125C22×C4×C11—22no—
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C2×C22⋊D11C22⋊C412yes—
130Q8×D11—82no—
131Q8×D11—82no—
132#4339—24no—
133C2×D44C22⋊C411yescharacteristic
134C2×C4×D11—24no—
135C2×C4×D11C22×C412yes—
136C2×C4×D11C2×D412yes—
137C2×C4×D11C2×D412yes—
138C2×Dic22—24no—
139C2×Dic22—21no—
140C2×Dic22—21no—
141C2×Dic22C22⋊C411yescharacteristic
142C11×M16—81no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4C22×C414yes—
150C42×C11C22×C411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2411yescharacteristic
154C22⋊Dic11—22no—
155C22⋊Dic11C22⋊C412yes—
156(C2×D11)⋊C4—24no—
157(C2×D11)⋊C4C22⋊C412yes—
158(C2×D11)⋊C4C22⋊C412yes—
159C4⋊Dic11—24no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11C22⋊C411yescharacteristic
163C4⋊Dic11C22⋊C411yescharacteristic
164C4⋊Dic11C22×C412yes—
165C4⋊Dic11C22×C412yes—
166Dic11⋊C4—24no—
167Dic11⋊C4—24no—
168Dic11⋊C4—24no—
169Dic11⋊C4—22no—
170Dic11⋊C4—22no—
171Dic11⋊C4C22⋊C412yes—
172Dic11⋊C4C22⋊C412yes—
173C4×Dic11—24no—
174C4×Dic11—22no—
175C4×Dic11C22×C412yes—
176C4×Dic11C2×D412yes—
177C4×Dic11C2×D412yes—
178#4318—81no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—22no—
182#4313—82no—
183#4313—82no—
184#3503—111no—
185#2991—111no—
186#2991—111no—
187#1561—111no—
188#1561—112no—
189#1549—112no—
190#1549D1111yescharacteristic, complemented
191#1546—112no—
192#1546—111no—
193#1544—111no—
194#1544—112no—
195C23×C11C2×C22⋊C411yescharacteristic
196C22×D11C2×C22⋊C412yes—
197Q8×C11—42no—
198Q8×C11—42no—
199Q8×C11—82no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—82no—
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C2×C22⋊C411yescharacteristic
209C2×C4×C11C2×C22⋊C411yescharacteristic
210C2×C4×C11C23×C411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C22⋊D11—24no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11C2×C22⋊C412yes—
217C2×Dic11C2×C22⋊C412yes—
218C2×Dic11C2×C22⋊C412yes—
219D44—22no—
220C4×D11—22no—
221C4×D11—22no—
222C4×D11—22no—
223C4×D11—22no—
224C4×D11—24no—
225C4×D11—84no—
226Dic22—41no—
227Dic22—41no—
228Dic22—41no—
229Dic22—41no—
230Dic22—84no—
231Dic22#10114yes—
232C8×C11—41no—
233C8×C11—42no—
234C8×C11—41no—
235C11⋊C8—42no—
236C11⋊C8—41no—
237C11⋊C8—41no—
238Q82—221no—
239#557—221no—
240#554—222no—
241#554—221no—
242D4×Q8—221no—
243D4×Q8—222no—
244#544—114no—
245#544—112no—
246#533—112no—
247#533—111no—
248C2×C4⋊Q8—112no—
249C2×C4⋊Q8C2×D1111yescharacteristic
250#520—112no—
251C4×#41—111no—
252C8×Q8—221no—
253C8×Q8—221no—
254#436—221no—
255#436—222no—
256#436—221no—
257#436—222no—
258#431—111no—
259#431—112no—
260#431—112no—
261#431C2×D1111yescharacteristic
262#423—111no—
263#423—112no—
264#423—112no—
265#423C2×D1111yescharacteristic
266#332—112no—
267#332—112no—
268#332—111no—
269#332—111no—
270#332—111no—
271#332—112no—
272#332—111no—
273#332—112no—
274#332C2×D1112yes—
275#332C2×D1112yes—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11C22×C22⋊C411yescharacteristic
280C2×D11—22no—
281C2×D11—22no—
282C2×D11—22no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—44no—
287C4×C11C2×#10112yes—
288C4×C11#57611yescharacteristic
289C4×C11#57711yescharacteristic
290C4×C11#57711yescharacteristic
291C4×C11#57811yescharacteristic
292Dic11—22no—
293Dic11—22no—
294Dic11—42no—
295Dic11—42no—
296Dic11C2×#10114yes—
297C2×#41—111no—
298C22×Q8—21no—
299C22×Q8—222no—
300C2×M16—21no—
301C2×M16—222no—
302C2×M16—222no—
303C2×M16—221no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—114no—
307C4⋊Q8—111no—
308C4⋊Q8—111no—
309C4⋊Q8—222no—
310C4⋊Q8—222no—
311C4⋊Q8—222no—
312C4⋊Q8—224no—
313C4⋊Q8C4×D1112yes—
314C4⋊Q8C22×D1112yes—
315#125—114no—
316#125—112no—
317#125—224no—
318#125—222no—
319C22⋊Q8—224no—
320C22⋊Q8—224no—
321C22⋊Q8—224no—
322C22⋊Q8—222no—
323C22⋊Q8—222no—
324C22⋊Q8—221no—
325C22⋊Q8—221no—
326C4×Q8—111no—
327C4×Q8—111no—
328C4×Q8—222no—
329C4×Q8—222no—
330C4×Q8—222no—
331C4×Q8—221no—
332C4×Q8—221no—
333C4×D4—112no—
334C4×D4—112no—
335C4×D4—111no—
336C4×D4—111no—
337C4×D4—222no—
338C4×D4—224no—
339#117—111no—
340#117—112no—
341#117—112no—
342#117—114no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—114no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4C4×D1112yes—
347C2×C42—112no—
348C2×C42C22×D1111yescharacteristic
349C4⋊C8—21no—
350C4⋊C8—112no—
351C4⋊C8—111no—
352C4⋊C8—111no—
353C4⋊C8—222no—
354C4⋊C8—222no—
355C4⋊C8—221no—
356C4⋊C8C22×D1111yescharacteristic
357C4⋊C8C22×D1112yes—
358C4⋊C8C22×D1111yescharacteristic
359C22⋊C8—21no—
360C22⋊C8—222no—
361C22⋊C8—222no—
362C22⋊C8—221no—
363C4×C8—21no—
364C4×C8—222no—
365C4×C8—222no—
366C4×C8—221no—
367C2×C11—41no—
368C2×C11C22×#10111yescharacteristic
369C2×C11#289711yescharacteristic
370C2×C11#289811yescharacteristic
371D11—42no—
372#41—224no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—81no—
376C2×Q8—81no—
377C2×Q8—111no—
378C2×Q8—224no—
379C2×Q8—221no—
380C2×Q8—221no—
381C2×Q8—882no—
382C2×Q8—882no—
383C2×D4—112no—
384C2×D4—111no—
385C22×C4—22no—
386C22×C4—112no—
387C22×C4—112no—
388C22×C4—112no—
389C22×C4—224no—
390C22×C4C2×C4×D1111yescharacteristic
391C22×C4D4×D1111yescharacteristic
392C22×C4D4×D1111yescharacteristic
393M16—81no—
394M16—882no—
395M16—882no—
396M16—881no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—22no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—222no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—112no—
407C4⋊C4—111no—
408C4⋊C4—112no—
409C4⋊C4—111no—
410C4⋊C4—112no—
411C4⋊C4—112no—
412C4⋊C4—224no—
413C4⋊C4—224no—
414C4⋊C4—224no—
415C4⋊C4—224no—
416C4⋊C4—222no—
417C4⋊C4—222no—
418C4⋊C4—221no—
419C4⋊C4—221no—
420C4⋊C4C2×C4×D1114yes—
421C22⋊C4—112no—
422C22⋊C4—112no—
423C22⋊C4—112no—
424C22⋊C4—224no—
425C22⋊C4—222no—
426C42—112no—
427C42—112no—
428C42—112no—
429C42—224no—
430C42—222no—
431C42C2×C4×D1111yescharacteristic
432C42D4×D1111yescharacteristic
433C42D4×D1111yescharacteristic
434C42C23×D1111yescharacteristic
435C11#1777711yescharacteristic, complemented, Sylow
436C23—112no—
437C23C22⋊C4×D1111yescharacteristic
438Q8—42no—
439Q8—42no—
440Q8—82no—
441Q8—114no—
442Q8—441no—
443Q8—441no—
444Q8—441no—
445Q8—441no—
446Q8—884no—
447D4—224no—
448D4—222no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—82no—
456C2×C4—112no—
457C2×C4—112no—
458C2×C4—112no—
459C2×C4—224no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—884no—
467C2×C4C22⋊C4×D1111yescharacteristic
468C2×C4C22⋊C4×D1111yescharacteristic
469C2×C4C22⋊C4×D1111yescharacteristic
470C2×C4C22×C4×D1111yescharacteristic
471C2×C4C2×D4×D1111yescharacteristic
472C2×C4C2×D4×D1111yescharacteristic
473C8—42no—
474C8—41no—
475C8—41no—
476C8—441no—
477C8—441no—
478C8—442no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—222no—
483C22—222no—
484C22—222no—
485C22C2×C22⋊C4×D1111yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—44no—
490C4—114no—
491C4—222no—
492C4—222no—
493C4—442no—
494C4—442no—
495C4D11×#10112yes—
496C4#1062329311yescharacteristic
497C4#1062329711yescharacteristic
498C4#1062330511yescharacteristic
499C4#1062330611yescharacteristic
500C2—41no—
501C2—442no—
502C2C2×D11×#10111yescharacteristic
503C2#1307714111yescharacteristic
504C2#1307714411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1549C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#1549D11
hypocenterC11#17777
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. #13067353C2semidirect
5. #13067352C2semidirect
6. #13067299C2semidirect
7. #13067288C2semidirect
8. #13067286C2semidirect
9. #13067280C2semidirect
10. #13067279C2semidirect
11. C11×#1549C2semidirect
190. #1549D11semidirect
435. C11#17777semidirect

Maximal subgroups

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

subgroupindex
#130824322
#130777462
#130777452
#130673532
#130673522
#130672992
#130672882
#130672862
#130672802
#130672792
C11×#15492
#1777711