Finite Group Databasebeta

← #14910162

Subgroups — #14910162

Order 2816.

500 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079266C211yesmaximal, characteristic, complemented
2#13070780C211yesmaximal, characteristic, complemented
3#13070773C211yesmaximal, characteristic, complemented
4#13070760C211yesmaximal, characteristic, complemented
5#13070750C211yesmaximal, characteristic, complemented
6#13070731C211yesmaximal, characteristic, complemented
7#13070717C211yesmaximal, characteristic, complemented
8#13070714C211yesmaximal, characteristic, complemented
9#13070700C211yesmaximal, characteristic, complemented
10#13070668C211yesmaximal, characteristic, complemented
11#13070668C211yesmaximal, characteristic, complemented
12#13070656C211yesmaximal, characteristic, complemented
13#13070651C211yesmaximal, characteristic, complemented
14#13070375C211yesmaximal, characteristic, complemented
15C11×#3175C211yesmaximal, characteristic, complemented
16C11×#542—21no—
17#10623066—21no—
18C11×#500C2211yescharacteristic
19C11×#495C2211yescharacteristic
20C11×#489—21no—
21C11×#468—21no—
22C11×#467C2211yescharacteristic
23C11×#466C2211yescharacteristic
24C11×#440—21no—
25C4×C11×Q16C2211yescharacteristic
26C4×C11×D8C2211yescharacteristic
27C11×#405C2211yescharacteristic
28C2×#66892C2211yescharacteristic
29C2×#66892C2211yescharacteristic
30C2×#66890C2211yescharacteristic
31C2×#66890C2211yescharacteristic
32#10622748—21no—
33#10622728C2211yescharacteristic
34#10622728C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37#10622326—21no—
38#10622324—21no—
39#10622308C2211yescharacteristic
40C4×D88C2211yescharacteristic
41C4×D88C2211yescharacteristic
42#10622296C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622129C2211yescharacteristic
48#10622129C2211yescharacteristic
49#10622129C2211yescharacteristic
50#10622129C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622128C2211yescharacteristic
53#10622127C2211yescharacteristic
54#10622127C2211yescharacteristic
55C4⋊(C11⋊C16)C2211yescharacteristic
56C4⋊(C11⋊C16)C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×SD16—21no—
61C2×C11×D8C2311yescharacteristic
62C2×C11×M16D411yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C4⋊Q8—21no—
65C11×#126—41no—
66C11×#124—21no—
67C11×#124—41no—
68C11×#123—41no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—41no—
71C11×#121—21no—
72C4×Q8×C11—21no—
73C4×D4×C11—21no—
74C11×#117D411yescharacteristic
75#66983—21no—
76#66983—21no—
77C2×D88—21no—
78C2×D88C2311yescharacteristic
79C2×D88C2311yescharacteristic
80#66947—41no—
81#66947—41no—
82#66937—41no—
83#66937—41no—
84#66927—21no—
85C4×D44—21no—
86C4×D44—21no—
87#66923—21no—
88C11×#107—21no—
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#103—21no—
92C11×#103—21no—
93C11×#102—21no—
94C11×#102—21no—
95C11×#97D411yescharacteristic
96C11×#97D411yescharacteristic
97C4×C8×C11C2311yescharacteristic
98C4×C8×C11C2311yescharacteristic
99#66892—41no—
100#66892—41no—
101#66890—41no—
102#66890—41no—
103#66885—21no—
104#66885—21no—
105#66885—21no—
106#66885—21no—
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66881—21no—
110#66876—41no—
111C2×C11⋊C16—41no—
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114C2×C11⋊C16C2311yescharacteristic
115C2×C11⋊C16C2311yescharacteristic
116#33823—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×Q8×C11—41no—
119C2×D4×C11—21no—
120C2×D4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11C2×D411yescharacteristic
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—41no—
128C2×D44—41no—
129C2×C4×D11—41no—
130C2×C4×D11—41no—
131C11×Q16—21no—
132C11×Q16—21no—
133C11×SD16—42no—
134C11×D8—21no—
135C11×D8—21no—
136C11×M16—41no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2411yescharacteristic
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4D811yescharacteristic
149C11×C4⋊C4D811yescharacteristic
150C11×C22⋊C4—41no—
151C11×C22⋊C4—41no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4—41no—
154C11×C22⋊C4—41no—
155C11×C22⋊C4D811yescharacteristic
156C11×C22⋊C4D811yescharacteristic
157C42×C11—41no—
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168D88—21no—
169D88—21no—
170D88—21no—
171D88—21no—
172D88—42no—
173C11⋊C16—21no—
174C11⋊C16—21no—
175C11⋊C16—21no—
176C11⋊C16—21no—
177#3176—111no—
178#3175D1111yescharacteristic, complemented
179#2229—111no—
180#2228—111no—
181#2226—111no—
182#2224—111no—
183#2220—111no—
184#2218—111no—
185#2217—111no—
186#2215—111no—
187#2210—111no—
188#2210—111no—
189#2207—111no—
190#2206—111no—
191#2151—111no—
192C23×C11—41no—
193C23×C11C2×D811yescharacteristic
194C22×D11—41no—
195C22×D11—41no—
196Q8×C11—41no—
197Q8×C11—41no—
198Q8×C11—161no—
199D4×C11—41no—
200D4×C11—41no—
201D4×C11—161no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—161no—
208C2×C4×C11C2×D811yescharacteristic
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C22⋊D11—161no—
215C22⋊D11—161no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218D44—41no—
219D44—41no—
220D44—41no—
221D44—41no—
222D44—161no—
223D44—161no—
224C4×D11—161no—
225C4×D11—161no—
226C8×C11—21no—
227C8×C11—21no—
228C8×C11—21no—
229C8×C11H(5,𝔽2)11yescharacteristic
230C8×C112−1+411yescharacteristic
231#542—21no—
232#540—221no—
233C2×SD32—111no—
234C2×SD32—111no—
235C2×D16—111no—
236C2×D16—111no—
237C2×M32—111no—
238C22×C16—111no—
239#500C2×D1111yescharacteristic
240#499—111no—
241#495C2×D1111yescharacteristic
242#493—111no—
243#490—221no—
244#489—21no—
245#469—221no—
246#468—21no—
247#467C2×D1111yescharacteristic
248#466—111no—
249#466—111no—
250#466C2×D1111yescharacteristic
251#442—221no—
252#440—21no—
253C4×Q16C2×D1111yescharacteristic
254C4×D8—111no—
255C4×D8—111no—
256C4×D8C2×D1111yescharacteristic
257#405C2×D1111yescharacteristic
258#367—111no—
259#367—111no—
260#366—111no—
261#366—111no—
262C4⋊C16—111no—
263C4⋊C16—111no—
264C4⋊C16—111no—
265C4⋊C16—111no—
266#358—111no—
267#358—111no—
268#357—111no—
269#357—111no—
270#357—111no—
271#357—111no—
272#357—111no—
273#357—111no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11C22×D811yescharacteristic
281C2×D11—81no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—81no—
286C2×D11—81no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—81no—
293C4×C11—81no—
294C4×C11—81no—
295C4×C11#53711yescharacteristic
296C4×C11#57511yescharacteristic
297Dic11—81no—
298Dic11—81no—
299C2×Q16C22×D1111yescharacteristic
300C2×SD16—21no—
301C2×D8—111no—
302C2×D8—111no—
303C2×D8—221no—
304C2×D8C22×D1111yescharacteristic
305C2×M16C22⋊D1111yescharacteristic
306C22×C8C22×D1111yescharacteristic
307C4⋊Q8—21no—
308#127—221no—
309#126—41no—
310#125—221no—
311#124—21no—
312#124—41no—
313#123—41no—
314#123—441no—
315#123—441no—
316C22⋊Q8—21no—
317C22⋊Q8—41no—
318#121—21no—
319#121—221no—
320#121—221no—
321#121—441no—
322#121—441no—
323C4×Q8—21no—
324C4×D4—21no—
325C4×D4—221no—
326C4×D4—221no—
327#117C22⋊D1111yescharacteristic
328SD32—441no—
329SD32—441no—
330D16—441no—
331D16—441no—
332M32—441no—
333C2×C16—111no—
334C2×C16—111no—
335C2×C16—111no—
336C2×C16—111no—
337C2×C16—441no—
338#107—21no—
339#107—111no—
340#107—111no—
341#107C22×D1111yescharacteristic
342#107C22×D1111yescharacteristic
343#106—221no—
344#103—21no—
345#103—21no—
346#102—21no—
347#102—21no—
348#102—221no—
349#102—221no—
350#102—221no—
351#102—221no—
352#97C22⋊D1111yescharacteristic
353#97C22⋊D1111yescharacteristic
354C4×C8C22×D1111yescharacteristic
355C4×C8C22×D1111yescharacteristic
356C2×C11—41no—
357C2×C11—161no—
358C2×C11#324511yescharacteristic
359C2×C11#341511yescharacteristic
360C2×C11#341611yescharacteristic
361D11—161no—
362D11—161no—
363C2×Q8—21no—
364C2×Q8—41no—
365C2×D4—21no—
366C2×D4—41no—
367C2×D4—221no—
368C2×D4—221no—
369C2×D4—441no—
370C2×D4—441no—
371C2×D4—441no—
372C2×D4—441no—
373C22×C4—41no—
374C22×C4—441no—
375C22×C4—441no—
376C22×C4C2×C22⋊D1111yescharacteristic
377Q16—21no—
378Q16—21no—
379SD16—42no—
380D8—21no—
381D8—21no—
382D8—221no—
383D8—221no—
384D8—221no—
385D8—221no—
386D8—442no—
387M16—41no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8C2×C22⋊D1111yescharacteristic
391C2×C8C2×C22⋊D1111yescharacteristic
392C2×C8C2×C22⋊D1111yescharacteristic
393C2×C8C23×D1111yescharacteristic
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—221no—
400C4⋊C4—221no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C4⋊C4#432311yescharacteristic
404C4⋊C4#432311yescharacteristic
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—441no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C22⋊C4—441no—
414C22⋊C4#432311yescharacteristic
415C22⋊C4#432311yescharacteristic
416C42—41no—
417C42C2×C22⋊D1111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C16—221no—
420C16—221no—
421C16—221no—
422C16—221no—
423C11#3382311yescharacteristic, complemented, Sylow
424C23—41no—
425C23—441no—
426C23—441no—
427C23C2×#432311yescharacteristic
428Q8—41no—
429Q8—41no—
430Q8—161no—
431D4—41no—
432D4—41no—
433D4—161no—
434D4—441no—
435D4—441no—
436D4—441no—
437D4—441no—
438D4—1761no—
439D4—1761no—
440D4—1761no—
441D4—1761no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—161no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—1761no—
451C2×C4—1761no—
452C2×C4C2×#432311yescharacteristic
453C2×C4C2×#432311yescharacteristic
454C2×C4C2×#432311yescharacteristic
455C2×C4C2×#432311yescharacteristic
456C2×C4C2×#432311yescharacteristic
457C2×C4C22×C22⋊D1111yescharacteristic
458C8—21no—
459C8—21no—
460C8—21no—
461C8#6704211yescharacteristic
462C8#6704311yescharacteristic
463C22—21no—
464C22—21no—
465C22—21no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—881no—
470C22—881no—
471C22—881no—
472C22—881no—
473C22—881no—
474C22—881no—
475C22C22×#432311yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—81no—
482C4—81no—
483C4—81no—
484C4—881no—
485C4—881no—
486C4#1062335311yescharacteristic
487C4#1062336411yescharacteristic
488C2—41no—
489C2—161no—
490C2—1761no—
491C2—1761no—
492C2#1307992311yescharacteristic
493C2#1308175511yescharacteristic
494C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3175C2
socleC22×C11C22×D8
hypercenter#3175D11
hypocenterC11#33823
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3175

Complements

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

NH ≅ G/Ntype
1. #13079266C2semidirect
2. #13070780C2semidirect
3. #13070773C2semidirect
4. #13070760C2semidirect
5. #13070750C2semidirect
6. #13070731C2semidirect
7. #13070717C2semidirect
8. #13070714C2semidirect
9. #13070700C2semidirect
10. #13070668C2semidirect
11. #13070668C2semidirect
12. #13070656C2semidirect
13. #13070651C2semidirect
14. #13070375C2semidirect
15. C11×#3175C2semidirect
178. #3175D11semidirect
423. C11#33823semidirect

Maximal subgroups

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

subgroupindex
#130792662
#130707802
#130707732
#130707602
#130707502
#130707312
#130707172
#130707142
#130707002
#130706682
#130706562
#130706512
#130703752
C11×#31752
#3382311