Finite Group Databasebeta

← #14910156

Subgroups — #14910156

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#13079255C211yesmaximal, characteristic, complemented
2#13070777C211yesmaximal, characteristic, complemented
3#13070770C211yesmaximal, characteristic, complemented
4#13070763C211yesmaximal, characteristic, complemented
5#13070753C211yesmaximal, characteristic, complemented
6#13070727C211yesmaximal, characteristic, complemented
7#13070717C211yesmaximal, characteristic, complemented
8#13070710C211yesmaximal, characteristic, complemented
9#13070700C211yesmaximal, characteristic, complemented
10#13070671C211yesmaximal, characteristic, complemented
11#13070671C211yesmaximal, characteristic, complemented
12#13070653C211yesmaximal, characteristic, complemented
13#13070648C211yesmaximal, characteristic, complemented
14#13070375C211yesmaximal, characteristic, complemented
15C11×#3176C211yesmaximal, characteristic, complemented
16C11×#540—21no—
17#10623065—21no—
18C11×#499C2211yescharacteristic
19C11×#493C2211yescharacteristic
20C11×#490—21no—
21C11×#469—21no—
22C11×#466C2211yescharacteristic
23C11×#466C2211yescharacteristic
24C11×#442—21no—
25C4×C11×D8C2211yescharacteristic
26C4×C11×D8C2211yescharacteristic
27C11×#405C2211yescharacteristic
28C2×#66891C2211yescharacteristic
29C2×#66891C2211yescharacteristic
30C2×#66890C2211yescharacteristic
31C2×#66890C2211yescharacteristic
32#10622747—21no—
33#10622729C2211yescharacteristic
34#10622728C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37#10622327—21no—
38#10622323—21no—
39C4×Dic44C2211yescharacteristic
40#10622309C2211yescharacteristic
41C4×D88C2211yescharacteristic
42#10622295C2211yescharacteristic
43#10622200C2211yescharacteristic
44#10622200C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622130C2211yescharacteristic
48#10622130C2211yescharacteristic
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×D8—21no—
60C2×C11×D8C2311yescharacteristic
61C2×C11×D8C2311yescharacteristic
62C2×C11×M16D411yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×#127—21no—
65C11×#125—21no—
66C11×#123—41no—
67C11×#123—41no—
68C11×#121—21no—
69C11×#121—21no—
70C11×#121—41no—
71C11×#121—41no—
72C4×D4×C11—21no—
73C4×D4×C11—21no—
74C11×#117D411yescharacteristic
75#66983—21no—
76#66977—21no—
77C2×Dic44C2311yescharacteristic
78C2×D88C2311yescharacteristic
79C2×#4314—21no—
80#66951—41no—
81#66949—41no—
82#66938—41no—
83#66936—41no—
84#66928—21no—
85C4×D44—21no—
86#66922—21no—
87C4×Dic22—21no—
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#106—21no—
91C11×#102—21no—
92C11×#102—21no—
93C11×#102—21no—
94C11×#102—21no—
95C11×#97D411yescharacteristic
96C11×#97D411yescharacteristic
97C4×C8×C11C2311yescharacteristic
98C4×C8×C11C2311yescharacteristic
99#66891—41no—
100#66891—41no—
101#66890—41no—
102#66890—41no—
103#66885—21no—
104#66885—21no—
105#66882—21no—
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66880—21no—
109#66880—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×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11—41no—
127C2×D44—21no—
128C2×C4×D11—41no—
129C2×Dic22—21no—
130C2×Dic22—41no—
131C11×D8—21no—
132C11×D8—21no—
133C11×D8—21no—
134C11×D8—21no—
135C11×D8—42no—
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⋊C4D811yescharacteristic
148C11×C4⋊C4D811yescharacteristic
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C11×C22⋊C4—41no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4D811yescharacteristic
154C11×C22⋊C4D811yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C22⋊Dic11—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167C4×Dic11—41no—
168Dic44—21no—
169Dic44—21no—
170D88—21no—
171D88—21no—
172#4314—42no—
173C11⋊C16—21no—
174C11⋊C16—21no—
175C11⋊C16—21no—
176C11⋊C16—21no—
177#3176D1111yescharacteristic, complemented
178#3175—111no—
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×C11—41no—
194C23×C11C2×D811yescharacteristic
195C22×D11—41no—
196D4×C11—41no—
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11—161no—
201D4×C11—161no—
202D4×C11—161no—
203D4×C11—161no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—161no—
209C2×C4×C11—161no—
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C22⋊D11—161no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220D44—41no—
221D44—41no—
222C4×D11—161no—
223Dic22—41no—
224Dic22—41no—
225Dic22—161no—
226C8×C11—21no—
227C8×C11—21no—
228C8×C11—21no—
229C8×C11H(5,𝔽2)11yescharacteristic
230C8×C112−1+411yescharacteristic
231#542—221no—
232#540—21no—
233C2×SD32—111no—
234C2×SD32—111no—
235C2×D16—111no—
236C2×D16—111no—
237C2×M32—111no—
238C22×C16—111no—
239#500—111no—
240#499C2×D1111yescharacteristic
241#495—111no—
242#493C2×D1111yescharacteristic
243#490—21no—
244#489—221no—
245#469—21no—
246#468—221no—
247#467—111no—
248#466—111no—
249#466C2×D1111yescharacteristic
250#466C2×D1111yescharacteristic
251#442—21no—
252#440—221no—
253C4×Q16—111no—
254C4×D8—111no—
255C4×D8C2×D1111yescharacteristic
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×C11—81no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11C22×D811yescharacteristic
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#53711yescharacteristic
295C4×C11#57511yescharacteristic
296Dic11—81no—
297Dic11—81no—
298Dic11—81no—
299C2×Q16—111no—
300C2×SD16—221no—
301C2×D8—21no—
302C2×D8—111no—
303C2×D8C22×D1111yescharacteristic
304C2×D8C22×D1111yescharacteristic
305C2×M16C22⋊D1111yescharacteristic
306C22×C8C22×D1111yescharacteristic
307C4⋊Q8—221no—
308#127—21no—
309#126—441no—
310#125—21no—
311#124—221no—
312#124—441no—
313#123—41no—
314#123—41no—
315#123—441no—
316C22⋊Q8—221no—
317C22⋊Q8—441no—
318#121—21no—
319#121—21no—
320#121—41no—
321#121—41no—
322#121—221no—
323C4×Q8—221no—
324C4×D4—21no—
325C4×D4—21no—
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—111no—
339#107—111no—
340#107—221no—
341#107C22×D1111yescharacteristic
342#107C22×D1111yescharacteristic
343#106—21no—
344#103—221no—
345#103—221no—
346#102—21no—
347#102—21no—
348#102—21no—
349#102—21no—
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—161no—
359C2×C11#324511yescharacteristic
360C2×C11#341511yescharacteristic
361C2×C11#341611yescharacteristic
362D11—161no—
363C2×Q8—221no—
364C2×Q8—441no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—221no—
372C2×D4—441no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—441no—
376C22×C4C2×C22⋊D1111yescharacteristic
377Q16—221no—
378Q16—221no—
379SD16—442no—
380D8—21no—
381D8—21no—
382D8—21no—
383D8—21no—
384D8—42no—
385D8—221no—
386D8—221no—
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—221no—
399C4⋊C4—221no—
400C4⋊C4—441no—
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—441no—
410C22⋊C4—441no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C22⋊C4—441no—
414C22⋊C4#432311yescharacteristic
415C22⋊C4#432311yescharacteristic
416C42—441no—
417C42C2×C22⋊D1111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C16—221no—
420C16—221no—
421C16—221no—
422C16—221no—
423C11#3382311yescharacteristic, complemented, Sylow
424C23—41no—
425C23—41no—
426C23—441no—
427C23C2×#432311yescharacteristic
428Q8—441no—
429Q8—441no—
430Q8—1761no—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—161no—
436D4—161no—
437D4—161no—
438D4—161no—
439D4—441no—
440D4—441no—
441D4—1761no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—161no—
447C2×C4—161no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
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—81no—
470C22—81no—
471C22—81no—
472C22—881no—
473C22—881no—
474C22—881no—
475C22C22×#432311yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—81no—
482C4—81no—
483C4—881no—
484C4—881no—
485C4—881no—
486C4#1062335311yescharacteristic
487C4#1062336411yescharacteristic
488C2—41no—
489C2—161no—
490C2—161no—
491C2—1761no—
492C2#1307992311yescharacteristic
493C2#1308175511yescharacteristic
494C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3176C2
socleC22×C11C22×D8
hypercenter#3176D11
hypocenterC11#33823
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3176

Complements

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

NH ≅ G/Ntype
1. #13079255C2semidirect
2. #13070777C2semidirect
3. #13070770C2semidirect
4. #13070763C2semidirect
5. #13070753C2semidirect
6. #13070727C2semidirect
7. #13070717C2semidirect
8. #13070710C2semidirect
9. #13070700C2semidirect
10. #13070671C2semidirect
11. #13070671C2semidirect
12. #13070653C2semidirect
13. #13070648C2semidirect
14. #13070375C2semidirect
15. C11×#3176C2semidirect
177. #3176D11semidirect
423. C11#33823semidirect

Maximal subgroups

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

subgroupindex
#130792552
#130707772
#130707702
#130707632
#130707532
#130707272
#130707172
#130707102
#130707002
#130706712
#130706532
#130706482
#130703752
C11×#31762
#3382311