Finite Group Databasebeta

← #14910216

Subgroups — #14910216

Order 2816.

488 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079255C211yesmaximal, characteristic, complemented
2#13070763C211yesmaximal, characteristic, complemented
3#13070760C211yesmaximal, characteristic, complemented
4#13070758C211yesmaximal, characteristic, complemented
5#13070755C211yesmaximal, characteristic, complemented
6#13070722C211yesmaximal, characteristic, complemented
7#13070717C211yesmaximal, characteristic
8#13070714C211yesmaximal, characteristic, complemented
9#13070710C211yesmaximal, characteristic, complemented
10#13070678C211yesmaximal, characteristic, complemented
11#13070675C211yesmaximal, characteristic, complemented
12#13070671C211yesmaximal, characteristic, complemented
13#13070668C211yesmaximal, characteristic, complemented
14#13070375C211yesmaximal, characteristic, complemented
15C11×#3175C211yesmaximal, characteristic, complemented
16C11×#542—21no—
17#10623065—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×#66893C2211yescharacteristic
29C2×#66892C2211yescharacteristic
30C2×#66891C2211yescharacteristic
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#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622130C2211yescharacteristic
48#10622130C2211yescharacteristic
49#10622129C2211yescharacteristic
50#10622129C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622128C2211yescharacteristic
53#10622128C2211yescharacteristic
54#10622128C2211yescharacteristic
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#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×#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#66893—41no—
100#66892—41no—
101#66891—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#33829—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×D44—21no—
125C2×C4×D11—41no—
126C2×Dic22—21no—
127C2×Dic22—41no—
128C11×Q16—21no—
129C11×Q16—21no—
130C11×SD16—42no—
131C11×D8—21no—
132C11×D8—21no—
133C11×M16—41no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2411yescharacteristic
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4D811yescharacteristic
146C11×C4⋊C4D811yescharacteristic
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C11×C22⋊C4—41no—
152C11×C22⋊C4D811yescharacteristic
153C11×C22⋊C4D811yescharacteristic
154C42×C11—41no—
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#3175—111no—
178#3175D1111yescharacteristic, complemented
179#2226—111no—
180#2226—111no—
181#2225—111no—
182#2225—111no—
183#2219—111no—
184#2218—111no—
185#2217—111no—
186#2217—111no—
187#2211—111no—
188#2211—111no—
189#2210—111no—
190#2210—111no—
191#2151—111no—
192C23×C11—41no—
193C23×C11C2×D811yescharacteristic
194C22×D11—41no—
195Q8×C11—41no—
196Q8×C11—41no—
197Q8×C11—161no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11—161no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—161no—
207C2×C4×C11C2×D811yescharacteristic
208C2×C4×C11C2×D811yescharacteristic
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C22⋊D11—161no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217D44—41no—
218D44—41no—
219C4×D11—161no—
220Dic22—41no—
221Dic22—41no—
222Dic22—161no—
223C8×C11—21no—
224C8×C11—21no—
225C8×C11—21no—
226C8×C11H(5,𝔽2)11yescharacteristic
227C8×C112−1+411yescharacteristic
228#542—21no—
229#542—221no—
230C2×Q32—111no—
231C2×SD32—111no—
232C2×SD32—111no—
233C2×D16—111no—
234C2×M32—111no—
235C22×C16—111no—
236#500—111no—
237#500C2×D1111yescharacteristic
238#495—111no—
239#495C2×D1111yescharacteristic
240#489—21no—
241#489—221no—
242#468—21no—
243#468—221no—
244#467—111no—
245#467C2×D1111yescharacteristic
246#466—111no—
247#466C2×D1111yescharacteristic
248#440—21no—
249#440—221no—
250C4×Q16—111no—
251C4×Q16C2×D1111yescharacteristic
252C4×D8—111no—
253C4×D8C2×D1111yescharacteristic
254#405C2×D1111yescharacteristic
255#367—111no—
256#367—111no—
257#367—111no—
258#367—111no—
259C4⋊C16—111no—
260C4⋊C16—111no—
261C4⋊C16—111no—
262C4⋊C16—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#358—111no—
267#357—111no—
268#357—111no—
269#357—111no—
270#357—111no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11C22×D811yescharacteristic
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—81no—
287C4×C11—81no—
288C4×C11—81no—
289C4×C11#53711yescharacteristic
290C4×C11#57511yescharacteristic
291Dic11—81no—
292Dic11—81no—
293Dic11—81no—
294C2×Q16—111no—
295C2×Q16C22×D1111yescharacteristic
296C2×SD16—21no—
297C2×SD16—221no—
298C2×D8—111no—
299C2×D8C22×D1111yescharacteristic
300C2×M16C22⋊D1111yescharacteristic
301C22×C8C22×D1111yescharacteristic
302C4⋊Q8—21no—
303C4⋊Q8—221no—
304#126—41no—
305#126—441no—
306#124—21no—
307#124—41no—
308#124—221no—
309#124—441no—
310#123—41no—
311#123—441no—
312C22⋊Q8—21no—
313C22⋊Q8—41no—
314C22⋊Q8—221no—
315C22⋊Q8—441no—
316#121—21no—
317#121—221no—
318C4×Q8—21no—
319C4×Q8—221no—
320C4×D4—21no—
321C4×D4—221no—
322#117C22⋊D1111yescharacteristic
323Q32—441no—
324SD32—441no—
325SD32—441no—
326D16—441no—
327M32—441no—
328C2×C16—111no—
329C2×C16—111no—
330C2×C16—111no—
331C2×C16—111no—
332C2×C16—441no—
333#107—21no—
334#107—111no—
335#107—111no—
336#107—221no—
337#107C22×D1111yescharacteristic
338#107C22×D1111yescharacteristic
339#103—21no—
340#103—21no—
341#103—221no—
342#103—221no—
343#102—21no—
344#102—21no—
345#102—221no—
346#102—221no—
347#97C22⋊D1111yescharacteristic
348#97C22⋊D1111yescharacteristic
349C4×C8C22×D1111yescharacteristic
350C4×C8C22×D1111yescharacteristic
351C2×C11—41no—
352C2×C11—161no—
353C2×C11#324511yescharacteristic
354C2×C11#341611yescharacteristic
355C2×C11#341611yescharacteristic
356D11—161no—
357C2×Q8—21no—
358C2×Q8—41no—
359C2×Q8—221no—
360C2×Q8—441no—
361C2×D4—21no—
362C2×D4—41no—
363C2×D4—221no—
364C2×D4—441no—
365C22×C4—41no—
366C22×C4—441no—
367C22×C4C2×C22⋊D1111yescharacteristic
368Q16—21no—
369Q16—21no—
370Q16—221no—
371Q16—221no—
372SD16—42no—
373SD16—442no—
374D8—21no—
375D8—21no—
376D8—221no—
377D8—221no—
378M16—41no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8C2×C22⋊D1111yescharacteristic
382C2×C8C2×C22⋊D1111yescharacteristic
383C2×C8C2×C22⋊D1111yescharacteristic
384C2×C8C23×D1111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4#432311yescharacteristic
396C4⋊C4#432311yescharacteristic
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—441no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C22⋊C4—441no—
407C22⋊C4#432311yescharacteristic
408C22⋊C4#432311yescharacteristic
409C42—41no—
410C42—441no—
411C42C2×C22⋊D1111yescharacteristic
412C42C2×C22⋊D1111yescharacteristic
413C16—221no—
414C16—221no—
415C16—221no—
416C16—221no—
417C11#3382911yescharacteristic, complemented, Sylow
418C23—41no—
419C23—441no—
420C23C2×#432311yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—161no—
424Q8—441no—
425Q8—441no—
426Q8—1761no—
427D4—41no—
428D4—41no—
429D4—161no—
430D4—441no—
431D4—441no—
432D4—1761no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—161no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—1761no—
443C2×C4C2×#432311yescharacteristic
444C2×C4C2×#432311yescharacteristic
445C2×C4C2×#432311yescharacteristic
446C2×C4C2×#432311yescharacteristic
447C2×C4C2×#432311yescharacteristic
448C2×C4C22×C22⋊D1111yescharacteristic
449C8—21no—
450C8—21no—
451C8—21no—
452C8#6704211yescharacteristic
453C8#6704311yescharacteristic
454C22—21no—
455C22—21no—
456C22—21no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—881no—
461C22—881no—
462C22—881no—
463C22C22×#432311yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4—881no—
473C4—881no—
474C4—881no—
475C4#1062335311yescharacteristic
476C4#1062336411yescharacteristic
477C2—41no—
478C2—161no—
479C2—1761no—
480C2#1307992311yescharacteristic
481C2#1308176011yescharacteristic
482C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3175C2
socleC22×C11C22×D8
prime radical#13070717C2
hypercenter#3175D11
hypocenterC11#33829
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. #13079255C2semidirect
2. #13070763C2semidirect
3. #13070760C2semidirect
4. #13070758C2semidirect
5. #13070755C2semidirect
6. #13070722C2semidirect
8. #13070714C2semidirect
9. #13070710C2semidirect
10. #13070678C2semidirect
11. #13070675C2semidirect
12. #13070671C2semidirect
13. #13070668C2semidirect
14. #13070375C2semidirect
15. C11×#3175C2semidirect
178. #3175D11semidirect
417. C11#33829semidirect

Maximal subgroups

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

subgroupindex
#130792552
#130707632
#130707602
#130707582
#130707552
#130707222
#130707172
#130707142
#130707102
#130706782
#130706752
#130706712
#130706682
#130703752
C11×#31752
#3382911