Finite Group Databasebeta

← #14910151

Subgroups — #14910151

Order 2816.

496 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#13079188C211yesmaximal, characteristic, complemented
2#13079184C211yesmaximal, characteristic, complemented
3#13070779C211yesmaximal, characteristic, complemented
4#13070777C211yesmaximal, characteristic, complemented
5#13070772C211yesmaximal, characteristic, complemented
6#13070730C211yesmaximal, characteristic, complemented
7#13070728C211yesmaximal, characteristic, complemented
8#13070725C211yesmaximal, characteristic, complemented
9#13070718C211yesmaximal, characteristic
10#13070679C211yesmaximal, characteristic, complemented
11#13070677C211yesmaximal, characteristic, complemented
12#13070671C211yesmaximal, characteristic, complemented
13#13070670C211yesmaximal, characteristic, complemented
14#13070370C211yesmaximal, characteristic, complemented
15C11×#2228C211yesmaximal, characteristic, complemented
16#10623222—21no—
17#10623088—21no—
18C11×#499C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20#10622770C2211yescharacteristic
21#10622768C2211yescharacteristic
22C2×#66891C2211yescharacteristic
23C2×#66890C2211yescharacteristic
24#10622681—21no—
25C4×#4324—21no—
26C2×Dic88C2211yescharacteristic
27C2×#66864C2211yescharacteristic
28C2×#66862C2211yescharacteristic
29C2×#66862C2211yescharacteristic
30#10622500C2211yescharacteristic
31#10622500C2211yescharacteristic
32#10622496C2211yescharacteristic
33#10622491C2211yescharacteristic
34#10622486C2211yescharacteristic
35#10622485C2211yescharacteristic
36#10622477—21no—
37#10622465—21no—
38#10622391—21no—
39#10622381—21no—
40C4×Dic44C2211yescharacteristic
41#10622309C2211yescharacteristic
42C4×C8×D11C2211yescharacteristic
43C11×#367C2211yescharacteristic
44C11×#366C2211yescharacteristic
45C11×C4⋊C16C2211yescharacteristic
46C11×#357C2211yescharacteristic
47C11×#357C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622141C2211yescharacteristic
50Dic11⋊C16C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×C11×D8C2311yescharacteristic
60C11×#125—21no—
61C4×D4×C11—21no—
62#66991—21no—
63#66989—21no—
64C2×#4324—21no—
65C4×C22⋊D11—41no—
66#66979—41no—
67C2×Dic44C2311yescharacteristic
68C2×Dic44C2311yescharacteristic
69C2×D88C2311yescharacteristic
70C2×#4314—21no—
71C2×C8×D11D411yescharacteristic
72C2×C8×D11C2311yescharacteristic
73#66951—41no—
74#66950—21no—
75#66950—21no—
76#66948—21no—
77#66947—41no—
78#66946—21no—
79#66946—41no—
80#66945—41no—
81#66943—21no—
82#66940—21no—
83#66936—41no—
84#66932—41no—
85#66928—21no—
86C42×D11D411yescharacteristic
87C4×Dic22—21no—
88C2×C11×C16C2311yescharacteristic
89C2×C11×C16C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#106—21no—
94C11×#102—21no—
95C4×C8×C11C2311yescharacteristic
96#66896—21no—
97#66891—41no—
98#66890—41no—
99#66882C2311yescharacteristic
100#66880—21no—
101C8×Dic11D411yescharacteristic
102C8×Dic11C2311yescharacteristic
103C2×C11⋊C16C2311yescharacteristic
104C2×C11⋊C16C2311yescharacteristic
105#66874—21no—
106#66874—21no—
107#66874—21no—
108#66873—21no—
109#66873—21no—
110#66872—21no—
111C4×C11⋊C8D411yescharacteristic
112Dic88—41no—
113#66864—41no—
114#66862—41no—
115#66862—41no—
116#33822—111nomaximal, Sylow
117C2×D4×C11—21no—
118C22×C4×C11—41no—
119C2×C22⋊D11—41no—
120C2×D44—21no—
121C2×D44—41no—
122C2×C4×D11—41no—
123C2×C4×D11D811yescharacteristic
124C2×C4×D11D811yescharacteristic
125C2×C4×D11C2×D411yescharacteristic
126C2×Dic22—21no—
127C2×Dic22—21no—
128C11×D8—21no—
129C11×D8—21no—
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2411yescharacteristic
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C22⋊C4—41no—
138C42×C11C2×D411yescharacteristic
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142#4324—42no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149C4⋊Dic11—21no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156C4×Dic11—41no—
157C4×Dic11—41no—
158C4×Dic11D811yescharacteristic
159C4×Dic11D811yescharacteristic
160C4×Dic11C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163Dic44—21no—
164Dic44—21no—
165Dic44—21no—
166Dic44—21no—
167D88—21no—
168D88—21no—
169#4314—42no—
170C8×D11—21no—
171C8×D11—21no—
172C8×D11—41no—
173C11×C16—21no—
174C11×C16—21no—
175C11⋊C16—21no—
176C11⋊C16—21no—
177#3168—111no—
178#3168—111no—
179#2229—111no—
180#2229—111no—
181#2228—111no—
182#2228D1111yescharacteristic, complemented
183#2220—111no—
184#2220—111no—
185#2219—111no—
186#2218—111no—
187#2211—111no—
188#2211—111no—
189#2210—111no—
190#2210—111no—
191#2150—111no—
192C23×C11—41no—
193C22×D11—41no—
194C22×D11C2×D811yescharacteristic
195D4×C11—41no—
196D4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—82no—
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C22⋊D11—82no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11C2×D811yescharacteristic
209C2×Dic11C2×D811yescharacteristic
210C2×Dic11C2×D811yescharacteristic
211D44—41no—
212D44—41no—
213D44—82no—
214C4×D11—21no—
215C4×D11—21no—
216C4×D11—41no—
217C4×D11—41no—
218C4×D11—82no—
219Dic22—41no—
220Dic22—41no—
221Dic22—41no—
222Dic22—41no—
223C8×C11—21no—
224C8×C11H(5,𝔽2)11yescharacteristic
225C8×C112−1+411yescharacteristic
226C11⋊C8—21no—
227C11⋊C8—21no—
228#529—221no—
229#529—221no—
230C2×Q32—111no—
231C2×SD32—111no—
232C2×SD32—111no—
233C2×D16—111no—
234C2×M32—111no—
235C2×M32—111no—
236#499—111no—
237#499C2×D1111yescharacteristic
238#495—111no—
239#495—111no—
240#488—221no—
241#488—221no—
242#467—111no—
243#467—111no—
244#466—111no—
245#466—111no—
246#465—221no—
247#465—221no—
248C4×Q16—111no—
249C4×Q16—111no—
250C4×SD16—221no—
251C4×SD16—221no—
252C4×D8—111no—
253C4×D8C2×D1111yescharacteristic
254C2×C4×C8—111no—
255#367—111no—
256#367C2×D1111yescharacteristic
257#366—111no—
258#366C2×D1111yescharacteristic
259C4⋊C16—111no—
260C4⋊C16—111no—
261C4⋊C16—111no—
262C4⋊C16C2×D1111yescharacteristic
263#358—111no—
264#358—111no—
265#358—111no—
266#358—111no—
267#357—111no—
268#357—111no—
269#357C2×D1111yescharacteristic
270#357C2×D1111yescharacteristic
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11C22×D811yescharacteristic
275C2×D11—21no—
276C2×D11—21no—
277C2×D11—21no—
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11—81no—
286C4×C11#53711yescharacteristic
287C4×C11#57511yescharacteristic
288Dic11—21no—
289Dic11—21no—
290Dic11—21no—
291Dic11—81no—
292Dic11—81no—
293Dic11—81no—
294C2×Q16—111no—
295C2×Q16—111no—
296C2×SD16—221no—
297C2×SD16—221no—
298C2×D8—111no—
299C2×D8C22×D1111yescharacteristic
300C22×C8—111no—
301C22×C8—111no—
302#126—441no—
303#126—441no—
304#125—21no—
305#125—221no—
306#124—221no—
307#124—221no—
308#123—441no—
309#123—441no—
310C22⋊Q8—221no—
311C22⋊Q8—221no—
312#121—221no—
313#121—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×D4—21no—
317C4×D4—221no—
318C4×D4—441no—
319C4×D4—441no—
320#117—441no—
321#117—441no—
322C2×C42—111no—
323Q32—441no—
324SD32—441no—
325SD32—441no—
326D16—441no—
327M32—441no—
328M32—441no—
329C2×C16—111no—
330C2×C16—111no—
331C2×C16C22×D1111yescharacteristic
332C2×C16C22×D1111yescharacteristic
333#107—111no—
334#107C22×D1111yescharacteristic
335#107C22×D1111yescharacteristic
336#107C22×D1111yescharacteristic
337#106—21no—
338#106—221no—
339#103—221no—
340#103—221no—
341#103—221no—
342#103—221no—
343#102—21no—
344#102—221no—
345#102—221no—
346#102—221no—
347C4×C8—111no—
348C4×C8—111no—
349C4×C8—111no—
350C4×C8C22×D1111yescharacteristic
351C2×C11—161no—
352C2×C11#324511yescharacteristic
353C2×C11#341411yescharacteristic
354C2×C11#341411yescharacteristic
355D11—41no—
356D11—161no—
357C2×Q8—221no—
358C2×Q8—221no—
359C2×D4—21no—
360C2×D4—221no—
361C2×D4—441no—
362C2×D4—441no—
363C22×C4—41no—
364C22×C4—111no—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—441no—
368Q16—221no—
369Q16—221no—
370Q16—221no—
371Q16—221no—
372SD16—442no—
373SD16—442no—
374D8—21no—
375D8—21no—
376D8—221no—
377D8—221no—
378C2×C8—111no—
379C2×C8—111no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8—441no—
383C2×C8D4×D1111yescharacteristic
384C2×C8C23×D1111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—221no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C22⋊C4—41no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C22⋊C4—441no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C22⋊C4—441no—
407C42—111no—
408C42—111no—
409C42—111no—
410C42—441no—
411C42—441no—
412C42D4×D1111yescharacteristic
413C16—21no—
414C16—21no—
415C16—221no—
416C16—221no—
417C11#3382211yescharacteristic, complemented, Sylow
418C23—41no—
419C23—111no—
420C23—441no—
421Q8—441no—
422Q8—441no—
423Q8—441no—
424Q8—441no—
425D4—41no—
426D4—41no—
427D4—441no—
428D4—441no—
429D4—882no—
430D4—882no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—82no—
435C2×C4—111no—
436C2×C4—111no—
437C2×C4—111no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—882no—
446C2×C4D8×D1111yescharacteristic
447C2×C4D8×D1111yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C8—21no—
450C8—221no—
451C8—221no—
452C8#6704011yescharacteristic
453C8#6704211yescharacteristic
454C22—81no—
455C22—81no—
456C22—81no—
457C22—221no—
458C22—221no—
459C22—221no—
460C22—881no—
461C22—881no—
462C22—881no—
463C22C2×D8×D1111yescharacteristic
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—221no—
470C4—221no—
471C4—221no—
472C4—881no—
473C4—881no—
474C4—881no—
475C4#1062316011yescharacteristic
476C4#1062330811yescharacteristic
477C2—161no—
478C2—441no—
479C2—1761no—
480C2#1307992511yescharacteristic
481C2#1308174811yescharacteristic
482C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2228C2
socleC22×C11C22×D8
prime radical#13070718C2
hypercenter#2228D11
hypocenterC11#33822
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #13079188C2semidirect
2. #13079184C2semidirect
3. #13070779C2semidirect
4. #13070777C2semidirect
5. #13070772C2semidirect
6. #13070730C2semidirect
7. #13070728C2semidirect
8. #13070725C2semidirect
10. #13070679C2semidirect
11. #13070677C2semidirect
12. #13070671C2semidirect
13. #13070670C2semidirect
14. #13070370C2semidirect
15. C11×#2228C2semidirect
182. #2228D11semidirect
417. C11#33822semidirect

Maximal subgroups

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

subgroupindex
#130791882
#130791842
#130707792
#130707772
#130707722
#130707302
#130707282
#130707252
#130707182
#130706792
#130706772
#130706712
#130706702
#130703702
C11×#22282
#3382211