Finite Group Databasebeta

← #14909325

Subgroups — #14909325

Order 2816.

526 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#13079183C211yesmaximal, characteristic, complemented
3#13070892C211yesmaximal, characteristic, complemented
4#13070875C211yesmaximal, characteristic, complemented
5#13070848C211yesmaximal, characteristic, complemented
6#13070715C211yesmaximal, characteristic, complemented
7#13070711C211yesmaximal, characteristic, complemented
8#13070706C211yesmaximal, characteristic, complemented
9#13070701C211yesmaximal, characteristic
10#13070472C211yesmaximal, characteristic, complemented
11#13070471C211yesmaximal, characteristic, complemented
12#13070465C211yesmaximal, characteristic, complemented
13#13070460C211yesmaximal, characteristic, complemented
14C4×C16×D11C211yesmaximal, characteristic, complemented
15C11×#2242C211yesmaximal, characteristic, complemented
16#10623222—21no—
17#10623211—21no—
18C11×#499C2211yescharacteristic
19C11×#495C2211yescharacteristic
20#10622801C2211yescharacteristic
21Q16×Dic11C2211yescharacteristic
22C2×#66893C2211yescharacteristic
23C2×#66892C2211yescharacteristic
24#10622784—21no—
25SD16×Dic11—21no—
26#10622770C2211yescharacteristic
27D8×Dic11C2211yescharacteristic
28C2×#66891C2211yescharacteristic
29C2×#66890C2211yescharacteristic
30#10622681—21no—
31#10622669—21no—
32C2×C16×D11C2211yescharacteristic
33C2×C16×D11C2211yescharacteristic
34#10622500C2211yescharacteristic
35#10622496C2211yescharacteristic
36#10622486C2211yescharacteristic
37#10622485C2211yescharacteristic
38#10622477—21no—
39#10622465—21no—
40#10622309C2211yescharacteristic
41C4×C8×D11C2211yescharacteristic
42#10622296C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#357C2211yescharacteristic
46C11×#357C2211yescharacteristic
47C4×C11×C16C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52C16×Dic11C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×SD16—21no—
61C2×C11×D8C2311yescharacteristic
62C11×#125—21no—
63C11×#124—21no—
64#66999—21no—
65Q8×Dic11—21no—
66#66991—21no—
67D4×Dic11—21no—
68C2×Dic44C2311yescharacteristic
69C2×D88C2311yescharacteristic
70C2×#4314—21no—
71C2×C8×D11D411yescharacteristic
72C2×C8×D11C2311yescharacteristic
73#66951—41no—
74#66950—21no—
75#66948—21no—
76#66947—41no—
77#66946—21no—
78#66946—41no—
79#66945—41no—
80#66940—21no—
81#66936—41no—
82(C22⋊D11)⋊C4—41no—
83#66932—41no—
84#66930—41no—
85#66928—21no—
86C42×D11D411yescharacteristic
87#66923—21no—
88C2×C11×C16C2311yescharacteristic
89C2×C11×C16C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#106—21no—
93C4×C8×C11C2311yescharacteristic
94#66899—21no—
95#66899—21no—
96#66896—21no—
97#66896—21no—
98#66893—22no—
99#66892—22no—
100#66891—22no—
101#66890—22no—
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66881—21no—
105C8×Dic11D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109#66874—21no—
110#66874—21no—
111#66873—21no—
112#66873—21no—
113C4×C11⋊C8D411yescharacteristic
114C16×D11—22no—
115C16×D11—22no—
116#33735—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C2×C22⋊D11—41no—
120C22×Dic11—41no—
121C2×D44—21no—
122C2×D44—41no—
123C2×C4×D11—41no—
124C2×C4×D11D811yescharacteristic
125C2×C4×D11D811yescharacteristic
126C2×C4×D11C2×D411yescharacteristic
127C2×Dic22—21no—
128C11×Q16—21no—
129C11×Q16—21no—
130C11×SD16—42no—
131C11×D8—21no—
132C11×D8—21no—
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2411yescharacteristic
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C22⋊C4—41no—
140C11×C22⋊C4—41no—
141C42×C11C2×D411yescharacteristic
142C22⋊Dic11—41no—
143C22⋊Dic11—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—
149(C2×D11)⋊C4—41no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11D811yescharacteristic
161C4×Dic11D811yescharacteristic
162C4×Dic11C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165Dic44—21no—
166Dic44—21no—
167D88—21no—
168D88—21no—
169#4314—42no—
170C8×D11—22no—
171C8×D11—21no—
172C8×D11—21no—
173C11×C16—21no—
174C11×C16—21no—
175C11⋊C16#4112yes—
176C11⋊C16#4112yes—
177#3168—111no—
178#3168—111no—
179#2253—111no—
180#2249—111no—
181#2242—111no—
182#2242D1111yescharacteristic, complemented
183#2217—111no—
184#2217—111no—
185#2216—111no—
186#2215—111no—
187C4×Q32—111no—
188C4×SD32—111no—
189C4×SD32—111no—
190C4×D16—111no—
191C2×C4×C16—111no—
192C23×C11—41no—
193C22×D11—41no—
194C22×D11C2×D811yescharacteristic
195Q8×C11—41no—
196Q8×C11—41no—
197D4×C11—41no—
198D4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C22⋊D11—82no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—82no—
210C2×Dic11C2×D811yescharacteristic
211C2×Dic11C2×D811yescharacteristic
212C2×Dic11C2×D811yescharacteristic
213D44—41no—
214D44—41no—
215D44—82no—
216C4×D11—22no—
217C4×D11—21no—
218C4×D11—21no—
219C4×D11—22no—
220C4×D11—82no—
221Dic22—41no—
222Dic22—41no—
223C8×C11#13512yes—
224C8×C11C2×#4111yescharacteristic
225C8×C11C2×#4111yescharacteristic
226C11⋊C8—21no—
227C11⋊C8—21no—
228#529—221no—
229#529—221no—
230C2×Q32—111no—
231C2×SD32—111no—
232C2×SD32—111no—
233C2×D16—111no—
234C22×C16—111no—
235C22×C16—111no—
236#499—111no—
237#499C2×D1111yescharacteristic
238#495—111no—
239#495C2×D1111yescharacteristic
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×D8—111no—
254C2×C4×C8—111no—
255#367—111no—
256#367—111no—
257#366—111no—
258#366—111no—
259#358—111no—
260#358—111no—
261#358C2×D1111yescharacteristic
262#358C2×D1111yescharacteristic
263#357—111no—
264#357—111no—
265#357C2×D1111yescharacteristic
266#357C2×D1111yescharacteristic
267C4×C16—111no—
268C4×C16—111no—
269C4×C16—111no—
270C4×C16C2×D1111yescharacteristic
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11C22×D811yescharacteristic
275C2×D11—21no—
276C2×D11—21no—
277C2×D11—81no—
278C2×D11—81no—
279C2×D11—81no—
280C2×D11#50812yes—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11—81no—
286C4×C11#53211yescharacteristic
287C4×C11C2×#13511yescharacteristic
288Dic11—21no—
289Dic11—21no—
290Dic11—81no—
291Dic11—81no—
292Dic11—81no—
293Dic11#50812yes—
294C2×Q16—111no—
295C2×Q16C22×D1111yescharacteristic
296C2×SD16—21no—
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—21no—
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—221no—
317C4×D4—221no—
318C4×D4—441no—
319C4×D4—441no—
320#117—441no—
321#117—441no—
322C2×C42—111no—
323Q32—222no—
324SD32—222no—
325SD32—222no—
326D16—222no—
327C2×C16—111no—
328C2×C16—111no—
329C2×C16—222no—
330C2×C16—222no—
331C2×C16C22×D1111yescharacteristic
332C2×C16C22×D1111yescharacteristic
333#107—111no—
334#107—111no—
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—221no—
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#316911yescharacteristic
353C2×C11C2×#50811yescharacteristic
354C2×C11C2×#50811yescharacteristic
355D11—22no—
356D11—161no—
357C2×Q8—21no—
358C2×Q8—221no—
359C2×D4—21no—
360C2×D4—221no—
361C2×D4—441no—
362C2×D4—441no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—111no—
366C22×C4—441no—
367C22×C4—441no—
368Q16—21no—
369Q16—21no—
370Q16—221no—
371Q16—221no—
372SD16—42no—
373SD16—442no—
374D8—21no—
375D8—21no—
376D8—221no—
377D8—221no—
378C2×C8—111no—
379C2×C8—111no—
380C2×C8—222no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8D4×D1111yescharacteristic
384C2×C8C23×D1111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—221no—
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—41no—
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—112no—
416C16—112no—
417C11#3373511yescharacteristic, complemented, Sylow
418C23—41no—
419C23—111no—
420C23—441no—
421Q8—41no—
422Q8—41no—
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—111no—
435C2×C4—111no—
436C2×C4—111no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—882no—
445C2×C4—882no—
446C2×C4D8×D1111yescharacteristic
447C2×C4D8×D1111yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C8—221no—
450C8—221no—
451C8#6696912yes—
452C8#41×D1111yescharacteristic
453C8#41×D1111yescharacteristic
454C22—81no—
455C22—81no—
456C22—81no—
457C22—112no—
458C22—221no—
459C22—221no—
460C22—881no—
461C22—881no—
462C22—881no—
463C22C2×D8×D1111yescharacteristic
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—112no—
470C4—221no—
471C4—221no—
472C4—881no—
473C4—881no—
474C4—881no—
475C4#1062319911yescharacteristic
476C4C2×#6696911yescharacteristic
477C2—161no—
478C2—222no—
479C2—1761no—
480C2#1307919411yescharacteristic
481C2D11×#50811yescharacteristic
482C2D11×#50811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2242C2
socleC22×C11C22×D8
prime radical#13070701C2
hypercenter#2242D11
hypocenterC11#33735
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2242

Complements

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

NH ≅ G/Ntype
1. #13079188C2semidirect
2. #13079183C2semidirect
3. #13070892C2semidirect
4. #13070875C2semidirect
5. #13070848C2semidirect
6. #13070715C2semidirect
7. #13070711C2semidirect
8. #13070706C2semidirect
10. #13070472C2semidirect
11. #13070471C2semidirect
12. #13070465C2semidirect
13. #13070460C2semidirect
14. C4×C16×D11C2semidirect
15. C11×#2242C2semidirect
182. #2242D11semidirect
417. C11#33735semidirect

Maximal subgroups

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

subgroupindex
#130791882
#130791832
#130708922
#130708752
#130708482
#130707152
#130707112
#130707062
#130707012
#130704722
#130704712
#130704652
#130704602
C4×C16×D112
C11×#22422
#3373511