Finite Group Databasebeta

← #14911270

Subgroups — #14911270

Order 2816.

484 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081019C211yesmaximal, characteristic
2#13081009C211yesmaximal, characteristic, complemented
3#13070902C211yesmaximal, characteristic, complemented
4#13070825C211yesmaximal, characteristic, complemented
5#13070819C211yesmaximal, characteristic, complemented
6#13070802C211yesmaximal, characteristic, complemented
7#13070797C211yesmaximal, characteristic, complemented
8#13070781C211yesmaximal, characteristic, complemented
9#13070754C211yesmaximal, characteristic, complemented
10#13070729C211yesmaximal, characteristic, complemented
11#13070712C211yesmaximal, characteristic, complemented
12#13070482C211yesmaximal, characteristic, complemented
13#13070404C211yesmaximal, characteristic, complemented
14C2×#10622142C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic, complemented
16#10623096—21no—
17#10623074—21no—
18C2×C11×M32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622729C2211yescharacteristic
22#10622729C2211yescharacteristic
23#10622728C2211yescharacteristic
24#10622728C2211yescharacteristic
25#10622719C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66864C2211yescharacteristic
30#10622463—21no—
31#10622460—21no—
32#10622350—21no—
33#10622348—21no—
34#10622335—21no—
35#10622335—21no—
36C4×Dic44C2211yescharacteristic
37C4×D88C2211yescharacteristic
38#10622296C2211yescharacteristic
39#10622295C2211yescharacteristic
40C11×C4⋊C16C2211yescharacteristic
41C11×C22⋊C16C2211yescharacteristic
42C11×C22⋊C16C2211yescharacteristic
43C11×#346C2211yescharacteristic
44#10622147C2211yescharacteristic
45#10622147C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622143C2211yescharacteristic
48#10622143C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622142C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622142C2211yescharacteristic
54#10622142C2211yescharacteristic
55#10622142C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C4×D4×C11D411yescharacteristic
62#66992—41no—
63D4×Dic11—41no—
64#66983—21no—
65#66983—21no—
66#66979—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70#66977—21no—
71#66977—21no—
72C2×Dic44C2311yescharacteristic
73C2×D88C2311yescharacteristic
74#66951—41no—
75#66943—41no—
76#66936—41no—
77(C22⋊D11)⋊C4—41no—
78#66931—41no—
79#66931—41no—
80C4×D44—21no—
81#66923—21no—
82#66922—21no—
83C4×Dic22—21no—
84C11×M32—22no—
85C2×C11×C16—22no—
86C2×C11×C16C2311yescharacteristic
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89C2×C11×C16C2311yescharacteristic
90C11×C4⋊C8D411yescharacteristic
91C11×C22⋊C8D411yescharacteristic
92C11×C22⋊C8D411yescharacteristic
93C4×C8×C11C2311yescharacteristic
94#66885—21no—
95#66885—21no—
96#66885—21no—
97#66882—21no—
98#66882—21no—
99#66882—21no—
100#66882—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66881—21no—
108#66881—21no—
109#66880—21no—
110#66880—21no—
111#66880—21no—
112#66864—22no—
113#33913—111nomaximal, Sylow
114C2×D4×C11D811yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C2×D44—21no—
123C2×C4×D11—41no—
124C2×Dic22—21no—
125C2×Dic22—41no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2411yescharacteristic
134C11×C4⋊C4D811yescharacteristic
135C11×C22⋊C4D811yescharacteristic
136C11×C22⋊C4D811yescharacteristic
137C42×C11C2×D411yescharacteristic
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159C4×Dic11—41no—
160C4×Dic11—41no—
161Dic44—21no—
162Dic44—21no—
163D88—21no—
164D88—21no—
165C11×C16—21no—
166C11×C16—21no—
167C11×C16—21no—
168C11×C16#4112yes—
169#3339—111no—
170#3338—111no—
171#2255—111no—
172#2237—111no—
173#2236—111no—
174#2233—111no—
175#2232—111no—
176#2229—111no—
177#2224—111no—
178#2220—111no—
179#2217—111no—
180#2175—111no—
181#2168D1111yescharacteristic, complemented
182#2159—111no—
183C2×#366—111no—
184C23×C11C2×D811yescharacteristic
185C23×C11C2×D811yescharacteristic
186C22×D11—41no—
187D4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11C2×D811yescharacteristic
193C2×C4×C11C2×D811yescharacteristic
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C22⋊D11—82no—
198C22⋊D11—161no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—161no—
207C2×Dic11—161no—
208C2×Dic11—161no—
209D44—41no—
210D44—41no—
211C4×D11—161no—
212Dic22—41no—
213Dic22—41no—
214Dic22—161no—
215C8×C11—21no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11C2×#4111yescharacteristic
219C8×C112−1+411yescharacteristic
220#554—221no—
221#553—221no—
222C2×SD32—111no—
223C2×M32C2×D1111yescharacteristic
224C22×C16C2×D1111yescharacteristic
225#500—111no—
226#499—111no—
227#484—221no—
228#484—221no—
229#482—221no—
230#481—221no—
231#478—221no—
232#477—221no—
233#467—111no—
234#467—111no—
235#466—111no—
236#466—111no—
237C4×Q16—111no—
238C4×D8—111no—
239C8×D4C2×D1111yescharacteristic
240#427—111no—
241C2×#107—111no—
242C2×#107—111no—
243C2×#107—111no—
244#367—111no—
245#367—111no—
246#367—111no—
247#366—111no—
248#366—111no—
249#366—111no—
250#366—111no—
251#366—111no—
252#366—111no—
253C4⋊C16C2×D1111yescharacteristic
254#358—111no—
255#358—111no—
256#358—111no—
257#357—111no—
258#357—111no—
259#357—111no—
260C22⋊C16C2×D1111yescharacteristic
261C22⋊C16C2×D1111yescharacteristic
262#346C2×D1111yescharacteristic
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11#51012yes—
269C22×C11C22×D811yescharacteristic
270C2×D11—81no—
271C2×D11—81no—
272C2×D11—81no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11#54711yescharacteristic
278C4×C11#57811yescharacteristic
279Dic11—81no—
280Dic11—81no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284Dic11—81no—
285Dic11—81no—
286C2×Q16—111no—
287C2×D8—111no—
288C22×C8C22×D1111yescharacteristic
289C22×C8C22×D1111yescharacteristic
290C4⋊Q8—221no—
291#126—441no—
292#125—221no—
293#125—441no—
294#123—441no—
295C22⋊Q8—221no—
296C22⋊Q8—221no—
297C22⋊Q8—441no—
298C22⋊Q8—441no—
299#121—221no—
300#121—221no—
301#121—441no—
302C4×Q8—221no—
303C4×D4—221no—
304C4×D4—441no—
305C4×D4—441no—
306C4×D4D4411yescharacteristic
307#117—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311SD32—222no—
312M32—22no—
313C2×C16—22no—
314C2×C16C22×D1111yescharacteristic
315C2×C16C22×D1111yescharacteristic
316C2×C16C22×D1111yescharacteristic
317C2×C16C22×D1111yescharacteristic
318#107—111no—
319#107—111no—
320#107—111no—
321#107—111no—
322#107—111no—
323#107—111no—
324#107—221no—
325#107—221no—
326#107—221no—
327#107—221no—
328#106—221no—
329#106—221no—
330C4⋊C8D4411yescharacteristic
331#103—221no—
332#103—221no—
333#103—221no—
334#102—221no—
335#102—221no—
336#102—221no—
337C22⋊C8D4411yescharacteristic
338C22⋊C8D4411yescharacteristic
339C4×C8C22×D1111yescharacteristic
340C2×C11—22no—
341C2×C11—41no—
342C2×C11#333411yescharacteristic
343C2×C11C2×#51011yescharacteristic
344C2×C11#341511yescharacteristic
345D11—161no—
346C2×Q8—221no—
347C2×Q8—441no—
348C2×D4—221no—
349C2×D4—441no—
350C2×D4—441no—
351C2×D4D8811yescharacteristic
352C22×C4—441no—
353C22×C4—441no—
354C22×C4—441no—
355C22×C4—441no—
356C22×C4C2×D4411yescharacteristic
357C22×C4C2×D4411yescharacteristic
358Q16—221no—
359Q16—221no—
360D8—221no—
361D8—221no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8C2×D4411yescharacteristic
367C2×C8C2×D4411yescharacteristic
368C2×C8C2×D4411yescharacteristic
369C2×C8C23×D1111yescharacteristic
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4D8811yescharacteristic
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C22⋊C4D8811yescharacteristic
393C22⋊C4D8811yescharacteristic
394C42—441no—
395C42—441no—
396C42C2×D4411yescharacteristic
397C16—21no—
398C16—21no—
399C16—21no—
400C16#434112yes—
401C11#3391311yescharacteristic, complemented, Sylow
402C23—441no—
403C23C2×D8811yescharacteristic
404C23C2×D8811yescharacteristic
405Q8—441no—
406Q8—441no—
407Q8—1761no—
408D4—22no—
409D4—441no—
410D4—441no—
411D4—882no—
412D4—1761no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—1761no—
425C2×C4—1761no—
426C2×C4—1761no—
427C2×C4—1761no—
428C2×C4C2×D8811yescharacteristic
429C2×C4C2×D8811yescharacteristic
430C2×C4C2×D8811yescharacteristic
431C2×C4C2×D8811yescharacteristic
432C2×C4C22×D4411yescharacteristic
433C8—21no—
434C8—21no—
435C8—21no—
436C8C2×#434111yescharacteristic
437C8#6704311yescharacteristic
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—881no—
444C22—881no—
445C22—881no—
446C22#1062252212yes—
447C22C22×D8811yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—881no—
453C4—881no—
454C4—881no—
455C4—881no—
456C4—881no—
457C4—881no—
458C4—881no—
459C4#1062308611yescharacteristic
460C4#1062328411yescharacteristic
461C2—22no—
462C2—41no—
463C2—1761no—
464C2#1308096411yescharacteristic
465C2C2×#1062252211yescharacteristic
466C2#1308175711yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
prime radical#13081019C2
hypercenter#2168D11
hypocenterC11#33913
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
2. #13081009C2semidirect
3. #13070902C2semidirect
4. #13070825C2semidirect
5. #13070819C2semidirect
6. #13070802C2semidirect
7. #13070797C2semidirect
8. #13070781C2semidirect
9. #13070754C2semidirect
10. #13070729C2semidirect
11. #13070712C2semidirect
12. #13070482C2semidirect
13. #13070404C2semidirect
14. C2×#10622142C2semidirect
15. C11×#2168C2semidirect
181. #2168D11semidirect
401. C11#33913semidirect

Maximal subgroups

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

subgroupindex
#130810192
#130810092
#130709022
#130708252
#130708192
#130708022
#130707972
#130707812
#130707542
#130707292
#130707122
#130704822
#130704042
C2×#106221422
C11×#21682
#3391311