Finite Group Databasebeta

← #14911325

Subgroups — #14911325

Order 2816.

476 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081048C211yesmaximal, characteristic, complemented
2#13081017C211yesmaximal, characteristic
3#13070903C211yesmaximal, characteristic, complemented
4#13070822C211yesmaximal, characteristic, complemented
5#13070812C211yesmaximal, characteristic, complemented
6#13070810C211yesmaximal, characteristic, complemented
7#13070809C211yesmaximal, characteristic, complemented
8#13070764C211yesmaximal, characteristic, complemented
9#13070732C211yesmaximal, characteristic, complemented
10#13070715C211yesmaximal, characteristic, complemented
11#13070478C211yesmaximal, characteristic, complemented
12#13070440C211yesmaximal, characteristic, complemented
13#13070401C211yesmaximal, characteristic, complemented
14#13070399C211yesmaximal, characteristic, complemented
15C11×#2229C211yesmaximal, characteristic, complemented
16#10623226—21no—
17#10623115—21no—
18C11×#499C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20#10622801C2211yescharacteristic
21#10622801C2211yescharacteristic
22C2×#66892C2211yescharacteristic
23#10622679—21no—
24#10622633—21no—
25C2×#66862C2211yescharacteristic
26C2×C16×D11C2211yescharacteristic
27#10622496C2211yescharacteristic
28#10622496C2211yescharacteristic
29#10622493C2211yescharacteristic
30#10622493C2211yescharacteristic
31#10622493C2211yescharacteristic
32D11×#107C2211yescharacteristic
33#10622479—21no—
34#10622476—21no—
35#10622427—21no—
36#10622427—21no—
37C4×D88C2211yescharacteristic
38C8×D44C2211yescharacteristic
39#10622295C2211yescharacteristic
40C11×#367C2211yescharacteristic
41C11×#366C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#358C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622129C2211yescharacteristic
53#10622128C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C11×#125—21no—
61C4×Q8×C11—21no—
62#66999—21no—
63#66999—21no—
64C2×D88C2311yescharacteristic
65C2×C8×D11C2311yescharacteristic
66C2×C8×D11C2311yescharacteristic
67#66951—41no—
68#66951—41no—
69#66951—41no—
70#66948—21no—
71#66948—21no—
72#66948—41no—
73#66947—41no—
74#66946—41no—
75#66945—21no—
76#66945—21no—
77#66945—21no—
78C4⋊C4×D11—21no—
79#66928—41no—
80C4×D44—21no—
81C4×D44D411yescharacteristic
82#66922—21no—
83C4×Dic22—41no—
84C2×C11×C16C2311yescharacteristic
85C2×C11×C16C2311yescharacteristic
86C11×#107C2311yescharacteristic
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#106—21no—
90C11×#103—21no—
91C4×C8×C11C2311yescharacteristic
92#66899—21no—
93#66899—21no—
94#66892—22no—
95#66885—21no—
96(C2×D11)⋊C8D411yescharacteristic
97(C2×D11)⋊C8D411yescharacteristic
98#66882—21no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102C2×C11⋊C16C2311yescharacteristic
103C2×C11⋊C16C2311yescharacteristic
104#66873—21no—
105#66873—21no—
106#66872—21no—
107#66872—21no—
108#66872—21no—
109#66871—21no—
110C4⋊(C11⋊C8)D411yescharacteristic
111#66862—22no—
112C16×D11—22no—
113#33917—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D44—21no—
116C2×D44—41no—
117C2×D44—41no—
118C2×D44D811yescharacteristic
119C2×C4×D11—41no—
120C2×C4×D11—41no—
121C2×C4×D11C2×D411yescharacteristic
122C2×C4×D11C2×D411yescharacteristic
123C2×Dic22—41no—
124C11×Q16—21no—
125C11×Q16—21no—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2411yescharacteristic
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C42×C11—41no—
135C42×C11C2×D411yescharacteristic
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4D811yescharacteristic
145(C2×D11)⋊C4D811yescharacteristic
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—41no—
150C4⋊Dic11D811yescharacteristic
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154C4×Dic11—41no—
155C4×Dic11—41no—
156C4×Dic11—41no—
157C2×C11⋊C8C2×D411yescharacteristic
158C2×C11⋊C8C2×D411yescharacteristic
159D88—21no—
160D88—21no—
161C8×D11—21no—
162C8×D11—21no—
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16—21no—
167C11⋊C16—21no—
168C11⋊C16#4112yes—
169#3342—111no—
170#3339—111no—
171#2255—111no—
172#2237—111no—
173#2235—111no—
174#2234—111no—
175#2234—111no—
176#2229D1111yescharacteristic, complemented
177#2226—111no—
178#2220—111no—
179#2217—111no—
180#2175—111no—
181#2168—111no—
182#2159—111no—
183#2158—111no—
184C22×D11—41no—
185C22×D11C2×D811yescharacteristic
186C22×D11C2×D811yescharacteristic
187Q8×C11—41no—
188Q8×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11C2×D811yescharacteristic
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11C2×D811yescharacteristic
200C2×Dic11C2×D811yescharacteristic
201D44—41no—
202D44—41no—
203D44—41no—
204D44—82no—
205D44—161no—
206C4×D11—21no—
207C4×D11—21no—
208C4×D11—21no—
209C4×D11—21no—
210C4×D11—161no—
211C4×D11—161no—
212Dic22—82no—
213C8×C11—21no—
214C8×C11C2×#4111yescharacteristic
215C8×C112−1+411yescharacteristic
216C11⋊C8—21no—
217C11⋊C8—21no—
218#556—221no—
219#553—221no—
220C2×SD32—111no—
221C2×M32—111no—
222C22×C16—111no—
223#500—111no—
224#499C2×D1111yescharacteristic
225#485—221no—
226#485—221no—
227#482—221no—
228#481—221no—
229#478—221no—
230#475—221no—
231#467—111no—
232#467—111no—
233#466—111no—
234#466—111no—
235C4×Q16C2×D1111yescharacteristic
236C4×D8—111no—
237C8×D4—111no—
238#427—111no—
239#427—111no—
240#427—111no—
241C2×#107—111no—
242#367—111no—
243#367—111no—
244#367—111no—
245#367—111no—
246#367C2×D1111yescharacteristic
247#366—111no—
248#366—111no—
249#366—111no—
250#366C2×D1111yescharacteristic
251C4⋊C16C2×D1111yescharacteristic
252#358—111no—
253#358C2×D1111yescharacteristic
254#358C2×D1111yescharacteristic
255#357—111no—
256#357—111no—
257#357—111no—
258C22⋊C16—111no—
259C22⋊C16—111no—
260#346—111no—
261C22×C11C22×D811yescharacteristic
262C2×D11—21no—
263C2×D11—21no—
264C2×D11—21no—
265C2×D11—21no—
266C2×D11—21no—
267C2×D11—21no—
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—81no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11#54711yescharacteristic
278C4×C11#57811yescharacteristic
279Dic11—21no—
280Dic11—21no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284C2×Q16C22×D1111yescharacteristic
285C2×D8—111no—
286C22×C8—111no—
287C22×C8—111no—
288C4⋊Q8—221no—
289#126—441no—
290#126—441no—
291#126—441no—
292#125—21no—
293#124—441no—
294#123—441no—
295C22⋊Q8—221no—
296C22⋊Q8—221no—
297#121—221no—
298#121—221no—
299#121—441no—
300C4×Q8—21no—
301C4×Q8—441no—
302C4×D4—111no—
303C4×D4—221no—
304C4×D4—441no—
305#117—221no—
306#117—221no—
307#117—221no—
308C2×C4⋊C4—221no—
309SD32—222no—
310M32—222no—
311C2×C16—111no—
312C2×C16—111no—
313C2×C16—222no—
314C2×C16C22×D1111yescharacteristic
315C2×C16C22×D1111yescharacteristic
316#107—111no—
317#107—111no—
318#107—111no—
319#107—221no—
320#107—221no—
321#107C22×D1111yescharacteristic
322#107C22×D1111yescharacteristic
323#107C22×D1111yescharacteristic
324#106—21no—
325#106—221no—
326#106—221no—
327#106—221no—
328C4⋊C8—111no—
329#103—21no—
330#103—221no—
331#103—221no—
332#102—221no—
333#102—221no—
334#102—221no—
335C22⋊C8—111no—
336C22⋊C8—111no—
337C4×C8C22×D1111yescharacteristic
338C2×C11#333411yescharacteristic
339C2×C11#341411yescharacteristic
340C2×C11#341611yescharacteristic
341D11—41no—
342D11—41no—
343D11—161no—
344C2×Q8—21no—
345C2×Q8—441no—
346C2×D4—111no—
347C2×D4—221no—
348C2×D4—441no—
349C2×D4—441no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—441no—
353C22×C4—441no—
354Q16—21no—
355Q16—21no—
356D8—221no—
357D8—221no—
358C2×C8—111no—
359C2×C8—111no—
360C2×C8—221no—
361C2×C8—221no—
362C2×C8—221no—
363C2×C8—221no—
364C2×C8D4×D1111yescharacteristic
365C2×C8C23×D1111yescharacteristic
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—111no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C22⋊C4—111no—
381C22⋊C4—111no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C42—41no—
391C42—441no—
392C42—441no—
393C42—441no—
394C42D4×D1111yescharacteristic
395C16—21no—
396C16—21no—
397C16—112no—
398C16—221no—
399C11#3391711yescharacteristic, complemented, Sylow
400C23—111no—
401C23—111no—
402C23—441no—
403Q8—41no—
404Q8—41no—
405Q8—882no—
406D4—441no—
407D4—441no—
408D4—441no—
409D4—882no—
410D4—1761no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—111no—
416C2×C4—111no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—1761no—
425C2×C4—1761no—
426C2×C4D8×D1111yescharacteristic
427C2×C4D8×D1111yescharacteristic
428C2×C4C2×D4×D1111yescharacteristic
429C8—21no—
430C8—221no—
431C8—221no—
432C8#6704011yescharacteristic
433C8#41×D1111yescharacteristic
434C22—221no—
435C22—221no—
436C22—221no—
437C22—221no—
438C22—221no—
439C22—221no—
440C22—881no—
441C22—881no—
442C22—881no—
443C22C2×D8×D1111yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—81no—
450C4—221no—
451C4—221no—
452C4—881no—
453C4—881no—
454C4—881no—
455C4#1062316211yescharacteristic
456C4#1062331011yescharacteristic
457C2—441no—
458C2—441no—
459C2—1761no—
460C2#1308096211yescharacteristic
461C2#1308175111yescharacteristic
462C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2229C2
socleC22×C11C22×D8
prime radical#13081017C2
hypercenter#2229D11
hypocenterC11#33917
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2229

Complements

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

NH ≅ G/Ntype
1. #13081048C2semidirect
3. #13070903C2semidirect
4. #13070822C2semidirect
5. #13070812C2semidirect
6. #13070810C2semidirect
7. #13070809C2semidirect
8. #13070764C2semidirect
9. #13070732C2semidirect
10. #13070715C2semidirect
11. #13070478C2semidirect
12. #13070440C2semidirect
13. #13070401C2semidirect
14. #13070399C2semidirect
15. C11×#2229C2semidirect
176. #2229D11semidirect
399. C11#33917semidirect

Maximal subgroups

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

subgroupindex
#130810482
#130810172
#130709032
#130708222
#130708122
#130708102
#130708092
#130707642
#130707322
#130707152
#130704782
#130704402
#130704012
#130703992
C11×#22292
#3391711