Finite Group Databasebeta

← #14911323

Subgroups — #14911323

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#13081043C211yesmaximal, characteristic, complemented
2#13081021C211yesmaximal, characteristic
3#13070900C211yesmaximal, characteristic, complemented
4#13070822C211yesmaximal, characteristic, complemented
5#13070811C211yesmaximal, characteristic, complemented
6#13070805C211yesmaximal, characteristic, complemented
7#13070804C211yesmaximal, characteristic, complemented
8#13070782C211yesmaximal, characteristic, complemented
9#13070761C211yesmaximal, characteristic, complemented
10#13070709C211yesmaximal, characteristic, complemented
11#13070481C211yesmaximal, characteristic, complemented
12#13070439C211yesmaximal, characteristic, complemented
13#13070404C211yesmaximal, characteristic, complemented
14#13070397C211yesmaximal, characteristic, complemented
15C11×#2220C211yesmaximal, characteristic, complemented
16#10623172—21no—
17#10623149—21no—
18C2×C11×SD32C2211yescharacteristic
19C2×C11×M32C2211yescharacteristic
20C11×#467C2211yescharacteristic
21C11×#466C2211yescharacteristic
22#10622801C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24#10622770C2211yescharacteristic
25D8×Dic11C2211yescharacteristic
26C8×C22⋊D11C2211yescharacteristic
27#10622719C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29#10622658—21no—
30#10622647—21no—
31C2×C16×D11C2211yescharacteristic
32#10622493C2211yescharacteristic
33#10622493C2211yescharacteristic
34#10622491C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622428—21no—
37#10622404—21no—
38#10622397—21no—
39#10622379—21no—
40C11×#366C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47C22⋊(C11⋊C16)C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622140C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×D8C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C22⋊Q8—21no—
63C11×#121—21no—
64#66999—21no—
65Q8×Dic11—21no—
66#66992—41no—
67#66991—21no—
68D4×Dic11—21no—
69D4×Dic11—41no—
70C4×C22⋊D11D411yescharacteristic
71#66979—21no—
72C2×C4⋊Dic11—21no—
73C2×C8×D11C2311yescharacteristic
74#66951—41no—
75#66945—21no—
76#66945—21no—
77#66943—21no—
78#66941—21no—
79#66940—41no—
80#66939—41no—
81#66938—41no—
82#66932—41no—
83#66932—41no—
84C11×SD32—22no—
85C11×M32—22no—
86C2×C11×C16C2311yescharacteristic
87C2×C11×C16C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#103—21no—
91C11×#102—21no—
92#66899—21no—
93#66899—21no—
94#66896—21no—
95#66896—21no—
96C22⋊(C11⋊C8)D411yescharacteristic
97(C2×D11)⋊C8D411yescharacteristic
98#66882—21no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66881—21no—
104Dic11⋊C8D411yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66872—21no—
109#66872—21no—
110#66872—21no—
111#66871—21no—
112C16×D11—22no—
113#33917—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—41no—
117C22×C4×C11C2×D411yescharacteristic
118C2×C22⋊D11—41no—
119C2×C22⋊D11D811yescharacteristic
120C22×Dic11—41no—
121C22×Dic11—41no—
122C2×C4×D11C2×D411yescharacteristic
123C2×Dic22—41no—
124C11×Q16—21no—
125C11×Q16—21no—
126C11×D8—21no—
127C11×D8—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2411yescharacteristic
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C22⋊Dic11—41no—
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11D811yescharacteristic
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4D811yescharacteristic
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4D811yescharacteristic
156C4×Dic11—41no—
157C4×Dic11—41no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16#4112yes—
167C11⋊C16—21no—
168C11⋊C16—21no—
169#3342—111no—
170#3339—111no—
171#2255—111no—
172#2237—111no—
173#2235—111no—
174#2234—111no—
175#2234—111no—
176#2229—111no—
177#2226—111no—
178#2220D1111yescharacteristic, complemented
179#2217—111no—
180#2175—111no—
181#2168—111no—
182#2159—111no—
183#2158—111no—
184C23×C11—41no—
185C23×C11C2×D811yescharacteristic
186C22×D11C2×D811yescharacteristic
187Q8×C11—41no—
188Q8×C11—41no—
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—82no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11C2×D811yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C22⋊D11—41no—
200C22⋊D11—161no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—161no—
206C2×Dic11—161no—
207C2×Dic11C2×D811yescharacteristic
208C2×Dic11C2×D811yescharacteristic
209C2×Dic11C2×D811yescharacteristic
210C4×D11—21no—
211C4×D11—21no—
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×SD32C2×D1111yescharacteristic
221C2×M32C2×D1111yescharacteristic
222C22×C16—111no—
223#500—111no—
224#499—111no—
225#485—221no—
226#485—221no—
227#482—221no—
228#481—221no—
229#478—221no—
230#475—221no—
231#467—111no—
232#467C2×D1111yescharacteristic
233#466—111no—
234#466C2×D1111yescharacteristic
235C4×Q16—111no—
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#367—111no—
247#366—111no—
248#366—111no—
249#366—111no—
250#366C2×D1111yescharacteristic
251C4⋊C16—111no—
252#358—111no—
253#358—111no—
254#358C2×D1111yescharacteristic
255#357—111no—
256#357—111no—
257#357C2×D1111yescharacteristic
258C22⋊C16—111no—
259C22⋊C16—111no—
260#346—111no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11C22×D811yescharacteristic
268C2×D11—21no—
269C2×D11—21no—
270C2×D11—21no—
271C4×C11—21no—
272C4×C11—81no—
273C4×C11—81no—
274C4×C11—81no—
275C4×C11#54711yescharacteristic
276C4×C11#57811yescharacteristic
277Dic11—21no—
278Dic11—21no—
279Dic11—21no—
280Dic11—81no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284C2×Q16C22×D1111yescharacteristic
285C2×D8C22×D1111yescharacteristic
286C22×C8—111no—
287C22×C8C22×D1111yescharacteristic
288C4⋊Q8—221no—
289#126—441no—
290#126—441no—
291#126—441no—
292#125—221no—
293#124—441no—
294#123—441no—
295C22⋊Q8—21no—
296C22⋊Q8—221no—
297#121—21no—
298#121—221no—
299#121—441no—
300C4×Q8—221no—
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—22no—
310M32—22no—
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—111no—
320#107—221no—
321#107—221no—
322#107C22×D1111yescharacteristic
323#107C22×D1111yescharacteristic
324#106—221no—
325#106—221no—
326#106—221no—
327#106—221no—
328C4⋊C8—111no—
329#103—21no—
330#103—221no—
331#103—221no—
332#102—21no—
333#102—221no—
334#102—221no—
335C22⋊C8—111no—
336C22⋊C8—111no—
337C4×C8—111no—
338C2×C11—41no—
339C2×C11—161no—
340C2×C11#333411yescharacteristic
341C2×C11#341411yescharacteristic
342C2×C11#341611yescharacteristic
343D11—41no—
344C2×Q8—21no—
345C2×Q8—441no—
346C2×D4—21no—
347C2×D4—41no—
348C2×D4—111no—
349C2×D4—441no—
350C22×C4—111no—
351C22×C4—441no—
352C22×C4—441no—
353C22×C4D4×D1111yescharacteristic
354Q16—21no—
355Q16—21no—
356D8—21no—
357D8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—111no—
361C2×C8—111no—
362C2×C8—221no—
363C2×C8—221no—
364C2×C8D4×D1111yescharacteristic
365C2×C8C23×D1111yescharacteristic
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—41no—
369C4⋊C4—111no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—111no—
383C22⋊C4—111no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C42—111no—
391C42—441no—
392C42—441no—
393C42—441no—
394C42—441no—
395C16—21no—
396C16—221no—
397C16—221no—
398C16#434112yes—
399C11#3391711yescharacteristic, complemented, Sylow
400C23—41no—
401C23—111no—
402C23D8×D1111yescharacteristic
403Q8—41no—
404Q8—41no—
405Q8—882no—
406D4—41no—
407D4—41no—
408D4—82no—
409D4—441no—
410D4—1761no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—111no—
417C2×C4—111no—
418C2×C4—111no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—1761no—
426C2×C4—1761no—
427C2×C4D8×D1111yescharacteristic
428C2×C4C2×D4×D1111yescharacteristic
429C8—21no—
430C8—221no—
431C8—221no—
432C8C2×#434111yescharacteristic
433C8#6704311yescharacteristic
434C22—21no—
435C22—21no—
436C22—21no—
437C22—81no—
438C22—81no—
439C22—81no—
440C22—221no—
441C22—221no—
442C22—221no—
443C22C2×D8×D1111yescharacteristic
444C4—21no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—221no—
449C4—221no—
450C4—221no—
451C4—881no—
452C4—881no—
453C4—881no—
454C4—881no—
455C4#1062314211yescharacteristic
456C4#1062330211yescharacteristic
457C2—41no—
458C2—161no—
459C2—441no—
460C2#1308096011yescharacteristic
461C2#1308174811yescharacteristic
462C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2220C2
socleC22×C11C22×D8
prime radical#13081021C2
hypercenter#2220D11
hypocenterC11#33917
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2220

Complements

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

NH ≅ G/Ntype
1. #13081043C2semidirect
3. #13070900C2semidirect
4. #13070822C2semidirect
5. #13070811C2semidirect
6. #13070805C2semidirect
7. #13070804C2semidirect
8. #13070782C2semidirect
9. #13070761C2semidirect
10. #13070709C2semidirect
11. #13070481C2semidirect
12. #13070439C2semidirect
13. #13070404C2semidirect
14. #13070397C2semidirect
15. C11×#2220C2semidirect
178. #2220D11semidirect
399. C11#33917semidirect

Maximal subgroups

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

subgroupindex
#130810432
#130810212
#130709002
#130708222
#130708112
#130708052
#130708042
#130707822
#130707612
#130707092
#130704812
#130704392
#130704042
#130703972
C11×#22202
#3391711