Finite Group Databasebeta

← #14911322

Subgroups — #14911322

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#13081047C211yesmaximal, characteristic, complemented
2#13070903C211yesmaximal, characteristic, complemented
3#13070824C211yesmaximal, characteristic, complemented
4#13070813C211yesmaximal, characteristic, complemented
5#13070804C211yesmaximal, characteristic, complemented
6#13070804C211yesmaximal, characteristic, complemented
7#13070777C211yesmaximal, characteristic, complemented
8#13070763C211yesmaximal, characteristic, complemented
9#13070727C211yesmaximal, characteristic, complemented
10#13070710C211yesmaximal, characteristic, complemented
11#13070480C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070402C211yesmaximal, characteristic, complemented
14#13070398C211yesmaximal, characteristic, complemented
15C11×#3339C211yesmaximal, characteristic
16C11×#553—21no—
17#10623073—21no—
18C11×#499C2211yescharacteristic
19C11×#482—21no—
20C11×#481—21no—
21C11×#478—21no—
22C11×#466C2211yescharacteristic
23C11×#466C2211yescharacteristic
24C4×C11×D8C2211yescharacteristic
25C8×D4×C11C2211yescharacteristic
26C11×#427C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C2×#66891C2211yescharacteristic
29#10622729C2211yescharacteristic
30#10622729C2211yescharacteristic
31#10622719C2211yescharacteristic
32#10622719C2211yescharacteristic
33C2×#66876C2211yescharacteristic
34C22×C11⋊C16C2211yescharacteristic
35#10622464—21no—
36#10622336—21no—
37#10622336—21no—
38C4×Dic44C2211yescharacteristic
39#10622295C2211yescharacteristic
40#10622200C2211yescharacteristic
41#10622200C2211yescharacteristic
42#10622200C2211yescharacteristic
43C22⋊(C11⋊C16)C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622130C2211yescharacteristic
46#10622130C2211yescharacteristic
47#10622130C2211yescharacteristic
48#10622128C2211yescharacteristic
49#10622128C2211yescharacteristic
50#10622128C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622128C2211yescharacteristic
53#10622127C2211yescharacteristic
54#10622127C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×D8C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×#126—41no—
63C11×#125—21no—
64C11×#123—41no—
65C11×#121—21no—
66C11×#121—21no—
67C11×#121—41no—
68C4×D4×C11—21no—
69C4×D4×C11—41no—
70C4×D4×C11D411yescharacteristic
71C11×#117—21no—
72C2×C11×C4⋊C4—21no—
73#66989—41no—
74#66979—21no—
75#66979—21no—
76#66977—21no—
77#66977—21no—
78C2×Dic44C2311yescharacteristic
79#66940—41no—
80#66932—41no—
81#66932—41no—
82#66922—21no—
83C4×Dic22—21no—
84C11×#107—21no—
85C11×#107C2311yescharacteristic
86C11×#107C2311yescharacteristic
87C11×#107C2311yescharacteristic
88C11×#106—21no—
89C11×#106—21no—
90C11×C4⋊C8D411yescharacteristic
91C11×#102—21no—
92C11×#102—21no—
93C11×#102—21no—
94C11×C22⋊C8D411yescharacteristic
95C11×C22⋊C8D411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97#66891—22no—
98#66882—21no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66881—21no—
103#66881—21no—
104#66880—21no—
105#66880—21no—
106#66880—21no—
107#66876—22no—
108C2×C11⋊C16—22no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#33917—111nomaximal, Sylow
114C2×D4×C11—21no—
115C2×D4×C11—41no—
116C2×D4×C11—41no—
117C2×D4×C11D811yescharacteristic
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C2×Dic22—21no—
123C2×Dic22—41no—
124C11×D8—21no—
125C11×D8—21no—
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⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4D811yescharacteristic
141C11×C22⋊C4—41no—
142C11×C22⋊C4—41no—
143C11×C22⋊C4—41no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4D811yescharacteristic
146C11×C22⋊C4D811yescharacteristic
147C42×C11—41no—
148C42×C11C2×D411yescharacteristic
149C22⋊Dic11—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152C22⋊Dic11—41no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163Dic44—21no—
164Dic44—21no—
165C11⋊C16—21no—
166C11⋊C16—21no—
167C11⋊C16—21no—
168C11⋊C16#4112yes—
169#3342—111no—
170#3339D1111yescharacteristic
171#2255—111no—
172#2237—111no—
173#2235—111no—
174#2234—111no—
175#2234—111no—
176#2229—111no—
177#2226—111no—
178#2220—111no—
179#2217—111no—
180#2175—111no—
181#2168—111no—
182#2159—111no—
183#2158—111no—
184C23×C11—41no—
185C23×C11C2×D811yescharacteristic
186C23×C11C2×D811yescharacteristic
187D4×C11—41no—
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—82no—
191D4×C11—161no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—161no—
200C2×C4×C11—161no—
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210Dic22—41no—
211Dic22—41no—
212Dic22—82no—
213C8×C11—21no—
214C8×C11—21no—
215C8×C11—21no—
216C8×C11C2×#4111yescharacteristic
217C8×C112−1+411yescharacteristic
218#556—221no—
219#553—21no—
220C2×SD32—111no—
221C2×M32—111no—
222C22×C16—111no—
223#500—111no—
224#499C2×D1111yescharacteristic
225#485—221no—
226#485—221no—
227#482—21no—
228#481—21no—
229#478—21no—
230#475—221no—
231#467—111no—
232#467—111no—
233#466C2×D1111yescharacteristic
234#466C2×D1111yescharacteristic
235C4×Q16—111no—
236C4×D8C2×D1111yescharacteristic
237C8×D4C2×D1111yescharacteristic
238#427—111no—
239#427—111no—
240#427C2×D1111yescharacteristic
241C2×#107C2×D1111yescharacteristic
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#366—111no—
251C4⋊C16—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255#357—111no—
256#357—111no—
257#357—111no—
258C22⋊C16—111no—
259C22⋊C16—111no—
260#346—111no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11C22×D811yescharacteristic
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11#54711yescharacteristic
279C4×C11#57811yescharacteristic
280Dic11—81no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284C2×Q16—111no—
285C2×D8C22×D1111yescharacteristic
286C22×C8C22×D1111yescharacteristic
287C22×C8C22×D1111yescharacteristic
288C4⋊Q8—221no—
289#126—41no—
290#126—441no—
291#126—441no—
292#125—21no—
293#124—441no—
294#123—41no—
295C22⋊Q8—221no—
296C22⋊Q8—221no—
297#121—21no—
298#121—21no—
299#121—41no—
300C4×Q8—221no—
301C4×Q8—441no—
302C4×D4—21no—
303C4×D4—41no—
304C4×D4C22⋊D1111yescharacteristic
305#117—21no—
306#117—221no—
307#117—221no—
308C2×C4⋊C4—21no—
309SD32—222no—
310M32—222no—
311C2×C16—111no—
312C2×C16—111no—
313C2×C16—111no—
314C2×C16—111no—
315C2×C16—222no—
316#107—21no—
317#107—111no—
318#107—111no—
319#107—111no—
320#107—221no—
321#107C22×D1111yescharacteristic
322#107C22×D1111yescharacteristic
323#107C22×D1111yescharacteristic
324#106—21no—
325#106—21no—
326#106—221no—
327#106—221no—
328C4⋊C8C22⋊D1111yescharacteristic
329#103—221no—
330#103—221no—
331#103—221no—
332#102—21no—
333#102—21no—
334#102—21no—
335C22⋊C8C22⋊D1111yescharacteristic
336C22⋊C8C22⋊D1111yescharacteristic
337C4×C8C22×D1111yescharacteristic
338C2×C11—41no—
339C2×C11—41no—
340C2×C11—161no—
341C2×C11#333411yescharacteristic
342C2×C11#341411yescharacteristic
343C2×C11#341611yescharacteristic
344C2×Q8—221no—
345C2×Q8—441no—
346C2×D4—21no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4#432311yescharacteristic
350C22×C4—41no—
351C22×C4—41no—
352C22×C4C2×C22⋊D1111yescharacteristic
353C22×C4C2×C22⋊D1111yescharacteristic
354Q16—221no—
355Q16—221no—
356D8—21no—
357D8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8C2×C22⋊D1111yescharacteristic
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C2×C22⋊D1111yescharacteristic
365C2×C8C23×D1111yescharacteristic
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4#432311yescharacteristic
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4#432311yescharacteristic
389C22⋊C4#432311yescharacteristic
390C42—41no—
391C42—441no—
392C42—441no—
393C42—441no—
394C42C2×C22⋊D1111yescharacteristic
395C16—112no—
396C16—221no—
397C16—221no—
398C16—221no—
399C11#3391711yescharacteristic, complemented, Sylow
400C23—41no—
401C23C2×#432311yescharacteristic
402C23C2×#432311yescharacteristic
403Q8—441no—
404Q8—441no—
405Q8—882no—
406D4—41no—
407D4—41no—
408D4—41no—
409D4—82no—
410D4—161no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—161no—
419C2×C4—161no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4C2×#432311yescharacteristic
425C2×C4C2×#432311yescharacteristic
426C2×C4C2×#432311yescharacteristic
427C2×C4C2×#432311yescharacteristic
428C2×C4C22×C22⋊D1111yescharacteristic
429C8—21no—
430C8—21no—
431C8—21no—
432C8#41×D1111yescharacteristic
433C8#6704311yescharacteristic
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C22×#432311yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—881no—
452C4—881no—
453C4—881no—
454C4—881no—
455C4#1062335511yescharacteristic
456C4#1062336911yescharacteristic
457C2—41no—
458C2—41no—
459C2—161no—
460C2#1308095911yescharacteristic
461C2#1308175011yescharacteristic
462C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3339C2
socleC22×C11C22×D8
hypercenter#3339D11
hypocenterC11#33917
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #13081047C2semidirect
2. #13070903C2semidirect
3. #13070824C2semidirect
4. #13070813C2semidirect
5. #13070804C2semidirect
6. #13070804C2semidirect
7. #13070777C2semidirect
8. #13070763C2semidirect
9. #13070727C2semidirect
10. #13070710C2semidirect
11. #13070480C2semidirect
12. #13070442C2semidirect
13. #13070402C2semidirect
14. #13070398C2semidirect
399. C11#33917semidirect

Maximal subgroups

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

subgroupindex
#130810472
#130709032
#130708242
#130708132
#130708042
#130707772
#130707632
#130707272
#130707102
#130704802
#130704422
#130704022
#130703982
C11×#33392
#3391711