Finite Group Databasebeta

← #14911223

Subgroups — #14911223

Order 2816.

504 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080964C211yesmaximal, characteristic
2#13070903C211yesmaximal, characteristic, complemented
3#13070816C211yesmaximal, characteristic, complemented
4#13070811C211yesmaximal, characteristic, complemented
5#13070807C211yesmaximal, characteristic, complemented
6#13070796C211yesmaximal, characteristic, complemented
7#13070770C211yesmaximal, characteristic, complemented
8#13070768C211yesmaximal, characteristic, complemented
9#13070731C211yesmaximal, characteristic, complemented
10#13070714C211yesmaximal, characteristic, complemented
11#13070478C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070405C211yesmaximal, characteristic, complemented
14C2×#10622127C211yesmaximal, characteristic, complemented
15C11×#3336C211yesmaximal, characteristic, complemented
16C11×#552—21no—
17#10623086—21no—
18C11×#499C2211yescharacteristic
19C11×#485—21no—
20C11×#483—21no—
21C11×#479—21no—
22C11×#467C2211yescharacteristic
23C11×#467C2211yescharacteristic
24C4×C11×Q16C2211yescharacteristic
25C8×D4×C11C2211yescharacteristic
26C11×#427C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C2×#66892C2211yescharacteristic
29#10622728C2211yescharacteristic
30#10622728C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66876C2211yescharacteristic
34C22×C11⋊C16C2211yescharacteristic
35#10622459—21no—
36#10622349—21no—
37#10622349—21no—
38C4×D88C2211yescharacteristic
39#10622295C2211yescharacteristic
40#10622202C2211yescharacteristic
41#10622202C2211yescharacteristic
42#10622202C2211yescharacteristic
43C22⋊(C11⋊C16)C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622129C2211yescharacteristic
46#10622129C2211yescharacteristic
47#10622129C2211yescharacteristic
48#10622128C2211yescharacteristic
49#10622128C2211yescharacteristic
50#10622128C2211yescharacteristic
51#10622127C2211yescharacteristic
52#10622127C2211yescharacteristic
53#10622127C2211yescharacteristic
54#10622127C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×#4341—41no—
60C2×C11×Q16C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#126—41no—
64C11×#125—21no—
65C11×#125—41no—
66C11×#123—41no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—21no—
69C4×Q8×C11—21no—
70C4×D4×C11D411yescharacteristic
71C11×#117—21no—
72C11×#117—41no—
73C2×C11×C4⋊C4—21no—
74#66983—21no—
75#66983—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×D88C2311yescharacteristic
79#66950—41no—
80#66939—41no—
81#66939—41no—
82C4×D44—21no—
83#66922—21no—
84C11×#107—21no—
85C11×#107C2311yescharacteristic
86C11×#107C2311yescharacteristic
87C11×#107C2311yescharacteristic
88C11×#106—21no—
89C11×#106—21no—
90C11×C4⋊C8D411yescharacteristic
91C11×#103—21no—
92C11×#103—21no—
93C11×#103—21no—
94C11×C22⋊C8D411yescharacteristic
95C11×C22⋊C8D411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97#66892—22no—
98#66885—21no—
99#66885—21no—
100#66885—21no—
101#66882—21no—
102#66882—21no—
103#66882—21no—
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66876—22no—
108C2×C11⋊C16—22no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#33910—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D4×C11D811yescharacteristic
116C22×C4×C11—41no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C2×C22⋊D11—41no—
120C2×C22⋊D11—41no—
121C22×Dic11—41no—
122C22×Dic11—41no—
123#4341—84no—
124C2×D44—21no—
125C2×C4×D11—41no—
126C2×Dic22—41no—
127C11×Q16—21no—
128C11×Q16—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2411yescharacteristic
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4D811yescharacteristic
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4D811yescharacteristic
151C11×C22⋊C4D811yescharacteristic
152C42×C11—41no—
153C42×C11—41no—
154C42×C11C2×D411yescharacteristic
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—41no—
162C4⋊Dic11—41no—
163C4⋊Dic11—41no—
164D88—21no—
165D88—21no—
166C11⋊C16—21no—
167C11⋊C16—21no—
168C11⋊C16—21no—
169C11⋊C16#4112yescomplemented
170#3336D1111yescharacteristic, complemented
171#3334—111no—
172#2255—111no—
173#2236—111no—
174#2235—111no—
175#2234—111no—
176#2232—111no—
177#2228—111no—
178#2227—111no—
179#2220—111no—
180#2217—111no—
181#2175—111no—
182#2168—111no—
183#2159—111no—
184C2×#366—111no—
185C23×C11C2×D811yescharacteristic
186C23×C11C2×D811yescharacteristic
187C22×D11—41no—
188Q8×C11—41no—
189Q8×C11—41no—
190D4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—82no—
200C2×C4×C11C2×D811yescharacteristic
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C22⋊D11—82no—
206C22⋊D11—82no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—82no—
211C2×Dic11—82no—
212D44—41no—
213D44—41no—
214C4×D11—82no—
215Dic22—82no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11C2×#4111yescharacteristic
220C8×C112−1+411yescharacteristic
221#552—21no—
222#547—221no—
223C2×SD32—111no—
224C2×M32—111no—
225C22×C16—111no—
226#500—111no—
227#499C2×D1111yescharacteristic
228#485—21no—
229#483—21no—
230#480—221no—
231#480—221no—
232#479—21no—
233#474—221no—
234#467C2×D1111yescharacteristic
235#467C2×D1111yescharacteristic
236#466—111no—
237#466—111no—
238C4×Q16C2×D1111yescharacteristic
239C4×D8—111no—
240C8×D4C2×D1111yescharacteristic
241#427C2×D1111yescharacteristic
242C2×#107—111no—
243C2×#107—111no—
244C2×#107C2×D1111yescharacteristic
245#367—111no—
246#367—111no—
247#367—111no—
248#366—111no—
249#366—111no—
250#366—111no—
251#366—111no—
252#366—111no—
253#366—111no—
254C4⋊C16—111no—
255#358—111no—
256#358—111no—
257#358—111no—
258#357—111no—
259#357—111no—
260#357—111no—
261C22⋊C16—111no—
262C22⋊C16—111no—
263#346—111no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11#50912yes—
270C22×C11C22×D811yescharacteristic
271C2×D11—81no—
272C2×D11—81no—
273C2×D11—81no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—81no—
279C4×C11—81no—
280C4×C11—81no—
281C4×C11—81no—
282C4×C11#54711yescharacteristic
283C4×C11#57811yescharacteristic
284Dic11—81no—
285Dic11—81no—
286Dic11—81no—
287C2×#41—441no—
288C2×Q16C22×D1111yescharacteristic
289C2×D8—111no—
290C22×C8C22×D1111yescharacteristic
291C22×C8C22×D1111yescharacteristic
292C4⋊Q8—221no—
293#126—41no—
294#125—21no—
295#125—41no—
296#123—41no—
297#123—441no—
298#123—441no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—441no—
302#121—221no—
303#121—221no—
304C4×Q8—21no—
305C4×D4—221no—
306C4×D4C22⋊D1111yescharacteristic
307#117—21no—
308#117—41no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312SD32—222no—
313M32—222no—
314C2×C16—111no—
315C2×C16—111no—
316C2×C16—111no—
317C2×C16—111no—
318C2×C16—222no—
319#107—21no—
320#107—111no—
321#107—111no—
322#107—111no—
323#107—221no—
324#107—221no—
325#107—221no—
326#107C22×D1111yescharacteristic
327#107C22×D1111yescharacteristic
328#107C22×D1111yescharacteristic
329#106—21no—
330#106—21no—
331C4⋊C8C22⋊D1111yescharacteristic
332#103—21no—
333#103—21no—
334#103—21no—
335#102—221no—
336#102—221no—
337#102—221no—
338C22⋊C8C22⋊D1111yescharacteristic
339C22⋊C8C22⋊D1111yescharacteristic
340C4×C8C22×D1111yescharacteristic
341C2×C11—22no—
342C2×C11—41no—
343C2×C11#333411yescharacteristic
344C2×C11C2×#50911yescharacteristic
345C2×C11#341711yescharacteristic
346D11—161no—
347#41—884no—
348C2×Q8—21no—
349C2×Q8—441no—
350C2×D4—221no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4#432311yescharacteristic
354C22×C4—41no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4—441no—
358C22×C4C2×C22⋊D1111yescharacteristic
359C22×C4C2×C22⋊D1111yescharacteristic
360Q16—21no—
361Q16—21no—
362D8—221no—
363D8—221no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8C2×C22⋊D1111yescharacteristic
369C2×C8C2×C22⋊D1111yescharacteristic
370C2×C8C2×C22⋊D1111yescharacteristic
371C2×C8C23×D1111yescharacteristic
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4#432311yescharacteristic
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4#432311yescharacteristic
395C22⋊C4#432311yescharacteristic
396C42—41no—
397C42—41no—
398C42C2×C22⋊D1111yescharacteristic
399C16—112no—
400C16—221no—
401C16—221no—
402C16—221no—
403C11#3391011yescharacteristic, complemented, Sylow
404C23—441no—
405C23C2×#432311yescharacteristic
406C23C2×#432311yescharacteristic
407Q8—41no—
408Q8—41no—
409Q8—882no—
410D4—22no—
411D4—441no—
412D4—441no—
413D4—882no—
414D4—882no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—82no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—882no—
428C2×C4—882no—
429C2×C4—882no—
430C2×C4C2×#432311yescharacteristic
431C2×C4C2×#432311yescharacteristic
432C2×C4C2×#432311yescharacteristic
433C2×C4C2×#432311yescharacteristic
434C2×C4C22×C22⋊D1111yescharacteristic
435C8—21no—
436C8—21no—
437C8—21no—
438C8#41×D1111yescharacteristic
439C8#6704311yescharacteristic
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—881no—
446C22—881no—
447C22—881no—
448C22#1062280612yes—
449C22C22×#432311yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—81no—
455C4—81no—
456C4—81no—
457C4—81no—
458C4—881no—
459C4—881no—
460C4—881no—
461C4#1062335511yescharacteristic
462C4#1062336911yescharacteristic
463C2—22no—
464C2—41no—
465C2—1761no—
466C2#1308095911yescharacteristic
467C2C2×#1062280611yescharacteristic
468C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3336C2
socleC22×C11C22×D8
prime radical#13080964C2
hypercenter#3336D11
hypocenterC11#33910
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3336

Complements

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

NH ≅ G/Ntype
2. #13070903C2semidirect
3. #13070816C2semidirect
4. #13070811C2semidirect
5. #13070807C2semidirect
6. #13070796C2semidirect
7. #13070770C2semidirect
8. #13070768C2semidirect
9. #13070731C2semidirect
10. #13070714C2semidirect
11. #13070478C2semidirect
12. #13070442C2semidirect
13. #13070405C2semidirect
14. C2×#10622127C2semidirect
15. C11×#3336C2semidirect
169. C11⋊C16#41semidirect
170. #3336D11semidirect
403. C11#33910semidirect

Maximal subgroups

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

subgroupindex
#130809642
#130709032
#130708162
#130708112
#130708072
#130707962
#130707702
#130707682
#130707312
#130707142
#130704782
#130704422
#130704052
C2×#106221272
C11×#33362
#3391011