Finite Group Databasebeta

← #14911545

Subgroups — #14911545

Order 2816.

480 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#13081508C211yesmaximal, characteristic, complemented
2#13070857C211yesmaximal, characteristic
3#13070852C211yesmaximal, characteristic, complemented
4#13070847C211yesmaximal, characteristic, complemented
5#13070780C211yesmaximal, characteristic, complemented
6#13070773C211yesmaximal, characteristic, complemented
7#13070763C211yesmaximal, characteristic, complemented
8#13070675C211yesmaximal, characteristic, complemented
9#13070675C211yesmaximal, characteristic, complemented
10#13070653C211yesmaximal, characteristic
11#13070525C211yesmaximal, characteristic, complemented
12#13070485C211yesmaximal, characteristic, complemented
13#13070480C211yesmaximal, characteristic, complemented
14C4×#66891C211yesmaximal, characteristic, complemented
15C11×#3396C211yesmaximal, characteristic
16C11×#559—21no—
17#10623098—21no—
18C11×#495C2211yescharacteristic
19C11×#495C2211yescharacteristic
20C11×#493C2211yescharacteristic
21C11×#463—21no—
22C11×#463—21no—
23C11×#460—21no—
24C8×Q8×C11C2211yescharacteristic
25C4×C11×Q16C2211yescharacteristic
26C4×C11×D8C2211yescharacteristic
27C4×C11×D8C2211yescharacteristic
28C2×#66893C2211yescharacteristic
29C2×#66891C2211yescharacteristic
30C2×#66891C2211yescharacteristic
31#10622464—21no—
32#10622442—21no—
33#10622442—21no—
34C4×Dic44C2211yescharacteristic
35C4×Dic44C2211yescharacteristic
36C4×Dic44C2211yescharacteristic
37#10622296C2211yescharacteristic
38#10622296C2211yescharacteristic
39#10622295C2211yescharacteristic
40#10622202C2211yescharacteristic
41#10622202C2211yescharacteristic
42#10622202C2211yescharacteristic
43#10622200C2211yescharacteristic
44#10622200C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622130C2211yescharacteristic
50#10622128C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622127C2211yescharacteristic
53C4⋊(C11⋊C16)C2211yescharacteristic
54C4⋊(C11⋊C16)C2211yescharacteristic
55C4⋊(C11⋊C16)C2211yescharacteristic
56#10622099C2211yescharacteristic
57#10622099C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×SD16—21no—
61C2×C11×SD16—21no—
62C2×C11×D8—21no—
63C2×C11×D8C2311yescharacteristic
64C2×C11×D8C2311yescharacteristic
65C11×#127—21no—
66C11×#124—21no—
67C11×#124—21no—
68C11×#124—41no—
69C11×#123—41no—
70C11×#123—41no—
71C4×Q8×C11—21no—
72C4×Q8×C11D411yescharacteristic
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11—41no—
76#66997—41no—
77C2×Dic44C2311yescharacteristic
78#66942—41no—
79#66942—41no—
80#66940—41no—
81#66923—21no—
82#66923—21no—
83#66922—21no—
84C4×Dic22—21no—
85C4×Dic22—21no—
86C4×Dic22—21no—
87C11×#107C2311yescharacteristic
88C11×C4⋊C8D411yescharacteristic
89C11×C4⋊C8D411yescharacteristic
90C11×C4⋊C8D411yescharacteristic
91C11×#103—21no—
92C11×#102—21no—
93C11×#102—21no—
94C4×C8×C11C2311yescharacteristic
95C4×C8×C11C2311yescharacteristic
96C4×C8×C11C2311yescharacteristic
97#66893—22no—
98#66891—22no—
99#66891—22no—
100#66882—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66881—21no—
105#66881—21no—
106#66880—21no—
107#66880—21no—
108#66880—21no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#33938—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×Q8×C11D811yescharacteristic
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11—41no—
122C2×Dic22—21no—
123C2×Dic22—41no—
124C11×Q16—21no—
125C11×Q16—21no—
126C11×SD16—81no—
127C11×SD16—81no—
128C11×D8—21no—
129C11×D8—21no—
130C11×D8—21no—
131C11×D8—21no—
132C11×D8—81no—
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2411yescharacteristic
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4D811yescharacteristic
140C11×C4⋊C4D811yescharacteristic
141C11×C4⋊C4D811yescharacteristic
142C11×C22⋊C4—41no—
143C11×C22⋊C4—41no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C42×C11—41no—
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163C4×Dic11—41no—
164C4×Dic11—41no—
165C4×Dic11—41no—
166Dic44—21no—
167Dic44#4112yes—
168C11⋊C16—21no—
169C11⋊C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3396D1111yescharacteristic
173#3383—111no—
174#2244—111no—
175#2243—111no—
176#2242—111no—
177#2229—111no—
178#2228—111no—
179#2226—111no—
180#2211—111no—
181#2211—111no—
182#2207—111no—
183#2183—111no—
184#2176—111no—
185#2175—111no—
186C4×SD32—111no—
187C23×C11—41no—
188C23×C11—41no—
189Q8×C11—41no—
190Q8×C11—41no—
191Q8×C11—41no—
192D4×C11—41no—
193D4×C11—41no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—82no—
197D4×C11—161no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—161no—
201C2×C4×C11—161no—
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C2×D811yescharacteristic
207C2×C4×C11C2×D811yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213Dic22—22no—
214Dic22—41no—
215Dic22—82no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11C2×#4111yescharacteristic
220C8×C112−1+411yescharacteristic
221#559—21no—
222#557—221no—
223C2×Q32—111no—
224C2×SD32—111no—
225C2×SD32—111no—
226#500—111no—
227#499—111no—
228#499—111no—
229#495C2×D1111yescharacteristic
230#495C2×D1111yescharacteristic
231#493C2×D1111yescharacteristic
232#479—221no—
233#479—221no—
234#475—221no—
235#463—21no—
236#463—21no—
237#460—21no—
238C8×Q8C2×D1111yescharacteristic
239C4×Q16—111no—
240C4×Q16—111no—
241C4×Q16—111no—
242C4×Q16C2×D1111yescharacteristic
243C4×D8C2×D1111yescharacteristic
244C4×D8C2×D1111yescharacteristic
245#367—111no—
246#367—111no—
247#366—111no—
248C4⋊C16—111no—
249C4⋊C16—111no—
250C4⋊C16—111no—
251#358—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255#357—111no—
256#357—111no—
257#357—111no—
258#357—111no—
259#357—111no—
260#357—111no—
261#346—111no—
262#346—111no—
263C4×C16—111no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
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—21no—
276C4×C11—21no—
277C4×C11—81no—
278C4×C11—81no—
279C4×C11#54811yescharacteristic
280C4×C11#57711yescharacteristic
281Dic11—42no—
282Dic11—81no—
283Dic11—81no—
284Dic11—81no—
285C2×Q16—111no—
286C2×Q16C22×D1111yescharacteristic
287C2×SD16—21no—
288C2×SD16—21no—
289C2×D8—21no—
290C2×D8C22×D1111yescharacteristic
291C2×D8C22×D1111yescharacteristic
292C4⋊Q8—221no—
293C4⋊Q8—441no—
294#127—21no—
295#125—221no—
296#125—221no—
297#125—441no—
298#125—441no—
299#124—21no—
300#124—21no—
301#124—41no—
302#123—41no—
303#123—41no—
304C4×Q8—21no—
305C4×Q8—221no—
306C4×Q8—221no—
307C4×Q8—221no—
308C4×Q8—441no—
309C4×Q8C22⋊D1111yescharacteristic
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—41no—
313Q32—222no—
314SD32—222no—
315SD32—222no—
316C2×C16—111no—
317C2×C16—111no—
318C2×C16—111no—
319C2×C16—111no—
320#107—111no—
321#107—111no—
322#107—111no—
323#107—221no—
324#107C22×D1111yescharacteristic
325#106—221no—
326#106—221no—
327C4⋊C8C22⋊D1111yescharacteristic
328C4⋊C8C22⋊D1111yescharacteristic
329C4⋊C8C22⋊D1111yescharacteristic
330#103—21no—
331#103—221no—
332#103—221no—
333#103—221no—
334#102—21no—
335#102—21no—
336C4×C8C22×D1111yescharacteristic
337C4×C8C22×D1111yescharacteristic
338C4×C8C22×D1111yescharacteristic
339C2×C11—161no—
340C2×C11—161no—
341C2×C11#335811yescharacteristic
342C2×C11#341411yescharacteristic
343C2×C11#341611yescharacteristic
344C2×Q8—21no—
345C2×Q8—221no—
346C2×Q8—441no—
347C2×Q8#432311yescharacteristic
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—41no—
351C2×D4—41no—
352C22×C4—41no—
353C22×C4—41no—
354Q16—21no—
355Q16—21no—
356Q16—112no—
357Q16—221no—
358SD16—81no—
359SD16—81no—
360D8—21no—
361D8—21no—
362D8—21no—
363D8—21no—
364D8—81no—
365C2×C8C2×C22⋊D1111yescharacteristic
366C2×C8C2×C22⋊D1111yescharacteristic
367C2×C8C2×C22⋊D1111yescharacteristic
368C2×C8C23×D1111yescharacteristic
369C4⋊C4—21no—
370C4⋊C4—41no—
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—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4#432311yescharacteristic
383C4⋊C4#432311yescharacteristic
384C4⋊C4#432311yescharacteristic
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C42—41no—
392C42—441no—
393C42—441no—
394C42—441no—
395C42C2×C22⋊D1111yescharacteristic
396C42C2×C22⋊D1111yescharacteristic
397C42C2×C22⋊D1111yescharacteristic
398C16—221no—
399C16—221no—
400C16—221no—
401C16—221no—
402C11#3393811yescharacteristic, complemented, Sylow
403C23—41no—
404C23—41no—
405Q8—41no—
406Q8—41no—
407Q8—41no—
408Q8—222no—
409Q8—441no—
410Q8—882no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—82no—
416D4—161no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—161no—
420C2×C4—161no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4C2×#432311yescharacteristic
426C2×C4C2×#432311yescharacteristic
427C2×C4C2×#432311yescharacteristic
428C2×C4C2×#432311yescharacteristic
429C2×C4C2×#432311yescharacteristic
430C2×C4C2×#432311yescharacteristic
431C2×C4C22×C22⋊D1111yescharacteristic
432C8—21no—
433C8—21no—
434C8—21no—
435C8#41×D1111yescharacteristic
436C8#6704311yescharacteristic
437C22—81no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C22×#432311yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—81no—
451C4—81no—
452C4—442no—
453C4—881no—
454C4—881no—
455C4—881no—
456C4#1062336211yescharacteristic
457C4#1062336711yescharacteristic
458C2—161no—
459C2—161no—
460C2#1308124711yescharacteristic
461C2#1308175011yescharacteristic
462C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3396C2
socleC22×C11C22×D8
prime radicalC11×#493C22
hypercenter#3396D11
hypocenterC11#33938
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3396

Complements

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

NH ≅ G/Ntype
1. #13081508C2semidirect
3. #13070852C2semidirect
4. #13070847C2semidirect
5. #13070780C2semidirect
6. #13070773C2semidirect
7. #13070763C2semidirect
8. #13070675C2semidirect
9. #13070675C2semidirect
11. #13070525C2semidirect
12. #13070485C2semidirect
13. #13070480C2semidirect
14. C4×#66891C2semidirect
402. C11#33938semidirect

Maximal subgroups

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

subgroupindex
#130815082
#130708572
#130708522
#130708472
#130707802
#130707732
#130707632
#130706752
#130706532
#130705252
#130704852
#130704802
C4×#668912
C11×#33962
#3393811