Finite Group Databasebeta

← #14911553

Subgroups — #14911553

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#13081629C211yesmaximal, characteristic
2#13081508C211yesmaximal, characteristic, complemented
3#13070858C211yesmaximal, characteristic
4#13070853C211yesmaximal, characteristic, complemented
5#13070848C211yesmaximal, characteristic, complemented
6#13070781C211yesmaximal, characteristic, complemented
7#13070774C211yesmaximal, characteristic, complemented
8#13070764C211yesmaximal, characteristic, complemented
9#13070679C211yesmaximal, characteristic, complemented
10#13070679C211yesmaximal, characteristic, complemented
11#13070657C211yesmaximal, characteristic
12#13070488C211yesmaximal, characteristic, complemented
13#13070482C211yesmaximal, characteristic, complemented
14C4×#66864C211yesmaximal, characteristic, complemented
15C11×#2183C211yesmaximal, characteristic, complemented
16#10623116—21no—
17#10623098—21no—
18C8×Q8×C11C2211yescharacteristic
19C2×Dic88C2211yescharacteristic
20C2×#66864C2211yescharacteristic
21C2×#66864C2211yescharacteristic
22#10622464—21no—
23#10622461—21no—
24#10622457—21no—
25#10622457—21no—
26#10622442—21no—
27#10622442—21no—
28C4×Dic44C2211yescharacteristic
29C4×Dic44C2211yescharacteristic
30C4×Dic44C2211yescharacteristic
31C4×Dic44C2211yescharacteristic
32#10622309C2211yescharacteristic
33#10622309C2211yescharacteristic
34#10622308C2211yescharacteristic
35C4×D88C2211yescharacteristic
36C4×D88C2211yescharacteristic
37#10622296C2211yescharacteristic
38#10622296C2211yescharacteristic
39#10622295C2211yescharacteristic
40C11×C4⋊C16C2211yescharacteristic
41C11×C4⋊C16C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×#346C2211yescharacteristic
44C11×#346C2211yescharacteristic
45C4×C11×C16C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52#10622143C2211yescharacteristic
53#10622143C2211yescharacteristic
54#10622142C2211yescharacteristic
55#10622141C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C4×Q8×C11D411yescharacteristic
60#67000—41no—
61#66997—41no—
62C2×Dic44C2311yescharacteristic
63C2×Dic44C2311yescharacteristic
64C2×D88—21no—
65C2×D88C2311yescharacteristic
66C2×D88C2311yescharacteristic
67C2×#4314—21no—
68C2×#4314—21no—
69#66947—41no—
70#66947—41no—
71#66946—41no—
72#66942—41no—
73#66942—41no—
74#66940—41no—
75#66928—21no—
76#66928—21no—
77#66927—21no—
78C4×D44—21no—
79C4×D44—21no—
80#66923—21no—
81#66923—21no—
82#66922—21no—
83C4×Dic22—21no—
84C4×Dic22—21no—
85C4×Dic22—21no—
86C4×Dic22—21no—
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89C2×C11×C16C2311yescharacteristic
90C2×C11×C16C2311yescharacteristic
91C11×C4⋊C8D411yescharacteristic
92C11×C4⋊C8D411yescharacteristic
93C11×C4⋊C8D411yescharacteristic
94C4×C8×C11C2311yescharacteristic
95C4×C8×C11C2311yescharacteristic
96C4×C8×C11C2311yescharacteristic
97#66885—21no—
98#66885—21no—
99#66882—21no—
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66881—21no—
105#66881—21no—
106#66880—21no—
107#66880—21no—
108#66880—21no—
109#66880—21no—
110Dic88—22no—
111#66864—22no—
112#66864—22no—
113#33938—111nomaximal, Sylow
114C2×Q8×C11D811yescharacteristic
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—41no—
118C2×D44—41no—
119C2×C4×D11—41no—
120C2×C4×D11—41no—
121C2×Dic22—21no—
122C2×Dic22—21no—
123C2×Dic22—41no—
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2411yescharacteristic
128C11×C4⋊C4D811yescharacteristic
129C11×C4⋊C4D811yescharacteristic
130C11×C4⋊C4D811yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D411yescharacteristic
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—41no—
145Dic11⋊C4—41no—
146Dic11⋊C4—41no—
147Dic11⋊C4—41no—
148Dic11⋊C4—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153C4×Dic11—41no—
154C4×Dic11—41no—
155C4×Dic11—41no—
156C4×Dic11—41no—
157Dic44—21no—
158Dic44—21no—
159Dic44—21no—
160Dic44#4112yes—
161D88—21no—
162D88—21no—
163D88—21no—
164D88—21no—
165D88—81no—
166#4314—81no—
167#4314—81no—
168C11×C16—21no—
169C11×C16—21no—
170C11×C16—21no—
171C11×C16—21no—
172#3396—111no—
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#2183D1111yescharacteristic, complemented
184#2176—111no—
185#2175—111no—
186C4×SD32—111no—
187C22×D11—41no—
188C22×D11—41no—
189Q8×C11—41no—
190C2×C4×C11C2×D811yescharacteristic
191C2×C4×C11C2×D811yescharacteristic
192C2×C4×C11C2×D811yescharacteristic
193C2×C4×C11C2×D811yescharacteristic
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203D44—41no—
204D44—41no—
205D44—41no—
206D44—41no—
207D44—82no—
208D44—161no—
209C4×D11—161no—
210C4×D11—161no—
211Dic22—22no—
212Dic22—41no—
213Dic22—41no—
214Dic22—41no—
215Dic22—82no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11C2×#4111yescharacteristic
220C8×C112−1+411yescharacteristic
221#559—221no—
222#557—221no—
223C2×Q32—111no—
224C2×SD32—111no—
225C2×SD32—111no—
226#500—111no—
227#499—111no—
228#499—111no—
229#495—111no—
230#495—111no—
231#493—111no—
232#479—221no—
233#479—221no—
234#475—221no—
235#463—221no—
236#463—221no—
237#460—221no—
238C8×Q8C2×D1111yescharacteristic
239C4×Q16—111no—
240C4×Q16—111no—
241C4×Q16—111no—
242C4×Q16—111no—
243C4×D8—111no—
244C4×D8—111no—
245#367—111no—
246#367—111no—
247#366—111no—
248C4⋊C16C2×D1111yescharacteristic
249C4⋊C16C2×D1111yescharacteristic
250C4⋊C16C2×D1111yescharacteristic
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#346C2×D1111yescharacteristic
262#346C2×D1111yescharacteristic
263C4×C16C2×D1111yescharacteristic
264C22×C11C22×D811yescharacteristic
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11#54811yescharacteristic
278C4×C11#57711yescharacteristic
279Dic11—42no—
280Dic11—81no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284Dic11—81no—
285C2×Q16—111no—
286C2×Q16—111no—
287C2×SD16—221no—
288C2×SD16—221no—
289C2×D8—111no—
290C2×D8—111no—
291C2×D8—221no—
292C4⋊Q8—221no—
293C4⋊Q8—441no—
294#127—221no—
295#125—221no—
296#125—221no—
297#125—441no—
298#125—441no—
299#124—221no—
300#124—221no—
301#124—441no—
302#123—441no—
303#123—441no—
304C4×Q8—221no—
305C4×Q8—221no—
306C4×Q8—221no—
307C4×Q8—221no—
308C4×Q8—441no—
309C4×Q8D4411yescharacteristic
310C4×D4—221no—
311C4×D4—221no—
312C4×D4—441no—
313Q32—222no—
314SD32—222no—
315SD32—222no—
316C2×C16C22×D1111yescharacteristic
317C2×C16C22×D1111yescharacteristic
318C2×C16C22×D1111yescharacteristic
319C2×C16C22×D1111yescharacteristic
320#107—111no—
321#107—111no—
322#107—111no—
323#107—111no—
324#107—221no—
325#106—221no—
326#106—221no—
327C4⋊C8D4411yescharacteristic
328C4⋊C8D4411yescharacteristic
329C4⋊C8D4411yescharacteristic
330#103—221no—
331#103—221no—
332#103—221no—
333#103—221no—
334#102—221no—
335#102—221no—
336C4×C8C22×D1111yescharacteristic
337C4×C8C22×D1111yescharacteristic
338C4×C8C22×D1111yescharacteristic
339C2×C11#335811yescharacteristic
340C2×C11#341411yescharacteristic
341C2×C11#341611yescharacteristic
342D11—161no—
343D11—161no—
344C2×Q8—221no—
345C2×Q8—221no—
346C2×Q8—441no—
347C2×Q8D8811yescharacteristic
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—441no—
351C2×D4—441no—
352C22×C4—441no—
353C22×C4—441no—
354Q16—112no—
355Q16—221no—
356Q16—221no—
357Q16—221no—
358SD16—881no—
359SD16—881no—
360D8—221no—
361D8—221no—
362D8—221no—
363D8—221no—
364D8—881no—
365C2×C8C2×D4411yescharacteristic
366C2×C8C2×D4411yescharacteristic
367C2×C8C2×D4411yescharacteristic
368C2×C8C23×D1111yescharacteristic
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—441no—
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⋊C4D8811yescharacteristic
383C4⋊C4D8811yescharacteristic
384C4⋊C4D8811yescharacteristic
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C42—441no—
392C42—441no—
393C42—441no—
394C42—441no—
395C42C2×D4411yescharacteristic
396C42C2×D4411yescharacteristic
397C42C2×D4411yescharacteristic
398C16—21no—
399C16—21no—
400C16—21no—
401C16—21no—
402C11#3393811yescharacteristic, complemented, Sylow
403C23—441no—
404C23—441no—
405Q8—41no—
406Q8—222no—
407Q8—441no—
408Q8—441no—
409Q8—441no—
410Q8—882no—
411D4—441no—
412D4—441no—
413D4—441no—
414D4—441no—
415D4—882no—
416D4—1761no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—1761no—
424C2×C4—1761no—
425C2×C4C2×D8811yescharacteristic
426C2×C4C2×D8811yescharacteristic
427C2×C4C2×D8811yescharacteristic
428C2×C4C2×D8811yescharacteristic
429C2×C4C2×D8811yescharacteristic
430C2×C4C2×D8811yescharacteristic
431C2×C4C22×D4411yescharacteristic
432C8—21no—
433C8—21no—
434C8—21no—
435C8#6704011yescharacteristic
436C8#41×D1111yescharacteristic
437C22—881no—
438C22—881no—
439C22—881no—
440C22—881no—
441C22—881no—
442C22—881no—
443C22C22×D8811yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—442no—
451C4—881no—
452C4—881no—
453C4—881no—
454C4—881no—
455C4—881no—
456C4#1062310711yescharacteristic
457C4#1062328211yescharacteristic
458C2—1761no—
459C2—1761no—
460C2#1308125211yescharacteristic
461C2#1308175211yescharacteristic
462C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2183C2
socleC22×C11C22×D8
prime radical#10622308C22
hypercenter#2183D11
hypocenterC11#33938
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #2183

Complements

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

NH ≅ G/Ntype
2. #13081508C2semidirect
4. #13070853C2semidirect
5. #13070848C2semidirect
6. #13070781C2semidirect
7. #13070774C2semidirect
8. #13070764C2semidirect
9. #13070679C2semidirect
10. #13070679C2semidirect
12. #13070488C2semidirect
13. #13070482C2semidirect
14. C4×#66864C2semidirect
15. C11×#2183C2semidirect
183. #2183D11semidirect
402. C11#33938semidirect

Maximal subgroups

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

subgroupindex
#130816292
#130815082
#130708582
#130708532
#130708482
#130707812
#130707742
#130707642
#130706792
#130706572
#130704882
#130704822
C4×#668642
C11×#21832
#3393811