Finite Group Databasebeta

← #14911544

Subgroups — #14911544

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#13081630C211yesmaximal, characteristic
2#13081507C211yesmaximal, characteristic, complemented
3#13070857C211yesmaximal, characteristic
4#13070851C211yesmaximal, characteristic, complemented
5#13070846C211yesmaximal, characteristic, complemented
6#13070781C211yesmaximal, characteristic, complemented
7#13070771C211yesmaximal, characteristic, complemented
8#13070761C211yesmaximal, characteristic, complemented
9#13070676C211yesmaximal, characteristic, complemented
10#13070676C211yesmaximal, characteristic, complemented
11#13070523C211yesmaximal, characteristic, complemented
12#13070485C211yesmaximal, characteristic, complemented
13#13070481C211yesmaximal, characteristic, complemented
14SD32×Dic11C211yesmaximal, characteristic, complemented
15C11×#2207C211yesmaximal, characteristic
16#10623244—21no—
17#10623100—21no—
18C2×C11×SD32C2211yescharacteristic
19C2×C11×SD32C2211yescharacteristic
20C11×#493C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22Q16×Dic11C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24C2×#66893C2211yescharacteristic
25#10622768C2211yescharacteristic
26#10622768C2211yescharacteristic
27#10622766—21no—
28#10622766—21no—
29D8×Dic11C2211yescharacteristic
30D8×Dic11C2211yescharacteristic
31#10622688—21no—
32#10622635—21no—
33#10622491C2211yescharacteristic
34#10622487C2211yescharacteristic
35#10622412—21no—
36#10622404—21no—
37C4×Dic44C2211yescharacteristic
38#10622296C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×C4⋊C16C2211yescharacteristic
41C11×#357C2211yescharacteristic
42C11×#357C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622200C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622143C2211yescharacteristic
49#10622142C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622140C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55C16×Dic11C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×D8—21no—
61C2×C11×D8C2311yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C11×#127—21no—
64C4×Q8×C11—21no—
65Q8×Dic11—21no—
66Q8×Dic11—21no—
67#66989—21no—
68#66989—21no—
69#66989—41no—
70#66988—41no—
71#66988—41no—
72D4×Dic11—21no—
73D4×Dic11—21no—
74D4×Dic11—41no—
75C2×#4324—21no—
76C2×#4324—21no—
77C2×Dic44C2311yescharacteristic
78#66943—21no—
79#66943—41no—
80#66941—21no—
81#66941—41no—
82#66923—21no—
83#66923—41no—
84C4×Dic22—21no—
85C4×Dic22—41no—
86C4×Dic22D411yescharacteristic
87C11×SD32—22no—
88C11×SD32—22no—
89C2×C11×C16C2311yescharacteristic
90C2×C11×C16C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#103—21no—
93C4×C8×C11C2311yescharacteristic
94#66899—21no—
95#66899—21no—
96#66896—21no—
97#66896—21no—
98#66893—22no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66881—21no—
103#66880—21no—
104Dic11⋊C8D411yescharacteristic
105Dic11⋊C8D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66872—21no—
111#66871—21no—
112C4⋊(C11⋊C8)D411yescharacteristic
113#33938—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C2×Dic22—21no—
122C2×Dic22—41no—
123C2×Dic22D811yescharacteristic
124C11×Q16—21no—
125C11×Q16#4112yes—
126C11×D8—21no—
127C11×D8—21no—
128C11×D8—21no—
129C11×D8—21no—
130C11×D8—81no—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2411yescharacteristic
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C42×C11—41no—
136C42×C11C2×D411yescharacteristic
137C22⋊Dic11—41no—
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142C22⋊Dic11—41no—
143#4324—81no—
144#4324—81no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151C4⋊Dic11D811yescharacteristic
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4D811yescharacteristic
158Dic11⋊C4D811yescharacteristic
159C4×Dic11—41no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11C2×D411yescharacteristic
163C4×Dic11C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166Dic44—21no—
167Dic44—21no—
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#2207D1111yescharacteristic
183#2183—111no—
184#2176—111no—
185#2175—111no—
186C4×SD32—111no—
187C23×C11—41no—
188C23×C11—41no—
189Q8×C11—22no—
190Q8×C11—41no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—41no—
194D4×C11—41no—
195D4×C11—82no—
196D4×C11—161no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C2×D811yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—161no—
207C2×Dic11—161no—
208C2×Dic11C2×D811yescharacteristic
209C2×Dic11C2×D811yescharacteristic
210C2×Dic11C2×D811yescharacteristic
211C2×Dic11C2×D811yescharacteristic
212Dic22—41no—
213Dic22—41no—
214Dic22—41no—
215Dic22—82no—
216C8×C11—21no—
217C8×C11C2×#4111yescharacteristic
218C8×C112−1+411yescharacteristic
219C11⋊C8—21no—
220C11⋊C8—21no—
221#559—221no—
222#557—221no—
223C2×Q32—111no—
224C2×SD32C2×D1111yescharacteristic
225C2×SD32C2×D1111yescharacteristic
226#500—111no—
227#499—111no—
228#499—111no—
229#495—111no—
230#495—111no—
231#493C2×D1111yescharacteristic
232#479—221no—
233#479—221no—
234#475—221no—
235#463—221no—
236#463—221no—
237#460—221no—
238C8×Q8—111no—
239C4×Q16—111no—
240C4×Q16—111no—
241C4×Q16—111no—
242C4×Q16C2×D1111yescharacteristic
243C4×D8—111no—
244C4×D8—111no—
245#367—111no—
246#367—111no—
247#366—111no—
248C4⋊C16—111no—
249C4⋊C16—111no—
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#357C2×D1111yescharacteristic
260#357C2×D1111yescharacteristic
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—42no—
274C4×C11—81no—
275C4×C11#54811yescharacteristic
276C4×C11#57711yescharacteristic
277Dic11—21no—
278Dic11—21no—
279Dic11—21no—
280Dic11—21no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284Dic11—81no—
285C2×Q16—111no—
286C2×Q16C22×D1111yescharacteristic
287C2×SD16—221no—
288C2×SD16—221no—
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—221no—
300#124—221no—
301#124—441no—
302#123—441no—
303#123—441no—
304C4×Q8—21no—
305C4×Q8—111no—
306C4×Q8—221no—
307C4×Q8—221no—
308C4×Q8—221no—
309C4×Q8—441no—
310C4×D4—221no—
311C4×D4—221no—
312C4×D4—441no—
313Q32—222no—
314SD32—22no—
315SD32—22no—
316C2×C16—111no—
317C2×C16—111no—
318C2×C16C22×D1111yescharacteristic
319C2×C16C22×D1111yescharacteristic
320#107—111no—
321#107—111no—
322#107—111no—
323#107—221no—
324#107C22×D1111yescharacteristic
325#106—221no—
326#106—221no—
327C4⋊C8—111no—
328C4⋊C8—111no—
329C4⋊C8—111no—
330#103—21no—
331#103—221no—
332#103—221no—
333#103—221no—
334#102—221no—
335#102—221no—
336C4×C8—111no—
337C4×C8—111no—
338C4×C8C22×D1111yescharacteristic
339C2×C11—161no—
340C2×C11—161no—
341C2×C11#335811yescharacteristic
342C2×C11#341411yescharacteristic
343C2×C11#341611yescharacteristic
344C2×Q8—21no—
345C2×Q8—111no—
346C2×Q8—221no—
347C2×Q8—441no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—41no—
351C2×D4—41no—
352C22×C4—441no—
353C22×C4—441no—
354Q16—21no—
355Q16—221no—
356Q16—221no—
357Q16#434112yes—
358SD16—881no—
359SD16—881no—
360D8—21no—
361D8—21no—
362D8—21no—
363D8—21no—
364D8—81no—
365C2×C8—111no—
366C2×C8—111no—
367C2×C8D4×D1111yescharacteristic
368C2×C8C23×D1111yescharacteristic
369C4⋊C4—21no—
370C4⋊C4—41no—
371C4⋊C4—111no—
372C4⋊C4—111no—
373C4⋊C4—111no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C42—41no—
392C42—111no—
393C42—111no—
394C42—441no—
395C42—441no—
396C42—441no—
397C42D4×D1111yescharacteristic
398C16—21no—
399C16—21no—
400C16—221no—
401C16—221no—
402C11#3393811yescharacteristic, complemented, Sylow
403C23—41no—
404C23—41no—
405Q8—22no—
406Q8—41no—
407Q8—441no—
408Q8—441no—
409Q8—441no—
410Q8—882no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—82no—
416D4—161no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—111no—
420C2×C4—111no—
421C2×C4—111no—
422C2×C4—111no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—1761no—
428C2×C4—1761no—
429C2×C4D8×D1111yescharacteristic
430C2×C4D8×D1111yescharacteristic
431C2×C4C2×D4×D1111yescharacteristic
432C8—21no—
433C8—221no—
434C8—221no—
435C8C2×#434111yescharacteristic
436C8#6704311yescharacteristic
437C22—81no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C2×D8×D1111yescharacteristic
444C4—21no—
445C4—21no—
446C4—42no—
447C4—81no—
448C4—221no—
449C4—221no—
450C4—221no—
451C4—221no—
452C4—881no—
453C4—881no—
454C4—881no—
455C4—881no—
456C4#1062312911yescharacteristic
457C4#1062330611yescharacteristic
458C2—161no—
459C2—161no—
460C2#1308124611yescharacteristic
461C2#1308174811yescharacteristic
462C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2207C2
socleC22×C11C22×D8
prime radicalC11×#493C22
hypercenter#2207D11
hypocenterC11#33938
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
2. #13081507C2semidirect
4. #13070851C2semidirect
5. #13070846C2semidirect
6. #13070781C2semidirect
7. #13070771C2semidirect
8. #13070761C2semidirect
9. #13070676C2semidirect
10. #13070676C2semidirect
11. #13070523C2semidirect
12. #13070485C2semidirect
13. #13070481C2semidirect
14. SD32×Dic11C2semidirect
402. C11#33938semidirect

Maximal subgroups

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

subgroupindex
#130816302
#130815072
#130708572
#130708512
#130708462
#130707812
#130707712
#130707612
#130706762
#130705232
#130704852
#130704812
SD32×Dic112
C11×#22072
#3393811