Finite Group Databasebeta

← #14911463

Subgroups — #14911463

Order 2816.

472 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081601C211yesmaximal, characteristic
2#13081507C211yesmaximal, characteristic, complemented
3#13070847C211yesmaximal, characteristic
4#13070846C211yesmaximal, characteristic
5#13070842C211yesmaximal, characteristic, complemented
6#13070781C211yesmaximal, characteristic, complemented
7#13070778C211yesmaximal, characteristic, complemented
8#13070751C211yesmaximal, characteristic
9#13070676C211yesmaximal, characteristic
10#13070664C211yesmaximal, characteristic, complemented
11#13070518C211yesmaximal, characteristic, complemented
12Q32×Dic11C211yesmaximal, characteristic, complemented
13C4×#66893C211yesmaximal, characteristic, complemented
14SD32×Dic11C211yesmaximal, characteristic
15C11×#2211C211yesmaximal, characteristic
16#10623202—21no—
17#10623100—21no—
18C2×C11×Q32C2211yescharacteristic
19C2×C11×SD32C2211yescharacteristic
20C11×#495C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22Q16×Dic11C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24Q16×Dic11C2211yescharacteristic
25#10622794C2211yescharacteristic
26C2×#66893C2211yescharacteristic
27#10622779—21no—
28#10622775—21no—
29#10622768C2211yescharacteristic
30D8×Dic11C2211yescharacteristic
31#10622667—21no—
32#10622635—21no—
33#10622491C2211yescharacteristic
34#10622487C2211yescharacteristic
35#10622412—21no—
36#10622404—21no—
37C4×Dic44C2211yescharacteristic
38#10622296C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×C4⋊C16C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622143C2211yescharacteristic
49#10622142C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55C16×Dic11C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×Q16C2311yescharacteristic
61C2×C11×SD16—21no—
62C2×C11×D8C2311yescharacteristic
63C11×#124—21no—
64C4×Q8×C11—21no—
65Q8×Dic11—21no—
66Q8×Dic11—21no—
67Q8×Dic11—21no—
68#66997—21no—
69C2×#4326—21no—
70#66989—21no—
71D4×Dic11—21no—
72C2×#4324—21no—
73C2×Dic44C2311yescharacteristic
74#66943—21no—
75#66943—41no—
76#66941—21no—
77#66941—41no—
78#66932—41no—
79#66932—41no—
80#66931—41no—
81#66930—41no—
82#66923—21no—
83#66923—41no—
84C4×Dic22—21no—
85C4×Dic22—41no—
86C4×Dic22D411yescharacteristic
87C11×Q32—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#66899—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#33931—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×D4×C11—21no—
117C22×Dic11—41no—
118C2×Dic22—21no—
119C2×Dic22—41no—
120C2×Dic22D811yescharacteristic
121C11×Q16—21no—
122C11×Q16—21no—
123C11×Q16—21no—
124C11×Q16#4112yes—
125C11×SD16—81no—
126C11×D8—21no—
127C11×D8—21no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2411yescharacteristic
130C11×C4⋊C4—21no—
131C11×C4⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C42×C11—41no—
135C42×C11C2×D411yescharacteristic
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138C22⋊Dic11—41no—
139#4326—81no—
140#4324—81no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—41no—
145C4⋊Dic11—41no—
146C4⋊Dic11—41no—
147C4⋊Dic11—41no—
148C4⋊Dic11D811yescharacteristic
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4D811yescharacteristic
157Dic11⋊C4D811yescharacteristic
158C4×Dic11—41no—
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#3393—111no—
173#3383—111no—
174#2242—111no—
175#2242—111no—
176#2241—111no—
177#2229—111no—
178#2229—111no—
179#2224—111no—
180#2211—111no—
181#2211D1111yescharacteristic
182#2209—111no—
183Q8×C16—111no—
184C4×Q32—111no—
185C4×Q32—111no—
186C4×SD32—111no—
187C23×C11—41no—
188Q8×C11—22no—
189Q8×C11—41no—
190Q8×C11—41no—
191Q8×C11—41no—
192D4×C11—41no—
193D4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11C2×D811yescharacteristic
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—82no—
205C2×Dic11C2×D811yescharacteristic
206C2×Dic11C2×D811yescharacteristic
207C2×Dic11C2×D811yescharacteristic
208C2×Dic11C2×D811yescharacteristic
209Dic22—22no—
210Dic22—41no—
211Dic22—41no—
212Dic22—82no—
213C8×C11—21no—
214C8×C11C2×#4111yescharacteristic
215C8×C112−1+411yescharacteristic
216C11⋊C8—21no—
217C11⋊C8—21no—
218#557—221no—
219#556—221no—
220C2×Q32—111no—
221C2×Q32C2×D1111yescharacteristic
222C2×SD32C2×D1111yescharacteristic
223#500—111no—
224#499—111no—
225#499—111no—
226#495—111no—
227#495C2×D1111yescharacteristic
228#494—111no—
229#479—221no—
230#479—221no—
231#475—221no—
232#464—221no—
233#464—221no—
234#461—221no—
235C8×Q8—111no—
236C4×Q16—111no—
237C4×Q16—111no—
238C4×Q16—111no—
239C4×Q16—111no—
240C4×Q16C2×D1111yescharacteristic
241C4×D8—111no—
242#367—111no—
243#366—111no—
244#366—111no—
245C4⋊C16—111no—
246C4⋊C16—111no—
247C4⋊C16C2×D1111yescharacteristic
248#358—111no—
249#358—111no—
250#358—111no—
251#358—111no—
252#358—111no—
253#358—111no—
254#358C2×D1111yescharacteristic
255#357—111no—
256#357—111no—
257#357C2×D1111yescharacteristic
258C4×C16—111no—
259C4×C16—111no—
260C4×C16—111no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11C22×D811yescharacteristic
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—42no—
268C4×C11—81no—
269C4×C11—81no—
270C4×C11#54811yescharacteristic
271C4×C11#57711yescharacteristic
272Dic11—21no—
273Dic11—21no—
274Dic11—21no—
275Dic11—81no—
276Dic11—81no—
277Dic11—81no—
278Dic11—81no—
279Dic11#50812yes—
280C2×Q16—111no—
281C2×Q16—221no—
282C2×Q16C22×D1111yescharacteristic
283C2×Q16C22×D1111yescharacteristic
284C2×SD16—21no—
285C2×SD16—221no—
286C2×D8C22×D1111yescharacteristic
287C4⋊Q8—221no—
288C4⋊Q8—221no—
289C4⋊Q8—441no—
290#126—441no—
291#126—441no—
292#125—221no—
293#125—221no—
294#125—441no—
295#125—441no—
296#124—21no—
297#124—221no—
298C22⋊Q8—441no—
299C4×Q8—21no—
300C4×Q8—111no—
301C4×Q8—221no—
302C4×Q8—221no—
303C4×Q8—221no—
304C4×Q8—221no—
305C4×Q8—441no—
306C4×D4—221no—
307#117—441no—
308Q32—22no—
309Q32—222no—
310SD32—22no—
311C2×C16—111no—
312C2×C16—111no—
313C2×C16C22×D1111yescharacteristic
314C2×C16C22×D1111yescharacteristic
315#107—111no—
316#107—111no—
317#107—111no—
318#107—221no—
319#107C22×D1111yescharacteristic
320#106—221no—
321#106—221no—
322C4⋊C8—111no—
323C4⋊C8—111no—
324C4⋊C8—111no—
325#103—21no—
326#103—221no—
327#103—221no—
328#103—221no—
329#103—221no—
330#102—221no—
331C4×C8—111no—
332C4×C8—111no—
333C4×C8C22×D1111yescharacteristic
334C2×C11—161no—
335C2×C11#335811yescharacteristic
336C2×C11C2×#50811yescharacteristic
337C2×C11#341711yescharacteristic
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—111no—
341C2×Q8—221no—
342C2×Q8—441no—
343C2×D4—21no—
344C22×C4—441no—
345Q16—21no—
346Q16—21no—
347Q16—21no—
348Q16—221no—
349Q16—221no—
350Q16—881no—
351Q16#434112yes—
352SD16—81no—
353SD16—881no—
354D8—21no—
355D8—21no—
356C2×C8—111no—
357C2×C8—111no—
358C2×C8D4×D1111yescharacteristic
359C2×C8C23×D1111yescharacteristic
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—111no—
363C4⋊C4—111no—
364C4⋊C4—111no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—441no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C4⋊C4—441no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—441no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C42—41no—
385C42—111no—
386C42—111no—
387C42—441no—
388C42—441no—
389C42—441no—
390C42—441no—
391C42D4×D1111yescharacteristic
392C16—21no—
393C16—21no—
394C16—221no—
395C16—221no—
396C11#3393111yescharacteristic, complemented, Sylow
397C23—41no—
398Q8—22no—
399Q8—41no—
400Q8—41no—
401Q8—41no—
402Q8—222no—
403Q8—441no—
404Q8—441no—
405Q8—882no—
406D4—41no—
407D4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—111no—
412C2×C4—111no—
413C2×C4—111no—
414C2×C4—111no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—882no—
420C2×C4D8×D1111yescharacteristic
421C2×C4D8×D1111yescharacteristic
422C2×C4C2×D4×D1111yescharacteristic
423C8—21no—
424C8—221no—
425C8—221no—
426C8C2×#434111yescharacteristic
427C8#6704311yescharacteristic
428C22—81no—
429C22—81no—
430C22—81no—
431C22C2×D8×D1111yescharacteristic
432C4—21no—
433C4—21no—
434C4—42no—
435C4—81no—
436C4—81no—
437C4—112no—
438C4—221no—
439C4—221no—
440C4—221no—
441C4—881no—
442C4—881no—
443C4—881no—
444C4—881no—
445C4#1062312911yescharacteristic
446C4#1062330611yescharacteristic
447C2—161no—
448C2#1308124611yescharacteristic
449C2D11×#50811yescharacteristic
450C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2211C2
socleC22×C11C22×D8
prime radicalC2×C11×D8C23
hypercenter#2211D11
hypocenterC11#33931
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2211

Complements

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

NH ≅ G/Ntype
2. #13081507C2semidirect
5. #13070842C2semidirect
6. #13070781C2semidirect
7. #13070778C2semidirect
10. #13070664C2semidirect
11. #13070518C2semidirect
12. Q32×Dic11C2semidirect
13. C4×#66893C2semidirect
396. C11#33931semidirect

Maximal subgroups

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

subgroupindex
#130816012
#130815072
#130708472
#130708462
#130708422
#130707812
#130707782
#130707512
#130706762
#130706642
#130705182
Q32×Dic112
C4×#668932
SD32×Dic112
C11×#22112
#3393111