Finite Group Databasebeta

← #14911474

Subgroups — #14911474

Order 2816.

484 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#13081625C211yesmaximal, characteristic
2#13081507C211yesmaximal, characteristic, complemented
3#13070849C211yesmaximal, characteristic, complemented
4#13070847C211yesmaximal, characteristic, complemented
5#13070838C211yesmaximal, characteristic
6#13070774C211yesmaximal, characteristic, complemented
7#13070771C211yesmaximal, characteristic, complemented
8#13070756C211yesmaximal, characteristic, complemented
9#13070680C211yesmaximal, characteristic, complemented
10#13070654C211yesmaximal, characteristic
11#13070518C211yesmaximal, characteristic, complemented
12Q32×Dic11C211yesmaximal, characteristic, complemented
13SD32×Dic11C211yesmaximal, characteristic, complemented
14C4×#66892C211yesmaximal, characteristic, complemented
15C11×#2211C211yesmaximal, characteristic, complemented
16#10623212—21no—
17#10623100—21no—
18C2×C11×Q32C2211yescharacteristic
19C2×C11×SD32C2211yescharacteristic
20C11×#495C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22#10622804C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24Q16×Dic11C2211yescharacteristic
25Q16×Dic11C2211yescharacteristic
26C2×#66892C2211yescharacteristic
27#10622778—21no—
28#10622776—21no—
29#10622764C2211yescharacteristic
30D8×Dic11C2211yescharacteristic
31#10622670—21no—
32#10622635—21no—
33#10622491C2211yescharacteristic
34#10622487C2211yescharacteristic
35#10622412—21no—
36#10622404—21no—
37C4×D88C2211yescharacteristic
38#10622296C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×C4⋊C16C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622142C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55C16×Dic11C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×Q16C2311yescharacteristic
61C2×C11×SD16—21no—
62C2×C11×D8C2311yescharacteristic
63C11×#124—21no—
64C4×Q8×C11—21no—
65#67000—21no—
66Q8×Dic11—21no—
67Q8×Dic11—21no—
68Q8×Dic11—21no—
69C2×#4325—21no—
70#66993—21no—
71D4×Dic11—21no—
72C2×#4323—21no—
73C2×D88C2311yescharacteristic
74#66943—21no—
75#66943—41no—
76#66941—21no—
77#66941—41no—
78#66939—41no—
79#66938—41no—
80#66936—41no—
81(C22⋊D11)⋊C4—41no—
82C4×D44—21no—
83#66923—21no—
84#66923—41no—
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#66892—22no—
99#66885—21no—
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66881—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#33932—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×D4×C11—21no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119C22×Dic11—41no—
120C2×D44—21no—
121C2×C4×D11—41no—
122C2×Dic22—41no—
123C2×Dic22D811yescharacteristic
124C11×Q16—21no—
125C11×Q16—21no—
126C11×Q16—21no—
127C11×Q16#4112yes—
128C11×SD16—81no—
129C11×D8—21no—
130C11×D8—21no—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2411yescharacteristic
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C42×C11—41no—
138C42×C11C2×D411yescharacteristic
139C22⋊Dic11—41no—
140#4325—81no—
141#4323—81no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152C4⋊Dic11D811yescharacteristic
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
166D88—21no—
167D88—21no—
168C11×C16—21no—
169C11×C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3396—111no—
173#3383—111no—
174#2242—111no—
175#2242—111no—
176#2240—111no—
177#2228—111no—
178#2228—111no—
179#2225—111no—
180#2211—111no—
181#2211D1111yescharacteristic, complemented
182#2207—111no—
183Q8×C16—111no—
184C4×Q32—111no—
185C4×SD32—111no—
186C4×SD32—111no—
187C23×C11—41no—
188C22×D11—41no—
189Q8×C11—22no—
190Q8×C11—41no—
191Q8×C11—41no—
192Q8×C11—41no—
193D4×C11—41no—
194D4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C22⋊D11—82no—
202C22⋊D11—161no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—161no—
207C2×Dic11C2×D811yescharacteristic
208C2×Dic11C2×D811yescharacteristic
209C2×Dic11C2×D811yescharacteristic
210C2×Dic11C2×D811yescharacteristic
211D44—41no—
212D44—41no—
213C4×D11—161no—
214Dic22—22no—
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×Q32C2×D1111yescharacteristic
224C2×SD32—111no—
225C2×SD32C2×D1111yescharacteristic
226#500—111no—
227#499—111no—
228#499—111no—
229#495—111no—
230#495C2×D1111yescharacteristic
231#493—111no—
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#358C2×D1111yescharacteristic
255#357—111no—
256#357—111no—
257#357—111no—
258#357—111no—
259#357—111no—
260#357C2×D1111yescharacteristic
261C4×C16—111no—
262C4×C16—111no—
263C4×C16—111no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11C22×D811yescharacteristic
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—42no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11#54811yescharacteristic
277C4×C11#57711yescharacteristic
278Dic11—21no—
279Dic11—21no—
280Dic11—21no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284Dic11#50812yes—
285C2×Q16C22×D1111yescharacteristic
286C2×Q16C22×D1111yescharacteristic
287C2×SD16—21no—
288C2×SD16—221no—
289C2×D8—111no—
290C2×D8—221no—
291C2×D8C22×D1111yescharacteristic
292C4⋊Q8—221no—
293C4⋊Q8—441no—
294#127—221no—
295#125—221no—
296#125—221no—
297#125—441no—
298#125—441no—
299#124—21no—
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—22no—
314SD32—22no—
315SD32—222no—
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#335811yescharacteristic
341C2×C11C2×#50811yescharacteristic
342C2×C11#341611yescharacteristic
343D11—161no—
344C2×Q8—21no—
345C2×Q8—21no—
346C2×Q8—111no—
347C2×Q8—441no—
348C2×D4—21no—
349C2×D4—221no—
350C2×D4—441no—
351C2×D4—441no—
352C22×C4—441no—
353C22×C4—441no—
354Q16—21no—
355Q16—21no—
356Q16—21no—
357Q16#434112yes—
358SD16—81no—
359SD16—881no—
360D8—21no—
361D8—21no—
362D8—221no—
363D8—221no—
364D8—881no—
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—41no—
386C22⋊C4—41no—
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#3393211yescharacteristic, complemented, Sylow
403C23—41no—
404C23—441no—
405Q8—22no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409Q8—222no—
410Q8—882no—
411D4—41no—
412D4—41no—
413D4—441no—
414D4—441no—
415D4—882no—
416D4—1761no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—111no—
421C2×C4—111no—
422C2×C4—111no—
423C2×C4—111no—
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—881no—
441C22—881no—
442C22—881no—
443C22C2×D8×D1111yescharacteristic
444C4—21no—
445C4—21no—
446C4—42no—
447C4—81no—
448C4—81no—
449C4—112no—
450C4—221no—
451C4—221no—
452C4—221no—
453C4—881no—
454C4—881no—
455C4—881no—
456C4#1062312911yescharacteristic
457C4#1062330611yescharacteristic
458C2—161no—
459C2—1761no—
460C2#1308124611yescharacteristic
461C2D11×#50811yescharacteristic
462C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2211C2
socleC22×C11C22×D8
prime radical#10622764C22
hypercenter#2211D11
hypocenterC11#33932
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
3. #13070849C2semidirect
4. #13070847C2semidirect
6. #13070774C2semidirect
7. #13070771C2semidirect
8. #13070756C2semidirect
9. #13070680C2semidirect
11. #13070518C2semidirect
12. Q32×Dic11C2semidirect
13. SD32×Dic11C2semidirect
14. C4×#66892C2semidirect
15. C11×#2211C2semidirect
181. #2211D11semidirect
402. C11#33932semidirect

Maximal subgroups

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

subgroupindex
#130816252
#130815072
#130708492
#130708472
#130708382
#130707742
#130707712
#130707562
#130706802
#130706542
#130705182
Q32×Dic112
SD32×Dic112
C4×#668922
C11×#22112
#3393211