Finite Group Databasebeta

← #14908927

Subgroups — #14908927

Order 2816.

532 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079256C211yesmaximal, characteristic
2#13077484C211yesmaximal, characteristic, complemented
3#13070821C211yesmaximal, characteristic, complemented
4#13070808C211yesmaximal, characteristic
5#13070766C211yesmaximal, characteristic, complemented
6#13070756C211yesmaximal, characteristic, complemented
7#13070680C211yesmaximal, characteristic, complemented
8#13070680C211yesmaximal, characteristic, complemented
9#13070533C211yesmaximal, characteristic
10#13070487C211yesmaximal, characteristic, complemented
11#13070483C211yesmaximal, characteristic, complemented
12Q32×Dic11C211yesmaximal, characteristic, complemented
13#13070465C211yesmaximal, characteristic, complemented
14#13070420C211yesmaximal, characteristic, complemented
15C11×#2188C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17#10623343—21no—
18#10623174—21no—
19C2×C11×Q32C2211yescharacteristic
20C2×C11×Q32C2211yescharacteristic
21C11×#467C2211yescharacteristic
22#10622838—21no—
23#10622804C2211yescharacteristic
24#10622797—21no—
25#10622797—21no—
26Q16×Dic11C2211yescharacteristic
27Q16×Dic11C2211yescharacteristic
28Q16×Dic11C2211yescharacteristic
29Q16×Dic11C2211yescharacteristic
30Q16×Dic11C2211yescharacteristic
31C2×#66892C2211yescharacteristic
32C2×#66892C2211yescharacteristic
33#10622728C2211yescharacteristic
34#10622719C2211yescharacteristic
35#10622714C2211yescharacteristic
36#10622662—21no—
37#10622487C2211yescharacteristic
38#10622485C2211yescharacteristic
39#10622430—21no—
40#10622408—21no—
41C11×#358C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622140C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55Dic11⋊C16C2211yescharacteristic
56C16×Dic11C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C22×Q8×C11—21no—
60C2×C11×Q16—22no—
61C2×C11×Q16—22no—
62C2×C11×Q16—21no—
63C2×C11×Q16C2311yescharacteristic
64C2×C11×Q16C2311yescharacteristic
65C2×C11×Q16C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C22⋊Q8—21no—
68#67000—21no—
69Q8×Dic11—21no—
70Q8×Dic11—21no—
71Q8×Dic11—21no—
72Q8×Dic11—21no—
73Q8×Dic11—21no—
74Q8×Dic11—41no—
75Q8×Dic11—41no—
76C2×#4325—21no—
77#66983—21no—
78#66979—21no—
79#66979—41no—
80#66979—41no—
81#66979D411yescharacteristic
82C2×#4318D411yescharacteristic
83C2×D88C2311yescharacteristic
84#66951—41no—
85#66950—41no—
86#66946—21no—
87#66941—21no—
88#66938—41no—
89#66936—41no—
90C11×Q32—22no—
91C11×Q32—22no—
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#103—21no—
96#66899—21no—
97#66899—21no—
98#66899—21no—
99#66899—21no—
100#66899—21no—
101#66892—22no—
102#66892—22no—
103#66885—21no—
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66881—21no—
108#66879D411yescharacteristic
109#66879D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C8×Dic11C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66873—21no—
115#66871—21no—
116#33681—111nomaximal, Sylow
117C2×Q8×C11—24no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—42no—
122C2×Q8×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C2×C22⋊D11—41no—
126C2×D44—21no—
127C2×C4×D11—41no—
128C2×Dic22—41no—
129C11×Q16—24no—
130C11×Q16—21no—
131C11×Q16—21no—
132C11×Q16—21no—
133C11×Q16—21no—
134C11×Q16#4112yes—
135C11×Q16#4112yes—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2411yescharacteristic
140C11×C4⋊C4—21no—
141C11×C4⋊C4—41no—
142C11×C22⋊C4—41no—
143C22⋊Dic11—41no—
144C22⋊Dic11D811yescharacteristic
145C22⋊Dic11D811yescharacteristic
146#4325—42no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—41no—
155C4⋊Dic11—41no—
156C4⋊Dic11—41no—
157C4⋊Dic11—41no—
158C4⋊Dic11—41no—
159C4⋊Dic11D811yescharacteristic
160C4⋊Dic11D811yescharacteristic
161Dic11⋊C4—41no—
162C4×Dic11—41no—
163C4×Dic11—41no—
164C4×Dic11—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167C4×Dic11—41no—
168C4×Dic11C2×D411yescharacteristic
169C4×Dic11C2×D411yescharacteristic
170#4318—41no—
171C2×C11⋊C8C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173D88—21no—
174D88—21no—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3175—111no—
180#2950—111no—
181#2237—111no—
182#2234—111no—
183#2227—111no—
184#2225—111no—
185#2211—111no—
186#2211—111no—
187#2188D1111yescharacteristic, complemented
188#2185—111no—
189#2176—111no—
190#2175—111no—
191C4×Q32—111no—
192C4×SD32—111no—
193#2164—111no—
194C23×C11C2×D811yescharacteristic
195C22×D11—41no—
196Q8×C11—22no—
197Q8×C11—22no—
198Q8×C11—44no—
199Q8×C11—41no—
200Q8×C11—41no—
201Q8×C11—41no—
202Q8×C11—41no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—44no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C22⋊D11—161no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11C2×D811yescharacteristic
217C2×Dic11C2×D811yescharacteristic
218C2×Dic11C2×D811yescharacteristic
219C2×Dic11C2×D811yescharacteristic
220D44—41no—
221D44—41no—
222C4×D11—161no—
223Dic22—161no—
224C8×C11—21no—
225C8×C11C2×#4111yescharacteristic
226C8×C11C2×#4111yescharacteristic
227C11⋊C8—21no—
228C11⋊C8—21no—
229C22×Q16C2×D1111yescharacteristic
230#542—221no—
231#519—221no—
232C2×Q32C2×D1111yescharacteristic
233C2×Q32C2×D1111yescharacteristic
234C2×SD32—111no—
235C2×SD32—111no—
236#500—111no—
237#495—111no—
238#489—221no—
239#468—221no—
240#467C2×D1111yescharacteristic
241#466—111no—
242#441—221no—
243#441—221no—
244#440—221no—
245C4×Q16—111no—
246C4×Q16—111no—
247C4×Q16—111no—
248C4×Q16—111no—
249C4×Q16—111no—
250C4×D8—111no—
251#427—111no—
252#419—221no—
253#405—111no—
254#367—111no—
255#367—111no—
256#366—111no—
257#366—111no—
258C4⋊C16—111no—
259C4⋊C16—111no—
260#358—111no—
261#358—111no—
262#358—111no—
263#358—111no—
264#358C2×D1111yescharacteristic
265#358C2×D1111yescharacteristic
266#357—111no—
267#357—111no—
268C22⋊C16—111no—
269C22⋊C16C2×D1111yescharacteristic
270#346—111no—
271C4×C16—111no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11C22×D811yescharacteristic
276C2×D11—81no—
277C2×D11—81no—
278C2×D11—81no—
279C4×C11—21no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11#52511yescharacteristic
285C4×C11#57511yescharacteristic
286Dic11—21no—
287Dic11—21no—
288Dic11—21no—
289Dic11—21no—
290Dic11—81no—
291Dic11—81no—
292Dic11—81no—
293C22×Q8—21no—
294C2×Q16—22no—
295C2×Q16—22no—
296C2×Q16—21no—
297C2×Q16C22×D1111yescharacteristic
298C2×Q16C22×D1111yescharacteristic
299C2×Q16C22×D1111yescharacteristic
300C2×SD16—221no—
301C2×D8—111no—
302C2×M16—111no—
303C22×C8C22×D1111yescharacteristic
304C4⋊Q8—221no—
305#126—441no—
306#124—221no—
307#124—441no—
308#123—441no—
309C22⋊Q8—21no—
310C22⋊Q8—441no—
311#121—221no—
312C4×Q8—221no—
313C4×Q8—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×Q8—221no—
317C4×Q8—441no—
318C4×Q8—441no—
319C4×D4—221no—
320#117—111no—
321#117—221no—
322#117—441no—
323#117—441no—
324Q32—22no—
325Q32—22no—
326SD32—222no—
327SD32—222no—
328C2×C16—111no—
329C2×C16—111no—
330C2×C16C22×D1111yescharacteristic
331C2×C16C22×D1111yescharacteristic
332#107—111no—
333#107—111no—
334#107—111no—
335#107—221no—
336#107C22×D1111yescharacteristic
337#106—221no—
338#103—21no—
339#103—221no—
340#103—221no—
341#103—221no—
342#103—221no—
343#103—221no—
344#102—221no—
345#102—221no—
346#97—111no—
347#97—111no—
348C4×C8—111no—
349C4×C8—111no—
350C2×C11—41no—
351C2×C11#310011yescharacteristic
352C2×C11#341611yescharacteristic
353C2×C11#341711yescharacteristic
354D11—161no—
355C2×Q8—24no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—42no—
360C2×Q8—41no—
361C2×Q8—441no—
362C2×D4—221no—
363C2×D4—441no—
364C22×C4—41no—
365C22×C4—441no—
366C22×C4D4×D1111yescharacteristic
367Q16—24no—
368Q16—21no—
369Q16—21no—
370Q16—21no—
371Q16—21no—
372Q16#434112yes—
373Q16#434112yes—
374SD16—442no—
375D8—221no—
376D8—221no—
377M16—441no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—111no—
381C2×C8—111no—
382C2×C8D4×D1111yescharacteristic
383C2×C8C23×D1111yescharacteristic
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—111no—
387C4⋊C4—111no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C22⋊C4—41no—
398C22⋊C4—111no—
399C22⋊C4—111no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C22⋊C4—441no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C42—111no—
406C42—111no—
407C42—441no—
408C42—441no—
409C42—441no—
410C42—441no—
411C42—441no—
412C42—441no—
413C16—21no—
414C16—21no—
415C16—221no—
416C16—221no—
417C11#3368111yescharacteristic, complemented, Sylow
418C23—441no—
419C23D8×D1111yescharacteristic
420Q8—22no—
421Q8—22no—
422Q8—44no—
423Q8—41no—
424Q8—41no—
425Q8—41no—
426Q8—41no—
427Q8—1761no—
428D4—441no—
429D4—441no—
430D4—1761no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—44no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—111no—
439C2×C4—111no—
440C2×C4—111no—
441C2×C4—111no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—1761no—
446C2×C4D8×D1111yescharacteristic
447C2×C4C2×D4×D1111yescharacteristic
448C8—21no—
449C8—221no—
450C8—221no—
451C8C2×#434111yescharacteristic
452C8C2×#434111yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—881no—
457C22—881no—
458C22—881no—
459C22C2×D8×D1111yescharacteristic
460C4—21no—
461C4—42no—
462C4—42no—
463C4—81no—
464C4—81no—
465C4—221no—
466C4—221no—
467C4—221no—
468C4—221no—
469C4—881no—
470C4—881no—
471C4—881no—
472C4#1062311711yescharacteristic
473C4#1062330411yescharacteristic
474C2—41no—
475C2—1761no—
476C2#1307861111yescharacteristic
477C2#1308176111yescharacteristic
478C2#1308176511yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2188C2
socleC22×C11C22×D8
prime radical#10622728C22
hypercenter#2188D11
hypocenterC11#33681
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2188

Complements

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

NH ≅ G/Ntype
2. #13077484C2semidirect
3. #13070821C2semidirect
5. #13070766C2semidirect
6. #13070756C2semidirect
7. #13070680C2semidirect
8. #13070680C2semidirect
10. #13070487C2semidirect
11. #13070483C2semidirect
12. Q32×Dic11C2semidirect
13. #13070465C2semidirect
14. #13070420C2semidirect
15. C11×#2188C2semidirect
187. #2188D11semidirect
417. C11#33681semidirect

Maximal subgroups

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

subgroupindex
#130792562
#130774842
#130708212
#130708082
#130707662
#130707562
#130706802
#130705332
#130704872
#130704832
Q32×Dic112
#130704652
#130704202
C11×#21882
#3368111