Finite Group Databasebeta

← #14908889

Subgroups — #14908889

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079259C211yesmaximal, characteristic, complemented
2#13077492C211yesmaximal, characteristic, complemented
3#13070799C211yesmaximal, characteristic, complemented
4#13070797C211yesmaximal, characteristic, complemented
5#13070782C211yesmaximal, characteristic, complemented
6#13070771C211yesmaximal, characteristic, complemented
7#13070654C211yesmaximal, characteristic, complemented
8#13070649C211yesmaximal, characteristic, complemented
9#13070539C211yesmaximal, characteristic, complemented
10#13070489C211yesmaximal, characteristic, complemented
11#13070481C211yesmaximal, characteristic, complemented
12#13070465C211yesmaximal, characteristic, complemented
13D16×Dic11C211yesmaximal, characteristic, complemented
14#13070420C211yesmaximal, characteristic, complemented
15C11×#2186C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17#10623358—21no—
18#10623150—21no—
19C2×C11×SD32C2211yescharacteristic
20C2×C11×D16C2211yescharacteristic
21C11×#466C2211yescharacteristic
22#10622845—21no—
23Q16×Dic11C2211yescharacteristic
24Q16×Dic11C2211yescharacteristic
25C2×#66892C2211yescharacteristic
26#10622777—21no—
27#10622777—21no—
28#10622764C2211yescharacteristic
29D8×Dic11C2211yescharacteristic
30D8×Dic11C2211yescharacteristic
31D8×Dic11C2211yescharacteristic
32C2×#66890C2211yescharacteristic
33#10622728C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35#10622714C2211yescharacteristic
36#10622652—21no—
37#10622491C2211yescharacteristic
38#10622485C2211yescharacteristic
39#10622398—21no—
40#10622377—21no—
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622140C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55Dic11⋊C16C2211yescharacteristic
56C16×Dic11C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622128C2211yescharacteristic
59C2×C11×#41—21no—
60C11×#135—22no—
61C11×#135—22no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×SD16—21no—
64C2×C11×D8C2311yescharacteristic
65C2×C11×D8C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#121—21no—
68Q8×Dic11—21no—
69Q8×Dic11—21no—
70#66993—21no—
71#66992—41no—
72#66991—41no—
73D4×Dic11—21no—
74D4×Dic11—21no—
75D4×Dic11—21no—
76D4×Dic11—41no—
77D4×Dic11—41no—
78C2×#4323—21no—
79#66983—21no—
80#66979—41no—
81#66979D411yescharacteristic
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—41no—
84C2×#4318D411yescharacteristic
85C2×D88C2311yescharacteristic
86#66946—21no—
87#66943—21no—
88#66939—41no—
89#66936—41no—
90C11×SD32—22no—
91C11×D16—22no—
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#102—21no—
96#66899—21no—
97#66899—21no—
98#66896—21no—
99#66896—21no—
100#66896—21no—
101#66892—22no—
102#66890—22no—
103#66885—21no—
104#66882—21no—
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66879D411yescharacteristic
109#66879D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C8×Dic11C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66873—21no—
115#66872—21no—
116#33679—111nomaximal, Sylow
117C11×#41—24no—
118C11×#41—42no—
119C2×Q8×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C22×C4×C11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128C2×C22⋊D11—41no—
129C22×Dic11—41no—
130C22×Dic11—41no—
131C22×Dic11—41no—
132C22×Dic11—41no—
133C2×D44—21no—
134C2×C4×D11—41no—
135C11×Q16—21no—
136C11×Q16#4112yes—
137C11×SD16—24no—
138C11×D8—21no—
139C11×D8—21no—
140C11×D8—21no—
141C11×D8#4112yes—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2411yescharacteristic
146C11×C4⋊C4—21no—
147C11×C22⋊C4—41no—
148C22⋊Dic11—41no—
149C22⋊Dic11—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11D811yescharacteristic
152C22⋊Dic11D811yescharacteristic
153#4323—42no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—41no—
160C4⋊Dic11—41no—
161C4⋊Dic11—41no—
162C4⋊Dic11—41no—
163C4⋊Dic11D811yescharacteristic
164C4⋊Dic11D811yescharacteristic
165Dic11⋊C4—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#3176—111no—
180#2951—111no—
181#2233—111no—
182#2232—111no—
183#2229—111no—
184#2228—111no—
185#2207—111no—
186#2206—111no—
187#2186—111no—
188#2186D1111yescharacteristic, complemented
189#2177—111no—
190#2175—111no—
191C4×SD32—111no—
192C4×D16—111no—
193#2164—111no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11C2×D811yescharacteristic
197C22×D11—41no—
198Q8×C11—22no—
199Q8×C11—41no—
200D4×C11—22no—
201D4×C11—44no—
202D4×C11—41no—
203D4×C11—41no—
204D4×C11—41no—
205D4×C11—161no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—44no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C22⋊D11—161no—
214C22⋊D11—161no—
215C22⋊D11—161no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—161no—
220C2×Dic11—161no—
221C2×Dic11—161no—
222C2×Dic11—161no—
223C2×Dic11C2×D811yescharacteristic
224C2×Dic11C2×D811yescharacteristic
225C2×Dic11C2×D811yescharacteristic
226C2×Dic11C2×D811yescharacteristic
227D44—41no—
228D44—41no—
229C4×D11—161no—
230C8×C11—21no—
231C8×C11C2×#4111yescharacteristic
232C8×C11C2×#4111yescharacteristic
233C11⋊C8—21no—
234C11⋊C8—21no—
235C2×#135C2×D1111yescharacteristic
236#540—221no—
237#520—221no—
238C2×SD32—111no—
239C2×SD32C2×D1111yescharacteristic
240C2×D16—111no—
241C2×D16C2×D1111yescharacteristic
242#499—111no—
243#493—111no—
244#490—221no—
245#469—221no—
246#466—111no—
247#466C2×D1111yescharacteristic
248#442—221no—
249#440—221no—
250#440—221no—
251C4×Q16—111no—
252C4×Q16—111no—
253C4×D8—111no—
254C4×D8—111no—
255C4×D8—111no—
256C4×D8—111no—
257C2×#107—111no—
258#417—221no—
259#405—111no—
260#367—111no—
261#367—111no—
262#366—111no—
263#366—111no—
264C4⋊C16—111no—
265C4⋊C16—111no—
266#358—111no—
267#358C2×D1111yescharacteristic
268#357—111no—
269#357—111no—
270#357—111no—
271#357—111no—
272#357—111no—
273#357C2×D1111yescharacteristic
274C22⋊C16—111no—
275C22⋊C16C2×D1111yescharacteristic
276#346—111no—
277C4×C16—111no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—42no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11C22×D811yescharacteristic
288C2×D11—81no—
289C2×D11—81no—
290C2×D11—81no—
291C4×C11—21no—
292C4×C11—42no—
293C4×C11—81no—
294C4×C11#52511yescharacteristic
295C4×C11#57511yescharacteristic
296Dic11—21no—
297Dic11—21no—
298Dic11—21no—
299Dic11—21no—
300Dic11—81no—
301Dic11—81no—
302Dic11—81no—
303C2×#41—21no—
304#135—22no—
305#135—22no—
306C2×Q16C22×D1111yescharacteristic
307C2×SD16—21no—
308C2×D8—111no—
309C2×D8—221no—
310C2×D8C22×D1111yescharacteristic
311C2×D8C22×D1111yescharacteristic
312C2×M16—111no—
313C22×C8C22×D1111yescharacteristic
314#127—221no—
315#125—221no—
316#123—441no—
317#123—441no—
318#121—21no—
319#121—221no—
320#121—441no—
321#121—441no—
322C4×Q8—221no—
323C4×Q8—221no—
324C4×D4—221no—
325C4×D4—221no—
326C4×D4—221no—
327C4×D4—221no—
328C4×D4—441no—
329C4×D4—441no—
330#117—111no—
331#117—441no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—441no—
334SD32—22no—
335SD32—222no—
336D16—22no—
337D16—222no—
338C2×C16—111no—
339C2×C16—111no—
340C2×C16C22×D1111yescharacteristic
341C2×C16C22×D1111yescharacteristic
342#107—111no—
343#107—111no—
344#107—111no—
345#107—221no—
346#107C22×D1111yescharacteristic
347#106—221no—
348#103—221no—
349#103—221no—
350#102—21no—
351#102—221no—
352#102—221no—
353#102—221no—
354#102—221no—
355#102—221no—
356#97—111no—
357#97—111no—
358C4×C8—111no—
359C4×C8—111no—
360C2×C11—41no—
361C2×C11—82no—
362C2×C11—161no—
363C2×C11#310011yescharacteristic
364C2×C11#341511yescharacteristic
365C2×C11#341611yescharacteristic
366D11—161no—
367#41—24no—
368#41—42no—
369C2×Q8—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—221no—
375C2×D4—441no—
376C2×D4—441no—
377C2×D4—441no—
378C22×C4—41no—
379C22×C4—441no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4D4×D1111yescharacteristic
385Q16—21no—
386Q16#434112yes—
387SD16—24no—
388D8—21no—
389D8—21no—
390D8—21no—
391D8—221no—
392D8—221no—
393D8—442no—
394D8#434112yes—
395M16—441no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—111no—
399C2×C8—111no—
400C2×C8D4×D1111yescharacteristic
401C2×C8C23×D1111yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—111no—
404C4⋊C4—111no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—441no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C4⋊C4—441no—
412C4⋊C4—441no—
413C22⋊C4—41no—
414C22⋊C4—111no—
415C22⋊C4—111no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C22⋊C4—441no—
420C22⋊C4—441no—
421C42—111no—
422C42—111no—
423C42—441no—
424C42—441no—
425C16—21no—
426C16—21no—
427C16—221no—
428C16—221no—
429C11#3367911yescharacteristic, complemented, Sylow
430C23—41no—
431C23—41no—
432C23—441no—
433C23D8×D1111yescharacteristic
434Q8—22no—
435Q8—41no—
436D4—22no—
437D4—44no—
438D4—41no—
439D4—41no—
440D4—41no—
441D4—161no—
442D4—441no—
443D4—441no—
444D4—1761no—
445D4—1761no—
446D4—1761no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—44no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—111no—
453C2×C4—111no—
454C2×C4—111no—
455C2×C4—111no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—1761no—
460C2×C4—1761no—
461C2×C4—1761no—
462C2×C4—1761no—
463C2×C4—1761no—
464C2×C4D8×D1111yescharacteristic
465C2×C4C2×D4×D1111yescharacteristic
466C8—21no—
467C8—221no—
468C8—221no—
469C8C2×#434111yescharacteristic
470C8C2×#434111yescharacteristic
471C22—21no—
472C22—21no—
473C22—21no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—881no—
481C22—881no—
482C22—881no—
483C22C2×D8×D1111yescharacteristic
484C4—21no—
485C4—42no—
486C4—81no—
487C4—221no—
488C4—221no—
489C4—221no—
490C4—221no—
491C4—881no—
492C4—881no—
493C4—881no—
494C4#1062311711yescharacteristic
495C4#1062330411yescharacteristic
496C2—41no—
497C2—82no—
498C2—161no—
499C2—1761no—
500C2#1307861111yescharacteristic
501C2#1308175411yescharacteristic
502C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2186C2
socleC22×C11C22×D8
hypercenter#2186D11
hypocenterC11#33679
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2186

Complements

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

NH ≅ G/Ntype
1. #13079259C2semidirect
2. #13077492C2semidirect
3. #13070799C2semidirect
4. #13070797C2semidirect
5. #13070782C2semidirect
6. #13070771C2semidirect
7. #13070654C2semidirect
8. #13070649C2semidirect
9. #13070539C2semidirect
10. #13070489C2semidirect
11. #13070481C2semidirect
12. #13070465C2semidirect
13. D16×Dic11C2semidirect
14. #13070420C2semidirect
15. C11×#2186C2semidirect
188. #2186D11semidirect
429. C11#33679semidirect

Maximal subgroups

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

subgroupindex
#130792592
#130774922
#130707992
#130707972
#130707822
#130707712
#130706542
#130706492
#130705392
#130704892
#130704812
#130704652
D16×Dic112
#130704202
C11×#21862
#3367911