Finite Group Databasebeta

← #14908817

Subgroups — #14908817

Order 2816.

586 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079192C211yesmaximal, characteristic
2C4×Q16×D11C211yesmaximal, characteristic, complemented
3#13070798C211yesmaximal, characteristic, complemented
4#13070795C211yesmaximal, characteristic, complemented
5#13070767C211yesmaximal, characteristic, complemented
6#13070766C211yesmaximal, characteristic, complemented
7#13070655C211yesmaximal, characteristic, complemented
8#13070654C211yesmaximal, characteristic, complemented
9#13070534C211yesmaximal, characteristic, complemented
10#13070531C211yesmaximal, characteristic, complemented
11#13070482C211yesmaximal, characteristic, complemented
12#13070480C211yesmaximal, characteristic, complemented
13#13070478C211yesmaximal, characteristic, complemented
14#13070417C211yesmaximal, characteristic, complemented
15C11×#2175C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C4×Q8×D11—21no—
18#10623079—21no—
19C2×C11×SD32C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21C4×C11×D8C2211yescharacteristic
22Q16×Dic11C2211yescharacteristic
23C2×#66892C2211yescharacteristic
24#10622770C2211yescharacteristic
25#10622764C2211yescharacteristic
26C2×#66891C2211yescharacteristic
27C4×#4326—21no—
28C4×#4323—21no—
29C2×#66864C2211yescharacteristic
30#10622496C2211yescharacteristic
31D11×#107C2211yescharacteristic
32#10622487C2211yescharacteristic
33#10622486C2211yescharacteristic
34D11×#103—21no—
35#10622403—21no—
36#10622388—21no—
37#10622373—21no—
38C4×Dic44C2211yescharacteristic
39C4×D88C2211yescharacteristic
40C4×C8×D11C2211yescharacteristic
41C11×#366C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×#346C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622147C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50#10622142C2211yescharacteristic
51#10622141C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×Q8×D11—21no—
60C2×#4339—41no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C4×Q8×C11—21no—
64C4×D4×C11—21no—
65Q8×Dic11—21no—
66C2×#4326—21no—
67#66993—21no—
68#66991—21no—
69C2×#4323—21no—
70C4×C22⋊D11—41no—
71Q16×D11—22no—
72Q16×D11—22no—
73C2×Dic44C2311yescharacteristic
74C2×D88C2311yescharacteristic
75C2×C8×D11D411yescharacteristic
76C2×C8×D11C2311yescharacteristic
77#66948—21no—
78C4⋊C4×D11—21no—
79C4⋊C4×D11—41no—
80#66941—21no—
81#66940—21no—
82#66940—41no—
83#66938—41no—
84#66937—41no—
85C4×D44—21no—
86C42×D11—41no—
87C42×D11D411yescharacteristic
88C4×Dic22—21no—
89C4×Dic22—41no—
90C11×SD32—22no—
91C2×C11×C16C2311yescharacteristic
92C2×C11×C16C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#103—21no—
96C11×#102—21no—
97C4×C8×C11C2311yescharacteristic
98#66899—21no—
99#66896—21no—
100#66892—22no—
101#66891—22no—
102#66885—21no—
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66880—21no—
106C8×Dic11D411yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66874—21no—
111#66873—21no—
112#66871—21no—
113#66871—21no—
114C4×C11⋊C8D411yescharacteristic
115#66864—22no—
116#33672—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C22×C4×C11—41no—
120C2×C22⋊D11—41no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123Q8×D11—24no—
124Q8×D11—42no—
125#4339—84no—
126C2×D44—21no—
127C2×D44—41no—
128C2×C4×D11—41no—
129C2×C4×D11—41no—
130C2×C4×D11—41no—
131C2×C4×D11D811yescharacteristic
132C2×C4×D11D811yescharacteristic
133C2×C4×D11C2×D411yescharacteristic
134C2×Dic22—21no—
135C2×Dic22—41no—
136C2×Dic22—41no—
137C11×Q16—21no—
138C11×Q16#4112yescomplemented
139C11×D8—21no—
140C11×D8—21no—
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2411yescharacteristic
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—41no—
146C11×C22⋊C4—41no—
147C42×C11—41no—
148C42×C11C2×D411yescharacteristic
149C22⋊Dic11—41no—
150#4326—24no—
151#4323—42no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163C4×Dic11—41no—
164C4×Dic11D811yescharacteristic
165C4×Dic11D811yescharacteristic
166C4×Dic11C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169Dic44—21no—
170Dic44#4112yescomplemented
171D88—21no—
172D88—21no—
173C8×D11—21no—
174C8×D11—21no—
175C8×D11—41no—
176C11×C16—21no—
177C11×C16—21no—
178C11⋊C16—21no—
179C11⋊C16—21no—
180#3169—111no—
181C2×C4×Q16—111no—
182#2232—111no—
183#2232—111no—
184#2227—111no—
185#2227—111no—
186#2207—111no—
187#2207—111no—
188#2185—111no—
189#2185—111no—
190#2175—111no—
191#2175—111no—
192#2175—111no—
193#2175D1111yescharacteristic, complemented
194#2163—111no—
195C23×C11—41no—
196C22×D11—41no—
197C22×D11C2×D811yescharacteristic
198Q8×C11—22no—
199Q8×C11—41no—
200D4×C11—41no—
201D4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—82no—
206C2×C4×C11C2×D811yescharacteristic
207C2×C4×C11C2×D811yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C22⋊D11—82no—
210C22⋊D11—82no—
211C22⋊D11—82no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11C2×D811yescharacteristic
216C2×Dic11C2×D811yescharacteristic
217C2×Dic11C2×D811yescharacteristic
218D44—41no—
219D44—41no—
220D44—82no—
221C4×D11—22no—
222C4×D11—21no—
223C4×D11—21no—
224C4×D11—22no—
225C4×D11—44no—
226C4×D11—82no—
227C4×D11—82no—
228Dic22—22no—
229Dic22—44no—
230Dic22—41no—
231Dic22—82no—
232C8×C11—21no—
233C8×C11C2×#4111yescharacteristic
234C8×C11C2×#4111yescharacteristic
235C11⋊C8—21no—
236C11⋊C8—21no—
237C22×Q16—111no—
238#532—221no—
239C2×C4×Q8—221no—
240C2×SD32—111no—
241C2×SD32—111no—
242C2×SD32—111no—
243C2×SD32C2×D1111yescharacteristic
244#500—111no—
245#493—111no—
246#486—221no—
247#466—111no—
248#466—111no—
249#466—221no—
250C4×Q16—111no—
251C4×Q16—111no—
252C4×Q16—111no—
253C4×Q16—221no—
254C4×Q16—221no—
255C4×Q16C2×D1111yescharacteristic
256C4×D8—111no—
257C4×D8—221no—
258C4×D8C2×D1111yescharacteristic
259C2×#107—111no—
260C2×#103—221no—
261C2×C4×C8—111no—
262#366—111no—
263#366—111no—
264#366—111no—
265#366C2×D1111yescharacteristic
266C4⋊C16—111no—
267C4⋊C16—111no—
268#358—111no—
269#358—111no—
270#358—111no—
271#358C2×D1111yescharacteristic
272#357—111no—
273#357—111no—
274#357—111no—
275#357C2×D1111yescharacteristic
276C22⋊C16—111no—
277C22⋊C16—111no—
278#346—111no—
279#346C2×D1111yescharacteristic
280C22×C11—81no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11C22×D811yescharacteristic
284C2×D11—21no—
285C2×D11—21no—
286C2×D11—81no—
287C2×D11—81no—
288C2×D11—81no—
289C2×D11#50912yes—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—42no—
293C4×C11—81no—
294C4×C11—81no—
295C4×C11#52511yescharacteristic
296C4×C11#57511yescharacteristic
297Dic11—21no—
298Dic11—21no—
299Dic11—42no—
300Dic11—81no—
301Dic11—81no—
302Dic11#51012yes—
303C2×#41—441no—
304C22×Q8—221no—
305C2×Q16—111no—
306C2×Q16—221no—
307C2×Q16—222no—
308C2×Q16—222no—
309C2×Q16C22×D1111yescharacteristic
310C2×D8—111no—
311C2×D8—221no—
312C2×D8C22×D1111yescharacteristic
313C22×C8—111no—
314C22×C8—111no—
315C4⋊Q8—221no—
316#127—221no—
317#124—441no—
318#121—221no—
319#121—221no—
320#121—441no—
321C4×Q8—21no—
322C4×Q8—221no—
323C4×Q8—221no—
324C4×Q8—221no—
325C4×Q8—441no—
326C4×Q8—441no—
327C4×D4—21no—
328C4×D4—221no—
329C4×D4—441no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—441no—
332C2×C42—111no—
333C2×C42—441no—
334SD32—22no—
335SD32—222no—
336SD32—222no—
337SD32—222no—
338C2×C16—111no—
339C2×C16—111no—
340C2×C16C22×D1111yescharacteristic
341C2×C16C22×D1111yescharacteristic
342#107—111no—
343#107—111no—
344#107—221no—
345#107—221no—
346#107C22×D1111yescharacteristic
347#107C22×D1111yescharacteristic
348#103—21no—
349#103—221no—
350#103—221no—
351#103—221no—
352#102—21no—
353#102—221no—
354#102—221no—
355#102—221no—
356C4×C8—111no—
357C4×C8—111no—
358C4×C8—111no—
359C4×C8C22×D1111yescharacteristic
360C2×C11—161no—
361C2×C11#310011yescharacteristic
362C2×C11C2×#50911yescharacteristic
363C2×C11C2×#51011yescharacteristic
364D11—22no—
365D11—161no—
366#41—884no—
367C2×Q8—21no—
368C2×Q8—224no—
369C2×Q8—221no—
370C2×Q8—441no—
371C2×Q8—441no—
372C2×Q8—442no—
373C2×D4—21no—
374C2×D4—221no—
375C2×D4—441no—
376C2×D4—441no—
377C2×D4—441no—
378C2×D4—441no—
379C22×C4—41no—
380C22×C4—111no—
381C22×C4—111no—
382C22×C4—111no—
383C22×C4—441no—
384C22×C4—441no—
385C22×C4—441no—
386Q16—21no—
387Q16—112no—
388Q16—224no—
389Q16—221no—
390Q16#433912yescomplemented
391D8—21no—
392D8—21no—
393D8—221no—
394D8—221no—
395D8—442no—
396C2×C8—111no—
397C2×C8—111no—
398C2×C8—221no—
399C2×C8—221no—
400C2×C8—441no—
401C2×C8D4×D1111yescharacteristic
402C2×C8C23×D1111yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
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—441no—
415C22⋊C4—441no—
416C22⋊C4—441no—
417C42—41no—
418C42—111no—
419C42—111no—
420C42—111no—
421C42—441no—
422C42—441no—
423C42—441no—
424C42D4×D1111yescharacteristic
425C16—21no—
426C16—21no—
427C16—221no—
428C16—221no—
429C11#3367211yescharacteristic, complemented, Sylow
430C23—41no—
431C23—111no—
432C23—441no—
433Q8—22no—
434Q8—41no—
435Q8—222no—
436Q8—444no—
437Q8—441no—
438Q8—882no—
439D4—41no—
440D4—41no—
441D4—441no—
442D4—441no—
443D4—882no—
444D4—882no—
445D4—882no—
446D4—882no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—82no—
451C2×C4—111no—
452C2×C4—111no—
453C2×C4—111no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—444no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—882no—
463C2×C4—882no—
464C2×C4D8×D1111yescharacteristic
465C2×C4D8×D1111yescharacteristic
466C2×C4C2×D4×D1111yescharacteristic
467C8—21no—
468C8—221no—
469C8—221no—
470C8C2×#433911yescharacteristic
471C8#41×D1111yescharacteristic
472C22—81no—
473C22—81no—
474C22—81no—
475C22—112no—
476C22—221no—
477C22—221no—
478C22—881no—
479C22—881no—
480C22—881no—
481C22C2×D8×D1111yescharacteristic
482C4—21no—
483C4—21no—
484C4—42no—
485C4—81no—
486C4—81no—
487C4—112no—
488C4—221no—
489C4—221no—
490C4—442no—
491C4—881no—
492C4—881no—
493C4#1062307811yescharacteristic
494C4#1062329911yescharacteristic
495C2—161no—
496C2—222no—
497C2—1761no—
498C2#1307861411yescharacteristic
499C2D11×#50911yescharacteristic
500C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2175C2
socleC22×C11C22×D8
prime radical#13079192C2
hypercenter#2175D11
hypocenterC11#33672
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
2. C4×Q16×D11C2semidirect
3. #13070798C2semidirect
4. #13070795C2semidirect
5. #13070767C2semidirect
6. #13070766C2semidirect
7. #13070655C2semidirect
8. #13070654C2semidirect
9. #13070534C2semidirect
10. #13070531C2semidirect
11. #13070482C2semidirect
12. #13070480C2semidirect
13. #13070478C2semidirect
14. #13070417C2semidirect
15. C11×#2175C2semidirect
138. C11×Q16#41semidirect
170. Dic44#41semidirect
193. #2175D11semidirect
390. Q16#4339semidirect
429. C11#33672semidirect

Maximal subgroups

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

subgroupindex
#130791922
C4×Q16×D112
#130707982
#130707952
#130707672
#130707662
#130706552
#130706542
#130705342
#130705312
#130704822
#130704802
#130704782
#130704172
C11×#21752
#3367211