Finite Group Databasebeta

← #14798879

Subgroups — #14798879

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077476C211yesmaximal, characteristic, complemented
2#13070083C211yesmaximal, characteristic, complemented
3#13070076C211yesmaximal, characteristic, complemented
4#13069893C211yesmaximal, characteristic, complemented
5#13069886C211yesmaximal, characteristic
6#13069521C211yesmaximal, characteristic, complemented
7#13069404C211yesmaximal, characteristic, complemented
8#13069112C211yesmaximal, characteristic, complemented
9#13069105C211yesmaximal, characteristic
10#13068741C211yesmaximal, characteristic, complemented
11#13068728C211yesmaximal, characteristic, complemented
12#13068725C211yesmaximal, characteristic, complemented
13#13068670C211yesmaximal, characteristic, complemented
14#13068416C211yesmaximal, characteristic, complemented
15C2×C11×#471C211yesmaximal, characteristic
16C2×C11×#137C2211yescharacteristic
17C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×#131C2211yescharacteristic
20#10623343C2211yescharacteristic
21#10623329C2211yescharacteristic
22C11×#471—22no—
23C11×#471—22no—
24C2×C11×#108C2211yescharacteristic
25C2×C11×#101C2211yescharacteristic
26C2×C11×#100C2211yescharacteristic
27#10622853C2211yescharacteristic
28#10622850C2211yescharacteristic
29#10622849C2211yescharacteristic
30#10622849C2211yescharacteristic
31C2×#66900C2211yescharacteristic
32#10622838C2211yescharacteristic
33#10622838C2211yescharacteristic
34C2×#66897C2211yescharacteristic
35#10622828C2211yescharacteristic
36#10622828C2211yescharacteristic
37#10622777—22no—
38SD16×Dic11—22no—
39#10622737C2211yescharacteristic
40#10622737C2211yescharacteristic
41C2×#66883C2211yescharacteristic
42#10622719C2211yescharacteristic
43#10622714C2211yescharacteristic
44#10622714C2211yescharacteristic
45#10622197C2211yescharacteristic
46#10622197C2211yescharacteristic
47#10622197C2211yescharacteristic
48#10622197C2211yescharacteristic
49#10622195C2211yescharacteristic
50#10622195C2211yescharacteristic
51#10622194C2211yescharacteristic
52#10622194C2211yescharacteristic
53#10622194C2211yescharacteristic
54#10622194C2211yescharacteristic
55C2×C11×#41C2311yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C11×#137—22no—
59C11×#137—41no—
60C11×AGL(1,ℤ/8)—22no—
61C11×AGL(1,ℤ/8)—41no—
62C2×C11×Q16—21no—
63C2×C11×SD16—21no—
64C2×C11×SD16—21no—
65C2×C11×SD16—21no—
66C2×C11×SD16—21no—
67C2×C11×SD16—21no—
68C2×C11×SD16—21no—
69C2×C11×SD16D412yes—
70C2×C11×SD16D412yes—
71C2×C11×D8—21no—
72C11×#131—21no—
73C11×#131—21no—
74C11×#131—21no—
75C11×#131—21no—
76C2×C11×M16—21no—
77C2×C11×M16C2311yescharacteristic
78C2×C11×M16C2311yescharacteristic
79C2×C11×M16C2311yescharacteristic
80C22×C8×C11—21no—
81C22×C8×C11C2311yescharacteristic
82C2×C22⋊Dic11—22no—
83Q8×Dic11—22no—
84Q8×Dic11—41no—
85D4×Dic11—22no—
86D4×Dic11—41no—
87#66979—22no—
88#66979C2311yescharacteristic
89#66979C2311yescharacteristic
90#66979C2311yescharacteristic
91#66979C2311yescharacteristic
92C2×#4318C2311yescharacteristic
93C2×#4318C2311yescharacteristic
94C2×#4318C2311yescharacteristic
95C2×#4318C2311yescharacteristic
96C11×#108—21no—
97C11×#108—21no—
98C11×#101—22no—
99C11×#100—22no—
100#66901—41no—
101#66901—41no—
102#66900—21no—
103#66900—41no—
104#66899—22no—
105#66899—41no—
106#66898—22no—
107#66897—21no—
108#66897—41no—
109#66896—22no—
110#66896—41no—
111#66886—41no—
112#66886—41no—
113#66883—21no—
114#66883—21no—
115#66882—21no—
116#66881—21no—
117#66879—21no—
118#66879—21no—
119C8×Dic11—21no—
120C8×Dic11—21no—
121#24987—111nomaximal, Sylow
122C24×C11—21no—
123C11×#41—21no—
124C11×#41—21no—
125C11×#41—21no—
126C11×#41—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C2×D412yes—
133C2×Q8×C11#4111yescharacteristic
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11C2×D412yes—
141C2×D4×C11#4111yescharacteristic
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—42no—
146C11×Q16—42no—
147C11×SD16—22no—
148C11×SD16—22no—
149C11×SD16—22no—
150C11×SD16—22no—
151C11×SD16—42no—
152C11×SD16—42no—
153C11×D8—42no—
154C11×M16—21no—
155C11×M16—21no—
156C11×M16—21no—
157C11×M16—21no—
158C11×M16—21no—
159C11×M16—21no—
160C11×M16—41no—
161C11×M16—41no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—41no—
166C2×C8×C11—41no—
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11#4111yescharacteristic
170C2×C8×C11#4111yescharacteristic
171C2×C8×C11#4111yescharacteristic
172C2×C8×C11#4111yescharacteristic
173C22⋊Dic11—21no—
174C22⋊Dic11—21no—
175C22⋊Dic11—21no—
176C22⋊Dic11—42no—
177C22⋊Dic11#4112yes—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—42no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—42no—
188#4318—21no—
189#4318—21no—
190#4318—21no—
191#4318—21no—
192#4318—21no—
193#4318—21no—
194#4318—21no—
195#4318—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×#471D1111yescharacteristic
201#2949—111no—
202#2082—111no—
203#2081—111no—
204#2049—111no—
205#2048—111no—
206#1977—111no—
207#1953—111no—
208#1905—111no—
209#1904—111no—
210#1833—111no—
211#1830—111no—
212#1829—111no—
213#1814—111no—
214#1757—111no—
215C23×C11—21no—
216C23×C11—22no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—161no—
220C23×C11C2×#4111yescharacteristic
221Q8×C11—22no—
222Q8×C11—21no—
223Q8×C11—22no—
224Q8×C11—21no—
225Q8×C11—41no—
226Q8×C11—41no—
227D4×C11—22no—
228D4×C11—21no—
229D4×C11—22no—
230D4×C11—21no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—41no—
234D4×C11—41no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C11H(5,𝔽2)11yescharacteristic
247C2×Dic11—22no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—162no—
252C8×C11—41no—
253C8×C11—41no—
254C8×C11—41no—
255C8×C11#12311yescharacteristic
256C8×C11#12311yescharacteristic
257C8×C11#12311yescharacteristic
258C8×C11#12311yescharacteristic
259C11⋊C8—41no—
260C11⋊C8—41no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263C2×#137C2×D1111yescharacteristic
264C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
265C22×SD16C2×D1111yescharacteristic
266C2×#131C2×D1111yescharacteristic
267#519—111no—
268#518—111no—
269#471—22no—
270#471—22no—
271#440—222no—
272C4×SD16—222no—
273#430—111no—
274#430—111no—
275C2×#108—111no—
276C2×#108C2×D1111yescharacteristic
277#427—111no—
278#421—111no—
279#421—111no—
280#419—111no—
281#419—111no—
282#418—111no—
283#418—111no—
284#413—111no—
285C2×#101—111no—
286C2×#101C2×D1111yescharacteristic
287C2×#100—111no—
288C2×#100C2×D1111yescharacteristic
289#410—111no—
290#405—111no—
291#405—111no—
292#344—111no—
293#344—111no—
294#344—111no—
295#344—111no—
296#344—111no—
297#344—111no—
298#344—111no—
299#344—111no—
300H(3,ℤ/4)—111no—
301H(3,ℤ/4)—111no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—42no—
305C22×C11—81no—
306C22×C11—82no—
307C22×C11—161no—
308C22×C11—161no—
309C22×C11#52911yescharacteristic
310C22×C11#54611yescharacteristic
311C22×C11#55511yescharacteristic
312C4×C11—41no—
313C4×C11—42no—
314C4×C11C2×#12311yescharacteristic
315C4×C11#54011yescharacteristic
316C4×C11#54611yescharacteristic
317C4×C11#55311yescharacteristic
318Dic11—42no—
319Dic11—81no—
320Dic11—81no—
321Dic11—81no—
322C2×#41C22×D1111yescharacteristic
323C22×Q8C22×D1111yescharacteristic
324C22×D4C22×D1111yescharacteristic
325#137—22no—
326#137—41no—
327AGL(1,ℤ/8)—22no—
328AGL(1,ℤ/8)—41no—
329C2×Q16—21no—
330C2×SD16—21no—
331C2×SD16—21no—
332C2×SD16—21no—
333C2×SD16—21no—
334C2×SD16—21no—
335C2×SD16—21no—
336C2×SD16C22⋊D1112yes—
337C2×SD16C22⋊D1112yes—
338C2×D8—21no—
339#131—21no—
340#131—21no—
341#131—21no—
342#131—21no—
343C2×M16—21no—
344C2×M16—111no—
345C2×M16—111no—
346C2×M16—111no—
347C2×M16—111no—
348C2×M16C22×D1111yescharacteristic
349C2×M16C22×D1111yescharacteristic
350C2×M16C22×D1111yescharacteristic
351C22×C8—21no—
352C22×C8C22×D1111yescharacteristic
353C4×Q8—222no—
354C4×Q8—441no—
355C4×D4—222no—
356C4×D4—441no—
357#117—111no—
358#117—111no—
359#117—111no—
360#117—111no—
361#117—222no—
362C2×C22⋊C4—222no—
363#108—21no—
364#108—21no—
365#108—221no—
366#108—221no—
367#108—441no—
368#108—441no—
369#107—221no—
370#106—221no—
371#104—441no—
372#104—441no—
373#103—222no—
374#103—441no—
375#102—222no—
376#102—441no—
377#101—22no—
378#101—221no—
379#101—441no—
380#100—22no—
381#100—221no—
382#100—441no—
383#99—222no—
384#97—221no—
385#97—221no—
386C4×C8—221no—
387C4×C8—221no—
388C2×C11—21no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11—81no—
392C2×C11—82no—
393C2×C11#242011yescharacteristic
394C24—21no—
395#41—21no—
396#41—21no—
397#41—21no—
398#41—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8#434111yescharacteristic
405C2×Q8C2×C22⋊D1112yes—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4#434111yescharacteristic
413C2×D4C2×C22⋊D1112yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—442no—
417C22×C4C23×D1111yescharacteristic
418Q16—42no—
419SD16—22no—
420SD16—22no—
421SD16—22no—
422SD16—22no—
423SD16—42no—
424SD16—42no—
425D8—42no—
426M16—21no—
427M16—21no—
428M16—21no—
429M16—21no—
430M16—21no—
431M16—21no—
432M16—41no—
433M16—41no—
434M16—221no—
435M16—221no—
436M16—221no—
437M16—221no—
438M16—221no—
439M16—221no—
440M16—221no—
441M16—221no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—41no—
446C2×C8—41no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8#434111yescharacteristic
452C2×C8#434111yescharacteristic
453C2×C8#434111yescharacteristic
454C2×C8#434111yescharacteristic
455C2×C8C2×C22⋊D1111yescharacteristic
456C2×C8C2×C22⋊D1111yescharacteristic
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—442no—
462C22⋊C4—112no—
463C22⋊C4—221no—
464C22⋊C4—221no—
465C22⋊C4—221no—
466C22⋊C4—442no—
467C42—221no—
468C42—221no—
469C42—221no—
470C42—221no—
471C42—442no—
472C11#2498711yescharacteristic, complemented, Sylow
473C23—22no—
474C23—21no—
475C23—41no—
476C23—41no—
477C23—161no—
478C23#41×D1111yescharacteristic
479Q8—22no—
480Q8—21no—
481Q8—22no—
482Q8—21no—
483Q8—41no—
484Q8—41no—
485D4—22no—
486D4—21no—
487D4—22no—
488D4—21no—
489D4—41no—
490D4—41no—
491D4—41no—
492D4—41no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—222no—
500C2×C4—441no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—1762no—
504C2×C4C2×#434111yescharacteristic
505C2×C4C2×#434111yescharacteristic
506C2×C4C2×#434111yescharacteristic
507C2×C4#6703711yescharacteristic
508C2×C4#6704211yescharacteristic
509C2×C4C22×C22⋊D1111yescharacteristic
510C8—41no—
511C8—41no—
512C8—41no—
513C8—441no—
514C8—441no—
515C8—441no—
516C8—441no—
517C8#6698811yescharacteristic
518C8#6698811yescharacteristic
519C8#6698811yescharacteristic
520C8#6698811yescharacteristic
521C22—41no—
522C22—41no—
523C22—42no—
524C22—82no—
525C22—81no—
526C22—161no—
527C22—161no—
528C22#1062313111yescharacteristic
529C22#1062314711yescharacteristic
530C22#1062336011yescharacteristic
531C4—41no—
532C4—42no—
533C4—442no—
534C4—881no—
535C4—881no—
536C4—881no—
537C4#1062314911yescharacteristic
538C4#1062315011yescharacteristic
539C4C2×#6698811yescharacteristic
540C4#1062333711yescharacteristic
541C2—21no—
542C2—21no—
543C2—21no—
544C2—82no—
545C2—81no—
546C2#1307210411yescharacteristic
subgroupG/H
centerC2#13072104
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#471C2
socleC2×C11#2420
prime radicalC2×C11×AGL(1,ℤ/8)C22
hypercenterC2×#471D11
hypocenterC11#24987
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#471

Complements

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

NH ≅ G/Ntype
1. #13077476C2semidirect
2. #13070083C2semidirect
3. #13070076C2semidirect
4. #13069893C2semidirect
6. #13069521C2semidirect
7. #13069404C2semidirect
8. #13069112C2semidirect
10. #13068741C2semidirect
11. #13068728C2semidirect
12. #13068725C2semidirect
13. #13068670C2semidirect
14. #13068416C2semidirect
472. C11#24987semidirect

Maximal subgroups

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

subgroupindex
#130774762
#130700832
#130700762
#130698932
#130698862
#130695212
#130694042
#130691122
#130691052
#130687412
#130687282
#130687252
#130686702
#130684162
C2×C11×#4712
#2498711