Finite Group Databasebeta

← #14795102

Subgroups — #14795102

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622704C211yesmaximal, characteristic, complemented
2C2×#10622448C211yesmaximal, characteristic
3#13076963C211yesmaximal, characteristic
4C4×#66950C211yesmaximal, characteristic
5#13070043C212yesmaximal
6#13069815C212yesmaximal
7#13069379C211yesmaximal, characteristic, complemented
8#13069358C212yesmaximal, complemented
9#13069304C212yesmaximal, complemented
10#13068622C211yesmaximal, characteristic, complemented
11C11×#1987C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999—21no—
14C2×#66950C2211yescharacteristic
15C2×C42×D11C2211yescharacteristic
16C2×C4×Dic22C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C4×C11×C4⋊C4C2211yescharacteristic
19#10622843—21no—
20C2×(C2×D11)⋊C8C2212yes—
21C2×#66880C2212yes—
22C2×#66879C2212yes—
23#10622704—24no—
24#10622600—21no—
25#10622600C2211yescharacteristic
26#10622600C2212yes—
27#10622598C2211yescharacteristic
28#10622587C2211yescharacteristic
29#10622586—21no—
30#10622586C2212yes—
31C2×#66874C2212yes—
32C2×#66872C2212yes—
33C2×#66871C2212yes—
34C4×(C2×D11)⋊C4—21no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11—21no—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622448—24no—
39#10622281—21no—
40#10622266—21no—
41C11×#340C2212yes—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×C4×D11D411yescharacteristic
47C22×C4×D11D411yescharacteristic
48C22×C4×D11C2311yescharacteristic
49C22×Dic22C2311yescharacteristic
50C22×C8×C11C2312yes—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59#66999—44no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11—21no—
72C2×C4×Dic11D411yescharacteristic
73C2×C4×Dic11D411yescharacteristic
74C2×C4×Dic11C2311yescharacteristic
75C22×C11⋊C8C2312yes—
76#66950—22no—
77#66950—22no—
78C42×D11—22no—
79C42×D11—22no—
80C4×Dic22—22no—
81C4×Dic22—22no—
82C11×C4⋊C8—22no—
83C11×#95—21no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—21no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90(C2×D11)⋊C8—24no—
91#66880—24no—
92#66879—24no—
93#66874—24no—
94#66872—24no—
95#66871—24no—
96C4⋊(C11⋊C8)D414yes—
97#24711—111nomaximal, Sylow
98C23×D11C2×D411yescharacteristic
99C2×Q8×C11—42no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—22no—
111C22×Dic11C2×D411yescharacteristic
112C22×Dic11C2×D411yescharacteristic
113C22×Dic11C2×D411yescharacteristic
114C2×C4×D11—22no—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—21no—
120C2×C4×D11—21no—
121C2×C4×D11—21no—
122C2×C4×D11—21no—
123C2×C4×D11—21no—
124C2×C4×D11—21no—
125C2×C4×D11—41no—
126C2×Dic22—21no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22#4112yes—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4#4112yes—
142C42×C11—42no—
143C42×C11C2×D412yes—
144C42×C11#4112yes—
145(C2×D11)⋊C4—24no—
146(C2×D11)⋊C4—42no—
147(C2×D11)⋊C4—44no—
148C4⋊Dic11—24no—
149C4⋊Dic11—21no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—21no—
153C4⋊Dic11—42no—
154C4⋊Dic11—42no—
155C4⋊Dic11—42no—
156Dic11⋊C4—44no—
157Dic11⋊C4—42no—
158C4×Dic11—22no—
159C4×Dic11—22no—
160C4×Dic11—21no—
161C4×Dic11—21no—
162C4×Dic11—42no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8C2×D414yes—
166C2×#477—111no—
167C2×#432—111no—
168#2857—111no—
169C4×C22⋊Q8—111no—
170#2075—112no—
171#2035—112no—
172#1987D1111yescharacteristic, complemented
173#1948—111no—
174#1944—112no—
175#1935—112no—
176#1803—111no—
177C23×C11C22×D411yescharacteristic
178C22×D11—21no—
179C22×D11—21no—
180C22×D11—21no—
181C22×D11—21no—
182C22×D11—21no—
183C22×D11—21no—
184C22×D11AGL(1,ℤ/8)12yes—
185Q8×C11—84no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—22no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11#12112yes—
198C2×C4×C11#12112yes—
199C2×C4×C11#13712yes—
200C2×C4×C11#13712yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C112−1+411yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—22no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—41no—
223C2×Dic11—42no—
224C2×Dic11—41no—
225C4×D11—44no—
226C4×D11—41no—
227C4×D11—41no—
228C4×D11—41no—
229C4×D11—41no—
230C4×D11—44no—
231Dic22—22no—
232Dic22—22no—
233Dic22—41no—
234Dic22—41no—
235C8×C11—42no—
236C11⋊C8—24no—
237C2×C4⋊Q8C2×D1111yescharacteristic
238C2×C22⋊Q8—111no—
239C2×C22⋊Q8—221no—
240C2×C4×Q8—111no—
241C22×C42—111no—
242#477—224no—
243#432—224no—
244C2×#107—112no—
245C2×#106—112no—
246C2×C4⋊C8—111no—
247C2×C4⋊C8C2×D1111yescharacteristic
248C2×#103—112no—
249C2×#103—112no—
250C2×C22⋊C8—112no—
251C2×#97—112no—
252#391—111no—
253#391—221no—
254#389—112no—
255#389—111no—
256#389—221no—
257#387—221no—
258#385—221no—
259#384—111no—
260#380—111no—
261#380—112no—
262#380—221no—
263C4×C4⋊C4—221no—
264C4×C4⋊C4C2×D1111yescharacteristic
265C4×C22⋊C4—221no—
266#340—112no—
267#340—112no—
268#340C2×D1112yes—
269#340C2×D1112yes—
270C22×C11C2×#12111yescharacteristic
271C22×C11#52511yescharacteristic
272C22×C11#53611yescharacteristic
273C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C11C2×#13711yescharacteristic
275C22×C11C2×#13711yescharacteristic
276C22×C11#57511yescharacteristic
277C2×D11—22no—
278C2×D11—22no—
279C2×D11—22no—
280C2×D11—41no—
281C2×D11—41no—
282C2×D11—41no—
283C2×D11—41no—
284C4×C11—22no—
285C4×C11—42no—
286C4×C11—81no—
287C4×C11—82no—
288C4×C11#47014yes—
289C4×C11#54711yescharacteristic
290C4×C11#54811yescharacteristic
291C4×C11#55211yescharacteristic
292C4×C11#55611yescharacteristic
293Dic11—42no—
294Dic11—41no—
295Dic11—41no—
296Dic11—41no—
297Dic11—82no—
298Dic11—81no—
299C22×Q8—21no—
300C22×Q8—111no—
301C23×C4—111no—
302C23×C4—111no—
303C23×C4—111no—
304C22×C8—112no—
305C22×C8C22×D1112yes—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C22⋊Q8—222no—
309C22⋊Q8—222no—
310C22⋊Q8—444no—
311C4×Q8—222no—
312C4×Q8—222no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—111no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4C22×D1112yes—
323C2×C4⋊C4C22×D1111yescharacteristic
324C2×C4⋊C4C22×D1111yescharacteristic
325C2×C22⋊C4—221no—
326C2×C22⋊C4—222no—
327C2×C22⋊C4—221no—
328C2×C42—21no—
329C2×C42—111no—
330C2×C42—111no—
331C2×C42—111no—
332C2×C42—222no—
333C2×C42—222no—
334C2×C42—221no—
335C2×C42C22×D1111yescharacteristic
336#107—224no—
337#106—224no—
338C4⋊C8—22no—
339C4⋊C8—114no—
340#103—224no—
341#103—224no—
342C22⋊C8—224no—
343#97—224no—
344#95—21no—
345#95—221no—
346#95—221no—
347#95—221no—
348#95—221no—
349#95—222no—
350#95—222no—
351C2×C11#241511yescharacteristic
352C2×C11C2×#47011yescharacteristic
353C2×C11#305511yescharacteristic
354C2×C11#311211yescharacteristic
355C2×C11#311611yescharacteristic
356C2×C11#323711yescharacteristic
357C2×C11#323811yescharacteristic
358D11—42no—
359C24—111no—
360C2×Q8—42no—
361C2×Q8—42no—
362C2×Q8—42no—
363C2×Q8—112no—
364C2×Q8—221no—
365C2×Q8—221no—
366C2×Q8—221no—
367C2×Q8—221no—
368C2×Q8—221no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—111no—
373C22×C4—111no—
374C22×C4—111no—
375C22×C4—222no—
376C22×C4—221no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—222no—
389C22×C4—441no—
390C22×C4D4×D1111yescharacteristic
391C22×C4D4×D1111yescharacteristic
392C22×C4C23×D1111yescharacteristic
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—114no—
397C2×C8—222no—
398C2×C8—222no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—42no—
405C4⋊C4—224no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—222no—
409C4⋊C4—222no—
410C4⋊C4—442no—
411C4⋊C4—444no—
412C4⋊C4—442no—
413C4⋊C4—442no—
414C4⋊C4—442no—
415C4⋊C4#434312yes—
416C22⋊C4—224no—
417C22⋊C4—444no—
418C22⋊C4—442no—
419C42—42no—
420C42—222no—
421C42—222no—
422C42—221no—
423C42—221no—
424C42—442no—
425C42#433912yes—
426C42D4×D1112yes—
427C11#2471111yescharacteristic, complemented, Sylow
428C23—112no—
429C23—221no—
430C23—221no—
431C23—221no—
432C23—221no—
433C23—221no—
434C23—221no—
435C23C2×D4×D1111yescharacteristic
436Q8—84no—
437Q8—222no—
438Q8—222no—
439Q8—441no—
440Q8—441no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—221no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—222no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—444no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—444no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—442no—
476C2×C4#6693712yes—
477C2×C4#6693712yes—
478C2×C4#6696812yes—
479C2×C4#6697112yes—
480C2×C4C2×#433911yescharacteristic
481C2×C4C2×D4×D1111yescharacteristic
482C2×C4C2×#434311yescharacteristic
483C2×C4#6704011yescharacteristic
484C2×C4#41×D1111yescharacteristic
485C2×C4#6704311yescharacteristic
486C8—42no—
487C8—224no—
488C22—222no—
489C22—222no—
490C22—222no—
491C22—441no—
492C22—441no—
493C22—441no—
494C22—441no—
495C22C2×#6693711yescharacteristic
496C22#1062315811yescharacteristic
497C22#1062315911yescharacteristic
498C22C2×#6696811yescharacteristic
499C22C2×#6697111yescharacteristic
500C22D11×AGL(1,ℤ/8)11yescharacteristic
501C22#1062330411yescharacteristic
502C4—22no—
503C4—42no—
504C4—81no—
505C4—82no—
506C4—441no—
507C4—442no—
508C4—441no—
509C4—441no—
510C4—882no—
511C4—881no—
512C4#1062242914yes—
513C4#1062311211yescharacteristic
514C4#1062311511yescharacteristic
515C4#1062320811yescharacteristic
516C4#1062325711yescharacteristic
517C2—442no—
518C2#1307204811yescharacteristic
519C2C2×#1062242911yescharacteristic
520C2#1307823311yescharacteristic
521C2#1307874011yescharacteristic
522C2#1307878011yescharacteristic
523C2#1307982811yescharacteristic
524C2#1307983611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1987C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1987D11
hypocenterC11#24711
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
1. C2×#10622704C2semidirect
7. #13069379C2semidirect
8. #13069358C2semidirect
9. #13069304C2semidirect
10. #13068622C2semidirect
11. C11×#1987C2semidirect
172. #1987D11semidirect
427. C11#24711semidirect

Maximal subgroups

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

subgroupindex
C2×#106227042
C2×#106224482
#130769632
C4×#669502
#130700432
#130698152
#130693792
#130693582
#130693042
#130686222
C11×#19872
#2471111