Finite Group Databasebeta

← #14795082

Subgroups — #14795082

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×#10622464C211yesmaximal, characteristic, complemented
2#13076968C211yesmaximal, characteristic
3C4×#66977C211yesmaximal, characteristic
4#13070049C212yesmaximal
5#13069820C212yesmaximal
6#13069567C211yesmaximal, characteristic, complemented
7#13069375C211yesmaximal, characteristic, complemented
8#13069354C212yesmaximal, complemented
9#13069306C212yesmaximal, complemented
10#13068622C211yesmaximal, characteristic, complemented
11C2×C11×#432C211yesmaximal, characteristic
12C22×C42×C11C2211yescharacteristic
13C2×#66977—21no—
14C2×#66977C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C2×C4×Dic22C2211yescharacteristic
17C11×#432—24no—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2212yes—
21C2×C11×#97C2212yes—
22#10622825—21no—
23#10622825C2211yescharacteristic
24#10622825C2212yes—
25#10622823—21no—
26C4×C22⋊Dic11—21no—
27C2×#66882C2212yes—
28C2×#66881C2212yes—
29C2×#66880C2212yes—
30C2×#66880C2212yes—
31#10622548C2211yescharacteristic
32C4×C4⋊Dic11C2211yescharacteristic
33#10622546—21no—
34C4×Dic11⋊C4—21no—
35#10622542—21no—
36#10622542C2211yescharacteristic
37#10622541—21no—
38#10622541C2211yescharacteristic
39#10622541C2212yes—
40#10622464—24no—
41#10622189C2212yes—
42#10622189C2212yes—
43#10622189C2212yes—
44#10622189C2212yes—
45C23×C4×C11D411yescharacteristic
46C23×C4×C11D411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×Dic22—21no—
49C22×Dic22C2311yescharacteristic
50C22×C8×C11C2312yes—
51C22×C8×C11C2312yes—
52C2×C42×C11—22no—
53C2×C42×C11—22no—
54C2×C42×C11D411yescharacteristic
55C2×C42×C11D411yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69#66977—22no—
70#66977—22no—
71#66977—44no—
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78#66922—22no—
79#66922—22no—
80C4×Dic22—22no—
81C4×Dic22—22no—
82C11×C4⋊C8—22no—
83C11×C4⋊C8D414yes—
84C11×C22⋊C8—24no—
85C11×#97—24no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—21no—
89C11⋊#95—21no—
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93#66882—24no—
94#66881—24no—
95#66880—24no—
96#66880—24no—
97#24710—111nomaximal, Sylow
98C24×C11C2×D411yescharacteristic
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—41no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C2×Dic22—21no—
124C2×Dic22—21no—
125C2×Dic22—21no—
126C2×Dic22—21no—
127C2×Dic22—21no—
128C2×Dic22—42no—
129C2×Dic22—42no—
130C2×Dic22—42no—
131C2×Dic22#4112yes—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11C2×D414yes—
138C42×C11—22no—
139C42×C11—22no—
140C42×C11—21no—
141C42×C11—21no—
142C42×C11C2×D412yes—
143C42×C11#4112yes—
144C22⋊Dic11—24no—
145C22⋊Dic11—44no—
146C22⋊Dic11—42no—
147C4⋊Dic11—22no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—21no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—42no—
157C4⋊Dic11—42no—
158C4⋊Dic11—42no—
159C4⋊Dic11#4112yes—
160Dic11⋊C4—24no—
161Dic11⋊C4—42no—
162Dic11⋊C4—44no—
163Dic11⋊C4—42no—
164C4×Dic11—42no—
165C4×Dic11—42no—
166C2×#475—111no—
167C2×#432D1111yescharacteristic
168#2857—111no—
169C4×C22⋊Q8—111no—
170#2077—112no—
171#2036—112no—
172#1988—111no—
173#1947—111no—
174#1943—112no—
175#1935—112no—
176#1803—111no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11#13712yes—
184C23×C11C22×D411yescharacteristic
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—44no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—44no—
202C2×C4×C11#12112yes—
203C2×C4×C11#12112yes—
204C2×C4×C11AGL(1,ℤ/8)12yes—
205C2×C4×C11#13712yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C112−1+411yescharacteristic
211C2×C4×C112−1+411yescharacteristic
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—42no—
228C2×Dic11—41no—
229C2×Dic11—42no—
230Dic22—22no—
231Dic22—22no—
232Dic22—41no—
233Dic22—41no—
234Dic22—84no—
235C8×C11—24no—
236C8×C11—42no—
237C2×C4⋊Q8—111no—
238C2×C22⋊Q8—111no—
239C2×C22⋊Q8—221no—
240C2×C4×Q8—111no—
241C22×C42C2×D1111yescharacteristic
242#475—224no—
243#432—24no—
244C2×#107—112no—
245C2×#106—112no—
246C2×C4⋊C8C2×D1111yescharacteristic
247C2×C4⋊C8C2×D1111yescharacteristic
248C2×#103—112no—
249C2×#103—112no—
250C2×C22⋊C8C2×D1112yes—
251C2×#97C2×D1112yes—
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—111no—
264C4×C4⋊C4—221no—
265C4×C22⋊C4—221no—
266#340—112no—
267#340—112no—
268#340—112no—
269#340—112no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11C2×#12111yescharacteristic
278C22×C11#52511yescharacteristic
279C22×C11#53611yescharacteristic
280C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C11C2×#13711yescharacteristic
282C22×C11C2×#13711yescharacteristic
283C22×C11#57511yescharacteristic
284C4×C11—22no—
285C4×C11—41no—
286C4×C11—41no—
287C4×C11—41no—
288C4×C11#46814yes—
289C4×C11#54711yescharacteristic
290C4×C11#54811yescharacteristic
291C4×C11#55211yescharacteristic
292C4×C11#55611yescharacteristic
293Dic11—42no—
294Dic11—42no—
295Dic11—82no—
296Dic11—81no—
297Dic11—82no—
298Dic11—81no—
299C22×Q8—111no—
300C22×Q8—221no—
301C23×C4D4411yescharacteristic
302C23×C4D4411yescharacteristic
303C23×C4C22×D1111yescharacteristic
304C22×C8C22×D1112yes—
305C22×C8C22×D1112yes—
306C4⋊Q8—222no—
307C4⋊Q8—222no—
308C22⋊Q8—222no—
309C22⋊Q8—222no—
310C22⋊Q8—444no—
311C4×Q8—222no—
312C4×Q8—222no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—111no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4—222no—
327C2×C22⋊C4—221no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—221no—
331C2×C42—221no—
332C2×C42D4411yescharacteristic
333C2×C42D4411yescharacteristic
334C2×C42C22×D1111yescharacteristic
335C2×C42C22×D1111yescharacteristic
336#107—224no—
337#106—224no—
338C4⋊C8—22no—
339C4⋊C8C22⋊D1114yes—
340#103—224no—
341#103—224no—
342C22⋊C8—24no—
343#97—24no—
344#95—221no—
345#95—221no—
346#95—221no—
347#95—221no—
348#95—221no—
349#95—222no—
350#95—222no—
351C2×C11—42no—
352C2×C11#241511yescharacteristic
353C2×C11C2×#46811yescharacteristic
354C2×C11#305611yescharacteristic
355C2×C11#311311yescharacteristic
356C2×C11#311511yescharacteristic
357C2×C11#323711yescharacteristic
358C2×C11#323911yescharacteristic
359C24C2×D4411yescharacteristic
360C2×Q8—112no—
361C2×Q8—221no—
362C2×Q8—221no—
363C2×Q8—221no—
364C2×Q8—221no—
365C2×Q8—221no—
366C2×Q8—442no—
367C2×Q8—442no—
368C2×Q8—442no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—41no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4C2×D4411yescharacteristic
388C22×C4C2×D4411yescharacteristic
389C22×C4C2×D4411yescharacteristic
390C22×C4C2×D4411yescharacteristic
391C22×C4C2×D4411yescharacteristic
392C22×C4C23×D1111yescharacteristic
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8C2×C22⋊D1114yes—
399C4⋊C4—112no—
400C4⋊C4—224no—
401C4⋊C4—221no—
402C4⋊C4—221no—
403C4⋊C4—222no—
404C4⋊C4—222no—
405C4⋊C4—222no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—222no—
409C4⋊C4—221no—
410C4⋊C4—444no—
411C4⋊C4—442no—
412C4⋊C4—442no—
413C4⋊C4—442no—
414C4⋊C4—442no—
415C4⋊C4—442no—
416C22⋊C4—224no—
417C22⋊C4—444no—
418C22⋊C4—442no—
419C42—22no—
420C42—22no—
421C42—21no—
422C42—21no—
423C42—442no—
424C42—442no—
425C42#433912yes—
426C42C2×C22⋊D1112yes—
427C11#2471011yescharacteristic, complemented, Sylow
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23#6696212yes—
435C23C22×D4411yescharacteristic
436Q8—222no—
437Q8—222no—
438Q8—441no—
439Q8—441no—
440Q8—884no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—222no—
459C2×C4—222no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—442no—
470C2×C4—441no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—442no—
476C2×C4#6696112yes—
477C2×C4#6696212yes—
478C2×C4#6698312yes—
479C2×C4#6698312yes—
480C2×C4C2×#433911yescharacteristic
481C2×C4#41×D1111yescharacteristic
482C2×C4#41×D1111yescharacteristic
483C2×C4#6704311yescharacteristic
484C2×C4#6704311yescharacteristic
485C2×C4C22×C22⋊D1111yescharacteristic
486C8—24no—
487C8—42no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22#1062305511yescharacteristic
496C22#1062305711yescharacteristic
497C22C2×#6696111yescharacteristic
498C22C2×#6696211yescharacteristic
499C22C2×#6696211yescharacteristic
500C22#1062327911yescharacteristic
501C22C2×#6698311yescharacteristic
502C4—22no—
503C4—41no—
504C4—41no—
505C4—41no—
506C4—442no—
507C4—442no—
508C4—881no—
509C4—882no—
510C4—881no—
511C4—882no—
512C4#1062274714yes—
513C4#1062306011yescharacteristic
514C4#1062306411yescharacteristic
515C4#1062335511yescharacteristic
516C4#1062336211yescharacteristic
517C2—42no—
518C2#1307203911yescharacteristic
519C2C2×#1062274711yescharacteristic
520C2#1307824611yescharacteristic
521C2#1307874711yescharacteristic
522C2#1307876811yescharacteristic
523C2#1307983211yescharacteristic
524C2#1307984811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#432C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#432D11
hypocenterC11#24710
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×#10622464C2semidirect
6. #13069567C2semidirect
7. #13069375C2semidirect
8. #13069354C2semidirect
9. #13069306C2semidirect
10. #13068622C2semidirect
427. C11#24710semidirect

Maximal subgroups

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

subgroupindex
C2×#106224642
#130769682
C4×#669772
#130700492
#130698202
#130695672
#130693752
#130693542
#130693062
#130686222
C2×C11×#4322
#2471011