Finite Group Databasebeta

← #14804283

Subgroups — #14804283

Order 2816.

1014 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622698C211yesmaximal, characteristic
2C2×#10622798C212yesmaximal, complemented
3#13073615C211yesmaximal, characteristic
4#13071676C211yesmaximal, characteristic, complemented
5#13069930C212yesmaximal, complemented
6#13069707C212yesmaximal, complemented
7#13069542C211yesmaximal, characteristic
8#13069332C211yesmaximal, characteristic, complemented
9#13068969C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C2×C11×#462C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#67000C2212yes—
16C2×Q8×Dic11C2212yes—
17C22×#4325C2212yes—
18C22×#4325C2212yes—
19C2×#66927C2211yescharacteristic
20C11×#462—24no—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2212yes—
23#10622843C2212yes—
24C2×#66899C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26#10622798—28no—
27C2×#66885C2212yes—
28C2×#66885C2212yes—
29C2×Dic11⋊C8C2212yes—
30#10622698—24no—
31#10622604—22no—
32#10622601C2212yes—
33#10622598—21no—
34#10622594—22no—
35C4⋊C4×Dic11—21no—
36#10622552—21no—
37#10622552—21no—
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622188C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11C2312yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D44—21no—
47C22×D44—21no—
48C22×D44C2312yes—
49C2×C11×Q16—24no—
50C2×C11×Q16—24no—
51C2×C11×Q16—42no—
52C22×C8×C11C2312yes—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8D414yes—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63#67000—24no—
64#67000—42no—
65Q8×Dic11—24no—
66Q8×Dic11—42no—
67C2×#4325—24no—
68C2×#4325—24no—
69C2×#4325—24no—
70C2×#4325—24no—
71C2×#4325—42no—
72C2×#4325—42no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11D411yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4×Dic11—21no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11C2312yes—
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87#66927—22no—
88#66927—22no—
89C11×C4⋊C8—22no—
90C11×#103—24no—
91#66899—22no—
92#66899D414yescomplemented
93C11⋊#95—21no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C11⋊#95D412yes—
97#66885—24no—
98#66885—42no—
99Dic11⋊C8—24no—
100C4×C11⋊C8—22no—
101#25369—111nomaximal, Sylow
102C23×D11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—21no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—21no—
113C2×Q8×C11C2×D412yes—
114C2×Q8×C11C2×D414yes—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11C2×D412yes—
124C22×Dic11C2×D412yes—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—42no—
132C2×D44—42no—
133C2×D44—42no—
134C2×D44—42no—
135C2×D44—81no—
136C2×D44—81no—
137C11×Q16—48no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—42no—
146C42×C11—42no—
147C42×C11C2×D412yes—
148C42×C11#4112yes—
149#4325—48no—
150#4325—48no—
151(C2×D11)⋊C4—44no—
152(C2×D11)⋊C4—44no—
153(C2×D11)⋊C4—82no—
154(C2×D11)⋊C4—82no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—44no—
161C4⋊Dic11C2×D412yes—
162C4×Dic11—22no—
163C4×Dic11—22no—
164C4×Dic11—44no—
165C4×Dic11—42no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8C2×D412yes—
171C2×C11⋊C8#4112yes—
172C2×#492—111no—
173C2×#464—112no—
174C2×#462D1111yescharacteristic, complemented
175#2548—111no—
176#2365—111no—
177#2055—112no—
178#2015—112no—
179#1982—111no—
180#1939—111no—
181#1880—112no—
182C4×#103—111no—
183C23×C11C22×D411yescharacteristic
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—42no—
191Q8×C11—22no—
192Q8×C11—24no—
193Q8×C11—22no—
194Q8×C11—24no—
195Q8×C11—42no—
196Q8×C11—42no—
197Q8×C11—41no—
198Q8×C11—41no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11#12112yes—
211C2×C4×C11#12112yes—
212C2×C4×C11#13512yes—
213C2×C4×C11#13712yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×C4×C11H(5,𝔽2)11yescharacteristic
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232D44—42no—
233D44—42no—
234D44—42no—
235D44—42no—
236D44—84no—
237D44—84no—
238C8×C11—42no—
239C11⋊C8—22no—
240C11⋊C8—22no—
241C22×Q16C2×D1112yes—
242C22×SD16—112no—
243C22×SD16—112no—
244C2×C4⋊Q8C2×D1111yescharacteristic
245C2×#127—111no—
246C2×#124—112no—
247C2×C4×Q8—112no—
248C2×C4×Q8C2×D1111yescharacteristic
249#492—224no—
250#464—228no—
251#462—24no—
252C2×C4⋊C8—112no—
253C2×C4⋊C8C2×D1111yescharacteristic
254C2×#103—111no—
255C2×#103—111no—
256C2×#103C2×D1112yes—
257C2×#102—112no—
258C2×#102—112no—
259C2×C4×C8—111no—
260#394—222no—
261#391—112no—
262#390—112no—
263#390—221no—
264#390—221no—
265#389—221no—
266#387—222no—
267C4×C4⋊C4—111no—
268C4×C4⋊C4—111no—
269C4×C4⋊C4—221no—
270#340—111no—
271#340—111no—
272#336—112no—
273C22×C11C2×#12111yescharacteristic
274C22×C11D4211yescharacteristic
275C22×C11#55011yescharacteristic
276C22×C11C2×#13511yescharacteristic
277C22×C11C2×#13711yescharacteristic
278C22×C11#57711yescharacteristic
279C22×C11#57711yescharacteristic
280C2×D11—82no—
281C2×D11—82no—
282C2×D11—82no—
283C2×D11—82no—
284C2×D11—82no—
285C2×D11—82no—
286C2×D11—82no—
287C4×C11—22no—
288C4×C11—44no—
289C4×C11—42no—
290C4×C11—81no—
291C4×C11#46414yescomplemented
292C4×C11#53211yescharacteristic
293C4×C11#54011yescharacteristic
294C4×C11D4211yescharacteristic
295C4×C11#54611yescharacteristic
296Dic11—42no—
297Dic11—42no—
298Dic11—42no—
299Dic11—81no—
300C22×Q8C22×D1111yescharacteristic
301C22×Q8C22×D1112yes—
302C22×D4—112no—
303C22×D4—221no—
304C22×D4—221no—
305C2×Q16—24no—
306C2×Q16—24no—
307C2×Q16—42no—
308C2×SD16—224no—
309C2×SD16—224no—
310C2×SD16—224no—
311C2×SD16—224no—
312C2×SD16—442no—
313C2×SD16—442no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8C22×D1112yes—
317C4⋊Q8—22no—
318C4⋊Q8C22⋊D1114yes—
319#127—222no—
320#127—222no—
321#124—224no—
322#124—442no—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8—224no—
326C4×Q8—442no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—111no—
332C2×C4⋊C4—111no—
333C2×C4⋊C4—111no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C22⋊C4—222no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C42—21no—
341C2×C42—112no—
342C2×C42—222no—
343C2×C42—221no—
344C2×C42C22×D1111yescharacteristic
345C4⋊C8—22no—
346C4⋊C8—224no—
347#103—24no—
348#103—114no—
349#103—222no—
350#102—224no—
351#102—442no—
352C4×C8—222no—
353#95—112no—
354#95—222no—
355#95—222no—
356#95—221no—
357C2×C11#242811yescharacteristic
358C2×C11C2×#46411yescharacteristic
359C2×C11#304311yescharacteristic
360C2×C11#327811yescharacteristic
361C2×C11#328411yescharacteristic
362C2×C11#339411yescharacteristic
363C2×C11#340011yescharacteristic
364D11—162no—
365C24—222no—
366C2×Q8—22no—
367C2×Q8—21no—
368C2×Q8—22no—
369C2×Q8—21no—
370C2×Q8—22no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—21no—
376C2×Q8D4×D1112yes—
377C2×Q8C2×C22⋊D1114yes—
378C2×D4—222no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—222no—
382C2×D4—222no—
383C2×D4—222no—
384C2×D4—442no—
385C2×D4—442no—
386C2×D4—442no—
387C2×D4—442no—
388C2×D4—881no—
389C2×D4—881no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—112no—
394C22×C4—112no—
395C22×C4—221no—
396C22×C4—221no—
397C22×C4D4×D1111yescharacteristic
398C22×C4D4×D1111yescharacteristic
399C22×C4C23×D1111yescharacteristic
400Q16—48no—
401SD16—448no—
402SD16—448no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—112no—
407C2×C8—112no—
408C2×C8—221no—
409C2×C8—221no—
410C2×C8—221no—
411C2×C8—221no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—42no—
417C4⋊C4—112no—
418C4⋊C4—222no—
419C4⋊C4—222no—
420C4⋊C4—221no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—444no—
424C22⋊C4—444no—
425C22⋊C4—444no—
426C22⋊C4—882no—
427C22⋊C4—882no—
428C42—42no—
429C42—222no—
430C42—222no—
431C42—444no—
432C42—442no—
433C42#434112yes—
434C42C2×C22⋊D1112yes—
435C11#2536911yescharacteristic, complemented, Sylow
436C23—442no—
437C23—442no—
438C23—442no—
439C23—442no—
440C23—442no—
441C23—442no—
442C23—442no—
443C23C2×D4×D1111yescharacteristic
444Q8—24no—
445Q8—22no—
446Q8—24no—
447Q8—22no—
448Q8—41no—
449Q8—42no—
450Q8—42no—
451Q8—41no—
452D4—442no—
453D4—442no—
454D4—442no—
455D4—442no—
456D4—884no—
457D4—884no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4#6697112yes—
482C2×C4#6697212yes—
483C2×C4#6699212yes—
484C2×C4#6699212yes—
485C2×C4C2×D4×D1111yescharacteristic
486C2×C4C2×#434111yescharacteristic
487C2×C4#6703711yescharacteristic
488C2×C4#41×D1111yescharacteristic
489C2×C4#6704211yescharacteristic
490C2×C4C22×C22⋊D1111yescharacteristic
491C8—42no—
492C8—222no—
493C8—222no—
494C22—882no—
495C22—882no—
496C22—882no—
497C22—882no—
498C22—882no—
499C22—882no—
500C22—882no—
501C22#1062313011yescharacteristic
502C22#1062314011yescharacteristic
503C22C2×#6697111yescharacteristic
504C22C2×#6697211yescharacteristic
505C22#1062330911yescharacteristic
506C22#1062330911yescharacteristic
507C22C2×#6699211yescharacteristic
508C4—22no—
509C4—44no—
510C4—42no—
511C4—81no—
512C4—442no—
513C4—442no—
514C4—442no—
515C4—881no—
516C4#1062279814yescomplemented
517C4#1062312711yescharacteristic
518C4#1062315011yescharacteristic
519C4D4×C22⋊D1111yescharacteristic
520C4#1062336011yescharacteristic
521C2—1762no—
522C2#1307220611yescharacteristic
523C2C2×#1062279811yescharacteristic
524C2#1307813911yescharacteristic
525C2#1308027711yescharacteristic
526C2#1308034111yescharacteristic
527C2#1308161111yescharacteristic
528C2#1308167311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenterC2×#462D11
hypocenterC11#25369
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
2. C2×#10622798C2semidirect
4. #13071676C2semidirect
5. #13069930C2semidirect
6. #13069707C2semidirect
8. #13069332C2semidirect
9. #13068969C2semidirect
10. C4×#66899C2semidirect
11. C2×C11×#462C2semidirect
92. #66899D4semidirect
174. C2×#462D11semidirect
291. C4×C11#464semidirect
435. C11#25369semidirect
516. C4#10622798semidirect

Maximal subgroups

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

subgroupindex
C2×#106226982
C2×#106227982
#130736152
#130716762
#130699302
#130697072
#130695422
#130693322
#130689692
C4×#668992
C2×C11×#4622
#2536911