Finite Group Databasebeta

← #14796428

Subgroups — #14796428

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622634C211yesmaximal, characteristic, complemented
2#13073789C211yesmaximal, characteristic
3Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
4#13070101C212yesmaximal, complemented
5#13070000C212yesmaximal
6#13069577C211yesmaximal, characteristic, complemented
7#13069334C211yesmaximal, characteristic, complemented
8#13068973C212yesmaximal
9#13068629C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic
11C2×C4×C11×SD16C211yesmaximal, characteristic
12C22×C11×SD16C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×Q8×Dic11C2212yes—
16C2×#66922C2211yescharacteristic
17C4×C11×SD16—24no—
18C2×C11×#106C2211yescharacteristic
19C2×C11×#103C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66899C2212yes—
23#10622834C2212yes—
24C2×#66896C2212yes—
25#10622825—21no—
26#10622825—21no—
27C2×Dic11⋊C8C2212yes—
28#10622634—24no—
29#10622598—22no—
30#10622598C2212yes—
31#10622590C2212yes—
32C2×#66871C2212yes—
33#10622560—22no—
34#10622548—21no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11—21no—
37C4×C4⋊Dic11C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622189C2212yes—
40#10622189C2212yes—
41#10622188C2212yes—
42#10622167C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×Dic22—21no—
47C2×C11×SD16—22no—
48C2×C11×SD16—22no—
49C2×C11×SD16Q814yescomplemented
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C4×Q8×C11—22no—
53C4×Q8×C11D414yes—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64Q8×Dic11—24no—
65Q8×Dic11—42no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11D411yescharacteristic
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2312yes—
75C2×C4×Dic11—22no—
76C2×C4×Dic11C2312yes—
77C22×C11⋊C8C2312yes—
78#66922—22no—
79#66922—22no—
80C11×#106—22no—
81C11×#103—22no—
82C11×#102—22no—
83C4×C8×C11—22no—
84#66899—24no—
85#66896—42no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95D412yes—
90Dic11⋊C8—42no—
91#66871—24no—
92C4⋊(C11⋊C8)—22no—
93#24814—111nomaximal, Sylow
94C24×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11C2×D412yes—
99C2×Q8×C11C2×Q812yes—
100C2×Q8×C11#4112yes—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11C2×Q812yes—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11C2×D412yes—
119C22×Dic11C2×D412yes—
120C2×Dic22—42no—
121C2×Dic22—81no—
122C2×Dic22—81no—
123C11×SD16—28no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11C2×Q812yes—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4C2×D412yes—
135C11×C22⋊C4—42no—
136C42×C11—24no—
137C42×C11C2×D412yes—
138C42×C11#4112yes—
139C22⋊Dic11—82no—
140C22⋊Dic11—82no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—44no—
148C4⋊Dic11—42no—
149C4⋊Dic11—42no—
150C4⋊Dic11—81no—
151C4⋊Dic11—82no—
152C4×Dic11—22no—
153C4×Dic11—22no—
154C4×Dic11—44no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×#477—111no—
159C2×C4×SD16D1111yescharacteristic
160#2563—111no—
161Q8×C4⋊C4—111no—
162#2085—112no—
163#2067—112no—
164#1990—111no—
165#1939—111no—
166#1880—112no—
167#1805—112no—
168#1802—111no—
169C23×C11—22no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11C22×D411yescharacteristic
177Q8×C11—22no—
178Q8×C11—22no—
179Q8×C11—22no—
180Q8×C11C22⋊Q814yes—
181D4×C11—22no—
182D4×C11—22no—
183D4×C11—41no—
184D4×C11—41no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—84no—
197C2×C4×C11#12112yes—
198C2×C4×C11#12112yes—
199C2×C4×C11#13512yes—
200C2×C4×C11#13712yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×Q811yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219Dic22—84no—
220C8×C11—22no—
221C8×C11—41no—
222C11⋊C8—42no—
223C22×SD16C2×D1111yescharacteristic
224C2×C4⋊Q8—111no—
225C2×C4×Q8—112no—
226C2×C4×Q8C2×D1111yescharacteristic
227C2×C4×D4C2×D1111yescharacteristic
228#477—224no—
229C4×SD16—24no—
230C2×#107—112no—
231C2×#106C2×D1111yescharacteristic
232C2×C4⋊C8—111no—
233C2×C4⋊C8—112no—
234C2×#103—112no—
235C2×#103C2×D1111yescharacteristic
236C2×#102—112no—
237C2×#102C2×D1111yescharacteristic
238C2×C4×C8C2×D1111yescharacteristic
239#393—222no—
240#390—112no—
241#389—112no—
242#389—222no—
243#384—111no—
244#384—221no—
245#382—112no—
246#380—221no—
247#380—221no—
248C4×C4⋊C4—111no—
249C4×C4⋊C4—221no—
250#340—112no—
251#340—112no—
252#340—112no—
253#336—112no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11C2×#12111yescharacteristic
262C22×C11#54611yescharacteristic
263C22×C11D4×Q811yescharacteristic
264C22×C11C2×#13511yescharacteristic
265C22×C11C2×#13711yescharacteristic
266C22×C11#57611yescharacteristic
267C22×C11#57711yescharacteristic
268C4×C11—24no—
269C4×C11—22no—
270C4×C11—42no—
271C4×C11—81no—
272C4×C11#46414yes—
273C4×C11C2×C22⋊Q811yescharacteristic
274C4×C11#53711yescharacteristic
275C4×C11#55211yescharacteristic
276C4×C11#55411yescharacteristic
277Dic11—42no—
278Dic11—42no—
279Dic11—82no—
280Dic11—82no—
281C22×Q8—221no—
282C22×Q8C22×D1111yescharacteristic
283C22×D4C22×D1111yescharacteristic
284C23×C4—21no—
285C2×SD16—22no—
286C2×SD16—22no—
287C2×SD16Dic2214yescomplemented
288C22×C8—112no—
289C22×C8C22×D1111yescharacteristic
290C22×C8C22×D1111yescharacteristic
291C4⋊Q8—222no—
292C4⋊Q8—222no—
293C4×Q8—22no—
294C4×Q8—224no—
295C4×Q8—442no—
296C4×Q8C22⋊D1114yes—
297C4×D4—22no—
298C4×D4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—112no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C22⋊C4—21no—
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C42—21no—
315C2×C42—112no—
316C2×C42—222no—
317C2×C42C22×D1111yescharacteristic
318#107—224no—
319#106—22no—
320C4⋊C8—222no—
321C4⋊C8—442no—
322#103—22no—
323#103—224no—
324#102—22no—
325#102—442no—
326C4×C8—22no—
327#95—112no—
328#95—222no—
329#95—222no—
330#95—222no—
331C2×C11—82no—
332C2×C11#241711yescharacteristic
333C2×C11C2×#46411yescharacteristic
334C2×C11#304511yescharacteristic
335C2×C11#330511yescharacteristic
336C2×C11#332911yescharacteristic
337C2×C11#338111yescharacteristic
338C2×C11#338511yescharacteristic
339C24—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—442no—
344C2×Q8—881no—
345C2×Q8—881no—
346C2×Q8C2×Dic2212yes—
347C2×Q8#433912yes—
348C2×Q8C2×C22⋊D1112yes—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4C2×Dic2212yes—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—112no—
362C22×C4—112no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4D4×D1111yescharacteristic
366C22×C4D4×D1111yescharacteristic
367C22×C4C23×D1111yescharacteristic
368SD16—28no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—222no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8C2×Dic2212yes—
378C4⋊C4—24no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—222no—
383C4⋊C4—222no—
384C4⋊C4—222no—
385C4⋊C4—222no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—444no—
389C4⋊C4—442no—
390C4⋊C4—442no—
391C4⋊C4—881no—
392C4⋊C4—882no—
393C4⋊C4C2×C22⋊D1112yes—
394C22⋊C4—42no—
395C22⋊C4—882no—
396C22⋊C4—882no—
397C42—24no—
398C42—222no—
399C42—222no—
400C42—444no—
401C42#434112yes—
402C42C2×C22⋊D1112yes—
403C11#2481411yescharacteristic, complemented, Sylow
404C23—22no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23C2×D4×D1111yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—22no—
415Q8—884no—
416Q8#6697714yes—
417D4—22no—
418D4—22no—
419D4—41no—
420D4—41no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—84no—
433C2×C4—222no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4#6696812yes—
446C2×C4#6696912yes—
447C2×C4#6699212yes—
448C2×C4#6699212yes—
449C2×C4C22×Dic2211yescharacteristic
450C2×C4C2×#433911yescharacteristic
451C2×C4C2×#434111yescharacteristic
452C2×C4#6704211yescharacteristic
453C2×C4#6704311yescharacteristic
454C2×C4C22×C22⋊D1111yescharacteristic
455C8—22no—
456C8—41no—
457C8—442no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22D4×Dic2211yescharacteristic
466C22#1062308111yescharacteristic
467C22C2×#6696811yescharacteristic
468C22C2×#6696911yescharacteristic
469C22#1062330011yescharacteristic
470C22#1062330111yescharacteristic
471C22C2×#6699211yescharacteristic
472C4—22no—
473C4—24no—
474C4—42no—
475C4—81no—
476C4—442no—
477C4—442no—
478C4—882no—
479C4—882no—
480C4#1062277914yes—
481C4#1062307211yescharacteristic
482C4#1062307411yescharacteristic
483C4C2×#6697711yescharacteristic
484C4#1062336411yescharacteristic
485C2—82no—
486C2#1307206711yescharacteristic
487C2C2×#1062277911yescharacteristic
488C2#1307815311yescharacteristic
489C2#1308056811yescharacteristic
490C2#1308091211yescharacteristic
491C2#1308148911yescharacteristic
492C2#1308152411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×C4×SD16D11
hypocenterC11#24814
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10622634C2semidirect
3. Q8×C4⋊Dic11C2semidirect
4. #13070101C2semidirect
6. #13069577C2semidirect
7. #13069334C2semidirect
9. #13068629C2semidirect
49. C2×C11×SD16Q8semidirect
287. C2×SD16Dic22semidirect
403. C11#24814semidirect

Maximal subgroups

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

subgroupindex
C2×#106226342
#130737892
Q8×C4⋊Dic112
#130701012
#130700002
#130695772
#130693342
#130689732
#130686292
#130686162
C2×C4×C11×SD162
#2481411