Finite Group Databasebeta

← #14796429

Subgroups — #14796429

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×C4×#4325C211yesmaximal, characteristic
2#13073790C211yesmaximal, characteristic
3Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
4#13070100C212yesmaximal, complemented
5#13069999C212yesmaximal
6#13069578C211yesmaximal, characteristic, complemented
7#13069332C211yesmaximal, characteristic, complemented
8#13068969C212yesmaximal
9#13068629C212yesmaximal, complemented
10#13068617C211yesmaximal, characteristic
11C2×C11×#477C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×Q8×Dic11C2212yes—
15C22×#4325C2211yescharacteristic
16C2×C4×D44C2211yescharacteristic
17C11×#477—24no—
18C2×C11×#107C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#103C2212yes—
21#10622844—22no—
22C2×#66899C2211yescharacteristic
23C2×#66885C2212yes—
24C2×Dic11⋊C8C2212yes—
25C4×#4325—24no—
26#10622601C2212yes—
27#10622600—21no—
28#10622600—21no—
29#10622598—22no—
30#10622598C2212yes—
31#10622590C2212yes—
32C2×#66873C2211yescharacteristic
33C2×#66872C2211yescharacteristic
34#10622548—21no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11—21no—
37C4×C4⋊Dic11C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×C8×C11C2312yes—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—22no—
50C4×Q8×C11—22no—
51C4×Q8×C11D414yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58Q8×Dic11—24no—
59Q8×Dic11—42no—
60C2×#4325—22no—
61C2×#4325—22no—
62C2×#4325Q814yescomplemented
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4×Dic11—22no—
75C2×C4×Dic11C2312yes—
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2311yescharacteristic
78C4×D44—22no—
79C4×D44—22no—
80C11×#107—24no—
81C11×C4⋊C8—22no—
82C11×#103—24no—
83#66899—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95D412yes—
88#66885—42no—
89Dic11⋊C8—42no—
90#66873—22no—
91#66872—22no—
92C4×C11⋊C8—22no—
93#24814—111nomaximal, Sylow
94C23×D11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—42no—
99C2×Q8×C11—81no—
100C2×Q8×C11—81no—
101C2×Q8×C11C2×D412yes—
102C2×Q8×C11C2×Q812yes—
103C2×Q8×C11#4112yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11C2×D412yes—
113C22×Dic11C2×D412yes—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44C2×Q812yes—
120C2×C4×D11—42no—
121C2×C4×D11—42no—
122C2×C4×D11—42no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4C2×D412yes—
132C42×C11—24no—
133C42×C11C2×D412yes—
134C42×C11#4112yes—
135#4325—28no—
136(C2×D11)⋊C4—42no—
137(C2×D11)⋊C4—82no—
138(C2×D11)⋊C4—82no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—44no—
146C4⋊Dic11—42no—
147C4⋊Dic11—81no—
148C4⋊Dic11—82no—
149C4×Dic11—22no—
150C4×Dic11—22no—
151C4×Dic11—44no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8C2×Q812yes—
158C2×#477D1111yescharacteristic, complemented
159C2×C4×SD16—111no—
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×C11C22×D411yescharacteristic
170C22×D11—22no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177Q8×C11—22no—
178Q8×C11—22no—
179Q8×C11—22no—
180Q8×C11—84no—
181Q8×C11C22⋊Q814yes—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11#12112yes—
194C2×C4×C11#12112yes—
195C2×C4×C11#13512yes—
196C2×C4×C11#13712yes—
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C22×Q811yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11H(5,𝔽2)11yescharacteristic
202C2×C4×C112−1+411yescharacteristic
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—42no—
215D44—22no—
216D44—22no—
217D44—41no—
218D44—41no—
219C4×D11—84no—
220C8×C11—42no—
221C11⋊C8—22no—
222C11⋊C8—41no—
223C22×SD16—111no—
224C2×C4⋊Q8C2×D1111yescharacteristic
225C2×C4×Q8—112no—
226C2×C4×Q8C2×D1111yescharacteristic
227C2×C4×D4—111no—
228#477—24no—
229C4×SD16—224no—
230C2×#107C2×D1112yes—
231C2×#106—111no—
232C2×C4⋊C8—112no—
233C2×C4⋊C8C2×D1111yescharacteristic
234C2×#103—111no—
235C2×#103C2×D1112yes—
236C2×#102—111no—
237C2×#102—112no—
238C2×C4×C8—111no—
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×C11C2×#12111yescharacteristic
255C22×C11#54611yescharacteristic
256C22×C11D4×Q811yescharacteristic
257C22×C11C2×#13511yescharacteristic
258C22×C11C2×#13711yescharacteristic
259C22×C11#57611yescharacteristic
260C22×C11#57711yescharacteristic
261C2×D11—42no—
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—81no—
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C4×C11—24no—
269C4×C11—22no—
270C4×C11—42no—
271C4×C11—82no—
272C4×C11#46414yes—
273C4×C11C2×C22⋊Q811yescharacteristic
274C4×C11#53711yescharacteristic
275C4×C11#55211yescharacteristic
276C4×C11#55411yescharacteristic
277Dic11—42no—
278Dic11—42no—
279Dic11—81no—
280Dic11—82no—
281C22×Q8—21no—
282C22×Q8C22×D1111yescharacteristic
283C22×D4—111no—
284C23×C4—221no—
285C2×SD16—114no—
286C2×SD16—222no—
287C2×SD16—222no—
288C22×C8—111no—
289C22×C8—111no—
290C22×C8C22×D1112yes—
291C4⋊Q8—22no—
292C4⋊Q8—22no—
293C4×Q8—22no—
294C4×Q8—224no—
295C4×Q8—442no—
296C4×Q8C22⋊D1114yes—
297C4×D4—222no—
298C4×D4—222no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4C22×D1112yes—
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C22⋊C4—221no—
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C42—21no—
315C2×C42—112no—
316C2×C42—222no—
317C2×C42C22×D1111yescharacteristic
318#107—24no—
319#106—222no—
320C4⋊C8—22no—
321C4⋊C8—442no—
322#103—24no—
323#103—222no—
324#102—222no—
325#102—442no—
326C4×C8—222no—
327#95—112no—
328#95—222no—
329#95—222no—
330#95—222no—
331C2×C11#241711yescharacteristic
332C2×C11C2×#46411yescharacteristic
333C2×C11#304511yescharacteristic
334C2×C11#330511yescharacteristic
335C2×C11#332911yescharacteristic
336C2×C11#338111yescharacteristic
337C2×C11#338511yescharacteristic
338D11—82no—
339C24—221no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—42no—
344C2×Q8—81no—
345C2×Q8—81no—
346C2×Q8Q8×D1112yes—
347C2×Q8#434312yes—
348C2×Q8C2×C22⋊D1112yes—
349C2×D4—112no—
350C2×D4—221no—
351C2×D4—221no—
352C2×D4—221no—
353C2×D4—221no—
354C2×D4—221no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—112no—
359C22×C4—112no—
360C22×C4—221no—
361C22×C4—222no—
362C22×C4—442no—
363C22×C4—442no—
364C22×C4—442no—
365C22×C4D4×D1111yescharacteristic
366C22×C4D4×D1111yescharacteristic
367C22×C4C23×D1111yescharacteristic
368SD16—228no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—112no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—221no—
376C2×C8—221no—
377C2×C8—221no—
378C4⋊C4—24no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—42no—
383C4⋊C4—222no—
384C4⋊C4—222no—
385C4⋊C4—221no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—221no—
389C4⋊C4—444no—
390C4⋊C4—442no—
391C4⋊C4—881no—
392C4⋊C4—882no—
393C4⋊C4C2×C22⋊D1112yes—
394C22⋊C4—442no—
395C22⋊C4—882no—
396C22⋊C4—882no—
397C42—24no—
398C42—222no—
399C42—222no—
400C42—444no—
401C42#434112yes—
402C42C2×C22⋊D1112yes—
403C11#2481411yescharacteristic, complemented, Sylow
404C23—222no—
405C23—441no—
406C23—441no—
407C23—441no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23C2×D4×D1111yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—22no—
415Q8—84no—
416Q8#6699914yes—
417D4—222no—
418D4—222no—
419D4—441no—
420D4—441no—
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—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—441no—
439C2×C4—442no—
440C2×C4—441no—
441C2×C4—442no—
442C2×C4—441no—
443C2×C4—442no—
444C2×C4—884no—
445C2×C4#6697112yes—
446C2×C4#6697212yes—
447C2×C4#6699212yes—
448C2×C4#6699212yes—
449C2×C4C2×#434111yescharacteristic
450C2×C4C2×Q8×D1111yescharacteristic
451C2×C4C2×#434311yescharacteristic
452C2×C4#6704211yescharacteristic
453C2×C4#6704311yescharacteristic
454C2×C4C22×C22⋊D1111yescharacteristic
455C8—42no—
456C8—222no—
457C8—441no—
458C22—442no—
459C22—442no—
460C22—442no—
461C22—881no—
462C22—881no—
463C22—881no—
464C22—881no—
465C22#1062316111yescharacteristic
466C22#1062316311yescharacteristic
467C22C2×#6697111yescharacteristic
468C22C2×#6697211yescharacteristic
469C22#1062330511yescharacteristic
470C22#1062330611yescharacteristic
471C22C2×#6699211yescharacteristic
472C4—22no—
473C4—24no—
474C4—42no—
475C4—82no—
476C4—442no—
477C4—442no—
478C4—881no—
479C4—882no—
480C4#1062279814yes—
481C4#1062316611yescharacteristic
482C4#1062317311yescharacteristic
483C4C2×#6699911yescharacteristic
484C4#1062336411yescharacteristic
485C2—882no—
486C2#1307206811yescharacteristic
487C2C2×#1062279811yescharacteristic
488C2#1307815911yescharacteristic
489C2#1308056311yescharacteristic
490C2#1308090711yescharacteristic
491C2#1308149011yescharacteristic
492C2#1308152511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#477C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#477D11
hypocenterC11#24814
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. Q8×C4⋊Dic11C2semidirect
4. #13070100C2semidirect
6. #13069578C2semidirect
7. #13069332C2semidirect
9. #13068629C2semidirect
11. C2×C11×#477C2semidirect
62. C2×#4325Q8semidirect
158. C2×#477D11semidirect
403. C11#24814semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43252
#130737902
Q8×C4⋊Dic112
#130701002
#130699992
#130695782
#130693322
#130689692
#130686292
#130686172
C2×C11×#4772
#2481411