Finite Group Databasebeta

← #14796424

Subgroups — #14796424

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×#10622704C211yesmaximal, characteristic, complemented
2C2×C4×#4324C211yesmaximal, characteristic
3C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
4#13070098C212yesmaximal, complemented
5#13070004C212yesmaximal
6#13069578C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13068974C212yesmaximal
9#13068628C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic
11C11×#2563C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4324C2211yescharacteristic
15C2×C4×Dic22C2212yes—
16C2×C4×Dic22C2211yescharacteristic
17C11×#393—22no—
18C11×#390C2212yes—
19C11×#382C2212yes—
20C11×#380—21no—
21C11×#380—21no—
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66896C2211yescharacteristic
24C2×#66896C2212yes—
25#10622704—24no—
26C4×#4324—24no—
27#10622589—21no—
28C4⋊C4×Dic11—21no—
29C2×#66874C2211yescharacteristic
30C2×#66874C2212yes—
31C2×#66872C2211yescharacteristic
32C2×#66871C2212yes—
33#10622548C2211yescharacteristic
34#10622541C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2212yes—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622260—22no—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×Q8×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×Dic22C2311yescharacteristic
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C4×D4×C11—22no—
50C4×D4×C11—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4—22no—
59C2×C42×C11C2312yes—
60C2×C42×C11C2311yescharacteristic
61C2×#4324—22no—
62C2×#4324—22no—
63C2×#4324Q814yescomplemented
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11—21no—
72C2×C4×Dic11—22no—
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2312yes—
75C22×C11⋊C8C2311yescharacteristic
76C4×Dic22—22no—
77C4×Dic22—24no—
78C4×Dic22—42no—
79C4×Dic22D414yes—
80C11×#95—22no—
81C11×#95—22no—
82C11×#95D412yes—
83#66896—22no—
84#66896—42no—
85C11⋊#95—22no—
86#66874—22no—
87#66874—24no—
88#66872—22no—
89#66871—24no—
90C4⋊(C11⋊C8)—22no—
91C4⋊(C11⋊C8)—42no—
92C4×C11⋊C8—22no—
93#24814—111nomaximal, Sylow
94C24×C11—21no—
95C2×Q8×C11—42no—
96C2×Q8×C11—81no—
97C2×Q8×C11—81no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11C2×Q812yes—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—22no—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22C2×D412yes—
121C2×Dic22C2×Q812yes—
122C2×Dic22#4112yes—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—42no—
130C11×C22⋊C4—42no—
131C11×C22⋊C4—82no—
132C11×C22⋊C4—82no—
133C42×C11—22no—
134C42×C11—22no—
135C42×C11C2×D412yes—
136C42×C11#4112yes—
137#4324—28no—
138C4⋊Dic11—21no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—42no—
142C4⋊Dic11—81no—
143C4⋊Dic11C2×D412yes—
144Dic11⋊C4—24no—
145Dic11⋊C4—44no—
146Dic11⋊C4—82no—
147C4×Dic11—24no—
148C4×Dic11—44no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8C2×Q812yes—
158C2×#477—111no—
159C2×C4×SD16—111no—
160#2563D1111yescharacteristic
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—84no—
178D4×C11—22no—
179D4×C11—22no—
180D4×C11—41no—
181D4×C11—41no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
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—41no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216Dic22—22no—
217Dic22—22no—
218Dic22—22no—
219Dic22C22⋊Q814yes—
220C11⋊C8—22no—
221C11⋊C8—41no—
222C11⋊C8—42no—
223C22×SD16—111no—
224C2×C4⋊Q8C2×D1111yescharacteristic
225C2×C4×Q8—111no—
226C2×C4×Q8—112no—
227C2×C4×D4C2×D1111yescharacteristic
228#477—224no—
229C4×SD16—224no—
230C2×#107—112no—
231C2×#106—111no—
232C2×C4⋊C8—111no—
233C2×C4⋊C8—112no—
234C2×#103—112no—
235C2×#103—111no—
236C2×#102—111no—
237C2×#102—112no—
238C2×C4×C8—111no—
239#393—22no—
240#390C2×D1112yes—
241#389—112no—
242#389—222no—
243#384—111no—
244#384—221no—
245#382C2×D1112yes—
246#380—21no—
247#380—21no—
248C4×C4⋊C4—221no—
249C4×C4⋊C4C2×D1111yescharacteristic
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—22no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—81no—
272C4×C11—82no—
273C4×C11#46414yes—
274C4×C11C2×C22⋊Q811yescharacteristic
275C4×C11#53711yescharacteristic
276C4×C11#55211yescharacteristic
277C4×C11#55411yescharacteristic
278Dic11—24no—
279Dic11—42no—
280Dic11—82no—
281C22×Q8—21no—
282C22×Q8—111no—
283C22×D4C22×D1111yescharacteristic
284C23×C4—21no—
285C2×SD16—114no—
286C2×SD16—222no—
287C2×SD16—222no—
288C22×C8—111no—
289C22×C8—112no—
290C22×C8—111no—
291C4⋊Q8—22no—
292C4⋊Q8—22no—
293C4×Q8—114no—
294C4×Q8—224no—
295C4×Q8—222no—
296C4×Q8—442no—
297C4×D4—22no—
298C4×D4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4C22⋊D1111yescharacteristic
308C2×C4⋊C4C22⋊D1111yescharacteristic
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C4⋊C4C22×D1112yes—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C42—221no—
315C2×C42—222no—
316C2×C42C22×D1112yes—
317C2×C42C22×D1111yescharacteristic
318#107—224no—
319#106—222no—
320C4⋊C8—222no—
321C4⋊C8—442no—
322#103—222no—
323#103—224no—
324#102—222no—
325#102—442no—
326C4×C8—222no—
327#95—22no—
328#95—22no—
329#95—222no—
330#95C22⋊D1112yes—
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—42no—
341C2×Q8—81no—
342C2×Q8—81no—
343C2×Q8—112no—
344C2×Q8—112no—
345C2×Q8—112no—
346C2×Q8—221no—
347C2×Q8—221no—
348C2×Q8—221no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4Q8×D1112yes—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—222no—
363C22×C4C2×C22⋊D1112yes—
364C22×C4C2×C22⋊D1112yes—
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367C22×C4C23×D1111yescharacteristic
368SD16—228no—
369C2×C8—112no—
370C2×C8—221no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8—221no—
376C2×C8—222no—
377C2×C8—221no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—42no—
385C4⋊C4—112no—
386C4⋊C4—224no—
387C4⋊C4—221no—
388C4⋊C4—222no—
389C4⋊C4—222no—
390C4⋊C4—444no—
391C4⋊C4—442no—
392C4⋊C4—882no—
393C4⋊C4—881no—
394C22⋊C4—42no—
395C22⋊C4—82no—
396C22⋊C4—82no—
397C42—22no—
398C42—22no—
399C42—224no—
400C42—444no—
401C42D4×D1112yes—
402C42#434112yes—
403C11#2481411yescharacteristic, complemented, Sylow
404C23—22no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23C22×C22⋊D1111yescharacteristic
412Q8—84no—
413Q8—114no—
414Q8—222no—
415Q8—222no—
416Q8—222no—
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—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—84no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4#6699112yes—
446C2×C4#6699112yes—
447C2×C4#6700312yes—
448C2×C4#6700412yes—
449C2×C4C2×D4×D1111yescharacteristic
450C2×C4C2×#434111yescharacteristic
451C2×C4C2×Q8×D1111yescharacteristic
452C2×C4#6704011yescharacteristic
453C2×C4#41×D1111yescharacteristic
454C2×C4#6704211yescharacteristic
455C8—222no—
456C8—441no—
457C8—442no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22C2×#6699111yescharacteristic
466C22Q8×C22⋊D1111yescharacteristic
467C22C2×#6700311yescharacteristic
468C22C2×#6700411yescharacteristic
469C22#1062336011yescharacteristic
470C22#1062336611yescharacteristic
471C22#1062336711yescharacteristic
472C4—22no—
473C4—42no—
474C4—42no—
475C4—81no—
476C4—82no—
477C4—224no—
478C4—442no—
479C4—882no—
480C4#1062266714yes—
481C4D11×C22⋊Q811yescharacteristic
482C4#1062316011yescharacteristic
483C4#1062316611yescharacteristic
484C4#1062317011yescharacteristic
485C2—82no—
486C2#1307206311yescharacteristic
487C2C2×#1062266711yescharacteristic
488C2#1307815111yescharacteristic
489C2#1308056011yescharacteristic
490C2#1308090411yescharacteristic
491C2#1308149111yescharacteristic
492C2#1308152611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2563C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2563D11
hypocenterC11#24814
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2563

Complements

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

NH ≅ G/Ntype
1. C2×#10622704C2semidirect
3. C4⋊C4×Dic22C2semidirect
4. #13070098C2semidirect
6. #13069578C2semidirect
7. #13069335C2semidirect
9. #13068628C2semidirect
63. C2×#4324Q8semidirect
403. C11#24814semidirect

Maximal subgroups

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

subgroupindex
C2×#106227042
C2×C4×#43242
C4⋊C4×Dic222
#130700982
#130700042
#130695782
#130693352
#130689742
#130686282
#130686162
C11×#25632
#2481411