Finite Group Databasebeta

← #14810744

Subgroups — #14810744

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623098C211yesmaximal, characteristic, complemented
2C2×#10622668C211yesmaximal, characteristic
3C2×#10622667C211yesmaximal, characteristic
4#13069767C212yesmaximal, complemented
5#13069762C212yesmaximal
6#13069564C211yesmaximal, characteristic, complemented
7#13069557C211yesmaximal, characteristic, complemented
8#13068974C212yesmaximal
9#13068960C212yesmaximal, complemented
10#13068449C211yesmaximal, characteristic, complemented
11C11×#2592C211yesmaximal, characteristic
12C2×C11×#124C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#66997—21no—
15C22×#4326C2211yescharacteristic
16C22×#4324C2211yescharacteristic
17#10623098—24no—
18#10623098—24no—
19C2×#66942—22no—
20C2×#66940—21no—
21C2×#66923C2212yes—
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22C2212yes—
24C2×C4×Dic22C2211yescharacteristic
25C11×#397—21no—
26C11×#393—21no—
27C11×#391C2212yes—
28C11×#390C2212yes—
29C11×#388—22no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2212yes—
33C2×#66896C2211yescharacteristic
34C2×#66896C2212yes—
35#10622668—24no—
36#10622667—24no—
37C2×#66874C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C22×Dic22—21no—
49C22×Dic22C2311yescharacteristic
50C11×#124—22no—
51C11×#124—22no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—22no—
61C2×C42×C11—21no—
62C2×C42×C11C2312yes—
63C2×C42×C11C2311yescharacteristic
64#66997—28no—
65C2×#4326—22no—
66C2×#4326—24no—
67C2×#4324—22no—
68C2×#4324—24no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2311yescharacteristic
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11—21no—
78C22×C11⋊C8C2312yes—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81#66942—216no—
82#66940—28no—
83#66923—24no—
84#66923—24no—
85#66922—22no—
86#66922D414yes—
87C4×Dic22—24no—
88C4×Dic22—22no—
89C4×Dic22—24no—
90C4×Dic22D414yes—
91C11×#95—21no—
92C11×#95—22no—
93C11×#95—22no—
94#66899—22no—
95#66899—24no—
96#66896—22no—
97#66896—24no—
98#66874—24no—
99C4⋊(C11⋊C8)—22no—
100#66867—22no—
101#25941—111nomaximal, Sylow
102C24×C11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—42no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C2×Dic22—24no—
124C2×Dic22—21no—
125C2×Dic22—22no—
126C2×Dic22—44no—
127C2×Dic22C2×D412yes—
128C2×Dic22#4114yes—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C22⋊C4—44no—
134C11×C22⋊C4—42no—
135C11×C22⋊C4—42no—
136C11×C22⋊C4—82no—
137C42×C11—22no—
138C42×C11—22no—
139C42×C11—81no—
140C42×C11C2×D412yes—
141C42×C11C2×D412yes—
142#4326—44no—
143#4324—44no—
144C4⋊Dic11—24no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11C2×D414yes—
148C4⋊Dic11C2×D412yes—
149Dic11⋊C4—28no—
150Dic11⋊C4—28no—
151Dic11⋊C4—28no—
152Dic11⋊C4—24no—
153C4×Dic11—28no—
154C4×Dic11—24no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×#557—111no—
163C2×#489—111no—
164C2×#464—111no—
165#2592D1111yescharacteristic
166#2026—112no—
167#2025—112no—
168#1987—111no—
169#1985—111no—
170#1880—112no—
171#1878—112no—
172#1763—111no—
173C23×C11—41no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11C22×D411yescharacteristic
179Q8×C11—44no—
180Q8×C11—41no—
181Q8×C11—41no—
182Q8×C11—42no—
183D4×C11—41no—
184D4×C11—41no—
185D4×C11—42no—
186C2×C4×C11—22no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11#12012yes—
201C2×C4×C11#12012yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4112yes—
205C2×C4×C112−1+412yes—
206C2×Dic11—22no—
207C2×Dic11—24no—
208C2×Dic11—22no—
209C2×Dic11—24no—
210C2×Dic11—44no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213Dic22—22no—
214Dic22—24no—
215Dic22—48no—
216Dic22#12414yes—
217C11⋊C8—41no—
218C11⋊C8—41no—
219C11⋊C8—42no—
220C22×Q16—111no—
221C22×SD16—111no—
222#557—224no—
223#557—224no—
224C2×C4⋊Q8—111no—
225C2×C4⋊Q8—221no—
226C2×#125—112no—
227C2×#125—222no—
228C2×#124C2×D1111yescharacteristic
229C2×C4×Q8—111no—
230C2×C4×Q8—112no—
231C2×C4×Q8—221no—
232C2×C4×Q8C2×D1111yescharacteristic
233#489—224no—
234#464—224no—
235C2×C4⋊C8—111no—
236C2×#103—112no—
237C2×#103—111no—
238C2×#103—112no—
239C2×#102—112no—
240C2×#102—111no—
241C2×#97—111no—
242#397—21no—
243#393—21no—
244#391C2×D1112yes—
245#390C2×D1112yes—
246#388—22no—
247C4×C4⋊C4C2×D1111yescharacteristic
248#340—112no—
249#340—112no—
250#340—112no—
251#336—112no—
252#336—112no—
253C22×C11—82no—
254C22×C11—82no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11C2×#12011yescharacteristic
259C22×C11#54812yes—
260C22×C11#57512yes—
261C22×C11#57711yescharacteristic
262C22×C11#57811yescharacteristic
263C4×C11—22no—
264C4×C11—22no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—82no—
268C4×C11—81no—
269C4×C11C2×#12411yescharacteristic
270C4×C11#53611yescharacteristic
271C4×C11#54812yes—
272Dic11—24no—
273Dic11—44no—
274Dic11—42no—
275C22×Q8—111no—
276C22×Q8—221no—
277C22×Q8C22⋊D1111yescharacteristic
278C22×Q8C22×D1111yescharacteristic
279C22×D4C22×D1111yescharacteristic
280C2×Q16—224no—
281C2×Q16—222no—
282C2×SD16—224no—
283C2×SD16—222no—
284C22×C8—111no—
285C22×C8—111no—
286C22×C8—112no—
287C4⋊Q8—114no—
288C4⋊Q8—228no—
289C4⋊Q8—222no—
290#125—224no—
291#125—224no—
292#125—2216no—
293#124—22no—
294#124—22no—
295C4×Q8—22no—
296C4×Q8—22no—
297C4×Q8—114no—
298C4×Q8—224no—
299C4×Q8—224no—
300C4×Q8—228no—
301C4×Q8—222no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—112no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4C22⋊D1111yescharacteristic
310C2×C4⋊C4C22⋊D1112yes—
311C2×C4⋊C4C22×D1112yes—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C42—21no—
317C2×C42—222no—
318C2×C42—221no—
319C2×C42C22×D1112yes—
320C2×C42C22×D1111yescharacteristic
321C4⋊C8—222no—
322#103—224no—
323#103—222no—
324#103—224no—
325#102—222no—
326#102—224no—
327#97—222no—
328#95—21no—
329#95—22no—
330#95—22no—
331C2×C11—161no—
332C2×C11#243611yescharacteristic
333C2×C11#300511yescharacteristic
334C2×C11#301311yescharacteristic
335C2×C11#337112yes—
336C2×C11#337712yes—
337C24—21no—
338C2×Q8—22no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—42no—
344C2×Q8—112no—
345C2×Q8—114no—
346C2×Q8—224no—
347C2×Q8—221no—
348C2×Q8—222no—
349C2×Q8—444no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—22no—
353C2×D4—22no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—222no—
359C22×C4C2×C22⋊D1112yes—
360C22×C4C2×C22⋊D1112yes—
361C22×C4C2×C22⋊D1111yescharacteristic
362C22×C4C2×C22⋊D1111yescharacteristic
363C22×C4C23×D1111yescharacteristic
364Q16—444no—
365SD16—444no—
366C2×C8—222no—
367C2×C8—221no—
368C2×C8—221no—
369C2×C8—222no—
370C2×C8—222no—
371C2×C8—222no—
372C2×C8—222no—
373C4⋊C4—22no—
374C4⋊C4—24no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—112no—
378C4⋊C4—114no—
379C4⋊C4—228no—
380C4⋊C4—228no—
381C4⋊C4—228no—
382C4⋊C4—224no—
383C4⋊C4—224no—
384C4⋊C4—221no—
385C4⋊C4—222no—
386C22⋊C4—44no—
387C22⋊C4—42no—
388C22⋊C4—42no—
389C22⋊C4—82no—
390C42—22no—
391C42—22no—
392C42—81no—
393C42—228no—
394C42—224no—
395C42D4×D1112yes—
396C42D4×D1112yes—
397C11#2594111yescharacteristic, complemented, Sylow
398C23—41no—
399C23—42no—
400C23—42no—
401C23—41no—
402C23—41no—
403C23C22×C22⋊D1111yescharacteristic
404Q8—44no—
405Q8—41no—
406Q8—41no—
407Q8—42no—
408Q8—114no—
409Q8—222no—
410Q8—224no—
411Q8—448no—
412D4—41no—
413D4—41no—
414D4—42no—
415C2×C4—22no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—222no—
430C2×C4—224no—
431C2×C4—222no—
432C2×C4—224no—
433C2×C4—444no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4#6699012yes—
437C2×C4#6699012yes—
438C2×C4C2×D4×D1111yescharacteristic
439C2×C4C2×D4×D1111yescharacteristic
440C2×C4#41×D1112yes—
441C2×C4#6704312yes—
442C8—441no—
443C8—441no—
444C8—442no—
445C22—82no—
446C22—81no—
447C22—82no—
448C22—81no—
449C22—81no—
450C22C2×#6699011yescharacteristic
451C22#1062335312yes—
452C22#1062336212yes—
453C22#1062336711yescharacteristic
454C22#1062336911yescharacteristic
455C4—22no—
456C4—22no—
457C4—42no—
458C4—42no—
459C4—82no—
460C4—81no—
461C4—224no—
462C4—444no—
463C4—442no—
464C4D11×#12411yescharacteristic
465C4#1062320611yescharacteristic
466C4#1062320812yes—
467C2—161no—
468C2#1307227111yescharacteristic
469C2#1307785611yescharacteristic
470C2#1307792811yescharacteristic
471C2#1308137812yes—
472C2#1308145212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2592C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2592D11
hypocenterC11#25941
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2592

Complements

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

NH ≅ G/Ntype
1. C2×#10623098C2semidirect
4. #13069767C2semidirect
6. #13069564C2semidirect
7. #13069557C2semidirect
9. #13068960C2semidirect
10. #13068449C2semidirect
397. C11#25941semidirect

Maximal subgroups

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

subgroupindex
C2×#106230982
C2×#106226682
C2×#106226672
#130697672
#130697622
#130695642
#130695572
#130689742
#130689602
#130684492
C11×#25922
#2594111