Finite Group Databasebeta

← #14808042

Subgroups — #14808042

Order 2816.

1094 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622692C211yesmaximal, characteristic, complemented
2C2×#10622694C211yesmaximal, characteristic, complemented
3#13076968C211yesmaximal, characteristic
4#13069809C214yesmaximal
5#13069578C211yesmaximal, characteristic, complemented
6#13069419C211yesmaximal, characteristic, complemented
7#13068884C214yesmaximal, complemented
8C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
9C2×C11×#533C211yesmaximal, characteristic
10C11×#533—24no—
11C11×#533—24no—
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#125—21no—
15C2×C11×C22⋊Q8—21no—
16C2×C11×C22⋊Q8C2212yes—
17C2×C4×Q8×C11—21no—
18C2×C4×Q8×C11C2212yes—
19C2×C11×#117—21no—
20C22×C42×C11C2211yescharacteristic
21C2×#66977—21no—
22C2×#66922C2211yescharacteristic
23C2×#66899C2214yes—
24C2×#66899C2214yes—
25#10622825—21no—
26#10622825C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28#10622694—24no—
29#10622692—24no—
30C2×#66872C2214yes—
31#10622548C2211yescharacteristic
32#10622542—21no—
33#10622541—21no—
34#10622541C2212yes—
35C2×C4×C11⋊C8C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622167C2214yes—
38#10622162C2212yes—
39C22×Q8×C11—21no—
40C22×Q8×C11C2312yes—
41C23×C4×C11D411yescharacteristic
42C23×C4×C11D411yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×Dic22—21no—
45C11×C4⋊Q8—22no—
46C11×C4⋊Q8—22no—
47C11×C4⋊Q8D414yes—
48C11×C4⋊Q8D414yes—
49C11×#125—28no—
50C11×C22⋊Q8—28no—
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—24no—
53C4×Q8×C11—28no—
54C4×Q8×C11—24no—
55C4×Q8×C11—24no—
56C11×#117—28no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—22no—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11D411yescharacteristic
68C2×C42×C11D411yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2312yes—
76C2×C4⋊Dic11C2312yes—
77#66977—44no—
78C2×Dic11⋊C4—22no—
79C22×C11⋊C8C2312yes—
80C22×C11⋊C8C2312yes—
81#66922—22no—
82#66922—22no—
83#66899—28no—
84#66899—28no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C22⋊(C11⋊C8)—24no—
88#66872—28no—
89C4×C11⋊C8—22no—
90C4×C11⋊C8—22no—
91#25672—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C2×Q8×C11—24no—
94C2×Q8×C11—22no—
95C2×Q8×C11—24no—
96C2×Q8×C11—24no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×Q8×C11C2×D414yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11SD1614yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—22no—
119C22×Dic11—22no—
120C2×Dic22—42no—
121C2×Dic22—42no—
122C2×Dic22—42no—
123C11×C4⋊C4—28no—
124C11×C4⋊C4—28no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4C2×D414yes—
130C11×C22⋊C4—28no—
131C42×C11—28no—
132C42×C11—22no—
133C42×C11—22no—
134C42×C11—21no—
135C42×C11—21no—
136C42×C11C2×D412yes—
137C42×C11C2×D412yes—
138C22⋊Dic11—44no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—24no—
142C4⋊Dic11—42no—
143C4⋊Dic11—42no—
144C4⋊Dic11—42no—
145Dic11⋊C4—44no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8#4114yes—
152C2×#533D1111yescharacteristic
153C2×#498—111no—
154C2×#487—111no—
155#2857—111no—
156#2035—114no—
157#1990—111no—
158#1956—111no—
159#1865—114no—
160C4×C22⋊C8—111no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11C2×SD1612yes—
168C23×C11C22×D411yescharacteristic
169Q8×C11—28no—
170Q8×C11—44no—
171Q8×C11—48no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—28no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—44no—
190C2×C4×C11#12012yes—
191C2×C4×C11#12012yes—
192C2×C4×C11C2×SD1612yes—
193C2×C4×C11C2×SD1612yes—
194C2×C4×C11#13512yes—
195C2×C4×C11#13712yes—
196C2×C4×C11#13712yes—
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4112yes—
200C2×C4×C112−1+412yes—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207Dic22—84no—
208C11⋊C8—24no—
209C11⋊C8—42no—
210#533—24no—
211#533—24no—
212C2×C4⋊Q8—111no—
213C2×C4⋊Q8C2×D1111yescharacteristic
214C2×C4⋊Q8C2×D1111yescharacteristic
215C2×#125—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—221no—
218C2×C22⋊Q8C2×D1112yes—
219C2×C4×Q8—21no—
220C2×C4×Q8C2×D1112yes—
221C2×#117—21no—
222C22×C42C2×D1111yescharacteristic
223#498—224no—
224#487—224no—
225C2×#106—114no—
226C2×#103—114no—
227C2×#103—114no—
228C2×C22⋊C8—112no—
229C2×C4×C8—111no—
230C2×C4×C8—111no—
231#391—221no—
232#389—112no—
233#389—221no—
234#384—111no—
235#380—112no—
236#380—221no—
237#340—114no—
238#336—112no—
239C22×C11—22no—
240C22×C11—22no—
241C22×C11—22no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—41no—
246C22×C11C2×#12011yescharacteristic
247C22×C11#53211yescharacteristic
248C22×C11#53611yescharacteristic
249C22×C11C22×SD1611yescharacteristic
250C22×C11C2×#13511yescharacteristic
251C22×C11C2×#13711yescharacteristic
252C22×C11C2×#13711yescharacteristic
253C4×C11—22no—
254C4×C11—41no—
255C4×C11—44no—
256C4×C11—41no—
257C4×C11—44no—
258C4×C11#44814yes—
259C4×C11#45214yes—
260C4×C11#54712yes—
261C4×C11#54812yes—
262Dic11—82no—
263Dic11—82no—
264C22×Q8—21no—
265C22×Q8—221no—
266C22×Q8C22×D1112yes—
267C23×C4C22⋊D1111yescharacteristic
268C23×C4C22⋊D1111yescharacteristic
269C23×C4C22×D1111yescharacteristic
270C22×C8—112no—
271C22×C8—112no—
272C4⋊Q8—22no—
273C4⋊Q8—22no—
274C4⋊Q8—222no—
275C4⋊Q8—222no—
276C4⋊Q8C22⋊D1114yes—
277C4⋊Q8C22⋊D1114yes—
278#125—28no—
279C22⋊Q8—28no—
280C22⋊Q8—24no—
281C22⋊Q8—24no—
282C22⋊Q8—444no—
283C4×Q8—28no—
284C4×Q8—24no—
285C4×Q8—24no—
286#117—28no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—112no—
293C2×C4⋊C4—112no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4—221no—
298C2×C4⋊C4C22×D1112yes—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—222no—
301C2×C42—22no—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42C22⋊D1111yescharacteristic
305C2×C42C22⋊D1111yescharacteristic
306C2×C42C22×D1111yescharacteristic
307C2×C42C22×D1111yescharacteristic
308#106—228no—
309#103—228no—
310#103—228no—
311C22⋊C8—224no—
312C4×C8—222no—
313C4×C8—222no—
314#95—222no—
315#95—222no—
316C2×C11—42no—
317C2×C11#243211yescharacteristic
318C2×C11C2×#44811yescharacteristic
319C2×C11C2×#45211yescharacteristic
320C2×C11#316711yescharacteristic
321C2×C11#318511yescharacteristic
322C2×C11#322911yescharacteristic
323C2×C11#323111yescharacteristic
324C24C2×C22⋊D1111yescharacteristic
325C2×Q8—24no—
326C2×Q8—22no—
327C2×Q8—24no—
328C2×Q8—24no—
329C2×Q8—42no—
330C2×Q8—42no—
331C2×Q8—442no—
332C2×Q8—442no—
333C2×Q8—442no—
334C2×Q8C2×C22⋊D1114yes—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4#432514yes—
349C22×C4C2×C22⋊D1111yescharacteristic
350C22×C4C2×C22⋊D1111yescharacteristic
351C22×C4C2×C22⋊D1111yescharacteristic
352C22×C4C2×C22⋊D1111yescharacteristic
353C22×C4C2×C22⋊D1111yescharacteristic
354C22×C4C23×D1111yescharacteristic
355C2×C8—114no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—222no—
361C4⋊C4—28no—
362C4⋊C4—28no—
363C4⋊C4—24no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—22no—
367C4⋊C4—224no—
368C4⋊C4—222no—
369C4⋊C4—222no—
370C4⋊C4—444no—
371C4⋊C4—442no—
372C4⋊C4—442no—
373C4⋊C4—442no—
374C4⋊C4C2×C22⋊D1114yes—
375C22⋊C4—28no—
376C22⋊C4—444no—
377C42—28no—
378C42—22no—
379C42—22no—
380C42—21no—
381C42—21no—
382C42C2×C22⋊D1112yes—
383C42C2×C22⋊D1112yes—
384C11#2567211yescharacteristic, complemented, Sylow
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23C2×#432512yes—
392C23C22×C22⋊D1111yescharacteristic
393Q8—28no—
394Q8—44no—
395Q8—48no—
396Q8—884no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—28no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4C2×#432512yes—
422C2×C4C2×#432512yes—
423C2×C4#6699512yes—
424C2×C4#6700312yes—
425C2×C4#6700412yes—
426C2×C4#6700612yes—
427C2×C4#6700612yes—
428C2×C4#41×D1112yes—
429C2×C4#6704312yes—
430C2×C4C22×C22⋊D1111yescharacteristic
431C2×C4C22×C22⋊D1111yescharacteristic
432C8—224no—
433C8—442no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22C22×#432511yescharacteristic
442C22C2×#6699511yescharacteristic
443C22C2×#6700311yescharacteristic
444C22C2×#6700411yescharacteristic
445C22#1062335611yescharacteristic
446C22#1062336311yescharacteristic
447C22C2×#6700611yescharacteristic
448C4—22no—
449C4—41no—
450C4—44no—
451C4—41no—
452C4—44no—
453C4—882no—
454C4—882no—
455C4#1062284014yes—
456C4#1062285214yes—
457C4#1062335512yes—
458C4#1062336212yes—
459C2—42no—
460C2#1307224011yescharacteristic
461C2C2×#1062284011yescharacteristic
462C2C2×#1062285211yescharacteristic
463C2#1307917611yescharacteristic
464C2#1307935711yescharacteristic
465C2#1307975711yescharacteristic
466C2#1307977111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#533D11
hypocenterC11#25672
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×#10622692C2semidirect
2. C2×#10622694C2semidirect
5. #13069578C2semidirect
6. #13069419C2semidirect
7. #13068884C2semidirect
384. C11#25672semidirect

Maximal subgroups

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

subgroupindex
C2×#106226922
C2×#106226942
#130769682
#130698092
#130695782
#130694192
#130688842
C4×C22⋊(C11⋊C8)2
C2×C11×#5332
#2567211