Finite Group Databasebeta

← #14808204

Subgroups — #14808204

Order 2816.

968 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623049C211yesmaximal, characteristic
2C2×#10622693C211yesmaximal, characteristic, complemented
3C2×#10622706C211yesmaximal, characteristic, complemented
4#13069819C212yesmaximal
5#13069812C212yesmaximal
6#13069580C211yesmaximal, characteristic, complemented
7#13069435C211yesmaximal, characteristic, complemented
8#13068883C212yesmaximal, complemented
9#13068869C212yesmaximal, complemented
10#13068382C211yesmaximal, characteristic
11C11×#2628C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#66977C2211yescharacteristic
15C2×#66977C2211yescharacteristic
16#10623049—24no—
17#10623049—24no—
18C2×#66942—21no—
19C2×#66942—21no—
20C2×#66932—21no—
21C2×#66932—21no—
22C2×#66923C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C11×#400—21no—
27C11×#399—21no—
28C11×#395—21no—
29C11×#393—21no—
30C11×#389C2212yes—
31C11×#382C2211yescharacteristic
32C11×#380C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34#10622706—24no—
35#10622693—24no—
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38C2×#66874C2212yes—
39C2×#66874C2212yes—
40C2×#66872C2212yes—
41C2×#66871C2212yes—
42C2×#66867C2211yescharacteristic
43C2×C4×C11⋊C8C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C22×Q8×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C22×Dic22C2311yescharacteristic
50C22×Dic22C2311yescharacteristic
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8—22no—
53C11×#117—22no—
54C11×#117—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4D411yescharacteristic
63C2×C11×C22⋊C4D411yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72#66977—22no—
73#66977—22no—
74#66977—22no—
75#66977—22no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11—21no—
84C22×C11⋊C8C2312yes—
85C22×C11⋊C8C2312yes—
86#66942—28no—
87#66942—28no—
88#66932—28no—
89#66932—28no—
90#66923—22no—
91#66923D414yes—
92#66922—22no—
93#66922D414yes—
94C4×Dic22—22no—
95C4×Dic22—22no—
96C4×Dic22—22no—
97C4×Dic22—22no—
98C11×#95—22no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—22no—
102C22⋊(C11⋊C8)—24no—
103#66874—24no—
104#66874—24no—
105#66874—24no—
106#66874—24no—
107#66872—24no—
108#66871—24no—
109#66867—22no—
110C4×C11⋊C8—22no—
111#25686—111nomaximal, Sylow
112C24×C11C2×D411yescharacteristic
113C2×Q8×C11—42no—
114C2×Q8×C11—82no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C2×Dic22—21no—
132C2×Dic22—21no—
133C2×Dic22—22no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22C2×D412yes—
138C2×Dic22C2×D412yes—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4—82no—
147C11×C22⋊C4—22no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—82no—
150C42×C11—21no—
151C42×C11—21no—
152C42×C11C2×D412yes—
153C42×C11C2×D412yes—
154C22⋊Dic11—24no—
155C22⋊Dic11—24no—
156C4⋊Dic11—24no—
157C4⋊Dic11—24no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11C2×D412yes—
161C4⋊Dic11C2×D412yes—
162Dic11⋊C4—24no—
163Dic11⋊C4—24no—
164Dic11⋊C4—24no—
165Dic11⋊C4—24no—
166Dic11⋊C4—24no—
167Dic11⋊C4—24no—
168C4×Dic11—24no—
169C4×Dic11—24no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8#4114yes—
176C2×#541—111no—
177C2×#501—111no—
178C2×#487—111no—
179#2628D1111yescharacteristic
180#2036—112no—
181#2035—112no—
182#1991—111no—
183#1960—111no—
184#1865—112no—
185#1863—112no—
186#1750—111no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11C22×D411yescharacteristic
193Q8×C11—84no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11#12012yes—
212C2×C4×C11#12012yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4112yes—
216C2×C4×C112−1+412yes—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227Dic22—24no—
228Dic22—24no—
229Dic22—42no—
230Dic22—42no—
231C11⋊C8—24no—
232C11⋊C8—42no—
233#541—224no—
234#541—224no—
235C2×C4⋊Q8—111no—
236C2×C4⋊Q8C2×D1111yescharacteristic
237C2×#126—221no—
238C2×#126—221no—
239C2×#125—111no—
240C2×#125—221no—
241C2×#125—221no—
242C2×C22⋊Q8—111no—
243C2×C22⋊Q8—111no—
244C2×C4×Q8—111no—
245C2×C4×Q8—111no—
246C2×#117C2×D1111yescharacteristic
247#501—224no—
248#487—224no—
249C2×#107—112no—
250C2×#106—112no—
251C2×#103—112no—
252C2×#103—112no—
253C2×#103—112no—
254C2×#103—112no—
255C2×C22⋊C8—112no—
256C2×#97—111no—
257C2×C4×C8—111no—
258#400—21no—
259#399—21no—
260#395—21no—
261#393—21no—
262#389C2×D1112yes—
263#382C2×D1111yescharacteristic
264#380C2×D1112yes—
265#340—112no—
266#340—112no—
267#336—112no—
268C22×C11—42no—
269C22×C11—41no—
270C22×C11—42no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11C2×#12011yescharacteristic
274C22×C11#53211yescharacteristic
275C22×C11#53611yescharacteristic
276C22×C11#57712yes—
277C22×C11#57812yes—
278C4×C11—22no—
279C4×C11—22no—
280C4×C11—41no—
281C4×C11—41no—
282C4×C11—41no—
283C4×C11—82no—
284C4×C11—82no—
285C4×C11#54712yes—
286C4×C11#54812yes—
287Dic11—42no—
288Dic11—42no—
289Dic11—42no—
290Dic11—42no—
291C22×Q8—21no—
292C22×Q8—111no—
293C22×Q8—111no—
294C23×C4C22×D1111yescharacteristic
295C22×C8—112no—
296C22×C8—112no—
297C4⋊Q8—22no—
298C4⋊Q8—22no—
299C4⋊Q8—114no—
300C4⋊Q8—222no—
301#126—228no—
302#126—228no—
303#125—114no—
304#125—228no—
305#125—228no—
306#125—222no—
307C22⋊Q8—222no—
308C22⋊Q8—222no—
309C22⋊Q8—222no—
310C22⋊Q8—222no—
311C4×Q8—222no—
312C4×Q8—222no—
313C4×Q8—222no—
314C4×Q8—222no—
315#117—22no—
316#117—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4C22⋊D1111yescharacteristic
330C2×C4⋊C4C22⋊D1111yescharacteristic
331C2×C4⋊C4C22×D1112yes—
332C2×C4⋊C4C22×D1112yes—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—221no—
335C2×C22⋊C4—221no—
336C2×C22⋊C4C22⋊D1111yescharacteristic
337C2×C22⋊C4C22⋊D1111yescharacteristic
338C2×C42—221no—
339C2×C42—221no—
340C2×C42C22×D1111yescharacteristic
341C2×C42C22×D1111yescharacteristic
342#107—224no—
343#106—224no—
344#103—224no—
345#103—224no—
346#103—224no—
347#103—224no—
348C22⋊C8—224no—
349#97—222no—
350C4×C8—222no—
351#95—22no—
352#95—21no—
353#95—21no—
354#95—22no—
355C2×C11—81no—
356C2×C11#243211yescharacteristic
357C2×C11#301011yescharacteristic
358C2×C11#301111yescharacteristic
359C2×C11#317812yes—
360C2×C11#324212yes—
361C24C2×C22⋊D1111yescharacteristic
362C2×Q8—42no—
363C2×Q8—82no—
364C2×Q8—112no—
365C2×Q8—112no—
366C2×Q8—221no—
367C2×Q8—221no—
368C2×Q8—222no—
369C2×Q8—222no—
370C2×Q8—222no—
371C2×Q8—222no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4C2×C22⋊D1111yescharacteristic
383C22×C4C2×C22⋊D1111yescharacteristic
384C22×C4C2×C22⋊D1111yescharacteristic
385C22×C4C2×C22⋊D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C23×D1111yescharacteristic
388C2×C8—114no—
389C2×C8—222no—
390C2×C8—222no—
391C2×C8—222no—
392C2×C8—222no—
393C2×C8—222no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—42no—
401C4⋊C4—82no—
402C4⋊C4—112no—
403C4⋊C4—112no—
404C4⋊C4—224no—
405C4⋊C4—224no—
406C4⋊C4—224no—
407C4⋊C4—224no—
408C4⋊C4—224no—
409C4⋊C4—224no—
410C4⋊C4—224no—
411C4⋊C4—224no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—82no—
417C22⋊C4—224no—
418C22⋊C4—224no—
419C42—21no—
420C42—21no—
421C42—224no—
422C42—224no—
423C42D4×D1112yes—
424C42D4×D1112yes—
425C11#2568611yescharacteristic, complemented, Sylow
426C23—21no—
427C23—21no—
428C23—21no—
429C23—22no—
430C23—22no—
431C23C22×C22⋊D1111yescharacteristic
432Q8—84no—
433Q8—224no—
434Q8—224no—
435Q8—442no—
436Q8—442no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4#6699012yes—
465C2×C4#6699012yes—
466C2×C4C2×D4×D1111yescharacteristic
467C2×C4C2×D4×D1111yescharacteristic
468C2×C4#6704012yes—
469C2×C4#41×D1112yes—
470C8—224no—
471C8—442no—
472C22—42no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—42no—
477C22C2×#6699011yescharacteristic
478C22#1062334711yescharacteristic
479C22#1062336311yescharacteristic
480C22#1062336712yes—
481C22#1062336912yes—
482C4—22no—
483C4—22no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—82no—
488C4—82no—
489C4—442no—
490C4—442no—
491C4—442no—
492C4—442no—
493C4#1062316212yes—
494C4#1062316412yes—
495C2—81no—
496C2#1307224511yescharacteristic
497C2#1307790011yescharacteristic
498C2#1307790911yescharacteristic
499C2#1307927812yes—
500C2#1307988412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2628C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2628D11
hypocenterC11#25686
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
2. C2×#10622693C2semidirect
3. C2×#10622706C2semidirect
6. #13069580C2semidirect
7. #13069435C2semidirect
8. #13068883C2semidirect
9. #13068869C2semidirect
425. C11#25686semidirect

Maximal subgroups

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

subgroupindex
C2×#106230492
C2×#106226932
C2×#106227062
#130698192
#130698122
#130695802
#130694352
#130688832
#130688692
#130683822
C11×#26282
#2568611