Finite Group Databasebeta

← #14810309

Subgroups — #14810309

Order 2816.

1260 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic22C211yesmaximal, characteristic
2C2×#10622682C211yesmaximal, characteristic, complemented
3C2×#10622676C211yesmaximal, characteristic, complemented
4#13069819C212yesmaximal, complemented
5#13069812C212yesmaximal, complemented
6#13069539C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic
8#13068550C212yesmaximal, complemented
9#13068550C212yesmaximal, complemented
10#13068449C211yesmaximal, characteristic, complemented
11C11×#2562C211yesmaximal, characteristic
12C23×Dic22C2212yes—
13C2×C11×#125C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×D4×Dic11—21no—
16C2×#66977C2212yes—
17D4×Dic22—24no—
18D4×Dic22—24no—
19C2×#66941—21no—
20C2×#66931—22no—
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#400—21no—
24C11×#394—21no—
25C11×#388—22no—
26C11×#380C2212yes—
27C11×#380C2212yes—
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622682—24no—
32#10622676—24no—
33C2×#66874C2211yescharacteristic
34C2×#66874C2211yescharacteristic
35C2×#66874C2212yes—
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38C2×#66874C2212yes—
39C2×#66874C2212yes—
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×#66867C2211yescharacteristic
44#10622167C2212yes—
45C22×D4×C11D411yescharacteristic
46C23×C4×C11C2312yes—
47C23×Dic11—22no—
48C22×Dic22—22no—
49C22×Dic22—24no—
50C22×Dic22—24no—
51C22×Dic22—24no—
52C22×Dic22—24no—
53C22×Dic22—42no—
54C22×Dic22—42no—
55C22×Dic22C2312yes—
56C22×Dic22C2311yescharacteristic
57C11×#125—22no—
58C11×#125—22no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4D412yes—
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—22no—
73D4×Dic11—28no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77#66977—24no—
78#66977—24no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—22no—
81C2×C4×Dic11—21no—
82C22×C11⋊C8C2312yes—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85#66941—28no—
86#66931—216no—
87#66922—22no—
88#66922D414yes—
89C4×Dic22—22no—
90C4×Dic22D414yes—
91C11×#95—21no—
92C11×#95—22no—
93C11×#95—22no—
94C22⋊(C11⋊C8)—42no—
95C22⋊(C11⋊C8)—42no—
96#66874—22no—
97#66874—22no—
98#66874—24no—
99#66874—24no—
100#66874—24no—
101#66874—42no—
102#66874—42no—
103#66872—22no—
104#66871—22no—
105C4⋊(C11⋊C8)—22no—
106#66867—22no—
107#25894—111nomaximal, Sylow
108C24×C11C2×D412yes—
109C2×D4×C11—24no—
110C2×D4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—28no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C22×Dic11—44no—
129C22×Dic11—44no—
130C2×Dic22—28no—
131C2×Dic22—21no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22—22no—
138C2×Dic22—44no—
139C2×Dic22—44no—
140C2×Dic22—48no—
141C2×Dic22—48no—
142C2×Dic22—48no—
143C2×Dic22—48no—
144C2×Dic22C2×D414yes—
145C2×Dic22C2×D412yes—
146C2×Dic22#4114yes—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—42no—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—44no—
158C11×C22⋊C4—82no—
159C42×C11—81no—
160C42×C11C2×D412yes—
161C42×C11C2×D412yes—
162C22⋊Dic11—28no—
163C4⋊Dic11—24no—
164C4⋊Dic11—24no—
165C4⋊Dic11—21no—
166C4⋊Dic11C2×D412yes—
167Dic11⋊C4—28no—
168Dic11⋊C4—24no—
169C4×Dic11—24no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×D4×Q8—111no—
178C2×#491—111no—
179C2×#479—111no—
180#2562D1111yescharacteristic
181#2036—112no—
182#2035—112no—
183#1981—111no—
184#1955—111no—
185#1787—112no—
186#1787—112no—
187#1763—111no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11#13714yes—
195C23×C11C22×D411yescharacteristic
196D4×C11—28no—
197C2×C4×C11—22no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
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—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11#12012yes—
216C2×C4×C11#12012yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4112yes—
220C2×C4×C11H(5,𝔽2)12yes—
221C2×Dic11—22no—
222C2×Dic11—24no—
223C2×Dic11—22no—
224C2×Dic11—24no—
225C2×Dic11—416no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230Dic22—22no—
231Dic22—24no—
232Dic22—24no—
233Dic22—24no—
234Dic22—416no—
235Dic22—42no—
236Dic22—42no—
237Dic22#12414yes—
238C11⋊C8—41no—
239C11⋊C8—41no—
240C11⋊C8—42no—
241C23×Q8—112no—
242D4×Q8—224no—
243D4×Q8—224no—
244C2×C4⋊Q8—111no—
245C2×C4⋊Q8—221no—
246C2×#125C2×D1111yescharacteristic
247C2×C22⋊Q8—112no—
248C2×C22⋊Q8—222no—
249C2×C4×Q8—111no—
250C2×C4×D4—221no—
251C2×C4×D4C2×D1111yescharacteristic
252#491—224no—
253#479—224no—
254C2×#107—111no—
255C2×#106—111no—
256C2×C4⋊C8—111no—
257C2×#103—111no—
258C2×#103—111no—
259C2×#103—112no—
260C2×#103—112no—
261C2×#103—112no—
262C2×#103—112no—
263C2×#103—112no—
264C2×C22⋊C8—112no—
265C2×C22⋊C8—112no—
266C2×#97—111no—
267#400—21no—
268#394—21no—
269#388—22no—
270#380C2×D1112yes—
271#380C2×D1112yes—
272C4×C4⋊C4C2×D1111yescharacteristic
273#340—112no—
274C22×C11—24no—
275C22×C11—24no—
276C22×C11—24no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11C2×#12011yescharacteristic
282C22×C11#54612yes—
283C22×C11C2×#13712yes—
284C22×C11#57711yescharacteristic
285C22×C11#57811yescharacteristic
286C4×C11—22no—
287C4×C11—22no—
288C4×C11—42no—
289C4×C11—81no—
290C4×C11—81no—
291C4×C11—82no—
292C4×C11C2×#12411yescharacteristic
293C4×C11#53511yescharacteristic
294C4×C11#54612yes—
295Dic11—24no—
296Dic11—44no—
297Dic11—42no—
298C22×Q8—111no—
299C22×Q8—112no—
300C22×Q8—224no—
301C22×Q8—224no—
302C22×Q8—224no—
303C22×Q8—224no—
304C22×Q8—222no—
305C22×Q8—442no—
306C22×Q8—442no—
307C22×D4C22⋊D1111yescharacteristic
308C23×C4—222no—
309C23×C4C22×D1112yes—
310C22×C8—112no—
311C22×C8—111no—
312C22×C8—111no—
313C4⋊Q8—114no—
314C4⋊Q8—228no—
315C4⋊Q8—222no—
316#125—22no—
317#125—22no—
318C22⋊Q8—2216no—
319C22⋊Q8—224no—
320C22⋊Q8—224no—
321C4×Q8—114no—
322C4×Q8—222no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—228no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4C22⋊D1111yescharacteristic
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C4⋊C4C22×D1112yes—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4C22⋊D1112yes—
341C2×C42—21no—
342C2×C42—221no—
343C2×C42C22×D1111yescharacteristic
344#107—222no—
345#106—222no—
346C4⋊C8—222no—
347#103—224no—
348#103—222no—
349#103—222no—
350#103—224no—
351#103—224no—
352#103—442no—
353#103—442no—
354C22⋊C8—442no—
355C22⋊C8—442no—
356#97—222no—
357#95—21no—
358#95—22no—
359#95—22no—
360C2×C11—44no—
361C2×C11#243511yescharacteristic
362C2×C11#300411yescharacteristic
363C2×C11#301311yescharacteristic
364C2×C11#331212yes—
365C2×C11#332012yes—
366C24C2×C22⋊D1112yes—
367C2×Q8—112no—
368C2×Q8—114no—
369C2×Q8—114no—
370C2×Q8—228no—
371C2×Q8—221no—
372C2×Q8—222no—
373C2×Q8—222no—
374C2×Q8—222no—
375C2×Q8—222no—
376C2×Q8—222no—
377C2×Q8—222no—
378C2×Q8—444no—
379C2×Q8—444no—
380C2×Q8—448no—
381C2×Q8—448no—
382C2×Q8—448no—
383C2×Q8—448no—
384C2×D4—24no—
385C2×D4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—221no—
396C22×C4—228no—
397C22×C4—221no—
398C22×C4—222no—
399C22×C4—444no—
400C22×C4—444no—
401C22×C4C2×C22⋊D1112yes—
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C2×C22⋊D1111yescharacteristic
404C22×C4C23×D1111yescharacteristic
405C2×C8—222no—
406C2×C8—221no—
407C2×C8—221no—
408C2×C8—222no—
409C2×C8—222no—
410C2×C8—222no—
411C2×C8—222no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—42no—
420C4⋊C4—42no—
421C4⋊C4—112no—
422C4⋊C4—228no—
423C4⋊C4—224no—
424C4⋊C4—224no—
425C4⋊C4—224no—
426C4⋊C4—221no—
427C22⋊C4—24no—
428C22⋊C4—44no—
429C22⋊C4—82no—
430C22⋊C4—228no—
431C42—81no—
432C42—224no—
433C42D4×D1112yes—
434C42D4×D1112yes—
435C11#2589411yescharacteristic, complemented, Sylow
436C23—22no—
437C23—22no—
438C23—22no—
439C23—22no—
440C23—22no—
441C23—22no—
442C23#6700414yes—
443C23C22×C22⋊D1111yescharacteristic
444Q8—114no—
445Q8—222no—
446Q8—224no—
447Q8—224no—
448Q8—224no—
449Q8—4416no—
450Q8—442no—
451Q8—442no—
452D4—28no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—222no—
472C2×C4—224no—
473C2×C4—222no—
474C2×C4—224no—
475C2×C4—4416no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4#6699012yes—
481C2×C4#6699012yes—
482C2×C4C2×D4×D1111yescharacteristic
483C2×C4C2×D4×D1111yescharacteristic
484C2×C4#41×D1112yes—
485C2×C4#6704212yes—
486C8—441no—
487C8—441no—
488C8—442no—
489C22—24no—
490C22—24no—
491C22—24no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22C2×#6699011yescharacteristic
497C22C2×#6700412yes—
498C22#1062336012yes—
499C22#1062336711yescharacteristic
500C22#1062336911yescharacteristic
501C4—22no—
502C4—22no—
503C4—42no—
504C4—81no—
505C4—81no—
506C4—82no—
507C4—224no—
508C4—444no—
509C4—442no—
510C4D11×#12411yescharacteristic
511C4#1062320511yescharacteristic
512C4#1062320712yes—
513C2—44no—
514C2#1307226411yescharacteristic
515C2#1307784911yescharacteristic
516C2#1307792811yescharacteristic
517C2#1308066112yes—
518C2#1308078112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2562C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2562D11
hypocenterC11#25894
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2562

Complements

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

NH ≅ G/Ntype
2. C2×#10622682C2semidirect
3. C2×#10622676C2semidirect
4. #13069819C2semidirect
5. #13069812C2semidirect
6. #13069539C2semidirect
8. #13068550C2semidirect
9. #13068550C2semidirect
10. #13068449C2semidirect
435. C11#25894semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
C2×#106226822
C2×#106226762
#130698192
#130698122
#130695392
#130694152
#130685502
#130684492
C11×#25622
#2589411