Finite Group Databasebeta

← #14810307

Subgroups — #14810307

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×Q8×D44C211yesmaximal, characteristic
2C2×#10622682C211yesmaximal, characteristic, complemented
3#13073783C211yesmaximal, characteristic
4#13069821C212yesmaximal, complemented
5#13069814C212yesmaximal, complemented
6#13069538C211yesmaximal, characteristic, complemented
7#13069413C211yesmaximal, characteristic
8#13068549C212yesmaximal, complemented
9#13068549C212yesmaximal, complemented
10#13068446C211yesmaximal, characteristic, complemented
11C2×C11×#479C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C2×C11×#125C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15Q8×D44—24no—
16Q8×D44—24no—
17C2×#66950—22no—
18C2×#66950C2212yes—
19C2×C4×D44—21no—
20C2×C4×D44C2211yescharacteristic
21C2×#66922—21no—
22C2×#66922C2211yescharacteristic
23C11×#479—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×#66899C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×#66880C2212yes—
33C2×#66880C2212yes—
34#10622682—24no—
35#10622604—21no—
36#10622603—22no—
37#10622600C2212yes—
38#10622600C2212yes—
39#10622599—21no—
40C2×#66874C2212yes—
41C2×#66874C2212yes—
42C4×C4⋊Dic11C2211yescharacteristic
43C2×#66867C2211yescharacteristic
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C2×Q8×D11—24no—
47C2×Q8×D11—24no—
48C2×Q8×D11—24no—
49C2×Q8×D11—24no—
50C2×Q8×D11—42no—
51C2×Q8×D11—42no—
52C22×D44D411yescharacteristic
53C22×C4×D11—22no—
54C22×C4×D11C2312yes—
55C22×Dic22—22no—
56C22×Dic22C2312yes—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C11×#125—22no—
60C11×#125—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11D414yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4D412yes—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11C2312yes—
80C2×C4×Dic11—21no—
81C22×C11⋊C8C2312yes—
82#66950—216no—
83#66950—24no—
84#66950—24no—
85C4×D44—28no—
86C4×D44—22no—
87C4×D44—22no—
88#66922—28no—
89#66922—22no—
90#66922D414yes—
91C11×#107—22no—
92C11×#106—22no—
93C11×C4⋊C8—22no—
94C11×#103—22no—
95C11×#103—22no—
96#66899—24no—
97C11⋊#95—21no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100(C2×D11)⋊C8—42no—
101(C2×D11)⋊C8—42no—
102#66880—42no—
103#66880—42no—
104#66874—24no—
105#66874—24no—
106#66867—22no—
107#25894—111nomaximal, Sylow
108C23×D11C2×D412yes—
109C2×Q8×C11—21no—
110C2×Q8×C11—22no—
111C2×Q8×C11C2×D412yes—
112C2×Q8×C11#4114yes—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11C2×D412yes—
123Q8×D11—48no—
124Q8×D11—48no—
125Q8×D11—48no—
126Q8×D11—48no—
127C2×D44—24no—
128C2×D44—22no—
129C2×C4×D11—28no—
130C2×C4×D11—22no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—44no—
137C2×C4×D11—44no—
138C2×Dic22—28no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—44no—
145C2×Dic22—44no—
146C2×Dic22C2×D414yes—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4C2×D412yes—
160C42×C11—24no—
161C42×C11C2×D412yes—
162C42×C11C2×D412yes—
163(C2×D11)⋊C4—28no—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4—44no—
166(C2×D11)⋊C4—82no—
167C4⋊Dic11—28no—
168C4⋊Dic11—22no—
169C4⋊Dic11—24no—
170C4⋊Dic11—24no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4×Dic11—81no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×D4×Q8—111no—
178C2×#491—111no—
179C2×#479D1111yescharacteristic, complemented
180#2562—111no—
181#2036—112no—
182#2035—112no—
183#1981—111no—
184#1955—111no—
185#1787—112no—
186#1787—112no—
187#1763—111no—
188C23×C11C22×D411yescharacteristic
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11#13714yes—
196Q8×C11—22no—
197Q8×C11—24no—
198Q8×C11#12414yes—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11#12012yes—
213C2×C4×C11#12012yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4112yes—
217C2×C4×C11H(5,𝔽2)12yes—
218C2×Dic11—22no—
219C2×Dic11—24no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227D44—28no—
228C4×D11—416no—
229C4×D11—42no—
230C4×D11—42no—
231C4×D11—42no—
232C4×D11—42no—
233Dic22—24no—
234Dic22—24no—
235Dic22—416no—
236Dic22—42no—
237Dic22—42no—
238C8×C11—41no—
239C8×C11—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×Q8C2×D1111yescharacteristic
250C2×C4×D4—111no—
251C2×C4×D4—221no—
252#491—224no—
253#479—24no—
254C2×#107C2×D1111yescharacteristic
255C2×#106C2×D1111yescharacteristic
256C2×C4⋊C8C2×D1111yescharacteristic
257C2×#103—112no—
258C2×#103—112no—
259C2×#103—112no—
260C2×#103—112no—
261C2×#103—112no—
262C2×#103C2×D1111yescharacteristic
263C2×#103C2×D1111yescharacteristic
264C2×C22⋊C8—112no—
265C2×C22⋊C8—112no—
266C2×#97—111no—
267#400—221no—
268#394—221no—
269#388—222no—
270#380—112no—
271#380—112no—
272C4×C4⋊C4—111no—
273#340—112no—
274C22×C11C2×#12011yescharacteristic
275C22×C11#54612yes—
276C22×C11C2×#13712yes—
277C22×C11#57711yescharacteristic
278C22×C11#57811yescharacteristic
279C2×D11—24no—
280C2×D11—24no—
281C2×D11—24no—
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—42no—
286C4×C11—24no—
287C4×C11—22no—
288C4×C11—22no—
289C4×C11—42no—
290C4×C11—81no—
291C4×C11—81no—
292C4×C11C2×#12411yescharacteristic
293C4×C11#53511yescharacteristic
294C4×C11#54612yes—
295Dic11—44no—
296Dic11—42no—
297Dic11—82no—
298C22×Q8—112no—
299C22×Q8—222no—
300C22×Q8—224no—
301C22×Q8—224no—
302C22×Q8—224no—
303C22×Q8—224no—
304C22×Q8—442no—
305C22×Q8—442no—
306C22×Q8C22×D1111yescharacteristic
307C22×D4—111no—
308C23×C4—112no—
309C23×C4—222no—
310C22×C8—112no—
311C22×C8C22×D1111yescharacteristic
312C22×C8C22×D1111yescharacteristic
313C4⋊Q8—114no—
314C4⋊Q8—228no—
315C4⋊Q8—222no—
316#125—22no—
317#125—22no—
318C22⋊Q8—224no—
319C22⋊Q8—2216no—
320C22⋊Q8—224no—
321C4×Q8—22no—
322C4×Q8C22⋊D1114yes—
323C4×D4—228no—
324C4×D4—222no—
325C4×D4—222no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—112no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C4⋊C4C22×D1111yescharacteristic
337C2×C22⋊C4—112no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C42—21no—
342C2×C42—221no—
343C2×C42C22×D1111yescharacteristic
344#107—22no—
345#106—22no—
346C4⋊C8—22no—
347#103—22no—
348#103—22no—
349#103—224no—
350#103—224no—
351#103—224no—
352#103—442no—
353#103—442no—
354C22⋊C8—442no—
355C22⋊C8—442no—
356#97—222no—
357#95—222no—
358#95—222no—
359#95—221no—
360C2×C11#243511yescharacteristic
361C2×C11#300411yescharacteristic
362C2×C11#301311yescharacteristic
363C2×C11#331212yes—
364C2×C11#332012yes—
365D11—44no—
366C24—112no—
367C2×Q8—21no—
368C2×Q8—22no—
369C2×Q8—114no—
370C2×Q8—228no—
371C2×Q8—222no—
372C2×Q8—222no—
373C2×Q8—222no—
374C2×Q8—222no—
375C2×Q8—222no—
376C2×Q8—444no—
377C2×Q8—444no—
378C2×Q8—448no—
379C2×Q8—448no—
380C2×Q8—448no—
381C2×Q8—448no—
382C2×Q8#434314yes—
383C2×Q8C2×C22⋊D1112yes—
384C2×D4—224no—
385C2×D4—222no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—112no—
391C22×C4—228no—
392C22×C4—222no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—444no—
401C22×C4—444no—
402C22×C4D4×D1111yescharacteristic
403C22×C4D4×D1111yescharacteristic
404C22×C4C23×D1111yescharacteristic
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—222no—
410C2×C8—222no—
411C2×C8—222no—
412C4⋊C4—24no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—42no—
419C4⋊C4—42no—
420C4⋊C4—228no—
421C4⋊C4—222no—
422C4⋊C4—224no—
423C4⋊C4—224no—
424C4⋊C4—222no—
425C4⋊C4—222no—
426C4⋊C4C2×C22⋊D1112yes—
427C22⋊C4—228no—
428C22⋊C4—224no—
429C22⋊C4—444no—
430C22⋊C4—882no—
431C42—24no—
432C42—881no—
433C42D4×D1112yes—
434C42C2×C22⋊D1112yes—
435C11#2589411yescharacteristic, complemented, Sylow
436C23—114no—
437C23—222no—
438C23—222no—
439C23—222no—
440C23—222no—
441C23—222no—
442C23—222no—
443C23C2×D4×D1111yescharacteristic
444Q8—22no—
445Q8—24no—
446Q8—224no—
447Q8—224no—
448Q8—4416no—
449Q8—442no—
450Q8—442no—
451Q8#6700014yes—
452D4—228no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—222no—
467C2×C4—224no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—4416no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4#6699012yes—
481C2×C4#6699012yes—
482C2×C4C2×D4×D1111yescharacteristic
483C2×C4C2×#434312yes—
484C2×C4#6704212yes—
485C2×C4C22×C22⋊D1111yescharacteristic
486C8—41no—
487C8—41no—
488C8—442no—
489C22—224no—
490C22—224no—
491C22—224no—
492C22—442no—
493C22—442no—
494C22—442no—
495C22—442no—
496C22#1062316112yes—
497C22#1062330111yescharacteristic
498C22#1062330211yescharacteristic
499C22D11×#13712yes—
500C22C2×#6699011yescharacteristic
501C4—22no—
502C4—24no—
503C4—22no—
504C4—42no—
505C4—81no—
506C4—81no—
507C4—442no—
508C4—444no—
509C4—882no—
510C4#1062316112yes—
511C4C2×#6700011yescharacteristic
512C4#1062336111yescharacteristic
513C2—444no—
514C2#1307226811yescharacteristic
515C2#1307784811yescharacteristic
516C2#1307792711yescharacteristic
517C2#1308066412yes—
518C2#1308078412yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#479C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×#479D11
hypocenterC11#25894
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
2. C2×#10622682C2semidirect
4. #13069821C2semidirect
5. #13069814C2semidirect
6. #13069538C2semidirect
8. #13068549C2semidirect
9. #13068549C2semidirect
10. #13068446C2semidirect
11. C2×C11×#479C2semidirect
179. C2×#479D11semidirect
435. C11#25894semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D442
C2×#106226822
#130737832
#130698212
#130698142
#130695382
#130694132
#130685492
#130684462
C2×C11×#4792
#2589411