Finite Group Databasebeta

← #14796411

Subgroups — #14796411

Order 2816.

894 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×#10622633C211yesmaximal, characteristic, complemented
2C2×C4×#4325C211yesmaximal, characteristic
3#13073565C211yesmaximal, characteristic
4#13070092C212yesmaximal, complemented
5#13069987C212yesmaximal
6#13069576C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13068971C212yesmaximal
9#13068621C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic
11Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C22×#4325C2211yescharacteristic
15C2×#66950—21no—
16C2×#66950—21no—
17C2×C4×D44C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C11×#389—22no—
20C11×#389C2212yes—
21C11×#384—21no—
22C11×#384C2211yescharacteristic
23C4×C11×C4⋊C4—21no—
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66899C2212yes—
27C4×#4325—24no—
28#10622633—24no—
29C2×#66873C2211yescharacteristic
30C2×#66873C2212yes—
31C2×#66872C2211yescharacteristic
32C2×#66872C2212yes—
33#10622552C2212yes—
34#10622548C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2212yes—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622290—22no—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22—21no—
47C4×Q8×C11—22no—
48C4×Q8×C11—24no—
49C4×Q8×C11—42no—
50C4×Q8×C11D414yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11—22no—
62C2×C42×C11C2312yes—
63C2×C42×C11C2311yescharacteristic
64C2×#4325—22no—
65C2×#4325—22no—
66C2×#4325Q814yescomplemented
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77C22×C11⋊C8C2311yescharacteristic
78#66950—44no—
79#66950—44no—
80C4×D44—22no—
81C4×D44—22no—
82#66922—22no—
83#66922—22no—
84C11×#95—22no—
85C11×#95D412yes—
86#66899—24no—
87#66899—22no—
88#66873—22no—
89#66873—42no—
90#66872—24no—
91#66872—22no—
92C4⋊(C11⋊C8)—22no—
93C4⋊(C11⋊C8)—42no—
94C4×C11⋊C8—22no—
95#24813—111nomaximal, Sylow
96C23×D11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11C2×D412yes—
101C2×Q8×C11C2×Q812yes—
102C2×Q8×C11#4112yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—22no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44C2×Q812yes—
119C2×C4×D11—42no—
120C2×C4×D11—42no—
121C2×C4×D11—42no—
122C2×Dic22—42no—
123C2×Dic22—42no—
124C2×Dic22—42no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—44no—
131C11×C4⋊C4—42no—
132C11×C4⋊C4—81no—
133C11×C4⋊C4—82no—
134C11×C4⋊C4SD1614yescomplemented
135C11×C4⋊C4C2×D412yes—
136C42×C11—24no—
137C42×C11—22no—
138C42×C11—22no—
139C42×C11—44no—
140C42×C11C2×D412yes—
141C42×C11#4112yes—
142#4325—28no—
143(C2×D11)⋊C4—44no—
144(C2×D11)⋊C4—42no—
145(C2×D11)⋊C4—44no—
146C4⋊Dic11—22no—
147C4⋊Dic11—21no—
148C4⋊Dic11—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11—44no—
151C4⋊Dic11—42no—
152C4⋊Dic11—44no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8C2×Q812yes—
162C2×#475—111no—
163C2×C4×SD16—111no—
164#2542—111no—
165Q8×C4⋊C4D1111yescharacteristic, complemented
166#2084—112no—
167#2065—112no—
168#1990—111no—
169#1939—111no—
170#1880—112no—
171#1803—112no—
172#1802—111no—
173C23×C11C22×D411yescharacteristic
174C22×D11—22no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—22no—
184Q8×C11C22⋊Q814yescomplemented
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11#12112yes—
202C2×C4×C11#12112yes—
203C2×C4×C11C2×SD1614yes—
204C2×C4×C11C2×SD1612yes—
205C2×C4×C11AGL(1,ℤ/8)12yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×Q811yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×C4×C112−1+411yescharacteristic
212C2×Dic11—42no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—41no—
217C2×Dic11—42no—
218D44—22no—
219D44—22no—
220D44—41no—
221D44—41no—
222C4×D11—84no—
223Dic22—84no—
224C11⋊C8—22no—
225C11⋊C8—41no—
226C11⋊C8—42no—
227C22×SD16—111no—
228C2×C4⋊Q8—111no—
229C2×C22⋊Q8—221no—
230C2×C22⋊Q8—221no—
231C2×C4×Q8C2×D1112yes—
232C2×C4×Q8C2×D1111yescharacteristic
233C2×C4×D4—111no—
234#475—224no—
235C4×SD16—224no—
236C2×#106—112no—
237C2×#106—111no—
238C2×C4⋊C8—111no—
239C2×C4⋊C8—112no—
240C2×#103—112no—
241C2×#103—111no—
242C2×#102—111no—
243C2×#102—112no—
244C2×C4×C8—111no—
245#399—222no—
246#390—112no—
247#389—22no—
248#389C2×D1112yes—
249#384—21no—
250#384—112no—
251#384C2×D1111yescharacteristic
252C4×C4⋊C4—21no—
253C4×C4⋊C4C2×D1111yescharacteristic
254#340—112no—
255#340—112no—
256#340—112no—
257#336—112no—
258C22×C11C2×#12111yescharacteristic
259C22×C11#54611yescharacteristic
260C22×C11D4×Q811yescharacteristic
261C22×C11C22×SD1611yescharacteristic
262C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C11#57711yescharacteristic
264C22×C11#57811yescharacteristic
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—81no—
272C4×C11—24no—
273C4×C11—24no—
274C4×C11—22no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—82no—
278C4×C11#46014yes—
279C4×C11C2×C22⋊Q811yescharacteristic
280C4×C11#53711yescharacteristic
281C4×C11#55211yescharacteristic
282C4×C11#55411yescharacteristic
283Dic11—82no—
284Dic11—81no—
285C22×Q8—221no—
286C22×Q8C22×D1111yescharacteristic
287C22×D4—111no—
288C23×C4—221no—
289C2×SD16—114no—
290C2×SD16—222no—
291C2×SD16—222no—
292C22×C8—111no—
293C22×C8—112no—
294C22×C8—111no—
295C4⋊Q8—222no—
296C4⋊Q8—222no—
297C22⋊Q8—444no—
298C22⋊Q8—444no—
299C4×Q8—22no—
300C4×Q8—24no—
301C4×Q8—42no—
302C4×Q8D4414yes—
303C4×D4—222no—
304C4×D4—222no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4C22⋊D1111yescharacteristic
316C2×C4⋊C4C22⋊D1111yescharacteristic
317C2×C4⋊C4C22×D1112yes—
318C2×C4⋊C4C22×D1111yescharacteristic
319C2×C22⋊C4—221no—
320C2×C22⋊C4—222no—
321C2×C22⋊C4—222no—
322C2×C42—21no—
323C2×C42—22no—
324C2×C42C22×D1112yes—
325C2×C42C22×D1111yescharacteristic
326#106—222no—
327#106—224no—
328C4⋊C8—222no—
329C4⋊C8—442no—
330#103—222no—
331#103—224no—
332#102—222no—
333#102—442no—
334C4×C8—222no—
335#95—22no—
336#95C22⋊D1112yes—
337C2×C11#241711yescharacteristic
338C2×C11C2×#46011yescharacteristic
339C2×C11#304611yescharacteristic
340C2×C11#329811yescharacteristic
341C2×C11#333211yescharacteristic
342C2×C11Q8×SD1611yescharacteristic
343C2×C11#338611yescharacteristic
344D11—82no—
345C24—221no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—442no—
350C2×Q8—442no—
351C2×Q8—442no—
352C2×Q8C2×D4412yes—
353C2×Q8#434112yes—
354C2×Q8Q8×D1112yes—
355C2×D4—112no—
356C2×D4—221no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—221no—
360C2×D4—221no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—222no—
365C22×C4—221no—
366C22×C4—442no—
367C22×C4—442no—
368C22×C4—442no—
369C22×C4C2×C22⋊D1112yes—
370C22×C4C2×C22⋊D1111yescharacteristic
371C22×C4C2×C22⋊D1112yes—
372C22×C4C2×C22⋊D1111yescharacteristic
373C22×C4C23×D1111yescharacteristic
374SD16—228no—
375C2×C8—112no—
376C2×C8—221no—
377C2×C8—221no—
378C2×C8—221no—
379C2×C8—222no—
380C2×C8—222no—
381C2×C8—221no—
382C2×C8—222no—
383C2×C8—221no—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—44no—
390C4⋊C4—42no—
391C4⋊C4—81no—
392C4⋊C4—82no—
393C4⋊C4—221no—
394C4⋊C4—222no—
395C4⋊C4—221no—
396C4⋊C4—222no—
397C4⋊C4—444no—
398C4⋊C4—442no—
399C4⋊C4—444no—
400C4⋊C4#432514yescomplemented
401C4⋊C4C2×D4412yes—
402C22⋊C4—444no—
403C22⋊C4—442no—
404C22⋊C4—444no—
405C42—24no—
406C42—22no—
407C42—22no—
408C42—44no—
409C42C2×D4412yes—
410C42#433912yes—
411C11#2481311yescharacteristic, complemented, Sylow
412C23—222no—
413C23—441no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23—441no—
418C23—441no—
419C23C22×C22⋊D1111yescharacteristic
420Q8—22no—
421Q8—22no—
422Q8—22no—
423Q8—884no—
424Q8#6695014yescomplemented
425D4—222no—
426D4—222no—
427D4—441no—
428D4—441no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—441no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—441no—
449C2×C4—442no—
450C2×C4—441no—
451C2×C4—884no—
452C2×C4#6698312yes—
453C2×C4#6698312yes—
454C2×C4C2×#432514yes—
455C2×C4C2×#432512yes—
456C2×C4#6700212yes—
457C2×C4C22×D4411yescharacteristic
458C2×C4C2×#433911yescharacteristic
459C2×C4C2×#434111yescharacteristic
460C2×C4#6703711yescharacteristic
461C2×C4C2×Q8×D1111yescharacteristic
462C2×C4#6704011yescharacteristic
463C8—222no—
464C8—441no—
465C8—442no—
466C22—442no—
467C22—442no—
468C22—442no—
469C22—881no—
470C22—881no—
471C22—881no—
472C22—881no—
473C22C2×#6698311yescharacteristic
474C22#1062333711yescharacteristic
475C22C22×#432511yescharacteristic
476C22Q8×C22⋊D1111yescharacteristic
477C22C2×#6700211yescharacteristic
478C22#1062336711yescharacteristic
479C22#1062336911yescharacteristic
480C4—22no—
481C4—24no—
482C4—24no—
483C4—42no—
484C4—42no—
485C4—82no—
486C4—881no—
487C4—882no—
488C4#1062264014yes—
489C4C2×#6695011yescharacteristic
490C4#1062304111yescharacteristic
491C4#1062304211yescharacteristic
492C4#1062304411yescharacteristic
493C2—882no—
494C2#1307206111yescharacteristic
495C2C2×#1062264011yescharacteristic
496C2#1307816611yescharacteristic
497C2#1308048111yescharacteristic
498C2#1308094311yescharacteristic
499C2Q8×#432511yescharacteristic
500C2#1308153311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingQ8×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterQ8×C4⋊C4D11
hypocenterC11#24813
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622633C2semidirect
4. #13070092C2semidirect
6. #13069576C2semidirect
7. #13069335C2semidirect
9. #13068621C2semidirect
11. Q8×C11×C4⋊C4C2semidirect
66. C2×#4325Q8semidirect
134. C11×C4⋊C4SD16semidirect
165. Q8×C4⋊C4D11semidirect
184. Q8×C11C22⋊Q8semidirect
400. C4⋊C4#4325semidirect
411. C11#24813semidirect
424. Q8#66950semidirect

Maximal subgroups

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

subgroupindex
C2×#106226332
C2×C4×#43252
#130735652
#130700922
#130699872
#130695762
#130693352
#130689712
#130686212
#130686132
Q8×C11×C4⋊C42
#2481311