Finite Group Databasebeta

← #14809914

Subgroups — #14809914

Order 2816.

1076 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic
2C2×#10622693C211yesmaximal, characteristic, complemented
3C2×#10622697C211yesmaximal, characteristic
4#13069954C212yesmaximal, complemented
5#13069949C212yesmaximal, complemented
6#13069573C211yesmaximal, characteristic, complemented
7#13069557C211yesmaximal, characteristic, complemented
8#13068876C212yesmaximal
9#13068862C212yesmaximal
10#13068444C211yesmaximal, characteristic
11C11×#2546C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#66999—21no—
16#10623110—24no—
17#10623110—24no—
18C2×#66949—21no—
19C2×#66949—21no—
20C2×C4⋊C4×D11—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×#66923C2211yescharacteristic
25C2×#66923C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C11×#398—21no—
28C11×#398—21no—
29C11×#391—21no—
30C11×#389C2212yes—
31C11×#389C2212yes—
32C4×C11×C4⋊C4C2211yescharacteristic
33#10622697—24no—
34#10622693—24no—
35C2×#66873C2212yes—
36C2×#66873C2212yes—
37C2×#66872C2212yes—
38C2×#66872C2212yes—
39C2×#66871C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622162C2212yes—
46#10622162C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11D411yescharacteristic
49C22×D44C2311yescharacteristic
50C22×C4×D11—21no—
51C22×C4×D11—21no—
52C22×C4×D11—21no—
53C22×Dic22—21no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—44no—
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71#66999—28no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C22×C11⋊C8C2312yes—
84C22×C11⋊C8C2312yes—
85#66949—28no—
86#66949—28no—
87C4⋊C4×D11—28no—
88C4×D44—22no—
89C4×D44—22no—
90C4×D44—22no—
91C4×D44—22no—
92C4×D44—22no—
93C4×D44D414yes—
94#66923—22no—
95#66923—22no—
96#66923—22no—
97#66923D414yes—
98#66922—22no—
99#66922—22no—
100C11×#95—21no—
101C11×#95—22no—
102C11×#95—22no—
103#66873—24no—
104#66873Q818yescomplemented
105#66872—24no—
106#66872—24no—
107#66871—24no—
108C4⋊(C11⋊C8)—22no—
109#66867—22no—
110#25851—111nomaximal, Sylow
111C23×D11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—41no—
115C2×Q8×C11—42no—
116C2×Q8×C11—42no—
117C2×Q8×C11—42no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11C2×D411yescharacteristic
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—
130C2×D44—21no—
131C2×D44—22no—
132C2×D44C2×D412yes—
133C2×D44C2×Q814yes—
134C2×C4×D11—24no—
135C2×C4×D11—24no—
136C2×C4×D11—24no—
137C2×C4×D11—42no—
138C2×C4×D11—42no—
139C2×C4×D11—82no—
140C2×C4×D11—82no—
141C2×Dic22—24no—
142C2×Dic22—82no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—44no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4—44no—
152C11×C4⋊C4C2×Q814yes—
153C42×C11—21no—
154C42×C11—21no—
155C42×C11—21no—
156C42×C11—21no—
157C42×C11—42no—
158C42×C11C2×D412yes—
159C42×C11C2×D412yes—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
163C4⋊Dic11—24no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11C2×D412yes—
168C4⋊Dic11C2×D412yes—
169C4⋊Dic11C2×D412yes—
170Dic11⋊C4—24no—
171Dic11⋊C4—24no—
172Dic11⋊C4—24no—
173Dic11⋊C4—24no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—24no—
178C2×C11⋊C8C2×Q814yes—
179C2×#554—111no—
180C2×#501—111no—
181C2×#476—111no—
182#2546D1111yescharacteristic, complemented
183#2059—112no—
184#2058—112no—
185#1989—111no—
186#1985—111no—
187#1864—112no—
188#1862—112no—
189#1762—111no—
190C23×C11C22×D411yescharacteristic
191C22×D11—22no—
192C22×D11—24no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—42no—
196Q8×C11—44no—
197Q8×C11—84no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—24no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11#12012yes—
217C2×C4×C11#12012yes—
218C2×C4×C11AGL(1,ℤ/8)12yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×Q812yes—
222C2×C4×C112−1+412yes—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230D44—22no—
231D44—24no—
232D44C4⋊Q814yescomplemented
233C4×D11—48no—
234C4×D11—84no—
235C4×D11—84no—
236Dic22—84no—
237C11⋊C8—24no—
238C11⋊C8—42no—
239#554—224no—
240#554—224no—
241C2×C4⋊Q8—21no—
242C2×C4⋊Q8—111no—
243C2×C4⋊Q8C2×D1111yescharacteristic
244C2×#125—111no—
245C2×#125—111no—
246C2×C22⋊Q8—221no—
247C2×C22⋊Q8—221no—
248C2×C22⋊Q8—221no—
249C2×C4×Q8C2×D1111yescharacteristic
250C2×C4×D4—111no—
251C2×C4×D4—111no—
252C2×C4×D4—111no—
253C22×C4⋊C4—221no—
254#501—224no—
255#476—224no—
256C2×#107—112no—
257C2×#106—112no—
258C2×#106—112no—
259C2×C4⋊C8—111no—
260C2×#102—112no—
261C2×#102—112no—
262C2×#97—111no—
263#398—21no—
264#398—21no—
265#391—21no—
266#389C2×D1112yes—
267#389C2×D1112yes—
268C4×C4⋊C4C2×D1111yescharacteristic
269#340—112no—
270#340—112no—
271#340—112no—
272#336—112no—
273#336—112no—
274C22×C11C2×#12011yescharacteristic
275C22×C11D4×Q812yes—
276C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C11#57511yescharacteristic
278C22×C11#57712yes—
279C2×D11—24no—
280C2×D11—44no—
281C2×D11—44no—
282C2×D11—42no—
283C2×D11—42no—
284C4×C11—22no—
285C4×C11—22no—
286C4×C11—22no—
287C4×C11—44no—
288C4×C11—41no—
289C4×C11—41no—
290C4×C11—41no—
291C4×C11—82no—
292C4×C11C2×C4⋊Q811yescharacteristic
293C4×C11#53611yescharacteristic
294C4×C11D4×Q812yes—
295Dic11—42no—
296Dic11—42no—
297Dic11—42no—
298C22×Q8—21no—
299C22×Q8—221no—
300C22×Q8C22⋊D1111yescharacteristic
301C22×D4—111no—
302C23×C4—221no—
303C23×C4—221no—
304C23×C4—221no—
305C22×C8—112no—
306C22×C8—112no—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309C4⋊Q8—44no—
310C4⋊Q8—222no—
311C4⋊Q8—222no—
312#125—114no—
313#125—222no—
314#125—222no—
315#125—222no—
316C22⋊Q8—228no—
317C22⋊Q8—228no—
318C22⋊Q8—228no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×D4—114no—
322C4×D4—222no—
323C4×D4—222no—
324C4×D4—222no—
325C4×D4—222no—
326C4×D4—222no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—111no—
332C2×C4⋊C4—111no—
333C2×C4⋊C4—228no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4C22⋊D1111yescharacteristic
340C2×C4⋊C4C22⋊D1111yescharacteristic
341C2×C4⋊C4C22⋊D1111yescharacteristic
342C2×C4⋊C4C22×D1112yes—
343C2×C4⋊C4C22×D1112yes—
344C2×C22⋊C4—221no—
345C2×C22⋊C4—221no—
346C2×C22⋊C4—221no—
347C2×C42—21no—
348C2×C42C22×D1111yescharacteristic
349C2×C42C22×D1111yescharacteristic
350C2×C42C22×D1111yescharacteristic
351#107—224no—
352#106—224no—
353#106—224no—
354C4⋊C8—222no—
355#102—118no—
356#102—224no—
357#97—222no—
358#95—21no—
359#95—22no—
360#95—22no—
361C2×C11#243411yescharacteristic
362C2×C11#300611yescharacteristic
363C2×C11#300911yescharacteristic
364C2×C11#338412yes—
365C2×C11#338812yes—
366D11—44no—
367C24—221no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—41no—
371C2×Q8—42no—
372C2×Q8—42no—
373C2×Q8—42no—
374C2×Q8—224no—
375C2×Q8—882no—
376C2×D4—112no—
377C2×D4—114no—
378C2×D4—221no—
379C2×D4—222no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—224no—
383C22×C4—224no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—224no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4—882no—
391C22×C4—882no—
392C22×C4C2×C22⋊D1111yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394C22×C4C2×C22⋊D1111yescharacteristic
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C2×C22⋊D1111yescharacteristic
398C22×C4C23×D1111yescharacteristic
399C2×C8—114no—
400C2×C8—222no—
401C2×C8—222no—
402C2×C8—222no—
403C2×C8—224no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—44no—
411C4⋊C4—44no—
412C4⋊C4—42no—
413C4⋊C4—112no—
414C4⋊C4—112no—
415C4⋊C4—112no—
416C4⋊C4—224no—
417C4⋊C4—224no—
418C4⋊C4—224no—
419C4⋊C4—224no—
420C4⋊C4—224no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4Q8×D1114yes—
425C22⋊C4—224no—
426C22⋊C4—224no—
427C22⋊C4—224no—
428C42—21no—
429C42—21no—
430C42—21no—
431C42—21no—
432C42—42no—
433C42D4×D1112yes—
434C42D4×D1112yes—
435C11#2585111yescharacteristic, complemented, Sylow
436C23—222no—
437C23—224no—
438C23—441no—
439C23—441no—
440C23—442no—
441C23C22×C22⋊D1111yescharacteristic
442Q8—44no—
443Q8—84no—
444Q8—884no—
445D4—114no—
446D4—222no—
447D4—224no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—24no—
458C2×C4—21no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—448no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—884no—
475C2×C4—884no—
476C2×C4#6698512yes—
477C2×C4#6699012yes—
478C2×C4#6699012yes—
479C2×C4C2×D4×D1111yescharacteristic
480C2×C4C2×D4×D1111yescharacteristic
481C2×C4C2×Q8×D1112yes—
482C2×C4#6704012yes—
483C8—224no—
484C8—442no—
485C22—224no—
486C22—442no—
487C22—442no—
488C22—444no—
489C22—444no—
490C22C2×#6698511yescharacteristic
491C22C2×#6699011yescharacteristic
492C22Q8×C22⋊D1112yes—
493C22#1062335311yescharacteristic
494C22#1062336812yes—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—41no—
499C4—41no—
500C4—41no—
501C4—44no—
502C4—82no—
503C4—442no—
504C4—442no—
505C4—442no—
506C4D11×C4⋊Q811yescharacteristic
507C4#1062325511yescharacteristic
508C4#1062325812yes—
509C2—444no—
510C2#1307225711yescharacteristic
511C2#1307786611yescharacteristic
512C2#1307789111yescharacteristic
513C2#1308151112yes—
514C2#1308155512yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2546C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2546D11
hypocenterC11#25851
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
2. C2×#10622693C2semidirect
4. #13069954C2semidirect
5. #13069949C2semidirect
6. #13069573C2semidirect
7. #13069557C2semidirect
11. C11×#2546C2semidirect
104. #66873Q8semidirect
182. #2546D11semidirect
232. D44C4⋊Q8semidirect
435. C11#25851semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
C2×#106226932
C2×#106226972
#130699542
#130699492
#130695732
#130695572
#130688762
#130688622
#130684442
C11×#25462
#2585111