Finite Group Databasebeta

← #14770403

Subgroups — #14770403

Order 2816.

1110 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623261C211yesmaximal, characteristic
2C2×#10622292C211yesmaximal, characteristic, complemented
3#13071528C211yesmaximal, characteristic, complemented
4#13069583C212yesmaximal, complemented
5#13069572C212yesmaximal, complemented
6#13069565C211yesmaximal, characteristic, complemented
7#13068615C212yesmaximal
8#13068613C211yesmaximal, characteristic
9#13068440C212yesmaximal
10C4×#66885C211yesmaximal, characteristic
11C11×#1990C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999—22no—
14#10623261—24no—
15#10623261C418yescomplemented
16C2×#66950—21no—
17C2×#66946C2212yes—
18C2×C4⋊C4×D11—21no—
19C2×#66943C2212yes—
20C2×#66940—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C11×#384C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66879C2212yes—
28C2×Dic11⋊C8C2212yes—
29#10622589C2212yes—
30C4⋊C4×Dic11C2212yes—
31#10622586—21no—
32#10622585—22no—
33C2×#66873C2212yes—
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622292—24no—
37C11×#340C2212yes—
38C11×#340C2212yes—
39#10622189C2211yescharacteristic
40#10622189C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×Q8×C11—21no—
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×C4×D11—22no—
48C22×Dic22D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8C2×C414yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C42×C11C2311yescharacteristic
59#66999—216no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11D411yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4D412yes—
71C2×C4×Dic11—21no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11C2312yes—
74C22×C11⋊C8C2312yes—
75#66950—28no—
76#66946—24no—
77#66946C2×C418yes—
78C4⋊C4×D11—28no—
79#66943—24no—
80#66943C2×C418yes—
81#66940—44no—
82C4×D44—22no—
83C4×D44C2×C414yes—
84C4×Dic22C2×C414yes—
85C4×Dic22D414yes—
86C4×C8×C11—22no—
87C11⋊#95—21no—
88C11⋊#95—22no—
89#66885—22no—
90#66885Q814yescomplemented
91#66879—24no—
92Dic11⋊C8—24no—
93#66873—24no—
94C4⋊(C11⋊C8)—22no—
95#22522—111nomaximal, Sylow
96C23×D11—21no—
97C2×Q8×C11—24no—
98C2×Q8×C11—81no—
99C2×Q8×C11—81no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11C2×D412yes—
109C22×Dic11C2×D412yes—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44C22×C412yes—
114C2×D44C2×Q812yes—
115C2×D44#4112yes—
116C2×C4×D11—28no—
117C2×C4×D11—24no—
118C2×C4×D11—42no—
119C2×C4×D11—42no—
120C2×C4×D11—82no—
121C2×C4×D11—82no—
122C2×Dic22—22no—
123C2×Dic22—22no—
124C2×Dic22C22⋊C414yes—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11C2×Q812yes—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—81no—
137C11×C4⋊C4C22×C414yes—
138C42×C11C22×C412yes—
139C42×C11C2×D412yes—
140(C2×D11)⋊C4—28no—
141(C2×D11)⋊C4—24no—
142C4⋊Dic11—28no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11C22⋊C414yes—
148C4⋊Dic11C22×C412yes—
149C4⋊Dic11C2×Q812yes—
150Dic11⋊C4—28no—
151Dic11⋊C4—44no—
152Dic11⋊C4—82no—
153Dic11⋊C4C22⋊C418yes—
154C4×Dic11—44no—
155C4×Dic11—42no—
156C4×Dic11C22×C414yes—
157C4×Dic11C2×D414yes—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×#554—111no—
162C2×#446—111no—
163Q8×C4⋊C4—111no—
164#1992—112no—
165#1990D1111yescharacteristic, complemented
166#1989—112no—
167#1987—111no—
168#1802—111no—
169#1802—112no—
170#1762—112no—
171C4×#102—111no—
172C23×C11C22×D411yescharacteristic
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180Q8×C11—84no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—24no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11C2×C22⋊C412yes—
190C2×C4×C11C2×C22⋊C412yes—
191C2×C4×C11AGL(1,ℤ/8)12yes—
192C2×C4×C11#13712yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×Q811yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C112−1+411yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11C2×C22⋊C414yes—
213C2×Dic11C2×C22⋊C414yes—
214D44—22no—
215D44—22no—
216D44—22no—
217D44C4×Q814yescomplemented
218C4×D11—48no—
219C4×D11—88no—
220Dic22—28no—
221C8×C11—22no—
222C8×C11—41no—
223C11⋊C8—42no—
224#554—118no—
225#554—224no—
226C2×C4⋊Q8C2×D1111yescharacteristic
227C2×#125—112no—
228C2×C22⋊Q8—221no—
229C2×C22⋊Q8—222no—
230C2×C4×Q8—111no—
231C2×C4×Q8—221no—
232C2×C4×D4—112no—
233C2×C4×D4—111no—
234C22×C4⋊C4—221no—
235#446—224no—
236C2×C4⋊C8—112no—
237C2×C4⋊C8—111no—
238C2×#102—111no—
239C2×#102—111no—
240C2×#102—112no—
241C2×#97—112no—
242C2×C4×C8C2×D1111yescharacteristic
243#389—222no—
244#389—221no—
245#384—112no—
246#384C2×D1111yescharacteristic
247C4×C4⋊C4—112no—
248C4×C4⋊C4—111no—
249#340—111no—
250#340—111no—
251#340—112no—
252#340—112no—
253#340—112no—
254#340C2×D1112yes—
255#340C2×D1112yes—
256C22×C11C22×C22⋊C411yescharacteristic
257C22×C11#54811yescharacteristic
258C22×C11D4×Q811yescharacteristic
259C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C11C2×#13711yescharacteristic
261C22×C11#57611yescharacteristic
262C22×C11#57711yescharacteristic
263C2×D11—24no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—42no—
270C4×C11—22no—
271C4×C11—44no—
272C4×C11—82no—
273C4×C11#41714yes—
274C4×C11C2×C4×Q811yescharacteristic
275C4×C11#51911yescharacteristic
276C4×C11#54811yescharacteristic
277C4×C11D4×Q811yescharacteristic
278Dic11—24no—
279Dic11—24no—
280Dic11—42no—
281Dic11—42no—
282Dic11—81no—
283C22×Q8—21no—
284C22×Q8—111no—
285C22×D4—111no—
286C23×C4—222no—
287C23×C4—221no—
288C22×C8—112no—
289C22×C8C22×D1111yescharacteristic
290C22×C8C22×D1111yescharacteristic
291C4⋊Q8—22no—
292C4⋊Q8C4×D1114yes—
293#125—118no—
294#125—224no—
295C22⋊Q8—228no—
296C22⋊Q8—2216no—
297C4×Q8—114no—
298C4×Q8—114no—
299C4×Q8—444no—
300C4×D4—118no—
301C4×D4—114no—
302C4×D4—224no—
303C4×D4—222no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—112no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—111no—
312C2×C4⋊C4—228no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4C22×D1112yes—
318C2×C4⋊C4C22×D1112yes—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—221no—
321C2×C42—112no—
322C2×C42—222no—
323C2×C42—221no—
324C2×C42C22×D1111yescharacteristic
325C4⋊C8—224no—
326C4⋊C8—222no—
327#102—114no—
328#102—224no—
329#102—222no—
330#97—224no—
331C4×C8—22no—
332#95—222no—
333#95—221no—
334C2×C11Q8×C22⋊C411yescharacteristic
335C2×C11C2×#41711yescharacteristic
336C2×C11#289711yescharacteristic
337C2×C11#336611yescharacteristic
338C2×C11#337211yescharacteristic
339C2×C11#338411yescharacteristic
340C2×C11#338511yescharacteristic
341D11—44no—
342C24—221no—
343C2×Q8—24no—
344C2×Q8—81no—
345C2×Q8—81no—
346C2×Q8—114no—
347C2×Q8—222no—
348C2×Q8—222no—
349C2×D4—112no—
350C2×D4—112no—
351C2×D4—112no—
352C2×D4—221no—
353C2×D4—221no—
354C2×D4—221no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—112no—
358C22×C4—112no—
359C22×C4—228no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—224no—
363C22×C4—221no—
364C22×C4—442no—
365C22×C4—442no—
366C22×C4—882no—
367C22×C4—882no—
368C22×C4D4×D1111yescharacteristic
369C22×C4D4×D1111yescharacteristic
370C22×C4C23×D1111yescharacteristic
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—222no—
377C2×C8—222no—
378C2×C8—222no—
379C2×C8Q8×D1112yes—
380C4⋊C4—24no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—42no—
385C4⋊C4—81no—
386C4⋊C4—114no—
387C4⋊C4—118no—
388C4⋊C4—112no—
389C4⋊C4—112no—
390C4⋊C4—228no—
391C4⋊C4—228no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4—221no—
396C4⋊C4—444no—
397C4⋊C4—882no—
398C4⋊C4C2×C4×D1114yes—
399C22⋊C4—228no—
400C22⋊C4—224no—
401C42—114no—
402C42—114no—
403C42—444no—
404C42—442no—
405C42C2×C4×D1112yes—
406C42D4×D1112yes—
407C11#2252211yescharacteristic, complemented, Sylow
408C23—222no—
409C23—222no—
410C23—222no—
411C23—441no—
412C23—441no—
413C23—441no—
414C23—441no—
415C23C2×D4×D1111yescharacteristic
416Q8—84no—
417Q8—228no—
418D4—114no—
419D4—222no—
420D4—222no—
421D4—222no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—24no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—114no—
431C2×C4—114no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—448no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—888no—
447C2×C4C22⋊C4×D1112yes—
448C2×C4C22⋊C4×D1112yes—
449C2×C4#6696712yes—
450C2×C4#6697112yes—
451C2×C4C22×C4×D1111yescharacteristic
452C2×C4C2×D4×D1111yescharacteristic
453C2×C4C2×Q8×D1111yescharacteristic
454C2×C4#6704011yescharacteristic
455C2×C4#41×D1111yescharacteristic
456C2×C4#6704311yescharacteristic
457C8—22no—
458C8—41no—
459C8—442no—
460C22—224no—
461C22—442no—
462C22—442no—
463C22—442no—
464C22—442no—
465C22—442no—
466C22—442no—
467C22C2×C22⋊C4×D1111yescharacteristic
468C22#1062320811yescharacteristic
469C22#1062325811yescharacteristic
470C22#1062328811yescharacteristic
471C22C2×#6696711yescharacteristic
472C22#1062329311yescharacteristic
473C22C2×#6697111yescharacteristic
474C4—22no—
475C4—44no—
476C4—82no—
477C4—224no—
478C4—224no—
479C4—442no—
480C4—442no—
481C4—881no—
482C4#1062241614yes—
483C4C4×Q8×D1111yescharacteristic
484C4#1062310311yescharacteristic
485C4#1062316311yescharacteristic
486C4#1062316411yescharacteristic
487C2—444no—
488C2#1307145011yescharacteristic
489C2C2×#1062241611yescharacteristic
490C2#1307713711yescharacteristic
491C2#1308132811yescharacteristic
492C2#1308140211yescharacteristic
493C2#1308152011yescharacteristic
494C2#1308153111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1990D11
hypocenterC11#22522
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. C2×#10622292C2semidirect
3. #13071528C2semidirect
4. #13069583C2semidirect
5. #13069572C2semidirect
6. #13069565C2semidirect
11. C11×#1990C2semidirect
15. #10623261C4semidirect
90. #66885Q8semidirect
165. #1990D11semidirect
217. D44C4×Q8semidirect
407. C11#22522semidirect

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×#106222922
#130715282
#130695832
#130695722
#130695652
#130686152
#130686132
#130684402
C4×#668852
C11×#19902
#2252211