Finite Group Databasebeta

← #14770396

Subgroups — #14770396

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×#10623074C211yesmaximal, characteristic
2C2×#10622292C211yesmaximal, characteristic, complemented
3C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
4#13069583C212yesmaximal, complemented
5#13069577C211yesmaximal, characteristic, complemented
6#13069570C212yesmaximal, complemented
7#13069564C211yesmaximal, characteristic, complemented
8#13068616C211yesmaximal, characteristic
9#13068614C212yesmaximal
10#13068443C212yesmaximal
11C4×C11×#102C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×D4×Dic11C2212yes—
14C22×C4⋊Dic11—21no—
15C2×#66977—21no—
16#10623074—24no—
17#10623074C418yescomplemented
18C2×#66943C2212yes—
19C2×#66931—22no—
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22—21no—
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×#66896C2212yes—
28C2×#66879C2212yes—
29C2×Dic11⋊C8C2212yes—
30#10622589C2212yes—
31C4⋊C4×Dic11C2212yes—
32#10622548C2211yescharacteristic
33#10622541—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35#10622292—24no—
36#10622260—22no—
37C11×#340C2211yescharacteristic
38C11×#340C2211yescharacteristic
39#10622189C2212yes—
40#10622189C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×Dic11—22no—
47C22×Dic22—21no—
48C22×Dic22D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×D4×C11—22no—
52C4×D4×C11C2×C414yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C22⋊C4—21no—
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—22no—
60D4×Dic11—24no—
61D4×Dic11C2×C418yes—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—28no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2312yes—
70#66977—28no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4D412yes—
75C2×C4×Dic11—22no—
76C2×C4×Dic11C2312yes—
77C22×C11⋊C8C2312yes—
78#66943—24no—
79#66943C2×C418yes—
80#66931—216no—
81#66922—22no—
82#66922C2×C414yes—
83C4×Dic22—44no—
84C4×Dic22C2×C414yes—
85C4×Dic22D414yes—
86C11×#102—22no—
87C11×#102Q814yescomplemented
88C4×C8×C11—22no—
89C11×#95—21no—
90#66896—24no—
91C11⋊#95—22no—
92#66879—24no—
93Dic11⋊C8—24no—
94C4⋊(C11⋊C8)—22no—
95#22522—111nomaximal, Sylow
96C24×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11C22×C412yes—
101C2×D4×C11C2×Q812yes—
102C2×D4×C11#4112yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—24no—
106C22×C4×C11—21no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—28no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—82no—
116C22×Dic11—82no—
117C22×Dic11C2×D412yes—
118C22×Dic11C2×D412yes—
119C2×Dic22—24no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22—81no—
123C2×Dic22—81no—
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—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4C22×C412yes—
136C11×C4⋊C4C2×Q812yes—
137C11×C22⋊C4—24no—
138C42×C11—42no—
139C42×C11C22×C412yes—
140C42×C11C2×D412yes—
141C22⋊Dic11—28no—
142C4⋊Dic11—28no—
143C4⋊Dic11—24no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—42no—
148C4⋊Dic11—81no—
149C4⋊Dic11C22⋊C414yes—
150C4⋊Dic11C22×C414yes—
151Dic11⋊C4—28no—
152Dic11⋊C4—44no—
153Dic11⋊C4—82no—
154Dic11⋊C4C22⋊C418yes—
155C4×Dic11—44no—
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#1990—111no—
166#1989—112no—
167#1987—111no—
168#1802—112no—
169#1802—111no—
170#1762—112no—
171C4×#102D1111yescharacteristic
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11C22×D411yescharacteristic
180D4×C11—22no—
181D4×C11—22no—
182D4×C11—22no—
183D4×C11C4×Q814yescomplemented
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—48no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11C2×C22⋊C412yes—
197C2×C4×C11C2×C22⋊C412yes—
198C2×C4×C11AGL(1,ℤ/8)12yes—
199C2×C4×C11#13712yes—
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×Q811yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C112−1+411yescharacteristic
205C2×C4×C112−1+411yescharacteristic
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—24no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—88no—
217C2×Dic11C2×C22⋊C414yes—
218C2×Dic11C2×C22⋊C414yes—
219Dic22—28no—
220Dic22—84no—
221C8×C11—22no—
222C8×C11—41no—
223C11⋊C8—42no—
224#554—118no—
225#554—224no—
226C2×C4⋊Q8—111no—
227C2×#125—112no—
228C2×C22⋊Q8—222no—
229C2×C22⋊Q8—221no—
230C2×C4×Q8—111no—
231C2×C4×Q8—221no—
232C2×C4×D4—112no—
233C2×C4×D4C2×D1111yescharacteristic
234C22×C4⋊C4—221no—
235#446—224no—
236C2×C4⋊C8—112no—
237C2×C4⋊C8—111no—
238C2×#102—112no—
239C2×#102C2×D1111yescharacteristic
240C2×#102C2×D1111yescharacteristic
241C2×#97—112no—
242C2×C4×C8C2×D1111yescharacteristic
243#389—222no—
244#389—221no—
245#384—112no—
246#384—111no—
247C4×C4⋊C4—112no—
248C4×C4⋊C4C2×D1111yescharacteristic
249#340—112no—
250#340—112no—
251#340—112no—
252#340—112no—
253#340—112no—
254#340C2×D1111yescharacteristic
255#340C2×D1111yescharacteristic
256C22×C11—24no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11C22×C22⋊C411yescharacteristic
264C22×C11#54811yescharacteristic
265C22×C11D4×Q811yescharacteristic
266C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C11C2×#13711yescharacteristic
268C22×C11#57611yescharacteristic
269C22×C11#57711yescharacteristic
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—81no—
274C4×C11#41714yes—
275C4×C11C2×C4×Q811yescharacteristic
276C4×C11#51911yescharacteristic
277C4×C11#54811yescharacteristic
278C4×C11D4×Q811yescharacteristic
279Dic11—24no—
280Dic11—24no—
281Dic11—44no—
282Dic11—82no—
283C22×Q8—111no—
284C22×Q8—221no—
285C22×D4C22×D1111yescharacteristic
286C23×C4—21no—
287C23×C4—222no—
288C22×C8—112no—
289C22×C8C22×D1111yescharacteristic
290C22×C8C22×D1111yescharacteristic
291C4⋊Q8—114no—
292C4⋊Q8—222no—
293#125—118no—
294#125—224no—
295C22⋊Q8—2216no—
296C22⋊Q8—228no—
297C4×Q8—114no—
298C4×Q8—114no—
299C4×Q8—444no—
300C4×D4—22no—
301C4×D4—118no—
302C4×D4—224no—
303C4×D4C4×D1114yes—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—112no—
308C2×C4⋊C4—228no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4C22×D1111yescharacteristic
317C2×C4⋊C4C22×D1111yescharacteristic
318C2×C4⋊C4C22×D1111yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—222no—
321C2×C42—21no—
322C2×C42—112no—
323C2×C42—222no—
324C2×C42C22×D1111yescharacteristic
325C4⋊C8—224no—
326C4⋊C8—222no—
327#102—22no—
328#102—224no—
329#102Dic2214yescomplemented
330#97—224no—
331C4×C8—22no—
332#95—21no—
333#95—222no—
334C2×C11—44no—
335C2×C11Q8×C22⋊C411yescharacteristic
336C2×C11C2×#41711yescharacteristic
337C2×C11#289711yescharacteristic
338C2×C11#336611yescharacteristic
339C2×C11#337211yescharacteristic
340C2×C11#338411yescharacteristic
341C2×C11#338511yescharacteristic
342C24—21no—
343C2×Q8—114no—
344C2×Q8—224no—
345C2×Q8—222no—
346C2×Q8—222no—
347C2×Q8—881no—
348C2×Q8—881no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4C2×Dic2212yes—
353C2×D4C2×C4×D1112yes—
354C2×D4#433912yes—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—24no—
358C22×C4—21no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—112no—
362C22×C4—112no—
363C22×C4—228no—
364C22×C4—222no—
365C22×C4—222no—
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×C8C2×Dic2212yes—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—114no—
385C4⋊C4—118no—
386C4⋊C4—114no—
387C4⋊C4—228no—
388C4⋊C4—228no—
389C4⋊C4—224no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4—444no—
394C4⋊C4—442no—
395C4⋊C4—881no—
396C4⋊C4—882no—
397C4⋊C4C2×Dic2212yes—
398C4⋊C4C2×C4×D1112yes—
399C22⋊C4—24no—
400C22⋊C4—228no—
401C42—42no—
402C42—114no—
403C42—114no—
404C42—444no—
405C42C2×C4×D1112yes—
406C42D4×D1112yes—
407C11#2252211yescharacteristic, complemented, Sylow
408C23—22no—
409C23—22no—
410C23—22no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23C2×D4×D1111yescharacteristic
416Q8—228no—
417Q8—884no—
418D4—22no—
419D4—22no—
420D4—22no—
421D4C4×Dic2214yescomplemented
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—48no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—114no—
435C2×C4—114no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—224no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—888no—
447C2×C4C22⋊C4×D1112yes—
448C2×C4C22⋊C4×D1112yes—
449C2×C4#6696412yes—
450C2×C4#6696812yes—
451C2×C4C22×Dic2211yescharacteristic
452C2×C4C22×C4×D1111yescharacteristic
453C2×C4C2×#433911yescharacteristic
454C2×C4C2×D4×D1111yescharacteristic
455C2×C4#6704311yescharacteristic
456C2×C4#6704311yescharacteristic
457C8—22no—
458C8—41no—
459C8—442no—
460C22—24no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22C2×C22⋊C4×D1111yescharacteristic
468C22D4×Dic2211yescharacteristic
469C22#1062308311yescharacteristic
470C22C2×#6696411yescharacteristic
471C22C2×#6696811yescharacteristic
472C22#1062330011yescharacteristic
473C22#1062330111yescharacteristic
474C4—22no—
475C4—42no—
476C4—42no—
477C4—81no—
478C4—224no—
479C4—224no—
480C4—444no—
481C4—882no—
482C4#1062238414yes—
483C4C2×C4×Dic2211yescharacteristic
484C4#1062304711yescharacteristic
485C4D4×Dic2211yescharacteristic
486C4#1062308311yescharacteristic
487C2—44no—
488C2C22⋊C4×Dic2211yescharacteristic
489C2C2×#1062238411yescharacteristic
490C2#1307713811yescharacteristic
491C2#1308132111yescharacteristic
492C2#1308139511yescharacteristic
493C2#1308151311yescharacteristic
494C2#1308152411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC4×#102D11
hypocenterC11#22522
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×#10622292C2semidirect
3. C4⋊C4×Dic22C2semidirect
4. #13069583C2semidirect
5. #13069577C2semidirect
6. #13069570C2semidirect
7. #13069564C2semidirect
17. #10623074C4semidirect
87. C11×#102Q8semidirect
183. D4×C11C4×Q8semidirect
329. #102Dic22semidirect
407. C11#22522semidirect
421. D4C4×Dic22semidirect

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106222922
C4⋊C4×Dic222
#130695832
#130695772
#130695702
#130695642
#130686162
#130686142
#130684432
C4×C11×#1022
#2252211