Finite Group Databasebeta

← #14763239

Subgroups — #14763239

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2#13077248C211yesmaximal, characteristic
3#13077247C211yesmaximal, characteristic
4#13069607C214yesmaximal, complemented
5#13069606C211yesmaximal, characteristic, complemented
6#13069605C211yesmaximal, characteristic, complemented
7#13069604C211yesmaximal, characteristic, complemented
8#13068698C214yesmaximal
9C11×#1997C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999C412yes—
12C2×Q8×Dic11C412yes—
13#10623259—21no—
14#10623259—21no—
15#10623259—21no—
16#10623259—21no—
17#10623259—21no—
18#10623259—21no—
19#10623259—21no—
20#10623259—21no—
21C2×#66950C412yes—
22C2×#66945C2212yes—
23C2×#66943C2212yes—
24C2×#66940C412yes—
25C2×C42×D11C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C11×#423C2211yescharacteristic
28C4×C11×M16C2211yescharacteristic
29#10622739C2212yes—
30#10622739C2212yes—
31#10622731C2212yes—
32M16×Dic11C2212yes—
33#10622537C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622448—21no—
36#10622448—21no—
37#10622446—21no—
38#10622446—21no—
39#10622318—21no—
40#10622318—21no—
41#10622298—21no—
42#10622298—21no—
43C11×#343C2214yes—
44#10622192C2214yes—
45#10622192C2214yes—
46#10622168C2214yes—
47C22×Q8×C11C2×C412yes—
48C22×C4×D11C2×C411yescharacteristic
49C22×C4×D11C2×C411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×Dic22C2×C412yes—
52C2×C11×M16C2312yes—
53C2×C11×M16C2312yes—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C2×C11×C4⋊C4C2×C412yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C42×C11C2311yescharacteristic
61#66999—22no—
62#66999—22no—
63#66999—22no—
64#66999—22no—
65Q8×Dic11—22no—
66Q8×Dic11—22no—
67Q8×Dic11—22no—
68Q8×Dic11—22no—
69C2×(C2×D11)⋊C4C2×C414yes—
70C2×C4⋊Dic11C2×C412yes—
71C2×C4⋊Dic11C2×C414yes—
72C2×C4⋊Dic11C2312yes—
73C2×Dic11⋊C4C2×C414yes—
74C2×C4×Dic11C2×C414yes—
75C2×C4×Dic11C2×C411yescharacteristic
76C2×C4×Dic11C2×C411yescharacteristic
77C2×C4×Dic11C2311yescharacteristic
78C2×#4318C2312yes—
79C2×#4318C2312yes—
80#66950—22no—
81#66950—22no—
82#66950—22no—
83#66950—22no—
84#66945—22no—
85#66945—22no—
86#66945—22no—
87#66945—22no—
88#66943—22no—
89#66943—22no—
90#66943—22no—
91#66943—22no—
92#66940—22no—
93#66940—22no—
94#66940—22no—
95#66940—22no—
96C42×D11D411yescharacteristic
97C42×D11D411yescharacteristic
98C42×D11D411yescharacteristic
99C42×D11D411yescharacteristic
100C42×D11D411yescharacteristic
101C42×D11D411yescharacteristic
102C42×D11D411yescharacteristic
103C42×D11D411yescharacteristic
104#66922—21no—
105#66922—21no—
106#66922—21no—
107#66922—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8—21no—
110C11×#97—21no—
111C4×C8×C11—21no—
112(C2×D11)⋊C8—22no—
113(C2×D11)⋊C8—22no—
114(C2×D11)⋊C8—22no—
115(C2×D11)⋊C8—22no—
116#66879—22no—
117Dic11⋊C8—22no—
118Dic11⋊C8—22no—
119C8×Dic11—22no—
120C4⋊(C11⋊C8)—21no—
121C4⋊(C11⋊C8)—21no—
122#66867—21no—
123C4×C11⋊C8—21no—
124#21831—111nomaximal, Sylow
125C23×D11C22×C411yescharacteristic
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—44no—
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C414yes—
132C22×C4×C11C2411yescharacteristic
133C22×Dic11C22×C411yescharacteristic
134C22×Dic11C22×C414yes—
135C22×Dic11C22×C411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—42no—
140C2×C4×D11—42no—
141C2×C4×D11C22⋊C411yescharacteristic
142C2×C4×D11C22⋊C411yescharacteristic
143C2×C4×D11C22⋊C411yescharacteristic
144C2×C4×D11C22⋊C411yescharacteristic
145C2×C4×D11C22⋊C411yescharacteristic
146C2×C4×D11C22⋊C411yescharacteristic
147C2×C4×D11C22⋊C411yescharacteristic
148C2×C4×D11C22⋊C411yescharacteristic
149C2×C4×D11C2×D411yescharacteristic
150C2×C4×D11C2×D411yescharacteristic
151C2×C4×D11C2×D411yescharacteristic
152C2×C4×D11C2×D411yescharacteristic
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—44no—
156C11×M16—22no—
157C11×M16—24no—
158C11×M16—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C42×C11C2×D411yescharacteristic
166C42×C11C2×D411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C42×C11C2×D411yescharacteristic
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—24no—
171C4⋊Dic11—24no—
172C4⋊Dic11—24no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—22no—
177Dic11⋊C4—24no—
178Dic11⋊C4—24no—
179C4×Dic11—24no—
180C4×Dic11—24no—
181C4×Dic11C22⋊C411yescharacteristic
182C4×Dic11C22⋊C411yescharacteristic
183C4×Dic11C22⋊C411yescharacteristic
184C4×Dic11C22⋊C411yescharacteristic
185C4×Dic11C22⋊C411yescharacteristic
186C4×Dic11C22⋊C411yescharacteristic
187C4×Dic11C22⋊C411yescharacteristic
188C4×Dic11C22⋊C411yescharacteristic
189C4×Dic11C2×D411yescharacteristic
190C4×Dic11C2×D411yescharacteristic
191C4×Dic11C2×D411yescharacteristic
192C4×Dic11C2×D411yescharacteristic
193#4318—24no—
194#4318—22no—
195#4318—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×#533—111no—
199#2920—111no—
200#2920—111no—
201#1998—114no—
202#1997—111no—
203#1997—111no—
204#1997—111no—
205#1997D1111yescharacteristic, complemented
206#1822—114no—
207C23×C11C23×C411yescharacteristic
208C22×D11—22no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11C2×C22⋊C411yescharacteristic
212C22×D11C2×C22⋊C411yescharacteristic
213Q8×C11—44no—
214Q8×C11—44no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—44no—
219C2×C4×C11C2×C22⋊C411yescharacteristic
220C2×C4×C11C2×C22⋊C411yescharacteristic
221C2×C4×C11C2×C22⋊C411yescharacteristic
222C2×C4×C11C2×C22⋊C411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C112−1+412yes—
226C2×C4×C112−1+412yes—
227C2×Dic11—22no—
228C2×Dic11—24no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—44no—
232C2×Dic11C2×C22⋊C411yescharacteristic
233C2×Dic11C2×C22⋊C411yescharacteristic
234C2×Dic11C2×C22⋊C411yescharacteristic
235C2×Dic11C2×C22⋊C411yescharacteristic
236C2×Dic11C2×C22⋊C411yescharacteristic
237C2×Dic11C2×C22⋊C411yescharacteristic
238C4×D11—21no—
239C4×D11—21no—
240C4×D11—22no—
241C4×D11—22no—
242C4×D11—21no—
243C4×D11—21no—
244C4×D11—22no—
245C4×D11—22no—
246C4×D11—22no—
247C4×D11—22no—
248C4×D11—41no—
249C4×D11—41no—
250C4×D11—41no—
251C4×D11—41no—
252Dic22—44no—
253Dic22—44no—
254C8×C11—42no—
255C8×C11—42no—
256C11⋊C8—42no—
257C11⋊C8—42no—
258#533—221no—
259#533—221no—
260#533—221no—
261#533—221no—
262#533—221no—
263#533—221no—
264#533—221no—
265#533—221no—
266C2×C4⋊Q8—111no—
267C2×C4⋊Q8C2×D1111yescharacteristic
268C2×#125—112no—
269C2×C22⋊Q8—112no—
270C2×C22⋊Q8—112no—
271C2×C4×Q8—112no—
272C2×C4×Q8—112no—
273C2×#117—112no—
274C22×C42—111no—
275#432—221no—
276#432—221no—
277#432—221no—
278#432—221no—
279#431—221no—
280#431—221no—
281#431—221no—
282#431—221no—
283#423—112no—
284#423—111no—
285#423C2×D1111yescharacteristic
286#407—112no—
287#407—112no—
288C4×M16—112no—
289C4×M16—111no—
290C4×M16C2×D1111yescharacteristic
291#343—114no—
292#343—114no—
293#343—114no—
294#343C2×D1114yes—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11C22×C22⋊C411yescharacteristic
298C22×C11#51912yes—
299C2×D11—21no—
300C2×D11—21no—
301C2×D11—21no—
302C2×D11—21no—
303C2×D11—21no—
304C2×D11—21no—
305C2×D11—44no—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—44no—
309C4×C11#41312yes—
310C4×C11#41312yes—
311C4×C11#53611yescharacteristic
312C4×C11#53612yes—
313C4×C11#53611yescharacteristic
314Dic11—21no—
315Dic11—21no—
316Dic11—21no—
317Dic11—21no—
318Dic11—21no—
319Dic11—21no—
320Dic11—44no—
321C22×Q8—112no—
322C22×Q8C4×D1112yes—
323C23×C4—111no—
324C23×C4—111no—
325C23×C4—111no—
326C2×M16—112no—
327C2×M16—112no—
328C2×M16C22×D1112yes—
329C2×M16C22×D1112yes—
330C4⋊Q8—21no—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8—221no—
335C4⋊Q8—221no—
336C4⋊Q8—221no—
337C4⋊Q8—221no—
338#125—222no—
339#125—222no—
340#125—222no—
341#125—222no—
342C22⋊Q8—222no—
343C22⋊Q8—222no—
344C22⋊Q8—222no—
345C22⋊Q8—222no—
346C22⋊Q8—222no—
347C22⋊Q8—222no—
348C22⋊Q8—222no—
349C22⋊Q8—222no—
350C4×Q8—222no—
351C4×Q8—222no—
352C4×Q8—222no—
353C4×Q8—222no—
354C4×Q8—222no—
355C4×Q8—222no—
356C4×Q8—222no—
357C4×Q8—222no—
358#117—222no—
359#117—222no—
360#117—222no—
361#117—222no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4C4×D1112yes—
367C2×C4⋊C4C22×D1112yes—
368C2×C22⋊C4—114no—
369C2×C42—111no—
370C2×C42—111no—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—111no—
374C2×C42—111no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—114no—
381C2×C42C22×D1111yescharacteristic
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—222no—
385C4⋊C8—222no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C22⋊C8—222no—
389C22⋊C8—222no—
390C22⋊C8—222no—
391C22⋊C8—222no—
392#97—21no—
393#97—222no—
394#97—221no—
395C4×C8—21no—
396C4×C8—222no—
397C4×C8—221no—
398C2×C11—22no—
399C2×C11#231011yescharacteristic
400C2×C11C2×#41311yescharacteristic
401C2×C11C2×#41311yescharacteristic
402D11—41no—
403D11—41no—
404C24—111no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—44no—
408C2×Q8—222no—
409C2×Q8—222no—
410C2×Q8—444no—
411C22×C4—111no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—111no—
417C22×C4—111no—
418C22×C4—111no—
419C22×C4—111no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—114no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—442no—
430C22×C4—442no—
431C22×C4C2×C4×D1111yescharacteristic
432C22×C4C2×C4×D1111yescharacteristic
433C22×C4C2×C4×D1114yes—
434C22×C4C23×D1111yescharacteristic
435M16—22no—
436M16—22no—
437M16—24no—
438M16—224no—
439M16—222no—
440M16—222no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—222no—
444C2×C8—222no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—224no—
450C4⋊C4—224no—
451C4⋊C4—224no—
452C4⋊C4—224no—
453C4⋊C4—222no—
454C4⋊C4—222no—
455C4⋊C4—222no—
456C4⋊C4—222no—
457C22⋊C4—224no—
458C22⋊C4—224no—
459C42—111no—
460C42—111no—
461C42—111no—
462C42—111no—
463C42—111no—
464C42—111no—
465C42—111no—
466C42—111no—
467C42—111no—
468C42—111no—
469C42—111no—
470C42—111no—
471C42—224no—
472C42—224no—
473C42D4×D1111yescharacteristic
474C42D4×D1111yescharacteristic
475C42D4×D1111yescharacteristic
476C42D4×D1111yescharacteristic
477C11#2183111yescharacteristic, complemented, Sylow
478C23—111no—
479C23—111no—
480C23—222no—
481C23—441no—
482C23—441no—
483C23C22×C4×D1111yescharacteristic
484Q8—44no—
485Q8—44no—
486Q8—444no—
487Q8—444no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—44no—
492C2×C4—111no—
493C2×C4—111no—
494C2×C4—111no—
495C2×C4—111no—
496C2×C4—111no—
497C2×C4—111no—
498C2×C4—222no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—224no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—444no—
517C2×C4C22⋊C4×D1111yescharacteristic
518C2×C4C22⋊C4×D1111yescharacteristic
519C2×C4C22⋊C4×D1111yescharacteristic
520C2×C4C22⋊C4×D1111yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4#6704012yes—
524C2×C4#6704312yes—
525C8—42no—
526C8—42no—
527C8—442no—
528C8—442no—
529C22—21no—
530C22—21no—
531C22—221no—
532C22—221no—
533C22—221no—
534C22—221no—
535C22—221no—
536C22—221no—
537C22—444no—
538C22C2×C22⋊C4×D1111yescharacteristic
539C22#1062310312yes—
540C4—21no—
541C4—21no—
542C4—44no—
543C4—221no—
544C4—221no—
545C4—221no—
546C4—221no—
547C4—221no—
548C4—221no—
549C4—444no—
550C4#1062235812yes—
551C4#1062236412yes—
552C4#1062315912yes—
553C4#1062320611yescharacteristic
554C4#1062325511yescharacteristic
555C2—22no—
556C2—441no—
557C2—441no—
558C2#1307119911yescharacteristic
559C2C2×#1062235811yescharacteristic
560C2C2×#1062236411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1997C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1997D11
hypocenterC11#21831
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
4. #13069607C2semidirect
5. #13069606C2semidirect
6. #13069605C2semidirect
7. #13069604C2semidirect
9. C11×#1997C2semidirect
205. #1997D11semidirect
477. C11#21831semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130772482
#130772472
#130696072
#130696062
#130696052
#130696042
#130686982
C11×#19972
#2183111