Finite Group Databasebeta

← #14787832

Subgroups — #14787832

Order 2816.

1184 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic, complemented
3C2×#10622631C211yesmaximal, characteristic, complemented
4#13069819C212yesmaximal, complemented
5#13069619C212yesmaximal, complemented
6#13069588C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068934C212yesmaximal, complemented
9#13068803C212yesmaximal, complemented
10#13068628C211yesmaximal, characteristic, complemented
11C11×#2535C211yesmaximal, characteristic
12C2×C11×#121C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×D4×Dic11—21no—
16C22×#4324C2211yescharacteristic
17C22×C4⋊Dic11C2212yes—
18C2×#66977C2212yes—
19#10623074—24no—
20#10623074—24no—
21C2×#66943—21no—
22C2×#66931—22no—
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C11×#397—21no—
26C11×#392—21no—
27C11×#386—22no—
28C11×#382C2211yescharacteristic
29C11×#380C2212yes—
30C2×#66896C2212yes—
31C2×#66896C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34#10622631—24no—
35#10622620—24no—
36C2×#66874C2211yescharacteristic
37C2×#66874C2212yes—
38C2×#66871C2211yescharacteristic
39C2×#66871C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×D4×C11—22no—
46C22×D4×C11D411yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11C2312yes—
50C23×Dic11—22no—
51C22×Dic22—21no—
52C22×Dic22C2311yescharacteristic
53C11×#121—24no—
54C11×#121—42no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4D412yes—
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—22no—
68D4×Dic11—28no—
69C2×#4324—22no—
70C2×#4324—22no—
71C2×#4324—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—24no—
75C2×C4⋊Dic11—24no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2312yes—
78#66977—24no—
79#66977—24no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—22no—
82C2×C4×Dic11—21no—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85C22×C11⋊C8C2311yescharacteristic
86#66943—28no—
87#66931—216no—
88#66922—22no—
89#66922D414yescomplemented
90C4×Dic22—22no—
91C4×Dic22D414yescomplemented
92C11×#95—22no—
93C11×#95—21no—
94C11×#95—21no—
95#66896—24no—
96#66896—22no—
97C22⋊(C11⋊C8)—24no—
98C22⋊(C11⋊C8)—42no—
99#66874—22no—
100#66874—42no—
101#66871—24no—
102#66871—22no—
103C4⋊(C11⋊C8)—22no—
104#66867—22no—
105#24130—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11C2×D412yes—
108C2×D4×C11—24no—
109C2×D4×C11—22no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—44no—
116C2×D4×C11—44no—
117C2×D4×C11—82no—
118C2×D4×C11#4112yes—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—42no—
128C22×C4×C11—82no—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—28no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11—82no—
138C22×Dic11—82no—
139C2×Dic22—24no—
140C2×Dic22—21no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—82no—
146C2×Dic22C2×D412yes—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—42no—
155C11×C22⋊C4—82no—
156C42×C11C2×D412yes—
157C42×C11C2×D412yes—
158C22⋊Dic11—28no—
159#4324—28no—
160C4⋊Dic11—28no—
161C4⋊Dic11—24no—
162C4⋊Dic11—21no—
163C4⋊Dic11—22no—
164C4⋊Dic11C2×D412yes—
165C4⋊Dic11C2×D414yes—
166Dic11⋊C4—28no—
167Dic11⋊C4—24no—
168C4×Dic11—24no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8#4112yes—
178C2×#554—111no—
179C2×#474—111no—
180C2×#440—111no—
181#2535D1111yescharacteristic
182#2036—112no—
183#2000—112no—
184#1993—111no—
185#1955—111no—
186#1874—112no—
187#1852—112no—
188#1805—111no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11#13714yes—
201C23×C11C22×D411yescharacteristic
202D4×C11—28no—
203D4×C11—22no—
204D4×C11—22no—
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—88no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—84no—
223C2×C4×C11#12012yes—
224C2×C4×C11#12012yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C2×C4×C112−1+411yescharacteristic
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—88no—
240Dic22—22no—
241Dic22—22no—
242Dic22—41no—
243Dic22—41no—
244Dic22—84no—
245C11⋊C8—22no—
246C11⋊C8—41no—
247C11⋊C8—42no—
248C22×SD16—111no—
249#554—224no—
250#554—224no—
251C2×C4⋊Q8—111no—
252C2×#125—221no—
253C2×C22⋊Q8—112no—
254C2×C22⋊Q8—222no—
255C2×#121C2×D1112yes—
256C2×C4×Q8—111no—
257C2×C4×D4—221no—
258C2×C4×D4C2×D1111yescharacteristic
259C2×C4×D4C2×D1111yescharacteristic
260C22×C4⋊C4—112no—
261#474—224no—
262#440—224no—
263C2×#107—111no—
264C2×#107—112no—
265C2×C4⋊C8—111no—
266C2×#103—111no—
267C2×#103—112no—
268C2×#102—111no—
269C2×#102—112no—
270C2×C22⋊C8—112no—
271C2×C22⋊C8—112no—
272C2×#97—111no—
273#397—21no—
274#392—21no—
275#386—22no—
276#382C2×D1111yescharacteristic
277#380C2×D1112yes—
278#340—112no—
279#340—112no—
280#340—112no—
281C22×C11—24no—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—44no—
290C22×C11—82no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11C2×#12011yescharacteristic
294C22×C11#54611yescharacteristic
295C22×C11#54711yescharacteristic
296C22×C11C2×#13712yes—
297C22×C11#57612yes—
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—42no—
301C4×C11—81no—
302C4×C11—82no—
303C4×C11#52511yescharacteristic
304C4×C11#53711yescharacteristic
305C4×C11#54811yescharacteristic
306C4×C11#55011yescharacteristic
307Dic11—42no—
308Dic11—44no—
309Dic11—42no—
310C22×Q8—111no—
311C22×Q8—221no—
312C22×D4—22no—
313C22×D4C22⋊D1111yescharacteristic
314C22×D4C22×D1111yescharacteristic
315C23×C4—21no—
316C23×C4—222no—
317C23×C4C22×D1112yes—
318C2×SD16—222no—
319C2×SD16—222no—
320C2×SD16—222no—
321C22×C8—111no—
322C22×C8—111no—
323C22×C8—112no—
324C4⋊Q8—114no—
325C4⋊Q8—222no—
326#125—228no—
327C22⋊Q8—2216no—
328C22⋊Q8—224no—
329C22⋊Q8—224no—
330#121—24no—
331#121—42no—
332C4×Q8—114no—
333C4×Q8—222no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—228no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—112no—
341C2×C4⋊C4—224no—
342C2×C4⋊C4—224no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4C22⋊D1111yescharacteristic
348C2×C4⋊C4C22×D1111yescharacteristic
349C2×C4⋊C4C22×D1112yes—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4C22⋊D1112yes—
355C2×C42—221no—
356C2×C42C22×D1111yescharacteristic
357#107—222no—
358#107—224no—
359C4⋊C8—222no—
360#103—222no—
361#103—442no—
362#102—222no—
363#102—224no—
364C22⋊C8—224no—
365C22⋊C8—442no—
366#97—222no—
367#95—22no—
368#95—21no—
369#95—21no—
370C2×C11—44no—
371C2×C11—82no—
372C2×C11#240711yescharacteristic
373C2×C11#300411yescharacteristic
374C2×C11#300811yescharacteristic
375C2×C11#331412yes—
376C2×C11#334612yes—
377C24—21no—
378C24C2×C22⋊D1112yes—
379C2×Q8—112no—
380C2×Q8—224no—
381C2×Q8—221no—
382C2×Q8—221no—
383C2×Q8—221no—
384C2×Q8—221no—
385C2×Q8—221no—
386C2×Q8—882no—
387C2×D4—24no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—44no—
395C2×D4—44no—
396C2×D4—82no—
397C2×D4#434112yes—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—42no—
407C22×C4—82no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4—222no—
411C22×C4—228no—
412C22×C4—882no—
413C22×C4—882no—
414C22×C4C2×C22⋊D1112yes—
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C2×C22⋊D1111yescharacteristic
417C22×C4C23×D1111yescharacteristic
418SD16—228no—
419C2×C8—112no—
420C2×C8—221no—
421C2×C8—221no—
422C2×C8—221no—
423C2×C8—222no—
424C2×C8—221no—
425C2×C8—222no—
426C2×C8—222no—
427C2×C8—221no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—112no—
434C4⋊C4—114no—
435C4⋊C4—228no—
436C4⋊C4—228no—
437C4⋊C4—224no—
438C4⋊C4—224no—
439C4⋊C4—221no—
440C4⋊C4—222no—
441C22⋊C4—24no—
442C22⋊C4—44no—
443C22⋊C4—42no—
444C22⋊C4—82no—
445C22⋊C4—228no—
446C42—224no—
447C42D4×D1112yes—
448C42D4×D1112yes—
449C11#2413011yescharacteristic, complemented, Sylow
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—41no—
458C23—42no—
459C23—41no—
460C23—42no—
461C23#6700414yes—
462C23C22×C22⋊D1111yescharacteristic
463Q8—222no—
464Q8—222no—
465Q8—441no—
466Q8—441no—
467Q8—884no—
468D4—28no—
469D4—22no—
470D4—22no—
471D4—41no—
472D4—41no—
473D4—88no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—84no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—224no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—888no—
498C2×C4#6699012yes—
499C2×C4#6699012yes—
500C2×C4C2×D4×D1111yescharacteristic
501C2×C4C2×D4×D1111yescharacteristic
502C2×C4C2×#434111yescharacteristic
503C2×C4#6703711yescharacteristic
504C2×C4#41×D1111yescharacteristic
505C2×C4#6704311yescharacteristic
506C8—222no—
507C8—442no—
508C8—441no—
509C22—24no—
510C22—24no—
511C22—24no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—44no—
518C22—82no—
519C22—81no—
520C22—81no—
521C22C2×#6699011yescharacteristic
522C22#1062333711yescharacteristic
523C22C2×#6700412yes—
524C22#1062335511yescharacteristic
525C22#1062336612yes—
526C4—22no—
527C4—22no—
528C4—42no—
529C4—82no—
530C4—81no—
531C4—442no—
532C4—442no—
533C4—444no—
534C4#1062312911yescharacteristic
535C4#1062313011yescharacteristic
536C4#1062313711yescharacteristic
537C4#1062313911yescharacteristic
538C2—44no—
539C2—82no—
540C2#1307195711yescharacteristic
541C2#1307784911yescharacteristic
542C2#1307788211yescharacteristic
543C2#1308069712yes—
544C2#1308110112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2535C2
socleC23×C11C22×D4
hypercenter#2535D11
hypocenterC11#24130
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#10623074C2semidirect
2. C2×#10622620C2semidirect
3. C2×#10622631C2semidirect
4. #13069819C2semidirect
5. #13069619C2semidirect
6. #13069588C2semidirect
7. #13069415C2semidirect
8. #13068934C2semidirect
9. #13068803C2semidirect
10. #13068628C2semidirect
89. #66922D4semidirect
91. C4×Dic22D4semidirect
449. C11#24130semidirect

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106226202
C2×#106226312
#130698192
#130696192
#130695882
#130694152
#130689342
#130688032
#130686282
C11×#25352
#2413011